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Title: Giant brains; or, Machines that think

Author: Edmund Callis Berkeley

Release date: September 14, 2022 [eBook #68991]
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Language: English

Original publication: United States: John Wiley & Sons, 1949

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*** START OF THE PROJECT GUTENBERG EBOOK GIANT BRAINS;
OR, MACHINES THAT THINK ***

GIANT BRAINS
OR
MACHINES THAT THINK
EDMUND CALLIS BERKELEY
Consultant in Modern Technology
President, E. C. Berkeley and Associates

JOHN WILEY & SONS, INC., NEW YORK
CHAPMAN & HALL, LIMITED, LONDON

Copyright, 1949
by
EDMUND CALLIS BERKELEY

All Rights Reserved

This book or any part thereof must not
be reproduced in any form without
the written permission of the publisher.

Second Printing, February, 1950

Printed in the United States of America

To my friends,
whose help and instruction
made this book possible

PREFACE
The Subject, Purpose, and Method
of this Book
The subject of this book is a type of machine that comes closer to being
a brain that thinks than any machine ever did before 1940. These new
machines are called sometimes mechanical brains and sometimes sequence-
controlled calculators and sometimes by other names. Essentially, though,
they are machines that can handle information with great skill and great
speed. And that power is very similar to the power of a brain.
These new machines are important. They do the work of hundreds of
human beings for the wages of a dozen. They are powerful instruments for
obtaining new knowledge. They apply in science, business, government,
and other activities. They apply in reasoning and computing, and, the harder
the problem, the more useful they are. Along with the release of atomic
energy, they are one of the great achievements of the present century. No
one can afford to be unaware of their significance.
In this book I have sought to tell a part of the story of these new
machines that think. Perhaps you, as you start this book, may not agree with
me that a machine can think: the first chapter of this book is devoted to the
discussion of this question.
My purpose has been to tell enough about these machines so that we can
see in general how they work. I have sought to explain some giant brains
that have been built and to show how they do thinking operations. I have
sought also to talk about what these machines can do in the future and to
judge their significance for us. It seems to me that they will take a load off
men’s as great as the load that printing took off men’s writing: a tremendous
burden lifted.
We need to examine several of the new mechanical brains:
Massachusetts Institute of Technology’s differential analyzer, Harvard’s
IBM automatic sequence-controlled calculator, Moore School’s ENIAC
(Electronic Numerical Integrator and Calculator), and Bell Laboratories’

general-purpose relay calculator. These are described in the sequence in
which they were finished between the years 1942 and 1946.
We also have to go on some excursions—for instance, the nature of
language and of symbols, the meaning of thinking, the human brain and
nervous system, the future design of machinery that can think, and a little
algebra and logic. I have also sought to discuss the relations between
machines that think and human society—what we can foresee as likely to
happen or be needed as a result of the remarkable invention of machines
that can think.

READING THIS BOOK

This book is intended for everyone. I have sought to put it together in
such a way that any reader can select from it what he wants.
Perhaps at first reading you want only the main thread of the story. Then
read only what seems interesting, and skip whatever seems uninteresting.
The subheadings should help to tell you what to read and what to skip.
Nearly all the chapters can be read with little reference to what goes before,
although some reference to the supplements in the back may at times be
useful.
Perhaps your memory of physics is dim, like mine. The little knowledge
of physics needed is explained here and there throughout the book, and the
index should tell where to find any explanation you may want.
Perhaps it is a long time since you did any algebra. Then Supplement 2
on mathematics may hold something of use to you. Two sections (one in
Chapter 5 and one in Chapter 6) labeled as containing some rather
mathematical details may be skipped with no great loss.
Perhaps you are unacquainted with logic that uses symbols—the branch
of logic called mathematical logic. In fact, very few people are familiar
with it. No discussion in the book hinges on understanding this subject,
except for Chapter 9 where a machine that calculates logical truth is
described. In all other chapters you may freely skip all references to
mathematical logic. But, if you are curious about the subject and how it can
be usefully applied in the field of mechanical brains, then begin with the

introduction to the subject in Chapter 9, and note the suggestions in the
section entitled “Algebra of Logic” in Supplement 2.
In any case, glance at the table of contents, the chapter headings and
subheadings, and the supplements at the back. These should give an idea of
how the book is put together and how you may select what may be
interesting to you.
Please do not read this book straight from beginning to end unless that
way proves to be congenial to you. If you are not interested in technical
details, skip most of the middle chapters, which describe existing
mechanical brains. If, on the other hand, you want more details than this
book contains, look up references in Supplement 3. Here are listed, with a
few comments, over 250 books, articles, and pamphlets related to the
subject of machinery for computing and reasoning. These cover many parts
of the field; some parts, however, are not yet covered by any published
information.
There are no photographs in this book, although there are over 80
drawings. Photographs of these complicated machines can really show very
little: panels, lights, switches, wires, and other kinds of hardware. What is
important is the way the machine works inside. This cannot be shown by a
photograph but may be shown by schematic drawings. In the same way, a
photograph of a human being shows almost nothing about how he thinks.

UNDERSTANDING THIS BOOK

I have tried to write this book so that it could be understood. I have
attempted to explain machinery for computing and reasoning without using
technical words any more than necessary. To do this seemed to be easy in
some places, much harder in others. As a test of this attempt, a count has
been made of all the different words in the book that have two syllables or
more, that are used for explaining, and that are not themselves defined.
There are fewer than 1800 of these words. In Supplement 1, entitled “Words
and Ideas,” I have digressed to discuss further the problem of explanation
and understanding.
Every now and then in the book, along comes a word or a phrase that
has a special meaning, for example, the name of something new. When it

first appears, it is put in italics and is explained or defined. In addition, all
the words and phrases having special meaning appear again in the index,
and next to each is the page number of its explanation or definition.
In many places, I have talked of mechanical brains as if they were
living. For example, instead of “capacity to store information” I have
spoken of “memory.” Of course, the machines are not living; but they do
have individuality, responsiveness, and other traits of living beings, just as a
political party pictured as a living elephant does. Besides, to treat things as
persons is a help in making any subject vivid and understandable, as every
song writer and cartoonist illustrates. We speak of “Old Man River” and
“Father Time”; we may speak of a ship or a locomotive as “she”; and the
crew on the first Harvard sequence-controlled calculator has often called
her “Bessy, the Bessel engine.”
Let us pause a little longer on the subject of understanding. What is the
understanding of something new? It is a state of knowing, a process of
knowing more and more. The more we know about something new, the
better we understand it. It is possible for almost anybody to understand
almost anything, I believe. What is mainly needed in order to grasp an idea
is a good collection of true statements about it and some practice in using
those statements in situations. For example, no one has ever seen or touched
the separate scraps of electricity called electrons. But electrons have been
described and measured; hundreds of thousands of people work with
electrons; they know and use true statements about electrons. In effect,
these people understand electrons.
Probably the hardest task of an author is to make his statements
understandable yet accurate. It is too much to hope for complete success. I
shall be very grateful to any reader who points out to me the statements that
he has not understood or that are in error.
As to the views I have expressed, I do not expect every reader to agree
with me. In fact, I shall be glad if many a reader disagrees with me. For
then someone else may say to both of us, “You’re both right and both wrong
—the truth lies atwixt and atween you.” Thoughtful and tolerant
disagreement is the finest climate for scientific progress.

BASIC FACTS

Many of the mechanical brains described in this book will do good
work for years; but their design is already out of date. Many organizations
are hard at work finding new tricks in electronics, materials, and
engineering and making new mechanical brains that are better and faster.
In spite of future developments, though, the basic facts about
mechanical brains will endure. These basic facts are drawn from the
principles of thinking, of mathematics, of science, of engineering, etc.
These facts govern all handling of information. They do not depend very
much on human or mechanical energy. They do not depend very much on
signs. They do not depend very much on the century, or the language, or the
country. For example, “II et III V sunt,” the Romans may have said; “deux
et trois font cinq,” say the French; “2 + 3 = 5,” say the mathematicians; and
we say, “two and three make five.” The main effort in this book has been to
make clear the basic facts about mechanical brains, for they are now a
masterly instrument for obtaining new knowledge.

Edmund Callis Berkeley
New York 11, N. Y.
June 30, 1949

ACKNOWLEDGMENTS
This book has been over seven years in the making and has evolved
through many different plans for its contents. It springs essentially from the
desire to see human beings use their knowledge better: we know enough,
but how are we to use what we know? Machines that handle information,
that make knowledge accessible, are a long step in the direction of using
what we know.
For help in causing this desire to come to fruition, I should like to
express my indebtedness especially to Professor (then Commander,
U.S.N.R.) Howard H. Aiken of Harvard University, whose stimulus, while I
was stationed for ten months in 1945-46 in his laboratory, was very great.
I should also like to express my appreciation to Mr. Harry J. Volk,
whose vision and enthusiasm greatly encouraged me in the writing of this
book.
For careful reviews and helpful comments on the chapters dealing with
existing mechanical brains, I am especially grateful to Dr. Franz L. Alt, Mr.
E. G. Andrews, Professor Samuel H. Caldwell, Dr. Grace M. Hopper, Mr.
Theodore A. Kalin, and Dr. John W. Mauchly, who are experts in their
fields. Dr. Ruth P. Berkeley, Dr. Rudolf Flesch, Mr. J. Ross Macdonald, Dr.
Z. I. Mosesson, Mr. Irving Rosenthal, Mr. Max S. Weinstein, and many
others have been true friends in reading and commenting upon many parts
of the manuscript. Mr. Frank W. Keller devoted much time and skill to
converting my rough sketches into illustrations. Mr. Murray B. Ritterman
has been of invaluable help in preparing and checking much of the
bibliography. Miss Marjorie L. Black has helped very greatly in turning
scraps of paper bearing sentences into an excellent manuscript for the
printer.
For permission to use the quotations on various pages in Chapters 11
and 12, I am indebted to the kindness of:
E. P. Dutton & Co., for quotations from Frankenstein,
by Mary W. Shelley, Everyman’s Library, No. 616.

Samuel French, for quotations from R. U. R., by Karel
Čapek.[1]
Modern Industry, for a quotation from the issue of
February 15, 1947.
Responsibility for the statements and opinions expressed in this book is
solely my own. These statements and opinions do not necessarily represent
the views of any organization with which I may be or have been associated.
To the best of my knowledge and belief no information contained in this
book is classified by the Department of Defense of the United States.

Edmund Callis Berkeley

CONTENTS

1. CAN MACHINES THINK?
What Is a Mechanical Brain? 1
2. LANGUAGES:
Systems for Handling Information 10
3. A MACHINE THAT WILL THINK:
The Design of a Very Simple Mechanical Brain 22
4. COUNTING HOLES:
Punch-Card Calculating Machines 42
5. MEASURING:
Massachusetts Institute of Technology’s
Differential Analyzer No. 2 65
6. ACCURACY TO 23 DIGITS:
Harvard’s IBM Automatic
Sequence-Controlled Calculator 89
7. SPEED—5000 ADDITIONS A SECOND:
Moore School’s ENIAC
(Electronic Numerical Integrator and Calculator) 113
8. RELIABILITY—NO WRONG RESULTS:
Bell Laboratories’
General-Purpose Relay Calculator 128
9. REASONING:
The Kalin-Burkhart Logical-Truth Calculator 144
10. AN EXCURSION:
The Future Design of Machines That Think 167

11. THE FUTURE:
Machines That Think, and
What They Might Do for Men 180
12. SOCIAL CONTROL:
Machines That Think, and
How Society May Control Them 196

SUPPLEMENTS
1. Words and Ideas 209
2. Mathematics 214
3. References 228
INDEX 257

Chapter 1
CAN MACHINES THINK?
WHAT IS A MECHANICAL BRAIN?
Recently there has been a good deal of news about strange giant
machines that can handle information with vast speed and skill. They
calculate and they reason. Some of them are cleverer than others—able to
do more kinds of problems. Some are extremely fast: one of them does
5000 additions a second for hours or days, as may be needed. Where they
apply, they find answers to problems much faster and more accurately than
human beings can; and so they can solve problems that a man’s life is far
too short to permit him to do. That is why they were built.
These machines are similar to what a brain would be if it were made of
hardware and wire instead of flesh and nerves. It is therefore natural to call
these machines mechanical brains. Also, since their powers are like those of
a giant, we may call them giant brains.
Several giant mechanical brains are now at work finding out answers
never before known. Two are in Cambridge, Mass.; one is at Massachusetts
Institute of Technology, and one at Harvard University. Two are in
Aberdeen, Md., at the Army’s Ballistic Research Laboratories. These four
machines were finished in the period 1942 to 1946 and are described in
later chapters of this book. More giant brains are being constructed.
Can we say that these machines really think? What do we mean by
thinking, and how does the human brain think?

HUMAN THINKING

We do not know very much about the physical process of thinking in the
human brain. If you ask a scientist how flesh and blood in a human brain
can think, he will talk to you a little about nerves and about electrical and
chemical changes, but he will not be able to tell you very much about how
we add 2 and 3 and make 5. What men know about the way in which a

human brain thinks can be put down in a few pages, and what men do not
know would fill many libraries.
Injuries to brains have shown some things of importance; for example,
they have shown that certain parts of the brain have certain duties. There is
a part of the brain, for instance, where sights are recorded and compared. If
an accident damages the part of the brain where certain information is
stored, the human being has to relearn—haltingly and badly—the
information destroyed.
We know also that thinking in the human brain is done essentially by a
process of storing information and then referring to it, by a process of
learning and remembering. We know that there are no little wheels in the
brain so that a wheel standing at 2 can be turned 3 more steps and the result
of 5 read. Instead, you and I store the information that 2 and 3 are 5, and
store it in such a way that we can give the answer when questioned. But we
do not know the register in our brain where this particular piece of
information is stored. Nor do we know how, when we are questioned, we
are able automatically to pick up the nerve channels that lead into this
register, get the answer, and report it.
Since there are many nerves in the brain, about 10 billion of them, in
fact, we are certain that the network of connecting nerves is a main part of
the puzzle. We are therefore much interested in nerves and their properties.

NERVES AND THEIR PROPERTIES

A single nerve, or nerve cell, consists of a cell nucleus and a fiber. This
fiber may have a length of anything from a small fraction of an inch up to
several feet. In the laboratory, successive impulses can be sent along a nerve
fiber as often as 1000 a second. Impulses can travel along a nerve fiber in
either direction at a rate from 3 feet to 300 feet a second. Because the speed
of the impulse is far less than 186,000 miles a second—the speed of an
electric current—the impulse in the nerve is thought by some investigators
to be more chemical than electrical.
We know that a nerve cell has what is called an all-or-none response,
like the trigger of a gun. If you stimulate the nerve up to a certain point,
nothing will happen; if you reach that point, or cross it,—bang!—the nerve

responds and sends out an impulse. The strength of the impulse, like the
shot of the gun, has no relation whatever to the amount of the stimulation.

Fig. 1. Scheme of a nerve cell.
The structure between the end of one nerve and the beginning of the
next is called a synapse (see Fig. 1). No one really knows very much about
synapses, for they are extremely small and it is not easy to tell where a
synapse stops and other stuff begins. Impulses travel through synapses in
from ½ to 3 thousandths of a second. An impulse travels through a synapse
only in one direction, from the head (or axon) of one nerve fiber to the foot
(or dendrite) of another. It seems clear that the activity in a synapse is
chemical. When the head of a nerve fiber brings in an impulse to a synapse,
apparently a chemical called acetylcholine is released and may affect the
foot of another fiber, thus transmitting the impulse; but the process and the
conditions for it are still not well understood.
It is thought that nearly all information is handled in the brain by groups
of nerves in parallel paths. For example, the eye is estimated to have about
100 million nerves sensitive to light, and the information that they gather is
reported by about 1 million nerves to the part of the brain that stores sights.
Not much more is yet known, however, about the operation of handling
information in a human brain. We do not yet know how the nerves are
connected so that we can do what we do. Probably the greatest obstacle to
knowledge is that so far we cannot observe the detailed structure of a living
human brain while it performs, without hurting or killing it.

BEHAVIOR THAT IS THINKING

Therefore, we cannot yet tell what thinking is by observing precisely
how a human brain does it. Instead, we have to define thinking by
describing the kind of behavior that we call thinking. Let us consider some
examples.
When you and I add 12 and 8 and make 20, we are thinking. We use our
minds and our understanding to count 8 places forward from 12, for
example, and finish with 20. If we could find a dog or a horse that could
add numbers and tell answers, we would certainly say that the animal could
think.
With no trouble a machine can do this. An ordinary 10-column adding
machine can be given two numbers like 1,378,917,766 and 2,355,799,867
and the instruction to add them. The machine will then give the answer,
3,734,717,633, much faster than a man. In fact, the mechanical brain at
Harvard can add a number of 23 digits to another number of 23 digits and
get the right answer in ³/₁₀ of a second.
Or, suppose that you are walking along a road and come to a fork. If you
stop, read the signpost, and then choose left or right, you are thinking. You
know beforehand where you want to go, you compare your destination with
what the signpost says, and you decide on your route. This is an operation
of logical choice.
A machine can do this. The mechanical brain now at Aberdeen which
was built at Bell Laboratories can examine any number that comes up in the
process of a calculation and tell whether it is bigger than 3 (or any stated
number) or smaller. If the number is bigger than 3, the machine will choose
one process; if the number is smaller than 3, the machine will choose
another process.
Now suppose that we consider the basic operation of all thinking: in the
human brain it is called learning and remembering, and in a machine it is
called storing information and then referring to it. For example, suppose
you want to find 305 Main Street in Kalamazoo. You look up a map of
Kalamazoo; the map is information kindly stored by other people for your
use. When you study the map, notice the streets and the numbering, and
then find where the house should be, you are thinking.

A machine can do this. In the Bell Laboratories’ mechanical brain, for
example, the map could be stored as a long list of the blocks of the city and
the streets and numbers that apply to each block. The machine will then
hunt for the city block that contains 305 Main Street and report it when
found.
A machine can handle information; it can calculate, conclude, and
choose; it can perform reasonable operations with information. A machine,
therefore, can think.

THE DEFINITION OF A MECHANICAL BRAIN

Now when we speak of a machine that thinks, or a mechanical brain,
what do we mean? Essentially, a mechanical brain is a machine that
handles information, transfers information automatically from one part of
the machine to another, and has a flexible control over the sequence of its
operations. No human being is needed around such a machine to pick up a
physical piece of information produced in one part of the machine,
personally move it to another part of the machine, and there put it in again.
Nor is any human being needed to give the machine instructions from
minute to minute. Instead, we can write out the whole program to solve a
problem, translate the program into machine language, and put the program
into the machine. Then we press the “start” button; the machine starts
whirring; and it prints out the answers as it obtains them. Machines that
handle information have existed for more than 2000 years. These two
properties are new, however, and make a deep break with the past.
How should we imagine a mechanical brain? One way to think of a
mechanical brain is shown in Fig. 2. We see here a railroad line with four
stations, marked input, storage, computer, and output. These stations are
joined by little gates or switches to the main railroad line. We can imagine
that numbers and other information move along this railroad line, loaded in
freight cars. Input and output are stations where numbers or other
information go in and come out, respectively. Storage is a station where
there are many platforms and where information can be stored. The
computer is a special station somewhat like a factory; when two numbers
are loaded on platforms 1 and 2 of this station and an order is loaded on
platform 3, then another number is produced on platform 4.

Fig. 2. Scheme of a mechanical brain.
We see also a tower, marked control. This tower runs a telegraph line to
each of its little watchmen standing by the gates. The tower tells them when
to open and when to shut which gates.
Now we can see that, just as soon as the right gates are shut, freight cars
of information can move between stations. Actually the freight cars move at
the speed of electric current, thousands of miles a second. So, by closing the
right gates each fraction of a second, we can flash numbers and information
through the system and perform operations of reasoning. Thus we obtain a
mechanical brain.
In general, a mechanical brain is made up of:
1. A quantity of registers where information (numbers
and instructions) can be stored.
2. Channels along which information can be sent.

3. Mechanisms that can carry out arithmetical and
logical operations.
4. A control, which guides the machine to perform a
sequence of operations.
5. Input and output devices, whereby information can
go into the machine and come out of it.
6. Motors or electricity, which provide energy.

THE KINDS OF THINKING A
MECHANICAL BRAIN CAN DO

There are many kinds of thinking that mechanical brains can do. Among
other things, they can:

1. Learn what you tell them.
2. Apply the instructions when needed.
3. Read and remember numbers.
4. Add, subtract, multiply, divide, and round off.
5. Look up numbers in tables.
6. Look at a result, and make a choice.
7. Do long chains of these operations one after another.
8. Write out an answer.
9. Make sure the answer is right.
10. Know that one problem is finished, and turn to another.
11. Determine most of their own instructions.
12. Work unattended.

They do these things much better than you or I. They are fast. The
mechanical brain built at the Moore School of Electrical Engineering at the
University of Pennsylvania does 5000 additions a second. They are reliable.
Even with hundreds of thousands of parts, the existing giant brains have
worked successfully. They have remarkably few mechanical troubles; in
fact, for one of the giant brains, a mechanical failure is of the order of once
a month. They are powerful. The big machine at Harvard can remember 72
numbers each of 23 digits at one time and can do 3 operations with these
numbers every second. The mechanical brains that have been finished are

able to solve problems that have baffled men for many, many years, and
they think in ways never open to men before. Mechanical brains have
removed the limits on complexity of routine: the machine can carry out a
complicated routine as easily as a simple one. Already, processes for
solving problems are being worked out so that the mechanical brain will
itself determine more than 99 per cent of all the routine orders that it is to
carry out.
But, you may ask, can they do any kind of thinking? The answer is no.
No mechanical brain so far built can:

1. Do intuitive thinking.
2. Make bright guesses, and leap to conclusions.
3. Determine all its own instructions.
4. Perceive complex situations outside itself and interpret them.

A clever wild animal, for example, a fox, can do all these things; a
mechanical brain, not yet. There is, however, good reason to believe that
most, if not all, of these operations will in the future be performed not only
by animals but also by machines. Men have only just begun to construct
mechanical brains. All those finished are children; they have all been born
since 1940. Soon there will be much more remarkable giant brains.

WHY ARE THESE GIANT BRAINS IMPORTANT?

Most of the thinking so far done by these machines is with numbers.
They have already solved problems in airplane design, astronomy, physics,
mathematics, engineering, and many other sciences, that previously could
not be solved. To find the solutions of these problems, mathematicians
would have had to work for years and years, using the best known methods
and large staffs of human computers.
These mechanical brains not only calculate, however. They also
remember and reason, and thus they promise to solve some very important
human problems. For example, one of these problems is the application of
what mankind knows. It takes too long to find understandable information
on a subject. The libraries are full of books: most of them we can never
hope to read in our lifetime. The technical journals are full of condensed

scientific information: they can hardly be understood by you and me. There
is a big gap between somebody’s knowing something and employment of
that knowledge by you or me when we need it. But these new mechanical
brains handle information very swiftly. In a few years machines will
probably be made that will know what is in libraries and that will tell very
swiftly where to find certain information. Thus we can see that mechanical
brains are one of the great new tools for finding out what we do not know
and applying what we do know.

Chapter 2
LANGUAGES:
SYSTEMS FOR HANDLING INFORMATION
As everyone knows, it is not always easy to think. By thinking, we mean computing,
reasoning, and other handling of information. By information we mean collections of ideas
—physically, collections of marks that have meaning. By handling information, we mean
proceeding logically from some ideas to other ideas—physically, changing from some
marks to other marks in ways that have meaning. For example, one of your hands can
express an idea: it can store the number 3 for a short while by turning 3 fingers up and 2
down. In the same way, a machine can express an idea: it can store information by
arranging some equipment. The Harvard mechanical brain can store 132 numbers between
0 and 99,999,999,999,999,999,999,999 for days. When you want to change the number
stored by your fingers, you move them: perhaps you need a half second to change the
number stored by your fingers from 3 to 2, for example. In the same way, a machine can
change a stored number by changing the arrangement of some equipment: the electronic
brain Eniac can change a stored number in ¹/₅₀₀₀ of a second.

LANGUAGES

Since it is not always easy to think, men have given much attention to devices for
making thinking easier. They have worked out many systems for handling information,
which we often call languages. Some languages are very complete and versatile and of
great importance. Others cover only a narrow field—such as numbers alone—but in this
field they may be remarkably efficient. Just what is a language?
Every language is both a scheme for expressing meanings and physical equipment that
can be handled. For example, let us take spoken English. The scheme of spoken English
consists of more than 150,000 words expressing meanings, and some rules for putting
words together meaningfully. The physical equipment of spoken English consists of (1)
sounds in the air, and (2) the ears of millions of people, and their mouths and voices, by
which they can hear and speak the sounds of English. For another example, let us take
numbers expressed in the Arabic numerals and the rules of arithmetic. The scheme of this
language contains only ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 or their equivalents, and some
rules for combining them. Sufficient physical equipment for this language might very well
be a ten-column desk calculating machine with its counter wheels, gears, keys, etc. If we
tried to exchange the physical equipment of these two languages, we would be blocked: the
desk calculating machine cannot possibly express the meaningful combinations of 150,000
words, and sounds in the air are not permanent enough to express the steps of division of
one large number by another.

SCHEMES FOR EXPRESSING MEANINGS

If we examine languages that have existed, we can observe a number of schemes for
expressing meanings. In the table on pp. 12-13 is a rough list of a dozen of them. From
among these we can choose the schemes that are likely to be useful in mechanical brains.
Schemes 11 and 12 are the schemes that have been predominantly used in machinery for
computing. Scheme 12 consisting of combinations of just two marks, ✓, ✕, provides one
of the best codes for mechanical handling of information. This scheme, called binary
coding (see Supplement 2), is also useful for measuring the quantity of information.

QUANTITY OF INFORMATION

How should we measure the quantity of information? The smallest unit of information
is a “yes” or a “no,” a check mark (✓) or a cross (✕), an impulse in a nerve or no impulse,
a 1 or a 0, black or white, good or bad, etc. This twofold difference is called a binary digit
of information (see Supplement 2). It is the convenient unit of information.

SCHEMES FOR EXPRESSING MEANINGS
Example:
/——————^—————————\
Principle Name of
No. Sign Used in Significance
of Scheme Scheme
(1) (2) (3) (4) (5) (6)
Sounds
1. Sound of new Bobwhite[2] Spoken kind of quail, Imitative;
word is like English so called bowwow
sound of from its note theory
referent
2. An utterance Pooh![3] Spoken The speaker Pooh-pooh
becomes a English expresses theory
new word disdain
3. New word is Chortle[4] Spoken “Chuckle” Analogical
like another English; and
word invented by “snort”
Lewis Carroll, blended
1896

Example:
/——————^—————————\
Principle Name of
No. Sign Used in Significance
of Scheme Scheme
(1) (2) (3) (4) (5) (6)
4. Word has Mother[5] Spoken Female Historical
been used English parent
through
the ages
Sights
5. Picture Egyptian; Picture of Imitative;
is like Ojibwa eye and pictographic
referent (American tears, to
Indian) mean grief
6. Pattern is English; Five; Ideographic;
symbol of French; cinq; mathematical;
an idea
5 German; fünf; symbolic;
etc. etc. numeric
Mapping of Sounds
7. Object Possible Picture of Rebus-
pictured English a knot to writing;
as the mean “not” phonographic
wanted
sound
8. Pattern is Ancient Sign for Syllable-
symbol for Cypriote the writing
a large (island of syllable
ound unit Cyprus) mu
9. Pattern is International The sound Phonetic
symbol for Phonetic zh, as writing
a small
Ʒ Alphabet of s in alphabetic
sound unit 87 characters “measure” writing;
Mapping of Sights or Symbols
10. Systematic ENIAC Abbreviations, Initial Alphabetic
combinations etc. letters coding

Example:
/——————^—————————\
Principle Name of
No. Sign Used in Significance
of Scheme Scheme
(1) (2) (3) (4) (5) (6)
of 26 of a
letters 5-word
title
11. Systematic Abbreviations, Social Numeric
combinations nomenclature, Security coding
135-03-1228
of 10 digits etc. No. of
a person
12. Systematic Checking “yes,” “no,” Binary
combinations lists, “no,” “yes,” coding
✓,✕,✕,✓,✓
of 2 marks etc. “yes,”
respectively

With 2 units of information or 2 binary digits (1 or 0) we can represent 4 pieces of
information:
00, 01, 10, 11
With 3 units of information we can represent 8 pieces of information:
000, 001, 010, 011, 100, 101, 110, 111
With 4 units of information we can represent 16 pieces of information:

0000 0001 0010 0011
0100 0101 0110 0111
1000 1001 1010 1011
1100 1101 1110 1111
Now 4 units of information are sufficient to represent a decimal digit 0, 1, 2, 3, 4, 5, 6, 7, 8,
9 and allow 6 possibilities to be left over; 3 units of information are not sufficient. For
example, we may have:

0 0000 5 0101
1 0001 6 0110
2 0010 7 0111

3 0011 8 1000
4 0100 9 1001
We say, therefore, that a decimal digit 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 is equivalent to 4 units of
information. Thus a table containing 10,000 numbers, each of 10 decimal digits, is
equivalent to 400,000 units of information.
One of the 26 letters of the alphabet is equivalent to 5 units of information, for, 5 binary
digits (1 or 0) have 32 possible arrangements, and these are enough to provide for the 26
letters. Any printed information in English can be expressed in about 80 characters
consisting of 10 numerals, 52 capital and small letters, and some 18 punctuation marks and
other types of marks; 6 binary digits (1 or 0) have 64 possible arrangements, and 7 binary
digits (1 or 0) have 128 possible arrangements. Each character in a printed book, therefore,
is roughly equivalent to 7 units of information.
It can be determined that a big telephone book or a big reference dictionary stores
printed information at the rate of about 1 billion units of information per cubic foot. If the
10 billion nerves in the human brain could independently be impulsed or not impulsed, then
the human brain could conceivably store 10 billion units of information. The largest library
in the world is the Library of Congress, containing 7 million volumes including pamphlets.
It stores about 100 trillion units of information.
We can thus see the significance of a quantity of information from 1 unit to 100 trillion
units. No distinction is here made between information that reports facts and information
that does not. For example, a book of fiction about persons who never existed is still
counted as information, and, of course, much instruction and entertainment may be found
in such a source.

PHYSICAL EQUIPMENT FOR
HANDLING INFORMATION

The first thing we want to do with information is store it. The second thing we want to
do is combine it. We want equipment that makes these two processes easy and efficient. We
want equipment for handling information that:
1. Costs little.
2. Holds much information in little space.
3. Is permanent, when we want to keep the information.
4. Is erasable, when we want to remove information.
5. Is versatile, holds easily any kind of information, and allows
operations to be done easily.
The amount of human effort needed to handle information correctly depends very much
on the properties of the physical equipment expressing the information, although the laws
of correct reasoning are independent of the equipment. For example, the great difficulty

with spoken sounds as physical equipment for handling information is the trouble of storing
them. The technique for doing so was mastered only about 1877 when Thomas A. Edison
made the first phonograph. Even with this advance, no one can glance at a soundtrack and
tell quickly what sounds are stored there; only by turning back the machine and listening to
a groove can we determine this. It was not possible for the men of 2000 b.c. to wait
thousands of years for the storing of spoken sounds. The problem of storing information
was accordingly taken to other types of physical equipment.

PHYSICAL EQUIPMENT FOR
HANDLING INFORMATION
Physical Arranged Operated or Low Little Perma- Eras- Vers-
No.
Objects in or on Produced by Cost? Space? nent? able? atile?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Mind
1. Nerve Human
Body ✕ ✓✓ ✓ ✓ ✓✓
cells brain
Sounds
2. Sounds Air Voice ✓✓ ✓✓ ✕✕ ✓✓ ✓✓
3. Sound- Wax Machines
tracks cylinders, and
✓ ✓ ✓✓ ✕ ✓✓
phonograph motors
records
Sights
4. Marks Sand Stick ✓ ✕ ✓ ✓✓ ✕
5. Colored Cave Paintbrush
painting walls, and paints
✕ ✕ ✓ ✕ ✕✕
canvases,
etc.
6. Marks, Clay, Stylus,
inscript- stone chisel ✕✕ ✓ ✓✓ ✕✕ ✓
ions
7. Marks Slate Chalk ✓ ✕ ✓ ✓✓ ✓
8. Marks Paper,
parchment, and ink, Pen ✓✓ ✓ ✓ ✕ ✓✓
etc. pencil

Physical Arranged Operated or Low Little Perma- Eras- Vers-
No.
Objects in or on Produced by Cost? Space? nent? able? atile?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
9. Letters, Paper Printing
etc. books press,
etc. movable
✓✓ ✓✓ ✓✓ ✕✕ ✓✓
type,
motor,
and hands
10. Photo- Film, Camera
graphs prints, ✓ ✓✓ ✓ ✕✕ ✓✓
etc.
11. Letters, Paper, Typewriter
etc. mimeograph and
✓ ✓✓ ✓ ✕ ✓✓
stencil, fingers
etc.
Body
12. Gestures Space Body ✓ ✕ ✕✕ ✓✓ ✕✕
13. Fingers Hands Body ✕ ✕ ✕✕ ✓✓ ✕✕
Objects
14. Pebbles Slab Hands ✓✓ ✓ ✓ ✓ ✕✕
15. Knots String Hands ✓✓ ✓ ✓ ✓ ✕✕
16. Tallies,
Stick Knife ✓✓ ✓ ✓✓ ✕✕ ✕✕
notches
17. Rods in
Beads a frame, Hands ✓ ✓ ✓ ✓✓ ✕✕
abacus
18. Ruled Rulers, Hands,
lines, scales, pressure, ✓ ✓ ✓ ✓ ✓
pointers dials etc.
Machines
19. Counter Desk Motor ✓ ✓ ✓ ✓✓ ✓
wheels, calculating and
gears, machines, hands

Physical Arranged Operated or Low Little Perma- Eras- Vers-
No.
Objects in or on Produced by Cost? Space? nent? able? atile?
(1) (2) (3) (4) (5) (6) (7) (8) (9)
keys, fire-control
lights, instruments,
etc. etc.
20. Punched Punch card Motor
cards machinery, and
and teletype, input ✓✓ ✓✓ ✓ ✕ ✓✓
paper etc. instructions
tape
21. Dial Motor
telephone, and
Relays ✕ ✓ ✓ ✓✓ ✓✓
other input
machinery instructions
22. Elect- Motor
ronic and
Machinery ✓ ✓ ✓ ✓✓ ✓✓
tubes input
instructions
23. Magnetic Motor
surfaces: and
wire, Machinery input ✓✓ ✓✓ ✓✓ ✓✓ ✓✓
tape, instructions
discs
24. Delay Motor
lines: and
Machinery ✕ ✓ ✕ ✓✓ ✓✓
electric, input
acoustic instructions
25. Electro- Motor
static and
Machinery ✕ ✓✓ ✕ ✓✓ ✓✓
storage input
tubes instructions

✓✓ yes, very.
✓ yes, adequately.

✕ not generally.
✕✕ not at all.

What are the types of physical equipment for handling information, and which are the
good ones? In the table on pp. 16-17 is a rough list of 25 types of physical equipment for
handling information. ✓✓ means “yes, very;” ✓ means “yes, adequately;” ✕ means “not
generally;” ✕✕ means “not at all.”
For example, our fingers (see No. 13) as a device for handling information are very
expensive for most cases. They take up a good deal of space. Certainly they are very
temporary storage; any information they may express is very erasable; and what we can
express with them alone is very limited. Yet, with a typewriter (see No. 11), our fingers
become versatile and efficient. In fact, our fingers can make 4 strokes a second; we can
select any one of about 38 keys; and, since each key is equivalent to 5 or 6 units of
information, the effective speed of our fingers may be about 800 units of information a
second.

LANGUAGES OF PHYSICAL OBJECTS

The use of pebbles (see No. 14) for keeping track of numerical information is shown in
the history of the words containing the root calc-of the word calculate. The Latin word
calcis meant pertaining to lime or limestone, and the Latin word calculus derived from it
meant first a small piece of limestone, and later any small stone, particularly a pebble used
in counting. All three of these meanings have left descendants: “chalk,” “calcite,”
“calcium,” relating in one way or another to lime; in medicine, “calculus,” referring to
stones in the kidneys or elsewhere in the body; and in mathematics, “calculate,” “calculus,”
referring to computations, once done with pebbles.
The pebbles, and the slab (for which the ancient Greek word is abax) on which they
were arranged and counted, were later replaced, for ease in handling, by groups of beads
strung on rods and placed in a frame (see No. 17). These constituted the abacus (see
Supplement 2 and the figure there). This was the first calculating machine. It is still used all
over Asia; in fact, even today more people use the abacus for accounting than use pencil
and paper. The skill with which the abacus can be used was shown in November 1946 in a
well-publicized contest in Japan. Kiyoshi Mastuzaki, a clerk in the Japanese
communications department, using the abacus, challenged Private Thomas Wood of the U.
S. Army, using a modern desk calculating machine, and defeated him in a speed contest
involving additions, subtractions, multiplications, and divisions.
The heaps of small pebbles, the notches in sticks, and the abacus had the advantage of
being visible and comparatively permanent. Storing and reading were relatively easy. They
were rather compact and easy to manipulate, certainly much easier than spoken words. But
they were subject to disadvantages also. Moving correctly from one arrangement to another
was difficult, since there was no good way for storing intermediate steps so that the process
could be easily verified. Furthermore, these devices applied to specified numbers only.

Also, there was no natural provision for recording what the several numbers belonged to.
This had to be recorded with the help of another language, writing.
The language of physical objects was picked up from obscurity by the invention of
motors and the demands of commerce and business. Commencing in the late 1800’s, desk
calculating machines (see No. 19) were constructed to meet mass calculation requirements.
They would add, subtract, multiply, and divide specific numbers with great accuracy and
speed. But until recently they still were adjuncts to the other languages, for they provided
figures one at a time for insertion in the spaces on the ledger pages or calculation sheets
where figures were called for.
Beginning in the 1920’s, a remarkable change has taken place. Instead of performing
single operations, machines have been developed to perform chains of operations with
many kinds of information. One of these machines is the dial telephone: it can select one of
7 million telephones by successive sorting according to the letters and digits of a telephone
number. Another of these machines is a fire-control instrument, a mechanism for
controlling the firing of a gun. For example, in a modern anti-aircraft gun the mechanism
will observe an enemy plane flying at several hundred miles an hour, convert the
observations into gun-aiming directions, and determine the aiming directions fast enough to
shoot down the plane. Punch-card machinery, machines handling information expressed as
punched holes in cards, enable the fulfillment of social security legislation, the production
of the census, and countless operations of banks, insurance companies, department stores,
and factories. And, finally, in 1942 the first mechanical brain was finished at Massachusetts
Institute of Technology.

THE CRUCIAL DEVICES FOR
MECHANICAL BRAINS

Let us consider the two modern physical devices for handling information which make
mechanical brains possible. These are relays and electronic tubes (Nos. 21 and 22). The last
three kinds of equipment listed in the table (magnetic surfaces, No. 23; delay lines, No. 24;
and electrostatic storage tubes, No. 25) were not included in any mechanical brains
functioning by the middle of 1948. The discussion of them is therefore put off to Chapter
10, where we talk about the future design of mechanical brains.

Fig. 1. Relay
Figure 1 shows a simple relay. There are two electrical circuits here. One has two
terminals—Pickup and Ground. The other has three terminals—Common, Normally Open,
and Normally Closed. When current flows through the coil of wire around the iron, it
makes the iron a magnet; the magnet pulls down the flap of iron above, overcoming the
force of the spring. When there is no current through the coil, the iron is not a magnet, and
the flap is held up by the spring. Now suppose that there is current in Common. When there
is no current in Pickup, the current from Common will flow through the upper contact, to
the terminal marked Normally Closed. When there is current in Pickup, the current from
Common will flow through the lower contact, to the terminal marked Normally Open. Thus
we see that a relay expresses a “yes” or a “no,” a 1 or 0, a binary digit, a unit of
information. A relay costs $5 to $10. It is rather expensive for storing a single unit of
information. The fastest it can be changed from 1 to 0, or vice versa, is about ¹/₁₀₀ of a
second.

Fig. 2. Electronic tube.
Figure 2 shows a simple electronic tube. It has three parts—the Cathode, the Grid, and
the Plate. The Grid actually is a coarse net of metal wires. Electrons can flow from the
Cathode to the Plate, provided the voltage on the Grid is such as to permit them to flow. So
we can see that an electronic tube is a very simple on-off device and expresses a “yes” or a
“no,” a 1 or 0, a binary digit, a unit of information. A simple electronic tube suitable for
calculating purposes costs 50 cents to a $1, only ⅒ the cost of a relay. It can be changed
from 1 to 0, or back again, in 1 millionth of a second.
Relays have been widely used in the mechanical brains so far built, and electronic tubes
are the essence of Eniac.
In the next chapter, we shall see how physical equipment for handling information can
be put together to make a simple mechanical brain.

Chapter 3
A MACHINE THAT WILL THINK:
THE DESIGN OF A VERY SIMPLE
MECHANICAL BRAIN
We shall now consider how we can design a very simple machine that will think. Let us call it Simon,
because of its predecessor, Simple Simon.

SIMON, THE VERY SIMPLE
MECHANICAL BRAIN

By designing Simon, we shall see how we can put together physical equipment for handling
information in such a way as to get a very simple mechanical brain. At every point in the design of Simon,
we shall make the simplest possible choice that will still give us a machine that: handles information,
transfers information automatically from one part of the machine to another, and has control over the
sequence of operations. Simon is so simple and so small, in fact, that it could be built to fill up less space
than a grocery-store box, about 4 cubic feet. If we know a little about electrical work, we will find it rather
easy to make Simon.
What do we do first to design the very simple mechanical brain, Simon?

SIMON’S FLESH AND NERVES—
REPRESENTING INFORMATION

The first thing we have to decide about Simon is how information will be represented: as we put it into
Simon, as it is moved around inside of Simon, and as it comes out of Simon. We need to decide what
physical equipment we shall use to make Simon’s flesh and nerves. Since we are taking the simplest
convenient solution to each problem, let us decide to use: punched paper tape for putting information in,
relays (see Chapter 2) and wires for storing and transferring information, and lights for putting
information out.

Fig. 1. Simon, the very simple mechanical brain.

For the equipment inside Simon, we could choose either electronic tubes or relays. We choose relays,
although they are slower, because it is easier to explain circuits using relays. We can look at a relay circuit
laid out on paper and tell how it works, just by seeing whether or not current will flow. Examples will be
given below. When we look at a circuit using electronic tubes laid out on paper, we still need to know a
good deal in order to calculate just how it will work.
How will Simon perceive a number or other information by means of punched tape, or relays, or
lights? With punched paper tape having, for example, 2 spaces where holes may be, Simon can be told 4
numbers—00, 01, 10, 11. Here the binary digit 1 means a hole punched; the binary digit 0 means no hole
punched. With 2 relays together in a register, Simon can remember any one of the 4 numbers 00, 01, 10,
and 11. Here the binary digit 1 means the relay picked up or energized or closed; 0 means the relay not
picked up or not energized or open. With 2 lights, Simon can give as an answer any one of the 4 numbers
00, 01, 10, 11. In this case the binary digit 1 means the light glowing; 0 means the light off. (See Fig. 1.)
We can say that the two lights by which Simon puts out the answer are his eyes and say that he tells his
answer by winking. We can say also that the two mechanisms for reading punched paper tape are Simon’s
ears. One tape, called the input tape, takes in numbers or operations. The other tape takes in instructions
and is called the program tape.

SIMON’S MENTALITY—POSSIBLE RANGE
OF INFORMATION

We can say that Simon has a mentality of 4. We mean not age 4 but just the simple fact that Simon
knows only 4 numbers and can do only 4 operations with them. But Simon can keep on doing these
operations in all sorts of routines as long as Simon has instructions. We decide that Simon will know just 4
numbers, 0, 1, 2, 3, in order to keep our model mechanical brain very simple. Then, for any register, we
need only 2 relays; for any answer, we need only 2 lights.
Any calculating machine has a mentality, consisting of the whole collection of different ideas that the
machine can ever actually express in one way or another. For example, a 10-place desk calculating
machine can handle numbers up to 10 decimal digits without additional capacity. It cannot handle bigger
numbers.

Fig. 2. Four directions.
What are the 4 operations with numbers which Simon can carry out? Let us consider some simple
operations that we can perform with just 4 numbers. Suppose that they stood for 4 directions in the order

east, north, west, south (see Fig. 2). Or suppose that they stood for a turn counterclockwise through some
right angles as follows:

0: Turn through 0°, or no right angles.
1: Turn through 90°, or 1 right angle.
2: Turn through 180°, or 2 right angles.
3: Turn through 270°, or 3 right angles.

Then we could have the operations of addition and negation, defined as follows:
Addition Negation
c=a+b c = -a

b: 0 1 2 3
a: a c
0 0 1 2 3 0 0
1 1 2 3 0 1 3
2 2 3 0 1 2 2
3 3 0 1 2 3 1

For example, the first table says, “1 plus 3 equals 0.” This means that, if we turn 1 right angle and then
turn in the same direction 3 more right angles, we face in exactly the same way as we did at the start. This
statement is clearly true. For another example, the second table says, “2 is the negative of 2.” This means
that, if we turn to the left 2 right angles, we face in exactly the same way as if we turn to the right 2 right
angles, and this statement also is, of course, true.
With only these two operations in Simon, we should probably find him a little too dull to tell us much.
Let us, therefore, put into Simon two more operations. Let us choose two operations involving both
numbers and logic: in particular, (1) finding which of two numbers is greater and (2) selecting. In this way
we shall make Simon a little cleverer.
It is easy to teach Simon how to find which of two numbers is the greater when all the numbers that
Simon has to know are 0, 1, 2, 3. We put all possible cases of two numbers a and b into a table:

b: 0 1 2 3
a:
0
1
2
3

Then we tell Simon that we shall mark with 1 the cases where a is greater than b and mark with 0 the
cases where a is not greater than b:
Greater Than

b: 0 1 2 3
a:

Greater Than
0 0 0 0 0
1 1 0 0 0
2 1 1 0 0
3 1 1 1 0

For example, “2 is greater than 3” is false, so we put 0 in the table on the 2 line in the 3 column. We see
that, for the 16 possible cases, a is greater than b in 6 cases and a is not greater than b in 10 cases.
There is a neat way of saying what we have just said, using the language of mathematical logic (see
Chapter 9 and Supplement 2). Suppose that we consider the statement “a is greater than b” where a and b
may be any of the numbers 0, 1, 2, 3. We can say that the truth value p of a statement P is 1 if the
statement is true and that it is 0 if the statement is false:
p = 1 if P is true, 0 if P is false
The truth value of a statement P is conveniently denoted as T(P) (see Supplement 2):
p = T(P)
Now we can say that the table for the operation greater than shows the truth value of the statement “a is
greater than b”:
p = T(a > b)
Let us turn now to the operation selection. By selecting we mean choosing one number a if some
statement P is true and choosing another number b if that statement is not true. As before, let p be the truth
value of that statement P, and let it be equal to 1 if P is true and to 0 if P is false. Then the operation of
selection is fully expressed in the following table and logical formula (see Supplement 2):
Selection
c = a·p + b·(1 - p)

p: 0 0 0 0 1 1 1 1
b: 0 1 2 3 0 1 2 3
a:
0 0 1 2 3 0 0 0 0
1 0 1 2 3 1 1 1 1
2 0 1 2 3 2 2 2 2
3 0 1 2 3 3 3 3 3

For example, suppose that a is 2 and b is 3 and the statement P is the statement “2 is greater than 0.” Since
this statement is true, p is 1, and
a·p + b·(1 - p) = 2(1) + 3(0) = 2
This result is the same as selecting 2 if 2 is greater than 0 and selecting 3 if 2 is not greater than 0.
Thus we have four operations for Simon that do not overstrain his mentality; that is, they do not
require him to go to any numbers other than 0, 1, 2, and 3. These four operations are: addition, negation,
greater than, selection. We label these operations also with the numbers 00 to 11 as follows: addition, 00;
negation, 01; greater than, 10; selection, 11.

SIMON’S MEMORY—
STORING INFORMATION

The memory of a mechanical brain consists of physical equipment in which information can be stored.
Usually, each section of the physical equipment which can store one piece of information is called a
register. Each register in Simon will consist of 2 relays. Each register will hold any of 00, 01, 10, 11. The
information stored in a register 00, 01, 10, 11 may express a number or may express an operation.

S1-2 S1-1
Relay energized Relay not energized

Fig. 3. Register S1 storing 10.

How many registers will we need to put into Simon to store information? We shall need one register to
read the input tape and to store the number or operation recorded on it. We shall call this register the input
register I. We shall need another register to store the number or operation that Simon says is the answer
and to give it to the output lights. We shall call this register the output register O. We shall need 5 registers
for the part of Simon which does the computing, which we shall call the computer: we shall need 3 to
store numbers put into the computer (C1, C2, C3), 1 to store the operation governing the computer (C4),
and 1 to store the result (C5). Suppose that we decide to have 8 registers for storing information, so as to
provide some flexibility for doing problems. We shall call these registers storage registers and name them
S1, S2, S3, ··· S8. Then Simon will have 15 registers: a memory that at one time can hold 15 pieces of
information.
How will one of these registers hold information? For example, how will register S1 hold the number 2
(see Fig. 3)? The number 2 in machine language is 10. Register S1 consists of two relays, S1-2 and S1-1.
10 stored in register S1 means that relay S1-2 will be energized and that relay S1-1 will not be energized.

THE CONTROL OF SIMON

So far we have said nothing about the control of Simon. Is he docile? Is he stubborn? We know what
his capacity is, but we do not know how to tell him to do anything. How do we connect our desires to his
behavior? How do we tell him a problem? How do we get him to solve it and tell us the answer? How do
we arrange control over the sequence of his operations? For example, how do we get Simon to add 1 and 2
and tell us the answer 3?
On the outside of Simon, we have said, there are two ears: little mechanisms for reading punched
paper tape. Also there are two eyes that can wink: light bulbs that by shining or not shining can put out
information (see Fig. 1). One of the ears—let us call it the left ear—takes in information about a particular
problem: numbers and operations. Here the problem tape or input tape is listened to. Each line on the
input tape contains space for 2 punched holes. So, the information on the input tape may be 00, 01, 10, or
11—either a number or an operation. The other ear—let us call it the right ear—takes in information about

the sequence of operations, the program or routine to be followed. Here the program tape or routine tape
or control tape is listened to. Each line on the program tape contains space for 4 punched holes. We tell
Simon by instructions on the program tape what he is to do with the information that we give him on the
input tape. The information on the program tape, therefore, may be 0000, 0001, 0010, ···, 1111, or any
number from 0 to 15 expressed in binary notation (see Supplement 2).
How is this accomplished? In the first place, Simon is a machine, and he behaves during time. He does
different things from time to time. His behavior is organized in cycles. He repeats a cycle of behavior
every second or so. In each cycle of Simon, he listens to or reads the input tape once and he listens to or
reads the program tape twice. Every complete instruction that goes on the program tape tells Simon a
register from which information is to be sent and a register in which information is to be received. The
first time that he reads the program tape he gets the name of the register that is to receive certain
information, the receiving register. The second time he reads the program tape he gets the name of the
register from which information is to be sent, the sending register. He finishes each cycle of behavior by
transferring information from the sending register to the receiving register.
For example, suppose that we want to get an answer out of Simon’s computer into Simon’s output
lights. We put down the instruction
Send information from C5 into O
or, more briefly,
C5 → O
But he does not understand this language. We must translate into machine language, in this case punched
holes in the program tape. Naturally, the punched holes in the program tape must be able to specify any
sending register and any receiving register. There are 15 registers, and so we give them punched hole
codes as follows:

Register Code Register Code
I 0001 C1 1010
S1 0010 C2 1011
S2 0011 C3 1100
S3 0100 C4 1101
S4 0101 C5 1110
S5 0110 O 1111
S6 0111
S7 1000
S8 1001
To translate the direction of transfer of information, which we showed as an arrow, we put on the program
tape the code for the receiving register first—in this case, output, O, 1111—and the code for the sending
register second—in this case, C5, 1110. The instruction becomes 1111, 1110. The first time in any cycle
that Simon listens with his right ear, he knows that what he hears is the name of the receiving register; and
the second time that he listens, he knows that what he hears is the name of the sending register. One reason
for this sequence is that any person or machine has to be prepared beforehand to absorb or take in any
information.
Now how do we tell Simon to add 1 and 2? On the input tape, we put:

Add 00
1 01

2 10
On the program tape, we need to put:
I → C4
I → C1
I → C2
C5 → O
which becomes:
1101, 0001;
1010, 0001;
1011, 0001;
1111, 1110

THE USEFULNESS OF SIMON

Thus we can see that Simon can do such a problem as:
Add 0 and 3.
Add 2 and the negative of 1.
Find which result is greater.
Select 3 if this result equals 2;
otherwise select 2.
To work out the coding for this and like problems would be a good exercise. Simon, in fact, is a rather
clever little mechanical brain, even if he has only a mentality of 4.
It may seem that a simple model of a mechanical brain like Simon is of no great practical use. On the
contrary, Simon has the same use in instruction as a set of simple chemical experiments has: to stimulate
thinking and understanding and to produce training and skill. A training course on mechanical brains could
very well include the construction of a simple model mechanical brain as an exercise. In this book, the
properties of Simon may be a good introduction to the various types of more complicated mechanical
brains described in later chapters.
The rest of this chapter is devoted to such questions as:
How do transfers of information actually take place in Simon?
How does the computer in Simon work so that calculation actually occurs?
How could Simon actually be constructed?
What follows should be skipped unless you are interested in these questions and the burdensome
details needed for answering them.

SIMON’S THINKING—
TRANSFERRING INFORMATION

The first basic thinking operation for any mechanical brain is transferring information automatically.
Let us see how this is done in Simon.

Fig. 4. Scheme of Simon.
Let us first take a look at the scheme of Simon as a mechanical brain (see Fig. 4). We have 1 input, 8
storage, 5 computer, and 1 output registers, which are connected by means of transfer wires or a transfer
line along which numbers or operations can travel as electrical impulses. This transfer line is often called
the bus, perhaps because it is always busy carrying something. In Simon the bus will consist of 2 wires,
one for carrying the right-hand digit and one for carrying the left-hand digit of any number 00, 01, 10, 11.
Simon also has a number of neat little devices that will do the following:
When any number goes into a register, the coils of the relays of the register
will be connected with the bus.
When any number goes out of a register, the contacts of the relays of the
register will be connected with the bus.
For example, suppose that in register C5 the number 2 is stored. In machine language this is 10. That
means the left-hand relay (C5-2) is energized and the right-hand relay (C5-1) is not energized. Suppose
that we want to transfer this number 2 into the output register O, which has been cleared. What do we do?
Let us take a look at a circuit that will transfer the number (see Fig. 5). First we see two relays in this
circuit. They belong to the C5 register. The C5-2 relay is energized since it holds 1; current is flowing
through its coil, the iron core becomes a magnet, and the contact above it is pulled down. The C5-1 relay
is not energized since it holds 0; its contact is not pulled down. The next thing we see is two rectifiers. The
sign for these is a triangle. These are some modern electrical equipment that allow electrical current to
flow in only one direction. In the diagram, the direction is shown by the pointing of the triangle along the
wire. Rectifiers are needed to prevent undesired circuits. Next, we see the bus, consisting of two wires.
One carries the impulses for left-hand or 2 relays, and the other carries impulses for the right-hand or 1
relays. Next, we see two relays, called the entrance relays for the O register. Current from Source 1 may
flow to these relays, energize them, and close their contacts. When the first line of the program tape is
read, specifying the receiving register, the code 1111 causes Source 1 to be energized. This fact is shown
schematically by the arrow running from the program tape code 1111 to Source 1. Finally, we see the coils
of the two relays for the Output or O register. We thus see that we have a circuit from the contacts of the
C5 register through the bus to the coils of the O register.

Fig. 5. Transfer circuit.
We are now ready to transfer information when the second line of the program tape is read. This line
holds 1110 and designates C5 as the sending register and causes Source 2 to be energized. This fact is
shown schematically by the arrow running from the second line of the program tape to Source 2. When the
second line is read, current flows:
1. From Source 2.
2. Through the contacts of the C5 register if closed.
3. Through the rectifiers.
4. Through the bus.
5. Through the entrance relay contacts of the O register.
6. Through the coils of the O register relays, energizing such of them as
match with the C5 closed contacts; and finally
7. Into the ground.
Thus relay O-2 is energized; it receives current because contact C5-2 is closed. And relay O-1 is not
energized; it receives no current since contact C5-1 is open. So we have actually transferred information
from the C5 register to the O register.
The same process in principle applies to all transfers:
The pattern of electrical impulses, formed by the positioning of one register, is
produced in the positioning of another register.

SIMON’S COMPUTING AND REASONING

Now so far the computing registers in Simon are a mystery. We have said that C1, C2, and C3 take in
numbers 00, 01, 10, 11, that C4 takes in an operation 00, 01, 10, 11, and that C5 holds the result. What
process does Simon use so that he has the correct result in register C5?
Let us take the simplest computing operation first and see what sort of a circuit using relays will give
us the result. The simplest computing operation is negation. In negation, a number 00, 01, 10, 11 goes into

the C1 register, and the operation 01 meaning negation goes into the C4 register, and the correct result
must be in the C5 register. So, first, we note the fact that the C4-2 relay must not be energized, since it
contains 0, and that the C4-1 relay must be energized, since it contains 1.
Now the table for negation, with c = -a, is:

a c
0 0
1 3
2 2
3 1
Negation in machine language will be:

a c
00 00
01 11
10 10
11 01
Now if a is in the C1 register and if c is in the C5 register, then negation will be:

C1 C5
00 00
01 11
10 10
11 01
But each of these registers C1, C5 will be made up of two relays, the left-hand or 2 relay and the right-
hand or 1 relay. So, in terms of these relays, negation will be:

C1-2 C1-1 C5-2 C5-1
0 0 0 0
0 1 1 1
1 0 1 0
1 1 0 1
Now, on examining the table, we see that the C5-1 relay is energized if and only if the C1-1 relay is
energized. So, in order to energize the C5-1 relay, all we have to do is transfer the information from C1-1
to C5-1. This we can do by the circuit shown in Fig. 6. (In this and later diagrams, we have taken one
more step in streamlining the drawing of relay contacts: the contacts are drawn, but the coils that energize
them are represented only by their names.)

Fig. 6. Negation— Fig. 7. Negation—
right-hand digit. left-hand digit.

Taking another look at the table, we see also that the C5-2 relay must be energized if and only if:

C1-2 C1-1
AND
HOLDS: HOLDS:
0 1
1 0
A circuit that will do this is the one shown in Fig. 7. In Fig. 8 is a circuit that will do all the desired
things together: give the right information to the C5 relay coils if and only if the C4 relays hold 01.

Fig. 8. Negation circuit.
Let us check this circuit. First, if there is any operation other than 01 stored in the C4 relays, then no
current will be able to get through the C4 contacts shown and into the C5 relay coils, and the result is
blank. Second, if we have the operation 01 stored in the C4 relays, then the C4-2 contacts will not be
energized—a condition which passes current—and the C4-1 contacts will be energized—another condition
which passes current—and:

If the number in C1 is: then C1-1: and C1-2: and the C5 relays energized are:
0 does not close does not close neither
1 closes does not close C5-2, C5-1
2 does not close closes C5-2 only
3 closes closes C5-1 only
Thus we have shown that this circuit is correct.
We see that this circuit uses more than one set of contacts for several relays (C1-2, C4-1, C4-2); relays
are regularly made with 4, 6, or 12 sets of contacts arranged side by side, all controlled by the same pickup
coil. These are called 4-, 6-, or 12-pole relays.

Fig. 9. Addition circuit.

Fig. 10. Greater-than circuit.
Circuits for addition, greater than, and selection can also be determined rather easily (see Figs. 9, 10,
11). (Note: By means of the algebra of logic, referred to in Chapter 9 and Supplement 2, the conditions for
many relay circuits, as well as the circuit itself, may be expressed algebraically, and the two expressions
may be checked by a mathematical process.) For example, let us check that the addition circuit in Fig. 9
will enable us to add 1 and 2 and obtain 3. We take a colored pencil and draw closed the contacts for C1-1
(since C1 holds 01) and for C2-2 (since C2 holds 10). Then, when we trace through the circuit,

remembering that addition is stored as 00 in the C4 relays, we find that both the C5 relays are energized.
Hence C5 holds 11, which is 3. Thus Simon can add 1 and 2 and make 3!

Fig. 11. Selection Circuit.

PUTTING SIMON TOGETHER

In order to put Simon together and make him work, not very much is needed. On the outside of Simon
we shall need two small mechanisms for reading punched paper tape. Inside Simon, there will be about 50
relays and perhaps 100 feet of wire for connecting them. In addition to the 15 registers (I, S1 to S8, C1 to
C5, and O), we shall need a register of 4 relays, which we shall call the program register. This register
will store the successive instructions read off the program tape. We can call the 4 relays of this register P8,
P4, P2, P1. For example, if the P8 and P2 relays are energized, the register holds 1010, and this is the
program instruction that calls for the 8th plus 2nd, or 10th, register, which is C1.
For connecting receiving registers to the bus, we shall need a relay with 2 poles, one for the 2-line and
one for the 1-line, for each register that can receive a number from the bus. For example, for entering the
output register, we actually need only one 2-pole relay instead of the two 1-pole relays drawn for
simplicity in Fig. 5. There will be 13 2-pole relays for this purpose, since only 13 registers receive
numbers from the bus; registers I and C5 do not receive numbers from the bus. We call these 13 relays the
entrance relays or E relays, since E is the initial letter of the word entrance.

Fig. 12. Select-Receiving-Register circuit.
The circuit for selecting and energizing the E relays is shown in Fig. 12. We call this circuit the Select-
Receiving-Register circuit. For example, suppose that the P8 and P2 relays are energized. Then this circuit
energizes the E10 relay. The E10 relay closes the contacts between the C1 relay coils and the bus; and so it
connects the C1 register to receive the next number that is sent into the bus. This kind of circuit expresses
a classification and is sometimes called a pyramid circuit since it spreads out like a pyramid. A similar
pyramid circuit is used to select the sending register.
We shall need a relay for moving the input tape a step at a time. We shall call this relay the MI relay,
for moving input tape. We also need a relay for moving the program tape a step at a time. We shall call this
relay the MP relay for moving program tape. Here then is approximately the total number of relays
required:

Relays Name Number
I, S, C, O Input, Storage, Computer, Output 30
P Program 4
E Entrance 13
MI Move Input Tape 1
MP Move Program Tape 1
Total 49
A few more relays may be needed to provide more contacts or poles. For example, a single P1 relay will
probably not have enough poles to meet all the need for its contacts.

Fig. 13. Latch relay.
Each cycle of the machine will be divided into 5 equal time intervals or times 1 to 5. The timing of the
machine will be about as follows:
Time Action
1 Move program tape.
Move input tape if read out of in last cycle.
2 Read program tape, determining the receiving register.
Read through the computing circuit setting up the C5 register.
3 Move program tape.
Energize the E relay belonging to the receiving register.
4 Read program tape again, determining the sending register.
5 Transfer information by reading through the
Select-Sending-Register circuit and the
Select-Receiving-Register circuit.
In order that information may remain in storage until wanted, register relays should hold their
information until just before the next information is received. This can be accomplished by keeping
current in their coils or in other ways. There is a type of relay called a latch relay, which is made with two
coils and a latch. This type of relay has the property of staying or latching in either position until the
opposite coil is impulsed (see Fig. 13). This type of relay would be especially good for the registers of
Simon.
If any reader sets to work to construct Simon, and if questions arise, the author will be glad to try to
answer them.

Chapter 4
COUNTING HOLES:
PUNCH-CARD CALCULATING MACHINES
When we think of counting, we usually think of saying softly to ourselves
“one, two, three, four, ···.” This is a good way to find the total of a small group
of objects. But when we have a large group of objects or a great many groups of
objects to be counted, a much faster way of counting is needed. A very fast way
of sorting and counting is punch-card calculating machinery. This is machinery
which handles information expressed as holes in cards. Punch-card machines
can:

Sort, count, file, select, and copy information,
Make comparisons, and choose according to instructions,
Add, subtract, multiply, and divide,
List information, and print totals.

For example, in a life insurance company, much routine handling of information
about insurance policies is necessary:
Writing information on newly issued policies.
Setting up policy-history cards.
Making out notices of premiums due.
Making registers of policies in force, lapsed, died, etc., for
purposes of valuation as required by law or good
management.
Calculating and tabulating premium rates, dividend rates,
reserve factors, etc.
Computing and tabulating expected and actual death rates;
and much more.
All these operations can be done almost automatically by punch-card machines.

ORIGIN AND DEVELOPMENT

When a census of the people of a country is taken, a great quantity of sorting
and counting is needed: by village, county, city, and state; by sex; by age; by
occupation; etc. In 1886, the census of the people of the United States which had
been taken in 1880 was still being sorted and counted. Among the men then
studying census problems was a statistician and inventor, Herman Hollerith. He
saw that existing methods were so slow that the next census (1890) would not be
finished before the following census (1900) would have to be begun. He knew
that cards with patterns of holes had been used in weaving patterns in cloth. He
realized that the presence or absence of a property, for example employed or
unemployed, could be represented by the presence or absence of a hole in a piece
of paper. An electrical device could detect the hole, he believed, since it would
allow current to flow through, whereas the absence of the hole would stop the
current. He experimented with sorting and counting, using punched holes in
cards, and with electrical devices to detect the holes and count them. A definite
meaning was given to each place in the card where a hole might be punched.
Then electrical devices handled the particular information that the punches
represented. These devices either counted or added, singly or in various
combinations, as might be desired.
More than 50 years of development of punch-card calculating machinery
have since then taken place. Several large companies have made quantities of
punch-card machines. A great degree of development has taken place in the
punch-card machines of International Business Machines Corporation (IBM),
and for this reason these machines will be the ones described in this chapter.
What is said here, however, may also in many ways apply to punch-card
machines made by other manufacturers—Remington-Rand, Powers, Control
Instrument, etc.

GENERAL PRINCIPLES

To use punch-card machines, we first convert the original information into
patterns of holes in cards. Then we feed the cards into the machines. Electrical
impulses read the pattern of holes and convert them into a pattern of timed
electrical currents. Actually, the reading of a hole in a column of a punch card is
done by a brush of several strands of copper wire pressed against a metal roller
(Fig. 1). The machine feeds the card (the bottom edge first, where the 9’s are
printed) with very careful timing over the roller; and, when the punched hole is
between the brush and the roller, an electrical circuit belonging to that column of
the card is completed. The machine responds according to its general design and
its wiring for the particular problem: it punches new cards, or it prints new

marks, or it puts information into new storage places. Clerks, however, move the
cards from one machine to another. They wait on the machines, keep the card
feeds full, and empty the card hoppers as they fill up. A human error of putting
the wrong block of cards into a machine may from time to time cause a little
trouble, especially in sorting. Actually, in a year, billions of punch cards are
handled precisely.

Fig. 1. Reading of punch cards.
The punch card is a masterpiece of engineering and standardization. Its exact
thickness matches the knife-blade edges that feed the cards into slots in the
machines, and matches the channels whereby these cards travel through the
machines. The standard card is 7⅜ inches long and 3¼ inches wide, and it has a
standard thickness of 0.0065 inch and other standard properties with respect to
stiffness, finish, etc.

Fig. 2. Scheme of standard punch card.
(Note: Positions 11 and 12 are not usually marked by printed numbers or letters.)

The standard IBM punch card of today has 80 columns and 12 positions for
punching in each column (Fig. 2). A single punched hole in each of the positions
known as 0 to 9 stands for each of the digits 0 to 9 respectively. The remaining 2
single punch positions available in any column are usually called the 11 position
and 12 position (though sometimes called the numerical X position and Y
position). These two positions do not behave arithmetically as 11 and 12.
Actually, in the space between one card and the next card as they are fed through
the machines, more positions occur. For example, there may be 4 more: a 10
position preceding the 9, and a 13, a 14, and a 15 position following the 12. The
16 positions in total correspond to a full turn, 360°, of the roller under the brush,
and to a complete cycle in the machine; and a single position corresponds to ¹/₁₆
of 360°, or 22½°. In some machines, the total number of positions may be 20. A
pair of punches stands for each of the letters of the alphabet, according to the
scheme shown.

A 12-1 J 11-1 Unused 0-1
B 12-2 K 11-2 S 0-2
C 12-3 L 11-3 T 0-3
D 12-4 M 11-4 U 0-4
E 12-5 N 11-5 V 0-5
F 12-6 O 11-6 W 0-6
G 12-7 P 11-7 X 0-7
H 12-8 Q 11-8 Y 0-8
I 12-9 R 11-9 Z 0-9
For example, the word MASON is shown punched in Fig. 3.

Fig. 3. Alphabetic punching. Fig. 4. Single-panel plugboard.

To increase the versatility of the machines and provide them with
instructions, many of them have plugboards (Fig. 4). These are standard
interchangeable boards filled with prongs on one side and holes or terminals
called hubs on the other side. The side with the prongs connects to the ends of
electrical circuits in the punch-card machine, which are brought together in one
place for the purpose. On the other side of the board, using plugwires, we can
connect the hubs to each other in different ways to produce different results. The
single-panel plugboard is 10 inches long and 5¾ inches wide. It contains 660
hubs in front and 660 corresponding prongs in the back. A double-panel
plugboard or a triple-panel plugboard applies to some machines. In less time than
it takes to describe it, we can take one wired-up plugboard out of a machine and
put in a new wired-up plugboard and thus change completely the instructions
under which the machine operates. Many of the machines have a number of
different switches that we must also change, when going from one kind of
problem to another.
The numbers that are stored or sorted in punch-card machines may be of any
size up to 80 digits, one in each column of the punch card. In doing arithmetic
(adding, subtracting, multiplying, and dividing), however, the largest number of
digits is usually 10. Beyond 10 digits, we can work out tricks in many cases.

TYPES OF PUNCH-CARD MACHINES

The chief IBM punch-card machines are: the key punch, the verifier, the
sorter, the interpreter, the reproducer, the collator, the multiplying punch, the
calculating punch, and the tabulator. Of these 9 machines, the last 6 have
plugboards and can do many different operations as a result.
There is a flow of punch cards through each of these machines. The machines
differ from each other in the number and relation of the paths of flow, or card
channels, and in the number and relation of the momentary stopping places, or
card stations, at which cards are read, punched, or otherwise acted on. We can
get a good idea of what a machine is from a picture of these card channels.

Key Punch

We use a key punch (Fig. 5) to punch original information into blank cards.
In the key punch there is one card channel; it has one entrance, one station, and
one exit. At the card station, there are 12 punching dies, one for each position in

the card column, and each card column is presented one by one for punching.
The numeric keyboard (Fig. 6) for the key punch has 14 keys:
One key for each of the punches 0 to 9, 11, and 12,
A space key, which allows a column of the punch card to
go by with no punch in it,
A release key, which ejects the card and feeds another
card.

Fig. 5. Key punch.

Fig. 6. Keyboard of key punch.
Of course, in using a key punch, we must punch the same kind of information
in the same group of columns. For example, if these cards are to contain
employees’ social security numbers, we must punch that number always in the
same card columns, numbered, say, 15 to 23, or 70 to 78, etc.

Verifier

The verifier is really the same machine as the key punch, but it has dull
punching dies moving gently instead of sharp ones moving with force. It turns on
a red light and stops when there is no punched hole in the right spot to match
with a pressed key.

Sorter

The sorter is a machine for sorting cards, one column at a time (Fig. 7). The
sorter has a card channel that forks; it has one entrance, one station, and 13 exits.
Each exit corresponds to: one of the 12 punch positions 0 to 9, 11, and 12; or
reject, which applies when the column is nowhere punched. It has one card
station where a brush reads a single column of the card. We can turn a handle and
move the brush to any column.

Fig. 7. Sorter.

Interpreter

The interpreter takes in a card, reads its punches, prints on the card the marks
indicated by the punches, and stacks the card. We call this process interpreting
the card, since it translates the punched holes into printed marks. The interpreter
(Fig. 8) has one card channel, with one entrance, 2 card stations, and one exit.
What the machine does at the second card station depends on what the machine
reads at the first card station and on what we have told the machine by switches
and plugboard wiring to do.

Fig. 8. Interpreter.

Reproducer

The reproducer or reproducing punch can:
Reproduce, or copy the punches in one group of cards into
another group of cards (in the same or different
columns).
Compare, or make sure that the punches in two groups of
cards agree (and shine a red light if they do not).
Gang punch, or copy the punches in a master card into a
group of detail cards.
Summary punch, or copy totals or summaries obtained in
the tabulator into blank cards in the reproducer.

Fig. 9. Reproducer.
The reproducer (Fig. 9) has 2 independent card channels, the cards not
mingling in any way, called the reading channel and the punching channel. We
can run the machine with only the punching channel working; in fact, IBM
equips some models only with the punching channel, particularly for “summary
punch” operation. The machine is timed so that, when any card is at the middle
station in either channel, then the next preceding card is at the latest station, and
the next following card is at the earliest station. At 5 stations, the machine reads a
card. At the middle station of the punching channel, the machine punches a card.
Using a many-wire cable, we can connect the tabulator to the reproducer and so
cause the tabulator to give information electrically to the reproducer. This
connection makes possible the “summary punch” operation. Here is an instance
with punch-card machines where, in order to transfer information from one
machine to another, we are not required to move cards physically from one
machine to another.

Collator

The collator is a machine that arranges or collates cards. It is particularly
useful in selecting, matching, and merging cards. The collator (Fig. 10) has 2
card channels which join and then fork into 4 channels ending in pockets called
Hoppers 1, 2, 3, and 4. The 2 card feeds are called the Primary Feed and the

Secondary Feed. Cards from the Primary Feed may fall only into the first and
second hoppers. Cards from the Secondary Feed may fall only into the second,
third, and fourth hoppers. The collator has 3 stations at which cards may be read.

No.1—Selected primaries
No.2—Merged cards and unselected primaries
No.3—Separate secondaries not selected
No.4—Selected secondaries
Fig. 10. Collator.
IBM can supply additional wiring called the collator counting device. With
this we can make the collator count cards as well as compare them. For example,
we could put 12 blank cards from the Secondary Feed behind each punched-card
from the Primary Feed in order to prepare for some other operation.

Calculating Punch

The calculating punch was introduced in 1946. It is a versatile machine of
considerable capacity. It adds, subtracts, multiplies, and divides. It also has a
control over a sequence of operations, in some cases up to half a dozen steps.
This machine (Fig. 11) has one card channel with 4 stations called,
respectively, control brushes, reading brushes, punch feed, and punching dies. At
station 1, there are 20 brushes; we can set these by hand to read any 20 of the 80
card columns. At station 2 there are 80 regular reading brushes. At station 3 the
card waits for a part of a second while the machine calculates, and, when that is
done, the card is fed into station 4, where it is punched or verified. The
multiplying punch is an earlier model of the calculating punch, without the
capacity for division.

Fig. 11. Calculating punch.

Tabulator

The tabulator can select and list information from cards. Also, it can total
information from groups of cards in counters of the tabulator and can print the
totals.

Fig. 12. Tabulator.
The tabulator (Fig. 12) has one card channel with two stations where cards
may be read, called the Upper Brushes and Lower Brushes. When the Lower
Brush station is reading one card, the Upper Brush station is reading the next
card. The tabulator also has another channel, which is for endless paper (and
sometimes separate sheets or cards). This channel has one station; here printing
takes place. Unlike the typewriter, the tabulator prints a whole row at a time. It
can print up to 88 numerals or letters across the sheet in one stroke. The cards
flowing through the card channel and the paper flowing through the paper
channel do not have to move in step; in fact, we need many different time
relations between them, and the number of rows printed on the paper may have
almost any relation to the number of punch cards flowing through the card
channel.
At the station where paper is printed, we can put on the machine a
mechanism called the automatic carriage. This is like a typewriter carriage,
which holds the paper for a typewriter, but we can control the movement of paper
through the automatic carriage by plugboard wiring, switch settings, and holes in
punch cards. Thus we can arrange for headings, spacing, and feeding of new

sheets to be controlled by the information and the instructions, with a great deal
of versatility.

HANDLING INFORMATION

We have now described briefly the chief available punch-card machines as of
the middle of 1948. The next question is: How do we actually get something
done by means of punch cards? Let us go back to the census example, even
though it may not be a very typical example, and see what would be done if we
wished to compile a census by punch cards.
The first thing we do is plan which columns of the punch card will contain
what information about the people being counted. For example, the following
might be part of the plan:
Information No. of Possibilities Columns
State 60 1-2
County 1,000 3-5
Township 10,000 6-9
City or village 10,000 10-13
Sex 2 14
Age last birthday 100 15-16
Occupation 100,000 17-21
... ... ...
Under the heading state, we know that there are 48 states, the District of
Columbia, and several territories and possessions—all told, perhaps 60
possibilities. So, 2 punch-card columns are enough: they will allow 100 different
sets of punches from 00 to 99 to be put in them. We then assign the code 00 to
Maine, 01 to New Hampshire, 02 to Vermont, etc., or we might assign the code
00 to Alabama, 01 to Arizona, 02 to Arkansas, etc.—whichever would be more
useful. Under the other headings, we do the same thing: count the possibilities;
assign codes. In this case, it will be reasonable to use numeric codes 0 to 9 in
each column in all places because we shall have millions of cards to deal with
and numeric codes can be sorted faster than alphabetic codes. Alphabetic codes
require 2 punched holes in each column, and sorting any column takes 2
operations.

The punch cards are printed with the chosen headings. We set up the codes in
charts and give them to clerks. Using key punches and verifiers, they punch up
the cards and check them. They work from the original information collected by
the census-taker in the field. Since the original information will come in
geographically, probably only one geographic code at a time will be needed, and
it will be simple to keep track of. As to occupation, however, it may be useful to
assign other clerks full-time to examining the original information and specifying
the right code for the occupation. Then the clerks who do the punching will have
only copying to do.
The great bulk of the work with the census will be sorting, counting, and
totaling. The original punch cards will be summarized into larger and larger
groups. For example, the cards for all males age 23 last birthday living in the
state of Massachusetts are sorted together. This group of cards may be put into a
tabulator wired to a summary punch. When the tabulator has counted the last
card of this group, the summary punch punches one card, showing the total
number in this group. Some time later a card like this will be ready for every
state. Then the whole group of state cards may be fed into the tabulator wired to
the reproducer acting as summary punch. When totaled, the number of males age
23 last birthday in the United States will be punched into a single card. After
more compiling, a card like this will be ready for all males in the United States at
each age. Then this group of cards may be fed into the tabulator wired to the
summary punch. Each card may be listed by the tabulator on the paper flowing
through it, showing the age and the number of males living at that age. At the end
of the listing, the tabulator will print the total number of all males in the list, and
the summary punch will punch a card containing this total.

ARITHMETICAL OPERATIONS

Punch-card machines can perform the arithmetical operations of counting,
adding, subtracting, multiplying, dividing, and rounding off.

Counting

Counting can be done by the sorter, the tabulator, and the collator. The
tabulator can print the total count. The tabulator and summary punch wired
together can put the total count automatically into another punch card. The sorter
shows the count in dials.

Adding and Subtracting

Adding and subtracting can be done by the tabulator, the calculating punch,
and the multiplying punch. In the calculating and multiplying punches, the sum
or difference is usually punched into the same card from which the numbers were
first obtained. The tabulator, however, obtains the result first in a counter; from
the counter, it can be printed on paper or punched into a blank card with the aid
of the summary punch.
Numbers are handled as groups of decimal digits, and the machines mirror
the properties of digits in the decimal system. Negative numbers are usually
handled as complements (see Supplement 2). For example, if we have in the
tabulator a counter with a capacity of six digits, the number-000013 is stored in
the counter as the complement 999987. We cannot store in the counter the
number +999987, since we cannot distinguish it from-000013. In other words, if
a counter is to be used for both positive and negative numbers, its capacity is
actually one digit less, since in the last decimal place on the left 0 will mean
positive and 9 will mean negative.

Multiplying and Dividing

Multiplying is done in the calculating and multiplying punches. In both cases,
the multiplication table is built into the circuits of the machine, and the system of
left-hand components and right-hand components is used (see Supplement 2).
Dividing is done in the calculating punch and is carried out in that machine
much as in ordinary arithmetic. By means of an estimating circuit the calculating
punch guesses what multiple of the divisor will go into the dividend. Then it
determines that multiple and tries it.

Rounding Off

Rounding off may be done in 3 punch-card machines, the calculating and
multiplying punches, and the tabulator. For example, suppose we have the
numbers 49.1476, 68.5327, and we wish to round them off to 2 decimal places.
The results will be 49.15 and 68.53. For the first number, we raise the .0076,
turning .1476 into .15, since .0076 is more than .005. For the second number, we
drop the .0027 since it is less than .005.
Each of these punch-card machines provides what is called a 5 impulse in
each machine cycle. When the number is to be rounded off, the 5 impulse is
plugged into the first decimal place that is to be dropped, and it is there added. If
the figure in the decimal place to be dropped is 0 to 4, the added 5 makes no

difference in the last decimal place that is to be kept. But, if the figure in the
decimal place to be dropped is 5 to 9, then the added 5 makes a carry into the last
decimal place that is to be kept, increasing it by 1, and this is just what is wanted
for rounding off.

LOGICAL OPERATIONS

Punch-card machines do many operations of reasoning or logic that do not
involve addition, subtraction, multiplication, or division. Just as we can write
equations for arithmetical operations, so we can write equations for these logical
operations using mathematical logic (see Chapter 9 and Supplement 2). If any
reader, however, is not interested in these logical equations, he should skip each
paragraph that begins with “in the language of logic,” or a similar phrase.

Translating

Reading and writing are operations perhaps not strictly of reasoning but of
translating from one language to another. Basically these operations take in a
mark in one language and give out a mark with the same meaning in another
language. For example, the interpreter takes in punched holes and gives out
printed marks, but the holes and the marks have the same meaning.
The major part of sorting is done by a punch-card sorting machine and can be
considered an operation of translating. In sorting a card, the machine takes in a
mark in the form of a punched hole on a punch card and specifies a place bearing
the same mark where the card is put. The remaining part of sorting is done by
human beings. This part consists of picking up blocks of cards from the pockets
of the sorter and putting the blocks together in the right sequence.

Comparing

Fig. 13. Comparer.
The first operation of reasoning done by punch-card machines is comparing.
For an example of comparing in the operation of the tabulator, let us take
instructing the machine when to pick up a total and print it. As an illustration,
suppose that we are making a table by state, county, and township of the number
of persons counted in a census. Suppose that for each township we have one
punch card telling the total number of persons. If all the cards are in sequence,
then, whenever the county changes, we want a minor total, and, whenever the
state changes, we want a major total. What does the machine do?
The tabulator has a mechanism that we shall call a comparer (Fig. 13). A
comparer has 2 inputs that may be called Previous and Current and one output
that may be called Unequal. The comparer has the property of giving out an
impulse if and only if there is a difference between the 2 inputs.
In the language of the algebra of logic (see Supplement 2 and Chapter 9), let
the pieces of information coming into the comparer be a and b, and let the
information coming out of the comparer be p. Then the equation of the comparer
is:
p = T(a ≠ b)
where “T (···)” is “the truth value of ···” and “···” is a statement, and where the
truth value is 1 if true and 0 if false.
In wiring the tabulator so that it can tell when to total, we use the comparer.
We feed into it the county from the current card and the county from the previous
card. Out of the comparer we get an impulse if and only if these two pieces of
information are different. This is just what happens when the county changes.
The impulse from the comparer is then used in further wiring of the tabulator: it
makes the counter that is busy totaling the number of persons in the county print
its total and then clear. In the same way, another comparer, which watches state
instead of county, takes care of major totals when the state changes.

Selecting

The next operation of reasoning which punch-card machines can do is
selecting. The tabulator, collator, interpreter, reproducer, and calculating punch
all may contain mechanisms that can select information. These mechanisms are
called selectors.
For example, suppose that we are using the tabulator to make a table showing
for each city the number of males and the number of females. In the table we
shall have three columns: first, city; second, males; third, females. Suppose that
each punch card in columns 30 to 36 shows the total of males or females in a
city. Suppose that, if and only if the card is for females, it has an X punch (or 11
punch) in column 79. What do we want to have happen? We want the number in
columns 30 to 36 to go into the second column of the table if there is no X in
column 79, and we want it to go into the third column of the table if there is an X
in column 79. This is just another way of saying that we want the number to go
into the males column if it is a number of males, and into the females column if it
is a number of females. We make this happen by using a selector.
A selector (Fig. 14) is a mechanism with 2 inputs and 2 outputs. The 2 inputs
are called X Pickup and Common. The 2 outputs are called X and No X. The X
Pickup, as its name implies, watches for X’s. The Common takes in information.
What comes out of X is what goes into Common if and only if an X punch is
picked up; otherwise nothing comes out. What comes out of No X is what goes
into Common if and only if an X punch is not picked up; otherwise nothing
comes out. From the point of view of ordering punch-card equipment, we should
note that there are two types of selectors: X selectors or X distributors, which
have a selecting capacity of one column—that is, one decimal digit—and class
selectors, which ordinarily have a selecting capacity of 10 columns or 10 decimal
digits. But we shall disregard this difference here, as we have disregarded most
other questions of capacity in multiplication, division, etc.

Fig. 14. Selector.
In the language of logic (see Chapter 9 and Supplement 2), if p, a, b, c are the
information in X Pickup, Common, X, and No X, respectively, then the equations
for a selector are:
b = a·p
c = a·(1 - p)
Returning now to the table we wish to make, we connect columns 30 to 36 of
the punch card to Common. We connect column 79 of the punch card to the X
Pickup. We connect the output No X to the males column of the table. We
connect the output X to the females column of the table. In this way we make the
number in the punch card appear in either one of two places in the table
according to whether the number counts males or females.
We might mention several more properties of selectors. A selector can be
used in the reverse way, with X Pickup, X, and No X as inputs and Common as
output (Fig. 15). What will come out of Common is (1) what goes into input No
X if there is no X punch in the column to which input X Pickup is wired, and (2)
what goes into input X if there is an X punch in the column to which input X
Pickup is wired.
In this case the logical equation for the selector is:
a = bp + c(1 - p)
Also, selectors can be used one after another, so that selecting based on 2 or 3 X
punches can be made.

Fig. 15. Selector.
In the language of logic, if p, q, r are the truth values of “there is an X punch
in column i, j, k,” respectively, then by means of selectors we can get such a
function as:
c = apq + b(1 - q)(1 - r)
Also, a selector may often be energized not only by an X punch but also by a
punch 0, 1, 2, ···, 9 and 12. In this case, the selector is equipped with an
additional input that can respond to any digit. This input is called the Digit
Pickup.

Digit Selector

Something like an ordinary selector is another mechanism called a digit
selector (Fig. 16). This has one input, Common, and 12 outputs, 0, 1, 2, 3, 4, 5, 6,
7, 8, 9, 11, 12. This mechanism is often included in the tabulator and may be
included in other punch-card machines. For example, suppose that we want to do
something if and only if column 62 of a punch card contains a 3 or a 4 or a 9.
Then we connect a brush that reads column 62 of the punch card to the Common
input of the digit selector. And we connect out from the digit selector jointly from
outputs 3, 4, and 9.

Fig. 16. Digit selector.
In the language of logic, if a is the digit going into Common, and if p is the
impulse coming out of the digit selector, then the equation of the mechanism in
this case is:
p = T(a = 3, 4, 9)

Sequencer

A fourth operation of reasoning done by punch-card machines is finding that
one number is greater than, or equal to, or less than another. This operation is
done in the collator and may be called sequencing. For example, suppose that we
have a file of punch cards for cities, showing in columns 41 to 48 the number of
people. Suppose that we wish to pick out the cards for cities over 125,000 in
population. Now the collator has a mechanism that has 2 inputs and 3 outputs
(Fig. 17). We may call this mechanism a sequencer, since it can tell the sequence
of two numbers. What goes into the Primary input is a number: let us call it a.
What goes into Secondary is another number: let us call it b. An impulse comes
out of Low Primary if a is less than b. An impulse comes out of Equal if a equals
b. An impulse comes out of Low Secondary if a is greater than b.

Fig. 17. Sequencer.
In the language of logic, if p, q, r are the three indications in Low Primary,
Equal, and Low Secondary, then:
p = T(a < b)
q = T(a = b)
r = T(a > b)
Returning to our example, we punch up a card with 125,000 in columns 43 to
48, and we put this card into the Secondary Feed. We take the punch cards for
cities and put them into the Primary Feed. In the plugboard, we connect the hubs
of the Secondary Brushes (that read the card in the Secondary Feed), columns 43
to 48, to the Secondary input of the Sequencer. We connect the hubs of the
Primary Brushes (that read the card in the Primary Feed), columns 41 to 48, to
the Primary input of the Sequencer. Then we connect the Low Primary output of
the Sequencer to a device that causes the city card being examined to fall into
pocket 1. We connect Equal output and Low Secondary output to a device that
causes the city card being examined to fall into pocket 2. Then, when the card for
any city comes along, the machine compares the number of people in the city
with 125,000. If the number is greater than 125,000, the card will fall into pocket
1; otherwise the card will fall into pocket 2. At the end of the run, we shall find in
pocket 1 all the cards we want.

NEW DEVELOPMENTS

We may expect to see over the next few years major developments in punch-
card machinery. It would seem likely that types of punch-card machines like the
following might be constructed:

A punch-card machine that performs any arithmetical or
logical operation at high speed and may perform a
dozen such operations in sequence during the time that
a punch card passes through the machine.
A punch-card machine that uses loops of punched paper
tape, which express either a sequence of values in a
table that the machine can consult or a sequence of
instructions that govern the operations of the machine.
Punch-card machinery that uses a larger card than the 80-
column card.
A punch-card machine that may have a fairly large amount
of internal memory, perhaps 30 or 40 registers where
numbers or words may be stored and referred to.

SPEED

The speed of various operations with present IBM punch-card machines is
about as shown in the table.
Machine Operation Time in Seconds
Key punch Punch 80 columns About 20 to 40
Verifier Check 80 columns About 20 to 40
Sorter Sort 1 card on 1 column 0.15
Interpreter Print 1 line 0.8
Reproducer Reproduce a card, all 80 columns 0.6
Collator Merge 2 cards 0.25
Multiplying punch Multiply by 8 digits 5.6
Calculating punch Add 0.3
Calculating punch Multiply by 8 digits 3.6
Calculating punch Divide, obtaining 8 quotient digits 9.0
Tabulator Print 1 line, numbers only 0.4
Tabulator Print 1 line, letters included 0.75
Tabulator Add numbers from 1 card 0.4

COST

Punch-card machines may be either rented or purchased from some
manufacturers but only rented from others. If we take the cost of a clerk as $120
to $150 a month, the monthly rent of most punch-card machines ranges from ⅒
of the cost of a clerk for the simplest type of machine, such as a key punch, to 3
times the cost of a clerk for a complicated and versatile type of machine, such as
a tabulator with many attachments. The rental basis is naturally convenient for
many kinds of jobs.

RELIABILITY

The reliability of work with punch cards and punch-card machines is often
much better than 99 per cent: in 10,000 operations, failures should be less than 2
or 3. This is, of course, much better than with clerical operations.
There are a number of causes for machine or card failures. Sometimes cards
may be warped and may not feed into the machines properly. Or, the air in the
room may be very dry, and static electricity may make the cards stick together.
Or, the air may be too humid; the cards may swell slightly and may jam in the
machine. A punch may get slightly out of true alignment, and punches in the
cards may be slightly off. A relay may get dust on its contact points and, from
time to time, fail to perform in the right way. Considerable engineering effort has
been put into remedying these and other troubles, with much success.
To make sure that we have correct results from human beings working with
punch-card machines, we may verify each process. Information that is punched
on the key punch may be verified on the verifier. Multiplications done with
multiplicand a and multiplier b may be repeated and compared with
multiplications done with multiplicand b and multiplier a. Cards that are sorted
on the sorter may be put through the collator to make sure that their sequence is
correct. It is often good to plan every operation so that we have a proof that the
result is right.
It is standard practice to have the machines inspected regularly in order to
keep them operating properly. On the average, for every 50 to 75 machines, there
will be one full-time service man maintaining them and taking care of calls for
repairs. Of course, as with any machinery, some service calls will be a result of
the human element; for example, a problem may have been set up wrongly on a
machine.

GENERAL USEFULNESS

Punch-card calculations are much faster and more accurate than hand
calculations. With punch cards, work is organized so that all cases are handled at
the same time in the same way. This process is very different from handling each
case separately from start to finish. As soon as the number of cases to be handled
is more than a hundred and each item of information is to be used five or more
times, punch cards are likely to be advantageous, provided other factors are
favorable. Vast quantities of information have been handled very successfully by
punch-card machines. Over 30 scientific and engineering laboratories in the
United States are doing computation by punch cards. Over a billion punch cards,
in fact, are used annually in this country.

Chapter 5
MEASURING:
MASSACHUSETTS INSTITUTE OF
TECHNOLOGY’S
DIFFERENTIAL ANALYZER NO. 2
In the previous chapter we talked about machines that move information
expressed as holes in cards. In this chapter we shall talk about machines that
move information expressed as measurements.

ANALOGUE MACHINES

A simple example of a device that uses a measurement to handle information
is a doorpost. Here the height of a child may be marked from year to year as he
grows (Fig. 1). Or, suppose that we have a globe of the world and wish to find the
shortest path between Chicago and Moscow. We may lay a piece of string on the
globe, pull it tight between those points, and then measure the string on a scale to
see about what distance it shows (Fig. 2).
Machines that handle information as measurements of physical quantities are
called analogue machines, because the measurement is analogous to, or like, the
information. A common example of analogue machine is the slide rule. With this
we calculate by noting the positions of ruled lines on strips that slide by each
other. These strips are made of fine wood, or of plastic, or of steel, in such fashion
that the ruled lines will hold true positions and not warp. If we space the rulings
so that 1, 2, 3, 4, 5, 6 ··· are equally spaced, then the slide rule is useful for
addition (Fig. 3). But if we space the rulings so that powers (for example, powers
of two—1, 2, 4, 8, 16, 32 ···) (Fig. 4) are equally spaced, we can do
multiplication. The spacings are then according to the logarithms of numbers (see
Supplement 2). Multiplication is more troublesome than addition, and so more
slide rules are made for multiplication than for addition.

Fig. 1. Measurement by doorpost.

Fig. 2. Measurement by string.

Fig. 3. Slide Rule for adding.

Fig. 4. Slide Rule for multiplying.
During World War II, the aiming and firing of guns against hostile planes was
done by machine. After sighting a plane, these machines automatically calculated
how to direct fire against it. They were much better and faster than any man.
These fire-control instruments were analogue machines with steel and electrical
parts built to fine tolerances. With care we can get accuracy of 1 part in 10,000
with analogue machines, but greater accuracy is very hard to get.

PHYSICAL QUANTITIES

Suppose that we wish to make an analogue machine. We need to represent
information by a measurement of something. What should we select? What
physical thing to be measured should we choose to put into the machine?
Different amounts of this physical quantity will match with different amounts of
the measurement being expressed. In the case of the doorpost, the string, and the
slide rule, the physical quantity is distance. In many fire-control instruments, the
physical quantity is the amount of turning of a shaft (Fig. 5). Many other physical
quantities have from time to time been used in analogue machines, such as
electrical measurements. The speedometer of an automobile tells distance
traveled and speed. It is an analogue machine. It uses the amount of turning of a
wheel, and some electrical properties. It handles information by means of
measurements. The basic physical quantity that it measures is the amount of
turning of a shaft.

Fig. 5. Measurement by amount of turning of a shaft.

DIFFERENTIAL ANALYZER

The biggest and cleverest mechanical brain of the analogue type which has
yet been built is the differential analyzer finished in 1942 at Massachusetts
Institute of Technology in Cambridge, Mass. The fundamental physical quantity
used in this machine is the amount of turning of a shaft. The name analyzer
means an apparatus or machine for analyzing or solving problems. It happens that
the word “analyzer” has been used rather more often in connection with analogue
machines, and so in many cases the word “analyzer” carries the meaning
“analogue” as well. The word “differential” in the phrase “differential analyzer”
refers to the main purpose of the machine: it is specially adapted for solving
problems involving differential equations. Now what is a differential equation?

DIFFERENTIAL EQUATIONS

In order to explain what a differential equation is, we need to use certain
ideas. These ideas are: equation; formula; function; rate of change; interval;
derivative; and integral. In the next few paragraphs, we shall introduce these
ideas briefly, with some explanation and examples. It is entirely possible for
anyone to understand these ideas rather easily, by collecting true statements about
them; no one should feel that because these ideas may be new they cannot be
understood readily.

PHYSICAL PROBLEMS

In physics, chemistry, mechanics, and other sciences there are many problems
in which the behavior of distance, of time, of speed, heat, volume, electrical
current, weight, acceleration, pressure, and many other physical quantities are
related to each other. Examples of such problems are:

Fig. 6. Paths of a shot from a gun, trajectories.
What are the various angles to which a gun should be raised
in order that it may shoot various distances? (See Fig. 6.) (The
paths of a shot from a gun are called trajectories.)
If a plane flies in a direction always at the same angle from
the north, how much farther will it travel than if it flew along the
shortest path? (See Fig. 7.) (A path always at the same angle

from the north is called a loxodrome, and a shortest path on a
globe is called a great circle.)
How should an engine be designed so that it will have the
least vibration when it moves fast?
In physical problems like these, the answer is not a single number but a
formula. What we want to do in any one of these problems is find a formula so
that any one of the quantities may be calculated, given the behavior of the others.
For example, here is a familiar problem in which the answer is a formula and not
a number:

Fig. 7. Paths of a flight.

Fig. 8. Room formulas.

How are the floor area of a room, its length, and its width related to each
other? (See Fig. 8.)

The answer is told in any one of three equations:
(floor area) equals (length) times (width)
(length) equals (floor area) divided by (width)
(width) equals (floor area) divided by (length)
The first equation shows that the floor area depends on the length of the room
and also on the width of the room. So we say floor area is a function of length and
width. This particular function happens to be product, the result of multiplication.
In other words, floor area is equal to the product of length and width.
Now there is another kind of function called a differential function or
derivative. A differential function or derivative is an instantaneous rate of change.
An instantaneous rate of change is the result of two steps: (1) finding a rate of
change over an interval and then (2) letting the interval become smaller and
smaller indefinitely. For example, suppose that we have the problem:
How are speed, distance, and time related to each other?
One of the answers is:
(speed) equals the instantaneous rate of change of
(distance) with respect to (time)
Or we can say, and it is just the same thing in other words:
(speed) equals the derivative of (distance) with respect to
(time)
Now we can tell what a differential equation is. It is simply an equation in
which a derivative occurs, such as the last example. Perhaps the commonest kind
of equation in physical problems is the differential equation.

SOLVING PHYSICAL PROBLEMS

Now we were able to change the equation about floor area into other forms, if
we wanted to find length or width instead of floor area. When we did this, we ran
into the inverse or opposite of multiplication: division.
In the same way, we can change the equation about speed into other forms, if
we want to find distance or time instead of speed. If we do this, we run into a new
idea, the inverse or opposite of the derivative, called integral. The two new
equations are:

(distance) equals the integral of (speed) with respect to
(time)
(time) equals the integral of [one divided by (speed)] with
respect to (distance)

These equations may also be called differential equations.
An integral is the result of a process called integrating. To integrate speed and
get distance is the result of three steps: (1) breaking up an interval of time into a
large number of small bits, (2) adding up all the small distances that we get by
taking each bit of time and multiplying by the speed which applied in that bit of
time, and (3) letting the bits of time get smaller and smaller, and letting the
number of them get larger and larger, indefinitely.
In other words,
(total distance) equals the sum of all the small (distances),
each equal to: a bit of (time) multiplied by the (speed) applying
to that bit

This is another way of saying as before,
(distance) equals the integral of (speed) with respect to
(time)
To solve a differential equation, we almost always need to integrate one or more
quantities.

ORIGIN AND DEVELOPMENT OF THE
DIFFERENTIAL ANALYZER

For at least two centuries, solving differential equations to answer physical
problems has been a main job for mathematicians. Mathematics is supposed to be
logical, and perhaps you would think this would be easy. But mathematicians
have been unable to solve a great many differential equations; only here and
there, as if by accident, could they solve one. So they often wished for better
methods in order to make the job easier.
A British mathematician and physicist, William Thomson (Lord Kelvin), in
1879 suggested solving differential equations by a machine. He went further: he
described mechanisms for integrating and other mathematical processes, and how
these mechanisms could be connected together in a machine. No such machine
was then built; engineering in those years was not equal to it. In 1923, a machine

of this type for solving the differential equations of trajectories was proposed by
L. Wainwright.
In 1925, at Massachusetts Institute of Technology, the problem of a machine
to solve differential equations was again being studied by Dr. Vannevar Bush and
his associates. Dr. Bush experimented with mechanisms that would integrate, add,
multiply, etc., and methods of connecting them together in a machine. A major
part of the success of the machine depended on a device whereby a very small
turning force would do a rather large amount of work. He developed a way in
which the small turning force, about as small as a puff of breath, could be used to
tighten a string around a drum already turning with a considerable force, and thus
clutch the drum, bring in that force, and do the work that needed to be done. You
may have watched a ship being loaded, seen a man coil a rope around a winch,
and watched him swing a heavy load into the air by a slight pull on the rope (Fig.
9). If so, you have seen this same principle at work. The turning force (or torque)
that pulls on the rope is greatly increased (or amplified) by such a mechanism,
and so we call it a torque amplifier.

Fig. 9. Increasing turning force;
winch, or torque amplifier.
By 1930, Dr. Bush and his group had finished the first differential analyzer. It
was entirely mechanical, having no electrical parts except the motors. It was so
successful that a number of engineering schools and manufacturing businesses
have since then built other machines of the Bush type. Each time, some
improvements were made in accuracy and capacity for solving problems. But, if
you changed from one problem to another on this type of machine, you had to do
a lot of work with screwdrivers and wrenches. You had to undo old mechanical
connections between shafts and set up new ones. Accordingly, in 1935, the men at

MIT started designing a second differential analyzer. In this one you could make
all the connections electrically.
MIT finished its second differential analyzer in 1942, but the fact was not
published during World War II, for the machine was put to work on important
military problems. In fact, a rumor spread and was never denied that the machine
was a white elephant and would not work. The machine was officially announced
in October 1945. It was the most advanced and efficient differential analyzer ever
built. We shall talk chiefly about it for the rest of this chapter. A good technical
description of this machine is in a paper, “A New Type of Differential Analyzer,”
by Vannevar Bush and Samuel H. Caldwell, published in the Journal of the
Franklin Institute for October 1945.

GENERAL ORGANIZATION OF
MIT DIFFERENTIAL ANALYZER NO. 2

A differential analyzer is basically made up of shafts that turn. When we set
up the machine to solve a differential equation, we assign one shaft in the
machine to each quantity referred to in the equation. It is the job of that shaft to
keep track of that quantity. The total amount of turning of that shaft at any time
while the problem is running measures the size of that quantity at that time. If the
quantity decreases, the shaft turns in the opposite direction. For example, if we
have speed, time, and distance in a differential equation, we label one shaft
“speed,” another shaft “time,” and another shaft “distance.” If we wish, we may
assign 10 turns of the “time” shaft to mean “one second,” 2 turns of the
“distance” shaft to mean “one foot,” and 4 turns of the “speed” shaft to mean
“one foot per second.” These are called scale factors. We could, however, use any
other convenient units that we wished.
By just looking at a shaft or a wheel, we can tell what part of a full turn it has
made—a half, or a quarter, or some other part—but we cannot tell by looking
how many full turns it has made. In the machine, therefore, there are mechanisms
that record not only full turns but also tenths of turns. These are called counters.
We can connect a counter to any shaft. When we want to know some quantity that
a shaft and counter are keeping track of, we read the counting mechanism.
The second differential analyzer, which MIT finished in 1942, went a step
further than any previous one. In this machine, a varying number can be
expressed either (1) mechanically as the amount of turning of a shaft, or (2)
electrically as the amount of two voltages in a pair of wires. The MIT men did
this by means of a mechanism called an angle-indicator.

Angle indicators have essentially three parts: a transmitter, a receiver, and
switches. The transmitter (Fig. 10) can sense the exact amount that a shaft has
turned and give out a voltage in each of two wires which tells exactly how much
the shaft has turned (Fig. 11). The receiving device (Fig. 12), which has a motor,
can take in the voltages in the two wires and drive a second shaft, making it turn
in step with the first shaft. By means of the switchboard (Fig. 13), the two wires
from the transmitter of any angle-indicator can lead anywhere in the machine and
be connected to the receiver of any other angle indicator.

Fig. 10. Scheme of angle-indicator transmitter.

Fig. 11. Indication of angle.

Fig. 12. Scheme of angle-indicator receiver.
In a differential analyzer, we can connect the shafts together in many different
ways. For example, suppose that we want one shaft b to turn twice as much as
another shaft a. For this to happen we must have a mechanism that will connect
shaft a to shaft b and make shaft b turn twice as much as shaft a. We can draw the
scheme of this mechanism in Fig. 14: a box, standing for any kind of simple or
complicated mechanism; a line going into it, standing for input of the quantity a;
a line going out of it, standing for output of the quantity b; and a statement saying
that b equals 2a.

Fig. 13. Switchboard.
One mechanism that will make shaft b turn twice as much as shaft a is a pair
of gears such that: (1) they mesh together and (2) the gear on shaft a has twice as
many teeth as the gear on shaft b (Fig. 15). On the mechanical differential
analyzer that MIT finished in 1930, a pair of gears was the mechanism actually
used for doubling. To make one shaft turn twice as much as another by this

device, we would: go over to the machine with a screwdriver; pick out from a box
two gears, one with twice as many teeth as the other; slide them onto the shafts
that are to be connected; make the gears mesh together; and screw them tight on
their shafts.

Fig. 14. Scheme of a doubling
mechanism.

Fig. 15. Example of a doubling
mechanism.

On the MIT differential analyzer No. 2, however, we are better off. A much
more convenient device for doubling is used. We make use of: a gearbox in
whichthere are two shafts that may be geared so that one turns twice as much as
the other, and two angle-indicator transmitters and receivers. Looking at the

drawing (Fig. 16), we can see that: shaft a drives shaft c to turn in step, shaft c
drives shaft d to turn twice as much, and shaft d drives shaft b to turn in step.
Here we can accomplish doubling by closing the pairs of switches that connect to
the gearbox shafts.
Angle indicators: T, transmitters, and R, receivers

Fig. 16. Another example of a doubling mechanism.
Above, we have talked about a mechanism with gears that would multiply the
amount of turning by the constant ratio 2. But, of course, in a calculation, any
ratio, say 7.65, 3.142, ···, might be needed, not only 2. In order to handle various
constant ratios, gearboxes of two kinds are in differential analyzer No. 2. The first
kind is a one-digit gearbox. It can be set to give any of 10 ratios, 0.1, 0.2, 0.3, ···,
1.0. The second kind is a four-digit gearbox. It can be set to give any one of more
than 11 thousand ratios, 0.0000, 0.0001, 0.0002, ···, 1.1109, 1.1110. We can thus
multiply by constant ratios.

Adders

We come now to a new mechanism, whose purpose is to add or subtract the
amount of turning of two shafts. It is called an adder. The scheme of it is shown
in Fig. 17: an input shaft with amount of turning a, another input shaft with
amount of turning b, and an output shaft with amount of turning a + b. The adder
essentially is another kind of gearbox, called a differential gear assembly. This
name is confusing: the word “differential” here has nothing to do with the word
“differential” in “differential analyzer.” This mechanism is very closely related to
the “differential” in the rear axle of a motor car, which distributes a driving thrust
from the motor to the two rear wheels of the car.

Fig. 17. Scheme of an adder mechanism.

Fig. 18. Example of an adding mechanism
(differential gear assembly).

A type of differential gear assembly that will add is shown in Fig. 18. This is a
set of 5 gears A to E. The 2 gears A and B are input gears. The amount of their
turning is a and b, respectively. They both mesh with a third gear, C, free to turn,
but the axis of C is fastened to the inside rim of a fourth, larger gear, D. Thus D is

driven, and the amount of its turning is (a + b)/2. This gear meshes with a gear E
with half the number of teeth, and so the amount of turning of E is a + b.
We can subtract the turning of one shaft from the turning of another simply by
turning one of the input shafts in the opposite direction.

Integrators

Another mechanism in a differential analyzer, and the one that makes it worth
while to build the machine, is called an integrator. This mechanism carries out
the process of integrating, of adding up a very large number of small changing
quantities. Figure 19 shows what an integrator is. It has three chief parts: a disc, a
little wheel, and a screw. The round disc turns horizontally on its vertical shaft.
The wheel rests on the disc and turns vertically on its horizontal shaft. The screw
goes through the support of the disc; when the screw turns, it changes the distance
between the edge of the wheel and the center of the disc.

Fig. 19. Mechanism of integrator.
Now let us watch this mechanism move. If the disc turns a little bit, the wheel
pressing on it must turn a little bit. If the screw turns a small amount, the distance
between the edge of the wheel and the center of the disc changes. The amount
that the wheel turns is doubled if its distance from the center of the disc is
doubled, and halved if that distance is halved. So we see that:

(the total amount that the wheel turns) equals the sum of
all the small (amounts of turning), each equal to: a
bit of (disc turning) multiplied by the (distance from
the center of the disc to the edge of the wheel) applying
to that bit

If we look back at our discussion of integrating (p. 72), we see that the capital
words here are just the same as those used there. Thus we have a mechanism that
expresses integration:
(the total amount that the wheel turns) equals the
integral of (the distance from the center of the disc to
the wheel) with respect to (the amount that the disc
turns)
The scheme of this mechanism is shown in Fig. 20.
For example, suppose that the screw measures the speed at which a car travels
and that the disc measures time. The wheel, consequently, will measure distance
traveled by the car. The mechanism integrates speed with respect to time and
gives distance.

Fig. 20. Scheme of integrator.
This mechanism is the device that Lord Kelvin talked about in 1879 and that
Dr. Bush made practical in 1925. The mechanical difficulty is to make the friction
between the disc and the wheel turn the wheel with enough force to do other
work. In the second differential analyzer, the angle indicator set on the shaft of
the wheel solves the problem very neatly.

Fig. 21. Graph of air resistance coefficient.

Function Tables

The behavior of some physical quantities can be described only by a series of
numbers or a graphic curve. For example, the resistance or drag of the air against
a passing object is related to the speed of the object in a rather complicated way.
Part of the relation is called the drag coefficient or resistance coefficient; a rough
graph of this is shown in Fig. 21. This graph shows several interesting facts: (1)
when the object is still, there is no air resistance; (2) as it travels faster and faster,
air resistance rapidly increases; (3) when the object travels with the speed of
sound, resistance is very great and increases enormously; (4) but, when the object
starts traveling with a speed about 20 per cent faster than sound, the drag
coefficient begins to decrease. This drawing or graph shows in part how air
resistance depends on speed of object; in other words, it shows the drag
coefficient as a function of speed (see Supplement 2).

Fig. 22. Pointer following graph.
Now we need a way of putting any function we wish into a differential
analyzer. To do this, we use a mechanism called a function table. We draw a
careful graph of the function according to the scale we wish to use, and we set the
graph on the outside of a large drum (Fig. 22). For example, we can put the
resistance coefficient graph on the drum; the speed (or independent variable)
goes around the drum, and the resistance coefficient (or dependent variable) goes
along the drum. The machine slowly turns the drum, as may be called for by the
problem. A girl sits at the function table and watches, turning a handwheel that
keeps the sighting circle of a pointer right over the graph. The turning of the
handwheel puts the graphed function into the machine. Instead of employing a
person, we can make one side of the graph black, leaving the other side white,
and put in a phototube (an electronic tube sensitive to amount of light) that will
steer from pure black or pure white to half and half (see Fig. 23).
We do not need many function tables to put in information, because we can
often use integrators in neat combinations to avoid them. We shall say more about
this possibility later.
We can also use a function table to put out information and to draw a graph.
To do so, we disconnect the handwheel; we connect the shaft of the handwheel to
the shaft that records the function we are interested in; we take out the pointer and
put in a pen; and we put a blank sheet of graph paper around the drum.

Fig. 23. Phototube following graph.
We have now described the main parts of the second MIT differential
analyzer. They are the parts that handle numbers. We can now tell the capacity of
the differential analyzer by telling the number of main parts that it holds:
Shafts About 130
One-digit gearboxes 12
Four-digit gearboxes 16
Adders About 16
Integrators 18
Function tables 3
On a simpler level, we can say that the machine holds these physical parts:
Miles of wire About 200
Relays About 3000
Motors About 150
Electronic tubes About 2000

INSTRUCTING THE MIT
DIFFERENTIAL ANALYZER NO. 2

Besides the function tables for putting information into the machine, there are
three mechanisms that read punched paper tape. The three tapes are called the A

tape, the B tape, and the C tape. From these tapes the machine is set up to solve a
problem.
Suppose that we have decided how the machine is to solve a problem.
Suppose that we know the number of integrators, adders, gearboxes, etc., that
must be used, and know how their inputs and outputs are to be connected. To
carry out the solution, we now have to put the instructions and numbers into the
machine.
The A tape contains instructions for connecting shafts in the machine. Each
instruction connects a certain output of one type of mechanism (adder, etc.) to a
certain input of another type of mechanism. When the machine reads an
instruction on this tape, it connects electrically the transmitting angle-indicator of
an output shaft to the receiving angle-indicator of another input shaft.
Now the connecting part of the differential analyzer behaves as if it were very
intelligent: it assigns an adder or an integrator or a gearbox, etc., to a new
problem only if that mechanism is not busy. For example, if a problem tape calls
for adder 3 (in the list belonging to the problem), the machine will assign the first
adder that is not busy, perhaps adder 14 (in the machine), to do the work. Each
time that adder 3 (in the problem list) is called for in the A tape, the machine
remembers that adder 14 was chosen and assigns it over again. This ability, of
course, is very useful.
The B tape contains the ratios at which the gearboxes are to be set. For
example, suppose that we want gearbox 4 (in the problem list) to change its input
by the ratio of 0.2573. The machine, after reading the A tape, has assigned
gearbox 11 (in the machine list). Then, when the machine reads the B tape, it sets
the ratio in gearbox 11 to 0.2573.
The answer to a differential equation is different for different starting
conditions. For example, when we know speed and time and wish to find distance
traveled and where we have arrived, we must know the point at which we started.
We therefore need to arrange the machine so that we can put in different starting
conditions (or different initial conditions, as the mathematician calls them).
The C tape puts the initial conditions into the machine. For example, reading
the C tape for the problem, the machine finds that 3000 should, at the start of the
problem, stand in counter 4. The machine then reads the number at which counter
4 actually stands, say 6728.3. It subtracts the two numbers and remembers the
difference, -3728.3. And whenever the machine reads that counter later, finding,
say, 9468.4 in it, first the 3728.3 is subtracted, and then the answer 5740.1 is
printed.

ANSWERS

Information may come out of the machine in either one of two ways: in
printed numbers or in a graph. In fact, the same quantity may come out of the
machine in both ways at the same time. To obtain a graph, we change a function
table from input to output, put a pen on it, and have it draw the graph.
The machine has 3 electric typewriters. The machine will take numerical
information out of the counters at high speed even while they are turning, and it
will put the information into relays. Then it will read from the relays into the
typewriter keys one by one while they type from left to right across the page.

HOW THE DIFFERENTIAL ANALYZER CALCULATES

Up to this point in this chapter, the author has tried to tell the story of the
differential analyzer in plain words. But for reading this section, a little
knowledge of calculus is necessary. (See also Supplement 2.) If you wish, skip
this section, and go on to the next one.
We have described how varying quantities, or variables, are operated on in
the machine in one way or another: adding, subtracting, multiplying by a
constant, referring to a table, and integrating. What do we do if we wish to
multiply 2 variables together? A neat trick is to use the formula:

xy = ∫ x dy + ∫ y dx
To multiply in this way requires 2 integrators and 1 adder. The connections that
are made between them are as follows:
Shaft x To Integrator 1, Screw
Shaft x To Integrator 2, Disc
Shaft y To Integrator 1, Disc
Shaft y To Integrator 2, Screw
Integrator 1, Wheel To Adder 1, Input 1
Integrator 2, Wheel To Adder 1, Input 2
Adder 1, Output To Shaft expressing xy
A product of 2 variables under the integral sign can be obtained a little more
easily, because of the curious powers of the differential analyzer. Thus, if it is
desired to obtain ∫ xy dt, we can use the formula:

xy dt = xd y dt

and this operation does not require an adder. The connections are as follows:
Shaft t To Integrator 1, Disc
Shaft y To Integrator 1, Screw
Integrator 1, Wheel To Integrator 2, Disc
Shaft x To Integrator 2, Screw
Integrator 2, Wheel To Shaft expressing ∫xy dt
In order to get the quotient of 2 variables, x/y, we can use some more tricks.
First, the reciprocal 1/y can be obtained by using the two simultaneous equations:

1
dy = log y,
y
1
- d(log y) = y
y
The connections are as follows:
Shaft y To Integrator 1, Disc and to Integrator 2, Wheel
Shaft log y To Integrator 1, Wheel and to Integrator 2, Disc
Shaft 1/y To Integrator 1, Screw, and negatively to Integrator 2, Screw
In order to get x/y, we can then multiply x by 1/y. We see that this setup gives
us log y for nothing, that is, without needing more integrators or other equipment.
Clearly, other tricks like this will give sin x, cos x, eˣ, x², and other functions that
satisfy simple differential equations.
An integral of a reciprocal can be obtained even more directly. Suppose that

1
y= dt
x

Then

1
Dₜ y = , Dy t = x,
x

t= x dy

The connections therefore are:
Shaft t To Integrator, Wheel
Shaft x To Integrator, Screw
Shaft y To Integrator, Disc
The light wheel then drives the heavy disc. Clearly only the angle-indicator
device makes this possible at all. Naturally, the closer the wheel gets to the center
of the disc, that is, x approaching zero, the greater the strain on the mechanism,
and the more likely the result is to be off. Mathematically, of course, the limit of
1/x as x approaches zero equals infinity, and this gives trouble in the machine.
There is no standard mathematical method for solving any differential
equation. But the machine provides a standard direct method for solving all
differential equations with only one independent variable. First: assign a shaft for
each term that appears in the equation. For example, the highest derivative that
appears and the independent variable are both assigned shafts. The integral of the
highest derivative is easily obtained, and the integral of that integral, etc. Second:
connect the shafts so that all the mathematical relations are expressed. Both
explicit and implicit equations may be expressed. Third: for any shaft there must
be just one drive, or source of torque. A shaft may, however, drive more than one
other shaft. Fourth: choose scale factors so that the limits of the machine are not
exceeded yet at the same time are well used. For example, the most that an
integrator or a function table can move is 1 or 2 feet. Also, the number of full
turns made by a shaft in representing its variable should be large, often between
1000 and 10,000.
Of course, as with all these large machines, anyone would need some months
of actual practice before he could put on a problem and get an answer efficiently.

AN APPRAISAL OF THE MACHINE

The second MIT differential analyzer is probably the best machine ever built
for solving most differential equations. It regularly has an accuracy of 1 part in
10,000. This is enough for most engineering problems. If greater accuracy is
needed, the second differential analyzer cannot provide it. Once in a while the
machine can reach an accuracy of 1 part in 50,000; but, to balance this, it is
sometimes less accurate than 1 part in 10,000.
The MIT differential analyzer No. 2 can find answers to problems very
quickly. The time for setting up a problem to be run on the machine ranges from 5
to 15 minutes. The time for preparing the tapes that set up the problem is, of
course, longer; but the punch for preparing the tape is a separate machine and
does not delay the differential analyzer. The time for the machine to produce a
single solution to a problem ranges usually from 3 minutes to a half-hour. It is
easy to put on a problem, run a few solutions, take the problem off, study the
results, change a few numbers, and then put the problem back on again. This
virtue is a great help in a search in a new field. While the study is going on, time
is not wasted, for the machine can be busy with a different problem.
Running a problem a second time is a good check on the reliability of an
answer. For, when the problem is run the second time, we can arrange that the
machine will route the problem to other mechanisms.
The machine has a control panel. Here the operator watching the machine can
tell what units are doing what parts of what problems. If a unit gives trouble or
needs to be inspected, the clerk can throw a “busy” switch. Then the machine
cannot choose that unit for work to be done. The machine contains many
protecting signals and alarms. It is idle for repairs less than 5 per cent of the time.
It is not easy to determine the total cost of the machine, for it was partially
financed by several large gifts. Also, much of the labor was done by graduate
students in return for the instruction that they gained. The actual out-of-pocket
cost was about $125,000. If the machine were to be built by industry, the cost
would likely be more than 4 times as much. A simple differential analyzer,
however, can be cheap. Small scale differential analyzers have been built for less
than $1000; their accuracy has been about 1 part in 100.
There are many things that this machine cannot do; it was not built to do
them. (1) It cannot choose methods of solution. (2) It cannot perform steps in
solving a problem that depend on results as they are found. (3) It cannot solve
differential equations containing two or more independent variables. Such
equations are called partial differential equations; they appear in connection with
the flow of heat or air or electricity in 2 or 3 dimensions, and elsewhere. (4) It
cannot solve problems requiring 6 or more digits of accuracy. (5) The machine,

while running, can store numbers only for an instant, since it operates on the
principle of smoothly changing quantities; however, when the machine stops, the
number last held by each device is permanently stored.
None of these comments, however, are criticisms of the machine. Instead they
show avenues of development for future machines. As was said before, for
solving most differential equations, this machine has no equal to date. The range
of problems which any differential analyzer can do depends mostly on the
number of its integrators. The second differential analyzer has 18 and provides for
expansion to 30. The machine is constructed, also, so that it can be operated in 3
independent sections, each working to solve a different problem. The differential
analyzer can operate unattended. After it has been set up and the first few results
examined, it can be left alone to grind out large blocks of answers.
An interesting example of the experimental use of a differential analyzer in a
commercial business is the following: In Great Britain, R. E. Beard of the Pearl
Assurance Company built a differential analyzer with 6 integrators. He applied
this machine to compute to 3 figures certain insurance values known as
continuous annuities and continuous contingent insurances. He has described the
machine and the application he made in a paper published in the Journal of the
Institute of Actuaries, Vol. 71, 1942, pp. 193-227.

Chapter 6
ACCURACY TO 23 DIGITS:
HARVARD’S IBM AUTOMATIC
SEQUENCE-CONTROLLED CALCULATOR
One of the first giant brains to be finished was the machine in the Computation
Laboratory at Harvard University called the IBM Automatic Sequence-Controlled
Calculator. This great mechanical brain started work in April 1944 and has been
running 24 hours a day almost all the time ever since. It has produced quantities of
information for the United States Navy. Although many problems that have been
placed on it have been classified by the Navy as confidential, the machine itself is
fully public. The way it was working on Sept. 1, 1945, has been thoroughly
described in a 540-page book published in 1946, Volume I of the Annals of the
Harvard Computation Laboratory, entitled Manual of Operation of the Automatic
Sequence-Controlled Calculator. Since then the machine has been improved in
many ways.
This machine does thousands of calculating steps, one after another, according
to a scheme fixed ahead of time. This property is what gives the machine its name:
automatic, since the individual operations are automatic, once the punched tape
fixing the chain of operations has been put on the machine, and sequence-
controlled, since control over the sequence of its operations has been built into the
machine.

ORIGIN AND DEVELOPMENT

More than a hundred years ago, an English mathematician and actuary, Charles
Babbage (1792-1871), designed a machine—or engine as he called it—that would
carry out the sequences of mathematical operations. In the 1830’s he received a
government grant to build an analytical engine whereby long chains of
calculations could be performed. But he was unsuccessful, because the refined
physical devices necessary for quantities of digital calculation were not yet
developed. Only in the 1930’s did these physical devices become sufficiently
versatile and reliable for a calculator of hundreds of thousands of parts to be
successful.

The Automatic Sequence-Controlled Calculator at Harvard was largely the
concept of Professor Howard H. Aiken of Harvard. It was built through a
partnership of efforts, ideas, and engineering between him and the International
Business Machines Corporation, in the years 1937 to 1944. The calculator was a
gift from IBM to Harvard University. Some very useful additional control units,
named the Subsidiary Sequence Mechanism, were built at the Harvard
Computation Laboratory in 1947 and joined to the machine.

Fig. 1. Scheme of Harvard IBM Automatic
Sequence-Controlled Calculator.

GENERAL ORGANIZATION

The machine (see Fig. 1) is about 50 feet long, 8 feet high, and about 2 feet
wide. It consists of 22 panels; 17 of them are set in a straight line, and the last 5
are at the rear of the machine. In the scheme of the machine shown in Fig. 1, the
details you would see in a photograph have been left out. Instead you see the
sections of the machine that are important because of what they do: input,
memory, control, and output. Why do we not see a section labeled “computer”?
Because in this mechanical brain the computing part of the machine is closely
joined to the memory: every storage register can add and subtract. We shall soon
discuss these sections of the machine more fully.

PHYSICAL DEVICES

Now in order for any brain to work, physical devices must be used. For
example, in the human body, a nerve is the physical device that carries information

from one part of the body to another. In the Harvard machine, an insulated wire is
the physical device that carries information from one part of the machine to
another. One side of every panel in the Harvard machine is heavily laden with a
great network of wires. Between the panels, you can see in many places cables as
thick as your arm and containing hundreds of wires. More than 500 miles of wire
are used.
The physical devices in the Harvard machine are numerous, as we would
expect. It is perhaps not surprising that this machine has more than 760,000 parts.
But, curiously enough, there are only 7 main kinds of physical devices in the
major part of the machine. They are: wire, two-position switches, two-position
relays (see Chapter 2), ten-position switches, ten-position relays, buttons, and cam
contacts (see below). These are the devices that handle information in the form of
electrical impulses. They can be combined by electrical circuits in a great variety
of ways. There are, of course, other kinds of physical devices that are important,
but they are not numerous, and they have rather simple duties. Looking at the
machine, you can see three examples easily. Physical devices of the first kind
convert punched holes into electrical impulses: 2 card feeds, 4 tape feeds. Those of
the second kind convert electrical impulses into punched holes: 1 card punch, 1
tape punch. Those of the third kind convert electrical impulses into printed
characters: 2 electric typewriters. We can think of a fourth kind of physical device
that would be a help, but, at present writing, it does not yet exist: a device that
converts printed characters into electrical impulses.
The Harvard machine, of course, is complicated. But it is complicated because
of the variety of ways in which relatively simple devices have been connected
together to make a machine that thinks.

Switches

A two-position switch (see Fig. 2) turned by hand connects a wire to either one
of 2 others. These 2 positions may stand for “yes” and “no,” 0 and 1, etc. There are
many two-position switches in the machine. A ten-position switch or dial switch
(see Fig. 3) turned by hand connects the wire running into the center of the switch
with a wire at any one of ten positions 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 around the edge.
There are over 1400 dial switches in the machine. How does turning the pointer on
the top of the dial make connection between the center wire and the edge wire?
Under the face of the dial is the part that works, a short rod of metal fastened to
the pointer (shown with dashes in Fig. 3). When the pointer turns, this rod also
turns, making the desired connection.

Fig. 2.Two-position switch.

Fig. 3. Dial switch.

Relays

Two-position relays—more often called just relays (see Chapter 2)—do the
automatic routing of the electrical impulses that cause computing to take place.

Each relay may take 2 positions, open or closed, and these positions may stand for
0 and 1. There are more than 3000 relays in the Harvard machine.
A magnet pulling one way and a spring pulling the other way are sufficient in
an ordinary relay to give 2 positions, “on” and “off,” “yes” and “no,” 0 and 1. But
how do we make a relay that can hold any one of 10 positions? Figure 4 shows
one scheme for a ten-position relay. The arm can take any one of 10 positions,
connecting the contact Common to any one of the contacts O, 1, 2, 3, 4, 5, 6, 7, 8,
and 9 so that current can flow. The gear turns all the time. When an impulse comes
in on the Pickup line, the clutch connects the arm to the gear. When an impulse
comes in on the Drop-out line, the clutch disconnects the arm from the gear. For
example, suppose that the ten-position relay is stopped at contact 2, as shown.
Suppose that we now pick up the relay, hold it just long enough to turn 3 steps,
and then drop it out. The relay will now rest at contact 5.

Fig. 4. Scheme of a ten-position relay,
or counter position.
In the Harvard machine, the ten-position relays, much like the scheme shown,
do the same work as counter wheels (Fig. 5) in an ordinary desk calculating
machine, and so they are often spoken of as counter positions in the Harvard
machine. They are very useful in the machine not only because they express the 10
decimal digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 but also because adding and subtracting
numbers is accomplished by turning them through the proper number of steps. In
fact, an additional impulse is provided when the counter position turns from 9 to 0,
for purposes of carry. A group of 24 counter positions makes up each storage
counter—or storage register—in the machine. There are 2200 of these counter
positions. Each is connected to a continuously running gear on a small shaft (Fig.
6). All these shafts are connected by other gears and shafts to a main drive shaft,

and they are driven by a 5-horsepower motor at the
back of the machine. When a counter position is
supposed to step, a clutch connects the drive to the
running gear, and the counter position steps. When the
counter position is supposed to stay unchanged, the
clutch is disconnected and the driving gear runs free. In
fact, when you first approach the Harvard machine,
about the first thing you are aware of is the running of
these gears and the intermittent whirring and clicking
of the counter positions as they step. The machine
gives a fine impression of being busy!

Fig. 5. Scheme of a
counter wheel.

Fig. 6. Scheme of counter 16.

Timing Contacts

A button (see Fig. 7) is a device for closing an electric circuit when and only
when you push it. A simple example is the button for ringing a bell: you push the
button, a circuit is closed, and something happens. When you let go, the circuit is
opened. The Harvard machine has a button for starting, a button for stopping, and
many others.

Fig. 7. Button. Fig. 8. Cam, with 5 lobes and contact.

A cam contact (see Fig. 8) is an automatic device for closing an electric circuit
for just a short interval of time. When the lobes on the cam strike the contact, it
closes and current flows. When the lobes have gone by, the spring pushes open the
contact, and no current flows. Just as a two-position relay is the automatic
equivalent of a two-position switch, and a ten-position relay is the automatic
equivalent of a ten-position switch, so a cam contact is the automatic equivalent of
a button.
All the cams in the machine have 20 pockets where small round metal lobes
may or may not be inserted. Each cam makes a full turn once in ³/₁₀ of a second
and is in time with all the others. Thus we can time all the electrical circuits in the
machine in units of ³/₂₀₀ of a second.

NUMBERS

Numbers in the machine regularly consist of 23 decimal digits. The 24th
numerical position at the left in any register contains only 0 for a positive number
and only 9 for a negative number. Nines complements (see Supplement 2) are used
for negative numbers. For example,-00284 is represented as 999715, supposing
that we had 5-digit numbers instead of 23-digit numbers. The sum of two nines
complements is automatically corrected so that it is still a correct nines
complement. The device that accomplishes this is called end-around-carry (see

Supplement 2). The decimal point is fixed for each problem; in other words, in any
problem, the decimal point is consistently kept in one place, usually between the
15th and 16th decimal columns from the right.

HOW INFORMATION GOES
INTO THE MACHINE

Numerical information may go into the machine in any one of 3 ways: (1) by
regular IBM punch cards, using standard IBM card feeds (panel 16); (2) by hand-
set dial switches (panels 1, 2); and (3) by long loops of punched tape placed on the
value tape feeds (panels 12 to 14). Three sets of 24 columns each punched on a
regular IBM punch card can be used to send 3 numbers and their signs into the
machine in one machine cycle. This is the fastest way for giving numbers to the
machine, but the most limited; for the cards must be referred to in order and can be
referred to automatically only once. Also, there is the risk that they may be out of
order. A card may be passed through the machine without reading; this saves some
sorting in preparing cards for the machine. Machines for preparing the cards are
regular IBM key punches, and machines for sorting them after preparation are
regular IBM card sorters.
In panels 1 and 2 there are 60 registers by which unchanging numbers like 1,
or 3.14159265···, or 7.65 may be put into the machine. These are called the
constant registers. Each constant register consists of 24 dial switches and contains
23 digits and a sign, 0 if positive and 9 if negative. Whenever the mathematician
says a certain constant is needed for a problem, the operator of the machine walks
over to these panels, and, while the machine is turned off, sets the dial switches for
the number, one by one, by hand. If we need 40 constants of 10 digits each for a
problem, then the operator sets 400 dial switches by hand and makes certain that
the remaining 14 switches in each of the 40 constant registers used are either at 0
or 9, depending on the sign of the number. Only then can he return to start the
machine.

Fig. 9. Value tape code.
The third means by which numerical information can be put into the machine
is the value tape feeds, in panels 12, 13, and 14. Here the machine can consult
tables of numbers. The numbers are punched on paper tape 24 holes wide, made of
punch-card stock. Tapes for the value tape feeds may be prepared by hand or by
the machine itself using punch cards or machine calculation. The tapes use equally
spaced arguments (see Supplement 2). The tape punch changes the decimal digits
in its keyboard into the following punching code (see Fig. 9):

0 0000 5 1100
1 1000 6 1010
2 0010 7 1001
3 0010 8 0110
4 0001 9 0101
Here the 1 denotes a punched hole and 0 no punched hole, and the 4 columns from
left to right of the code correspond to 4 rows of the paper tape from bottom to top.
To make sure the value tape is correct, the machine itself can read the value tape
and check it mathematically or compare it with punch-card values.

HOW INFORMATION COMES
OUT OF THE MACHINE

Information comes out of the machine in any one of three ways: (1) by
punching on IBM cards with a regular IBM card punch that is built into the
machine (panel 17), (2) by typing on paper sheets with electric typewriters (panels
16 and 17), and (3) by punching paper tape 24 holes wide of the same kind as is
fed into the machine.

Usually, one of the electric typewriters is used to print a result for a visual
check and to print it before the machine makes a specified check of the value.
Then, about 10 seconds later, after the result has been checked as specified in the
machine, the checked result is printed by the second typewriter. In the second
typewriter, a special one-use carbon ribbon of paper is used to produce copy for
publication by a photographic process.
The card punch writes a number more rapidly than an electric typewriter. This
extra speed is sometimes very useful. However, the punch’s chief purpose is to
record intermediate results on punch cards. Then, if there is a machine failure, and
if the problem has been well organized, the problem may be run over from these
intermediate results, instead of requiring a return to the original starting
information. The tape punch used for preparing tape by hand can also be operated
by cable from the machine.

HOW INFORMATION IS HANDLED
IN THE MACHINE

The machine is a mechanical brain. So, between taking in information and
putting out information, the machine does some “thinking.” It does this thinking
according to instructions. The instructions go into the machine as: (1) the setting
of switches, or (2) the pressing of buttons, or (3) the wiring of plugboards, or (4)
feeding in tape punched with holes. The instructions are remembered in the
machine in these 4 ways, and we can call these sets of devices the control of the
machine.
To illustrate: One of the buttons pressed for every problem is the Start Key:
when you press it, the machine starts to work on the problem. One of the switches
with which you give instructions is a switch that turns electric typewriter 1 on or
off. One of the plugboards contains some hubs by which you can tell the machine
how many figures to choose in the quotient when dividing, for clearly you do not
need a quotient of 23 figures every time the machine divides. You can have 5
choices in any one problem; you can specify them by plugging, and you can call
for any one of 5 choices of quotient size from time to time during the problem. In
many cases, when we wish the machine to do the same thing for all of a single
problem and do it whenever the occasion arises, we can put the instruction into the
wiring of a plugboard. We use plugboard wiring, for example, in fixing the
decimal point in multiplication, so that the product will read out properly, and in
guiding the operation of the typewriters, so that printing will take place in the
columns where we want it.

Sequence of Steps

The most important part of the control of the machine is the sequence-tape
feed and its sequence-control tape. These tell the machine a great part of what
operations are to be performed.

Fig. 10. Sequence-control tape code.
At the end of the room where the machine is, there is the special tape punch
mentioned above. It holds a big spool of card stock that is thin, flexible, smooth,
and tough. With one keyboard we may prepare value tape. With another keyboard
we prepare the sequence-control tape. The tape (see Fig. 10) contains places for 24
round punched holes in each row. Some and only some of these holes are punched.
Each row of punched holes is equivalent to an instruction to the machine and is
called a line of coding or coding line. In general, the instruction has the form:

Take a number out of Register A;
put the number into Register B;
and perform operation C.

The first group of 8 holes at the left is called the A field or the out-field. Here
we tell the machine where a number is to be taken from. The middle group of 8
holes is called the B field or the in-field. Here we tell the machine where a number
is to be put. The last group of 8 holes is called the C field or the miscellaneous
field. Here we tell the machine part or all of the operation that is to be performed.
To illustrate (see Fig. 10), we have holes 3, 2, 1 punched in the A field, holes 3,
2 punched in the B field, and hole 7 punched in the C field. Now 321 is the code—
or machine language, or machine call number—for storage counter 7; 32 is the
code for storage counter 6; and 7 in the C field is the code (in this case, and
generally) for “Add, and read the next line of coding.” So, if we punch out this
line of coding and put the tape on the machine, we tell the machine to read the
number in counter 7, add it into counter 6, and proceed to the next line of coding
and read that.

The holes in each group of 8 holes from left to right are numbered: 8, 7, 6, 5,
4, 3, 2, 1. The code 631, for example, means that holes 6, 3, 1 are punched and that
no holes are punched at 8, 7, 5, 4, 2. Since it is more natural, the code is read from
left to right, or 631, instead of from right to left in the sequence 136.
The devices in the machine have in-codes, used in the in-field, and out-codes,
used in the out-field. For each of the 72 regular storage counters, the in-code and
the out-code are the same. The first 8 storage counters have the codes 1, 2, 21, 3,
31, 32, 321, 4, 41; the last 2 storage counters, the 71st and the 72nd, have the
codes 7321, 74.
The constant registers—often called constant switches, or just switches—
naturally have only out-codes, since numbers can be entered into the constant
registers only by setting dial switches by hand. The first 8 constant registers have
the out-codes 741, 742, 7421, 743, 7431, 7432, 74321, 75, and the 59th and 60th
constant registers have the out-codes 821, 83.

Transferring, Adding, and Clearing

Each storage counter has the property that any number transferred into it is
added into it. For example, the instruction

Take the number in switch 741;
transfer it into storage register 321

is coded:
741, 321, 7
The 7 in the third column is an instruction to the sequence-tape feed to turn up to
the next coding line and read it. If any number is already stored in register 321, the
content of 741 will be added to it, and the total will then be stored in 321.
Resetting or clearing a regular storage register is accomplished by a coding
that is a departure from the usual scheme of “out” and “in.” The instruction

Clear register 321;
read the next coding line

is coded:
321, 321, 7

Similarly, you can clear any other regular storage register if you repeat its code in
the out-and in-fields. However, a few of the storage registers in the machine have
special reset codes, and these may occur in any of the three fields A, B, C.
As the result of a recent modification of the machine, you can easily double
the number in any storage register. For example, the instruction

Double the number in register 321;
read the next coding line

is coded:
321, 321, 743

Subtracting

If the number in switch 741 is to be subtracted from the number in storage
counter 321, the instruction is changed into:

Take the negative of the number in switch 741;
transfer it into storage register 321;
read the next line of coding

The coding line becomes:
741, 321, 732
By putting 32 in the C field, we cause the number in switch 741 to be subtracted
from whatever number is in register 321.
We have 2 more choices in adding and subtracting. The value of the number
without regard to sign—in other words, its absolute value (see Supplement 2)—
may be added or subtracted. The instruction
Add the absolute value of
is expressed by a C field code 2, and the instruction
Add the negative of the absolute value of
is expressed by a C field code 1.

Multiplying

When we wish to multiply one number by another and get a product, we have
3 numbers. We tell the machine about each of these numbers on a separate line of
coding. Multiplication is signaled by sending a number into the multiplicand
counter. The multiplicand counter has an in-code 761. If the multiplicand is in
321, the instruction is:

Take the number in 321;
enter it as multiplicand;
read the next coding line

The coding is:
321, 761, 7
On the third following coding line, the multiplier is sent into the multiplier
counter. If the multiplier is in switch 741, the instruction is:

Take the number in 741;
enter it as multiplier;
read the next coding line

The coding is:
741, ——, 7
We do not punch anything in the middle field: the machine is “educated” and
“knows” that it has started a multiplication and needs a multiplier, and it expects
this multiplier in the third coding line. To have no code for the multiplier counter
is, of course, a departure from the general rule, but it saves some punching and
permits the use of this space for certain other codes, thus saving some operating
time.
We need not confuse the 761 in-code for the multiplicand counter with the 761
out-code, which happens to be the out-code of the 25th constant register, because
neither can occur in the other’s field. We may, of course, use other registers
besides 321 and 741 for supplying the multiplicand and multiplier.
To get the product and put it into any storage counter D, we use two lines of
coding one right after the other:
—— —— 6421
8761 D ——

The product counter has the out-code 8761. When the product is desired, it is
called for, transferred into counter D, and the multiplication unit is automatically
cleared. It takes time, however, for the machine to perform a multiplication. That
is the reason for the preceding coding line and the 6421 in the C field. While the
multiplication is going on, we can instruct the machine to do other things that we
want done. We can insert or interpose coding lines in between the multiplier line
and the product line. For example, if we have a multiplier of 10 digits, we can
insert 8 coding lines and maybe more. The 6421 code essentially tells the machine
to finish both the multiplication and the interposed instructions, and, as soon as the
later one of these two tasks is finished, to transfer out the product to counter D.
Up to the middle of 1946, the wiring of the machine was a little different and
less convenient. When the product was obtained by the multiplication unit, it had
to be accepted and transferred at once into one of the 72 storage registers.

Dividing

Division is called for by first sending the divisor into the divisor counter, and
this has a code 76 in the B field. If the divisor is in counter 321, the instruction
may be:

Take the number in 321;
enter it as divisor;
read the next coding line

The coding will then be:
321, 76, 7
Three coding lines later, the dividend is called for, and the coding, if the dividend
is in switch 7431, is:
7431, ——, 7
We can send the quotient, when ready, into any desired counter Q by the following
two lines of coding:
—— —— 642
876 Q ——
In the same way as with multiplication, we can insert a number of coding lines in
between the dividend line and the first quotient line.

Both multiplication and division are carried out in the same unit of the
machine, the multiply-divide unit. The machine first constructs a table of the
multiples of the multiplicand or divisor: 1 times, 2 times, 3 times, ···, 9 times. In
multiplication this table is then used by selecting multiples according to the digits
of the multiplier one after another. In division the table is used by comparing
multiples of the divisor against the dividend and successive remainders, finding
which will go and which will not. Since the numbers in the machine are normally
of 15 to 23 digits, any particular multiple will be used, on the average, several
times, and so this process is relatively efficient. Actually the multiplicand and the
divisor go into the same counter. Division, however, has the code 76 and
multiplication the code 761, and so the difference is essentially an operation code
not in the third or C field.

Consulting a Table

When we desire the machine to consult a table of values (i.e., a function—see
Supplement 2), we punch the table with its arguments and function values on a
tape, and we put the tape on a value tape feed mechanism. The instruction to the
machine may be:

Take the number in register A;
find the value of the function for this number,
and enter it in register B.

The coding is:
—— —— 73
A 7654 61
—— —— 762
—— —— 543
—— —— 75431
841 7654 ——
A 763 6421
8762 B 73
—— 8763 7
Without explaining this coding line by line, we can say that this is what happens:

The machine reads the argument in register A. The machine
reads the argument in the table at which the value tape
feed is resting.
It subtracts them, and thereby determines how far away the
desired argument is.
The machine then turns the tape that required distance.
It checks that the new argument is the wanted argument.
It reads the value of the function entered at that point on
the function tape.

Selecting

There is a storage counter in the machine that is called the selection counter.
The selection counter is counter 70 and has the code 732. It has all the properties
of an ordinary storage counter and, in addition, one extra property: depending on
the sign of the number stored in the selection counter, it is possible to select
whether some other number shall be treated positively or negatively. In other
words, addition of a number anywhere in the machine may take place either
positively or negatively, if the number stored in the selection counter is positive or
negative, respectively.
For example, suppose that x is the number in the selection counter. Suppose
that y is the number in some other counter A. Suppose that z is the number in
counter B. Suppose that we use the coding:
A, B, 7432
What we get in B, because of the 7432 in the third or C field, is z plus y if x is
positive or zero, and z minus y if x is negative. In the language of the algebra of
logic (see Chapter 9 and Supplement 2), where T( ...) is “the truth value of ...,” the
number in b equals:
z + y·T(x ≥ 0) - y·T(x < 0)
(The nines complement of 0, namely 999···9 to 24 digits, is treated by the machine
as negative.)
Why do we need an operation like this in a mechanical brain? Among other
reasons, what we want to do with a number, in mathematics, often depends on its
sign. It may happen that a table is, for negative arguments, the negative of what it
is for positive arguments; in other words, F(-x) =-F(x). This is true, for instance,

for a table of cubes {F(x) = x³} or for a table of trigonometric tangents (see
Supplement 2). If so, we certainly do not want to take the time and trouble to list
the whole table. We put down only half the table and then, if x is negative, use the
negative of the value in the table. In order to apply such a time-saving rule when
using the machine, we need the selection counter or its equivalent.

Checking

There is another special counter in the machine that is called the check
counter. It also has all the properties of an ordinary storage counter and, in
addition, one extra property: If the sign of the number stored in the check counter
on a certain coding line is negative, then on the next coding line the machine may
be stopped. In other words, suppose that the check counter stores a certain
tolerance t. Suppose, under the instructions we give the machine, that it calculates
a positive number x that ought to be less than this tolerance. Suppose that
something may go wrong and that x actually may be greater than t. Then we put a
check into our instructions. We tell the machine:

When you have found x, subtract it from t.
If the result is positive, go ahead.
If the result is negative or zero, stop!

Here is the coding. Suppose that the tolerance t is in switch 751. Suppose that
the number x to be checked is in counter 4321. Then the instructions and coding
are:

Clear the check counter — — 7
Put in the tolerance, from switch 751 751 74 7
Subtract the absolute value of the number to be checked 4321 74 71
Stop, O Mechanical Brain, if your result be negative! — — 64
An operation like this is very useful in a mechanical brain. It enables the
calculation to be interrupted if something has gone wrong. Of course, other
operations of checking besides this one are used—for example, inspecting for
reasonableness the results printed on typewriter 1.

Other Operations

There are other operations in the machine. There are two pairs of storage
registers that can be coupled together so that we can handle problems requiring
numbers of 46 digits instead of 23. Registers 64 and 65 can be coupled, and
registers 68 and 69 can be coupled. There is another storage counter, No. 71, that
has an extra property. We can read out the number it holds times 1, or times 10¹²,
or times 10⁻¹², as may be called for. As a result of this counter, we can do problems
requiring 144 registers storing numbers of 11 digits each, instead of 72 registers
storing 23 digits each. Bigger statistical problems can be handled, for example.
There are some minor sequences of operations, or subroutines, that can be
called for by a single code. The subroutine may be a whole set of additions,
subtractions, multiplications, divisions, and choices, having a single purpose: to
compute some number by a process of rapid approximation (see Supplement 2).
There are built-in subroutines for some special mathematical functions: the
logarithm of a number to the base 10, the exponential of a number to the base 10,
and the sine of a number. (See Supplement 2.)
There are also 10 changeable subroutines, each of 22 coding lines, which can
be called in, when wanted, by the main sequence-control tape or by each other.
These subroutines constitute the Subsidiary Sequence Mechanism, and are
extremely useful. They have A, B, and C fields just like the main sequence-control,
but they are given information by plugging with short lengths of wire instead of by
feeding punched paper tape.

RAPID APPROXIMATION FOR A LOGARITHM

Up to this point in this chapter the author has tried to tell the facts about the
Harvard machine in plain words. But for reading this section, a little knowledge of
calculus is necessary. (See also Supplement 2.) If you wish, skip this section and
go on to the next one.
What is the process that the machine uses to compute any desired logarithm to
23 digits? Suppose that we take for an example the process by which the machine
computes log10 49.3724. We choose a 6-digit number for simplicity; the machine
would handle a 23-digit number in the same way. The process uses 2 fundamental
equations involving the logarithm: the sum relation
log (a·b·c···) = log a + log b + log c···
and the series relation

logₑ(1 + h) = h - h² + h³ - h⁴ + ···, │h│ < 1

2 3 4
The error in this series is less than the first neglected term. Now, the machine
stores the base 10 logarithms (to 23 decimal places) of the following 36 numbers:

1 1.1 1.01 1.001
2 1.2 1.02 1.002
... ... ... ...
9 1.9 1.09 1.009
First, the number 49.3724 is examined in a counter called the Logarithm-In-
Out counter, and the position of the decimal point is determined, giving the
characteristic of the logarithm. The number 49.3724 has the characteristic 1. Next,
4 successive divisions are performed, in which the 4 divisors are (1) the first digit
of the number, (2) the first 2 digits of the quotient, (3) the first 3 digits of the next
quotient, and (4) the first 4 digits of the subsequent quotient; thus,

4.93724
= 1.23431
4
1.23431
= 1.02860
1.2
1.02860
= 1.00843
1.02
1.00843
= 1.00043
1.008
For simplicity we have kept only 6 digits, although the machine, of course, would
keep 23. It is interesting to note that the machine is able to sense digits and thus
determine the 4 divisors; this is an arithmetical and numerical process and one that
cannot be done in ordinary algebra. We now have:
log₁₀ 49.3724 = 1 + log₁₀ 4 + log₁₀ 1.2 + log₁₀ 1.02
+ log₁₀ 1.008 + log₁₀ 1.00043
To compute log₁₀ 1.00043 to 21 decimals we use

h² h³ h⁴ h⁵ h⁶
log₁₀e · h- + - + -
2 3 4 5 6

with h = 0.00043. Only 6 terms of the series relation are needed. For, the error is
less than h⁷/7, which is less than 10⁻²¹/7, since h < ¹/₁₀₀₀. The machine uses the
series relation in the form

log₁₀ (1 + h) = {([{(c₆h + c₅) h + c₄}h + c₃]h + c₂)h + c₁}h
where
c₁ = M, c₂ = -M/2, c₃ = M/3, ···,
and M = log₁₀_e= 0.434294···.
The 6 values of the c’s are also stored in the machine. When any logarithm is to be
computed, the sum of the characteristic, of the 4 logarithms of the successive
divisors, and of the first 6 terms of the series relation gives the logarithm. The
maximum time required is 90 seconds.

AN APPRAISAL OF THE CALCULATOR

The IBM Automatic Sequence-Controlled Calculator at Harvard is a landmark
in the development of machines that think. Its capacity for many problems for
which it is suited is far beyond the capacity of a hundred human computers.

Speed

The time required in the machine for adding, subtracting, transferring, or
clearing numbers is ³/₁₀ of a second. This is the time of one machine cycle or of
reading one coding line. Multiplication takes at the most 6 seconds, and an
average of 4 seconds. Division takes at the most 16 seconds, and an average of 11
seconds. Each, however, requires only 3 lines of coding, or ⁹/₁₀ of a second’s
attention from the sequence mechanism; interposed operations fill the rest of the
time. To calculate a logarithm, an exponential, or a sine to the full number of digits
obtainable by means of the automatic subroutine takes at the most 90, 66, and 60
seconds, respectively. To get three 24-digit numbers from feeding a punch card
takes ⅓ second. To punch a number takes from ½ second up to 3 seconds. To print
a number takes from 1½ seconds up to 7 seconds.

Cost and Value

The cost of the machine was somewhere near 3 or 4 hundred thousand dollars,
if we leave out some of the cost of research and development, which would have
been done whether or not this particular machine had ever been built. A staff of 10
men, consisting of 4 mathematicians, 4 operators, and 2 maintenance men, are
needed to keep the machine running 24 hours a day. This might represent, if
capitalized, another 1 or 2 hundred thousand dollars. If a capital value of $500,000
is taken as equivalent to $50,000 a year, then the cost of the machine in operation
24 hours a day is in the neighborhood of $150 a day or $6 an hour.
The value of the machine, however, is very much greater. If 100 human beings
with desk calculators were set to work 8 hours a day at $1.50 an hour, the cost
would be $1200 a day, or 8 times as much. Yet it is very doubtful that the work
they could produce would equal that turned out by the machine, either in quality or
quantity, when the machine is well suited to the problem.

Reliability

By reliability we mean the extent to which the results produced by the machine
can be relied on to be right. The machine contains no built-in device for making its
operations reliable. So, if we wish to check a multiplication, for example, we can
do the multiplication a second time, interchanging the multiplier and the
multiplicand. But if, say, digit 16 of the product were not transferring correctly, we
would get the same wrong result both ways and we would not have a sufficient
check. Thus, when we set up a problem for the machine to do, one of the big tasks
we have is checking. We have to work out ways of making sure that the result,
when we get it, is right and ways of instructing the machine to make the tests we
want. This is not a new task. Whenever you or I set out to solve a problem, we
have to make sure—usually by doing the problem twice, and preferably by doing
it a different way the second time—that our answer, when we get it, is correct. One
of the chief tasks for the mathematician, in making a sequence-control tape for the
machine, is to put into it sufficient checks to make sure that the results are correct.
We can use a number of different kinds of partial checks: the check counter;
differences, and smoothness (see Supplement 2); watching the results printed on
typewriter 1; mathematical checks; comparison with known specific values; etc.
In actual experience on the machine, human failures, such as failure to state
the problem exactly or failure to put it on the machine correctly, have given about
as much trouble as mechanical failures. The machine operates without mechanical

failure about 90 to 95 per cent of the time. The balance of the time the machine is
idle while being serviced or repaired. The machine is serviced by mechanics
trained and supervised at Harvard.
Often when we change the machine from one problem to another problem, we
find some kind of trouble. Consequently, we need to work out in detail the first
part of any calculation placed on the machine. We then compare the results step by
step with the results produced by the machine. Any mathematician working with
the machine needs considerable training in order to diagnose trouble quickly and
guide the maintenance men to the place where repair or replacement is needed.
Once you find the trouble, you can fix it easily. Without disturbing the soldered
connections, you can easily pull out from its socket a relay that is misbehaving and
plug in a new relay. With a screwdriver you can change a counter position—detach
it from its socket and replace it by another one that is working correctly.
One “bug” that will long be remembered around the Laboratory was a case
involving a 5 that would incorrectly come in to a number every now and then. It
did not happen often—only once in a while. After a week of search the bug was
finally located: the insulation on a wire that carried a 5 had worn through in one
spot, and once in a while this wire would shake against a post that could carry
current and took in the 5!

Efficiency

In many respects, this machine is efficient and well-balanced. Its reading and
writing speed is close to its calculating speed. We can punch or print a result on
the average for every 10 additions or 1½ multiplications. The memory of 72
numbers in the machine is extremely useful; a smaller memory is a serious
limitation on the achievements of a computing machine. The machine can do
many kinds of arithmetic and logic. It is well educated and can compute
automatically some rather complicated mathematical functions, like logarithm or
sine. It has done difficult and important problems. It has computed and tabulated
(see Supplement 2) Bessel functions, definite integrals, etc. It can solve differential
equations (see Chapter 5) and many other problems in mathematics, physics, and
engineering.
On the other hand, no calculator will ever again be built just like this one,
useful though it is. Electronic computing is easily 100 times as fast as relay
computing; nearly every future calculator will do its computing electronically.
Many other improvements will be made. For example, in this calculator, there are
72 addition-subtraction mechanisms, yet only one of these can be used at a time.
Also, the machine has only one combined multiply-divide unit. So we have to

organize any computation with few multiplications, and with still fewer divisions,
for they take longer still.
Until 1947, we had to organize any computation in this calculator into one
single fixed sequence of operations. In other words, there was no way to move
from one subroutine to another subroutine depending on some indication that
turned up in our computation. Recently, the Harvard Computation Laboratory
decided to remedy this condition and provided the Subsidiary Sequence
Mechanism equivalent to 10 subroutines of 22 lines of coding each. These are on
relays and plug wires and may be called for by the sequence-control tape or by
each other. This provision has added greatly to the efficiency of the calculator.
Whatever else can be said about the Harvard IBM Automatic Sequence-
Controlled Calculator, it must be said that this was the first general-purpose
mechanical brain using numbers in digit form and able to do arithmetic and logic
in hundreds of thousands of steps one after another. And great credit must go to
Professor Howard H. Aiken of Harvard and the men of International Business
Machines Corporation who made this great mechanical brain come into existence.

Chapter 7
SPEED—5000 ADDITIONS A SECOND:
MOORE SCHOOL’S ENIAC
ELECTRONIC NUMERICAL INTEGRATOR AND
CALCULATOR
Another of the giant brains that has begun to work is named ENIAC. This name
comes from the initial letters of the full name, Electronic Numerical Integrator and
Calculator. Eniac was born in 1942 at the Moore School of Electrical Engineering, of the
University of Pennsylvania, in Philadelphia. Eniac’s father was the Ordnance Department
of the U. S. Army, which provided the funds to feed and rear the prodigy.
In the short space of four years, Eniac grew to maturity, and in February 1946 he
began to earn his own living by electronic thinking. Eniac promptly set several world’s
records. He was the first giant brain to use electronic tubes for calculating. He was the
first one to reach the speed of 5000 additions a second. He was the first piece of
electronic apparatus containing as many as 18,000 electronic tubes all functioning
together successfully. As soon as Eniac started thinking, he promptly made relay
calculators obsolete from the scientific point of view, for they have a top speed of perhaps
10 additions a second.
At the age of 5, he moved to Maryland at a cost of about $90,000, and his permanent
home is now the Ballistic Research Laboratories at the U. S. Army’s Proving Ground at
Aberdeen, Md.

ORIGIN AND DEVELOPMENT

In the Department of Terrestrial Magnetism in the Carnegie Institution of Washington,
a great deal of information about the earth is studied. Many kinds of physical
observations are there gathered and analyzed: electricity in the atmosphere, magnetism in
the earth, and the weather, for example. In 1941, a physicist, Dr. John W. Mauchly, was
thinking about the great mass of numerical information they had to handle. He became
convinced that much swifter ways of handling these numbers were needed. He was
certain electronic devices could be used for computing at very high speeds, yet he found
no one busy applying electronics in this field. With hopes of finding some way of
developing electronic computing, he joined the staff of the Moore School of Electrical
Engineering in the autumn of 1941.
The Moore School in 1934 and 1935 had built a differential analyzer; and, from that
time on, the school had made a number of improvements in it. In 1941, with war
imminent, the differential analyzer was put hard at work calculating tables for the Army’s

Ballistic Research Laboratories. These tables were mostly firing tables, tables of the paths
along which projectiles travel when fired—trajectories; obviously, you cannot fire a gun
usefully, unless you know how to aim it. The amount of calculation of trajectories was so
huge that Dr. Mauchly suggested that a machine using electronic tubes be constructed to
calculate them. A good deal of discussion took place between men at the Moore School,
men at the Ballistic Research Laboratories, and men from the Ordnance Department in
Washington. A contract for research into an electronic trajectory computer was concluded
with the Ordnance Department of the U. S. Army. Mauchly and one of the young
electronics engineers studying at Moore School, J. Presper Eckert, Jr., set to work on the
design.
Gradually the design of a machine took form, and the crucial experiments on
equipment were completed. In 1943, the design was settled as a special-purpose machine
to calculate trajectories. Later on, the group modified the plans here and there to enable
the machine to calculate a very wide class of problems. A group of Moore School
electronics engineers and technicians during 1944 and 1945 built the machine, using as
much as possible standard radio tubes and parts. Here, again, in spite of the successful
progress of the electronic machine, the rumor that it was a “white elephant” was allowed
to spread in order to protect the work from prying enemy ears.

GENERAL ORGANIZATION

The main part of Eniac consists of 42 panels, which are placed along the sides of a
square U. Each of these panels is 9 feet high, 2 feet wide, and 1 foot thick. They are of
sheet steel, painted black, with switches, lights, etc., mounted on them. At the tops of all
the panels are air ducts for drawing off the hot air around the tubes. Large motors and
fans above the machine suck the heated air away through the ducts. There are also 5
pieces of equipment which can be rolled from place to place and are called portable, but
there is no choice as to where they can be plugged in. We shall call this equipment panels
43 to 47.

Panels

Now what are these panels, and what do they do? Each panel is an assembly of some
equipment. The names of the panels are shown in the accompanying table. The
arrangement of Eniac at the Ballistic Research Laboratories as shown in the table is
slightly different from the arrangement of Eniac at Moore School.

NAMES OF PANELS OF ENIAC
Panel Name
No. (and additional names in some cases)
1 Initiating Unit

Panel Name
No. (and additional names in some cases)
2 Cycling Unit
3, 4 Master Programmer, panels 1, 2
5 Accumulator 1
6 Accumulator 2
7 Accumulator 3
8 Accumulator 4 (Quotient)
9 Divider-Square-Rooter
10 Accumulator 5 (Numerator I)
11 Accumulator 6 (Numerator II)
12 Accumulator 7 (Denominator—Square Root I)
13 Accumulator 8 (Denominator—Square Root II)
14 Accumulator 9 (Shift I)
15 Accumulator 10 (Shift II)
16 Blank panel for new unit (Converter)
17 Accumulator 11 (Multiplier)
18 Accumulator 12 (Multiplicand)
19-21 Multiplier, panels 1, 2, 3
22 Accumulator 13 (Left-Hand Partial Products I)
23 Accumulator 14 (Left-Hand Partial Products II)
24 Accumulator 15 (Right-Hand Products I)
25 Accumulator 16 (Right-Hand Products II)
26 Blank panel for new unit (100 Registers)
27 Accumulator 17
28 Accumulator 18
29 Accumulator 19
30 Accumulator 20
31, 32 Function Table 1, panels 1, 2
33, 34 Function Table 2, panels 1, 2
35, 36 Function Table 3, panels 1, 2
37-39 Constant Transmitter, panels 1, 2, 3
40-42 Printer, panels 1, 2, 3
43-45 Portable Function Tables A, B, and C
46 IBM Card Reader

Panel Name
No. (and additional names in some cases)
47 IBM Summary Punch
Note: The accumulators from which a number can be sent to the
printer are now accumulators 1, 2, and 15 to 20.
In reading over the table, we find a number of words that need explaining. Some of
the explanation we can give in the summary of the units of Eniac:

SUMMARY OF UNITS OF ENIAC
Quantity Device Significance
20 Accumulators Store, add, and subtract numbers
1 Multiplier Multiplies
1 Divider-Square-Rooter Divides, and obtains twice the square root
of a number (see Supplement 2)
3 Function Tables Part of the memory, for referring to
tables of numbers
1 Constant Transmitter Stores numbers from the card reader and
from hand-set switches
1 Printer Punches machine results into cards
1 Cycling Unit Controls the timing of the various parts
of the machine
1 Initiating Unit Has controls for starting a calculation,
for clearing, etc.
1 Master Programmer Holds the chief controls for coordinating
the various parts of the machine
An accumulator is a storage counter. It can hold a number; it can clear a number; it
can transmit a number either positively or negatively; and it can receive a number by
adding the number in and thus holding the sum of what it held before and the number
received. Eniac when first built had only 20 accumulators, and so it could remember only
20 numbers at one time (except for constant numbers set in switches). This small memory
was the most serious drawback of Eniac; panel 26 was designed, therefore, to provide a
great additional memory capacity.
The divider-square-rooter, as its name tells, is a mechanism that can divide and that
can find twice the square root of a number. Eniac is one of the several giant brains that
have had square root capacity built into them, particularly since square root is needed for
solving trajectories.

Many panels of Eniac have double duty and some have triple duty. For example,
panel 24 is an accumulator, but it also (1) stores the right-hand partial products (see
Supplement 2) of the multiplier and (2) was a register, when Eniac was at Moore School,
from which information to be punched in the printer could be obtained. Clearly, if we
have a multiplication to do, we cannot also use this accumulator for storing a number that
is to remain unchanged during the multiplication.

Parts

The total number of parts in Eniac is near half a million, even if we count electronic
tubes as single parts. There are over 18,800 electronic tubes in the machine. It is
interesting to note that only 10 kinds of electronic tubes are used in the calculating
circuits and only about 60 kinds of resistors and 30 kinds of capacitors. A resistor is a
device that opposes the steady flow of electric current through it to a certain extent (called
resistance and measured in ohms). A capacitor is a device that can store electrical energy
up to a certain extent (called capacitance and measured in farads). All these tubes and
parts are standard parts in radios. All types are identified by the color labels established in
standard radio manufacturing. It is the combinations of these parts, like the combinations
of pieces in a chess game, that give rise to the marvelous powers of Eniac.
The combinations of parts at the first level are called plug-in units. A plug-in unit is a
standard box or tray or chassis made of sheet steel containing a standard assembly of
tubes, wires, and other parts. It can be pushed in or pulled out of a standard socket with
many connections. An example of a plug-in unit is a decade, or, more exactly, an
accumulator decade. This is just a counter wheel or decimal position expressed in Eniac
language: it can express successively all the digits from 0 to 9 and then pass from 9 to 0,
giving rise to a carry impulse. It is striking that a mechanical counter to hold 10 digits can
be made up of 10 little wheels, ¼ inch wide and an inch high. But an accumulator in
Eniac, to hold 10 digits, is a set of 10 decades each 2 inches wide and 2½ feet high.
There are only about 20 kinds of plug-in units altogether. Each plug-in unit is
interchangeable with any other of the same kind. So, if a decade, for example, shows
trouble, you can pull it out of its socket and plug in a spare decade instead.

Numbers

Numbers in Eniac are of 10 decimal digits with a sign that may be plus or minus. The
decimal point is fixed. However, when you are connecting one accumulator with another,
you can shift the decimal point if you want to. Also, 2 accumulators may be coupled
together so as to handle numbers of 20 digits.

HOW INFORMATION GOES
INTO THE MACHINE

There are three ways by which information—numbers or instructions—can go into
the Eniac. Numbers can be put into the machine by means of punch cards fed into the
Card Reader, panel 46, or switches on the Constant Transmitter, panels 37 to 39. Numbers
or instructions can also go into the machine by means of the Function Tables, panels 43 to
45. Here there are dial switches, which are set by hand. Instructions can also go into the
machine by setting the switches, plugging the inputs and outputs, etc., of the wires or
lines along which numbers and instructions travel.

HOW INFORMATION COMES
OUT OF THE MACHINE

There are two ways by which numerical information can come out of the machine.
Numbers can come out of the machine punched on cards by the Summary Punch, panel
47. They are then printed in another room by means of a separate IBM tabulator. Also,
numbers can be read out of the machine by means of the lights in the neon bulbs mounted
on each accumulator. You can read in the lights of a panel the number held by the
accumulator, if the panel is not computing.

HOW INFORMATION IS MANIPULATED
IN THE MACHINE

Eniac handles information rather differently from any other of the big brains. Instead
of having only one bus or “railroad line” along which numbers can be sent, Eniac has
more than 10 such lines. They are called digit trays and labeled A, B, C, ···. Each
contains 11 digit trunk lines or digit trunks—10 to carry the digits of a number, and the
11th to carry the sign. Instead of having only one telegraph line along which instructions
can be sent, Eniac has more than 100 such lines. They are called program trunk lines or
program trunks and labeled A1, A2, ···, A11, B1, B2, ···, B11, ···, etc. They are
assembled in groups of 11 to a tray; the program trays, in fact, look just like the digit
trays, except for their connectors and their purpose, which are different. Below, we shall
make clear how the program trays carry control information.
Now, actually, Eniac has many more trunk lines than we have just stated, for each of
the lines we have mentioned can be divided into numerous separate sections by the
removal of plug connections. How we choose to do this depends on the needs of the
problem, the space between the panels, the time when the line is used, etc.

Transferring Numbers, Adding,
and Subtracting

Basically, a number is represented in Eniac by an arrangement of on and off electronic
tube elements in pairs, called flip-flops. There is one flip-flop enclosed in a single tube
(type 6SN7) for each value 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 for each of the 10 digits stored in an

accumulator. So we have at least 100 flip-flops for each accumulator, and thus at least
100 electronic tubes are required to store 10 digits. Actually, an accumulator needs 550
electronic tubes. So we see that there is not very much of a future in this type of
arrangement. The newer electronic brains use different devices for storage of numbers.
In order to show what number is stored in an accumulator, there are 100 little neon
bulbs mounted on the face of each accumulator panel. Each bulb glows when the flip-flop
that belongs to it is on. For example, suppose that the 4th decade in Accumulator 11 holds
the digit 7. Then the 7th flip-flop in that decade will be on, and all the others will be off.
The 7th neon bulb for that decade will glow.
Now suppose that the number 7 is in the 4th decade in Accumulator 11 and is to be
added into, say, the 4th decade in Accumulator 13. And suppose that it is to be subtracted
from the 4th decade in Accumulator 16. What do we do, and what will Eniac do?
First, we pick out 2 digit trays, say B and D. Accumulator 11 has 2 outputs, called the
add output and the subtract output. We plug B into the add output and D into the subtract
output. Then we go over to Accumulators 13 and 16. They have 5 inputs, that is, 5 ways
of being plugged to receive numbers from digit trunks. These inputs are named with
Greek letters, α, β, γ, δ, ε. We choose one input, say γ, for Accumulator 13, and we plug
B into that input. We choose one input, say ε, for Accumulator 16, and we plug D into
that input.
Now we have the “railroad” switching for numbers accomplished. We have set up a
channel whereby the number in Accumulator 11 will be routed positively into
Accumulator 13 and negatively into Accumulator 16. Now let us suppose that, at some
definite time fixed by the control, Accumulator 11 is stimulated to transmit and
Accumulators 13 and 16 are conditioned to receive. When this happens, a group of 10
pulses comes along a direct trunk from the cycling unit, and a group of 9 pulses comes
along another trunk. We can think of each pulse as a little surge of electricity lasting about
2 millionths of a second. The ten-pulses, as the first group is called, are 10 millionths of a
second apart. The nine-pulses, as the second group is called, are also 10 millionths of a
second apart but are sandwiched between the ten-pulses. When the 1st ten-pulse comes
along, the 7th flip-flop in Accumulator 11 goes off, the 8th flip-flop goes on, the
following nine-pulse goes through and goes out on the subtract line to Accumulator 16.
Then the 2nd ten-pulse comes along, the 8th flip-flop goes off, the 9th flip-flop goes on,
and the next nine-pulse goes out on the subtract line to Accumulator 16. Now the decade
sits at 9, and for this reason the next ten-pulse changes an electronic switch (actually
another flip-flop) so that all later nine-pulses will go out on the add line. This ten-pulse
also turns off the 9th flip-flop and turns on the 0th flip-flop without causing any carry.
Now the 4th of the ten-pulses comes along, turns the 0th flip-flop off, and turns the 1st
flip-flop on, and the next nine-pulse goes out on the add line to Accumulator 13. The next
6 of the ten-pulses then come along and change Accumulator 11 back to the digit 7 as
before, and the next 6 of the nine-pulses go out to Accumulator 13. Thus Eniac has added
7 into Accumulator 13, has added 2, the nines complement of 7 (see Supplement 2), into

Accumulator 16, and has left Accumulator 11 holding the same number as before. This is
just the result that we wanted.
In this way, the nines complement of any digit in a decade is transferred out along the
subtract line, and the digit unchanged is transmitted out along the add line. As the pulses
arrive at any other accumulator, they add into that accumulator.

Multiplying and Dividing

Eniac performs multiplication by a built-in table of the products in the 10-by-10
multiplication table, using the method of left-hand components and right-hand
components (see Supplement 2). For example, suppose that the 3rd digit of the multiplier
is 7 and that the 5th digit of the multiplicand is 6. Then, when Eniac attends to the 3rd
digit of the multiplier, the right-hand digit of the 42 = 6 × 7 is gathered in one
accumulator, and the left-hand digit 4 is gathered in another accumulator. After Eniac has
attended to all the digits of the multiplier, then Eniac performs one more addition and
transfers the sum of the left-hand digits into the right-hand digits accumulator.
Eniac does division in rather a novel way. First, the divisor is subtracted over and over
until the result becomes negative or 0. Then the machine shifts to the next column and
adds the divisor until the result becomes positive or 0. It continues this process,
alternating from column to column. For example, suppose that we divide 3 into 84 in this
way. We have:

____ _
3 ) 84 ( 32
-3
+54
-3
+24
-3
-6
+3
-3
+3
0

After we subtract 3 the third time, the result becomes negative,-6; in the next column,
after we add 3 twice, the result becomes 0. The quotient is

_
32, which is the same as 30 - 2, or 28;

and 3 × 28 is 84. Thus the process checks.

Consulting a Table

Eniac has three Function Tables. Here you can store numbers or instructions for the
machine to refer to. Each Function Table has 104 arguments (see Supplement 2). For each
argument, you can store 12 digits and 2 signs that may be plus or minus. This capacity
can be devoted to one 12-digit number with a sign, or to two 6-digit numbers each with a
sign, or to six 2-digit instructions. The three Function Tables are panels 43, 44, and 45. To
put in the numbers or instructions, you have to go over to these panels and set the
numbers or instructions, digit by digit, turning dial switches by hand. It is slow and hard
to do this right, but once it is done, Eniac can refer to any number or instruction in any
table in ¹/₁₀₀₀ of a second. This is much faster than the table reference time in any other of
the giant brains built up to 1948.

Programming

We said above that Eniac has over 100 control lines or program trunks along which
instructions can be sent. These instructions are expressed as pulses called program pulses.
Now how do we make these pulses do what we want them to do? For example, how can
we instruct Accumulator 11 to add what it holds into Accumulator 13?
On each unit of Eniac there are plug hubs or sockets (called program-pulse input
terminals) to which a program trunk may be connected. A program pulse received here
can make the unit act in some desired way. On each accumulator of Eniac, we find 12
program-pulse input hubs. Corresponding to each of these hubs, there is a nine-way
switch, called a program-control switch. The setting of this switch determines what the
accumulator will do when the program-pulse input hub belonging to the switch receives a
program pulse. For instance, there are switch settings for: receive input on the α line,
receive input on the β line, etc.; and transmit output on the add line, etc. There is even a
switch setting that instructs the accumulator to do nothing, and this instruction may be
both useful and important.
Now, in order that Accumulator 11 may transfer a number to Accumulator 13, we
need: (1) a digit tray, say B, for the number to travel along; (2) a program trunk line, say
G3, to tell Accumulator 11 when to send the number and Accumulator 13 when to receive
it; and (3) certain plugging as follows:
1. We plug from program trunk G3 into a program-pulse input
hub, say No. 5, of Accumulator 11;
2. We plug from the same program trunk G3 into a program-
pulse input hub, say No. 7, of Accumulator 13;
3. We set program-control switch No. 5 of Accumulator 11 to
“add”;

4. We set program-control switch No. 7 of Accumulator 13 to
some input, say γ.
5. We plug from digit tray B into the add output of Accumulator
11.
6. We plug from digit tray B into the γ input of Accumulator 13.
Now, when the program pulse comes along line G3, it makes Accumulator 13 transmit
additively along digit tray B into Accumulator 13. And that is the result that we wanted.
As each mechanism of Eniac finishes what it is instructed to do, it may or may not put
out a program pulse. This pulse in turn may be plugged into any other program trunk line
and may stimulate another mechanism to act. Then, when this mechanism finishes, it too
may or may not put out a program pulse, and so on.
In general, there are two different ways to instruct Eniac to do a problem. One way is
to set all the switches, plug all the connections, etc., for the specific problem. This is a
long and hard task. Very often, even with great care, it is done not quite correctly, and
then the settings must be carefully checked all over again. A second method (called the
von Neumann programming method) is to store all the instructions for a problem in one or
two function tables of Eniac and then tell Eniac to read the function tables in sequence
and to do what they say. The rest of the machine is then wired up in a standard fashion.
This method of instructing Eniac was proposed by Dr. John von Neumann of the Institute
of Advanced Study at Princeton, N. J. Eniac has been modified to the slight extent needed
so that this method can be used when desired. In this method, each instruction is a
selected one of 60 different standard instructions or orders—one of them, for example,
being “multiplication.” Each standard order is expressed by 2 decimal digits. The 60
standard orders are sufficient so that Eniac can do any mathematical problem that does
not overstrain its capacity. Since each of the 3 Function Tables can hold 600 2-digit
instructions, the machine can hold a program of 1800 instructions under the von
Neumann programming method.

AN APPRAISAL OF ENIAC
AS A COMPUTER

As a general-purpose calculating machine, Eniac suffers from unbalance. That is to
say, Eniac operates rapidly and successfully in some respects, and slowly and
troublesomely in other respects. This is altogether to be expected, however, in a calculator
as novel as Eniac and made to so large an extent out of standard radio parts. It was
certainly better to finish a calculator like this one and then start on a new one, as the
Moore School of Electrical Engineering did, than to prolong design and construction
indefinitely in order to make improvements.

Speed

Eniac adds or subtracts very swiftly at the rate of 5000 a second. Eniac multiplies at
the rate of 360 to 500 a second. Division, however, is slow, relatively; the rate is about 50
a second. Reading numbers from punched cards, 12 a second for 10-digit numbers, is
even slower. As a result of these rates, you find, when you put a problem on Eniac, that
one division delays you as long as 100 additions or 8 multiplications. Division might have
been speeded somewhat by (1) rapidly convergent approximation (see Supplement 2) to
the reciprocal of the divisor and (2) multiplying by the dividend; this might have taken 5
or 6 multiplication times instead of 8. Also, the use of a standard IBM punch-card feed
and card punch slows the machine greatly. One way to overcome this drawback might be
to install one or two additional sets of such equipment, which might increase input and
output speed.

Ease of Programming

Eniac has a very rapid and flexible automatic control over the programming of
operations. Eniac has more than 10 channels along which numbers can be transferred and
more than 100 channels along which program-control pulses can be transferred. There are
many ways for providing subroutines. Eniac has the additional advantage that there is no
delay in giving the machine successive instructions: all the instructions the machine may
need at any time are ready at the start of the problem, and indications occurring in the
calculation can change the routine completely.
All these advantages, however, are paid for rather heavily by the slow methods for
changing programming. You have to plug large numbers of program trunk lines and digit
trunk lines, or you have to set large numbers of switches, or both. Also, when you wish to
return to a previous problem, you must do all the plugging and switch setting over again.
Many delays in the operation of the machine are due to human errors in setting the
machine for a new problem. Here again, we must remember that Eniac was originally
designed as a special-purpose machine for solving trajectories. To calculate a large family
of trajectories very little changing of wires and switches would be needed.

Memory

The most severe limitation on the usefulness of Eniac was, at the outset, the fact that
it had only 20 registers for storing numbers. There are large numbers of problems that
cannot be simply handled with so small an internal memory. Even the Harvard IBM
calculator (see Chapter 6) is often strained during a problem because of the number of
intermediate results that must be stored for a time before combining. The Ballistic
Research Laboratories, however, contracted for extensions to Eniac to provide more
memory and easier changing of instructions.

Reliability

Checking results with Eniac is not easy. There is no built-in guarantee that Eniac’s
results are correct. A large calculator can and does make both constant and intermittent
errors. Ways for checking with Eniac are:
Mathematical, if and when available, and this will be seldom.
Running the problem a second time, and this will, at most, prove
consistency.
Deliberate testing of small parts of the problem, which is very
useful and is standard practice but leads only to a probability
that the final result is correct.
You can operate Eniac one addition at a time, and even one pulse at a time, and see what
the machine shows in its little neon bulbs. This is a very useful partial check.

Cost

The cost of Eniac is higher than that of some of the other large mechanical brains—
over half a million dollars. Because some of the work was done at the Moore School by
students, the cost was probably less than it otherwise would have been. The largest part of
the cost was the designing of the machine and the construction of the panels; the tubes
were only a small portion of the cost. The tubes used in the calculating circuits cost only
20 to 90 cents. However, no later electronic calculator need cost as much, for many
improvements can now be seen.
The power required for Eniac is about 150 kilowatts or about 200 horsepower, most
of which is used for the heaters of the electronic tubes. The largest number of electronic
tubes mentioned for future electronic calculators is about 3000, so we can see that they
are likely to use less than a quarter of the power needed for Eniac.
Eniac will doubtless give a number of years of successful operation and be extremely
useful for problems that employ its assets and are not excluded by its limitations. In fact,
at the Ballistic Research Laboratories, for a typical week of actual work, Eniac has
already proved to be equal to 500 human computers working 40 hours with desk
calculating machines, and it appears that soon two or three times as much work may be
obtained from Eniac.

Chapter 8
RELIABILITY—NO WRONG RESULTS:
BELL LABORATORIES’
GENERAL-PURPOSE RELAY CALCULATOR
In 1946, Bell Telephone Laboratories in New York finished two general-purpose
relay calculators—mechanical brains. They were twins. One was shipped in July 1946 to
the National Advisory Committee for Aeronautics at Langley Field, Virginia. The other,
after some months of trial operation, was shipped in February 1947 to the Ballistic
Research Laboratories at the U. S. Army’s Proving Ground, Aberdeen, Md.
Each machine is remarkably reliable and versatile. It can do a wide variety of
calculations in a great many different ways. Yet the machine never takes a new step
without a check that the old step was correctly performed. There is, therefore, a chance of
better than 99.999,999,999 per cent that the machine will not let a wrong result come out.
The automatic checking, of course, does not prevent (1) human mistakes—for example,
instructing the machine incorrectly—or (2) mechanical failures, in which the machine
stops dead in its tracks, letting no result at all come out.

ORIGIN AND DEVELOPMENT

In Bell Telephone Laboratories the telephone system of the country is continually
studied. Their research produced the common type of dial telephone system: a masterly
machine for selecting information.
Now when a telephone engineer studies an electric circuit, he often finds it very
convenient to use numbers in pairs: like 2, 5 or-4,-1. Here the comma is a separation sign
to keep the two numbers in the pair separate and in sequence. Mathematicians call
numbers of this kind, for no very good reason, complex numbers; of course, they are far
less complex than why the sun shines or why plants grow.
When Bell Laboratories test the design of new circuits, girl computers do arithmetic
with complex numbers. Addition and subtraction are easy: each means two operations of
addition or subtraction of ordinary numbers. For example, 2, 5, plus-4,-1 equals 2-4, 5-1,
which equals-2, 4. And 2, 5 minus-4,-1 is the same as 2, 5 plus 4, 1; and this equals 2 + 4,
5 + 1, which equals 6, 6. Multiplication of two complex numbers, however, is more work.
If a, b and c, d are two complex numbers, then the formula for their product is (a × c)-(b
× d), (a × d) + (b × c). To get the answer, we need 4 multiplications, 1 subtraction, and
1 addition. Division of two complex numbers requires even more work. If a, b and c, d
are two complex numbers, the formula for the quotient of a, b divided by c, d is:

[(a × c) + (b × d)] ÷ [(c × c) + (d × d)],
[(b × c) - (a × d)] ÷ [(c × c) + (d × d)]
For example,
(2, 5) ÷ (-4, -1) = [(2 × -4 = -8) + (5 × -1 = -5)] ÷ [(-4 × -4 = 16) + (-1 × -1 = 1)],
[(5 × -4 = -20) - (2 × -1 = -2)] ÷ [16 + 1] = -(¹³/₁₇), -(¹⁸/₁₇)
Thus, division of one complex number by another needs 6 multiplications, 2 additions, 1
subtraction, and 2 divisions of ordinary numbers—and always in the same pattern or
sequence.

The Complex Computer

About 1939, an engineer at Bell Telephone Laboratories in New York, Dr. George R.
Stibitz, noticed the great volume of this pattern arithmetic. He began to wonder why
telephone switching equipment could not be used to do the multiplications and divisions
automatically. He decided it could. All that was necessary was that the relays (see
Chapter 2) used in regular telephone equipment should have a way of remembering and
calculating with numbers. Regular telephone equipment would take care of the proper
sequence of operations. Regular equipment known as teletypewriters would print the
numbers of the answer when it was obtained. A teletypewriter consists essentially of a
typewriter that may be operated by electrical impulses. It has a keyboard that may
produce electrical impulses in sets corresponding to letters; and it can receive or transmit
over wires.
Dr. Stibitz coded the numbers: each decimal digit was matched up with a group of
four relays in sequence, and each of these relays could be open or closed. If 0 means
open and 1 means closed, here is the pattern or code that he used:

Decimal
Relay Code
Digit
0 0011
1 0100
2 0101
3 0110
4 0111

5 1000
6 1001

Decimal
Relay Code
Digit
7 1010
8 1011
9 1100
With regular telephone relays and regular telephone company techniques, Dr. Stibitz
and Bell Telephone Laboratories designed and constructed the machine. It was called the
Complex Computer and was built just for multiplying and dividing complex numbers. Six
or eight panels of relays and wires were in one room. Two floors away, some of the girl
computers sat in another room, where one of the teletypewriters of the machine was
located. When they wished, they could type into the machine’s teletypewriter the
numbers to be multiplied or divided. In a few seconds back would come the answer. In
fact, there were two more computing rooms where teletypewriters of the machine were
stationed. To prevent conflicts between stations, the machine had a circuit like the busy
signal from a telephone.
In 1940, a demonstration of the Complex Computer took place: the computing panels
remained in New York, but the teletypewriter input-output station was set up at
Dartmouth College in Hanover, N. H. Mathematicians gave problems to the machine in
Dartmouth, it solved them in New York, and it reported the answers in Dartmouth.

Special-Purpose Computers

With this as a beginning, Bell Laboratories developed another machine for a wide
variety of mathematical processes called interpolating (see Supplement 2). Then, during
World War II, Bell Laboratories made more special-purpose computing machines. They
were used in military laboratories charged with testing the accuracy of instruments for
controlling the fire of guns. These computers took in a set of gun-aiming directions put
out by the fire-control instrument in some test. They also took in the set of observations
that went into the fire-control instrument on that test. Then they computed the differences
between the gun-aiming produced by the fire-control instrument and the gun-aiming
really required by the observations. Using these differences, the fire-control instrument
could be adjusted and corrected. These special-purpose computers were also useful in
checking the design of new fire-control instruments and in checking changes due to new
types of guns or explosives.
Regularly, after each of these special-purpose computers was finished, people began
to put other problems on it. It seemed to be fated that, as soon as you had made a
machine for one purpose, you wanted to use it for something else. Accordingly, in 1944,
two agencies of the U. S. Government together made a contract with Bell Telephone
Laboratories for two general-purpose relay computers. These two machines were finished
in 1946 and are twins.

ORGANIZATION OF THE
GENERAL-PURPOSE COMPUTER

When a man sits down at a desk to work on a computation, he has six things on his
desk to work with: a work sheet; a desk calculator, to add, subtract, multiply, and divide;
some rules to be followed; the tables of numbers he will need; the data for the problem;
and an answer sheet. In his head, he has the capacity to make decisions and to do his
work in a certain sequence of steps. These seven subdivisions of calculation are all found
in the Bell Laboratories’ general-purpose relay computer. The general-purpose computer
is a computing system, in fact, more than it is a single machine. The part of the system
which does the actual calculating is called, in the following paragraphs, the computer, or
else, since it is in two halves, Computer 1 and Computer 2.

Physical Units

The computing system delivered to the Ballistic Research Laboratories fills a room
about 30 by 40 feet and consists of the following:
2 computers: panels of relays, wiring, etc., which add, subtract,
multiply, divide, select, decide, control, etc.
4 problem positions: tables each holding 12 mechanisms for
feeding paper tape, which read numbers and instructions
punched on tape and convert them into electrical impulses.
2 hand perforators: keyboard devices for punching instructions
and numbers on paper tape.
1 processor: a table holding mechanisms for feeding 2 paper
tapes and punching a third paper tape, used for checking
numbers and instructions punched on tape.
2 recorders: each a table holding a teletypewriter, a tape punch,
and a tape feed, used for recording answers and, if
necessary, consulting them again.
The 2 computers correspond to the work sheet, the desk calculator, and the man’s
capacity to make decisions and to carry out a sequence of steps. The 4 problem positions
correspond to the problem data, the rules, and the tables of numbers. The 2 recorders
correspond to the answer sheet. The 2 hand perforators and the processor are auxiliary
machines: they translate the ordinary language of arithmetic into the machine language of
punched holes in paper tape.
This is the computing system as organized for the Ballistic Research Laboratories at
Aberdeen. The one for the National Advisory Committee for Aeronautics has only 3
problem positions. The computer system may, in fact, be organized with 1 to 10
computers and with 1 to 20 problem positions.

The great bulk of this computing system, like the mechanical brains described in
previous chapters, is made up of large numbers of identical parts of only a few kinds.
These are: standard telephone relays; wire; and standard teletype transmitters,
mechanisms that read punched paper tape and produce electrical impulses.

Numbers

The numbers that the Bell machine contains range from 0.1000000 to 0.9999999
times a power of 10 varying from 10,000,000,000,000,000,000 to
0.000,000,000,000,000,000,1, or, in other words, from 10¹⁹ to 10⁻¹⁹. The machine also
contains zero and infinity: zero arises when the number is smaller than 10⁻¹⁹, and infinity
arises when the number is equal to or greater than 9,999,999,000,000,000,000. (See
Supplement 2.)
The system used in the machine to represent numbers on relays is called biquinary—
the bi-, because it is partly twofold like the hands, and the -quinary because it is partly
fivefold like the fingers. This system is used in the abacus (see Chapter 2 and Supplement
2). In the machine, for each decimal digit, 7 relays are used. These relays are called the
00 and 5 relays, and the 0, 1, 2, 3, and 4 relays. If, as before, 0 indicates a relay that is not
energized and 1 indicates a relay that is energized, then each decimal digit is represented
by the positioning of the 7 relays as follows:

Decimal
Relays
Digit
00 5 0 1 2 3 4
0 1 0 10000
1 1 0 01000
2 1 0 00100
3 1 0 00010
4 1 0 00001

5 0 1 10000
6 0 1 01000
7 0 1 00100
8 0 1 00010
9 0 1 00001
Then, for any decimal digit, one and only one of the 00 and 5 relays is energized, and one
and only one of the 0, 1, 2, 3, and 4 relays is energized. If more or less than exactly one
relay in each set is energized, then the machine knows that it has made a mistake, and it

stops dead in its tracks. Thus any accidental failure of a relay is at once caught, and the
chance of two compensating failures occurring at the same time is extremely small.

HOW INFORMATION GOES
INTO THE MACHINE

In order to put a problem into this machine—just as with the other machines—first a
mathematician who knows how the problem is to be solved, and who knows how to
organize it for the machine, lays out the scheme of calculation. Then, a girl goes to one of
the hand perforators. Sitting at the keyboard, she presses keys and punches out feet or
yards of paper tape expressing the instructions and numbers for the calculation. Each
character punched—digit, letter, or sign—has one or more of a maximum of 6 holes
across the tape. Another girl, using the other hand perforator, also punches out the
instructions and numbers for the calculation. If she wishes to erase a wrong character, she
can press an erase key that punches all 6 holes, and then the machine will pass by this
row as if it were not there.
Three kinds of tapes are produced for the machine:
Problem tapes, which contain information belonging to the
particular problem.
Table tapes, which contain tables of numbers to be referred to
from time to time.
Routine tapes, which contain the program, or routine, or
sequence of steps that the machine is to carry out.
In each of these tapes one character takes up ⅒ of an inch along the tape. In the case of a
table tape, however, an ordinary 1-digit number requires 4 characters on the tape, and a
7-digit number requires 11 characters on the tape. On a table tape there will be on the
average about 1 inch of tape per number.

The Processor

The two paper tapes prepared on the perforator should agree. But whether or not they
agree, a girl takes them over to the processor and puts them both in. The processor has
two tape feeds, and she puts one tape on each and starts the machine. The processor
compares them row by row, making sure that they agree, and punches a new tape row by
row. If the two input tapes disagree, the processor stops. You can look to see which tape
is right, and then you can put the correct punch into the new tape with a keyboard
mounted on the processor. As the processor compares the two input tapes, it also converts
any number written in the usual way into machine language. For example, the processor
will automatically translate 23,188 into +.231 8800 × 10⁺⁵. The processor also puts in
certain safeguards. If you want it to, the processor will also make a printed record of a

tape. Also, when a tape becomes worn from use in the machine, you can put it into the
processor and make a fresh copy.

The Problem Positions

Next, the girl takes the punched tape made by the processor over to a problem
position that is idle. Two of the problem positions are always busy guiding the two
computers. The other two problem positions stand by, ready to be loaded with problems.
A problem position looks like a large covered-over table. Under the covers are 12
tape feeds, or tape transmitters. All these transmitters look exactly alike except for their
labels and consist of regular teletype transmitters. Six-hole paper tape can be fed into any
transmitter. Six metal fingers sense the holes in the paper tape and give out electrical
impulses at proper times. At the front of the problem position is a small group of switches
that provide complete control over the problem while it is on the machine. These are
switches for starting, disconnecting, momentary stop, etc.
One tape transmitter is the problem tape transmitter. It takes in all the data for the
problem such as the starting numbers. The first thing it does at the start of a problem is to
check (by comparing tape numbers) that the right tapes are in the right feeds.
Five transmitters are routine tape transmitters. Each of these takes in the sequence of
computing steps. The routine tapes also contain information for referring to table tapes
and instructions for printing and punching tape. The machine can choose according to
instructions between the five routine tapes and can choose between many different
sections on each tape. Therefore, we can use a large number of different routines in a
calculation, and this capacity makes the machine versatile and powerful.
Six transmitters are table tape transmitters. They read tables of numbers when
directed to. A table tape can be as long as 100 feet and will hold numbers at the rate of 1
inch per number, so that about 1200 numbers of seven decimal digits can be stored on a
table tape.
When we look up a number in a table, such as the following,
2½ 3 3½ ···
1 1.02500 1.03000 1.03500
2 1.05063 1.06090 1.07123
3 1.07689 1.09273 ···
4 1.10381 ··· ···
5 1.13141 ···
6 1.15969
7 ···
8 ···

9 ···
10
··· ···
we look along the top and down the side until we find the column and row of the number
we are looking for. These are called the arguments of the tabular value that we are
looking for (see Supplement 2). Now when we put this table on a tape to go into the Bell
Laboratories machine, we write it all on one line, one figure after another, and we punch
it as follows:
2-½ 1-5 1.02500 1.05063 1.07689 1.10381 1.13141
6-10 1.15969 ··· 11-15 ··· ··· ··· 3 1-5
1.03000 1.06090 ··· ··· 3½ 1-5 1.03500 ···
You will notice that the column labels 2½, 3, 3½ have been put on the tape, each in front
of the group of numbers they apply to. The row labels 1 to 5, 6 to 10, ··· have also been
put on the tape, each in front of the group of numbers they apply to. The appropriate
column and row numbers, or arguments, must be put often on every table tape, so that it
is easy for the machine to tell what part of the table tape it is reading.
In the Bell Laboratories machine, we do not need to put equal blocks of arguments
like 1-5, 6-10 ··· on the table tape. Instead we can put individual arguments like 1, 2, 3, 4
···, or, if we wish, we can use blocks of different sizes, like 1-3, 4-15, 16-30···. For some
tables, such as income tax tables, it is very useful to have varying-sized blocks of
arguments. The machine, when hunting for a certain value in the table, makes a
comparison at each block of arguments.
The machine needs about 6 seconds to search a foot of tape. If we want to set up a
table economically, therefore, we need to consider the average length of time needed for
searching.

Fig. 1. Scheme of a recorder.

HOW INFORMATION COMES
OUT OF THE MACHINE

At either one of the two recorders (Fig. 1), information comes out of the machine,
either in the form of printed characters or as punched tape. The recorder consists of a
printer, a reperforator, and a tape transmitter. One recorder table belongs to each
computer and records the results it computes. The printer is a regular teletypewriter
connected to the machine. It translates information produced by the machine as electrical
impulses and prints the information in letters and digits on paper. The reperforator is an
automatic tape punch. It translates information produced by the machine in the form of
electrical impulses and punches the information on paper tape. Next to the tape punch is a
tape transmitter. After the tape comes through the punch, it is fed into the transmitter.
Here the machine can hunt for a previous result punched in the tape, read that result, and
use it again.

HOW INFORMATION IS MANIPULATED
IN THE MACHINE

The main part of the computing system consists of 27 large frames loaded with relays
and wiring, called the computer, or Computer 1 and Computer 2. In this “telephone

central station,” all the “phone calls” from one number to another are attended to. There
are 8 types of these frames in the computer:

Frames Number
Storing register frames 6
Printer frames 2
Problem frames 2
Position frames 2
Calculator frames 6
Control frames 2
Routine frames 4
BTL (Block-Trig-Log) frames 2
Permanent table frames 1
Total 27
In most but not quite all respects, the two halves, Computer 1 and Computer 2, can
compute independently. The storing register frames hold enough relays to store 30
numbers. The registers for these numbers are named A, B, C, D, ···, M, N, O in two
groups of 15 each. One group belongs to Computer 1 and the other to Computer 2. In
each Computer, the calculator frames hold enough relays for storing two numbers (held
in the X and Y registers) and for performing addition, subtraction, multiplication,
division, and square root. In each Computer, the problem frame stores the numbers that
are read off the problem tape and the table tapes, and the printer frame stores the
numbers that are read into the printer. The printer frame also stores indications, for
example, the signs of numbers, plus or minus, for purposes of combining them. These
frames also hold the relays that control the printer, the problem tape, and the table tapes.
Jointly for both Computers, the position frames connect a problem in some problem
position to a Computer that becomes idle. For example, one problem may finish in the
middle of the night; the machine automatically and unattended switches to another
problem position and proceeds with the instructions there contained. A backlog of
computing on hand can be stored in two of the problem positions, while the other two
control the two Computers. In each Computer, the routine frames hold the relays that
make the Computer follow the routine instructions. Jointly for both Computers, the
remaining frames—the control frames, the BTL frames, and the permanent table frames
—hold the relays that control: the alarms and lights for indicating failures; some circuits
called the BTL controls; the tape processor; and the mathematical tables that are
permanently wired into the machine. The permanent table frames hold the following
mathematical functions (see Supplement 2): sine, cosine, antitangent, logarithm, and
antilogarithm.

Storing

Numbers can be stored in the machine in the 30 regular storing registers of both
Computers together. They can also be stored, at the cost of tying up some machine
capacity, in the other registers: the 4 calculator registers, the 2 problem registers, the 2
table registers, and the 2 printer registers. Numbers can also be punched out on tape, in
either of the two printers, and later read again from the tape. Labels identifying the
numbers can also be punched and read again from the tape.
Each register in the machine stores a number in the biquinary notation, as explained
above. In programming the machine, after mentioning a register it is necessary—as a part
of the scheme for checking—to tell the machine specifically whether to hold the number
in the register or to clear it.

Addition and Subtraction

The calculator frames can add two numbers together, if so instructed in the routine
tape. Suppose that the two numbers are in the registers B and D and that we wish to put
the sum in register F. Suppose that we wish to clear the D number but hold the B number
after using them. The code on the routine tape is B H + D C = F. H and C coming right
after the names of the registers always designate “hold” and “clear,” respectively.
The calculator frames can, likewise, subtract a number. The routine instruction B H-D
C = F means:

Take the number in register B (hold it);
subtract the number in D (clear it);
put the result in F

Multiplication and Division

The calculator frames perform multiplication by storing the digits of the multiplier,
adding the multiplicand over and over, and shifting, until the product is obtained.
However, if the multiplier is 1989, for example, the calculator treats it as 2000-11. This
short-cut applies to digits 6, 7, 8, 9 and cuts the time required for multiplying. The
routine instruction is B H × D C = F.
The calculator performs division by repeated subtraction. The routine instruction is B
H ÷ D C = F. The operation signs +,-, ×, ÷ actually appear on the keyboard of the
perforator and on the printed tape produced by the printer.

Discrimination

Discrimination is the term used in the Bell Laboratories computer for what we have
previously called selection, or comparison, or sequencing. The discriminator is a part of
the calculator that compares or selects or decides—“discriminates.” The discriminator
can decide whether a number is zero or not zero. In the language of the algebra of logic
(see Chapter 9 and Supplement 2), if a is a number, the discriminator can find T(a = 0).
The discriminator can also decide whether a number is positive or negative. In the
language of logic, it can find T(a > 0) or T(a < 0). The actions that a discriminator can
cause to be taken are:

Stop the machine.
Stop the problem, and proceed to another problem.
Stop the routine going on, and proceed with a new routine.
Permit printing, or prevent printing; etc.

In this way the discriminator can:

Distinguish between right and wrong results.
Tell that a certain result is impossible.
Recognize a certain result to be the answer.
Control the number of repetitions of a formula.
Change from one formula to another formula.
Check a number against a tolerance; etc.

PROBLEMS

Among the problems that have been placed on the machine successfully are: solving
the differential equation of a trajectory (see Chapter 5) and solving 32 linear
simultaneous equations in 32 unknowns (see Supplement 2). In the second case, the
routine tapes were designed to apply equally well to 11 to 100 linear equations in 11 to
100 unknowns. However, the machine can do a very broad class of problems, including,
for example, computing a personal income tax. This calculation with all its complexity of
choices cannot be placed on any of the mechanical brains described in previous chapters.
The machine can, of course, be used to calculate any tables that we may wish to refer to.

AN APPRAISAL OF THE CALCULATOR

The Bell Telephone Laboratories general-purpose relay computer is probably the best
mechanical brain made up to the end of 1947, in regard to the two important factors of
reliability and versatility.

Reliability

The machine produces results that are practically 100 per cent reliable, for the
machine checks each step before taking the next one. The checking principle is that
exactly a certain number of relays must be energized. For example, as we said before, for
each decimal digit there are 7 relays. Exactly 2 of these relays must be energized—no
more, no less. If this does not happen, the machine stops at once without losing any
numbers. Lights shine for many circuits in the control panel, and, if you compare what
they ought to show with what they do show, you can usually find at once the location of
the mistake. The trouble may be a speck of dirt between two contact points on a relay,
and, when it is brushed away, the machine can go right ahead from where it stopped.
According to a statement by Franz L. Alt, director of the computing laboratory at the
Ballistic Research Laboratories, in December 1947, “the Bell machine had not given a
single wrong result in eight months of operation, except when operators interfered with
its normal running.”
To guard against the risk of putting tapes in the wrong transmitters, the machine will
check by the instructions contained in the tapes that the right tapes are in the right places.

Time Required

The time required to do problems on this mechanical brain is perhaps longer than on
the others. The numbers are handled digit by digit on the input tapes, and the typewriter
in the recorder moves space by space in order to get to the proper writing point. These are
slow procedures. The speeds of numerical operation are: addition, ³/₁₀ second;
multiplication, 1 second on the average; division, 2.7 seconds on the average; square
root, 4.5 seconds on the average; logarithm, about 15 seconds.

Staff

In order to operate the machine, the staff required is: one maintenance man; one
mathematical engineer; about six girls for punching tape, etc., depending on the number
of problems to be handled at the rate of about one problem per week per girl. Unlike any
of the other mechanical brains built by the end of 1947, this machine will run unattended.

Maintenance

The relays in the machine will operate for years with no failure; they have the
experience of standard telephone techniques built into them. Under laboratory conditions
this type of relay had by 1946 operated successfully much more than 100 million times.
The tape feeding and reading equipment in the machine may be maintained by periodic
inspection and service. The total number of teletype transmitters in the machine is 38. If
one fails, it is easy to plug in a spare.
The total power required for the machine is about 28 horsepower. Batteries are
furnished so that, if the power supply should be interrupted, the machine can still operate

for as long as a half-hour.

Cost

The cost of production of this machine in the size of 4 problem positions and 2
computers has been roughly estimated as half a million dollars. This cost includes
material, manufacture, installation, and testing. No development cost is included in this
figure. Instead, the cost of development has been reckoned as squaring with patents and
other contributions of the work to the telephone switching art.
It is unlikely that the general-purpose relay computer will be manufactured generally.
The pressure of orders for telephones, the need to catch up with the backlog of demand,
and the development of electronic computers—all indicate that the Bell system will
hardly go further with this type of computer. In an emergency, however, the Bell system
would probably construct such machines for the government, if requested. In the
meantime, many principles first used in the general-purpose relay computer are likely to
find applications in telephone system work. In fact, a present major development being
pursued in the telephone sections of Bell Laboratories is the application of the computer
principles to the automatic computation of telephone bills.

Chapter 9
REASONING:
THE KALIN-BURKHART
LOGICAL-TRUTH CALCULATOR
So far we have talked about mechanical brains that are mathematicians. They are fond of
numbers; their main work is with numbers; and the other kinds of thinking they do are
secondary. We now come to a mechanical brain that is a logician. It is fond of reasoning—
logic; its main work is with what is logically true and what is logically false; and it does not
handle numbers. This mechanical brain was finished in June 1947. It is called the Kalin-
Burkhart Logical-Truth Calculator. As its name tells, it calculates logical truth. Now what
do we mean by that?

TRUTH

To be true or false is a property of a statement. Usually we say that a statement is true
when it expresses a fact. For example, take the statement “Salt dissolves in water.” We
consider this statement to be true because it expresses a fact. Actually, in this case we can
roughly prove the fact ourselves. We take a bowl, put some water in it, and put in a little salt.
After a while we look into the water and notice that no salt whatever is to be seen.
Of course, this statement, like many another, occurs in a context where certain things are
understood. One of the understandings here, for example, is “a small amount of salt in a
much larger amount of water.” For if we put a whole bag full of salt in just a little water, not
all the salt will dissolve. Nearly every statement occurs in a context that we must know if we
are to decide whether the statement is true or false.

LOGICAL TRUTH

Logical truth is different from ordinary truth. With logical truth we appeal not to facts
but to suppositions. Usually we say that a statement is logically true when it follows
logically from certain suppositions. In other words, we play a game that has useful, even
wonderful, results. The game starts with “if” or “suppose” or “let us assume.” While the
game lasts, any statement is logically true if it follows logically from the suppositions.
For example, let us take five statements:

1. “The earth is flat like a sheet of paper.”
2. “The earth is round like a ball.”
3. “John Doe travels as fast as he can, without turning
to left or to right, for many days.”

4. “John Doe will fall off the earth.”
5. “John Doe will arrive back at his starting point.”

Let us also take a certain context in which: We know what we mean by such words as
“earth,” “flat,” “falling,” etc.; we have other statements and understandings such as “if John
Doe walks off the edge of a cliff, he will fall,” “a flat sheet of paper has an edge,” etc. In this
context, if statements 1 and 3 are supposed, then statement 4 is logically true. On the other
hand, if statements 2 and 3 are supposed, then statement 5 is logically true. Of course, for
many centuries, nearly all men believed statement 1; and the importance of the years 1492 to
1521 (Columbus to Magellan) is linked with the final proof that statement 2 expresses a fact.
So, depending on the game, or the context, whichever we wish to call it, almost any
statement can be logically true. What we become interested in, therefore, is the connections
between statements which make them follow logically.

LOGICAL PATTERNS

Perhaps the most familiar example of “following logically” is a pattern of words like the
following:

1. All igs are ows.
2. All ows are umphs.
3. Therefore, all igs are umphs.

If statements 1 and 2 are supposed, then statement 3 is logically true. In other words,
statement 3 logically follows from statements 1 and 2. This word pattern is logically true, no
matter what substitutions we make for igs, ows, and umphs. For example, we can replace igs
by men, ows by animals, and umphs by mortals, and obtain:

4. All men are animals.
5. All animals are mortals.
6. Therefore, all men are mortals.

The invented words “igs,” “ows,” “umphs” mark places in the logical pattern where we can
insert any names we are interested in. The words “all,” “are,” “therefore” and the ending s
mark the logical pattern. Of course, instead of using invented words like “igs,” “ows,”
“umphs” we would usually put A’s, B’s, C’s. This logical pattern is called a syllogism and is
one of the most familiar. But there are even simpler logical patterns that are also familiar.

THE SIMPLEST LOGICAL PATTERNS

Many simple logical patterns are so familiar that we often use them without being
conscious of doing so. The simple logical patterns are marked by words like “and,” “or,”
“else,” “not,” “if,” “then,” “only.” In the same way, simple arithmetical patterns are marked
by words like “plus,” “minus,” “times,” “divided by.”

Let us see what some of these simple logical patterns are. Suppose that we take two
statements about which we have no factual information that might interfere with logical
supposing:

1. John Doe is eligible for insurance.
2. John Doe requires a medical examination.

In practice, we might be concerned with such statements when writing the rules governing a
plan of insurance for a group of employees. Here, we shall play a game:
(1) We shall make up some new statements from statements 1 and
2, using the words “and,” “or,” “else,” “not,” “if,” “then,”
“only.”
(2) We shall examine the logical patterns that we can make.
(3) We shall see what we can find out about their logical truth.
Suppose we make up the following statements:
3. John Doe is not eligible for insurance.
4. John Doe does not require a medical examination.
5. John Doe is eligible for insurance and requires a medical
examination.
6. John Doe is eligible for insurance, and John Doe is eligible for
insurance.
7. John Doe is eligible for insurance, or John Doe requires a
medical examination.
8. If John Doe is eligible for insurance, then he requires a medical
examination.
9. John Doe requires a medical examination if and only if he is
eligible for insurance.
10. John Doe is eligible for insurance or else he requires a medical
examination.
Now clearly it is troublesome to repeat quantities of words when we are interested only in
the way that “and,” “or,” “else,” “not,” “if,” “then,” “only” occur. So, let us use just 1 and 2
for the two original statements, remembering that “1 and 2” means here “statement 1 and
statement 2” and does not mean 1 plus 2. Then we have:

3: not-1
4: not-2
5: 1 and 2
6: 1 and 1

7: 1 or 2
8: if 1, then 2
9: 1 if and only if 2
10: 1 or else 2
Here then are some simple logical patterns that we can make.

CALCULATION OF LOGICAL TRUTH

Now what can we find out about the logical truth of statements 3 to 10? If we know
something about the truth or falsity of statements 1 and 2, what will logically follow about
the truth or falsity of statements 3 to 10? In other words, how can we calculate the logical
truth of statements 3 to 10, given the truth or falsity of statements 1 and 2?
For example, 3 is not-1; that is, statement 3 is the negative or the denial of statement 1.
It follows logically that, if 1 is true, 3 is false; if 1 is false, 3 is true. Suppose that we use T
for logically true and F for logically false. Then we can show our calculation of the logical
truth of statement 3 in Table 1.
Table 1 Table 2
1 not-1 = 3 2 not-2 = 4

T F T F
F T F T
Our rule for calculation is: For T put F; for F put T. Of course, exactly the same rule applies
to statements 2 and 4 (see Table 2). The T and F are called truth values. Any meaningful
statement can have truth values. This type of table is called a truth table. For any logical
pattern, we can make up a truth table.
Let us take another example, “and.” Statement 5 is the same as statement 1 and
statement 2. How can we calculate the logical truth of statement 5? We can make up the
same sort of a table as before. On the left-hand side of this table, there will be 4 cases:

1. Statement 1 true, statement 2 true.
2. Statement 1 false, statement 2 true.
3. Statement 1 true, statement 2 false.
4. Statement 1 false, statement 2 false.

On the right-hand side of this table, we shall put down the truth value of statement 5.
Statement 5 is true if both statements 1 and 2 are true; statement 5 is false in the other cases.
We know this from our common everyday experience with the meaning of “and” between
statements. So we can set up the truth table, and our rule for calculation of logical truth, in
the case of and, is shown on Table 3.

Table 3
1 2 1 and 2 = 5

T T T
F T F
T F F
F F F
“and” and the other words and phrases joining together the original two statements to
make new statements are called connectives, or logical connectives. The connectives that we
have illustrated in statements 7 to 10 are: or, if ··· then, if and only if, or else.
Table 4 shows the truth table that applies to statements 7, 8, 9, and 10. This truth table
expresses the calculation of the logical truth or falsity of these statements.

Table 4
1 or 2 if 1, then 2 1 if and only if 2 1 or else 2
1 2 =7 =8 =9 = 10

T T T T T F
F T T T F T
T F T F F T
F F F T T F
The “or” (as in statement 7) that is defined in the truth table is often called the inclusive
“or” and means “and/or.” Statement 7, “1 or 2,” is considered to be the same as “1 or 2 or
both.” There is another “or” in common use, often called the exclusive “or,” meaning “or
else” (as in statement 10). Statement 10, “1 or else 2,” is the same as “1 or 2 but not both”
or “either 1 or 2.” In ordinary English, there is some confusion over these two “or’s.”
Usually we rely on the context to tell which one is intended. Of course, such reliance is not
safe. Sometimes we rely on a necessary conflict between the two statements connected by
“or” which prevents the “both” case from being possible. In Latin the two kinds of “or”
were distinguished by different words, vel meaning “and/or,” and aut meaning “or else.”
The “if ··· then” that is defined in the truth table agrees with our usual understanding
that (1) when the “if clause” is true, the “then clause” must be true; and (2) when the “if
clause” is false, the “then clause” may be either true or false. The “if and only if” that is
defined in the truth table agrees with our usual understanding that (1) if either clause is true,
the other is true; and (2) if either clause is false, the other is false.
In statement 6, there are only two possible cases, and the truth table is shown in Table 5.

Table 5

1 1 and 1 = 6

T T
F F
We know that 6 is true if and only if 1 is true. In other words, the statement “1 and 1 if and
only if 1” is true, no matter what statement 1 may refer to. It is because of this fact that we
never use a statement in the form “1 and 1”: it can always be replaced by the plain statement
“1.”

LOGICAL-TRUTH CALCULATION BY
EXAMINING CASES AND REASONING

Now you may say that this is all very well, but what good is it? Almost anybody can use
these connectives correctly and certainly has had a great deal of practice using them. Why
do we need to go into truth values and truth tables?
When we draft a contract or a set of rules, we often have to consider several conditions
that give rise to a number of cases. We must avoid:
1. All conflicts, in which two statements that disagree apply to the
same case.
2. All loopholes, in which there is a case not covered by any
statement.
If we have one statement or condition only, we have to consider 2 possible cases: the
condition satisfied or the statement true; the condition not satisfied or the statement false. If
we have 2 conditions, we have to consider 4 possible cases: true, true; false, true; true, false;
false, false. If we have 3 conditions, we have to consider 8 possible cases one after the other
(see Table 6).

Table 6
1st 2nd 3rd
Case
Condition Condition Condition
1 T T T
2 F T T
3 T F T
4 F F T

5 T T F
6 F T F
7 T F F

8 F F F
Instead of T’s and F’s, we would ordinarily use check-marks (✓) and crosses (✕), which, of
course, have the same meaning. We may consider and study each case individually. In any
event, we must make sure that the proposed contract or set of rules covers all the cases
without conflicts or loopholes.
The number of possible cases that we have to consider doubles whenever one more
condition is added. Clearly, it soon becomes too much work to consider each case
individually, and so we must turn to a second method, thoughtful classifying and reasoning
about classes of cases.
Now suppose that the number of conditions increases: 4 conditions give rise to 16
possible cases; 5, 6, 7, 8, 9, 10, ··· conditions give rise to 32, 64, 128, 256, 512, 1024, ···
cases respectively. Because of the large number of cases, we soon begin to make mistakes
while reasoning about classes of cases. We need a more efficient way of knowing whether
all cases are covered properly.

LOGICAL-TRUTH CALCULATION
BY ALGEBRA

One of the more efficient ways of reasoning is often called the algebra of logic. This
algebra is a part of a new science called mathematical logic. Mathematical logic is a science
that has the following characteristics:

It studies chiefly nonnumerical reasoning.
It seeks accurate meanings and necessary consequences.
Its chief instruments are efficient symbols.

Mathematical logic studies especially the logical relations expressed in such words as “or,”
“and,” “not,” “else,” “if,” “then,” “only,” “the,” “of,” “is,” “every,” “all,” “none,” “some,”
“same,” “different,” etc. The algebra of logic studies especially only the first seven of these
words.
The great thinkers of ancient Greece first studied the problems of logical reasoning as
these problems turned up in philosophy, psychology, and debate. Aristotle originated what
was called formal logic. This was devoted mainly to variations of the logical pattern shown
above called the syllogism. In the last 150 years, the fine symbolic techniques developed by
mathematicians were applied to the problems of the calculation of logical truth, and the
result was mathematical logic, much broader and much more powerful than formal logic. A
milestone in the development of mathematical logic was The Laws of Thought, written by
George Boole, a great English mathematician, and published in 1854. Boole introduced the
branch of mathematical logic called the algebra of logic, also called Boolean algebra. In late
years, all the branches of mathematical logic have been improved and made easier to use.
We can give a simple numerical example of Boolean algebra and how it can calculate
logical truth. Suppose that we take the truth value of a statement as 1 if it is true and 0 if it is

false. Now we have numbers 1 and 0 instead of letters T and F. Since they are numbers, we
can add them, subtract them, and multiply them. We can also make up simple numerical
formulas that will let us calculate logical truth. If P and Q are statements, and if p and q are
their truth values, respectively, we have Table 7.

Table 7
Statement Truth Value
not-P 1-p
P and Q pq
P or Q p + q - pq
if P, then Q 1 - p + pq
P if and only if Q 1 - p - q + 2pq
P or else Q p + q - 2pq
For example, suppose that we have two statements P and Q:

P: John Doe is eligible for insurance.
Q: John Doe requires a medical examination.

To test that the truth value of “P or Q” is p + q-pq, let us put down the four cases, and
calculate the result (see Table 8).

Table 8
p q p + q - pq

1 1 1+1-1=1
0 1 0+1-0=1
1 0 1+0-0=1
0 0 0+0-0=0
Now we know that P or Q is true if and only if either one or both of P and Q are true, and
thus we see that the calculation is correct.
The algebra of logic (see also Supplement 2) is a more efficient way of calculating
logical truth. But it is still a good deal of work to use the algebra. For example, if we have
10 conditions, we shall have 10 letters like p, q to handle in calculations. Thus we need a
still more efficient way.

CALCULATION OF CIRCUITS BY
THE ALGEBRA OF LOGIC

In 1937 a research assistant at Massachusetts Institute of Technology, Claude E.
Shannon, was studying for his degree of master of science. He was enrolled in the
Department of Electrical Engineering. He was interested in automatic switching circuits and
wondered why an algebra should not apply to them. He wrote his thesis on the answer to this
question and showed that:

(1) There is an algebra that applies to switching circuits.
(2) It is the algebra of logic.

A paper, based on his thesis, was published in 1938 in the Transactions of the American
Institute of Electrical Engineers with the title “A Symbolic Analysis of Relay and Switching
Circuits.”

Fig. 1. Switches in series.
For a simple example of what Shannon found out, suppose that we have two switches, 1,
2, in series (see Fig. 1). When do we get current flowing from the source to the sink? There
are 4 possible cases and results (see Table 9).

Table 9
Switch 1 Switch 2 Current
is closed is closed flows
Yes Yes Yes
No Yes No
Yes No No
No No No
Now what does this table remind us of? It is precisely the truth table for “and.” It is just
what we would have if we wrote down the truth table of the statement “Switch 1 is closed
and switch 2 is closed.”

Fig. 2. Switches in parallel.

Fig. 3. Switch open—current flowing.
Suppose that we have two switches 1, 2 in parallel (see Fig. 2). When do we get current
flowing from the source to the sink? Answer: when either one or both of the switches are
closed. Therefore, this circuit is an exact representation of the statement “Switch 1 is closed
or switch 2 is closed.”
Suppose that we have a switch that has two positions, and at any time must be at one and
only one of these two positions (see Fig. 3). Suppose that current flows only when the switch
is open. There are two possible cases and results (see Table 10).

Table 10
Switch 1 Current
is closed flows
Yes No
No Yes
This is like the truth table for “not”; and this circuit is an exact representation of the
statement “Switch 1 is not closed.” (Note: These examples are in substantial agreement with

Shannon’s paper, although Shannon uses different conventions.)
We see, therefore, that there is a very neat correspondence between the algebra of logic
and automatic switching circuits. Thus it happens that:
1. The algebra of logic can be used in the calculation of some
electrical circuits.
2. Some electrical circuits can be used in the calculations of the
algebra of logic.
This fact is what led to the next step.

LOGICAL-TRUTH CALCULATION
BY MACHINE

In 1946 two undergraduates at Harvard University, Theodore A. Kalin and William
Burkhart, were taking a course in mathematical logic. They noticed that there were a large
number of truth tables to be worked out. To work them out took time and effort and yet was
a rather tiresome automatic process not requiring much thinking. They had had some
experience with electrical circuits. Knowing of Shannon’s work, they said to each other,
“Why not build an electrical machine to calculate truth tables?”
They took about two months to decide on the essential design of the machine:
1. The machine would have dial switches in which logical
connectives would be entered.
2. It would have dial switches in which the numbers of statements
like 1, 2, 3 ··· would be entered.
3. It would scan the proper truth table line by line by sending
electrical pulses through the dial switches.
4. It would compute the truth or falsehood of the whole
expression.

CONSTRUCTION AND COMPLETION OF THE
KALIN-BURKHART LOGICAL-TRUTH CALCULATOR

With the designs in mind, Kalin and Burkhart bought some war surplus materials,
including relays, switches, wires, lights, and a metal box about 30 inches long by 16 inches
tall, and 13 inches deep. From March to June, 1947, they constructed a machine in their
spare time, assembling and mounting the parts inside the box. The total cost of materials was
about $150. In June the machine was demonstrated in Cambridge, Mass., before several
logicians and engineers, and in August it was moved for some months to the office of a life
insurance company. There some study was made of the possible application of the machine
in drafting contracts and rules.

GENERAL ORGANIZATION
OF THE MACHINE

The logical-truth calculator built by Kalin and Burkhart is not giant in size, although
giant in capacity. Like other mechanical brains, the machine is made up of many pieces of a
rather small number of different kinds of parts. The machine contains about 45 dial switches,
23 snap switches (or two-position switches), 85 relays, 6 push buttons, less than a mile of
wire, etc. The lid of the metal box is the front, vertical panel of the machine.

UNITS OF THE MACHINE

The machine contains 16 units. These units are listed in Table 11, in approximately the
order in which they appear on the front panel of the machine—row by row from top to
bottom, and from left to right in each row.

Table 11
UNITS, THEIR NAMES, AND SIGNIFICANCE
Unit Row Part No. Mark Name Significance
1 1 Small red 12 — Statement truth- Output: glows if
lights value lights statement is
assumed true
in the case
2 1 2-position 12 ~ Statement denial Input: if up,
snap switches switches statement
is denied
3 2 14-position 12 V Statement Input of
dial switches switches statements
4 3 4-position 11 k Connective Input of
dial switches switches connectives:
∧ (and),
∨ (or),
▲ (if-then),
▼ (if and only if)
5 4 11-position 11 A Antecedent Input of
dial switches switches antecedents
6 5 11-position 11 C Consequent Input of consequents
dial switches switches

UNITS, THEIR NAMES, AND SIGNIFICANCE
Unit Row Part No. Mark Name Significance
7 6 2-position 11 S Stop switches Input: if up, associates
snap switches connective to main
truth-value light
8 6 2-position 11 ~ Connective denial Input: if up, statement
snap switches switches produced by connective
is denied
9 7 Red light and 1 Start Automatic start Input: causes the calc.
large button to start down a truth
table automatically
10 7 Red light and 1 Start Power switch Input: turns the power
2 buttons Stop on or off
11 7 2-position 1 Stop “Stop-on-true-or- Input: causes the calc.
snap switch false” switch to stop either on
and red button true cases or on
false cases
12 7 Yellow light 1 — Main truth-value Output: glows if the
light statement produced
by the main connective
is true for the case
13 7 Large button 1 Man. Manual pulse Input: causes the calc.
Pulse button to go to the next
line of a truth table
14 7 11-position 1 kⱼ Connective check Output: glows when any
dial switch switch and light specified connective
is true
15 7 13-position 1 TT “Truth-table-row- Input: causes the calc.
dial switch Row stop” switch to stop on the
Stop last row of the
truth table
16 Be- Continuous 1 — Timing control Input: controls the
tween dial knob knob speed at which the
6 & 7 and button calculator scans rows
of the truth table

Some of the words appearing in this table need to be defined.
Connective here means “and,” “or,” “if ··· then,” “if and only if.” Only
these four connectives appear on the machine; others when needed can be
constructed from these. The symbols used for these connectives in
mathematical logic are ∧, ∨, ▲, ▼ . These signs serve as labels for the
connective switch points. In this machine, when there is a connective
between two statements, the statement that comes before is called the
antecedent and the statement that comes after is called the consequent.

HOW INFORMATION GOES
INTO THE MACHINE

Of the 16 units 13 are input units. They control the setup of the machine so that it can
solve a problem. Of the 13 input units, those that have the most to do with taking in the
problem are shown in Table 12.

Table 12
Name of Kind of
Unit Mark Switch Settings
Switches Switch
3 Statement V₁ to Dial Statements 1 to 12 or
V₁₂ constant T or F
2 Statement ~ Snap Affirmative (down)
denial or negative (up)
4 Connective k₁ to Dial ∧ (and),
k₁₁ ∨ (or),
▲ (if-then),
▼ (if and only if)
8 Connective ~ Snap Affirmative (down) or
denial negative (up)
5 Antecedent A₁ to Dial V or various k’s
A₁₁
6 Consequent C₁ to Dial V or various k’s
C₁₁
7 Stop S₁ to Snap Not connected (down)
S₁₁ or connected (up)
The first step in putting a problem on the machine is to express the whole problem as a
single compound statement that we want to know the truth or falsity of. We express the
single compound statement in a form such as the following:

VkVkVkVkVkVkVkVkVkVkVkV
where each V represents a statement, each k represents a connective, and we know the
grouping, or in other words, we know the antecedent and consequent of each connective.
For example, let us choose a problem with an obvious answer:
Problem. Given: statement 1 is true; and if statement 1 is true, then
statement 2 is true; and if statement 2 is true, then statement 3 is true; and
if statement 3 is true, then statement 4 is true. Is statement 4 true?
How do we express this whole problem in a form that will go on the machine? We
express the whole problem as a single compound statement that we want to know the truth
or falsity of:

If [1 and (if 1 then 2) and (if 2 then 3) and (if 3 then 4)], then 4
The 8 statements occurring in this problem are, respectively: 1 1 2 2 3 3 4 4. These are the
values at which the V switches (the statement dial switches, Unit 2) from V₁ to V₈ are set.
The 7 connectives occurring in this problem are, respectively: and, if-then, and, if-then,
and, if-then, if-then. These are the values at which the k switches (the connective dial
switches, Unit 4) from k₁ to k₇ are set.
A grouping (one of several possible groupings) that specifies the antecedent and
consequent of each connective is the following:

1 and 1 if-then 2 and 2 if-then 3 and 3 if-then 4 if-then 4
| | | | | |
k₂ k₄ k₆
| | | |
k₁ k₅
| |
k₃
| |
k₇
The grouping has here been expressed graphically with lines but may be expressed in the
normal mathematical way with parentheses and brackets as follows:

{[ 1 and (1 if-then 2) ] and [(2 if-then 3) and (3 if-then 4) ] } if-then 4.
So the values at which the antecedent and consequent dial switches are set are as shown in
Table 13.

Table 13

Antecedent Consequent
Connective Set at Set at
Switch Switch
k₁ A₁ V C₁ k₂
k₂ A₂ V C₂ V
k₃ A₃ k₁ C₃ k₅
k₄ A₄ V C₄ V
k₅ A₅ k₄ C₅ k₆
k₆ A₆ V C₆ V
k₇ A₇ k₃ C₇ V
In any problem, statements that are different are numbered one after another 1, 2, 3, 4 ···.
A statement that is repeated bears always the same number. In nearly all cases that are
interesting, there will be repetitions of the statements. If any statement appeared with a
“not” in it, we would turn up the denial switch for that statement (Unit 2).
The different connectives available on the machine are “and,” “or,” “if ··· then,” “if and
only if.” If a “not” affected the compound statement produced by any connective, we would
turn up the denial switch for that connective (Unit 8).
The last step in putting the problem on the machine is to connect the main connective of
the whole compound statement to the yellow light output (Unit 12). In this problem the last
“if-then,” k₇, is the main connective, the one that produces the whole compound statement.
So we turn Stop Switch 7 (in Unit 7) that belongs to k₇ into the up position. There are a few
more things to do, naturally, but the essential part of putting the information of the problem
into the machine has now been described.

HOW INFORMATION COMES OUT
OF THE MACHINE

Of the 16 units listed in Table 11, 3 are output units, and only 2 of these are really
important, as shown in Table 14.

Table 14
Unit Name of Light Mark Kind of Light
1 Statement truth value V₁ to V₁₂ Small, red
13 Main truth value Large, yellow
The answer to a problem is shown by a pattern of the lights of Units 1 and 13. The pattern of
lights is equivalent to a row of the truth table. Each little red light (Unit 1) glows when its
statement is assumed to be true, and it is dark when its statement is assumed to be false. The
yellow light (Unit 13) glows when the whole compound statement is calculated to be

logically true, and it is dark when the whole compound statement is calculated to be
logically false.
The machine turns its “attention” automatically to each line of the truth table one after
the other, and pulses are fed in according to the pattern of assumed true statements. We can
set the machine to stop on true cases or on false cases or on every case, so as to give us time
to copy down whichever kind of results we are interested in. When we have noted the case,
we can press a button and the machine will then go ahead searching for more cases.

A COMPLETE AND CONCRETE EXAMPLE

The reader may still be wondering when he will see a complete and concrete example of
the application of the logical-truth calculator. So far we have given only pieces of examples
in order to illustrate some explanation. Therefore, let us consider now the following
problem:
Problem. The A. A. Adams Co., Inc., has about 1000 employees.
About 600 of them are insured under a contract for group insurance with
the I. I. Insurance Co. Mr. Adams decides that more of his employees
ought to be insured. As a part of his study of the change, he asks his
manager in charge of the group insurance plan, “What are the possible
statuses of my employees who are not insured?”
The manager replies, “I can tell you the names of the men who are not
insured, and all the data you may want to know about them.”
Mr. Adams says, “No, John, that won’t be enough, for I need to know
whether there are any groups or classes that for some basic reason I
should exclude from the change I am considering.”
So the manager goes to work with the following 5 statuses and the following 5 rules, and
he produces the following answer. Our question is, “Is he right, or has he made a mistake?”
Statuses. A status for any employee is a report about that employee, answering all the
following 5 questions with “yes” or “no.”
1. Is the employee eligible for insurance?
2. Has the employee applied for insurance?
3. Has the employee’s application for insurance been approved?
4. Does the employee require a medical examination for
insurance?
5. Is the employee insured?
Rules. The rules applying to employees are:
A. Any employee, to be insured, must be eligible for insurance,
must make application for insurance, and must have such
application for insurance approved.

B. Only eligible employees may apply for insurance.
C. The application of any person eligible for insurance without
medical examination is automatically approved.
D. (Naturally) an application can be approved only if the
application is made.
E. (Naturally) a medical examination will not be required from
any person not eligible for insurance.
Answer by the Manager. There are 5 possible combinations of statuses for employees
who are not insured, as shown in Table 15.

Table 15
Possible Status 1, Status 2, Status 3, Status 4, Status 5,
Combination Application Examination
of Statuses Eligible Applied Approved Required Insured
1 Yes Yes Yes Yes No
2 Yes Yes Yes No No
3 Yes Yes No Yes No
4 Yes No Yes No No
5 No No No No No
The question may be asked why employees who are eligible, who have applied for
insurance, who have had their applications approved, and who require no medical
examination (combination 2) are yet not insured. The answer is that the rules given do not
logically lead to this conclusion. As a matter of fact, there might be additional rules, such as:
any sick employee must first return to work; or any period from date of approval of
application to the first of the following month must first pass.
The first step in putting this problem on the Kalin-Burkhart Logical-Truth Calculator is
to rephrase the rules, using the language of the connectives that we have on the machine.
The rules rephrased are:
A. If an employee is insured, then he is eligible, he has applied for
insurance, and his application has been approved.
if 5, then 1 and 2 and 3

B. If an employee has applied (under these rules) for insurance,
then he is eligible.
if 2, then 1

C. If an employee is eligible for insurance, has applied, and
requires no medical examination, his application is
automatically approved.

if 1 and 2 and not-4, then 3

D. If an employee’s application has been approved, then he has
applied.
if 3, then 2

E. If an employee is not eligible, then he does not require a
medical examination (under these rules).
if not-1, then not-4

To get the answer we seek, we must add one more rule for this answer only:
F. The employee is not insured.
not-5

We now have a total of 4 + 2 + 4 + 2 + 2 + 1 occurrences of statements, or 15 occurrences.
This is beyond the capacity of the existing machine. But fortunately Rule F and Rule A
cancel each other; they may both be omitted; and this gives us 10 occurrences instead of 15.
In other words, all the possible statuses under “Rule B and Rule C and Rule D and Rule E”
will give us the answer we seek.
The rephrasing and reasoning we have done here is perhaps not easy. For example, going
from the logical pattern
Only igs may be ows
to the logical pattern
If it is an ow, then it is an ig
as we did in rephrasing Rule B, deserves rather more thought and discussion than we can
give to the subject here. A person who is responsible for preparing problems for the Logical-
Truth Calculator should know the algebra of logic.
Choosing an appropriate grouping, we now set on the machine:

{( 2,
if then 1) and [if (1 and 2) and not-4, then 3]} and
[(if 3, then 2) and (if not-1, then not-4)]
The setting is as shown in Table 16. After this setting, the machine is turned on and set to
stop on the “true” cases. The

Table 16
SETTING OF THE PROBLEM
ON THE
LOGICAL-TRUTH CALCULATOR

Unit

3 Statement Dial No. V₁ V₂ V₃ V₄ V₅ V₆ V₇ V₈ V₉ V₁₀ V₁₁ V₁₂
3 Statement Dial Setting 2 1 1 2 4 3 3 2 1 4 F F
2 Statement Denial Switch
Setting — — — — up — — — up up — —
4 Connective Dial No. k₁ k₂ k₃ k₄ k₅ k₆ k₇ k₈ k₉ k₁₀ k₁₁
4 Connective Dial Setting ▲ ∧ ∧ ∧ ▲ ∧ ▲ ∧ ▲ off off
8 Statement Denial Switch
Setting ————————— — —
5 Antecedent Dial No. A₁ A₂ A₃ A₄ A₅ A₆ A₇ A₈ A₉ A₁₀ A₁₁
5 Antecedent Dial Setting V k₁ V k₃ k₄ k₂ V k₇ V off off
6 Consequent Dial No. C₁ C₂ C₃ C₄ C₅ C₆ C₇ C₈ C₉ C₁₀ C₁₁
6 Consequent Dial Setting V k₅ V V V k₈ V k₉ V off off
7 Stop Switches, associating
connective to Main
Truth-Value Light ————————— — —
possible statuses of employees who are not insured are shown in Table 17. As we look down
the last column in Table 17, we observe 6 occurrences of T, instead of 5 as the manager
determined (see Table 15). Thus, when we compare the manager’s result with the machine
result, we find an additional possible combination to be reported to Mr. Adams, combination
7:
Employee eligible, employee has not applied, employee’s
application not approved, employee requires a medical
examination, employee not insured.

Table 17
SOLUTION OF THE PROBLEM
BY THE CALCULATOR

LEGEND:
{A} THE EMPLOYEE IS ELIGIBLE FOR INSURANCE
{B} THE EMPLOYEE HAS APPLIED FOR INSURANCE
{C} THE EMPLOYEE’S APPLICATION FOR INSURANCE
HAS BEEN APPROVED
{D} THE EMPLOYEE REQUIRES A MEDICAL EXAMINATION
{E} THE EMPLOYEE IS INSURED
{F} CASE, OR COMBINATION NO.

{G} THE COMBINATION DOES NOT CONTRADICT THE RULES,
I.E., THE YELLOW LIGHT IS ON

{A} {B} {C} {D} {E} {F} {G}
Status: 1 2 3 4 5
T T T T F 1 T
F T T T F 2 F
T F T T F 3 F
F F T T F 4 F
T T F T F 5 T
F T F T F 6 F
T F F T F 7 T
F F F T F 8 F
T T T F F 9 T
F T T F F 10 F
T F T F F 11 F
F F T F F 12 F
T T F F F 13 F
F T F F F 14 F
T F F F F 15 T
F F F F F 16 T
Because of the medical examination, this additional class of employee would need to be
considered rather carefully in any change of the group insurance plan.

AN APPRAISAL OF THE CALCULATOR

In appraising the Kalin-Burkhart Logical-Truth Calculator, we must remember that this
is a first model. It was the only machine of its kind up to the end of 1948; and it worked.
The cost of the machine, as stated before, was about $150 of parts and perhaps $1000 of
labor. This is less than ¹/₁₀₀ of the cost of the other giant brains described in previous
chapters. Yet we can properly call this machine a mechanical brain because it transfers
information automatically from one part to another of the machine, has automatic control
over the sequence of operations, and does certain kinds of reasoning.
The machine is swift. It can check up to a 100 cases against a set of rules in less than 1
minute. It can check: 128 cases for 7 conditions in 1¼ minutes, 256 cases for 8 conditions in

2½ minutes, and 4096 cases for 12 conditions in 38 minutes. That is the limit of the present
machine. Of course, setting up the machine to do a problem takes some more time.
The programming of this machine to do a problem is less complicated than the
programming of most of the big machines previously described. Of course, in order to
prepare a problem for the machine, the preparer needs to know a fair amount of the algebra
of logic. This, however, is not very hard. As to reliability, the machine has in practice been
out of order less than 2 per cent of operating time.
The big barrier to wide use of the machine, of course, is lack of understanding of the
field of problems in which it can be applied. Even in this modern world of ours, we are in
rather a primitive stage in regard to recognizing problems in logical truth and knowing how
to calculate it. Here, however, is an electrical instrument for logical reasoning, and it seems
likely that its applications will multiply.

Chapter 10
AN EXCURSION:
THE FUTURE DESIGN OF MACHINES THAT
THINK
In the previous chapters we have described four giant mechanical brains
finished by the end of 1946: Massachusetts Institute of Technology’s
Differential Analyzer No. 2, Harvard’s IBM Automatic Sequence-
Controlled Calculator, Moore School of Electrical Engineering’s Electronic
Numerical Integrator and Calculator (Eniac), and Bell Telephone
Laboratories’ General-Purpose Relay Computer. All these brains have
actually worked long enough to have demonstrated thoroughly some facts
of great importance.

WHAT EXISTING MACHINES HAVE PROVED

The existing mechanical brains have proved that information can be
automatically transferred between any two registers of a machine. No
human being is needed to pick up a physical piece of information produced
in one part of the machine, personally move it to another part of the
machine, and there put it in again. We can think of a mechanical brain as
something like a battery of desk calculators or punch-card machines all
cabled together and communicating automatically.
The existing mechanical brains have also proved that flexible, automatic
control over long sequences of operations is possible. We can lay out the
whole routine to solve a problem, translate it into machine language, and
put it into the machine. Then we press the “start” button; the machine starts
whirring and prints out the answers as it obtains them. Mechanical brains
have removed the limits on complexity of routine: the machine can carry
out a complicated routine as easily as a simple one.
The existing giant brains have shown that a machine with hundreds of
thousands of parts will work successfully. It will operate accurately, it will

run unattended, and it will have remarkably few mechanical troubles.
These machines have shown that enormous speeds can be realized:
5000 additions a second is Eniac’s record. High speed is needed for many
problems in science, government, and business. In fact, there are economic
and statistical problems, now settled by armchair methods, for which high-
speed mechanical brains may make it possible to compute answers rather
than guess them.
Also, these machines have been shown to be reasonable in cost. The
cost of each of the large calculators is in the neighborhood of $250,000 to
$500,000. If we assume a ten-year life, which is conservative, the cost is
about $3 to $6 an hour for 24-hour operation. Since each mechanical brain
can, for problems for which it is suited, do the work of a hundred human
computers, such a machine can save its cost half a dozen times. And these
machines are only engineers’ models, built without the advantages of
production-line assembly.
The cost of giant mechanical brains under design in 1947 and 1948 is in
the neighborhood of $100,000 to $200,000. The main reason for the
reduction from the previous cost is the use of cheaper automatic memory.
As designs improve and charges for research and development are paid off,
the cost should continue to go down.

NEW DEVICES FOR HANDLING INFORMATION

In the laboratories working on new mechanical and electronic brains,
scientists are doing a lot of thinking about new devices for handling
information. Research into devices for storing information shows that
magnetic wire as used in sound recording is a rather good storage medium.

Magnetic Wire

For example, on a hundredth of an inch of fine steel wire we can “write”
a magnetized spot by means of a small “writing” electromagnet. The
electromagnet is simply some copper wire coiled around some soft iron
shaped in a U. When current flows through the coil, the iron becomes a
magnet, and the tips of the U magnetize the little section of the wire

between them. The magnetized spot can be of two kinds, say north-south or
south-north, depending on which way the current flows. We can “read” this
difference by means of another small “reading” electromagnet. We can
erase the spot by means of a stronger “erasing” magnet that produces a
uniform magnetic state throughout the wire. The difference between north-
south and south-north corresponds to the difference between 1 and 0, or
“yes” and “no,” etc., and is a unit of information (see Chapter 2). Many
other variations are possible. For example, the presence or absence of a
magnetized spot may be the unit of information, or the “writing,” “reading,”
and “erasing” electromagnets all may be the same.
Magnetic wire sound recordings made in the 1890’s are still good. This
fact shows that magnetic wire may be a more permanent medium for
storing information than is paper. Stray magnetic forces are likely to have
no harmful effect on information stored on magnetic wire, for these forces
would not be strong enough or detailed enough to change greatly the
difference between the magnetized spot and its neighboring neutral area.
A reel of magnetic wire a mile long and ³/₁₀₀₀ of an inch thick costs
about $5. At 80 magnetized spots to the inch, a mile of wire can store about
5 million units of information. Hence, the cost of storing one unit of
information is about ¹/₁₀₀₀₀ of a cent. The time needed for changing a
magnetized spot from 1 to 0 or from 0 to 1 is about ¹/₁₀₀₀₀ of a second.

Magnetic Tape

There is, however, a storage device that may be even more useful, and
this is magnetic tape (see Fig. 1). The usual size of such tape is ¼ inch wide
and 2 or 3 thousandths of an inch thick. Magnetic tape may be made of
plastic with magnetic powder all through it, or it may be of paper coated
with magnetic powder, or it may be of stainless steel or a magnetic alloy, or
it may be of brass or a nonmagnetic alloy coated with a magnetic plating.
Magnetic tape has the added advantage that from 4 to 20 channels
across the tape can be filled with magnetized spots, and the cost then
becomes about ¹/₁₀₀₀₀₀ of a cent per spot. It seems possible that 1000 units
of information can be stored in a quarter of a square inch of magnetic tape.
This means that more than 1 million units of information can be stored in a

cubic inch of space filled with magnetic tape, and about 2 billion units of
information in a cubic foot, except that some of the space should be allotted
to the reels and other equipment that hold the tape (see Fig. 2). This is
closer packing than printed information in the telephone book, and yet with
magnetic tape we can get to the information automatically.

Fig. 1. Magnetic tape.

Fig. 2. Tape reels.
Think of the enormous files in libraries, government, and business.
Think of the problems of space and cost and access which these files imply.

We can then see that this new development may well be of extraordinary
importance.

Mercury Tanks

Fig. 3. Mercury tank.

Scientists are investigating other storage devices having still more
remarkable properties, but these have the disadvantage that, when the
power goes off, the information vanishes. One of these new storage devices
is called a mercury tank (see Fig. 3). It consists mainly of a section of iron
or steel pipe filled with mercury. At each end of this pipe, touching the
mercury, is a thin slab of a crystal of quartz. Quartz, which is a common
stone, and which nearly all sand is made of, changes its shape when pulsed
with electricity. We put a pattern of electrical pulses into the quartz slab at
one end of the mercury tank; for example, we could have the pattern 1101
meaning “pulse, pulse, no pulse, pulse.” The electrical pulses going into the
quartz slab make the quartz vibrate. Thus ripples are produced in the
mercury, and waves in the pattern 1101 meaning “wave, wave, no wave,
wave” travel down the tank and strike the quartz slab at the far end. The
quartz slab there changes its shape in the rhythm 1101, and it converts the
waves back into electrical pulses in the same pattern. Then we take the

pulses out of the far end along a wire, make them stronger again with an
amplifier, give them the right form again, and feed them back into the front
end of the mercury tank. The mercury tank is a clever use of the principle of
an echo, as when you call across a valley and the rocks answer you back.
We can store a pattern of 400 pulses (each a unit of information, a 1 or a 0,
and each a millionth of a second in duration), in a mercury tank about 20
inches long. A mercury tank and an echo are examples of delay lines
—“lines” along which waves are “delayed.”

Electrostatic Storage Tube

Another of the memory devices being developed is called an
electrostatic storage tube (see Fig. 4). This is a big electronic tube with a
screen across one end. The screen may be of two layers: one of copper,
which conducts electricity, and one of mica, a material that does not. In the
other end of the tube is a beam of electrons, which we can turn on and off
and shoot at any of 2 or 3 thousand specific points or spots on the screen.

Fig. 4. Electrostatic storage tube.

There are two sizes of electric charge or quantity of electrons; we can
call these 1 and 0. In about a millionth of a second, we can put either size of
charge on one of the spots of the screen. With other circuits we can keep it
there as long as we want, if the power does not flicker off. We can
“remember” perhaps 2 or 3 thousand units of information in one of these
electronic tubes. We can read, write, or erase any unit of information in a
few millionths of a second.
Neither the mercury tank nor the electrostatic storage tube had, by the
end of 1947, been put into a working mechanical brain. But there is good
reason to believe that they will be successful devices and will open up a
new era of speed in storing and referring to information. In fact, several
laboratories are developing electronic calculating circuits using these
devices which will perform up to 100,000 additions a second or 10,000
multiplications a second. Our minds certainly stagger at the thought of such
speeds.

NEW OPERATIONS

Many kinds of combining operations have already been built into one or
more mechanical brains. The operations may be arithmetical: addition,
subtraction, multiplication, division, looking up numbers in tables, etc. Or
the operations may be logical: comparing, selecting, checking, etc.
Additional logical operations will be built into some of the mechanical
brains now being constructed: sorting, collating, matching, merging, etc.

NEW IDEAS IN PROGRAMMING

Programming—the way to give instructions to machines—is also being
studied in the laboratories. Several new ideas of importance have developed
as a result.
One idea is that the machine should be able to store its instructions or
program or routine in its memory in just the same physical ways as it stores
numbers. There is basically no reason why numbers only should be stored
in some registers, and instructions only stored in other registers.
Another idea is that the machine should have in its permanent memory
any subroutine it may need. For example, a subroutine should always be
available in the machine for finding square root. At any time when a square
root was needed, we would only have to call on the machine for the
subroutine of square root. The machine would then consult the right part of
its memory and carry out the subroutine for square root.
A third idea, and one of the most interesting, is that the machine should
be able to compute its own instructions. For example, consider a program
for finding the product of two matrices (see Supplement 2), each of 100
terms in an array of 10 columns and 10 rows, resulting in a new matrix of
100 terms. The whole program can be made to consist of about 50 orders.
Only one of them is “multiply,” and only one of them is “add”; the other
orders consist of how to choose expressions to be multiplied or added, etc.
Such problems as these are often fascinating to mathematicians, who
love to play with the intricate ideas needed.

NEW IDEAS IN RELIABILITY

Reliability has a number of aspects:

1. No wrong results allowed out of the machine.
2. Few failures.
3. Rapid location of failures.
4. Quick repair or replacement of parts that fail.
5. Easy maintenance.
6. Unattended operation overnight.

For example, Bell Laboratories proved that mechanical brains can be built
so that no wrong results are allowed to come out. In other words, the
machine checks itself all the time as it goes along and stops at once if the
check shows that something is wrong. This is likely to be a standard feature
of new automatic thinking machinery.
The frequency of failures in the machinery being designed in the
laboratories may be of the order of one or two mechanical failures a week.
For any type of failure an alarm circuit and trouble lights will show what
part of the machine needs attention. Plug-in parts for replacement are
already in use in at least two of the four mechanical brains described and
should be available in all the new machines. It is possible to build a
machine that will automatically change from failing equipment to properly
functioning equipment. For some years though, this may be too expensive
to be reasonable.
The use of magnetic tape for storage reduces greatly the number of parts
and so increases reliability. For example, instead of 18,000 electronic tubes
in an electronic brain, there may be less than 3000.
A final degree of reliability is gained when most of the time the machine
operates unattended. Then, there is no human operator standing by who
may fail to do the correct thing at the moment when the machine needs
some attention. In fact, the motto for the room housing a mechanical brain
should become, “Don’t think; let the machine do it for you.” Unattended
operation from the end of one working day to the beginning of the next,
with the machine changing itself from one problem to another problem, has
already been proved possible on the Bell Laboratories machine.

AUXILIARY DEVICES

In order to use a mechanical brain, we have to give it and take from it
language that it understands, machine language. A mechanical brain that
can do 10,000 additions a second can very easily finish almost all its work
at once. How can we, slow as we are, keep our friend, the giant brain, busy?
We have found so far several answers to this question, none of them yet
very good.
Devices for preparing input will be very important. For each brain, we
shall need a great many of these devices. For, at best, we type at a rate, say,
of 4 characters a second, selecting any one of some 38 keys, each of which
is equivalent to about 6 units of information. This is about 800 units of
information per second. The machine, however, is likely to be able to gulp
information from its input mechanism at the amazing rate of 60,000 units of
information per second, equal to 75 people typing with no mistakes and no
resting. Fortunately, at least some of the time the machine will be busy
computing!
For an input-preparation device, we may get something that can be
fastened to an ordinary typewriter and that will produce magnetic tape
agreeing with what is printed by the typewriter. Since the input information
must be carefully verified, we shall need a second magnetic tape device
such as exists for paper tape on the Bell Laboratories machine: the
processor. The processor takes two hand-prepared tapes, compares them,
reports any differences, and produces a third tape. The third tape copies the
two original tapes if they agree, and it receives corrected information as
furnished by a girl at a keyboard if the two original tapes disagree.
For information already on punch cards, we need an input device that
will read punch cards and write on magnetic tape. Where information is on
punched paper tape, we need a machine that will read punched paper tape
and write on magnetic tape.
Problem data, tables of numbers, and routine instructions will go into
the mechanical brain. They will all be prepared on regular input devices.
The machine will accept information in the form in which it is most
convenient for you and me to prepare it. Then, the machine will be
instructed to change the information into the form with which it is most
convenient for the machine to operate.

Many output devices will also be needed, since the machine will be able
to produce information very swiftly. These output devices might be cabled
to the machine. A kind of traffic control system would govern them. Each
will have a magnetic tape that will be loaded up swiftly with information.
Then the output device will unload its information more slowly, in any form
that we may desire: printing, graphs, film, punch cards, or punched paper
tape.
The machine is likely to be able to put out information on magnetic tape
at the same high speed of 60,000 units of information per second or 10,000
characters per second. But the best printing speed of an electric typewriter
is about 10 or 12 characters a second. Card-punching speed is about 130
characters a second. Punch-card tabulator speed can reach a maximum of
about 200 characters a second. Thus we see that here, too, we may be
snowed under with the information that the giant brain puts out, if we fail to
ask the giant only for what we really want.

MECHANICAL BRAINS UNDER CONSTRUCTION

This chapter would not be complete without mention of the great
mechanical brains that were actually under construction at the end of 1947.
In power they are intermediate between the machinery now being designed,
described in this chapter, and the earlier machines described in the previous
chapters of this book.
The mechanical brains under construction on December 31, 1947, were:
Harvard’s Sequence-Controlled Relay Calculator
Mark II, constructed at the Harvard Computation
Laboratory, tested there July 1947 to January
1948, and delivered to the Naval Proving Ground,
Dahlgren, Va., in 1948.
The IBM Selective-Sequence Electronic Calculator,
constructed in the IBM laboratories, Endicott, N.
Y., and installed in 1947 at the office of
International Business Machines, 590 Madison
Ave., New York, N. Y.

Moore School of Electrical Engineering’s EDVAC
(Electronic Digital Variable Automatic Computer)
being constructed partly at Moore School and
partly elsewhere, and to be delivered to the
Ballistic Research Laboratories, Aberdeen, Md.
Harvard’s Sequence-Controlled Electronic Calculator
Mark III, being constructed at the Harvard
Computation Laboratory, and to be delivered to the
Naval Proving Ground, Dahlgren, Va.
We shall cover briefly (and perhaps a little technically) some of the
main features of the first two of these machines; for, during 1948, they
began to do problems. The other two had not been finished by the end of
1948 and so would be difficult to describe correctly, for mechanical brains
grow, and design changes go on until they are finished—and even
afterwards.
Some information about these machines can be obtained from the
organizations referred to above and from reports that should appear from
time to time in some of the journals mentioned in Supplement 3. There is
also a regular section entitled “Automatic Computing Machinery” in the
quarterly Mathematical Tables and Other Aids to Computation, where it is
likely that current information may be found.

Harvard’s Mark II

The Harvard Sequence-Controlled Calculator Mark II began to do
problems under test during July 1947. This machine is at least twelve times
as powerful as Mark I (see Chapter 6) and was constructed entirely by the
Harvard Computation Laboratory. The machine contains about 13,000
relays of a new type that will operate reliably within ¹/₁₀₀ of a second.
Numbers in the machine are regularly of 10 decimal digits between
1.000,000,000 and 9.999,999,999, inclusive, multiplied by a power of 10
between 1,000,000,000,000,000 and 0.000,000,000,000,001, inclusive.
For storage of numbers, the machine has 100 relay registers totaling
about 1200 decimal digits. Also, it can consult any one of 8 tape feeds for

numbers and any one of 4 tape feeds for instructions. Effectively, the
machine can read one number and one instruction from paper tape in ¹/₃₀ of
a second.
The machine performs all arithmetical and most logical operations. In
every second it can carry out 4 multiplications, 8 additions (or subtractions),
and 12 transfers. Division is performed by rapid approximation using the
other operations.
In each second the machine can perform 30 instructions. An instruction
is expressed by 6 digits between 0 and 7 which you can select and, in effect,
by 3 more digits fixed by the time (within the second) when the machine
reads the instruction. For example, in the 9th instruction of the 30
instructions in each second, we can specify a multiplicand. But, if we do not
want to multiply right then—a rare event if we are coding wisely—we leave
the 9th instruction empty. The machine may operate as a whole, attending to
one problem; or the machine may be separated into halves, and each half
will attend to its own problem.

The IBM Selective-Sequence
Electronic Calculator

The IBM Selective-Sequence Electronic Calculator was announced
publicly on January 27, 1948, after some months of trial running. It is a
large and powerful mechanical brain, and it is the intention of International
Business Machines to devote it to solving scientific problems. The staff of
the Watson Scientific Computing Laboratory in New York will be mainly in
charge of the machine.
The machine contains about 12,500 electronic tubes and about 21,500
relays. Numbers in the machine are regularly of either 14 or 19 decimal
digits. Instructions are expressed as numbers. For storage of information,
the machine has a capacity of 8 registers totaling 160 decimal digits of very
rapid memory in electronic tubes. Also, it has about 150 registers totaling
3000 decimal digits of less rapid memory in relays. Also, it can consult any
one of 66 paper tape feeds; each row on a paper tape can hold up to 78
punched holes or 19 decimal digits, and the machine can consult 25 rows on

one tape in one second. These paper tapes together give the machine about
400,000 decimal digits of memory.
For arithmetical and logical operations, the machine has an arithmetical
unit using electronic tubes. This unit can carry out about 50 multiplications
or about 250 additions per second, including the transfers of numbers. In
each second the machine can read and perform 50 instructions, and each
instruction consists, usually, of getting two numbers out of two relay
registers, performing an operation, and putting the result into a third relay
register.

Eckert-Mauchly’s Binac

As this book went to press, another mechanical brain, the Electronic
Binary Automatic Computer, or BINAC, was announced on August 22,
1949. This machine was constructed by the Eckert-Mauchly Computer
Corporation, Philadelphia, Pa., for Northrop Aircraft, Inc., Hawthorne,
Calif.
This machine has some remarkable properties. It does addition or
subtraction at the rate of 3500 per second. It does multiplication or division
at the rate of 1000 per second. The input is from a keyboard or magnetic
tape; the output is to magnetic tape or an electric typewriter. Binac has 512
registers of very rapid memory in mercury tanks, and each register holds 30
binary digits. The machine actually is a pair of twins: the storage, the
computing element, and the control are double, and each twin runs in step
with the other and checks every operation of the other. In tests in July the
machine ran over 10 consecutive hours with no error. Each twin has only
700 electronic tubes. Binac handles all numbers in binary notation, except
that the keyboard and the typewriter express numbers in octal notation (see
Supplement 2). Finally, Binac is only 5 feet high, 4 feet long, and one foot
wide.

Chapter 11
THE FUTURE:
MACHINES THAT THINK,
AND WHAT THEY MIGHT DO FOR MEN
The pen is mightier than the sword, it is often said. And if this is true,
then the pen with a motor may be mightier than the sword with a motor.
In the Middle Ages, there were few kinds of weapons, and it was easy
for a man to protect himself against most of them by wearing armor. As
gunpowder came into use, a man could no longer carry the weight of armor
that would protect him, and so armor was given up. But in 1917, armor,
equipped with a motor and carrying the man and his weapons, came back
into service—as the tank.
In much the same way, in the Middle Ages, there were few books, and it
was easy for a man to handle nearly all the information that was in books.
As the printing press came into use, man’s brain could no longer handle all
recorded information, and the effort to do so was given up. But in 1944, a
brain to handle information, equipped with a motor and supporting the man
and his reasoning, came into existence—as the sequence-controlled
calculator.
In previous chapters we have examined some of the giant mechanical
brains that have been finished; we have also considered the design of such
machines. Now in this chapter we shall discuss the future significance of
machines that think, of motorized information. We shall discuss what we
can foresee if we look with imagination into the future.
There are two questions we need to ask: What types of machines that
think can we foresee? What types of problems to be solved by these
machines can we foresee?

FUTURE TYPES OF MACHINES THAT THINK

The machines that already exist show that some processes of thinking
can already be performed very quickly:

Calculating: adding, subtracting,...
Reasoning: comparing, selecting,...
Referring: looking up information in lists,...

We can expect other processes of thinking to come up to high speed through
the further development of thinking machines.

Automatic Address Book

Nowadays when we wish to send out announcements of an event, like
going to South America for a year, we may copy the addresses of our
friends onto the envelopes by hand. In the future, we can see our address
book as a spool of magnetic tape. When we wish to send out
announcements, we put a stack of blank envelopes into the machine that
will read the magnetic tape, and we press a button. Out will come the
envelopes addressed.
If we wish to select only those friends of ours whose last names we put
down on a list, we can write the list on another magnetic tape, place it also
in the machine, and set a few switches. Then the machine will read the
names on the list, find their addresses in the address-book tape, and prepare
only the envelopes we want. If a friend’s address changes, we can notify the
machine. It will find his old address, erase it, and enter the new address.

Automatic Library

We can foresee the development of machinery that will make it possible
to consult information in a library automatically. Suppose that you go into
the library of the future and wish to look up ways for making biscuits. You
will be able to dial into the catalogue machine “making biscuits.” There will
be a flutter of movie film in the machine. Soon it will stop, and, in front of
you on the screen, will be projected the part of the catalogue which shows
the names of three or four books containing recipes for biscuits. If you are

satisfied, you will press a button; a copy of what you saw will be made for
you and come out of the machine.
After further development, all the pages of all books will be available
by machine. Then, when you press the right button, you will be able to get
from the machine a copy of the exact recipe for biscuits that you choose.
We are not yet at the end of foreseeable development. There will be a
third stage. You will then have in your home an automatic cooking machine
operated by program tapes. You will stock it with various supplies, and it
will put together and cook whatever dishes you desire. Then, what you will
need from the library will be a program or routine on magnetic tape to
control your automatic cook. And the library, instead of producing a
pictorial copy of the recipe for you to read and apply, will produce a routine
on magnetic tape for controlling your cooking machine so that you will
actually get excellent biscuits!
Of course, you may have other kinds of automatic producing machinery
in your home or office. The furnishing of routines to control automatic
machinery will become a business of importance.

Automatic Translator

Another machine that we can foresee would be used for translating from
one language to any other. We can call it an automatic translator. Suppose
that you want to say “How much?” in Swedish. You dial into the machine
“How much?” and press the button “Swedish,” and the machine will
promptly write out “Hur mycket?” for you. It also will pronounce it, if you
wish, for there would be little difficulty in recording on magnetic tape the
pronunciation of the word as spoken by a good speaker of the language. The
machine could be set to repeat the pronunciation several times so that the
student could really learn the sound. He could learn it better, probably, by
hearing it and trying to say it than he could by using any set of written
symbols.

Automatic Typist

We now come to a possible machine that uses a new principle. This
principle is that of being able to recognize signs. This machine would
perceive writing on a piece of paper and recognize that all the a’s that
appear on the paper are cases of a, and that all the b’s that appear on it are
instances of b, and so forth. The machine could then control an electric
typewriter and copy the marks that it sees. The first stage of this machine
would be one in which only printed characters of a high degree of likeness
could be recognized. In later stages, handwriting, even rather illegible
handwriting, might be recognizable by the machine. We can call it an
automatic typist.
The elements of the automatic typist would be the following:
1. Phototubes (electronic tubes sensitive to the
brightness of light), which could sense the
difference between black and white (these already
exist).
2. A memory of the shapes of 52 letters, 10 digits, and
punctuation marks. Fine distinctions would be
required of this memory in some cases—like the
difference between the numeral 5 and the capital
letter S.
3. A control that would cause the machine to tune
itself, so that a good matching between the marks
it observed and the shapes it remembered would
be reached.
4. A triggering control so that, when the machine had
reached good enough matching between its
observations and its memory, the machine would
proceed to identify the marks, read them, and
transfer them.
5. An electric typewriter, which would respond to the
transferred instructions. (This also already exists.)
This machine is perhaps not so farfetched as it might seem. During
World War II, gun-aiming equipment using the new technique radar
reached a high stage of development. Many shots that disabled and sank

enemy ships were fired in total darkness by radar-controlled guns. On the
glowing screen in the control room, there were two spots, one that marked
the target and one that reported the point at which the gun was aimed. These
two spots could be brought almost automatically into agreement. In the
same way, a report from a phototube telling the shape of an observed mark
and a report from the memory of the machine telling the shape of a similar
mark could be compared by the machine for likeness and, if judged enough
alike, could be approved as identical.
Even the phrase “enough alike” can be applied by a machine. During
World War II, tremendous advances were made in machinery for
deciphering enemy messages. Machines observed various features and
patterns in enemy messages, swiftly counted the frequency of these
features, and carried out statistical tests. Then the machines selected those
few cases in which the patterns showed meaning instead of randomness.
A machine like the automatic typist, if made flexible enough, would be,
of course, extremely useful. A great load of dull office work is now being
thrown on clerks whose task is to translate from writing and typing into
languages that machines can read, such as punch cards. At the present time,
if punch-card machines are widely used in a big company, the company
must employ large numbers of girls whose sole duty is to read papers and
punch up cards. A still bigger chore is the work of typists in all kinds of
businesses whose main duty is to read handwriting, etc., and then copy the
words on a typewriter.

Each square in the grill
is watched by a phototube.

Fig. 1. Scheme for distinguishing A and H by 15 phototubes.

Research has already begun on various features of the automatic typist
because of its obvious labor-saving value. For example, many patents have
been issued on schemes for dividing the area occupied by a letter or a digit
into an array of spots, with a battery of phototubes each watching a spot.
The reports from the phototubes together will distinguish the letter or digit.
For example, if we consider A and H placed in a grill of fifteen spots, 5 long
by 3 wide (see Fig. 1), then the phototubes can distinguish between A and H
by sensing black or white in the spot in the middle of the top row. When we
consider how easily and swiftly a human being does this, we can once more
marvel at the recognizing machine we all carry around with us in our heads.

Automatic Stenographer

Another development that we can foresee is one that we can call the
automatic stenographer. This is a machine that will listen to sounds and
write them down in properly spelled English words. The elements of this
machine can be outlined:

1. Microphones, which can sense spoken sounds
(these already exist).
2. A memory storing the 40 (more or less) phonetic
units or sounds that make up English, such as the
23 consonant sounds,

p b l ng
f v m th
t d n r
s z h y
k g w
ch j
sh zh (heard in “pleasure”)
and the 17 vowel sounds,

Long Short Other
A (“ate”) a (“cat”) ar (“are”)
E (“eat”) e (“end”) aw (“awe”)
I (“isle”) i (“in”) er (“err”)
O (“owe”) o (“on”) ow (“owl”)
U (“cute”) u (“up”) oi (“oil”)
OO (“roof”) oo (“book”)
3. A collection of the rules of spelling in English,
containing many statements like
The sound b is always spelled b
The sound sh may be spelled sh (ship), s (sugar), ti
(station), ci (physician), ce (ocean) or tu
(picture) and other statements based on
context, word lists, derivation, etc. These are
the statements by means of which a good

English speller knows how to spell even words
that he hears for the first time.
4. A triggering control so that, when the machine
reaches good enough matching between its
observations of sounds, its memory of sounds, and
its knowledge of spelling rules, the machine will
identify groups of sounds as words, determine
their spelling, and report the letters determined.
5. An electric typewriter, which would type the
reported letters.
With this type of machine, you would dictate your letters into a machine
(now existing) that would record your voice. Then the record would be
placed on the automatic stenographer, and out would come your letters
written and spaced as they should be.

Automatic Recognizer

We can foresee a recognizing machine with very general powers.
Suppose that we call it an automatic recognizer (see Fig. 2). It will have the
following elements:
1. Input. This element will consist of a set of
observing instruments, capable of perceiving
sights, sounds, etc. There will be ways of
positioning or tuning these instruments.
2. Memory. This element will store knowledge. It may
store the patterns of observations that we are
interested in; or it may store general rules on how
to find patterns of observations that we will be
interested in. It will contain knowledge about
acceptable groups of patterns, about actions to be
performed in response to patterns, etc.
3. Program 1. The element “Program 1” performs a
set of standard instructions. Under these
instructions, the machine:

Compares group after group of observations with
the information in the memory.
Compares these groups with patterns furnished, or
seeks to organize the observations into
patterns.
Counts cases and tests frequencies.
Finds out how much matching with patterns there
is.
Tunes the observing instruments in ways to
increase matching.

Fig. 2. Scheme of an automatic recognizer.

4. Program 2. The element “Program 2” performs
another set of standard instructions. Under these
instructions, the machine, if it is tuned well,
matches sets of observations one after another with
the patterns and so reads them.
5. Triggering Control. This element shifts the control
of the machine from Program 1 to Program 2. It
does this when the machine reaches “good
matching.” We shall set the meaning of this into
the machine in much the same way as we set
“warm” into a thermostat.
6. Output. This element performs any action that we
want, depending on recognized patterns read and
any other knowledge or instructions stored in the
memory.
The automatic recognizer will be capable of extraordinary tasks. With
microphones and a large memory, this type of machine would be able to
hear a foreign language spoken and translate it into spoken or written
English. With phototubes and with an expanded filtering and decoding
capacity as in deciphering machines, the automatic recognizer should be
able to read a dead language, even those (such as Minoan or Etruscan) that
have so far resisted efforts to read it. The machine would derive rules for
the translation of the language and translate any sample.
An automatic recognizer could perhaps be equipped with many
sensitive, tiny observing instruments that could be placed around or in the
brain and nervous systems of animals. Then the machine might enable us to
find out what activity in the nervous system corresponds with what activity
in the animal.

TYPES OF PROBLEMS THAT MACHINES
WILL SOLVE IN THE FUTURE

We turn now to the second question regarding the future of machines
that think: What types of problems can we foresee as solved by these
machines?

Problems of Control

Probably the foremost problem which machines that think can solve is
automatic control over all sorts of other machines. This involves controlling
a machine that is running so that it will do the right thing at the right time in
response to information. For example, suppose that you are mowing a lawn
with a mowing machine. You watch the preceding strip so as to stay next to
it. You watch the ends of the strips, where you turn around. If a stick is
caught in the cutting blade, you stop and take it out. Now it is entirely
possible to put devices on the mowing machine so that all these things will
be taken care of automatically. In fact, in the case of plowing a large field, a
tractor-plow can be equipped with a device that guides it next to the
preceding furrow. Thus, once the first furrow around the edge has been
made, riderless tractors will plow a whole field and stop in the middle.
For another example, take a gas furnace for heating steam to keep a
house warm. Such a furnace has automatic controls, which respond to the
following information whenever reported:

House too warm.
House not warm enough.
Too much steam pressure.
Not enough water in boiler.
Gas flame not lit.
Daytime.
Nighttime.

In fact, your own meaning of “warm” can be put into the control system:
you set the dial on your thermostat at the temperature that “warm” is to be
for you.
In the future many kinds of automatic control will be common. We shall
have automatic pilots for flying and landing airplanes. We shall have
automatic missiles for destructive purposes, such as bombing and killing,
and for constructive purposes, such as delivering mail and fast freight. An
article in the magazine Fortune for November 1946 described the automatic
factory (see Supplement 3). This is a factory in which there would be

automatic arms for holding stuff being manufactured, and automatic feed
lines for supplying material just where it is needed. All this factory would
be controlled by machines that handle information automatically and
produce actions that respond to information.
This prospect fills us with concern as well as with amazement. How
shall we control these automatic machines, these robots, these
Frankensteins? What will there be left for us to do to earn our living? But
more of this in the next chapter.

Problems of Science

Other problems for which we can foresee the use of machines that think
are the understanding, and later the controlling, of nature. One of these
problems is weather forecasting and weather control.

The Weather Brain

We can imagine the following type of machine—a weather brain. A
thousand weather observatories all over the country observe the weather at
8 a.m. The observations are fed automatically through a countrywide
network of communication lines into a central station. Here a giant
machine, containing a great deal of scientific knowledge about the weather,
takes in all the data reported to it. At 8:15 the weather brain starts to
calculate; in half an hour it has finished, having produced an excellent
forecast of the weather for the whole country. Then it proceeds to transmit
its forecast all over the country. By 8:50 every weather station, newspaper,
radio station, and airport in the country has the details. In October 1945, Dr.
V. K. Zworykin of the Princeton Laboratories of the Radio Corporation of
America proposed solving the problem of weather forecasting in this way
by a giant brain.
The weather brain will have a second stage of application. From time to
time and here and there, the weather is unstable: it can be triggered to
behave in one way or another. For example, recently, pellets of frozen
carbon dioxide—often called Dry Ice—have been dropped from planes and
have caused rain. In fact, a few pounds of Dry Ice have apparently caused
several hundred tons of rain or snow. In similar ways, we may, for example,

turn away a hail storm so that hail will fall over a barren mountain instead
of over a farming valley and thus protect crops. Or we may dispel
conditions that would lead to a tornado, thus avoiding its damage. Both
these examples involve local weather disturbances. However, even the
greatest weather disturbances, like hurricanes and blizzards, may eventually
be directed to some extent. Thus the weather may become to some degree
subject to man’s control, and the weather brain will be able to tell men
where and when to take action.

Psychological Testing

Another scientific problem to which new machinery for handling
information applies is the problem of understanding human beings and their
behavior. This increased understanding may lead to much wiser dealing
with human behavior.
For example, consider tests of aptitudes. If you take one of these tests,
you may be asked to mark which word out of five suggested ones is nearest
in meaning to a given word. Or your test may be 40 simple arithmetical
problems to be solved in 25 minutes. Or you may be given a sheet with 20
circles, and be asked to put 3 dots in the first, 7 dots in the second, 4 dots in
the third, 11 dots in the fourth, and so on, irregularly; you may be given a
total of 45 seconds to do this as well as you can. Now, if a vocational
counselor gives you one of these tests, and if you get 84 out of 100 on it, he
needs to know just what he has measured about you. Also, he needs to
know whether he can reasonably forecast that, as a result of your grade of
84, you will be good at writing articles, or good at supervising the work of
other people, or good at designing in a machine shop. He needs to know the
records of people with scores of about 84 on this test and to have evidence
supporting his forecasts.
If we wish to make the most use of the tests, we need to carry out a
good deal of statistics, mathematics, and logic. For example, it will turn out
that answers to some questions are much more significant than answers to
others, and so we can greatly improve the quality of the tests by keeping
only the more significant questions. Powerful machinery for handling
calculations will be very useful in the field of aptitude testing.

But, you may ask, what if the person analyzing your answers has to use
interpretations and judgments? If the judgments and interpretations can be
expressed in words, and if the words can be translated into machine
language, then the machine can carry out the analysis. Usually the
difference between a rule and a judgment is simply this: a rule in a case in
which it is hard to express all the factors being considered is called a
judgment.

Psychological Trainer

It is conceivable that machines that think can eventually be applied in
the actual treatment of mental illness and maladjustment. Consider what a
physician does. In treating a psychiatric case, such as a neurosis, a
physician uses words almost entirely. He asks questions. He listens to the
patient’s answers. Each answer takes the physician nearer and nearer to a
diagnosis. By and by the physician knows what most of the difficulty is.
Then he must present his knowledge slowly to the patient, gradually
guiding the patient to understanding. It is a psychological truth that telling a
man in ten minutes what is wrong with him does not cure him. The
physician seeks to free the patient from the tormenting circles of habit and
worry in which he has been trapped. Often the diagnosis is short and the
treatment is long; the reasons for the neurosis may soon be clear to the
physician, but they may take months to become clear to the patient.
Now let us consider the following kind of machine as an aid to the
physician. We might call this kind of machine a psychological trainer, for
in many ways it is like the training machines used in World War II for
training a pilot to fly an airplane. The psychological trainer would have the
following properties:
1. The machine is able to show sound movies—
produce pictures and utter words.
2. It is able to put before the patient: situations,
problems, questions, experiences, etc.
3. It is able to take in responses from the patient.
4. It is able to receive a program of instructions from
the physician.

5. Depending on the responses of the patient and on
the program from the physician, the training
machine can select more material to put before the
patient.
6. The training machine produces a record of what it
presented and of how the patient responded, so
that the physician and the patient can study the
record later.
What sort of films would the machine hold? The machine could be
loaded with a number of films which would help in the particular type of
neurosis from which the patient was suffering.
What sort of responses could the patient make? The patient might have
buttons in front of him which he could press to indicate such answers as:
Yes I don’t know Repeat
No It depends Go ahead
Also, the patient might hold a device—like a lie detector, perhaps—which
would report his state of tenseness, etc., and so report what he really felt.
Where would the machine’s questions come from? From one or more
physicians very clever in the treatment of mental illness.
Suppose that the patient is inconsistent in his answers? The machine,
discovering the inconsistencies, could return to the subject and ask related
questions in a different way. As soon as several questions related to the
same point are answered consistently, the machine could exclude groups of
questions that no longer apply and could proceed to other questions that
would still apply.
Patients would vary in their ability to go as fast as the machine could.
So from time to time the machine would ask questions to test the effect of
what it had presented; and, depending on the answers, the machine would
go faster or would bring in additional material to clarify some point.
This machine might have a few advantages over ordinary treatment. For
example, with the machine, treatment does not depend on the physician’s
making the right answer in a split second, as it may in a personal interview.

Also, the patient might be franker with the machine than with the physician,
for it might be arranged that the patient could review his record, and then
decide whether to confess it to his physician.
Such a machine would enable physicians to treat many more patients
than they now can. In fact, it is estimated that nearly 50 per cent of persons
who consult physicians are suffering only from mental illness. Such a
machine would therefore be a great help.

Problems of Business

Another large group of problems for which we can foresee the use of
machines that think is found in business and economics.
For example, consider production scheduling in a business or a factory.
The machine takes in a description of each order received by the business
and a description of its relative urgency. The machine knows (that is, has in
its memory) how much of each kind of raw material is needed to fill the
order and what equipment and manpower are needed to produce it. The
machine makes a schedule showing what particular men and what particular
equipment are to be set to work to produce the order. The machine turns out
the best possible production schedule, showing who should do what when,
so that all the orders will be filled in the best sequence. What is the “best”
sequence? We can decide what we think is the best sequence, and we can
set the machine for making that kind of selection, in the same way as we
decide what is “warm” and set the thermostat to produce it!
On a much larger scale, we can use mechanical brains to study
economic relations in a society. Everything produced in a society is made
by consuming some materials, labor, equipment, and skill. The output
produced by one man or factory or industry becomes the input for other
men, factories, industries. In this way all economic units are linked together
by many different kinds and degrees of dependence. The situation is, of
course, complicated: it changes as time goes on and as people want
different things produced. Economists have already set up simple models of
economic societies and have studied them. But with machines that think, it
will be possible to set up and study far more complicated models—models
that are very much like the society we live in. We can then answer questions

of economics by calculation instead of by arguments and counting noses.
We shall be able to solve definitely such problems as: “How will a rise in
the price of steel affect the farming industry?” “How much money must be
paid out as wages and salaries so that consumer purchasing power will buy
back what industry produces?”

Machines and the Individual

What about the ordinary everyday effects of these machines upon you
and me as an individual? We can see that the new machinery will apply on a
small scale even to us. Small machines using a few electronic tubes—much
like a radio set, for example—and containing spools of magnetic wire or
magnetic tape will doubtless be available to us. We shall be able to use them
to keep addresses and telephone numbers, to figure out the income tax we
should pay, to help us keep accounts and make ends meet, to remember
many things we need to know, and perhaps even to give us more
information. For there are a great many things that all of us could do much
better if we could only apply what the wisest of us knows.
We can even imagine what new machinery for handling information
may some day become: a small pocket instrument that we carry around with
us, talking to it whenever we need to, and either storing information in it or
receiving information from it. Thus the brain with a motor will guide and
advise the man just as the armor with a motor carries and protects him.

Chapter 12
SOCIAL CONTROL:
MACHINES THAT THINK
AND HOW SOCIETY MAY CONTROL THEM
It is often easier for men to create a device than to guide it well
afterwards: it is often easier for a scientist to study his science than to study
the results for good or evil that his discoveries may lead to. But it is not
right nor proper for a scientist, a man who is loyal to truth as an ideal, to
have no regard for what his discoveries may lead to.
This principle is now being widely recognized. Many scientists today—
both as individuals and as groups, and especially the atomic scientists—are
considering the results of their scientific discoveries; and they are sharing in
the effort to render those results truly useful to humanity.
It would be easy to leave out of this book any discussion of how
machines that think may be controlled, any consideration of how they may
be made truly useful to humanity. But that would be hardly right or proper.
In concluding a book such as this one, that touches on many aspects of
machines that think, we need to consider what can and should be done to
make such machines of true benefit to all of humanity.
So, we come to the most important of all our questions: What sort of
control over machines that think do we need in human society?

MACHINE THAT BOTH THINKS AND ACTS

From a narrow point of view, a machine that only thinks produces only
information. It takes in information in one state, and it puts out information
in another state. From this viewpoint, information in itself is harmless; it is
just an arrangement of marks; and accordingly, a machine that thinks is
harmless, and no control is necessary.

Although it is true that the information produced only becomes good or
evil after other machinery or human beings act on the information, in reality
a machine with the power to produce information is constructed only for the
reason of its use. We want to know what such machines can tell us only
because we can then proceed to act much more efficiently than before. For
example, a guided missile needs a mechanical brain only because then it
can reach its target. In all cases mechanical brains are inseparable from their
uses.
For the purposes of this chapter, the narrow view will be rejected
because it dodges the issue. We shall be much concerned with the
combination of a machine that thinks with another machine that acts; and
we shall often call this combination the robot machine.

READING THIS CHAPTER

Now, before launching further into the discussion, we need to say that
the conclusions suggested in this chapter are not final. Even if they are
expressed a little positively in places, they are nevertheless subject to
change as more information is discovered and as the appraisal of
information changes with time. Also, almost any conclusions about social
control—including, certainly, the conclusions in this chapter—are subject to
controversy. But controversy is good: it leads to thought. The more minds
that go to work on solving the problem of social control over robot
machines and other products of the new technology—which is rushing upon
us from the discoveries of the scientists—the better off we all will be. If,
while stimulating disagreement, the ideas expressed in this chapter should
succeed in stimulating thought and deliberation, the purpose of this chapter
will be well fulfilled.
Up to this point in this book, the emphasis has been on possibilities of
benefits to humanity that may arise from machines that think. In this
chapter, devoted as it is to the subject of control, the emphasis is on
possibilities for harm. Both possibilities are valid, and the happening of
either depends upon the actions of men. In much the same way, atomic
energy is a great possibility for benefit and for harm. It is the nature of
control to put a fence around danger; and so it is natural in this chapter that

the weight of attention should shift to the dangerous aspects of machines
that think.
Perhaps a reader may feel that a chapter of this kind is rather out of
place in a book, such as this one, that seeks to be scientific. If so, he is
reminded that, in accordance with the general suggestions for reading this
book stated in the preface, he should omit this chapter.

FRANKENSTEIN

Perhaps the first study of the consequences of a machine that thinks is a
prophetic novel called Frankenstein, written more than a hundred years
ago, in 1818. The author, then only 21 years old, was Mary W. Godwin,
who became the wife of the poet Percy Bysshe Shelley.
According to the story, a young Swiss, an ardent student of physiology
and chemistry, Victor Frankenstein, finds the secret of life. He makes an
extremely ugly, clever, and powerful monster, with human desires.
Frankenstein promptly flees from his laboratory and handiwork. The
monster, after seeking under great hardships for a year or two to earn fair
treatment among men, finds himself continually attacked and harmed on
account of his ugliness, and he becomes embittered. He begins to search for
his creator for either revenge or a bargain. When they meet:
“I expected this reception,” said the daemon.
“All men hate the wretched; how then must I be hated
who am miserable beyond all living things! Yet you my
creator detest and spurn me, thy creature, to whom thou art
bound by ties only dissoluble by the annihilation of one of
us. You purpose to kill me. How dare you sport thus with
life? Do your duty towards me, and I will do mine towards
you and the rest of mankind. If you will comply with my
conditions, I will leave them and you at peace; but if you
refuse, I will glut the maw of death, until it be satiated with
the blood of your remaining friends.”
Frankenstein starts to comply with the main condition, which is to make a
mate for the monster; but Frankenstein cannot bring himself to do it. So the
monster causes the death one after another of all Frankenstein’s family and

closest friends; and the tale finally ends with the death of Frankenstein and
the disappearance of the monster.
As the dictionary says about Frankenstein, “The name has become a
synonym for one destroyed by his own works.”

ROSSUM’S UNIVERSAL ROBOTS

Perhaps the next study of the consequences of a machine that thinks is a
remarkable play called R.U.R. (for Rossum’s Universal Robots), first
produced in Prague in 1921. Karel Čapek, the Czech dramatist who wrote
it, was then only 31. The word “robot” comes from the Czech word
“robota,” meaning compulsory service.
According to the play, Rossum the elder, a scientist, discovered a
“method of organizing living matter” that was “more simple, flexible, and
rapid” than the method used by nature. Rossum the younger, an engineer,
founded a factory for the mass production of artificial workmen, robots.
They had the form of human beings, intelligence, memory, and strength; but
they were without feelings.
In the first act, the factory under Harry Domin, General Manager, is
busy supplying robots to purchasers all over the world—for work, for
fighting, for any purpose at all, to anyone who could pay for them. Domin
declares:
“... in ten years, Rossum’s Universal Robots will produce so
much corn, so much cloth, so much everything that things
will be practically without price. There will be no poverty.
All work will be done by living machines. Everybody will
be free from worry and liberated from the degradation of
labor. Everybody will live only to perfect himself.... It’s
bound to happen.”
In the second act, ten years later, it turns out that Domin and the others
in charge of the factory have been making some robots with additional
human characteristics, such as the capacity to feel pain. The newer types of
robots, however, have united all the robots against man, for the robots
declare that they are “more highly developed than man, stronger, and more
intelligent, and man is their parasite.”

In the last act, the robots conquer and slay all men except one—an
architect, Alquist, who in the epilogue provides a final quirk to the plot.

FACT AND FANCY

Now what is fact and what is fancy in these two warnings given to us a
hundred years apart?
Of course, it is very doubtful that a Frankenstein monster or a Rossum
robot will soon be constructed with nerves, flesh, and blood like an animal
body. But we know that many types of robot machines can even now be
constructed out of hardware—wheels, motors, wires, electronic tubes, etc.
They can handle many kinds of information and are able to perform many
kinds of actions, and they are stronger and swifter than man.
Of course, it is doubtful that the robot machines, by themselves and of
their own “free will,” will be dangerous to human beings. But as soon as
antisocial human beings have access to the controls over robot machines,
the danger to society becomes great. We want to escape that danger.

Escape from Danger

A natural longing of many of us is to escape to an earlier, simpler life on
this earth. Victor Frankenstein longed to undo the past. He said:
“Learn from me, if not by my precepts, at least by my
example, how dangerous is the acquirement of knowledge,
and how much happier that man is who believes his native
town to be the world, than he who aspires to become greater
than his nature will allow.”
Any sort of return to the past is, of course, impossible. It is doubtful that
men could, even if they wanted to, stop the great flood of technical
knowledge that science is now producing. We all must now face the fact
that the kind of world we used to live in, even so recently as 1939, is gone.
There now exist weapons and machines so powerful and dangerous in the
wrong hands that in a day or two most of the people of the earth could be
put to death. Giant brains are closely related to at least two of these
weapons: scientists have already used mechanical brains for solving

problems about atomic explosives and guided missiles. In addition, thinking
mechanisms designed for the automatic control of gunfire were an
important part of the winning of World War II. They will be a still more
important part of the fighting of any future war.
Nor can we escape to another part of the earth which the new weapons
will not reach. At 300 miles an hour, any spot on earth can be reached from
any other in less than 48 hours. A modern plane exceeds this speed; a rocket
or guided missile doubles or trebles it.
Nor can we trust that some kind of good luck will pull us through and
help men to escape the consequences of what men do. Both Frankenstein
and Domin reaped in full the consequences of what they did. The history of
life on this earth that is recorded in the rocks is full of evidence of races of
living things that have populated the earth for a time and then become
extinct, such as the dinosaurs. In that long history, rarely does a race
survive. In our own day, insects and fungi rather than men have shown
fitness to survive and spread over the earth: witness the blight that
destroyed the chestnut trees of North America, in spite of the best efforts of
scientists to stop it.
There seems to be no kind of escape possible. It is necessary to grapple
with the problem: How can we be safe against the threat of physical harm
from robot machines?

UNEMPLOYMENT

The other chief threat from robot machines is against our economic life.
Harry Domin, in R.U.R., you remember, prophesied: “All work will be done
by living machines.” As an example, in the magazine Modern Industry for
Feb. 15, 1947, appeared a picture of a machine for selling books, and under
the picture were the words:
Another new product in robot salesmen—Latest in the
parade of mechanical vending machines is this book
salesman.... It is designed for use in hospitals, rail terminals,
and stores. It offers 15 different titles, selected manually, and
obtained by dropping quarter in slot. Cabinet stores 96
books.

Can you feel the breath of the robot salesman, workman, engineer,——, on
the back of your neck?
At the moment when we combine automatic producing machinery and
automatic controlling machinery, we get a vast saving in labor and a great
increase in technological unemployment. In extreme cases, perhaps, the
effect of robot machines will be the disappearance of men from a factory.
Such a factory will be like a modern power plant that turns a waterfall into
electricity: once the machinery is installed, only one watchman is ordinarily
needed. But, in most cases, this will be the effect: in a great number of
factories, mines, farms, etc., the labor force needed will be cut by a great
proportion. The effect is not different in quality, because the new
development is robot machinery; but the amount of technological
unemployment coming from robot machines is likely to be considerably
greater than previously.
The robot machine raises the two questions that hang like swords over a
great many of us these days. The first one is for any employee: What shall I
do when a robot machine renders worthless all the skill I have spent years
in developing? The second question is for any businessman: How shall I
sell what I make if half the people to whom I sell lose their jobs to robot
machines?

SOCIAL CONTROL
AND ITS TWO SIDES

The two chief harmful effects upon humanity which are to be expected
from robot machines are physical danger and unemployment. These are
serious risks, and some degree of social control is needed to guard against
them.
There will also be very great advantages from robot machines. The
monster in Frankenstein is right when he says, “Do your duty towards me,
and I will do mine towards you and the rest of mankind.” And Harry Domin
in R.U.R. is right as to possibility when he says, “There will be no
poverty.... Everybody will be free from worry.” Social control must also be
concerned with how the advantages from robot machines are to be shared.

The problem of social control over men and their devices has always
had two sides. The first side deals with what we might plan for control if
men were reasonable and tolerant. This part of the problem seems relatively
easy. The other side deals with what we must ordinarily arrange, since most
men are often unreasonable and prejudiced and, as a result, often act in
antisocial ways. This part of the problem is hard. Let us begin with the
easier side first.

TYPES OF CONTROL—
IF MEN WERE REASONABLE

In seeking to fulfill wants and achieve safety, men have used hundreds
of types of control. The main types are usually called political and
economic systems, but there are always great quantities of exceptions. The
more mature and freer the society, the greater the variety of types of control
that can be found in it.
Probably the most widely used type of control in this country is private
and public control working together, as private ownership and public
regulation—for example, railroads, banks, airlines, life insurance
companies, telephone systems, and many others. It would be reasonable to
expect private ownership and public regulation of a great many classes of
robot machines, to the end that they would never threaten the safety of
people.
Another common type of control is public ownership and operation;
examples are toll bridges, airports, city transit systems, and water-supply
systems. Atomic energy was so clearly fraught with serious implications
that in 1946 the Congress of the United States placed it entirely under
public control expressed as the Atomic Energy Commission. There is a
class of robot machinery which has already reached the stage of acute
public concern: guided missiles and automatic fire-control. It would be
reasonable that in this country all activity in this subdivision should be
under close control by the Department of Defense.
In the international arena, again, the problem becomes soluble if we
assume men to be reasonable. An international agency, such as an organ of
the United Nations, would take over inspection and control of robot

machine activities closely affecting the public safety anywhere in the world.
Particularly, this agency would concern itself with guided missiles, robot
pilots for planes, automatic gunfire control, etc. Much manufacturing skill
is needed to make such products as these: the factories where they could be
manufactured would thereby be determined. Also, a giant brain is a useful
device for solving scientific problems about weapons of mass destruction.
So the agency would need to inspect the problems being solved on such
machines. This agency would be responsible to a legislature or an executive
body representing all the people in the world—if men were reasonable.
In regard to the effects of robot machines on unemployment, again, if
men were reasonable, the problem would be soluble. The problem is
equivalent to the problem of abundance: how should men distribute the
advantages of a vast increase in production among all the members of
society in a fair and sensible way? A vast increase in production is not so
impossible as it may seem. For example, in 1939, with 45 million
employed, the United States index of industrial production was at 109, and,
in 1943, with 52½ million employed, the index of production was at 239.
If men were reasonable, the net profits from robot machinery would be
divided among (1) those who had most to do with devising the new
machinery, and (2) all of society. A rule would be adopted (probably it
could be less complicated than some existing tax rules) which would take
into account various factors such as rewards to the inventors, incentives to
continue inventing, adequate assistance to those made unemployed by the
robot machines, reduction of prices to benefit consumers, and contributions
to basic and applied scientific research.
In fact, under the assumption “if men were reasonable,” it would hardly
be necessary to devote a chapter to the problem of social control over robot
machines!

OBSTACLES

The discussion above of how robot machines could be controlled
supposing that men were reasonable, seems, of course, to be glaringly
impractical. Men are not reasonable on most occasions most of the time. If
we stopped at this point, again we would be dodging the issue. What are the
obstacles to reasonable control?

There are, it seems, two big obstacles and one smaller one to reasonable
types of social control over robot machines. The smaller one is ignorance,
and the two big obstacles are prejudice and a narrow point of view.

Ignorance

By ignorance we mean lack of knowledge and information. Now
mechanical brains are a new and intricate subject. A great many people will,
through no fault of their own, naturally remain uninformed about
mechanical brains and robot machines for a long time. However, there is a
widespread thirst for knowledge these days: witness in magazines, for
example, the growth of the article and the decline of the essay. There is also
a fairly steady surge of knowledge from the austere scientific fountain of
new technology. We can thus see both a demand and a supply for
information in such fields as mechanical brains and robot machines. We can
expect, therefore, a fairly steady decline in ignorance.

Prejudice

Prejudice is a much more serious obstacle to reasonable control over
robot machines. It will be worth our while to examine it at length.
Prejudice is frequent in human affairs. For example, in some countries,
but not in all, there is conflict among men, based on their religious
differences. Again, in other countries, but not in all, there is wide
discrimination among men, based on the color of their skin. Over the whole
world today, there is a sharp lack of understanding between conservatives,
grading over to reactionaries, on the one hand, and liberals, grading over to
radicals, on the other hand. All these differences are based on men’s
attitudes, on strongly held sets of beliefs. These attitudes are not affected by
“information”; the “information” is not believed. The attitudes are not
subject to “judgment”; they come “before judgment”: they are prejudices.
Even in the midst of all the science of today, prejudice is widespread. In
Germany, from 1933 to 1939, we saw one of the most scientific of countries
become one of the most prejudiced.
Prejudice is often difficult to detect. We find it hard to recognize even in
ourselves. For a prejudice always seems, to the person who has it, the most

natural attitude in the world. As we listen to other people, we are often
uncertain how to separate information, guesses, humor, prejudice, etc.
Circumstances compel us to accept provisionally quantities of statements
just on other people’s say-so. A good test of a statement for prejudice,
however, is to compare it with the scientific view.
Prejudice is most dangerous for society. Its more extreme
manifestations are aggressive war, intolerance (especially of strange people
and customs), violence, race hatred, etc. In the consuming hatred that a
prejudiced man has towards the object of his prejudice, he is likely to
destroy himself and destroy many more people besides. In former days, the
handy weapon was a sword or a pistol; not too much damage could be done
when one man ran amuck. But nowadays a single use of a single weapon
has slain 70,000 people (the atom bomb dropped at Hiroshima), and so a
great many people live anxious and afraid.
What is prejudice? How does it arise? How can it be cured, and thus
removed from obstructing reasonable control over robot machines and the
rest of today’s amazing scientific developments?
Prejudice is a disease of men’s minds. It is infectious. The cause and
development of the disease are about as follows: Deprive someone of
something he deeply needs, such as affection, food, or opportunity. In this
way hurt him, make him resentful, hostile; but prevent him from expressing
his resentments in a reasonable way, giving him instead false outlets, such
as other people to hurt, myths to believe, hostile behavior patterns to
imitate. He will then break out with prejudices as if they were measles. The
process of curing the disease of prejudice is about as follows: Make friends
with the patient; win his trust. Encourage him to pour out his half-forgotten
hates. Help him to talk them over freely, by means of questions but not
criticisms, until finally the patient achieves insight, sees through his former
prejudices, and drops them.
In these days prejudice is a cardinal problem of society. It is perhaps
conservative to say that a chief present requirement for the survival of
human society—with the atom bomb, bacterial warfare, guided missiles,
etc., near at hand—is cure of prejudice and its consequences, irrational and
unrestrained hate.

Narrow Point of View

A narrow point of view regarding what is desirable or good is the third
obstacle to rational control over robot machines. What do we mean by this?
Our point of view as a two-year-old is based on pure self-interest. If we
see a toy, we grab it. There is no prejudice about this; it is entirely natural—
for two-year-olds. As we grow older, our point of view concerning what is
good or desirable rapidly broadens: we think of others and their advantage
besides our own. For example, we may become interested in a conservation
program to conserve birds, or soil, or forests, and our point of view
expands, embraces these objectives, which become part of our personality
and loyalties.
Unfortunately, it seems to be true that the expanding point of view, the
expanding loyalties, of most people as they grow up are arrested
somewhere along the line of: self, family, neighborhood, community,
section of country, nation. An honorable exception is the scientists’ old and
fine tradition of world-wide unity and loyalty in the search for objective
truth.
Now the problem of rational control over robot machines and other
parts of the new technology is no respecter of national boundaries. To be
solved it requires a world-wide point of view, a loyalty to human society
and its best interests, a social point of view.
Almost all that you and I have and do and think is the result of a long
history of human society on this earth. All men on the earth today are
descendants of other men who lived 1000, 2000, 3000 ... years ago, whether
they were Romans or Chinese or Babylonians or Mayas or members of any
other race. To ride in a subway or an airplane, to talk on the telephone, to
speak a language, to calculate, to survive smallpox or the black death, etc.
—all these privileges are our inheritance from countless thousands of other
human beings, of many countries, and nearly all of whom are now dead.
During our lives we pass on to our own children an inheritance in which our
own contribution is remarkably small. Since each person is the child of two
others, the number of our forefathers is huge, and we are all undoubtedly
blood cousins. Because of this relationship, and because we owe to the rest
of society nearly all that we are, we have a social responsibility—we need

to hold a social point of view. Each of us needs to accept and welcome a
world-wide social responsibility, as a member of human society, as a
beneficiary and trustee of our human inheritance. Otherwise we are drones,
part of the hive without earning our keep. The social point of view is
equitable, it is inspiring, and it is probably required now in order for human
beings to survive. We need to let go of a narrow point of view.

CONCLUSION

We have now outlined the problem of social control over robot
machines, supposing that human beings were reasonable. We have also
discussed the practical obstacles that obstruct reasonable control.
It is not easy to think of any yet organized group of people anywhere
that would have both the strength and the vision needed to solve this
problem through its own efforts. For example, a part of the United Nations
might have some of the vision needed, but it does not have the power.
Consequently, it is necessary and desirable for individuals and groups
everywhere to take upon themselves an added load of social responsibility
—just as they tend to do in time of war. People often “want to do their
share.” Through encouragement and education, the basic attitude of a
number of people can contain more of “This is our business; we have a
responsibility for helping to solve this problem.” We also need public
responsibility; we need a public body responsible for study, education,
advice, and some measure of control. It might be something like an Atomic
Energy Commission, Bacterial Defense Commission, Mental Health
Commission, and Robot Machine Commission, all rolled into one.
When, at last, there is an effective guarantee of the two elements
physical safety and adequate employment, then at last we shall all be free
from the threat of the robot machine. We can then welcome the robot
machine as our deliverer from the long hard chores of many centuries.

Supplement 1
WORDS AND IDEAS
The purpose of this book is to explain machines that think, without
using technical words any more than necessary. This supplement is a
digression. Its purposes are to consider how to explain in this way and to
discuss the attempt made in this book to achieve simple explanation.

WORDS AS INSTRUMENTS
FOR EXPLAINING

Words are the chief instruments we use for explaining. Of course, many
other devices—pictures, numbers, charts, models, etc.—are also used; but
words are the prime tools. We do most of our explaining with them.
Words, however, are not very good instruments. Like a stone arrow-
head, a word is a clumsy weapon. In the first place, words mean different
things on different occasions. The word “line,” for example, has more than
fifty meanings listed in a big dictionary. How do we handle the puzzle of
many meanings? As we grow older we gather experience and we develop a
truly marvelous capacity to listen to a sentence and then fit the words
together into a pattern that makes sense. Sometimes we notice the time lag
while our brain hunts for the meaning of a word we have heard but not
grasped. Then suddenly we guess the needed meaning, whereupon we grasp
the meaning of the sentence as a whole in much the same way as the parts
of a puzzle click into place when solved.
Another trouble with words is that often there is no good way to tell
someone what a word means. Of course, if the word denotes a physical
object, we can show several examples of the object and utter the word each
time. In fact, several good illustrations of a word denoting a physical thing
often tell most of its meaning. But the rest of its meaning we often do not
learn for years, if ever. For instance, two people would more likely disagree
than agree about what should be called a “rock” and what should be called a
“stone,” if we showed them two dozen examples.

In the case of words not denoting physical objects, like “and,” “heat,”
“responsibility,” we are worse off. We cannot show something and say,
“That is a ···.” The usual dictionary is of some help, but it has a tendency to
tell us what some word A means by using another word B, and when we
look up the other word B we find the word A given as its meaning. Mainly,
however, to determine the meanings of words, we gather experience: we
soak up words in our brains and slowly establish their meanings. We seem
to use an unconscious reasoning process: we notice how words are used
together in patterns, and we conclude what they must mean. Clearly, then,
words being clumsy instruments, the more experience we have had with a
word, the more likely we are to be able to use it, work with it, and
understand it. Therefore explanation should be based chiefly on words with
which we have had the most experience. What words are these? They will
be the well-known words. A great many of them will be short.

SET OF WORDS FOR EXPLAINING

Now what is the set of all the words needed to explain simply a
technical subject like machines that think? For we shall need more words
than just the well-known and short ones. This question doubtless has many
answers; but the answer used in this book was based on the following
reasoning. In a book devoted to explanation, there will be a group of words
(1) that are supposed to be known already or to be learned while reading,
and (2) that are used as building blocks in later explanation and definitions.
Suppose that we call these words the words for explaining. There are at
least three groups of such words:
Group 1. Words not specially defined that are so
familiar that every reader will know all of them;
for example, “is,” “much,” “tell.”
Group 2. Words not specially defined that are familiar,
but perhaps some reader may not know some of
them; for example, “alternative,” “continuous,”
“indicator.”
Group 3. Words that are not familiar, that many
readers are not expected to know, and that are
specially defined and explained in the body of the

book; for example, “abacus,” “trajectory,”
“torque.”
In writing this book, it was not hard to keep track of the words in the
third group. These words are now listed in the index, together with the page
where they are defined or explained. (The index, of course, also lists
phrases that are specially defined.)
But what division should be made between the other two groups? A
practical, easy, and conservative way to separate most words between the
first and second groups seemed to be on the basis of number of syllables.
All words of one syllable—if not specially defined—were put in Group 1.
Also, if a word became two syllables only because of the addition of one of
the endings “-es,” “-ed,” “-ing,” it was kept in Group 1, for these endings
probably do not make a word any harder to understand. In addition, there
were put into Group 1:

1. Numbers; for example, “186,000”; “³/₁₀”.
2. Places: “Philadelphia”; “Massachusetts”.
3. Nations, organizations, people, etc.: “Swedish”; “Bell”.
4. Years and dates: “February”; “1946”.
5. Names of current books or articles and their authors.

Of course, not all these words would be familiar to every reader (for
example, “Maya”), but in the way they occur, they are usually not puzzling,
for we can tell from the context just about what they must mean.
All remaining words for explaining—chiefly, words of two or more
syllables and not specially defined—were put in Group 2 and were listed
during the writing of this book. Many Group 2 words, of course, would be
entirely familiar to every reader; but the list had several virtues. No hard
words would suddenly be sprung like a trap. The same word would be used
for the same idea. Every word of two or more syllables was continually
checked: is it needed? can it be replaced by a shorter word? It is perhaps
remarkable that there were fewer than 1800 different words allowed to stay
in this list. This fact should be a comfort to a reader, as it was to the author.
Now there are more words in this book than words for explaining. So
we shall do well to recognize:

Group 4. Words that do not need to be known or
learned and that are not used in later explanation
and definitions.
These words occur in the book in such a way that understanding them,
though helpful, is not essential. One subdivision of Group 4 are names that
appear just once in the book, as a kind of side remark, for example, “a
chemical, called acetylcholine.” Such a name will also appear in the index,
but it is not a word for explaining. Another subdivision of Group 4 are
words occurring only in quotations. For example, in the quotation from
Frankenstein on page 198, a dozen words appear that occur nowhere else in
the book, including “daemon,” “dissoluble,” “maw,” “satiate.” Clearly we
would destroy the entire flavor of the quotation if we changed any of these
words in any way. But only the general drift of the quotation is needed for
understanding the book, and so these words are Group 4 words.
In this way the effort to achieve simple explanation in this book
proceeded. But even supposing that we could reach the best set of words for
explaining, there is more to be done. How do we go from simple
explanation to understanding?

UNDERSTANDING IDEAS

Understanding an idea is basically a standard process. First, we find the
name of the idea, a word or phrase that identifies it. Then, we collect true
statements about the idea. Finally, we practice using them. The more true
statements we have gathered, and the more practice we have had in
applying them, the more we understand the idea.
For example, do you understand zero? Here are some true statements
about zero.
1. Zero is a number.
2. It is the number that counts none or nothing.
3. It is marked 0 in our usual numeral writing.
4. The ancient Romans, however, had no numeral for
it. Apparently, they did not think of zero as a
number.

5. 0 is what you get when you take away 17 from 17,
or when you subtract any number from itself.
6. If you add 0 to 23, you get 23; and if you add 0 to
any number, you get that number unchanged.
7. If you subtract 0 from 48, you get 48; and if you
subtract 0 from any number, you get that number
unchanged.
8. If you multiply 0 by 71, you get 0; and if you
multiply together 0 and any number, you get 0.
9. Usually you are not allowed to divide by 0: that is
against the rules of arithmetic.
10. But if you do, and if you divide 12 by 0, for
example—and there are times when this is not
wrong—the result is called infinity and is marked
∞, a sign that is like an 8 on its side.
This is not all the story of zero; it is one of the most important of numbers.
But, if you know these statements about zero, and have had some practice
in applying them, you have a good understanding of zero. Incidentally, a
mechanical brain knows all these statements about zero and a few more;
they must be built into it.
For us to understand any idea, then, we pursue three aims:

1. We find out what it is called.
2. We collect true statements about it.
3. We apply those statements—we use them in situations.

We can do this about any idea. Therefore, we can understand any idea, and
the degree of our understanding increases as the number of true statements
mastered increases.
Perhaps this seems to be a rash claim. Of course, it may take a good
deal of time to collect true statements about many ideas. In fact, a scientist
may spend thirty years of his life trying to find out from experiment the
truth or falsehood of one statement, though, when he has succeeded, the fact
can be swiftly told to others. Also, we all vary in the speed, perseverance,

skill, etc., with which we can collect true statements and apply them.
Besides, some of us have not been taught well and have little faith in our
ability to carry out this process: this is the greatest obstacle of all. But, there
is in reality no idea in the field of existing science and knowledge which
you or I cannot understand. The road to understanding lies clear before us.

Supplement 2
MATHEMATICS
In the course of our discussion of machines that think, we have had to
refer without much explanation to a number of mathematical ideas. The
purpose of this supplement is to explain a few of these ideas a little more
carefully than seemed easy to do in the text and, at the end of the supplement,
to put down briefly some additional notes for reference.

DEVICES FOR MULTIPLICATION

Suppose that we have to multiply 372 by 465. With the ordinary school
method, we write 465 under the 372 and proceed about as follows: 5 times 2
is 10, put down the 0 and carry the 1; 5 times 7 is 35, 35 and 1 is 36, put
down the 6 and carry the 3; 5 times 3 is 15, 15 and 3 is 18, put down the 8
and carry the 1; ... The method is based mainly on a well-learned subroutine
of continually changing steps:

1. Select a multiplicand digit.
2. Select a multiplier digit.
3. Refer to the multiplication table with these digits.
4. Obtain the value of their product, called a partial product.
5. Add the preceding carry.
6. Set down the right-hand digit.
7. Carry the left-hand digit.

We can, however, simplify this subroutine for a machine by delaying the
carrying. We collect in one place all the right-hand digits of partial products,
collect in another place all the left-hand digits, and delay all addition until the
end.
For example, let us multiply 372 by 465 with this method:

Right-Hand Left-Hand Usual Method
Digits Digits for Comparison
372 372 372
× 465 × 465 × 465
550 131 1860
822 141 2232
288 120 1488
37570 13541 172980

Final Addition
37570
+ 13541
172980
37570 is called the right-hand component of the product. It is convenient to
fill in with 0 the space at the end of 13541 and to call 135410 the left-hand
component of the product.
This process is called multiplying by right- and left-hand components. It
has the great advantage that no carrying is necessary to complete any line of
the original multiplications. Some computing machines use this process.
Built into the hardware of the machine is a multiplication table up to 9 × 9.
The machine, therefore, can find automatically the right-hand digit and the
left-hand digit of any partial product. In a computing machine that uses this
process, all the left-hand digits are automatically added in one register, and
all the right-hand digits are added in another register. The only carrying that
is needed is the carrying as the right-hand digits are accumulated and as the
left-hand digits are accumulated. At the end of the multiplication, one of the
registers is automatically added into the other, giving the product.
Another device used in computing machines for multiplying is to change
the multiplier into a set of digits 0 to 5 that are either positive or negative. For
example, suppose that we want to multiply 897 by 182. We note that 182
equals 200 minus 20 plus 2, and so we can write it as

222.

The minus over the 2 marks it as a negative digit 2. Then to multiply we
have:

897
222
1794
-1794
1794
163254

The middle 1794 is subtracted. This process is usually called short-cut
multiplication. Everybody discovers this trick when he decides that
multiplying by 99 is too much work, that it is easier to multiply by 100 and
subtract once.

BINARY OR TWO NUMBERS

We are well accustomed to decimal notation in which we use 10 decimal
digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and write them in combinations to designate
decimal numbers. In binary notation we use two binary digits 0, 1 and write
them in combinations to designate binary numbers. For example, the first 17
numbers, from 0 to 16 in the decimal notation, correspond with the following
numbers in binary notation:
Decimal Binary Decimal Binary
0 0
1 1 9 1001
2 10 10 1010
3 11 11 1011
4 100 12 1100
5 101 13 1101
6 110 14 1110
7 111 15 1111
8 1000 16 10000

In decimal notation, 101 means one times a hundred, no tens, and one. In
binary notation, 101 means one times four, no twos, and one. The successive
digits in a decimal number from right to left count 1, 10, 100, 1000, 10000, ...
—successive powers of 10 (for this term, see the end of this supplement). The
successive digits in a binary number from right to left count 1, 2, 4, 8, 16, ...
—powers of 2.
The decimal notation is convenient when equipment for computing has
ten positions, like the fingers of a man, or the positions of a counter wheel.
The binary notation is convenient when equipment for computing has just
two positions, like “yes” or “no,” or current flowing or no current flowing.
Addition, subtraction, multiplication, and division can all be carried out
unusually simply in binary notation. The addition table is simple and consists
only of four entries.

+ 0 1
0 0 1
1 1 10
The multiplication table is also simple and contains only four entries.

× 01
0 00
1 01
Suppose that we add in binary notation 101 and 1001:

Binary
Check
Addition
101 5
+ 1001 9
1110 14
We proceed: 1 and 1 is 10; write down 0 and carry 1; 0 and 0 is 0, and 1 to
carry is 1; and 1 and 0 is 1; and then we just copy the last 1. To check this we

can convert to decimal and see that 101 is 5, 1001 is 9, and 1110 is 14, and
we can verify that 5 and 9 is 14.
One of the easiest ways to subtract in binary notation is to add a ones
complement (that is, the analogue of the nines complement) and use end-
around-carry (for these two terms, see the end of this supplement). A ones
complement can be written down at sight by just putting 1 for 0 and 0 for 1.
For example, suppose that we subtract 101 from 1110:

Subtraction by
Direct
Check Adding Ones
Subtraction
Complement
1110 14 1110
- 101 - 5 + 1010
1001 9 (1)1000
↓
⎯→ 1
1001
Multiplication in the binary notation is simple. It amounts to (1) adding if
the multiplier digit is 1 and not adding if the multiplier digit is 0, and (2)
moving over or shifting. For example, let us multiply 111 by 101:

Binary
Check
Multiplication
111 7
× 101 ×5
111
111
100011 35
The digit 1 in the 6th (or nth) binary place from the right in 100011 stands for
1 times 2 to the 5th (or n-1 th) power, 2 × 2 × 2 × 2 × 2 = 32. The result
100011 is translated into 32 plus 2 plus 1, which equals 35 and verifies.

Division in the binary notation is also simple. It amounts to (1)
subtracting (yielding a quotient digit 1) or not subtracting (yielding a quotient
digit 0), and (2) shifting. We never need to try multiples of the divisor to find
the largest that can be subtracted yet leave a positive remainder. For example,
let us divide 1010 (10 in decimal) into 10001110 (142 in decimal):

1110 (14 in decimal)
————
1010)10001110
1010
1111
1010
1011
1010
10 (remainder, 2 in decimal)

In decimal notation, digits to the right of the decimal point count powers
of ⅒. In binary notation, digits to the right of the binary point count powers
of ½: ½, ¼, ⅛, ¹/₁₆.... For example, 0.1011 equals ½ + ⅛ + ¹/₁₆, or ¹¹/₁₆.
If we were accustomed to using binary numbers, all our arithmetic would
be very simple. Furthermore, binary numbers are in many ways much better
for calculating machinery than any other numbers. The main problem is
converting numbers from decimal notation to binary. One method depends on
storing the powers of 2 in decimal notation. The rule is: subtract successively
smaller powers of 2; start with the largest that can be subtracted, and count 1
for each power that goes and 0 for each power that does not. For example, 86
in decimal becomes 1010110 in binary:

86
64 64 goes 1
22 32 does not go 0
16 16 goes 1
6 8 does not go 0
4 4 goes 1

2 2 goes 1
2 1 does not go 0
0
It is a little troublesome to remember long series of 1’s and 0’s; in fact, to
write any number in binary notation takes about 3⅓ times as much space as
decimal notation. For this reason we can separate binary numbers into triples
beginning at the right and label each triple as follows:
Triple Label
000 0
001 1
010 2
011 3
100 4
101 5
110 6
111 7
For example, 1010110 would become 1 010 110 or 126. This notation is often
called octal notation, because it is notation in the scale of eight.

BIQUINARY OR TWO-FIVE NUMBERS

Another kind of notation for numbers is biquinary notation, so called
because it uses both 2’s and 5’s. Essentially this notation is very like Roman
numerals, ancient style. By ancient style we mean, for example, VIIII instead
of IX. In the following table we show the first two dozen numbers in decimal,
biquinary, and ancient Roman notation:
Decimal Biquinary Roman
0 0
1 1 I
2 2 II
3 3 III

Decimal Biquinary Roman
4 4 IIII
5 10 V
6 11 VI
7 12 VII
8 13 VIII
9 14 VIIII
10 100 X
11 101 XI
12 102 XII
13 103 XIII
14 104 XIIII
15 110 XV
16 111 XVI
17 112 XVII
18 113 XVIII
19 114 XVIIII
20 200 XX
21 201 XXI
22 202 XXII
23 203 XXIII
The biquinary columns alternate in going from 0 to 4 and from 0 to 1. The
digits from 0 to 4 are not changed. The digits from 5 to 9 are changed into 10
to 14. We see that the biquinary digits are 0 to 4 in odd columns and 0, 1 in
even columns, counting from the right.
This is the notation actually expressed by the abacus. The beads of the
abacus show by their positions groups of 2 and 5 (see Fig. 1).

Fig. 1. Abacus and notations.

SOME OPERATIONS OF ALGEBRA

One of the operations of algebra that is important for a mechanical brain
is approximation, the problem of getting close to the right value of a number.
Take, for example, finding square root (see the end of this supplement). The
ordinary process taught in school is rather troublesome. We can set down
another process, however, using a desk calculator to do division, which gives
us square root with great speed.
Suppose that we want to find the square root of a number N, and suppose
that we have x₀ as a guessed square root correct to one figure. For example, N
might be 67.2 and x₀ might be 8, chosen because 8 × 8 is 64, and 9 × 9 is 81,
and it seems as if 8 should be near the square root of 67.2. Here is the
process:

1. Divide x₀ into N, and obtain N / x₀.
2. Multiply x₀ + N / x₀ by 0.5 and call the result x₁.

Now repeat:

1. Divide x₁ into N and obtain N / x₁.
2. Multiply x₁ + N / x₁ by 0.5 and call the result x₂.

Every time this process is repeated, the new x comes a great deal closer to the
correct square root. In fact it can be shown that, if x₀ is correct to one figure,
then:
Is Correct To
Approximation
··· Figures
x₁ 2
x₂ 4
x₃ 8
x₄ 16
Let us see how this actually works out with 67.2 and a 10-column desk
calculator.
Round 1: 8 divided into 67.2 gives 8.4. One half of 8
plus 8.4 is 8.2. This is x₁.
Round 2: 8.2 divided into 67.2 gives 8.195122. One
half of 8.2 plus 8.195122 is 8.197561. This is x₂.
Round 3: 8.197561 divided into 67.2 gives
8.197560225. One half of 8.197561 and
8.197560225 is 8.1975606125. This is x₃.
Checking x₃, we find that 8.1975606125 divided into
67.2 gives 8.1975606126 approximately.
In this case, then, x₃ is correct to more than 10 figures. In other words, with a
reasonable guess and two or three divisions we can obtain all the accuracy we
can ordinarily use. This process is called rapid approximation, or rapidly
convergent approximation, since it converges (points or comes together) very
quickly to the number we are seeking.

Another important operation of algebra is interpolation, the problem of
putting values smoothly in between other values. For example, suppose that
we have the table:

x y
5 26
6 37
7 50
8 65
9 82
Suppose that we want to find the value that y (or yₓ) ought to have when x has
the value of 7.2. This is the problem of interpolating y so as to find y at the
value of 7.2, y₇ˌ₂.
One way of doing this is to discover the formula that expresses y and then
to put x into that formula. This is not always easy. Another way is to take the
difference between y₇ and y₈, 15, and share the difference appropriately over
the distance 7 to 7.2 and 7.2 to 8. We can, for example, take ²/₁₀ of 15 = 3,
add that to y₇ = 50, and obtain an estimated y₇ˌ₂ = 53. This is called linear
interpolation, since the difference 0.2 in the value of x is used only to the first
power. It is a good practical way to carry out most interpolation quickly and
approximately.
Actually here y = x² + 1, and so the true value of y₇ˌ₂ is (7.2 × 7.2) + 1, or
52.84, which is rather close to 53. Types of interpolation procedures more
accurate than linear interpolation will come much nearer still to the true
value.

ALGEBRA OF LOGIC

We turn now to the algebra of logic. The first half of Chapter 9,
“Reasoning” (through the section “Logical-Truth Calculation by Algebra”),
introduces this subject. There the terms truth values, truth tables, logical
connectives, and algebra of logic are explained. The part of Chapter 3, “A
Machine That Will Think,” that discusses the operations greater-than and
selection, also explains some of the algebra of logic. It introduces, for
example, the formula

p = T(a > b) = 1, 0
This is a way of saying briefly that the truth value of the statement “a is
greater than b” equals p; p is 1 if the statement is true and 0 if the statement is
false. The truth value 1 corresponds with “yes.” The truth value 0
corresponds with “no.”
With mechanical brains we are especially interested in handling
mathematics and logic without any sharp dividing line between them. For
example, suppose that we have a register in which a ten-digit number like
1,765,438,890 may be stored. We should be able to use that register to store a
number consisting of only 1’s and 0’s, like 1,100,100,010. Such a number
may designate the answers to 10 successive questions: yes, yes, no, no, yes,
no, no, no, yes, no. Or it may tell 10 successive binary digits. The register
then is three times as useful: it can store either decimal numbers or truth
values or binary digits. We need, of course, a way to obtain from the register
any desired digit. For this purpose we may have two instructions to the
machine: (1) read the left-hand end digit; (2) shift the number around in a
circle. The second instruction is the same as multiplying by 10 and then
putting the left-most digit at the right-hand end. For example, suppose that
we want the 3rd digit from the left in 1,100,100,010. The result of the first
circular shift is 1,001,000,101; the result of the second circular shift is
0,010,001,011; and reading the left-most digit gives 0. A process like this has
been called extraction and is being built into the newest mechanical brains.
Using truth values, we can put down very neatly some truths of ordinary
algebra. For example:

(the absolute value of a) =
a × (the truth of a greater than or equal to 0)
- a × (the truth of a less than 0)

|a| = a · T(a ≥ 0) - a · T(a < 0)
For another example:

Either a is greater than b,
or else a equals b,
or else a is less than b

T(a > b) + T(a = b) + T(a < b) = 1

Many common logical operations, like selecting and comparing, and the
behavior of many simple mechanisms, like a light or a lock, can be expressed
by truth values. Chapter 4, on punch-card mechanisms, contains a number of
examples.

pronoun, variable

In ordinary language, a pronoun, like “he,” “she,” “it,” “the former,” “the
latter,” is a word that usually stands for a noun previously referred to. A
pronoun usually stands for the last preceding noun that the grammar allows.
In mathematics, a variable, like “a,” “b,” “x,” “m₁,” “m₂” closely resembles a
pronoun in ordinary language. A variable is a symbol that usually stands for a
number previously referred to, and usually it stands for the same number
throughout a particular discussion.

multiplicand, dividend, augend, etc.

In the The Name The Name The Name
Equation of a is: of b is: of c is:
a+b=c augend addend sum
a-b=c minuend subtrahend remainder
a×b=c multiplicand multiplier product
a÷b=c dividend divisor quotient
Augend and addend are names of registers in the Harvard Mark II
calculator (see Chapter 10).

subtraction by adding, nines complement

Two digits that add to 9 (0 and 9, 1 and 8, 2 and 7, 3 and 6, 4 and 5) are
called nines complements of each other. The nines complement of a number a

is the number b in which each digit of b is the nines complement of the
corresponding digit of a; for example, the nines complement of 173 is 826.
Ordinary subtraction is the same as addition as of the nines complement, with
a simple correction; for example, 562 less 173 (equal to 389) is the same as
562 plus 826 (equal to 1388) less 1000 plus 1.

end-around-carry

The correction “less 1000 plus 1” of the foregoing example may be
thought of as carrying the 1 (in the result 1388) around from the left-hand end
to the right-hand end, where it is there added. So the 1 is called end-around-
carry.

tens complement

Two digits that add to 10 are called tens complements of each other. The
tens complement of a number a, however, is equal to the nines complement of
the number plus 1. For example, the tens complement of 173 is 827. When
subtracting by adding a tens complement, the left-most digit 1 in the result is
dropped. For example, 562 less 173 (equal to 389) is the same as 562 plus
827 (equal to 1389) less 1000.

power, square, cube, reciprocal, etc.

A power of any number a is a multiplied by itself some number of times.
a × a × a ... × a where a appears b times is written aᵇ and is read a to the bth
power. a², a to the 2nd power, is a × a and is called a squared or the square of
a. a³, a to the 3rd power, a × a × a, is called a cubed, or the cube of a. a⁰, a to
the zero power, is equal to 1 for every a. a¹, a to the power 1, is a itself. The
first power is often called linear. a to some negative power is the same as 1
divided by that power; that is, a⁻ᵇ = 1/aᵇ. a⁻¹, a to the power minus 1, is 1/a,
and is called the reciprocal of a. a¹ᐟ², a to the one-half power, is a number c
such that c × c = a, and is called the square root of a and often denoted by √a.

table, tabular value, argument, etc.

An example of a table is:

0.025 0.03
1 1.02500 1.03000
2 1.05063 1.06090
3 1.07689 1.09273
The numbers in the body of the table, called tabular values, depend on or are
determined by the numbers along the edge of the table, called arguments. In
this example, if 1, 2, 3 are choices of a number n, and if 0.025, 0.03 are
choices of a number i, then each tabular value y is equal to 1 plus i raised to
the nth power. n and i are also called independent variables, and y is called
the dependent variable. The table expresses a function or formula or rule. The
rule could be stated as: add i to 1; raise the result to the nth power.

constant

A number is said to be a constant if it has the same value under all
conditions. For example, in the formula:
(area of a circle) = π × (radius)²,
π is a constant, equal to 3.14159 ...,
applying equally well to all circles.

infinity

Mathematics recognizes several kinds of infinity. One of them occurs
when numbers become very large. For example, the quotient of 12 divided by
a number x, as x becomes closer and closer to 0, becomes indefinitely large,
and the limit is called infinity and is denoted ∞.

equation, simultaneous, linear

An example of two linear simultaneous equations is:

7x + 8t = 22
3x + 5t = 11
x and t are called unknowns—that is, unknown variables—because the
objective of solving the equations is to find them. These equations are called
simultaneous because they are to be solved together, at the same time, for
values of x and t which will fit in both equations. The equations are called
linear because the only powers of the unknowns that appear are the first
power. Values that solve equations are said to satisfy them. It is easy to solve
these two equations and find that x = 2 and t = 1 is their solution. But it is a
long process to solve 10 linear simultaneous equations in 10 unknowns, and
it is almost impossible (without using a mechanical brain) to solve 100 linear
simultaneous equations in 100 unknowns.

derivative, integral,
differential equation, etc.

See the sections in Chapter 5 entitled “Differential Equations,” “Physical
Problems,” and “Solving Physical Problems.” There these ideas and, to some
extent, also the following ideas were explained: formula, equation, function,
differential function, instantaneous rate of change, interval, inverse,
integrating. See also a textbook on calculus. If y is a function of x, then a
mathematical symbol for the derivative of y with respect to x is Dₓ y, and a
symbol for the integral of y with respect to x, is ∫y dx. An integral with given
initial conditions (see p. 83) is a definite integral.

exponential

A famous mathematical function is the exponential. It equals the constant
e raised to the x power, eˣ, where e equals 2.71828.... The exponential lies
between the powers of 2 and the powers of 3. It can be computed from:
x² x³
eˣ = 1 + + +...
1·2 1·2·3
It is a solution of the differential equation Dₓy = y. See also a textbook
on calculus. The exponential to the base 10 is 10ˣ.

logarithm

Another important mathematical function is the logarithm. It is written
log x or logₑ x and can be computed from the two equations:
log uv = log u + log v
x² x³
log(1 + x) = x - + -... x² < 1
2 3
It is a solution of the differential equation Dₓy = 1/y. If y is the logarithm of
x, then x is the antilogarithm of y. The logarithm to the base 10 of x, log₁₀ x,
equals the logarithm to the base e of x, logₑ x, divided by logₑ 10. See also
textbooks on algebra and calculus.

sine, cosine, tangent, antitangent

These also are important mathematical functions. The sine and cosine are
solutions of the differential equation Dₓ(Dₓy) =-y and are written as sin x
and cos x. They can be computed from
x³ x⁵
sin x = x - + -...
1 · 2· 3 1 · 2 · 3· 4· 5

x² x₄
cos x = 1 - + -...
1·2 1 · 2 · 3· 4
The tangent of x is simply sine of x divided by cosine of x. If y is the tangent
of x, then x is the antitangent of y. See also references on trigonometry and
on calculus. Trigonometric tables include sine, cosine, tangent, and related
functions.

Bessel functions

These are mathematical functions that were named after Friedrich W.
Bessel, a Prussian astronomer who lived from 1784 to 1846. Bessel functions
are found as some of the solutions of the differential equation

x² Dₓ(Dₓy) + x Dₓy + (x² - n²)y = O
This equation arises in a number of physical problems in the fields of
electricity, sound, heat flow, air flow, etc.

matrix

A matrix is a table (or array) of numbers in rows and columns, for which
addition, multiplication, etc., with similar tables is specially defined. For
example, the matrix

1 2

3 4
plus the matrix
5 20

60 100
equals the matrix
6 22

63 104
(Can you guess the rule defining addition?)
Calculations using matrices are useful in physics, engineering, psychology,
statistics, etc. To add a square matrix of 100 terms in an array of 10 columns
and 10 rows to another such matrix, 100 ordinary additions of numbers are
needed. To multiply one such matrix by another, 1000 ordinary
multiplications and 900 ordinary additions are needed. See references on
matrix algebra and matrix calculus.

differences, smoothness, checking

On p. 221, a sequence of values of y is shown: 26, 37, 50, 65, 82.
Suppose, however, the second value of y was reported as 47 instead of 37.
Then the differences of y as we pass down the sequence would not be 11, 13,
15, 17 (which is certainly regular or smooth) but 21, 3, 15, 17 (which is
certainly not smooth). The second set of differences would strongly suggest a
mistake in the reporting of y. The smoothness of differences is often a useful
check on a sequence of reported values.

Supplement 3
REFERENCES
A book like the present one can cover only a part of the subject of machines that
think. To obtain more information about these machines and other topics to which
they are related there are many references that may be consulted. There are still few
books directly on the subject of machines that think, but there are many articles and
papers, most of them rather specialized.
The purpose of this supplement is to give a number of these references and to
provide a brief, general introduction to some of them. The references are subdivided
into groups, each dealing with a branch of the subject. The references in each group
are in alphabetical order by name of author (with “anonymous” last), and under each
author they are in chronological order by publication date. Some publications,
especially a forum or symposium, are listed more than once, according as the topic
discussed falls in different groups. In this supplement, the sign three dots ( ...) next to
the page numbers for an article indicates that the article is continued on later,
nonconsecutive pages.
It seemed undesirable to try to make the group of references dealing with a subject
absolutely complete, so long as enough were given to provide a good introduction to
the subject. It proved impractical to try to make the citation of every single reference
technically complete, so long as enough citation was given so that the reference could
certainly be found. Furthermore, in a list of more than 250 references, errors are
almost certain to occur. If any reader should send me additions or corrections, I shall
be more than grateful.

THE HUMAN BRAIN

No one yet knows specifically how particular ideas are thought about in the
human brain. The references listed in this section, however, contain some information
about such topics as:
The structural differences, development, and evolution of the
brains of animals, apes, primitive man, and modern man.
The effect on the brain of blood composition, body
temperature, supply of oxygen, and other biochemical
factors.

The structure and physiology of the brain, the nervous
system, and nerve impulses.
The theory of learning, intelligence, and memory.

Barcroft, Joseph, The Brain and Its Environment,
New Haven: Yale University Press, 1948, 117 pp.
Beach, Frank A., Payday for Primates, Natural
History, vol. 56, no. 10, Dec. 1947, pp. 448-451.
Beach, Frank A., Can Animals Reason? Natural
History, vol. 57, no. 3, Mar. 1948, pp. 112-116 ...
Berry, R. J. A., Brain and Mind, or the Nervous
System of Man, New York: The Macmillan Co.,
1928, 608 pp.
Boring, Edwin G., A History of Experimental
Psychology, New York: Century Co., 1929, 699
pp.
Franz, Shepherd I., The Evolution of an Idea; How
the Brain Works, Los Angeles: University of
California, 1929, 35 pp.
Herrick, C. Judson, The Thinking Machine, Chicago:
University of Chicago Press, 1929, 374 pp.
Herrick, C. Judson, Brains of Rats and Men,
Chicago: University of Chicago Press, 1930, 382
pp.
Lashley, Karl S., Brain Mechanisms and
Intelligence, Chicago: University of Chicago
Press, 1929, 186 pp.
Pieron, Henri, Thought and the Brain, London:
Kegan, Paul, Trench, Trübner & Co., 1927, 262
pp. Also New York: Harcourt, Brace & Co.
Schrödinger, Erwin, What is Life?, New York: The
Macmillan Co., 1945, 90 pp.
Sherrington, Charles S., The Brain and Its
Mechanism, Cambridge, England: The University
Press, 1933, 35 pp.

Tilney, Frederick, The Brain from Ape to Man, New
York: P. B. Hoeber, Inc., 1928, 2 vol., 1075 pp.
Wiener, Norbert, Cybernetics, or Control and
Communication in the Animal and the Machine,
New York: John Wiley & Sons, 1948, 194 pp.
Anonymous, Ten Billion Relays, Time, Feb. 14, 1949,
p. 67.

MATHEMATICAL BIOPHYSICS

There has recently been another approach to the problem: How
does a brain think? A group of men, many of them in and near
Chicago, have been saying: “We know the properties of nerves,
nerve impulses, and simple nerve networks. We know the activity of
the brain. What mathematical model of nerve networks is necessary
to account for the activity of the brain?” These men have used
mathematics, statistics, and mathematical logic in the effort to attack
this problem, and they support a Bulletin of Mathematical
Biophysics.

Householder, Alston S., A Neural Mechanism for
Discrimination, Psychometrika, vol. 4, no. 1, Dec.
1939, pp. 45-58.
Householder, Alston S., and Herbert D. Landahl,
Mathematical Biophysics of the Central Nervous
System, Bloomington, Ind.: Principia Press, 1945.
Landahl, Herbert D., Contributions to the
Mathematical Biophysics of the Central Nervous
System, Bulletin of Mathematical Biophysics, vol.
1, no. 2, June 1939, pp. 95-118.
Landahl, Herbert D., Warren S. McCulloch, and
Walter Pitts, A Statistical Consequence of the
Logical Calculus of Nervous Nets, Bulletin of
Mathematical Biophysics, vol. 5, no. 4, Dec. 1943,
pp. 135-137.

Landahl, Herbert D., A Note on the Mathematical
Biophysics of Central Excitation and Inhibition,
Bulletin of Mathematical Biophysics, vol. 7, no. 4,
Dec. 1945, pp. 219-221.
Lettvin, Jerome Y., and Walter Pitts, A
Mathematical Theory of the Affective Psychoses,
Bulletin of Mathematical Biophysics, vol. 5, no. 4,
Dec. 1943, pp. 139-148.
McCulloch, Warren S., and Walter Pitts, A Logical
Calculus of the Ideas Immanent in Nervous
Activity, Bulletin of Mathematical Biophysics,
vol. 5, no. 4, Dec. 1943, pp. 115-133.
Rashevsky, N., Mathematical Biophysics, Chicago:
University of Chicago Press. Revised edition,
1948, 669 pp.
Rashevsky, N., Mathematical Biophysics of
Abstraction and Logical Thinking, Bulletin of
Mathematical Biophysics, vol. 7, no. 3, Sept.
1945, pp. 133-148.
Rashevsky, N., Some Remarks on the Boolean
Algebra of Nervous Nets in Mathematical
Biophysics, Bulletin of Mathematical Biophysics,
vol. 7, no. 4, Dec. 1945, pp. 203-211.
Rashevsky, N., A Suggestion for Another Statistical
Interpretation of the Fundamental Equations of the
Mathematical Biophysics of the Central Nervous
System, Bulletin of Mathematical Biophysics, vol.
7, no. 4, Dec. 1945, pp. 223-226.
Rashevsky, N., The Neural Mechanism of Logical
Thinking, Bulletin of Mathematical Biophysics,
vol. 8, no. 1, Mar. 1946, pp. 29-40.

LANGUAGES: WORDS AND SYMBOLS
FOR THINKING

Hardly any field of techniques for thinking is more fascinating
than language. The following list of references, of course, is short; it
is meant chiefly as an introduction pointing out a number of different
paths into the field of language and languages. Such topics as the
following are introduced by the references in this list:

The origin of languages and alphabets.
The languages of the world, and speech communities.
The comparison of words and structure from language to language.
The significance of grammar and syntax.
The problem of clear meanings.
Writing and speaking that is easy to understand.

Bloomfield, Leonard, Language, New York: Henry
Holt & Co., 1933, 564 pp.
Bodmer, Frederick, and Launcelot Hogben, The
Loom of Language, New York: W. W. Norton &
Co., 1944, 692 pp.
Flesch, Rudolf, The Art of Plain Talk, New York:
Harper & Brothers, 1946, 210 pp.
Graff, Willem L., Language and Languages: An
Introduction to Linguistics, New York: D.
Appleton & Co., 1932, 487 pp.
Hayakawa, S. I., Language in Action, New York:
Harcourt, Brace & Co., 1941, 345 pp.
Jespersen, Otto, The Philosophy of Grammar, New
York: Henry Holt & Co., 1929 (third printing),
359 pp.

Jespersen, Otto, Analytic Syntax,
In this book, by means of a well-contrived system of
letters and signs, the great linguistic scholar
Jespersen depicts all the important inter-relations
of English words and parts of words in connected
speech.

Ogden, C. K., The System of Basic English, New
York: Harcourt, Brace & Co., 1934, 320 pp.

Schlauch, Margaret, The Gift of Tongues, New
York: Modern Age Books, 1942, 342 pp.
Walpole, Hugh R., Semantics: The Nature of Words
and Their Meanings, New York: W. W. Norton &
Co., 1941, 264 pp.

LANGUAGES:
MACHINES FOR THINKING

For many years, nearly all references about machines as a
language for thinking have been specialized and limited. Colleges
with scholars who write textbooks usually have not had a variety of
expensive and versatile computing machinery. As a result, the main
environment for stimulating possible authors has until recently been
missing. The list of references is accordingly brief.

Aiken, Howard H., and others, Proceedings of a
Symposium on Large-Scale Digital Calculating
Machinery, Cambridge, Mass.: Harvard
University Press, 1948, 302 pp.
Comrie, John Leslie, The Application of Commercial
Calculating Machines to Scientific Computing,
Mathematical Tables and Other Aids to
Computation, vol. 2, no. 16, Oct. 1946, pp. 149-
159.
Crew, E. W., Calculating Machines, The Engineer,
vol. 172, Dec. 1941, pp. 438-441.
Fry, Macon, Designing Computing Mechanisms,
Cleveland, Ohio: Penton Publishing Co., 1946, 48
pp. (Reprinted from Machine Design, Aug. 1945
through Feb. 1946.)
Hartree, D. R., Calculating Machines: Recent and
Prospective Developments and Their Impact on
Mathematical Physics, Cambridge, England: The
University Press, 1947, 40 pp.