Transcriber’s Notes:
Underscores “_” before and after a word or phrase indicate _italics_
in the original text.
A single underscore after a symbol indicates a subscript.
Small capitals have been converted to SOLID capitals.
Illustrations have been moved so they do not break up paragraphs.
Typographical and punctuation errors have been silently corrected.
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.
[1] Copyright 1923 by Doubleday, Page and Co.; all rights reserved;
quotations reprinted by permission of Karel Čapek and Samuel French.
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.
[Illustration: 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.
[Illustration: 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 SIGN USED IN SIGNIFICANCE NAME OF
NO. 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![2] Spoken The speaker Pooh-pooh
becomes a English expresses theory
new word disdain
3. New word is Chortle[2] Spoken “Chuckle” Analogical
like another English; and
word invented by “snort”
Lewis Carroll, blended
1896
4. Word has Mother[2] Spoken Female Historical
been used English parent
through
the ages
_Sights_
5. Picture [picture Egyptian; Picture of Imitative;
is like of eye] Ojibwa eye and pictographic
referent (American tears, to
Indian) mean grief
6. Pattern is 5 English; Five; Ideographic;
symbol of French; cinq; mathematical;
an idea German; fünf; symbolic;
etc. etc. numeric
_Mapping of Sounds_
7. Object [picture Possible Picture of Rebus-
pictured of knot] English a knot to writing;
has the mean “not” phonographic
wanted
sound
8. Pattern is [picture Ancient Sign for Syllable-
symbol for of star] Cypriote the writing
a large (island of syllable
sound unit Cyprus) _mu_
9. Pattern is Ʒ International The sound Phonetic
symbol for Phonetic _zh_, as writing
a small 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
of 26 of a
letters 5-word
title
11. Systematic 135-03-1228 Abbreviations, Social Numeric
combinations nomenclature, Security coding
of 10 digits etc. No. of
a person
12. Systematic ✓,✕,✕,✓,✓ Checking “yes,” Binary
combinations lists, “no,” coding
of 2 marks etc. “no,”
“yes,”
“yes,”
respectively
[2] The preceding word is the spoken word, not the written one.
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 PERM- ERAS- VERS-
NO. OBJECTS IN OR ON PRODUCED BY COST? SPACE? ANENT? 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, Pen ✓✓ ✓ ✓ ✕ ✓✓
parchment, and ink,
etc. pencil
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. Beads Rods in Hands ✓ ✓ ✓ ✓✓ ✕✕
a frame,
abacus
18. Ruled Rulers, Hands, ✓ ✓ ✓ ✓ ✓
lines, scales, pressure,
pointers dials etc.
_Machines_
19. Counter Desk Motor ✓ ✓ ✓ ✓✓ ✓
wheels, calculating and
gears, machines, hands
keys, fire-control
lights, instruments,
etc. etc.
20. Punched Punch card Motor ✓✓ ✓✓ ✓ ✕ ✓✓
cards machinery, and
and teletype, input
paper etc. instructions
tape
21. Relays Dial Motor ✕ ✓ ✓ ✓✓ ✓✓
telephone, and
other input
machinery instructions
22. Elect- Machinery Motor ✓ ✓ ✓ ✓✓ ✓✓
ronic and
tubes input
instructions
23. Magnetic Machinery Motor ✓✓ ✓✓ ✓✓ ✓✓ ✓✓
surfaces: and
wire, input
tape, instructions
discs
24. Delay Machinery Motor ✕ ✓ ✕ ✓✓ ✓✓
lines: and
electric, input
acoustic instructions
25. Electro- Machinery Motor ✕ ✓✓ ✕ ✓✓ ✓✓
static and
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.
[Illustration: 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.
[Illustration: 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.
[Illustration: TWO-HOLED TAPE READER: Simon’s left ear that listens to
numbers and operations.
FOUR-HOLED TAPE READER: Simon’s right ear that listens to instructions.
LIGHT BULBS: Simon’s eyes that wink answers.
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.
[Illustration: 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_|_c_
_a_ +————————— ————+————
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_+—————————
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.
[Illustration: S1-2 Relay energized]
[Illustration: S1-1 Relay not energized
FIG. 3. Register _S_1 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 (_C_1, _C_2, _C_3), 1 to store the operation governing the
computer (_C_4), and 1 to store the result (_C_5). 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 _S_1, _S_2, _S_3, ··· _S_8. 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 _S_1 hold the number 2 (see Fig. 3)? The number 2 in
machine language is 10. Register _S_1 consists of two relays, _S_1-2
and _S_1-1. 10 stored in register _S_1 means that relay _S_1-2 will be
energized and that relay _S_1-1 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 _C_5 into _O_
or, more briefly,
_C_5 → _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 _C_1 1010
_S_1 0010 _C_2 1011
_S_2 0011 _C_3 1100
_S_3 0100 _C_4 1101
_S_4 0101 _C_5 1110
_S_5 0110 _O_ 1111
_S_6 0111
_S_7 1000
_S_8 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, _C_5, 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_ → _C_4
_I_ → _C_1
_I_ → _C_2
_C_5 → _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.
[Illustration: 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 _C_5 the number 2 is stored. In
machine language this is 10. That means the left-hand relay (_C_5-2) is
energized and the right-hand relay (_C_5-1) 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
_C_5 register. The _C_5-2 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 _C_5-1 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 _C_5 register through the bus to the
coils of the _O_ register.
[Illustration: 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 _C_5 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 _C_5 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 _C_5 closed contacts; and
finally
7. Into the ground.
Thus relay _O_-2 is energized; it receives current because contact
_C_5-2 is closed. And relay _O_-1 is not energized; it receives no
current since contact _C_5-1 is open. So we have actually transferred
information from the _C_5 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 _C_1, _C_2, and _C_3 take in numbers 00, 01, 10, 11, that _C_4
takes in an operation 00, 01, 10, 11, and that _C_5 holds the result.
What process does Simon use so that he has the correct result in
register _C_5?
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 _C_1 register, and the operation 01 meaning negation goes into the
_C_4 register, and the correct result must be in the _C_5 register. So,
first, we note the fact that the _C_4-2 relay must not be energized,
since it contains 0, and that the _C_4-1 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 _C_1 register and if _c_ is in the _C_5 register,
then negation will be:
_C_1 | _C_5
—————+—————
00 | 00
01 | 11
10 | 10
11 | 01
But each of these registers _C_1, _C_5 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:
_C_1-2 _C_1-1 | _C_5-2 _C_5-1
——————————————+——————————————
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 _C_5-1 relay is energized
if and only if the _C_1-1 relay is energized. So, in order to energize
the _C_5-1 relay, all we have to do is transfer the information from
_C_1-1 to _C_5-1. 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.)
[Illustration: FIG. 6. Negation—right-hand digit.]
[Illustration: FIG. 7. Negation—left-hand digit.]
Taking another look at the table, we see also that the _C_5-2 relay
must be energized if and only if:
_C_1-2 AND _C_1-1
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 _C_5 relay coils if and only if the _C_4 relays hold
01.
[Illustration: FIG. 8. Negation circuit.]
Let us check this circuit. First, if there is any operation other than
01 stored in the _C_4 relays, then no current will be able to get
through the _C_4 contacts shown and into the _C_5 relay coils, and the
result is blank. Second, if we have the operation 01 stored in the _C_4
relays, then the _C_4-2 contacts will not be energized—a condition
which passes current—and the _C_4-1 contacts will be energized—another
condition which passes current—and:
IF THE NUMBER AND THE _C_5 RELAYS
IN _C_1 IS: THEN _C_1-1: AND _C_1-2: ENERGIZED ARE:
0 does not close does not close neither
1 closes does not close _C_5-2, _C_5-1
2 does not close closes _C_5-2 only
3 closes closes _C_5-1 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 (_C_1-2, _C_4-1, _C_4-2); 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.
[Illustration: FIG. 9. Addition circuit.]
[Illustration: 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 _C_1-1 (since _C_1
holds 01) and for _C_2-2 (since _C_2 holds 10). Then, when we trace
through the circuit, remembering that addition is stored as 00 in the
_C_4 relays, we find that both the _C_5 relays are energized. Hence
_C_5 holds 11, which is 3. Thus Simon can add 1 and 2 and make 3!
[Illustration: 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_, _S_1 to _S_8, _C_1 to _C_5, 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 _P_8, _P_4, _P_2, _P_1.
For example, if the _P_8 and _P_2 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 _C_1.
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 _C_5 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.
[Illustration: 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 _P_8 and _P_2 relays are energized. Then
this circuit energizes the _E_10 relay. The _E_10 relay closes the
contacts between the _C_1 relay coils and the bus; and so it connects
the _C_1 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 _m_oving _i_nput 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 _m_oving _p_rogram 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 _P_1 relay will probably not have enough poles to
meet all the need for its contacts.
[Illustration: 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
_C_5 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.
[Illustration: 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.
[Illustration: 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.
[Illustration: FIG. 3. Alphabetic punching.]
[Illustration: 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.
[Illustration: FIG. 5. Key punch.]
[Illustration: 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.
[Illustration: 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.
[Illustration: 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.
[Illustration: 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.
[Illustration: 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.
[Illustration: 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.
[Illustration: 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:
NO. OF
INFORMATION 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
[Illustration: 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.
[Illustration: 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.
[Illustration: 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.
[Illustration: 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_.
[Illustration: 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.
[Illustration: FIG. 1. Measurement by doorpost.]
[Illustration: FIG. 2. Measurement by string.]
[Illustration: FIG. 3. Slide Rule for adding.]
[Illustration: 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.
[Illustration: 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:
[Illustration: 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:
[Illustration: FIG. 7. Paths of a flight.]
[Illustration: 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_.
[Illustration: 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.
[Illustration: FIG. 10. Scheme of angle-indicator transmitter.]
[Illustration: FIG. 11. Indication of angle.]
[Illustration: 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 2_a_.
[Illustration: 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.
[Illustration: FIG. 14. Scheme of a doubling mechanism.]
[Illustration: 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.
[Illustration: 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.
[Illustration: FIG. 17. Scheme of an adder mechanism.]
[Illustration: 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.
[Illustration: 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.
[Illustration: 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.
[Illustration: 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).
[Illustration: 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.
[Illustration: 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_ = │_x d_│ │ _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 ⌠ 1
│ ———— _dy_ = log _y_, │ - ———— _d_(log _y_) = _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_
1
Then _Dₜy_ = —————, _D{_y} t_ = _x_,
_x_
⌠
and _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.
[Illustration: 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.
[Illustration: FIG. 2. Two-position switch.]
[Illustration: 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.
[Illustration: FIG. 4. Scheme of a ten-position relay, or counter
position.]
[Illustration: FIG. 5. Scheme of a counter wheel.]
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!
[Illustration: 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.
[Illustration: FIG. 7. Button.]
[Illustration: 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.
[Illustration: 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 0100 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.
[Illustration: 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_) = _x_³} 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 log_{10} 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
_h_² _h_³ _h_⁴
logₑ(1 + _h_) = _h_ - ———— + ———— - ———— + ···, │_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,
4.93724/4 = 1.23431
1.23431/1.2 = 1.02860
1.02860/1.02 = 1.00843
1.00843/1.008 = 1.00043
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
( _h_² _h_³ _h_⁴ _h_⁵ _h_⁶ )
log₁₀_e_ · (_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 _h_⁷/7, which is less than 10⁻²¹/7, since
_h_ < ¹/₁₀₀₀. The machine uses the series relation in the form
log₁₀ (1 + _h_) = {([{(_c_₆_h_ + _c_₅)_h_ + _c_₄}_h_
+ _c_₃]_h_ + _c_₂)_h_ + _c_₁}_h_
where
_c_₁ = _M_, _c_₂ = -_M_/2, _c_₃ = _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 NO. NAME (AND ADDITIONAL NAMES IN SOME CASES)
1 Initiating Unit
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
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.