JEHAN SHUMAN was used to dealing with the men in authori-
ty on long-embattled Earth. He was only a civilian but he
originated programming patterns that resulted in self-direct-
ing war computers of the highest sort. Generals consequent-
ly listened to him. Heads of congressional committees, too.
There was one of each in the special lounge of New
Pentagon. General Weider was space-burnt and had a small
mouth puckered almost into a cipher. Congressman Brant
was smooth-cheeked and clear-eyed. He smoked Denebian
tobacco with the air of one whose patriotism was so no-
torious, he could be allowed such liberties.
Shuman, tall, distinguished, and Programmer-first-class,
faced them fearlessly.
He said, "This, gentlemen, is Myron Aub."
"The one with the unusual gift that you discovered quite
by accident," said Congressman Brant placidly. "Ah." He
inspected the little man with the egg-bald head with amia-
ble curiosity.
The little man, in return, twisted the fingers of his hands
anxiously. He had never been near such great men before. He
was only an aging low-grade Technician who had long ago
failed all tests designed to smoke out the gifted ones among
mankind and had settled into the rut of unskilled labour.
There was just this hobby of his that the great Programmer
had found out about and was now making such a frightening
fuss over.
General Weider said, "I find this atmosphere of mystery
childish."
"You won't in a moment," said Shuman. "This is not some-
thing we can leak to the firstcomer.Aub!" There was some-
thing imperative about his manner of biting off that
one-syllable name, but then he was a great Programmer
speaking to a mere Technician. "Aub! How much is nine
times seven?"
Aub hesitated a moment. His pale eyes glimmered with a
feeble anxiety. "Sixty-three," he said.
Congressman Brant lifted his eyebrows. "Is that right?"
"Check it for yourself, Congressman."
The Congressman took out his pocket computer, nudged
the milled edges twice, looked at its face as it lay there in
the palm of his hand, and put it back. He said, "Is this the
gift you brought us here to demonstrate? An illusionist?"
"More than that, sir. Aub has memorized a few opera-
tions and with them he computes on paper."
"A paper computer?" said the general. He looked pained.
"No, sir," said Shuman patiently. "Not a paper comput-
er. Simply a sheet of paper. General, would you be so kind
as to suggest a number?"
"Seventeen," said the general.
"And you, Congressman?"
"Twenty-three."
"Good! Aub, multiply those numbers and please show the
gentlemen your manner of doing it."
"Yes, Programmer," said Aub, ducking his head. He fished
a small pad out of one shirt pocket and an artist's hairline
stylus out of the other. His forehead corrugated as he made
painstaking marks on the paper.
General Weider interrupted him sharply. "Let's see that."
Aub passed him the paper, and Weider said, "Well, it
looks like the figure seventeen."
Congressman Brant nodded and said, "So it does, but I
suppose anyone can copy figures off a computer. I think I
could make a passable seventeen myself, even without prac-
tice."
"If you will let Aub continue, gentlemen," said Shuman
without heat.
Aub continued, his hand trembling a little. Finally he said
in a low voice, "The answer is three hundred and ninety-
one."
Congressman Brant took out his computer a second time
and flicked it. "By Godfrey, so it is. How did he guess?"
"No guess, Congressman," said Shuman. "He computed
that result. He did it on this sheet of paper."
"Humbug," said the general impatiently. "A computer is
one thing and marks on paper are another."
"Explain, Aub," said Shuman.
"Yes, Programmer.Well, gentlemen, I write down seven-
teen and just underneath it, I write twenty-three. Next I say
to myself: seven times three"
The Congressman interrupted smoothly, "Now, Aub, the
problem is seventeen times twenty-three."
"Yes, I know," said the little Technician earnestly, "but I
start by saying seven times three because that's the way it
works. Now seven times three is twenty-one."
"And how do you know that?" asked the Congressman.
"I just remember it. It's always fwenty-one on the computer.
I've checked it any number of times."
"That doesn't mean it always will be though, does it?"
said the Congressman.
"Maybe not," stammered Aub. "I'm not a mathematician.
But I always get the right answers, you see."
"Go on."
"Seven times three is twenty-one, so I write down twenty-
one. Then one times three is three, so I write down a
three under the two of twenty-one."
"Why under the two?" asked Congressman Brant at once.
"Because" Aub looked helplessly at his superior for
support. "It's difficult to explain."
Shuman said, "If you will accept his work for the moment,
we can leave the details for the mathematicians."
Brant subsided.
Aub said, "Three plus two makes five, you see, so the
twenty-one becomes a fifty-one. Now you let that go for a
while and start fresh. You multiply seven and two, that's
fourteen, and one and two, that's two. Put them down like
this and it adds up to thirty-four. Now if you put the
thirty-four under the fifty-one this way and add them, you
get three hundred and ninety-one and that's the answer."
There was an instant's silence and then General Weider
said, "I don't believe it. He goes through this rigmarole and
makes up numbers and multiplies and adds them this way and
that, but I don't believe it. It's too complicated to be anything
but horn-swoggling."
"Oh no, sir," said Aub in a sweat. "It only seems compli-
cated because you're not used to it. Actually, the rules are
quite simple and will work for any numbers."
"Any numbers, eh?" said the general. "Come then." He
took out his own computer (a severely styled Gl model)
and struck it at random. Make a five seven three eight on
the paper. That's five thousand seven hundred and thirty-
eight."
"Yes, sir," said Aub, taking a new sheet of paper.
"Now," (more punching of his computer), "seven two three
nine. Seven thousand two hundred and thirty-nine."
"Yes, sir."
"And now multiply those two."
"It will take some time," quavered Aub.
"Take the time," said the general.
"Go ahead, Aub," said Shuman crisply.
Aub set to work, bending low. He took another sheet
of paper and another. The general took out his watch finally
and stared at it. "Are you through with your magic-making,
Technician?"
"I'm almost done, sir.Here it is, sir. Forty-one million,
five hundred and thirty-seven thousand, three hundred and
eighty-two." He showed the scrawled figures of the result.
General Weider smiled bitterly. He pushed the multiplica-
tion contact on his computer and let the numbers whirl to
a halt. And then he stared and said in a surprised squeak,
"Great Galaxy, the fella's right."
The President of the Terrestrial Federation had grown
haggard in office and, in private, he allowed a look of
settled melancholy to appear on his sensitive features. The
Denebian war, after its early start of vast movement and
great popularity, had trickled down into a sordid matter of
manoeuvre and countermanceuvre, with discontent rising stead-
ily on Earth. Possibly it was rising on Deneb, too.
And now Congressman Brant, head of the important Com-
mittee on Military Appropriations, was cheerfully and smooth-
ly spending his half-hour appointment spouting nonsense.
"Computing without a computer," said the president im-
patiently, "is a contradiction in terms."
"Computing," said the Congressman, "is only a system for
handling data. A machine might do it, or the human brain
might. Let me give you an example." And, using the new
skills he had learned, he worked out sums and products
until the president, despite himself, grew interested.
"Does this always work?"
"Every time, Mr. President. It is foolproof."
"Is it hard to learn?"
"It took me a week to get the real hang of it. I think you
would do better."
"Well," said the president, considering, "it's an interesting
parlour game, but what is the use of it?"
"What is the use of a newborn baby, Mr. President? At
the moment there is no use, but don't you see that this
points the way towards liberation from the machine. Consider,
Mr. President," the Congressman rose and his deep voice
automatically took on some of the cadences he used in public
debate, "that the Denebian war is a war of computer against
computer. Their computers forge an impenetrable field of
counter-missiles against our missiles, and ours forge one
against theirs. If we advance the efficiency of our comput-
ers, so do they theirs, and for five years a precarious and
profitless balance has existed.
"Now we have in our hands a method for going beyond
the computer, leapt rogging it, passing through it. We will
combine the mechanics of computation with human thought;
we will have the equivalent of intelligent computers; billions
of them. I can't prediet what the consequences will be in
detail but they will be incalculable. And if Deneb beats us to
the punch, they may be unimaginably catastrophic."
The president said, troubled, "What would you have me
do?"
"Put the power of the administration behind the establish-
ment of a secret project on human computation. Call it
Project Number, if you like. I can vouch for my committee,
but I will need the administration behind me."
"But how far can human computation go?"
"There is no limit. According to Programmer Shuman, who
first introduced me to this discovery"
"I've heard of Shuman, of course."
"Yes. Well, Dr. Shuman tells me that in theory there is
nothing the computer can do that the human mind cannot
do. The computer merely takes a finite amount of data and
performs a finite number of operations upon them. The hu-
man mind can duplicate the process."
The president considered that. He said, "If Shuman says
this, I am inclined to believe himin theory. But, in prac-
tice, how can anyone know how a computer works?"
Brant laughed genially. "Well, Mr. President, I asked the
same question. It seems that at one time computers were de-
signed directly by human beings. Those were simple compu-
ters, of course, this being before the time of the rational use of
computers to design more advanced computers had been es-
tablished."
"Yes, yes. Go on."
"Technican Aub apparently had, as his hobby, the recon-
struction of some of these ancient devices and in so doing he
studied the details of their workings and found he could im-
itate them. The multiplication I just performed for you is
an imitation of the workings of a computer."
"Amazing!"
The Congressman coughed gently, "If I may make another
point, Mr. President The further we can develop this
thing, the more we can divert our Federal effort from com-
puter production and computer maintenance. As the human
brain takes over, more of our energy can be directed into
peacetime pursuits and the impingement of war on the ordi-
nary man will be less. This will be more advantageous for
the party in power, of course."
"Ah," said the president, "I see your point. Well, sit down,
Congressman, sit down. I want some time to think about
this. But meanwhile, show me that multiplication trick
again. Let's see if I can't catch the point of it."
Programmer Shuman did not try to hurry matters. Loesser
was conservative, very conservative and liked to deal with
computers as his father and grandfather had. Still, he con-
trolled the West European computer combine, and if he could
be persuaded to join Project Number in full enthusiasm, a
great deal would be accomplished.
But Loesser was holding back. He said, "I'm not sure I
like the idea of relaxing our hold on computers. The human
mind is a capricious thing. The computer will give the same
answer to the same problem each time. What guarantee
have we that the human mind will do the same?"
"The human mind, Computer Loesser, only manipulates
facts. It doesn't matter whether the human mind or a machine
does it. They are just tools."
"Yes, yes. I've gone over your ingenious demonstration
that the mind can duplicate the computer, but it seems to me
a little in the air. I'll grant the theory but what reason have
we for thinking that theory can be converted to practice?"
"I think we have reason, sir. After all, computers have
not always existed. The cave men with their triremes, stone
axes, and railroads had no computers."
"And possibly they did not compute."
"You know better than that. Even the building of a rail-
road or a ziggurat called for some computing, and that must
have been without computers as we know them."
"Do you suggest they computed in the fashion you demon-
strate?"
"Probably not. After all, this methodwe call it 'graph-
itics,' by the way, from the old European word 'grapho'
meaning 'to write'is developed from the computers them-
selves so it cannot have antedated them. Still, the cave men
must have had some method, eh?"
"Lost arts! If you're going to talk about lost arts"
"No, no. I'm not a lost art enthusiast, though I don't say
there may not be some. After all, man was eating grain be-
fore hydroponics, and if the primitives ate grain, they must
have grown it in soil. What else could they have done?"
"I don't know, but I'll believe in soil-growing when I see
someone grow grain in soil. And I'll believe in making fire
by rubbing two pieces of flint together when I see that, too."
Shuman grew placative. "Well, let's stick to graphitics. It's
just part of the process of etherealization. Transportation by
means of bulky contrivances is giving way to direct mass
transference. Communications devices become less massive
and more efficient constantly. For that matter, compare your
pocket computer with the massive jobs of a thousand years
ago. Why not, then, the last step of doing away with com-
puters altogether? Come, sir. Project Number is a going con-
cern; progress is already headlong. But we want your help.
If patriotism doesn't move you, consider the intellectual ad-
venture involved."
Loesser said sceptically, "What progress? What can you do
beyond multiplication? Can you integrate a transcendental
function?"
"In time, sir. In time. In the last month I have learned
to handle division. I can determine, and correctly, integral
quotients and decimal quotients."
"Decimal quotients? To how many places?"
Programmer Shuman tried to keep his tone casual. "Any
number!"
Loesser's lower jaw dropped. "Without a computer?"
"Set me a problem."
"Divide twenty-seven by thirteen. Take it to six places."
Five minutes later, Shuman said, "Two point oh seven six
nine two three."
Loesser checked it. "Well, now, that's amazing. Mulitiplica-
tion didn't impress me too much because it involved in-
tegers after all, and I thought trick manipulation might do
it. But decimals"
"And that is not all. There is a new development that is,
so far, top secret and which strictly speaking, I ought not to
mention. Stillwe may have made a breakthrough on the
square root front."
"Square roots?"
"It involves some tricky points and we haven't licked the
bugs yet, but Technician Aub, the man who invented the
science and who has an amazing intuition in connection
with it, maintains he has the problem almost solved. And he
is only a Technician. A man like yourself, a trained and tal-
ented mathematician, ought to have no difficulty."
"Square roots," muttered Loesser, attracted.
"Cube roots, too. Are you with us?"
Loesser's hand thrust out suddenly. "Count me in."
General Weider stumped his way back and forth at the
head of the room and addressed his listeners after the fashion
of a savage teacher facing a group of recalcitrant students. It
made no difference to the general that they were the civilian
scientists heading Project Number. The general was the over-
all head, and he so considered himself at every waking mo-
ment.
He said, "Now square roots are all fine. I can't do them
myself and I don't understand the methods, but they're fine.
Still, the Project will not be sidetracked into what some
of you call the fundamentals. You can play with graphitics
any way you want to after the war is over, but right now we
have specific and very practical problems to solve."
In a far corner. Technician Aub listened with painful at-
tention. He was no longer a Technician, of course, having
been relieved of his duties and assigned to the project, with
a fine-sounding title and good pay. But, of course, the social
distinction remained and the highly placed scientific leaders
could never bring themselves to admit him to their ranks
on a footing of equality. Nor, to do Aub justice, did he,
himself, wish it. He was as uncomfortable with them as they
with him.
The general was saying, "Our goal is a simple one, gentle-
men: the replacement of the computer. A ship that can
navigate space without a computer on board can be con-
structed in one fifth the time and at one tenth the expense
of a computer-laden ship. We could build fleets five times,
ten times, as great as Deneb could if we could but eliminate
the computer.
"And I see something even beyond this. It may be fantastic
now, a mere dream; but in the future I see the manned
missile!"
There was an instant murmur from the audience.
The general drove on. "At the present time, our chief bot-
tleneck is the fact that missiles are limited in intelligence.
The computer controlling them can only be so large, and for
that reason they can meet the changing nature of anti-
missile defences in an unsatisfactory way. Few missiles, if
any, accomplish their goal and missle warfare is coming to
a dead end; for the enemy, fortunately, as well as for
ourselves.
"On the other hand, a missile with a man or two within,
controlling flight by graphitics, would be lighter, more mo-
bile, more intelligent. It would give us a lead that might
well mean the margin of victory. Besides which, gentlemen,
the exigencies of war compel us to remember one thing. A
man is much more dispensable than a computer. Manned
missiles could be launched in numbers and under circum-
stances that no good general would care to undertake as far
as computer-directed missiles are concerned"
He said much more but Technician Aub did not wait.
Technician Aub, in the privacy of his quarters, laboured
long over the note he was leaving behind. It read finally
as follows:
"When I began the study of what is now called graphitics,
it was no more than a hobby. I saw no more in it than an
interesting amusement, an exercise of mind.
"When Project Number began, I thought that others were
wiser than 1; that graphitics might be put to practical use
as a benefit to mankind, to aid in the production of really
practical mass-transference devices perhaps. But now I see
it to be used only for death and destruction.
"I cannot face the responsibility involved in having invent-
ed graphitics."
He then deliberately turned the focus of a prot,ein-depolar-
izer on himself and fell instantly and painlessly dead.
They stood over the grave of the little Technician while
tribute was paid to the greatness of his discovery.
Programmer Shuman bowed his head along with the rest
of them, but remained unmoved. The Technician had done
his share and was no longer needed, after all. He might
have started graphitics, but now that it had started, it would
carry on by itself overwhelmingly, triumphantly, until manned
missiles were possible, with who knew what else.
Nine times seven, thought Shuman with deep satisfaction,
is sixty-three, and I don't need a computer to tell me so.
The computer is in my own head.
And it was amazing the feeling of power that gave him.