"But perhaps you can hint that by seeing me they
may head off a campaign by Feingold and Martin to
strengthen the rights of robots further."
"Wouldn't that be a lie, Andrew?"
"Yes, Paul, and I can't tell one. That is why you
must call."
110
ISAAC ASIMOV
"Ah, you can't lie, but you can urge me to tell a lie,
is that it? You're getting more human all the time, An-
drew."
It was not easy to arrange, even with Paul's suppos-
edly weighted name.
But it was finally carried through and, when it was,
Harley Smythe-Robertson, who, on his mother's side,
was descended from the original founder of the corpo-
ration and who had adopted the hyphenation to indi-
cate it, looked remarkably unhappy. He was ap-
proaching retirement age and his entire tenure as
president had been devoted to the matter of robot
rights. His gray hair was plastered thinly over the top
of his scalp, his face was not made up, and he eyed
Andrew with brief hostility from time to time.
Andrew said, "Sir, nearly a century ago, I was told
by a Merton Mansky of this corporation that the
mathematics governing the plotting of the positronic
pathways was far too complicated to permit of any
but approximate solutions and that therefore my own
capacities were not fully predictable."
"That was a century ago." Smythe-Robertson hesi-
tated, then said icily, "Sir. It is true no longer. Our
robots are made with precision now and are trained
precisely to their jobs."
"Yes," said Paul, who had come along, as he said, to
make sure that the corporation played fair, "with the
result that my receptionist must be guided at every
point once events depart from the conventional, how-
ever slightly."
Smythe-Robertson said, "You would be much more
displeased if it were to improvise."
Andrew said, 'Then you no longer manufacture ro-
bots like myself that are flexible and adaptable."
OPUS 200 111
"No longer."
"The research I have done in connection with my
book," said Andrew, "indicates that I am the oldest
robot presently in active operation."
"The oldest presently," said Smythe-Robertson,
"and the oldest ever. The oldest that will ever be. No
robot is useful after the twenty-fifth year. They are
called in and replaced with newer models."
"No robot as presently manufactured is useful after
the twenty-fifth year," said Paul pleasantly. "Andrew
is quite exceptional in this respect."
Andrew, adhering to the path he had marked out
for himself, said, "As the oldest robot in the world and
the most flexible, am I not unusual enough to merit
special treatment from the company?"
"Not at all," said Smythe-Robertson freezingly.
"Your unusualness is an embarrassment to the com-
pany. If you were on lease, instead of having been a
sale outright through some mischance, you would long
since have been replaced."
"But that is exactly the point," said Andrew. "I am a
free robot and I own myself. Therefore I come to you
and ask you to replace me. You cannot do this without
the owner's consent. Nowadays, that consent is ex-
torted as a condition of the lease, but in my time this
did not happen."
Smythe-Robertson was looking both startled and
puzzled, and for a moment there was silence. Andrew
found himself staring at the holograph on the wall. It
was a death mask of Susan Calvin, patron saint of all
roboticists. She was dead nearly two centuries now,
but as a result of writing his book Andrew knew her
so well he could half persuade himself that he had
met her in life.
Smythe-Robertson said, "How can I replace you for
112
ISAAC ASIMOV
you? If I replace you as a robot, how can I donate the
new robot to you as owner since in the very act of
replacement you cease to exist?" He smiled grimly.
"Not at all difficult," interposed Paul. "The seat of
Andrew's personality is his positronic brain, and it is
the one part that cannot be replaced without creating
a new robot. The positronic brain, therefore, is An-
drew the owner. Every other part of the robotic body
can be replaced without affecting the robot's person-
ality, and those other parts are the brain's possessions.
Andrew, I should say, wants to supply his brain with
a new robotic body."
That's right," said Andrew calmly. He turned to
Smythe-Bobertson. "You have manufactured androids,
haven't you? Robots that have the outward appear-
ance of humans complete to the texture of the skin?"
Smythe-Robertson said, "Yes, we have. They
worked perfectly well, with their synthetic fibrous
skins and tendons. There was virtually no metal any-
where except for the brain, yet they were nearly as
tough as metal robots. They were tougher, weight for
weight"
Paul looked interested. **I didn't know that How
many are on the market?"
"None," said Smythe-Robertson. They were much
more expensive than metal models and a market sur-
vey showed they would not be accepted. They looked
too human."
Andrew said, "But the corporation retains its exper-
tise, I assume. Since it does, I wish to request that I
be replaced by an organic robot, an android."
Paul looked surprised. "Good Lord," he said.
Smythe-Bobertson stiffened. "Quite impossiblel"
"Why is it impossible?" asked Andrew. "I will pay
any reasonable fee, of course."
OPUS 200 113
Smythe-Robertson said, "We do not manufacture
androids."
"You do not choose to manufacture androids," inter-
posed Paul quickly. That is not the same as being
unable to manufacture them."
Smythe-Robertson said, "Nevertheless, the manu-
facture of androids is against public policy."
There is no law against it," said Paul.
"Nevertheless, we do not manufacture them, and we
will not."
Paul cleared his throat. "Mr. Smythe-Robertson," he
said, "Andrew is a free robot who is under the pur-
view of the law guaranteeing robots^ rights. You are
aware of this, I take it?"
"Only too well."
This robot, as a free robot, chooses to wear clothes.
This results in his being frequently humiliated by
thoughtless human beings despite the law against the
humiliation of robots. It is difficult to prosecute
vague offenses that don't meet with the general disap-
proval of those who must decide on guilt and inno-
cence."
"U. S. Robots understood that from the start. Your
father's firm unfortunately did not."
"My father is dead now," said Paul, "but what I see
is that we have here a clear offense with a clear tar-
get."
"What are you talking about?" said Smythe-
Robertson.
"My client. Andrew Martin—he has Just become my
client—is a free robot who is entitled to ask U. S. Ro-
bots and Mechanical Men, Inc., for the right of re-
placement, which the corporation supplies anyone
who owns a robot for more than twenty-five years. In
fact, the corporation insists on such replacement."
114
ISAAC ASIMOV
Paul was smiling and thoroughly at his ease. He
went on, 'The positronic brain of my client is the
owner of the body of my client—which is certainly
more than twenty-Bve years old. The positronic brain
demands the replacement of the body and offers to
pay any reasonable fee for an android body as that
replacement. If you-refuse the request, my client un-
dergoes humiliation and we will sue.
"While public opinion would not ordinarily support
the claim of a robot in such a case, may I remind you
that U. S. Robots is not popular with the public gen-
erally. Even those who most use and profit from ro-
bots are suspicious of the corporation. This may be a
hangover from the days when robots were widely
feared. It may be resentment against the power and
wealth of U. S. Robots, which has a worldwide mono-
poly. Whatever the cause may be, the resentment ex-
ists and I think you will find that you would prefer
not to withstand a lawsuit, particularly since my client
is wealthy and will live tor many more centuries and
will have no reason to refrain from fighting the battle
forever."
Smythe-Robertson had slowly reddened. "You are
trying to force me to—"
"I force you to do nothing," said Paul. "If you wish
to refuse to accede to my client's reasonable request,
you may by all means do so and we will leave without
another word . . . But we will sue, as is certainly our
right, and you will find that you will eventually
lose."
Smythe-Robertson said, "Well—" and paused.
"I see that you are going to accede," said Paul. "You
may hesitate but you will come to it in the end. Let
me assure you, then, of one further point. If, in the
process of transferring my client's positronic brain
OPUS 200
115
from his present body to an organic one, there is any
damage, however slight, then I will never rest till I've
nailed the corporation to the ground. I will, if neces-
sary, take every possible step to mobilize public opin-
ion against the coi-noration if one brain path of my
client's platinum-iridium essence is scrambled." He
turned to Andrew and said, "Do you agree to all this,
Andrew?"
Andrew hesitated a full minute. It amounted to the
approval of lying, of blackmail, of the badgering and
humiliation of a human bein^. But not physical harm,
he told himself, not physical harm.
He managed at last to come out with a rather faint
"Yes."
It was like being constructed again. For days, then for
weeks, finally for months, Andrew found himself not
himself somehow, and the simplest actions kept giving
rise to hesitation.
Paul was frantic. "They've damaged you, Andrew.
We'll have to institute suit."
Andrew spoke very slowly. "You mustn't. You'll
never be able to prove— something— m-m-m-m—"
"Malice?"
"Malice. Besides, I grow stronger, better. Ifs the tr-
tr-tr-"
Tremble?"
"Trauma. After all, there's never been such an op-
op-operation before."
Andrew could feel his brain from the inside. No one
else could. He knew he was well, and during the
months that it took him to learn full coordination and
full positronic interplay, he spent hours before the
mirror.
Not quite humani The face was stiff—too stiff—and
116
ISAAC ASIMOV
the motions were too deliberate. They lacked the care-
less free flow of the human being, but perhaps that
might come with time. At least he could wear clothes
without the ridiculous anomaly of a metal face going
along with it.
Eventually he said, "I will be going back to work."
Paul laughed and said, "That means you are well.
What will you be doing? Another book?"
"No," said Andrew seriously. "I live too long for any
one career to seize me by the throat and never let me
go. There was a time when I was primarily an artist
and I can still turn to that. And there was a time when
I was a historian and I can still turn to that. But now I
wish to be a robobiologist"
"A robopsychologist, you mean."
"No. That would imply the study of positronic
brains and at the moment I lack the desire to do that.
A robobiologist, it seems to me, would be concerned
with the working of the body attached to that brain."
"Wouldn't that be a roboticist?"
"A roboticist works with a metal body. I would be
studying an organic humanoid body, of which I have
the only one, as far as I know."
"You narrow your field," said Paul thoughtfully. "As
an artist, all conception was yours; as a historian, you
dealt chiefly with robots, as a robobiologist, you will
deal with yourself."
Andrew nodded. "It would seem so."
Andrew had to start from the very beginning, for he
knew nothing of ordinary biology, almost nothing of
science. He became a familiar sight in the libraries,
where he sat at the electronic indices for hours at a
time. looking perfectly normal in clothes. Those few
who knew he was a robot in no way interfered with
him.
OPUS 200
117
He built a laboratory in a room he had added to his
house, and his library grew, too.
Years passed, and Paul came to him one day and
said, "It's a pity you're no longer working on the his-
tory of robots. I understand U. S. Robots is adopting a
radically new policy,"
Paul had aged, and his deteriorating eyes had been
replaced with photoptic cells. In that respect, he had
drawn closer to Andrew. Andrew said, "What have
they done?"
"They are manufacturing central computers, gigan-
tic positronic brains, really, which communicate with
anywhere from a dozen to a thousand robots by mi-
crowave. The robots themselves have no brains at all.
They are the limbs of the gigantic brain, and the two
are physically separate.
"Is that more efficient?"
"U. S. Robots claims it is. Smythe-Robertson estab-
lished the new direction before he died, however, and
it's my notion that it's a backlash at you. U. S. Robots
is determined that they will make no robots that will
give them the type of trouble you have, and for that
reason they separate brain and body. The brain will
have no body to wish changed; the body will have no
brain to wish anything.
"It's amazing, Andrew," Paul went on, "the influ-
ence you have had on the history of robots. It was
your artistry that encouraged U. S. Robots to make
robots more precise and specialized; it was your freb-
dom that resulted in the establishment of the principle
of robotic rights; it was your insistence on an android
body that made U. S. Robots switch to brain-body
separation."
Andrew said, "I suppose in the end the corporation
will produce one vast brain controlling several billion
118
ISAAC ASIMOV
robotic bodies. All the eggs will be in one basket
Dangerous. Not proper at all."
"I think you're right," said Paul, "but I don't suspect
it will come to pass for a century at least, and I won't
live to see it. In fact, I may not live to see next year."
"Paul!" said Andrew in concern.
Paul shrugged. "We're mortal, Andrew. We're not
like you. It doesn't matter too much, but it does make
it important to assure you on one point. I'm the last ot
the human Martins. There are collaterals descended
from my great-aunt, but they don't count. The money
I control personally will be left to the trust in your
name, and, as far as anyone can foresee the future, you
will be economically secure."
"Unnecessary," said Andrew with difficulty. In all
this time, he could not get used to the deaths of the
Martins.
Paul said, "Let's not argue. That's the way it's going
to be. What are you working on?"
"I am designing a system for allowing androids—
myself—to gain energy from the combustion of hydro-
carbons, rather than from atomic cells."
Paul raised his eyebrows. "So that they will breathe
and eat?"
"Yes."
"How long have you been pushing in that direc-
tion?"
"For a long time now, but I think I have designed
an adequate combustion chamber for catalyzed con-
trolled breakdown."
"But why, Andrew? The atomic cell is surely infi-
nitely better."
"In some ways, perhaps, but the atomic cell is inhu-
man."
OPUS 200
119
It took time, but Andrew had time- In the first place,
he did not wish to do anything till Paul had died in
peace.
With the death of the great-grandson of Sir, Andrew
felt more nearly exposed to a hostile world, and for
that reason was the more determined to continue the
path he had long ago chosen.
Yet he was not really alone. If a man had died, the
firm of Feingold and Martin lived, for a corporation
does not die any more than a robot does. The firm
had its directions and it followed them soullessly. By
way of the trust and through the law firm, Andrew
continued to be wealthy. And in return for their own
large annual retainer, Feingold and Martin involved
themselves in the legal aspects of the new combustion
chamber.
When the time came for Andrew to visit U. S. Ro-
bots and Mechanical Men, Inc., he did it alone. Once
he had gone with Sir and once with Paul. This time,
the third tune, he was alone and manlike.
U. S. Robots had changed. The production plant
had been shifted to a large space station, as was the
case with more and more industries. With them had
gone many robots. The Earth itself was becoming
parktike, with its one-billion-person population stabi-
lized and perhaps not more than 30 percent of its at
least equally large robot population independently
brained.
The director of research was Alvin Magdescu, dark
of complexion and hair, with a little pointed beard
and wearing nothing above the waist but the breast-
band that fashion dictated. Andrew himself was well
covered in the older fashion of several decades back.
Magdescu said, "I know you, of course, and I'm
rather pleased to see you. You're our most notorious
120
ISAAC ASIMOV
product, and it's a pity old Smythe-Robertson was so
set against you. We could have done a great deal with
you."
"You still can," said Andrew.
"No, I don't think so. We're past the time. We*ve }iad
robots on Earth for over a century, but that's chang-
ing. It will be back to space with them and those that
stay here won't be brained."
"But there remains myself, and I stay on Earth."
'True, but there doesn't seem to be much of the ro-
bot about you. What new request have you?"
"To be still less a robot. Since I am so far organic, I
wish an organic source of energy. I have here the
plans—"
Magdescu did not hasten through them. He might
have intended to at Brst, but he stiffened and grew
intent. At one point he said, "This is remarkably ingeni-
ous. Who thought of all this?"
"I did." said Andrew.
Magdescu looked up at him sharply, then said, "It
would amount to a major overhaul of your body, and
an experimental one, since it has never been at-
tempted before. I advise against it Remain as you
are."
Andrew's face had limited means of expression, but
impatience showed plainly in his voice. "Dr. Mag-
descu, you miss the entire point. You have no choice
but to accede to my request. If such devices can be
built into my body, they can be built into human bod-
ies as well. The tendency to lengthen human life by
prosthetic devices has already been remarked on.
There are no devices better than the ones I have de-
signed and am designing.
"As it happens, I control the patents by way of the
6rm of Feingold and Martin. We are quite capable of
OPUS 200 121
going into business for ourselves and developing the
kind of prosthetic devices that may end by producing
human beings with many of the properties of robots.
Your own business will then suffer.
"If, however, you operate on me now and agree to
do so under similar circumstances in the future, you
will receive permission to make use of the patents and
control the technology of both robots and the prosthe-
tization of human beings. The initial leasing will not
be granted, of course, until after the first operation is
completed successfully, and after enough time has
passed to demonstrate that it is indeed successful."
Andrew felt scarcely any First Law inhibition to the
stern conditions he was setting a human being. He
was learning to reason that what seemed like cruelty
might, in the long run, be kindness.
Magdescu looked stunned. He said, "I'm not the one
to decide something like this. That's a corporate deci-
sion that would take time."
T can wait a reasonable time," said Andrew, "but
only a reasonable time." And he thought with satisfac-
tion that Paul himself could not have done it better.
It took only a reasonable time, and the operation was
a success.
Magdescu said, "I was very much against the opera-
tion, Andrew, but not for the reasons you might think.
I was not in the least against the experiment, if it had
been on someone else. I hated risking your positronic
brain. Now that you have the positronic pathways in-
teracting with simulated nerve pathways, it might be
difficult to rescue the brain intact if the body went
bad."
"I had every faith in the skill of the staff at U. S.
Robots." said Andrew. "And I can eat now."
122
ISAAC ASIMOV
"Well, you can sip olive oil. It will mean occasional
cleanings of the combustion chamber, as we have ex-
plained to you. Rather an uncomfortable touch, I
should think."
"Perhaps, if I did not expect to go further. Self-
cleaning is not impossible. In fact, I am working on a'
device that will deal with solid food that may be ex-
pected to contain incombustible fractions—indigestible
matter, so to speak, that will have to be discarded."
"You would then have to develop an anus."
*The equivalent."
"What else, Andrew?"
"Everything else."
"Genitalia, too?"
"Insofar as they will fit my plans. My body is a can-
vas on which I intend to draw—"
Magdescu waited for the sentence to be completed,
and when it seemed that it would not be, he com-
pleted it himself. "A man?"
"We shall see," said Andrew.
Magdescu said, "It's a puny ambition, Andrew.
You're better than a man. You've gone downhill from
the moment you opted for organicism."
"My brain has not suffered."
"No, it hasn't. I'll grant you that. But, Andrew, the
whole new breakthrough in prosthetic devices made
possible by your patents is being marketed under
your name. You're recognized as the inventor and
you're honored for it—as you are. Why play further
games with your body?"
Andrew did not answer.
The honors came. He accepted membership in sev-
eral learned societies, including one that was devoted
to the uew science he had established; the one he had
i
OPUS 200 123
called robobiology but which had come to be termed
prosthetology.
On the one hundred fiftieth anniversary of his con-
struction, there was a testimonial dinner given in his
honor at U. S. Robots. If Andrew saw irony in this, he
kept it to himself.
Alvm Magdescu came out of retirement to chair the
dinner. He was himself ninety-four years old and was
alive because he had prosthetized devices that, among
other things, fulfilled the function of liver and kid-
neys. The dinner reached its climax when Magdescu,
after a short and emotional talk, raised his glass to
toast "the Sesquicentennial Robot,"
Andrew had had the sinews of his face redesigned
to the point where he could show a range of emotions,
but he sat through all the ceremonies solemnly pas-
sive. He did not like to be a Sesquicentennial Robot.
It was prosthetology that finally took Andrew off the
Earth. In the decades that followed the celebration of
the Sesquicentennial, the Moon had come to be a
world more Earthlike than Earth in every respect but
its gravitational pull, and in its underground cities
there was a fairly dense population.
Prosthetized devices there had to take the lesser
gravity into account and Andrew spent five years on
the Moon working with local prosthetologists to make
the necessary adaptations. When not at his work, he
wandered among the robot population, every one of
which treated him with the robotic obsequiousness
due a man.
He came back to an Earth that was humdrum and
quiet by comparison and visited the offices of Fein-
gold and Martin to announce his return.
The current head of the firm, Simon DeLong, was
124
ISAAC ASIMOV
surprised. He said, "We had been told you were re-
turning, Andrew" (he had almost said "Mr. Martin"),
"but we were not expecting vou till next week."
"I grew impatient," said Andrew brusquely. He was
anxious to get to the point. "On the Moon, Simon, I
was in charge of a research team of twenty human
scientists. I gave orders that no one questioned. The
Lunar robots deferred td me as they would to a
human being. Why, then, am I not a human being?"
A wary look entered DeLong's eyes. He said, "My
dear Andrew, as you have just explained, you are
treated as a human being by both robots and human
beings. You are therefore a human being de facto."
"To be a human being de facto is not enough. I
want not only to be treated as one, but to be legally
identified as one. I want to be a human being de
jure."
"Now that is another matter," said DeLong. "There
we would run into human prejudice and into the un-
doubted fact that however much you may be like a
human being, you are not a human being."
"In what way not?" asked Andrew. "I have the
shape of a human being and organs equivalent to
those of a human being. My organs, in fact, are identi-
cal to some of those in a prosthetized human being. I
have contributed artistically, literarily, and scientifi-
cally to human culture as much as any human being
now alive. What more can one ask?"
"I myself would ask nothing more. The trouble is
that it would take an act of the World Legislature to
define you as a human being. Frankly, I wouldn't ex-
pect that to happen."
To whom on the Legislature could I speak?"
*To the chairman of the Science and Technology
Committee perhaps."
OPUS 200 125
"Can you arrange a meeting?"
"But you scarcely need an intermediary. In your po-
sition, you can—"
"No. You arrange it." (It didn't even occur to An-
drew that he was giving a flat order to a human
being. He had grown accustomed to that on the
Moon.) "I want him to know that the firm of Fein-
gold and Martin is backing me in this to the hilt."
"Well, now—"
"To the hilt, Simon. In one hundred seventy-three
years I have in one fashion or another contributed
greatly to this firm. I have been under obligation to
individual members of the firm in times past. I am
not now. It is rather the other way around now and I
am calling in my debts."
DeLong said, "I will do what I can."
The chairman of the Science and Technology Com-
mittee was of the East Asian region and she was a
woman. Her name was Chee Li-Hsing and lipr trans-
parent garments (obscuring what she wanted ob-
scured only by their dazzle) made her look plastic-
wrapped.
She said, "I sympathize with your wish for full hu-
man rights. There have been times in history when
segments of the human population fought for full hu-
man rights. What rights, however, can you possibly
want that you do not have?"
"As simple a thing as my right to life. A robot can
be dismantled at any time."
"A human being can be executed at any time."
"Execution can only follow due process of law.
There is no trial needed for my dismantling. Only the
word of a human being in authority is needed to end
me. Besides—besides—" Andrew tried desperately to
126 ISAAC ASIMOV
allow no sign of pleading, but his carefully designed
tricks of human expression and tone of voice betrayed
him here. "The truth is, I want to be a man. I have b,-
wanted it through six generations of human beings."
Li-Hsing looked up at him out of darkly sympa-
thetic eyes. "The Legislature can pass a law declaring'
you one—they could pass a law declaring a stone
statue to be defined as a man. Whether they will ac-
tually do so is, however, as likely in the first case as
the second. Congresspeople are as human as the rest
of the population, and there is always that element of
suspicion against robots."
"Even now?"
"Even now. We would all allow the fact that you
have earned the prize of humanity, and yet there
would remain the fear of setting an undesirable pre-
cedent."
"What precedent? I am the only free robot, the only
one of my type, and there will never be another. You
may consult U. S. Robots."
"'Never' is a long time, Andrew—or, if you prefer,
Mr. Martin—since I will gladiv give you my personal
accolade as man. You will find that most congress-
people will not be willing to set the precedent, no
matter how meaningless such a precedent might be.
Mr. Martin, you have my sympathy, but I cannot tell
you to hope. Indeed—"
She sat back and her forehead wrinkled. "Indeed, if
the issue grows too heated, there might well arise a
certain sentiment, both inside the Legislature and out-
side, for the dismantling you mentioned. Doing away
with you could turn out to be the easiest way of re-
solving the dilemma. Consider that before deciding to
push matters."
Andrew said, "Will no one remember the technique
OPUS 200 127
of prosthetology, something that is almost entirely
mine?"
"It may seem cruel, but they won't. Or if they do, it
will be remembered against you. It will be said you
did it only for yourself. It will be said it was part of a
campaign to roboticize human beings, or to humanity
robots; and in either case evil and vicious. You have
never been part of a political hate campaign, Mr.
Martin, and I tell vou that you will be the object of
vilification of a kind neither you nor I would credit,
and there would be people who'll believe it all. Mr.
Martin, let your life be." She rose and, next to An-
drew's seated figure, she seemed small and almost
childlike.
Andrew said, "If I decide to fight for my humanity,
will you be on my side?"
She thought, then said, "I will be—insofar as I can
be. If at any time such a stand would appear to
threaten my political future,-1 may have to abandon
you, since it is not an issue I feel to be at the very root
of my beliefs. I am trying to be honest with you."
"Thank you, and I will ask no more. I intend to
fight this through whatever the consequences, and I
will ask you for your help only for as long as you can
give it."
It was not a direct fight. Feingold and Martin coun-
seled patience and Andrew muttered grimly that he
had an endless supply of that. Feingold and Martin
then entered on a campaign to narrow and restrict the
area of combat.
They instituted a lawsuit denying the obligation to
pay debts to an individual with a prosthetic heart on
the grounds that the possession of a robotic organ re-
128
ISAAC ASIMOV
moved humanity, and with it the constitutional rights
of human beings.
They fought the matter skillfully and tenaciously,
losing at every step but always in such a way that the
decision was forced to be as broad as possible, and
then carrying it by way of appeals to the World Court.
It took years, and millions of dollars.
When the final decision was handed down, DeLong
held what amounted to a victory celebration over the
legal loss. Andrew was, of course, present in the com-
pany offices on the occasion.
"We've done two things, Andrew," said DeLong,
"both of which are good. First of all, we have estab-
lished the fact that no number of artifacts in the hu-
man body causes it to cease being a human body. Sec-
ondly, we have engaged public opinion in the
question in such a way as to put it fiercely on the side
of a broad interpretation of humanity since there is
not a human being in existence who does not hope for
prosthetics if that will keep him alive."
"And do you think the Legislature will now grant
me my humanity?" asked Andrew.
DeLong looked faintly uncomfortable. "As to that, I
cannot be optimistic. There remains the one organ
that the World Court has used as the criterion of hu-
manity. Human beings have an organic cellular brain
and robots have a platinum-iridium positronic brain if
they have one at all—and you certainly have a posi-
tronic brain . . . No, Andrew, don't get that look in
your eye. We lack the knowledge to duplicate the
work of a cellular brain in artificial structures close
enough to the organic type to allow it to fall within
the Court's decision. Not even you could do it"
"What should we do, then?"
"Make the attempt, of course. Congresswoman U-
OPUS 200 129
Hsing will be on our side and a growing number of
other congresspeople. The President will undoubtedly
go along with a majority of the Legislature m this
matter."
"Do we have a majority?"
"No, far from it. But we might get one if the public
will allow its desire for a broad interpretation of hu-
manity to extend to you. A small chance, I admit, but
if you do not wish to give up, we must gamble for it."
"I do not wish to give up."
Congresswoman Li-Hsing was considerably older
than she had been when Andrew had first met her.
Her transparent garments were long gone. Her hair
was now close-cropped and her coverings were tubu-
lar. Yet still Andrew clung, as closely as he could
within the limits of reasonable taste, to the style of
clothing that had prevailed when he had first adopted
clothing over a century before. ^
She said, "We've none as far as we can, Andrew.
We'll try once more after recess, but, to be honest, de-
feat is certain and the whole thing will have to be
given up. All mv most recent efforts have only earned
me a certain defeat in the coming congressional cam-
paign."
"I know," said Andrew, "and it distresses me. You
said once you would abandon me if it came to that.
Whv have you not done so?"
"One can change one's mind, you know. Somehow,
abandoning you became a higher price than I cared to
pav for just one more term. As it is, I've been in the
Legislature for over a quarter of a century. It's
enough."
"Is there no way we can change minds, Chee?"
"We've changed all that are amenable to reason.
130 ISAAC ASIMOV
The rest—the majority—cannot be moved from their
emotional antipathies."
"Emotional antipathy is not a valid reason for vot-
ing one way or the other."
"I know that, Andrew, but they don't advance emo-
tional antipathy as their reason."
Andrew said cautiously, "It all comes down to the
brain, then, but must we leave it at the level of cells
versus positrons? Is there no way of forcing a func-
tional definition? Must we say that a brain is made of
this or that? May we not say that a brain is something—
anything—capable of a certain level of thought?"
"Won't work," said Li-Hsing. "Your brain is man-
made, the human brain is not. Your brain is con-
structed, theirs developed. To any human being who is
intent on keeping up the barrier between himself and
a robot, those differences are a steel wall a mile high
and a mile thick."
"If we could get at the source of their antipathy—
the very source of—"
"After all your years," said Li-Hsing sadly, "you are
still trying to reason out the human being. Poor An-
drew, don't be angry, but it's the robot in you that
drives you in that direction."
"1 don't know," said Andrew. "If I could bring my-
self-"
If he could bring himself—
He had known for a long time it might come to
that. and in the end he was at the surgeon's. He found
one, skillful enough for the job at hand, which meant
a robot surgeon, for no human surgeon could be
trusted in this connection, either in ability or in inten-
tion,
The surgeon could not have performed the opera-
OPUS 200 131
tion on a human being, so Andrew, after putting off
the moment of decision with a sad line of questioning
that reflected the turmoil within himself, put the First
Law to one side by saying, "I, too, am a robot."
He then said, as firmly as he had learned to form
the words even at human beings over these past dec-
ades, "I order you to carry through the operation on
me."
In the absence of the First Law, an order so firmly
given from one who looked so much like a man acti-
vated the Second Law sufficiently to carry the day.
Andrew's feeling of weakness was, he was sure, quite
imaginary. He had recovered from the operation. Nev-
ertheless, he leaned, as unobtrusively as he could
manage, against the wall. It would be entirely too re-
vealing to sit.
Li-Hsing said, "The final vote will come this week,
Andrew. I've been able to delay it no longer, and we
must lose . . . And that will be it, Andrew."
Andrew said, "I am grateful for your skill at delay.
It gave me the time I needed, and I took the gamble I
had to."
"What gamble is this?*' asked Li-Hsing with open
concern.
"I couldn't tell you, or the people at Feingold and
Martin. I was sure I would be stopped. See here, if it
is the brain that is at issue, isn't the greatest differ-
ence of all the matter of immortality? Who really cares
what a brain looks like or is built of or how it was
formed? What matters is that brain cells die; must die.
Even if every other organ in the body is maintained or
replaced, the brain cells, which cannot be replaced
without changing and therefore killing the personal-
ity, must eventually die.
132
ISAAC ASIMOV
"My own positronic pathways have lasted nearly
two centuries without perceptible change and can last
for centuries more. Isn't that the fundamental bar-
rier? Human beings can tolerate an immortal robot,
for it doesn't matter how long a machine lasts. They
cannot tolerate an immortal human being, since their
own mortality is endurable only so long as it is univer-
sal. And for that reason they won't make me a human
being."
Li-Hsing said, "What is it you're leading up to, An-
drew ?"
"I have removed that problem. Decades ago, my
positronic brain was connected to organic nerves.
Now, one last operation has arranged that connection
in such a way that slowly—quite slowly—the potential
is being drained from my pathways."
Li-Hsing's finely wrinkled face showed no expres-
sion for a moment. Then her lips tightened. "Do you
mean you've arranged to die, Andrew? You can't have.
That violates the Third Law."
"No," said Andrew, "I have chosen between the
death of my body and the death of my aspirations and
desires. To have let my body live at the cost of the
greater death is what would have violated the Third
Law."
Li-Hsing seized his arm as though she were about
to shake him. She stopped herself. "Andrew, it won't
work. Change it back."
"It can't be. Too much damage was done. I have a
year to live—more or less. I will last through the hun-
dredth anniversay of my construction. I was weak
enough to arrange that."
"How can it be worth it? Andrew, you're a fool."
"If it brings me humanity, that will be worth it. If it
OPUS 200 133
doesn't, it will bring an end to striving, and that will
be worth it, too."
And Li-Hsing did something that astonished her-
self. Quietly, she began to weep.
It was odd how that last deed caught at the imagina-
tion of the world. All that Andrew had done before
had not swaved them. But he had finally accepted
even death in order to be human, and the sacrifice
was too great to be rejected.
The final ceremony was timed, quite deliberately,
for the two hundredth anniversary. The World Presi-
dent was to sign the act and make it law, and the cer-
emonv would be visible on a global network and
would be beamed to the Lunar state and even to the
Martian colon v.
Andrew was in a wheelchair. He could still walk,
but only shakily.
With mankind watching, the'Worid President said,
"Fifty years ago, vou were declared a Sesquicen-
tennial Robot, Andrew." After a pause, and in a more
solemn tone, he said, "Today we declare you a Bicen-
tennial Man, Mr. Martin."
And Andrew, smiling, held out his hand to shake
that of the President.
Andrew's thoughts were slowly fading as he lay in
bed.
Desperately he seized at them. Mani He was a man!
He wanted that to be his last thought. He wanted to
dissolve—die—with that.
He opened his eves one more time and for one last
time recognized Li-Hsing waiting solemnly. There were
others, but those were only shadows, unrecognizable
134
ISAAC ASIMOV
shadows. Only Li-Hsing stood out against the deepen-
ing gray. Slowly, inchingly, he held out his hand to her
and very dimly and faintly felt her take it.
She was fading in his eyes, as the last of his
thoughts trickled away. ,
But before she faded completely, one last fugitive
thought came to him and rested for a moment on his
mind before everything stopped.
"Little Miss," he whispered, too low to be heard.
PART 3
MATHEMATICS
It takes a lot of ingenuity for me to write about math-
ematics, since I know so little about it.
Why bother to write about it, then? Because I love
it, that's why. What I must do {and here is where the
ingenuity comes in) is find some portion of mathe-
matics so incredibly simple that I can understand it.
Once I've done that, all I have to do is write about it
in such a way (more ingenuity) that no one detects
my essential ignorance.
For children, I wrote How Did We Find Out About
Numbers? {Book 142), and in it I presented a section
on Roman numerals, which I had learned how to use
when I was seven or eight and which, fortunately, I
had never forgotten. Here it is:
from How DID WE FIND OUT ABOUT NUMBERS?
(1973)
About two thousand years ago, large sections of Eu-
rope, Asia, and Africa were ruled from the city of
Rome- The Roman Empire, as it was called, used a
system of numerals based on five.
The Romans used symbols taken from their alpha-
bet. Fortunately, the people of Europe and America
138
ISAAC ASIMOV
use the1 Roman alphabet so the Roman symbols are
familiar to us.
The Romans began by letting the number one be
written as I. For two, three, and four they had II, III,
and IIII. So far it looks like the Egyptian system, bilt
the Romans only allowed four of any symbol to be
used before inventing a new symbol. Instead of writ-
ing five as the Egyptian IIIII they wrote it as V.
Instead of writing six as IIIIII they wrote it VI.
Nine was VIIII. If they wrote ten as VIIIII, that
would mean five of the symbol I and they didn't al-
low that. They used a new symbol for ten, which was
X.
The list of symbols up to one thousand is as fol-
lows:
I == one
V = five
X == ten
L == fifty
C == one hundred
D = five hundred
M ^ one thousand
By using special symbols for five, fifty, and five
hundred, the Romans never had to use more than four
of any of the symbols for one. ten, or one hundred.
To write twenty-two they wrote XXII. Seventy-
three is LXXIII. Four hundred eighteen is
CCCCXVIII. One thousand nine hundred ninety-nine
IS MDCCCCLXXXXVIIII.
If you try to write one thousand nine hundred
ninety-nine by the Egyptian system, you would need
one symbol for thousand, and nine symbols each for
hundred, ten, and one. That would mean twenty-eight
OPUS 200 139
symbols all together. In Roman numerals only sixteen
symbols are needed.
The Egyptian system uses only four different kinds
of symbols, while the Roman system uses seven. In
the Roman system you need less counting but more
memorizinff.
When these Roman numerals were first developed,
it didn't matter in what order the symbols were
placed. Whether you wrote XVI or XIV or IXV or
VIX, it all came to sixteen. No matter in what order
you add ten, five, and one, you end up with sixteen.
Of course, it is easier to add up a number if you
arrange the symbols according to some convenient
system. The usual way is to put all the symbols of the
same sort together. The largest symbol is on the left
and as you move to the right you write down smaller
and smaller symbols. Thus seventy-eight would al-
ways be written LXXVIII, working down from L to X
to V to I.
The later Romans thought of a way of still further
decreasing the number of a particular symbol that
had to be written down. As long as symbols were al-
ways written from left to right and from large to
small, why not sometimes reverse the order?
When you put the smaller symbol after the larger
one in the usual way you add the two. Therefore, VI
is "five plus one," or six. If on the other hand you put
the smaller symbol before the larger one, you subtract
it from the larger. In this way IV is "five minus one,"
or four.
By writing four as IV instead of IIII you have to
write and read only two symbols instead of four, but
you have to notice the positions and remember to sub-
tract instead of add.
In the same way, XL is forty while LX is sixty and
140
ISAAC ASIMOV
XC is ninetv while CX is one hundred ten and CM is
nine hundred while MC is one thousand one hundred.
The vear nineteen seventy-three can be written
MCMLXXIII instead of MDCCCCLXXIII-eight
symbols instead of twelve. One thousand nine
hundred ninetv-nine can be written MCMXCIX in-
stead of MDCCCCLXXXXVIIH-seven symbols in-
stead of sixteen.
Of course, once vou start using the subtracting no-
tion, vou can't scramble the order of the symbols any-
more. It becomes important to place each symbol ex-
actly.
The western part of the Roman Empire broke up
|ust about one thousand five hundred years ago. The
people of western Europe kept on using Roman nu-
merals for more than seven hundred years after the
Roman Empire had come to an end.
If Roman numerals are easy to grasp and explain, Ara-
bic numerals are even easier, especially since every-
one in our culture over the age of six already knows
about them (or is supposed to}. That means I can un-
derstand them, too, and need only find some aspect of
them that isn't entirely familiar.
Suppose we let the Arabic numerals represent
larger and larger numbers. How can we represent
such very large numl}ers and where do we stop?
To answer questions like that, I have my F & SF
essays. My first F & SF essay appeared in the Novem-
ber 1958 issue, and since then I have continued them
at monthly intervals, without missing an issue, for
twenty years. Six collections of F & SF essays are in-
cluded among my first hundred books, but I did not
stop there. Among my second hundred books are
OPUS 200 141
seven more collections (plus four additional collec-
tions that included older F & SF essays, rearranged
and updated, from my first hundred books).
One of these new collections. Of Matters Great and
Small (Book 159), which Doubleday published in
1975, contains the following essay on very much larger
numbers:
"Skewered!" (1974)
I don't write many mathematical articles in this series,
and for a very good reason. I don't have a mathemati-
cal mind and I am not one of those who, by mere
thought, finds himself illuminated by a mathematical
concept.
I have, however, a nephew, Daniel Asimov by
name, who does have a mathematical mind. He is the
other Ph.D. in the family and he is now an Assistant
Professor of Mathematics at the University of Minne-
sota.
Some years ago, when he was yet a student at
M.I.T., Danny had occasion to write to Martin Gard-
ner and point out a small error in Gardner's excellent
"Mathematical Recreations" column in Scientific
American. Gardner acknowledged the error and wrote
me to tell me about it and to ask a natural question.
"Am I correct in assuming," said he, "that Daniel Asi-
mov is your son?"
Well! As everyone who knows me knows, I am only
a little past thirty right now and was only a little past
thirty at the time, some years ago, when this was tak-
ing place. I therefore wrote a letter to Gardner and
told him, with some stiff ness: "I am not old enough,
142
ISAAC ASIMOV
Martin, to have a son who is old enough to be going
to M.I.T. Dannv is the son of mv vounger brother."
Friends of mine who have heard me tell this story
keep assuring me that my statement involves a logical
contradiction, hut, as I sav, I do not have a mathemat-
ical mind, and I just don't see that.
And yet I must write another mathematical article
now because over eleven vears ago I wrote one in
which I mentioned Skewe-s* number as the largest fi-
nite number that ever showed up in a mathematical
proof.w Ever since then, people have been asking me
to write an article on Skewes" number. The first re-
quest came on September 3, 1963, almost immediately
after the article appeared. On that date, Mr. R. P.
Boas of Evanston, Illinois, wrote me a long and fasci-
nating letter on Skewes' number, with the clear inten-
tion of helping me write such an article.
I resisted that, along with repeated nudges from
others in the vears that followed, until March 3, 1974,
when, at Boskone 11 (a Boston science fiction con-
vention at which I was guest of honor), I was cor-
nered by a fan and had Skewes' number requested of
me- So I gave in. Eleven years of chivvying is
enough.! I am Skewered.
First, what is Skewes' number? Not the numerical
* See "T-Formation," reprinted in Adding a Dimension
(New York: Doubleday, 1964).
f 111 admit that I've been chivvied longer than that in some
respects. For seventeen years I have been requested, with
varying degrees of impatience, to write another U)e Baley
novel; and for over twenty years to write another Foundation
novel. So please don't anybody write letters that begin with
"If eleven years of chivvying is enough, why don't you——."
Because I'm doing all I can, that's why.
OPUS 200 143
expression, but the significance. Here's the story as I
got it from Mr. Boas (though I will paraphrase it, and
if I get anything wrong, it's my fault, not his).
It involves prime numbers, which are those num-
bers .that cannot be divided evenly by any number
other than themselves and one. The numbers 7 and 13
are examples.
There are an infinite number of prime numbers,
but as one goes up the list of numbers, the fraction of
these numbers that are prime decreases. There is a
formula that tells you the number of primes to be
found in the list of numbers up to a given number,
but like everything else about prime numbers, the for-
mula is not neat and definite. It only tells you approx-
imately how many primes there will be up to some
limiting number.
Up to the highest limit that has actually been
tested, it turns out that the actual number of primes
that exist is somewhat less than is predicted by the
formula.
In 1914, however, the British mathematician John
Edensor Littlewood demonstrated that if one length-
ened the string of numbers one investigated for
primes, one would find that up to some limits there
would indeed be less than the formula predicted, but
that up to other limits there would be more than the
formula predicted.
In fact. if one continued up the line of numbers for-
ever, the actual total number of primes would switch
from less than the formula prediction to more than the
formula prediction to less than the formula prediction,
and so on—and make the switch an infinite number of
times. If that were not so, Littlewood demonstrated,
there would be a contradiction in the mathematical
structure and that, of course, cannot be allowed.
144
ISAAC ASIMOV
The only trouble is that as far as we have actually
gone in the list of numbers, not even one shift has
taken place. The number of primes is always less than
the formula would indicate. Of course, mathemati-
cians might just go higher and higher up the list of
numbers to see what happens, but that isn't so easy.
The higher one goes, the longer it takes to test num-
bers for primehood.
However, it might be possible to do some theoreti-
cal work and determine some number below which
the first switch from less than the prediction to more
than the prediction must take place- That will at least
set a limit to the work required.
Littlewood set S. Skewes (pronounced in two sylla-
bles, by the way, Skew'ease) the task of finding that
number. Skewes found that number and it proved to
be enormously large; larger than any other number
that ever turned up in the course of a mathematical
proof up to that time, and it is this number that is
popularly known as "Skewes' number."
Mind you, the proof does not indicate that one must
reach Skewes' number before the number of primes
shifts from less than the prediction to more. The proof
merely says that some time before that number is
reached—perhaps long long before—the shift must
have occurred.
A number as large as Skewes' number is difficult to
write. Some shorthand device must be used and the
device used is the excellent one of exponential nota-
tion.
Thus, 1000 = 10 X 10 X 10, so 1000 can be written as
10s (ten to the third power), where the little 3 is
called an "exponent." The little 3 signifies that 1000
can be considered the product of three 10s, or that it
can be written as 1 followed by three zeros. In gen-
OPUS 200 145
eral, 10s (ten to the xth power) is the product of x 10s
and can be written as a 1 followed bv x zeros.
Since 10,000,000,000 is written as a 1 followed by 10
zeros, it can be written exponentially as 101" (ten to
the tenth power). In the same way, a 1 followed by
ten billion zeros, something that would be imprac-
tical to write, can be expressed exponentially as
lO10-"00-000-"'10 (ten to the ten billionth power). But
since ten billion is itself 1010, lo10.000.000.0"0 can be
written, even more briefly, as 101010.
Writing exponentials is always a strain when an arti-
cle is being written for a nonspecialized outlet- This is
especially so when one is forced to place exponents on
exponents. To avoid driving the Noble Printer crazy
and to make the notation look prettier, I have in-
vented a notation of my own. I make the exponent a
figure of normal size and it is as though it is being
held up by a lever, and its added weight when its size
grows bends the lever down. Thus, instead of writing
ten to the third power as 103, I will write it as
10\3.
In the same way, ten to the ten billionth power can
be written as 10\ 10,000,000,000 or as l0\10^10.
Using this "Asimovian exponential notation,"
Skewes' number becomes 10\10\,10\34.
Now let's see what Skewes' number might be in or-
dinary nonexponential notation. To do that, we must
consider the components of the exponential notation
from right to left. Starting at the right, we know what
34 is, we move leftward and consider 10'\34. This is
ten to the thirty-fourth power and can be written as a 1
followed by 34 zeros thus: 10,000,000,000,000,000,000,-
000,000,000.000,000, or, in words, ten decillion (Ameri-
can style). This means that Skewes' number can
146 ISAAC ASIMOV
be written ten 10\10\10,000,000,000,000.000,000.000,-
000,000,000,000.
So far, so good, if a bit disconcertingly formidable.
The next step is to move one place to the left and ask
how we might write: 10\ 10.000,000,000,000.000,000,-
000,000,000,000,000. Easy. You just put down a 1 and
then follow it by ten million billion billion billion
(or ten decillion, if you prefer) zeros.
If vou were to try to write such a number by begin-
ning with a 1 and then writing ten decillion zeros,
each the size of a hydrogen atom, you would require
nearly exactly the entire surface of the Earth to write
the number. Furthermore, if you wrote each zero in a
trillionth of a second and kept it up at that rate with-
out cessation, it would take a thousand trillion years
to write the entire number.
Anyway, let's call this number the "Earth-number,"
because it takes the Earth as a blackboard to write it.
and imagine that we can write it. Now we can write
Skewes' number as 10\ Earth-number, and this means
we now know how to write Skewes' number in the
usual fashion. We start with a one and then follow it
with an Earth-number of zeros.
This is tremendously more than the ten decillion ze-
ros it took merely to write the Earth-number. A num-
ber itself is much greater than the number of zeros it
takes to write it. It takes only one zero to write 10, but
the result is a number that is ten times greater than
the number ^>f zeros required to write it. In the same
way it takes ten zeros to write 10,000,000,000, but the
number written is ten billion, which is a billion times
greater in size than the number of zeros used to write
it.
Similarly it takes only ten decillion zeros to write
OPUS 200 147
the Earth-number, but the Earth-number itself is
enormously greater than that number or zeros.
To write not ten decillion zeros, but an Earth-
number of zeros, would require far more than the sur-
faces of all the objects in the known universe, even
with each zero the size of a hydrogen atom. A trillion
such universes as ours might suffice, and that is just
to write the Earth-number in a one followed by zeros.
Skewes' number itself, written by a one followed by
an Earth-number of zeros, is enormousiy, ENORMOUSLY
greater than the Earth-number tliat suffices to count
those zeros.
So let's forget about counting zeros; that will get us
nowhere. And if we abandon counting zeros, we don't
need to have our exponents as integers. Every number
can be expressed as a power of ten if we allow deci-
mal exponents. For instance, by using a logarithm ta-
ble, we can see that 34=10\1.53. So instead of writ-
ing Skewes' number as 10^10^10^34, we can write
it as 10\10'\10\10\1.53. (Such fractional expo-
nents are almost always only approximate, however.)
There are some advantages to stretching out the
large numbers into as many tens as is required to
make the rightmost number fall below ten. Then we
can speak of a "single-ten number," a "double-ten
number," a "triple-ten number," and so on. Skewes'
number is a "quadrupie-ten number."
We can't count objects and reach Skewes' number in
any visualizable way. Counting zeros is no help either.
Let us instead try to count permutations and combi-
nations,
Let me give you an example. In the ordinary deck
of cards used to play bridge, there are fifty-two dif-
ferent cards. (The number 52 is itself a single-ten
148
ISAAC ASIMOV
number, as are all the numbers between 10 and
10,000,000,000; 52^10\1.716.)
In the game of bridge, each of four people is dealt
thirteen cards. A player can, with equal probability,
get any combination of thirteen cards, and tlie order
in which he gets them doesn't matter. He rearranges
that order to suit himself. The total number of differ-
ent hands lie can get by receiving anv thirteen cards
out of tlie fifty-two (and I won't bother vou with how
it i.s calculated) is about 635.000,000,000. Since this
number is higher than ten billion, we can be sure it is
beyond tlie single-ten-number stage. Exponentially, it
can lie expressed as 6.35X10\11. Logarithms can
help us remove that multiplier and put its value into
the exponent at the cost of making that exponent a
decimal. Thus 6.35 X10\.11= 10\11.80. Since 11.80 is
over ten, we can express that, exponentially, as
11.80 = 10'\1.07.
Consequently, we can sav that the total number of
different hands a single bridge plaver can hold is
10'\10\J..07. Using onlv thirteen cards, we have, in a
perfectly understandable way, reached a double-ten
number. We might almost feel that we were halfway
to the quadruple-ten number that is Skewes*.
So let's take all fifty-two cards and let's arrange to
have the order count as well as the nature of the
cards. You begin with a deck in which tlie cards are-in
a certain order. You shuffle it and end witli a differ-
ent order. You shuffle it again and end with yet an-
other order. How many different orders are there?
Remember that any difference in order, however
small, makes a different order. If two orders arc iden-
tical except for the interchange of two adjacent cards,
they are two different orders.
To answer that Question, we figure that the first
OPUS 200 149
card can be any of the fiftv-two, the second any of the
remaining fifty-one, the third any of the remaining
fifty, and so on. The total number of different orders
is52X51X50X . . . 4X3X2X1, In other words, the
number of different orders is equal to the product of
the first fifty-two numbers. This is called "factorial
fifty-two" and can be written "521"
The value of 52! is, roughly, a one followed by
sixty-eight zeros; in other words, a hundred decillion
deciltion. (You are welcome to work out the multipli-
cation if you doubt this, but if you try, please be pre-
pared for a long haul.) This is an absolutely terrific
number to get out of one ordinary deck of cards that
most of us use constantly without any feeling of being
overwhelmed. The number of different orders into
which that ordinary deck can be placed is about ten
times as great as all the subatomic particles in our en-
tire Milky Way galaxy.
It would certainly seem that'if making use of thir-
teen cards with order indifferent lifted us high up.
making use of all fifty-two and letting order count
"will do much better still—until we try our exponential
notation. The number of orders into which fifty-two
different cards can be placed is 10\68 == 10\10\1.83.
That may strike you as strange. The number of or-
ders of fifty-two cards is something like a trillion tril-
lion decillion times higher tlian the number of bridge
hands of thirteen cards; yet, while the latter is
10\10\1.07, the former is only 10\10\1.83. Were
still in the "double-ten numbers" and we haven't even
moved up much,
The trouble is that the more tens we add to such
exponential numbers, the harder it is to move that
rightmost component. For instance, a trillion is ten
times as great as a hundred billion, and counting a
150
ISAAC ASIMOV
trillion objects would be an enormously greater task
than counting a hundred billion. Write tliem exponen-
tially, however, and it is 10\.12 as compared with
10\11, and the rightmost components are only a unit
apart. Write the twelve and the eleven as powers of
ten so that vou can make use of double-ten numbers,
and a trillion becomes 10\10\1.08, while a hundred
billion is 10\10\1.04 and the difference is scarcely
noticeable.
Or put it another way. The number'10\3 (which is
1000) is ten times as high as 10\2 (which is 100),
but the degree to which 10\10\3 is greater than
10\10\2 would require a 1 followed by 900 zeros to
be expressed. As for comparing -10\10\10\3 and
10\10\10\2, I leave that to you.
This is disheartening. Perhaps reaching the
quadruple-ten numbers won't be that easy after all.
Let's try one more trick with fifty-two cards. Sup-
pose each of the cards can be any card at all. Suppose
the deck can have two tens of diamonds or three aces
of clubs, or, for that matter, fifty-two threes of hearts.
The total number of orders of such a chameleonic
deck could be calculated by imagining that the first
card could be any one of fifty-two, and the second
card could be any one of fifty-two, and so on for all
fifty-two. To calculate the number of different orders,
you would have to take the product of
52 X 52 X 52 X ... 52 X 52 X 52; fifty-two 52s. This
product which could be written 52\52 I might call
"superfactorial fifty-two," but if so, I would be using
a term I have just made up, so don't blame the mathe-
maticians.
Superfactorials are immensely larger than factorials.
Factorial fifty-two can be expressed by a one fol-
lowed by sixty-eight zeros, but superfactorial fifty-
OPUS 200 151
two is one followed by ninety zeros—ten billion tril-
lion times higher. Yet express it exponentially and
superfactorial 52 == 10\90 = 10\10'\1.95.
No good. We're still in the double-ten numbers.
Well just have to forget playing cards. We must
have more than fifty-two units to play with, and we
had better go all the way up; all the way up.
A generation or so ago, the British astronomer Ar-
thur S, Eddington calculated that the total number of
electrons, protons, and neutrons in the universe was
10\79, or 10\10\1.90. This number is arrived at if
we suppose that the sun is an average star, that there
are about a hundred billion stars in the average gal-
axy, and that there are a hundred billion galaxies in
the universe.
In addition to electrons, protons, and neutrons, of
course, there are numbers of unstable particles un-
known to Eddington, but their numbers are compara-
tively few. There are, liowever, massless particles such
as neutrinos, photons, and gravitons, which do not gen-
erally behave like particles but which are very numer-
ous in the universe.
If we wisli, we can suppose that the number of
massless particles speeding through space at any time
is nine times the number of massed particles (proba-
bly a grievous overestimate) and make the total num-
ber of subatomic particles in the universe 10\80, or
10\IO\1.903.
Now, at least, we are starting with a double-ten
number and that ought to do it. Skewes' number, here
we come. All we have to do is take the superfactorial
of ,10\.80, something we can express as
(l0\80)\(10\80).
Working tliat out (and I hope I'm doing it cor-
rectly), we get 10\10\81.9, or 10\10\10\1.91.
152
ISAAC ASIMOV
And that lifts us into the "triple-ten numbers" for
the first time. In fact, if we compare the superfac-
torial of the total number of subatomic particles in the
universe (which is IO'VIO'YIO^I.91) -with Skewes*
number (which, as a triple-ten number, ' is
IOVIO^JOV.34), we might think we were almost
there.
We need to begin with something more than the
number of subatomic particles in the universe—how
about the amount of space in the universe?
The smallest unit of space we can conveniently deal
with is the volume of a neutron, a tiny globe that is
about 10'\ —13 centimeters in diameter, or one ten-
trillionth of a centimeter.
The observable universe has a radius of 12.5 bil-
lion light-years, or 1.25 X 10\10 light-years, and
each light-year is equal to just under 10\l3 kilo-
meters. Hence, the observable universe has a ra-
dius of roughly 10\23 kilometers. Since 1 kilo-
meter = 100,000, or 10\5, centimeters, the observable
universe has a radius of roughly 10X28 centimeters.
From this we can calculate the volume of the observ-
able universe to be roughly equal to 4.2 X 10\84 cubic
centimeters.
A neutron, with a diameter of ION.—13 centimeters,
has a volume that is equal to roughly 5 X 10\ — 40 cu-
bic centimeters. That means that the volume of the
observable universe is -roughly 2XlO\124, or
10\.124.3 times the volume of a single neutron.
Suppose we call the volume of space equal to that
of a neutron a "vacuon." We can then say that there
are 10X124.3 vacuous in the universe and call that the
"vacuon-number."
The vacuon-number is nearly a billion billion bil-
OPUS 200 153
lion billion billion times greater than the number of
subatomic particles in the universe, so we can feel
pretty confident about the superfactorial of the
vacuon-number, which is (10^124.3)^(10^124.3).
except that this comes out to 10\10\1Q\2.10...
Despite the vastly greater quantity of empty space
than of matter in the universe, -the rightmost compo-
nent of the triple-ten number went up only from 1.91
to 2.10, with 34 as the goal. That's enough to depress
us, but wait-
In considering the number of vacuons in the uni-
verse, we imagined it as existing at a moment in time.
But time moves, and the universe changes. A sub-
atomic particle that occupies one place at one moment
may occupy another place at another moment. The
most rapidly moving particles are, of course, the mass-
less ones which move at the speed of light.
The speed of light is Just about 3 X 10'\10 centime-
ters per second, and the smallest distance one can
move with some significance is the diameter of a neu-
tron, which is 10\ —13 centimeters. A photon will
flash the width of a neutron, then, in about
3 X 10\ —24 seconds. We can consider this the small-
est unit of time that has physical meaning and call it
the "chronon."0
To imagine a long period of time, let's consider
what we can call the "cosmic cycle," one period of ex-
pansion and contraction of the universe (assuming it
is oscillating). Some have guessed the length of the
cosmic cycle to be 80,000,000,000, or 8 X 10\10, years.
* Stanley G. Weinbaum once imagined ;>pace and time
quantized in this fashion in one of his science fiction stories
and med the word "chronoii" for his ultimate particle of
time.
154
ISAAC ASIMOV
The number of chronons in one cosmic cycle, then,
is roughly l0\42.
In every chronon of time, the universe is slightly
different from what it was in the preceding chronon
or what it will be in the next chronon, because,'if
nothing else, every free-moving photon, neutrino, and
graviton has shifted its position by the width of one
neutron in some direction or other with each chronon
that passes.
Therefore we might consider the total number of
vacuons not only in the present universe, but also in
the one that existed in the last chronon, the one that
will exist in the next chronon, and, in general, all the
universes in all the chronons through a cosmic cycle,
(To be sure, the expansion and contraction of the uni-
verse alters its vacuon content—these increasing in
number with expansion and decreasing with contrac-
tion—but we can suppose that the present size of the
universe is about average.)
In that case, then, the total number of vacuons
through every chronon of the cosmic cycle is just
about l<r\ 166.3. What this means is that if you wish
to place a proton somewhere in the universe at some
instant in time, you have (under the conditions I've
described-) a choice of 10'\166.3 different positions.
But if you take the superfactorial of this enor-
mous "total-vacuon number," you end up with
10\10\10\2.27.
We have hardly moved. I Just can't seem to move
those triple-ten numbers and make progress toward
Skewes* number. I am Skewered.
In fact, it's worse tlian that. According to Mr. Boas,
Skewes' determination of Skewes' number depended
on the supposition that something called the "Rie-
OPUS 200 155
mann- hypothesis" is true. It probably is, but no one
has proved it to be so.
In 1955 Skewes published a paper in which he cal-
culated the value of the number below which the
number of primes must be higher at some point than
the formula would predict, if the Riemann hypothesis
were not true.
tt turns out _that the Riemann-hypothesis-not-true
case yields a number that is far higher than Skewes'
number. The new number, Or what I suggest we call
the Super-Skewes number, is 10\10\10\1000, or
10\10\10\10\3.
The Super-Skewes number and Skewes' number are
both quadruple-ten numbers-10\10\10\10\3 and
10\10\10\10\1.53 respectively-and the differ-
ence in the rightmost component seems to be small.
However, vou saw what difficulty there was in budg-
ing the triple-ten numbers upward. Well, moving the
quadruple-ten numbers upward is far harder still, and
Skewes' number is virtually zero in comparison to the
Super-Skewes number.
If I had reached Skewes' number, I would still have
had the Super-Skewes number ahead of me. I would
have been Super-Skewered.
PART 4
PHYSICS
My major work, as far as physics is concerned, is my
three-volume Understanding Phvsics, which is in-
cluded among my first hundred books. Once that was
done, there was little I could do in physics but forage
about the edges of the subject and approach a differ-
ent audience.
Among the small books for eight-year-olds that I
wrote for Follett, and mentioned earlier, there is one
book on physics— Light (Boo^ 208). From that book,
here is the description of the spectrum:
from LIGHT (1970)
Light energy comes out of atoms in tiny amounts
called photons." Different kinds of atoms give off
different kinds of photons; each kind carries a differ-
ent amount of energy.
Photons of light are said to move up and down rap-
idly as they speed outward. Scientists think of them as
speeding along in a wavy motion. Photons travel as
"light waves."
The photons in light cause our eyes to see certain
colors. Certain low-energy photons make us see the
color red. Those with a little more energy make us see
160 ISAAC ASIMOV
orange. With still a little more energy we see yellow
. . . then green . . . then blue, and finally violet.
Sunlight is made up of different kinds of light
waves. Each kind has its own length, its own kind of
photons, and its own amount of energy. The light
waves in a sunbeam can be spread out separately. A
special piece of glass with three flat sides will do this.
Such a piece of glass is called a "prism."
When separated light from a prism falls on a white
wall, vou can see a band of assorted colors. These are
made by the sorted-out light waves. Those having the
lowest energy cause you to see the red at one end of
the band. Those having the highest energy cause you
to see violet at the other end. You can also see other
colors in between. A beautiful band is made when
you separate the light waves in sunlight. It is called
the "solar spectrum." Other kinds of light give differ-
ent spectrum patterns.
A rainbow looks like a spectrum because it is a
spectrum. After a rainstorm, the air is still filled with
tiny droplets of water. Each droplet acts like a prism.
When the sun comes out and shines through the drop-
lets, the photons are sorted out. Then we see a rain-
bow, a spectrum in the sky.
Back in 1966, the editor of Science Digest asked if I
would do a small item for him. The magazine had a
department called "Please Explain," in which readers'
questions were answered. One question was a poser
that dealt with how often body cells are replaced..
Knowing the answer wasn't enough; it had to be
given in five hundred words and made both thorough
and clear. Being a cheerful idiot not much given to
worry and introspection, 1 undertook to answer the
OPUS 200 161
question for a reasonably small sum and did so. My
essay was published in the June 1966 issue of the
magazine.
What followed was absolutely predictable—which
doesn't mean to say that I predicted it, for I am often
thoroughly astonished when the predictable comes to
pass. In a couple of months, the magazine asked me to
do another essay on another catchy question, then an-
other, and another, and before the year was out, I
found that what I was doing was, in effect, a monthly
column.
I was fust getting ready to ask the editor if that was
what he really had in mind, when I received an issue
of the magazine in which the department was no
longer headed "Please Explain"; it had become "Isaac
Asimov Explains." That made it clear to the meanest
intelligence (meaning mine, for instance} that indeed
it was a column 1 was writing.
The column continued for over nine years before I
managed to get out of it. In 1974, there was a change
of editor, and when the new editor told me he wanted
to reorganize the magazine, I promptly asked him if
he wanted to end the column. He did.
I didn't consider it a tragic event, because I had
completed a goal I had set myself some years before, I
had written a hundred of these essays, and it had
been my intention to put the essays into book form
once a hundred of them had been done.
Houghton Mifflin published the collection in 1973 as
Please Explain (Book 143). Here are three selections
dealing with physics:
162 ISAAC AS1MOV
from PLEASE EXPLAIN (2973)
What is the speed of gravitation?
A longer but perhaps clearer way of putting the ques-
tion is this: Suppose the sun suddenly ceased to exist
and vanished into nothingness. How long would it be
before the earth would cease to be held by its gravita-
tional field?
A similar question might be: How long after the
sun disappears would the earth cease receiving its
light?
We know the answer to the second question quite
well. We know that the sun is just under 93 million
miles from earth and we also know that light travels
at 186,282 miles per second through a vacuum. The
last bit of light leaving the sun, just before it disap-
peared, would take 8.3 minutes to reach the earth. In
other words, we would see the sun disappear 8.3 min-
utes after it really disappeared.
The reason it is easy to answer the question about
light is that there are a number of ways of actually
measuring the speed at which light travels. These
measurements are made practical by our ability to de-
tect changes in the very faint light emitted by a dis-
tant heavenly body, and by our own ability to pro-
duce quite strong beams of light.
We don't have these advantages with gravitational
fields. It is very difficult to study faint changes in
weak gravitational fields, and we can't produce strong
gravitational effects extending over long distances
here on earth.
So we have to fall back on theory. There are four
types of interactions known in the universe: (1)
OPUS 200
163
v
strong nuclear, (2) weak nuclear, (3) electromag-
netic, and (4) gravitational. Of these, the first two are
short-range, falling off very rapidly with distance. At
distances greater than the width of an atomic nucleus,
the nuclear interactions are so weak they can be ig-
nored. The electromagnetic and gravitational interac-
tions are long-range, however. They fall off only at
the square of the distance. This means they can make
themselves felt even over astronomical distances.
Physicists believe that everv interaction between
two bodies takes place through the exchange of sub-
atomic particles. The more massive the exchange parti-
cle, the shorter-ranged the interaction. Thus, the
strong nuclear interaction results from the exchange of
pions, which are 270 times as massive as electrons.
The weak nuclear interaction results from the ex-
change of even more massive W-particles (which
haven't been detected yet, by the way).
If an exchange particle has no mass at all, then the
interaction is as long-range as possible, and this is the
case with the electromagnetic interaction. The ex-
change particle there is the massless photon. A stream
of such massless photons makes up a beam of light or