October 3, 2025 • 30 mins
A surreal sci-fi series exploring speculative concepts, dreams, and philosophical what-ifs. Each episode is a cerebral journey into the mind’s deepest questions.
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Speaker 1 (00:39):
Mine. Well, welcome to a half hour of mind Way
short Stories.
Speaker 2 (01:00):
Roads of speculative fiction.
Speaker 3 (01:12):
This is Michael Hanson, this time with a Stanley Weinbaum
story copyright nineteen thirty six by Better Publications Incorporated, entitled
The Brink of Infinity. One would hardly choose the life
of an assistant professor of mathematics at an Eastern university
(01:33):
is an adventurous one. Professors in general are reputed to
drown out of quiet, scholarly existence, and an instructor of
mathematics might seem the driest and least lively of men,
since the subject is perhaps the most desiccated. And yet
even the lifeless science of figures has added its dreamers Clerk, Maxwell, Obachevsky, Einstein.
Speaker 1 (01:51):
And the rest.
Speaker 3 (01:52):
And don't forget that Alice in Wonderland was written by
a dreamer who happened also to be a mathematician. Not
that I class myself for them. I'm practical enough to
leave fantasies alone. Teaching is my business. At least teaching
is my main business. I do a little statistical work
for investrial corporations when the occasion presents itself. In fact,
(02:13):
you'll find my name in the classified section. Abner Errand's
statistician and consulting mathematician. I eek out my professional salary,
and I do at time strike something interesting. Of course,
in the main such work consists of graphic trends of
consumption for manufacturers, of population increase for public utilities, and
occasionally some up and coming advertising agency will consult me.
(02:36):
Not exactly exciting work, but it helps financially, so I
was not particularly surprised that July morning to receive a call.
The university had been closed for several weeks. The summer
session was about to open without, however, the benefit of
my presence. I was taking a vacation. Even the modest
holiday I planned canvite deeply enough into the financial foundation
(02:58):
of an assistant professor's put. The work sounded like one
of those fairly lucrative and rather simple propositions.
Speaker 1 (03:06):
This is quite strong.
Speaker 3 (03:08):
I'm an experimental chemist, and I've completed the rather long
series of experiments. I want them tabulated and the results analyzed.
Do you do that sort of work? Yes, I do.
It will be necessary for you to call here for
your data. It's impossible for me to leave. They're followed
(03:32):
in address on West seventieth Streets. Well. I had called
for data before, generally the stuff was delivered or mailed
to me, but his request was not extraordinary, so I
agreed and added that i'd be over shortly. No use
delaying my vacation if I could help it. I took
the subway. Taxis are needless luxury to a professor, and
(03:54):
the car of my own was an unrealized ambition. It
wasn't long before I entered one of the hound the
script round houses that still survived west of the other.
Strawn let me in, and I perceived the reason for
his request. The man was horribly crippled. His whole left
side was warped like a gnarled oak, and he was
hard foot to hobble about the house for the rest.
(04:16):
Stringy dark hair, little tense eyes. He greeted me pleasantly enough.
When I entered a small library, while my host hobbled
over to a littered desk, seating himself facing me, The
deep set eyes looked me over and he chuckled, are
you a good mathematician, doctor Errands? My work has been satisfactory.
(04:37):
I've been doing statistical work for several years. Of course,
of course, I don't doubt your practical ability. Are you, however,
well burst in the more abstract branches the theory of numbers,
for instance, or the hyperspatial mathematics. I don't see that
(04:58):
any of this is necessary in statistic analysis of experimental results,
if you'll give me your data of the going. As
a matter of fact, doctor Aarons, the experiment is not
completed yet. Indeed, to tell the truth, it's just beginning.
(05:18):
What do you mean now, if this is your idea
of a joke, Josh, the moment strong leveled of very
effective looking blue barreled automatic at me. I sat down again,
open morked. I can pess to a feeling the panic
at the side of the cripples, beady little eyes bearing
along the ugly weapon. A common politeness dictates that you
(05:43):
at least hear me out, doctor Aaron, As I was saying,
the experiment is just beginning. As a matter of fact,
you are the experiment. What do you mean. You're a mathematician,
aren't you, And that makes you fair game for me.
(06:07):
A mathematician, my good friend is no more to me
than something to be hunted down, and I'm doing it.
The man was crazy the realization dawned them as I
strove to hold myself come best to reason with him,
I thought, but but why we're a harmless lot? E harmless, eh, harmless?
(06:30):
Where it was one of your colleagues that did this,
he indicated, his withered leg in his withered arm. He
did this with his lying calculations. Listen to me, doctor ERNs,
I am a chemist or wise once. I used to
work with explosives and was pretty good too. And then
(06:54):
one of you damned calculators figured out a formula for me,
a misplace decimal point.
Speaker 1 (07:02):
You are all their.
Speaker 2 (07:03):
Gain to me.
Speaker 3 (07:05):
He paused, and the sneer came back to his lips.
That's simple justice, now, isn't it. You can imagine how
thoroughly terrified I was sitting there facing a homicidal maniac
with a loaded gun in his hand. Humor him. I'd
heard that was best treatment used persuasion reasons. Now, mister Strong,
(07:32):
you are certainly entitled to justice, Yes, you most certainly are.
But surely, mister Strong, you are not serving the ends
of justice by venting your anger on me. Surely that
is not justice. A very specious argument, doctor warings, you
are simply unfortunate in that your name is the first
(07:54):
in the classified section of the directory. Had you were
kindly given me a chance, any slightest chance to save
my body from this that you see, I might be forgiving.
But I trusted that fool's calculations. As it is, I'm
giving you more of a chance than I had, far more. If,
(08:17):
as you claim you are a good mathematician, you shall
have your opportunity to escape. I have no quarrel with
the real students of figures, but only only with the dollars,
the fakes, their blunderers. Yes, you will have your chance.
(08:39):
I saw no other alternative but to continue the ghastly force. Certainly,
open opposition to any of his suggestions might only inflame
them any act of violence. So I'm really questioned, and
what is your proposition, mister Strawn. It is just this.
You are a mathematician, and you say it, good one,
(09:00):
Very well. We shall put your claim to the test.
I'm thinking of a mathematical quantity, a numerical expression. If
you prefer, you have ten questions to discover it. If
you do so, you are free, as far as I
am concerned. But if you fail, well, if you fail,
(09:26):
I shall recognize you is one of the tribe of
blunderers against whom I war, and the outcome will not
be passion. It was several moments before I found my
voice and began the babble protests. But mister Strawn, that's
an utter impossibility. The range of numbers is infinite. How
(09:47):
can identify one with ten questions? Give me a fair test, man,
This one offers not a chance in a million in
a billion. He silenced me with a wave of the
blue barrel A member doctor Aaron's. I did not say
it was our number. I said a numerical expression, which
(10:09):
is vastly wider. I'm giving you this hint without deducting
the question. You must appreciate my magnanimity. The rules of
our little game are as follows. You may ask me
any questions except the direct question. What is the expression?
(10:29):
I am bound to answer you and pull into the
best of my knowledge any question except the direct inquiry.
You may ask me as many questions at a time
as you wish, up to your limit of ten. But
in any event I will answer not less than two
per day. That should give you sufficient time or reflection.
(10:52):
And my time too is limited. But mister strong, that
may keep me here five days. You know that by
tomorrow my wife will have the police searching for me.
You are not being fair, doctor Aarons. I know you
are not married. I checked up on you before you
came here. I know you will not be missed. Don't
(11:15):
attempt to lie to me. Rather help me serve the
ends of justice. You should be more than willing to
prove your worth to survive. Is one of the true mathematicians.
And now, sir, you will please precede me through that
door and up those stairs. There was nothing to do
but obey. The study gun in his hand was enough authority,
(11:38):
at least to an unadventurous soul like myself. I rose
and stalked out of the room at his direction, left
the stairs and through a door he indicated Beyond was
a windowless little cell ventilated by a skylight. And the
first glance revealed that this was barred a piece of
furniture of the type known as a day bed. The
(11:58):
straight chair, were stuff chairing the desk may look the
furnishings here is your students. Sell on the desk is
a craft of water, and is you see and on
the bridge Dictionary that's the only reference allowed in our
little game. Now it's ten minutes to four by four tomorrow.
You must have asked me two questions and have them
(12:22):
well thought out. The ten minutes over our gift from me.
Lest you doubt my generosity, I'll see that your meals
are on time. My best wishes, Doctor Aaron's. The door
clicked shut, and I at once commenced the survey of
the room. The skylight was hopeless in the door. Even
(12:43):
more so I was securely and ingloriously imprisoned. I spent
perhaps half an hour in painstaking and fruitless inspection, But
the room had been well designed or adapted to the strips.
The massive door was barred on the outside, the skylight
was guarded by heavy iron grating, and the walls offered
no slightest hope. I was most certainly a prisoner. My
(13:07):
mind turned to Strawns insane game. Perhaps I could solve
a mad mystery. At least I could keep him from
violence for five days, and something might occur in the interim.
I found cigars on the desk, and forcing myself to
a degree of calm, I lit one and sat down
to think. Certainly, there was no use in getting at
his lunatic concept from a quantitative angle. I could waste
(13:30):
all ten questions too easily by asking is it greater
or less than a million? Is it greater or less
than a thousand? Is it greater or less than a hundred?
Impossible to pin the thing down by that sort of elimination,
when it might be a negative number, a fraction, a decimal,
or even an imaginary number like the square root of
minus one, or for that matter, any possible combination of these.
(13:53):
And that reflection gave me my impulse for the first question.
By the time the cigar had been consumed to a
tattered stub, i'd formulated my initial inquiry, nor had I
very long to wait. It was just past six when
the door opened. Stand away from the door, doctor Aarons,
(14:13):
I complied perforce. The madman entered, pushing before him a
tea caddy bearing a really respectable meal. He propelled the
cart with his wither left hand, the right brandish the
evil automatic. I trust you have used your time well.
At least I have my first question. Hey, good, doctor
(14:34):
Aaron's very good. Let us hear it well. Among numbers
expressions of quantity, mathematicians recognized two broad distinctions, two fields
in which every possible numerical expression may be classified. These
two classifications are known as real numbers, on the one hand,
including every number, both positive and negative, all fractions, decimals,
(14:55):
and multiples of these numbers, and on the other hand,
the class of imaginary numbers, which includes all products of
operations on the quantity called I, otherwise expressed as the
square root of minus one. Have cars, Doctor Aaron's, that's elementary. Now, then,
is this quantity of yours real or imaginary? A very
(15:19):
fair question, sir, very fair, And the answer may assist
you is that it is either. A light seemed to
burst in my brain. Any student of numbers knows that
only one figure is both real and imaginary, the one
that marks the point of intersection between the real and
(15:40):
imaginary number graphs. I've got it, The phrase kept running
through my mind like a crazy drum beat. I've got it.
With an effort, I kept my appearance of calm, mister strong,
is the quantity you have in mind?
Speaker 1 (15:57):
Zero?
Speaker 3 (16:01):
A nasty superior laugh that rasped in my ears. It
is not, doctor Aarons, I know as well as you
that zero is both a real and imaginary number. Let
me card your attention to my answer. I did not
say that my concept was both real and imaginary. I
(16:24):
said it was either. Hey, let me further remind you
that you have eight gases remaining, since I am forced
to consider this premature shot in the dark as one chance,
good evening, he was gone. I heard the bar outside
the door settle into its socket with a thump. I
stood in the throes of despair and cast scarcely a
(16:47):
glance at the rather sumptuous repast he'd served me, and
slumped back into my chair. It seemed hours before my
thoughts were coherent again. Actually, I never knew the interval,
since I did not plants at my watch. However, sooner
or later I recovered enough to pour a tumbler of
wine and eat a bit of the roast beef Labooleon
was hopelessly cold, and then I settled down to the
(17:10):
consideration of my third question. From Strawn's several hints in
the wording of his terms and the answers to my
first and second queries, I tabulated what information I could glean.
He had specifically designated a numerical expression that eliminated the
axes and Y's of Algeboic usage. The quantity was either
(17:31):
real or imaginary, and was not zero. Well, the square
of any imaginary is a real number. If the quantity
contained more than one figure, or if an exponent was used,
then I felt sure his expression was merely the square
of an imaginary One could consider such a quantity either
real or imaginary. A means of determining this by a
(17:55):
single question occurred to me. I scribbled a few symbols
on a sheet of paper, and then been a sudden
and thorough exhaustion. I threw myself on the day bed
and slept. I dreamed Strang was pushing me into a
nightmarriage sea of grinning mathematical monsters. The creaking of the
door aroused me. Sunbeams illuminated the skylight I'd slept out
(18:19):
the night. Strawn entered, balancing the tray on his left arm,
holding the epp present weapon in his free hand. He
placed a half dozen covered dishes on the tea cart,
removing the remains of the evening meal to his tray.
A poor appetite, doctor aarons you should not permit your anxiety.
He to serve the ends of justice to upset you
(18:42):
no questions yet, no matter, you have until four tomorrow
for you hear next to I do have a question.
A numerical quantity, mister Strawn, can be expressed as an
operation on numbers us. Instead of being the numeral four,
one may prefer to express it as a product such
(19:04):
as two times two, or is a sum three plus one,
or is a quotient eight divided by two, or as
a remainder five minus one, or even in some other ways,
as a square such as two squared, or as a
root such as the square root of sixteen a cube
root of sixty four. All are different methods of expressing
(19:25):
the single quantity four. Now Here I've written out the
various mathematical symbols of operations, and my question is this
which if any of these symbols is used in the
expression you have in mind? Very neatly put back there, Aerons,
You've succeeded in combining several questions in one. This symbol
(19:48):
this is the one used, He indicated the first one
in my list, the subtraction sign a simple dash, and
my hope to use the triviality of upon were dashed
as well, for that sign eliminated my carefully thought out
theory of a product or square of imaginaries to form
(20:09):
a real number. You can't change imaginary to reel by
additionary's attraction. It takes multiplication, squaring, or division to perform
that mathematical magic. Once more, I was thoroughly at sea,
and for a long time I was unable to marshal
my thoughts, And so the hours dragged into days with
a tantalizing slow swiftness. The tortures that condemned in a
(20:31):
prison death of us, I seemed check made it at
every turn curious paradoxical answers defeated my questions. My fourth query,
are there any imaginaries in your quantity? Elicited a cool
definite null. My fifth how many digits are used in
this expression? Brought forth and equally definite tool. Now what
(20:54):
two digits connected by a minus sign? Can you name
whose remainders either real or imaginary? And I thought it
was an impossibility. I thought the maniac was merely torturing me.
And yet somehow Strawn's madness seemed too ingenious, too clever,
for such an answer. He was, sincere, in his perverted
search for justice, had strong the ant on my sixth question,
(21:18):
I had an inspiration. By the terms of our games.
Strawn was to answer any questions, say the direct one.
What is the ex question that'saw our way out? On
his next appearance, I met him with feverish excitement, barely
waiting for his entrance to begin my querians. Mister Strong,
here's a question you're bound by your own rules to answer. Now,
(21:39):
suppose we place an equal sign after your quantity. What
number or numbers will complete the equation? What is the
quantity equal to? Very clever, doctor Aarons, a very clever question.
And the answer is anything, anything, anything, Then you're a
(22:05):
fraud in your Game's a damnable trickery. There's no such expression,
my dearie is doctor I got mathematician could find it,
and he departed laughing. I spent a sleepless night, hour
after hour, I said at that hateful best, checking my
scraps of information, thinking, trying to remember fragments of all
(22:26):
but forgotten theories, and I found solutions, not one, but several.
With four questions two days left to me, the solution
of the problem began to loom very close. The things
binged in my brain, my judgment counseled me to proceed slowly,
to check my progress with another question, But my nature
was rebelling against the incessant strain. Stake it all on
(22:49):
your last four questions, asked them all at once, and
then the agony. One way or another. I thought I
saw the answer. Oh, the fiendish, insane cleverness of the man.
He had pointed to the minus sign on my list
deliberately misled me. For all the time the symbol had
meant the bar of a fraction. Do you see the
two symbols are identical, just a simple dash, but one
(23:11):
means subtraction, the other division one minus one means zero,
but one divided by one means one. And by division,
his problem could be solved, for there is a quantity
that means literally anything real number or imaginary, and that
quantity is zero divided by zero. Yes, zero divided by zero.
You think offhand that the answer would be zero or
(23:32):
perhaps one, but it isn't. Not necessarily look at it
this way. Take the equation two times three equal six.
That's another way of saying that two goes into six
three times. Now take zero times six equal zero. Perfectly correct,
isn't it?
Speaker 1 (23:47):
Well?
Speaker 3 (23:47):
In that equation zero goes into zero six times, or
zero divided by zero equal six, and so on. For
any number, real or imaginary, zero divided by zero equals anything.
And that's what I figured the fiend had done, pointed
to the minus sign when he met the bar of
a fraction or division. Strawn came into the room grinning
(24:10):
at dawn. Are your questions ready, doctor Erons, I believe
you have for remaining, mister Strawn, Is your concept zero
divided by zero? Now? Sir?
Speaker 1 (24:24):
It is not.
Speaker 3 (24:26):
I was not disheartened. There was just one other symbol
I had been thinking of. They would meet the requirement,
one other possibility. My eighth question followed, then, is it
infinity divided by infinity? It is not, doctor Errands. I
was a little panicky, and the end loomed awfully near.
(24:49):
There was one way to find out if the thing
was fraudulent or not, and I used my ninth question,
mister Strawn, when you designated the dash as the mathematical
symbol used in your did you mean it as the
barb of fraction? Or is the sign of subtraction as
the subtraction sign? Doctor Arents, you have one more question
(25:10):
where you wait until tomorrow to ask it. The fiend
was grinning in huge enjoyment, thoroughly confident he was in
the intricacies of his insane gain. I hesitated in the
torture of frenzied and decision, the appalling prospect of another
agonized knight of doubts, decided me, Oh, I'll ask it now,
(25:33):
mister Strawn. It had to be right. There weren't any
other possibilities. I'd exhausted all of them an hour after
hour of miserable conjecture. So I asked, is the expression
the one you're thinking of infinity minus infinity?
Speaker 1 (25:50):
It was?
Speaker 3 (25:51):
I knew by the madman's clair mas disappointment that devil
must have told you, and I think they were flexive.
Faulth his lipsy lowered the gun in his hand as
I edged toward the door. He made no move to
stop me, but stood in a sort of desolate silence
until I gained the top of the stairway. And then
wait a minute, you're tell Then wait just a minute,
(26:13):
doctor Aarons. I was down the stairs in two leaps
and tugging at the door. The strong came after me.
As gun leveled, I heard it crash as the door
opened an I slipped out into the welcome daylight. Yes,
I recorded in and the police got him. He was crazy,
but his story was true. He had been mangled in
experimental laboratory explosion. Oh the problem, you see. Infinity is
(26:39):
the greatest expression of number possible, a number greater than
any conceivable Figure it out like this. The mathematician symbol
for infinity is a tipsy eight. Well, take the question
infinity plus six equals infinity. That's true because you can't
add anything to infinity that'll make it any greater than
it is. It's the greatest possible number already. Then by
(27:02):
the same transposition, infinity minus infinity equal six, and so on.
The same system applies to any conceivable number, real or imaginary.
Speaker 1 (27:14):
There you are.
Speaker 3 (27:15):
Infinity minus itself may equal any quantity, absolutely, any number,
real or imaginary, from zero to infinity. No, there was
nothing wrong with Quirt Strong's mathematics.
Speaker 2 (27:32):
O O O O O O O O O O
O O h O O O o O.
Speaker 3 (28:21):
We've heard the Brink of Infinity. A story by Stanley Weinbaum,
copyright nineteen thirty six by Better Publications Incorporated, and we
printed in the Lancer book titled A Martian Odyssey. This
is Michael Hansen. Technical operation for this program by Steve Gordon.
(28:41):
Mind Webbs is produced at w h A Radio in Madison,
a service the University of Wisconsin.
Speaker 2 (28:48):
Extensions its.
Speaker 4 (29:16):
Insti It says it's
Speaker 3 (30:02):
To
Mine. Well, welcome to a half hour of mind Way
short Stories.
Speaker 2 (01:00):
Roads of speculative fiction.
Speaker 3 (01:12):
This is Michael Hanson, this time with a Stanley Weinbaum
story copyright nineteen thirty six by Better Publications Incorporated, entitled
The Brink of Infinity. One would hardly choose the life
of an assistant professor of mathematics at an Eastern university
(01:33):
is an adventurous one. Professors in general are reputed to
drown out of quiet, scholarly existence, and an instructor of
mathematics might seem the driest and least lively of men,
since the subject is perhaps the most desiccated. And yet
even the lifeless science of figures has added its dreamers Clerk, Maxwell, Obachevsky, Einstein.
Speaker 1 (01:51):
And the rest.
Speaker 3 (01:52):
And don't forget that Alice in Wonderland was written by
a dreamer who happened also to be a mathematician. Not
that I class myself for them. I'm practical enough to
leave fantasies alone. Teaching is my business. At least teaching
is my main business. I do a little statistical work
for investrial corporations when the occasion presents itself. In fact,
(02:13):
you'll find my name in the classified section. Abner Errand's
statistician and consulting mathematician. I eek out my professional salary,
and I do at time strike something interesting. Of course,
in the main such work consists of graphic trends of
consumption for manufacturers, of population increase for public utilities, and
occasionally some up and coming advertising agency will consult me.
(02:36):
Not exactly exciting work, but it helps financially, so I
was not particularly surprised that July morning to receive a call.
The university had been closed for several weeks. The summer
session was about to open without, however, the benefit of
my presence. I was taking a vacation. Even the modest
holiday I planned canvite deeply enough into the financial foundation
(02:58):
of an assistant professor's put. The work sounded like one
of those fairly lucrative and rather simple propositions.
Speaker 1 (03:06):
This is quite strong.
Speaker 3 (03:08):
I'm an experimental chemist, and I've completed the rather long
series of experiments. I want them tabulated and the results analyzed.
Do you do that sort of work? Yes, I do.
It will be necessary for you to call here for
your data. It's impossible for me to leave. They're followed
(03:32):
in address on West seventieth Streets. Well. I had called
for data before, generally the stuff was delivered or mailed
to me, but his request was not extraordinary, so I
agreed and added that i'd be over shortly. No use
delaying my vacation if I could help it. I took
the subway. Taxis are needless luxury to a professor, and
(03:54):
the car of my own was an unrealized ambition. It
wasn't long before I entered one of the hound the
script round houses that still survived west of the other.
Strawn let me in, and I perceived the reason for
his request. The man was horribly crippled. His whole left
side was warped like a gnarled oak, and he was
hard foot to hobble about the house for the rest.
(04:16):
Stringy dark hair, little tense eyes. He greeted me pleasantly enough.
When I entered a small library, while my host hobbled
over to a littered desk, seating himself facing me, The
deep set eyes looked me over and he chuckled, are
you a good mathematician, doctor Errands? My work has been satisfactory.
(04:37):
I've been doing statistical work for several years. Of course,
of course, I don't doubt your practical ability. Are you, however,
well burst in the more abstract branches the theory of numbers,
for instance, or the hyperspatial mathematics. I don't see that
(04:58):
any of this is necessary in statistic analysis of experimental results,
if you'll give me your data of the going. As
a matter of fact, doctor Aarons, the experiment is not
completed yet. Indeed, to tell the truth, it's just beginning.
(05:18):
What do you mean now, if this is your idea
of a joke, Josh, the moment strong leveled of very
effective looking blue barreled automatic at me. I sat down again,
open morked. I can pess to a feeling the panic
at the side of the cripples, beady little eyes bearing
along the ugly weapon. A common politeness dictates that you
(05:43):
at least hear me out, doctor Aaron, As I was saying,
the experiment is just beginning. As a matter of fact,
you are the experiment. What do you mean. You're a mathematician,
aren't you, And that makes you fair game for me.
(06:07):
A mathematician, my good friend is no more to me
than something to be hunted down, and I'm doing it.
The man was crazy the realization dawned them as I
strove to hold myself come best to reason with him,
I thought, but but why we're a harmless lot? E harmless, eh, harmless?
(06:30):
Where it was one of your colleagues that did this,
he indicated, his withered leg in his withered arm. He
did this with his lying calculations. Listen to me, doctor ERNs,
I am a chemist or wise once. I used to
work with explosives and was pretty good too. And then
(06:54):
one of you damned calculators figured out a formula for me,
a misplace decimal point.
Speaker 1 (07:02):
You are all their.
Speaker 2 (07:03):
Gain to me.
Speaker 3 (07:05):
He paused, and the sneer came back to his lips.
That's simple justice, now, isn't it. You can imagine how
thoroughly terrified I was sitting there facing a homicidal maniac
with a loaded gun in his hand. Humor him. I'd
heard that was best treatment used persuasion reasons. Now, mister Strong,
(07:32):
you are certainly entitled to justice, Yes, you most certainly are.
But surely, mister Strong, you are not serving the ends
of justice by venting your anger on me. Surely that
is not justice. A very specious argument, doctor warings, you
are simply unfortunate in that your name is the first
(07:54):
in the classified section of the directory. Had you were
kindly given me a chance, any slightest chance to save
my body from this that you see, I might be forgiving.
But I trusted that fool's calculations. As it is, I'm
giving you more of a chance than I had, far more. If,
(08:17):
as you claim you are a good mathematician, you shall
have your opportunity to escape. I have no quarrel with
the real students of figures, but only only with the dollars,
the fakes, their blunderers. Yes, you will have your chance.
(08:39):
I saw no other alternative but to continue the ghastly force. Certainly,
open opposition to any of his suggestions might only inflame
them any act of violence. So I'm really questioned, and
what is your proposition, mister Strawn. It is just this.
You are a mathematician, and you say it, good one,
(09:00):
Very well. We shall put your claim to the test.
I'm thinking of a mathematical quantity, a numerical expression. If
you prefer, you have ten questions to discover it. If
you do so, you are free, as far as I
am concerned. But if you fail, well, if you fail,
(09:26):
I shall recognize you is one of the tribe of
blunderers against whom I war, and the outcome will not
be passion. It was several moments before I found my
voice and began the babble protests. But mister Strawn, that's
an utter impossibility. The range of numbers is infinite. How
(09:47):
can identify one with ten questions? Give me a fair test, man,
This one offers not a chance in a million in
a billion. He silenced me with a wave of the
blue barrel A member doctor Aaron's. I did not say
it was our number. I said a numerical expression, which
(10:09):
is vastly wider. I'm giving you this hint without deducting
the question. You must appreciate my magnanimity. The rules of
our little game are as follows. You may ask me
any questions except the direct question. What is the expression?
(10:29):
I am bound to answer you and pull into the
best of my knowledge any question except the direct inquiry.
You may ask me as many questions at a time
as you wish, up to your limit of ten. But
in any event I will answer not less than two
per day. That should give you sufficient time or reflection.
(10:52):
And my time too is limited. But mister strong, that
may keep me here five days. You know that by
tomorrow my wife will have the police searching for me.
You are not being fair, doctor Aarons. I know you
are not married. I checked up on you before you
came here. I know you will not be missed. Don't
(11:15):
attempt to lie to me. Rather help me serve the
ends of justice. You should be more than willing to
prove your worth to survive. Is one of the true mathematicians.
And now, sir, you will please precede me through that
door and up those stairs. There was nothing to do
but obey. The study gun in his hand was enough authority,
(11:38):
at least to an unadventurous soul like myself. I rose
and stalked out of the room at his direction, left
the stairs and through a door he indicated Beyond was
a windowless little cell ventilated by a skylight. And the
first glance revealed that this was barred a piece of
furniture of the type known as a day bed. The
(11:58):
straight chair, were stuff chairing the desk may look the
furnishings here is your students. Sell on the desk is
a craft of water, and is you see and on
the bridge Dictionary that's the only reference allowed in our
little game. Now it's ten minutes to four by four tomorrow.
You must have asked me two questions and have them
(12:22):
well thought out. The ten minutes over our gift from me.
Lest you doubt my generosity, I'll see that your meals
are on time. My best wishes, Doctor Aaron's. The door
clicked shut, and I at once commenced the survey of
the room. The skylight was hopeless in the door. Even
(12:43):
more so I was securely and ingloriously imprisoned. I spent
perhaps half an hour in painstaking and fruitless inspection, But
the room had been well designed or adapted to the strips.
The massive door was barred on the outside, the skylight
was guarded by heavy iron grating, and the walls offered
no slightest hope. I was most certainly a prisoner. My
(13:07):
mind turned to Strawns insane game. Perhaps I could solve
a mad mystery. At least I could keep him from
violence for five days, and something might occur in the interim.
I found cigars on the desk, and forcing myself to
a degree of calm, I lit one and sat down
to think. Certainly, there was no use in getting at
his lunatic concept from a quantitative angle. I could waste
(13:30):
all ten questions too easily by asking is it greater
or less than a million? Is it greater or less
than a thousand? Is it greater or less than a hundred?
Impossible to pin the thing down by that sort of elimination,
when it might be a negative number, a fraction, a decimal,
or even an imaginary number like the square root of
minus one, or for that matter, any possible combination of these.
(13:53):
And that reflection gave me my impulse for the first question.
By the time the cigar had been consumed to a
tattered stub, i'd formulated my initial inquiry, nor had I
very long to wait. It was just past six when
the door opened. Stand away from the door, doctor Aarons,
(14:13):
I complied perforce. The madman entered, pushing before him a
tea caddy bearing a really respectable meal. He propelled the
cart with his wither left hand, the right brandish the
evil automatic. I trust you have used your time well.
At least I have my first question. Hey, good, doctor
(14:34):
Aaron's very good. Let us hear it well. Among numbers
expressions of quantity, mathematicians recognized two broad distinctions, two fields
in which every possible numerical expression may be classified. These
two classifications are known as real numbers, on the one hand,
including every number, both positive and negative, all fractions, decimals,
(14:55):
and multiples of these numbers, and on the other hand,
the class of imaginary numbers, which includes all products of
operations on the quantity called I, otherwise expressed as the
square root of minus one. Have cars, Doctor Aaron's, that's elementary. Now, then,
is this quantity of yours real or imaginary? A very
(15:19):
fair question, sir, very fair, And the answer may assist
you is that it is either. A light seemed to
burst in my brain. Any student of numbers knows that
only one figure is both real and imaginary, the one
that marks the point of intersection between the real and
(15:40):
imaginary number graphs. I've got it, The phrase kept running
through my mind like a crazy drum beat. I've got it.
With an effort, I kept my appearance of calm, mister strong,
is the quantity you have in mind?
Speaker 1 (15:57):
Zero?
Speaker 3 (16:01):
A nasty superior laugh that rasped in my ears. It
is not, doctor Aarons, I know as well as you
that zero is both a real and imaginary number. Let
me card your attention to my answer. I did not
say that my concept was both real and imaginary. I
(16:24):
said it was either. Hey, let me further remind you
that you have eight gases remaining, since I am forced
to consider this premature shot in the dark as one chance,
good evening, he was gone. I heard the bar outside
the door settle into its socket with a thump. I
stood in the throes of despair and cast scarcely a
(16:47):
glance at the rather sumptuous repast he'd served me, and
slumped back into my chair. It seemed hours before my
thoughts were coherent again. Actually, I never knew the interval,
since I did not plants at my watch. However, sooner
or later I recovered enough to pour a tumbler of
wine and eat a bit of the roast beef Labooleon
was hopelessly cold, and then I settled down to the
(17:10):
consideration of my third question. From Strawn's several hints in
the wording of his terms and the answers to my
first and second queries, I tabulated what information I could glean.
He had specifically designated a numerical expression that eliminated the
axes and Y's of Algeboic usage. The quantity was either
(17:31):
real or imaginary, and was not zero. Well, the square
of any imaginary is a real number. If the quantity
contained more than one figure, or if an exponent was used,
then I felt sure his expression was merely the square
of an imaginary One could consider such a quantity either
real or imaginary. A means of determining this by a
(17:55):
single question occurred to me. I scribbled a few symbols
on a sheet of paper, and then been a sudden
and thorough exhaustion. I threw myself on the day bed
and slept. I dreamed Strang was pushing me into a
nightmarriage sea of grinning mathematical monsters. The creaking of the
door aroused me. Sunbeams illuminated the skylight I'd slept out
(18:19):
the night. Strawn entered, balancing the tray on his left arm,
holding the epp present weapon in his free hand. He
placed a half dozen covered dishes on the tea cart,
removing the remains of the evening meal to his tray.
A poor appetite, doctor aarons you should not permit your anxiety.
He to serve the ends of justice to upset you
(18:42):
no questions yet, no matter, you have until four tomorrow
for you hear next to I do have a question.
A numerical quantity, mister Strawn, can be expressed as an
operation on numbers us. Instead of being the numeral four,
one may prefer to express it as a product such
(19:04):
as two times two, or is a sum three plus one,
or is a quotient eight divided by two, or as
a remainder five minus one, or even in some other ways,
as a square such as two squared, or as a
root such as the square root of sixteen a cube
root of sixty four. All are different methods of expressing
(19:25):
the single quantity four. Now Here I've written out the
various mathematical symbols of operations, and my question is this
which if any of these symbols is used in the
expression you have in mind? Very neatly put back there, Aerons,
You've succeeded in combining several questions in one. This symbol
(19:48):
this is the one used, He indicated the first one
in my list, the subtraction sign a simple dash, and
my hope to use the triviality of upon were dashed
as well, for that sign eliminated my carefully thought out
theory of a product or square of imaginaries to form
(20:09):
a real number. You can't change imaginary to reel by
additionary's attraction. It takes multiplication, squaring, or division to perform
that mathematical magic. Once more, I was thoroughly at sea,
and for a long time I was unable to marshal
my thoughts, And so the hours dragged into days with
a tantalizing slow swiftness. The tortures that condemned in a
(20:31):
prison death of us, I seemed check made it at
every turn curious paradoxical answers defeated my questions. My fourth query,
are there any imaginaries in your quantity? Elicited a cool
definite null. My fifth how many digits are used in
this expression? Brought forth and equally definite tool. Now what
(20:54):
two digits connected by a minus sign? Can you name
whose remainders either real or imaginary? And I thought it
was an impossibility. I thought the maniac was merely torturing me.
And yet somehow Strawn's madness seemed too ingenious, too clever,
for such an answer. He was, sincere, in his perverted
search for justice, had strong the ant on my sixth question,
(21:18):
I had an inspiration. By the terms of our games.
Strawn was to answer any questions, say the direct one.
What is the ex question that'saw our way out? On
his next appearance, I met him with feverish excitement, barely
waiting for his entrance to begin my querians. Mister Strong,
here's a question you're bound by your own rules to answer. Now,
(21:39):
suppose we place an equal sign after your quantity. What
number or numbers will complete the equation? What is the
quantity equal to? Very clever, doctor Aarons, a very clever question.
And the answer is anything, anything, anything, Then you're a
(22:05):
fraud in your Game's a damnable trickery. There's no such expression,
my dearie is doctor I got mathematician could find it,
and he departed laughing. I spent a sleepless night, hour
after hour, I said at that hateful best, checking my
scraps of information, thinking, trying to remember fragments of all
(22:26):
but forgotten theories, and I found solutions, not one, but several.
With four questions two days left to me, the solution
of the problem began to loom very close. The things
binged in my brain, my judgment counseled me to proceed slowly,
to check my progress with another question, But my nature
was rebelling against the incessant strain. Stake it all on
(22:49):
your last four questions, asked them all at once, and
then the agony. One way or another. I thought I
saw the answer. Oh, the fiendish, insane cleverness of the man.
He had pointed to the minus sign on my list
deliberately misled me. For all the time the symbol had
meant the bar of a fraction. Do you see the
two symbols are identical, just a simple dash, but one
(23:11):
means subtraction, the other division one minus one means zero,
but one divided by one means one. And by division,
his problem could be solved, for there is a quantity
that means literally anything real number or imaginary, and that
quantity is zero divided by zero. Yes, zero divided by zero.
You think offhand that the answer would be zero or
(23:32):
perhaps one, but it isn't. Not necessarily look at it
this way. Take the equation two times three equal six.
That's another way of saying that two goes into six
three times. Now take zero times six equal zero. Perfectly correct,
isn't it?
Speaker 1 (23:47):
Well?
Speaker 3 (23:47):
In that equation zero goes into zero six times, or
zero divided by zero equal six, and so on. For
any number, real or imaginary, zero divided by zero equals anything.
And that's what I figured the fiend had done, pointed
to the minus sign when he met the bar of
a fraction or division. Strawn came into the room grinning
(24:10):
at dawn. Are your questions ready, doctor Erons, I believe
you have for remaining, mister Strawn, Is your concept zero
divided by zero? Now? Sir?
Speaker 1 (24:24):
It is not.
Speaker 3 (24:26):
I was not disheartened. There was just one other symbol
I had been thinking of. They would meet the requirement,
one other possibility. My eighth question followed, then, is it
infinity divided by infinity? It is not, doctor Errands. I
was a little panicky, and the end loomed awfully near.
(24:49):
There was one way to find out if the thing
was fraudulent or not, and I used my ninth question,
mister Strawn, when you designated the dash as the mathematical
symbol used in your did you mean it as the
barb of fraction? Or is the sign of subtraction as
the subtraction sign? Doctor Arents, you have one more question
(25:10):
where you wait until tomorrow to ask it. The fiend
was grinning in huge enjoyment, thoroughly confident he was in
the intricacies of his insane gain. I hesitated in the
torture of frenzied and decision, the appalling prospect of another
agonized knight of doubts, decided me, Oh, I'll ask it now,
(25:33):
mister Strawn. It had to be right. There weren't any
other possibilities. I'd exhausted all of them an hour after
hour of miserable conjecture. So I asked, is the expression
the one you're thinking of infinity minus infinity?
Speaker 1 (25:50):
It was?
Speaker 3 (25:51):
I knew by the madman's clair mas disappointment that devil
must have told you, and I think they were flexive.
Faulth his lipsy lowered the gun in his hand as
I edged toward the door. He made no move to
stop me, but stood in a sort of desolate silence
until I gained the top of the stairway. And then
wait a minute, you're tell Then wait just a minute,
(26:13):
doctor Aarons. I was down the stairs in two leaps
and tugging at the door. The strong came after me.
As gun leveled, I heard it crash as the door
opened an I slipped out into the welcome daylight. Yes,
I recorded in and the police got him. He was crazy,
but his story was true. He had been mangled in
experimental laboratory explosion. Oh the problem, you see. Infinity is
(26:39):
the greatest expression of number possible, a number greater than
any conceivable Figure it out like this. The mathematician symbol
for infinity is a tipsy eight. Well, take the question
infinity plus six equals infinity. That's true because you can't
add anything to infinity that'll make it any greater than
it is. It's the greatest possible number already. Then by
(27:02):
the same transposition, infinity minus infinity equal six, and so on.
The same system applies to any conceivable number, real or imaginary.
Speaker 1 (27:14):
There you are.
Speaker 3 (27:15):
Infinity minus itself may equal any quantity, absolutely, any number,
real or imaginary, from zero to infinity. No, there was
nothing wrong with Quirt Strong's mathematics.
Speaker 2 (27:32):
O O O O O O O O O O
O O h O O O o O.
Speaker 3 (28:21):
We've heard the Brink of Infinity. A story by Stanley Weinbaum,
copyright nineteen thirty six by Better Publications Incorporated, and we
printed in the Lancer book titled A Martian Odyssey. This
is Michael Hansen. Technical operation for this program by Steve Gordon.
(28:41):
Mind Webbs is produced at w h A Radio in Madison,
a service the University of Wisconsin.
Speaker 2 (28:48):
Extensions its.
Speaker 4 (29:16):
Insti It says it's
Speaker 3 (30:02):
To
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