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delighted. Objectively, he knew the boy was neat and trim rather than
handsome, yet subjectively
(and privately, of course: he was very proper now), he always felt the boy was
"good-looking." This feeling puzzled him until one day he had to move a stack
of old college annuals, and browsing as one will, he suddenly came upon his
own senior picture. His best student was enough like his youthful self to be a
double, or at least a younger brother.
Shortly after that, the professor confided the story of his escapade to the
boy. He could not have said why he did so, and it certainly was not wise; but
the student was beginning to betray the same weird talent the professor had
for trans-
lating topological abstractions into hardware that did peculiar things; and
somehow the tale just told itself. He had become very fond indeed of his
disciple. The boy, who affected the total amorality which was the fashion of
his generation, was nevertheless shocked; but he was also intrigued. He picked
up the box and shook it. "Maybe she's alive," he said. "After all, inside it's
only been an instant. Let's unlock it."
"Don't be ridiculous," the professor said, taking the cube back and setting it
on his desk in a definite manner. "In the first place, she's not alive. While
she's in the construction, there's no evidence of the crime. Second, if she
were alive, she might go to the police; or worse yet, she might expect me to
take up that dreadful, boring liaison with her again. And in the third place,
we can't unlock it. That was the whole point of breaking the sword. The cube's
a closed system now, and no part of the interior is available to this aspect
of time and space. Eventually she'll be equally distributed through the entire
universe. Absolutely not! I forbid you to think about it. When are you going
to give me that paper on topological re-intervertebrates?"
Conversation languished, and the student shortly took his leave. A day or two
later, the professor found the boy fiddling the edges of the cube with a
device made of mirrors, and they had a genuine quarrel; but gradually they
fell back almost into their former sympathetic teacher-student relation.
One day the student appeared in the professor's apartment with a tiny
glittering piece of metal in his hand, the shape of which was extraordinarily
hard to see. The whole thing seemed to flicker in and out of the
mathematician's sight.
"What the hell have you got there?" he asked the boy in irritation.
"It's a chrome-plated, self-powered, retractable, inverted, universally
jointed, and fully gurgitated Mobius strip," the
young man said.
The professor laughed. Every schoolboy knows a Mobius strip is a band, one end
of which has been given a half twist before joining it to the other end to
make a circlet. The consequence of that little twist (try it) is that the
Mobius strip is a geometric figure which has only one side and one edge,
though common sense, looking at it, can plainly discern two sides and two
edges. However, a pencil drawn down the center of "one side" will meet its own
mark and there will then be seen to be a line drawn on "both sides" . . .
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because there is only one side, you see?
But every schoolboy knows that's all a Mobius strip is: just a curiosity.
Anything else you do to it changes it from being a Mobius strip. So it can't
be improved by chroming it or powering it or anything else. The professor
pointed all this out to his student in a rather overbearing manner. He
finished by saying, "And I suppose you're going to tell me it has some
practical application."
"Yes," said the boy, "it has." And before the professor could stop him, he had
reached across the desk, penetrated into the shiny cube with one half of the
glittering M5bius strip, and fished out the shattered remnant of a short Roman
stabbing sword.
In an instant, the old familiar bulgy cylinder was present on the desk,
full-size, and in another, a completely naked young woman had leaped out of it
onto the floor. In stupefac-
tion, the professor saw a pink, three-cornered scar, obviously just healing,
on her rib cage, and noticed there were still drops of water glistening on her
flank.
"Sweetheart!" she cried. "What -was that butcher knife? I
had to dodge like crazy!" And she engulfed the student in a squid-like
embrace. A moment later she saw the professor and recoiled.
"Who is this bald-headed old creep?" she said. "I draw the line at voyeurs,
honey." And with a wink and a nod, she and the student dumped the professor
into the expanded cube and collapsed it about him.
Even in the endless instant which is the inside of his device, time has begun
to seem long to the topologist. He knows the girl and the student are long
since dust in the whirling, kaleidoscopic world outside. He is beginning to be
transparent, so he knows his substance is slowly plating out along the entire
cylindrico-spherical space-time continuum.
He has realized that when he is fully distributed, the universe will be at an
end; and he has composed a most astounding paper in his head explaining the
whole phenomenon. His only regret is that he will never be able to send it to
the Journal of Topology for publication.
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