SWORD GAME

H. H. Hollis
Late in the afternoon of an ugly fall day, a forty-year-old
topologist, employed to teach mathematics at a university he
despised, bored by his students and frightened that he had
done everything of significance in his life that he would ever
do, blundered head-down into a group of students handing
out flowers and handbills. Before he could retrieve his
dropped book bag and move on to continue composing in his
head a memorable letter of resignation, his eye had fallen on
a grubby teen-age girl and he was hopelessly entrapped.
Thinking to break the spell, he boldly said to her, "Aren't
you in my class in elementary topology?"
She licked the raspberry snow cone she was holding and
said, without a trace of a smile, "You must be mad. I'm not
a student, just a wandering Gypsy fortune teller." She held
out the snow cone for him to take a lick. "Do you have a
place where we could go, and I would tell your fortune?"
The mathematician knew she was no Gypsy, for your
modern, urban Romany never allows himself to be as dirty
as she was. He was certain she was putting him on, but
his mood of desperate boredom was such that he said,
"Cra-a-a-zy, Gypsy! Fall up to my pad, and we'll tell fortunes
and other lies till the world melts."
They left hand in hand under the eyes of forty witnesses.
Within their own subculture, however, the rebel students
conformed to a rigid code; and they would have died rather
than give information to the fuzz or even to the Dean of the
Faculty; so the professor's absolute breach of propriety in
picking up a student went unremarked and unreported.
When he had taken off her clothes, the girl was every bit
as dirty as she appeared to be, but this only made him more
determined to take advantage of her. Later, he persuaded her
to shower by promising to bathe with her; and she looked,
when she left, with her rum-colored hair in two long plaits,
like a fresh-scrubbed Girl Scout.
The crust turned out to be her equivalent of the makeup
squares use; when he came past the common the next day,
she was as delectably grimy as ever, and she held a fresh
snow cone purple with grape syrup.
The two joined hands and went directly to his apartment.
The young woman hardly spoke until late in the evening, after
they had showered together. She was toweling her hair and
the information came indistinctly. "I went to the Provost's
office today," she said, "and told him about us."
The professor was so uncharacteristically content he con-
templated the ruin of his academic career with pleasure. "All
right, big mouth, how are we going to live?"
  "I'm not really a Gypsy," she said, "but I really was in a
carnival once, when I ran away before. I know how to dodge
swords in a sword basket. Could you be an East Indian sword
magician? We could pick up a show somewhere and travel
right along with them."
"By God," cried the topologist, "I can do better than that!
It's been a long time since I did any engineering work, but I
have a little laboratory curiosity that will just fill the bill.
Come with me to the animal house in the basement of the
Psychology Department, and I'll show you something you
won't believe."
"Try me, baby," replied his inamorata. "You'd be surprised
at what / can believe."
They repaired to the noisome cages in which the experi-
mental animals were kept, and the professor secured a sturdy
mouse. Selecting a few strips of clear plastic from a rack, he
lit a burner and uncorked a container of plastic adhesive. In
a few minutes, the topologist had cobbled up a container
which defied the eye to define its exact shape, but which most
often seemed to be a lumpy cylinder. In a trice, he thrust the
mouse in and clapped the square top down. The mouse could
be seen through the plastic, but he seemed to be in a single
fixed position, floating in midair with his paws  and tail
extended just as when he was inserted.
Heating a pointed rod, the professor pierced a hole first in
one side of the bulgy cylinder and then in the other. In a
moment, when the long pin had cooled, he introduced its
sharp point 'through the hole again, and having located the
mouse properly, skewered the rodent through the heart so
that the point of the sharpened rod came out the second hole.
Swinging the cylinder over the girl's hand with a little shake,
the professor deposited a tiny drop of bright arterial mouse
blood on her wrist.
As she looked at the crimson drop, tears appeared,
sparkling on her eyelids. "Big deal, big man," she said.
"Mouse murder. I don't think a wild mouse would walk into
that plastic pipe, do you?"
"Heart of my heart," he replied, "it's not a pipe. It isn't
even a cylinder, and it certainly isn't a mousetrap. This is a
tesseract, as you would know if you had ever read a popular
work on topology."
"Oh, all right, I know what a tesseract is: an expanded
cube, a cube with a cube on each face. That mouse cage
doesn't look like six cubes surrounding a cube to me."
"No, otherwise our mouse would be dead all over. This is
a tesseract which is a temporal illusion."
"A temporal illusion!"
"Yes, my dear," he said, "a temporal illusion. Topology
teaches us that mathematical properties can be quite indepen-
dent of apparent shape. A circle is still a circle, even though
it looks like a scalloped pie crustas it may, if it is drawn
on a wavy surface. This mouse cage is a cubed cage which
is partly displaced along the dimension of time. That's why
it appears formless and shifting. Here, feel it."
Sure enough, to the touch it was solid enough: a cube with
a cube on each face; but even when held in the hand and
sensed by touch, the object still appeared to be a rippling
cylinder and the mouse still appeared to be stock still.
"This mouse looks dead. Eccch!" she said.
Deftly the topologist withdrew the tiny sword, pried off the
top, and shook Mr. Mouse out in his hand, where the charm-
ing little fellow at once sat up on his haunches and waved his
forepaws, as if demanding cheese.
"How did you do .that?" cried the girl.
"Simple, really," replied the tinker. "The exterior flickers in
and ou~of this moment of time, because of the subtle twist I
imparted to the shape when I made it; but the inside is fixed
in time, because much of the internal mass is stretched all the
way around the very large but finite continuum of space and
time which is our universe. This little rascal's 'time' has
passed so slowly that the powerful regenerative and repair
processes of his body have worked as if instantaneously, and
the apparently mortal wound I dealt him was no more than
a pin prick. Do you think you could get into a large tesseract
like this one and let me run a rapier through you . . . knowing
it would do you no harm?"
She clapped her hands in pleasure. "Oh yes, lover! That'll
be so much more of a mind buster than some old wicker
basket that everybody knows I dodge the sword in."
So they hied themselves to a plastic supply house and
thence to a dog-and-pony show that was in the neighborhood,
and for a long time, everything went like a guided trip with
Tim Leary. Audiences were transfixed by the girl's beauty.
She was considerably cleaner under 'the difficult circumstances
of carnival trouping than she had been when soap and water
were conveniently to be had, and when the topologist drove
a sharpened fencing foil through her lovely body, clad as
lightly as local ordinance allowed, the crowds gasped. When
the box was rotated to show the point of the sword encarna-
dined, strong men fainted. Later they would press forward
and pay a dollar apiece to examine the tiny wound as it closed
up and disappeared, usually midway up her delightfully
articulated rib cage.
Trouping the carnival together was an idyll. Still, even if
forty years is not old, neither is it young; and the doctor of
mathematics at last realized that he was bored again. The
girl's vocabulary never enlarged itself appreciably,  and the
snow cone remained her favorite confection. The difference
in their ages was sufficient for their basic sex attitudes to be
irreconcilable. For him, a certain overtone of the forbidden
gave carnal love its highest stimulation; but for her, sex was
just another natural function, like perspiring or excreting, so
that the level of their love-making remained at mere technical
proficiency.
After the fashion her generation had adopted, she was
faithful. There 'might be others later, her manner implied by
its playfulness; but for now, she did not share her favors out.
He was denied even the sour spice of jealousy.
At the end of their last appearance each evening, she was
often wearing only transparent pantaloons and a shiny little
brief, and when they had walked back to their quarters, she
would hold up her arms, and stamping her naked feet softly
like a harem dancer, say, "Help me get ready for my bath,
lover." If he approached and began to roll down the waist-
band of her sateen pants, she would drop her arms and begin
to undress him too. Later they would bathe each other.
They had almost no other conversation.
At last the idyll became an enslavement to the professor.
He found some respite when he learned that a Hindu torture-
man, their neighbor in the show, who slept on nails, poured
boiling lead in his eyes, and so on, was a Failed M.A. in
Mathematics from the University of Rawalpindi. By talking
to him, the topologist was able to keep from going quite mad.
Still,  he was  a little off.  He loathed the girl  and dreamed
only of what he would do when she left him; but she would
not leave, and continued to raise her arms to him and stamp
her feet, as exquisitely irritating as a kitten which continues
to claw one's sock after one has done playing with it.
He began to do everything badly, even their turn in the
show, which had never much interested him after he put the
big tesseract together. Once he missed the hole with his thrust,
and the plastic deflected the point of the foil into his toe.
This was a real wound, in real time, not spread along the
space-time continuum, and was extremely painful for a week.
Each time he limped, the pain made him more resolved to be
quit of her, until at last his fertile topological mind .saw the
way.
He had a regular armorefs store of swords with which he
made play in their act, and one evening he laid handy, next
their bed, a very passable imitation of a Roman short sword.
In its day, that design had been a great technological break-
through for the weapons makers, and it was beautifully
shaped for destructive stabbing.
When they came in that night, he skimmed off her tawdry
cape with a flourish, and as she lifted her round arms and
stamped one foot, he peeled the bottom of her costume off in
one extravagant gesture, and then gave her. the pleasure of
chasing him and tearing off his garments. As they were
toweling each other after their ritual coupling and bathing,
he kissed her, tender but preoccupied, as it were, and said,
"My dear, would you mind letting me practice that last pass
in the act? I just don't seem to be putting that foil home
right."
She was so pleased to have him pleasant again that she
scampered into the spare tesseract they had in the quarters,
a few drops from the bath still glistening on one flank. She
turned her face up to him with a grin that almost made him
reconsider the irreversible act he had planned. Then he
remembered the months of boredom and hardened his heart.
Decisively, he tapped the top home. Without a tremor, he
put the Roman short sword as nearly into her heart as he
could judge its location through the subtle time shifting in
the plastic. With that, he snapped off the blade, so that the
sword also was within the spread, slowed effect of the moving
time field, and gave the construction a knowledgeable kick
or two which caused it to collapse into itself. Instead of a
knobby cylinder, as it had appeared when it was an expanded
cube blurred by time, it now appeared to be a single cube
about six inches on a side, with an abstract pattern in each
face.
The collapsed cube was much heavier than it looked, but
not nearly as heavy as the girl, for a substantial part of her
mass was distributed along the whole of the cylindrico-
spherical space-time continuum. As he gazed at the mirror-
like surface of one square face, an eye and eyebrow slowly
spread flatly across the plane; but there was neither panic nor
recognition as he stared into it. He realized that to the occu-
pant of this peculiar box, his movements were so fast in
appearance as to be a mere blur. Whistling, the professor
packed the weighty cube into his bag and strolled off the lot,
casually remarking to his old Hindu neighbor, "So long, we're
jumping this flea circus." By changing into one of his
wrinkled natural shoulder suits at the bus station, he simply
disappeared as Grax, the Swordsman of Time (his carnival
billing), and reincarnated himself as a topologist of con-
siderable talent who had been vaguely on sabbatical for
a while.
The frustrations that had so nearly consumed him before
his adventure seemed to have been burned and purged away.
He settled with pleasure into a new academic routine and
became expert in its execution. Once in five years, perhaps,
he had a really promising student; but the scarcity no longer
bothered him. As he advanced up the ladder of academic
tenure and preferment, he was able to place a few brilliant
people about himself, and life was as good, he now knew, as
it was ever going to be.
The heavy cube was a paperweight on the desk in his
apartment. No one else ever recognized the shifting abstract
patterns in its silvery sides as the topologized contours of a
dead human being. At great intervals, 'there would drift across
one face or another of the prism some recognizable anatomi-
cal feature with which the professor was intimately ac-
quainted, and he would feel a vague regret for his act and a
light stirring, as of the ashes in a cold grate, of his appetite
for the one adventure of his life. He would stuff his pipe, turn
the pages of the Journal of Topology, and immerse himself
once more in the calm, sweet life of the university.
When he was sixty years old and almost bald, there ap-
peared in his classes the student of his dreams, who under-
stood everything he said in his arcane specialty, and replied
with fresh and elegant insights into the intuitive- sort of math
in which they both 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" . . . 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.