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ElapticAI-512

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Mathematics and the Imagination: The captives were not truly bound so
long as freedom of leg movement permitted them to convert their bonds
into a simply-connected manifold.
[Illustration]
By way of illustration (and for your own amusement) tie a 36" piece of
string to each of your wrists. Tie a second piece of string to each of
the wrists of a friend in such a fashion that the second piece loops
the first. By experiment, you will discover it is quite possible to
disengage yourself from your companion without breaking or cutting the
string.
Another interesting example of topological freedom is that achieved
in removing the vest without first removing the coat. Try it. The
coat may be unbuttoned, but your arms must not slip out of the coat
sleeves. Ed.]
"Topogra-which?" asked Hank interestedly. "I didn't know it had no
name, Mr. Grimper. Just 'peared to me like as if a circle's got an
inside an' an outside, an' we was in the inside, so we wasn't tied up
at all, rightly speakin'. Well, let's git out o' here!"
Well he might make the suggestion. For all this had taken time. As we
labored to free each other we had heard an excited hubbub gathering
outside, the wail of fire sirens had sounded, the yammer of voices
raised in command, and a stream of water was already beginning to
play upon one wall. But in the meantime, the fire had gained headway.
The walls of this room were ruddy sheets of flame. The narrow circle
of safety in which we stood was rapidly dwindling. And my skin was
beginning to crack and blister with oven-fierce heat.
I croaked despairingly, "But how, Hank? We're free, yes! But the doors
are still locked, and the windows "
"Why, the skylight, Jim!" drawled Hank. "That's our exit Hey! Grab
him!"
I whirled just in time to catch the falling frame of government agent
Grimper. The thin man had come to an end of his endurance. His heart
was stout and courageous out of all proportion to his physical makeup.
With a stifled cry he had fainted dead away!
Well, there you are! One moment we were on our road to a Happy Ending,
and bing! all of a sudden the Three Gray Ladies slap us in the puss
with a damp mackerel! I stared at Hank fearfully, and moistened parched
lips.
"Wh-what will we do with him, Hank? W-we can't just leave him here to
die!"
Hank stroked a lean and thoughtful jaw.
"Sort o' complicates matters, don't it?" he queried. "Let's see we
couldn't h'ist him up, could we?"
I said bitterly, "I can't, Hank. I hate to admit it but I'd be a
damned liar if I pretended otherwise. I'm so weak, and my armpits so
badly strained, that it will be all I can do to lift myself. Can can
you?"
Hank shook his head miserably.
"Nup. I didn't jump off'n that chain just now, Jim, I fell off.
Hangin' up there like jerked meat wrenched somethin' in my back. I
calc'late I c'n climb that chain myself, but I couldn't h'ist nobody
else's weight.
"Wait a minute! Weight!" He repeated the word more loudly. A
gleam brightened in his eye. "Sure! Dead weight! That's the answer!
Here gimme a hand, Jim. We got to lash him to one strand o' this
pulley-chain. Use them ropes. Got it? Okay tie him tight, now."
"He he's tied!" I puffed. The smoke was beginning to get me now.
Tears were coursing down my cheeks. Time was getting perilously short.
"W-what do we do next?"
"Git on the other end o' that chain," ordered Hank, "an' climb!"
"W-what? And leave him dangling here below? But it only saves our
lives, Hank! See, the flames are right on us. We won't have time to
reach the skylight and haul him up "
"Do whut I tell you!" roared Hank, "An' hurry!"
There was more vehemence in his voice than I'd heard at any previous
time. It shocked, startled me into activity. I leaped for the side of
the draw-chain opposite to that upon which Grimper was hanging limp;
began climbing like a monkey, hand-over-hand. The dangling chain drew
taut above me, and I saw that Hank, too, was climbing. I looked for
Grimper
And Grimper was above me! As Hank and I climbed one side of the
chain, the agent's inert body was being hauled up the other. He
reached the cool sanctuary of the skylight before we did, lifted
to safety by our combined weights, before I remembered the old
monkey-weight-and-pulley puzzle that one time caused a near-riot in a
staid academy of savants!
So all's well that ends well. It was an easy matter to unlash Grimper