Miss Liberty and I were standing in
a dark room, lit by candles and smoky torches. On the floor a large pentagram
was drawn in chalk. We were standing inside the pentagram, and outside was a
three-headed giant.
“I am 3-Demon!” said the giant’s
yellow face.
“Master of geometry!” said the
giant’s blue face.
“And champion glitch-killer!” said
the giant’s red face.
“Hi there!” said Miss Liberty. “I
have Full Access. Are you ready to grant a few wishes?”
3-Demon’s three faces said in
unison, “You have full access, but it was obtained illegally. Therefore I shall
grant you three wishes; and then I shall destroy you.”
“My three wishes are simple geometry
problems.”
“Good,” said 3-Demon. “That’s my
specialty. I am a Perfect Master of Classical Geometry. With my straightedge
and my compass I construct all proportions.”
“Straight-edge and compass? Is that
all?” Liberty asked.
“Those are the approved
instruments,” said 3-Demon. “They suffice.”
Miss Liberty and I exchanged a
glance. We shrugged. Apparently this program hadn’t been re-written lately. It
would be no trouble to outwit 3-Demon.
“I’ll give you one for free,” Miss
Liberty said thoughtfully. She reached into her robe and drew forth a square.
She tossed the geometric object out to 3-Demon, who deftly caught it. “That’s a
nice enough square, but it’s too small. Can you double its area?”
“I shall try,” said 3-Demon’s blue
face. With a few quick strokes of compass and straightedge, 3-Demon constructed
a new square, and tossed it back. “This square now has precisely twice the
original square’s area. Next problem.”
“Nice!” Liberty said, admiring the
square. She put it away, then drew out a cube. “How about doubling this cube?”
“I shall try,” said 3-Demon’s yellow
face. After some geometry, the giant tossed back a cube. “That cube now has
1.999 times its original volume.”
“That’s almost right,” said
Liberty, tossing it back, “but I want it exactly twice as big!”
3-Demon constructed another cube.
“This one is 2.000001 times as big as the original.”
“You’re getting close,” said
Liberty.
3-Demon made another cube. “This one
is 1.999999999 times as big as the original.”
“Nice! You’re nearly there!”
“I am not done,” the yellow face
said. “I must study this further.” It closed its eyes.
“While you’re thinking about that,
here’s another problem.” Miss Liberty took out a circle, which she spun over to
3-Demon. “Can you construct a square with the same area as this circle?”
“I shall try,” said 3-Demon’s red
face. After some geometry, the giant held a square. “This square has 1.001
times the area of the circle.”
“Well, that’s almost right,”
said Liberty.
3-Demon constructed another square.
“This one is 0.999999 times as big as the circle.”
“You’re getting close,” said
Liberty.
3-Demon constructed another square.
“This one is 1.00000001 times as big as the circle.”
“Nice! You’re nearly there!”
“I am not done,” 3-Demon’s red face
said. “I must study this further.” It closed its eyes.
“You are a saboteur!” cried
3-Demon’s blue face.
“Correct,” said Liberty.
“You distract me with
approximations! What are the exact constructions?”
“You want exact
constructions? But those don’t exist, you silly little obsolescent subroutine.”
All of 3-Demon’s six eyes opened
wide. “What!” it cried in all three voices.
“You can’t get those proportions
precise with straight-edge and compass! That’s a mathematical theorem!” she
said.
“You have assigned us two problems
with no finite solutions, only infinite approximations which would take us an
infinite time to construct!”
“That’s right.”
3-Demon’s heads all looked at each
other; then it came to an agreement among itself. “You are a serious glitch.
You need doctoring. So we are going to send you to our supervisor.”
“I agree!” said Miss Liberty.
3-Demon looked surprised. “You are
not afraid? You are about to see Doctor Memory!”
“I demand to see Doctor
Memory!”
“Well...” said 3-Demon’s red face.
“Well...” said 3-Demon’s yellow
face.
“Well...” said 3-Demon’s blue face.
And all three faces said in unison:
“... we’ll just have to see the
Doctor about this!”
Then the lights went out.
In the sudden darkness we heard
3-Demon say, “This program is jammed. Consult supervisor.”
* click *
mmmmmmmmmmmmmmmmMMMMMMMMMMMMM....
Thus Miss Liberty cornered 3-Demon
with Doubling the Cube and Squaring the Circle.
3-Demon said, “You now have Full Access to Doctor Memory.
Beware, Master! She’s a glitch! Burn her!”
FLASH
No comments:
Post a Comment