Wednesday, October 24, 2012

Feghoot's Proof

Ferdinand Feghoot QED, Doctor of Quantum Geometry

By the year 2202, interstellar travel had been achieved and thousands of planets were colonized, due to the invention of a simple FTL teleportation device--called the "Nick Machine", a technological spinoff from the research boom in quantum tantra. The major barrier in 2202 to travel between the stars was no longer technical but psychological as various human-based cultures created their own "no-fly lists" at every teleport node in order to prevent the spread of what each of them considered "evil" into the galaxy.

This network of no-fly zones divided the galaxy into virtual ideological gulags (VIGs) inside which certain citizens were confined against their wills, isolated forever from the advantages of interplanetary travel. And the surest way to find yourself on a no-fly list was to criticize this system or even to mention the existence of VIGs.

Ferdinand Feghoot had recently concluded a mutually beneficial love affair with one of the top quantum tantrikas on planet Literati and, after a lunar cycle of intimate farewells with the tantrika and her friends, he arrived at the Literati Airport to "fly" (instantaneously) to the Red Zone in Aldebaran a hundred light years away.

To his dismay he discovered that his name was flagged on the Literati "no-fly" list as a notorious interplanetary punster. The Literatis were firm believers in the sacredness of language and regarded all puns as sins against the purity of the spoken word.

"Feghoot, You shall not pass," said the gate-keeper at the Nick Machine. "You are well known, FF, as a multiple offender against the sanctity of language." See here, here and here. And he stamped Feghoot's boarding pass with a big red X.

"Wait, wait, there's been some mistake," said our hero. "Praise the Word. I am not that heretical lout. I am Ferdinand Feghoot QED, Professor of Quantum Geometry, on my way to an important science convention on Aldebaran III where I will be giving the keynote speech. If I am delayed even 10 minutes your whole planet will be disgraced by this incident. And you, sir, will probably be sent to the language mines."

"I may have been born in Sarfattistan, Feghoot, but I'm no gullible dupe," the crossing guard replied. "If you're such an important professor, show me something impressive to prove it."

"Praise the Word. I'm glad you asked, kind sir. I am just on my way to the Red Zone to present my latest result in Quantum Geometry which I would be happy to share with you. What most people don't know about reality is that ordinary plane geometry is subject to a fundamental quantum uncertainty--measured in "Plank units", named after an old American word for a flat piece of lumber. And I, Ferdinand Feghoot QED, Praise the Word, have devised the simplest proof in the entire galaxy of Fundamental Geometric Uncertainty. Feghoot's Proof is so simple I can even demonstrate it to you, sir".

"America?," the guard asked. "Isn't that the empire that was ruthlessly plundered by the ---?"

"Yes, yes, but that's ancient history. Do you or do you not want to see this proof? No one else has ever seen it. It's brand new. You'll be the first. I'll show it to you only if you print me up a fresh boarding pass."

"OK, person who's calling himself Doctor Feghoot. But I'm keeping this new pass in my hand till I see that proof."

"Fair enough," said Feghoot. "Now hand me that old pass."

Upon receiving the old pass, Feghoot pulled a pair of scissors from his backpack and cut the pass into four pieces which he arranged into a right triangle. The triangle was 5 Glips in height and 13 Glips long. "What is the area of this triangle?" asked Feghoot.

"Every child knows that, Feghoot. I'm not impressed. Area of any triangle is 1/2 Base times Height. Base is 13 Glips; Height is 5 Glips. Area is 32 and a 1/2 square Glips."

"That's correct, sir. Now watch closely," said Feghoot as he re-arranged the four pieces of the cut-up boarding pass. "What is the area of this new triangle?"

"Why, the base and the height of this new triangle are the same, so the area is the same also. The answer is 32 and a 1/2 square Glips."

"But observe, sir. This new triangle has a hole in it exactly one square Glip in size. Where did that hole come from? From Quantum Geometry, I say. That hole represents precisely the one quantum of uncertainty that dwells invisibly in all triangles. Dwells invisibly until now. Dwells invisibly until revealed by Feghoot's Proof. Now hand me my boarding pass. I'm off to show this to my colleagues"

Feghoot steps into the Nick Machine, inserts his new boarding pass, and is instantly present in a distant Nick Machine on Aldebaran III.

Meanwhile the crossing guard (and you and I) are left with the paradox of the hole in the triangle.

Hole in the Triangle paradox


Alec MacCall said...

Clearly, Pythagoras did not encounter this paradox. It either would have set us back (forcing him to take up another profession, such as goatherder), or (according to Feghoot's interpretation)forward, either way a couple of thousand years.

J said...

Hey Nick, what do you think of this dark maatter web that's beginning to be described - looks kind of neurony/networky, eh?

Len Anderson said...

Neither of these two "illustrations" is a triangle. The configured "areas" are each wrong by the same amount, namely 0.5. The hypotenuse of each figure is bowed—one inward, the other outward. It is really difficult to see how this could make a difference of 0.5 in the area, so maybe there are some other variations that are yet harder to see.