Friday, December 19, 2008

Strange Loop

Starting from Moebius strip(I would say its a simple kind of strange loop), we come across many strange loops. It may sometimes be visual, or audible or sometimes hardly noticeable. Shepard tones are example of audible strange loops. Dorste effect is an example of visual strange loop.
These strange loops could be easily noticeable(I can't say understandable).

Some of the strange loops need bit more smartness even to notice. Not every one can see the beauty in it. Well! people say its strange, but I call it beauty. It needs cleverness to form such a strange loop.

Here is an example
Every natural number can be unambiguously described in fourteen words or less.
I can prove the above statement using smart arguments.
Proof:
1.Suppose there is some natural number which cannot be unambiguously described in fourteen words or less.
2.Then there must be a smallest such number. Let's call it n.
3.But now n is "the smallest natural number that cannot be unambiguously described in fourteen words or less".
4.This is a complete and unambiguous description of n in fourteen words, contradicting the fact that n was supposed not to have such a description!
5.Since the assumption (step 1) of the existence of a natural number that cannot be unambiguously described in fourteen words or less led to a contradiction, it must be an incorrect assumption.
6.Therefore, all natural numbers can be unambiguously described in fourteen words or less!

Fantastic! Isn't? Of course there is something wrong in the proof. But the way its constructed is beautiful. Not every one can see the self referential statement here.

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