Re: chaos <=> paradox. Prove me wrong. A challenge.

From: Will Twentyman (wtwentyman_at_read.my.sig)
Date: 10/05/04 

Date: Tue, 05 Oct 2004 07:47:31 -0400

Lefty wrote:
> Elegance and simplicity - I suppose we would like the world to be that way
> and often times we find that it is.
>
> Most mathematicians hate paradoxes because they are confounding, and they
> hate to be confounded by something.

Please stop saying this. I have not met a mathematician who feels
anything close to dislike, much less hate, for paradoxes. If a
mathematician encounters a contradiction, it indicates that work needs
to be done to remove it. Once that work is done, the contradiction is
reduced to a paradox because it now only *appears* to contain a
contradiction.

> But the simple fact that there is something which is contradictory and
> unresolvable - I dont know if this is neccesarily just another example of
> linguistics.

A paradox is not a contradiction. Contradictions occur as one of the
major techniques of proof in mathematics.

> Take for example- "This statement is false". A paradoxical sentence.
> It contradicts itself logically.

It is a paradox only under the assumption that it can be assigned a
truth value. Once you realize it is not a statement (having a truth
value), the apparent contradiction goes away.

> My question is this - In writing such a sentence, did you perform a feat of
> literature, or was it a physics experiment ? After all, if you can compose
> paradoxical prose, then perhaps the universe is "allowing" it somehow. I
> thnk it's a property of space/time. That's my 2 cents.
>
> Maybe in a different universe it would not be possible to compose a
> paradoxical statement depending on the nature of that universe.
>
> If paradoxes can exist in the physical universe, then the laws of physics
> can probably be broken. I can hear you laughing. But then, our expectation
> that the "laws" of physics inviolable is an entirely human projection. God
> never made such a promise to anyone.

An apparent paradox in the physical universe merely indicates a flaw in
our understanding of it.

> And ultimately, yes - it is a load of crap unless it can be proved. So tell
> me - how does one prove "any" mathamatical property in the real universe ?

Mathematics isn't about reality. We just describe it within the bounds
of reality.

> I
> dont think that this has ever been done. Can you prove that straight lines
> exist in space ? Do points exist in space ? Is space continuous ? And what
> about infinity ? Does counting things make sense ? Does randomness exist in
> space ?

no, no, maybe, no, yes, yes.

Of course, are just my oppinions.

> There is probably a trick to make it work, but nobody has unlocked that
> secret either. Any suggestions ?

A trick to making what work? Paradox or math? 

-- 
Will Twentyman
email: wtwentyman at copper dot net

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