Registered: Aug 2002
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Well, forgive the title, but I couldn't think of a better one. Hopefully you wanks will look past that and read on.

I have for many years now found the ideas of entropy and absolutism -- the sort of dialectic between randomness and certainty -- wholly captivating. Perhaps it is a function of my world view, but I see this present in a wide array fields: physics, art, morality, philosophy, and even mathematics. It occurs to me that it has been an ever-present concern for man. The themes of chaos and order are really nothng new. Mythology is infused with it. It has been argued that ancient cave paintings are man's first attempts at codifying the world around him through art. Symbolic reasoning is perhaps man's greatest gift. I suppose then, that I shouldn't be surprised to see this age-old dialectic carried on in whatever form that reasoning may assume.

Anyhow.

I read a similar article to the one that follows by this same mathematician several years ago. The following isn't quite as elegant. Probably that is due at least in part because this is a transcript from a speech, whereas what I read before wasn't. Nevertheless, it does hit on all the same themes. Providing you can tolerate some squiggly symbols and mathematical hand-waving, perhaps you will find some value in it.

Go here. I would have quoted the text for the lazy, but the formatting would be irrepairably lost. Plus, there are links and pictures that some might find interesting.

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Dunno if anyone finds any value in this or not, but I find this sort of thing endlessly fascinating. Here is a corresponding article linked from the one above. It discusses the findings of two physicists who argue that the basic structures of the universe arise from nothing but noise. They were able to simulate this using a very simple computer model which, over time, produced some of the familiar structures of space-time via random interactions.

Amazing stuff if you ask me.

[scanned from the magazine]
Cover
page 1
page 2
page 3
page 4
page 5

[pdf version]
link

[hrm, better html version]
link

Last edited by tessellated on 12-04-2004 at 10:48 PM

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Page 1's a blueprint for a roller coaster,ya?


There is no spoon.

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I always found it interesting that Michael Moorcock set up his central battle not as the hackneyed old 'good versus evil' but as 'order versus entropy'.

I'm not familiar with Chown's statement of Godel's incompleteness theorem; I thought that it was that there are statements whose truth or falsity cannot be deduced, thus they are undecidable (in the sense of being both unproveable and unrefutable) and thus can be added, without contradiction, as additional axioms. The 'Continuum Hypothesis' is the example normally given. I also think that the Incompleteness Theorem only applies to axiomatic sets that include arithmatic.

In his book 'Pi in the Sky', John Barrow talks a little about possible implications, for physics, of the incompleteness theorem.

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quote:

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Originally posted by Smug Git
I always found it interesting that Michael Moorcock set up his central battle not as the hackneyed old 'good versus evil' but as 'order versus entropy'.

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There's only one straight line that goes through 2 points. Was he referring to this?

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The idea of 'true theorems that can't be deduced' is what I objected to. Axioms are 'true by definition' and these 'incompleteness theorem' propositions are things that can be added as axioms or their negation can be added as an axiom, and I didn't think that was particularly clear from what he said.

I'm often rather dubious of exciting new developments of this nature that appear in popular science magazines, because often enough they make something new and exciting out of something that really isn't revolutionary (such as the furore about 'Chaos Theory', which if it was a revolution, was a fucking slow one). There is something compelling about entropy though, particularly when you look at the statistical mechanical model (basically Boltzmann's picture). It is pretty weird to think about it, even though it is pretty intuitive (more than it is in the thermodynamical model, say).

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I totally agree.

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YUP. Me too.

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Hmm. Ok, I guess I see your objection, but I don't really think it impacts the article in any way.

True too that science magazines often oversell their product -- market forces and all that rot. I was never particularly enamored of Chaos Theory. I think it owes most of its popularity due to all the pretty calendars sold in mall kiosks or the toy fractal programs on the internet. That this Chaitin fellow showed that randomness is intimately bound up in the structure of math, or rather that some of the structure of math lacks any structure, I find pretty mind-blowing. As you know, there is a long history of interplay between math and physics. The New Scientist article is just a specific example. I'd like to find others if they exist.

What these guys really need to do is produce something resembling a physical law from their computer model.

Last edited by tessellated on 12-05-2004 at 12:38 AM

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"Absolutely Nothing" -- basically describes what goes on here every day!

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I read the article. It was interesting but it made my head hurt. I'm sick and my head already hurts, so it's not the article's fault. I lost him during his explanation of program-complexity theory. I didn't quite get why you can't prove any lower bounds on the program-size complexity of individual objects and I lost him from there. I'll read the article again and then read the link you provided and the links in the article and see if that helps.

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i woke up, read the article and now i sleep again.

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this is a useless post that will not add anything to the discussion. but i thought that i should make it to remind you all that i still excist
-gorilla biscuit

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this is another useless post adding nothing to the discussion except a cheap attempt at humour but I thought I would make it anyway to remind you all that I'm a hypocrite.
-Hawley Griffin

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have i ever made a usefull post?

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YES!

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you are not helping

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quote:

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Originally posted by Hawley Griffin
have i ever made a usefull post?

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har har now youre flaming skills suck less

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Ignatz, here is another version of his lecture. Maybe it will help clarify...or maybe it will only confuse! :P

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If the barber doesn't shave himself, then he shaves himself because he shaves everyone who doesn't shave himself.

Of course, you have to remember that the self he shaves isn't the self he shaves on the shelf while shelling for sea shell shavings which he sells. Now if he shaves the self he's shelving, can he save the self who's shelling for shavings? Ask Shelley, silly!

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Hmm, speaking of which he talks about Boltzmann and statistical mechanics directly, Smug, comparing his idea of program-size complexity to entropy.

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