the self-referential universe
 

I recently came across the mathematically cute topic of self-referential sentences -- sentences that make statements about their own content. It is interesting that one can start out with a self-referential sentence that says something blatantly false about its own content, and then iterate it using a very simple technique, and you will eventually be led to a sentence that says true things about its own content (or possibly to a set of sentences that say true things about one another).

Now, ordinarily I wouldn't care too much (it's a very "pure math" type of subject), but this one gave me a very peculiar feeling. After thinking about it a while, I think I found out why. The universe can be thought of as a bunch of information (a "sentence"), and in fact it's a self-referential sentence -- we humans (scientists/physicists, specifically) are a part of the sentence, and we make statements about the rules governing the sentence itself. And in fact, we have a kind of iterative process (called science) whereby we take current statements, compares them to experiment, and then construct refined statements which get us a little closer to the truth (analogous to attraction to a "fixed point").

I'm not sure what else to say -- I suppose I'm wondering if this similarity is anything more than superficial, and if it can be used to make non-obvious statements about the nature of science, or the universe itself. Any opinions or ideas?

Re: the self-referential universe
 

Informally speaking, Kurt Godel's Incompleteness Theorem for formal theories of arithmetic is based on the peculiar nature of self-referential sentences. Godel's Theorem showed that the massive project undertaken by Russell and Whitehead in Principia Mathematica to reduce all mathematical truths to logic was impossible.

Re: the self-referential universe
 

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Informally speaking, Kurt Godel's Incompleteness Theorem for formal theories of arithmetic is based on the peculiar nature of self-referential sentences. Godel's Theorem showed that the massive project undertaken by Russell and Whitehead in Principia Mathematica to reduce all mathematical truths to logic was impossible.

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It's also the basic reason that no general solution to the halting problem can exist in computer science. Probably there is something analogous to be said about physics, which is by its nature self-referential.

Re: the self-referential universe
 

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[ QUOTE ]
Informally speaking, Kurt Godel's Incompleteness Theorem for formal theories of arithmetic is based on the peculiar nature of self-referential sentences. Godel's Theorem showed that the massive project undertaken by Russell and Whitehead in Principia Mathematica to reduce all mathematical truths to logic was impossible.

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It's also the basic reason that no general solution to the halting problem can exist in computer science. Probably there is something analogous to be said about physics, which is by its nature self-referential.

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Well then, let us be so bold as to say it: physics is impossible! [img]/images/graemlins/smile.gif[/img]

Re: the self-referential universe
 

it's late and my state is altered, but your post reminds me of the idea that I am God, and that I invented myself and the world out of nothing.

for example, the world does not really exist, i am merely imagining it.
if the world doesn't exist, then how am i able to exist to imagine myself? given the rules of my imaginary world, i could exist, therefore i can exist in said imagination.

the mechanism is similar to your self-referential sentance.

this is essentially the same idea (that i saw mentioned in another thread here) that says: everything that possibly could happen is happening, all at once, in different planes/worlds.

Re: the self-referential universe
 

Re: the self-referential universe
 

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http://www.amazon.com/Self-Aware-Uni.../dp/0874777984

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That's interesting -- my undergrad quantum mechanics course used Amit Goswami's QM textbook...

Re: the self-referential universe
 

These ideas are explored to great lengths by Douglas Hofstadter,
http://en.wikipedia.org/wiki/Douglas_Hofstadter

in "Gödel, Escher, Bach", and more recently
"I am a strange loop".
http://en.wikipedia.org/wiki/I_Am_a_Strange_Loop

If you are interested in the idea of 'loopiness', I'd just recommend to read the books.

Re: the self-referential universe
 

Exactly what I was thinking. And Godel Escher Bach is an easy read, nice and dumbed down for people like me. [img]/images/graemlins/smile.gif[/img]