**From:** *geodesicallyincomplete@warpmail.net*

**Date:** Sun Apr 27 2003 - 13:30:46 MDT

**Next message:**Eliezer S. Yudkowsky: "Re: Infinite universe"**Previous message:**Simon Gordon: "Re: Infinite universe"**In reply to:**Perry E. Metzger: "Re: Infinite universe"**Next in thread:**Spudboy100@aol.com: "Re: Infinite universe"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

"Perry E. Metzger" <perry@piermont.com> wrote:

*> I missed that -- could you give me a quick quote from it so I can do a
*

*> search through the paper for the section?
*

"Indeed, if this exponential growth of the number of bubbles has been

going on forever, there will be an uncountable infinity of such parallel

universes [...]" (pages 5-6 of the .pdf)

*> Mmmm. Well, if the universe was too simple, what would we do for fun in
*

*> coming millennia? :)
*

It's not so much the possibility that there might be a lot more to think

about that bothers me (that's a good thing) as the possibility that all

these ideas are going in completely the wrong direction and will collapse

because of various paradoxes lurking on my horizon of comprehension.

A few comments on formal systems.

It's not obvious to me they should all have a finite number of axioms.

Googling, I see people talk about "recursively axiomatized formal

systems", which means that their set of axioms is recursive, which means

it doesn't have to be finite. Their number remains countable, though.

By "mathematical structure" Tegmark means an equivalence class of formal

systems. This is explained further in his older paper at

http://xxx.lanl.gov/abs/gr-qc/9704009.

In the same paper, he argues set-theoretic models (which are themselves

formal systems) have the same physical existence as the formal systems of

which they are models. In that sense, the universe (and others) can be

seen as a set.

Nus (prophet of the universal quantifier)

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