**From:** Eliezer S. Yudkowsky (*sentience@pobox.com*)

**Date:** Sat Apr 26 2003 - 19:13:47 MDT

**Next message:**Paul Hughes: "RE: Infinite universe"**Previous message:**Simon Gordon: "Re: Infinite universe"**In reply to:**Perry E. Metzger: "Re: Infinite universe"**Next in thread:**Perry E. Metzger: "Re: Infinite universe"**Reply:**Perry E. Metzger: "Re: Infinite universe"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Perry E. Metzger wrote:

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*> In the Level I universe (using the terminology we've been discussing),
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*> there are countably many universes for obvious reasons. In the
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*> Level III universe, there would also (I think) be countably many
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*> universes, because there are only finitely many quantum states any
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*> given volume of space could assume. At Level II, I must confess I
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*> don't understand the whole "chaotic perpetual inflation" thing well
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*> enough to grok but I'd guess "countable". At Level IV, if
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*> metamathematics follows the rules we've established for it in the last
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*> 120 years or so (i.e. we are talking about formal systems), by
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*> definition the set of all possible formal systems is countable.
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But a *single* Level IV Process could conceivably contain uncountably many

universes - aleph-one, aleph-two, or beyond - while still being just one

formal system according to your enumeration. There may be uncountably

many universes contained in other Level IV Processes - for example, a

Process might contain universes that run on reals or fields of reals.

Actually, Bayesia itself appears to be made up of fields of real and

complex numbers, but in a way that leads to only countably many universes.

Furthermore, the measure of these countably many universes appears to be

divided up among a finite number of distinguishable computational

processes at any finite time. After any finite amount of time within any

finite volume of space, there are a finite number of different possible

material configurations, a finite causal history (past light cone) for any

spacetime event, a finite cognitive embodiment for any distinguishable

thinking entity, and a finite number of finite subjective experiences that

are possible given a finite thinking time. Even if time grows without

upper bound, the t coordinate always has a finite value at any given

point; it never assumes a specific number called "infinity". Though

perhaps chaotic perpetual inflation means that any universe has an

infinite past history from "before" its Big Bang... still, it doesn't look

like this materially alters the point.

Thus, Bayesia consists of datums of possible diversity aleph-two (the

quantum fields), which interact in such way as to create a countable

number of universes, with their measure divided up among an enumerable

(but perhaps unbounded) number of distinguishable computational processes.

Perhaps much the same relation would likely hold of any Level IV Process

capable of containing conscious observers, regardless of how high an order

of infinity the number of universes was. And if so, perhaps we should

just expect to find ourselves in one of the simpler or most commonly

occurring Processes that gives rise to conscious observers, without having

an anthropic prejudice in favor of explanations that predict "finitely" or

"countably" or "uncountably" many observers.

-- Eliezer S. Yudkowsky http://intelligence.org/ Research Fellow, Singularity Institute for Artificial Intelligence

**Next message:**Paul Hughes: "RE: Infinite universe"**Previous message:**Simon Gordon: "Re: Infinite universe"**In reply to:**Perry E. Metzger: "Re: Infinite universe"**Next in thread:**Perry E. Metzger: "Re: Infinite universe"**Reply:**Perry E. Metzger: "Re: Infinite universe"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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