Dear Jürgen, what you say about TOEs is fine, just one question:
aren't we supposed to KNOW about everything before we put everything into an
equation? (algorithmic or not).
(first: omniscient, then make equation out of 'it').
John Mikes
<jamikes.domain.name.hidden>
"
http://pages.prodigy.net/jamikes"
----- Original Message -----
From: <juergen.domain.name.hidden>
To: <everything-list.domain.name.hidden>
Sent: Thursday, February 08, 2001 11:54 AM
Subject: Algorithmic TOEs vs Nonalgorithmic TOEs
> Algorithmic theories of everything (TOEs) are limited to universe
> histories describable by finite computer algorithms. The histories
> themselves may be infinite though, computable by forever running programs.
>
> To predict a future we need some conditional probability distribution
> on possible futures, given the past. Algorithmic TOEs are limited
> to distributions computable in the limit, that is, there must be some
> (possibly forever running) finite computer program that approximates
> with arbitrary precision the probability of any possible future.
>
> What about NONalgorithmic TOEs? For instance, once one assumes that
> the cardinality of possible futures equals the cardinality of the real
> numbers one has a NONalgorithmic assumption.
>
> I postulate that the restricted, algorithmic TOEs are preferable over
> nonalgorithmic TOEs, for two reasons: they are simpler, yet there is
> no evidence that they are too simple. They are simpler not just in some
> vague, model-dependent, quantitative way but even in a fundamental and
> qualitative way, because they are fully describable by finitely many
> bits of information, while NONalgorithmic TOEs are not. We can write
> a book that completely describes an algorithmic TOE. We cannot write a
> book that completely describes a nonalgorithmic TOE.
>
> Algorithmic TOEs vs nonalgorithmic TOEs - it's really like describable
> things vs nondescribable things.
>
> I join those who claim that things one cannot describe do not exist.
> For instance, most real numbers do not exist. Huh? Isn't there a
> well-known set of axioms that uniquely characterizes the real numbers?
> No, there is not. The Loewenheim-Skolem Theorem implies that any first
> order theory with an uncountable model such as the real numbers also
> has a countable model. No existing proof concerning any property of
> the real numbers really depends on the "continuum of real numbers",
> whatever that may be. Our vague ideas of the continuum are just that:
> vague ideas without formal anchor.
>
> Some might think there is an algorithmic way of going beyond
> algorithmic TOEs, by writing a never halting program that outputs
> all beginnings of all possible universe histories in a continuum
> of histories --- let us call this an "ensemble approach":
> http://www.idsia.ch/~juergen/everything/html.html
>
> But while there is a clever ensemble approach that needs only countably
> many time steps to output ALL infinite histories that are INDIVIDUALLY
> computable within countable time, and to output their FINITE complete
> descriptions, there is no ensemble approach that outputs ALL histories of
> a continuum: http://rapa.idsia.ch/~juergen/toesv2/node27.html The ensemble
> approach is firmly grounded in the realm of algorithmic TOEs, and cannot
> go beyond those. An ensemble approach can output all incompressible finite
> strings, all with finite descriptions, but it cannot output anything that
> is not computable in the limit. In particular, the ensemble approach
> cannot provide us with things such as infinite random strings, which
> simply do not exist!
>
> The algorithmic constraint represents a strong, plausible, beautiful,
> satisfying bias towards describability. What we cannot even describe
> we must ignore anyway. The algorithmic constraint by itself is already
> sufficient to show that only histories with finite descriptions can have
> nonvanishing probability, and that only histories with short descriptions
> can have large probability: http://rapa.idsia.ch/~juergen/toesv2/ More
> is not necessary to demonstrate that weird universes with flying rabbits
> etc. are generally unlikely. Why assume more than necessary?
>
> Provocative (?), actually straightforward conclusion:
> henceforth we should ignore nonalgorithmic TOEs.
>
Received on Thu Feb 08 2001 - 15:08:56 PST