On 03 Oct 2011, at 01:40, Russell Standish wrote:

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On Sun, Oct 02, 2011 at 01:42:19PM +0200, Bruno Marchal wrote:Hi Russell, On 02 Oct 2011, at 11:37, Russell Standish wrote:In David Deutsch's Beginning of Infinity chapter 8, he criticisesSchmidhuber's Great Programmer idea by saying that it is giving uponexplanation in science,Actually I did address this point on the FOR list years ago. Somehow, I share David's critics on Schmidhuber's idea of a great programmer when seen as an *explanation* (of everything). My (older, btw) publications makes this point clear. The Universal Dovetailer (which can be seen as an effective and precise version of the "great programmer", and which is a tiny part of elementary arithmetical truth) makes it possible to *formulate* (not solve!) the mind body problem mathematically, but Schmidhuber use it as an explanation gap. He missed the fact that if we are machine we cannot know in which computations we are and we have to recover the physical laws, not from one computation but from an internal (self-referential) statistics on infinities of computations, and that statistics has to be recovered entirely from the self-reference ability of machine.Sure - Schmidhuber, with his speed prior, assumed that the specific implementation of the universal reference machine has physical consequences, but we, thanks to your work, know better. David's criticism was quite specific - because the specific implementation of the UTM doesn't have any physical consequences, therefore one is somehow giving up on obtaining the ulimate explanation. My response was that surely the question becomesuninteresting (David's terminology) - or even meaningless (as youstate below).

`It means that from a comp view, to fix a UTM for physical reality like`

`a quantum computer, would be a treachery, would be bound to be wrong,`

`and would miss the opportunity of the necessary Solovay split for`

`distinguishing quanta and qualia.`

... snip ...But this was an answer to David's remark that "the great programmers" explains too much, and so don't explain anything.I'm aware of this criticism, which applies to ensemble theories ingeneral. IMHO, the only way to address that critique is with somesort ofobserver-relative anthropic selection - but that is a whole othertopic!

`OK. The time has not yet come to dig on the heart of the ASSA/RSSA`

`thread :)`

as the hardware on which the "Great Program" runs is unknowable.Of course the contrary is true. If we are machine, we know (up to some recursive equivalence) what runs us, and where the possible hardware come from. Any first order specification of any universal machine or theory will do the job. I use elementary arithmetic because we are all familiar with it. The laws of physics cannot depend on that choice.We're actually saying the same thing here.

OK.

David, why do you say that? Surely, the question of what hardware is implementing the Great Simulators simply becomes uninteresting, much likethe medieval arguments about the number of angels dancing on theheadof a pin. It is unknowable, and it doesn't matter, as any universal machine will do.I disagree with this. The notion of primitive hardware is precisely shown to be meaningless. The laws of physics are shown to be machine independent. Eventually the initial universal system plays the role of a coordinate system, and the laws of physics does not depend on it.Isn't this stating the above in a stronger form? "Meaningless", rather than "unknowable"?

`Yes. But it is important to chose one which facilitates the derivation`

`of the couplings consciousness/matter, or quanta/qualia.`

`We can choose a quantum computer, but this will make the extraction of`

`quanta very confusing, with a risk of "treachery" at each step. Given`

`that self-reference is born in arithmetic (OK, in Gödel's Principia`

`Mathematica, but soon on much weaker theories, which makes the result`

`more general), and given that arithmetic is taught in high school, I`

`think it is the better choice. Especially that arithmetic distinguish`

`nicely universality (the everything) and Löbianity (the observer`

`person multiplied in the everything), by the passage from Robinson`

`arithmetic to Peano Arithmetic. It helps to use mathematical logics to`

`solve a problem in computer science. The universality notion used in`

`AUDA is the notion of sigma_1 completeness. The restriction of the`

`probability to UD accessible states, in translated in arithmetic by`

`the restriction of p to the sigma_1 sentence.`

`And then I appreciate the numbers and number theory, but well I`

`appreciate also the combinators and more abstract applicative algebra`

`too.`

`To do the work we have to choose a theory (as conceptually simple as`

`possible), then this gives the phi_i and the w_i, which defines the`

`computations and their domains.`

Bruno

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