On 03 Oct 2011, at 01:40, Russell Standish wrote:
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 criticises
Schmidhuber's Great Programmer idea by saying that it is giving up
on
explanation 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 becomes
uninteresting (David's terminology) - or even meaningless (as you
state 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 in
general. IMHO, the only way to address that critique is with some
sort of
observer-relative anthropic selection - but that is a whole other
topic!
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 like
the medieval arguments about the number of angels dancing on the
head
of 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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Prof Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics [email protected]
University of New South Wales http://www.hpcoders.com.au
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