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.
The consequence is that, a priori, the laws of physical cannot be
digital, the physical reality cannot be Turing emulable, nor can
consciousness. Both matter and mind becomes global feature of the
fabric of reality. Mechanism (I am a machine) entails that the
everything which is not me, cannot be a machine (like arithmeyical
truth cannot be emulated by any machines). In fact mechanism is
incompatible with digital physics.
Mechanism (I am a machine) entails that the "everything which is not
me", cannot be a machine (like arithmetical truth cannot be emulated
by any machines). In fact mechanism is incompatible with digital
physics.
But this was an answer to David's remark that "the great programmers"
explains too much, and so don't explain anything. In fact it explains
nothing, but its effective version makes it possible to formulate the
mind body problem, and to solve it both conceptually, and technically
(but this leads to mathematical open problems, some of which have been
solved since).
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.
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.
The second question I have to David is why you say "The whole point of
universality is lost if one conceives of computation as being somehow
prior to the physical world."?
Good question. I am interested in what David can say about this. The
notion of universality has been discovered by mathematician, and is
indeed a provably arithmetical property of numbers, relatively to
numbers.
I do appreciate that mathematically, hypercomputers exist, an example
being the infinity hotel example you give in your book.
I will have to read that. In fact I think that hypercomputation is a
red herring. Basically our reality must seem "hypercomputed" (and even
worst that that) once we are digital machine. The analytical (which is
above the arithmetical, which is itself above the computable (sigma_1
arithmetical), and the physical are internal aspect of the computable,
once we assume that "we" (not the universe) are Turing emulable.
So a
consequence of something like Schmidhuber's theory is that
hypercomputers can never exist in our physical world.
The opposite conclusion than mechanism. But digital physics entails
mechanism, and mechanism entails the falsity of digital physics. This
means that digital physics is a contradictory notion.
I suppose you would say that if physics were generated by machine, why
the class of Turing universal machine, and not some hyper-(hyper-)
machine? Whereas in a physics-first scenario, physics can only support
Turing computation.
If "I" (whatever I am) is a machine, then the universe (whatever
responsible for me to exist) cannot be a machine, nor explicitly
generated by a machine (but it can be, and need to be *apparent* to
machines points of view). This follows from the Universal Dovetailer
Argument (and I wait some replies on it on the FOR list).
Surely though, we can reverse the question in the physics-first case -
why can't physics support hypercomputation?
Good question. Actually some solution of Einstein equation for gravity
allows some form of hypercomputation, but I doubt this can resist the
unknown theory unifying QM and GR. But classical computers + random
oracle (which cannot be simulated by classical computer without using
the self-multiplication stuff) can be simulated with a quantum
computer. In fact both digital mechanism and quantum physics implies
the availability of "true" random oracle.
Cheers
I'm copying this to the everything-list, as people there are
interested in this topic too.
Thanks,
Bruno
----------------------------------------------------------------------------
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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