From: Marc Geddes (marc_geddes@yahoo.co.nz)
Date: Mon Aug 16 2004 - 00:30:03 MDT
--- Eliezer Yudkowsky <sentience@pobox.com> wrote:
> Marc Geddes wrote:
> >
> > Given that the language of science used to
> describe
> > the physical world is mathematical, and given the
> > Turing arguments (showing the mapping between
> maths
> > and algorithms), it follows that any of the
> equations
> > being used to describe a finite portion of
> physical
> > reality are back translatable into an algorithm.
>
> This does not follow automatically because physics
> is continuous, while
> Turing machines and Church's lambda calculus are
> discrete. It is only
> recently that new physical concepts such as
> holographic bounds on
> entanglement have begun to justify the appealing
> notion that the continuous
> distributions of quantum physics are finitely
> parameterizable. Previously
> the Church-Turing thesis only suggested that physics
> was computable in the
> sense that it could be computed to within epsilon.
> Turing machines don't
> handle real numbers, unless you choose a countable
> subset of symbolically
> describable real numbers. This is why I don't
> believe in real numbers,
> only finite objects that pretend to be distributions
> over real intervals.
Well, real numbers might exist in the sense that they
are a property of the multiverse as a whole. But in
our particular space-time region (what we call 'the
observable universe') we need finite objects to make
sense out of it.
>
> Albeit it was already a mathematical theorem that if
> our universe
> ultimately consists of a finite or countable set of
> axioms (i.e.,
> equations), and the axioms are satisfiable by any
> model, they must be
> satisfiable by a countable model.
>
> --
> Eliezer S. Yudkowsky
> http://intelligence.org/
> Research Fellow, Singularity Institute for
> Artificial Intelligence
>
Well, if my suggested metaphysics is corret (total
equiavlence beteen mathematics, mind, matter) then
reality as a whole (the multiverse) cannot have a
finite set of axioms. My reasoning: Godel's Theorem
says that there would have some truths which 'escaped'
the finite set of axioms. But this would mean that
mathematics was greater than physical reality (if
physical reality only consisted of a finite set of
axioms). Therefore the multiverse as a whole must be
a system with infinite axioms.
On the other hand, our particular location in the
multiverse (the 'observable universe') might indeed be
a system with a finite number of axioms. I don't
know.
I've been dropping way too many hints to the SL4 list
of late. I want Sing Inst to give me a run for my
money yes, that will be entertaining, but I don't want
them actually BEATING ME to FAI ;)
=====
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-H.G.Wells
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