From: Eliezer Yudkowsky (sentience@pobox.com)
Date: Sun Aug 15 2004 - 02:40:58 MDT
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.
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
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