**From:** Eliezer Yudkowsky (*sentience@pobox.com*)

**Date:** Sun Aug 15 2004 - 02:40:58 MDT

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Marc Geddes wrote:

*>
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*> Given that the language of science used to describe
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*> the physical world is mathematical, and given the
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*> Turing arguments (showing the mapping between maths
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*> and algorithms), it follows that any of the equations
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*> being used to describe a finite portion of physical
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*> reality are back translatable into an algorithm.
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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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