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Hal Finney wrote:

*> > M. Pour-El and I. Richards [Computability in Analysis and Physics, Springer,
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*> > Berlin, 1989] have proven that ......................
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*> I haven't seen this result, but it is well known that Newtonian physics
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*> has similar properties. In fact you can do an infinite amount of
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*> computation in finite time using Newtonian point sources. I wouldn't be
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*> surprised if this QM result relied on similar unrealistic idealizations.
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Freeman Dyson wrote something about that result.

<The superiority of analog-life is not so surprising if you are familiar

with the mathematical theory of computable numbers and computable functions.

Marian Pour-El and Ian Richards, two mathematicians at the University of Minnesota,

proved a theorem twenty years ago that says, in a mathematically precise way,

that analog computers are more powerful than digital computers.

They give examples of numbers that are proved to be non-computable

with digital computers but are computable with a simple kind of analog computer.

The essential difference between analog and digital computers is that an analog

computer deals directly with continuous variables while a digital computer deals

only with discrete variables. Our modern digital computers deal only with zeroes and ones.

Their analog computer is a classical field propagating though space and time and

obeying a linear wave equation. The classical electromagnetic field obeying the Maxwell

equations would do the job. Pour-El and Richards show that the field can be focussed

on a point in such a way that the strength of the field at that point is not computable

by any digital computer, but it can be measured by a simple analog device.

The imaginary situation that they consider has nothing to do with biological information.

The Pour-El-Richards theorem does not prove that analog-life will survive better in a cold.>

http://www.edge.org/3rd_culture/dyson_ad/dyson_ad_index.html

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