Subj : Re: Polymorphism sucks [Was: Paradigms which way to go?]
To   : comp.programming,comp.object
From : Dmitry A. Kazakov
Date : Tue Aug 16 2005 01:33 pm

On Mon, 15 Aug 2005 11:35:35 -0500, Chris Sonnack wrote:

> Dmitry A. Kazakov writes:
> 
>> Hmm, was Shannon aware of Hilbert's program? I think he was.
>> Anyway in the times after Goedel, we know that there is no
>> way to "break" everything down to 1s and 0s.
> 
> Are we possibly talking about two different things here?  Yes,
> Goedel showed we can't fully analyse any non-trivial system,
> but I believe Shannon hasn't been superceded in the sense that
> anything that *can* be expressed or computed can be expressed
> or computed in binary.

Which contains a hidden tautology, of course. Everything = anything
computable in 1s and 0s? (:-))

>> And even if there were one, neither fuzziness nor randomness
>> can be expressed in a deterministic system without some
>> incomputable elements.
> 
> But they are incomputable by *any* means, right?

That's an interesting question. It depends on the hardware. We don't know
if the Universe can offer us anything beyond Turing machine. In particular,
can our biological "hardware" compute incomputable? Nobody knows it for
sure. Then there is quantum computing. So far people are busy trying to
make 1/0s computing out of it. But let's look in another direction. What if
quantum computing is more than that? Purely fictitious, let you can compute
random distributions, rather than their realizations (the only thing we can
do now), then this class of computing will be incomputable for any Turing
machine.

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de

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