Subj : Re: Polymorphism sucks [Was: Paradigms which way to go?]
To   : comp.programming,comp.object
From : Mark Nicholls
Date : Thu Aug 18 2005 05:32 am

>
> >> 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.

But the turing machine is a theoretical machine, it is not the universe
that constrains it (in terms of physics) but the maths, and that is
only constrained by the wit of man.

> In particular,
> can our biological "hardware" compute incomputable?

Isn't this the point about 'belief', i.e. that human rational is not
constrained by formal logic, it cannot be inconsistent with formal
logic (well it can be, but provability is a subset of 'truth'), but we
believe we can deduce the correctness of some assertions that are
beyond the scope of formal logic....(thus our previous discussion about
god, and aethiesm as a belief system, rather than within the scope of a
logical or scientific discussion).

> 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.
>

I haven't got a clue what quantum computing is, but you should be able
to model it, even if it doesn't exist....as long as it obeys the
axioms.

Would it be capable of belief in the absence of formal proof? Could it
discern the truth?

.