Subj : Re: Polymorphism sucks [Was: Paradigms which way to go?]
To   : comp.programming,comp.object
From : Mark Nicholls
Date : Fri Aug 19 2005 04:22 am


Dmitry A. Kazakov wrote:
> On 18 Aug 2005 04:32:05 -0700, Mark Nicholls wrote:
>
> >>>> 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.
>
> But computer is a physical object. You can build it of atoms, you cannot do
> it out of thoughts.

A turing machine is not.

> Many people strongly believe that the physical world is
> equivalent to a giant FSM, which is even weaker than a TM.

TM?

>
> >> In particular,
> >> can our biological "hardware" compute incomputable?
> >
> > Isn't this the point about 'belief',
>
> That could be that sort of questions Goedel's incompleteness is about.

That was really my point about the god discussion, science is limited
by maths, and that is limited, belief needs to be consistent with the
maths, but can live in the gaps.

>
> > 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.
>
> There are two objections to this:
>
> 1. You cannot say what follows from the axioms (Goedel.)

you can say a lot, but not everything.

>
> 2. Not that I would insist on it, but it is thinkable that the minimal set
> of axioms required to adequately describe what's going on [by means of our
> logic] could be bigger than the number of the states of all our brains.

Goedel would imply that the set of axioms required for the system to be
complete is unbounded, if the states of our brains are finite, then we
cannot 'know' everything.

>
> > Would it be capable of belief in the absence of formal proof? Could it
> > discern the truth?
>
> An extended Turing test, a capability to believe in irrational as a
> criterion of intelligence? (:-))
>

irrational may be strong....though people often believe irrational
things.....unprovable certainly.

so it is reasonable to believe in god
it is reasonable to not believe in god
it is irrational to assert that you know the answer......it would be
harsh on the proponent of aethiesm as a fact to assert that that made
him unintelligent!

.