Subj : Re: Polymorphism sucks [Was: Paradigms which way to go?]
To   : comp.programming,comp.object
From : Dmitry A. Kazakov
Date : Thu Aug 18 2005 08:23 pm

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

> 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.)

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.

> 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? (:-))

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

.