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Orchid XP v7 <voi### [at] dev null> wrote:
> (Evidently some people actually believe
> that the human mind is capable of deductions that are beyond
> Turing-completeness.
"Turing-completeness" doesn't mean "can calculate everything that can
be calculated", but "can calculate everything a Turing machine can calculate".
--
- Warp
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Warp wrote:
> Orchid XP v7 <voi### [at] devnull> wrote:
>> (Evidently some people actually believe
>> that the human mind is capable of deductions that are beyond
>> Turing-completeness.
>
> "Turing-completeness" doesn't mean "can calculate everything that can
> be calculated", but "can calculate everything a Turing machine can calculate".
Are you saying there are things that can be calculated but not by a
Turing machine?
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Orchid XP v7 <voi### [at] devnull> wrote:
> Are you saying there are things that can be calculated but not by a
> Turing machine?
As far as I can see, the Church-Turing thesis ("if an algorithm
(a procedure that terminates) exists then there is an equivalent Turing
Machine or applicable lambda-function for that algorithm") is a
hypothesis, not an axiom:
http://en.wikipedia.org/wiki/Church-Turing_thesis
The concept of hypercomputability, while theoretical, has been
considered.
http://en.wikipedia.org/wiki/Hypercomputation
--
- Warp
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From: John VanSickle
Subject: Re: A random interjection: the Halting Problem
Date: 30 Dec 2007 16:59:07
Message: <477814ab@news.povray.org>
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Warp wrote:
> John VanSickle <evi### [at] hotmailcom> wrote:
>> Which has the implication that computers will never be capable of
>> handling the process of software engineering without some level of human
>> assistance.
>
> Humans are bound to the same limitations as computers.
This has not been proven for all limitations pertaining to computers.
Regards,
John
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Warp wrote:
> Humans are bound to the same limitations as computers. If it has been
> proven that a certain problem is not solvable, a human cannot solve it
> either.
Not necessarily. Turing machines don't have a source of random input,
while humans do. Humans may or may not be deterministic.
--
Darren New / San Diego, CA, USA (PST)
It's not feature creep if you put it
at the end and adjust the release date.
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Darren New <dne### [at] sanrrcom> wrote:
> Turing machines don't have a source of random input
Would it change the properties of a turing machine if it had a source
of true randomness (eg. a command like "put a random value here")?
--
- Warp
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From: Darren New
Subject: Re: A random interjection: the Halting Problem
Date: 1 Jan 2008 15:34:02
Message: <477aa3ba@news.povray.org>
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Warp wrote:
> Darren New <dne### [at] sanrrcom> wrote:
>> Turing machines don't have a source of random input
>
> Would it change the properties of a turing machine if it had a source
> of true randomness (eg. a command like "put a random value here")?
I'm not sure. It would make it very difficult to have a UTM simulate it,
for example, that doesn't have that instruction, so I'd have to guess
"yes". :-)
--
Darren New / San Diego, CA, USA (PST)
It's not feature creep if you put it
at the end and adjust the release date.
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