Re: Poll: Are PCs Turing Machines?
From: Stephen Harris (cyberguard1048-usenet_at_yahoo.com)
Date: 12/08/04
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Date: Wed, 08 Dec 2004 12:46:18 GMT
"Mitch Harris" <harrisq@tcs.inf.tu-dresden.de> wrote in message
news:31nubiF3d9i8aU1@news.dfncis.de...
> Will Twentyman wrote:
> >
>> There are no physical Turing Machines.
>
> That just seems to be a common way of sidestepping the issue. The
> only explanation I can see of your statement is that TMs are
> considered to be only theoretical constructs.
Yes, that is exactly right. And the people who don't know this
are the people who have only a vague notion of what a TM is.
You can find 50+ definitions on the web which say a TM is an
abstract, or theoretical, or hypothetical, or notional device.
That is the definition which I don't think you learned. There are
only philosophical issues for those who don't know the definition.
>But that seems to me to
> be similar to saying, there are no physical examples of the number 2,
> because, of course, 2 is an abstraction. When you have two apples,
> you don't have literally the number 2. But everything you want to say
> about the number of those apples is in the 2.
>
Not similar to me. You can link twoness to reality. You can point and
say there are two PCs but never point and say there is one Turing tape.
TM tapes are often described as potentially infinite. Infinity is not a
number.
The memory of the TM is boundless. The memory of a PC cannot
be boundless so it does not physically exemplify a TM nor can it
ever without postulating infinite physical parallel universes which
the Many Worlds interpretation does not do.
Where does the physical energy to operate the TM come from?
Nor is there any time constraint on how long a TM computes or
how fast as given in Turing's 1936 paper. These are not properties
which are part of physical reality.
A TM can be partially simulated by a PC. Except for the boundless
memory and the lack of a physically imposed time constraint. But
this is exactly why a TM can compute more finite digits of Pi than
any physical computer, even if it (PC) uses all the matter in the universe
for its memory. And that is the issue this thread is about. Not that PCs
are similar in many respects to TMs, nor denying that PCs drew some of
their inspiration from TMs. Though PCs are closer to von Neumann machines.
> --
> Mitch Harris
> (remove q to reply)
>
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