Re: Poll: Are PCs Turing Machines?

spinoza1111_at_yahoo.com
Date: 12/13/04 

Date: 13 Dec 2004 02:27:40 -0800

Interesting, because you assume based on present knowledge that there
exists at least one calculation that always and forever will require an
unbounded number of digits.

This may be true OR it may be an artifact of our knowledge. In the case
of pi the dependency, I understand, is on something called the Riemann
hypothesis, the solution of which may crack the problem of digit
patterns recurring in pi, in which case, a TM could calculate it to
arbitrary precision WITHOUT running out of "storage".

But at heart there is a major confusion when you make the answer to the
question "can a PC simulate a Turing machine?" dependent on physics.

Whether a PC simulates a Turing machine is a question unrelated to
physical and empirical data. You see, the assertion that the universe's
particle count is finite is an empirical assertion, not true in all
possible worlds because an infinite universe is physically possible, if
not verifiable.

>>From a philosophical standpoint, a PC does indeed simulate, emulate,
act like a Turing machine and these silly ass physical arguments only
serve to confuse the issue. For you don't understand computer science
until you understand not only that PCs simulate TMs but also that there
is no possible PC that goes beyond the limits described by Turing's
formalism.

I realize that it is popular to naturalize and fetishize technical
development and to claim that one goes beyond TM formalisms using
usually some clap trap from AI which turns out on investigation to be
spaghetti code, no more and no less.

Recall that we said "simulate". When an ordinary computer simulates
another, it may not be as powerful without the validity of a simulation
being placed in question. So it is for the Turing machine.

There is an unpleasant, even nasty theological undertone here in which
the Turing machine, based as it was on the daily struggles of working
people (for Turing was probably inspired by a Bletchley or City clerk
at work) is taken from the people and made into something which at this
juncture we simply do not need.

This is another goddamn Platonic myth in which one is supposed to stand
in awe of a completed infinity, pi in the sky, and the social effect of
these myths is of course to reinforce Guardian power.

Ultimately, the reaction towards Turing's discovery is emotional, and
it varies.

To some, it is a finished infinity and as such the concern only of a
professoriat which is permitted to concern itself with such
marginalities. To others it is an illumination, a story, a legend which
teaches a usable Truth.

Mark Nudelman wrote:
> spinoza1111@yahoo.com wrote:
> > Mark Nudelman wrote:
> >> I didn't say that a PC couldn't handle an input of X=10^1000. I
> >> said that it couldn't perform a calculation that requires 10^1000
> >> _storage cells_. (For example, multiplying two numbers, each of
> >> which has 10^1000 digits.) There isn't enough matter in the
universe
> >> to even begin to build a computer that could hold a 10^1000 digit
> >> number.
> >
> > Doesn't have to hold complete numbers: think "events". Is sent
digits
> > just in time. Emits significant digits of product and revises them
> > when carry forward occurs.
>
> You're trying to enhance the PC by adding some kind of input / output
device
> to hold unprocessed input and temporary results. I would consider
that
> equivalent to just making the PC's memory bigger. But where in the
universe
> are you going to hold the input before you give it to the TM, and
where will
> you store the intermediate results? The problem is NOT that a PC is
not big
> enough to hold a 10^1000 digit number -- the problem is that the
universe
> isn't big enough. Moving the storage outside the PC doesn't solve
the
> problem.
>
> > But even if you want to have and to "hold" a 10e4 number, think
> > biocomputation and the coming ability to inscribe data on
molecules,
> > on cells thereby oops creating designer diseases.
>
> I deliberately chose the example to invalidate this kind of solution.
Even
> if you inscribed your data on elementary particles, and even if
there's a
> lot more matter in the universe than we think -- even if the
observable
> universe was packed solid with electron-sized memory cells, there
still
> wouldn't be nearly enough memory to hold a 10^1000 digit number (by
which I
> mean an integer containing 10^1000 digits -- I'm not sure what you
mean by
> "a 10e4 number").
>
> --Mark

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