Re: Arthur O'Dwyer on the feasibility of simulating a Turing Machine

From: Edward G. Nilges (spinoza1111_at_yahoo.com)
Date: 02/29/04

  • Next message: Edward G. Nilges: "Re: Arthur O'Dwyer on the feasibility of simulating a Turing Machine" 
    Date: 28 Feb 2004 17:34:54 -0800

    Calum <calum.bulk@ntlworld.com> wrote in message news:<c1q1sr$t0d$1@newsg4.svr.pol.co.uk>...
    > Edward G. Nilges wrote:
    > > Ian Woods <newspub2@wuggyNOCAPS.org> wrote in message news:<Xns949CEAB025450newspubwuggyorg@217.32.252.50>...
    > >
    > >>spinoza1111@yahoo.com (Edward G. Nilges) wrote in
    > >>news:f5dda427.0402270201.44a84f6b@posting.google.com:
    > >>
    > >>
    > >>>Ian Woods <newspub2@wuggyNOCAPS.org> wrote in message
    > >>>news:<Xns949B6A55F24D3newspubwuggyorg@217.32.252.50>...
    > >>>
    > >>>>spinoza1111@yahoo.com (Edward G. Nilges) wrote in
    > >>>>news:f5dda427.0402252138.41cb7360@posting.google.com:
    > >>
    > >><snip>
    > >>
    > >>>>>There are
    > >>>>>hundreds of working TM simulators of which I've written about
    > >>>>>three.
    > >>>>
    > >>>>None of which will run all of the programs which a TM can run. The
    > >>>>conclusion? They're not a full implementation of a TM.
    > >>>
    > >>>(Sigh) You've just managed to deny Church's thesis and you have said
    > >>>that modern computers aren't Turing complete.
    > >>
    > >>Are you claiming that every program computable on a TM is computable on a
    > >>modern computer?
    > >>
    > >
    > > Given enough time and memory space, yes. Furthermore I've already
    > > shown you how to trade time for memory so as to avoid the problem of
    > > "a finite amount of matter".
    >
    > I don't really "get" your argument about achieving infinite storage from
    > a finite universe. Let me paraphrase what I believe you said: I have a
    > memory that is only one binary digit. But that's okay, because I can
    > store a sequence of digits there, effectively turning my 1-bit memory
    > into unlimited storage. So how can this ingenious invention of yours be
    > used for practical benefit, and cutting my RAM costs considerably?

    Let's reduce the question to whether a "stationary" Turing Machine
    could be a UTM, not moving its tape and using ONE square for all
    memory.

    Because the alphabet of TMs is unconstrained it could store one of an
    infinite number of decimal digits, infinitely long, on the one square.

    Similarly its state is an unbounded integer.

    Could this contraption work as a UTM?

    [These sorts of questions make more sense and are more precise than
    diffuse discussions by physics majors.]
    >
    > Of course, there may be some other esoteric physics that might help us.
    > e.g. White holes, quantum superpositioning, that potentially _do_
    > allow unlimited storage, however I doubt the information holding
    > capacity of such things would be _infinite_. And hey, how would you
    > read it all?
    >
    > And then of course, even if you could trade time for space, you don't
    > have infinite time either. Even if you flipped your 1-bit memory at 1
    > TeraHertz for 10 billion years, you still have finite storage.
    >
    > So back to square one?
    >
    > Calum

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