Re: Poll: Are PCs Turing Machines?

From: |-|erc (h_at_r.c)
Date: 12/14/04

  • Next message: |-|erc: "Re: Poll: Are PCs Turing Machines?" 
    Date: Tue, 14 Dec 2004 09:39:17 +1000

    "Mark Nudelman" <markn@greenwoodsoftware.com> wrote in
    > > 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.
    >
    > Yes, I do make such an assumption. This assumption seems fairly trivial.
    > In my example, I don't even care about the calculation itself, only that the
    > input is a 10^1000 digit number. There's no conceivable way to even store
    > such a number without a corresponding amount of memory.
    >
    > > 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".
    >
    > I don't think the randomness of digits in pi has anything to do with the RH,
    > but I could be wrong. But calculating pi wasn't my example.
    >
    > > 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.
    >
    > This is true, but the question was, "can a PC simulate a TM". I assumed
    > "PC" meant a real PC, existing in our universe. If you want to hypothesize
    > a universe in which there is an infinite amount of matter, which can be
    > formed into an infinite amount of memory units in a finite time, and in
    > which there is no speed-of-light limit on information transfer, then, yeah,
    > a PC can probably simulate a TM. But I don't think that was the question
    > that was asked.
    >

    Argument 1
    The question is: Is there a TM that logically represents a PC?
    or, for any PC, is there a TM that logically represents it?

    ie. are PC's Turing Machines?
    as in, are Traffic Lights automations?
    YES

    Argument 2.
    Everything possible in the real world can be represented / simulated functionally.
    All functions can be represented by TMs.
    Therefore anything can be represented by a TM.
    Therefore PC's can be represented by a TM.
    Therefore PC's are TM's.

    Most people have the infinite memory argument backwards.

    Is a TM a #FSM? NO a FSM would run out of memory for many TM's.

    Herc
    #FSM = finite state machine

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    • Re: Poll: Are PCs Turing Machines?
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