[net.math] Mind and Turing Machines

ellis@spar.UUCP (Michael Ellis) (11/09/85)

    If I'm not mistaken, the AMOUNT of time taken as a very primitive Turing
    machine slogs laboriously thru its tape is a matter which we must
    clearly put aside. There was never any doubt at all from the very
    beginning that one might perform such tasks in a less laborious fashion.
    All that matters here is the machine's ability, given inputs {I1, I2,..}
    to produce outputs {O1, O2, ..} regardless of time. If the difference
    between time-at-input and time-at-output is yet another functional
    requirement, then it is only fair that us enginerds should get a chance
    to do a bit of redesign..

    Turing was the perfect mathematician in this sense -- having
    masterminded a particularly simple-brained approach, he expanded its
    theoretical conclusions without regard towards any physical
    consideration whatsoever.

    Clearly, there are many practical gadgets to improve on linear
    sequential search times -- binary trees, hashing functions -- so what?
    Why not use brute force -- an ENORMOUS amount of random access memory!

    With Todd Moody's extravagant method, we can simply reduce all of human
    intelligence to a gargantuan storage medium of single bits,
    corresponding to the truth (or falsity, if 0) of any search key --
    namely a yes/no question in phrased in some ideal (Tractatus-like, for
    instance) language.  

    Theoretically, that's all mind is, right?

-michael

    "The skeptic argues that when I answered `125' to the problem `68+57',
     my answer was an unjustified leap into the dark; my past history is
     equally compatible with the hypothesis that I meant quus, not plus, and
     should have therefore said `5'". - Kripke/Wittgenstein

    "No course of action could be determined by a rule.." - Wittgenstein

rich@sdcc12.UUCP (rich) (11/12/85)

Can a Turing machine write an inductive proof on an infinite set of
sequences? {An such problem will do}. 

Then, again, from sentential you probably could build such a turing
machine from the correct set of lemmas. But who wrote the lemmas.
Probably some old drunk. Ah ha!!!! Humanity beats out the machine
again.

    -rich
    {I never was much for induction on infinite sequences anyway}