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.." - Wittgensteinrich@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}