GUT and P=NP
Patrick Juola
juola at suod.cs.colorado.edu
Tue Jul 26 09:54:05 PDT 1994
> > One last word on this. Try and represnet a continum of states by an
> > infinite turing machene. Go ahead, I dare you. You can't.<=big period.
>Could I not let each position on the tape represent a real value in
>[0...1]?
Cantor demonstrated, near the turn of the century, that no such system
can represent all reals in [0,1]. Boring technical explanation follows.
['cept it doesn't 'cause I edited it out.]
Perhaps I misunderstood the original poster, but I assumed that
s/he was suggesting simply encoding a particular real number into
the infinite tape using standard binary encoding. There's no
cardinality problem there at all -- but of course the tape will only
hold a single real number. Standard tape compression techniques
will buy you enough space for a countably infinite set of reals.
Of course, the dead hand of Cantor forbids a continuous set of reals
encoded onto a TM, but we all know that he's just a Dead White Male
and therefore can be ignored.... 8-)
- kitten
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