🚀 go-pugleaf

This thread is getting me down, because intelligent people are making
fools of themselves. So now I'm going to have another go at making a
fool of MYself. :-)

I think the observation here is that actual computers are NOT
(equivalent to) turing machines BECAUSE they have finite resources.
Note that it doesn't matter WHAT the bound on resources is; so long as
it is there, and has some value in each case, the theoretical
observation that this is NOT REALLY a turing machine holds.

So the question is, *can we get any mileage out of that*? What useful
theorems could we prove if we were to grant (or assume, if it makes
you feel better - maybe your computer is A LOT bigger than mine :-)
that there IS SOME upper bound on machine state complexity?

Now, I don't do theory, and I haven't spent a lot of time worrying
about the structure of the appropriate theorems (though it does seem
pretty obvious that a FINITE computer has an easy check for programme
termination: wait until it has run enough cycles to be in EVERY state.
By this point it has either halted or it is in an infinite loop, by
a pigeonhole argument. It's not PRACTICAL, of course, but that
doesn't mean it has no practical CONSEQUENCES); but it doesn't seem at
all incoherent that it MIGHT be very important.

And it certainly means there's room for different perspectives on
what's "possible".
----------------------------------------------------------------------
stephen p spackman         Center for Information and Language Studies
systems analyst                                  University of Chicago
----------------------------------------------------------------------