At 03:25 AM 12/18/00 -0500, you wrote:
>James Rogers <jamesr@best.com>
>
> > So while I may not know how a finite-state machine will terminate,
> I can
> > always give a relatively precise answer as to what it will do *next*.
>
>A logical absurdity, if you can ALWAYS tell what it would do next then you
>can tell if it will terminate before it reaches box X or not. And when
>you say
>you can always tell what its next step will be you can only do so by doing
>exactly
>what the machine itself is doing, looking at the next even number and
>seeing if it's
>the sum of two primes or not. You have no shortcut, no proof, you don't even
>have a way to make a fast estimate, so if you and the machine are running on
>similar hardware at the same speed then by the time you "predict" what it
>will do
>next it will have already done it.
What you are stating and what I am stating are both logically consistent
and not incompatible; I'm not sure you read it correctly.
As long as the predictive error rate of the predictor is *non-zero*, which
will always be the case, then certainty will approach zero as the function
projects farther and farther into the future. Every sequential prediction
into the future aggregates the probable error rate, so the effective result
is that it is impossible to predict the final outcome for any machine that
doesn't terminate rapidly but it is possible to predict the next sequential
result with excellent accuracy whether the machine terminates or not.
-James Rogers
jamesr@best.com
This archive was generated by hypermail 2b30 : Mon May 28 2001 - 09:50:37 MDT