From: James Rogers (jamesr@best.com)
Date: Sat Dec 21 1996 - 17:16:57 MST
At 10:28 PM 12/20/96 -0600, you wrote:
>John K Clark wrote:
>
>>
>> >James:
>> >The computer is a tool designed to do deterministic
>> >computation. If you are foolhardy enough to try to do a
>> >non-deterministic computation on a computer, you do so at
>> >your own risk.
>>
>> All algorithms are deterministic but not all algorithms are predictable. If
>> it's foolhardy to write or run the above program there is no way to tell
>> you're a fool in a finite amount of time. If it has not stopped at one
>> trillion perhaps it will stop at a trillion and two. It may have been running
>> for 10 billion years but that tells you nothing, 10 billion years is no
closer
>> to being an infinite amount of time than one second is. It could stop in the
>> next 5 minutes, it might stop in another 99 trillion years, it might never
>> stop. There is no way to tell.
True, but then this boils down to computational complexity, not our
understanding of computers. For deterministic problems, a computer can
always come up with a deterministic solution provided we are willing to wait.
The fact that we are not willing to wait is a personal problem.
It is also the reason I replaced my IBM XT years ago ;-)
>
>There have been computers turned loose on problems that were thought to
>be non-deterministic, like proving Fermat's theorem. And Viola! after
>the N zillionth step they stopped with a solution. Someone probably has
>one running right no to prove that no even number greater than 4 is not
>the sum of two primes.
>
As I stated previously, our real problem isn't in our understanding of
computers, but in our ability to determine whether or not a problem has a
deterministic solution before trying it on a computer. The length required
to complete a computation is not a problem of the computer design, but of
our unwillingness to wait for the computation to complete.
-James Rogers
jamesr@best.com
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