From: Mu In Taiwan (mu.in.taiwan@gmail.com)
Date: Tue Oct 13 2009 - 13:42:00 MDT
>
>
> and as I said before if it were not true then no program would be of any
> use.
>
>
You are wrong. This is not what you said before. In your 'no shit sherlock'
post, your original claim is about the consequences of our being able to
show particular things e.g. with proofs.
Further, you are wrong in this post too, with this altered second claim.
There are programs that can be proven not to halt (if they were run on a
theoretical turing machine) but that are useful. For example, it is easy to
imagine optimization algorithms that continually improve their result over
time but do not stop running. These programs are of use because by using a
clock (or non-repeating incrementing counter as someone suggested) or an
human-driven external interrupt, we can prevent such a program from
continuing to run and take the most recent partial result as useful output.
QED, programs that are non-halting in principle on a turing machine can be
practically useful, directly contrary to your second claim. Another example:
imagine a turing machine that runs forever and is a thermostat for a room.
The fact that the program does not halt, does not mean it is not useful.
Heck, I can even run an 'infinite' loop on my computer and use it to heat
the room, to test the stability of the processor under stress and so on. The
theoretical question of whether algorithms halt on a turing machine is
orthogonal to the issue of utility.
You will of course simply ignore these counterexamples, as you have ignored
so many other counterexamples in other posts in this thread.
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