Re: Halting Problem: What Constitutes Pathological Input

On 06/05/2025 05:55, olcott wrote:

*EVERYONE IGNORES THIS*
It is very simple the mapping from inputs to outputs
must have a well defined sequence of steps.

What you're ignoring is that not every well defined sequence of steps we can imagine writing will necessarily produce a correct mapping from inputs to outputs.
To convince yourself of this, try to construct an algorithm that will universally and correctly decide whether any program you are given will halt for the input you're given. When you think you have done so, let Turing know, and he will show you how to build a program that your 'universal' program can't analyse.
Your problem is not that you don't understand Turing's logic, but that you can't believe the place it takes you. Logic isn't a matter of belief, of course, any more than Pythagoras is; it's more of a failure to accept the counter-intuitive result that there really are some programs that can't be written.
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
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