Re: Halting Problem: What Constitutes Pathological Input

On 05/05/2025 22:31, dbush wrote:

On 5/5/2025 5:08 PM, olcott wrote:

<snip>

No TM can compute the square root of a dead rabbit either.

 Strawman.  The square root of a dead rabbit does not exist,

Don't be so sure. I have several on my mantelpiece and two more on order. For once, olcott is right; there is no way to compute them. They do, however, need thorough and regular polishing. Black polish or brown? Well, that's undecidable.

but the question of whether any arbitrary algorithm X with input Y halts when executed directly has a correct answer in all cases.

Indeed it has.

It's just that no algorithm exists that can compute that mapping, as proven by Linz and other and as you have *explicitly* agreed is correct.

He's coming round to the idea, albeit slowly. He can't bring himself to describe the mapping as 'incomputable' or 'undecidable', but he's started to claim that such a mapping is 'incorrect', which is a tacit acknowledgement that it exists.
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Richard Heathfield
Email: rjh at cpax dot org dot uk
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