Re: Halting Problem: What Constitutes Pathological Input

On 5/5/2025 6:19 PM, olcott wrote:

On 5/5/2025 5:03 PM, dbush wrote:

On 5/5/2025 5:47 PM, olcott wrote:

On 5/5/2025 4:40 PM, Richard Heathfield wrote:

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.
>

>
When the input to HHH(DD) is mapped to the
behavior that this input actually specifies
IT DOES NOT HALT.
>

>
In other words, HHH doesn't meet the requirements to be a solution to the halting problem:
>

 A deeper understanding proves that those requirements

Are very useful, as an algorithm that could meet those requirements would allow unknowable truths to be knowable.