XPost: comp.theory, sci.math, sci.logic

On 4/7/2022 12:31 PM, Mike Terry wrote:

On 07/04/2022 01:24, Dennis Bush wrote:

On Wednesday, April 6, 2022 at 8:20:16 PM UTC-4, olcott wrote:

On 4/6/2022 7:17 PM, Dennis Bush wrote:

On Wednesday, April 6, 2022 at 8:10:14 PM UTC-4, olcott wrote:

On 4/6/2022 6:44 PM, Ben Bacarisse wrote:

olcott <[email protected]> writes:

On 4/6/2022 6:27 PM, Ben Bacarisse wrote:

... Your hobby seems to be posting here. Are you having fun
posting here?

I am enjoying posting here because progress continues to occur.

That's fine. I'd like to think I am helping to entertain you.

I have
my whole proof boiled down to the correct understanding of a single >>>>>>> (very difficult to understand) sentence.

Except for the two questions you can't answer without it all
unravelling!

You merely continue to greatly disrespectfully refuse to pay enough
attention:

It is the case that the correctly simulated input to embedded_H can
never possibly reach its own final state under any condition at all. >>>>> Therefore embedded_H is necessarily correct to reject its input.

But how can we verify that the input was correctly simulated?

The exection trace that is specified by its TM description.

But another halt decider simulates the same input to completion.  So
the claim that the input "can never possibly reach its own final state
under any condition at all" is false:

Given an embedded_H that aborts its simulation which we'll call
embedded_Ha, is embedded_Ha (and therefore Ha) correct to reject
<Ha^><Ha^>?

Now we have Hb, which has the exact same halting criteria as Ha except
it defers aborting for k steps. Hb simulates <Ha^><Ha^> and is able to
reach the input's final state of <Ha^.qn> while remaining in UTM mode
and accepts this input. This tells us that embedded_Ha is not correct
to reject <Ha^><Ha^> because it aborted too soon.

PO really really really really really believes that when his simulator observes his "infinite recursive behaviour" pattern, that really really really really means that the simulation is exhibiting infinite recursive behaviour, and so would never halt however far it is continued.

It does not matter to PO that he has actually run the computation
outside of the simulator, and observed himself that the computation is halting!!!!!!

If you are a guard assigned to watch the front door any nothing comes in
the front door then you are correct to report that nothing has come in
the front door no matter what comes in anywhere else.

The actual behavior of the actual input to embedded_H is the front door.

The actual behavior of any damn thing else anywhere else IS NOT THE
FRONT DOOR.

embedded_H computes the mapping from its inputs
from its inputs
from its inputs
from its inputs
from its inputs
from its inputs not any damn other place else.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

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