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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: Why does Olcott care about simulation, anyway?
Date: Sun, 2 Jun 2024 20:34:08 -0400
Organization: i2pn2 (i2pn.org)
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On 6/2/24 8:16 PM, immibis wrote:
> The halting problem says you can't find a Turing machine that tells 
> whether executing each other Turing machine will halt. Simulation has 
> nothing to do with the question.

Because it looks like an out to solve the question. He doesn't actual 
seem to care about halting (which is why he is so ignorant about it) but 
cares about the fact that the Halting Theorem (or pulling the same sort 
of proof) can show so many other things can't be done in other fields.

There ARE some principles that allow the use of a certain type of 
simulation, that of the UTM which is defined to just recreate the 
behavior of the machined described, and a simple way to do that is to 
build a simulator. (UTMs are not actually defined by simulation, but by 
results).

Olcott, in his typical method of playing with things he doesn't really 
understand, things that by tweeking the rules on the simulation, he 
might be able to get something close enough to Halting and using a UTM, 
that he can sneek his bad proof by, trying to replace the UTM simulation 
forever to show non-halting to trying to invoke an "induction-like" 
infinte set of "related" machines to try to argue that his infinite set 
of  "correct" (but partial) simulation is just as good the one infinite 
simulation in showing non-halting.

Not how he needs to keep things a bit undefined to avoid making the scam 
to obvious, and blocking his shell game.

The key of the shell game is making an H that aborts simulating a 
machine using it, some how "equal" to a DIFFERN machine built on a 
DIFFERENT H that does simulate forever, and get stuck.

If he can make you think these to input are "the same" because they are 
based things with the same name and doing things sort of the in the same 
way, just one is finite and the other never halts, he can pull a 
switcher-roo and show that the input to his actual H, which does halt, 
can be argued to not-halt as it was ok to swap it with the other machine.

Ultimately, this comes down to his H needs to change its behavior when 
the "pathological machine" uses it, which is why his H^ uses an 
embedded_H instead of just a copy of H, so he can try to argue it could 
be different.