answer to https://www.youtube.com/watch?v=t37GQgUPa6k&lc=UgzkBgBPBHBFOuxl_0J4AaABAg.8r0OIdsywPs9SFJwTlsK1g

@Leo Jackouski  i'm not sure where exactly you've gotten stuck on Barrie being just the N part, but please stop. Barrie is X, the sequence of P -> H -> N. You want a source? Wikipedia says "Penrose 1990, p. 57–63" (And the title of that one is "The Emperor's New Mind: Concerning computers, Minds and the Laws of Physics") ... And not sure if this counts as a source, but here's a compsci Q&A on the topic: https://cs.stackexchange.com/a/65406 (Barrie is called P for "perverse" there)

"Where is the instruction to tell the number or processor to loop the number indefinitely?" -- it is embedded in the number itself. Most of the bytes in the exe file will represent instructions/opcodes and their arguments, while at the same time the sequence of all these bytes is (can be seen as) a binary number. Why do you deny that "a series of 1's and 0's" can in fact be "simply a number"?

"How does a program "analyse" another program, without making any reference to (reading) it?" -- first of all, we don't need to know. It just does, by virtue of the fact that it is (supposedly) a solution for the problem. Secondly, reading something is not really a reference. The action of reading just passively accepts what is available, no matter what it is; while a reference is an _indirection_ that allows deferred access to something that is expected.

It is not just _MY_ definition of Barrie, but the way i've learned the concept, and the way it _works_ for the proof. If you think the two videos disagree with this interpretation, then [a] you could try assuming you haven't fully understood what the video was trying to say, and watch again with the foreknowledge of this interpretation; if that fails then [b] perhaps the video wasn't clear. But the concept that SHOULD have been presented by the video is the P -> H -> N sequence. Describing it would naturally focus on the N part (even Tom Scott in his https://youtu.be/eqvBaj8UYz4?t=338 says it like that), that's the most important part but it's not the _whole_ of X. Barrie's input will not be the output of H, that always just goes into N. X's input will always be a "schematic."

Yes, that is what X is: copy (P), pass to H, then pass to N, and finish. That's Barrie.

(Fwiw, Turing wasn't yet aware of programs as we know them today. I've just gone over his paper as published in the Proceedings of the London Mathematical Society, and it's focused on enumerable [real] numbers as representations of computability.)

PS "Barrie(Hal(Barie(barrie)))" -doesn't make sense- isn't self-consistent, you can't have the inner Barrie take a number as input, while the outer one taking just a flag.