On Friday, January 29, 2021 at 7:30:42 AM UTC-7 Bruno Marchal wrote:
> On 28 Jan 2021, at 02:07, Alan Grayson <[email protected]> wrote: > > > > On Wednesday, January 27, 2021 at 9:20:15 AM UTC-7 Bruno Marchal wrote: > >> >> On 17 Jan 2021, at 03:03, Pierz Newton-John <[email protected]> wrote: >> >> >> >> On Sun, 17 Jan 2021 at 3:49 am, Alan Grayson <[email protected]> wrote: >> >>> *What would be the mechanism or process for other worlds to interact >>> with each other, that is to interfere with each other? This is the gorilla >>> in the room that many MWI enthusiasts ignore; awesome speculation with zero >>> grounding in empirical evidence. Something definitely awry with this pov. >>> AG* >> >> >> I’m not an “enthusiast”. It’s a physical theory not a football team. If >> anything I dislike the idea of all those alternative variants of me and my >> life. If MWI is disproved I’ll be perfectly happy. It’s just that it >> unfortunately makes more sense in my assessment than any other alternative, >> so I entertain it as the most likely explanation for the observed data. To >> say it has zero grounding in empirical data is simply false - it’s the >> theory that simply takes the empirical data to its logical conclusion >> without adding a collapse postulate. The wave function is the whole thing. >> Asking what the mechanism is for worlds to interfere with one another is >> the same as asking what the mechanism is for the Schrödinger wave function >> to interfere with itself. In the dual slit experiment it’s an observed >> fact. It makes no sense for it to behave that way if we stick to the old >> view of matter as little hard balls, but there you go. When we talk of >> “worlds”, it just refers to a ramifying quantum state, and it is in the >> nature of quantum states to interfere with themselves per the dual slit >> experiment, even if they become large and complex. Interference ceases when >> two branches of the universal quantum state diverge far enough that they >> completely decohere. When you say “what is the mechanism?” that really >> means “what is the mathematical description?” in physics. Anything else is >> just imprecise circumlocution like the word “world” in this context. So the >> mechanism for interference is the Schrödinger equation, which predicts such >> interference. MWI adds precisely nothing to that mathematical description. >> >> >> >> Yes. To avoid the MWI, the early founders of QM *added* an axiom: the >> wave collapse postulate. But it introduce a non intelligible dualism with >> an unknown theory of mind. It makes everything more complicated, for reason >> of philosophical taste, which is alway dubious. Occam Razor favour the >> theory with as much axioms as possible. >> >> Especially if one believe in Mechanism. This asks us to believe that >> 2+2=4 & Co., which entails the existence of all computations, with a >> extraordinary complex redundancy of those computations, implying the >> existence of a (Lebgues) Measure on their first person limit (the >> “observer” cannot be aware of the number of steps of the universal >> dovetailing (which occur in all models of any theory of arithmetic). So ... >> >> Bruno >> > > *Are irrational numbers, other than say PI or e, and possibly a few > others, computable? AG * > > > > By Cantor theorem, the set of irrational numbers is non countable. The set > of computable things is countable, so there are uncountably many irrational > number which are not computable. > > Some precise irrational numbers exists, like the one build from the > characteristic function of non computable set, like the halting set (the > set of code of non halting programs) or TOT (the set of code of total > computable functions…). > > In arithmetic most sets of numbers, including many having some use, are > not computable. > > In computer science, most attribute of programs are not computable. For > example, there is no algorithm to decide if a given code compute the null > function, or any function, actually. > > The computable part of mathematics is a very tiny part of mathematics. > > Bruno > *That's what I thought. Why then is computability an important concept? AG * -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/50e2ffc8-6377-4cac-913f-b4f267a87ba9n%40googlegroups.com.
