> On 29 Jan 2021, at 19:55, Alan Grayson <[email protected]> wrote: > > > > 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] >> <applewebdata://3A4CE09A-4371-448B-92D9-479F9E716F5D>> 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
One reason is based on Descartes’ idea that our bodies are machine, which really means that their working involved only local distinct causations, handling of finitely describable information, etc. This is used by Darwin, and made more explicit by the geneticists, from Mendel, Morgan to molecular genetic and the DNA relative codings. But there ia another reason, which is that the notion of computability is the only notion in epistemology which has a precise purely mathematical definition, thanks to the Church-Turing thesis (or the Kleene-Post thesis). Like Gödel eventually understood (he mlssed that thesis), there is a sort of mathematical miracle at play, as most metamathematical notion, like truth, provable, definable do lack an equivalent thesis. Technically: computability (and related generalisation, like relative computability, or computability with Turing’s “oracle”) are the only notion which are close for Cantor’s transcendental diagonalisation method, which indeed break down easily any pretension of universality quasi everywhere in mathematics. The universal machine is only partially computable, and the very notion of computability enforces the existence of non computable notion having an important rôle in the “life of the machine” in arithmetic. Bruno > > > > -- > 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] > <mailto:[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 > > <https://groups.google.com/d/msgid/everything-list/50e2ffc8-6377-4cac-913f-b4f267a87ba9n%40googlegroups.com?utm_medium=email&utm_source=footer>. -- 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/8DFA9336-11C1-4C77-AF77-C1385BC89F06%40ulb.ac.be.
