If (Indexical, Digital) Mechanism is assumed, the laws of physics are not necessarily Turing emulable, and a part of physics is necessarily not Turing emulable. The reason is that the domain of indeterminacy bear on a non computable subset of computations (in arithmetic).
It is important to realise that Mechanism (roughly "I am a machine") is inconsistent with the idea that the physical universe, and any "reality", like a model of arithmetic, are non computer emulable reality. The computable is only a very tiny part of the arithmetical truth. Given that all computations are realised in arithmetic, the physical reality is a non computable statistics on those (infinitely many) computations going through our state. I have derived the many-world interpretation of arithmetic before realising that physicists were already there. Only later I got the (shadow of) the quantum logical formalism. I don't think that something like gravitation is globally Turing emulable, but I am not sure. Bruno On Saturday, July 3, 2021 at 2:13:15 PM UTC+2 Tomas Pales wrote: > On Saturday, July 3, 2021 at 1:55:59 PM UTC+2 Bruno Marchal wrote: > >> >> With Mechanism the physical laws remains persistent because they are the >> same for all universal machine, and they come from the unique statistics on >> all computations (in arithmetic, in lambda calculus, in any Turing >> universal theory or system). >> > > Can't there be a machine that computes gravitational interaction with > gravitational constant 6.674 x 10 to the -11 up until some time t and then > continues the computation with gravitational constant 5 x 10 to the -11, or > just halts? That would be an instability or cessation of gravitational law. > > -- 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/7635743c-eda0-4e74-aed5-139bafaad6cen%40googlegroups.com.
