In First Order Logic, Real Numbers are the one which simplifies. The first order theory of the real is decidable, unlike the first order theory of the natural numbers. The digital, or discrete, reality is more complex than the reals, which fits all holes, and provides (in the complex extensions) all roots for the polynomials. Also, Nicolas Gisin use the Aristotelian act of faith (defining “real” by “physical”), which requires a non Mechanist theory of mind. With Mechanism, real number are phenomenological constructs by digital entities. It is real, but not ontologically real.
Bruno > On 30 Nov 2019, at 20:15, Philip Thrift <cloudver...@gmail.com> wrote: > > > https://arxiv.org/abs/1803.06824 <https://arxiv.org/abs/1803.06824> > > (V2: several mineurs changes ) ! > > Indeterminism in Physics, Classical Chaos and Bohmian Mechanics. Are Real > Numbers Really Real? > > Nicolas Gisin > <https://arxiv.org/search/quant-ph?searchtype=author&query=Gisin%2C+N> > (Submitted on 19 Mar 2018 (v1 <https://arxiv.org/abs/1803.06824v1>), last > revised 31 May 2019 (this version, v3)) > It is usual to identify initial conditions of classical dynamical systems > with mathematical real numbers. However, almost all real numbers contain an > infinite amount of information. I argue that a finite volume of space can't > contain more than a finite amount of information, hence that the mathematical > real numbers are not physically relevant. Moreover, a better terminology for > the so-called real numbers is ``random numbers'', as their series of bits are > truly random. I propose an alternative classical mechanics, which is > empirically equivalent to classical mechanics, but uses only > finite-information numbers. This alternative classical mechanics is > non-deterministic, despite the use of deterministic equations, in a way > similar to quantum theory. Interestingly, both alternative classical > mechanics and quantum theories can be supplemented by additional variables in > such a way that the supplemented theory is deterministic. Most physicists > straightforwardly supplement classical theory with real numbers to which they > attribute physical existence, while most physicists reject Bohmian mechanics > as supplemented quantum theory, arguing that Bohmian positions have no > physical reality. > Comments: 8 pages. Presented at the David Bohm Centennial Symposium, > London, Octobre 2017 V2: several mineurs changes and additions > Subjects: Quantum Physics (quant-ph); History and Philosophy of Physics > (physics.hist-ph) > Cite as: arXiv:1803.06824 <https://arxiv.org/abs/1803.06824> [quant-ph] > (or arXiv:1803.06824v3 <https://arxiv.org/abs/1803.06824v3> [quant-ph] > for this version) > > > > @philipthrift > > -- > 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 everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/8dd42147-b6ba-4716-9dfa-2a422964f79f%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/8dd42147-b6ba-4716-9dfa-2a422964f79f%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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/E6EC62CF-7FA2-4973-B750-7477AFF946EE%40ulb.ac.be.
