> On 28 Sep 2018, at 17:09, smitra <smi...@zonnet.nl> wrote: > > On 28-09-2018 00:34, kujawskilucja...@gmail.com wrote: >> Hello I think this good forum for this topic - what do you think about >> Mathematical Universe, there are very big arguments for that >> hypothesis: >> - applicability of mathematic, to natural sciences >> - all we discovere are structures and I didnt find explanation of the >> diference beetwen physical structures and mathematical structures. >> - scientists and philosophers of science tend to affirm belive in >> diverse structure and homogeneous substance (neutral monism) or >> mathematicism vide Ladyman, Ross, French, Tegmark etc. >> What are your thoughts. >> Regards > > I've written up my thoughts here: > > https://fqxi.org/data/essay-contest-files/Mitra_without.pdf > > Whether or not there exists a mathematical multiverse is, of course, > debatable.
Lawyere has tried, with CAT, the category of all categories, but this did not work, and he discover the toposes, independently of Grothendieck who discovered them in abstract geometry. The notion of the whole of mathematics is not definable in mathematics, and I am not sure it makes any sense. Fortunately, with mechanism; we can limit ourselves to the arithmetical truth, and eventually to the sigma_1 arithmetical truth, which is related to the universal dovetailer (which is sigma_1 provability). G* proves them equivalent, but G does not, so the equivalence of sigma_1 truth and sigma_1 provability is known only by “God". > However, a multiverse of any sort that's large enough to give rise of > identical copies of observers, will affect the laws of physics. Assuming mechanism, or wekemening of it. Yes. > Since the laws of physics are what we observe them to be, this means that > what we observe already includes the effects of the multiverse, i.e. the laws > of physics actually describe some sector of the multiverse rather than a > particular universe. > > This then means that if the mathematical multiverse hypothesis is correct, > the laws of quantum mechanics should be considered to give an effective > description of that multiverse. The set of all your copies considered as > algorithms that are in the same state (your state simply refers to what > algorithm is running including what information is being processed), are > distributed over the entire multiverse, they are not all in the same > universe. To derive the effective laws of physics, one needs to do statistics > over the ensemble of identical observers. This involves performing summations > over the multiverse, but these summations are with a constraint that says > that some given observer is present. Mathematically it is more convenient to > perform unrestricted summations, a convenient way to take into account > constraints is by including them using phase factors. > > For example, if we want to compute a summation over a function f(n1, n2, n3, > n4,....) where the nj are integers, we can just sum over n1, n2,...etc., > independently. But suppose that we need to sum over f(n1, n2, n3, n4,....), > such that some other function g(n1,n2,n3,...) is kept fixed to some constant > value M. The way one handles that is by summing over the function f(n1, n2, > n3, n4,....) Exp[i t g (n1,n2,...)] without any restrictions. This summation > then becomes a function of the parameter t. By taking the Fourier transform > of this function, one can extract the component of Exp[i t M] of that > function, obviously only terms of the original summation such that > g(n1,n2,...) takes the value M, contribute to that. > > In case of keeping track of a given observer, one needs to include a vast > number of constraints, one can then get to a something similar to the path > integral formulation of QM. But I have no rigorous arguments at this moment > that one can really reproduce QM this way. The universal machine have been proved to say this, but in a more “arithmeticalist setting”. The physical reality becomes the border of the Turing universal machine's mindscape. Bruno > > > Saibal >> -- >> 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 post to this group, send email to >> everything-list@googlegroups.com. >> Visit this group at https://groups.google.com/group/everything-list >> [1]. >> For more options, visit https://groups.google.com/d/optout [2]. >> Links: >> ------ >> [1] https://groups.google.com/group/everything-list >> [2] https://groups.google.com/d/optout > > -- > 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 post to this group, send email to everything-list@googlegroups.com. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. -- 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 post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
