On Wednesday, September 25, 2019 at 5:26:21 AM UTC-6, Bruno Marchal wrote: > > > On 24 Sep 2019, at 14:55, Alan Grayson <[email protected] <javascript:>> > wrote: > > > > On Tuesday, September 24, 2019 at 6:38:50 AM UTC-6, Bruno Marchal wrote: >> >> >> On 23 Sep 2019, at 13:11, Alan Grayson <[email protected]> wrote: >> >> >> >> On Monday, September 23, 2019 at 3:48:56 AM UTC-6, Bruno Marchal wrote: >>> >>> >>> On 20 Sep 2019, at 03:17, Alan Grayson <[email protected]> wrote: >>> On Thursday, September 19, 2019 at 6:56:25 PM UTC-6, stathisp wrote: >>>> >>>> On Fri, 20 Sep 2019 at 09:47, Alan Grayson <[email protected]> wrote: >>>> >>>>> On Thursday, September 19, 2019 at 2:31:18 PM UTC-6, stathisp wrote: >>>>>> >>>>>> On Fri, 20 Sep 2019 at 01:15, Alan Grayson <[email protected]> >>>>>> wrote: >>>>>> >>>>>>> On Thursday, September 19, 2019 at 7:47:44 AM UTC-6, Quentin Anciaux >>>>>>> wrote: >>>>>>>> >>>>>>>> Le jeu. 19 sept. 2019 à 15:37, Alan Grayson <[email protected]> >>>>>>>> a écrit : >>>>>>>> >>>>>>>>> On Thursday, September 19, 2019 at 5:02:11 AM UTC-6, Bruno Marchal >>>>>>>>> wrote: >>>>>>>>> >>>>>>>> On 16 Sep 2019, at 17:18, Alan Grayson <[email protected]> wrote: >>>>>>>>> >>>>>>>> On Monday, September 16, 2019 at 9:00:46 AM UTC-6, Bruno Marchal >>>>>>>>> wrote: >>>>>>>>> >>>>>>>> On 14 Sep 2019, at 05:22, Alan Grayson <[email protected]> wrote: >>>>>>>>> >>>>>>>> >>>>>>>>>>> On Friday, September 13, 2019 at 4:08:23 PM UTC-6, John Clark >>>>>>>>>>> wrote: >>>>>>>>>>>> >>>>>>>>>>>> On Thu, Sep 12, 2019 at 10:26 PM Alan Grayson < >>>>>>>>>>>> [email protected]> wrote: >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>>> *> Carroll also believes that IF the universe is infinite, >>>>>>>>>>>>> then there must exist exact copies of universes and ourselves. >>>>>>>>>>>>> This is >>>>>>>>>>>>> frequently claimed by the MWI true believers, but never, AFAICT, >>>>>>>>>>>>> proven, or >>>>>>>>>>>>> even plausibly argued. What's the argument for such a claim?* >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> Of course it's been proven! It's simple math, there are only a >>>>>>>>>>>> finite number of ways the atoms in your body, or even the entire >>>>>>>>>>>> OBSERVABLE >>>>>>>>>>>> universe, can be arranged so obviously if the entire universe is >>>>>>>>>>>> infinite >>>>>>>>>>>> then there is going to have to be copies, an infinite number of >>>>>>>>>>>> them in >>>>>>>>>>>> fact. Max Tegmark has even calculated how far you'd have to go >>>>>>>>>>>> to see such a thing. >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> What I think you're missing (and Tegmark) is the possibility of >>>>>>>>>>> UNcountable universes. In such case, one could imagine new >>>>>>>>>>> universes coming >>>>>>>>>>> into existence forever and ever, without any repeats. Think of the >>>>>>>>>>> number >>>>>>>>>>> of points between 0 and 1 on the real line, each point associated >>>>>>>>>>> with a >>>>>>>>>>> different universe. AG >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> Tegmark missed this? >>>>>>>>>>> >>>>>>>>>>> Deutsch did not, and in his book “fabric of reality”, he gave >>>>>>>>>>> rather good argument in favour of Everett-type of multiverse having >>>>>>>>>>> non >>>>>>>>>>> countable universe. That makes sense with mechanism which give >>>>>>>>>>> raise to a >>>>>>>>>>> continuum (2^aleph_0) of histories, but the “equivalence class” >>>>>>>>>>> brought by >>>>>>>>>>> the measure can have lower cardinality, or bigger. Open problem, to >>>>>>>>>>> say the >>>>>>>>>>> least. >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> *What you're not addressing is that with uncountable universes -- >>>>>>>>>> which I haven't categorically denied could arise -- it's not obvious >>>>>>>>>> that >>>>>>>>>> any repeats necessarily occur. I don't believe any repeats occur. AG >>>>>>>>>> * >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> I assume the mechanist hypothesis, which shows that the repeat >>>>>>>>>> exist, indeendly of the cardinality of the number of histories. At >>>>>>>>>> some >>>>>>>>>> point the difference are not more relevant, due to the Digital >>>>>>>>>> mechanist >>>>>>>>>> truncate, which makes the repeats even more numerous in the non >>>>>>>>>> countable >>>>>>>>>> case. >>>>>>>>>> >>>>>>>>> >>>>>>>>> *I don't believe in repeats and I haven't seen any proofs that >>>>>>>>> they occur, just assertions from the usual suspects. AG * >>>>>>>>> >>>>>>>> >>>>>>>> Imagine a movie in 1280x720 pixels, then the same in 1920x1080 >>>>>>>> pixels then in 3840x2160 pixels... always the same but with more and >>>>>>>> more >>>>>>>> "precision", once you are at the correct substitution level (the level >>>>>>>> at >>>>>>>> which your consciousness is preserved) then any more precise >>>>>>>> simulation >>>>>>>> thant the ones at the correct level (which exists by assumption and >>>>>>>> there >>>>>>>> are an infinity of them) does not make any difference, but there are >>>>>>>> an >>>>>>>> infinity of them (at the correct level and below it). >>>>>>>> >>>>>>> >>>>>>> Let's suppose we correspond possible universes with the positive >>>>>>> integers, and also assume there's a property with uncountable outcomes, >>>>>>> such as a continuous mass in some range for any particle of your >>>>>>> choice. No >>>>>>> matter how many countable universes you can imagine, there's no >>>>>>> necessity >>>>>>> for any repeats of the mass of your particle; hence, no repeats of any >>>>>>> universe. AG >>>>>>> >>>>>> >>>>>> If finite precision of a continuous quantity is used, the outcomes >>>>>> are not uncountable. >>>>>> >>>>>>> -- >>>>>> Stathis Papaioannou >>>>>> >>>>> >>>>> I specifically used a COUNTABLE model as a possible counter example of >>>>> the necessary existence of copies. AG >>>>> >>>> >>>> Do you think the number of mental states a human can possibly have is >>>> finite, countably infinite or uncountably infinite? >>>> >>>> >>>> -- >>>> Stathis Papaioannou >>>> >>> >>> What I have shown is that it's hypothetically possible to have countable >>> universes wherein there are no repeats, no exact copies. AG >>> >>> >>> It is a theorem, about *all* universal machinery phi_i that all >>> programs repeat, with different codings. >>> >>> For all i there is a j such that i ≠ j, and for all x phi_j(x) = >>> phi_i(x). That is obvious for a programmer, you can always add spurious >>> instructions, for example. >>> >>> So, in the arithmetical reality (which is Turing universal) then if you >>> can survive with a digital brain, you survive in all infinitely many >>> computations which extends your current experiences. >>> There is arguably a non countable set of (infinite!) computational >>> extension, but at all time, a brain or a machine cannot distinguish more >>> than a finite or countable states. >>> >>> Bruno >>> >> >> If you have a countable set of programs, none of which can calculate an >> irrational number, how could they produce copies of everything? They have >> no contact with a set so large. AG >> >> >> First, the UD does compute many irrational numbers, like sqrt(2), PI, e, >> etc. Those are computable real number, in the sense that an galorothm can >> generate all decimals. >> >> But then you forget the first person indeterminacy, and the step 4 of the >> UDA. The consciousness of the emulated entities cannot be aware of any >> delay, and so will fork on a non computable set of “stream”, given by the >> program dovetailing on all initial sequence of all (Turing) Oracles. >> >> I cannot generate one precise non-computable real number, but I can >> generate them all. The following path illustrates this: >> >> 0 >> 1 >> >> 00 >> 01 >> 10 >> 11 >> >> 000 >> 001 >> 010 >> 011 >> 100 >> 101 >> 110 >> 111 >> >> Etc. >> >> This generate each infinite sequence of 0 and 1, including all non >> computable real numbers, in the limit, and as the machine cannot be aware >> of the delays of “reconstitution’ in the universal dovetailing, their first >> person indeterminacy domain is not countable. >> >> Bruno >> > > Because irrational numbers have non repeating decimal representations, > they can't be exactly calculated by any finite process. Period! AG > > > OK, but that is not the standard definition of “computable” for a real > number. Basically, a real number is computable if we have an algorithm to > generate all its decimal (and actually we ask a bit more but I do not want > enter in the details). > > Computable real number are represented in arithmetic by the code of total > computable functions (the set of such code can be shown to be NOT > computable). >
??? Can you elaborate? AG > > With your definition, only finite function and set would be computable, > and that would make the notion of computability trivial. > > Bruno > You agreed on a related thread that "most" real numbers are NOT computable since we don't have mathematical representations of them, unlike the case with PI. I think that set is dense in the reals with the cardinality of the continuum. My point was to suggest another problem with your version of the MWI; the severe restriction of what worlds are possible under the arithmetic MW scenario. 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/67d32f3f-0ba5-4f5e-8450-6505c363c4ea%40googlegroups.com.
