On Wednesday, September 25, 2019 at 6:15:27 AM UTC-6, Alan Grayson wrote: > > 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]> 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. >>> >> No. This you definitely NOT do. AG > 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/13a6a56b-d513-4851-bddc-e84c6e9c4158%40googlegroups.com.
