> On 28 Sep 2019, at 11:18, Alan Grayson <[email protected]> wrote: > > > > On Saturday, September 28, 2019 at 2:28:14 AM UTC-6, Bruno Marchal wrote: > >> On 27 Sep 2019, at 18:42, Alan Grayson <[email protected] <javascript:>> >> wrote: >> >> >> >> On Friday, September 27, 2019 at 10:31:02 AM UTC-6, Bruno Marchal wrote: >> >>> On 27 Sep 2019, at 11:23, Alan Grayson <[email protected] <>> wrote: >>> >>> >>> >>> On Wednesday, September 25, 2019 at 5:47:10 AM UTC-6, Bruno Marchal wrote: >>> >>>> On 24 Sep 2019, at 17:03, Alan Grayson <[email protected] <>> wrote: >>>> >>>> >>>> >>>> On Tuesday, September 24, 2019 at 8:52:50 AM UTC-6, Alan Grayson wrote: >>>> >>>> >>>> On Tuesday, September 24, 2019 at 8:37:23 AM UTC-6, Bruno Marchal wrote: >>>> >>>>> On 23 Sep 2019, at 15:18, Alan Grayson <[email protected] <>> wrote: >>>>> >>>>> >>>>> >>>>> On Monday, September 23, 2019 at 5:21:38 AM UTC-6, Alan Grayson wrote: >>>>> >>>>> >>>>> On Monday, September 23, 2019 at 2:44:05 AM UTC-6, Bruno Marchal wrote: >>>>> >>>>>> On 21 Sep 2019, at 17:00, Alan Grayson <[email protected] <>> wrote: >>>>>> >>>>>> >>>>>> >>>>>> On Wednesday, September 18, 2019 at 4:02:09 AM UTC-6, Alan Grayson wrote: >>>>>> I think he means one can replace a human brain and/or nervous system >>>>>> with computer microchips and consciousness will be preserved, or >>>>>> perfectly simulated so the person who says "Yes doctor", will awake from >>>>>> the surgery thinking he/she's the same person, like awakening from >>>>>> unremarkable surgery. From my pov, this belief is a huge, huge stretch >>>>>> since we can even define what consciousness IS. AG >>>>>> >>>>>> Bruno; does "Yes doctor" mean that a patient accepts as fact that >>>>>> removing his/her brain and/or nervous system and replacing it with >>>>>> microcircuits preserving the same functions, yields a surgical result >>>>>> such that the patient upon awakening seems to him or herself, and >>>>>> others, as the same "person" who previously approved the surgery? >>>>> >>>>> The patient cannot accept this as a fact. It is something he can hope >>>>> only. Then, if mechanism is true, by definition he was correct, but even >>>>> after the operation, he cannot claim that as a fact, despite its personal >>>>> impression. He might have lose a faculty and not be aware of it, like >>>>> people can become blind and be unaware of the change, in some special >>>>> brain disease (anosognosia). >>>>> >>>>> >>>>> >>>>>> Is this the essence of mechanism? If not, please elaborate. TIA, AG >>>>> >>>>> >>>>> Yes, it is mechanism, but it requires an act of faith. >>>>> >>>>> Now, to be sure, taking a plane, or even a bike, requires some faith too, >>>>> but here, that play an important role in the sequel, and so that nuance >>>>> has to be taken into account. >>>>> >>>>> Rational machine have a surrational corona extending what they can >>>>> justify. That corona has a precise mathematical structure, and is used to >>>>> derive the laws of physics from arithmetic. >>>>> >>>>> Bruno >>>>> >>>>> Can you name one law you have established or proved using your theory? AG >>>> >>>> I have written a theorem prover generating the propositional physical laws. >>>> >>>> It predicts many laws including the very existence of non trivial >>>> physical laws, and the quantum nature of the observable. It predicts >>>> general statements, like the bottom of the physical reality is highly >>>> symmetrical (and plausibly necessarily reversible). >>>> >>>> Then it predicts the qualia and consciousness, at a place where physics is >>>> either wrong or dismiss its existence and makes it into an illusion. >>>> >>>> Keep in mind that Mechanism is not an hypothesis in physics, but in >>>> cognitive science. This predicted the possibility of AI (the reason what I >>>> have mocked 40 years ago). >>>> >>>> I am not so much proposing a new theory than showing that all physicalist >>>> theory of everything are wrong if we assume Mechanism (like Descartes, >>>> Darwin, and many others more or less explicitly). >>>> >>>> >>>> >>>> >>>>> >>>>> Calculating everything, even if that were possible, >>>> >>>> The possibility of this is a theorem in arithmetic + Church’s thesis. >>>> >>>> >>>> >>>> >>>> >>>>> doesn't mean you know anything! >>>> >>>> >>>> We agree on that. You know the main axiom from which I derive everything >>>> is named “the Modesty axiom” by Rohit Parikh and Raymond Smullyan. >>>> >>>> Not only I don’t know everything, but I know-for-sure only my >>>> consciousness, and only god knows if I know more than that. But I have >>>> theories/beliefs, and I show how to test them. >>>> >>>> >>>> >>>>> How would you know our universe uses inverse square for gravity (to a >>>>> good approximation) and not inverses of higher order? >>>> >>>> That kind of thing is explained by many theorems in mathematics already. A >>>> beautiful illustration is given in the following very nice video which >>>> computes the sum of the inverse of saure numbers 1 + 1/4 + 1/9 + 1/16 + >>>> 1/25 + … using (and explaining) the inverse square laws. >>>> >>>> https://www.youtube.com/watch?v=d-o3eB9sfls >>>> <https://www.youtube.com/watch?v=d-o3eB9sfls> >>>> >>>> I can’t use this with Mechanism though, because we have not yet extracted >>>> any notion of physical space (although I do have ideas how to get them, >>>> but the math get very complex. A recent progress has been made as it is >>>> related to possible deep relation between the theory of brads and knots >>>> and very large cardinal in set theory (the cardinal of Laver). >>>> >>>> >>>> >>>> >>>> >>>> >>>>> Also, since no computer can calculate a single irrational number, >>>> >>>> That is false. A computer can calculate PI, e, sqrt(2), sqrt(3), sqrt(5) >>>> etc.. all irrational. >>>> >>>> No. A computer cannot calculate any irrational exactly. >>> >>> Nor could a human. >>> >>> >>> >>>> It can only approximate them, such as PI. AG >>>> >>>> With PI, you at least have a series representation and can approximate it >>>> to any degree desirable, >>> >>> OK. And that is how we define what is a computable real number. We can >>> compute the approximations. Actually we need also to be able to compute a >>> modulus of convergence, to assure that addition of the computable real >>> numbers is a computable operation. Turing get this wrong in his paper, but >>> corrected this in a footnote in most re-publication of his paper. >>> >>> >>> >>> >>>> but with most of the others you don't even know how to represent them >>>> mathematically and thus haven't a prayer for calculating them. AG >>> >>> Yes, in classical logic/theories, most real numbers are not computable. >>> Note that in intuitionistic mathematics, Brouwer has introduce the axioms >>> that all real numbers are computable, but as I use classical logic, that >>> does not concern us. Yet that play a role in the logic of the subject ([]p >>> & p, S4Grz, …). >>> >>> Listen; you can't compute, even approximately, a real number you have no >>> way of defining. >> >> No problem with this. I cannot compute a non computable real. OK. >> >> >> >> >>> In fact, the act of defining it, would be tantamount to computing it! >> >> Hmm… OK (with a large sense of tantamount). >> >> But what I can still do, is generating it, even if I will generate many >> other real numbers, and be unable to recognise where is the one which is >> uncomputable. >> >> >> >> >> >>> So this is all nonsense. >> >> You confuse generating the decimal of a real number, and just that one >> (computable real number), and generating a real number, among many one. That >> are different procedures. >> >> >> >> >> >>> But let's suppose the monkey at the keyboard produces a text defining the >>> axioms of QM, along with a multitude of other theories. Without a physical >>> universe to test these theories, there's no way to determine which one is >>> "true”. >> >> With mechanism, no universe, nor god, could do that. But the relative state >> of the machine have just the math showing that the physical reality will >> look like a quantum multiverse, so no need to add a universe when actually, >> it cannot do the work we would expect it to do, without violating Mechanism. >> >> Your machine can generate other theories, such as one corresponding to >> universes which don't obey QM. > > The universal dovetailer does not generate theories. It generates all > computations, and the physical universe is the unique structure emerging from > the statistics on all computation. Physics is theory-independent, or > universal-machine-independent. That is why the “TOE” is anything Turing > equivalent to Arithmetic (without induction). Physics is independent of the > phi_i. It is the same for all universal machine. There is only one physics > (with Mechanism). That’s the beauty of it. > > > > >> Presumably, all of these are assumed to produce physically appearing >> universes. > > No. > > > >> I don't see that anything has been proven, or even that any of these >> universes must exist just because some axioms are typed by the monkey. > > You are right. Monkey's typing does not produce any universe. Study my > papers, perhaps, you would have seen that your monkey does not generate any > universe. A physical universe becomes a first person plural appearance > associated to a unique statistics on all relative computations. A monkey can > only type a texte, and no texte ever produced anything y itself. Don’t > confuse a computation emulated in a reality, and a description of a > computation (in any reality). > > In fact, with Mechanism, it is proven that the physical universe is not > described by *any* computation. Mechanism is at the antipodes of “digital > physics” which is simply inconsistent (Digital physics implies Mechanism, but > Mechanism negates digital Physics, so Digital physics, as a fundamental > theory is self-contradictory). > > > >> And regardless of how you parse words, you cannot compute most irrational >> numbers; only a few that have known mathematical expressions like PI and e. >> AG > > On the contrary. I cannot compute a few non computable real numbers, but I > can generate them all, and that explains why the universal dovetailer > executes all computations with all Turing’s Oracles. > > You must have a special definition of "computable number”.
I use the standard one. What is slightly less standard is my definition all generable real numbers. Computable implies generable, but generable does not imply computable. > As I see it, other than PI, e, and possibly a few other irrational numbers, > no computer can fully compute any of them, The set of computable real numbers is (obviously) countable. The set of non computable real numbers is not countable, so yes, much more are not computable. > which have the cardinality of the continuum. Indeed. > You can't even define those numbers so how the heck can you compute them? I can write a procedure which generate them all, without computing any. A real number is generable if there is an algorithm which generate them, and the dovetailing on the initial segment of the reals do generate them all. What I cannot do is generate them individually, or namely. I have given the procedure for doing so. > You could take a string representing some rational number, and then insert > digits randomly, to produce an approximation of some irrational number. It > will always be an approximation since your program will never halt. That would all irrational real number not computable, but of course all sqrt(x) when x is not a square are computable. A real number is computable when you can write a program generating the decimals of it, and generating only the decimals of it. That is also an infinite task. > And how will you define that random string you're inserting without > referencing some quantum measurements, say of spin? I generate them all by dovetailing, so I get all their approximations, and they all converge in the limit. That works for their role as oracle. Most of the real numbers generated in that way are not nameable (there is only a countable set of nameable numbers). At the start, I have: 0... And 1... Those initial segment denote already an non countable set of numbers or infinite binary sequence, the non countable set of those beginning by 0, and the non countable set of those beginning with 1. Then I get four uncountable sets: 00... 01... and, 10... 11… Etc. All real number are generated in that way, although at no moment did I name or describe any one of them individually. That is why we cannot use Cantor argument to claim that one real number will be missing. That can be related to Brouwer’s fan in intuitionist mathematics, or Kleene-Brouwer trees, or to descriptive set theory, which study the set of reals, or the subset of N, with different topologies. It makes sense in measure theory. Bruno > AG > > Bruno > > > >> >> >> >> >> >>> Frankly, I don't see what's been discovered by "computability". AG >> >> A precise mathematical notion of universality. >> >> Bruno >> >> >> >> >> >>> >>> Bruno >>> >>>>> they can only calculate to a measure zero (the rationals) of what exists; >>>>> not to mention the finite time constraint for any of these calculations. >>>>> AG >>>> >>>> If you study my papers, you will see that the physical laws are not >>>> computable: they emerge from the first person indeterminacy (step 3) and >>>> the delay invariance (step 2 and 4). The universal machine is partially >>>> computable only, which means that she is partially not computable, also, >>>> and that plays a key role, for both consciousness and matter. >>>> >>>> Bruno >>> >>> >>> -- >>> 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/ee2e1087-327f-495e-9b0d-f192665dff0b%40googlegroups.com >>> >>> <https://groups.google.com/d/msgid/everything-list/ee2e1087-327f-495e-9b0d-f192665dff0b%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 [email protected] <javascript:>. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/everything-list/d44c3b79-c88b-4c0d-b7b0-87f5ecbdce59%40googlegroups.com >> >> <https://groups.google.com/d/msgid/everything-list/d44c3b79-c88b-4c0d-b7b0-87f5ecbdce59%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 [email protected] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/c9526687-5f40-4763-a522-5cdd92346162%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/c9526687-5f40-4763-a522-5cdd92346162%40googlegroups.com?utm_medium=email&utm_source=footer>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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