Interesting-sounds like it may, in theory open up hypothetically, a boost to hypercomputing. Maybe something that could take better advantage of quantum computing. Thanks!
-----Original Message----- From: Jason Resch <jasonre...@gmail.com> To: Everything List <everything-list@googlegroups.com> Sent: Tue, Jul 24, 2018 10:06 pm Subject: Re: Do we live within a Diophantine equation? On Tue, Jul 24, 2018 at 7:47 PM, spudboy100 via Everything List <everything-list@googlegroups.com> wrote: Yielding (Here comes the awful question) The knowledge of our Diophantine-connected existence, does what for us? Implications?? Provides a TOE that assumes no more than Integers and their relations. Possibly permits the derivation of all physical laws purely from number theory. Jason -----Original Message----- From: Jason Resch <jasonre...@gmail.com> To: Everything List <everything-list@googlegroups.com> Sent: Mon, Jul 23, 2018 11:40 pm Subject: Re: Do we live within a Diophantine equation? Other mathematics might work, but this seems to be the absolute simplest and with the least assumptions. It comes from pure mathematical truth concerning integers. You don't need set theory, or reals, or machines with infinite tapes. You just need a single equation, which needs math no more advanced than whats taught in elementary school. I can't imagine a TOE that could assume less. Jason On Mon, Jul 23, 2018 at 9:15 PM, spudboy100 via Everything List <everything-list@googlegroups.com> wrote: Very well, but, why this class of equation? Why not some ther branch of mathematics? Facetiously, what not a toaster-oven, or a Hafnium, or Chloride atom? What is innate about Diophantine, that yields such awe? Does it propagate exponentially? Does it yield new information? -----Original Message----- From: Jason Resch <jasonre...@gmail.com> To: Everything List <everything-list@googlegroups.com> Sent: Mon, Jul 23, 2018 7:19 pm Subject: Re: Do we live within a Diophantine equation? There is a diophantine equation whose solutions correspond to every possible execution of every halting program. Just as a simple equation defines/creates all the richness of the Mandlebrot set, this simple equation defines/creates all the richness of computable first-person experience. So in a certain sense you could say we live within such an equation. Jason On Mon, Jul 23, 2018 at 2:09 PM, spudboy100 via Everything List <everything-list@googlegroups.com> wrote: navigation Jump to search Finding all right triangles with integer side-lengths is equivalent to solving the Diophantine equation a2 + b2 = c2. In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integer solutionsare sought or studied (an integer solution is a solution such that all the unknowns take integer values). A linear Diophantine equationequates the sum of two or more monomials, each of degree 1 in one of the variables, to a constant. An exponential Diophantine equation is one in which exponents on terms can be unknowns. **I'd guess no-based on the above description** -----Original Message----- From: Bruno Marchal <marc...@ulb.ac.be> To: everything-list <everything-list@googlegroups.com> Sent: Mon, Jul 23, 2018 7:24 am Subject: Re: Do we live within a Diophantine equation? On 21 Jul 2018, at 18:02, John Clark <johnkcl...@gmail.com> wrote: On Thu, Jul 19, 2018 at 9:17 AM, Jason Resch <jasonre...@gmail.com> wrote: >> If "Abbey" is the being before the teleportation then obviously by >> definition "Abbey" will not exist after the teleportation. Are you sure you >> really want to go with that definition? > Okay we can go with your definition as anyone who remembers being Abby, what > is important is that our language and definitions are consistent. Yes, some definitions are more useful than others but the most important thing is that they be used consistently > So we have: "Earth Abby" - The Abby at time 0 on Earth "Abby-1" - The Abby who ends up at her intended destination on Mars, at time 1 "Abby-2" - The Abby who ends up at her admirer's destination on Mars, at time 1 "Abby" - Anyone who remembers being Earth Abby (includes Earth Abby, Abby-1, Abby-2) After duplication it would be misleading to call anything "THE Abby". Abby-1 is just Abby plus something extra, lets call it M. And Abby-2 is just Abby plus something extra that is different, lets call it W. Both are Abby but Abby-1 is not Abby-2. Yes, we agree on this since day one. But to answer to the step-3 question, we must keep in mind that it refers to the first person self lived by, obviously with computationalism, both copies. >> I define "Abby" as anyone who remembers being Abbey before the duplication. >> Do you disagree? > No, we can go with that. Indeed. OK, and since 2 people meet the definition of "Abbey" then there is simply no getting around the fact that "Abbey" will see 2 entirely different things at exactly the same time. That is the 3-1 description, but that does not answer the question about the 1-description, as lived by any copies, which obviously cannot have a first person perception of the two cities at once FROM that first person perspective. Whenever I say something like that Bruno says but that contradicts blah blah, but if true then the only alternative is to change the definition of "Abbey" or change the blah blah. And then of course Bruno would accuse me of playing with words as he does whenever I try to be precise, as if precise thinking is not necessary in a matter of this sort. My answer has always been the same: you dismiss the difference between the 1p self (both of which obviously cannot feel to be in two places at once from their local current perspective after the duplication) and the 3p perspective. Your answer is alway like “the hell with the pee-pee” or “the hell with the diary”, etc. Just do the thought experience, with anyone in Helsinki, and test the result by interviewing all copies, which is the only way to figure out what their personal experience. Then very elementary math shows that all attempt to make the prediction fails, but that they can still infer distribution of probabilities (for example in the iterated case scenario). So here, you are just conflating again first and third person account. In the math part, that becomes the (common) confusion between belief ([]p) and knowledge ([]p & p). Bruno >> If the future doesn't unfold as I expected and my retirement investments go >> bad then I will have lost some money, but if I develop Alzheimer's disease >> in retirement and lost my past then I will have lost far more than money, I >> will have lost my identity. The past and the future are not symmetrical, we >> can remember the past but not the future. > But the important point is we have expectations about the future, and > physical theories attempt to predict likelihoods of various future outcomes Yes but those theories have nothing to do with our self identification so why are we even talking about it? > which we (at time now) have no memory of, but nonetheless expect to > experience in the future. Do you agree on this point? I agree that very often our expectations about the future turn out to be entirely wrong but when that happens we do not loose our identity or consciousness. So I repeat, why are we even talking about this? > the only point in having a brain is to predict and prepare for the future.I > was suggesting the same thing as you did regarding Alzheimers. If memories > are erased and we have no access to other evidence, the past can become > indeterminant, similarly to the future. The future is always indeterminate to us, when the past also becomes indeterminate to us that might be a good definition of death. That's what makes Alzheimers so horrible, it doesn't kill you all at once, you merge into oblivion slowly by degrees and you can feel your mind going. I wouldn't wish that on my worse enemy, I hope I don't live long enough to get it. >> So what was that one bit of information that "Abby" gained? Did "Abby" (and >> I am the only one who has given a precise definition of that word and stuck >> with it) end up seeing W or M? > The bit is gained by "Abby-1" and "Abby-2". Abby-1 will say "Huh, I am experiencing life as Abby-1 rather than Abby-2" -- let's call this outcome "0" Abby-2 will say "Huh, I am experiencing life as Abby-2 rather than Abby-1" -- let's call this outcome "1" Each of Abby-1 and Abby-2 have gained a bit of information. But, assuming she was told the truth by the experimenters, Abby already knew that would happen before the duplication, no new information was gained by her in a Shannon informational sense. The only difference between Abby-1 and Abby-2 is that Abby-1 saw M and Abby-2 saw W, so when Abby sees W she is not surprised she will not ask herself why she is not Abby-1 because she already knows the answer, because she did not see M. The amount of information is a measure of surprise and there is zero surprise in any of this so there is zero information. > The bit of information was "I got to use my swimsuit today" or "I had to use > my winter coat", What's with this "or" business? John Clark is using his swimsuit today AND John Clark is using his winter coat today, and John Clark knew all this yesterday before the duplication. Nothing is surprising in any of this. > But you don't have to take my word for it. Max Tegmark explained the same in > a thought experiment he describes in "Our Mathematical Universe", starting on > page 194: >"The fundamental reason that quantum mechanics appears random even though the >wave function evolves deterministically is that the Schrodinger equation can >evolve a wavefunction with a single you into one with clones of you in >parallel universes. " I agree with Tegmark. Let's modify Bruno's thought exparament, its the same in that you are duplicated and transported to Moscow and Washington however you were NOT told you would be duplicated, you were told you would be transported to Washington OR Moscow (or just told you would be transported to some unspecified city). In that case you really would receive new information when you saw Washington for example, although the scientists performing the exparament who had more information about what was really going on from the beginning would not. When we flip a coin and see that it lands heads we really do gain a bit of information because we don't know with anything even close to certainty that Many Worlds is really true. But suppose we somehow obtained ironclad proof that it was, what then? If the results of a coin flip would have different consequences for me then I'd start making plans for both eventualities before the flip and none of my thought processes would end up being waisted. Now lets suppose we somehow obtained ironclad proof that Many Worlds was NOT true and the coin flip really was fundamentally random, then I'd still make plans for both possibilities even though half of that brainwork would end up being a waist of time, that can't be helped, it just comes from living in a universe that is truly random. So I'd live my life the same way regardless of if I thought Many Worlds was true or if I thought fundamental randomness existed. > Is it not also interesting, that they all reach similar conclusions, namely, > that computation sits at the basis of reality, I don't want to talk too much about the nature of reality, that topic can quickly suck you down into a metaphysical quagmire, but I will say computation certainly sits at the basis of understanding because information is the ONLY thing that we can understand. And the thing that makes matter interesting is that it can perform computations and nothing else can. > and moreover that "all computations exist" The 7918th Busy Beaver Number is finite and can be proven to exist, BUT a computation to produce the 7918th Busy Beaver Number can be proven NOT to exist. The 5th Busy Beaver Number is also finite and can also be proven to exist, a computation to produce the 5th Busy Beaver Number may or may not exist, nobody knows, and whats more there is no guarantee anybody will ever know if such a computation exists or not. > if taken as true, could explain the appearance of our physical reality, that > physics itself might be explained from a more fundamental ensemble of > computations? I don't see how it could because nobody has found a way to make a calculation without using matter or energy; I know typing ASCII characters onto a computer screen won't work because that is just a list of instructions to DO something, and matter/energy is the the only thing ever found that can change, that is to say DO something. John K Clark -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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