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 < [email protected]> wrote: > navigation <https://en.wikipedia.org/wiki/Diophantine_equation#mw-head> > Jump to search > <https://en.wikipedia.org/wiki/Diophantine_equation#p-search> > <https://en.wikipedia.org/wiki/File:Rtriangle.svg> > <https://en.wikipedia.org/wiki/File:Rtriangle.svg> > Finding all right triangles with integer side-lengths > <https://en.wikipedia.org/wiki/Pythagorean_triple> is equivalent to > solving the Diophantine equation *a*2 + *b*2 = *c*2. > In mathematics <https://en.wikipedia.org/wiki/Mathematics>, a *Diophantine > equation* is a polynomial equation > <https://en.wikipedia.org/wiki/Polynomial_equation>, usually in two or > more unknowns <https://en.wikipedia.org/wiki/Equation>, such that only > the integer <https://en.wikipedia.org/wiki/Integer> solutions > <https://en.wikipedia.org/wiki/Zero_of_a_function#Polynomial_roots>are > sought or studied (an integer solution is a solution such that all the > unknowns take integer values). A *linear Diophantine equation*equates the > sum of two or more monomials <https://en.wikipedia.org/wiki/Monomials>, > each of degree <https://en.wikipedia.org/wiki/Degree_of_a_polynomial> 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 <[email protected]> > To: everything-list <[email protected]> > 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 <[email protected]> wrote: > > On Thu, Jul 19, 2018 at 9:17 AM, Jason Resch <[email protected]> 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. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > 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 [email protected]. > To post to this group, send email to [email protected]. > 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 [email protected]. > To post to this group, send email to [email protected]. > 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. 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