> On 23 Jul 2018, at 21:09, 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 a2 + b2 = c2.
> 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 equationequates 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**
>
Why? I use “diophantine equation” in that precise sense. I have often given an
example of universal (in the Turing sense of course) diophantine equation, or
of a universal system of Diophantine equation .
I can put it again, of course it is not obvious that it is Turing universal.
That comes from the work of Matiyasevic, and also Jones:
================
(unknowns range on the non negative integers (= 0 included)
31 unknowns: A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, W, Z,
U, Y, Al, Ga, Et, Th, La, Ta, Ph, and two parameters: Nu and X.
X is in W_Nu iff phi_Nu(X) stop if and only if
BEGIN:
Nu = ((ZUY)^2 + U)^2 + Y
ELG^2 + Al = (B - XY)Q^2
Qu = B^(5^60)
La + Qu^4 = 1 + LaB^5
Th + 2Z = B^5
L = U + TTh
E = Y + MTh
N = Q^16
R = [G + EQ^3 + LQ^5 + (2(E - ZLa)(1 + XB^5 + G)^4 + LaB^5 + +
LaB^5Q^4)Q^4](N^2 -N)
+ [Q^3 -BL + L + ThLaQ^3 + (B^5 - 2)Q^5] (N^2 - 1)
P = 2W(S^2)(R^2)N^2
(P^2)K^2 - K^2 + 1 = Ta^2
4(c - KSN^2)^2 + Et = K^2
K = R + 1 + HP - H
A = (WN^2 + 1)RSN^2
C = 2R + 1 Ph
D = BW + CA -2C + 4AGa -5Ga
D^2 = (A^2 - 1)C^2 + 1
F^2 = (A^2 - 1)(I^2)C^4 + 1
(D + OF)^2 = ((A + F^2(D^2 - A^2))^2 - 1)(2R + 1 + JC)^2 + 1
END
================
>
> -----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]
> <mailto:[email protected]>> wrote:
>
> On Thu, Jul 19, 2018 at 9:17 AM, Jason Resch <[email protected]
> <mailto:[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
>
>
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