> On 14 Jun 2020, at 20:02, Telmo Menezes <[email protected]> wrote: > > > > Am So, 14. Jun 2020, um 09:40, schrieb Bruno Marchal: >> >>> On 13 Jun 2020, at 22:22, Telmo Menezes <[email protected] >>> <mailto:[email protected]>> wrote: >>> >>> >>> >>> Am Sa, 13. Jun 2020, um 05:01, schrieb Brent Meeker: >>>> >>>> >>>> On 6/12/2020 9:25 PM, Telmo Menezes wrote: >>>>> >>>>> >>>>> Am Sa, 13. Jun 2020, um 04:08, schrieb Brent Meeker: >>>>>> >>>>>> >>>>>> On 6/12/2020 8:12 PM, Telmo Menezes wrote: >>>>>>> >>>>>>> >>>>>>> Am Fr, 12. Jun 2020, um 18:39, schrieb 'Brent Meeker' via Everything >>>>>>> List: >>>>>>>> >>>>>>>> >>>>>>>> On 6/12/2020 2:55 AM, Telmo Menezes wrote: >>>>>>>>> Hello all, >>>>>>>>> >>>>>>>>> I've been reading here often the claim that physics is about the >>>>>>>>> "real stuff" and math is a human construction that helps us make >>>>>>>>> sense of the real stuff, but it is just an approximation of reality. >>>>>>>>> So here's a thought experiment on this topic. >>>>>>>>> >>>>>>>>> Let us imagine I program a digital computer to keep iterating through >>>>>>>>> all possible integer values greater than 2 of the variables a, b, c >>>>>>>>> and n. If the following condition is satisfied: >>>>>>>>> >>>>>>>>> a^n + b^n = c^n >>>>>>>>> >>>>>>>>> then the computer turns on a light. I let it run for one year. Will >>>>>>>>> the light turn on during that year? >>>>>>>>> >>>>>>>>> So my questions are: >>>>>>>>> >>>>>>>>> (1) Can you use theoretical physics to make a correct prediction? >>>>>>>> >>>>>>>> Yes. Theory of theoretical physics includes arithmetic and in fact >>>>>>>> your question assumes it. >>>>>>> >>>>>>> So we can conclude that arithmetic is part of physical reality, >>>>>> >>>>>> No, you can conclude it's part of theories of physics. >>>>>> >>>>> >>>>> It points to underlying reality at least as much as a physical theory >>>>> does, that's my point. >>>> >>>> I agree. But what points is distinct from the thing pointed to. >>>> >>>> >>>>> >>>>>> >>>>>>> at least as much as any other thing that physics talks about? >>>>>>> >>>>>>>>> (2) Can you use math to make a correct prediction? >>>>>>>> >>>>>>>> Not unless the math can predict how fast the computer runs >>>>>>> >>>>>>> It doesn't matter how fast the computer runs, and we know this thanks >>>>>>> to a mathematical proof, not a theory in physics. And that's how we >>>>>>> know how this particular physical system will behave. >>>>>> >>>>>> No we don't. What happens when you runs out of registers to contain the >>>>>> numbers? >>>>>> >>>>> >>>>> In that case an exception is triggered and nothing happens. The light >>>>> doesn't turn on. Will it turn on before exhausting whatever memory space >>>>> is available? >>>> >>>> Not if it perfectly reliable. But then why not just postulate a computer >>>> whose light is burned out? Is there something special about Fermat's >>>> last theorem, now that we know the answer? You've made it seem profound, >>>> but it's logically equivalent to a program that says, "Don't turn on the >>>> light." >>> >>> I'm not trying to sound profound. What I am trying to do is to confront the >>> idea that empiricism is the only way to figure out a world where the only >>> real things are the ones that "kick back". As far as I can tell, this very >>> real question can only be solved in the platonic realm. No actual >>> experimentation will help settle it -- although I concede that it will help >>> adjust your bayesian priors. I think this is interesting. >>> >>> When Andrew Wiles proved Fermat's last theorem, was he doing physics? >>> >>> - If yes, then he provided an answer for a question about systems that >>> "kick back" without any empirical grounding whatsoever. >>> >>> - If no, then physics has to share the stage with math. >>> >>> Do you believe I am missing an option? >> >> No. Nice argument. >> >> >> >>> >>>> >>>>> >>>>>> >>>>>>> >>>>>>>> and how reliable it is. >>>>>>> >>>>>>> If we use Newton's laws to predict the movement of a ball, we assume >>>>>>> that someone will not show up and kick it around, that the ball is not >>>>>>> unbalanced, etc. >>>>>> >>>>>> Newton also assumed physics was deterministic. >>>>>> >>>>> >>>>> What's your point? >>>> >>>> Newton was wrong. As far as we know now, nothing can be perfectly >>>> reliable because all physical processes include some randomness. >>> >>> Are you sure? I don't possess your level of sophistication in theoretical >>> physics, but as far as I understand, there are two types of randomness: >>> >>> (1) Non-linear dynamics. In such cases, it's not that we cannot write laws >>> that perfectly describe the system, but in practice we would need extremely >>> high to infinite precision to be sure about the outcome (e.g. weather >>> prediction, throwing dice, etc). I assume we all agree on this, and it >>> doesn't make Newton wrong -- perhaps only a bit ignorant, but we can >>> forgive him given that he lived a long time ago. >>> >>> (2) Fundamental / primary randomness as a brute fact of reality. This is >>> kind of this topic of this mailing list, right? If MWI is correct, then >>> this sort of randomness is, in a sense, an illusion created by our limited >>> perception of all there is. There is no definite answer to this question, >>> correct? >>> >>> So, if we agree that we only care about (2) here, I would say that I do not >>> share your certainty. >>> >>>> >>>>> >>>>>> >>>>>>> Maybe I can suggest a system with an uneven number of redundant >>>>>>> computers and such a simple voting mechanism that a probability of >>>>>>> failure is infinitesimal, like NASA used to do. >>>>>> >>>>>> An idealization. >>>>>> >>>>> >>>>> Language itself is an idealization. This sort of refutation is applicable >>>>> to anything one can say. >>>> >>>> Exactly so. Which is why you should no more confuse arithmetic with >>>> reality than you do Sherlock Holmes. >>>> >>> >>> The only reality that you and me have access to is idealized. Is there such >>> thing as a non-idealized reality? This is a metaphysical question. I won't >>> bother you with discussion on the ontological status of Sherlock Holmes. >> >> Your thought experience is actually by itself a good answer to Brent. If >> Fermat’s mathematical truth was of the type of Sherlock Homes sort of >> reality, it would not be possible to use it to make any physical prediction. >> >> Mathematics is always done when doing physics, and indeed, that is why we >> have a computer in the head, it computes all the time. >> In fact when we look at what the physicists do, what we see are people who >> bet on some measurable numbers, and infer or extrapolate mathematical >> relation between those measurable numbers. Such relations are never proved, >> only inferred, but they might become theorem, in some metaphysics (and that >> is necessarily the case in Mechanist Metaphysics). >> >> Then some “mystic” people infer that there is a non mathematical origin to >> those mathematical relations, that they might called God, or Universe, or >> Matter, but that is the part which looks like Sherlock Holmes … >> We can test Mechanism/physicalism, but we cannot really test >> mathematicalism, because a machine cannot distinguish a non computable >> reality from a (mathematical) oracle. The dream argument strikes again. > > So my previous joke is not so bad…
I agree :) > But I'm not sure I understand correctly what you mean here with "mathematical > oracle", can you clarify? Take a set S of number. An oracle is some entity that can answer the question “does n belong to S” and give the answer to the machine which will act accordingly. You can see it as a supplementary control structure like “If x belongs to S do this else do that”. Of course, if S is a computable/recursive set, the oracle is equivalent with a subroutine. The interest is when S is a non computable set, like the halting set H (the set of all I such that ph_i stop), for example. A natural question was: can we solve all problem in arithmetic if we give H as oracle to a Turing machine? The answer is no, for example the set TOT (the set of all I such that phi_i(x) is a total function) is still not computable. That means that TOT is more non solvable than H. A machine with TOT as oracle can solve “is n in H”, but a machine with H as oracle can still not solve all question of the type “is n in Tot”. This has led Turing, Post, Kleene to the study of the degrees of unsolvability, which classifies the degree of complexity of the non computable set of numbers definable in arithmetic. For example, the Turing machine with oracle will contain a new type of quadruplet like q_i S_j q_k q_r, and it means “if the number of one on my tape belong to the set O (the oracle) then I will be in the state q_k, else I will be in the state q_r. People note phi_i^O the phi_i that are partial computable with the oracle O. That gives a relativise theory of computability. As O is not computable, that is akin to a definition of computable with the help of some “god”. That one has a non computable ability, like knowing H, or TOT. All limitations results remains valid. It was thought that such gods/oracles could help to overcome incompleteness, but that is not the case… Turing is the one introducing such “God" in computability theory, and he called them Oracle. Bruno > > Telmo > >> Assuming some non-mechanism, all positions remains open. >> >> Bruno >> >> >> >> >> >> >>> >>> Telmo >>> >>>> Brent >>>> As far as the laws of mathematics refer to reality, they are not >>>> certain, and as far as they are certain, they do not refer to >>>> reality. >>>> -- Albert Einstein >>> >>> >>> -- >>> 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/14b0505e-2256-4a27-9716-d5137bb47084%40www.fastmail.com >>> >>> <https://groups.google.com/d/msgid/everything-list/14b0505e-2256-4a27-9716-d5137bb47084%40www.fastmail.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/93EA8663-7A99-4CF6-987C-3BA602A6437E%40ulb.ac.be >> >> <https://groups.google.com/d/msgid/everything-list/93EA8663-7A99-4CF6-987C-3BA602A6437E%40ulb.ac.be?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/b3ce69c4-2ec7-4193-920f-5c3a35c497be%40www.fastmail.com > > <https://groups.google.com/d/msgid/everything-list/b3ce69c4-2ec7-4193-920f-5c3a35c497be%40www.fastmail.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]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/EA5697E8-D02A-41EF-9FB8-19DBF5133FC0%40ulb.ac.be.
