Am So, 14. Jun 2020, um 09:40, schrieb Bruno Marchal: > >> On 13 Jun 2020, at 22:22, Telmo Menezes <[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... But I'm not sure I understand correctly what you mean here with "mathematical oracle", can you clarify? 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]. >> 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]. > 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]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/b3ce69c4-2ec7-4193-920f-5c3a35c497be%40www.fastmail.com.
