> On 13 Jun 2020, at 23:18, 'Brent Meeker' via Everything List > <[email protected]> wrote: > > > > On 6/13/2020 1:22 PM, Telmo Menezes 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. > > The empirical grounding was implicitly assumed in supposing that the computer > implemented the computation as mathematicians intended so that Wiles proof > could be translated into some conclusion about the physical process. It's > really no different than any other testing of mathematics by running a > computer. On the math-fun list, to which I subscribe, there is a discussion > right now of whether one should define 0^0=1. I pointed out that in Lisp > (expt 0 0) returns 1. Does that prove that Lisp is doing physics? or that > the computer programmer made some assumption about mathematical axioms?
Incompleteness explains why the mathematical reality will look empirical by the internal self-aware creature of the arithmetical reality. Physics becomes necessarily the product of a sort of mathematical experience. In particular, the physical reality is not a mathematical reality among others. It is much more fundamental than that, and can be described a universal digital-machine (mathematical) experience made by almost all universal machine in any Turing universal/complete realm. The conceptually hard problem of consciousness is reduced to a conceptually simple, but mathematically complicated mathematical problem: to derive physics from the mathematical psychology of the universal numbers, which are dreaming, because the arithmetical reality is “build that way” (to talk like Hardy). Science is born from the discovery of mathematics, behind the psychological, and physical, appearances. Bruno > > Brent > >> >> - If no, then physics has to share the stage with math. >> >> Do you believe I am missing an option? >> >>> >>>> >>>>> >>>>>> >>>>>>> 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. >> >> 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/c46da115-5a4d-231f-150d-4e236cf7e30a%40verizon.net > > <https://groups.google.com/d/msgid/everything-list/c46da115-5a4d-231f-150d-4e236cf7e30a%40verizon.net?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/6DDA9BD5-F40A-48EE-8B19-783AA68D3440%40ulb.ac.be.
