Am Sa, 13. Jun 2020, um 08:07, schrieb Jason Resch: > > > On Fri, Jun 12, 2020 at 4:56 AM Telmo Menezes <[email protected]> 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? >> (2) Can you use math to make a correct prediction? >> >> Notice that I am asking a question that is as hard-nosed as it can be. No >> metaphysics, just a question about an observable event in a physical system >> during a well-defined time period. Will the light turn on? >> >> What gives? >> > > > Excellent question Telmo! I arrived at a very similar thought-experiment in > the past, writing: > >> In fact, incompleteness is not limited to mathematics and mathematical >> problems, but extends into physical systems too. Consider an intricate >> arrangement of dominoes. The question of how long it takes for the last >> domino to fall after the first is toppled is a purely physical question >> having some definite answer.
Dominos is an an excellent idea for this, much better than mine. >> Likewise, a physical computer is a physical system, and questions about its >> future behavior can be framed as a physical problem. For example, we could >> ask how long after pushing the power button will it take for the screen to >> light up. But things get murky in the case the computer runs a computation >> before turning the screen on. >> >> Let’s say the computer runs a search for a proof of some unproven statement >> when it is turned on, and only when it completes does it light up the >> screen. Now the physical question of how long it takes for this physical >> light to switch on is reduced to a mathematical problem. Where things become >> very unclear is when due to incompleteness, the computer might never find >> such a proof. >> >> It turns out that some physical questions cannot be answered without solving >> fundamental problems in the foundation of mathematics. > > So where things get hairy is when the computer is not only looking for some > example which may or may not exist, but a proof which may not doesn't exist > in the generally assumed/accepted system of axioms. Then if we want to answer > this purely physical question of "will this light ever turn on?", we need to > delve into foundations of mathematics. We get dragged into the mathematical > debate of what system of axioms allows a proof to be found, and is that > system of axioms consistent? > > There's no way of escaping it that I see. Exactly. There is something truly bizarre and at the same time unescapable about this. Telmo > Jason > > > -- > 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/CA%2BBCJUhL%3DSq0QFes7hffhXGtOdemSgMLigyu5uLzHvsFKSafYw%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CA%2BBCJUhL%3DSq0QFes7hffhXGtOdemSgMLigyu5uLzHvsFKSafYw%40mail.gmail.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/d3e946e8-3491-4eef-bd4b-b6c70c0768ee%40www.fastmail.com.
