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. 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. 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.
