Roger Penrose – Is Mathematics Invented or Discovered? [video]

Post by analbumcover » Fri, Apr 17, 2020, 8:19 PM UTC

pron wrote: post #265

analbumcover wrote: post #236

Earlier quoted context omitted.

But that's the whole point, patents are awarded to things deemed inventions not things deemed discoveries. If you can't delineate between the two you can't say what is and what is not patentable. Fourier analysis couldn't have been patented, despite numerous commercial applications. It's just the patent system is setup to only reward low-level innovation, so it arbitrarily excludes research level innovation by termin…

Yes, what is patented is some commercial application of some knowledge, and that application is the invention. It doesn't matter whether the knowledge itself is invented or discovered. When an algorithm is patented, we're no more patenting math than we're patenting Newton's laws when a car brake is invented. We're patenting a commercial application of either, and that must be the invention.

Post by deltron3030 » Fri, Apr 17, 2020, 8:24 PM UTC

polytely wrote: post #225

deltron3030 wrote: post #183

Earlier quoted context omitted.

>I've long stopped believing in free will because everything points at it being an illusion of our brain because we're a product of this world and we had no chance of influencing the conditions which brought us to life Free will doesn't depend on the universe being deterministic or not. Things that haven't happened yet are likely going to happen in a certain way based on the trajectory, but it doesn't mean that you c…

>but it doesn't mean that you can't change your own path in a meaningful way, you're free to take a harder path vs. an easier or more obvious one. This is of course debatable, there is some evidence to suggest that the feeling that you took a certain path is illusionary. Your brain made the decision, then you became cognizant of the options and you felt yourself making the decision[0], but if you could rewind the uni…

Post by nikofeyn » Fri, Apr 17, 2020, 8:29 PM UTC

lisper wrote: post #184

The question assumes that there is a difference between invention and discovery. There isn't. Invention is a kind of discovery. The apparent distinction arises from our separation of physical and mental processes. But this is a purely artificial separation, a human conceit, because (unless you're a dualist) mental processes are physical processes. Specifically, mental processes are computational processes, which are…

Post by Koshkin » Fri, Apr 17, 2020, 8:36 PM UTC

peterburkimsher wrote: post #94

DeathArrow wrote: post #2

Intuitionist mathematics claims that mathematics is purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles existing in an objective reality. [0] In intuitionist mathematics there is only potential infinity, no actual infinity. Constructive set theory differs from Zermelo set theory. That has many consequences in practice. Applying intuitionist mathematics t…

Tell me more about the difference between "potential infinity" and "actual infinity". Recursive functions in computer programming, or fractals in maths, are infinite but can be described. Each small part looks like the whole, but the whole can never be fully known within a finite universe. Is that "potential" or "actual" infinity? I've been thinking a lot about infinity this past week, mostly because of Conway's lect…

Post by Koshkin » Fri, Apr 17, 2020, 8:41 PM UTC

mmmBacon wrote: post #164

danck wrote: post #49

If you only look at mathematics I think it's simply: - Axioms are invented - Conclusions are discovered The magic part for me is that some axioms have been chosen so well that their conclusions are confirmed in the real world.

This is an excellent point. When I took algebra as an undergraduate I was blown away by the fact that you can choose any axioms and then derive an algebra based on those axioms. I was blown away because prior to that course I just assumed that our “standard” axioms were immutable.