Invented to describe what's being discovered.
Roger Penrose – Is Mathematics Invented or Discovered? [video]
31–40 of 322 posts
Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]
#32I am not sure of the implications. Does it even matter if Math is invented or discovered? Maybe it's both, and it isn't a contradiction between invention and discovering? We describe things having a certain radiation wavelength as having the color yellow. In that sense, yellow it's an invention. That doesn't mean the radiation doesn't exist. But to complicate things a bit, some things don't exist unless we observe th…
If it is discovered, then it means there exists math which we don't have to 'invent' and can simply be found like some buried treasure.
Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]
#33The expression is invented but the underlying relationships are discovered. It's silly to think that the sqaure root of negative one is something real to be discovered. It's just a stand-in to express complex relationships more succinctly. The same for negative numbers, for that matter. It would be equally silly to think that the underlying relationships are invented. Nobody invented prime numbers, they were discover…
> The same for negative numbers, for that matter.
It might be expressed differently, but the concept of addition seems very fundemental, and additive inverses (negative numbers) are a very real part of addition.
> It's silly to think that the sqaure root of negative one is something real to be discovered
If we assume the aliens also have a need for multiplication, combining it with multiplication we get polynomials, and to factor polynomials you need complex numbers.
Besides, if they think of quantum mechanics they'll surely need some way to express what we call the complex numbers too.
Even if they don't think of them as "numbers", they'll absolutely discover analogous concepts and theorems.
Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]
#34The expression is invented but the underlying relationships are discovered. It's silly to think that the sqaure root of negative one is something real to be discovered. It's just a stand-in to express complex relationships more succinctly. The same for negative numbers, for that matter. It would be equally silly to think that the underlying relationships are invented. Nobody invented prime numbers, they were discover…
It's just as silly to think of the "real numbers" as being discovered. They don't exist in the real world, after all.
If aliens ever draw a square and wonder what it's diagonal is, they'll have to face the idea of irrational numbers.
Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]
#35Earlier quoted context omitted.
Don't they, though? The path of an orbit in vacuum should follow pi, unless coordinates are discrete (which they might be, I suppose)
You could argue that it is only the model we construct using maths that contains pi.
The real question would be whether all simple, precise models of the concept contain something that can be identified as pi.
Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]
#36I am not sure of the implications. Does it even matter if Math is invented or discovered? Maybe it's both, and it isn't a contradiction between invention and discovering? We describe things having a certain radiation wavelength as having the color yellow. In that sense, yellow it's an invention. That doesn't mean the radiation doesn't exist. But to complicate things a bit, some things don't exist unless we observe th…
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Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]
#37The answer is: "both".
Where do Mathematicians look to discover Mathematics? In the depths of their own minds.
The part where you "look and think deeply" is discovery. The part where you "express your discovery in a coherent language" is invention.
Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]
#38Could the same be said about just about everything?
Like Music. Is a Song just a combination of notes, beats, intervals, voice etc. waiting to be discovered? Or is it something that a musician invents in her brain through talent, experience, practice and trail and error.
Or for that matter, a startup idea? A product/service that would bring immense value to its consumers, but it is not there yet, waiting to be discovered.
I guess philosophers must have dwelled on such questions before.
Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]
#39I am not sure of the implications. Does it even matter if Math is invented or discovered? Maybe it's both, and it isn't a contradiction between invention and discovering? We describe things having a certain radiation wavelength as having the color yellow. In that sense, yellow it's an invention. That doesn't mean the radiation doesn't exist. But to complicate things a bit, some things don't exist unless we observe th…
> Does it even matter if Math is invented or discovered? It matters for philosophical inquiry. Does philosophy matter? It matters for people who find it valuable, the same way art, music or literature matters.
You think logic, the art of making distinctions, the study of critical thinking and the foundation of mathematics only matter in the same way art does?
Re: Roger Penrose – Is Mathematics Invented or Discovered? [video]
#40I am not sure of the implications. Does it even matter if Math is invented or discovered? Maybe it's both, and it isn't a contradiction between invention and discovering? We describe things having a certain radiation wavelength as having the color yellow. In that sense, yellow it's an invention. That doesn't mean the radiation doesn't exist. But to complicate things a bit, some things don't exist unless we observe th…
> But to complicate things a bit, some things don't exist unless we observe them.
Is this intepretation of quantum mechanics still the canonical one?