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

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

#141

Post by DagAgren »

ineedasername wrote: post #134
ebj73 wrote: post #132

A vaguely, but tangentially related fact, is that Stephen King actually considers the stories in his books as discovered, rather than invented. He talks about it in his book 'On Writing'. He considers the stories to be sort of preexisting things, and his job as a writer to unearth and discover them, rather than invent them. It's about his frame of mind while writing, I guess, but still.

It's a common theme among sculptors too: the shape is already in the stone, they just have to uncover it.

Is it? The only time I have ever heard this expressed is as a bad joke.

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

#142

Post by analbumcover »

pron wrote: post #42
thomasahle wrote: post #29

Earlier quoted context omitted.

> Does it even matter if Math is invented or discovered? It impacts whether mathematics should be patentable, since patents generally covers inventions, but not discoveries.

Patents cover inventions that are applications of knowledge. For example, chemistry is certainly discovered, but applying the use of a certain molecule as a glue or as a drug is very much patentable. Physics is also discovered, but a special lever system that is a direct application of Newtonian mechanics is patentable. The knowledge that a certain mathematical formula could be written and has certain properties is n…

I don't see how you are distinguishing between inventions and discoveries. The "discovery" of a mathematical proof is just an application of knowledge, why aren't they patentable? The "invention" of the light bulb, on the other hand, is just the discovery that putting various particles together in a certain configuration produces light in a predictable manner, why is this patentable? I don't see how a clear delineation between the two can be made.

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

#143

Post by otabdeveloper4 »

itvision wrote: post #97

There's one thing I cannot wrap my head around. Math is purely abstract science yet it describes the world around us to the utmost precision. Does that mean that this world is simply ... a math model which means everything around us is ... not real? 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 infl…

> Math ... describes the world around us to the utmost precision.

It does no such thing. The models we create using mathematical language do.

Math is a precise language that can be used to describe the world around us precisely. It can also be used to describe utter nonsense or utter fantasy precisely.

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

#145

Post by kevin_thibedeau »

red75prime wrote: post #106
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.

Arithmetic existed long before its axiomatization. Arithmetic was useful and no one stumbled upon contradictions in it. So it was natural to suppose that it can be described by some axiomatic system. Peano found it.

It is a system for modeling concepts invented by man. Everything that falls out of such a system is a product of the invention. Numbers don't inherently exist. Everything derived from that concept can't be a "discovery".

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

#146

Post by ironSkillet »

analbumcover wrote: post #129
mikorym wrote: post #16

Earlier quoted context omitted.

The reason why intuitionist mathematics is useful in QM is because it can be viewed as resource based logic. But remember that (as far as I know) you can do intuitionist mathematics in classical mathematics, but not the other way around. So you can think of intuitionist mathematics as being embedded in classical mathematics.

It's the other way around, classical logic is a restriction of intuitionistic logic that arises when you affirm the Law of Excluded Middle.

I think you're both right in a certain sense. The set of provable statements in intuitionist logic is a subset of what is provable in classical logic, which is what I believe the parent was referring to.

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

#147

Post by noodles_ftw »

ken47 wrote: post #137
noodles_ftw wrote: post #125

Earlier quoted context omitted.

Why is there a need to insult anyone when it is you yourself that lacks understanding of the matter. We believers believe that God was uncreated, He is unlike His creation. Only created things have a creator. And God created time itself, so there is no before or after Him. He was always there. So there's no other answer than "that's impossible" to your question. Of course this is hard to understand, but what would yo…

You ascribe beliefs to me via stereotype. I don't "believe" in the Big Bang Theory. I'm content knowing that I don't know. It doesn't strike me as rational to speak in such absolutes about subjects which are beyond human comprehension. To each their own.

> It seems like humans trying to understand a hypothetical God are not unlike ants trying to understand quantum physics.

> You ascribe beliefs to me via stereotype.

Not that I feel offended by the first quote, since I don't believe in a hypothetical god, but how am I the one stereotyping you? If you don't believe in God, which you made clear in your first comment, then you disbelieve in Him. So that means you're an atheist, right?

Or am I misunderstanding the concept of being an atheist? To each their own of course.

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

#149

Post by r721 »

itvision wrote: post #97

There's one thing I cannot wrap my head around. Math is purely abstract science yet it describes the world around us to the utmost precision. Does that mean that this world is simply ... a math model which means everything around us is ... not real? 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 infl…

https://en.wikipedia.org/wiki/Mathematical_universe_hypothes...

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

#150

Post by Tainnor »

guerrilla wrote: post #39
goatlover wrote: post #28

Earlier quoted context omitted.

> 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?

There is a distinction between logic, which is just the study of formal systems where you can prove theorems as in any other area of mathematics, and the philosophy of maths and particularly of mathematical logic. The same applies for set theory.

The first one can assert that (in classical first order logic) e.g. there are uncountable models of the natural numbers; this is irrefutable. The second one asks things like "is classical first-order logic even true and/or adequate in an epistemic sense" (this is different from the more pragmatic question of "is classical FOL useful for the problem at hand")? Similarly, something like Gödel's incompleteness theorems are unequivocally true but the question of what they "mean" deep down is nothing that really affects mathematicians' work in general.

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