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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]

#101

Post by kd5bjo »

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 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?

You can only reach this conclusion if you categorize math as "not real". If everything we interact with is a perfect mathematical object, I prefer to take that as evidence that all mathematical objects may be real, however abstract they seem.

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

#102

Post by red75prime »

jbotz wrote: post #93
hliyan wrote: post #67

Earlier quoted context omitted.

I've always thought math as we know it is a result of both deep underlying relationships between natural constructs and how we perceive them. For example, a species who has no sense of vision will not develop geometry the same way we would. A species that has a sense of vision that also includes a direct distance perception (as opposed to our stereoscopic vision) will probably come up with a very different form of ge…

"two of our own species [discovered calculus]"..? Which two species are those? I assume by "own own" you mean Terran species, and one of them is Homo Sapiens, which is the other one? Really curious...

Leibniz and Newton. Two [members] of our own species.

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

#103

Post by novalis78 »

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…

What’s depressing about being a nanotchmological robot attempting to conquer the solar system and spread his technology and nanotechnology? It sounds rather exciting and fascinating. Perhaps if the depression is too severe you need to check out your programming ;-)

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

#105

Post by tirant »

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…

Mathematics has not been static throughout history. It has evolved at the same pace our science and discoveries have evolved, and as such it has incorporated all necessary elements to help describe new phenomena. To the point that now is able to describe never observed phenomena.

So no, our world is not unreal because it can be described with maths. Maths have evolved to describe it. Same as human language has evolved to support our close environment and our human interactions.

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

#106

Post by red75prime »

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.

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

#108

Post by lmm »

magicalhippo wrote: post #76

If B follows from A via logic, but A is invented, isn't B invented as well then? Just to take a recent example which was mentioned here, Geometric Algebra[1]. There you assume you have some objects which aren't numbers but which when squared equals a given number. By doing that a bunch of nice results have been discovered. However to me the basic premise, take some objects which aren't numbers but which square to a n…

> If B follows from A via logic, but A is invented, isn't B invented as well then?

Not really, because you have no choice about B - it's true (or rather it follows from A) whether you want it to or not. You could have picked a different A, but once you picked A then B was fixed.

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

#109

Post by voldacar »

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?

you think too poorly of art

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

#110

Post by phaemon »

hliyan wrote: post #67
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…

I've always thought math as we know it is a result of both deep underlying relationships between natural constructs and how we perceive them. For example, a species who has no sense of vision will not develop geometry the same way we would. A species that has a sense of vision that also includes a direct distance perception (as opposed to our stereoscopic vision) will probably come up with a very different form of ge…

And yet, most blind mathematicians are geometers, which suggests your theory is incorrect.
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