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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]

#91

Post by keiferski »

DeathArrow wrote: post #43
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.

>It matters for philosophical inquiry. I was thinking more of tangible implications. Maybe there are some.

Philosophical implications are perhaps the most tangible implications there are: they shape the conception of reality and society that you live in. They only seem intangible because they are subtle and pervasive.

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

#92

Post by noodles_ftw »

guerrilla wrote: post #77
noodles_ftw wrote: post #65

Earlier quoted context omitted.

> I'll never understand how someone otherwise so apparently intelligent can be so religious. Why not? Religious people believe that God is the Most Wise. Mathematics in nature attest to that attribute of God (as well as to other attributes of Him). An intelligent and religious person would recognize that, knowing it is God who came up with all the rules that keep the universe in balance. I'll never understand why som…

If you want to understand why some people believe that science and creationism don't go hand in hand, then studying epistemology would help you do that. Most introductory texts will cover what you need.

Sounds like I got something new to learn during this lockdown, thank you. After a quick look at the wikipedia page on epistemology (very interesting), I'm not sure how this explains why some people believe that science and creationism don't go hand in hand.

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

#93

Post by jbotz »

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…

"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...

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

#94

Post by peterburkimsher »

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 lectures. I'm trying to figure out whether the following logic makes sense.

- Assuming that the universe is finite -> Infinity cannot be approximated with finite numbers (MIP* = RE) [1] -> Numbers cannot have infinite strings of digits -> The future can never be perfectly preordained (Gisin) [2] -> Free will exists (Conway) [3]

This is not a proof that free will exists! But I think this is a consistency proof that free will is finite.

Now you're telling me that there's another kind of infinity, and I want to know what that means for this thought.

[1] https://www.quantamagazine.org/landmark-computer-science-pro...

[2] https://www.quantamagazine.org/does-time-really-flow-new-clu...

[3] https://www.youtube.com/watch?v=tmx2tpcdKZY&feature=youtu.be...

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

#95

Post by fsflover »

zelos wrote: post #40
DeathArrow wrote: post #24

I 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?

This is a philosophical question. "No experimental evidence exists that distinguishes among these interpretations."

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

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

#97

Post by itvision »

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 influencing the conditions which brought us to life, and even after our minds and consciousnesses form it's hard to believe they are fully autonomous and not simply a function of the processess in our brains we're simply not aware of.

If you think about all of it, it becomes utterly depressing as you begin to realize you're a biological robot, a byproduct of the universe evolution which couldn't care less about our species and this little tiny blue planet.

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

#98

Post by peterburkimsher »

raghavtoshniwal wrote: post #70

Last week I came across another fascinating podcast by Penrose that you folks might also like: https://www.youtube.com/watch?v=orMtwOz6Db0

Thanks for the link. At 1:02:57, Penrose proposes "infinite cycles of the big bang"

https://youtu.be/orMtwOz6Db0?t=3777

Is that multiverse theory disproven by Wolfram's latest blog post?

"could there be other universes? The answer in our setup is basically no."

https://writings.stephenwolfram.com/2020/04/finally-we-may-h...

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

#99

Post by [deleted] »

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...

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