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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]

#131

Post by used_noise »

phaemon wrote: post #110
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…

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

I'm not convinced that blind mathematicians count as their own species, nor that they echolocate, and so it doesn't seem to say much about his theory one way or the other.

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

#132

Post by ebj73 »

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.

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

#133

Post by miscPerson »

andreareina wrote: post #111
guerrilla wrote: post #39

Earlier quoted context omitted.

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?

I think not the whole of logic, but this particular distinction -- what changes in the world if one is true versus the other? Is there even a difference that is manifest? It's like the question of what underlies quantum mechanics -- is the Copenhagen interpretation correct? Everett? Some flavor of deBroglie-Bohm? If there's no way to tell the difference, does it matter? It matters as far as the philosophy of it matte…

Copenhagen requires an extraneous assumption — which may turn out to have practical implications.

At the very least, we know it isn’t parsimonious, though that wasn’t clear until after it was developed (and the philosophical inclination to preserve locality was reasonable).

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

#134

Post by ineedasername »

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.

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

#135

Post by coldtea »

TheOtherHobbes wrote: post #126
peterburkimsher wrote: post #94

Earlier quoted context omitted.

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…

Free will is a philosophical concept which is essentially dualist. It's an attempt to reconcile two subjective experiences - the feeling of making a decision, and the fact that sometimes we can't predict the actions of others - with universal determinism. There's no reason why universal determinism and free will need to be related. So trying to "prove" free will with math makes as much sense as "proving" free will wi…

>Free will is a philosophical concept which is essentially dualist.

Is it though? I came to the conclusion that one could consider free will the self-realization of a person in space-time -- in other words, free will is the only and only choice one can make (at each decision they face), that they make because of who they are thus far.

In that sense, "free will" is the same as the "person" (or the person's essense) -- and would it make sense for it to be any other way? Randomness wouldn't be free will, and having a second entity (e.g. a soul in dualism) do the decision making just moves the question and degree upwards (from "how the person has free will?" to "how the person's soul has free will?")

If a person faced with a choice A or B could go either way, then I wouldn't call that really free will (even though for some reason that's what most people have in mind when talking about the subject).

Either a person is a concrete personality/being and that manifests through its choices (which means that when faced with the A or B dillema they can only chose one or the other based on who they are), or they have some degree of randomness in their decision making (which makes them less of a person in my eyes -- randomness is not tied to our person, it is, as the name reveals, random).

When some people say "free will" they actually mean "free (independent) from the person". But that's not a will then -- a will denotes something being tied to a person (a person is their will).

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

#136

Post by henrik_w »

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…

I really liked this perspective from Bartosz Milewski in this (very good) podcast episode: mathematics is not inherent to the world, it is inherent to the human brain (paraphrased, around minute 32 in the episode)

https://corecursive.com/035-bartosz-milewski-category-theory...

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

#137

Post by ken47 »

noodles_ftw wrote: post #125
ken47 wrote: post #112

Earlier quoted context omitted.

And who/what created God -- e.g. who is God's God? And so on? It seems like humans trying to understand a hypothetical God are not unlike ants trying to understand quantum physics.

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.

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

#138

Post by gibspaulding »

danck wrote: post #60
vanderZwan wrote: post #54

Earlier quoted context omitted.

Isn't that simply because axioms that don't lead to consistent conclusions are rejected?

You can invent and pick axioms in many ways that (probably) won't lead to inconsistencies. But they won't all be powerful enough or relevant in the real world.

Doesn't this imply that, while you can invent all the axioms you like, you must discover which ones are consistent with each other and with experimental results.

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

#139

Post by otabdeveloper4 »

TheOtherHobbes wrote: post #126
peterburkimsher wrote: post #94

Earlier quoted context omitted.

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…

Free will is a philosophical concept which is essentially dualist. It's an attempt to reconcile two subjective experiences - the feeling of making a decision, and the fact that sometimes we can't predict the actions of others - with universal determinism. There's no reason why universal determinism and free will need to be related. So trying to "prove" free will with math makes as much sense as "proving" free will wi…

You're conflating different kinds of randomness here.

A coin flip and a hand of cards are both random, but obviously cards are 'more random'.

This can be quantified - 'more random' is information complexity, or information entropy. (Two names for the same thing.)

If free will exists, then it must necessarily be a singularity of infinite information complexity, which is the same thing as a singularity of infinite randomness.

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

#140

Post by RashadSaleh »

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.

I doubt that he actually said that but I could be wrong.
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