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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]

#241

Post by lazyant »

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…

Not exactly the same but 2-dimensional beings on a curved surface can discover the 3rd dimension using math, we did this proof in a differential geometry class.

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

#242

Post by alanbernstein »

lisper wrote: post #233
jhedwards wrote: post #231

Earlier quoted context omitted.

OK let me invent something: A fignaft is a small pink bird from the island of slamp. It has a short triangular beak well adapted to plucking seeds out of the hard cones of the humnit bush. It was nearly hunted to extinction by the umaglots, until their chief shaman declared the bird to be a repository of the souls of men lost at sea. Since then it has made a remarkable recovery. In contrast to the mental process requ…

OK let me invent something: gnoiwiof wefoin wf oinwfe oinfowin wfeoi fwenoifwe Do you count that as in invention? If not, what distinguishes it from your "invention"?

You seem to be protesting that the bird invention is nonsense, and no more meaningful than random letters. Regardless of the answer to your question, I think you might be overlooking a different point.

Here is my invention: a new piece of jewelry, a double ring, which you wear on both a finger and a toe at the same time. This is a realizable physical object that (presumably) has never existed before. Is it a discovery?

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

#243

Post by toasterlovin »

lisper wrote: post #184

The question assumes that there is a difference between invention and discovery. There isn't. Invention is a kind of discovery. The apparent distinction arises from our separation of physical and mental processes. But this is a purely artificial separation, a human conceit, because (unless you're a dualist) mental processes are physical processes. Specifically, mental processes are computational processes, which are…

I think a useful dichotomy is between whether an intellectual product's existence is possible without the existence of the person who created it. Copyrightable works typically could not exist without their creator. Only Prince was capable of creating When Doves Cry and only Jane Austen was capable of writing Pride and Prejudice. But inventions share with mathematical discoveries that they can (and often are) created or discovered separately by more than one person.

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

#244

Post by lavp »

lazyant wrote: post #241
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…

Not exactly the same but 2-dimensional beings on a curved surface can discover the 3rd dimension using math, we did this proof in a differential geometry class.

I would love to see a proof of it if you happen to have it!

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

#245

Post by dorgo »

lisper wrote: post #232
dorgo wrote: post #223

Earlier quoted context omitted.

lol, yes, you discover how mathematicians think, but what they think is still an invention. In the end, I agree that if we expand the definition of the universe beyond physical world to contain "everything" then yes, every invention is also a discovery.

> what they think is still an invention Is there anything that any human thinks (other than straight-out mimicry) that is not an invention? If I type: squirgle florb snozbar would you say that I have invented something? Because if the answer to that is yes, then I'll concede the point (and observe that "invention" is not a particularly interesting concept). But if the answer is no, then I challenge you to draw a dist…

neither inventions nor discoveries have to be interesting.

>squirgle florb snozbar

yes, you invented something (i think you can even claim copyright on that). I agree that it is not very interesting. mathematicians usually/sometimes produce more interesing inventions.

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

#246

Post by lisper »

dorgo wrote: post #245
lisper wrote: post #232

Earlier quoted context omitted.

> what they think is still an invention Is there anything that any human thinks (other than straight-out mimicry) that is not an invention? If I type: squirgle florb snozbar would you say that I have invented something? Because if the answer to that is yes, then I'll concede the point (and observe that "invention" is not a particularly interesting concept). But if the answer is no, then I challenge you to draw a dist…

neither inventions nor discoveries have to be interesting. >squirgle florb snozbar yes, you invented something (i think you can even claim copyright on that). I agree that it is not very interesting. mathematicians usually/sometimes produce more interesing inventions.

> yes, you invented something

OK, I guess we'll have to agree to disagree then. I would not call that an invention (and I think most people would agree).

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

#247

Post by karmakaze »

symplee wrote: post #172
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.

Isn't it the other way around? Axioms are chosen because there are no observable counter examples in the real world.

Not at all, pure math is in part about exploring axiomatic systems that may or may not have a physical counterpart. The latter is immaterial.

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

#248

Post by guerrilla »

ukj wrote: post #220
guerrilla wrote: post #190

Earlier quoted context omitted.

My question asking if you value products of philosophy that have become essential to our society neither contains an unjustified assumption and thus is not a loaded question and still stands and thus has not backfired.

It was loaded. It contains an unjustified assumption that “logic, the art of making distinctions, the study of critical thinking and the foundation of mathematics" and [other?] art belong in different categories. It also takes an incomplete view on "critical thinking". Drawing distinctions is complemented by abstracting similarities. The creation of knowledge (in all its forms) is itself a form of artistic self-expre…

It literally asks that as a question, posing it as the hypothesis under question.

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

#249

Post by lazyant »

lavp wrote: post #244
lazyant wrote: post #241

Earlier quoted context omitted.

Not exactly the same but 2-dimensional beings on a curved surface can discover the 3rd dimension using math, we did this proof in a differential geometry class.

I would love to see a proof of it if you happen to have it!

https://fsw01.bcc.cuny.edu/luis.fernandez01/web/texts/dgcs.p...

Ctrl-F for "2D" (2-dimensional creatures), although I can't find the "discovery", maybe I remember it wrong.

Btw, this was one of the mindfucks I learned studying physics. Other ones are:

  - dimensional analysis: checking if formulas can be wrong, and more importantly, finding formulas (eg, period of a pendulum) just by analyzing units that can be involved (no constants obv)  
  - similarly, rate of growths in dimensions: why giants can't exist (bone resistance is proportional to section area and load (weight) is proportional to volume  
  - Conservation laws derive easily from symmetries (energy from invariance in time, momentum from invariance in direction etc)

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

#250

Post by ukj »

guerrilla wrote: post #248
ukj wrote: post #220

Earlier quoted context omitted.

It was loaded. It contains an unjustified assumption that “logic, the art of making distinctions, the study of critical thinking and the foundation of mathematics" and [other?] art belong in different categories. It also takes an incomplete view on "critical thinking". Drawing distinctions is complemented by abstracting similarities. The creation of knowledge (in all its forms) is itself a form of artistic self-expre…

It literally asks that as a question, posing it as the hypothesis under question.

Your question was answered before you even asked it.

> It matters for people who find it valuable, the same way art, music or literature matters.

Key phrase "the same way".

There's nothing wrong with being wrong, yet you strike me as a person who doesn't like it.

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