Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

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

youtube.com

Post reply on HN
Print view View original

51–60 of 322 posts

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

#51

Post by DeathArrow »

jeffdavis wrote: post #9

The expression is invented but the underlying relationships are discovered. It's silly to think that the sqaure root of negative one is something real to be discovered. It's just a stand-in to express complex relationships more succinctly. The same for negative numbers, for that matter. It would be equally silly to think that the underlying relationships are invented. Nobody invented prime numbers, they were discover…

>The same for negative numbers

Are you sure negative numbers are not "real" in the same way natural numbers are?

That would mean particles like electrons with a negative charge are not "real", too. And someone can argue that his negative bank balance is not "real".

As for complex numbers, I fail to see how they are less real than real numbers. Real numbers are points on the real axis, while complex numbers are points in R^2 plane. If we question the reality of real numbers, we can also question the reality of the plane.

Mr Euclid would frown to hear that.

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

#52

Post by ukj »

guerrilla wrote: post #48
ukj wrote: post #47

Earlier quoted context omitted.

It's the same kind of activity - creation. The significance of the creation (if it has any at all) is not necessarily the concern of the creator. Some people do Mathematics for its sheer beauty.

You could say the same about structural engineers.

If you buy into Wittgenstein's rule-following paradox.

You could say anything about anything.

> no course of action could be determined by a rule, because any course of action can be made out to accord with the rule

If I had my own way of (mis?)interpreting him, I think he was alluding to what we now call "strict evaluation" in Programming Language Theory. A diligent rule-follower.

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

#53

Post by guerrilla »

inopinatus wrote: post #50
guerrilla wrote: post #46

Earlier quoted context omitted.

Good thing the founders of modern science, mathematics, ethics and political theory didn't share the same opinion.

Ridiculous hubris, to claim to speak on their behalf, to claim to know the opinion of so many and diverse minds, and in such a crude misdirection to boot.

Good thing they wrote volumes about it which have debated and summarized to the hilt.

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

#54

Post by vanderZwan »

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

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

#55

Post by guerrilla »

ukj wrote: post #52
guerrilla wrote: post #48

Earlier quoted context omitted.

You could say the same about structural engineers.

If you buy into Wittgenstein's rule-following paradox. You could say anything about anything. > no course of action could be determined by a rule, because any course of action can be made out to accord with the rule If I had my own way of (mis?)interpreting him, I think he was alluding to what we now call "strict evaluation" in Programming Language Theory. A diligent rule-follower.

Structural engineering the same kind of activity - creation.

The significance of the creation (if it has any at all) is not necessarily the concern of the creator.

Some people do structural engineering for its sheer beauty.

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

#56

Post by cpsempek »

justforfunhere wrote: post #38

Could the same be said about just about everything? Like Music. Is a Song just a combination of notes, beats, intervals, voice etc. waiting to be discovered? Or is it something that a musician invents in her brain through talent, experience, practice and trail and error. Or for that matter, a startup idea? A product/service that would bring immense value to its consumers, but it is not there yet, waiting to be discov…

I think I get your point and I‘m open to ideas which drive home your point in a more precise way. However, the main difference between concerning ourselves with whether or not mathematical objects exists vs music or start-up ideas is their place in building a foundation for understanding reality. Science has been a productive program for understanding reality. It happens to be underpinned by math. And as a result, we have encountered some pretty interesting relationships between what the math tells us and what we observe. For instance, neutrinos and black holes were known to exist mathematically before they were ever observed and measured “in reality”. It’s not clear to me that music and start-up ideas hold up to math when it comes to being a tool for understanding or describing our reality, or perception the rig. Math is somehow fundamental to many successful enterprises which seek to describe and explain reality. Therefore, it becomes the point of focus of much philosophical inquiry when seeking to understand reality. Hence the foundational question, do mathematical objects exist? And not, does music or blockchain kittens exist?

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

#57

Post by iovrthoughtthis »

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 that art does not?

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

#58

Post by ukj »

guerrilla wrote: post #55
ukj wrote: post #52

Earlier quoted context omitted.

If you buy into Wittgenstein's rule-following paradox. You could say anything about anything. > no course of action could be determined by a rule, because any course of action can be made out to accord with the rule If I had my own way of (mis?)interpreting him, I think he was alluding to what we now call "strict evaluation" in Programming Language Theory. A diligent rule-follower.

Structural engineering the same kind of activity - creation. The significance of the creation (if it has any at all) is not necessarily the concern of the creator. Some people do structural engineering for its sheer beauty.

[Scientific discoveries|Mathematics|Ethics|Political science] are the same kind of activity - creation.

The significance of the creation (if it has any at all) is not necessarily the concern of the creator.

Some people do [Scientific discoveries|Mathematics|Ethics|Political science] for its sheer beauty.

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

#59

Post by iovrthoughtthis »

guerrilla wrote: post #46
inopinatus wrote: post #44

Earlier quoted context omitted.

I’d say they don’t matter nearly so much as art. The most cosmically significant export of humanity to date is Voyager’s golden record.

Good thing the founders of modern science, mathematics, ethics and political theory didn't share the same opinion.

I would like some stuff to read on this if possible.

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

#60

Post by danck »

vanderZwan wrote: post #54
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 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.
Post reply on HN