Roger Penrose – Is Mathematics Invented or Discovered? [video] • Hacker News Board

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

#71

Post by Y_Y » Fri, Apr 17, 2020, 9:46 AM UTC

mikorym wrote: post #14

Y_Y wrote: post #11

Earlier quoted context omitted.

It's just as silly to think of the "real numbers" as being discovered. They don't exist in the real world, after all.

They are necessary for the continuum. If you throw away real numbers, then you lose major things in physics. I think for example you lose the wave function in QM. It is not a question of whether they exist in nature, but rather whether they are the more superior technique, or not, to explain nature.

Wavefunctions are in fact generally complex-valued. I don't know if that supports your argument or not.

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

#72

Post by inopinatus » Fri, Apr 17, 2020, 9:47 AM UTC

DeathArrow wrote: post #66

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.

While art is certainly very important, I believe it doesn't have the same impact upon our lives as math has. And if you believe art is about creativity, you can find beauty and art in in mathematics and other sciences. Many great mathematicians were also art lovers, they appreciated music, they appreciated paintings and other forms of art. I don't think there's a dichotomy between art and sciences.

I agree 100% with everything you say. However, I don’t believe that the “impact on lives” of scientific advances, whilst certainly being of tremendous interest and importance to the humans, carries into much universal significance.

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

#73

Post by weego » Fri, Apr 17, 2020, 9:49 AM UTC

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…

It matters because what if you can't actually describe the underlying foundations of the universe and reality with absolute accuracy as a mathematical equation. We get very close, but if we're always off even by ten to the minus whatever, have we really 'solved' it.

Maybe there is some other conceptual framework that we've not or are not able to cognitively express that underpins things.

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

#74

Post by Y_Y » Fri, Apr 17, 2020, 9:52 AM UTC

yiyus wrote: post #27

Y_Y wrote: post #11

Earlier quoted context omitted.

It's just as silly to think of the "real numbers" as being discovered. They don't exist in the real world, after all.

Depending on how philosophical you want to get, it is not so clear what exists and what does not. Neither it is absolutely clear what means to be discovered. I think that ideas can be discovered. In my opinion, theorems, or more precisely the proof of these theorems, for instance, are discovered. In the sense that they are not an invention, they "emerge" from more fundamental definitions. You seem to be of the opinio…

On the contrary. I think that "real" and "imaginary" numbers are both discovered and neither concept has more reality than the other.

I think that even chess rules have a meaningful "existence" (in a Platonic sense) even if they are in some sense arbitrary. We can't discover "the one true rule system" but we can discover various possible systems and also theorems about them.

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

#75

Post by guerrilla » Fri, Apr 17, 2020, 9:55 AM UTC

ukj wrote: post #58

guerrilla wrote: post #55

Earlier quoted context omitted.

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.

Yes, that's my point. It applies to anything that is creative and dismisses the original point through abstraction.

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

#76

Post by magicalhippo » Fri, Apr 17, 2020, 10:02 AM UTC

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 number, feels very much like an invention. So as such wouldn't the nice results be inventions as well?

[1]: https://bivector.net/doc.html

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

#77

Post by guerrilla » Fri, Apr 17, 2020, 10:04 AM UTC

noodles_ftw wrote: post #65

guerrilla wrote: post #41

I'll never understand how someone otherwise so apparently intelligent can be so religious. Weird, the systems that we spent massive amounts of energy designing to precisely describe reality do that better than all the ones that we threw out along the way!

> 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.

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

#78

Post by ukj » Fri, Apr 17, 2020, 10:06 AM UTC

guerrilla wrote: post #75

ukj wrote: post #58

Earlier quoted context omitted.

[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.

Yes, that's my point. It applies to anything that is creative and dismisses the original point through abstraction.

You didn't make a point. You asked a loaded question.

It backfired on you.

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

#79

Post by jl6 » Fri, Apr 17, 2020, 10:08 AM UTC

noodles_ftw wrote: post #65

guerrilla wrote: post #41

I'll never understand how someone otherwise so apparently intelligent can be so religious. Weird, the systems that we spent massive amounts of energy designing to precisely describe reality do that better than all the ones that we threw out along the way!

> 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…

Careful with your use of the word creationism. I guess you mean it in the sense of the very vague and general claim that “god created the universe”, but in my experience it is used to refer to a much more specific set of claims, such as “the Earth is about 6000 years old”, which is absolutely not compatible with science.

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

#80

Post by Kaiyou » Fri, Apr 17, 2020, 10:08 AM UTC

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…

Combining the words "most" and "species" feels a little bit silly. Among all the millions of species on this planet only humans have displayed the intelligence necessary to contemplate any of this.