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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]

#81

Post by feanaro »

t_von_doom wrote: post #69
DeathArrow wrote: post #51

Earlier quoted context omitted.

>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…

While negatively charged particles are real, the 'negative' charge is a way to distinguish them from a 'positive' charge. It's a naming convention more than it is an actual negative value. We could easily call them 'black' and 'white' particles and the system itself would stay the same

This is not true. You're losing a crucial property in your translation, namely that the negative numbers are the additive inverse of the positive numbers. In other words, it's essential for electrodynamics that a + (-a) = 0. You could add this requirement to you 'black' and 'white' terminology, but then you've just arrived at negative numbers under a different name.

Don't let the naming confuse you. The name "negative" might be a peculiar, human-specific thing, but the concepts of addition and additive inverses are not.

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

#82

Post by joyj2nd »

Y_Y wrote: post #11
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…

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

I read that we can advance physics the most by research into mathematics. Sooner or later the oddest math finds application in nature, which is odd. See also: https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...

Negative numbers do of cause have their application in nature (negative charge etc.). But it is possible to do correct mathematics that have no interpretation in real live. E.g. 6 Students walk into an empty classroom, 10 walk out, you have -4 Students left.

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

#83

Post by feanaro »

joyj2nd wrote: post #82
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.

I read that we can advance physics the most by research into mathematics. Sooner or later the oddest math finds application in nature, which is odd. See also: https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness... Negative numbers do of cause have their application in nature (negative charge etc.). But it is possible to do correct mathematics that have no interpretation in real live. E.g. 6 Students walk int…

> E.g. 6 Students walk into an empty classroom, 10 walk out, you have -4 Students left.

The only trouble here is in the assigned interpretation. You do have -4 students left compared to the initial state but there is no reason to assume the initial state was 0.

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

#84

Post by Phenomenit »

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've always figured it's our visions ability to perceive wholes, one of something. A clear conceptual border between two entities.

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

#85

Post by noodles_ftw »

jl6 wrote: post #79
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…

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.

According to Wikipedia: 'Creationism is the religious belief that nature, and aspects such as the universe, Earth, life, and humans, originated with supernatural acts of divine creation.'.

I choose my words carefully. I get what you're saying though, but I think that's more of a subjective matter.

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

#86

Post by morelisp »

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?

> the art of making distinctions, the study of critical thinking and the foundation of mathematics only matter in the same way art does?

A major movement (or several, depending on how you slice it) in modern philosophy takes aesthetics as first philosophy - so yes, arguably they matter exactly the same way art does.

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

#89

Post by feanaro »

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.

> If you throw away real numbers, then you lose major things in physics. I think for example you lose the wave function in QM.

Then again, have you ever observed a non-computable number as a component of the value of a wave function in nature? Real numbers add a lot of cruft which can never be practically observed (due to not being computable).

One of the main reasons we lose things is that our results have been built upon the real numbers since they were easier to conceptualize and to work with, but it's possible that a lot can be recovered (maybe even everything we care about) using only the computable numbers. For instance, see https://en.wikipedia.org/wiki/Computable_analysis for some results in recovering analysis (limits, differentiation, integration, etc) using the computable numbers.

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

#90

Post by hliyan »

Phenomenit wrote: post #84
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…

I've always figured it's our visions ability to perceive wholes, one of something. A clear conceptual border between two entities.

Yes, but it's possible to perceive distict objects without vision, except the separation is in time, rather than space. Or, depends on the number of sense organs available (e.g. a blind person can sense two different objects simultaneously by holding one in each hand).
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