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[Chris Whitman]

I mean, that's a bit like saying religion is a cultural idea. Obviously these things have an objective existence independent of humanity. Good thing I picked the right set of ideas and those just so happened to be the ideas of the culture I was born into!

[Problem Machine]

It's almost as if it were actually conceived of by humans and did not possess an independent existence.

Isn't the entire point of applied mathematics that it has descriptive/predictive power though?

[brog]

And composing a proof of something is not a direct human influence?

By the way, I refuse to accept any novel as a piece of art because it's just one of the 60^1000000 or so possible configurations of letters.  All the author does is pick one of these, it already exists in the space of possibilities, that doesn't count as a creative effort in my opinion.

[Problem Machine]

I think mathematics are art in the same way that a still life is art; a skillful description of an extant object (though in this case it's more of a behavior, but yes). I do agree that human influence is necessary for something to be artistic (art = artifice = artificial), but obviously that would include mathematical proofs, as they would not exist in their current form without their creators.
It's not really debatable whether that form matters; just as all poems about trees are not equal, all mathematical proofs of a particular property are not equal.

[Chris Whitman]

Isn't the entire point of applied mathematics that it has descriptive/predictive power though?

Yeah, and spooky predictive power at that, and all kinds of very unexpected elegance and interrelation.

The point is, though, the definition of an n-connected topological space was invented by a dude. Cauchy proved that the limit of a convergent sequence of continuous functions is continuous and it was considered true for many years even though there were known counter examples, just because mathematical rigour wasn't thought of in the same way then as it is now.

Math is very elegant and interesting, and the math we have describes a lot about the universe we live in, but it's ultimately constructed by people, and there may be new math in the future which describes other things better than we can understand now. Bertrand Russell wrote a bit about the idea, I think.

[Problem Machine]

I completely agree I just thought that what you were saying before was a little misleading.

[Chris Whitman]

No, that's... pretty much in line with what I was saying before. Invented by people to describe the universe; not written into the universe.

[Chris Whitman]

But yes, while we're all in agreement I would like to say that brog is actually overestimating the number of likely novels by a significant margin, due to the relatively low entropy of English.

So novels are totally not art.

[increpare]

Bertrand Russell wrote a bit about the idea, I think.

That's something of a catch-all statement; you could probably put it in your signature and nobody would think it out of place in any particular context

(I haven't read much of Russell on maths in general, beyond the introduction to the principia (which is a delight, to be sure).  Lakatos is about as far as I've gotten, alas).

[PaleFox]

Math is as much an art as anything else - even if it is just a proof. There are many ways to prove something, and some are more picturesque than others (an elevator in space, for example, was used by Einstein). However, equations are also about beauty, or personal choice: is one way of stating it more aesthetic than another?

It's kind of like choosing which way to best portray a scene or still life, except it's the universe.

[agj]

I didn't know about the ballerina, so I looked for the video. Wow, I can't see it rotating counter clockwise at all. Always clockwise. And I'm pretty sure that I'm mostly left brained (not in the neurological sense, but in the everyday sense), so there's that.

[Corpus]

Sometimes I can make it switch direction at will, but other times, try as I might, it's locked in one direction of rotation.

[team_q]

The Ballerina/brainness is a pile of crap, but its a cool optical illusion, to switch, try looking at her feet.

[Corpus]

Pile of crap? I think not, sir.

Looks like your experience with it was something of a... no brainer

[team_q]

As in, there isn't a connection between the hemisphere of the brain you use and how the ballerina twirls.

[Zaphos]

I find if I cover up the ballerina and just look at her lower-most foot and its shadow, I can visualize that as oscillating back and forth instead of rotating.  If I then uncover the ballerina, she will be rotating to match whichever direction the foot was moving at that time ...

[Corpus]

I must refute your claim with the greatest of vehemence, TeamQuiggan. Do you not know Science when you see it, sir?

Interesting, Zapdos

[team_q]

Gwaffaw! Do you dare challenge a man of science at which he is most proficient! When trolling the great googles, I found a blog, which, I'm sure you will note has SCIENCE in its title! Look upon and despair! Surely you could not stop such a stunning logical coup d'état!

[Alex May]

All I can see when I look at the ballerina is boobies.

[ஒழுக்கின்மை (Paul Eres)]

I managed to make it switch once. I could never do that after that, though. It's incredibly difficult.