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mathema the transcendental virgin

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mathema is pure form. immaculate as read-only-memory is immaculate. the virgin as a symbol for the transcendental. not only number but ideal shape --i like to see ratio made visible. there is something about number represented spatially.....

i'm not looking for debate, but rather a discussion of the aesthetics of math. the number e is something special, is it not? the ratio of continuous to simple interest, literally a "transcendental number." it seems like a great symbol for life itself...

any one else struck by the beauty of math?

Quote:

More generally, an account that starts at $1, and yields (1+R) dollars at simple interest, will yield eR dollars with continuous compounding.

Quote:

Suppose that a gambler plays a slot machine that pays out with a probability of one in n and plays it n times. Then, for large n (such as a million) the probability that the gambler will win nothing at all is (approximately) 1 ⁄ e.

@Reconstructo,

An immortal, eternal virgin, yes, one who is frozen in time. Must Time destroy her beauty, or can there be temporal mathematical beauty, too?

I wish I could appreciate more of her beauty, but she wears thick and ugly clothing. She is veiled. I am ugly myself, and she doesn't like me.

I find the theorem on unique factorisation of integers into primes beautiful. It is also beautiful that it can be generalised to other kinds of numbers, to polynomials, and other objects.

As for "temporal mathematical beauty": is this seen in the design of algorithms for digital computers? (Except for those written in a purely functional programming language, of course!)

@Twirlip,

Twirlip;137462 wrote:

An immortal, eternal virgin, yes, one who is frozen in time. Must Time destroy her beauty, or can there be temporal mathematical beauty, too?

I love and hate this virgin. Too clean. Too empty.

---------- Post added 03-08-2010 at 03:34 PM ----------

Twirlip;137462 wrote:

I find the theorem on unique factorisation of integers into primes beautiful.

Yes, it's something like a finger print. "Prime" is a potent word. The irreducible. I think philosophy is a lust to discover the primes of thought.

@Reconstructo,

Reconstructo;137444 wrote:

any one else struck by the beauty of math?

Maths is a very broad field, with a lot of variety, I think most people would consider something mathematical to be beautiful, if they looked at enough. But I think that's true for pretty much any field that's broad and varied. For example, disease is quite repugnant but, if the edition of Encyclopedia Britannica that my mother owns is reliable, any animal with advanced rabies, even a sheep, will attack a dog, and rabies reaches full strength when harboured by dogs. I think this has a kind of beauty, of course it's a different beauty from the beauty of Archimedes' informal method of proof, but that, again, is quite different from the beauty of Vietnamese cuisine, etc.
There's also the question of mathematical pathologies and false proofs, can these be beautiful? or just amusing?
In the case of maths, is it really a question of beauty, or is it appreciation? It might be interesting to consider ugly proofs, does anyone have any examples?

@ughaibu,

ughaibu;137723 wrote:

Maths is a very broad field, with a lot of variety, I think most people would consider something mathematical to be beautiful, if they looked at enough. But I think that's true for pretty much any field that's broad and varied. For example, disease is quite repugnant but, if the edition of Encyclopedia Britannica that my mother owns is reliable, any animal with advanced rabies, even a sheep, will attack a dog, and rabies reaches full strength when harboured by dogs. I think this has a kind of beauty, of course it's a different beauty from the beauty of Archimedes' informal method of proof, but that, again, is quite different from the beauty of Vietnamese cuisine, etc.
There's also the question of mathematical pathologies and false proofs, can these be beautiful? or just amusing?
In the case of maths, is it really a question of beauty, or is it appreciation? It might be interesting to consider ugly proofs, does anyone have any examples?

Yes, there's beauty in almost anything, if one can see the structure. Perhaps this gives math is special attraction, as it is made almost of pure form, pure structure.
A ugly proof could be beautiful to the degree that it was the extreme or the mean of ugly proofs in general?
Rabies is creepy. But I can see what you mean. It's a sort of demon. The sheep will attack a dog (strange) and then the rabies have their most "obedient" vessel. (I don't actually ascribe conscious motive to rabies, of course.)

@Reconstructo,

On this page there's a short discussion of ugly and elegant proofs, according to Einstein's taste: Menelaus Theorem: proofs ugly and elegant - A. Einstein's view from Interactive Mathematics Miscellany and Puzzles

@Reconstructo,

I went from studying the visual side of math into the study of Shogi, of all things. This is Japanese chess, and in some ways it's superior to "Chess." At the moment, I like this phrase: ratio is visual. Not that ratio is only visual...

At the moment, I see strategic board games as dynamic mathematical sculptures. Does anyone around here enjoy chess, shogi, stratego ? Has anyone here ever created such a game, or modified one? It's always been an interest of mine. Lately, I've cooked up a variant of Shogi that further emphasizes its mono-directionality.

Anyone else see the art/beauty in this sort of thing?

@Reconstructo,

Reconstructo;141678 wrote:

I went from studying the visual side of math into the study of Shogi, of all things.

I play at BrainKing, if you'd like a game, feel free to send me an invitation.

@ughaibu,

ughaibu;141780 wrote:

I play at BrainKing, if you'd like a game, feel free to send me an invitation.

Thanks. Have you ever tried FICS? You didn't say what you played. FICS is chess. I'm a big fan of lightning chess. 1 minute total game time on each side. It's brutal man. It's like two octopuses in a knife fight.

---------- Post added 03-22-2010 at 09:50 PM ----------

Games like chess and shogi are math all the way, but heavy on that visual-geometrical element. The Shogi variants have eaten up my free time. To sculpt a game is perhaps more fun than playing any particular game. It reminds me of those sculptors who made mobiles, or dynamic sculpture in general. Except in this case we are dealing with 2 dimension conceptual sculpture. A sculpture of a world that is designed to be activated by the human desire to win.

@Reconstructo,

Reconstructo;142399 wrote:

You didn't say what you played. FICS is chess.

At the moment I only play shogi, three checks chess and tablut.

Reconstructo;142399 wrote:

The Shogi variants have eaten up my free time.

I've secured permission for BrainKing to host Kyoto shogi and renge shogi, but no action on that yet.

@ughaibu,

ughaibu;142422 wrote:

At the moment I only play shogi, three checks chess and tablut.I've secured permission for BrainKing to host Kyoto shogi and renge shogi, but no action on that yet.

I just looked up tablut. Seems like a nice game. I didn't know of 3 checks chess. Looked it up. Sounds good. I would give 3 checks chess a try, for sure.

@Reconstructo,

Reconstructo;149398 wrote:

I just looked up tablut. Seems like a nice game. I didn't know of 3 checks chess. Looked it up. Sounds good. I would give 3 checks chess a try, for sure.

I can hard-ly play GO...or Chess.

[CENTER]Used to play Chequers with great-grand-father Greenland we called him. He lived there (retired peoples Home). I remember he smoked cigars and my Mother cleaning afterwards.
[/CENTER]

Pepijn Sweep
ud Jisp

Is tablut abbess ?

:bigsmile:

@Pepijn Sweep,

Pepijn Sweep;149407 wrote:

I can hard-ly play GO...or Chess.

[CENTER]Used to play Chequers with great-grand-father Greenland we called him. He lived there (retired peoples Home). I remember he smoked cigars and my Mother cleaning afterwards.
[/CENTER]

Pepijn Sweep
ud Jisp

Is tablut abbess ?

:bigsmile:

Tablut

Checkers is a great little game in itself. The kings can move backward, and that is their only power. And yet in a forward world it's quite a power. Also the simple symbolism of stacked pieces. Pretty great. And let's not forget the triple or quadruple jump. In Chess, you can only capture one piece at a time.

@Reconstructo,

Reconstructo;149410 wrote:

Tablut

Checkers is a great little game in itself. The kings can move backward, and that is their only power. And yet in a forward world it's quite a power. Also the simple symbolism of stacked pieces. Pretty great. And let's not forget the triple or quadruple jump. In Chess, you can only capture one piece at a time.

I was Young and he was Old. Still we had a Game. He biked 5 miles to come, and 5 miles to go back; at 85!!. I am sorry I don't play it any-more.
Smile

@Reconstructo,

YouTube - Fractal Zoom Sierpinski Carpet
YouTube - Fractal Zoom Sierpinski Carpet

@ughaibu,

ughaibu;138084 wrote:

On this page there's a short discussion of ugly and elegant proofs, according to Einstein's taste

@jeanlee411,

jeanlee411;161096 wrote:

I went from studying the visual side of math into the study of Shogi, of all things. This is Japanese chess, and in some ways it's superior to "Chess." At the moment, I like this phrase: ratio is visual. Not that ratio is only visual...

At the moment, I see strategic board games as dynamic mathematical sculptures. Does anyone around here enjoy chess, shogi, stratego ? Has anyone here ever created such a game, or modified one? It's always been an interest of mine. Lately, I've cooked up a variant of Shogi that further emphasizes its mono-directionality.

Anyone else see the art/beauty in this sort of thing?

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