h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

No. There is not mathematics in nature - there is nature all over mathematics because mathematicians keep having to re-invent it. That's my point.

Not sure what you mean about the art thing....

Mathematics, in essence, is the study of patterns. There are patterns everywhere in nature. Whether we invent or discover the patterns is another thing entirely, but they are present in nature.

As for the art thing, what about the golden ratio/number
http://milan.milanovic.org/math/english/golden/golden4.html
for starters. Never mind the mathematics ideas used in true perspectives during and since the renaissance, to mention two...

You wouldn't want to believe everything you read about the Golden Ratio:

"Pythagoras ... proved that it was the basis for the proportions of the human figure"

Since it is not true, it would be very difficult to prove it.

Well, maths has certainly had an influence on art, which was the point of the (maybe not wholly accurate) remark.

Would Escher's tessellating (sp?) pattern pieces count as having a mathematical influence? I'd say so.

Apparently, although Escher's work was full of mathematical patterns, he wasn't conscious of them when he made them. Just goes to show, patterns don't have to be intentional to be there.

I'm sure that bees aren't conscious of the shape of their honeycombs when they make them. I'm likewise sure that spiders don't deliberate much over the patterns of their webs.

I think the difference here is one of semantics, and to a certain degree we're all arguing the same point:

Consider the statement "mathematics exists in nature". To me implies that nature somehow obeys mathematical principles. I find this a hugely arrogant stance to suggest that somehow nature adheres to a flimsy model mankind came up with. Nature was around way before mathematics was. It's kind of like saying an apple was called an apple before there was the English language.

"There are elements of nature in mathematics" is a more palatable statement to me. Over the years man has tried to model nature with mathematics, and has extended the model to make it cover some aspects of nature which it did not adequately describe. Chaos theory and fractals being examples of that.

The art thing can have a similar argument - is the mathematics in the art, or are the mathematicians simply interpreting the art through their favoured model......? That's a question which really only the artist can answer, and it seems that Escher for one did answer it. I'll admit that given Da Vinci's love of science and mathematics, it seems unlikely that he didn't use its principles as inspiration for some of his work.

I guess to me (and this is a purely personal standpoint) the concepts of mathematics and art are entirely opposing systems for analysing and understanding nature. I subscribe to the art method of looking at the world, cos that's just the way my brain works.

Speaking of patterns and math, check this out
http://www.wolframscience.com/
very interesting ideas.

Sorry if anyone got the wrong end of the stick, there. I wasn't really arguing for or against anything. I was just musing some examples out loud.

<>

I'd say that there are patterns in nature which we describe using maths. Things like gravity require pretty simple maths, and are linear, which means a slight error in the question leads to a slight error in the answer. In 'nature' (meaning living things presumably), the maths we'd use to describe things is non-linear, which lets us see the patterns by which, for example, a flower grows, but couldn't let us predict the exact shape of a flower even if we knew the equations to describe its growth.

Re mathematics and art; hmm, don't really have an opinion that doesn't relate to patterns.

pedro, Escher did have some contact with mathematics and mathematicians, particularly later in his life. The 'Circle Limit' pictures were inspired by his collaboration with Coxeter.

http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Escher.html

Escher certainly had some mathematical influence and this influence did appear to grow as he got older but he is something of an extreme example I think that the influence mathematics has had on art is high especially things like the golden ratio.

Your question - "if mathematics is just something we invented, how come it is so spectacularly good at making predictions about the real world?" - is easy. Mathematics is a language we devised as a method of describing (and predicting) relationships in the world. If it did not work - it would die. Over time its success has grown. Just like evolution. It has taken a long time. As such its success should be good. Spectacular?
As for zero - it was not invented other than as a part of mathematical language. There was no "moment of discovery" as such. All intelligent people understood what it was - simply a state of absence. No food = zero food.

Wether mathematics existed in Nature before, that is basically that philosophical "If it walks like a duck and talks like a duck, is it a duck?" argument. But certainly there are a lot of things in nature that follows mathematical patterns, where the patterns were discovered in maths before they were in nature.

Cubism was apparently inspired by the idea of a fourth spatial dimension.

Read:
Godel, Escher, Bach (an etarnal golden braid) by Douglas Hofstadter
aka GEB .

It is not only a highly challenging mathamatical tome, but is entertaining, rewarding, and full of M. C. Escher artwork. The author relates the works of three pioneers; Kurt Godel, a number theory mathmatician, J.S. Bach, a classical music composer, and M.C. Escher, a visual artist.

I can't begin to describe how amazing this book is (especially if you can get to the end), but I think it is an insight to how the arts and maths are what they are (and often aren't what they seem!)

Each chapter is two parts; first a dialogue between ficticious characters that describes a paradox or situation that will be the topic of the accompanying scientific evaluation. The science is then examined in depth.

I think it shows that there is always more to understand, as well as detail that slips from our grasp. Still, between the two lies Beauty, Bueaty, and Baeuty.

{but not zero, it doesn't exist)

I don´t think zero was discovered because it has no use except for maths.

"I'm hungry. How many apples do you have?"
"None"
"Ah well, then, guess I'll just starve."

Et voila. Zero, with any maths in sight.

The book sounds fascinating.

Zero is weird if you think about it too much. Right now I have 1 spoon and 1 napkin sitting on my desk; there is 2 types of things that i have one of. But I also have zero plates on my desk, and zero pencils, and zero elephants...I have an infinate number of types of things that I have zero of.

Also, in higher mathematics that deals much with INfinity, I think zero and infinity have some sort of weird relationship. 1/infinity = 0 (since a fraction thought of as splitting a pie, and if you split a pie an infinate number of times, you would have all split and no pie.) I know this is accepted as true in some forms of calculus. So then, by using simple algebra, does 1/0 = infinity? And 0 x infinity = 1?

speaking of weird math, .999999999999999999999999999999999999999999 = 1. that's one of the weirdest things ever.

.9 recurring can easily be proved to equal 1
1/0=infinity is fair enough but so does 2/0
as infinity is technically indefined theese are nonsense statements that are only useful in psedumaths like:
Let a=b let a = 1
a=b
a^2=ab
a^2-b^2=ab-b^2
(a+b)(a-b)=b(a-b)
cancel the a-b
a+b=b
as a=1 b=1
1+1=1
Therefore
2=1
However infinty has proved useful in many mathematical ideas most notably calculus.