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Thursday, January 30, 2014

Mathematical Beauty and Creativity

http://vimeo.com/77330591 - Beauty of Mathematics

http://www.firstpost.com/topic/organization/pixar-pixar-and-math-disney-pixars-brave-wonder-moss-video-EnaA9ZRPXiE-35299-1.html - Wonder moss

http://fineartamerica.com/featured/4-flow-of-life-flow-of-pi-cristian-ilies-vasile.htmll - Flow of life / flow of pi

I got thinking about this topic when a friend on Facebook liked this quote. I fully agree with this quote in all aspects and I want to draw attention to point II. Music is mathematical - pitch, frequency, rhythm and meter - really all of music can be described by mathematics.  Destin from Smarter Every Day did a great video of a beatboxer (Flula) in slow motion In it he shows how overtones produce a unique sound signature. It also goes over the different mathematical components that make up sound. I'm not saying that music can be replaced by mathematics, only described by it. We can do the same with art. In fact, in the special features of the Disney-Pixar move Brave they describe how math is used to create the amazing world shown in the film. Really, mathematics is a language that can be used to describe just about everything within our world. Not just the sciences but also the arts. I am not saying that it can be used to predict things. Nassim Nicholas Taleb would tell us that anytime we have a human element involved, predictions go out the window. But mathematics can be used to describe it in its present state.

Many think of mathematics as cold and unfeeling. Statistics and probability are guidelines not rules. The mathematical analysis of a painting will never look the same as the painting itself. Algorithms can't put their heart and soul into producing a piece of music like a composer might. To call someone "calculating" is usually considered, if not an outright insult, a derogatory remark used for villains and along the lines of "heartless." I think that this view of mathematics is one of the big reasons that many see the arts and mathematics as mutually exclusive. It is not uncommon for me to hear, "I'm one of those English people / art people / music people and so can't do math." I think my previous examples demonstrate that mathematics is not separate from the arts, but rather is something that can help us understand it even more.

So rather than continue my reasons why people don't like math, I want to demonstrate some of the beauty of mathematics. It is my hope that the following examples may be appreciated regardless of mathematical ability. Just like art or music you don't have to know how to create it in order to enjoy it.

First, fractals.
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Simply Googling "fractals" and looking at the images will give you lots of cool pictures, both from nature and artificial. Fractals are produced you have a design replicate itself so that ever successive generation or iteration looks like the initial one. The picture above shows how every new iteration branches the same way that the first do. If you were to zoom in (or out on a fractal you would find yourself looking at the same image, they are infinite in their presentation. One of the most famous fractals is the Dragon CurveNumberphile did a great video on the Dragon curve and how it works.

The second example I want to look at is an artist by the name of Cristian Ilies Vasile. Numberphile introduced me to his art in one of their videos - Pi is Beautiful. Looking like a web of colored lines Cristian plotted the digits 0-9 in a circle and then starting with 3 he drew a line to 1 then to 4, back to 1 and continued along the digits of pi. He's done the same with e and the golden ratio. Like the Dr. James Grime points out, this is math for art's sake. There is no real mathematical use for these pictures, but they are quite striking. Check out the link on Cristian's name above. I would love to pick up one of his pictures myself and am hoping to in the near future.

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