Art vs. Mathematics?

Question

I'm writing an essay that discusses the roles of imagination and reason in the Arts and Mathematics. My thesis is that imagination and reason play a role in both subjects but that too much reason in art or too much creativity in math blurs the line between the two. Examples I've come up with are tessellations and fractals; I'm looking for some other examples where the line between art and math becomes blurred. Anything really will help. THanks!

Answer 1

Relationship between Beauty and Math:
We find things beautiful because of their mathematical proportions.

The best example is the Golden Ratio, sometimes called "phi". Sculpture, architecture and paintings are more beautiful when they display objects sized according to this ratio.

Famous examples include the Parthenon, the Mona Lisa and Salvador Dali's "The Sacrament of the Last Supper".

"Leonardo da Vinci's illustrations in De Divina Proportione and his views that some bodily proportions exhibit the golden ratio have led some scholars to speculate that he incorporated the golden ratio in his own paintings. Some suggest that his Mona Lisa, for example, employs the golden ratio in its geometric equivalents."

Most psychologists believe that a beautiful human face can be measured mathematically, in that they can measure the symmetry of a face, and, in general, the more symmetrical a face, the more perceived beauty.

Mathematicians employee imagination when they speculate on unproven relationships. Then they attempt to construct a link between what they can prove and their hoped-for result. If they can build a chain of proven steps, then they have achieved their goal.

How they *imagine* some unproven result can be a leap of intuition, and generally they attempt to prove relationships that they find beautiful or symmetrical. Airplane designers have a saying that "if a plane looks good, it will fly well", and a similar concept applies to math. Mathematicians rarely attempt to prove concepts they find "ugly".

Artists only rarely envision a finished product and attempt to arrive at it (famous example: carving away all the parts of a block of marble that are not part of the finished statue).

More often they incrementally build from some starting place. They typically employ a lot of trial and error and imagine where their piece could go if they continued in that direction, relying on their aesthetic sense to determine what is working and what is not.

As an amateur photographer, I seek beauty where ever I go, but I cannot force the natural elements to assume some pre-planned relationship. I can try-out various relationships between potential photographic elements, but all I can do is imagine how a shot might turn out after manipulating the elements I stumble upon. My best photos are a combination of serendipity and constant searching, along with the application of a few general principles.

In summary, you could say that the biggest difference between a mathematician and an artist is in the size of their initial intuitive leaps.

Answer 2

An artist can not function without mathematics and in mathematics there is the beauty of art. Consider the art of fooling the eye. The illusion and the confusing.

Answer 3

I am an artist, I have an art dealer and an art degree and making art is my priority in life right now. Math has little or nothing to do with my work, although I have been told that my work reminds people of fractals. I don't start a painting wanting to make forms that look like fractals, but recurring patterns occur unconsciously in my paintings (which are abstract). I know a few artists who use procedures such as counting and precise documentation. Nicolas Symes measures and counts every addition to his sculptures. The show I saw of his includes notebooks of this documentation. here's a link, you can watch him at work on youtube . http://www.pmgallery.ca/Catalog2_View_Summary.php?ID=20&mode=1
at the Alley Jaunt show in toronto, Stephen Lavigne matches tiny paint swatches to every colour of every object left in his garage (the garages are the gallery spaces of the Alley Jaunt show). He then used the information and the numbers and colours etc. to make paintings. http://www.eye.net/eye/issue/issue_08.17.06/arts/artsweek_4.php
The practices of both of these artists are highly methodical, even mathimatical? One example of when maybe too much math has hindered someone's work when a fellow student in school counted every pencil mark he made as he made it. The resulting piece was many pencil lines a couple of meters in length piled onto of one anothe on a large piece of paper. He quoted a number to correspond with the pencil marks, I found the work to be empty, but that's just my opinion.
Anyways, I hope this helps with your project in some way or another, I am personally really bad at math, but that just makes me a really inept accountant but maybe not a bad artist?

Answer 4

Go back to the Greeks...math and art..the "golden mean" , the "music of the spheres", Pythagorean philosophy...
or
"sacred geometry"
or
cathedral architecture
or
ancient Egyptian math "encoded" in their glyphs


however,
your assumption as to the "artistic" interpretation(s) of fractals is somewhat specious...the mathematical basis for Mandelbrot and Julia sets, for "strange attractors", as well as other fractal forms had been known for a long time....it was only with the application of an analog computer that the forms were seen...
the "artistic" interpretations/aspects are nominally given by non-mathematical persons..because the formulae are easily programmable, fractal math can generate a plethora of forms...many of which can be utilized as "art"....

"too much creativity in math"....I think not...
read the bios of Newton and Gauss...they attributed [at least in part] their "insights" that furthered math to their imagination/"creative" view of the then known mathematical assumptions...

while the counter positive may be true..."art" that is too mathematical...may be stretching the definition of art..as in fractals and tessellations..it is only artifice

Answer 5

I find much of Hyperdimentional Geometry both facinating and beautiful.

Look into the work of a man called Michu Kuka for more about Hyperdimentional Geometry and you might also find the work of Stephen Wolfram helpful, especialy his book A New Kind of Science.

Answer 6

an artist must have a grasp, of mathematics.

Mathematicians must create art with their numbers.

both forms must balance.

Answer 7

Algebra.

It was the one branch of math that I did well in because it involves a great deal of imagination.