Archive for May, 2012

Those who fall in love with practice without science are like pilots who board a ship without rudders or compass. -Leonardo da Vinci

Q: Why do the Mona Lisa’s eyes appear to follow her viewers around the room?

A: Because Leonardo da Vinci was an expert at creating illusions…based on science and observation.

The development of perspective was hugely important in Renaissance art. Many artists of this time were obsessed with painting the world as it actually existed, rather than the way it appeared  to exist. The discovery of linear perspective allowed artists to create art that followed the laws of nature to create dimension, rather than merely using height and width to create the illusion of depth. Then they (the artists of the Renaissance) tossed in a few rockin’ shadows and created the most realistic two dimensional paintings made to date.

But back to Mona. I remember one time sitting on the couch eating dinner watching a television show. I saw something on the screen behind one of the actors and craned my neck to get a look behind him to see what it was. That was the moment that I truly understood the difference between two dimensions and three. No matter if I even stood up and walked across the room, I would never be able to see behind the fellow, unless he moved out of the way.  In a painting this limitation of two dimensions is even more prevalent because Mona Lisa will never acquiesce to a request to budge over so we can see whats going on behind her. She can never ever change what she’s doing. So if she is painted to be looking at the viewer, she will always be looking at the viewer, no matter where the viewer is standing. Once the perspective is set, it will remain forever.

Projective geometry, the mathematics underlying the rules of perspective, was born in the Renaissance and indeed may have ushered in the art of the High Renaissance. One-point perspective appeared first in the works of Masaccio and Masolino in the first half of the fifteenth century, coming to full fruition in the works of Leonardo da Vinci in the second half of the century. Although the scheme was firmly established with Leonardo, it saw further refinement in subsequent centuries with the introduction of two-point perspective a century later and three-point perspective much later–after cameras with tiltable lenses for architectural renditions were invented in the twentieth century. (Bülent Atalay, Math and the Mona Lisa)

(My other favorite artist, Albrecht Dürer)


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(Leonardo Da Vinci-self portrait circa 1512)

Leonarda da Vinci has long been my favorite artist. I thought about doing a blog posting on him several times over, but never could focus all the awesomeness into one idea succinct enough for a post. But, as will happen when the time is right, I scored a copy of a book entitled Math and the Mona Lisa: The Art and Science of Leonardo da Vinci by Bülent Atalay. From this score came the succinct thought that I needed. Leonardo da Vinci is known of as a renaissance man. Indeed, it was probably he as a subject, who first generated the term, because of his knowledge, curiosity and deep comprehension of so many varied, and seemingly polar opposite, subjects. Math and art. Science and religion. Circles and squares. These are all supposed opposites, and are also all ideas that Leonardo da Vinci was able to connect with his fabulous and inventive mind (a mind that is referred to as being seemingly superhuman, by some)

Since there are so many great ideas presented in Atalay’s book, I’ll just focus on a few and I’ll spread them out over a couple of postings. Too much goodness just goes to my head! I’ll start off with a quote:

For mathematicians and physicists it is undeniable that there exists inherent beauty in mathematics. This is the aesthetics of mathematics. Perspective, proportion, and symmetry in any context are quantifiable. Accordingly, art indeed possesses quantifiable aspects. There is the symmetry expressible in mathematical terms and then there are ‘nature’s numbers.’ These notations figure into the mathematics of aesthetics. The associated quantification  can be formulated at various levels of mathematical sophistication…The Fibonnaci series gives rise to the notion of dynamic symmetry, the golden section, or the ‘divine proportion,’ which Fibonacci himself could not have anticipated. Three hundred years after Fibonacci formulated the series Leonardo da Vinci illustrated a book called De divinia proportione. But the integration of science and art has many more strands than Fibonacci’s mathematics and Leonardo’s art: It also draws in elements of architecture, astronomy, biology, chemistry, geology, engineering, mathematics, philosophy, physics–encompassing the extraordinary range of Leonardo da Vinci’s interests. For him these were branches of the same tree, part of a grand unified structure, the universe. (Ataly, pg 14)

For those of you who skipped the quote, it basically said that beauty is often quantifiable through perspective, proportion, and symmetry and that for Leonardo da Vinci science, mathematics and art were all various parts of the same whole.

Up next…how is the Mona Lisa able to stare at you wherever you go? It’s beautiful…and it’s math.

(Leonardo Da Vinci-Flower of Life drawing)

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