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Math and the Mona Lisa: The Science of Looking at Art (October 15, 2004, Two)

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Program Summary

From the corner of your eye, you catch the mysterious smile for which Leonardo da Vinci’s Mona Lisa is famous. When you try to study it directly, though, the smile is gone. Is it magic? No. Is it all in your head? Well, yes. The unsettling appearance and disappearance of the smile is the result of the physical structure of our eyes.

The center of the retina is best at perceiving small, sharp detail, while the periphery is better at distinguishing large, blurry images. Leonardo used a technique called sfumato, deliberately painting the upturned edges of the mouth in a hazy fashion; our center vision can’t see the fuzzy smile when we gaze at it straight on, but when we move our eyes to another part of the picture, our peripheral vision picks it up.

Did da Vinci understand the anatomical reason for this phenomenon? He couldn’t have; knowledge of how vision works was centuries away. It was an optical illusion that he stumbled upon, then never used again. But it lives on as one of the most dramatic tricks of the eye ever invented. Ira and his guests discuss this and the math and science behind other stunning visual effects in art.

Guests

Bulent Atalay, author of "Math and the Mona Lisa: The Art and Science of Leonardo daVinci" (Smithsonian Books, 2004)
and professor of physics at the University of Mary Washington in Fredericksburg, Virginia

Margaret Livingstone, author of "Vision and Art: The Biology of Seeing" (Harry N Abrams, 2002) and professor of neurobiology at the Harvard Medical School in Boston, Massachusetts

Related Links and Resources

BBC News, February 18, 2003: ”Mona Lisa Smile Secrets Revealed”
Bulent Atalay: Scientist-Artist
College Street Journal, October 18, 2002: “The Biology of Seeing: Harvard Neuroscientist Continues Visual Studies Series October 24”
SFGate.com, November 27, 2000: “The Mystery of Mona Lisa's Smile Linked to Flickering Eyes”

Books Discussed

"Math and the Mona Lisa: The Art and Science of Leonardo daVinci" by Bulent Atalay (Smithsonian Books, 2004)

"Vision and Art: The Biology of Seeing" by Margaret S. Livingstone (Harry N Abrams, 2002)

For Discussion:

• Why does Mona Lisa’s smile seem to appear and disappear?
• What is sfumato?
• What is the “primitive brain” in humans? How is it different from the rest of our brain?
• What is luminance? What is the role of the primitive brain in creating luminance in art?
• What are the golden triangle and the golden rectangle in art? What are the mathematical principles behind them? Why are we attracted to art pieces that use these principles?

Activities

Eye spy. Take a look at sight at Neuroscience for Kids: Vision, which discusses the structure of the eye and how it affects how and what we see. The Retina and Visual Pathway pages give details about light and color, and lots of fun experiments at the Gallery of Visual Illusions and Vision Experiments demonstrate the science.

When you’re smiling... For an in-depth explanation of spatial frequency (the cause of Mona’s magic smile), read Mona Lisa’s Smile from Science Netlinks. A link at the bottom of the page will take you to Purdue University’s Visual Perception Online Laboratory for some sophisticated optical illusion experiements.

Da Vinci’s da bomb. Get up close and personal with Leonardo da Vinci at the Boston Museum of Science, an online exhibit that delves into the genius’ life, art, and inventions. At the Multimedia Zone you’ll find interactive explanations of his art techniques that incorporate math and science, including a section on sfumato. Shockwave is required.

I’ve got a secret. Thinkquest’s Why Is Mona Lisa Smiling? asks not how she smiles, but why? And the answer is astounding. This project uses a morphing program to explore the intriguing theory that the secret Mona Lisa guards is that da Vinci actually painted himself.

The golden hour. What is the golden triangle? Get answers about Fibonnaci numbers and the golden ratios at Mr. Narain's Golden Ratio WebSite. The Activities page links the golden ratio to art, architecture, and nature, and involves students in several activities to demonstrate the amazing properties. In The Perfect Face, students measure the proportions of well-known “beautiful people” and try to construct their own perfect face.

Use the search box below to perform a Google search within any of the specifc sites or general domains mentioned in this Activities section.

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