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February 28, 2008
Lakshminarayanan Mahadevan, a professor of applied mathematics at Harvard, “practic[es] the old-fashioned method of scientific inquiry called natural philosophy, where one wonders about everything,” writes Jonathan Shaw in Harvard Magazine, where he takes a deliciously leisurely ramble through Mahadevan’s “Physics of the Familiar,” complete with video clips of demonstrations. The professor’s motto: “Just because something is familiar doesn’t mean you understand it.” Shaw writes:
Mahadevan sees trees lifting water from roots to crown, or perhaps a drop of paint drying in the sun, and wants to understand in a deep sense what is happening right before his eyes. . . .
What will happen as the drop of paint dries? . . .
[A] skin will form. That is the natural consequence of liquid solvent leaving the surface fastest. “Now you have a skin, which is covering a drop, which is sitting on a surface, and you want to remove more liquid from inside. That is like drying a raisin,” says Mahadevan. When you remove some of the volume from beneath a fixed amount of surface skin, “the only thing the skin can do is wrinkle.”
Paint often wrinkles—but sometimes it cracks. This seems odd, he points out, because in wrinkling, things are pushed together, whereas cracks form when things are pulled apart. What accounts for these antithetical behaviors?
The answer, he explains, depends on whether and how the drop is attached to the surface. “For example, if I have sliced the grape in half and stuck it down on a surface,” then it can’t shrink easily because it is stuck to the substrate, and it will rip. “On the other hand, if the drying grape is not attached,” removing liquid from the inside will cause it to wrinkle as it shrinks.
Changing one little parameter changes the outcome.
Pure curiosity is fruitful because the universe is a uni-verse: the same mathematical and physical laws that operate in a drop of drying paint are at work in the behavior of the earth’s crust, and in the newly discovered wrinkling and cracking of the surface of the planet Mercury. As a byproduct of understanding these phenomena, we may learn to engineer useful materials. “The simplest answers often are very powerful,” Mahadevan says, “since they allow one to move from one problem to another, often via analogy.”
As Shaw concludes—inviting the reader to visit Mahadevan’s Web site—the professor is “a testament to science driven primarily by curiosity.” Now how about watching grass grow?
(Annie Gottlieb) |
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