Math Trek

The Ignobility of Wrinkles

Researchers win Ig Nobel Prize for study of rumpled sheets

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1:44am, October 17, 2007
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Grab one end of a bedsheet, hand the other end to a partner, and spread it out as if you're going to fold it. But instead of folding it, engage in a tug-of-war, with one of you pulling on the head end of the sheet and the other pulling on the foot end. The sheet will stretch a bit lengthwise and at the same time compress a bit widthwise. That combination will create a funny-looking set of wrinkles with furrows along the length of the sheet.

A mathematician and physicist working together have found an explanation for this wrinkling pattern. For their study of sheet wrinkles, they have won this year's Ig Nobel Prize in physics. The prize, sponsored by the magazine The Annals of Improbable Research, celebrates research that "first makes people laugh, and then makes them think." Ten prizes are awarded each year in various fields of science.

Sheet wrinkle experts Lakshminarayanan Mahadevan, a mathematician at Harvard University, and Enrique Cerda Villablanca, a physicist at the Universidad de Santiago de Chile, are sharing the prize in physics. It does not include a monetary award.

Mahadevan says he is "neither proud nor sheepish, just amused" to receive the honor. "There is no reason that good science cannot be good fun," he comments, "and I think our research is just one more example of that."

Marc Abrahams, editor of the magazine and administrator of the prizes, says that when he contacted Mahadevan to tell him about the award, "He wasn't too surprised about it. He knew at least roughly what the prize was about, and he's done a lot of colorful research. But he seemed to be surprised that it was for this. I could hear the silence on the other end, and I thought I could hear the words he was thinking, which were, 'What's funny about that?'"

The humor was not lost on everyone, though. "It was fun at the ceremony to see the difference in the audience's first reaction to the scientists' first reaction," says Abraham. "The audience laughed as soon as the prize was announced."

But Abrahams won't reveal why the research amuses him. "Explaining why something is funny is something I don't get into," he says.

Despite the light-heartedness of the prize, the team's work has been in earnest. The pair has deduced "a general theory of wrinkling" which explains why wrinkles form and predicts their number and size based on the characteristics of the fabric.

The theory also offers some insight into the wrinkles that form on people's skin, although it can't predict how many wrinkles any one person will get. Skin forms a flexible surface attached to a more rigid subsurface made of muscles.

The researchers' theory explains why our most obvious wrinkles tend to appear on relatively bony areas like the cheeks and forehead. The skin and fat are both thinner there. Fat provides a stretchy, cushioned connection to the firm muscle beneath, so where there's less fat beneath the skin, the skin connects to a more rigid subsurface. Also, thin skin is more pliable than thicker skin. The rigid subsurface and flexible surface combine to create larger, more visible wrinkles.

The team also examined the patterns that appear when fabric drapes over a solid object such as the body. The equations they developed to describe those possible patterns have many different solutions, and that fact corresponds to our experience that cloth can fall into many different shapes. The researchers say their results could improve our ability to depict moving clothing in computer-generated animation.

Past Ig Nobel prizes in mathematics and physics have been awarded for research contributions such as the following:

  • Calculating the number of photographs you must take to (almost) ensure that each person's eyes will be open in a group photo;
  • Calculating the odds that Mikhail Gorbachev was the Antichrist (answer: 710,609,175,188,282,000 to 1); and
  • Figuring out why a stick of dry spaghetti often breaks into more than two pieces when you bend it.

Cerda Villablanca was unable to attend the ceremony, but his sister Mariella accepted the prize on his behalf. "My brother dedicates his Ig Nobel prize to all the wrinkled people in the world," she said.

Mahadevan accepted his prize with a bit of doggerel:

Wrinkle, wrinkle, on my skin

How, I wonder, did you begin?

By sagging and swelling and shrinking too,

While stretching and bending were mixed into a brew,

'Til, aha! A formula that fits on a pin.


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