Engines of Our Ingenuity

No. 2179:
SCIENCE BREAKTHROUGHS OF 2006

by John H. Lienhard

Today, the big science news of 2006. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

Sience magazine lists breakthroughs for 2006. Most are biological. Number Ten has to do with new forms of RNA, and Seven with the rise of several new species during the year. Numbers Four and Two also have to do with evolution: Paleontologists found a long-missing link between fish and reptiles -- a 375-million-year-old fish with strong, jointed front fins that served as embryonic legs. And they've found partial Neanderthal DNA. It suggests that Neanderthals might've interbred with Cro-Magnon humans.

Number Three on the list was confirmation that the great ice sheets over Greenland and the Arctic are melting at an accelerating rate. Such coastal regions as New Orleans and Bangladesh will likely vanish under water in a century or two. Placing that result in the Number Three spot might sound crass, considering the potential cost in human suffering. Perhaps it's not ranked higher as a scientific discovery simply because it's so unsurprising.

Yet that same criticism might be leveled at Science magazine's Number One breakthrough, a proof of Poincaré's conjecture. It was actually about objects in four-dimensional space, but we can get the idea by imagining certain smooth bodies in three dimensions -- ones on whose surface we can lay a closed elastic loop of string anywhere, then shrink the string to a point. Of course if we do that on a doughnut, loops surrounding the hole will be stopped.

In 1900, Poincaré proposed that all four-dimensional bodies with no such holes can be deformed into higher order spheres.

That's pretty abstruse and, while people were sure it was true, no one could prove it. Finally Russian mathematician Grigori Perelman used new mathematical tools, and he invented others, to prove Poincaré was right. He built on earlier work; then other mathematicians filled in details. Perelman was offered the Fields Medal, a kind of Nobel Prize in math, for that work.

But he refused it -- made dark comments about ethical lapses among mathematicians. Arguments have raged over his real reasons ever since. All that makes fine Grand Guignol theatre, no doubt.

But we need to consider how the breakthroughs were ranked. Was it right to place a terribly arcane mathematical result ahead of the hot-button issues of evolution and global warming?

I think it was. We can't let science turn into hot-button forums. Those issues must be faced. We're doomed if problem-solvers don't make wise use scientific results -- if politicians and engineers fail to face reality.

Yet we're also in trouble without people who look for the truth of things -- without reference to daily hot buttons. We need the unskewed knowledge they provide to deal with problems in the long run. So congratulations Grigori, you've unraveled another old mystery, and you're entitled to your Number One post. Of course, the rest of us had better keep our eye on that global thermometer.

I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.

(Theme music)


For the breakthroughs, see the articles in the 22 December, 2006 issue of Science, pp. 1848-1855.

For more on Grigori Perelman, see S. Nasar and D. Gruber, Manifold Destiny: A Legendary Problem and the Battle over Who Solved It. New Yorker, August 28, 2006, pp. 44-57.

My thanks to Martin Golubitsky, UH Mathematics Department, for his counsel.


distorted spheres

The Engines of Our Ingenuity is Copyright © 1988-2007 by John H. Lienhard.