

It leans off to one side, rocks to and fro as if gathering strength and then, presto, tips itself back into a ''standing'' position as if by magic. It doesn't have a hidden counterweight inside that helps it perform this trick, like an inflatable punching-bag doll that uses ballast to bob upright after you whack it. No, the Gomboc is something new: the world's first self-righting object.

The Gomboc is a result of a long mathematical quest. In 1995, the Russian mathematician Vladimir Arnold mused that it would be possible to create a ''mono-monostatic'' object -- a three-dimensional thingy that purely by dint of its geometry had only one possible way to balance upright.


After several more years of scratching their heads, they finally hit upon a shape that looked promising. They designed it on a computer, and when it came back from the manufacturer, they nervously tipped it over, wondering if all their work would be for naught. Nope: the Gomboc performed perfectly [43]. ''It's a very nice mathematical problem because you can hold the proof in your hands -- and it's quite beautiful,'' Varkonyi says.

Yet the scientists now say that Mother Nature may have beaten them in the race after all. They have noticed that the Gomboc closely resembles the shell of a tortoise or a beetle, creatures whose round-shelled backs help them right themselves when flipped over. ''We discovered it with mathematics,'' Domokos notes, ''but evolution got there first.'' CLIVE THOMPSON

SMOG-EATING CEMENT This year a new weapon against smog was introduced in the United States: cement. Called TX Active, it was developed by the Italian company Italcementi. Enrico Borgarello, Italcementi's head of research and development, says the product can literally ''kill'' pollution.

The cement's chemical composition is enhanced with titanium dioxide, which under the right conditions can neutralize some harmful pollutants. When exposed to sunlight or ultraviolet light, the titanium dioxide is ''activated,'' Borgarello says, and pollutants that come in contact with the surface of the cement are oxidized. Hazardous nitrogen oxides and sulfur oxides, for example, are transformed into harmless nitrates or sulfates, which simply rinse off the building with rainwater. This also keeps it especially clean.

Italcementi developed the cement for the architect Richard Meier, who wanted a very white material for his Jubilee Church in Rome. Titanium dioxide, commonly used to make paints bright white, was added to the standard cement's mix. It was only later that Italcementi realized that TX Active had pollution-busting properties. For instance, in Bergamo, where Italcementi is based, a stretch of road downtown was coated with a layer of TX Active. Borgarello says that residents reported better-smelling air within 4.5 square miles. The company says their research shows that if 15 percent of the surface area of Milan were covered in TX Active, air pollution would be reduced by 50 percent.

Thomas Cahill, an atmospheric scientist at the University of California, Davis, is skeptical of the full extent of the company's claims. He cautions that the ''benefits, while they might be real in limited cases, are not a 'cure' for pollution.''

Borgarello says that he envisions TX Active as an agent of change for air quality -- and for cement's reputation as an uninspired, antienvironmental material. ''You destroy the green, and you put a building in with cement,'' he says. ''Now we put this material in, and we are contributing to quality of life.'' lia miller

STARCH MADE US HUMAN [44] Traditionally, when scientists spared a thought for our hunting and gathering forebears, they focused on the hunters and the meat they brought in. But it may be that it was our ancestors' less glamorous ability to gather, eat and digest roots, bulbs and tubers -- the wild versions of what became carrots, onions and potatoes -- that increased the size of our brains and made the hunt and the territorial expansion that came with it possible.

In a paper published in September in Nature Genetics, George Perry, a graduate student at Arizona State University, Nathaniel Dominy, an anthropology professor at the University of California, Santa Cruz, and their colleagues demonstrate something significant: unlike our fellow primates, modern humans have many copies of a gene that makes a protein in our saliva that is crucial for breaking down starch into glucose. Our brains run on glucose. DNA and saliva samples taken from populations all over the world -- from locals in Arizona and Japan to the Hadza, hunter-gatherers in Tanzania, and the Yakut, Siberian animal herders and fishermen -- showed that if you have more copies of the gene amylase 1, you have more of the protein. Groups like the Japanese, who eat diets high in starches, have on average a higher number of copies of the gene. ''In human evolution, starch may have played a particularly important role,'' Perry says. After all, if you possessed the ability to efficiently convert starch into the glucose that fuels your brain, ''you'd have a big advantage nutritionally,'' Dominy says.