IT FAZED me the first time I saw one. I was in Wales, where they call it a rebellious celt, but it's also called a rattleback or just a celt. "It" is a 10-centimetre-long plastic toy with a base shaped like the hull of a boat. When you spin it one way, it turns a few times before the ends start to rattle up and down. The more it pitches, the slower it rotates until it stops spinning altogether. Then the most intriguing thing happens: the celt starts to spin in the opposite direction. It's as if some unseen hand is playing a joke on the laws of physics. What on Earth is driving it?

The first attempt to analyse celts was a century ago. But it took until the mid-1980s for full mathematical descriptions to emerge, one by Hermann Bondi, then Master of Churchill College, Cambridge, and the other by Mont Hubbard, professor of mechanical engineering at the University of California, Davis.

Bondi and Hubbard agree that the celt's astonishing trick needs three main ingredients. First, the curved base must have two different radii--one long radius for the lengthwise curve and one shorter radius for the tighter curve across its width. Next, the axes of symmetry of the celt must be skewed slightly from its principal axes of inertia (see top Diagram). Any rigid object has three principal axes of inertia. They sit at right angles to each other and if you spin the object about one of them, there is no tendency to rotate about the other two. Finally, there must be a different distribution of mass about each of the two horizontal axes of inertia--a long, thin shape, say. 

Given these characteristics, the maths predicts how the celt should behave. The trouble begins, however, when you try to translate the equations into a physical explanation for what's going on. "It's only clear through the equations," says Hubbard. "I don't intuitively understand it."

But there are at least a few hints about what's going on. Let's start halfway through the celt's journey, while it is pitching up and down like a rocking horse (see lower Diagram). Friction acts horizontally--at the point of contact between the celt and the surface--to prevent the celt from slipping. One component of this frictional force creates a torque that tends to rotate the celt about its vertical axis. 

"To make it more complicated, the point of contact is moving all the time and the torque changes," says Hubbard. If the inertial and symmetrical axes of the celt coincided, the average torque over a single oscillation would be zero. But for the celt, there is a net torque in one direction. And it is this that reverses the angular momentum, says Bondi.

Another way to understand how the celt works is in terms of energy. It emerges from the maths that each direction of spin is linked to a different mode of oscillation: if clockwise rotation feeds the pitching oscillation, then anticlockwise spin would feed a side-to-side, or rolling, oscillation. So, when the celt spins clockwise, any tiny pitching oscillation grows exponentially. It feeds off the rotational energy and so slows down the spin. "But even when there is zero spin, the torque still acts," says Hubbard. So the direction of spin changes. Some celts will reverse spin directions again by trading rotational energy with the rolling oscillation.

It seems that we'll have to wait for a better physical description of how the celt behaves. Still, after a hundred years of probing the toy, it's unlikely that scientists will stop now. "The thing about scientists is that they really like toys," says Brian Pippard of the University of Cambridge, who's devised a way to make a celt from part of a wine bottle. "They have an interest in anything that looks odd. And they're not happy until they can describe how it happens."