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ANCIENT traders and modern mathematicians may have been getting their sums
wrong. It seems you can鈥檛 get a consistent measure of goods by randomly pouring
spheres such as oranges or grains into a vessel, say American researchers. Their
findings have sparked off a debate about the meaning of randomness.

Since biblical times, barter economies have relied on the assumption that the
same amounts of produce will always fill a container of known volume.
Mathematicians also believed that if you pour spheres randomly and shake them
around enough, they settle down into a maximum density, a state called random
close packing. But while exhaustive experiments with peas and ball bearings gave
a maximum density for randomly packed spheres of around 64 per cent, nobody has
been able to predict this value theoretically.

Now Salvadore Torquato, a materials scientist from Princeton University, says
this whole concept is misplaced. 鈥淲e showed in a computer simulation that you
can go beyond the 64 per cent limit,鈥� he says.

Using a computer model, Torquato and his colleagues simulated 500 spheres in
a cube, and squeezed the sides inwards at different rates to mimic the effects
of shaking until the spheres jammed together. Pushing in the walls at different
speeds yielded structures with densities ranging from 64 per cent to 74 per
cent. 鈥淏oth density and order vary continuously,鈥� says Torquato.

The scientists argue that the concept of random close packing is meaningless
because a 鈥渞andom鈥� state and an 鈥渙rdered鈥� state are simply regions on a
continuous scale, with no sharp distinction between them. Princeton chemist
Roberto Car supports his colleagues. 鈥淭hey proved that a concept that has been
around for a long time is not defined and incorrect.鈥�

But chemical engineer Geoff Mason from Loughborough University disagrees. 鈥淚
believe there鈥檚 a boundary,鈥� he says. 鈥淚t is possible to get random packing up
to a density of around 64 per cent, but after that you鈥檒l start to get order in
the system.鈥� Computational scientist Les Woodcock at the University of Singapore
also believes there are well-defined limits to random close packing. 鈥淚 disagree
profoundly with their assertions,鈥� he says.