TO A man with a hammer, Mark Twain once said, everything looks like a nail. One hammer that has seen lots of use in recent years is the type of mathematical relationship known as a power-law distribution. Such distributions have been observed in phenomena as diverse as earthquake magnitudes, the sizes of personal fortunes, and the number of visits made to websites. They have not, however, shown up in diagnostic medicine—at least, not until now. In this week's Physical Review Letters, Yoshiharu Yamamoto of the University of Tokyo and his colleagues explain how the movements of people suffering from clinical depression can be described by a power law—and how this law is so different from that of healthy people that it looks truly diagnostic.

Like many mathematical functions, a power law plots two variables against each other to form a characteristic curve on a graph. Dr Yamamoto collected the data for his own particular power-law curves by fitting his experimental subjects—about half of whom were healthy, and half of whom had been diagnosed as having clinical (or “major”) depression—with accelerometers. These devices measure how often someone changes his rate of movement by recording each time his acceleration exceeds a certain threshold.

The basic results confirmed a known feature of depressed people. The normal daily rhythm that would lead to a high, steady number of counts during daylight hours and low counts during the night was replaced by occasional bursts of activity. The surprise came when the team started plotting their results out on graphs.

The curves produced by plotting the lengths of low-activity periods against their frequency were strikingly different in healthy and depressed people. This reflects not inactivity by the depressed (though they were, indeed, less active) but a difference in the way that the healthy and the depressed spread their resting periods over the day. Depressed people experience longer resting periods more frequently and shorter ones less frequently than healthy people do.

That discovery may provide another way of diagnosing major depression—although if it were indeed to become a diagnostic tool, someone would first have to show that the pattern for those experiencing minor, non-clinical depression was not the same as that shown by the clinically depressed. Another diagnostic tool would be welcome, though, because current diagnoses often depend on self-reporting, which can be unreliable.

But Dr Yamamoto's result is not merely of practical significance. It also raises an interesting question about the nature of depression itself. That is because, when he looked for similar power-law curves in other areas, the one which he thought most resembled that exhibited by the depressed turned out to be the pattern of electrical activity shown by nerve cells isolated in a Petri dish and unable to contact their neighbours.

It is both unnerving and intriguing that a mental disorder which isolates people from human society, and which must surely have its origins in some malfunction of the nerve cells, is reflected in the behaviour of cells that have themselves been isolated. Maybe this is just a coincidence—another example of Mark Twain's hammer. But maybe it is not.