You have to hand it to those extra-terrestrials: they aren't just smart, they're artistic and witty. Every summer since the 1970s, they have parked their UFOs in fields around the world, and set about creating beautiful patterns somewhat prosaically named "crop circles". And this summer they've outdone themselves, having just created a 90-metre wide design in a field in Wiltshire, England, which contains a secret message and a mathematical joke.
At first glance, the circle looks like a half-finished maze. But its broken arcs apparently contain a code which, when deciphered, reveals a formula from higher mathematics. Known as Euler's Identity, it links together five of the most important numbers in maths: zero, one, pi, "e" and the square-root of negative one, usually denoted by the letter "i". But in what we must presume is an example of alien humour, they've tweaked the last letter, turning it from "i" into a cheery "Hi".
Some spoilsports may well presume something else, namely that the whole thing is simply a hoax. That's doubtless the view of most scientists, who have long dismissed crop circles as symbolic only of the wide-eyed credulity of the public. After years of tiresome questions about the circles, mainstream scientists were delighted by the confession in 1991 of two British pranksters that they had been making crop circles since the late 1970s.
In the process, however, they also put an end to any concerted effort to understand what may be a genuine meteorological phenomenon. For while the vast majority of crop circles are certainly no more "inexplicable" than an outdoor sculpture, a handful hint at something rather more enigmatic. They are certainly not an invention of the New Age, as they have been noted by apparently reputable witnesses for well over a century. In July 1880, John Rand Capron, a solicitor and amateur scientist from Guildford, England, wrote to the leading science journal Nature about finding what appeared to be crop circles while walking across the Surrey countryside to visit a nearby farm.
Capron described how a field of wheat appeared to have been hit by some force which had left a series of "circular spots", each with a few stalks of wheat standing up at its centre, with the rest flattened down as if hit by a hammer-blow from the sky. He suspected a recent thunderstorm may have played some role in forming the circles, adding that: "They were suggestive to me of some cyclonic wind action."
Since then, similar crop circles have been reported in fields across the world, from the United States to Japan, Russia to China. Yet very few scientists have taken the phenomenon seriously, for fear of being seen as credulous. One of those with the courage to do so is the physicist Dr Terence Meaden, deputy director of the Tornado and Storm Research Organisation at Oxford Brookes University in the UK.
During the late 1980s, Dr Meaden suggested that crop circles may be created by spinning vortices of air formed when a weather front passed over a range of hills. Such vortices draw air up into their cores, becoming doughnut-shaped and increasingly unstable. They then collapse in an explosive event that releases a downward blast of air - levelling crops that happened to be underneath into a circular pattern.
As well as accounting for the shape of crop circles, Dr Meaden's theory even offers an explanation for reports of flashes of light seen during the formation of crop circles. These, he suggested, may be electrical discharges produced by dust becoming frictionally charged as they whirled around inside the vortex - a well-known effect in dust storms. Dr Meaden's "vortex plasma" theory appeared to gain support in June 1990, when scientists at Waseda University, Tokyo, claimed to have recreated such vortices in the laboratory, forming circular patterns in plates of fine aluminium powder.
Yet just a month later, the whole crop circle debate veered into the realms of the ridiculous. A pattern appeared in a field in Wiltshire, England which looked like some kind of alien "message". It was seized upon by ageing hippies, New Age believers - and the designers of the Led Zeppelin boxed set album released later that year. And it marked the end of any hope of a major scientific effort to understand the original phenomenon.
Only a handful of researchers have since risked their reputations by continuing to take it seriously. In 1994, research published in the journal Physiologia Plantarum by Dr William Levengood, a Michigan-based biophysicist, pointed to evidence for swelling, malformations and charring of the crops forming the circles. Meanwhile, a team of physicists led by Dr Yuri Varaksin of the Moscow-based Joint Institute of High Temperatures of the Russian Academy of Sciences recently published results from experiments suggesting that vortices formed in unstable air can create the circles and swirls seen in crops.
Intriguingly, a connection between vortices of air and heat has been invoked before, to explain another controversial phenomenon: ball lightning. Long dismissed by scientists as a delusion, the existence of these glowing spheres of light is now widely accepted, and is the subject of mainstream research. They are thought to be the result of thunderbolts blasting into the ground, creating a ball of incandescent dust.
Could there be a link between ball lightning and crop circles? Perhaps. This might explain why crop circles have a habit of turning up at this time of the year in the northern hemisphere, when the atmosphere is laced with thermal instabilities. It would certainly not surprise Capron, who suspected the crop circles he saw almost exactly 130 years ago may have been linked to thunderstorm. On the other hand, Capron would probably have been both surprised and saddened by the reluctance of today's scientific community even to countenance such things. But then, unlike the amateur Capron, the professional scientist of the 21st century is more concerned with maintaining reputation and research funding than in gaining insights into the weirder manifestations of nature.
Robert Matthews is Visiting Reader in Science at Aston University, Birmingham, England