Chatting further, the academic told me that he had discovered the hidden meaning of the numerical message in the crop circle and that he thought the next one would appear at a certain spot, and have something to do with the mathematical term pi.
"Pie in the sky," was what I thought, but I smiled encouragingly and said nothing.
I confess that I had felt like an infidel approaching Mecca as I neared the small town of Calne for four days of crop circle chasing with the wonderfully named Megalithic Tours. Although I was doing my best to keep an open mind, I was not a believer. I believed that crop circles existed, of course – I'm not that sceptical: I had just assumed they were created by jaunty outdoor types with ropes, planks and a penchant for complicated geometric patterns.
I felt even more of a heretic as we drove up an obscure country lane to the Silent Circle cafe (silentcircle.co.uk/MAP.1.html), our first port of call. Here was everything the dedicated croppie could wish for: crop circle books, crop circle DVDs (sample strap-line: "Warning: this documentary contains material that will change your view of this world for ever…"), crop circle stickers and, inevitably, crop circle clothing. My joke that instead of T-shirts they should be selling crop tops fell, alas, on stony ground.
Crucially for our little group, the cafe is the place where devotees go to find out whether any new crop circles have appeared overnight. Neil, our laid-back tour guide, duly spoke with the owner and broke the sad news to us that no fresh formations had been reported.
Happily, this still left us with plenty that had been recently created in the vicinity. (Why it should be Wiltshire that plays host to the vast majority of planet Earth's crop circles is just another of the myriad mysteries in which the whole business is enveloped.)
In the minibus, Neil handed out a pack of papers bearing aerial photos of the latest circles and breezily announced: "One arrived at Alton Barnes a couple of days ago – let's go and see that, shall we?"
Image below: Dixe Wills's group explores a crop circle in Wiltshire
"There it is," a member of the group cried out, and away we trooped, carefully picking our way along paths cut by tractor wheels.
This was my first ever crop circle visit, and I confess, my heart quickened. Neil asked if anyone "felt" anything as we wandered about the stricken wheat but, crushingly, no one did. Pulling myself together, I examined the bent stalks for what I'd been told were the telltale signs of the use of planks but, frustratingly, the evidence was inconclusive.
Neil has written several guidebooks that touch on unexplained phenomena, so I was keen to hear his take on the circles. "I don't know how they're made," he replied, with a commendable lack of guile, "I just think they're wonderful works of art."
This seemed to be the consensus among the group, although several people also said they had photographed "orbs" hovering over the circles.
"And there's another inexplicable thing," added Neil. "Quite a few times I've found little balls of molten iron under the crushed stems. That's odd, isn't it?"
So was set the pattern of our days: a visit to the Silent Circle cafe followed by a trip through Wiltshire hills and the glorious Vale of Pewsey (pewsey-uk.co.uk) to track down the circles – with non-crop-related jaunts to Marlborough, Avebury and an Iron Age fort for good measure. We bagged seven circles in all: each one a little masterpiece. My favourites were one that looked like four deer heads, another that showed five mad scorpions chasing each other, and a third that resembled, er, a giant sperm.
And the circles had one last trick up their sleeve: on the day we left, one appeared at the place foretold by our American friend. It comprised two huge pi signs. Those aliens – they're messing with my head, you know.
• The Weekend Crop Circle Quest with Megalithic Tours (01772 728181, megalithictours.com) costs £350 (including three nights' B&B at Calne's Lansdowne Hotel); the next trip is on 6 July 2012, but Megalithic can arrange tailor-made tours for groups. More information from visitwiltshire.co.uk