When I saw the photos of the Wilton Windmill crop circle (the photo here is by Steve Alexander), reported on 22nd May, I was immediately struck by the possibility of a message encoded in 8-bit binary.

After transcribing the binary digits, I translated each byte (8 bits) into its corresponding ASCII character with this handy online converter, starting from the direction of the windmill, and working clockwise around the circle and out from the centre. (If you’re having trouble following this, see the animation linked at the bottom of the article).

The result was this:

*e^(hi)pi)1=0*

It looked like some kind of equation, and when I looked it up, Google asked if I meant: e^(i)pi)1=0, for which the top result was Euler’s identity: *e ^{iπ}+1=0*. This has been called “the most beautiful theorem in mathematics”. No surprise that it should turn up in a crop circle then!

One of the things that had caught my attention on initially seeing the pictures of the crop formation had been the way that it referenced both the turning wheel of the windmill and the twelve-part division of the zodiacal cycle, the cosmic wheel. On looking a little deeper into the mathematics, it becomes clear that the formation also represents Euler’s formula, of which Euler’s Identity is a special case, in graphical form – as a circle, with radii represented at different angles. On reflection, this is a very cleverly executed and elegant design, in which mathematical and symbolic meanings are fused into a single ‘identity’.

Not being a mathematician, I wasn’t sure about the odd notation of the formula as expressed in the crop circle, but I assumed that, for the circle-maker, it could be a way to get around the limitations of ASCII text, and was a near enough approximation for me to get the intended result.

One thing that bothered me was the inclusion of the anomalous ‘h’ in the message/formula. Certainly, with the absent ‘+’, it made up the number of characters to the symbolic number twelve.

Perhaps significantly, the ‘h’, with the adjacent ‘i’, reads ‘hi’ – an embedded message from the circle-maker? It was only when a Facebook contact suggested that ‘h’ could be a reference to the Planck constant, taking us from the world of maths into the world of physics, that I realised a possible new layer of meaning within the embedded message. Could the makers have left a ‘Planck’ in the design as a subtle joke on all the croppies who might pronounce this a ‘genuine’ crop circle as opposed to a circle made with a plank?! I wonder if anyone has looked down that arc that represents the binary digit in question – could there be a physical plank there?

Less flippantly, I think that the more likely scenario is that the circle-makers made a genuine mistake. The binary encoding for ‘h’ – 01101000 is just one binary digit different to that for ‘(‘ – 00101000. The extra opening bracket would pair up with the otherwise unpaired closing bracket in the message to give us e^((i)pi)1=0.

This animated explanation of the 2010 Wilton Windmill crop circle design that I put together should make everything clear!

Also, here’s my original blog post.

Update: See my essay ‘Closing the Circle’ in the wonderful Daily Grail journal Darklore 5 for a more detailed treatment. The essay is also available as a free sample pdf.