Not quite as good as visiting these awesome places, but we can at least keep you up to date on what's happening.

Planck found in 'Euler's Identity' Crop Circle?!

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).

Wilton Windmill Crop Circle May 2010

The result was this:


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+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!

Wilton Windmill Crop Circle May 2010

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.

Vallee on Crop Circles Part Trois

Jacques Vallee has posted the third instalment of his four-part series on crop circles over at Boing Boing. This time around, Jacques discusses the hoaxer theory, the weakness of 'New Age' explanations, and once again returns to the question of advanced technology being used:

I once met several of these artists at a conference in Switzerland, where they were presenting their techniques and the resulting data. When I asked them, "How dare you fool people this way?" they answered that art in general was about fooling people to create a sense of awe, beauty or simply a brief, healthy disconnect with ordinary reality. Crop CircleOne of them pointed out that "When you look at the Mona Lisa you think you look at a woman, but you have been fooled: there is no woman there; someone just applied some paint to a rectangular piece of canvas. Well, we do the same thing, except that our canvas happens to be a cornfield."

When you put it that way it is perfectly all right for teams of artists to run through the fields at night and produce things like the spider, the bicycle or more elaborate geometric designs. People like Jim Schnabel have participated in the game and there are even international competitions in circle making, with recognition for the most complex productions. No wonder people are convinced that all the circles are made for fun by a team of humans crushing the corn for kicks when the subject comes up in discussions among scientists or businessmen today. The difficult question is, "does this explain ALL the circles, or only the relatively simple ones?" The artists I spoke to in Switzerland confessed that some of the extraordinary designs were beyond their ability to produce them. While the initial "weather phenomenon" theory of Terence Meaden and others has not survived, there are still people who firmly believe the complex designs are made by Aliens and some who state they are a warning from Gaia. Among the technical community there are also those who pursue the idea first expressed by Dr. Jean-Pierre Petit, Jean-Jacques Velasco and others, looking to military electronics as the key to the mystery.

As I've mentioned previously, I don't feel there's much evidence supporting the 'aerial weapon' theory, and it certainly doesn't shake hands politely with the rule of parsimony. I *do* however support Jacques in raising these questions and exploring them. For all the attacks in the comments, few people seem to have noted the final paragraph, in which Jacques makes clear that he does not think the weapon hypothesis is the most logical. He just wants to explore possibilities:

From the point of view of rational analysis the weight of evidence is still on the side of the skeptics who assure us that all crop circles are made by artists and lovable, jolly old men like Doug and Dave. But there are facts that don't quite fit, and the alternatives are worth considering.

And, viewing some of his words in these blog posts - and the comments left by readers - I also do get the feeling that these 'crop circle' posts are as much about Jacques exploring people's beliefs and rationalisations as they are about glyphs in fields. Certainly, he knows and is interested in the replies being posted - more than the commenters seem to appreciate...I had a bit of a giggle when I read this line: "Since we have obviously hit a nerve it may be interesting to drill a bit further."

I'm looking forward to the final instalment of the series, which Jacques says will explore the "construction and manipulation of belief systems" - ground which he covered in depth in his classic book Messengers of Deception: UFO Contacts and Cults (Amazon US and Amazon UK), re-released in 2008 by Daily Grail Publishing.

Previously on TDG:

Timescapes: Death is the Road to Awe

A wonderful short time-lapse video to make you feel that sense of wonder and awe at time beyond time, and space beyond space. Tom Lowe's Timescape: Death is the Road to Awe:

The name of the piece takes its name from the evocative music heard in the clip, from Clint Mansell's excellent soundtrack to the movie The Fountain. (Add to that his recent work on Moon, and the stunning Requiem for a Dream soundtrack - check out 'Lux Aeterna' for instance - and Mansell is one of the most interesting musical artists in the world today in my opinion.)

Going Around in (Crop) Circles

Over the past fortnight, legendary paranormal researcher Jacques Vallee has posted two guest-blogs on (the insanely popular website) Boing Boing, on the topic of crop circles. In the first, "In Search of Alien Glyphs", he details his own alternative theory for their construction (first set out in "Crop Circles: 'Signs from Above' or Human Artifacts?":

In Sept. 1991, I published in a New Age magazine my own hypothesis about the Crop Circles phenomenon. Crop CircleI speculated they involved a military aerial device (not a space-based instrument) for generating such designs using focused microwave beams, such as a "maser." At the time nobody wanted to hear that the beautiful pictures in English corn fields might be crafted by a technical team inside some lab, bouncing signals from a hovering platform and using individual corn stalks as simple pixels to calibrate a lethal device. So my paper was met with dead silence.

Vallee then related his own theory to recent news regarding military use of microwaves. The comments from the Boing Boing crowd were as would be expected - a few supportive of the theory, or at least of Vallee's outside-the-box thinking - but mostly along the lines of...

Just for giggles, why not try some *gasp* actual science?

Look at the stalks. Have they been blasted with microwaves, or just bent by a guy with a two-by-four on a rope?

This fails even as a troll. Stupid conspiracy theories shouldn't have easily testable disproof.

Nevertheless, Vallee followed up his post with a second last week, titled "Alien Glyphs, Human Myths, Blogging Bliss". He began by addressing the many comments to his previous post, by saying his blog entry "could be considered, among other things, as a social science test of the role of belief systems in the manipulation of memes and factual data," going on to "explain why the hypothesis is not a joke but a logical result from observation and from the process of asking the right questions."

On the first point, I fully agree with Jacques. For every crazy gullible believer out there, there's also some armchair expert who thinks any 'skeptically-oriented' explanation that they hear solves the case - without reading any further. In the crop circle case, it's largely the 'Doug and Dave' headline, though if the 'skeptic' has read a bit more deeply, it would be the claims of groups like the Circlemakers and some of their public demonstrations. Belief systems are of all kinds, and aren't just restricted to crazy woos.

On the second point, I can only claim partial agreement. As all readers would know, I am *heavily* in favour of people putting forward alternative, out-of-the-box explanations of mysterious phenomena (as long as they are recognized as such). And Jacques has been clear on multiple occasions that it is just that. So I say good on him for doing so.

However, for me, parsimony suggests that crop circles are, quite simply, made by human artists with relatively simple equipment.

Megalithomania 2010

The 2010 Megalithomania conference (8-9 May at Glastonbury) is looking pretty awesome. Speakers include our good friends Paul Devereux ('Archaeoacoustics and Sacred Geography'), Robert Bauval ('Black Genesis: The Origins of Egypt') and Walter Cruttenden ('The Lost Star of Myth and Time'), as well as Aubrey Burl ('Megalithic Observations') and Andrew Collins ('Beneath the Pyramids: A Lost World'). For those that aren't within reach of Glastonbury, remember to check out the DVDs available of the 2008 and 2009 events (and hopefully, 2010), which include the likes of Graham Hancock and Robert Temple discussing their pet topics.

Google Stonehenge-View

Earlier this year Google asked users to vote in a poll on the tourist attraction they most wanted to see in the 'Street View' mode of Google Maps. Stonehenge topped the poll, and so now you can tour Stonehenge from the comfort of your own home (and while on TDG no less!). Mouse-over the image and follow the arrows to walk around (and through) the famous monument:

View Larger Map

Well worth going the full-screen option to take it in properly, as it's wonderfully up close and personal. (And no, they didn't drive one of those Street View camera cars around the megaliths - it was apparently done with a custom trike suited to off-road mapping). Thanks to the Standing with Stones folk for the heads-up.

Megalithic Mystery

Here's a fascinating video from the wonderful Standing with Stones documentary, a two hour journey exploring the Neolithic and Bronze Age sites of the British Isles. In this particular video, presenter Rupert Soskin is baffled by what appears to be a carved piece of petrified wood in a burial chamber on Anglesy:

When I traveled to the UK ten years ago one of my favourite experiences was visiting megalithic sites - from Stonehenge through to small barely-known arrangements in farmer's fields. The atmosphere of these places is heavy with a sense of vast time. Here's a wonderful time-lapse video that gives you the feel of these sacred sites; the realisation that the Earth has spun countless times, and all sorts of biological creatures have come and gone, while these stones just sat there as mute witnesses: "Lapse of Memory" by Tony Partington assembles more than 70,000 panoramic high-dynamic range images into a one-of-a-kind viewing experience:

If megaliths interest you, I definitely recommend picking up a copy of the Standing with Stones documentary - an authoritative visual guide that is worth every cent (or penny). The linked website has a number of other sample videos for watching, and there's also a companion book to the DVD which is available from Amazon US and UK.

Atlas Obscura

Here's a great resource for the Fortean travelers out there: Atlas Obscura:

Welcome to the Atlas Obscura, a compendium of this age's wonders, curiosities, and esoterica. The Atlas Obscura is a collaborative project with the goal of cataloging all of the singular, eccentric, bizarre, fantastical, and strange out-of-the-way places that get left out of traditional travel guidebooks and are ignored by the average tourist. If you're looking for miniature cities, glass flowers, books bound in human skin, gigantic flaming holes in the ground, phallological museums, bone churches, balancing pagodas, or homes built entirely out of paper, the Atlas Obscura is where you'll find them.

TDG readers will probably enjoy sections such as "Incredible Ruins" (Baalbek, Gobekli Tepe etc), "Relics and Reliquaries" and "Instruments of Science" (HAARP, Tesla Coils etc) - topics can be browsed on the right hand side of the page. Found via the always fascinating Boing Boing.

Original 'Croppie' Passes Away

The UK's 'sacred landscape' community has suffered another loss, on the back of the death last month of John Michell: Pat Delgado, one of the most influential writer/researchers on the topic of crop circles, passed away on the weekend aged 90. Delgado co-authored the bestselling book Circular Evidence with Colin Andrews, and in doing so introduced many people to the mystery of the 'agriglyphs'. He largely retired from the scene after the 'Doug and Dave' revelations in 1991, in which he was the central 'victim' to pronounce that their faked circle was "genuine". He later said (in 1996) that he had come to the conclusion that the complex patterns should be considered "artistic" man-made designs, rather than hoaxes, but that the truly "genuine" circles "are simple single circles and their history probably goes back thousands of years."

Crop Circles and Black Helicopters

More interesting revelations from this week's release by the UK Ministry of Defence of secret documents pertaining to the UFO subject...though in this case, it is crop circles. One of the mysterious themes propagated (pun not intended) in the crop circle mythos is that of 'black helicopters' being present at the scene of newly-formed glyphs. According to the latest MoD documents released, that was simply the military sight-seeing:

The MoD tried to stop military helicopter crews photographing crop circles for fear that this contradicted the official line that they had no interest in the phenomenon.

In 1991, the Centre For Crop Circle Studies wrote to the MoD, saying aircraft had hovered over fields where the patterns had appeared and on at least one occasion taken pictures. This concerned the MoD so much that they wrote to Army and Navy chiefs, asking them to ensure this did not happen again.

But both services refused, saying they would "not be taken seriously" by air crews if they issued such an edict and suggesting the department was being "over-sensitive towards the UFO lobby".

The documents also reveal a dialogue between the MoD and British Prime Minister Margaret Thatcher regarding the circles, as well as one strange case in which a circle was said to be formed by four 'bright' whirlwinds (interesting note about the "swishing" sound, given my own research...although in this case that's probably a likely sound with a windstorm in fields of crops).

As mentioned previously, you can download the relevant documents from the website of The National Archives.