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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).

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.

      1. potato
        In the interest of keeping the mind open to interesting possibilities, it’s fun to think that this and other circles (ones not outright proven to be made with boards and ropes) are the work of Everett-model quantum neighbors. Given that the Boltzmann equation was recently solved, given that Andre Kubetzka & team have just discovered how to manipulate the path of electrons & measure it, and given that progress on the quantum “world” is being made more and faster with each given day, this could be interpreted as a greeting & invitation to say hello from humans very much like us just a fraction of a percent out of phase with us at the atomic scale. This would naturally account for the fact that the authors know ascii, of course they would they’re nearly identical to us & if they know how to manipulate vegetation in neighboring states of atomic phase they would also find it natural to assume we know ascii and would figure it out.

        Or it could just be a-holes with boards, ropes, and way too much time on their hands. Whichever 😉

        1. Told ya so!
          And he even got it wrong, they told the info was coded in binary, no mention of ASCII or the formula— or the Planck.

          …Aaand, Lucy Pringle is still riding on your tail coat.

  1. “Hi” Said the Crop Circle?
    It’s amazing that an intelligence, be it human or not, could figure out a way to integrate ‘Euler’s Identity’ into an 8-bit windmill-shaped crop circle?

    But I find it more amazing that they would add one letter to supposedly make the message a silly greeting, or to suggest that the circle might have been made with “planks.”

    Is it possible, instead, that the creators of the message, assuming they wanted to teach us something important, added a very significant factor to the equation that changes everything:

    H, for he Human equation?

    Just a thought, but perhaps the real message is intended to teach us that we Humans have more effect on space-time, on reality, and our own future, that even we currently understand.

    1. Maybe they’re not so
      Maybe they’re not so intelligent and just made a mistake. The binary encoding for ‘(‘ – 00101000 – is just one binary digit different to that for ‘h’ – 01101000.

      That would give us e^((i)pi)1=0

      I’ve updated the article to reflect this point.

      1. difficulties
        We must also consider the difficulties these artists were most likely facing. Possible the work was constructed in darkness. Most likely in bad weather (it is in the UK, right?). The aliens might not be used to the local beer either. And then only one mistake in going clockwise / counter clockwise. Perhaps they use digital watches too, making the distinction even trickier.

        1. It was HOT this last weekend.
          It was HOT this last weekend. The biggest difficulty facing any human circlemakers in that field would have been pushing over all those 5ft high oilseed rape plants (without snapping them, if they were any good).

  2. Daily Mail gives you credit (NOT!)
    Oh, Lucy…

    Working from the centre outwards, people are suggesting it has a connection to Leonhard Euler’s theorem e^(i)pi+1=0 which is thought to be one of the most beautiful theorems in mathematics.’

    To any Daily Mail reporters reading TDG: you need to give, in order to receive.

  3. Image cropping
    [quote=Perceval]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?![/quote]

    Love it! 🙂

    Lucy Pringle’s not big on the whole credit thing is she. At least they squeezed an (unlinked) ‘Grailseeker’ into this page of nonsense:

      1. Missing link
        [quote=Perceval]There’s a link to my animation, that’s credit enough.[/quote]

        When I checked, the only link I could find was the one you mentioned yourself in your comment added way down the page. Did I miss another one? I see that they’ve since added credit at the top of the page to you though, so all good.

        1. crop circle business
          Yeah, at they updated the page. The original info down the page appeared shortly after I emailed them.

          It’s a comments page, but I was not tempted to pay the £21 joining fee to post my own comment, hence my email, so I guess they just added my bit at the bottom of the current comments, then re-edited as time allowed.

          I can’t help wondering how much money has changed hands with all those national newspaper articles I wasn’t credited in. In retrospect, I should have called the papers in the first instance, rather than Lucy Pringle, who makes a business out of promoting crop circles – you live and learn!

          Perhaps there’s a moral argument against making money from a farmer’s flattened crops, but I could have used some cash to pay for the time I spent on the whole affair!

          1. business
            Perhaps I should mow the grasses and weeds differently next week and you can call the press.

            If the law enforcement people were serious, they would have found the plank by now.

    1. Would you credit it?
      The whole ‘credit’ thing is interesting. While it’s only right that people should credit their sources, it’s worth remembering that the makers themselves seek no credit for their work.

      Perhaps that’s more for legal reasons than anything else!

  4. Forgetomori
    Good article about the crop decoding at Forgetomori:

    The correct equation “e^((i)pi)+1=0” takes 13 characters. Could it be encoded in 12? Yes, you could also write the equation as “e^(i*pi)+1=0”, for instance. Why would the circlemakers choose a deliberately wrong rendition of the “most beautiful theorem in mathematics”*? Another error?

    Perhaps, but this could also be interpreted as part of the joke, a blatantly clear message that this is no perfect message. If for nothing else, it should be clear that intergalactic aliens would hardly use the ASCII code established in 1968, with a mathematical notation of parenthesis, Euler’s number, the imaginary unit and even how one would write the Greek letter ‘pi’ in roman characters, just the way one would enter such equation in Google.

  5. Another error
    If the final “)” was a “+”, the equation would read e^(hi)pi+1=0 which makes more sense.

    There’s just a single bit difference between ) and + :

      ) = 0101001
      + = 0101011
    bit error -^

    I think someone put their plank down the wrong way…

    1. Yes, there are quite a number
      Yes, there are quite a number of possibilities here.

      As Kentaro Mori points out, there are better ways to encode Euler’s Identity in 12 ASCII characters. Either the circle-makers didn’t think this through, went for a less elegant encoding and then botched it in a rather ironic way (most likely in my view), or they deliberately encoded another layer of hidden meaning.

      This latter possibility, however, opens the whole thing up to endless speculation, especially on the part of the ‘believers’ who seek to find alternatives to the ‘error hypothesis’. One suggestion I have yet to see is that, if there’s such a thing as human error, there must also be ‘alien error’!

      It’s a shame that sloppy work on the part of the circle-makers should spoil an otherwise neat idea.

      I don’t mean to mock those who are attempting in good faith to investigate crop formations on the ground, as the physical evidence is an important aspect of the phenomenon. Part 2 of Linda Moulton Howe’s report on this formation is a good summary of this (Part 1 is her interview with me).

      On the assertion in part 2 of the Earthfiles report that you can’t push against the plant stems without cracking them (65% were bent apparently) I would question whether that statement was made based on pushing against individual stems or multiple stems (i.e. with a plank). A plank would spread the load, so each stem would take less weight, much like the way a snowshoe stops you sinking in the snow.

      While I’m linking, here’s a mention on Boing Boing (with predictable comments thread!).

    1. Unoriginal
      The whole movement of crop circles is a bit unoriginal to begin with; in fact it’s sort of a tradition by now!

      It’s still a beautiful formation, though. Imagine if we could teach children Math and Physics like this 🙂

  6. Sorry to necropost but you’re the only other person I’ve found that came up with this same conclusion! Just wanted to say hi! 😀

    I love a good puzzle! I started looking at these after a recent Why Files episode and I’ve found myself far enough into the web to land here along side you after searching for the “incorrect” ASCII decode.

    Aliens, humans… it could be hyper intelligent slime mold that made these for all I care… I just enjoy finding and decoding patterns in this. Such a fun game.

    The rotary encoded Pi circle was a beautifully executed piece of art and I’m glad there’s more stuff to play with. The Windmill was a rather quick and easy dig.

    Off now to find more difficult riddles to solve. Ta!

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