Extraordinary claims. Ordinary investigations.

Circlemakers say “Hi” (here’s a plank to stomp with)


Of course, the Mail (and so many other vehicles) reports the story with a slightly different take:

Crop circle hiding ‘beautiful’ maths formula appears in rape seed field
An extraordinary crop circle based on the ‘world’s most beautiful maths theorem’ has appeared in a field next to a windmill in Wiltshire. The complex disc, which measures 300ft across, appeared to the east of Wilton Windmill near Marlborough in a blazing yellow rape seed field. It appeared on Saturday [May 23] just 25miles from another circle that popped up a fortnight ago by the Iron Age hill fort of Old Sarum.”

They quote Lucy Pringle, who says that “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.”

What they didn’t quote was who first suggested this decoding, and as Greg Taylor remarked on UfoUpdates, it was Daily Grail editor Richard Andrews (“Grailseeker”). This is important not only for crediting where credit is due, but because Andrews explains how he decoded the formation.

It was simply a matter of decoding the radial lines: starting from the center, notice how each have 8 bars going either up or down. This can be interpreted as an 8-bit binary code, not unlike the kind of barcode used for mail in the US and other countries. And 8-bits can be always interpreted as encoding ASCII characters, especially when we have previous formations using ASCII. And that’s how you get the message “e^(hi)pi)1=0”.

Click the image below for a nice animation by Andrews explaining the decoding:


Now, as Andrews explains, “e^(hi)pi)1=0” is not exactly Euler’s identity, which can be written as “e^((i)pi)+1=0”. He suggests this was intentional: Planck found in ‘Euler’s Identity’ Crop Circle?!

“One thing bothered me though, and that was the inclusion of the anomalous ‘h’ in the message/formula. Certainly, with the absent ‘+’, it made up the number of characters to twelve, which would make the crop circle easier to produce on the ground and more windmill-like, as well as referencing a highly symbolic number.

More significantly though, with the adjacent ‘i’, it reads ‘hi‘ – an embedded message from the maker perhaps? It was only when Jim Gilliland suggested in this Facebook thread 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 what could be the full meaning of 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?!”

It would be an elegant Trojan Horse joke by the circlemakers. It would not be the first time, the 1991 Milk Hill script can also be decoded with a very humorous message (which you can read on ‘The Field Guide’). And perhaps even more elegant because it can also be interpreted as an error: there’s only one flipped bit between the ascii code for ‘h’=01101000 and the correct ‘(’=00101000. Flipping the bit happens in the best families.

Now, could this be a deliberate error? Notice how even if they didn’t flip the bit, the formula equation would still be incorrect because it’s missing a ‘+’, as Andrews noticed. A mathematician would be quick to point out how this missing plus sign is perhaps one the most important parts of the equation, because that means that transcendental numbers and the imaginary unit can equal a number as comprehensible as a negative integer –1.

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.

A clear message that the only mystery here is that created by humans, for humans.

With a Plan(c)k, perhaps.

– – –

*As Max Reinhold Jahnke points out, “this expression is known as Euler’s identity, Euler’s theorem is another thing (there are several of them, the most famous refers to algebra/number theory). It’s also not correct to call it a formula, since it only has constantes. =)”.

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Posted in Fortean | 4 comments

4 Comments so far

  1. […] (EXTRA) A deeper analysis of the cleverly encoded crop circle from last week. But the presumption it was *human* intelligence is still suspicious..: forgetomori – Circlemakers say “Hi” (here’s a plank to stomp with) […]

  2. Jeremy June 17th, 2010 5:38 pm

    Where are all the pictures of the poorly crafted crop circles? The first attempts.

  3. Amanda December 22nd, 2010 2:50 pm

    No mystery. I know someone who used to make them. Everything is planned in advance, hence very few mistakes but mistakes do happen which then have attached to them some mystical significance.
    The 2001 Milk Hill formation was one that this person helped make.


    I’m not mentioning any names as those who believe in crop formations being alien or mystical can get very violent if their beliefs are threatened. In one instance they started to stone a group of people making a crop formation and have been known to stalk circle makers.

    People are making a fortune from this non-mystery. There are those who will do any-thing to keep the mystery going, otherwise they will lose money. If you believe their rubbish you are being conned and are wasting your money.

  4. Mat March 26th, 2011 12:39 am

    “No mystery (!?!)”

    It’s amazing how many people on the internet will hear a debunking and then instantly stop researching, as if they managed to hit to truth perfectly on the head at first go. This is of course a logical fallacy and pandering to ones own ego.

    With the greatest of respect Amanda, you are one of these people who has heard about the circles, knows there are the deliberate hoaxers (which are incidently, are never as flawless as the ‘real’ circles)and decided that because this is what the mainstream has decided, its can’t be real so there’s no more point researching.

    The fact is that crop circles or “devil’s circles” go way way way way back in history. Added to the fact that every time any of these ‘circle makers’ have tried to make a circle in front of a scientific panel, they have routinely failed every single time to mimic the level of detail, the criss cross effect of the crops or the faultless designs made by whatever is making the true crop circle designs. The only people who can do it to this standard are advertising companies who take weeks to plan, scout out and sculpt their advertisments.

    How for example, do you explain the famous Arecibo message http://www.enterprisemission.com/glyph2.htm, constructed in one night right next to Chilbolton military base, which is patroled 24 hours a day, yet nobody saw it being made. it also presents a direct answer to the famous Arecibo message sent out into space by Carl Segan. Many fraudulent cases are easy to debunk, try looking at the difficult ones.

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