The Square Recircled

Posted by on July 26, 2015

To my delight I found that the 2015 season had kicked off on 9th April, with a crop circle in the magic field at Barbury Castle. Images can be found on the Crop Circle Connector but, for personal reasons I am unable to include one here. I believe my survey (1) is accurate.

Barbury

1. Barbury Castle, 9th April 2015, diagram.

 

The first formation of each season is greeted with great excitement and this one was remarkable in several respects. First, it arrived in green Oilseed Rape. I could be mistaken, but I do not recall a circle appearing before the crop had ripened to produce its golden flowers. Second, it landed in virtually the precise location of the 2008 Pi formation, falling, as did its predecessor, across the field’s bridle path, shown here in green. This is an exceptional occurrence. Crop circles generally position themselves in areas of clear crop; their interaction with (or overlaying of) pre-existing landscape features is rare.

A personal note. The majestic Milk Hill formation of 2001 (2) was the last circle I was able to walk through. It was seven years later, in this field at Barbury Castle 2008 (3), that Gary King, having noticed that the bridle pathran straight through the formation, was able to take me into it in my wheelchair.

Milk Hill

2. Milk Hill, 12th August 2001.

 

9 Barbury Castle

3. Barbury Castle, 1st June 2008.

 

Before looking at Barbury Castle 2015 in more detail, I believe we should revisit its crucial predecessor. Barbury Castle 2008 was an astonishment. It was formed with precision and elegance and it remains one

of the most articulate and significant crop circles I have ever seen. By its inventive use of radial and concentric geometries it indicated, unquestionably, 3.141592654…, the Pi number. The crop circle included even a small circle to represent the decimal point and three rings to represent “…”, the ellipsis at the end of the ten element sequence.

For those unfamiliar with the marvellous Barbury Pi system, I will go through it again here. Diagram (4) shows how the formation may be considered as being radially sliced from the centre like a pizza, into ten sectors, each of 36°.

Barbury 08

4. Barbury Castle, 1st June 2008, diagram

 

The formation is also divided into ten concentric rings. None of these rings, numbered 1 to 10 on the diagram, forms a complete circle. Instead each is an arc or part of that circle. Starting at the central circle, the path moves out to join the end of arc 1. It moves through three sectors (we note 3), bypasses the tiny circle (we note the decimal point) and moves outward again to join the end of arc 2. Arc 2 takes us through one sector (we note 1) and moves out to join the end of arc 3 which in turn takes us through four sectors and we note 4. We have now, using this ingenious and beautiful system, registered 3.14 and if we continue we will discover 3.1415392654…

What intelligence, which civilisation, has the creativity to encode Pi with such style and wit? And why do they return to this idea with such patience and single-mindedness? Why is it so important? To them? To us?

A FURTHER REVELATION

Bert Janssen, also bemused by the incongruity of a crop circle that positioned itself directly over a landscape feature, made a brilliant connection. He understood that the bridle path indicated one side of the square (shown in blue in diagram 4) that Squared the Circle. This insight showed, yet again, the crop circle phenomenon’s need to pair the two elements. Pi and Squaring the Circle (I will use the abbreviation StC from now on) have been interwoven through the crop circle narrative over many seasons. We often find one that refers however subtly, to the other. Could Pi, π, as the mathematical constant used in calculations involving anything circular, be seen also as a metaphorical key to the door between the Square and the Circle?

For millennia, in many cultures the square has represented the physical realm, the World, while the circle has been emblematic of the spiritual and Heaven. Thus StC is freighted with profound meaning. It symbolises the bridge between the material and the divine and between Earth and Heaven.

An exercise in sacred Geometry is the drawing of a square with exactly the same perimeter length (the four sides) as the circumference of the circle. Measurement is not allowed! In drawing this diagram which expresses their equality, StC is emblematic of a marriage or reconciliation between Heaven and Earth, between the sublime and the material realms.

The Crop Circles have referred to StC for many years and indeed it is unusual now to have a season without an StC example. Equally we have seen references to Pi. Pi, as referred to in the 2008 formation is an irrational or endless number calculated, currently to well over three million digits. A simpler method of deriving Pi is twenty-two divided by seven. This gives a result of 3.142857… not precisely the “real” Pi but close enough for the majority of applications. The crop circles have given us circles containing 22 and 7 and, during 2000 there were several formations embodying 29, the sum of these two numbers. The Pi symbol itself (π) has appeared only once, in 1999 at Avebury Manor.

The almost obsessive repetition of these ideas suggest that the Circles are signalling our inevitable shift towards the Spiritual and, boy, do we need it now.

(Whatever the case, StC seems inappropriate. Who could wish to make the circle more square or Heaven more Earthly? Surely Circling the Square or CtS is more optimistic.)

BARBURY CASTLE 2015

Though there had been a seven-year gap, the fact that Barbury 2015 was (like its seminal 2008 predecessor) placed directly over a bridle path was an unmissable invitation for me to visit. By the time I got in, the field had fully blossomed and the height of the plants had increased substantially. The formation, initially so cleanly impressed, was now largely grown-out. The tramlines, which in 2008 ran East-West have now been switched to North-South. Rape/Canola is a robust crop and its formations are notoriously difficult to measure. However I believe my drawing (1) is reasonably accurate.

The dominant feature of the formation was a fine ring with a small circle of about 15 feet diameter on it. I was not able to measure the diameter of the ring but my estimate was about 90 feet. Barbury Pi 2008 was about double that. The path forming the ring was about 3 feet wide and the bridle path is about 8 feet wide. The separate little configuration of pathways and the larger satellite circle (about 26 feet diameter) to the north west of the formation remain enigmatic.

There are, for me, too many similarities between Barbury Pi 2008 and this year’s formation for it to be dismissed as coincidence. I believe Barbury 2015 was a reminder for those who choose to notice. There was no reference whatsoever to Pi, but a powerful souvenir of the way 2008 squared the circle.

THE SEGMENT

Diagram (5) produced kindly for me by Allan Brown accurately illustrates the squared circle or, as I prefer, the circled square. In comparing Barbury ’08 and Barbury ’15 I noticed the segments, four in 2008 and just one in 2014. Figure (5) shows four segments in pink. A segment is created when a line (a chord) separates part of a circle. It occurred to me that, whenever the square was correctly circled, the proportions of this segment, this orange slice, must by definition be exactly the same. Once again, I turned to Allan Brown who informed me (6) that, if the width of the segment (red arrows) is 1, then the depth of the segment (blue arrows) must be 0.1773. This, I believe, is a newly observed proportional constant.

Squared Circle

5. Squared circle, diagram.

Segment

6. Squared circle, diagram showing segment.

 

The proportions of the segments of the two formations appeared remarkably similar but, without solid site measurements, a confirmation was impossible. And of course the realisation that the segment base line, the chord, the bridle path, is eight feet wide (7) throws any hope of geometrical accuracy out of the window.

Barbury 15

7. Barbury Castle, 2015, diagram showing segment.

 

An eight foot thick line, an eight foot wide chord, suggests that we are about to enter another realm! Obviously Allan Brown’s exact proportion will be included here but so will a thousand others. The ancient philosopher’s conundrum The Thickness of the Geometer’s Line is useful here.

 

A SPECULATION

Allowing for my overwhelmingly optimistic bias here (which I imagine many would call delusion) I feel that the Barbury Castle formation, the first of the season, was a reference to its distinguished precursor of 2008. Neither the placement of the circle over the bridle path nor the similarity of their respective segments can be glibly dismissed as meaningless coincidence.

We tend, in our endless search for the sensational, to let our eyes slide too quickly over what we initially feel to be unremarkable. The crop circle narrative is both allusive and elusive, and, like all great teachers, it expects our committed attention. Barbury 2015 could be seen simply as a large ring with both a small orbital circle and an attached system of enigmatic pathways.

But it was more than that. I believe that this modest event was a hint, a prompt. The 2008 event was unquestionably a true classic of the crop circle project perhaps we are being gently reminded of its importance. And perhaps we are also being urged to look more slowly and to notice more deeply.

 

Acknowledgements and thanks

Photography: Steve Alexander.

Diagrams and graphics: Michael Glickman, Allan Brown, Ofmil Haynes Jr.

Conversation and advice: John Martineau, Karen Alexander, Gary King, Albert Lamb.

5 Comments

  1. Always so happy to get a notice that you’ve posted something new! Wonderful insights. Thank you for sharing.

  2. Thank you Michael. So fascinating. Your love, appreciation, and passion for the circles is always felt in your writings and deepens my awe for them.

  3. Thank you Michael for your observations, insight and analysis. I agree that we are crossing into a spiritual realm and also realize that we have been treading this pathway/bridge for some time now. And, YES, we certainly do need it. Thanks for the enlightenment. I am in awe.

    Grace

  4. I am a visual artist with a background in studio art, art history, philosophy and religion, currently doing graphite and charcoal drawings of mythologies for quantum mechanics, mystical poetry, pre-Socratic and Eastern thought. As such I am constantly involved with transitions from geometric matrices to organic form and, perforce, spiritual/earthly implications. I have seen ghosts and have had intense mystical experiences so it is blatantly obvious to me that there are other dimensions that I can relate to. Crop circles blow my head off! I find it difficult to describe their authors as ‘alien.’ Whoever is making these things is already so far inside of me that I get weak in the knees
    thinking about it. I have not as yet incorporated crop circles in my work; I believe I am about to!

  5. Yes, “…look more slowly and notice more deeply” into this beautiful cultural and civil (and sometimes uncivil) phenomenon. Here, early in the season, is an important visual poetic metaphorical mathematical message that clearly suggests a tone for deeper consideration and reflection within and through the cycles of Time, and much less need for racing and chase.
    This is not fox hunting.
    Each CC field formation is part and parcel of a much larger cultural-whole and civil contemplative conversation…