Posted by Michael Glickman on September 21, 2013

Fig.1 – Water Eaton 12th May 2012

The crop circles offer us a conversation in symbolic form. They do not work through our ears with sound or through our nose with smell. They are presented to our eyes as shape, form and structure and, for those with the discernment to look more carefully, they also introduce the magical sisters, number and geometry.

Now, nothing like this has happened before. There are no precedents. There is no instruction manual we can refer to. And in the absence of any guidance I have made my own rules: look longer, see more deeply and rely on intuition. Occasionally this has worked.
I believe we are obliged to consider the symbolism of these signs and to infer, though this is rarely possible, their meaning and intent. My own inference (and this is a speculation only) is that the Circle Mistresses and Masters, subscribing to the ancient Earth/Square conjunction, invent their overwhelming variations on squareness to suggest to us the infinite choices and possibilities now becoming available to the world.

In this first section I look, chronologically, at five formations of early 2012.

WATER EATON, 12TH MAY
The Water Eaton formation of 12th May 2012 [Fig.1] was a concentrically doubled Celtic Cross. For clarity, [Fig.2] shows a simple Quintuplet, similar to a dice five-spot, and its sibling, the Celtic Cross which has the four satellite circles, often called the daughters, on a fine orbit ring.

Fig.2 – Typical Quintuplet and Celtic Cross

The Quintuplet and the Celtic Cross have been familiar components of the phenomenon since the 1980s. They are often incorporated into larger formations and they tend to obey the following rules:

A – The central circle (often the ‘Mother’ circle) is larger than the four satellite or ‘daughter’ circles.
B – The daughter circles have the same diameter.
C – The daughter circles are the same distance from the mother.
D – The axes locating the daughters are substantially at 90° to each other.

Rule D is particularly important here. The quintuplet type was the first occasion in the history of the circles that orthogonal or right-angle geometry was employed and from here the square is only a small step away. If lines are drawn to connect the centres of the satellite, outrider or daughter circles, a square is formed.

The Celtic Cross obeys the following additional rules:

E – An orbit ring runs through the centres of the satellites.
F – The orbit ring is normally very thin.

Of course, these rules are occasionally broken or shifted but, in general, the quintuplet type seems to respect its own traditions. At Water Eaton for example, the internal form conforms and has four identical satellites while the outer, enclosing form has two pairs of circles of differing size and shape.

Fig.3 – Gallery of quintuplets

[Fig.3] is a page from Allan Brown’s seminal study of the quintuplets. This important study, tragically still unpublished, analyses all known quintuplets and Celtic crosses and demonstrates, using a variety of geometric protocols, that the majority of these forms accurately square the circle.

SQUARING THE CIRCLE: A SHORT NOTE
The subject of Squaring the Circle is regularly mentioned. Some notes might be useful.

The deeper meaning of the square and the circle has already been discussed. The Squaring of the Circle might be considered the final act of sacred geometry in that it signifies, symbolically, the final reconciliation of earth and heaven. There are two important provisos.

First, the phrase “Squaring the Circle” implies the making of Heaven more Earthly.
Surely, this cannot be the object of the exercise, no matter how symbolic. The intention must be to make Earth more Heavenly. Thus the phrase “Circling the Square” might be more appropriate.

Second, both of the methods of squaring the circle arithmetically (whether by perimeter and circumference or by area) rely on the use of the constant Pi, 3.1415926535…, which is an irrational or infinite number. The infinity of Pi suggests that just as, arithmetically at least, the square can never be precisely circled, so Earth can never be made totally and comprehensively Heavenly.

We are, however, our obliged to keep on trying.

CHILCOMB DOWN 1st JULY
The Chilcomb Down formation [fig.4] is probably the most perfect multi-point perspective figure the crop circles have ever presented to us.

Fig.4 – Chilcomb Down 1st July 2012

Initially, the crop circles were flat two-dimensional images. This changed in 1999 with the Allington [Fig.5] and Honey Street cubes which were, I believe, the first essays in three-dimensional representation. These were Isometric Projections, an architectural and engineering technique that is based on 60° geometry and which produces a simulation of true perspective. [Fig.6] shows how cubes, in Isometric Projection, are based on hexagons.

Fig.5 – Allington Down 23rd June 1999

Fig.6 – Allington Down framed by hexagon

The Uffington Towers of 8th July 2006 and the West Kennett Longbarrow temple of 28th June 2007 were both examples of single point perspective where the perspective lines converge onto a single vanishing point.

Chilcomb Down is certainly the most realistic representation of a three dimensional object that I have seen in the crop circles; but what is it and, crucially, what might it mean?

For me it is a display case. The top and four sides are plate glass in a metal framework with a spherical connector at each corner. Proportionally, it is not quite a cube. It is stylish (and stylised) and it seems precisely engineered. Perhaps this most accurate of three-point perspectives is a metaphor for the crop circle phenomenon itself and, more significantly, a comment on how humanity regards the annual display.

A thought. I believe that the 2012 shift is moving us from the Third to the Fifth Dimension. The third dimension, mechanical reality, has been pretty good for us but it comes with constraints and limitations. Our evolution to Five will be painful; is painful.
Maybe the exquisitely crafted, supremely real, Chilcomb Down formation shows us that, no matter how hard we peer through our current material 3D lens, nothing will be revealed. The display case is empty!

To see and understand the crop circles fully we must hold ourselves, for a moment at least, distant from the current consensus world-view.

ALDBOURNE 22nd JULY

Fig.7 – Aldbourne 22nd July 2012

What initially seems a square immaculately formed by four thin paths reveals a fourth side misplaced and misaligned by about ten degrees. Three of the corners meet with remarkable precision at the edge of the containing circle while the errant fourth side collides clumsily with its sibling [fig.8]. This “mistake” is celebrated and emphasised with a delicate motif of a small circle and a small ring.

I put “mistake” in quotes because it brings up a widespread misunderstanding. Many believe that any glitch, anomaly or irregularity will be unquestionable evidence that the formation is man-made. This superficial notion ignores the fact that these “mistakes” are very often time-consuming and hard to make. In addition, the anomaly often serves to emphasize other significances in the event.

Fig.8 – Aldbourne detail

Returning to Aldbourne, there can be no doubt that the misplacing of the fourth side is intentional. No contractor who could form corners so meticulously could possibly make such an obvious blunder. I have tried (rather inadequately I fear) to correct the perspective and thus to define the angle by which the fourth side is so conspicuously displaced. It reads a little under 10° for me; perhaps someone out there could do it more accurately.

Why is our attention being drawn so specifically to this angle? Neither the number nor the angle appear to offer any immediate clue. Once again a transparently simple crop formation responds to an innocent question with yet more conundrums. And once again, having sought clarification, I am even more perplexed.

[Fig.9] shows, in green, the slim triangle sliced off the square.

Fig.9 – Aldbourne green triangle

It is curious, and perhaps significant that Chilcomb Down is remarkably accurate, Aldboune, two days later, is equally remarkably wrong.

BISHOPS CANNINGS DOWN 24th JULY
This formation adopts a most familiar crop circle device; one square laid over another at 45° forming an octagram or eight pointed star. We have seen several of these and, in every case, the centre, like a good chocolate is always surprising. I confess that I had observed this formation only briefly and I assumed initially that the centre contained a pursuit pattern of diminishing squares defined by thin lines.

Fig.10 – Bishops Cannings Down red decagram

Fig.11 – Bishops Cannings Down blu decagram

Fig.12 – Bishops Cannings Down green triangle

The reality was far richer. In fact no single geometric shape is formed by the lines. Instead the lines describe two similar but independent, almost labyrinthine, paths. The first path, shown in red in [Fig.10], starts at the top corner and goes from 1 to 7 to 13 to 19 to 5 to 11 to 17 to 3 to 9 to 15 to 1. The second, shown in blue in [Fig.11] starts at 2 and goes from 2 to 8 to 14 to 20 to 6 to 12 to 18 to 4 to 10 to 16 to 2.

Each of these pathways mark out a decagram, a ten-pointed star. They are irregular in that their points, instead of conforming to a circle, are constrained here by a square.

A footnote. [Fig.12] shows a triangle, in green, which is arrestingly similar to that in [Fig.9]. Naturally, I hoped they would magically prove to be identical but, sadly, Aldbourne is just under 10° while Bishops Cannings is just over 11°. Ah well! And even if they had been identical that would have served simply to deepen the mystery.

HANNINGTON 28th JULY

Fig.13 – Hannington 28th July 2012

The major 12 x 12 square was sized to fit precisely into the circle and, though three of the corners, 1A, 1L and 12L are laid, it is easy to see (especially at 1L) how perfectly the square has been accommodated. The fourth corner, 12L, is of particular interest. It is the only corner with a standing square but crop circle protocols consistently resist bringing adjacent blocks of standing wheat into collision; they always engineer gaps or gateways for us. The perimeter of the enclosing circle has been minimally and elegantly adapted to allow a small access way around standing square 12L. I believe this is this first time that an enclosing perimeter has been modified in this way.

The defining linear grid is clearly visible even where the squares have been laid. The rotational swirl of the flattening is also clear. The flattened square 11J is unique in that it has a prominent standing tuft.

Fig.14 – Hannington numbered

This formation is clearly as articulate and meaningful as, for example, the 2008 Barbury Castle Pi formation. Indeed, I hoped that the lonely standing dot of 11J might represent, as at Barbury, the decimal point that released the whole cascade. It was not to be. Hannington remains silently, and tauntingly, enigmatic.

A final point. Earlier photographs show all 65 standing squares clean and untouched.

The later images shown here indicate some modifications. 1, 2 and 3B have rings carefully set into the squares. 6B seems to have a flattened triangular feature while 1D has a diagonal cross and 3L a rudimentary spiral. There are others. I feel these small changes are too careful (and too unassertive) to be the work of human spoilers but some disagree. Whatever the source, these marks add mystery to mystery.

Part 2 of The Squares and Cubes of 2012 will follow shortly.

Acknowledgements and thanks
Photography: Steve Alexander, Eva-Marie Brekkesto, Ann White
Diagrams and graphics: Ofmil Haynes Jr
General advice: Karen Alexander, Albert Lamb
Trigonometry consultants: Robin Heath, John Martineau