Quirky Quintuplet: Back to Square One?

Eaton Water Copse, nr Hannington, Wilts May 12th 2012
Oilseed Rape (canola)
Click on any of the images to enlarge them.

The third formation of the year was reported on May the 12th and was located at the rather elaborately named ‘Eaton Water Copse’ (near to Hannington) in Wilts, just North of Swindon. While there are many that would argue that Swindon does not have many endearing qualities, one only has to look at the countryside surrounding it to see that even though its town centre may not be the most picturesque, its encompassing landscape more than makes up for it. The rolling hills and grand expanses of farmers fields; a collage all shapes, sizes and colours, make a beautiful frame for the concrete and red brick town centre.

Swindon holds a very special place in my heart, not because I have ever spent much time there, or because I have any particularly fond memories of events there, but because it is the home of one of my favourite literary heroines ‘Thursday Next’ – Jasper Ffordes wonderfully funny, clever and unconventional creation. Sorry I digress!

The formation was a quintuplet; this is a ‘five dot on a dice’ design, one circle in the centre and four circles surrounding it in equidistant positions. It is a classical crop circle design-type. There has been a whole catalogue of variations on this pattern, with circles of varying sizes, some connected by a ring, others not, even one where (most unusually), the four orbiting circles touched the centre circle. Researcher and geometer Michael Glickman affectionately identifies them as the mother circle (in the centre) and her daughters (orbiting circles). This is so endearing that it is now how I think of them as well!

A glimpse through any of the early books about the phenomenon will throw up a whole raft of quintuplets. While the quintuplet is essentially about the number four (it is four-fold in nature), it does have a curious connection to five through its anchoring centre circle. The quintuplet has long fascinated crop circle researchers/geometers (as evidenced above), because it has been such a reoccurring design, but it was geometer Allan Brown that really propelled the quintuplet into superstardom. He showed that almost every quintuplet-shaped crop circle carried a hidden property. That hidden property was that they all Squared the Circle.

In seasons past it may have been easy to forget the humble quintuplets in the face of other more complex and intricate designs, but after Allan Brown’s seminal contribution to the subject, it is almost impossible to look at each new quintuplet without asking “I wonder how it squares the circle?”

For those of you that don’t know about the Squaring of the Circle, and for those who need a quick refresher, it is a curious and rather old riddle – how to create (with just a compass and straight edge), a circle and a square who’s perimeters or areas are equal. This may seem like a strange conundrum indeed, but there was a rationale behind this, it was not just some arbitrary geometrical or arithmetical exercise. In fact it carried a great and noble symbolic significance and that was nothing less than the reconciliation of Heaven and Earth. Traditionally, and symbolically, the circle represents heaven, whether by its unity (it encompasses all), or by its similarity in shape to the canopy of the sky (the heavens). Numerous philosophers and theologians including Empedocles, Hermes Trismegistus, St. Augustine, Pascal, Voltaire and more have summed the concept up when they said, “God is a circle whose centre is everywhere and circumference nowhere”. Similarly, the square has been traditionally and symbolically associated with the Earth, material reality. It is the original foundation block of matter, or as geometer Michael Schneider calls it “Mother Substance”. Therefore to unite the circle and the square was seen as a great symbolic act. Ever wonder why many temples and churches carry a dome? This is exactly why. They marry the circle (the dome), with the square (the body of the building). In this way these buildings create a sacred space; they are a place where heaven and earth meet. One cannot talk of the Squaring of the Circle without talking of Leonardo Da Vinci’s ‘Vitruvian Man’; his famous drawing depicting a man stood inside both a circle and a square. Often cited as an exercise illustrating the portions of the human form, this work of art also carries an esoteric (hidden) meaning. Mankind too, is a meeting of heaven and earth, the divine and the profane. Man has an immortal, incorporeal soul and a temporal, material body.

The Squaring of the Circle carries within it this great human truth, but it also carries another and that truth is best expressed in the way in which we must seek to accomplish this task – with just a compass and a straight edge. With modern computers we can easily (okay then perhaps it’s not easy, but it is possible), to calculate the exact circumference or area of a circle, but traditionally this was not so. It is why we are all drilled at school in the delights of ‘pi’. Pi is an irrational number (a number that has no whole number solution – or whose decimal places go on ad infinitum), and we use it to approximate the perimeter or area of a circle by applying the formula 2 ∏ R (or ∏ R2) – pi is 22/7 or 3.142… Just as the true measure of a circle can never be fully known to the geometer, neither can the full measure of God or Heaven ever be fully known by man. However, conversely, with the square this is a simple calculation, symbolising that although man may be able to measure and manipulate the material world, he is unable to say such of the divine and its realm.

Many have speculated upon the inclusion of the Squaring of the Circle in crop circle design. But it seems to me that it is one of the fundamentals in creating a sense of sacredness in their spaces. I have often pondered as to why so many intuitively feel that there is a spiritual component to the circles, perhaps this is one reason. While many may not be aware of the subtle nuances of the geometry of the formation they might be visiting, I think intuitively we are drawn to such spaces and they in turn evoke such feelings. Perhaps this incorporeal marriage of the circle and the square in some crop circles can be sensed unconsciously, intuitively, even spiritually?

As I am fond of doing, I would like to relate some of these concepts to those of the philosopher Jean Gebser’s theory of consciousness change. If you are new to this blog, I apologise – please read previous blogs. Gebser talked of consciousness ‘mutation’ rather than evolution, one of his overriding concerns was that people should understand that when conscious changes (mutates), it does not throw off and discard the coats of the old, but it integrates them, sews them into a new garment – in other words all previous stages of consciousness (our origins) remain ever present. There is a tendency to think that consciousness change means only the end of the old and the beginning of the new, but it more of an assimilation of the new with everything we already are, I believe it is why Gebser called his fifth and next conscious stage ‘The Integral’. To me, the reoccurrence of the quintuplets are the ever-present origin of the circle phenomenon, still present and yet being constantly integrated into everything has come after them, season after season, symbolically, this is just magical.

The Eaton Water Copse formation had one other geometric secret and that was that it contained a golden section proportion – just like its predecessor at Yarnbury Castle last month. In my last blog I talked at length about the Golden Section as a transcending third component, and I would like to revisit some of that here.

The Golden Section (or Phi) is found in the proportions of all living things. It is found in the proportions of the human body and in the division and organisation of branches and leaves on trees and plants, to name just two of an almost infinite list of living systems this proportion governs and in which it is found. It is for this reason that the Golden Section is often referred to as ‘the fingerprint of the divine’. Like the tide leaves a wave upon the sand, so the divine, in creating life, leaves its own unique fingerprint on everything it touches via the Golden Section. The human mind has been shown to have an unconscious/intuitive connection to this proportion; simply, we consider it beautiful. Whether in the proportions of a face, a rose or in the spiral of a far-away galaxy, we are drawn to it like a moth to a flame, we seem to recognise its intrinsically ‘spiritual’ nature. Once again the Golden Section has, for thousands of years, been designed into the proportions of sacred buildings, some even growing by increments of phi as they were enlarged and added to. I go back to me earlier question of why many believe there is a spiritual component to the crop circles – it’s built in!

If the Golden section is a transcending third, a way of bridging the duality of our three-dimensional world, then what about the Squaring of the Circle? It seems to me that this too is yet another way in which the duality of reality can be reconciled. If the crop circles are some kind of catalyst, inspiration and commentary upon the changes we are undergoing at this moment in time it seems to me they are perfectly in sync with us!

Both the Golden Section and the Squaring of the Circle also seemed linked with the quantum mechanical notions of complementiarity and entanglement. Each is a model of complimentiarity; the idea that there is another way of complementing another that does not equate to precise equality, or quantity, but is based more on the quality of the relationship. Each is also an entanglement of parts, where each is an essential part of the other (and a greater whole) and when conjoined, create ‘spooky’ effects on human consciousness and the human spirit.

Steve and I finally got to fly over the Water Eaton Copse formation several days after it had been reported, it looked simply stunning in the yellow sea of the oilseed rape field it occupied. As we flew the farmer was spraying in the field, no doubt with some toxic cocktail some in our society have sanctioned because it is expedient and profitable. I am told he wants no visitors, believe you me, the last thing anyone wants to do is to breathe that in, or get it on their skin. I think it’s best we leave the farmer alone. Instead, you can see a collection of Steve’s beautiful photographs of this circle (and the one nearby at Ashmead Break) on our 2012 Image Library – we hope you enjoy them!

KAREN ALEXANDER – MAY 19th 2012