Transcendental Triangulation: Two Becomes Three

Yarnbury Castle, April 28th 2012 – Oilseed Rape (canola)
Click on any of the images to enlarge them.

The second formation of the 2012 crop circle season arrived on the 28th of April. Located by Yarnbury Castle hill-fort, it was just a stone’s throw away from Stonehenge along the A303. By the time we had managed to arrange to fly over it the circle was several days old, the inclement English weather had kept us at bay. The night the circle had appeared had been no better, heavy rain and strong winds had buffeted the British Isles. It has been the wettest April on record, according to the UK Met (Meteorological) Office. Paradoxically, almost the entirety of Southern England has a hosepipe ban in place; it would need to rain consistently until December before the ban could be lifted the water utility companies tell us, even though there has been widespread flooding. Such is our topsy-turvy world in 2012.

Yarnbury Castle (or Hill-fort) fig.02 and 03, is of course, not a fortification in the traditional sense. There are no buildings or battlements. Dating back to the iron-age these types of earthworks are simple enclosures with a bank and a ditch, which would have probably encircled a settlement. Apparently, the scoop shapes inside the formation are a mix of old quarry marks and 18th century sheep pen enclosures. Yarnbury Castle looks magnificent from the air it is one of the larger hill-forts in the UK with well defined banks and ditches. Alas, there is no public access to this amazing landmark on foot; the fort is on private property.

The crop circle at Yarnbury, was on the opposite side of the road to the hill-fort in a field of yellow oilseed rape. We flew over the formation in the late afternoon/early evening and the light was a warm buttery gold. A stormy weather front had just cleared the southern half of the UK leaving amazing visibility, we could see all the way to the coast to Portsmouth’s Spinnaker Tower and the Needles by the Isle of Wight (50 miles or so away). It was hard to think we had driven up from the south coast just an hour before, I don’t think I’ve ever seen the visibility so crystal clear. The landscape beneath us was a patchwork of brilliant green and bright yellow fields. I noted how early in the year it still was, many of the trees we flew over had not yet fully got their leaves.

The circle itself was by the side of the field close to one of its edges, I would estimate it was in the region of 80-90ft in diameter. It looked as if the formation was on a bit of a rise. The design reminded me of the 2007 Oliver’s Castle formation fig.04, if for no other reason that it too was in oilseed rape and was a circle with a wide outer ring and concentric arcs inside. The 2007 formation had been on a much larger scale though, and remained pristine, as it was not ever subjected to the ravages of stormy weather. I had seen images of the formation on the internet before we flew, so I knew the field had sustained some wind and rain damage, but the circle surprised me as it looked much more defined than I had imagined, and much neater too. Oilseed rape is a much coarser crop than say barley or wheat, and the smaller the formation, or the more detailed it is, the less defined it can look in this awkward, unwieldy crop.

The flight over, I wanted to get the design on the drawing board. I could see that we had a circle with a wide outer ring and that we had some intersecting concentric arcs. I could also see what appeared to be another arc intersecting in an opposite direction and that the concentric arcs had been flattened in an opposing pattern either side of this. As I began to draft out a preliminary drawing, I realised that what might be helpful would not just be to draw the formation itself, but also to draw in the radiating geometry. There are times when in order to see a fuller picture of a formation that it is informative to draw all the shapes that make up the design, even if they are not visible in the field. Sometimes it can reveal hidden aspects or explain the placement of certain elements. This particular formation makes much more sense when you can see the radiating shapes.

The design begins with a double circle, two circles in a Vesica Piscis relationship fig.05. To create the concentric rings, one of the circles is divided into six, a central circle with five equally spaced concentric rings. Then using the point at which the top arc intersects the large wide ring around the perimeter of the formation another circle of equal diameter is drawn, which connects with the bottom perimeter of the formation in the centre. What you realise is that although this formation appears to be about duality; the Vesica, the opposing flattened arcs, it has this partially hidden third element. Here was a pattern that talked much of duality, but which also had a mysterious third element – the third circle. This third circle was not in the traditional ‘third’ position that would turn the vesica created by the first two circles into a triquetra (or a tri-vesica if you will), but was placed in a slightly skewed position. See fig.06 We had a ‘irrational’ positioning of the third, rather than a logical progression of the design in to three equal parts. This is significant.

For anyone who heard the presentation I recently gave to the Earth Spirit Conference in Vermont, you will know that the idea of duality within the crop circles is something that interests me greatly. I have often talked at length in these blogs too, of the notion that something is beginning to change in human perception and that this may be symbolised in the use of duality, opposition, the vesica, interference patterns etc. in the design of many crop circles. During my Vermont presentation I showed a whole raft of crop circles whose design contained some element of duality, and those were the only ones I had time to show!

Much is talked about of a shift in human consciousness in crop circle, circles. I think symbolically this prevalence of two-ness is directly related to this idea. Our current three-dimensional, mental/rational consciousness state, is based on duality. We define our reality – our worldview – through opposites; night/day, black/white, right/wrong, real/not real, left/right… the list is almost endless, but what the crop circles have also shown us, with uncanny regularity, is a progressive triangulation of duality. This is important because it complements what is going on in other worldview-shifting subjects. Quantum physics is a much-quoted subject by paranormal researchers, and it is, as often as not, misquoted too, but it does have something very interesting to say about duality, and the way in which the quantum world-view changes our understanding of the duality of reality. In the classic ‘Double Slit’ experiment it was shown that light can be both a particle and a wave. We hear this so often now that it is no longer surprising, but we should be surprised, very surprised, astonished in fact, if we are really engaged in thinking about the full implication of this fact. Quantum physics changes opposition to complementiarity, it says that something can be two-things at the same time, in other words, it transcends duality and unites seeming opposites into a new vision of unity. I think it is almost too fascinating for words that the crop circles seem to mirror this. We have had vesicas, mirror image opposites, interference patterns, yin/yang formations as crop circles, but we have also had triangulations, interference patterns with three points and even a triple yin/yang – surely a very irrational notion!

Jung talked of a transcending third, he called it the ‘transcendent-function’. Jung said, “As a rule it occurs when analysis has constellated the opposites so powerfully that a union or synthesis of the personality becomes an imperative necessity…” However, the uniting third is not a logical synthesis, but an unexpected and seemingly irrational solution. There is something important here about how duality cannot be resolved through logic alone, it needs an ‘irrational third’ to transcend it, because to simply unite opposites is to cancel them out, or they annihilate each other! The key word here is ‘transcend’. If we are ever to move to a new state of human consciousness we have to find our ‘irrational transcending third’, to make that leap to a deeper more complete worldview. We have to understand how something can be two things at the same time without destroying, or cancelling-out the opposites.

In another uncanny echo of this stuff of consciousness change, the crop circles carry with them their own corrosive duality which seems to lie at the core of its being; that is the argument of real vs. not real. How can these two opposites be transcended? It is an interesting question. What could be a transcending-third?

It seems that we have reached a point, where just as Jung describes, our world-view and society has constellated the opposites to such a degree that it has become corrosive to ourselves and our civilization with extremism, materialism and over identification with the ego. A synthesis of sorts is fast becoming an imperative necessity! It is clear to me that this change is already been worked upon by our unconscious and perhaps collective unconscious, and is echoed in the crop circles. Finding our transcendental third could be our passport to a new and more harmonious reality, it is the quest of our age!

Phi as the Transcendental Third

I have recently been engaged in some playful speculation (as is my nature) with fellow crop circle researcher Jonathan DeVierville. As we have talked about the multifold symbolism of the crop circles, we have been discussing the triangulation of opposites and the idea of Jung’s transcendental third in relation to consciousness shift and the crop circles. So, as above, so below, as without, so within, we wondered if there might be a geometric model for the transcendental third and we have been wondering out loud (well over Skype) about the role, function, symbolism and philosophy of Phi (the Golden Section/Mean). Phi is essentially a ratio, but it is a three-way ratio. Traditionally ratios are two-way 1:2 etc. but Phi has three harmonious proportions.

In fig.07a, we can see the way this works: AB is to AC as AC is to CB, or the lesser is to the greater is as the greater is to the whole. The golden section is a way of ‘splitting’ or dividing something so that each part retains its own unique relationship to the whole, yet each part is not equal in the quantative sense. This is a fascinating notion as it is an irrational way of dividing something, unlike dividing by two, which is logical, practical and equal. Phi is known in ‘mathematical speak’ as an irrational number because it has no whole number resolution, its decimal points stretch to infinity. But I wonder if its irrationality is more than just mathematical?

Did you know Phi (capital P) is 1.618… and phi (small p) is 0.618…?!

As I looked at the Yarnbury formation, I was drawn to the relationship between the two sides of the linear curved line in the bottom section of the formation, I wondered if the unusual placement of the third circle which created that curve had some deeper significance, so I decided I would see if there was a phi relationship at work. I downloaded a blue print from the internet to make a golden section caliper. After I had made the caliper (cut out of card and joined together with a few split pins), I placed it on my drawing of the formation and fig.07 shows the result. I shared this with researcher and geometer Michael Glickman, who like me found it interesting, even if both of us agreed we didn’t fully understand it. But here is the picture, make of it what you will – are we being shown the transcendental third in the golden section? Is the Golden section at work in the Yarnbury formation? I guess only more playful, creative thinking and contemplation will tell!

KAREN ALEXANDER – MAY 7th 2012