Phive Pointed Star
Phive Pointed Star
Last time in Squareness Reconsidered of 6th March 2017 I wrote of the importance of John Martineau’s early work on the geometry of the crop circles. Published originally in 1993 as The Sophistication of Agriglyph Geometry it dealt comprehensively with a range of geometrical shapes but the importance of the pentagram as a controlling form was clear.
Image (2) shows how, in a Celtic Cross formation at Goodworth Clatford in 1988, the pentagram with its points precisely on the orbit ring, uses its inner pentagon to size the central circle.
It might be useful here to remind everyone of the difference between pentagrams, five pointed (3) and pentagon, five sided (4).
Image (5) shows the seminal Upton Scudamore quintuplet of 1987. Here the points of the star rest on a circle enclosing the formation while the central circle is located by the pentagram’s arm crossing. Interestingly, the red horizontal line bisecting the centre circle and two of the satellites also uses the pentagram lines.
HUMANITY AND THE STAR OF LIFE
Figure (6) shows the traditional man in the star. There are many variations of this image but they all emphasise the five-fold nature of humanity and, by extension, most creatures. We have four limbs and one head. In classic numerology, five is the number of Life and thus the pentagram, the geometrical manifestation of five, is known as the Star of Life.
TWO UNIVERSAL RATIOS
Each of the five points of the pentagram is formed by a specific triangle. They are isosceles triangles; two of their three sides are of equal length. (7) shows one of these in detail. If the angle between the two equal sides is 36° the ratio of the shorter to the two longer sides is, inevitably, Phi the Golden Section (8).
The second of the two fundamental ratios is 1 to 1, Unison or, as some prefer, Symmetry.
HUMANITY AND THE RATIOS
When we are born (9) our navel is at our mid-point. As we grow to maturity the navel migrates upwards on the body (10) taking a new permanent and proportionate position. For the infant, the navel is halfway between the feet and the crown of the head. For the adult, if we take the ground to navel as 1, then the navel to head will tend towards 0.1618, the Golden Section. “Tend towards…” because as biological creatures these ratios will be generally though never precisely approached.
The two ratios, the Golden Section and Unison, leave evidence of a profound and perpetual sign on our bodies (11). Phi, the Golden Section, positions the navel, the thumbprint of our forebears, the Past. In the adult the location of the genitals, the herald of our descendants, the Future, is confirmed by Unison, Symmetry.
For me this verges on magic! Not only are the two prime ratios etched on our bodies but they also locate us poetically in time.
BYTHORN: THE CONFIRMATION
1992 and 1993 had both been disappointing years, especially after the excitements of 1991. And then, far outside the usual territory and on 5th September 1993 long after the usual season’s end, there came news of a beautiful star formation at Bythorn in Cambridgeshire (12).
Despite its distance I was able to visit Bythorn three times on one of which I measured it with John Martineau. For 1993 this was a remarkably elaborate formation. Perhaps the most intriguing feature was that, as the first realised crop circle pentagram, it confirmed John’s work of some years earlier.
Bythorn remains for me, after almost a quarter century, one of the most charmed and articulate of crop circles.
It was, curiously, positioned the wrong way up! It was oriented exactly to the south instead of north which, in our culture, signifies upwards. Many national flags feature pentagrams; they never point down. Figure (13) shows, incongruously, the man in the inverted star.
A possible interpretation would be that Bythorn warns us that humanity – for the moment at least – is upside down.
THE PATHWAY AS LABYRINTH
Photograph (14) shows the pathway running around one of the ten surrounding petals. This pathway was, as we shall see, an important, defining and original feature of this crop circle. It ran consistently clockwise defining the pentagram star and around the ten petals. It was exactly forty inches wide throughout its length.
Before Bythorn, crop was either laid or standing. The Bythorn path extended the palette significantly in that it established here two clearly differentiated categories of laid crop.
Diagram (15) illustrates the route of the path through the formation. It is unicursal or single-pathed, the characteristic which separates labyrinths from mazes. The maze presents many confusing options and requires left-brain reasoning while the labyrinth offers no choices and often engenders a contemplative or meditative experience.
The Bythorn labyrinth can be seen as five overlaid elongated hearts and (16) shows an individual heart form and how it might be approached. Starting at the bottom point of the heart you proceed, clockwise always, up the left hand straight side, you bounce over the two top lobes and descend the right hand side. At the bottom you move clockwise, bounce again over the next two lobes and continue through the whole formation. You will have noticed that the red directional pointers are all 36° isosceles triangles.
I never physically walked this labyrinthine route; by the time I understood it, the formation had been harvested. However it serves well as a meditative practice.
AN AVAILABLE ALTERNATIVE
Look again at the photograph of Bythorn (18). There is a ring of ten “petals” surrounding the pentagram and there are ten gaps between each pair. Five of these gaps perfectly house the five points of the pentagram but the remaining five are empty. The empty gaps are also, surprisingly, chamfered to leave a precise 36° housing (19 + 20). What could this suggest?
I believe that, though they have presented us with a symbolically upside-down Star of Life, they have also offered us (generous as always) an immediate and easy remedy. The position of the properly oriented north-pointing star is laid out for us; its five empty housings (21) ready to be filled.
A Brazilian, Rogerio de Almeida Freitas, warned that “We are the unwanted companions in this part of the Galaxy, since we commit all sorts of crimes against the dignity of life.” Perhaps the symbolic depiction of us as wrong-way-up-mankind reinforces the de Almeida Freitas quote.
The crop circles never give advice or instruction. Instead, their veiled and enigmatic communications invariably to offer a choice.
At Bishops Cannings Down on 13th July 1997 the second crop circle pentagon appeared (22). Like its predecessor at Bythorn, the Bishops Cannings star was upside-down and pointed exactly south. While Bythorn provided tailored 36° locations for the star points, Bishop Cannings had five arrays of three bars forming 36° angle guides (23). They showed the way to easily and correctly reorientate the star. That this second pentagram seemed to confirm and reassert the messages of the first was reassuring.
On 20th June 1998 the third pentagram (24) arrived at Avebury Trusloe in a corner of a field adjoining the A4 highway. Like Bythorn it had an elegant surrounding necklace of ten petals but in this case they all were simple three-sided forms without the 36 ° chamfer. Unlike Bythorn there was no defined pathway but the ground lay was spectacularly ordered. Though the formation was essentially circular its perimeter was enhanced with ten graceful shallow scallops.
I was very impressed with the north/south choices offered us by both the Bythorn and the Bishop Cannings stars and naturally I hoped that this narrative would continue here. There was no clue in the design of the crop circle itself but the true difficulty was that it somehow became impossible to sensibly read my compass in the formation. This was a routine matter that I had performed often but here, inexplicably, I could not find north!
The question of “crop circle befuddlement” is relevant here. People had noticed that within certain circles, left-brain reasoning activity proves to be difficult while visitors simply experiencing and contemplating the formation are never troubled. A surveyor, on returning home with his professional equipment after measuring a crop circle, found that he could not understand his own notes! A senior researcher, visiting the Barbury Castle Tree of Life of 3rd May 1997 found herself leaving the formation, bewildered and without the measurements she had specifically gone there to take. Andreas Mueller, a skilled veteran crop circle field researcher, experienced as I did, compass incongruities in the Avebury Trusloe formation.
There was a remarkable triad of crop circles incorporating small pentagrams in 2000. The first of these (25) was seen at Silbury Hill on 24th July 2000. It was a pentagram of pentagrams, all of them (including a sixth at the centre) made up of five small and precise equilateral triangles.
A couple of weeks later on 7th August 2000 a restrained and elegant formation (26) arrived below the Pewsey white horse. Among other features it had an incredibly slender crescent moon and three perfect tiny pentagrams.
The next day on 8th August the final member of the trio (27) arrived in Horton. I have a real and strong affection for this crop circle; it was placed in the nearest arable field to my home, just three minutes away.
For many years I have put my drawings of the season’s circles on my living room wall as they were completed and I have lived though the winter with this annual wallpaper of form. After the 2000 season I noticed that the formations were somehow organising themselves into groups of three. Now clearly I am not suggesting here that the drawings were physically moving around the wall; simply, they seemed to group together usefully. There were four of these trios and I was curious to discover what kind of triangles, if any, they would make if laid out on the map.
There is neither the time nor the space to examine the four triads so I will concentrate on the small pentagram group (28). I was hoping, as you will understand, that the formations, when located, would form a perfect PHI generating isosceles triangle of 36°. It was not to be. In fact, the angle between the two long sides was 32°. However, those two sides, that is Silbury to Pewsey and Horton to Pewsey were virtually identical in length at about 6.9 miles!
Now consider for a moment the kind of surveying, engineering and geometric skill that would be required to construct accurately in the landscape a triangle of nearly seven miles in size. Bear in mind also that all three formations at the corners of the triangles were beautifully positioned in their fields. There was no crashing into roads or hedges.
What can this mean? What can we learn from this?
Returning to the deceptively simple Horton crop circle (27). Diagram (29) shows, again, the fascination the phenomenon has with the number seven and its geometries. The red sevenfold star (a “fat” heptagram) precisely sizes and encloses the central circle while the blue sevenfold star (a “thin” heptagram) sizes the starred circle on the orbit ring (30), a green duplicate of which has been placed in the centre for clarity.
Again, what might this mean? Who out there cares so profoundly about us that they need to charm us with this super-order?
THE 1998 DOUBLED STARS
During the 1998 there were two remarkable events which, perhaps, continued the north-or-south, upside-down-or-not narrative.
The first of these formations was at Dadford on the 4th July 1998 and featured two equally sized pentagrams overlaying a thin ring. I obviously felt that this might cast some light on the Bythorn and Bishops Cannings pair, both of which displayed a real south-pointing star and an implicit north-pointing one.
Dadford was unusual in three respects. Firstly it was miles away in Buckinghamshire and it required the longest journey I ever took to a crop circle. Secondly, it was accompanied in the field by three curious logos or trademarks, at least one of which was repeated two or three times elsewhere. Finally, it was, being adjacent to the Silverstone motor racing circuit, the noisiest crop circle I ever visited!
I was anxious to discover which of the pentagrams at Dadford, the overlaid or the underlaid, pointed to the north and, to this end, I took my tape measure, notebook and above all my compass. I was convinced that Dadford would move the story forward yet here is my shameful confession. I was befuddled! I know I spent time in the formation and I know I took both measurements and bearings. But, at the end of the visit I had neither notes nor memories of either.
This disgrace, which I now freely admit, was compounded by the fact that on the 8th August a very similar formation with two overlaid pentagrams arrived at Beckhampton. Dadford’s stars were the same size but at Beckhampton the underlying pentagram was the larger. Instead of a ring, the formation overlaid a pentagon.
Unlike distant Dadford, Beckhampton is only moments away and now I must admit my final overwhelming shame! I never visited it. Nine years later I cannot recall what stopped me going up the road to investigate a potentially crucial formation. My friends will accept “befuddlement” while my adversaries will cry “shoddy research”.
A TENTATIVE HYPOTHESIS
I believe the Crop Circle phenomenon could, if it wished, take over the global media and, in the appropriate language, give us all the answers.
But like all brilliant teachers, they know that what we discover for ourselves will embody deeper meaning. And so they approach us enigmatically with metaphors, allusions, implications and symbols.
What I am clinging to is the idea that the ancient pentagram acts here, in some way, as a symbol broadly representing mankind. We have heard that we are “unwanted companions in this part of the Galaxy” and (if my idea is even remotely right) humanity is depicted, through the symbolism of the pentagram, as upside down. However, they seem always to offer us the possibility of recovery. There is always an alternatively oriented star available.
Image (33) shows the complex Ranscombe Bottom formation of 23rd July 2016. This was one of the more intricate and elaborate formations of the season, playing imaginative geometrical games with large and small pentagrams. And yet the diagram (34) shows its inexorable return to its upward or downward duality. It still offers choice.