One of the most interesting traits of the CROP CIRCLES phenomenon, beyond their exquisite beauty, is the fact that they often embed advanced mathematical knowledge, such as the graphic lay-out of Chaos Theory’s algorithms and Mandelbrot-type fractal sets. In fact, this mathematical knowledge is so sophisticated that it often takes a few intuitive minds a long while, and cross-examination between them, to finally decipher these crop circles. The crop glyphs clearly are giant enigmas and coded artworks asking to be studied and solved; and in so doing, it clearly launches a process of intelligent communication with Exo-Planetary Intelligent Civilizations or EPICs, using visual mathematics and symbols as a common language.
The sophistication in both the crystal-clear designs and the maths involved, as well as our incapacity to reproduce the technological process for creating them (beyond making a couple of fuzzy blotches), rule out any explanation based on forgery.
In this respect, I truly believe that the significance of the crop circles—viewed as graphic mathematical means of communicating with us orchestrated by alien civilizations—has been hugely underestimated. With the mathematical glyphs and their high artistic and esthetic touch, we definitely have a clear message of good will and peaceful exchange with at least one EPIC, showing us in the clearest way that we have some sure allies of Earth in our neighboring worlds.
As this means of communication seems to be evolving, let’s keep in touch with the current formations and their analysis by crop circles experts.
Below is the analysis of one of the most stunning mathematical puzzles posed by a crop circle, the embedment of the number Pi (π) within the Barbury Castle formation of June 1st, 2008 in England, and its astounding decoding by expert Michael Glickman and some of his colleagues.
Don’t miss reading the full article and checking with Michael’s reports on current crop circles, on his blog!
Extract of the article ”Why Pi ?” posted by Michael Glickman on his blog on June 28, 2012.
See the whole article by Michael Glickman at (copy- paste the address below):
MICHAEL GLICKMAN ON CROP CIRCLES
Why-Pi? (THE 2000 SEASON)
“But perhaps the narrative was advanced by another, more crucial, feature of Avebury Trusloe [crop circle]. The date was the twenty-second of July or 22/7.
Now anyone familiar with the simplest mathematical ideas will recognise 22/7 or 22 over 7 or 22 divided by 7 as the most popular formula for Pi or π, the constant used in all calculations involving circles or circularity.
Graphic [Fig.5] shows the difference between “pure” Pi and the conventional working 22/7 version. Arithmetically, they are very close to each other. They are both irrational or “endless” numbers. Apparently, the pure version has been calculated to over six million digits. The diagram [Fig.6] demonstrates the relationship between circumference (22) and diameter (7).
Pi (π) = 3.141592
22/7 = 3.142857
[Extraction of] Fig.5 & 6 – Two versions of P: Pi number & Circumference and diameter
The authors of the crop circle phenomenon regularly display prodigious inventiveness, but I can see the difficulty in signing, “divided by” in the wheat. They simply added the 22 and the 7 together and assumed that, sooner or later, we would work it out.
A COUPLE OF CONFIRMATIONS
The dazzling Picked Hill formation [Fig.7] of 13th August 2000 brought clear support to the Pi theory. This beautiful and elaborate design had 44 radial elements and 14 concentric rings. 44/14 = 22/7 = π. In diagram [Fig.8] eleven of the radial elements are numbered in red for clarity while the green triangles show a unit from each concentric circle.
|Fig.7 – Picked Hill crop circle, August 13th, 2000|
|Fig.8 – Picked Hill diagram|
A 2001 hypothesis
I believed in 2001, as I believe today, that the authors and engineers of the circles are playing fair. They seem to me to have consistently demonstrated a rigorous integrity. There is wit, but there are no tricks.
How then was I (were we) to respond to this? Here was a clear demonstration of will and intent. These events were too consistent and too clear to be brushed under the carpet as “coincidence”. I felt that the reiterated references to Pi were undeniable and unchallengeable. What might this mean?
I have referred often to the ancient conundrum of Squaring the Circle but I want here to consider it more in philosophical and symbolic terms than in relation to number or geometry. If the Square is the token of the world and of material reality and the Circle is taken to be the symbol of God and the spiritual realm then the Squaring of the Circle, or, as I prefer, the Circling of the Square is emblematic of a marriage, or at least reconciliation, between the two.
Pi, the constant in the ordering of all things circular, might thus be seen as the master-key; a symbolic toolbox to aid us in our endeavours to manifest heaven (or a small part of it) here.
THE BARBURY CASTLE PI FORMATION
|Fig.10 – Barbury Castle crop circle - 1st June 2008|
A large and intricate formation [Fig.10] appeared on 1st June 2008 in a field of barley below the Barbury Castle hill fort. Barley is a graceful crop, which seems always to add glamour to a crop circle but this formation was almost shockingly good looking. Beneath the beauty was a hint of purpose in its elaborate stepped spiral.
The pattern was ten-fold radially (that is, like a pizza it was divided into ten slices of 36°) and ten-fold concentrically (that is the path was made of several arcs, each of which was a part of one of ten concentric circles). It took many long hours to work out the meaning embodied in the formation.
The path was swept outwards from the central black circle. Using diagram [Fig.11] we move onto the first red arc and we see that it covers three 36° slices. We then see the small red circle representing the decimal point. We note 3. (three point…) before we move out on to the next, lilac[-color] arc (one slice) and then to yellow (four slices). We have now established 3.14… and the diagram will continue to build the Pi number.
Fig.11 – Barbury Pi Diagram
The wedges, the pizza slices, were exactly 36° and the concentric arc pathways were precisely 10’9” centre to centre.
This remains for me one of the most beautiful crop circles that I have seen and it is an astonishment that, beneath this charm, lies an elegant and innovative method of encoding the Pi number.
This would have been enough, but after some days, Bert Janssen a researcher from Holland, discovered that the bridle path (on the right of the photograph) formed one side of the square which squares the circle. This is a miracle of precise placement. The intelligence and foresight required to achieve this accuracy of juxtaposition is breathtaking.
Four years later, I look back on the Barbury Pi formation with respect and wonder. I can recall few crop events that integrated beauty and meaning with such assurance.
Acknowledgements and thanks [for the whole article].
Photography: Steve Alexander, Ulrich Kox.
Diagrams and graphics: Johan Andersson, Ofmil Haynes Jr.”
[In brackets: additions of my own.]
*****end of the extract *****
I suggest to you to meditate a few moments on the enlarged ‘Fig 8 – Picked Hill diagram’ and try to distinguish: 1. The lotus petals around the central black core (Take a point on the outside border of this core, blink and half close your lids, and look for all the embedded petals growing outward around this point).
2. The concentric circles, starting from the center (It’s more easy that way). Then
3. All possible sets: Get the whole picture from farther away in one glance, and move from one inner structure to another one, searching all you can find, e.g. the spirals clockwise and anti-clockwise, the spirals moving toward the center or out of the center, the lotus petals embedded into one another (by sliding slowly the point on the inner black border around this border), the concentric circles, the mandalas of lotus petals, and more. Then, the ultimate:
4. Watch how all these sets are dynamical and follow their movement: soon you’ll see that the center is a vortex of dynamical energy.
Dazzling! Don’t you agree?
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