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25 June 2017
Evening Sedition

"The Flowering of Geometry"

Doric, Ionic, and Corinthian Columns

No architecture is so haughty as that which is simple.

— John Ruskin

I found myself walking through lower Manhattan reflecting upon neo-classical architecture, specifically the different types of columns: Doric, Ionic, and Corinthian.

The famous Roman architect Vitruvius, the inspiration behind da Vinci's Vitruvian Man, is credited with naming the three main types of Roman columns and entablature (horizontal piece running across the tops of columns). The differences between them are ones of proportion, symbolism, and opulence.

Greek Stamp with Doric Column

Doric is the oldest and most spartan; it represents a man. (I use the word spartan in terms of being undecorated, not in terms of being from Sparta, which it wasn't.) The column notably has no base but has triglyphs and metopes. (A metope is the space between triglyphs.) This style is from the Greek mainland.

Greek Stamp with Ionic Column

Ionic is far less solid than Doric, being based on the proportions of a mature woman. (The Greeks valued slenderness in their women, including small breasts and hips.) Also unlike Doric, it has a column base but no triglyphs. The volutes are the key flourish of note. (Volutes are the scrollwork patterns in the capital.) This style is from the eastern Aegean.

Greek Stamp with Corinthian Column

Corinthian is the latest and most stylizied; some might say opulent. It is based on the dimensions of a young maiden and is capped with a circular belle formed from rows of acanthus leaves and volutes. (Corinthian was very popular for neo-classical architecture, particularly in Washington, DC.) Acanthus is an ornamental plant with spiny leaves; the reason for its inclusion in the Corinthian style have to do with the legend of its origin.

9. It is related that the original discovery of this form of capital was as follows. A freeborn maiden of Corinth, just of marriageable age, was attacked by an illness and passed away. After her burial, her nurse, collecting a few little things which used to give the girl pleasure while she was alive, put them in a basket, carried it to the tomb, and laid it on top thereof, covering it with a roof-tile so that the things might last longer in the open air. This basket happened to be placed just above the root of an acanthus. The acanthus root, pressed down meanwhile though it was by the weight, when springtime came round put forth leaves and stalks in the middle, and the stalks, growing up along the sides of the basket, and pressed out by the corners of the tile through the compulsion of its weight, were forced to bend into volutes at the outer edges.

10. Just then Callimachus, whom the Athenians called katatêxitechnos for the refinement and delicacy of his artistic work, passed by this tomb and observed the basket with the tender young leaves growing round it. Delighted with the novel style and form, he built some columns after that pattern for the Corinthians, determined their symmetrical proportions, and established from that time forth the rules to be followed in finished works of the Corinthian order.

"The Origins of the Three Orders, and the Proportions of the Corinthian Capital" Vitruvius Pollio, The Ten Books on Architecture, Chapter I, Book IV

Greek architecture is the flowering of geometry.

— Ralph Waldo Emerson

"Moping Melancholy, and Moon-Struck Madness."

"Melencholia I" by Albrecht Dürer

"Melencholia I", Albrecht Dürer, 1514, 9 1/2 x 7 3/8 inches (24 x 18.5 cm) (various museums)

I hold that the perfection of form and beauty is contained in the sum of all men.

— Albrecht Dürer, Four Books on Human Proportions, 1528

I first encountered Albrecht Dürer's "Melencolia I" twenty-five years ago, when I was in high school. (I remember seeing it in Science, not the JAAS journal, which I also leafed through, but in their magazine designed to compete with Scientific American.) Since then, I've thought about it from time to time, but never dug into exactly what all the symbolism meant.

A few weeks ago I was thinking about Dürer again — he was a very smart and accomplished fellow, and his accomplishments include inventing etching (hey, baby, want to come up and see my etchings?), making numerous advances in art, and creating a mechanical device for accurately drawing perspective — and was inspired to again dig out Melencolia I for a look. That led me to some searches for the symbolism — an option that was not easy twenty-five years ago — and after doing so I was inspired to write it up.

I spent a bit of time digging out Webpages and papers on Melencolia I, and have only included the ones with detailed analysis, and those not in the realm of the delusional, spiritual, or occult. The "The Melencolia Code" by David Finkelstein, a physics professor at Georgia Institute of Technology, has the best writeup of the lot, so I'll be quoting extensively from him. This isn't to say he's correct, just that he summed up the arguments cogently and succinctly. I won't write up all of the symbolism, just enough to give you a flavor for the piece.

The Melencolia I (1514) of Albrecht Durer (1471-1528) might be the most studied engraving ever made, and it influenced European art for centuries. It represents science well before Newton. Many riddlers have tried to decode it. The art historian Erwin Panofsky saw in it Durer’s own melancholy frustration at the gap between artistic and divine creation. Frances Yates, historian of the Hermetic tradition, took its melancholia to be an inspired creative fever, not sadness at all, and read the engraving as a declaration of the harmony between microcosm and macrocosm. The art historian Patrick Doorly sees it as an illustration for Plato’s Greater Hippias, a dialogue on beauty; the angelic melancholy represents the inability to define absolute beauty. Long before I heard of their studies, I saw in it a feeling about science that I could not quite read. Was the angel truly melancholy? If so, was it for knowing too little? Or too much? Is the angel dreaming of a Final Theory? Isn’t she actually smiling slightly? What is the joke?

"The Melencolia Code" by David R. Finkelstein, School of Physics, Georgia Institute of Technology, Page 3

The Name and the Bat

"Melancholia I" by Albrecht Dürer

To unscramble it [the name Melencolia I] I proceeded as follows. Since so many Durers, father, mother, and repeated son, already hide in the engraving, I guessed that the motto might hide another. This amounts to a prediction. To test it I went to Durer’s coat of arms to see how he might depict himself. There I found if I did not invent the caelo rebus by which Durer represents his art. CAELO indeed fits into MELENCOLIA. The leftover letters quickly arrange themmselves into the common noun LIMEN, commonly meaning gateway, doorway, threshold, lintel, walls, house, home, boundary path, and limit, according to context. MELENCOLIA then decodes to LIMEN CAELO, gateway in heaven. This describes the Durer coat of arms itself quite accurately, fulfilling the prediction that the anagram hid a name for Durer. It indirectly supports the rebus theory of the coat of arms. It also applies well to the dim archway in the heavens that frames it, and will acquire further meaning as we go.

The speed with which this prediction checked out suggested that I read Durer correctly. The proposition before us is that Durer constructed the motto MELENCOLIA I from the covert one LIMEN CAELO I, put melancholic elements and the mooonbow to fit them, and added the hell-bat to signal that the cover message was ironic.

"The Melencolia Code" by David R. Finkelstein, School of Physics, Georgia Institute of Technology, Page 11

The Solid

"Melancholia I" by Albrecht Dürer

There are observations about the geometrical figure to the right of Melencolia. Geometrically, the polyhedron is simply a cube or rhombohedron which has been truncated at the upper vertex. Somebody has proposed that the shape is a very elaborate optical illusion. It is made to appear as though it is a truncated cube, with 90 degree angles, but in reality, it has no 90 degree angles at all. Panofsky describes it simply as a "truncated rhomboid." It is possible to proportion it so that the vertices project onto a 4-by-4 square grid like that of the magic square (T. Lynch, "The geometric body in Durer's engraving Melancholia I," Journal of the Warburg and Courtauld Inst., pp. 226-232, 1982.). Schreiber (P. Schreiber, "A New Hypothesis on Durer's Enigmatic Polyhedron in His Copper Engraving 'Melencholia I'," Historia Mathematica, 26, pp. 369-377, 1999. ) proposes that it comes from a rhombohedron with 72-degree face angles, which has been truncated so it can be inscribed in a sphere....and on and on.

"Dürer's Polyhedra" by George Hart

Dürer's solid is the 8-faced solid depicted in an engraving entitled Melancholia I by Albrecht Dürer (The British Museum, Burton 1989, Gellert et al. 1989), the same engraving in which Dürer's magic square appears, which depicts a disorganized jumble of scientific equipment lying unused while an intellectual sits absorbed in thought. Although Dürer does not specify how his solid is constructed, Schreiber (1999) has noted that it appears to consist of a distorted cube which is first stretched to give rhombic faces with angles of 72°, and then truncated on top and bottom to yield bounding triangular faces whose vertices lie on the circumsphere of the azimuthal cube vertices.

"Dürer's Solid" Mathworld

What triggered my own new interest in Melencolia I and Durer were two faces that I found hiding in the polyhedron in April 2004. Anyone who steps back several paces from a good print and focuses on the shading of the front face of the polyhedron patiently for a minute or so, will soon find or construct a face, either a man with his head cocked to the right or a woman with her head erect. Both are there, at di erent angles and scales, apparently waiting to be seen for centuries. Some viewers see the man first and some the woman; one cannot see both at once. Both disappear if we come too close. Digitizing and reducing the engraving for the internet sometimes outlines one of the faces crisply, bringing it completely out of hiding. That is how I found the woman by chance and was drawn into this study. Absent such electronic aids, the faces emerge from the polyhedron slowly the first time but are inescapable thereafter. They are subtle and draw much on our own perceptive process, so that as we see them taking shape, we are not entirely clear whether they are really there or are our own projections. One can resolve these doubts to some extent. We may note that we cannot find such faces in all of Durer’s shadings. We can verify the faces we see with other viewers. We may assume that Durer’s vision was more sensitive to variations of shade than most, and infer that if we see these faces then so did Durer, and therefore they are part of his intention.

In 1604, long after popular demand had worn out Durer’s original copper plate, the Dutch engraver Jan Wierix (ca. 1553-1619) produced a new engraving of Melencolia I from scratch, so to speak. In order to distinguish his copy from the original he left out a flourish between “Melencolia” and “I” in the motto. Less publicly, he also systematically changed both hidden faces to hidden devil’s masks. By this change he left a secret sign that he saw the hidden faces and rejected what they stood for. This convinces me that they are not of my creation. And later they will lead us to the function of the polyhedron.

...

One can read the surface of the polyhedron in three ways: as blank, as a woman’s face, or as a man’s face. This is the only such triple image I find in Durer’s work. The two hidden faces resemble somewhat Durer’s last portraits of his mother and father, and have the same poses. Durer’s father died in 1507 at the age of 75 and a Durer portrait shows him beardless at 70, but five years is enough for the small beard on the hidden face of the man. Durer did his last portrait of his mother two months before her death and Melencolia I soon after. There is not enough detail in the hidden faces for positive recognition but since the ages, poses, and general features match, and the picture has already been recognized as autobiographical, perhaps they represent his mother and father. They have another function that I will point out later. They are part of a joke that Durer is playing on us.

I am less certain of a third hidden face. The black axle-hole in its center of the millstone might pass for a silhouette profile of a lean young man, presumably Albrecht again. Unlike the two parental ghosts, this hidden face reverses figure and ground, a common way to hide faces at the time.

"The Melencolia Code" by David R. Finkelstein, School of Physics, Georgia Institute of Technology, Pages 5-6

The Magic Square

"Melancholia I" by Albrecht Dürer

We need not look far [to find the meaning of the magic square]. The sum of the whole table is 136. Pursuing the autobiographical hypothesis, I computed the Latin gematria for “Albrecht Durer,” ignoring the non-Latin umlaut. The sum is 135. Since there is no “u” in the Latin alphabet, the name should really be “Albrecht Dvrer, ” but this would not change the sum, since “v” would then replace “u” as letter 21 of the alphabet. There is a significant discrepancy of 1 between 135 and 136. One must separate the 1 from the rest of the table to make the sum “Albrecht Durer.” This amounts to a prediction: that Durer did so. Returning to the engraving to check this prediction, we see that he made the 1 unmistakably taller than all the other numerals, as I did in transcribing the Durer Table above. This again di erentiates the Durer Table from the Jupiter Table. In addition, one wing of the angel brushes the 1 in the table, and only that numeral, verifying it divinity.

By splitting the sum into 136= 1 +135 Durer again puts himself into his own Table, next to God. The magic square provides two more Durer signatures within a symbol of the divinity of mathematics.

"The Melencolia Code" by David R. Finkelstein, School of Physics, Georgia Institute of Technology, Page 9

The Comet

"Melancholia I" by Albrecht Dürer

The great comet 1471Y1 was first seen on Christmas Day in Durer’s birth year, and Durer wrote of seeing a comet in 1503. The physical natures of meteors and comets were not yet known in 1514. Even Galileo would still believe that comets were formed from atmospheric vapors leaving the Earth. But da Vinci already mocked the idea that events in the sky foretold events on Earth, and so did Durer.

"The Melencolia Code" by David R. Finkelstein, School of Physics, Georgia Institute of Technology, Page 21

The Balance (Scales)

"Melancholia I" by Albrecht Dürer

The balance is one of the few scientific instruments in the picture. They all hang on the wall and the artisan tools litter the yard, as the experimental philosopher is sanctified above the craftsman. The scales hang on the side wall between the angel and the putto, level and balanced. One dish touches the putto, the other the angel. There is a balance between putto and angel, first literally, there it hangs between them, and then metaphorically, they have equal weight in some sense; perhaps equal divinity. The putto-angel equation seems to be a literally central message of the engraving. This fully supports Yate’s interpretation of the triumphant artist and of a balance between the Intellectual and Terrestrial spheres represented by the angel and the putto.

"The Melencolia Code" by David R. Finkelstein, School of Physics, Georgia Institute of Technology, Pages 14-15

The Angel

"Melancholia I" by Albrecht Dürer

If she had melancholia, it would have to be the creative form of the humor, not the depressive. In fact she is visibly not creating. Her compasses are held in a way that puts them out of service. Her book is sealed. The unresolved tension between her positive expression and attitude and the apparently negative legend is part of the hold that the engraving has on us.

She looks at nothing in the scene. The polyhedron, the putto, and the dog are directly to her right, and the globe is beneath her line of sight. She looks up out of the frame, right past what is going on in the sky behind her, meteor, hell-bat, moonbow and all. This is consistent with her representing the faculty of Contemplation that connects its user to the Intellectual Sphere of Forms and angels. What the angel is doing is remarkable. She is doing nothing.

I propose that her main function in this engraving is that of the knight between Death and the Devil: to ignore evil. She sees nothing and does nothing. She is unlike the putto, who studies the dog intentlly and draws it. But neither see the bizarre night sky.

"The Melencolia Code" by David R. Finkelstein, School of Physics, Georgia Institute of Technology, Page 14

Sources and Further Reading

  1. "Dürer's Solid" Mathworld
  2. "The Melencolia Code" by David R. Finkelstein, School of Physics, Georgia Institute of Technology
  3. "The Melencolia Code" by David R. Finkelstein, School of Physics, Georgia Institute of Technology (CitizenArcane copy)
  4. "Dürer's Polyhedra" by George Hart
  5. Melencholia I, Albrecht Dürer, 1514, Metropolitan Museum of Art

Oh, and since I know you were wondering, the title line is from Paradise Lost, by John Milton, (book XI, l, 485). I'll leave you with one more thought:

Gone is the mystical mathetic vision of absolute truth, the perspective of infinity, but also the self-deification and the gloom. Both halves of the picture live on Earth. Knowledge, with all its limits, is no longer a light in the night sky but a record of actual experience.

"The Melencolia Code" by David R. Finkelstein, School of Physics, Georgia Institute of Technology, Page 22

Vitruvian’s the Name. Vitruvian Man.

Vitruvian Man

Vitruvian Man, Leonardo da Vinci, circa 1492

The "Vitruvian Man" is an image that everbody — at least anyone with even the most rudimentary knowledge of history and art — knows, and yet whose name seems to be unknown by everybody. Circa 1492, while the Spanish were funding what would become the systematic rape, pillage, and looting of the New World — and the return of virulent syphilis; I think the native peoples didn't give as good as they got, but it was a nice thank-you present to the Europeans — Leonardo da Vinci was exploring the relationship between architecture and the human body's proportions.

The outgrowth of that exploration was "Vitruvian Man"; the name originates with the Roman architect Vitruvius, who was one of the first to argue in De Architectura (original latin and English translation), written between 27 and 23 BC, that human proportions should be the basis for architecture. (Vitruvius also argued that the job of the architect was to design useful and aesthetically pleasing buildings, a lesson that Frank Gehry would do well to learn.) But, back to Vitruvian Man.

Da Vinci was certain to have read Vitruvius' treatise on role of the human body's proportions in temple architecture:

1. The design of Temples depends on symmetry, the rules of which Architects should be most careful to observe. Symmetry arises from proportion, which the Greeks call a)nalogi/a. Proportion is a due adjustment of the size of the different parts to each other and to the whole; on this proper adjustment symmetry depends. Hence no building can be said to be well designed which wants symmetry and proportion. In truth they are as necessary to the beauty of a building as to that of a well formed human figure,

2. which nature has so fashioned, that in the face, from the chin to the top of the forehead, or to the roots of the hair, is a tenth part of the height of the whole body. From the chin to the crown of the head is an eighth part of the whole height, and from the nape of the neck to the crown of the head the same. From the upper part of the breast to the roots of the hair a sixth; to the crown of the head a fourth. A third part of the height of the face is equal to that from the chin to under side of the nostrils, and thence to the middle of the eyebrows the same; from the last to the roots of the hair, where the forehead ends, the remaining third part. The length of the foot is a sixth part of the height of the body. The fore-arm a fourth part. The width of the breast a fourth part. Similarly have other members their due proportions, by attention to which the ancient Painters and Sculptors obtained so much reputation.

3. Just so the parts of Temples should correspond with each other, and with the whole. The navel is naturally placed in the centre of the human body, and, if in a man lying with his face upward, and his hands and feet extended, from his navel as the centre, a circle be described, it will touch his fingers and toes. It is not alone by a circle, that the human body is thus circumscribed, as may be seen by placing it within a square. For measuring from the feet to the crown of the head, and then across the arms fully extended, we find the latter measure equal to the former; so that lines at right angles to each other, enclosing the figure, will form a square.Link to the editor's note at the bottom of this page

4. If Nature, therefore, has made the human body so that the different members of it are measures of the whole, so the ancients have, with great propriety, determined that in all perfect works, each part should be some aliquot part of the whole; and since they direct, that this be observed in all works, it must be most strictly attended to in temples of the gods, wherein the faults as well as the beauties remain to the end of time."

De Architectura by Vitruvius, Book III, Chapter 1 (original latin and English translation)

Notice the key portion:

It is not alone by a circle, that the human body is thus circumscribed, as may be seen by placing it within a square. For measuring from the feet to the crown of the head, and then across the arms fully extended, we find the latter measure equal to the former; so that lines at right angles to each other, enclosing the figure, will form a square.

De Architectura by Vitruvius, Book III, Chapter 1 (original latin and English translation)

Now, this starts to possibly explain why da Vinci drew the figure the way he did. While it might be that he was simply following Vitruvius' instructions, there may be another explanation rooted in mathematics. Da Vinci may actually have been attempting to solve the famous mathematical problem of "squaring the circle".

The secret concerns a geometric algorithm in human form. In this unity, Leonardo saw the solution to the problem known as squaring the circle.Leonardo‘s man is an algorithm! Squaring the circle is an ancient geometrical problem whereby of a pair of compasses and a ruler are used in an attempt to construct a circle and square of equal area.

In the 19th century it was proven beyond doubt that this is not possible in a finite number of constructional steps. Solutions do exist in infinite numbers of steps, however. The algorithm in the Vitruvian Man is based on an approach in-volving a continuation into infinity.

For the first time, the reconstruction of the algorithm provides an insight into the unique and bold image of man which Leonardo da Vinci has bequeathed to us in the form of this mystery. The Vitruvian Man may not be the sole mystery of this type. You can now witness the unfolding of the mystery with the aid of computer animations.

"The Secret of the Vitruvian Man" by Klaus Schroeer

This seems cumbersome and forced, however. It may simply be that da Vincia was following Vitruvius' lead in delighting in the joy of the human body's proportions. Vitruvian Man might, therefore, be just an exploration of human geometry. There are, of course, other explanations, involving everything from sacred mathematics to alchemical imagery. Consider this one — the massive geometry lesson not being quoted — blending geometry with alchemy:

The most fundamental composition consists of a circle, a square, and a triangle, a sigillum known to magicians and alchemist, sometimes called the Universal Seal of Light or the Seal of Hermes. The compositional triangle on this drawing is concealed, even though that it outlines important segments. It is drawn in the circle within the square and it coincides with the progression of squares as depicted on the illustration.

The main proportional lines come from the progression of squares, every second square is half the size of the original, and the measures thus obtained are the same as described by Vitruvius.

Distinguished is also the triangle with the size of a square and apex in the navel.

It seems that the drawing, or better the original design as explained by Vitruvius, contains many layers of geometry and symbolism that concord in one single image delineating the proportions of the human body. This idea of 'reason' governing 'form' was the fundamental theme of the Renaissance and is traceable in best architecture and art in general. It would not be odd if Leonardo had a close contact with scholars that spread the source of the Renaissance thought which didn't distinguish between art, science, and magick in terms of conflicting or opposing discourses as is the case today.

"Vitruvian Man: On Planning of Temples" by Morphvs

Regardless of its purpose, we can always appreciate the drawing as pure art. You can see the original at the Accademia di Belle Arti in Venice, Italy, in the unlikely event you ever end up there.

And, lest I forget to mention it, yesterday (15 April) was da Vinci's birthday. (Tax day, too.) Google, of course, observed it with a special logo (replicated here for after it vanishes):

Google Logo for Da Vinci's Birthday

Sources and Further Reading

  1. De Architectura by Vitruvius (original latin)
  2. De Architectura by Vitruvius (English translation)
  3. "Vitruvian Man: On Planning of Temples" by Morphvs
  4. "The Secret of the Vitruvian Man" by Klaus Schroeer

"A Jack Hammer Riveting Into Your Skull"

For those of you wavering on the question of Miles' sanity, this clinches it. Metal Machine Music is an hour's worth of the equivalent of a dentist's drill drilling into an infected tooth, a jack hammer riveting into your skull. Except it's perhaps less melodic than that. Miles has officially gone over the edge. You know the sound of fingernails on a chalkboard? This is worse -- a lot worse.

— Andy Whitman

Album Cover for Metal Machine Music (front)

I was passing by a bar around lunchtime and heard what could only be described as pure noise. But it wasn't just noise; something was hauntingly familiar. Then I realized what it was: Lou Reed's Metal Machine Music. (I think the only drink they serve at that bar must be EverClear straight up with an Oxycontin chaser.) If you haven't ever heard this album you're missing... well, absolutely nothing. Yeah, I know, there are those who swear by it, but they use jackhammers by day and say "what?" by night. This is music that could be used to torture Iraqi detainees. In all fairness, however, it isn't pure noise and it did take some creativity to introduce that feedback. Reed obviously did all of this in a studio using instruments, and not actual machinery. So it is an exercise in creativity, but that doesn't mean I want to listen to it. (If you don't believe me, you should listen to some short snippets.) Anyway, here's some commentary on Metal Machine Music:

The album was a two-record set titled Metal Machine Music and was met with much derision from the record-buying public, who went back to their respective record stores in droves and demanded refunds, claiming the album was "defective."

...

Along with Igor Stravinsky's La Sacre du Printemps (The Rite of Spring), which caused a riot at its 1913 debut, Metal Machine Music is one of a handful of compositions to elicit an almost universally negative response from the public.

...

But the idea that Lou Reed then left the studio is false --- or, at the very least, if Lou Reed did leave, then somebody stuck around --- because there is a lot happening on this album. It sounds like Lou took some basic recordings of feedback and subjected them to all sorts of electronic manipulation [...]

...

In other words, as Harry Dean Stanton put it in the film Twister [a film from ca. 1990, not the more recent blockbuster]: "I suppose you can acquire a taste for anything, but why do it?" Or something like that.

Joe Castleman

8-Track Tape for Metal Machine Music (front)

8-Track Tape for Metal Machine Music (front)

The waves of distortion are a bit to get through, and by the time that the record has ended you know that you have completed quite a task. Your ears, if the piece is turned up loud, feel as though they have been through a war.

Stylus Magazine

8-Track Tape for Metal Machine Music (back)

8-Track Tape for Metal Machine Music (back)

Except to add, "I think my ear canals are bleeding...", what can I say about Metal Machine Music Part III (16:13) that hasn't already been said; it's densely scrawled in the same violent frenzy as the rest.

David J. Opdyke

I bet if you need it for your 8-track collection you can find it on eBay.

At the end of the finishing assault, Metal Machine Music Part IV, Reed had engineers create a locked groove so that the record literally wouldn't stop playing its final wrenching seconds until someone manually lifted the needle (or pulled the plug).

— David J. Opdyke

A Plank, A Rope, And Thou?

Fractal Circles Crop Circle

On a moonless night in July 1990 I found myself in the middle of a Wiltshire field with a plank, a rope, and... well, you can guess the rest.

— Mike J. quoted in "I Was A Teenage Plasma Vortex"

In yesterday's entry about sand circles, I said that the Circlemakers had, as far as I knew, used the technique first. This induced me to write up their more famous work: crop circles. No matter what the UFOlogists say, crop circles are the work of humans. And most of them were the work of the bad boys of circle making over at Circlemakers.org. (Sorry to suck all the mystery out of the world. Well, not really. I mean the being sorry part, not about the removing the mystery part.) A few years ago I saw a documentary on the Discovery Channel about how they wield their talents and it is both amazing and beautiful. All that sacred geometry comes from using lengths of rope to do the measuring. Who knew?

In their own words:

Doug Bower, assisted by his pal Dave, made his first circle in a Hampshire wheat field sometime during the summer of 1978. They made it on their hands and knees with a four-foot metal bar normally used to secure the back-door of Doug's Southampton studio.

"I'd always been interested in UFOs and flying saucers", he remembers, "...so I thought I'd make it look like one had landed." Whatever initially inspired him - divine guidance, the 1966 circle in a Queensland reed-bed, close to where Doug lived at the time, or simple ale-induced prankishness - the leap from provincial trampler to extraterrestrial super-force was swift.

Doug's daytime work-bench doodles transmogrified by night into gleaming sun-blessed articles of faith. This genius - fast-possessing others - couldn't be re-bottled.

Thousands of circles have since appeared world-wide in wheat, barley, oil-seed rape... grass, oats, linseed, peas, maize, mustard and rye... Gradually, inevitably, the circles grew appendages; curled scrolls unravelled into straw-perfect aisles; simple circles' sets became cathedral-like floor-plans - vast temporary sacred sites morphogenised the Gaiaic cry of nautili, whales, serpents, snails, scorpions, and spider's webs.

Equally spectral were the people who studied them; a veritable zoo of new-scientists, cerealogists, ufologists, vicar's-voiced dowsers, orgone revivalists, channellers, and myriad mystics, all seeking phenomenal genuineness in one form or another.

That genuineness proved elusive. Once wrapped in darkness with the warblers and the rabbits, cold air hitting the throat like mint as they raced around and around and around in decreasing spirals; dew-soaked wheat whooshing and splaying under skidding rollers, crunching under planks; ever-widening swaths laid flat as a mat in their path; Doug, and his many imitators, have since retired unseen.

The Circlemakers by Rob Irving

Wavy Line and Concentric Circles Crop Circle

Want to make your own? It isn't hard.

Although the circles have appeared worldwide in wheat, oats, spinach, grass, peas, rice, linseed, maize, oil-seed rape, sunflowers, mustard, barley, sugar-beet, rye, and a multitude of other crops, most cereal artists prefer to concentrate upon just three. These are grown and harvested in a smooth, overlapping progression; oil-seed rape in April through May, barley throughout May and June, and wheat from June until early September. In this guide we will give you all the information you will need to work with these plants, and eventually, with a little practice, produce genuine, dowsable, scientifically proven un-hoaxable circles patterns.

Equipment

The tools you will need are relatively unsophisticated; a 30 metre surveyors tape - this is preferable to string which tends to tangle easily... a 1-2 metre board or plank with a rope attached to each end to form a loop - this is known as a stalk-stomper... dowsing rods - these should be made of copper, and purchased from an expensive new age shop, or, in an emergency, a couple of bent coat-hangers will do... and a plastic garden roller (available from reputable garden centres, or, if only for occasional use, these may be rented from tool-hire shops for about £2 a night). A luminous watch is also useful as a summer night can be surprisingly brief.

Circlemakers guide to making crop circles

Windmill Crop Circle

The Windmill Hill formation is often cited as being too complicated to have been made by humans. Well, they've got a nice rebuttal to that argument:

According to Silva these formations were tiny - a sixth and tenth of the size respectively compared to the Windmill Hill formation, which he states "dwarfs man made attempts".

The Windmill Hill formation was 375ft across, (It was measured by researcher Paul Vigay, amongst others who created a very accurate scale diagram from his measurements) though it is often inaccuarately cited as being nearly 1000ft across.

Our formation was 200ft across (made by three of us in 2.5 hrs). Matthew Williams' formation was a respectable 218ft across, made in only 2hrs by two people. Not the minute size that Silva alleges.

Myth Men By Rod Dickinson

Sparsholt Crop Circle

The Sparsholt formation is often cited as "proof" that aliens were making crop circles. Who else, after all, would combine a portrait of an "alien" with "DNA" evidence. (Nobody ever asks why the aliens don't just land on the Whitehouse lawn. Didn't anyone ever see "The Day The Earth Stood Still"?)

It's a massive ring which houses what looks like a 360 degree three-dimensional representation of a twisting DNA strand! According to reports there are 1296 squares that make up the grid that the DNA is laid out on and the formations stretched for over 200ft. Interestingly, the formations center is located between tram lines in standing crop, as you can see from the aerial photos there is no trace in the crop, now how did THEY do that?

Circlemakers: Top of the Crops 2002

Star Pattern Crop Circle

High Fidelity. Errr… "High-Tide Phidelity"

Double-Weave Design

Kris Northern a "designer, musician, and information architect (amongst other things)" has been creating sand circles. These are like crop circles, but are made using beach sand. It's an interesting, and attractive, medium for art, but the Circlemakers did it first.

How do you get it so perfect?

It is through a combination of being meticulous, sacred geometry and working with the cycles of nature in mind (ie the ebb and flow of the tides). We use a simple tool-kit of string, a couple hand rakes and a smoothing trowel.

What does it mean?

Each piece might have its own personal meaning to the creator but the common thread between all the designs is self similarity, harmony, balance and pleasing design. Each piece should have its own unique meaning to each person viewing it.

Where do you get your designs from?

We design them all from scratch... this isn't to say that we are the first to create them. Sometimes we stumble upon a design that many others before us have discovered. Generally we use Adobe Illustrator to create a prototype of the design so that we dont get lost in the maze of lines when we are inside of it.

Why do you do it?

Primarily because it is fun for us; we love geometry and design so to see these designs on a staggering scale is a real thrill. We use the work as a chance to practice mindfulness and really relax and put our full attention into it. Also if given the choice between sitting in front of a computer and learning this or a fully interactive experience with our friends on the beautiful tidal flats of ocean beach I dont think there's much of weighing of options.

Isn't hard to leave the designs behind?

While I can't speak for everyone else involved I have no attachments to the pieces. Their impermance is probably one of my favorite aspects of them, it's not something that can be taken for granted, it's not something a person can come back later and check it out when they have more time, they either enjoy it in the moment or they dont, and that is one of the most valuable lessons Ive learned in life.

How long does it take?

We spend anywhere from 1 hour to 2 1/2 hours on a piece on the beach, though creating the initial design on our computers might be the better part of a night trying different combinations and techniques.

What do you guys do when you arent making crop circles?

We are all free-lance artists.

Phidelity

Raking Sand

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