Conspiracy for the Day - December 9, 1993 (+quot;Quid coniuratio est?+quot;) Euclid's Crop

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Conspiracy for the Day -- December 9, 1993 ============================================ ("Quid coniuratio est?") ----------------------------------------------------------------- Euclid's Crop Circles by Ivars Peterson [From *Science News*, Feb. 1, 1992.] [Excerpts] It's no wonder that farmers with fields in the plains surrounding Stonehenge, in southern England, face late-summer mornings with dread. On any given day at the height of the growing season, as many as a dozen are likely to find a field marred by a circle of flattened grain. The study of these mysterious crop circles has grown into a thriving cottage industry of sightings, measurements, speculations and publications. Serious enthusiasts call themselves cereologists, after Ceres, the Roman Goddess of agriculture. Most crop deformations appear as simple, nearly perfect circles of grain, flattened in a spiral pattern. But a significant number consist of circles in groups, circles inside rings, or circles with spurs and other appendages. Within these geometric forms, the grain itself may be laid down in various patterns. Explanations of the phenomenon range from the bizarre to the unnatural. To some people, the circles -- which began appearing about a decade ago -- represent the handiwork of extraterrestrial invaders, or crafty tradesmen bent on mischief after an evening at the pub. [The paranormal-type scenarios] suffered a severe blow late last summer, when two elderly landscape painters, David Chorley and Douglas Bower, admitted to creating many of the giant, circular wheat-field patterns that cropped up over the last decade in southern England. But this newspaper-orchestrated, widely publicized admission didn't settle the whole mystery. Gerald S. Hawkins, a retired astronomer, felt compelled to write to Bower and Chorley last September, asking how they managed to discover and incorporate a number of ingenious, previously unknown geometric theorems -- of the type that appear in antique textbooks -- into what he called their "artwork in the crops." [Hawkins had begun his investigations in 1990. He] found the crop formations sufficiently intriguing to begin a systematic study of their geometry. Using data from published ground surveys and aerial photographs, he painstakingly measured the dimensions and calculated the ratios of the diameters and other key features in 18 patterns that included more than one circle or ring. In 11 of these structures, Hawkins found ratios of small whole numbers that precisely matched the ratios defining the diatonic scale. These ratios produce the eight tones of an octave in the musical scale corresponding to the white keys on a piano. The existence of these ratios prompted Hawkins to begin looking for geometrical relationships among the circles, rings and lines of several particularly distinctive patterns that had been recorded in the fields. Their creation had to involve more than blind luck, he insists. Over the next few months, Hawkins discovered three more geometric theorems, all involving diatonic ratios arising from the ratios of areas of circles, among various crop-circle patterns. Hawkins came to realize that his four original theorems, derived from crop-circle patterns, were really special cases of a single, more general theorem. Remarkably, he could find none of these theorems in the works of Euclid, the ancient Greek geometer who established the basic techniques and rules of what is known as Euclidean geometry. He was also surprised at his failure to find the crop-circle theorems in any of the mathematics textbooks and references, ancient and modern, that he consulted. This suggests that the hoaxer or hoaxers "had to know a tremendous lot of old-fashioned geometry," he argues. The hoaxers apparently had the requisite knowledge not only to prove a Euclidean theorem but also to conceive of an original theorem in the first place -- a far more challenging task. To show how difficult such a task can be, Hawkins often playfully refuses to divulge his fifth theorem, inviting anyone interested to come up with the theorem itself before trying to prove it. "It's a good test," he says. "It's easy to prove the theorem but so difficult to conceive it." What Hawkins now has is a kind of intellectual fingerprint of the hoaxers involved. "One has to admire this sort of mind, let alone how it's done or why it's done," he says. ----------------------------------------------------------------- I encourage distribution of "Conspiracy for the Day." ----------------------------------------------------------------- CfD Recommends: The video documentary entitled "The JFK Assassination: The Jim Garrison Tapes" (Watch it with someone you love.) ----------------------------------------------------------------- CfD Mailing List -- If you would like "Conspiracy for the Day" delivered to your e-mail address, just send a message to me at bfrg9732@uxa.cso.uiuc.edu saying REQUEST CfD. If you later decide to cancel, send a message saying CANCEL CfD. ----------------------------------------------------------------- Today's conspiracy brought to you by....... Brian Francis Redman ................................................... : Aperi os tuum muto, : : et causis omnium filiorum qui pertranseunt. : : Aperi os tuum, decerne quod justum est, : : et judica inopem et pauperem. : : -- Liber Proverbiorum XXXI: 8-9 : :.................................................: (bfrg9732@uxa.cso.uiuc.edu) (72567.3145@compuserve.com)

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