Zef Damen, Ph.D, has one of the most dazzling websites on the entire internet.

On the site, he offers geometrical reconstructions of many recent crop circles. Damen is a Dutch engineer with many patents and other notable professional accomplishments. Interestingly, Dr. Damen specializes in pattern recognition, which has been a frequent topic of ours on detectovision.com. Chessplayers use pattern recognition to cut their work down over the tournament board, and sabermetric baseball analysts use historical "player template" precedents to judge the future performance of their favorite young baseball players.

Damen doesn't discuss pattern recognition much on his site, that I can tell. He does, however, show a stunning talent for it with his "reverse engineering" of crop circles through geometry.

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As a very simple example, consider the following crop circle:

Dr. Damen points out that this pattern-in-the-field can be precisely diagrammed through the application of five steps of geometry:

1. Draw a circle, and extend the centerlines.

2. Inscribe two equilateral triangles, pointing in reverse direction.

3. Construct a circle passing through the intersections of the two triangles.

4. Construct another circle, with its center at the point of one of the triangles, so that it is tangent to the second (smaller) circle.

5. Construct two more circles at the other points of the same triangle.

As one considers Dr. Damen's construction of this pattern in AutoCAD ....

... one is tempted to believe that this is how circle hoaxers laid out their perfect symmetry in the field.

These beautiful reconstructions form a sort of "floor plan" of the formations, and as Damen points out, help us to "better understand" the diagrams. He cautions that his motivation is decidedly NOT to investigate HOW the patterns are created in the fields. His motivation seems to be simply to "understand" the geometry (as if we lesser mortals "understand" sequences of numbers or shapes in the way that Damen does).

Because of the geometry used, the diagrams can be reconstructed using unlined rulers. Note that distances are never defined by measurement, but always by reference to previously-drawn shapes.

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The problem arises when you move from 5-step geometry to 46-step geometry! :- ) Dr. Damen also reverse-engineers the AutoCAD sequence leading to this formation:

In fact, some of Damen's reconstructions involve over 70 (!!) steps and then match the final crop layout precisely.

I don't know:  maybe AutoCAD can automate this process through geometry-recognition algorithms.  :- )  If so, somebody let me know.  But assuming it can't, Zef Damen has one whale of a knack for pattern recognition.

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This presents an incredible puzzle. How could human beings, hoaxing these circles, construct them (in 6 hours of darkness) so as to match such intricate geometrical patterns? For example, how do hoaxers get the "sweep" of the circular angles so consistent with respect to other circles in the diagram and with respect to the 46-fold geometry?

Damen also notes that in the final diagrams, "superfluous parts are often removed" and in the field, this would be impossible!

On the other hand, Damen also points out that most of the crop circle layouts are not quite precise: they are a foot or two off here and there. If they were being done by advanced civilizations, why wouldn't such a civilization use computers and therefore avoid such imprecisions?

The crop circles seem too good to be done by humans, and seem not precise enough to be done by higher beings or transcendent beings. What a puzzle.

Cheers,

jemanji

images:

http://www.zefdamen.nl/CropCircles/Reconstructions/2008/HoneyStreet08/ho...

http://www.zefdamen.nl/CropCircles/Reconstructions/2008/HoneyStreet08/ho...

http://www.zefdamen.nl/CropCircles/Reconstructions/2008/SouthField08/sou...