Crop circle

"Crop circles" have been popping up for something like 15 years now, and the "conventional wisdom" is that...well, what do you think about 'em?

Yeah, the CW is that they're hoaxes, produced by groups who love to fool the credulous.

This meme began when some TV network found two guys in the U.K. who had produced simple circular shapes in wheat fields in a few hours by using rope and two-by-fours. One guy would hold one end of the rope in the center and the other guy would walk out until the rope was taut, then walk forward, dragging his 2x4 on the wheat, bending it all in the same direction.

Ha ha. Stupid rubes who believe in aliens... etc. Case closed.

I hadn't heard much about crop circles in the past five years or so but then yesterday chanced on this photo:


My first thought was "Now that's one hell of an elaborate hoax." There are a LOT of circles there--including the little ones, almost 400. Lots of time there. Presumably hoaxers would have to be very highly motivated to invest that much work--in something that wouldn't have any financial payoff.

Of course it's the elaborate detail that makes any hoax convincing.

But some other factors jumped out:  While the perfect symmetry of the six curving arms is easy enough to lay out with a drawing compass, laying it out with a taut rope in a field would likely damage the areas between the arms--something that's not visible. 

Then there's the precise sizes of the 13 circles on each of the arms, so that they fill the entire length of each curving arm exactly, while just touching each other.  While the necessary diameters of each could be found by trial and error on a computer screen, accurately executing the different sizes on each arm would be extremely difficult.

What are the odds of getting zero mistakes in such a task? And remember that the crew wouldn't be able to see the figure from the air so they wouldn't know if a mistake had been made.

Then there's the perfect symmetry of the bends in the axes of the four to six smaller circles off 48 of the larger ones:  It's simple to strike a perpendicular to the main curved arm at any point, but each smaller circle departs from the perpendicular by exactly the same small angle, every time.  To do this even with a surveyor's rig, over 250 times without a mistake--at night--would be extremely unlikely.

Because the six main arms curve as they get farther away from the center, the bend axes of the side circles take a very large number of different heading.  Just keeping track of which circle a hoaxer was in would start to get prohibitive.

And remember, these things appear during a single night.

I realize humans are amazingly creative and have put some elaborate hoaxes over on the rest of us, but how elaborate does a figure like the one shown have to be before a rational person finally concludes that the probability of the thing being done by hoaxers in a single night approaches zero?