# Signs

Generally speaking, I have an open-door office policy: if my door is open, then I am available for help.   More often than not, the only folks who will turn up at my door are my students seeking help on their homework, but occasionally a random person will show up and something very weird will happen.

Here’s such an example.   I’m at work on the computer when a student I do not recognize knocks on my door.

Student: Hey.   I heard you had a pretty cool office.

Me: Well, I try.

Student: So… do you believe in crop circles?

Me: In that crop circles exist?   Yeah, sure.

Student: No, I mean, do you believe in crop circles?

Me: I think that crop circles are a particularly evocative form of human guerrilla art.   They’re not made by aliens.

Student: Well, why not?   There’s a lot of evidence for that.

Me: Actually, there’s a lot of evidence to suggest that most elaborate crop circles are, in fact, man-made.   A small team of guys with wooden planks, wires, and a decent GPS can bang out extraordinarily intricate crop circle designs in about an hour.   In fact, there’s even a group called “Circlemakers” who pride themselves on being able to reproduce seemingly impossible crop circle designs.

Student: Yeah, but some of them might be made by aliens.

Me: Well,  there is some flimsy evidence to support that some crop circles — particularly  isolated, non-elaborate ones —  are not man-made.   However, if something is not man-made, only poor logic dictates that it must  therefore by aliens.   It might, for example,  be formed by some kind of natural phenomena that is not yet completely understood.

Student: But still…

Me: Look at it this way: which is more likely?   That crop circles are  man-made, or that  there exist  alien intelligences with technology so advanced as to permit  undetectable interplanetary flight who have utterly nothing better to do with their time than to tag a planet with graffiti you’d find in a head shop?

On a related note, one of my favorite crop circles is the Barbury Castle circle, which appeared in June of 2008.   Rather than being one of the overly ornate fractal-looking designs, the Barbury Castle circle is, well, a circle with a zagged spiral winding out from its center.   It doesn’t look like much from the get-go, but it hides a secret.

If you’ve never seen it before, you might try to see if you can decode the secret meaning of this crop circle.   It’s a fun puzzle in recreational mathematics.   I’ll fill you in on its solution after the break.

Astrophysicist Mike Reed figured it out.   He noticed that the “jags” — the  small radial segments  — on the otherwise mostly circular  spiral occurred only at multiples of 36 degrees.   He overlayed a polar grid on the crop circle with 10 uniform sectors (each measuring 36 degrees), and found the following:

If we start counting (from the center) the number of sectors each circular portion of the spiral passes through before it “jumps”, we obtain the numerical sequence  [3141592654].   In fact, if we include the four extra small circles — the tiny one at the green arrow and the three larger ones at the end of the arc — as “dots”  where they occur in the sequence, we obtain [3.141592654…]

… which is, of course, an  approximation of $pi$, correct to ten significant digits.   Somebody out there’s pretty frickin’ clever.

It’s just not aliens.

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