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 
It’s just not aliens.
