Here’s a surprise: A new geoglyph has been found in the soil of the Nazca Desert in southern Peru.

This one, evidently a cat, appears to be the oldest yet — it may have been engraved in the earth as early as 200 B.C. and has been waiting all this time to be discovered.

“The figure was barely visible and was about to disappear because it is situated on quite a steep slope that’s prone to the effects of natural erosion,” the culture ministry wrote.

“It’s quite striking that we’re still finding new figures,” said chief archaeologist Johny Isla, “but we also know that there are more to be found.”

Back in 2009 I worried that, if vampires are constantly converting humans, eventually we must all succumb.

Apparently this fear is not unfounded. In 2006 physicists Costas Efthimiou and Sohang Gandhi worked out that if the first vampires had turned up in 1600, if they’d needed to feed only once a month, and if the world population at that time had been 536,870,911 (as estimated), then the vampire population would have increased geometrically and the last human would have succumbed in June 1602, after a bloodbath of only two and half years.

Worse, in 1982 a team of Austrian mathematicians led by R. Haiti and A. Mehlmann found that intelligent vampires could calculate a bloodsucking frequency that would maximize total utility per vampire and keep the human race alive indefinitely — and solutions exist no matter whether they’re “asymptotically satiated vampires,” “blood-maximizing vampires,” or “unsatiable vampires.”

Later they expanded on this to show that cyclical bloodsucking patterns are optimal. That’s not very comforting.

(Dino Sejdinovic, “Mathematics of the Human-Vampire Conflict,” Math Horizons 16:2 [November 2008], 14-15.)

Shuffle a deck and deal three cards face down. A friend looks at the cards and turns up two that are the same color. What’s the probability that the remaining card is also of this color?

The answer is not 1/2 but 1/4. Three randomly selected cards might have any of eight equally possible arrangements of color. In only two of these (RRR and BBB) are all the colors the same. So the chance of this happening is 2/8 = 1/4.

(Martin Gardner, “Modeling Mathematics With Playing Cards,” College Mathematics Journal 31:3 [May 2000], 173-177.)

10/18/2020 UPDATE: A number of readers have pointed out that the probabilities here aren’t quite accurate. Gardner was trying to show how various mathematical problems can be illustrated using a deck of cards and contrived this example within that constraint, focusing on the “seeming paradox” of 1/4 versus 1/2. But because the cards are dealt from a finite deck without replacement, if the first card is red then the second card is more likely to be black, and so on. So the final answer here is actually slightly less than 1/4 — which, if anything, is even more surprising, I suppose! Thanks to everyone who wrote in about this.