In a lecture at the University of Edinburgh in the 1970s, artificial intelligence pioneer I.J. Good pointed out that a robot cricket player doesn’t necessarily need a complex knowledge of physics in order to catch a ball — instead it might emulate humans, who follow a simple rule: “If the ball appears to be rising in the sky, run backwards. If it is falling, run towards it.”

Similarly, Hope College mathematician Tim Pennings noticed that his Welsh corgi, Elvis, seemed to follow the optimal path when chasing a ball thrown into Lake Michigan — Elvis seemed to realize that he ran faster than he swam, and so could minimize his retrieval time by racing intelligently along the beach before jumping into the water. But how did he make these judgments?

“We confess that although he made good choices, Elvis does not know calculus,” Pennings wrote. “In fact, he has trouble differentiating even simple polynomials.”

(Timothy J. Pennings, “Do Dogs Know Calculus?” College Mathematics Journal 34:3 [2003], 178-182.)

Here’s a little oddity that I just came across. John Conway’s Game of Life is a familiar recreation that takes place on a grid of squares. At the start each square is either “alive” or “dead,” and then on each turn the status of each square is updated:

1. Any live cell with fewer than two live neighbors dies (as if by underpopulation)
2. Any live cell with two or three live neighbors lives on
3. Any live cell with more than three live neighbors dies (as if by overpopulation)
4. Any dead cell with exactly three live neighbors becomes a live cell (as if by reproduction)

This produces some surprising creatures, such as the “glider,” a self-propagating “spaceship” that travels diagonally:

Gliders can be generated by an oscillating factory called a “gun”:

Here’s the oddity: It would seem that each gun will produce an infinite fleet, since its gliders all depart in the same direction. But that’s not true if the grid of squares is written on a torus — then the gliders snake around the figure and destroy their maker: