@cstross My cat also chases his tail. He has a favourite toy that is one of those sort of fluffy tail things on a string on a stick that can be waved around. My 8yo son has taken to draping the string on the toy over the cat's back end so that he not only has his own tail to chase, he also has the tail on his toy that then follows him around. The result is somewhere between ecstasy and terminal confusion.