My 4.5-year-old, Devon, just told me "The twenty-first is the 20th." Translation: the first day of the "20's" is the 20th. Ranks right up there with my older boy's assertion that kids have kidneys; grown-ups have grown-up knees.

Suppose God gives Gabriel an ideal trumpet with radius 1/x feet, for x greater than or equal to 1. If Gabriel wants to embed the surface with gold, how much gold will he need? My calculus is a little rusty, but Bob Pease says that the surface area is the integral of 2 pi (1/x) dx, or ln x from 1 to infinity, which is infinite. The volume of the horn is the integral of pi (1/x^2) dx, or -pi (1/x) from 1 to infinity, which is only pi cubic feet. Gabriel can't plate the surface, but he can plug the horn solid and then ream it out. Weird. [Electronic Design, 9/12.]

-- Ken