language of probability rather than the less-intuitive language of Lebesgue
measure.- Technically, the temperature sliding down from 70 degrees to 69.9999 degrees
is discontinuous unless it passed through every real number between 70 and
69.9999; this is a consequence of the intermediate value theorem for continuous
functions. The purpose of this illustration was to give the reader the idea of a
nonjumpy transition without getting overly technical. - One of these equations is the Navier-Stokes equation, a partial differential equa-
tion whose solution is one of the Clay Mathematics Institute’s millennium prob-
lems. - G. J. Sussman and J. Wisdom, “Numerical Evidence That the Motion of Pluto Is
Chaotic,” Science 241: pp. 433–37. - See http:// www .jaworski .co .uk/ m10/ 10 _reviews .html. I can’t believe this is still
around! - For those interested in reading further about the history and early development
of chaos, I recommend James Gleick’s Chaos: Making a New Science (New York:
Viking, 1987). Gleick is a terrific science writer, a worthy heir to Paul de Kruif,
Isaac Asimov, and Carl Sagan. Chaos has advanced considerably since this book
was published, though.
184 How Math Explains the World