Joel: >> Really? So what is the exact circumference >> of a circle with a diameter of 2 inches?

Karl: > 2pi. Russell: > The exact circumference is pi. Really, where did you > learn your mathematics! And please explain for me how this calculation involved the continuum or infinite binary expansion of the symbol "pi" in any meaningful way. All you have really said was: 2 * broccoli = 2 broccoli I am unimpressed. It seems to me there is a great deal more information in PI than just the 2 bytes it takes to convey it in an email message. Maybe Mathematica was a poor choice for your counterexample, since it too runs on discrete hardware and software that could easily be run on a CA. So far you have not convinced me that a CA could not perform these same calculations. Do you have some other example? Joel