Δαφνη Ευτυχια Αρθουρος

After rehearsal, justgus37 and I grabbed a bite to eat. And we chatted about number systems and computers. A tangential comment led to musing about the meaning of a base with a non-integer radix. So we spent a while trying to figure out how to count in base-two-and-a-half.

It had been a while since I played with math (as opposed to using it or teaching it). I'd remembered it was fun, but I'd forgotten how intoxicating it can be. That giddy feeling as something surprising suddenly clicks into sense. "Drunk on math". We were entertained by the discovery that in a non-integer base there will numbers with lower values than shorter numbers -- that is, a number N digits long that is less than a number N-1 digits long (for example, 100_{two-and-a-half} < 22_{two-and-a-half} ... note that 100_{two-and-a-half} = 6.25_ten, and 22_{two-and-a-half} = 7_ten). Once I've closed a few of the too-many open browser windows, I'm going to have to ask Google what's already been written on this subject.

It seems somehow fitting that the place where we were discussing this is called Plato's.