Touching all the bases

Most people these days count in base ten. And most computers count in base two. In school we learn that there are other possibilities: like base one, or three or four or five. But nobody ever talks about base 1.7, or base 3.4, do they? Why is that? At this point you might be thinking “why would anybody want to count in base 1.7?” That’s a very sensible question. Well, ok then, I’ll tell you.

Let’s take the number 42 for example. It has two digits in base ten, right? Well, in base two it has six digits – 101010₂ – in base three it has four digits – 1120₃ – and in base four it has three digits – 222₄. In base one it’s a lot bigger:

That’s 42 zeros, in case you were wondering. But suppose you wanted to use about twenty digits to represent 42? Then you might want something between base one and base two.

Does this sound crazy? Well, it will probably get crazier. Tomorrow I’ll talk about why I’m thinking about this. It’s a tale that goes from brains that overheat when they think too hard, to problems with grandmothers, to computers that learn on their own, to armies of short people in elevators.

All this and more! Stay tuned.