I ran into a friend today on my walk. He was running down the Blaine Street steps just as I approached to walk up them. We walked up together.
He was carrying with him five small stones, pebbles really. Each one represented a trip down and then back up again. When we got to the top, he tossed it into a pile of stones that accumulated in a hollow at the base of a tree where two thick branches diverged. Then he had just four small stones.
Being a student of the computer sciences, I thought, does that mean he takes five or six trips? Do the stones count five to one or five to zero? Being not very good at the computer sciences, I presumed five trips.
Taking an extra trip at zero stones always feels to me like just that, an extra trip. This is why I’m bad at the computer sciences, because zero isn’t a number to me; whereas to computer scientists, zero is exactly one half of the only two numbers that make up all the rest of the numbers.
The numeral 0 as an integer seems to have worked its way into use in various mathematical texts roughly around the common era year 500, or possibly 600, but definitely by the year 700. Before that, one examined the context in which numerals were used. It was also common to count in sexagesimal, base 60, which is why there are sixty seconds in a minute, sixty minutes in an hour, and three hundred sixty degrees in a circle. Dividing circles into sixties is easier than dividing them into tens.
It’s also because counting on one hand to twelve is easier than counting to ten on two hands. One counts on the three finger bones, on each of four fingers of one hand, with the thumb. Do this four times and you’ve counted to sixty. Six times that is three hundred sixty.
And the world goes ’round.
Can’t quite do that in base 10. Not as easily anyway. Once we started doing fractions, though, base 10 really started to shine. That is, when we started using money. If I could get a shekel for every 160 grains of barley, great. But owing you a shekel that was worth 1/60th of a mana was a pain in the fingers. Owing you a shekel that was worth 1/50th of a mana, now that math could be done on paper. Heck, that kind of math could even be done quickly in the head and it would be easy enough for everyone to agree on the outcome.
It’s no great coincidence that the spread of mercantile mathematics, the base 10 numerical system, and monetary systems all evolved together.
We haven’t seen a corresponding computer-scienceization of custom. The common person still sees zero as a thing that isn’t done, instead of a thing that is.
When we make the move to qubits, we’ll have a zero that can hold a whole bit in itself. Then a light switch can be both on and off at the same time. As well, it can be off and off, on and on, and off and on.
At that point, I can tell my friend he needs only carry one quantum rock with him on the stairs.
On the first four trips, the rock will keep count of each trip. But on the last trip, he leaves the rock in the crook of the tree and runs down and back up alone.