math tuesday

 In the beginning there were just the natural numbers, the numbers Joe Sixrock, sitting outside his cave, idly watching the clouds roll by in the sunny days of prehistory, and thinking why look now I have as many fingers up as those birds perched on the tree.  Then another alit and he put up another finger and now he was onto something.  He was counting.  As he was living in a hunter gatherer society he had plenty of time on his hands and he could have worked out all the mathematics that fill our university math libraries today. 

Well it would have taken some time and practically speaking he would have needed something to write all this down, but it was not a problem, because he wasn't interested in doing anything like that, he just wanted to keep track of things, and from what we know from current hunter gatherer tribes his numbers didn't exceed five or six and after that it was just many, and that was good enough for him.  

As we developed agriculture and now had things to count, it must have become obvious that we couldn't just go on thinking of new names for each number, and if you looked at a whole bunch of notches on a log you really couldn't tell how many there were without going through the arduous process of counting each one.  You needed some other kind of unit, and five became as clear as the back of one's hand.  Since you have two hands you get ten.  They could have included their feet and got to twenty, but they didn't, they stopped at five and ten, and then they had five tens (L) and ten tens (C) and five ten-tens (D) and ten ten-tens (M), and then I guess they had enough, though you can see that if they ever had to write a million they would be in a bind.  The Sumerians by contrast came up with a base of 60, and after all those years we still have 60 minute hours.

Just looking at those Roman numerals you have to think geez, isn't there a better way.  But those Romans were tough so nobody said anything until about five hundred years later when the Arabs were top dogs and one look at their number notation system and it was clear that this was a better way, and along the way the way the Arabs picked up the zero from the Indians, and now you could represent a million succinctly with 1,000,000.  Which is pretty nifty, but a billion becomes a little iffy.  You could use the exponential thing with 1*10^10, but eventually as you go higher and higher you are going to need an exponent for the exponent not to fill the page, and then you will need an exponent for that exponent, and so on and so on and dooby dooby do on.  Infinity is always a problem.