OK, guys, we’re about to get really heavy here. Put on some incense, pull out the floor pillows, and sit down in your best thinking pose – this chapter is about to bust out some grade-A philosophy.
So, have you heard the one about Achilles (super-human Greek soldier from the Trojan war) and the turtle (really slow animal with a big shell)? They decide to race. Turns out, if the turtle gets a head start of about ten feet, Achilles can never catch up with it. By the time Achilles moves ten feet, the turtle has already moved ahead six inches. By the time Achilles moves six inches, the turtle has already moved half an inch. By the time Achilles does that half an inch, the turtle has already moved a hundredth of an inch. He moves a hundredth, it moves a thousandth. And so on and so forth. This was a famous ancient Greek conundrum that seemed to have no solution. On the one hand, we feel like that must be wrong – obviously fast Achilles can catch up with and overtake the turtle. But on the other hand – look at the math. It all seems to check out.
The solution is that the puzzle ignores the way time actually flows. By breaking time down into smaller and smaller units, it ignores basic rules of continuity – which is actually its own mathematical concept (the idea of limits that calculus differentials and integrals explore).
Right, OK then. One question though: what does all this have to do with War and Peace?
Tolstoy says that another place we see this same mistake of breaking continuous time into fake units is in the study of history. When we decide to study some big historical event – say, a war – we automatically give it some kind of starting and ending point, as if that’s how time and human actions really occurred. Tolstoy argues that you can’t do this without sacrificing meaning. If we throw away what happened before our arbitrary starting date, then we’re necessarily going to come to a lot of false and mistaken conclusions about causes, effects, and what happened because of what.
He proposes to go with calculus instead of the Achilles-turtle branch of math – to break time up into little tiny fragments, but only with the idea of then somehow putting them all back together into something as close to a universal presentation of history as possible. This kind of history would have to include not just the VIPs like Napoleon, but also the peasants and low-level soldiers around him.
Huh. Interesting, no? How is history different when we include the thoughts and actions of usually ignored groups of people?