Reading for Friday, 13 February
My first year of university came back to me in this chapter (along with my recent reading of the book, Mathematics: Is God Silent?) with Tolstoy’s example of Achilles and the tortoise.
This was actually an ancient Greek mistake which they made. Back in those days, they didn’t have a concept of a limit – which in mathematics means (very roughly) that if you add increasingly smaller numbers to something, eventually you’ll head towards a single number called the “limit”.
Before they knew about this, the Greeks had this conundrum that if Achilles (who runs 10 times the speed of a tortoise) and a tortoise were in a race and the tortoise was given a head start (let’s say 100 metres), then the tortoise would always win. The logic went something like this:
Let’s say Achilles can run 10 metres per second and the tortoise can go 10 centimetres in one second (which is actually a fairly fast tortoise, now I think about it, but I can’t be bothered changing the numbers now) then in 10 seconds, Achilles would have run 100 metres. But the tortoise, in the same time, would have been one metre ahead.
And by the time Achilles ran that one metre, the tortoise would have gone a tenth of a metre forward. So, logically speaking, the Greeks said, Achilles could never overtake the tortoise.
Now, you and I might have thought that the logical solution to all of this is to get a fast runner down and a tortoise and see who wins . . . not so the Greeks. Their thinking was that if logically speaking the tortoise would win – that was the truth – regardless of what evidence in the physical world might exist to the contrary. To them, the logic was more important than explaining the real world with it.
Anyway, fascinating story, but Tolstoy is here using it in a larger sense to talk about the continuous flow of history and that you can’t really look at things in little segments, but need to look at things continuously. I must admit, it is a mind-blowing concept when you think how many things were caused by a little something somewhere else which caused something somewhere else, which had an influence somewhere else. All of these things could be traced back and back and back until – yes, it can sometimes seem hard to come to an ultimate cause for any particular little event (except for a God who organised the whole thing, which is what Tolstoy hints at).
But, in his view, no one person can really be claimed to have caused anything – least of all a general, which leads us into the next chapter . . .