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 . . .


14 thoughts on “One-Year War and Peace 11.1 – Calculus

  1. I, too, remember the Achilles and the tortoise paradox very well – and in fact was telling some friends about it only a week ago (although I have to confess that I was trying to explain it after maybe jut a few too many wines, and I think I even had the tortoise chasing Achilles at one stage). But it’s a good example of the limitations of our way of conceptualising and explaining things, which I guess is Tolstoy’s main point here – that we have to change our perceptions of things, because the ways in which we have traditionally explained and made sense of the world really just don’t accord with what’s really going on.

    In a way, I think the idea of tracing everything back to the beginning of everything is not exactly what Tolstoy means – I think what he is telling us here is that it is the totality of history, the totality of its components, that we have to look at, instead of the dog-chasing-its-tail futility of trying to understand how this event was caused by that event which was caused by another event. We need to understand the broader, bigger rules of history – the thyings that govern the masses, as he puts it.

    It’s interesting because, at the moment, I am also reading Trotsky’s “Revolution Betrayed” and he says almost exactly the same thing – that we understand the history (and, from Trotsky’s point of view, the destruction) of the post-revolutionary Soviet Union not by examining Stalin so much as by examining the people, and the class relationships, that supported him.

    I think that so far in War and Peace Tolstoy has been showing us how the big picture is made up of a billion little pictures. And now he’s moving on to explain to us that it’s the big picture that ultimately helps us to understand what’s really going on in all the little ones.

  2. Interesting point, actually, Ian. So in a way, with that kind of philosophy, War and Peace really *had* to be this long and have so many characters, because it’s Nikolai’s patriotism that sends him off to war, Dolokhov’s personality that makes him go reckless in battle, Andrei’s bitterness that makes him serve where he does, etc.

    And if we were to take the sum of all these little actions (plus the people we’re not even reading about), then we would get a picture of the overall flow of history.

    It’s funny, because it’s almost the complete opposite of a conspiracy-oriented view of history, where everything is being engineered by a few . . .

  3. Carly, thank you so much for this link. I am really tempted to give it a go, although I have to admit that all the technical requirements about recording it mean absolutely nothing to me. I couldn’t even tell you where the microphone is on my computer (but I know there’s one somewhere)!! But I am very tempted to try to overcome my technophobic inhibitions and become involved – I soooooo much love reading out the text of W&P! Thanks again!

  4. Well, I’d do it myself, just for the sake of helping to get the thing together, but I don’t have a good reading voice. I’m kinda’ scratchy – sometimes people call me SIR! Y’know?

    An old diehard smoker here.

    Actually, all you need is the mike – plug it in – wherever? Dunno’ . . . you can download a recording program from the web.

    They’re doing the MAUDE translation, btw.

    They have some good readers – and they’ve got some that are kinda’ hard to listen to.

  5. About the math?

    I’m not bad at basic math – multiplication, division, etal . . . but I never took calculus, algebra and all that jazz. Don’t regret it either – just looking at it gives me a headache.

  6. what were the key ideas of the chapter? and how did tolstoy apply his knowledge of calculus even though he did not become a scientist or an engineer

    1. Hi Wilson,

      It’s been so long since I read this chapter that I’d recommend just having a look at it yourself. It won’t really spoil any of the story for you, because it’s right up the end in the second appendix.

      Hi Carly! I should pick another book, shouldn’t I?

  7. I just got a notification on this thread . . . are we bringing it back up again? Or starting a new book? A new book would be a grand idea.

    BTW – hi, everybody . . . nice to see y’all again – especially you, Matt and my old pal, Ian.


  8. I want the spoilers, what were the key ideas and how tolstoy applied his knowledge of calculus even though he didn not become a scientist or engineer

  9. You’ll have to depend on Matt and Ian for that – I had no understanding of what that was all about. But Tolstoy sounded like a pretty smart man.

    When are they making that moooooovie? Anthony Hopkins was asked to play Tolstoy, but he ended up turning it down. I wonder if they’re going ahead with the movie – or maybe it’s already done?

  10. Wilson – sorry, mate, I’m not really into spoilers. It’s a tiny, short chapter, and you could easily look it up on Project Gutenberg and read it for yourself.

    Carly, if you’re talking about a movie about Leo Tolstoy, it came out last year, I believe, with Christopher Plummer as Tolstoy, and it’s called “The Last Station”. I haven’t seen it myself, but I think it would be interesting.

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