Department of Analogies
Sarang, in comments, says:
"I should point out that I _don't_ think my objections are of the pedantic-asshole type. As I see it, the macro-regularities follow certain laws and the micro-regularities follow some, apparently entirely different, laws. You can pretend that these sets of laws are 'continuously connected,' but as far as I can tell, they are entirely different, and also as far as I can tell, there's a watershed at say N = 10000 people at which the micro-laws cease to be continuously connected to the macro-laws."
No one is accusing Sarang of asshole pedantry (pederasty is another matter). But let me say what I think Tolstoy's analogy is and isn't doing.
I think Tolstoy is primarily objecting to the idea that particular events happened because Napoleon did one thing and not another. And indeed, Napoleon did have command of an empire, and his whim really did matter. But Tolstoy would say, I think, that Napoleon's control of his empire, and his army, depended on everyone obeying his orders, which in turn depended on their own decisions, their own "will." You can't understand the French invasion of Russia merely by reference to Napoleon's ambitions.
A true account of the French invasion would be much more fine-grained. Why did each soldier choose to obey his orders (or why did some desert, or whatever)? Why did gun-makers make the necessary guns? Why did so many non-French serve? etc. etc.
But anyway, I think continuity of historical theories is actually a red herring. It may be that as you include more and more dimensions in your model, you get discontinuities, and I don't think it matters. The point is to abandon crude, "discrete" accounts of history and embrace the multitude of factors that come into play. In my analogy, to zoom in, to take a close look at each section of coastline, to avoid the easy "because Napoleon said so" answers.
And I think ultimately the upshot is that history is intractable. History is the confluence of so many individual decisions and outcomes that the only true depiction of the world is the world itself. One can only zoom in so far before outstripping one's data and ability to process it. And this is my problem with Tolstoy's stance - I think he overreacts to the "great man" theories of history that repulsed him. In a sense, he was dealing with the same issues that Krugman deals with in, again, my favorite Krugman essay.
You understand history as well as you can with the tools you have. But remember, Tolstoy was writing at a time when it was becoming feasible to understand things much better than previously. His desire for a more continuous account of history is entirely understandable and defensible.
And, finally, the literalism of his analogy - sure, he doesn't seem to have been up to speed on calculus (though who am I to criticize?). But War and Peace is a novel (or an epic, or whatever Tolstoy thought it was). And this isn't a case of Tolstoy making sweeping statements about a discipline he knew nothing about, as with the Sokal hoax. In the first place, Tolstoy isn't commenting on mathematics, he's commenting on history, which, given the setting of War and Peace, I think he earned the right to do. Additionally, I think his commentary is at the very least coherent and informed, which is apparently not true of the commentary protested by Sokal.
So I don't think literalism is called for. At the very least, I feel that I got something out of the analogy. It reflects the philosophy that Andrei had embraced during the invasion, and I think it's something we've all thought about in one form or another. I'm actually thrilled to be able to see something the way Tolstoy saw it, even if I can't be sure that I precisely appreciate his point.
"I should point out that I _don't_ think my objections are of the pedantic-asshole type. As I see it, the macro-regularities follow certain laws and the micro-regularities follow some, apparently entirely different, laws. You can pretend that these sets of laws are 'continuously connected,' but as far as I can tell, they are entirely different, and also as far as I can tell, there's a watershed at say N = 10000 people at which the micro-laws cease to be continuously connected to the macro-laws."
No one is accusing Sarang of asshole pedantry (pederasty is another matter). But let me say what I think Tolstoy's analogy is and isn't doing.
I think Tolstoy is primarily objecting to the idea that particular events happened because Napoleon did one thing and not another. And indeed, Napoleon did have command of an empire, and his whim really did matter. But Tolstoy would say, I think, that Napoleon's control of his empire, and his army, depended on everyone obeying his orders, which in turn depended on their own decisions, their own "will." You can't understand the French invasion of Russia merely by reference to Napoleon's ambitions.
A true account of the French invasion would be much more fine-grained. Why did each soldier choose to obey his orders (or why did some desert, or whatever)? Why did gun-makers make the necessary guns? Why did so many non-French serve? etc. etc.
But anyway, I think continuity of historical theories is actually a red herring. It may be that as you include more and more dimensions in your model, you get discontinuities, and I don't think it matters. The point is to abandon crude, "discrete" accounts of history and embrace the multitude of factors that come into play. In my analogy, to zoom in, to take a close look at each section of coastline, to avoid the easy "because Napoleon said so" answers.
And I think ultimately the upshot is that history is intractable. History is the confluence of so many individual decisions and outcomes that the only true depiction of the world is the world itself. One can only zoom in so far before outstripping one's data and ability to process it. And this is my problem with Tolstoy's stance - I think he overreacts to the "great man" theories of history that repulsed him. In a sense, he was dealing with the same issues that Krugman deals with in, again, my favorite Krugman essay.
You understand history as well as you can with the tools you have. But remember, Tolstoy was writing at a time when it was becoming feasible to understand things much better than previously. His desire for a more continuous account of history is entirely understandable and defensible.
And, finally, the literalism of his analogy - sure, he doesn't seem to have been up to speed on calculus (though who am I to criticize?). But War and Peace is a novel (or an epic, or whatever Tolstoy thought it was). And this isn't a case of Tolstoy making sweeping statements about a discipline he knew nothing about, as with the Sokal hoax. In the first place, Tolstoy isn't commenting on mathematics, he's commenting on history, which, given the setting of War and Peace, I think he earned the right to do. Additionally, I think his commentary is at the very least coherent and informed, which is apparently not true of the commentary protested by Sokal.
So I don't think literalism is called for. At the very least, I feel that I got something out of the analogy. It reflects the philosophy that Andrei had embraced during the invasion, and I think it's something we've all thought about in one form or another. I'm actually thrilled to be able to see something the way Tolstoy saw it, even if I can't be sure that I precisely appreciate his point.
posted by James | 10:18 PM
10 Comments:
James, what's pederasty?
One of Sokal's targets was the use of ill-conceived scientific analogies to shed prestige on dumb humanities arguments. Tolstoy's calculus analogy falls squarely into this category.
I think that coarse- and fine-grained views are capable of coexistence; one has a theory of why soldiers obey orders and a theory of wars that assume they do obey orders.
Perhaps Tolstoy's arguments served a useful polemical purpose way back when, but I've always seen them as being just a lot of handwaving about historical necessity. Also, as you appear to agree, continuity -- which, if anything, is what the analogy is about -- appears to be a red herring.
Continuity has a precise meaning, if I remember correctly - something about the limit of y as x approaches a particular value from each side being the same as the actual value of the function at that point. I could have that wrong, but anyway that's the sense in which I think continuity is not particularly important. So for instance, if taking into account an additional dimension leads to a qualitatively different conception of history, then I don't think that's problematic for Tolstoy's analogy.
I take it that Tolstoy is railing against incomplete answers to historical questions - answers that are arbitrarily truncated. And this truncation is, in the analogy, the imposition of discreteness on a phenomenon that is actually continuous. Procrusteanism.
The analogy works for me, perhaps because this is the way I was taught calculus. We started with a problem that had to be solved, and we saw that the answer became more accurate as we divided up the graph into more and more pieces. Then we took the limit as the number of pieces approached infinity, and got our answer.
So basically, Tolstoy is urging us not to look for one explanation, or two explanations, but rather to recognize the multitude of causes that bring about each event. The more we take into account, the more complete and accurate our picture becomes. This may not be "continuity" in the technical sense, but it's easy to see how one's explanations can be more or less fine-grained.
Now, as Sarang has pointed out, there are all kinds of problems with this. Tolstoy was apparently wrong about infinitesimals, for instance.
But I don't think Tolstoy's view of history was dumb, even if I think it was problematic. And I don't think the analogy was ill-conceived, because it fulfilled its purpose, at least for me. It took an idea that was familiar to me and used it to explain an idea that was not. I don't think you should ask much more of an analogy than that, but this one happened to be aesthetically pleasing to me as well.
I feel that in the process of defending the analogy you've severely attenuated Tolstoy's point. The original idea was that fine-graining and integrating would permit one to address previously intractable problems, "just as" calculus allows you to solve Zeno's paradox. Read this way, the analogy connects a rather wild-eyed historical claim to a fallacious scientific one. Taken your way, the claim seems almost tautologous: more information usually means a more accurate picture.
But whatever. I don't want to insist that Tolstoy's theory of history is dumb, not least because it's been years since I read W/P and I skipped over large tracts of historical theorizing.
Stop procrustinating.
Right, but I think Tolstoy was correct, so far as it goes. You really can't fully understand history without doing what he suggests. My own objection is that there is a tradeoff, that one can only spend so much time and effort on understanding history. A partial understanding will have to do (and for many purposes will suffice).
So I think one can take his point to be that, since we can't differentiate and integrate (or whatever), we can't really comprehend history. And you can disagree with that, but it's an interesting idea and one that is reflected in the viewpoint of Andrei and, to a lesser extent, Kutuzov.
Well, if no one else is going to assume the mantle of pedantic asshole...
This debate is going nowhere.
I stand by my original reaction, that Tolstoy sought to imbue a simple idea with profundity by cloaking it in ill-fitting finery.
So I suppose my position is somewhere between you two's.
I mean, it's obvious that history is "intractable" in the sense that we can't completely know the state of the (relevant) world at any given point in time, much less over a period of time. We have to essentially use a model, whose design should be based on our ends. Illustrating the non-discrete nature of history via comparison to the fundamental achievement of calculus is, though not inaccurate, something of an indiscretion.
Now you may object that I'm torching a straw man. You may say: "No, the beauty/utility of the analogy is that it elegantly elucidates the underlying misconception of Napoleocentric theories -- it reveals that someone whose view is too sweeping is overlooking the dust of history. In other words, Tolstoy really brings home the point."
And then some. He proves too much. The thing is, it's impossible to "integrate" history, and it's silly to think that good history should strive to do so. The search for explanatory power is not coextensive with the search for information. Like I said on day one, "there are useful models, and there are stupid ones." Not much going on here.
But Tolstoy doesn't get it. He epically concludes: "Historical science in its movement always takes ever smaller units for examination, and in this way strives to approach the truth."
And Dean Keaton replies: "No, you're missing the point."
Don't miss the forest for the analogy.
Not to put too fine a point on it, but I agree that more detailed and nuanced accounts of history are on balance better, that people should check their assumptions against reality, etc.
You just can't say anything worthwhile without some approximation, and if you know how you're going to approximate, it makes sense to make a smooth map of certain parts of the coastline.
Or something.
Alan -- I think my last post _was_ basically giving up on the debate. I think my position on this is substantially the same as yours with some expletives thrown in.
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