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"The movement of humanity, arising as it does from innumerable arbitrary human wills, is continuous. To understand the laws of this continuous movement is the aim of history. . . . Only by taking infinitesimally small units for observation (the differential of history, that is, the individual tendencies of men) and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history"

-Leo Tolstoy, war and peace

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What's the difference between metaphor and analogy? –  Mitch Jul 9 '11 at 1:34
    
@Mitch: Feel free to ask that as a Question. But briefly, I think an analogy generally involves a more extended comparison than a metaphor. In OP's case it's a close-run thing, but I'd call it analogy because the nature of the correspondence is sufficiently complex that Tolstoy feels he needs to use quite a lot of words to guide the reader into his meaning. –  FumbleFingers Jul 9 '11 at 13:51
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I would say it's an analogy, which generally in literature implies the primary subject being compared to something more familiar, in hopes of conveying insights into the true nature of the subject.

In Tolstoy's case, it doesn't matter that his audience probably aren't particularly familiar with differential calculus. He explicitly defines the feature relevant to his analogy; exacting measurement of tiny differences enables one to graph a complex function to present a revealing image.

His purpose being to show that a true understanding of human history in the global and long-term sense can best be achieved by focussing on the minute particulars of specific incidents involving particular people at some given place and time.

Today he'd be more likely to use the analogy of a hologram, which has the interesting property that if you shatter it, you can still retrieve the whole original picture from each small part.

Unfortunately for Tolstoy (who had no great reputation as a mathematician), measuring exact values anywhere on the line of a complex function doesn't actually tell you much about what may happen elsewhere on the graph. And the smaller the piece of broken hologram you look at, the fuzzier the image you can get from it becomes. It's not an analogy that can be taken too far.

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+1 Very nice. .. Very nice.... –  Thursagen Jul 9 '11 at 1:17
    
@Ham and Bacon: I expect someone who knows more than me about calculus could pick me up on the details of that bit. But I'm pretty sure about the holograms, and about what Tolstoy was trying to convey. So I reckon he would have liked that analogy even better if he'd known of it. –  FumbleFingers Jul 9 '11 at 1:44
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I would call this an implied metaphor. Without actually declaring the comparator, Tolstoy is likening humanity to something massive and moving, possibly a river or a glacier — in any case, something composed of minute forces that push the mass along. He then suggests that a kind of calculus could be applied to the progress, measuring smaller and smaller bits, until a larger pattern emerges.

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You read a lot into the word movement, an almost imperceptible 'metaphor' which I think is not central to the passage. The focus is on comparing the study of human affairs on a global scale to calculus; I suggest this is best called an analogy. –  FumbleFingers Jul 9 '11 at 1:17
    
@FumbleFingers: Funny, I thought I mentioned calculus in a third of the sentences I wrote. –  Robusto Jul 9 '11 at 3:06
    
Of course. But the way I read it, most of your answer is taken up with the metaphorical use of the word movement. All that you say is true; I just didn't think that first part was likely to be what OP meant when he asked whether the passage was a metaphor or an analogy. I may be wrong, of course, but I still think it's only the calculus bit he's asking about. –  FumbleFingers Jul 9 '11 at 3:19
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