Friday, May 14, 2010

We simply move forward in a rather unimpressive fashion

A number of years ago I read Horst Althaus's Hegel: An Intellectual Biography, and I recall being struck by a short passage concerning Hegel's intentions to visit Bamberg.  The episode was relatively inconsequential, but it has been the one point of the book that has remained with me in a very significant way.  In correspondence with Schelling in 1800 he writes,
"I am looking for inexpensive board, the opportunity of good beer for my physical constitution, the chance of meeting a few people", and then significantly adds: "I should prefer to live in a Catholic rather than a Protestant town; I should very much like to observe that religion at first hand."  What he was looking for, and later avowedly found, in Bamberg was 'Catholicism' as an unadulterated expression of the 'mediaeval world', as one particular stage in the course of 'world history'.  He was willing to expose himself directly to the phenomenon in order to experience it for himself as a still living and experienced reality. (46)

Taken without too much reflection, this sort of idea sounds perfectly normal.  In the United States, a possible analogy (at least for someone like me who grew up on the East Coast) might be traveling to Lancaster, Pennsylvania to encounter in the Amish an earlier world "as a still living and experienced reality".

A moment's consideration, however, will present the idea as absurd.  Georg Hegel and the Catholic townspeople of southern Germany were all just as much present at the turn of the 19th century; in the same way I am no more at home in the 21st century than an Amish family that doesn't use electricity.  The corollary can also be affirmed, that the 19th century Catholic is as little "medieval" as is Hegel himself.  Time doesn't eddy for the sake of particular communities, nor is anyone ever "ahead of their time".  We simply move forward in a rather unimpressive fashion, all of us just like everybody else.

Of course, the reason why Catholicism was for Hegel a window to the past is obvious enough... I'm not saying the man made no sense.  Periodization is not strictly the same thing as timing, and someone could conceivably be described as "medieval" on the basis of their culture if it were in some sense true to the culture of their chronological predecessors.  A tradition needs to be identifiable with its origins by some sort of transaction in order to be identifiable at all.  But this shouldn't blind us to the fact that we are all equally up-to-date (in the literal sense) without even trying.  Merely by maintaining a pulse we stand on the cutting edge of the entirety of human history.

This realization should deflate two opposing tendencies: nostalgia, whereby we seek either a return to the past or a return of the past in the present; and progressivism, whereby we understand the present and posturing towards the future as identifiable with certain particular causes or technologies.  Both of these tendencies conveniently forget that our neighbor occupies the same position that we do, and that this temporal solidarity can't be abrogated by the mythology that we have attached to our understanding of what counts as out-dated or contemporary.

On the other hand, this realization can open up two possibilities that both oppose these unhelpful tendencies and can stand complementary to each other: we can recognize the continuation of past practices (however quaint it may seem) as coherent and good within the present so long as it contributes to edifying interaction with our circumstances, and we can recognize the break with past practices (however severe it may seem) as worthwhile so long as it is adequate for the preservation of meaning and the fulfilling of work within the world that we now face.

17 comments:

  1. I lived across the street from Colonial Williamsburg for four years and I can tell ya - the past ain't what it used to be.

    That having been said, can't we at least speak in terms of averages? Isn't progressivism viable if we say that the average technological development is moving upwards and onwards, and if we look to the future for the fulfillment of that expectation? Isn't it plausible to understand nostalgia as a cultural restatement of the principle of entropy? It seems to me that as long as we set the parameters of what we're talking about clearly enough, the concepts are still useful.

    Or, we can ditch these Newtonian proclivities, embrace Einstein, and declare (hopefully not too ethnocentrically) that culture moves through time at different speeds and any visual evidence to the contrary is an illusion. The fabric of culture-time is actually distorted by the gravity of gesellschaft.

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  2. Evan,

    I'm not sure if I understand your distinction between 'periodization' and 'timing'. There is a sense, an almost mechanical (and therefore almost meaningless) one in which we have temporal solidarity, according to which we all human beings are just alive accidentally at the same time. But I gather that you mean, really, much more than just temporal solidarity, but something thicker, something existential or cultural, gesturing at some shared background that makes our apparent differences fuse, if only just a bit, sufficient for collective enterprises.

    If that's right, then I can't make good sense out of the rest of what you are say. The temporal homogeneity you describe cannot produce or account for the variation that we know is actually real variation (which I know you know is real). There's an important point to make about the self-deception among contemporaries who don't recognise themselves in their supposed opponents—a real problem, yes. But if I were actually to believe that we're all equally up-to-date, all in the same position, etc., so that, e.g., the Amish are just as at home in the 21st as the urban, then I wouldn't be able to make that important point.

    If that were the case, the sort of temporal solidarity you describe (if I understand you) would be conceptually sterile, which, in contrast to your intention, I imagine, is nicely evoked by the imagery of a shared pulse. Not really much solidarity, that. Certainly, I don't think that it is doughty enough to fend off nostalgia and progressivism, real problems, I think.

    I’m not convinced, however, that they are problems insofar as they don't recognise that we are all engaged in a world we share at the same time, or something like what you’re getting at. The reason I'm unconvinced is because we understand our world, we interpret it, in light of how we understand its coming about and its potential for further goings on. The laudator temporis acti understands his world more in respect of its past, the Whig more in light of where she senses it is going. None of us though understands it just in terms of the present moment. Indeed, we can't so understand it. If we think we can, I would begin to try to evoke the implicit ways we narrate the past we imagine as having taken place, and the future we imagine will, or would like to see, take place, the ways which are covered over by our ahistorical self-understandings.

    I like your writing, by the way.

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  3. There are too many good points here. I have a feeling this will be a long response. I'll respond to Daniel here and follow up with Adam.

    That having been said, can't we at least speak in terms of averages? [...] It seems to me that as long as we set the parameters of what we're talking about clearly enough, the concepts are still useful.

    Of course this is the case, and that's why I said that Hegel made some sense in what he was doing. I also have no problem in speaking of directional development that can point us into the future ("medical technology has increased life expectancy by 5 years and we expect such developments to continue if x, y, z", etc.). Saying that things were done better in a certain past society is fine too, and if we want to make that what nostalgia means, then that's fine too. The point, as you said, is to set parameters. The parameters you set don't seem problematic alongside the parameters I'm trying to explain away, however. I think I can totally affirm them.

    Or, we can ditch these Newtonian proclivities, embrace Einstein [...]"

    The thing is, this is neither Newtonian nor Einsteinian. At the very most, Einstein might buy one culture traveling corporately at incredibly high speeds across the galaxy a few seconds over another culture... if you can explain how that changes very much of my point, I'm all ears. The analogy you make brings in something different, a "culture-time", and I'm not sure that this changes my point. I'm perfectly willing to recognize that Lancaster County and Washington D.C. are quite different cultures, and that some sort of cultural "gravity" of modernity might be working on the difference. But calling this thing temporal doesn't make it so.

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  4. There is a sense, an almost mechanical (and therefore almost meaningless) one in which we have temporal solidarity, according to which we all human beings are just alive accidentally at the same time. But I gather that you mean, really, much more than just temporal solidarity, but something thicker, something existential or cultural, gesturing at some shared background that makes our apparent differences fuse, if only just a bit, sufficient for collective enterprises.

    The sense I’m going for is the “mechanical” sense that you refer to, although I don’t see how it’s almost meaningless. An Amish man and I can share a meal with one another, while I can’t do the same with a similarly suburban, college-educated library staffperson who happened to die ten years ago. I can enlist in the Army and kill a man in Iraq, but there is no way that an American living in the 1890’s could be killed by AIDS. Now, these accidents of time are of course not especially meaningful insofar as formative influences can be transmitted without any sort of personal coexistence… I might very well be more greatly influenced by the family traits passed down by a great grandfather I never knew than by a coworker that I see every day. But I’m not trying to argue against cultural difference or traditional influence. I’m simply saying that I am of my coworker’s context in a way that I will never be of my great grandfather’s. And I think I would want to affirm quite the opposite of what you say in your last sentence here… we have the collective enterprise already simply by the accident of temporal solidarity. There’s no fusing of difference here, because the temporal co-existence is immediate and effortless. There is no process involved that prepares me to be able to have a meal with an Amish man. The solidarity doesn’t have to be “thicker” than any difference, because it’s there regardless. And the differences are neither simply apparent nor in need of being “fused”… I’m happy to let them be as they are.

    The temporal homogeneity you describe cannot produce or account for the variation that we know is actually real variation (which I know you know is real). […] if I were actually to believe that we're all equally up-to-date, all in the same position, etc., so that, e.g., the Amish are just as at home in the 21st as the urban, then I wouldn't be able to make that important point.

    But the Amish are at home, aren’t they? They’ve never struck me as fearfully out of place, at least. What I think you mean is that they are not as at home in an urban context as an urban person is, and that’s perfectly true, and vice versa. But I’m not clear on what this has to do the 21st century in particular. Aren’t we simply establishing cultural difference here? My concern is that cultural and temporal identity is being fused, and that seems to be what you’re doing here as well.

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  5. If that were the case, the sort of temporal solidarity you describe (if I understand you) would be conceptually sterile, which, in contrast to your intention, I imagine, is nicely evoked by the imagery of a shared pulse. Not really much solidarity, that. Certainly, I don't think that it is doughty enough to fend off nostalgia and progressivism, real problems, I think.

    Again, the point may be underwhelming and so “almost meaningless” or “conceptually sterile”. That doesn’t really concern me. I’d hardly want to bother with treating the fact that we are both living alongside one another as anything philosophically significant in itself. It simply happens to be the case. What fends off nostalgia/progressivism, however, is not that our temporal co-existence is something monumental, but rather that simply as a boring old fact of the matter it renders certain things incoherent, like the idea that an Amish person is “from another century”, or that we’re going to bomb Afghanistan “into the Stone Age”. What is incredible is not any sort of realization of solidarity. Rather, that is mundane, and by paying more attention to it we realize that our application of temporal concepts to non-temporal differences is in-credible.

    I’m not convinced, however, that [nostalgia/progressivism] are problems insofar as they don't recognise that we are all engaged in a world we share at the same time, or something like what you’re getting at.

    Certainly Hegel didn’t really think he was going back in time. In that sense, of course you’re right and I wouldn’t disagree. The point is to scrutinize our conceptualization of things, however, because while we may recognize a shared world, our patterns of thought may also mean that we forget as well. My concern is not that we would fail to predict ourselves bumping into someone walking in the opposite direction on the street. Of course there’s recognition of mutual presence. The question is how significant that recognition is allowed to become for more complex relationships. As cultural difference is expressed in temporal terms so that we have two modes of temporality in play, the risk for subtle confusion inevitably increases a bit. Really (and perhaps it’s just because I have him on the brain from last week’s readings), this is similar to Henri Bergson’s concern about conflating time with space… when something unextended is understood as extended, pseudo-problems like Zeno’s Paradox are introduced.

    The reason I'm unconvinced is because we understand our world, we interpret it, in light of how we understand its coming about and its potential for further goings on. The laudator temporis acti understands his world more in respect of its past, the Whig more in light of where she senses it is going. None of us though understands it just in terms of the present moment. Indeed, we can't so understand it.

    Quite right. I’d agree with everything you say here, and I don’t think anything I’ve been arguing contradicts any of this.

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  6. Another useful question to think about might be... how are the differences that you two seek to preserve against my supposedly homogenizing talk of "temporal solidarity" not fully accounted for in the last paragraph of my post?

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  7. Can you say something basic about Bergson's understanding of the conflation of temporal and cultural concepts? I know he thinks it is deleterious, and the distinction is obvious enough. But I gather from what little I've read of him that he thinks it's consequential.

    I'll respond at greater length later.

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  8. The work that struck me as analogous was Time and Free Will, although I have not read much more of Bergson and duration certainly continues to be a theme elsewhere. Here Bergson is concerned about time being understood as measurable like space is... as an extensive phenomenon that can be divided out by, for instance, the hands of a clock or the swings of a pendulum, rather than duration, "the form which the succession of our conscious states assumes when our ego lets itself live, when it refrains from separating its present states from its former states" (100). The concern about spatializing time as a shorthand is that it creates misunderstandings about time, like Xeno's paradox where Achilles never catches the tortoise because as he overtakes previous steps of the tortoise he is always faced with new ones that were gained in the meantime. The paradox can only surface by "forgetting that space alone can be divided and put together again in any way we like, and thus confusing space with motion" (113-14). (apologies for all the quotes... I haven't been too long in the school of Bergson, so I'm trying to reassure myself by buttressing my own account a bit)

    Solving silly paradoxes like this may not seem especially meaningful... it's not any more incredible to say that Achilles overtakes the tortoise than to say that an Amish man and I are living at the same time... but again, it's the mundane point that realizes how in-credible certain misunderstandings really are. Bergson's eventual concern is to present the problem of free will and determinism as a similar pseudo-problem, which is created by understanding time as a succession of extended and divisible simultaneities liable to prior determination.

    Understanding cultural difference in terms of temporal difference is a similar sort of unhelpful conflation, although if we go too far with the Bergson analogy we will have to establish a better vocabulary, because I've already begun to go down a different track than him. Bergson, for instance, wants to move away from time as a succession of separable simultaneities, where as I'm using a simultaneity... Hegel and the Catholics in 1800 or the Amish and myself in 2010... to point out my own distinction. Also, Bergson and I are using "homogenous" in different ways... again with me using it (although following your lead) to distinguish (folks across time all being a part of one temporal home distinguished from cultural difference) whereas he used it as a marker for the unhelpful conflation (time being seen as a homogenous backdrop of the sort that space is).

    So I'm not using time in the same way that Bergson is (although I think I could get us on the same page easily enough). In fact, I may be making something of the opposite point... that "space" is being understood in terms of "time" rather than the other way around. That is, communities with differing practices in different spaces (here in the city or in rural Pennsylvania, Protestants in Frankfurt or Catholics in Bamberg, etc.) are being understood as in different times ("not at home in the 21st century" or "a living medieval community"). There is an underlying unity of argument, however, because just as in the example of Xeno's paradox where Bergson points out that space but not time can be rearranged as we choose, I'm also saying that space (various cultures spread out and intermingling) can be rearranged as we choose, but not time (we can't simply place an Amish person out of the century that we all share just as fully and comfortably).

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  9. It's also worth noting that, far from flattening human communal experience as simply a homogenous moving-forward, my argument here is trying to create conceptual space for a more textured and diverse account of our world. The heart of my point is that our century has room for more than simply technocratic city folk, just as Hegel's century had room for more than simply cosmopolitan Protestants. I'm trying to draw attention to the artificiality of saying that any time has non-temporal criteria for establishing its own legitimacy. The point is not to say that it's a small world after all... quite the opposite, actually.

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  10. First, I should say I mean 'homogeneity' here rather basically (being 'the same, immediate source of something'), innocent of connotations of ideological activity (which, I forgot, is the vogue the verb form has enjoyed for some time).

    Thanks for your Bergson summary. That's helpful. He seems to me, so I will read him one day. For the meanwhile, however, I look askance at his attempt, as with all attempts by philosophers, to show how problems, especially enduring ones, are really pseudo-problems; I wish others would be similarly incredulous with me. I don’t think big problems can in fact be gotten rid of in this way; historians know this well. If avoidance of the problems of free will and determinism is the terminus ad quem of Bergson's critique of the spatialising of time, then I come to suspect his critique. And like you said, it's little reward that following him here somehow unravels Zeno's paradox.

    But if--if Bergson's critique of the spatiality of time is weak, then this might adversely affect your own variation on it, which criticises the identifying of cultural differences with temporal ones. You say that such an identity is absurd, when clearly it is not, as you seem to say also: for Hegel made some sense, you admit, in what he was saying.

    So I can't gather from what you're saying that you really think that the application of temporal concepts to cultural differences is incoherent, unbelievable, incredible. Misunderstandings between groups there might be, but it is intolerable to proper understanding when we make over misunderstandings into pseudo-misunderstandings.

    You talk about sitting down to take food with an Amish, that we can do this, and we can't do it with dead people. But more really, we can't do this. Do you really think all it takes to have a meal with an Amish is just the mere fact that you could do so, if both of your bodies happened upon a table and bread simultaneously? I can hardly take a meal with some of my own colleagues, much the less Amish. And when I do, I'm hardly helped, when perplexed by the odd life-form talking to me from across the table in the commons, by thinking that, after all, our feet walk the same globe, our hearts pulse the same rhythms. That's what I mean when I say this sort of temporal dimension is meaningless and unhelpful because mechanical. The fact is that this strange person does really inhabit a different world than I, and the difference is one of traditions of discourse and vocabulary, patterns of thought of recollection, and so on. Sure enough, if I speak up, I'll become rather strange to her too.

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  11. But here I wonder if the problem is the concept of culture, or world, assumed in the contrast between 'temporal' differences and 'cultural' ones. Cultures (i.e., shared symbolic networks of belief, action, and attitude), as with most things, can be understood only in respect of their histories, which are effaced only at the price of proper understanding. I know you aren't aiming to efface those histories. But if it's artificial to say that a time has non-temporal criteria for establish its own legitimacy (which I'm completely unconvinced of--without, I'd have to argue, being either culpably nostalgic or progressivistic), it seems just as preposterous--more so, I think, really--to say that our present situation, our shared simultaneity has any better claim to legitimacy.

    A more comprehensive understanding of our time would have to account for the fact, not simply explain away as illusory, that it seems undeniably so, contrary to the heart of your point, that there is little room in our world for those who are not 'technocratic city folk', as it were. The fact that you are making your initial point actually draws attention to the more basic feature of experience, i.e., that we do find the Amish strange, that we would, if cultured Protestants, find southern German Catholics medieval. As for me, I wish there could be the room you describe, as I don't find myself being either intensely technocratic or Amish. But Marx would laugh incredulously at the idea that shared time could be anything more than a palliative for the disease of alienation.

    So then, in your last para., when you talk about past practices, continuing or breaking them, they're still being evaluated on the basis of the good of the present ('edifying interaction with our circumstances', 'the preservation of meaning', 'the fulfilling of work, etc.'), as if the present were a standpoint which represents goods that could be codified apart from their respective pasts and futures. For each, the past and future here, as always, are the inescapable frameworks for understanding what exactly constitutes work worth doing, worlds worth living in, in short, the present as always interpreted reality. The whole point of the past (also as always interpreted) is to call certain interpretations of the present into question, to make it seem not obvious to us that the present is the right, best, highest, most noble, etc. way of going about things, or that it is so, etc. etc.

    This was the point I was trying to make in my originally last para., about which you at last said you have no disagreements. I think you must disagree, however, if we've understood each other. The differences that we find ourselves with (right? It’s in our differences, not our simultaneous cohabitation, that is 'immediate and effortless', not the other way round) are the basis of our public discourse. Some, as the Amish, prescind from that public discourse, and over time, their strangeness will increase for that withdrawal. You cannot by fiat undo that strangeness; it has to be narrated away, not conceptualised away, so to speak.

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  12. I don’t think big problems can in fact be gotten rid of in this way; historians know this well. If avoidance of the problems of free will and determinism is the terminus ad quem of Bergson's critique of the spatialising of time, then I come to suspect his critique.

    One of the main problems with folks who think too hard, in my opinion, is that they see "big problems" as things through which they've got to get in order to reach what ends up being the place where they started. We've either got free will or we haven't, and whatever mental paradoxes we create or end up solving around free will as a thought problem aren't going to effect the fabric of the world in which we live. We'll still either have free will or not at the end of the day. For this reason, I don't understand the point of harboring suspicion against someone who thinks they've solved a difficulty of thought that continues to endure for others, merely because they think they've solved it. In the end, there never were and never will be any problems with how-things-are except the ones that we entertain, simply because things are how they are. Now, Bergson very well might be wrong about what he says, but so might Zeno. You don't seem to be pointing out their fallibility, though... rather, you seem to be suspicious merely of the fact that Bergson has made his peace with an issue that others haven't.

    You say that such an identity is absurd, when clearly it is not, as you seem to say also: for Hegel made some sense, you admit, in what he was saying.

    Sure. Bergson could follow Zeno's line of reasoning well enough too, and understood why it made people scratch their heads. Lots of people don't buy the ontological argument but still admit that there's a sensibility and even an allure about the point that it tries to make. I don't see why this seems to strike you as a hedging on my opinion of the matter, or an inner contradiction of my argument.

    Do you really think all it takes to have a meal with an Amish is just the mere fact that you could do so, if both of your bodies happened upon a table and bread simultaneously?

    Yes. One doesn't need to convince a date to stay the night in order to have had a veritable meal with them. Heck, the meal doesn't even need to be enjoyable. The conversation could be boring, too.

    The fact is that this strange person does really inhabit a different world than I, and the difference is one of traditions of discourse and. vocabulary, patterns of thought of recollection, and so on. Sure enough, if I speak up, I'll become rather strange to her too.

    Sure. Again, I haven't denied strangeness or difference in the way that you've denied (or at least severely downplayed) the significance of shared time.

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  13. if it's artificial to say that a time has non-temporal criteria for establish its own legitimacy [...] it seems just as preposterous--more so, I think, really--to say that our present situation, our shared simultaneity has any better claim to legitimacy.

    It's here! It's simply the case. Right now. It is its own legitimacy, and it is its own argument against the idea that the present isn't here presently, but rather is stuck in another century or ahead of its time. By legitimacy I don't mean that those of us who are present are ready to face some sort of throne of judgment. I simply mean that we don't need to justify our presence amidst one another by citing any commonality outside of the fact of our presence itself.

    A more comprehensive understanding of our time would have to account for the fact, not simply explain away as illusory, that it seems undeniably so, contrary to the heart of your point, that there is little room in our world for those who are not 'technocratic city folk', as it were. The fact that you are making your initial point actually draws attention to the more basic feature of experience, i.e., that we do find the Amish strange, that we would, if cultured Protestants, find southern German Catholics medieval.

    That may be the case... I'm not making any claims of being comprehensive. Nor (and here I think you don't take enough care with what I'm saying) am I arguing that any difference is "illusory". What is illusory is a specific sort of difference that is being posited... that of certain people not really belonging to their own time. That's something quite different than saying "our world" has little room for certain people. What I'm saying is that "our time" does have room. I do have to disagree with you, however, about what is most basic to our experience. Certainly a shared time is much more basic to our experience than any cultural accidents, in fact I'd argue that this is exactly why shared time strikes you as so insignificant in the first place! But surely it is far from insignificant... it only seems insignificant because you've come to depend upon it, and you don't see it rupturing any time soon. Were it somehow to do so, however, you would surely realize the significance of such a basic aspect of our shared reality.

    when you talk about past practices, continuing or breaking them, they're still being evaluated on the basis of the good of the present [...] as if the present were a standpoint which represents goods that could be codified apart from their respective pasts and futures.

    Not at all, and in fact, Bergson's whole idea of duration (as opposed to a spatialized conception of time) goes against the idea that life can be partitioned out this way. We of course hold within ourselves everything that came before. Otherwise, to use Bergson's argument again, the present would be almost a sort of unconsciousness insofar as it's partitioned off with itself. The point, however, is that we can't now act in the past, we could only do so then, when it was the present. Simply saying that we always act now as if we're acting now isn't a matter of being historically myopic... it's a matter of being coherent. And I agree with you that the past can call certain interpretations of the present into question, but how? Not by literally doing so, of course, but rather by being presently mediated through an interpreter in the present!

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  14. The differences that we find ourselves with (right? It’s in our differences, not our simultaneous cohabitation, that is 'immediate and effortless', not the other way round) are the basis of our public discourse.

    I could be fine with this formulation, but it also seems that we are talking about two different things and I am not sure that you realize we're talking about two different things, so I want to stop and attempt to clarify. When you say that difference comes first and that it is "immediate and effortless", you are speaking with regard to a sort of discursive cohabitation, our "public discourse". When I spoke above of similarity as first, "immediate and effortless", and not a matter of a subsequent "fusing" of difference, I was speaking with regard to "temporal cohabitation" rather than "discursive cohabitation". I would, however, like to revise one statement that I said. While at the time I wanted to speak of similarity as "first" or "already", I think I'd be happy to abandon such precedence. It really doesn't matter any more than it matters how "thick" the similarity is because, as I said above, it's "there regardless", amidst the difference that I'm happy to grant, and haven't done anything to deny.

    Some, as the Amish, prescind from that public discourse, and over time, their strangeness will increase for that withdrawal. You cannot by fiat undo that strangeness; it has to be narrated away, not conceptualised away, so to speak.

    I'm still confused as to why you think I'm trying to "undo" their strangeness simply by saying that I don't agree with certain conceptions of their strangeness. What I'm trying to do away with is unhelpful understandings of something that we both seem to agree is the case.

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  15. RE: "The concern about spatializing time as a shorthand is that it creates misunderstandings about time, like Xeno's paradox where Achilles never catches the tortoise because as he overtakes previous steps of the tortoise he is always faced with new ones that were gained in the meantime"

    I've never understood what's so paradoxical about this paradox. The examples where the runner covers half the distance in each time period it IS a "paradox" if you want to call it that - if you want to say that "infinitely close" isn't close enough. But the Achilles and tortoise thing is ridiculous. Let's assume that Achilles covers X units of space in t units of time, and the tortoise covers Y units of space in t units of time, and X>Y. If T is the time it takes for Achilles to cover the initial distance between the two, and (T+1)*YX, then the new distance between Achilles and the tortoise is (T*Y). It will take (T*Y)/X units of time for Achilles to cover that distance, in which time the tortoise will have moved (T*Y^2)/X units of space. Again, if at that time ((T*Y^2)/X)+1)*Y > X, Achilles will overrrun the tortoise in the next unit of time. If not, we cycle through again. Except now that tortoise will have covered (T*Y^3)/X^2 units of space, and Achilles will only catch the tortoise in the next unit of time if ((T*Y^3)/X^2)+1)*Y > X. A pattern is starting to emerge. Achilles will catch the tortoise at some point if as n approaches infinity:
    ((T*Y^(n+1))/X^n)+1) < X/Y

    If we rearrange this we get (Y/X)^n < (X-Y)/(TY^2). Since Zeno posits that Y<X, we know that (Y/X)^n converges to zero as n goes to infinity, and we know that (X-Y)/(TY^2) has to be positive, which means Achilles will overtake him. If you're concerned about the "converges to 0" language, just pick values for X and Y and the starting distance and you'll confirm that Achilles always catches the tortoise in finite time.

    Period, end of story. Why is this such a paradox? Am I misunderstanding something? If so, what?

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  16. I guess my point is that "spatializing time" in the sense of just thinking about it as another dimension makes Zeno's paradox extremely UNparadoxical. It's only by confusing the concept of time as something other than the fourth dimension that Zeno's paradox becomes paradoxical.

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  17. No, you're right... and it's of course not as if we had to wait until Bergson to get a "solution" to this paradox... it remains a venerated thought problem, but not because anyone takes it especially serious as actually explaining much about reality. The point for Bergson is that it's symptomatic (or maybe better, illustrative) of the problem that he sees. But he's not simply arguing that time as spatialized is itself the problem.

    Bergson also isn't against us owning clocks. He recognizes, I think, that time can be represented in measured and "spatialized" terms, just as I recognize that Hegel can talk of people as "medieval" in a useful way. The point is to be vigilant about recognizing where such figures of speech can lead to conscious or unconscious misunderstandings.

    With Zeno, though, Bergson does identify the real problem saying, "they think they are justified in reconstructing Achilles' whole movement, not with Achilles' kind of step, but with the tortoise's kind: in place of Achilles pursuing the tortoise they really put two tortoises, regulated by each other, two tortoises which agree to make the same kind of steps or simultaneous acts, so as never to catch the tortoise." (113) So it's not as if he's saying that Zeno goes wrong simply by explaining time as another dimension.

    Do note... my initial reference to Bergson on Zeno said, "space alone can be divided and put together again in any way we like"... the problem with time as a spatialized sort of dimension isn't simply that it's represented this way, but rather that it is mistakenly manipulated in the way that only space can be manipulated. I don't think that Bergson has a problem with mundane sorts of tallying time, so long as we use it purely as a useful reference rather than a basis for an understanding of what time is.

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