Wednesday, April 05, 2006

Unchanging Time and the Infinite Past

You sometimes hear people argue that there couldn't be an infinite past, or else the present couldn't have been "reached" yet. But this is a bad argument. Alejandro succinctly explains:
Time being infinite in the negative direction just means that for every instant t there is a previous instant t’. It doesn’t imply that anything has to “do” an infinite task.

As I noted in that same comments thread: it does not take time for "now" to be reached, any more than it takes distance for “here” to be reached. We may posit an infinite space without supposing anything to cross it. Similarly, we may posit an infinite temporal dimension without supposing anything (the “moving ‘now’”?) to have traversed that.

The problem lies in conceiving of "the passage of time" as being a kind of movement. We imagine the present-marker "starting" at the beginning of time, and moving forward into the future. But this picture belies a deep incoherence. It takes a second dimension - time - to move along some dimension. (Think of a graph plotting the change in y-axial distance against the x-axis of time.) But what is the present-marker moving through, as we track its changing temporal location? It can't be moving through the first-order timeline, since that is rather what it is moving along. We need to posit another temporal dimension, a 'meta-time', in which it can traverse first-order 'time'. This leads to infinite regress, and an absurd commitment to infinitely many temporal dimensions.

We must conclude that there is no present-marker, or "moving 'now'". All times are on an equal ontological footing, the same way that all distances are. 'Now' is no more a privileged time (or "one true present") than 'here' is a privileged location or "one true place". The significance is merely indexical. Now is the time I'm at, and here is the place. But there are other places and times, no less real and existing than my own.

To avoid regress, we must recognize that time exists atemporally. Each moment stands in temporal relations (e.g. "before" or "after") to other moments, and indexically represents itself as 'present'. And that's just how it is, eternally. The moments themselves don't change. Rather, "change" is merely the fact of one moment differing from those which stand in the 'before' relation to it.

Besides which, even if they were possible, any external changes to time itself could have no impact on our experiences. At this moment in April, I have memories of March, which I conceive of as "last month". But if God were to rewind time, to “replay” the universe backwards, we couldn't tell the difference! God would see April first, but what he would see is me with my memories of March (and of course no memory of the "future" moments which God had previously shifted the present-marker from). He would later see those memories form, back in March. But the order in which God views things, from "outside time" (so to speak), cannot affect the experiences we have within our chronology.

Consider the movie Memento, where the viewed chronology is all jumbled up. The first scene we see is the last event to occur within the movie's chronology. As the movie progresses, we get to see earlier events. The fact that our external view is jumbled up doesn't affect the true chronology of events internal to the movie. Those events stand in 'before' and 'after' relations simply in themselves, quite independently of our viewing the movie.

The idea of the "moving 'now'" or present-marker is like the external movie projector. It highlights a sequence of moments, one after the other. But it needn't show those moments in the correct sequence (as represented internally by those moments themselves). So even if there could be a "moving 'now'", it would be strictly irrelevant to the proper chronology of things. April occurs after March, no matter what order the moving 'now' might happen to show them in. The 'now' could move backwards through time, but it would make no difference -- either to our experiences, or to the first-order temporal facts.

Since it makes no difference anyway, we clearly don't need the moving 'now' at all, any more than a set of movie frames needs a projector in order for there to be facts about the movie's chronology. It is enough for the frames, or moments, to exist. They internally represent their own chronology. No external highlighting is needed.

We could imagine a movie with infinitely many frames. Perhaps we couldn't watch it from start to finish, just like a moving 'now' couldn't traverse an infinite past to reach the present. (Aside: this might actually be possible via hyper-acceleration, however!) But in neither case is such external highlighting necessary. Each frame/moment exists, and represents itself as 'present', and as 'after' other moments. And that's all we need. It's perfectly coherent to recognize that there could be a moment -- perhaps this one -- to which infinitely many other moments stand in the 'before' relation. That is, we could have an infinite past.


  1. I agree with you that to imagine the present as "moving" into the future is a deeply flawed way to concieve time. But I'm not sure if the mistake Jonathan was making (the argument that the present cannot have been "reached" if time is infinite in the negative direction) can be pinned down to this image you criticize here. They seem to me to be two related but independent mistakes.

    To see what I mean, imagine an (possibly) inmortal being moving with constant speed in an homogeneous space. If the being has short-term memory, he can wonder: "Have I existed and been moving forever, or has my motion started somewhere?" And he may reason that if he has been moving forever, he has traversed an infinite distance to get "here"; but an infinite distance cannot be traversed, so his motion must have had a beginning.

    This being is not falling into the fallacy you criticize in this post, because he is literally and truly moving. But I think he is commiting the same kind of fallacy Jonathan commits, and his reasoning is not valid. This shows the "an infinite past cannot be traversed" fallcy to be somewhat independent of the "time as a moving now" fallacy.

    The being's reasoning fails because an infinite distance can be traversed -if it is done in an infinite time. (Also in a finite time with hyperacceleration, but even with infinite time there is no contradiction). And even if the "moving now" view of time could be articulated coherently, the "speed of time" could not be other than "one second per second", and so the "now" could have traversed the infinite past because it would have had an correspondingly infinite amount of "meta-time" or whatever you call it to do it; there is no need for hyperacceleration there.

  2. I think I remember trying to explain this to you...
    anyway... good post !


    "The being's reasoning fails because an infinite distance can be traversed -if it is done in an infinite time."
    I like Richard's explination better because there is some value in sidestepping the unresolvable equasion where you start talking about infinite distances being traversed in infinite time when this is not really required.

  3. Don Jr, if someone claims that an infinite past is impossible or contradictory based on a wrong definition of it, and I provide the correct definition and note that it is obviously self-consistent, then I have indeed refuted the claim.

    You may answer that I have not proved the definition to be self-consistent. True, I haven't because I thought that was obvious: it is analogous to what means for the negative numbers to extend to negative infinity. So it can't give rise to a contradiction, quite independently of whether an A or a B theory of time is correct, whether the present "moves" or not, or all those discussions, which I agree are a red herring with respect to Jonathan's original argument. And I don't see what further argument for the possibility could I make.

    By the way, there might seem to be a contradiction between my comment quoted by Richard and my comment on this thread, in which I seem to say that the traveller would be in fact doing an infinite task and taking an infinite time to do it. There is really no contradiction because what I meant now by that is simply that: 1) for every t, the traveller moves at the same speed v, 2) for every t, there is a previous t'. There is still no "infinite task to be completed" in the sense Jonathan was thinking. This also answers to Genius: I am not really dividing two infinities. My point was simply that both space and time could be infinite in that example (in the sense of infinity that I defined in the quote Richard makes) and without any need for hyper-acceleration.

  4. Alejandro - that's a fascinating example you mention in your first comment. I still want to say that there are connections between the two issues, but perhaps not such strict ones as I'd assumed.

    Don Jr. - I don't see how presentism helps. So we say that movie frames only exist while they're being shown in the projector. (Perhaps each frame pops into existence, ex nihilo, when it's their turn to be shown; and promptly disintegrates immediately afterwards.) That doesn't change the fact that the external order of viewing is utterly irrelevant to the temporal relations represented within a frame. Again, when watching Memento, we see the latest events first, even if the later frames (of earlier events) haven't popped into existence yet.

    Everyone agrees that past moments did exist, and that future ones will do so, and that suffices to construct a timeline -- the "first-order temporal dimension" discussed in the post. There are still internal facts about the movie's (universe's) chronology that aren't affected by external viewings of it. That remains true even if frames (moments) only exist during presentation.

  5. This is an old point; Thomas Aquinas pointed out something like it in exactly this context in the thirteenth century, and he was just clarifying a point that had already been made by Muslim Aristotelians. I'm not convinced, though, that it has anything to do, one way or another, with A-theory or B-theory. (I've gone on record denying that there is any clear way to make a distinction between A-theory and B-theory, so that's perhaps unsurprising.)

    I'm also not convinced that the traversal in the objection is supposed to be an infinite traversal by time, rather than a traversal by the world as measured by infinite time. (Neither way saves the argument, I think, but the latter seems much less straw-mannish; and in that way of understanding the problem, I think Don Jr. is right that your analysis is just "an exact model of the problem".)

  6. While I was reading this post, a connection occurred to me.

    Brian Greene writes in The Fabric of the Cosmos that the idea of a "moving light", highlighting moments in sequence so that each one briefly becomes the "now", is unsupported: physicists have found nothing in the laws of physics that corresponds to such a moving light. But it's not just a matter of this idea being unsupported by evidence. In fact, this idea is actually contradicted by the evidence, specifically the evidence of Einstein's special relativity.

    The main idea behind special relativity is that there is no one, universal time. On the contrary, observers on relative motion will disagree on which events are simultaneous, and there is no way, even in principle, to declare one of them right and the other wrong. (Gedankenexperiment: A moving train car has two photon detectors set up at either end of the car. Equidistant between them is a device that, when activated, emits a pair of photons, one in each direction. While the car is in motion, the device is activated. According to observers on the train, the photon detectors go off simultaneously; according to observers watching from the platform, the detector near the front of the train car goes off first. Neither is more right or more wrong than the other; it's all a matter of perspective.)

    One of the more interesting implications of this is that observers separated by a great distance, even if they are moving at ordinary speeds, will disagree dramatically on which events are simultaneous - which means they will disagree on what does or does not exist at a given moment. For example, according to the equations of special relativity, if an observer 10 billion light-years from Earth walks away from us at 10 miles per hour, his list of "things that exist now" will encompass events that, from a stationary observer's perspective on Earth, lie 150 years in the future.

    In this sense, presentism is false. There is not one unique present that's the same for everyone; Richard is correct when he says that all moments must exist timelessly, and that the notion of "present" is merely indexical. That is exactly what special relativity says.

  7. Yeah, I've a separate post on Presentism and Relativity which discusses the interesting argument Ebonmuse mentions.

    Brandon, thanks for the pointer, I wasn't aware of the issue's pedigree.

    Don Jr., could you explain what presentism is and how it avoids the problem? My understanding was that it is simply the claim that only the present time (the time highlighted by the moving 'now') really exists. This seems to be exactly the idea of a 'moving time' that I was arguing against! You say that other times need to "be existent" for the problem to arise, but that isn't so, as the analogy of the presentist movie clip (where only the currently presented frame exists) illustrates.

    I'm not sure what you mean by "the phenomenological now", or why you think I'm committed to any such thing. I hold that I'm conscious of 'now' in much the same way that I'm conscious of 'here'. There's no one present-marker. Every single moment has its own internal, indexical, self-representation of being 'now'. And there are no external markers. So I don't think your comments apply to me at all.

  8. Excellent to see physics in philosophy !

  9. Hah, I've been beaten to the punch! It just goes to show I need to do a lot more reading of your archives, I suppose.

    Incidentally, does anyone know when the 28th Philosophers' Carnival will be up? It seems a bit late.

  10. Presentism requires that the present is always changing. You believe that March used to be objectively present, but now April is instead. That's all the "movement" I need for my arguments. (You deny that March any longer "exists", but that doesn't help you here. I've explained in previous comments how we can construct a timeline, even if you insist that only one point of the line truly exists at any given moment.) You then object that "pretty much all theories of time will be subject to [the] complaint." But static conceptions of time, like that which I advocate in the main post, have no problem here (as you finally admit in your last paragraph). The problem applies to all dynamic theories of time, it's true. But those are precisely what I was trying to argue against.

    "if they're all equally existent, with no external influence, then why do we seem to experience them in succession?"

    I address this in my discussion of how external influence is utterly superfluous. Our memories are built into the present moment. They aren't sensitive to external orderings, any more than the characters in a movie are sensitive to the fact that we're watching them backwards. What they (we) have access to are the orderings as represented in the internal chronology. So at any given moment, I will have memories of the recent past. What more stands in need of explanation? What more could be explained? Presentism doesn't add anything here, it offers merely the illusion of explanation. Again, my main post showed how its external claims are superfluous to our internal experiences.

    (Perhaps there is the locative indexical fact - why am I experiencing this moment rather than some other one? But this is a separate and broader issue. We can just as well ask why am I me and not someone else. The first-personal nature of phenomenal experience is puzzling, but it's no special problem for a static conception of time.)

  11. Yes, by all means, please do reconsider your response in light of my later clarifications! (There would be little point in my talking to you otherwise!) In actual fact the core of my criticisms does not "require... the entire line or dimension of time to be existent." That's just an assumption you've made, and which I've repeated rebuked. The core of my objection is to the idea of the "one true present" changing over time, which presentism is quite obviously committed to.

    The idea of the 'present-marker' is simply that of an ontologically privileged present. (If the name confuses you in this respect, just return to the idea of the "one true present", which I take to be synonymous, and which - again - the presentist is quite obviously committed to.) It doesn't make any claims about the privileges enjoyed by other times on the scale, and particularly whether or not they can be truly said to "exist".

    The latter point seems merely terminological in any case - as Brandon might agree - since everyone agrees that all times have existed or will exist at some point, but also that they're no part of this moment in time. The remaining question seems to be whether to restrict our quantifiers to those objects that exist at present, or whether to broaden its scope to include other moments. Perhaps for this reason, presentism is sometimes instead characterized as the view which takes "temporal becoming" seriously. The 13th April isn't yet privileged to be the 'one true present'. (Indeed, it doesn't even "exist" yet.) But it will be, tomorrow. So the present must "move" or change from here to there, or rather now to then, even if you insist that what it leaves behind - the "past" - will subsequently no longer exist. The temporal dynamism I criticize is at the very heart of presentism, and your attempts to dodge this by disputing the existence of the whole timeline are, well, simply irrelevant.

    As for phenomenology, I'll grant there are some puzzling questions there. But I see that as much less serious than the incoherence of dynamism. Especially since dynamism couldn't offer any better answers, as explained in my section on 'superfluity' which you insist on ignoring.

    Whatever experiences we have, we have them internally to our represented chronology. That includes experiences of time "in succession" (which I expect is heavily dependent on short-term memory, hence my previous comment). Now, the "temporal becoming" of presentism is an external feature. The 're-ordering' issues are relevant because there's no reason why the external chronology needs to match the internal one, as the movie projector analogies show. (I'm not sure what part of it is failing to make sense for you. It's unfortunate, because I find that analogy incredibly illuminating, and this mutual incomprehension may explain why we seem to be talking past each other here.) Even if presentism were true, there's no reason to think that the previous objective/external moment was from our past, rather than our future. As I extended the analogy, God could be playing the universe backwards, and we wouldn't know it. This external ("viewing") process can have no impact on our experiences, since the latter occur internally to moments; and the former merely offers a presentation of the moments, it does not alter their contents. So the external process cannot explain our experiences. I have the experiences I do because of the intrinsic nature of the universe at each moment in time. The external relations between these moments, such as the presentist's "temporal becoming", are not accessible to me, stuck as I am always inside the "frame" of each moment.

  12. > There would be little point in my talking to you otherwise!

    haha is there an implicit "because I sure as hell wont reconsider mine!" hidden in there?
    Just kidding - mostly.

  13. The internal chronology is that which we have access to from within a moment: the set of "before" and "after" relations that hold between moments. For example, April 13 is determinately after April 12, according to the internal chronology of our world. (It's "time as we know it". Again, I find the analogy to the movie characters helpful here. The story internally represents some events as 'before' or 'after' others. This doesn't require any external support, as the superfluity of the projector shows. The temporal relations hold intrinsically, no matter whether we go to the bother of actually playing the movie through.) Externally, of course, anything could happen, and we'd never notice. This shows that external dynamism (as posited by presentism, etc.) cannot do anything to explain our experiences.

    Your long comment keeps repeating the irrelevant fact that presentism doesn't think the other points on the timeline exist, without addressing my point that presentism is obviously committed to the dynamism of a changing "one true present". It's extremely frustrating.

    I addressed your concerns in my very first comment, and several times since, but let me try one last time before giving up on this conversation. Here's the thing: it doesn't help to say the other points on the timeline (the other "light bulbs", as you put it) don't "exist". The only difference is the insistence that only one light bulb exists at a time. You say the previous lightbulb winks out of existence when its turn is done, and the next one pops into existence bright and ready. So what? That doesn't change anything. The light still moves from one bulb to the next: it's just that the unlighted ones immediated cease to exist. (Even if only one bulb exists at a time, we can easily reconstruct the whole string of them, based on what has or will exist.) So please, shut up about existence already. Let's face the undeniable presentist claim of "temporal becoming" -- that's what's really relevant here.

    You believe that April 12 used to be, but is no longer, the one true present. This entails that the present has changed ("moved", perhaps metaphorically speaking) from April 12 to 13. All your irrelevant handwaving about "existence" merely serves to obscure this crucial point, effectively changing the topic. If you want to continue the discussion, you have to address this point.

  14. I'd like to add a comment that talking about "time" is complicated because we use time and temporal metaphors "all the time". For instance, I think it is quite tautological that only one moment of time "exists at a time." Just like my apartment is the only apartment which exists "at my apartment". You certainly wouldn't want to say that every moment of time exists at each moment of time. The passage of time is so ingrained in our thinking that these kinds of conversations are almost impossible.

    I am reminded of conversations I've had with friends in which I've tried to explain that the question "what happened before the Big Bang?" just isn't a well-posed question because the word "before" is inappropriate.

    Also, on a separate note, the analogy that "at this time" is similar to "at this place" is not merely a good analogy. It is also physically correct. Time and space really are intertwined. They are not separate objects.

  15. I think the point is if a perspective or piece of logic doesnt exist it cannot be used to logicaly disprove anything.
    eg a statement like "X god exists so humanism is immoral"
    So the question remains "can you prove the perspective exists?"
    If not maybe you are just introducing a "false" fact.

    For example while I can concieve of momento example I expect the laws of physics preclude it from genuinely happening. (one could argue that as being a side effect of presentism?)

    I am as it happens more convinced by the space time duality and more than 4 dimensions (ie not giving time some sort of ultimate status) and I dont see presentism as a very useful perspective it just makes it slightly harder to conceptuaize certain problems.

  16. With respect to Alejandro's statement "that for every instant t there is a previous instant t' ", should this not read "for every instant t there are previous instants t' "? The former makes time sound discrete, which it may be, but shouldn't this come with an argument?

    Also, did Relativity not show us that "before" and "after" are in fact relative?

  17. Actually, relativity preserves before/after causality for all luminal and subluminal processes. What it doesn't preserve is simultaneity.

    But that's not the point.

    All this talk of objective time, as far as I'm concerned, neglects something absolutely crucial:

    I experience a subjective flow of time. That illusion, that sensation, is absolutely real for me.

    If time really is a motionless "loaf" of coordinates, I couldn't possibly have that illusion! There would be nothing for me to move through in order to think I'm moving! I'd just simultaneously exist for all of my spatial and temporal extent.

    Since I don't, there must be an objective motion to time, or at least to something like time ("meta-time" as you call it).

    No, we don't need an infinite regression.

    All we need is this:
    There is an independent variable to the universe. A parameter if you will.

    All other entities evolve according to the motion of this parameter.
    This motion is constant and continuously forward (by definition).

    May as well call it t. (Or tau, if you really love your relativity).


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