Showing posts with label instantaneous change. Show all posts
Showing posts with label instantaneous change. Show all posts

24 May 2014

Priest (11.2) In Contradiction, ‘The Instant of Change’, summary

 

by Corry Shores
[
Search Blog Here. Index-tags are found on the bottom of the left column.]

[Central Entry Directory]
[Logic & Semantics, Entry Directory]
[Graham Priest, entry directory]
[Priest’s In Contradiction, entry directory]



Graham Priest


In Contradiction:
A Study of the Transconsistent


Part III. Applications

Ch.11. The Metaphysics of Change I:
The Instant of Change


11.2 The Instant of Change



Brief Summary:

Things in the physical world change states through time. There are instants of such change when we have no more reason to say that it is in the prior or the following state. In such cases, it is true that the thing is both in a state and not in that state. This is a true contradiction, a dialetheia, that is a real and common situation in the physical world.



Summary


Priest will illustrate a problem with the instant of change.

As I write, my pen is touching the paper. As I come to the end of a word I lift it off. At one time it is on; at another it is off (that is, not on). Since the motion is continuous, there must be an instant at which the pen leaves the paper. At that instant, is it on the paper or off? [160]

[We have things and their interactions here operating in a describable way, so we will call it system s. There is a moment in time in question, the instant when the pen leaves the paper, which we will call t0. We also have different states the pen can be in, either on or off the paper, called s0 and s1. We will describe the state of being on the page in the statement called α (which reads “The pen is on the paper”). Otherwise, the pen would be off the paper, and then it will be in the next succeeding state, s1. After the pen leaves the paper, it is not the case that “the pen is on the paper”, which is a proposition we would then write as ¬α. Now we want to know, at the moment it leaves the paper, what state is it in? There are four possibilities. Either 1) it is only on the paper, 2) it is only off the paper, 3) it is neither on the paper nor off, or 4) or it is both on the paper and off the paper in the same instant.]

We may formulate the problem more generally. Before a time t0, a system s is in a state s0, described by α. After t0 it is in a state s1, described by ¬α. What state is it in at t0? A priori, there are four possible answers:
(A) s is in s0 and s0 only.
(B) s is in s1 and s1 only.
(Γ) s is in neither s0 nor s1.
(Δ) s is in both s0 and s1.
(160)

Also, there may not be an answer which holds for all cases, because “Different changes may be changes of different kinds.” (160) If we just assume classical logic, then all changes will have to be of types either A or B. But since we are testing the viability of classical logic for explaining change, we cannot assume from the beginning it is the only means to find the answer. Priest will argue that there are changes of type Δ, that the pen is both on the page and off it the instant it makes that transition.


Previously in section 4.7 Priest ruled out the possibility of Γ type changes, so at least one of α or ¬α must hold. [His argument there has to do with liar paradoxes, for example, ‘This sentence is false’. If it is false, then it is true, but if it is true, then it is false. Therefore it is both true and false. That is not a problem for dialetheians. However, those who reject this need to explain what is wrong with the argumentation that leads to the paradox. One solution is to say that there are truth gaps, that is, that there are sentences which are neither true nor false. Priest in that section showed how their arguments failed, and thus in this current section, he does not find the third option, that it is neither in one state nor the other, convincing.] Now we must argue that not all changes are of types A or B (being either on or off the paper exclusively). So recall that at  t0 the pen leaves the paper. Is it on or off? It seems we do not have a better reason to say one over the other. This means we might prefer a symmetrical answer like Γ or Δ (the pen is neither on nor off the paper, or the pen is both on and off the paper). We might break this asymmetry by identifying being on with being zero distance from. [It seems Priest might be saying something like the following here. Consider its motion coming off the paper. Because of infinite divisibility, there is no first point when it is off the paper. Thus maybe we might say that it cannot be both, because the final on point is determinable, but the first off point is not. However, this does not apply for objects falling to the ground for example. This is perhaps because there is a final terminating point for the motion without there being a continuation after it. Priest writes: “There is, however, a way of breaking the asymmetry in this case. Since the motion is continuous, there is, presumably, a last instant at which the distance between the point of my pen and the paper is zero, but no first point at which it is non-zero. (Perhaps more precisely, there is a last point at which the electrical repulsion between my pen and the paper is equal to the weight of the pen, but no first point at which this is not the case.) If we identify being on with being zero distance from, this makes the change of type A. But the identification is highly suspect. An arrow is fired into the ground. At the instant of impact, before the point of the arrow penetrates the ground, is the arrow on the ground?” (160)]


Priest says that even if we can preserve asymmetry in the above example, it will not work in all cases. If we discover some solution, then we have a symmetrical relation between the state before of not having it and the state after of having it.

A particularly striking example of this is a phenomenological one. For days I have been puzzling over a problem. Suddenly the solution strikes me. Now, at the instant the solution strikes me, do I or do I not know the answer? The situation is, again, symmetrical. Before, I did not know the answer; after, I did. Moreover, one cannot suppose that in this case there is some tie-breaking ulterior fact. My epistemological state is all there is, and that is symmetrical. It makes little sense to suppose that I either did or did not determinately know the answer at the instant of change, though I am unaware which. (161)

In the next example, Priest has us consider us walking into a room. There will be a point when we have no more reason to say we are in than we are out. Thus there are cases where we have enough reason to give answers of type A or B.

I am in a room. As I walk through the door, am I in the room or out of (not in) it? To emphasize that this is not a problem of vagueness, suppose we identify my position with that of my centre of gravity, and the door with the vertical plane passing through its centre of gravity. As I leave the room there must be an instant at which the point lies on the plane. At that instant am I in or out? Clearly, there is no reason for saying one rather than the other. It might be suggested that in this and similar cases we are free to stipulate that I was, say, in. Unfortunately this is not a solution, but simply underlines the problem. I am free to stipulate in this way only because neither being in nor not being in has a better claim than the other: I am neither determinately out rather than in, nor determinately in rather than out. Thus, intrinsically, the change is symmetrical, and therefore not of type A or type B. (161)


So we are arguing for type Δ changes (both on and off). Someone might argue against them by opening the possibility for Γ type changes (neither on nor off). They might do this by rejecting the exhaustion principle which says that if α is not true then ¬α is true. [Perhaps then in the case of the pen, it can both be that the pen is not on the table but also not-not on the table, or in other words, that the pen is neither on nor off the table.] This is possible if the arguments from section 4.7 can be met. Nonetheless, the above example still gives us ample reason to suppose that there are type Δ changes.


There is another issue to address. Instead of instants of time, there might only be intervals. If so, then there are no instants of change, and thus no contradictions [because it is never at the same time that the pen is on or off the paper]


There are some problems however with arguing that time is not composed of instants. Science operates as though time can be represented by the real line. Calculus’ application in physics presupposes this. Thus to say that they are wrong about instants is to say that much of their work [or at least methodology, maybe conclusions] are wrong. [[However, there is also a way to conceive of the instant as an infinitesimal interval. This would make it both a combination of states without any passage of duration between them.]]

a good part of science is based on the | assumption that physical continua have a structure that can be represented by the real line, and therefore that we can speak of instants of time. In particular, any science that uses the differential and integral calculus presupposes this. Therefore, this proposal, if adopted, would cause the demise of a good part of science. Or, to put it more tellingly, the proposal flies in the face of well corroborated scientific theories. Its correctness is, therefore, highly suspect. (161-162)


Another problem with the theory that time is composed of intervals and not units is that it fails to account for how (or when) change happens. If two successive intervals have different states, where does the change take place? It cannot be between them, because there are no instants between intervals. But it cannot be in either one, because there is only one state and not a change of states. Thus tie would just be a sequence of still moments. This is the cinematic account of change [we discuss it further in sect.12.2].

suppose that during a certain time a system, s, changes discretely from state s0 to states s1. Then there must be two abutting intervals, X and Y, X wholly preceding Y, such that s0 holds throughout X and s1 holds throughtout [sic] Y. Now, given that there is no instant dividing X and Y, we cannot ask what state s is in at it. However, just because there is no such instant, there is no time at which the system is changing. X is before the change. Y is after it. Thus, in a sense, there is no change in the world at all, just a series of states patched together. The universe would appear to be more like a sequence of photographic stills, shown consecutively, than something in a genuine state of flux or change. We might call this the cinematic account of change. As we will see, it has a habit of surfacing in consistent accounts of change. I will discuss it in more detail in section 12.2. For the present, let us just note that the cinematic account is highly counter-intuitive. (162)

Also, intervals would have to be divisible, which means at one line of subdivision there could be a case of α ∧ ¬α.

it is not even clear that dialetheism can be avoided by eschewing instants of time in favour of intervals; for, unless there are atomic intervals, a possibility that raises the shades of Zeno and exacerbates both the previous problems, intervals must be indefinitely subdivisible. Now, note that the fact that a holds at an interval, X, does not necessarily imply that it holds at every subinterval of X (or else the sun’s shining on a certain day would imply that it shone during every part of the day). There is therefore nothing, in principle, to rule out the possibility of an interval such that every subinterval where a holds has a subinterval where :a holds and vice versa. What holds at this interval? What could it be but α ∧ ¬α?
(162)



Priest, Graham. In Contradiction: A Study of the Transconsistent. Oxford/New York: Oxford, 2006 [first published 1987]

3 Feb 2014

Notes from Barry Dainton’s Time and Space for comparison with his “Sensing Change”


by Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]

[Central Entry Directory]

[The Dainton – Gallagher Phenomenal Time Debate, entry directory]


[All underlining, boldface, and bracketed commentary are my own. Proofreading is incomplete, so mistakes are still currently present.]



Notes from Barry Dainton’s

Time and Space

for comparison with his “Sensing Change”



In Barry Dainton’s article “Sensing Change,” he describes his overlap model of the specious present of our phenomenal awareness.

Of course, anyone who believes that concrete reality is itself confined to what the present instant contains will find the Extensional approach problematic. If the past simply does not exist, contents located in the past cannot be co-conscious with contents located in the present. (This thought may well underlie the Retentionalist doctrine that only items that are momentary and simultaneous can be phenomenally unified.) But while this view of time—Presentism—may have some appeal at the level of commonsense, it does not sit easily with the four-dimensional space-time ontology that (many believe) Einstein’s theories of relativity require. By allowing phenomenal unity to connect contents that are separated by time as well as space, it is the Extensional approach that is more in tune with the findings of contemporary physics. (Dainton “Sensing Change” 380)

Dainton writes more about the four-dimensional space-time view of temporality in his book Time and Space. What might be implied in this is that Dainton’s overlap model is also more in tune with contemporary physics because it is extensionalist. So we will see if his writings in Time and Space might determine this.

In the first chapter of Time and Space Dainton introduces McTaggart’s distinction between A- and B-series. The temporal character of events in the A-series are understood in terms of their relation to the now-moment from which we see them. This means that events are understood as being located either in the present now, or in the future that comes after the present now or the past that happened before the present. Events understood in terms of the B-series however are not seen as though there is a origin point which can make these distinctions. An event can come before or after, or be simultaneous with another, like how we think of historical events, but the temporal character of the B-series is not one that allows for present, future, and past. (TS 11)

Dainton then makes the following distinctions.

• The Block view: all times and events timelessly coexist, and all are equally real; temporal passage is unreal.

• The dynamic view: temporal passage is real, and time is not an ensemble of coexisting times and events. In short, the block-universe view is false.

• The tensed theory: A- concepts such as past, present and future have an essential and ineliminable role to play in any metaphysically adequate account of the nature of time.

• The tenseless theory: B- concepts such as earlier than, later than and simultaneous with are all we need for a metaphysically adequate account of time. (TS 11-12)


Because the overlap model is one in which the present ceaseless passes, it would seem to observe the dynamic view and not the block view. The question is then, does the contemporary physics that Dainton refers to here also take the dynamic view? In the overlap model, it is the present which is extended and passing. Do physicist think in the four-dimensional view that there is a one second long present that passes through time?

In the third chapter Dainton looks more closely at the four-dimensional ‘block’ view of time, which might be the view he says is popular in contemporary physics and required by Einstein’s relativity theories.

Beginning the first section, titled “Time without Passage,” he writes:

Many contemporary philosophers are convinced that McTaggart was essentially correct: our world is a block-like four-dimensional ensemble, lacking a moving present, wherein all times and events are equally real. (TS 27)

A bit later he writes:

Of all the models of time that we will be considering, the B-theory is currently the most popular among philosophers and physicists, but in many respects it is also the strangest and most counterintuitive. (TS 27)

In the fourth chapter he further claims that for B-theorists time does not really have a moving now that flows with time’s passage:

But if the B-theory is true, time is not going anywhere: there is no moving “now”, no slippage into the past, no crystallization from mere possibility into present actuality. (TS 44)

In chapter 5 he formulates a particular claim that in chapter 6 he critically examines:

The world is a four-dimensional ensemble, and all times and events are equally real and coexist. (TS 63)

In the 6th chapter he examines presentism, which he mentions in the paragraph we cited from “Sensing Change”. Presentism thinks that only the present is real. Here in Time and Space he says something similar:

Once one becomes aware of the Block view, and the scientific considerations (especially Einstein’s special theory of relativity) that can be mustered in its favour, denying reality to everything but the present can easily come to seem absurd. (TS 81)

In the 7th chapter Dainton examines the phenomenology of time. He begins first with phenomenological data of the phenomena of change and persistence.

Let us start by gathering some basic phenomenological data. Our typical experience is a combination of persistence and change. You are, let us suppose, lying in a deckchair gazing at the sky, where you can see a few white clouds moving very slowly against the unvarying blue backdrop. You see the occasional bird overhead. Sometimes they circle around for a while, and often they fly right on by. When you do see a bird in flight you are directly aware of its motion: the flapping of wings; the sometimes fast, sometimes slow changes of position. You are as fully and immediately aware of these movements and changes as you are of the unchanging blue of the sky. The same holds quite generally for other modes of consciousness. We see change, but we also hear it (a rapid sequence of notes played on a piano), feel it (slowly move your finger across the palm of your hand) and imagine it (recreate in your imagination the final shot in a tennis tournament – a ball goes out, a player leaps with joy, the crowd roars). In addition, there can be changes in what we smell and taste, and in our emotional state (a surge of anger). And then there is the inner soliloquy, the conversation we have with ourselves in thought, conducted sometimes in words, sometimes in images, sometimes in neither, which rarely ceases during our waking hours.

All this is obvious: consciousness is alive with change and variation. More elusive is the subtle but distinctive sort of dynamism that is characteristic of unchanging sensations. Return to the deckchair scenario. For some moments now you have been staring at an empty region of blue sky and nothing has changed. Your inner monologue has (if only briefly) ground to a halt, you have seen no movement, your visual field is filled with an unvarying expanse of blue. But is your consciousness entirely still or frozen? Have you come to a complete stop? No. Throughout this period you remain conscious, and conscious of the blue presence continuing on; you have a (dim, background, passive) awareness of the blue constantly being renewed from moment to moment. This passive awareness of continuation and renewal is perhaps more vivid in the case of auditory experience. Imagine hearing a sustained but unwavering note played on a cello: you hear a continuous and continuing flow of sound. This feature – call it “immanent phenomenal flow” – is possessed by all forms of experience (think of the burning sensation on the tongue caused by biting on a chilli pepper), and is a dynamic feature of experience that is independent of changes of the ordinary qualitative sort (the chilli- induced burning is felt as continuing on even when its intensity and qualitative character remains constant). Phenomenal flow is especially important in the case of easily overlooked but ever- present bodily experiences: the feeling of one’s limbs being disposed one way rather than another, the feeling of being vertical rather than horizontal or upside down, the feelings of pressure on one’s skin caused by clothes, seats, shoes and so on. When we are not moving about, our bodily experience is largely unvarying in quality, and so goes largely unnoticed, but it remains a constant – and constantly flowing – presence within our consciousness. (TS 104)

Thus we may distinguish two temporal phenomenal traits, passage (change) and flow (persistence):

• our experience of change is as direct and immediate as our experience of colour or shape;

• our experiences possess the feature of phenomenal flow. (TS 104)

Phenomenal flow, by the way, involves an awareness of the newness even of persistent things in our awareness:

As well as providing an explanation of how we can have an immediate experience of change, the model provides an account of phenomenal flow, the impression we have that a qualitatively unvarying sensation is continuously refreshed and renewed. (TS 110)

We also note that again Dainton in this book, like in other writings including “Sensing Change” claims that contents in his awareness do not linger.

If the two- dimensional model were true, we could expect that:

experiences would never end abruptly, they would always linger on for a short while as they are represented in successive awarenesses as possessing diminishing presentedness;

• at each moment we would be aware of our current experience together with a constantly shifting complex of representations of recent experiences, and so our consciousness would be choked with the residues of recent experiences.

But this is wrong on both counts. As far as I can tell, my consciousness is not clogged up with fading residues of prior experiences, and experiences do not always linger; they sometimes do end abruptly. It could be objected, “Ah, but the residues are very brief. That’s why you don’t notice them. Likewise, for the shifting constellations of representations.” This reply is unconvincing. If we cannot discern the posited representations, there is no reason to suppose that they have any phenomenological reality, and hence no reason to suppose that they contribute to our actual experience of change and persistence. (TS 111)

[[Dainton also at times refers to the blur behind a fast moving object. In cases when he mentions these he does not explain why these are not instances of lingering contents, and in cases when he says we never have lingering contents, he does not mention cases of blurred moving objects in order to clarify how they are not instances of lingering.]]

We also note here that in “Sensing Change” Dainton says that what is in the extensive specious present of his overlap model is present because it has the full force and vivacity of present things.

What quality, added to a pain sensation, would make that sensation seem to be in the past rather than in the present? If I am now experiencing some sensation, won’t the experience seem to be occurring now irrespective of any peculiar qualities it might possess? Someone might say, “Presentedness is not an additional property that experiences have. It is akin to Hume’s ‘force and vivacity’. It is simply a measure of the intensity of an experience; as experiences lose presentedness they become progressively fainter, until they fade away altogether.” But this won’t work. Do some parts of the image in Figure 7.5 appear “more past” than others? [This figure shows a star-shaped image of light where the center is bright and diminishes toward the edges](112)

[[But when discussing non-extensional models, he examine a similar concept called presentedness, which is a quality that retentional contents have to diminishing degrees as they move further away from the present toward the past. He says that presentedness cannot be understood as Hume’s full force and vibrancy, because presently given weak phenomena like faint sounds or light do not now sound as if in the past. Those advocating for a diminishing presentedness might say that what makes the content seem more past is not merely its faintness as much as how much fainter it is from when it first presented itself. The faint sound now gets even fainter and as it does, and only as it does, it appears less and less present. It is also unclear how it is that Dainton’s criticism of presentedness does not apply to his concept of presence which is defined in exactly the same terms as presentedness. If a sound is currently very faint, does it seem less present than other concurrent sounds which are prominent? If not, how exactly do we make a clear distinction between presentness and presence with respect to currently faint phenomena?]]

When describing his overlap model, he explains how contents separated by others are not transitively co-conscious, and he also says that the specious present is less than a second.

Since the specious present is of limited duration (probably less than a second), the relationship of co- consciousness over time (diachronic co- consciousness) cannot be transitive. (114)

Later there is a paragraph which might help us better understand how the features of the overlap model might be in tune or not in tune with the contemporary physics understanding of time. It is not here clear if he is saying that moments outside the present are real in the same way as those inside the specious present. He only says that they are real in the present, but he puts in it a way that might suggest we cannot say something about the reality of those outside it.

However, in assessing the plausibility of what is being offered here, we must not lose sight of the model of time with which we are dealing. The overlap theory tells us that for me to experience C flowing into D, or D flowing into E, my experiencing of C must be co-conscious with my experiencing of D, and my experiencing of D must similarly be co-conscious with my experiencing of E. When two experiences are (diachronically) co-conscious, they are experienced together, in a unified temporally extended episode of experiencing. It is difficult to see how C could be related to D in this way if C is unreal when D occurs – and similarly for D and E. In order for C and D to be part of one unified experience, C and D must surely coexist. But according to the Dynamic Presentist, since C and D occur in succession, they do not coexist. (118)

[[A presentist might also say that to perceive C flowing into D is to perceive the passage between and thus to have both simultaneously in consciousness in that instant of their passage.]]

[[More generally speaking, it is not clear if the overlap model assumes time makes up a B-series, because the present has an extensive structure where successive moments co-exist, or if because the present is always in motion that it makes it not a B-series. If it is not a B-series on account of the movement of the present, then it is unclear how it is compatible with contemporary theories of physics which seem to construe time as B-series.]

Then he specifically addresses the question of whether the overlap model is compatible with other metaphysically intelligible views of time, and he says that it is “neutral” with respect to them. First he looks at the block view, which is like the B-series conception. All moments have their place, none are present, and there is no flowing now. But the way he describes it here suggests that within the four-dimensional block a stream of consciousness is like a small part that is only aware of tiny moving portion of it. It does not explain the relationship between the movement of the stream of consciousness and the non-movement of the block. So he explains why it is that the specious present is only a small part of the whole block, but he does not explain why in the block a small part of it is moving.

What of the other models of time that we have considered and found metaphysically intelligible? For better or worse, the overlap theory seems entirely neutral with respect to these.

Consider the Block view. The overlap theory tells us that co-consciousness extends over short periods to create temporally extended “phenomenal presents”, that successive phenomenal presents overlap, and that the contents of these phenomenal presents have an inherent dynamic character. That our experience is structured in this way guarantees that we will have the impression that our consciousness is confined to a forward-moving present even if, in reality, past and future experiences are just as real as present ones. From the four-dimensional perspective, a stream of consciousness is akin to a glowing filament embedded in a long glass block; the filament is aglow throughout its entire length, but this is not discernible to the subject of these experience, who is only ever aware of those tiny stretches of experience joined by co-consciousness. (119)

Dainton contrasts his overlap theory to ones which conceive of the present as durationless. He claims that such models cannot account for the phenomenon of passage. But one argument against Dainton’s position, which he does not address, is that physics understands an instant of motion as being like the smallest part of passage. In one sense it is durationless in that it is not an extent of time, but it is not the same as a lack of temporality. It in a way is greater than a zero amount of time and less than any givable finite amount of time. At any such instant of motion, we can calculate the instantaneous velocity of the motion. In a sense, the object is both in motion and at rest. It is at rest because it does not travel any extent of space or occupy any extent of time, however it is in motion because it is still in passage between locations, and thus it can have a certain rate of making that passage even though no extend of time or space transpires. Dainton in fact discusses and describe this operation in physics, and he even notes that modern scientific and technological calculations depend on it. This suggests that the instantaneous view of parts of motion are compatible with contemporary views of time in physics. What is interesting is that he does not consider this view of the instant when examining possible models of time consciousness where the present is instantaneous. Could not the present in our phenomenal consciousness be an instant which is aware off the smallest part of change? He explains instantaneous velocity when discussing the at-at account of motion, which can solve Zeno’s paradox of the arrow. An arrow in flight occupies a series of points in space coordinated to instants in time where it is found at those locations. But it is not at motion in any of the points, so it is never at any point or moment in flight. Dainton explains how those who think time and space are continuous can reply that since the arrow was at a different location prior to any in its motion, then it is changing location across time and thus is in movement. It is at certain points at certain times, and at intermediate points between them. He then looks at the calculus way of looking at this to show how even in the instant the arrow would have an instantaneous velocity, which suggests that no matter how small of a part of its motion we look at, it is at motion in that instant.

17.1 The “Arrow”

Imagine an arrow in flight. At every instant during its flight, the arrow is at some specific location, occupying a volume of space that corresponds exactly to the arrow’s own size. Since instants are durationless, and motion takes time, the arrow is not in motion at (or during) these instants. Yet the arrow’s entire flight is composed of these instants, and nothing but these instants. If the arrow is not in motion at any of the instants that jointly make up its flight, it is not in motion at all.

This is Zeno’s “Arrow” paradox. The reasoning obviously generalizes – what holds for the arrow holds for any object in motion – and so if the argument is sound, motion does not and cannot occur. The argument is sometimes taken as being directed – along with “Stadium”, which we will be looking at shortly – against the doctrine that space and time are discrete, rather than continuous. While this may well be true for the Stadium, it is not obviously true in the case of the Arrow. In any event, the Arrow reasoning certainly poses a significant problem for those who believe space and time are continuous rather than discrete, the conception of the continuum with which we are currently concerned. If space and time are composed of dimensionless points, and the arrow’s flight involves its occupying a continuous succession of different locations, we are undeniably confronted with the problem of explaining how it is possible for the arrow to have moved, given that it is not (seemingly) moving during any of the momentary stages which constitute its flight.

The at-at theory

Those who subscribe to the orthodox conception of the continuum have a response to the Arrow challenge that is widely, although by no means universally, accepted as adequate. The proposal runs as follows. Whether or not an object is in motion at a given time t does not depend on the object’s condition or state at time t. Rather, it depends on how the object behaves at those temporal instants neighbouring t. If at these neighbouring times the object is at precisely the same location as it is at t, then we say that it is not moving at t; but if it is at different locations, then we say that it is moving at t. Since everyone can agree that an object is moving if it is changing its location over time, this simple account seems to give us all we might want. Or as Russell puts it, “Motion consists merely in the fact that bodies are sometimes in one place and sometimes in another, and that they are | at intermediate places at intermediate times” (1917: 84) [Russell, B. 1917. “Mathematics and Metaphysicians”. In his Mysticism and Logic. London: George Allen & Unwin]; hence the “at-at” label for this view.

It will be useful to take a closer look at what proponents of the at-at account are proposing. Suppose we start with an interval I1, running from half a second before t to half a second after t (see Figure 17.1). We calculate the arrow’s average velocity over I1 by dividing the distance travelled over the course of this interval by the time taken, which in this case is one second. This gives us an initial, reasonably accurate, approximation of the object’s velocity at t. To get more accurate approximation we repeat the procedure for a shorter interval I2, which is also centred on t, but running (we can suppose) from a quarter of a second before it to a quarter of a second after it. By working out the average velocities over shorter and shorter t-centred intervals we will generate increasingly accurate estimates of our object’s velocity at t itself. In standard fashion we now introduce the limit-value of the series at t: it is the average velocity to which the series of ever-decreasing intervals converges as the end-points of the intervals approach arbitrarily close to t itself. We can now stipulate that our object’s instantaneous velocity at t is simply this limit-value.

This procedure can be applied quite generally to deliver the instantaneous velocities of any moving object at any time. Indeed, the procedure just outlined is essentially that used in the calculus, where velocity is the “first derivative” of change of position with respect to time (acceleration, the rate of change of velocity, is the “second derivative”). Since the day of Newton and Leibniz, calculus has been at the heart of physics and applied mathematics, and it is undeniable that much of the success of the former is due to the latter; without the methods of the calculus we would not be able to calculate the rates of change of interdependent quantities in the precise and accurate ways our science and technology require. (TS 289-290)

Dainton. Time and Space fig17.1

Figure 17.1 from page 290 of Barry Dainton's Time and Space (2010 2d ed)

As we can see, time is understood here as an extension, and this is specifically Dainton’s claim, that contemporary theories in physics regard time as extensive in their four-dimensional models. Our question is whether or not the overlap model’s other features are compatible with this four-dimensional view. We might for example wonder, do these contemporary conceptions of time think that within the extent of time there is a one second long moving present? One way Dainton might locate something like this in Einstein’s special relativity theory is in how there is no absolute simultaneity. Events that in one frame seem simultaneous might in another seem successive.

In the context of STR, simultaneity is not absolute but frame-relative. Spatially separated events that are simultaneous from the perspective of one inertial frame are not simultaneous from the perspective of other inertial frames, and since the perspectives of all inertial frames are equally valid, there is no sense in the idea that the events in question are “really” simultaneous or not. (TS 322)

So the present cannot be seen as an instant that all frames share. So we consider all possible observations. In one such comparison, there will be events that in one frame seem simultaneous and in another seem successive, and we are looking at the pairing where magnitude of the extent of time in the succession of events is greatest for any other comparison of frames. This difference in magnitude would be the extensive present, because it is the extent of time during which all other observations fit the same events. So while in the frame where the events seem maximally successive, in another they are simultaneous. The presence in the simultaneous case is extensively stretched in the successive case, and this is the extent of the present. This brings us closer to seeing how the extensive overlap model might be closer to contemporary physics and Einstein’s relativity in particular, but there is still a lot that is not clear about this account. Does that mean that because our specious present is one second long, this extent of time is the greatest possible temporal difference between all frames in the universe? And are we suggesting that when we view the specious present we are somehow perceptive of the temporally difference between reference frames of which we are not otherwise perceptively aware of? Perhaps, but Dainton does not clarity if and how this might be so.


When discussing general relativity, Dainton more specifically addresses when it is compatible with B-series conceptions of time and dynamic conceptions of time. He writes that “Nothing in GTR is obviously incompatible with the Block conception;” (381) and “A certain class of GTR models are surprisingly friendly to those versions of dynamism that posit a universe-wide tide of becoming” (TS 381). However, in this section Dainton does not clarify whether or not in any version of relativity theory that there is a moving extensive present of a second or so in duration.

Thus at least in his book Time and Space, Dainton does not give us reason to think that all the important features of the overlap model of the specious present [the present is an extent of time of about one second long where all phases or contents of that present are equally present with those outside its scope being past and future] correspond with the features of time as conceived in contemporary physics and in particular in Einstein’s relativity theories. The main point of difference would be that while both see time as extensive, it is unclear if physical theories think there is a moving present of a length of about one second long. We recall how Dainton writes in “Sensing Change:”

But while this view of time—Presentism—may have some appeal at the level of commonsense, it does not sit easily with the four-dimensional space-time ontology that (many believe) Einstein’s theories of relativity require. By allowing phenomenal unity to connect contents that are separated by time as well as space, it is the Extensional approach that is more in tune with the findings of contemporary physics. (Dainton “Sensing Change” 380)

It seems that while extensional approaches in general are compatible with the way that contemporary theories of physics portray time as being part of a four-dimensional space-time manifold, the overlap model of the specious present as a specific extensional model of time does not correspond with the way that contemporary physics understands the ‘present’ within the extent of space-time. Thus unless Dainton can maker further clarification, it does not seem safe to claim that his overlap model is compatible with contemporary theories of time in physics.

Works cited:


Barry Dainton. (2010, 2nd edition [1st edition 2001]) Time and Space. Durham: Acumen.

Barry Dainton (2008) “Sensing Change.” Philosophical Issues, 18: 362–384.

 

4 Jul 2012

Difference & Sensation: Deleuze's Spinozistic Affect


by Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]

[Central Entry Directory]
[Corry Shores, Entry Directory]

The following is my presentation at the Nederlands Genootschap voor Esthetica (Dutch Association of Aesthetics) Utrecht Expertmeeting Kunstfilosofie in Utrecht, November 2011


Corry Shores

Difference & Sensation:
Deleuze's Spinozistic Affect



Photobucket
(Animation above is my own, made with GIMP and Unfreeze,
image from Spinoza, Opera vol. 2, archive.org
, p.233)

Deleuze is commonly considered an anti-phenomenologist. However, I would like to explore the phenomenological value of his aesthetical ideas regarding affection and bodily sensation. The aim of this presentation is to offer a Spinozistic interpretation of certain concepts in Deleuze’s Francis Bacon book. For this aim, I draw primarily upon Deleuze’s writings on Spinoza’s affection. We will regard affection phenomenologically as involving a sort of affective awareness of bodily-given phenomena. We do this because Deleuze explains Spinoza’s kinds of knowledge in terms of the rhythm of affection.

Deleuze specifically refers to affective awareness as ‘the phenomenon of passage.’ It is the lived transition that we undergo when affections transfer us from one bodily state to another.


There are two primary dimensions, then, to such affective alterations.

One is the physical composition of bodies that becomes changed by the affection. The other is the dynamic of the alteration. Deleuze combines these two dimensions of affection, the compositional and the dynamic, by analyzing two sorts of infinities in Spinoza’s theory of affection, namely, extensive and intensive infinities. There is a cryptic diagram in Spinoza’s Twelfth Letter: the ‘letter on infinity.’ Deleuze’s novel interpretation of the diagram shows how it illustrates the two infinities.


Spinoza writes of the diagram that “all the inequalities of the space lying between the two circles ABCD in the diagram exceed any number, as do all the variations of the speed of matter moving through that area.”


We find similar diagrams in Spinoza’s Principles of Cartesian Philosophy. In the left diagram, both semi-circles share the same center. The space between their circumferences is everywhere the same. However, if the semi-circles do not share the same center, then the space between their circumferences will be everywhere unequal.


He also has us consider the circulation of water moving through the space between offset circles. And on account of the geometry of the non-concentric circles, every place along the circuit has a different width and hence “the fluid body that moves through the tube ABC receives an indefinite number of degrees of speed.”

The infinity diagram would then seem to be a hybrid of these two other figures.


Yet, Spinoza explains in his 81st letter that the infinity here is not obtained from the fact that there are more parts than can be counted. Instead, the diagram according to Deleuze, illustrates a mode’s infinite division into differential relations between infinitely small partitions.

Now, although Spinoza’s ‘letter on the infinite’ predates the inception of differential calculus, Deleuze locates in it what he considers to be seminal calculus notions. To explain the concept of infinitely small vanishing values, Deleuze guides us through the remarkably simple and illuminating visualization in one of Leibniz’ letters.


The diagonal line moves to the right, which diminishes the top triangle, all while increasing the bottom one; yet, because the triangles stay proportionally similar throughout the alteration, the ratio between the smaller one’s legs always remains proportional to the ratio between the larger one’s legs.


Photobucket
(Animation above is my own, made with OpenOffice Draw and Unfreeze)

The vanished triangle, Deleuze says, is not actually there, but is there “virtually,” because the vanishing lines have not yet entirely merged together at the corner. So the infinitely small legs of the smaller triangle are still distinct from each other and from the corner they are collapsing upon; and yet, they also do not extend beyond it. Thus, they do not bear extensive magnitudes but rather only intensive ones, which we will treat as degrees of variation. The philosophical idea here – difference without terms – is essential to Deleuze’s Spinozistic notion of affection. And it will allow us to see how Deleuze can use Spinoza’s diagram to illustrate both the intensive and extensive infinities that are involved in affection.

Photobucket
(Thanks en.wikipedia.org/ A.Greg)

Extensive bodies, for Spinoza, are divisible until reaching what he calls simplest bodies. Simplest bodies form compounds when ones moving at the same or at different speeds maintain a fixed relation in their mutual motions and when “the laws or nature of one part adapts itself to the laws or nature of another part in such wise that there is the least possible opposition between them.”

These infinitely small simplest bodies are never found alone, but rather only in infinite sets. These sets reciprocally unite with other infinite sets to compose a more complex body. These compound bodies are then combined with other bodies, and so on to higher orders until reaching the whole of Nature.

Photobucket
pulsing blue balls animated gif
heart cell beating
circulatory system pulsing beating pumping animated gif
circulatory system animation
Egypt protest bridge animated gif
amazon river animated gif
earth from space animated gif
solar system gif
spiral galaxy animated gif
galaxies animated gif


(Credits in order)
(colliding particles: Thanks A.Greg / en.wikipedia.org)
(blue molecule: Thanks M.L. Rahman / faculty.bracu.ac.bd)
(heart cell: Thanks Bluegrass Pundit / scinewsblog)
(heart beating: Thanks Sterile Barrier Solutions / sbsmed.net)
(circulatory system: Thanks John U / quietmoment.org)
(Egypt bridge protest: Thanks Freemanfilmsuk / youtube.com)
(Amazon river: Thanks BestofAttenborough /youtube.com)
(earth: Thanks UweTube / youtube.com)
(solar system: Thanks animated-sun.weebly.com)
(spiral galaxy: Thanks Kanal von beltoforion1 /youtube.com)
(galaxies: Thanks BrainMind.com / youtube.com)

In his letter on blood, Spinoza has his correspondent imagine a tiny worm so small that it can swim through the blood and observe how its tiniest particles collide and communicate their motion. The worm would see that the simple bodies of blood, the lymph and chyle, continually affect one another’s speeds. Yet, because they maintain their mutual affections without one destroying the other, they together make up the composite body that is our blood. The ratio of their speeds is a level of power that must stay within certain limits.


For otherwise, the simple bodies could decompose and enter into other relations. This happens, for example, when arsenic enters the blood. They will not combine. Rather, on account of their incompatible levels of power, arsenic will decompose our blood.

This sends a chain reaction of affective shockwaves throughout the body, decomposing all the other higher orders of differentially related parts. If it decreases our whole body’s power below a certain threshold, we die. Our body no longer expresses our modal essence, but instead its rearranged parts express the essences of other modes, such as the worms and soil we recompose into.

Thus, Deleuze interprets the infinity diagram as showing how a finite body extending between the limits of its size is divisible into an infinity of simplest bodies.

Photobucket
(Animation above is my own, made with GIMP and Unfreeze,
image from Spinoza, Opera vol. 2, archive.org, p.233)


Now to understand intensive infinities, first consider a ball on a chain swung in a circle. There are competing forces acting on the ball: on the one hand, it wants to fly outward, but on the other hand, its chain pulls it inward. As a result, the ball is always tending to go some certain way at each moment in its circular motion. If we were to cut the ball loose, it would not fly-off in a spiral, but instead outward in a straight line. This would also be the tangent to a circle’s curve at that point.
Photobucket
(Animation above is my own, made with OpenOffice Draw and Unfreeze)

The tangent on curves is like a tendency in the line’s change of direction at that place that is only implied in the movement. Physicists use techniques to find the instantaneous velocity of a moving object; it is something like the speed it is tending to go at that moment.


But how can a velocity be instantaneous? Well, nonetheless, it is a real quantity in the physical world, although it exists only as a virtuality.

Now, for a curve moving in a somewhat more irregular path, finding its tendency-toward-change is more complex, and here is where we might use Leibniz’ method.

Photobucket
(Animation above is my own, made with OpenOffice Draw and Unfreeze)

Photobucket
(Thanks Dr. Siddique / faculty.uncfsu.edu)

Sometimes we can almost feel where a certain part of the curve is heading just by judging its pattern of change. We can also create a triangle showing how the curve’s dimensions extend in a certain region. Then, like with Leibniz’ triangles, we slowly diminish the two triangle legs, and the third diagonal side gives us the tangent, which also tells us which way the curve is tending at that place.

Now, when sets of simplest bodies affectively impact the parts of our own bodies, their shocking collision corresponds with the production of an idea of that object in our imagination. “I look at the sun,” says Deleuze, “and the sun little-by-little disappears and I find myself in the dark of night; it is thus a series of successions, of coexistences of ideas, successions of ideas.” These ideas also correspond to an increase or decrease in our power of acting, and the variations are continuous.

He has us imagine that we encounter on the street our enemy Peter who makes us afraid. Yet, we suddenly turn our glance toward our friend Paul, whose charm reassures us. While moving from the ideas of Peter to Paul, we underwent a continuous increase in our power of action. These variations, Deleuze explains, are ever-altering quantities: “In other words, there is a continuous variation in the form of an increase-diminution-increase-diminution of the power of acting or the force of existing of someone according to the ideas which she has,” and “this kind of melodic line of continuous variation will define affect.”

In the 22nd letter, we find “nothing else pertains to an essence than that which it possesses at the moment it is perceived.” Deleuze reinterprets this as, “there belongs to an essence only the present, instantaneous affection that it experiences.” Deleuze offers an example of this instantaneity of an affective alteration.


We are meditating in a dark room. Then without warning, someone enters the room and abruptly turns on the lights, which completely dazzles us and renders us no longer able to maintain mental focus.

We pass between two very different states in a “lightning fast” alteration: “Two successive affections, in cuts. The passage is the lived transition from one to the other.” Every passage between affections is then necessarily an increase of power or a decrease of power. So if instead we are looking for our glasses in the complete dark, and then someone turns on a dim light, we appreciate him, because then the light increased our power of action. What we note here especially is that the affection’s increase or decrease is seen as instantaneous, which means it does not extend in time. Rather, it is an intensity.

Hence Deleuze’s other illustrative use of the diagram. A body has a certain range of affective power, and when an affection takes it beyond its limits, the body’s parts decompose into other bodies, like when arsenic enters the blood. So consider how there is a largest and smallest limit in the diagram, and throughout it is a continuum of an infinity of differential variations. Deleuze has us conceive this range of variation as representing the range of affective power that we can sustain before we decompose. So this is the intensive infinity.

Photobucket
(Animation above is my own, made with GIMP and Unfreeze,
image from Spinoza, Opera vol. 2, archive.org, p.233)


Now, according to Deleuze, we obtain Spinoza’s second kind of knowledge through our interactive contact with affecting bodies. As we saw with arsenic, the affections of other bodies can decompose us. Yet, in many cases when we are threatened by certain affections, we might know how to modify our own bodies so that we may sustain ourselves.

Deleuze cites an example in Dante’s Inferno. A damned soul is pelted with rain. Yet, rather than let the rain destroy him, he continually modifies the relations of his own body’s parts by twisting around, so that he may co-sustain with the rain’s affections. By making changes in the relations of our body-parts, we send waves of affective alteration throughout us on the level of our simplest bodies.


These internal self-affective shock-waves are in a dance of sorts with the external waves of affection, and their perpetuated interaction is what Deleuze here calls “rhythm.” Another example he offers is swimming. While in the water, a wave draws near us. When it strikes, we and the wave affect each other’s simplest-body arrangements. In that very instant we might be learning how to adjust to the wave’s decompositional forces. By modifying our own body’s composition, we may stay afloat and swim in conjunction with the wave, causing our body and the wave to become a compound, a larger body.

Another illustration better expresses how the rhythm of affection is a matter of differential relations. Deleuze explains that a violin and a piano playing independently do not really produce affective rhythm. However, they may achieve a rhythmic relationship during a joint performance if the violin plays in response to the piano all while simultaneously the piano performs in response to the violin. In this way, they each affectively modify one another while at the same time they modify themselves, which sustains their dual improvisation. And according to Deleuze, Cézanne also describes this rhythmic interaction when he wrote about “how to compose the canvas-easel relation with the relation of wind, and how to compose the relation of the easel with the sinking sun, and how to end up in such a way that I might paint on the ground, that I might paint lying on the ground.”

This portrayal of Spinoza’s affection will now serve to interpret some difficult terminology in Deleuze’s Francis Bacon book. Deleuze writes here that in simple sensations, rhythm “appears as the vibration that flows through the body without organs, it is the vector of the sensation, it is what makes the sensation pass from one level to another.”


The vector here is like the intensity of the affective variation to change its quantitative value. We could then conceive the body without organs as the Spinozistic body composed of continually altering differential relations. Hence, Deleuze writes that the body without organs is “an intense and intensive body. It is traversed by a wave that traces levels or thresholds in the body according to the variations of its amplitude. Thus the body does not have organs, but thresholds or levels.” As the damned soul in Dante’s Inferno twists his once protected side toward the pelting rain, waves of affective variation now impact the newly exposed part directly. It then becomes the site of sensation, where the internal waves of self-affection meet the external waves of affective variation. Yet this status is temporary, because he continually twists in the rain, making instead other parts of his body the new sites of affective reception.

Deleuze continues: “When the [internal] wave encounters external forces at a particular level, a sensation appears. An organ will be determined by this encounter, but it is a provisional organ that endures only as long as the passage of the wave and the action of the force, and which will be displaced in order to be posited elsewhere.” Sensational rhythm, Deleuze explains, can be the unpredictable variance of intensity waves that continually alters our bodily composition.

Thus Deleuze’s body without organs and its waves of sensational intensity can be viewed in light of his conception of the Spinozistic body and its continuous variations of affection, with the concept of ‘rhythm’ playing a similar role in both cases.

This provides us with a more substantial explanation for one of Deleuze’s few attacks on traditional phenomenology, in this case regarding the body without organs in contrast to the phenomenological lived body.

He writes: "this rhythmic unity of the senses can be discovered only by going beyond the organism. The phenomenological hypothesis is perhaps insufficient because it merely invokes the lived body. But the lived body is still a paltry thing in. We can seek the unity of rhythm only at the point where rhythm itself plunges into chaos, into the night, at the point where the differences of level are perpetually and violently mixed. Beyond the organism, but also at the limit of the lived body, there lies […] the body without organs."


Thus, Deleuze breaks from traditional phenomenology’s manner of conceiving the composition of the body as being made of harmoniously integrated parts that work organically with each other and with the world around them during phenomenal experiences. Nothing in its environment would stand out and appear to such a body that is completely accustomed to all the affective influences around it. Rather, for phenomena to appear to us, our bodies would need to sense things that stand out; we would need to detect differences.

A Deleuze-inspired phenomenology would explain bodily-given phenomena that appear to our affective awareness as being based on differential relations within us, throughout the phenomenal world around us, and between our bodies and the world.


Image credits:

Blue and red particles in motion
http://en.wikipedia.org/wiki/File:Translational_motion.gif
Thanks A.Greg

Blue molecule in motion
http://faculty.bracu.ac.bd/~mlrahman/Research.html
Thanks M.L. Rahman

Heart cell
http://scinewsblog.blogspot.com/2011/04/scientists-turn-blood-cells-into.html
Thanks Bluegrass Pundit

Heart beating
http://sbsmed.net/
Thanks Sterile Barrier Solutions

Circulatory system animated gif
http://www.quietmoment.org/my_weblog/2011/03/mysteries-of-the-human-body.html
Thanks John U.

Egypt protestors on a bridge
http://www.youtube.com/watch?v=rXbRdumboZ0
Thanks Freemanfilmsuk

Amazon river
http://www.youtube.com/watch?v=dn53PtW0AnA
Thanks BestofAttenborough

Earth
http://www.youtube.com/watch?v=hALtHnu4WEo
Thanks UweTube

Solar system
http://animated-sun.weebly.com/animated-solar-system.html
Thanks animated-sun.weebly

Spiral Galaxy
http://www.youtube.com/watch?v=AD9OV1Zrs4I
Thanks Kanal von beltoforion1

Galaxies
http://www.youtube.com/watch?v=X5zVlEywGZg
Thanks BrainMind.com

Spinoza. Opera, vol. 2. Edited by Carl Gebhardt. Heidelberg: Winter, 1972.
http://archive.org/details/operaquotquotre00landgoog

Geometrical Derivative animation:
http://faculty.uncfsu.edu/msiddiqu/Maple_Animations.htm
http://faculty.uncfsu.edu/msiddiqu/images/images/Gif_Folder/Definition%20of%20Derivative18.gif
Thanks Dr. Siddique of Fayetteville State University

12 Sept 2011

Unity under Displacement: The Moving Integration with Absence as the Phenomenon of Time. §g ch2 prt3 of Merleau-Ponty, Phenomenology of Perception

by Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]

[Central Entry Directory]
[Merleau-Ponty, Entry Directory]


Unity under Displacement:
The Moving Integration with Absence
as the Phenomenon of Time

Maurice Merleau-Ponty

Phénoménologie de la perception
Phenomenology of Perception

Part III. Being-for-Itself and Being-in-the-World
Troisième Partie: L'être-pour-soi et l'être-au-monde

Ch. 2. La temporalité
Ch. 2. Temporality


What does time's continuous movement from absence to presence got to do with you?

We might look back at our youth as being a better time of our lives. These moments have passed. We are aware of them only through the eyes of the present, which sees them differently than they were originally seen by our younger self, because each moment since then has given new ways and reasons to reflect upon these former times. It might even seem that our youth is drifting away from us like a boat cast to sea, while death looms on the horizon, sailing slowly but determinedly toward us to take us away. But so long as we are living, perhaps whenever we feel time directly, it is not as a distance to our youth but rather as the continuous movement of new moments passing in and out of our lives. When do we feel time? What does time feel like? Does it feel like a motion? That same motion was with us when we were young, and will be there with us until the end. There is one time of our lives.


Brief Summary

The phenomenon of time is its integrated motion in and out of absences (future to past) that are thoroughly tied to and announced implicitly in any given present moment of this continuous movement. We are not retentionally aware at moment C of past moments A and B, because B through the eyes of moment C has become modified to B', and A then to A''. They are all a part of one act of retentional awareness, so they are no longer successive moments. Their temporal successive character is given phenomenally in their continuous modification from A' to A'' for example. Each moment differentiates itself from the others, on account of their having been once present to the exclusion of the presence of the others. But this exclusion is possible on the basis of the continuous motion which brought any one moment into the present and which takes it out as well. The present is not a pure present, because it implicitly announces the future's 'destiny', just as it implicitly announces the destined passing of the past moments. The future and past cross over each other in the present moment. So there is one unified time that is made of diverse moments of presencing and that is in a continuous motion of transition in and out of absence.


Points relative to Deleuze

Merleau-Ponty's phenomenon of time is its givenness to us as a continuous motion of dispacements from absence to presence to absence, with all motions being integrated with the rest such that at any moment, the others are given implicitly somehow. Each moments A, B, C, and D, held in our retentional awareness, have contents which differentiate each one from the others. But they are no longer successive in the temporal sense, because back when they were in the process of passing through presence, their neighbors were absent; yet in our retentional awareness, all moments, all neighbors, are given together in our present moment of consciousness. The phenomenon of time is their continuous motion from the future to the past through the present, which involves their going deeper and deeper into our retentional awareness, being modified each time from the new perspective we take at each new moment.

The Deleuzean phenomenon of time will also involve the differentiation between A, B, and C, and in fact will be more clearly based on it. What allows moment A to move to moment B is the fact they are different to begin with, for otherwise we would remain at moment A. The Deleuzean phenomenon of time is not the movement from the one to the other, but rather that flashing moment when their differences are given. In other words, we do not have time because we go from instant A continuously to instant B. During the passage between them, they in a way are both given simultaneously as the differences between them. So there is a shock from one moment to the next. The logic of becoming is something like: (A and B) when A implies not-B and B implies not-A. At the original seat of the phenomenon of time, at its primordial core, what we phenomenally feel most directly when time appears to us, is not its motion, but the paradoxical co-givennes of incompatible (incompossible) states of affairs. So phenomenologically speaking, the origin of phenomenal time is the sudden flashes of differential relations that shock us. If we look in the mirror and for the first time notice a sign of age, like a wrinkle, for a brief instant we feel three years time having passed. Time is not the linear time-line A, B, C, D, nor is it the continuous movement of absence to presence to absence, of A to B concurrent with A to A'. Time is instead the contentless, purely affective difference between A and B, between A and D, between A and A'', and so on. It is in fact the discontinuity from A to B that gives the passage its temporal character, not the continuity. Thus what gives the present its temporal character is not its continuous passage from future to the past, but rather the fact that the present is discontinuous with these other moments, standing out completely from them as not fitting in completely with them. The parts of the present that give us temporal affections are not the continuities, the announcements of the future; those go unnoticed because they do not tell us anything. The temporally phenomenal content of the present are its shocking standings-out from the past and future. Deleuzean phenomenal time is always sudden, always based on paradoxical combinations and incompatibilities whose differential shocks between them alert our attention to what is immediately given.



Review Paragraph §f

Previously Merleau-Ponty discussed Husserl's triangle diagram for retentional awareness.


(From Phenomenology of Perception 479 / 484)

Animation:

Photobucket
Current moment A in the next moment became something in our retentional awareness, A'. In yet another succeeding moment, we are not just attending to A retentionally, we are rather intending A'', which is a retention of a retention of A. It might seem that each moment we are retentionally aware of something not unified with the original A. Yet, we regard them as all being intentional awareness of one A. This is because there is a continuous passage of their going further into the past, so we can get back to A when we are at C. During moment C, we have in our mind a retention of prior moment B, so this is B'. B' has in its retentional awareness prior retention A'. But because B' was modified by C, that makes A' modified as well, making it A''. When we trace events back to A, we do so by seeing A'', which is A under the view of two layers of retentional modification. Merleau-Ponty says that these new layers of consciousness do not block our view of the past moment, but they also do not give us a direct view of it either. It is rather like seeing the bottom of a stream through the clear water moving above it. But this still does not give us a phenomenal experience of time, because it does not include the absence involved in succession. He also notes that we have a more primordial intentional awareness of the feeling of our current moment of awareness leaning up against the absences of the past and future whose forces are pushing and pulling the current moment away. There is a paradox here. This involves an absolute difference between things which are not unified, because it is between absence and presence, and yet it is also on the basis of this differential relation that all moments are connected immediately upon one another and thus time's uncombinable parts are as well the grounds for time's unification.


Summary
§g

To solve these problems, Merleau-Ponty reminds us that what we are considering is an instant of our mental awareness, which I think is each diagonal line in the diagram. Thus we are not dealing with discrete moments A B C, because our instant has just C, B', and A'' all as parts of the same moment of consciousness. There are not a multiplicity of various different retentions and protentions in this one instant of awareness. (1945: 481d / 486d) Also, it is not firstly that there is an arising present which then causes secondarily the past to pile up, and the future be anticipated differently. This is because our awareness of the present is itself the movement of the future into the present, and the present into the past. All three are in motion simultaneously.
The upsurge of a | fresh present does not cause a heaping up of the past and a tremor of the future; the fresh present is the passage of future to present, and of former present to past, and when time begins to move, it moves throughout its whole length. (481b / 486-487)
The instants A, B, and C are not given in one instant each as successive moments. They are rather given as the movement from A'-B to A''-B'-C. What makes A B and C different in one moment of consciousness is not that they are successive, because they here are not, but rather that they differentiate among one another within our awareness. What gives them their temporal character in such a present immediate experience is not so much the temporal gap between A, B, and C, which is now gone; rather the phenomenon of time here is the awareness of A' becoming A'' and B becoming B'. These are retentions, which means the phenomenon of time is our awareness of some event in the past being continuously seen through a continuously thickening lens of other intervening retentional moments linking to it.
The ‘instants’ A, B and C are not successively in being, but differentiate themselves from each other, and correspondingly A passes into A′ and thence into A″. In short, the system of retentions collects into itself at each instant what was, an instant earlier, the system of protentions. There is, then, not a multiplicity of linked phenomena, but one single phenomenon of running-off. Time is the one single movement appropriate to itself in all its parts, as a gesture includes all the muscular contractions necessary for its execution. When we pass from B to C, there is, as it were, a bursting, or a disintegration of B into B′, of A′ into A″, and C itself which, while it was on the way, announced its coming by a continuous emission of Abschattungen, has no sooner come into existence than it already begins to lose its substance. (481c.d / 487a.b)
I wonder if one way to view this would be something like a reverb or the visual trail left behind fast moving objects. Maybe what can make these phenomena seem magical is not just hearing the simultaneity of the past and the present, but also hearing the movement of the present into the past, represented as its continual fading. A reverb might give us all at once conscious moments A, B, and C of our experience of a sound. The phenomenon of time in Merleau-Ponty's sense would then be us hearing the action of the fading out as the sound extends, because perhaps us hearing the fading of the beginning of the sound, the A moment, corresponds with it receding deeper into our retentional awareness; so the diminishing vividness of the sound in our ears would match the diminishing vividness in our retentional awareness. So when we hear a reverb, while hearing moment C, the prior moment has faded somewhat, so it is not B but rather B', and the first moment is even more faded, and is thus A'' rather than A.

When time appears to us as something we notice, what we sense is a sort of outward blooming from the reality that is given to us now. The present moment A soon becomes B. So A becomes B. But also, A makes a transition not just to B, but also to being something in our retentional awareness, so A also becomes A'. What links A with A', the present intention with its immediately succeeding retention, is not some synthesis of the two on the basis of their identification with one another. The transitional movement from one state to the next is what binds them together. Merleau-Ponty's phenomenon of time is like an awareness of the continuous motion of intentional contents slipping down the retentional diagonal of Husserl's diagram.
It is nothing but a general flight out of the Itself, the one law governing these centrifugal movements, or again, as Heidegger says, an ek-stase. While B becomes C, it becomes also B′; and simultaneously A which, while becoming B, had also become A′, lapses into A″. A, A′ and A″ on the one hand, and B and B′ on the other, are bound together, not by any identifying synthesis, which would fix them at a point in time, but by a transition-synthesis (Übergangssynthesis), in so far as they issue one from the other, and each of these projections is merely one aspect of the total bursting forth or dehiscence. Hence time, in our primordial experience of it, is not for us a system of objective positions, through which we pass, but a mobile setting which moves away from us, like the landscape seen through a railway carriage window. (481-482 / 487bc.d)
Merleau-Ponty then describes the passage of time as like a sort of movement coming first from a distance into explicit physical expression and then fading back into a distance. When a new moment comes, it was in a way germinating somehow within what we are immediately aware-of. Slowly it comes to bloom, and in this way it sort of fades-in to full volume in the present. Then reaching its peak, it fades back into the retentional margins of our awareness.
the disintegration undoes what the passage from future to present had achieved: C is the culmination of a long concentration which has brought it to maturity; as it was being built up, it made its approach known by progressively fewer Abschattungen, for it was approaching bodily. When it came into the present it brought with it its genesis, of which it was merely the ultimate expression, and the impending presence of what was to come after it. So that, when D comes into being and pushes C into the past, C is not suddenly bereft of its being; its disintegration is forever the inverse or the consequence of its coming to maturity. In short, since in time being and passing are synonymous, by becoming past, the event does not cease to be. (482b.c / 488a.b)
What we call objective time - we might think of it as time outside our consciousness - can be found in the sliding overlap of the future and the past in the present. He uses the term 'destiny' to explain how it is that the basis of time involves something absent that as well is fully given in presence. Because everything comes to be through this overlapping passage of future to past through the present, what comes to be was destined previously to arrive now, and it as well, as something temporal, is now destined to pass out of existence in the next moment.
The origin of objective time, with its fixed positions lying beneath our gaze, is not to be sought in any eternal synthesis, but in the mutual harmonizing and overlapping of past and future through the present, and in the very passing of time. Time maintains what it has caused to be, at the very time it expels it from being, because the new being was announced by its predecessor as destined to be, and because, for the latter, to become present was the same thing as being destined to pass away. (482c / 488b.c, boldface mine)
For Bergson, duration is essentially a continuous flow of newness. Merleau-Ponty says that Bergson should not have reduced the essence of time to just its continuity. The continuous passage of time means that the movement from future to present to past proceeds by gradations so imperceptible that they all blend together. This in a way denies the absolute difference between the presence of the present and the absence of the future and past.
Bergson was wrong in explaining the unity of time in terms of its continuity, since that amounts to confusing past, present and future on the excuse that we pass from one to the other by imperceptible transitions; in short, it amounts to denying time altogether. (482d / 488c)
Merleau-Ponty says that Bergson was however right to think of time's continuity as an essential temporal phenomenon. Merleau-Ponty goes on to analyze what he thinks it is that makes up the phenomenon of time's continuity. He seems to be saying that the continuity is the horizonal integration of the present with the absent past and future. What makes moment C what it is, is that it is both an anticipation of D at the same time a passing into the past. Continuity is always an active motion of passage. Each moment is thoroughly integrated with the others and none are completely distinguishable from one another, on account of the continuous passage.
Bergson was wrong in explaining the unity of time in terms of its continuity, since that amounts to confusing past, present and future on the excuse that we pass from one to the other by imperceptible transitions; in short, it amounts to denying time altogether. But he was right to stick to the continuity of time as an essential phenomenon. It is simply a matter of elucidating this. Instant C and instant D, however near they are together, are not indistinguishable, for if they were there would be no time; what happens is that they run into each other and C becomes D because C has never been anything but the anticipation of D as present, and of its own lapse into the past. (482-483 / 488d, boldface mine)
This means that the future and the past are spoken through the present, even if in a much less obvious way. Thus the phenomenon of time is not an experience of a series of nows, each with its own view of the past and future, which secondarily requires our consciousness to string them together synthetically. Rather, the phenomenon of time is their motional unity, their continuous transitioning into and through one another. There is one time as the motion of coming into explicit awareness of the present through a continual transitional movement from future to the past through the present. The absence of the past and future is given now, but not as an open announcement in the present, but rather as what is announcing itself as coming and as having passed already.
This amounts to saying that each present reasserts the presence of the whole past which it supplants, and anticipates that of all that is to come, and that by definition the present is not shut up | within itself, but transcends itself towards a future and a past. What there is, is not a present, then another present which takes its place in being, and not even a present with its vistas of past and future followed by another present in which those vistas are disrupted, so that one and the same spectator is needed to effect the synthesis of successive perspectives: there is one single time which is self-confirmatory, which can bring nothing into existence unless it has already laid that thing’s foundations as present and eventual past, and which establishes itself at a stroke. (483b / 488-489)


Merleau-Ponty, Maurice. Phenomenology of Perception. Transl. Colin Smith. London/New York: Routledge, 1958.

Merleau-Ponty, Maurice. Phénoménologie de la perception. Paris: Éditions Gallimard, 1945.