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

by Corry Shores
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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)

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.

 

Simultaneity is Absolute. §81. Ch.4.One or Many Durations? Bergsonism. Deleuze

by Corry Shores
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Gilles Deleuze

Le bergsonisme

Bergsonism

Ch.4.

Une ou plusieurs durées ?

One or Many Durations?

Previously Deleuze discussed Bergson's reaction to Einstein's theory of broken-up simultaneities. Bergson shows that the theory presupposes simultaneities which are absolute. One of these absolute simultaneities is the flow of all flows (which is concurrent with our own consciousness), and hence simultaneities cannot break apart.

§81 Time is One, Because It's a Special Kind of Many

[Recall Bergson's distinction between virtual and actual multiplicities (see §78 of Bergsonism). There is one flow of all flows. Only secondarily may we divide it up into discrete numerically different constituent flows. Because it requires a second act to extract the constituent flows, the universal flow of duration is a virtual multiplicity. But after our mental acts of division, it becomes an actual multiplicity. Einstein's relativity performs such a division, and looks at other flows from the perspective of a particular one out of the group. As a result, we might come to conclude that there is a plurality of times. But these other times are not real lived times. All lived times are concurrent with each other, with the ultimate flow, and with our conscious duration. Einstein wants it both ways. He would like to assign other flows a different temporality, which would not be livable, while in the same stroke call them 'times', as though they were in the same category as lived time. This lived time is only found in the virtual multiplicity. So by trying to have it both ways,] Einstein confuses the virtual with the actual (85a). [Recall also Bergson's distinction between image and symbol from §79. Physicists use math to produce a symbolic representation of the time in other moving systems. But they are not so much imagining the people in the other systems as much as they fictionalize or merely symbolize them. For if the physicists really imagined the other people, they would also take-on their conscious perspective, and thereby find their own system to be the system of reference.] Relativity physicists regard their symbolic tokens, which stand for fictionalized observers, as being in another sense real conscious beings. This explains how they also confuse the virtual with the actual.

So we began with the question, is duration one or multiple? We found that in one sense it is multiple. But this is a virtual multiplicity, which means it is primarily united and only secondarily divided into spatially-distinct actual fluxes. Hence "Only the hypothesis of a single time can, according to Bergson, account for the nature of virtual multiplicities" (85b). Scientists normally spatialize time by representing successive moments along a drawn time-line. But then we see the line all at once. The moments are no longer successive, but rather simultaneous and instantaneous. This deprives them of their real durational character. Einstein spatializes time in yet a new and different way. At different places in space are objects moving at different speeds. The object in one place, moving at its speed, will have a different time-flow than another object moving a different speed through its place. Deleuze writes: "By confusing the two types - actual spatial multiplicity and virtual temporal multiplicity - Einstein has merely invented a new way of spatializing time" (85bc). However, this spatialization of time has advanced the sciences profoundly. [In footnote 24, or the one on p.87 of the French, Deleuze cites two parts of Duration and Simultaneity (reference to be added later). The first one could be: "We have just seen how the notation of a fourth dimension is introduced automatically, so to speak, into the theory of relativity. This undoubtedly accounts for the often expressed opinion that we are indebted to this theory for the earliest suggestion of a four-dimensional environment merging time and space" (Bergson 103a). The second one, regarding the advantages of assuming a space-time manifold, could be: "And much is gained, for the expression with which we provide him is that of a new physical truth: it points out how the 'transmission' of light behaves with regard to the 'translation' of bodies" (119c).]

And yet, the mathematics involved in these four-dimensional calculations does not tell us something about the real nature of time. Although it is beneficial to science, it only produces symbols for a temporality that no one could possibly experience.

this achievement is that of a symbol for expressing composites, not that of something experienced that is capable, as Proust would say, of expressing "a little time in the pure state." (85c)

cette conquête est celle d'un symbole pour exprimer les mixtes, non pas celle d'un vécu capable d'exprimer, comme dirait Proust, « un peu de temps à l'état pur ». (87c)

And as we noted, time, as a virtual multiplicity, is more fundamentally a unity. Deleuze writes:

Being, or Time, is a multiplicity. But it is precisely not "multiple"; it is One, in conformity with its type of multiplicity. (85cd)

L'Être, ou le Temps, est une multiplicité ; mais précisément il n'est pas «multiple », il est Un, conformément à son type de multiplicité. (87cd)

Deleuze, Gilles. Bergsonism. Transl. Hugh Tomlinson and Barbara Habberjam. New York: Zone Books, 1991.Deleuze, Gilles.

Deleuze, Gilles. Le bergsonisme. Paris : Presses Universitaires de France, 1966.

Bergson's Einstein §74. Ch.4.One or Many Durations? Bergsonism. Deleuze

by Corry Shores
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[The following summarizes parts of Deleuze's Bergsonism. My commentary is in brackets. Paragraph subheadings are my own.]

Gilles Deleuze

Le bergsonisme

Bergsonism

Ch.4.

Une ou plusieurs durées ?

One or Many Durations?

Previously Deleuze discussed Bergson's position on whether there is just one duration or many of them. Bergson often describes duration as a heterogeneous qualitative multiplicity. So we might expect him to say that there are many durations. Oddly, Bergson holds that there is just one duration. This is his monist hypothesis of time.

§74 Bergson's Einstein

Deleuze wonders how we might account for Bergson's surprising position. It is the product of Bergson's confrontation with Einstein's relativity theory. Both Einstein and Bergson draw their notion of multiplicity from Riemann. However, they come to opposing positions regarding whether there is a plurality or unity of time.

Deleuze will review Bergson's summary of Einstein's relativity theory. [It can be found in greater detail in the first chapter of Bergson's Duration and Simultaneity].

We in the first place conceive of bodies in motion. [Their movement is reciprocal. While in a steadily moving train, we walk around and feel as though we are on stable ground. But we might observe through the window a person along the track rapidly coming-and-going. For us on the train, the person is in motion. But for this same person observing the train from the ground, the locomotive is the moving body, while she remains immobilized, standing on firm ground. This can be explained using Newtonian physics. But when dealing with the speed of light, we encounter a problem. First consider a man walking on a boat. He feels himself travel at the speed of his gait. But a woman on the docks sees him travel not just his walking speed, but also she adds to that the speed of the boat. So the walking-man's speed depends on the perspective of reference. This is not so for light. It goes the same speed for the person on the boat as it does for the person observing from the dock. But this is strange, because for the man on the boat, the light goes a certain distance. But for the woman on the dock, it goes a different distance; for, the boat moves underneath the light, in a sense. To explain how the light goes the same speed for different distances, Einstein theorized that] time dilates and space contracts [on a moving body, from the perspective of the reference position, which is provisionally considered as immobile, so that accurate calculations are made that will accord with all other moving systems, which also must take this phenomenon into account. But as a result of the distortions in time, what seems simultaneous on the boat is really not so from the perspective of the woman on the dock. Hence] simultaneities in mobile systems are not so for fixed ones. Einstein also theorized that motion, rest, and acceleration are all relative. [So for the woman on the dock, the boat-man is moving and is wrong about his simultaneities. But for him, his own boat is stable, and the dock moves away from him. So for the boat observer, what seems to be simultaneities on the dock for the dock person are not simultaneities for the boat person. Thus,] "these contractions of extensity, these dilations of time, these ruptures of simultaneity become absolutely reciprocal" (Deleuze 79bc). [So we have one time for the boat person, which he thinks differs for the time on the dock. Yet the person on the dock has her own time, which likewise she thinks differs from the boat's time. Hence] "there would be a multiplicity of times, a plurality of times, with different speeds of flow, all real, each one peculiar to a system of reference" (79c).

Now, if we want to situate a point somewhere, we need to indicate both its spatial and temporal position. So the only unity of time is the fourth temporal dimension united with its spatial dimensions [see this entry on the Mankowski diagrams for this correlation between time and space]. But this unity does not hold universally throughout the cosmos. The relations between time and space for moving bodies depend upon the relative speed of the observer. So in this way "It is precisely this Space-Time block that actually divides up into space and into time in an infinity of ways, each one peculiar to a system" (79d). [All of this is Bergson's summary of Einstein's theory of relativity. Bergson builds from the same premises to conclude that there is only one duration, and not the plurality that Einstein posits].

Deleuze, Gilles. Bergsonism. Transl. Hugh Tomlinson and Barbara Habberjam. New York: Zone Books, 1991.Deleuze, Gilles.

Deleuze, Gilles. Le bergsonisme. Paris : Presses Universitaires de France, 1966.

The One of Time. F: L'observateur fantasmatique. Ch. 4. Concerning the Plurality of Times. Duration and Simultaneity. Henri Bergson

by Corry Shores

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[The following summarizes part of chapter 4 in Bergson's Duration and Simultaneity. Paragraph headings are my own. My personal commentary is in brackets.]

The One of Time

Henri Bergson

Duration and Simultaneity

Ch. 4. Concerning the Plurality of Times

Subheading F:

L'observateur fantasmatique

Previously Bergson further elaborated his explanation for why relativity does not imply that there are multiple times, break-ups of simultaneities, or contractions of lengths. Rather, when we fully take-up relativity theory's premise that all motion is reciprocal, we thereby conclude that there is just one duration shared by all conscious observers, no matter their relative speed.

§117 The Physicist Becomes Philosopher

Bergson will now summarize the chapter. He returns to the hypothesis of the physicist on the earth. The scientist repeats over and again the Michelson-Morley experiment. But instead of him worrying about physics calculations, the physicist will now take-up the philosophical concern regarding what is real. Hence "his gaze never leaves the moving line of demarcation that separates the symbolic from the real, the conceived from the perceived. Instead of adopting the language of relativity, the physicist will now use such terms as 'reality' & 'appearance', and 'true measurements' & 'false measurements' " (80d). Nonetheless, he will adopt the theory. By translating the theory into this philosophical language, we may better evaluate it and modify it.

§118 The Constancy of Light's Motion

[Recall what the experiment sought to find. During different times of the year, the earth moves a different speed. The light apparatus of course moves with the earth. The experimenters expected the light to also move a different speed during different times of the year. But it did not. Light travels the same speed no matter how fast its origin moves. Also, they rotated the light path so that it would be moving at different angles from the earth's direction of motion. Again, light traveled the same speed in all cases. Hence,] "The speed of light is thus the same in every direction, the same for every speed of the earth" (81a). Bergson asks, why?

§119 The Physicist's World is Immobile

The physicist solves this problem by noting that motion is relative. The earth is only in motion relative to another perspective. We just as well may make the earth itself our unmoving system to which all other motion is relative.

§120 But There May be Physicists on Other Worlds

But then someone taking the perspective of another planet would see ours as the one in motion, and hence there would be no grounds to explain the common speed of light on earth as resulting from earth's immobility.

§121 Extra-Terrestrial Physicists

But the physicist on earth replies on the basis of relativity theory. He notes that the extraterrestrial observer will still measure light as moving the same speed. This is because the earth's units of time for the extraterrestrial onlooker "appear to him longer than" they appear to the earth observer. Another reason light would prove to go the same speed is because the earth observer uses rulers whose lengths have contracted. [Consider the person on earth, who synchronizes clocks at a distance. He does so by sending light to the other one, who bounces it back. They then adjust for the time light takes to make its trip for that given distance, and they synchronize their clocks accordingly. But from the perspective of someone on another planet, the earth is in motion relative to themselves. So as long as the light does not move perpendicular to the earth's motion, the distance it travels on the trip down will be different from the distance it travels on the way back. So the earth person's clocks could not really be synchronized. One of the clocks would have to lag behind the other.] The lag between clocks increases with the speed of the earth. It does so in a way that maintains a balanced inverted proportion. The faster the speed, the greater the lag. [This lagging, in a sense, gives the light more time to travel the greater distance that the earth travels with increased speed]. So the earth observer, unaware of the lag, never notices it, and he always obtains the same speed for light, because somehow the time distortions counterbalance the effects of the earth's speed.

This is the way the earth observer would reason. The conclusions accord with the extraterrestrial's observations. But what the earth observer is saying is that he obtains the correct measurements for his own system only because his own mistakes cancel each other out. This allows him to still obtain the constant speed of light. But for the extraterrestrial observer, all the earth-physicist's measurements and calculations are incorrect. Yet, let's consider if this imagined extraterrestrial observer were to come to life, and were to take his own planet as immobile. He would likewise need to also see his own calculations as mistaken, from the perspective of the earth observer, and despite the errors, he still obtains the same speed of light.

§122 Seeing Double from Too Much Relativity Theory

The relativity theorists in a way gives us double-vision, as if by pressing down on our eyeballs so that we see double. The additional image allows us to regard our own systems as a fixed reference and still bring all the other seemingly discordant ones into accord with our own;

the first image perceived, the experiment first begun, doubles into a phantasmal image where duration slows down, where simultaneity incurvates into succession, and where, for that very reason, lengths change. This diplopia, artificially induced in the experimenter, is to reassure him, or rather, to secure him against the risk he thinks he is running (which he really would be running in certain cases) in arbitrarily making himself the center of the world, in referring everything to his personal system of reference, and in nevertheless building up a physics that he would like to be universally valid. He can rest easy from now on; he knows that the laws he formulates will be confirmed, no matter from what vantage point we view nature. For the phantasmal image of his experiment, an image which shows him how this experiment would look, if the experimental device were in motion, to a motionless observer provided with a new system of reference, is no doubt a temporal and spatial distortion of the first image, but a distortion that leaves the relations among parts of the framework intact, keeps its connections and relations being precisely what we call the laws of nature. (84b.d)

§123 The Science-Fiction Phantasy of Relativity

Nonetheless, the terrestrial observer must never forget that the other observer is imagined, all while he himself is real. And yet still, the earth physicist may imagine as many of these other phantasmal observers as he pleases, in fact he may imagine "as many as there are speeds, an infinity of them" (83a).

All will appear to him as building up their representation of the universe, changing the measurements he has taken on earth, obtaining for that very reason a physics identical with his. From then on, he will work always at his physics while remaining unreservedly in his chosen observation post, the earth, and will pay them no more heed. (83a)

§124 One Giant Leap for an Imagined Man

Yet physics moves great leaps forward by positing these imaginary observers.

§125 Relativity is a Philosophical Tool.

It Proves There is Single Time and not Multiple Time,

as Many Relativity Theorists Believe

We are located on earth. From here we posit phantasmal physicists at all other locations of the universe. But for each of these phantasmal physicists there could be a real one in its place, who likewise posits other phantasmal physicists strewn about the cosmos.

But we want to know what is real. And we would like to determine if there is single time or multiple time. To do so, "We must pay no attention to phantasmal physicists, we must take account only of real physicists" (83bc). So, do all real physicists perceive the same time?

Normally a philosopher would struggle to "declare with certainty that two people live the same rhythm of duration. He cannot even give this statement a rigorous, precise meaning" (83c). Nonetheless, relativity theory allows us to do so. What we find is that in systems moving reciprocally to each other, the observers in these systems are interchangeable; "doing away with the privileged system is the very core of the theory of relativity. Hence, this theory, far from ruling out the hypothesis of a single time, calls for it and gives it a greater intelligibility" (83c, boldface mine).

Bergson, Henri. Duration and Simultaneity. Ed. Robin Durie. Transl. Mark Lewis and Robin Durie. Manchester: Clinamen Press, 1999.

The original French version is available online at:

http://www.archive.org/details/dureetsimultan00berguoft

Simultaneous Relativities. E: Les deux simultanéitiés. Ch. 4. Concerning the Plurality of Times. Duration and Simultaneity. Henri Bergson

by Corry Shores

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[The following summarizes part of chapter 4 in Bergson's Duration and Simultaneity. Paragraph headings are my own. My personal commentary is in brackets.]

Simultaneous Relativities

Henri Bergson

Duration and Simultaneity

Ch. 4. Concerning the Plurality of Times

Subheading E:

Les deux simultanéitiés

Previously Bergson explained that the theory of relativity leads us to conclude that there is just one universal real time.

§83 Distance & Simultaneity

Bergson will now deal with the issue of the breakup of simultaneities.

First he will review what he has said about intuitive simultaneity [see §42]. Bergson will also give simultaneity this formal definition: "it is an identity between the readings of clocks synchronized through an exchange of; optical signals, and concluding that simultaneity is relative to the synchronizing" ["c'est une identité entre les indications d'horloges réglées les unes sur les autres par un échange de signaux optiques, conclure de là que la simultanéité est relative au procédé de réglage."] (60a/116b).

Bergson acknowledges that we compare clocks to determine an event's time. However, "the simultaneity of an event with the clock reading that gives us its time does not follow from any synchronizing of events with clocks, it is absolute" (60b).

[Note Einstein's definition of simultaneity: We have to take into account that all our judgments in which time plays a part are always judgments of simultaneous events. If, for instance, I say, "That train arrives here at 7 o'clock," I mean something like this: "The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events" (Einstein The Principle of Relativity 39, qtd. in Mook & Vargish 56bc).]

[Recall the issue of synchronizing clocks that are at a distance (look about midway into this entry from chapter 1. Or perhaps better, look at section 3.4 of this entry, which shows more clearly how distant clocks would be synchronized by a third person midway between them).] Image two people each have a clock, but they stand at a distance to each other. A third person stands equidistant between them. The clock-operators send signals to the center person. The signals take the same amount of time, because they are equally distant from the center person, and light always travels the same speed. This third person regards both clocks as being in his own system of reference. So even distant simultaneities suppose there being the immediate sort of simultaneity that we see between a clock and a nearby event. (60c.d)

§84 Distant Clocks in One Mind

Bergson returns to the examples of systems S and S', which are in motion with respect to each other. We begin by taking system S as our system of reference. By doing so, we immobilize it. In this system, the clocks have been synchronized by using an exchange of optical signals. Because the system is motionless, the signals make the same trip out and back.

We will now designate points where distant clocks are located: points Cm and Cn. An observer stands between these two clocks, and can "embrace from there, in a single act of instantaneous vision, any two events occurring at points Cm and Cn respectively when these two clocks show the same time" (61a). In particular, he will "embrace in this instantaneous perception the two concordant readings on the two clocks" (61ab). In this way, all simultaneities indicated by the clocks will then "be converted into intuitive simultaneity inside the system" (61).

§85 Distant Clocks Worlds Away

Now we will turn to system S'. An observer in this system regards it as his reference system. So he too immobilizes it. He likewise synchronizes his clocks. "Hence, when two of his clocks show the same time, the simultaneity they indicate could be lived and become intuitive" (61).

§86 The Nature of Simultaneity

Simultaneity in these cases is intuitive. "Thus, there is nothing artificial or conventional in simultaneity whether we apprehend it in one or the other of the two systems" (61bc).

§87 Conventions of Succession

We will now see how an observer in S judges events in S'. For S, the S' system is in motion. Consider the example of a person walking on a boat. She seems to herself to be walking at a certain speed. But from the perspective of someone on the dock, she moves both her speed plus the boat's speed. The person in S is like someone on the dock, watching moving system S'. The optical signals between clocks move distances that include the motion of the system itself. So the signals do not make the same trip one way as the do on their return. The exception of course is if the clocks are positioned perpendicular to the system's motion. Here we see they make diagonal lines, which are equal.

Now recall what we said about the moving system and the disruption of simultaneity, from our simplification.

We see that the moving system sees each beam at a different time, but the stationary person sees them at the same time. The situation with S and S' is different. Here we are dealing with the optical signals going from one clock to the other and back. Unless the light's path is perpendicular to the system's relative motion, the path will be different there and back. But light will be the same speed. That means time and space in the moving system distorted from the perspective of the motionless observer. So the clocks that have been synchronized from the point of view of system S', are instead successive from the viewpoint of system S.

Note what it is that the observer in S considers to be a succession. The clocks on moving system S' were synchronized. But they did so under the assumption that light had the same distance to travel from one clock to the next. But from the viewpoint of S, they had a different distance. So the clocks in system S' read the same time only one-after-the-other. But if the person on S took the perspective of S', he could have considered the concordant readings of the clocks as simultaneous. So we see that the definition of 'succession' is merely a convention. Yet as we noted, the simultaneity of events in one person's consciousness, however, is not relative and hence not conventional.

=

§87 Ultimate Simultaneity

Bergson will now verify that in fact simultaneity is not conventional.

We assume that S' is a duplicate of S. The same history unfolds in each. And they are moving relative to each other. So it is arbitrary which one we consider motionless. We choose S, then, as our reference system.

The faster S' moves away, the more time and space will seem to distort, and the more simultaneities will become successively separated.

We will say that events A, B, C, D of system S are simultaneous for the observer in S. There are thus identical events in S', events A', B', C', D'. These are simultaneous for the observer in S'.

We will now imagine a supreme consciousness that is "capable of instantly sympathizing or telepathically communicating with the two consciousnesses in S and S' " (62b). Because he experiences what both observers experience, and because both observers experience simultaneity, the supreme consciousness as well perceives A, B, C, D and A', B', C', D' each as simultaneities.

Now, we can also imagine that S' returns to S. [We saw in section C of this chapter already that the time spans for each person would be the same. See this entry for more compelling reason to reject the solutions to the twin paradox which say the times are different]. So both observers in the different systems lived the same total duration. Now, let's imagine that we divide this extent of time into equal slices. There would be the same number of slices for both observers. Let's say that events A, B, C, D happen at moment M, which lies at the extremity of a slice. Then the moment M', when A', B', C', D' are simultaneous, also occurs at the extremity of the corresponding slice. Because the slices are equal, that means if we juxtapose both durations, M and M' will be aligned with each other. Hence M and M' are simultaneous. Thus A, B, C, D and A', B', C', D' as well are simultaneous altogether. "We can therefore continue to imagine, as in the past, instantaneous slices of a single time and absolute simultaneities of events" (62d).

§88 Physicists are Not In-Synch with Philosophers

But physicists would not come to the same conclusion. They see things this way: S is at rest, and S' is in motion. Experiments in S give the same results as those in S'. But how do we get the same results when light in the one system travels different distances? We see things this way only when we first take the point of view of the observer in S. By doing so, the observer in S' becomes merely something imagined in the S observer's mind. We cannot say that both observers are conscious at the same time, because doing so means that we make both of them the system of reference. But that means their systems would be motionless, yet we already stated that they are in reciprocal motion. "To be sure, we shall leave men in the moving one; but they will have momentarily abdicated their consciousness or, at least, their faculties of observation; they will retain, in the eyes of the single physicist, only the physical side of their person as long as it is a question of physics" (63b).

But Bergson's argument involved us taking both observers' consciousnesses together equally. So Bergson's rendition will not hold under the physicist's conception, which necessitates that one observer's consciousness be provisionally eliminated. We then take the perspective of the motionless observer. He sees light moving the same speed in system S' as it does in his own system. However, he also sees light maintaining this speed even though it covers different distances and even though the observer in S' clocks the light as taking the same amount of time. The observer in S then regards the simultaneities in S' to really be successions. So, because S' synchronized its clocks, and because those synchronies were really successions, that allows for light to be considered as always traveling the same speed. Thus the observer in S chooses to define simultaneity in terms of the synchronization of clocks. However, Bergson showed before that even these synchronizations involved the simultaneities of distant events perceived or conceived in the mind of one person's consciousness. Hence this physics definition of simultaneity does not also prevent us from defining simultaneity as the "real, lived simultaneities, not governed by clock synchronizations" (63d).

§89 Curves of Time

Because physicists have their own way to conceive simultaneity and succession, we must distinguish between the two different varieties. One type involves the lived experience of duration, while the other is a product of mathematical abstractions. "The first is inside events, a part of their materiality, proceeding from them. The other is merely laid down over them by an observer outside the system. The first says something about the system itself; it is absolute. The second is changeable, relative, imaginary; it turns upon the difference, changing with speed, between this system's immobility for itself and its mobility with respect to another; there is an apparent incurvation from simultaneity into succession. The first simultaneity and the first succession belong to an aggregate of things; the second, to the observer's image of them, obtained in mirrors that distort the more, the greater the speed attributed to system" (64-65). The laws of physics requiring that simultaneity incurvate into succession are the same for both the moving and immobilized observer.

§90 You Cannot Steal Someone's Simultaneity

Bergson now supposes that he is in system S'. So he considers it immobilized. Bergson stands equidistantly between the locations of two distant events O' and A'. Bergson synchronizes the clocks at the two events by taking into account that the light signal makes the same trip from O' to A' as it does on the way back. We call P the trip from O' to A', and we call Q the trip back.

Bergson now has two ways to recognize simultaneity in this situation.

1) The Intuitive Way: He could view what happens at both A' and O' in one act of consciousness.

2) The Derivative Way: He could consult the clocks and see that both events concurred with the same time on each clock.

For the person inside system S', trips P and Q are equal. But from outside system S' who regards S' as in motion, these distances seem unequal. So we first take the perspective of S' and say that the trips are equal, then we leave that perspective and take up other ones, and see them as unequal. And the faster that system S' seems to be going from our different perspective, the more unequal P and Q become. "I then declare that the events that were simultaneous before are becoming successive, and that their temporal separation is increasing" (64d). Yet, Bergson says, this is merely a convention used to "preserve the integrity of physical laws" (64d). And in fact, these laws were devised by first assuming that simultaneity and succession are relative, given one's point of view. (underlining and boldface mine)

So, Bergson wonders, when considering simultaneity and succession in this manner, are we dealing with real simultaneity or succession? Recall first how we defined real time: "there is no time without a before and an after verified or verifiable by a consciousness that compares one with the other, were this consciousness only an infinitesimal consciousness coextensive with the interval between two; infinitely adjacent instants" (65b). The person in S' perceives a simultaneity or a succession, and both are thus real. It is true that we might take-up a point-of-view outside this system, and see as successions what are simultaneities for the consciousness of a person on S'. But that then is using a mathematical convention, which yields a conventional reality. It does not change the fact that the person on S' experiences real simultaneity and real succession.

§91 The Physicist's Sleight of Hand Simultaneity

Now consider before we stepped outside system S'. At that previous time, we considered distant events simultaneous because our mind grasped them together. The simultaneity in our consciousness is intuitive or innate simultaneity. And then we come to consider the distant events as simultaneous, so this is a learned simultaneity. However, in this case, the two types of simultaneity coincide. But when we regard S' as being in motion, then the two simultaneities no longer coincide. The faster we consider S' to be going, the less simultaneous the events seem to be. So we would no longer call the learned simultaneity a simultaneity. We might have to invent some other word for it. But we still need to speak of the clocks being read, which means that an event is simultaneous with the clock's position. Now, consider how a perspective deemed motionless with respect to S'. From this perspective we could use math to determine that events which seem successive on S' are in fact simultaneous. So we keep this intuitive meaning for simultaneity, but transpose its reality from one perspective to another. Bergson says to the physicist

the passing from stability to mobility having doubled the meaning of the work, you slip all the materiality and solidity of the first meaning into the second. I would say that instead of forewarning the philosopher against this error, you want to draw him into it, did I not realize the advantage you derive, as a physicist, from using the word simultaneity in both senses: you remind yourself in this way that learned simultaneity began as innate simultaneity and can always turn into it again should thought immobilize the system anew. [66b]

§92 A Unilateral Shift in Argumentation

Bergson will return to the view of unilateral relativity where there is an absolute time and an absolute clock-time. This is the time of the observer located in privileged system S. We again assume that S' first coincides with S, then moves-off.

§93 Physicists Confuse Reality with Science

We will also say that the clocks in S' are synchronized using optical signals, in the ways we mentioned before. So distant clocks will show the same time when, from the perspective of absolute time, they should be different. The simultaneities in S break-up and become successions in S' on account of its motion. The observer in S' sees them still as simultaneities, even though they are really successions.

But Einstein's theory is bilateral, so all motion is reciprocal, and there are no privileged systems. Hence "the observer in S is as much in the right in seeing succession in S' as is the observer in S' in seeing simultaneity there" (66d boldface mine). Thus regarding journeys P and Q "The observer in S' is not mistaken, since, for him, P is equal to Q: the observer in S is no more mistaken, since, for him, the P and Q of system S' are unequal" (66d). Now, in this double (bilateral) relativity, we have regarded some system as privileged. Then, the mathematics works-out the same as if it were single (unilateral) relativity. So in our minds, we think of double relativity as if it were single relativity.

We then act as if - the two passages P and Q appearing unequal when the observer is outside S' - the observer inside S' were mistaken in designating these passages as equal, as if events in the physical system S' had been broken up in actuality at the dissociation of the two systems, when it is merely the observer outside S' who rules them broken up in following his own definition of simultaneity. We forget that simultaneity and succession have then become conventional, that they retain of the original simultaneity and succession merely the property of corresponding to the equality or inequality of the two journeys P and Q. It was then still a question of an equality and inequality found by an observer inside the system and therefore final and unchanging. [67ab]

§94 Lightning & Relativity

Bergson will now explain why it is natural to confuse these two viewpoints when we read certain pages in Einstein's writing. The physicist might not be interested in drawing these distinctions, because they are mathematically indiscriminable. However, philosophers will view time differently depending on whether they take-up the single or double relativity theory.

Bergson now discusses the train example, which matches our demonstration from before. In this case, lightning strikes two parts of a train track. Someone stands in the middle, equally distant from both flashes. This person sees the flashes as simultaneous. However, the people in the train are moving toward one of the flashes in the process.

To understand how, we imagine that the middle of the train and the center point of the track are aligned when the lightning strikes on both ends of the track. The train moves forward and sees the one flash in front of it before later seeing the one behind it. The stationary person midway between both flashes, however, sees both flashes at the same time.

This is Bergson's diagram:

Hence "Events simultaneous with respect to the track are no longer so with respect to the train, and vice versa (relativity of simultaneity). Each system of reference has its own time; a time reading has meaning only if we indicate the system of comparison used for the measurement of time" (68cd).

§95 Bergson is More Egalitarian Than Einstein

We see that in our example, Einstein chooses the person along the track to be the frame of reference. This is why the train is moving in the direction of the arrow. But Bergson draws the situation with arrows along the track moving the other way, to indicate the reciprocal motion between the train and the track.

the philosopher, who wants to know what to believe regarding the nature of time, who wonders whether or not the track and the train have the same real time - that is, the same lived or livable time the philosopher must always remember that he does not have to choose between the two systems; he will place a conscious observer in both and will seek out the lived time of each. [69a].

So Bergson draws additional arrows. He also adds letters A' and B' to mark the extremities of the train.

§96 Train's and Thunderbolts

We will now say that lighting strikes. But we will not say that the place the bolts strike is on the ground or on the train. "The points from which they set out no more belong to the ground than to the train; the waves advance independently of the motion" (69bc).

§97 The World is Upside Down

So we are regarding the train and the track as mutually and reciprocally moving past each other. We see then that we cannot say that either system has some priority. We could take the perspective of the train, or of the track. Hence, the two systems are interchangeable. [Whatever would make events not-simultaneous for the train would also make them not simultaneous for the track. Now let's consider if we made the train the immobilized systems, and the ground moves in relation. Then point M' would perceive the flashes simultaneously, and point M on the track would not, because the track is moving-off toward one of the bolts all while fleeing the other. Hence Bergson writes,] "It then becomes evident at once that the two systems are interchangeable, and that exactly the same thing will occur at M' as at the corresponding point M. If M is the middle of AB, and if it is at M that we perceive a simultaneity on the track, it is at M', the middle of B'A', that we shall perceive this same simultaneity in the train" (69c).

§98 Different Times are the Same

[So we see that for either perspective, train or track, simultaneity is the same thing. When we talk to either the train or the track observer, we find that they both experienced a simultaneity; they both experienced the same temporality. Bergson writes:] "Accordingly, if we cling to the perceived, to the lived, if we question a real observer on the train and on the track, we shall find that we are dealing with one and the same time - what is simultaneity with respect to the track is simultaneity with respect to the train" (69cd).

§99 Philosophers See Things Their Own Way

[But if we think about things like physicists, we would say that both the train observer and the track observer could not have been both at the midpoint and also observed a simultaneity. This is because we would take one perspective over the other, in Einstein's example, we take the track's perspective. This allows us to formulate our mathematics and make our physical determinations. But when we ask ourselves about the reality of the lived experience of time, we will not prefer one observer's experience over the other, so we have to assume that the train-observer sees the ground-observer fly-off into the distance. Hence from the train-observer's perspective, it is the ground-observer who reaches one flash before the other. So because we take both perspectives, we are concerned with the real nature of time as it was experienced by each observer. Bergson writes:]

But, in marking the double set of arrows, we have given up adopting a system of reference; we have mentally placed ourselves on the track and in the train at one and the same time; we have refused to turn physicist. We were not, in fact, looking for a mathematical representation of the universe; the latter must naturally be conceived from one point of view and conform to the laws of mathematical perspective. We were asking ourselves what is real, that is, observed and actually recorded. (69d, boldface and underline mine)

§100 The Reality Behind Relativity

The physicist makes a distinction, however, between the chosen system of reference versus all the other systems. So the physicist regards his own recordings as what are so, and he transposes into his own system the possible recordings of the other moving observes. Yet his calculations then will no longer be what those other observers actually experienced. They will be mere abstractions; "his notation of it will then no longer correspond to anything perceived or perceptible; it will therefore no longer be a notation of the real but of the symbolic" (70, boldface mine). But the same will hold for the observer in the train, who transposes all other systems to his own. There will be a discrepancy between a) the observer's recordings for the observers he sees and b) the recordings that those observers themselves obtain. However, the same laws of nature will hold for each. And this is the ground for us saying there is a universe independent of our observations. "The magnitudes appearing in these two visions will be generally different, but, in both, certain relations among magnitudes, which we call the laws of nature, will remain the same, and this identity will precisely express the fact that the two representations are of one and the same thing, of a universe independent of our representation" (70b).

§101 Philosophers Do Not Like the Physicist's Privileges

Bergson returns to the train example. The physicist at point M sees the simultaneity of the two flashes of lightning. But he cannot also be at point M' as well. So he can only "say that he ideally sees the recording at M' of a nonsimultaneity between the two flashes" (70b). All his mathematical representations of the world depend on him considering the earth his system of reference. So from his perspective, the train moves, and thus the train does not see a simultaneity at M'. But for the ground observer, M' is just a mathematical representation. It is not a fully conscious being who takes his own system as the system of reference. He just imagines an observer. So for the ground observer, 'what is simultaneity with respect to the track is not so with respect to the train. But there is an observer on the train as well, and for him, the track is the one that is speeding towards one flash and away from the other. So for the train observer, the ground point M' does not perceive the simultaneity. Hence as well, 'what is simultaneity with respect to the track is not so with respect to the train' (70d). So we see that if we take both the track and the train viewpoints, we are no longer dealing with scientific constructions. We are dealing with reality. This is the consequence of taking up Einstein's theory in its fullest. But physicists cannot do so. They must assume provisionally unilateral relativity. So for them, there is a multiplicity of times, because they take one perspective to be real, the immobilized system, and all the rest to be abstractions. But when we do not choose a privileged system, there is only just one time experienced by every observer.

A philosophy which assumes the viewpoints of both track and train, which then notes as simultaneity in the train what it notes as simultaneity on the track, no longer stands halfway between perceived reality and scientific construction; it is completely in the real, and is moreover, only completely appropriating Einstein's conception which is that of the reciprocity of motion. But that idea, as complete, is philosophical and no longer physical. To convey it in physicist's language we must take the position of what we called the hypothesis of unilateral relativity. And as this language asserts itself we do not perceive that we have for a moment adopted this hypothesis. We then speak of a multiplicity of times that are all on the same plane, all real, therefore, if one of them is real. But the truth is that the latter differs fundamentally from the others. It is real, because it is really lived by the physicist. The others, merely thought of, are auxiliary, mathematical, symbolic. [70-71, boldface mine]

§101 Diverging Lines of Time

Bergson will explain this point another way. We are to imagine a system S'. On it are three points, M', N', and P'.

The system moves in the direction of this line. M' and P' are at an equal distance, l, from N'. Suppose they all share the same event. We know that the event cannot happen simultaneously, for an observer that is not moving the speed of this system. Also consider a determinate event happening for N' at a certain moment. Depending on the relative speed between this system and the observing system, the event will happen at some other time for the other points. So the event is not determinate at the other points [it could happen at any time, depending on the relative speed of the observer].

We will call this system's speed v. Recall in chapter 1 our discussion of the breakup of simultaneities. We described how each clock separated by l lagged by

seconds. So now suppose that there is an event at N' that seems for the observer there to also be simultaneous at M' and P'. From the perspective of an observer moving at a different speed, "it is the past at M' and the future at P' that enter within the present context of the observer at N'. What, at M' and P', is a part of the present of the observer at N' appears to this outside observer as being the farther back in the past history of place N', the farther forward in the future history of place P, the greater the system's speed" (72b).

Bergson will now drop, in opposite directions, two lines M'H' and P'K', which are perpendicular to M'P'.

We will assume that the events in the past history of M' are spaced along M'H'. And those events of the future history of place P' are spaced along P'K'. [What is really simultaneous with N' is something in the past at M' and something in the future at P'.] So we will draw a line from past event E' at place M', through N', to F'. All these events will be simultaneous for an outside observer moving at a certain relative speed. We may call this line the "line of simultaneity" (72b). Event E' is at a interval

in the past, and F' is at the same interval into the future. [As the speed increases, time distorts event more; hence] the line M'N'P' continues to diverge as the system's speed increases (72c).

§102 Mirages of Time

Bergson notes that we might be misled into certain paradoxical conclusions. For example, imagine that we are at point N' in the center. And suppose it were possible for us to instantaneously leap to point P'. We might think that we would then be able to see a part of the future, as if we would jump to point F'.

Bergson says this is a mirage. In fact, the Minkowski scheme serves to intensify this illusion. Bergson will not yet go into detail regarding Minkowski's diagrams. He will now merely convey some of Minkowski's ideas, using the above figure.

§103 The Presence of the Past and Future

So recall that the line of simultaneity E'N'F' diverges from line M'N'P' the faster the relative speed.

But nothing goes faster than light. So there is a limit to how much the line may diverge. Recall as well that the diagonal line raises or lowers according to how many

seconds the time dilates. This tells us the length of lines M'E' and P'F', whose lengths represent the extent of the temporal distortion. The v stands for the velocity of the system, and the c stands for the speed of light. So let's substitute the speed of light for the speed of the system, and see what the limit is for the length of lines M'E' and P'F'.

So the distance cannot exceed.

Consider also how we think that time goes on and on into the past and future, and the extent of this time is beyond what anyone could foresee in system S'. This is because there is a certain limit to how far the diagonal line can reach up or down the lines representing the past and future at the ends of the line. So "nothing of this past or future can be a part of the present of the observer at N' (73bc).

However, note also that the future and past at the lines' extremities are supposedly contemporaneous with the event at N', from the perspective of the exterior observer. So we cannot also say that these events are absolutely future and past. In a sense, they are present as well. So if the observer at N' could have an instantaneous vision of the extremities, then the past and future would be contemporaneous with his present. But exactly how far into the past and future that he sees will be a matter of how fast the system is moving, relatively. (73c)

§104 Relativity Theorists Claim that Prophesy is Theoretically Possible

Relativity theoreticians make this claim that an observer at N' could presently perceive the future at P', if he were to have "the gift of instantaneous vision at a distance" (73d). However, such theoreticians say, light cannot travel fast enough to the observer at N', so he cannot have such instantaneous vision. And hence he cannot see into the future at P'; "that future can with impunity be included in the present of the person at N'; practically, it remains nonexistent for him" (74a).

§105 Unfolding the Mirage of Time

Bergson will now evaluate whether or not this distortion of time is a mirage.

Recall that for relativity theory, "the temporal relations among events unfolding in a system depend solely upon the speed of that system, not upon the nature of those events" (74b).

Now let's assume that S' is a double of S. That means the events will unfold in the same way in both systems.

§106 Doubled Observation

So we will also assume that in system S there is a line MNP. It begins by coinciding with line M'N'P. Then the two diverge after system S' moves-off from system S. Hence "an observer located at M' and one at M, being at two corresponding places in two identical systems, each witnesses the same history of the place, the same march of events" (74b). The same goes for the observers at N and N', and also for the observers at P and P'.

We will focus on the observers at the midpoints, N and N'.

§107 Determining What is Indeterminate

Consider the situation for the observer at N. Because he is motionless, the events at M and P are simultaneous. They are not indeterminate as with the events at M' and P'. The time that these events lag from the event at N' depends on the relative speed of S'. But S is considered immobile, so its events at M and P are determinate.

§108 Relatively, It's All the Same

We will now imagine that system S' somehow instantaneously (without acceleration) moves away at a certain speed. All the while, the system S' remains for the person at N' a motionless system. So for the observer at N', the events at M' and P' are simultaneous and not in the past or future, just as for the observer at N the events and M and P are simultaneous with the present.

The two systems S and S' are in a state of complete reciprocity; it is for the convenience of study, to erect a physics, that we have immobilized one or the other into a system of reference. All that a real, flesh-and-blood observer observes at N, all that he would instantaneously, telepathically observe at no matter how remote a point in his system would be identically perceived by a real flesh-and-blood observer located at N' in S'. Hence, that portion of history of places M' and P' which really enters the present of the observer at N' for him, what he would perceive at M' and P' if he had the gift of instantaneous vision at a distance, is determinate and unchanging, whatever the speed of S' in the eyes of the observer inside system S. It is the same portion that the observer at N would perceive at M and P. [74-75]

§109 Time & Reciprocity

Systems S and S' are in reciprocal motion. So it does not matter which perspective we take; the systems are interchangeable. This means that "the clocks of S' run for the observer at N' absolutely like those of S for the observer at N" (75a). And also on account of this reciprocity, "When the clocks located at M, N, P, and which are optically synchronized, show the same time and when there is then by relativist definition, simultaneity among the events occurring at these points, the same is true for the corresponding clocks in S'; and there is then, still by definition, simultaneity among the events occurring at M', N', P' - events respectively identical with the former ones" (75b).

§110 Simultaneity & Immobility

Yet to make our calculations, we immobilize one system, even though they are in reciprocal motion. When we do so, the simultaneities of the clocks in S are absolutely simultaneous.

§111 Time Has Come Unhinged

But then, the observer in S notices that the distances and times distort in system S'. The clocks that are simultaneous for the people in S' are not simultaneous in the eyes of the observer; "the clocks that show the same time in system S' do not, in his eyes, underline contemporaneous events" (75d). The events that seem contemporaneous for those in S' appear successive to the observer in S; "or rather, they appear as having to be noted down as successive, by reason of his definition of simultaneity" (75d).

§112 Relativity is not Reality;

It's Just a Mathematical Shorthand

Consider if the speed of S' increases. For the observer at S, "the observer at N drives farther into the past of point M' and projects farther into the future of point P' - by the numbers he assigns them - events, occurring at these points, which are contemporaneous both for him in his own system and also for an observer located in system S' " (75-76).

By doing so, the observer at S no longer considers the consciousness of the observer in the other system.

For this last observer, it must be added, there is no further question of a flesh-and-blood existence; he has been surreptitiously drained of his content, in any case, of his consciousness; from observer he has become simply observed, since it is the observer in N who has been given the status of physicist-builder of all science. (76a)

The physicist in S calculates that time is distorted in the other system. But this is just a calculation that he needs to perform so that his measurements for moving systems may come into accord.

as v increases, our physicist notes as pushed back ever farther into the past of place M', advanced ever more into the future of place P', the always identical event which, whether it be at M' or P', is part of the really conscious present of an observer at N', and consequently part of his own. There are not, therefore, different events at place P' which enter by turns, for increasing speeds of the system, into the real present of the observer at N'. But the same event of place P', which is part of the present of the observer at N', under the assumption of the system's immobility, is noted by the observer at N as belonging to a future ever more remote for the observer at N', as the speed of the mobilized system S' increases. If the observer at N did not so note, it must be added, his physical conception of the universe would become incoherent, for his written measurements of phenomena occurring in a system would express laws that he would have to vary with the system's speed; thus, a system identical with his, whose every point would have identically the same history as the corresponding point in his, would not be governed by the same physics (at least in what concerns electromagnetism). [76b.c]

§113 Physics Makes Philosophers Delusional

Recall from §104 the position of relativity theorists. They say that the person at N' could theoretically see into the future, if he had instantaneous vision across great distances. But light takes time to travel, so no such vision is possible. Hence also no such ability to see the future is possible either. Yet we have seen that if we do take-on this observer's perspective, moving in system S, then we would no longer consider that system to be in motion, and hence there would just be simultaneities present to him, both theoretically and practically. Yet the relativity theorist does think that the future is present yet unavailable to the person at N'. Bergson notes: "Certainly no physical or mathematical error will result from this statement; but great would be the delusion of the philosopher who would take the physicist at his word" (77bc).

§114 The Appearance of Relativity

So we see that there is not the perpendicular lines extending from M' and P'.

These are merely mathematical abstractions that are created when we fix one outside observer. So it might seem from the diagram that there is a continuum of past and future moments that could become simultaneous with N', depending on the speed of the observer.

For the observer at N', therefore, there is not, at M' and P', next to events that we consent to leave in the "absolute past" or in the "absolute future," a whole mass of events which, past and future at those two points, enter his present whenever we attribute the appropriate speed to system S'. There is, at each of these points, only one event making up a part of the real present of the observer at N', whatever the speed of the system; it is the very one that, at M and P, is part of the present of the observer at N. But this event will be noted down by the physicist as located more or less back in the past of M', more or less forward in the future of P', according to the speed attributed to the system. It is always, at M' and P', the same couple of events that form together with a certain event at N' the present of Paul located at this latter point. But this simultaneity of three events appears incurvated into past-present-future when beheld in the mirror of motion by Peter picturing Paul. [77c.d, boldface and underline mine]

§115 Illusions of Relativity

Bergson will now attack this problem from another direction. So let's assume again that S is identical to S', and the two systems are superposed upon each other. Then, S' breaks off and "instantly attained its speed" (77d).

Let's take-on the relativist hypothesis that time really does change. And let's also assume that the observer at N has instantaneous vision at a distance. This means he would see the future at P'. Now let's also assume that he has instantaneous communication. And recall that the systems are identical. So the observer at N could then forewarn the person at P what is to come.

[However, as we saw, the same would hold for the person in S', that he would be able to look into the future in the S system.] Really what happens is that on account of certain principles of optics, time just appears distorted in the other system. But this is an optical illusion. If the person at N had instantaneous vision at a distance, he would see the same things happening at P' which are also happening at P. "This 'skewed vision' makes the line of simultaneity passing through points M, N, P in system S appear the more oblique in system S', duplicate of S, the greater the speed of system S', the duplicate of what is occurring at M thus finds itself pushed back into the past, the duplicate of what is occurring at P, pulled forward into the future; but the long and short of it is that we have here only an effect of mental torsion" (78d); "the line of simultaneity between the three points M', N', P' appears turned about N' by a certain angle, so that one of its extremities lags behind in the past while the other encroaches upon the future" (79a, boldface mine).

§116 The Long and the Short of Longitudinal Contraction

Recall also that according to relativity theory, distances contract in the moving system, from the perspective of the immobilized one. Bergson will now show that the longitudinal contraction is also an optical illusion like the breakup of simultaneities. Bergson has us consider points A' and B' in moving system S'.

System S' is moving along, until at one moment coinciding parallel to its stationary double, system S. When it does so, points A' and B' settle over points A and B. Now, there are clocks at A' and B'. They were synchronized together, so they show the same time.

But let's now take the perspective of the person at S. For him, system S' is moving relative to his own system. So he thinks that the clock at B' lags behind the one at A'. So that means A and A' coincide first, but then B' will coincide with B slightly after. For this to be possible, figures the person at S, that means the length of A'B' is shorter than AB.

But, for the observer in S', his own system is the motionless one. So for S', the clock at A appears to be lagging behind B. Hence A coincides with A' only after B coincides with B'. So he will figure that the length of AB has contracted.

Bergson now wonders if AB and A'B' really have the same length or if in reality they do not. Bergson calls real whatever is perceived or perceptible. But the measurements and calculations that S and S' reckon for each other's systems are merely mathematical abstractions. We can only go by what is really perceived or perceivable. That means we must turn to Peter and Paul and ask them what their perceptions are of the lengths in their own system. Both of them consider their length to be at rest, so they both obtain the same measure. When we consider their systems in motion, that means we may interchange their perspectives. And that means both their measurements will be the same.

Hence, in the thesis of special relativity, the extended can no more really contract than time slow down or simultaneity actually break up. But, when a system of references has been adopted and thereby immobilized, everything happening in other systems must be expressed perspectively, according to the greater or lesser difference that exists, on a size-scale, between the speed of the system referred to and the speed, zero by hypothesis, of the referrer system. [80bc]

Mook, Delo E. & Thomas Vargish. Inside Relativity. Princeton: Princeton University Press, 1987.

Bergson, Henri. Duration and Simultaneity. Ed. Robin Durie. Transl. Mark Lewis and Robin Durie. Manchester: Clinamen Press, 1999.

The original French version is available online at:

http://www.archive.org/details/dureetsimultan00berguoft