Synthesis 3: The Undoing

We've finally made it to the third film in the trilogy.  The ending is predictable Deleuze -- the forces of chaos triumph and everything you thought you understood comes undone.  The pattern of the three passive syntheses of time is pretty clear.  The first constitutes all of time as the ever mobile passing present -- a time composed of atomic elements.  The second synthesizes all of time as the whole of the past -- a time composed as a monolithic fractal whole.  The third, and in some sense the deepest, constitutes all of time as the future -- as the form of change that merely defines a before and an after but that is otherwise completely empty, composed of nothing more than this distinction itself.

If the first two syntheses are defined by different types of contraction, the third will be associated with a sort of contraction that actually blows everything apart.  If the first two states show us different types of repetition, the third will be based on a strange type of repetition that produces absolute novelty.  And if the first two syntheses shows us different forms of difference itself, the third will show us a pure and transcendental difference-in-itself that is simultaneously the most common thing in the universe (existence in time).  The third synthesis is pure paradox, time as the unchanging form of change itself, time as the concept of change, some paradoxical point where difference and repetition touch.

Let's try to go through in detail what all this poetry means.

This section (broken into two pieces on pg. 85-96) begins with a contrast between the Cartesian and the Kantian conceptions of the cogito, the I or self in "I think therefore I am".  Kant makes short work of the self-evident certainty of Descartes' formulation.  Descartes is right; there's no doubt that some thinking is happening, existing right now, as I have the experience of thinking about this question.  What's not obvious at all is that this thinking is "mine".  Does my thinking at now1 belong to the same "me" as my thinking at now2?  If so, where did the continuity of this me come from?  Without this presumed continuity of my self-identical being, does the fact of my current thinking experience prove anything more than "there exists some thinking" right now?  It certainly doesn't seem to prove that any sort of stable, solid, continuous I exists.  But you just can't get famous for tweeting: "I think therefore ... there is some thinking going on".

Deleuze phrases this critique as an objection to the way Descartes' slight-of-hand magically converts a bare undetermined existence (mere existence or naked Being, if you will) into a solid thing or substance that can have properties like thinking.  In other words, he has smuggled in the assumption that the I that's doing the being here will have the same form as the familiar I that (we assume) does our thinking.  But is the I that thinks really the same as the I that is?  Or does thinking require being without really telling us very much about it?

It is as though Descartes's Cogito operated with two logical values: determination and undetermined existence. The determination (I think) implies an undetermined existence (I am, because 'in order to think one must exist') - and determines it precisely as the existence of a thinking subject: I think therefore I am, I am a thing which thinks. The entire Kantian critique amounts to objecting against Descartes that it is impossible for determination to bear directly upon the undetermined. The determination ('I think') obviously implies something undetermined ('I am'), but nothing so far tells us how it is that this undetermined is determinable by the 'I think': "in the consciousness of myself in mere thought I am the being itself, although nothing in myself is thereby given for thought." Kant therefore adds a third logical value: the determinable, or rather the form in which the undetermined is determinable (by the determination).  This third value suffices to make logic a transcendental instance.

The emphasis here on the form in which being can appear to us (rather than focusing on the being in itself) seems to be the essence of the Kantian transcendental.  I don't know enough about Kant to say much of anything interesting, but I did review Louis White Beck's introduction to my copy of Prolegomena To Any Future Metaphysics, which contains this helpful footnote:

It is important to distinguish between "transcendent" and "transcendental."  The former means "transcending the limits of experience," and hence metaphysical in the usual sense of the word; the latter means "lying at the base of experience," and hence epistemological in the ordinary sense.

Perhaps there are a whole set of transcendental forms that do not "... signify something passing beyond all experience but something that indeed precedes it a priori, but that is intended simply to make knowledge of experience possible" (as Kant himself puts it).  The one we're interested in now though is Time.  We experience out thoughts as happening in time.  All of our experience is experience-in-time.  This is the only form in which we can experience either our thinking or our being.

Kant's answer is well known: the form under which undetermined existence is determinable by the 'I think' is that of time ... The consequences of this are extreme: my undetermined existence can be determined only within time as the existence of a phenomenon, of a passive, receptive phenomenal subject appearing within time.

If the only way we can get at our existence is though time, then Descartes' existential equation no longer shows us what he claims.  My thinking doesn't reveal the presence and activity of a substantial underlying self that exists continuously.  In fact, since I can't get at the being of this self except through thinking, what this being is like in itself remains a mystery.  All I can know is that this being appears within time, because my knowledge is limited to how my experience of thinking works.  For this being to be consistent across time, for it to be my being or thinking in the sense of a "property of underlying me", we need to add another assumption.  For Descartes, that assumption was God.

Descartes could draw his conclusion only by expelling time, by reducing the Cogito to an instant and entrusting time to the operation of continuous creation carried out by God.  More generally, the supposed identity of the I has no other guarantee than the unity of God himself. For this reason, the substitution of the point of view of the 'I' for the point of view of 'God' has much less importance than is commonly supposed, so long as the former retains an identity that it owes precisely to the latter. God survives as long as the I enjoys a subsistence, a simplicity and an identity which express the entirety of its resemblance to the divine.

Recall that Descrates' God played a very prominent and unusual role in a philosophy that was supposed to doubt everything that could be doubted.  He guarantees the unity of the world, safeguards our senses from deceptions by evil geniuses who want to farm out our brains to vats, and, of course, implicitly gives us a model for the substantial and enduring self.  In practice, like we observed at the outset, the logic probably moves in the opposite direction -- Descartes assumes that God is a continuous unified substance because he experiences his own self that way (as so many of us do).  In any case, whatever unity we posit that holds across time -- whether God, Self, or World -- is not a unity we can actually experience, since all of our experience arises and passes within time.  

Without recourse to Descartes' God, how will Kant guarantee to us that the I that appears in my thoughts is the same from moment to moment?  And if each flickering thought -- even if the contents of that thought are an image of a persistent self -- can only appear as a thing within time, then how will Kant guarantee that we exist as stable thinking entities?  Finally, if we take apart one side of the equation (our unity as thinker) and take apart the other (our unity as exister), then what's left of the equation?   

For Deleuze, the answer is basically nothing.  He thinks that Kant has opened up a real can of worms here.  He has created an unbridgeable gulf between thinking and being.  He has killed God and dissolved the self.  "My" thinking can no longer prove my existence.  There is thinking, which means there is existence, but this existence isn't the property or activity of a substantial me.  It (thinking or being) seems to "just happen"; I'm not the subject or author of it.  

Kant's answer is well known: the form under which undetermined existence is determinable by the 'I think' is that of time ... The consequences of this are extreme: my undetermined existence can be determined only within time as the existence of a phenomenon, of a passive, receptive phenomenal subject appearing within time. As a result, the spontaneity of which I am conscious in the 'I think' cannot be understood as the attribute of a substantial and spontaneous being, but only as the affection of a passive self which experiences its own thought - its own intelligence, that by virtue of which it can say I - being exercised in it and upon it but not by it.  Here begins a long and inexhaustible story: I is an other, or the paradox of inner sense. The activity of thought applies to a receptive being, to a passive subject which represents that activity to itself rather than enacts it, which experiences its effect rather than initiates it, and which lives it like an Other within itself. To 'I think' and 'I am' must be added the self - that is, the passive position (what Kant calls the receptivity of intuition); to the determination and the undetermined must be added the form of the determinable, namely time.

In fact, the only tenuous thread left connecting anything is the meta-level form in which all things appear -- time.  Since this form must apply to any contents, we might characterize it as "empty".  Yet this exact same transcendental form of time that connects all contents, perpetually separates undetermined being-in-itself from any more concrete determination of it (say, as a thinking type of being).  As a result, we might call it a "fracture" or a "fault" through our very core, something that separates us from ourselves.  The empty form of time separates thinking from being, even as it relates them a priori.  

It is as though the I were fractured from one end to the other: fractured by the pure and empty form of time. In this form it is the correlate of the passive self which appears in time. Time signifies a fault or a fracture in the I and a passivity in the self, and the correlation between the passive self and the fractured I constitutes the discovery of the transcendental, the element of the Copernican Revolution.

We'll come back to this concept of the fractured I and its relationship to the form of time in many posts, I'm sure.  It's a strange and paradoxical one, because the fracture holds the pieces together by the thinnest of threads even as it separates them.  It represents Difference in itself, a difference that has been made internal to ... something which is not exactly a unity, namely, difference itself.  "... time is the most radical form of change, but the form of change does not change".  

The Geometry of Experience

One thing I've discovered in meditating is that experience can present itself in different geometrical forms.  Sometimes there's a feeling that I am the center of my experience -- the commonplace idea we call having a point of view.   Sometimes, in contrast, I am not the center of my experience.  Somehow, the experience contains a center, but that center is experienced as being somewhere else.  This might be part of what people mean when they say they have an "out of body" experience.  Even more strangely, an out of body experience is really just the tip of the iceberg.  That experience still conforms in every respect to our typical unified self-centered (I don't mean this term in a judgmental sense) everyday experience.  It's like an exact double of that experience, just with the location shifted somewhere else.  

Things can get much weirder, it turns out.  Consider a patchwork of experience with multiple centers, none of which coincide, and which don't together constitute a space.  An out of body experience often still contains a reference to the initial position of the body.  As in, "I was floating above myself".  An experience that contains multiple centers may lack this reference completely.  "I" may not necessarily be any of the centers, nor a point located by some sort of triangulation of them.  The centers can each define a separate patch of space, but these patches may not exist in any relation to one another.  There is no single unified space in which they can be embedded.  You can't even call this an out of body experience because there's simple no reference left to the body.

Or is there?  Multiple centers that can't be unified explodes (literally) our normal concept of the body.  But there are still centers here.  Each center unifies something, even if they are irreducibly multiple and can't be put together.  Each center still functions as a body.  Call it an "out of the three body problem" experience.  I've even had an odd experience that is best described as being "out of someone else's body".  Put that in your pipe and smoke it.

The next question is obvious.  And the answer is yes.  

You can have an experience that lacks a center entirely.  How might you go about describing this experience that lacks all of the reference points we usually use to describe our world?  As a set of waves folded within waves?  As an infinitely fast movement that traverses every point and fills all of space?  Would "space" then be the center of the experience?  What makes this "an" experience?  If it doesn't have a center in space, does it at least have a center in time, presumably halfway between when it starts and stops?  

I don't really know how to answer these questions, but I think Deleuze is getting at something like this experience when he talks about the Eternal Return.  It's an experience that breaks open the universe and has no center to its repetition.  It's an experience that dissolves all identity and constitutes a world of pure difference.  It's very difficult to describe.  And as a result, I think a lot of Deleuze's writing style is dedicated to trying to trace this experience out, so that as you follow along with him, you have the experience for yourself.  He's not just trying to tell you what the experience is like, or ask whether it is "true" (whatever that would mean in the context of an experience).  He's trying to show you how to have the experience.  You have to follow the words and  images and the movement of the concepts, tracing them again and again, practicing the pattern, till you have some sort of epiphany where now you sorta know what he means because you've had some new experience yourself.  His whole theory of pedagogy, and his whole literary style rest on this technique because the type of experience he's trying to get at requires this approach. 

We learn nothing from those who say: 'Do as I do'. Our only teachers are those who tell us to 'do with me', and are able to emit signs to be developed in heterogeneity rather than propose gestures for us to reproduce.

Is there any better description of the difficulty inherent in teaching someone how to meditate?

The Second Coming of Repetition

I think we're finally at the point of closing out this second section of the second chapter (pgs. 79-85) that deals with the second passive synthesis.

We know that for something like memory to exist there has to first be a passive synthesis of the past with itself to constitute an entire space of time, in which individual memories would be actively located.  Past = Time.  We've also figured out that this synthesis needs to have a fractal form where each present contracts all of the past, that is, all of time, all of the possible presents, including itself, expressed in a certain manner.  Time, or the past as a Whole, is then an infinite number of possible contractions each of which is itself infinite.  Present = Fractal Past = Time.

I'd have to think more about the subtle mutation it undergoes in a new context, but the pure past Deleuze describes here seems to be basically the same concept as the Plane of Consistency or the Plane of Immanence as these appear in his later writing with Guattari.  Maybe this gives us a hint as to why he wants to call this the Past, when it seems to be what we would normally call Time, since it really includes all of the past, present, and future.  The past always appears to us as a pre-existent background that's just given a priori.   You can't change the past.  Each time it re-presents or re-iterates all of itself as a present, it lays out an entire time line that locates the present in a now fully determined space.  Even though each slice contains all of time, including the present and future, this time is present-ed as given to us and already determined, just as we experience the conventional past.  

This fractal pre-determination also explains why Deleuze reaches for the word "destiny".  

Consider what we call repetition within a life - more precisely, within a spiritual life. Presents succeed, encroaching upon one another. Nevertheless, however strong the incoherence or possible opposition between successive presents, we have the impression that each of them plays out 'the same life' at different levels. This is what we call destiny. Destiny never consists in step-by-step deterministic relations between presents which succeed one another according to the order of a represented time. Rather, it implies between successive presents non-localisable connections, actions at a distance, systems of replay, resonance and echoes, objective chances, signs, signals and roles which transcend spatial locations and temporal successions. We say of successive presents which express a destiny that they always play out the same thing, the same story, but at different levels: here more or less relaxed, there more or less contracted. This is why destiny accords so badly with determinism but so well with freedom: freedom lies in choosing the levels.

Destiny seems like a good word to describe the experience of the entirety of time being given at once.  It isn't the same thing as deterministic cause and effect, where one given moment determines the next adjacent moment in a step-by-step progression in a single direction.  With destiny, the movement is infinitely fast in both directions, so to speak (What is Philosophy? emphasizes the infinite movement and infinite speeds of thought).  The present as fractal past simultaneously determines all of the past and all of the future as a single whole, without going through the stepwise connection of other presents.  My life, my succession of presents, is really just re-presenting this whole past from different points of view, with each point of view simultaneously containing the whole.  

But let's leave further explorations of the paradoxes of destiny and metempsychosis as exercises for the reader and find out what difference and repetition mean in the context of the second synthesis.  This is probably the main point of the whole section, and brings us back to the two kinds of repetition we met way back in the introduction: repetition of forms, and repetition of processes.

Between the two repetitions, the material and the spiritual, there is a vast difference. The former is a repetition of successive independent elements or instants; the latter is a repetition of the Whole on diverse coexisting levels (as Leibniz said, 'everything can be said to be the same at all times and places except in degrees of perfection').  As a result, the two repetitions stand in very different relations to 'difference' itself. Difference is drawn from one in so far as the elements or instants are contracted within a living present. It is included in the other in so far as the Whole includes the difference between its levels.  One is bare, the other clothed; one is repetition of parts, the other of the whole; one involves succession, the other coexistence; one is actual, the other virtual; one is horizontal, the other vertical. The present is always contracted difference, but in one case it contracts indifferent instants; in the other case, by passing to the limit, it contracts a differential level of the whole which is itself a matter of relaxation and contraction. In consequence, the difference between presents themselves is that between the two repetitions: that of the elementary instants from which difference is subtracted, and that of the levels of the whole in which difference is included. And following the Bergsonian hypothesis, the bare repetition must be understood as the external envelope of the clothed: that is, the repetition of successive instants must be understood as the most relaxed of the coexistent levels, matter as a dream or as mind's most relaxed past.

In the first passive synthesis of habit, repetition is material repetition, the repetition of an organic form.  Atomic instants, no two of which are ever exactly the same, were contracted into a present, and a general difference drawn from the expectation that this new form would itself repeat.  The difference introduced into the world, drawn from the world's habit of repeating certain elements, was the very existence of that new form.  Every thing was the passing present, forced to continually reconstruct itself and reiterate its difference, or risk dissolution.

In the second passive synthesis, everything is the past, but a past which encompasses all of time including the present and the future.  This past repeats itself on an infinity of different levels, but each level contains an image of the whole just like a fractal.  The object being repeated here is always the past as a whole, though each time it appears in a new guise, through the selection of a new level.  This is how we should think of the repetition of a process that is able to produce many possible forms, and starts to explain why there seems to be some ambiguity between whether to call this a repetition of the process, or simply to say that the process is ongoing or continues.  It's the same whole past that keeps appearing and re-appearing, organized in different ways.  But all these different levels are internal to a single past because of its curious fractal structure.  Each level is a particular present that contains within it a certain layout of the set of all the possible presents.  The difference that characterizes the present has shifted from being an external difference, drawn out of the present in the first synthesis, to being an internal difference, included within the present in the second.  The first synthesis produces one form, the identity of which is repeated again and again.  The second synthesis is a repeating process that produces an infinity of possible forms..  

Interpreting the two syntheses as repetition of form and repetition of process, respectively, helps with up a couple of other nagging thoughts I've had.  

The first stems from the reference to Bergson in the last quote.  Last time I mentioned in passing that one way of conceiving all of time was as a set of unrelated atomic instants that appear and pass away.  You might call this an experience of time (the past as a whole) in its least contracted state.  Since each slice or level of the past is always a repetition of an entire set of possible presents (or a continuation of the ongoing process of the past) we might think of one mode or level of operation of this process as the production of a whole series of unrelated atomic instants.  Deleuze has been calling the second synthesis "noumenal" or "spiritual" or "virtual".  The repetition of the entire past is the repetition of a process, a thing without material form.  Is Bergson suggesting that one mode of this spiritual repetition, this continual reiteration of the whole of time, might be to realize the loosest and least contracted form of time -- precisely the set of atomic instants that we associate with a materialist view of the universe?  Matter as mind's most relaxed part?  And conversely mind as matter's most contracted state?  Does one mode of the spiritual process spit out the material and temporal form of the universe?

The second issue that might be illuminated by looking at the second synthesis as the repetition of process is this question of the present as "passage to the limit".  How is one level of the past, one infinite set of possible presents, each of which is more or less contracted or relaxed, selected from the others and contracted into a present?  By passing to the limit.  Deleuze says it here, and in my mind it echoes his description of the 'obligation' of each of Spinoza's modes (pg.40).  I don't have a fully worked out thought here, but in the context of a process (and we should think here of Deleuze's paradigmatic process, embryogenesis) "passing to the limit" doesn't imply going outside the ongoing process but passing through a phase transition within that process.  So maybe we should be thinking of the levels of the past as lines drawn immanently within it that describe the phase transitions inherent within some ongoing process.  I guess this process would be something like the unfolding of time.  The same system can be ice, water, or steam depending on the context.  To pass to the limit might be to cross some threshold that precipitates a new behavior from the same old process.

Expansion, Contraction, and the levels of the Past

Deleuze gives us the concept of a pure past, which is essentially equal to all of time, as a solution to the problem of active memory.  Before a subject can have a present memory, there has to be 1) a subject (first passive synthesis of habit) and 2) a temporal space that a former present and a current present can be embedded in (second passive synthesis of memory).  We're still working on translating the paradoxes that characterize this pure past into simpler terms.  So far, we've concluded that the past is a sort of substantial element from which time is fashioned. 

I think maybe the key to understanding this second synthesis is to think more about how Time could be a substance.  This conception clearly takes us away from thinking about time as a collection of atomic presents, a heap of presents that accumulate one by one.  Instead, we have to think of time as one whole substance that somehow contains all the various presents within itself. Basically, each present is an expression or slice of time that contains all of time as seen from a certain angle or perspective.  In this sense, each moment is a reiteration of the whole of time, with all of the past and future telescoped down to one point of present.  If this sounds pretty weird, consider that perhaps the problem of memory itself is the weird thing -- what exactly is a memory if everything that "is" always is in the present?

Deleuze describes this continual remixing of the past as a whole with recourse to the same cone image from Bergson we saw in the context of the cinema books.

... the present designates the most contracted degree of an entire past, which is itself like a coexisting totality. Let us suppose, in effect, in accordance with the conditions of the second paradox, that the past is not conserved in the present in relation to which it is past, but is conserved in itself, the present present being only the maximal contraction of all this past which coexists with it. It must first be the case that this whole past coexists with itself, in varying degrees of relaxation ... and of contraction. The present can be the most contracted degree of the past which coexists with it only if the past first coexists with itself in an infinity of diverse degrees of relaxation and contraction at an infinity of levels (this is the meaning of the famous Bergsonian metaphor of the cone, the fourth paradox in relation to the past).

Just in case, here's the diagram again, where, as Bergson says: 

At S is the present perception which I have of my body, that is to say, of a certain sensory-motor equilibrium. Over the surface of the base AB are spread, we may say, my recollections in their totality. Within the cone so determined the general idea oscillates continually between the summit S and the base AB. In S it would take the clearly defined form of a bodily attitude or of an uttered word; at AB it would wear the aspect, no less defined, of the thousand individual images into which its fragile unity would break up.

This time though, we need to interpret the diagram a little differently.  Rather than seeing this as a light cone that defines all the parts of the past that are able to interact with our present observation at S, he wants us to read each of these circular slices (AB, AB', AB", and even the infinitesimal circle at S) as a possible level of the past that could express its entirety in the same way that S seems to by being at the bottom of the funnel.  In other words, our experienced present could be S in this diagram, or it could be AB'.  These would be different experiences summing up the entire past, but they would equally all be possible presents.  AB is the experience of our entire past as a set of distinct individual memories (like a dream or like Funes) available to consciousness, and S is the experience of that entire past focused as it bears on my present action.  Clearly, at S, most of the past is experienced unconsciously.  

I'll quote Bergson at length on this because he is such a remarkably lucid writer.

Let us, for a moment, suppose our psychical life reduced to sensori-motor functions alone. In other words, suppose ourselves placed be considered, on the in the diagrammatic figure at the point S, which corresponds to the they coincide; greatest possible simplification of our mental life. In this state every perception spontaneously prolongs itself into appropriate reactions; for analogous former perceptions have set up more or less complex motor apparatus, which only await a recurrence of the same appeal in order to enter into play. Now there is, in this mechanism, an association of similarity, since the present perception acts in virtue of its likeness to past perceptions; and there is also an association of contiguity, since the movements which followed those former perceptions reproduce themselves, and may even bring in their train a vast number of actions coordinate with the first. Here then we seize association of similarity and association of contiguity at their very source, and at a point where they are almost confounded in one - not indeed thought, but acted and lived. They are not contingent forms of our psychical life; they represent the two complementary aspects of one and the same fundamental tendency, the tendency of every organism to extract from a given situation that in it which is useful, and to store up the eventual reaction in the form of a motor habit, that it may serve other situations of the same kind.

Let us jump now to the other extremity of our mental life, and, following our line of thought, go from the psychical existence which end, secondly, is merely 'acted,' to that which is exclusively 'dreamed.' In other words, let us place ourselves on the base AB of memory where all the events of our past life are set out in their smallest details. A consciousness which, detached from action, should thus keep in view the totality of its past, would have no reason to dwell upon one part of this past rather than upon another. In one sense, all its recollections would differ from its present perception, for, if we take them with the multiplicity of their detail, no two memories are ever precisely the same thing. But, in another sense, any memory may be set alongside the present situation: it would be sufficient to neglect in this perception and in this memory just enough detail for similarity alone to appear. Moreover, the moment that the recollection is linked with the perception, a multitude of events contiguous to the memory are thereby fastened to the perception - an indefinite multitude, which is only limited at the point at which we choose to stop it. The necessities of life are no longer there to regulate the effect of similarity, and consequently of contiguity; and as, after all, everything resembles everything else, it follows that anything can be associated with anything. In the first case the present perception continued itself in determinate movements; now it melts into an infinity of memories, all equally possible. At AB association would provoke an arbitrary choice, and in S an inevitable deed.

But these are only two extreme limits, at which the psychologist must place himself alternately for convenience of study, and which are really never reached in practice. There is not, in man at least, a purely sensori-motor state, any more than there is in him an imaginative memory: life without some slight activity beneath it. Our psychical life, as we have said, oscillates normally between these two extremes. On the one hand, the sensori-motor state S marks out the present direction of memory, being nothing else, in fact, than its actual and acting extremity; and on the other hand this memory itself, with the totality of our past, is continually pressing forward, so as to insert the largest possible part of itself into the present action. From this double effort result, at every moment, an infinite number of possible states of memory, states figured by the sections A'B', A''B'' of our diagram. These are, as we have said, so many repetitions of the whole of our past life. But each section is larger or smaller according to its nearness to the base or to the summit; and moreover each of these complete representations of the past brings to the light of consciousness only that which can fit into the sensori-motor state, and consequently that which resembles the present perception from the point of view of the action to be accomplished. In other words, memory, laden with the whole of the past, responds to the appeal of the present state by two simultaneous movements, one of translation, by which it moves in its entirety to meet experience, thus contracting more or less, though without dividing, with a view to action; the other of rotation upon itself, by which it turns towards the situation of the moment, presenting to it that side of itself which may prove to be the most useful. To these varying degrees of contraction correspond the various forms of association by similarity.

Everything happens, then, as though our recollections were repeated an infinite number of times in these many possible reductions of our past life. 

As you can see, Deleuze takes a lot of the idea of the first passive synthesis of habit straight from Bergson.   Our active sensory-motor experience at S is based on all the past habits defining our organism.  From this perspective, we are input-output machines that have been wired up by evolution and learning, and our present of action and reaction is the contraction of that entire past down to a point that constitutes us, now.  You can also see the kernel of the idea for the second synthesis is taken from Bergson as well.  If we aren't acting, but are instead involved in the experience of reminiscing or dreaming, we can experience the past on various different levels, or in different aspects.  

But Delezue modifies this understanding of what the cone represents by taking the active subject out of the memory.  It's somewhat ambiguous, but Bergson here seems to be saying that we as human thinkers can slice up the past and experience it in various ways that are disconnected from the active present, that is, we can experience and represent it as a past.  Deleuze removes the "we" from this activity, making it passive, as if the past were recollecting itself, without the need for a human subject to do any remembering.  He actually frequently transforms Bergson in this way, taking what seems to be a subjective, human psychological process, and turning it into an objective and ontological process that goes beyond human experience and grounds it.  In this case, our ability to focus on different parts of the past as a whole depends on the past's own ability to focus all of itself into an infinity of different presents.  Our active synthesis of any two parts of the past as a memory is dependent on the passive synthesis of the entire past with itself in an infinity of different possible ways, each of which is a way of representing the whole of the past as a present.  

I've been saying that the present somehow focuses all of the past, but it's probably more accurate to say that the past synthesizes all of the possible presents into a single present.  It's this set of all possible presents, the past as a whole, that can be focused or contracted in different ways to produce different levels, each of which is a distinct present.  As we've now come to expect, the past has a fractal structure.  Each present is actually equal to the set of all possible presents considered from a certain perspective.  We could conceive of the past (Time as a whole) in a relaxed fashion, as a set of individual atomic moments with no inherent relation between them, or as contracted into a tightly organized whole.  These would be two different experiences of the past, of the set of all presents, but each is equally a single possible present experience.  The whole structure reminds me of how each of Leibniz's monads contains an expression of the whole world.  The cone image illustrates the "fourth paradox in relation to the past".  Each slice is a part of the past that expresses the whole of the past; a single event that can be mapped to an infinite series.  

Giving the past a fractal structure is the only way I can find to make sense of Deleuze's repeated description of the present as a contraction of a level of the past that is itself relatively contracted or relaxed.  For example, here:

It must first be the case that this whole past coexists with itself, in varying degrees of relaxation ... and of contraction.

Or here:

We say of successive presents which express a destiny that they always play out the same thing, the same story, but at different levels: here more or less relaxed, there more or less contracted.

Or again here:

The present is always contracted difference, but in one case it contracts indifferent instants; in the other case, by passing to the limit, it contracts a differential level of the whole which is itself a matter of relaxation and contraction.

Or finally here:

In short, what we live empirically as a succession of different presents from the point of view of active synthesis is also the ever-increasing coexistence of levels of the past within passive synthesis. Each present contracts a level of the whole, but this level is already one of relaxation or contraction.

If each present lays out an infinite series of presents, because each level of the past reiterates the whole past, this fractal past also accounts for why the present is reflected in the past as a supplementary dimension.  The current present has to contain itself as part of the entire past that it contracts.

... if the new present is always endowed with a supplementary dimension, this is because it is reflected in the element of the pure past in general, whereas it is only through this element that we focus upon the former present as a particular.

I'll have to continue next time with the way the fractal past helps us understand why difference and repetition appear differently in the first and second synthesis.