Early in this second chapter, Deleuze gives two examples of other philosophers who have touched on the problem of repetition.
We've already covered his reference to Hume in exhaustive detail. We saw that his account of why we believe in causality involved a two step process. Step one: nature presents to us A and B in constant conjunction and our imagination passively synthesizes them as related events, two ends of a chain. These are what I have been calling the habits of nature (as they pertain to our organism). Deleuze will also term these contractions, durations, contemplations, or lived presents. They are what happens "in general", and below the level of conscious representation. Step two: our mind then begins to habitually move from the idea of A or the appearance of any particular A to the idea of B. This mental habit is actually what we mean by our feeling of causality. This is an active synthesis performed by a full blown human mind.
We haven't talked about his reference to Bergson, but the point is largely the same; we want to highlight the way the active synthesis our mind performs when comparing distinct copies of a thing is based on a prior passive synthesis, made by our imaginative subconscious, that these are in fact qualitatively "the same" thing. Bergson is actually a pretty clear writer though, so it's worth quoting the source in full.
Whilst I am writing these lines, the hour strikes on a neighbouring clock, but my inattentive ear does not perceive it until several strokes have made themselves heard. Hence I have not counted them; and yet I only have to turn my attention backwards to count up the four strokes which have already sounded and add them to those which I hear. If, then, I question myself carefully on what has just taken place, I perceive that the first four sounds had struck my ear and even affected my consciousness, but that the sensations produced by each one of them, instead of being set side by side, had melted into one another in such a way as to give the whole a peculiar quality, to make a kind of musical phrase out of it. In order, then, to estimate retrospectively the number of strokes sounded, I tried to reconstruct this phrase in thought : my imagination made one stroke, then two, then three, and as long as it did not reach the exact number four, my feeling, when consulted, answered that the total effect was qualitatively different. It had thus ascertained in its own way the succession of four strokes, but quite otherwise than by a process of addition, and without bringing in the image of a juxtaposition of distinct terms. In a word, the number of strokes was perceived as a quality and not as a quantity: it is thus that duration is presented to immediate consciousness, and it retains this form so long as it does not give place to a symbolical representation derived from extensity.
The point of both examples is to describe two different levels of repetition -- active and passive. The rest of this first part of the chapter turns out to be entirely about the passive synthesis. Presumably we'll come back to the active one at some later point.
But why give two examples, if they illustrate the same point? Deleuze does this to illustrate a different type distinction we can make within the concept of repetition, namely the distinction between the repetition of elements and the repetition of cases. The cases-elements distinction is orthogonal, as it were, to the active-passive distinction. We can get a handle on it if we plow through this paragraph, which totally baffled me for a while.
No doubt Bergson's example is not the same as Hume's. One refers to a closed repetition, the other to an open one. Moreover, one refers to a repetition of elements of the type A A A A ... (tick, tick, tick, tick ...), the other to a repetition of cases such as AB AB AB A ... (tick-tock, tick-tock, tick-tock, tick ...). The principal distinction between these two forms rests upon the fact that in the second case difference not only appears in the contraction of the elements in general but also occurs in each particular case, between two elements which are both determined and joined together by a relation of opposition. The function of opposition here is to impose a limit on the elementary repetition, to enclose it upon the simplest group, to reduce it to a minimum of two (tock being the inverse of tick). Difference therefore appears to abandon its first figure of generality and to be distributed in the repeating particular, but in such a way as to give rise to new living generalities. Repetition finds itself enclosed in the 'case', reduced to the pair, while a new infinity opens up in the form of the repetition of the cases themselves. It would be wrong, therefore, to believe that every repetition of cases is open by nature, while every repetition of elements is closed. The repetition of cases is open only by virtue of the closure of a binary opposition between elements. Conversely, the repetition of elements is closed only by virtue of a reference to structures of cases in which as a whole it plays itself the role of one of the two opposed elements: not only is four a generality in relation to four strokes, but 'four o'clock' enters into a duality with the preceding or the following half-hour, or even, on the horizon of the perceptual universe, with the corresponding four o'clock in the morning or afternoon. In the case of passive synthesis, the two forms of repetition always refer back to one another: repetition of cases presupposes that of elements, but that of elements necessarily extends into that of cases (whence the natural tendency of passive synthesis to experience tick-tick as tick-tock).
Let's get that translated into Plain English. It's a bit of a technical point, but it actually helps to illuminate a bunch of other opaque bits in this section.
Basically we have two types of repetition:
1 = Bergson = repetition of elements = closed repetition = general form of difference = A, A, A, A, ... = {A}
2 = Hume = repetition of cases = open repetition = particular form of difference = AB, AB, AB, A ... = {AB}
The question is how these two are related. The answer is that they are constantly converting into one another. How so?
We have to start by thinking about the initial problem of this chapter -- don't we paradoxically have to have some difference to be able to talk about a repetition? At first we imagined that this difference was created in the mind of the person doing the recognizing of the repetition. Later we discovered a passive synthesis that operated below the level of the mind, but nevertheless still drew a general sort of difference from the repetition.
Repetition 1 -- of elements -- illustrates this synthesis pretty well because it shows us a difference we might call "the general fact that there is A". Starting from the assumption of an atomized world, all those individual instances of A weren't exactly the same. Technically, there is no A. But they were good enough for government work, as my father used to put it, and somehow, for some purpose, they were contracted into the existence of a thing we call A. The general difference drawn from the world's habit of repeating something like A is that there is an A. In other words, the difference drawn is the existence, really the very creation, of A. This sounds a bit circular because it is. Hold off on that part though.
Repetition 2 -- of cases -- obviously could illustrate the same point because it shows us the general fact that there exists the connection AB. But there's a more specific form of difference at work in this type of repetition because there's a difference within each of the elements, the difference between A and B. At first this seems to make it a totally different case from repetition 1. But Deleuze is going to show us how to get from 1 to 2 and back again.
What do you need to have to have an A? How can the difference "there exists A" be created in the world? Well, we need there to be at least one repetition of A. That is, we need to have seen what an A is at least twice. For there to be "an" A, there need to be at least two instances A1 and A2.
[This is one of the odd aspects of Deleuze's concept of repetition. "A" single multiplicity requires at least 2 heterogenous elements. On a side side note, it occurs to me that this may be the more interesting approach to the concept of non-duality as you sometimes hear it in Buddhism -- it obviously means "not two"; but if they wanted to say "one", then why not just say that instead? Seems like non-dual means not-two, but also not-one either.]
Now we've re-conceived the general fact that there is such a thing as an A as the particular difference that holds together A1 and A2. We've reduced the repetition of A to its minimum, which turns out to be that there was an A1 followed by an A2. If you just rename these A and B, you can see how we went from the closed repetition of the element A to the open repetition of cases where we assert that all A will be followed by B. If you think back to Bergson's clock and think about the ticking rather than the chiming, you'll notice that for some odd perceptual reason we often reduce a long string of identical instances to an alternation of two types. I'm sitting here listening to my gutter drip as I type, and there's a duck-rabbit sort of gestalt flip that takes me from hearing drip-drip-drip-drip to hearing drip-drop-drip-drop.
We can also go back the opposite way if we think about how the two ends of the chain are held together as one relation. After all, the story of repetition 2 is that the case AB is repeated as if it were an element in its own right. Earlier when I wrote that the existence of A required A1 and A2 you may have been tempted to object that you could perfectly well think of only one copy of a thing, or, in fact, you could even conceive of no copies of a thing. All you have to do is think about the idea of that thing, and think that the one instance you saw is unique. Actually though, this reasoning involves a hidden second copy of A. It requires the idea of A, the set of all A, {A}. A repetition of elements is closed, it keeps repeating the form of element A, only by virtue of this idea {A} that serves as a second element that differs from any particular A. Which is to say that {A} functions as B in an open repetition of the case called: "a particular A will be followed by the idea of A" -- ie. AB = A{A}. So you might define the repetition of the element A to be the same thing as the repetition of the case A{A}.
When Bergson says something as simple as "the clock struck four" there are actually a number of ideas at work that serve to "make" the general difference "four o'clock". First, you need the idea of four, as a qualitative description of a characteristic of the "musical phrase" of the chiming. That idea has to distinguish it from 3 or 5 strokes, or even from hearing a music that contains no individual strokes at all. You also need the idea of four o'clock as a sort of meaningful event to begin with. Why else would you have made note of the fact that these sounds should be grouped together and distinguished from the rest of the commotion around you? The general identity of the repeated element four o'clock depends upon its particular place in a repeating case that we call "telling time". The repetition of this overall context, this series of four o'clocks, is necessary for us to distinguish it as an entity and differentiate it from 3:00 and 5:00. Finally, you need to have an idea of this particular 4:00 that distinguishes the 4AM element from the 4PM, which is the largest difference of elements before the case itself would repeat.
To summarize in less technical terms: for an element to be repeated, it has to be embedded in a meaningful context or case that recognizes it as a repetition. But for the context to be defined enough to function as the means of identifying a repetitive element, it itself needs to be repeated as an element. The two convert back and forth into one another and the cycle never ends, very much along the lines we saw earlier with the twin repetitions of organism and environment.
Difference therefore appears to abandon its first figure of generality and to be distributed in the repeating particular, but in such a way as to give rise to new living generalities.
... the generality originally formed by the contraction of 'ticks' is redistributed in the form of particularities in the more complex repetition of 'tick-tocks', which are in turn contracted.'
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