I am quickly learning that most of the published guides to Difference and Repetition are not very helpful for explicating its opening pages (though they are very good at situating the book's broader arguments within a context of influences [e.g., Nietzsche and Bergson] and enemies [e.g., Kant and Hegel]). Though I was able to find a secondary source to help me deal with repetition and the law a few days ago, I want to try and deal with Deleuze's claims about repetition and scientific experiment (the subject of his fifth paragraph) on my own.
Deleuze opens with a feint against himself, "From the point of view of scientific experiment, it seems difficult to deny a relationship between repetition and law" (3). This designation of scientific experiment as a point of view gives some insight into what Deleuze is actually up to in this weird introduction. He began (as we saw in SR 1.1) by differentiating generality and repetition as distinct points of view, then moved on to the law and repetition, and now takes up scientific experiment and repetition. In each case, he brings together two terms that do not have an immediately obvious relationship (at least for me). And yet, in each case, Deleuze manages to accomplishes two things:  he convinces me that there is a common sensical relation between repetition and these three other points of view, and  he persuades me that it is important to determine why this common sensical relation is wrong (or, at the very least, that it leaves the term repetition unconceptualized). One might say that Deleuze has to compose each of these problems before I can actually sense the urgency of his philosophical response to them. (Bergson: "stating the problem is not simply uncovering, it is inventing" [Creative Mind 37].)
It was pretty old hat, even in DR's publication year, to associate law with science. As far as I know, scientists no longer strive to discover "natural laws" that explain (and/or determine) natural phenomena. They have worked for some time now with theories (not laws) that are supported by mathematics, trials, observations, and experiments but that (in themselves) are not proven or complete. And yet, all the same, scientific experimentation does seem more directly relevant to a philosophical project on repetition than either generality or law does. We still associate the word "repeatable," after all, with the scientific method, which grounds scientific experiments. (At least that's what I learned in high school chemistry and physics. Perhaps things have changed...)
In order get at the "conditions" under which "experimentation" is said to "ensure" or to value repetition, Deleuze distinguishes between the "free state" in which natural phenomena occur "among vast cycles of resemblance" and experimentation's "relatively closed environments" (3). From the point of view of this free state, "any inference is possible." In other words, I can infer from the orderly cycles of the tide, the phases of the moon, the patterns of the stars in the night sky, the visible qualities of animals and animal types, and the regularity of the passing seasons that there is some sort of design to all of this vastness. And yet, if I have Darwin's mind and archive and I begin noticing patterns that seem to disrupt this particular sense of orderliness, I infer something else altogether from the composite of trans-species resemblance and environment: not design at all, but evolution by natural selection. Deleuze is not claiming that all inferences are equally valid from the point of view of this free state, merely that so many conflicting and contradictory and mutually exclusive inferences are possible when one situates oneself in an archive where "everything reacts on everything else, and everything resembles [or, I might append, potentially resembles] everything else" (3).
What do experiments do? They arrange precise, relatively controlled conditions and enumerate a finite number of factors according to which they measure or observe expectant or emerging phenomena. Deleuze expands this point:
Consequently, there is no need to question the application of mathematics to physics: physics is already mathematical, since the closed environments or chosen factors also constitute systems of geometrical co-ordinates. In these conditions, phenomena necessarily appear as equal to a certain quantitative relation between the chosen factors. Experimentation is thus a matter of substituting one order of generality for another: an order of equality for an order of resemblance. Resemblances are unpacked in order to discover an equality which allows the identification of a phenomenon under the particular conditions of the experiment. (3)
(Is there a counter-mathematical movement in (or against) physics? If not, why the first sentence? Is there some point here about the competition between theoretical and experimental physics?) Given Deleuze's admiration for science, I think it is a mistake to read this passage as a disparagement of scientific experimentation. He seems merely to be conceptualizing (or trying conceptualize while looking outward from within the domain of philosophy) scientific experiment itself as a kind of function. A scientist sets up an experimental condition (z=f(x, y)), such that certain expected phenomena (x and y) become substituted by "a certain quantitative relation between the chosen factors" (z). Take a crude experiment that tests the mathematical probability that out of 100 coin tosses, I should see approximately 50 heads and 50 tails appear. I employ five tossers, each of whom will toss five respective coins twenty times. I run this experiment five times. Eventually, I will be able to substitute a numeric equality (which I then compare with my initial hypothesis) for an initial order of resemblance (in which the appearances of heads and tails are recognized and recorded). I will eventually identify, in other words, the appearances and re-appearances of heads and tails with numeric representations that break down how many times heads and tails appeared, how much these appearances deviated from the hypothetical calculation (if at all), how many streaks appeared (that is, several recurrences of heads or tails in a row), and if there seemed to be any variation between the different tossers' results.
(Note: I apologize to any scientists reading this crude example. Remember, I can barely follow Deleuze's philosophical and historical allusions let alone be responsible to the actualities of scientific experimentation! I would, of course, welcome correction. Or a better example!)
What does any of this have to do with repetition? How does this example tell us about the purported repeatability of scientific experiments? "Repetition appears here," Deleuze continues, "only in the passage from one order of generality [i.e., resemblance] to another [i.e., equivalence]" (3). In other words, scientific experiments do not repeat the phenomena they purport to study but merely a jump between orders of generality that concern these phenomena, from qualitative resemblances (x, y) which might be difficult to isolate in the free state of nature to a quantitative equivalence (z). "The formula" or what I called the function of scientific experimentation "says that in similar situations one will always be able to select and retain the same factors, which represent the being-equal of the phenomena [that is, the being-equal of its resemblances to its equivalencies]" (3).
What is Deleuze's point here? Namely, that it is a mistake to presuppose that repetition for itself constitutes the scientific claim, "given the same circumstances, then [such and such will appear again]" (3). The reappearance of such and such in scientific experimentation is not a repetition of this such and such "in principle" but a representation of the phenomena under preset conditions: finite factors, materials, and coordinates (3). My example of the coin tosses works here, for my experiment is a mere representation of a coin's singularity (or a set of coins' singularities). It represents a coin, in other words, as an object that, when thrown in the air, will land on one side or the other. It cannot encompass the coin's potential relation to other phenomena in a free state insofar as it cannot replicate all possible conditions under which a coin might fall, or be tossed. In fact, these potential relations and alternative conditions do not altogether matter to me. My experiment strategically reduces the coin in itself as well as its potential relation to other things to a non-natural, preconceived situation in which its two-sided resemblance to other objects becomes translated into a useful order of equivalencies. I write "useful" because it is useful to know how to read and study probabilities. But this usefulness still does not express (does not repeat) the singularity of the coin in itself; it merely represents it (thus reducing it) within an order of generality. For the experiment, the materials that make up the coin, my affection for the coin, the history of the various hands through which the coin has passed, the signs and scars of usage on its surface and edge—all of the elements that make the coin non-exchangeable outside qualitative and quantitative orders—have nothing to do with the "hypothetical repetition" (i.e., the purported repeatability) of my experiment.
But isn't this all a matter of confused (and confusing) semantics, of taking issue a bit too aggressively with the colloquial use of the word "repetition"? Perhaps. And yet something interesting is happening these pages: namely, that out of this quibbling and strict division between repetition and generality, law, and experimentation one begins to see a rather novel philosophical respect for the uniqueness of singular things developing. While there's nothing wrong with speaking of coins in general (or requiring voting laws that rely on the general determination of citizenship or setting up the conditions of an experiment that can, in general, be "repeated" by anyone anywhere), Deleuze's seemingly naïve insistence on a thing's singularity (and not its particularity) actually does open up some philosophical problems. The first among them, though Deleuze does not say this here, is that he is not inventing a concept of repetition that is just stubbornly contrary; rather, he is inventing a concept that takes repetition literally. We use this word all the time, he seems to be saying, but can we actually come up with a robust conceptualization of it? Or is it condemned to the colloquial and the general? Repetition happens all the same, he seems to be saying, but do we really understand? Can we find a way to talk about it? And, if so, what sort of consequences might this have for how we see and interact with others, with things, and with the world? (In this sense, the thrust of his opening method is not altogether different from Martin Heidegger's in Being and Time (1925): "[The] question [of the meaning of being] has today been forgotten [. . .] It is said that 'Being' is the most universal and the emptiest of concepts. As such it resists every definition" (2). As with Heidegger and being, so it is with Deleuze and repetition . . . and difference.]
But I have left out a few things: namely, that Deleuze does not deny that repetition has a part to play in scientific experiment. The experiment itself might not repeat the phenomenon it studies, but the phenomenon, "in order to appear," still "takes advantage of the artificial passage from one order of generality to another" (3). What does this mean? While the experiment does not "account for what gives rise to repetition"—no more than the celebration of the fall of the Bastille accounts or repeats the initial conditions of its singular fall—the function of the scientific experiment—like a festival or celebration of independence or a bathroom mirror—nevertheless serves as a kind of stage or passageway for "the power of a single time" or "a singular power" to repeat itself to the nth power. These connections between scientific experiment, the festival, and the mundane bathroom mirror suggests something about Deleuze's repetition: namely, that it serves as the very ground of the order of generality (in other words, generality requires the repetition of singularities even if it cannot account or represent singularities) and that repetition requires some sort of passageway or condition (whether artificial or natural, free or constrained) in order to appear. But what is the nature or the mechanics of that appearance? What is a singularity?
Questions which he will hopefully take up later in the book. Questions, then, for another time. Next time: back to repetition and law, specifically moral law.