When I asked earlier what place repetition could have in a law-like material universe, I was actually getting one page ahead of myself. The simplest image we have for how laws work would be something like a mathematical law -- let's say the law governing the position of a body in a vacuum falling due to gravity y=1/2at^2. You plug in a particular example of the independent variable, combine it with a constant, and it determines the particular value of the dependent variable. Later, the dependent variable you are interested in will have changed to a new particular value.
On the other hand, generality belongs to the order of laws. However, law determines only the resemblance of the subjects ruled by it, along with their equivalence to terms which it designates. Far from grounding repetition, law shows, rather, how repetition would remain impossible for pure subjects of law - particulars. It condemns them to change.
Anything subject to a law is condemned to change in this mechanical way. It has no freedom; it can't not change, it is impermanent. Even the constant "a=g" here is dependent on another law, Newton's law of gravitaion F=GmM/r^2. Etc ... etc ... Even the constants are variables one you look one level higher. The only thing that's ultimately really preserved here is the form of the law. An unchanging form for an ever changing world.
I'll have to come back to this later, but I believe this is why Deleuze thinks of any change in this type of world as a "false movement":
Kierkegaard and Nietzsche are among those who bring to philosophy new means of expression. In relation to them we speak readily of an overcoming of philosophy. Furthermore, in all their work, movement is at issue. Their objection to Hegel is that he does not go beyond false movement - in other words, the abstract logical movement of 'mediation'. They want to put metaphysics in motion, in action.
Even though there's continual change in a law-like world -- in fact, everything governed by the laws is condemned to change in accordance with them, never to repeat itself -- there's really, "nothing new under the sun". There's not any real development or evolution, just the mechanical working through of the consequences of something that we presume stands outside Nature (ie. the form of the law).
But doesn't science base itself explicitly on discovering the ways in which Nature repeats itself? If we read of a "replication crisis" it must be because "normal" science (when it's not having a crisis) is all about exact reproducibility of experimental results, right? Well, sure it does. Think about the way it goes about this in practice though. There's all kinda of stuff going on everywhere in Nature all the time. From this constant chaos we grab onto this thing, which seems to kinda resemble that other thing. Once we decide that these two phenomena are related, we try to isolate some quantitative aspect of them while holding every other way in which they might differ constant.
Consider how it works with the apple and the moon. Newton, spliffed out under a tree: "Dude, it's like they're both sorta falling, man". But an apple and the moon are quite obviously different. And it's actually a pretty long road to make a connection between the way that they are indeed similar, and the experimental setup that allows you to exclude all the factors like friction, the influence of other planets, etc ... that would prevent them from being substituted for m and M in the equation above. In short, an experiment is an elaborately "artificial" setup whose goal, at the limit, is to try and hold the entire universe constant in order to convert our perception of the similarity of two things into a law about how they are interchangeable in one particular quantitative aspect. I'm just re-writing this passage in my own terms:
From the point of view of scientific experiment, it seems difficult to deny a relationship between repetition and law. However, we must ask under what conditions experimentation ensures repetition. Natural phenomena are produced in a free state, where any inference is possible among the vast cycles of resemblance: in this sense, everything reacts on everything else, and everything resembles everything else (resemblance of the diverse with itself). However, experimentation constitutes relatively closed environments in which phenomena are defined in terms of a small number of chosen factors (a minimum of two - for example, Space and Time for the movement of bodies in a vacuum). Consequently, there is no reason 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.
If you consider what it is that's "repeating" here, it's not really Nature, so much as your experimental set-up. Obviously, that's part of Nature too, but looking at it this way I think changes your idea of what's going on in a subtle but important way. The whole thing kinda reminds me of the debate that surrounds Wigner's famous Unreasonable Effectiveness of Mathematics in the Natural Sciences: "Some men went fishing in the sea with a net, and upon examining what they caught they concluded that there was a minimum size to the fish in the sea." This isn't meant to imply that you didn't learn something "real" and "true" about the universe by going fishing -- if you bring this net, these are the fish you will catch. It's just that it might not be what you thought you learned.
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