Quantitative and Qualitative Multiplicities

I’ve written previously about spatial and temporal integration. Luhmann argued that in modern society temporal integration becomes more powerful than spatial integration. Here is an excerpt from The Stanford Encyclopedia of Philosophy on Bergson. It illustrates the concept of quantitative multiplicity:

For Bergson, we must understand the duration as a qualitative multiplicity — as opposed to a quantitative multiplicity. As the name suggests, a quantitative multiplicity enumerates things or states of consciousness by means of externalizing one from another in a homogeneous space. In contrast, a qualitative multiplicity consists in a temporal heterogeneity, in which “several conscious states are organized into a whole, permeate one another, [and] gradually gain a richer content” (Time and Free Will, p. 122). Bergson even insists that the word ‘several’ is inappropriate to qualitative multiplicity because it suggests numbering. In Time and Free Will, Bergson provides examples of a quantitative multiplicity; the example of a flock of sheep is perhaps the easiest to grasp (Time and Free Will, pp. 76–77). When we look at a flock of sheep, what we notice is that they all look alike. We sense no qualitative change as we move from one to another. We also notice that we can enumerate the sheep. We are able to enumerate them because each sheep is spatially separated from or juxtaposed to the others; in other words, each occupies a discernible spatial location. Therefore, quantitative multiplicities, as Bergson says, are homogeneous and spatial. Moreover, because a quantitative multiplicity is homogeneous, we can represent it with a symbol, for instance, a sum: ‘25’.

Quantitative multiplicity allows us to speak of a flock or the flock–in other words, one flock, a sum of individual sheep. Quantitative multiplicity rests on a spatial orientation, where objects observed as belonging to the same class (sheep in this case) can be counted. There is a still background where the sheep can be counted. But when we observe sheep, they are usually moving toward or away from one another. Moreover, this motion cannot be segmented; the motion is indivisible, continuous, and heterogeneous.

Qualitative multiplicity is about difference, or how something become different from itself. In the experience of duration, each moment is different than the previous one. But we cannot slice up time into segments and then juxtapose these segments. If we consider the days of a week, “Tuesday is different from Monday because Monday only includes itself and Sunday, while Tuesday includes itself, Monday, and Sunday.” So Monday and Tuesday are not identical segments; they are not like the identical-looking sheep. Tuesday is qualitatively different than Monday.

And, if we draw different distinctions, the sheep are not structurally identical; some are older, weaker, etc. They are qualitatively different. We are drawing distinctions like young/not young, strong/not strong to show qualitative differences.

In a rhyzome, the

variable distances are not extensive quantities divisible by each other; rather, each is indivisible, or “relatively indivisible,” in other words, they are divisible below or above a certain threshold, they cannot increase or diminish without their elements elements changing in nature. A swarm of bees . . . What is the significance of these indivisible distances that are ceaselessly transformed, and cannot be divided or transformed without their elements changing in nature each time? Is it not the intensive character of this kind of multiplicity’s elements and the relations between them? Exactly like a speed or a temperature, which is not composed of other speeds speeds and temperatures but rather is enveloped in or envelopes others, each of which makes a change in nature.

Deleuze & Guattari, A Thousand Plateaus, 30-31

This seems to mean that the difference in speed between 30 mph and 40 mph is not the same as the difference between 40 mph and 50 mph, and the difference in temperature between 30 degrees and 40 degrees is not the same as the difference between 40 degrees and 50 degrees.

The issue of natural causation also links Luhmann to Bergson.

Bergson thinks that Kant has confused space and time in a mixture, with the result that we must conceive human action as determined by natural causality. Bergson offers a twofold response. On the one hand, in order to define consciousness and therefore freedom, Bergson proposes to differentiate between time and space, “to un-mix” them, we might say. On the other hand, through the differentiation, he defines the immediate data of consciousness as being temporal, in other words, as the duration (la durée). In the duration, there is no juxtaposition of events; therefore there is no mechanistic causality. It is in the duration that we can speak of the experience of freedom.

In other words, we cannot say that A causes B in a mechanistic way. There are multiple casualties. For instance, we claim that a particular virus causes the flu, but this leads to the question of what caused the virus. And did whatever caused the virus also, by extension, cause the flu symptoms? How far back can we legitimately go in tracing causes? Also, how far into the future can we attribute effects? For instance, a parent neglects his child, and that child grows up to neglect his child. Can we blame the grandparent for his grandchild’s treatment? Is the grandparent folded into the parent like Monday is folded into Tuesday? Or did events unrelated to the grandparent contribute to the grandchild’s neglect? It’s more likely that the causes are multiple and complex. It comes down to attribution.

A virus can perturb an organism, but the organism’s structure determines how, or even if, it will change. And these changes are observed through a prism of distinctions.

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