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More noodling on intersectionality (more on the 1%, the 20%, and the 80%)

[UPDATE I realized I left the legend off Figure 2, so the colors in the Venn Diagram must have seemed random. They're pretty random anyhow, since in order to get the color to blend properly, I had to use beige to mean white, which is another instance of the fact that developing a sense of visualization and a visual vocabulary isn't all that easy. Anyway, if (a) anybody read this, and (b) reading it, found Figure 2 to be the source of bafflement, Figure 2 is improved. --lambert]

Some may think this series (part one) is dry.... To which I would respond so is the edge of a sword, until it's used....

If we think of the 80/20/1 as sets of people (classes), how do we figure out how to put one person in one set, and another in another?

Informally we might say with a litmus test: In the case before us, one litmus test is whether they purchase labor power (the 1%) or sell it (the 99%, with other litmus tests to classify the "pillars of the regime" into the 20% from the 80%)[1]. More formally, we might say, for "litmus test," "set membership function," as we see in Figure 1. And as you can see, I'm still learning to sketch (and might even have to give up, or learn both to draw, and especially to print and/or write, better):

(I picked the gold (1%), red (20%), and blue (80%) color from the color of an archery target. Again, not having exercised my visual imagination much, I'm not sure these colors work.)

First, I was about to write that the hierarchical relation expressed in this diagram is just the same as that expressed in the previous noodle, with triangles -- pause to note that if we could get the visual notation right, we could do sketches on napkins, and so forth -- but in fact it isn't. The set of all humans is included within both outermost circle and enclosing triangle, but where the triangle has the 80, the 20, and the 1 contiguous, this figure has the 1 contained within the 20, and the 20 contained within the 80. I don't think that's appropriate (it doesn't express the idea that "the rich are different" in the way the triangle does, where the 1% are above the 20%, not within them.)

That said, when we introduce a notation for the set membership function:

f(x,R) Equation 1

that makes the relations we need to work out clear. (I drew the function on a "chalkboard" for fun.) Suppose we have "J," a human ("Jay," "Jaye," "Jeh", "J" for Jack, "J" for Jacqueline) and we want to classify them. The function has two parameters: x, and R. "J" is x; a (social) Relation is R. In other words, we ask ourselves -- this being a capitalist system -- what J's Relation to capital is. If J owns capital (and hence purchases labor power), J goes in the 1%. And so on. In fact, J works at Walmart, hence is part of the 80%, as Figure 1 shows.

Now, to be fair, I suppose by "clear" I mean, "Forces us to think through the sort of question I want us to think through." And what's wrong with that? But suppose we want a more complicated set membership function? One that expresses -- say -- the "white working-class men" that Hillary Clinton is supposed to have a hard time appealing to. Figure 2:

Visually, Figure 2 puts "J" inside three overlapping sets. (One reason I started drawing circles is that I wanted to draw Venn diagrams to express overlap, the idea that "J" can belong to several sets at the same time. Having drawn them, I'm not sure I like the result. How do we handle "L," "M," and "N" without going crazy with colors and overlaps?

However, once again the set membership notation clears things up:

f(x; C, R, G) Equation 2
f("J"; white, working-class, male)

Note that this notation can also be used for "fuzzy sets." The people who like this sort of notation seem to be enthusiastic about it; see here, here, and here.

At this point, I should add a ton of caveats:

1) I'm not seeking to prove anything; I'm seeking clarity of expression.

2) I'm not trying to model anything; the set membership functions produce a snapshot, and nothing dynamic. (I suppose one could add variable, call it T, for time, and that might even work conceptually, but I'm not sure it would communicate effectively.

However, I do claim that inventing (or discovering) a notation and following through on its implications can provide useful results. For example, we might ask ourselves "How is that f("J"; white, working-class, male) is ubiquitous in the pages of WaPo, f("J"; black, working-class) appears only rarely, and the much more -- maximally? -- inclusive f("J"; working-class) hardly ever appears at all? Could there be a reason for this seemingly arbitrary choice regarding set membership function of interest?

More to come....

NOTE
[1] Caveat that this is a toy example. In reality, social relations are a good deal more complex. So we need a notation that is capable of handling such complexity!

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