I have the beginnings of an idea for another book, which would pick up the threads of some of my posts a while ago about equality.

The mathematical backbone would be four chapters on four mathematical topics: equality, equivalence, isomorphism, adjointness. Admittedly I barely know enough to write the first two, would struggle with the third, and have a way to go before I could seriously tackle the last. But nevertheless, I think that’s the sequence to follow. The interest would be in the way that equality is conserved through progressively “weaker” (but more general) constructions of alikeness.

Interleaved between these would be chapters on equal intelligence, sexual equality, economic equality and political equality.

The chapter on equal intelligence would deal with Ranciere, perhaps Chomsky, and the notion of “distributed” cognition. The point about distributed cognition is that “a thought” is not the property of a single thinking intelligence, but something that takes form as an anonymous multiplicity. The equal capacity to sustain a thought that Badiou talks about is not an equal intellectual facility with formal matter, but the fact that anyone and everyone can be summoned to participate in the construction of such a multiplicity. That may seem a bit weak: after all, every member of our manifestly unequal society “participates” in it in at least some sense. I think one has to find a way to distinguish between “democratic” participation in (that is, subordination to) the life of the state, which is the articulation of unequally distributed powers, and participation in the construction of a new configuration of the general will. But that’s political equality - and it’s worth remarking that political equality and thinking equality seem to be closely tied. Not surprising, really: more and more, one hears these days that political (and economic) inequality is just the expression of a naturally unequal distribution of intellectual powers…

Sexual equality is a sticky one. I think seeing off various idealisations of sexual identity would be a good start. The point is not to afford equal dignity to diverse “lifestyles”, but to affirm that they’re all equally worthless. (I could really warm to this theme). A modest ambition here would be to be the first person to treat Gayle Rubin’s Thinking Sex with the contempt it really deserves. Thinking sex, sexual intelligence, would first of all require a nihilating fury against commercial sexuality in all its forms. Equality is not for sale.

I have no idea what one might say about economic equality, which tells a story all by itself. Is it thinkable? I can’t think of any other starting point besides “to each according to his needs, from each according to his ability”. This assumes diverse needs and abilities, but places them under a regime of equality. “To each…from each…” calls for a mechanism of distribution; “according to…according to…” calls for techniques of measurement; “…his needs…his ability” enjoins an asymmetric reciprocity. The “logic of the market” poses as a solution to these requirements, but functions instead in the service of capitalisation. It’s a familiar problem, but I’m unable to pose - even in a far off, utopian manner - an adequate solution. Perhaps there isn’t one, or at least not one that can be arrived at by pure cogitation in the midst of present conditions. We need some room to experiment, a sense of the possible.