I just finished Absolute Recoil. My diagnosis:
— You’ve got the exchange abstraction. Nothing much to worry about. Very common in these ages of the world [Weltalter]. You just need some relativity as such: take one each morning after breakfast.

Long answer: The book elaborates a variety of absolutes relative to one another and relative to themselves (‘self-relating negativity’, ‘absolute recoil’) but it does not investigate relativity as relativity as the oppositional determination of absoluteness.

A dialectic is needed between relativity and absoluteness like the dialectic of necessity and contingency formulated in Less Than Nothing.

Do I have a solution? I’d written a mathematical formulation a few years ago:

It has some implications for the book’s resolution:

“den is less than nothing”.
— Yes. It is the unicity ‘less than zero’ that I indicate by a dot:
0′ = ·

“objet a is more than one, but less than two: 1 + a.”
— No. Objet a is ‘less than one’ (‘to be or not to be’), where the outer dot (‘not to be’) embodies the shadowy double:
1′ = · {·}

“In short, the objet a is den processed through the One.”
— Here we have the exchange abstraction. There’s the input, the blackbox and the output: ‘Technology.’ (*)

“[sinthome is] the Two, a couple (yin-yang, masculine-feminine, the two classes in society), plus the One of Y a d’l’Un which makes the sexual (or class) relationship impossible and possible at the same time as its constitutive obstacle (chimney sweep, Jew, rabble): 2 + a.”
— No. What is expressed here is a dilemma (‘this one or that one’), which is ‘less than two’, where the outer dot (‘none of them’) embodies the dilemma:
2′ = · {·} { · {·} }

Note that there could be 3 or more elements, and the outer dot (‘none of the above’) would still embody the antagonism:
3′ = · {·} { · {·} } { · {·} { · {·} } }

In this light, I have an answer to this Freudian question: Why did he make up the story of the three prisoner women? I think it was a passage a l’acte to mark the absence of relativity as relativity in the book, to mark the abstaining from relativity as such.

(*): See Alfred Sohn-Rethel 1951 Intellectual Labour and Manual Labour (which was cited in The Sublime Object of Ideology). In fact I have a paper on necessity, contingency and Sohn-Rethel, but I have submitted it to a conference just a few days ago — OK, I’ve got the exchange abstraction too, well, I’m working on it.


On this topic:

1) objet petit a = “less than zero” = “less than the empty set”

2) Qualia is uncertainty, uncertainty is conditional counting

3) Virtuality is what is left behind by conditional subtraction

4) encapsulation is relativity

5) relativity?

6) Conditional Counting of Qualia

7) Why N-1 in standard deviation?



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