Compositionality and Generative Effects

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Our third meeting took place on the 17th of August 2020. We summarize and discuss parts of Systems, Generativity and Interactional Effects by Elie Adam.

The basic idea is that we can assign some observable data to systems such that when we join these systems together, the observable data of the joined system does not match the join of the observed data of the component systems. That is, the effect is produced by the phenomenal assignment rather than the systems themselves. Adam shows a wide range of examples of this, from pandemics to graphs to grammars, and proposes a way of formally capturing the generative effect itself as a mathematical object. Roughly, if we join together two systems and then "modulo out the explainable" data, we are left with only the interesting bits. This is generally non-linear, so the question is whether one can linearize it. Adam uses cohomology theory to do this, which amounts to finding the proper object which would make an inexact sequence exact.

STP is interested in using these tools to understand political movements on the one hand and economic crises on the other. We identify how the Marx's theory of surplus value fits the Adam's model, as the assignment of price onto the system of labour power (commodified labour) and of means of production which then exhibits "loss of exactness" when the two systems are joined in the final product. If we assume, as Marx does, that capitalism relies on this generative effect to reproduce itself, then Adam's tools for describing such an "evolving" or "devolving" system will certainly be useful to us.