# Parametricity

There is a nice idea – which I learned from the work of David Harvey (or in podcast form) – of analyzing society in terms of a number of “moments”, or aspects of society at a given moment in time. Harvey chooses 7:

• Technology

• Relation to nature

• Mental conceptions of the world

• Social relations

• Institutional arrangements

• The patterns and activities of daily life

• Labor and production processes

I prefer to think of these as 7 “coordinates” on the state of society. In other words, the actual state of society is very high dimensional, but we can approximately represent it using the above 7 coordinates each giving some information about society.

An important point stressed by Harvey is that all 7 of these coordinates are related to each other. For example, possessing a certain technology – say the internal combustion engine – along with the daily life fact of driving to work, implies a certain relation to nature: namely, living in a rapidly warming climate.

That is, one cannot choose each coordinate independently of the others. If the state of society as a whole is represented by a 7-tuple of individual states in each coordinate, only a subset of all the possible 7-tuples correspond to really possible societies while the others refer to contradictory or otherwise impossible societal structures.

This is a useful model for thinking about how historical change occurs and how best to help make it happen, since it gives one a set of handles to start analyzing a given historical moment. Also, as we will discuss more later, it encourages thinking about how changes in many different areas are required to create lasting historical change, thus encouraging more sophisticated and ultimately more effective action.

## Making this model mathematical

Mathematically speaking, if $S$ is the set of all 7-tuples with the above coordinates, then we might imagine there is a relation $\mathsf{stable} \subseteq S$ which consists of those states which represent stable, coherent, really possible societies. This connects with Harvey’s description of these 7 coordinates as being in relation to each other, not determining each other. Mathematically, each coordinate in stable societies cannot be represented as a pure function of the others. We must use a full-fledged mathematical relation (i.e., a subset of a Cartesian product) to model it.

## A more sophisticated model

Going further, we might object to the rigidity of the above model. In reality it is not true that a society is either stable/coherent or it’s not. In reality, all societies are contradictory, some are just more contradictory than others. The degree of “contradictoriness” or “instability” should intuitively measure how quickly society would tend to exit that state. For example, a capitalist society with actual political democracy would very quickly cease to be capitalist (since the majority could use the mechanisms of democracy to institute socialism) and thus such a society would be highly unstable, and indeed attempts to put society into such a state have been very fraught.

We might model this with a function $\mathsf{instability} \colon S \to \mathbb{R}$ which measures how unstable a given society is. You can think of this as something like the “potential energy” of that social arrangement.

The coherent/stable/really possible societies are then those with instability close to 0. The set $\mathsf{stable}$ above would correspond to the set of states $s \in S$ where $\mathsf{instability}(s) = 0$.

Drawing the model out a bit, we might even imagine that history proceeds on a trajectory through $S$ over time just as a physical system does. The state of society has momentum, and its evolution over time is a combination of continuing on in the direction of its momentum and trying to locally change to reduce the value of $\mathsf{instability}$. It’s interesting to note that Harvey already seems to implicitly think in this model already: at 12:50 of this recording he talks about changes in one coordinate increasing the “energy” in other coordinates.

## The utility of this model

Harvey says this model is important because it indicates that to majorly change the state of society, you typically have to make major changes in all of the 7 coordinates. Changing only a subset of them will push you out of the “high-stability subset” (since the actual high-stability subset does not lie in an axis-aligned subspace) and then over time, you will roll back down the hill into an societal state unlike the one you were trying to reach.

He uses this model to explain the historical failure of many socialist revolutions. In certain cases they succeeded in revolutionizing (i.e., dramatically moving) some of the coordinates, but not others. As a result, the societal states they entered were not stable, and overtime aspects regressed to obtain stable configurations which fell short of the ultimate goal of communism. Of course there are spatial/geographic/geo-political contingencies that must be taken into account as well, but I think this does explain part of the historical failures.

By making this model mathematical, we gain access to sophisticated notions like “the set of stable societies does not locally approximately lie in axis-aligned subspaces”, or to be able to talk more precisely about things like the “momentum of history”. We also gain access to language about our position in the historical landscape (e.g., we might say we’ve been propelled in a direction which has put us very near to a cliff in regards to our relation to nature, as the fallout from the climate crisis makes it likely we’ll slide right off).