Recollection and Repetition: Ergodic and Non-Ergodic Processes in the Sciences

July 23rd, 2015
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Article of the Week from Fixing the Economists

by Philip Pilkington

Say what you will, this problem is going to play an important role in modern philosophy because repetition is a decisive expression for what ‘recollection’ was for the Greeks. Just as they taught that all knowledge is recollection, thus will modern philosophy teach that life itself is a repetition.

— Soren Kierkegaard, ‘Repetition

Follow up:

Just a bit of a follow-up here to my last post on the limits of probability theory. I got two fantastic responses that I think require me to clarify things somewhat. One was from Lord Keynes in the comments of his blog, the other was from Tom Hickey of Mike Norman Economics in the comments of mine.

First off, I should lay out the reason it seems clarification is necessary. In the last post I was largely concerned with laying out the properly relevant philosophical questions underlying probability theory. I think I succeeded in doing that but I only really hinted at what my own opinions on the matter were. So, let’s go into that a bit.

Lord Keynes’ response was basically that in the social sciences the future mirrors the past only in a very limited sense and that in the natural sciences there are many processes in which the future fully mirrors the past — he gives examples of cycles of seasons and so on. Cast in different terminology what Lord Keynes is saying is that determinism is very limited in social science if it indeed exists at all, but that it does exist to a large extent in the natural sciences. Or, one more time to ensure that we all know what the words we are using mean, that social science is based on material that is largely non-ergodic while the natural sciences are based on material that is ergodic.

I largely agree with this assessment although I think I’d go one further. In my response to Lord Keynes I brought up a metaphysical distinction that I think useful in discussing these issues. The metaphysical distinction is the question of whether we view reality as being based on deterministic constants — Infinite Laws — or simply on repetitions — Finite Regularities. Actually, this metaphysical distinction is the same one as Kierkegaard laid out in the opening quote: that between recollection and repetition.

Think about this for a moment. What does it mean to say that the universe is deterministic? Well, we’ve already phrased this in a different and useful way: it means that the future mirrors the past in some sense or other. Let’s cast this in Kierkegaard’s language to see how it fits: a deterministic universe is characterised by the future ‘recollecting’ the past. The idea here is that the future is determined fully by the ‘memory’ of the past. Everything that is in the future is always already contained in the past. The future is thus a sort of congealed memory of the past.

Okay, that’s a good description of a deterministic universe, one which is just the infinite unfolding of any number of abstract Laws. But what about a non-deterministic universe? Well, this I would argue, is a universe of repetition. In such a universe the future does contain the past — it can never truly break free — but it nevertheless adds something new that was not there before. Kierkegaard sums up the two metaphysical positions nicely:

Repetition and recollection are the same movement, just in opposite directions, because what is recollected has already been and is thus repeated backwards, whereas genuine repetition is recollected forwards. (‘Repetition and Philosophical Crumbs‘, Pp3)

Kierkegaard was, of course, interested in the meaning these two different metaphysical views had for ethics; he claimed that recollection makes a man unhappy and repetition makes him happy. However, as we have just seen, they also have a lot to say about how we understand more practical matters; like economics and science.

Back to Lord Keynes’ examples. In the social sciences — and I shall prove this logically in a moment — the universe we deal with is no doubt the non-deterministic, non-ergodic universe of repetition. Thus it is pointless trying to discover fixed, timeless Laws as, for example, the neoclassicals try to do. Instead we must seek out the repetitions themselves. What I mean by this is that we need to try to find regularities. So, we might look at spending multipliers; at propensities to save in different income groups; basically: macroeconomic trends. Using these trends — but understanding always that as they repeat through time they change — we can make judgements about what might happen or what policies might be appropriate.

What about the natural sciences then? What about the changes in seasons or the movement of the celestial bodies? Lord Keynes says that these are ergodic processes. I’m not sure that they are. Obviously for all intents and purposes we can act ‘as if’ they are ergodic processes; as if they are subject to recollection rather than repetition. We can do this just as we can use Newton’s laws of gravitation for most engineering problems even though we know these laws to be overturned by Einstein’s relativity theory. But I don’t think that these are truly ergodic processes. I think they are just repetitions with a far longer time horizon to those that we deal with in the social sciences. Eventually the cycle of the seasons will change, as will the movement of the celestial bodies. We won’t be around to see this, as we are quite literally a product of and contained within this particular repetition, but we should recognise that it is nevertheless a repetition.

Like all metaphysical judgements we can agree to disagree on this point. To each his own. But back to more pressing matters for a moment. I said that I would prove logically that in the social sciences we deal with repetitions — that is, with non-ergodic, non-deterministic processes — so allow me to do that. I will repeat here what I said to Tom Hickey in my response to his comment.

Imagine for a moment that it were possible to discover certain Laws dictating my behavior. Now imagine that you discovered these. In order for them to continue to be valid you would have to keep them secret from me otherwise, using this knowledge, I could reflexively change my behavior and invalidate these Laws. The same is true if we determine Laws for large groups of people. Once they became commonly known people would change their behavior. This reflexivity suggests that there is a non-deterministic process at work — a repetition rather than a recollection.

In human affairs there is a degree of freedom that negates any notion that we can come up with deterministic Laws that dictate behavior. The very process of trying to discover such Laws is in itself an act of creative repetition. Think, for instance, of a neoclassical policymaker trying to impose so-called ‘market forces’ on a public sector institution. He acts as if he is just renaturalising this institution in some way — as if he is bringing it back in line with the Laws of the market after it has been made impure through regulation. But what he is really doing is creating a new institutional framework through an act of creative repetition.

This is the nature of all human endeavor and it is this that the neoclassicals ignore. Such ignorance not only generates bad theory but it also gives them an authority they would not otherwise have; it naturalises their decisions and their ideas — their repetitions — in a way that lends them power. Like the organised religions of the past, this is what neoclassical economics is all about.


The above discussion takes its leave from Kierkegaard’s ethical considerations of repetition. His book is brilliant but very obscure and, for those interested in the topic, I do not recommend it. From a social sciences perspective the definitive work on repetition is that of the French sociologist Gabriel Tarde. A good outline is his Social Laws: An Outline of Sociology which is available online. From a metaphysical perspective the definitive, if difficult work is that of Gilles Deleuze — most notably his Difference and Repetition. Finally, although many evolutionary economists are doing work similar to what I just discussed, the most interesting work that I ever came across in economics that uses the framework I am talking about — albeit not using the terminology I have laid out above — is Joan Robinson’s forgotten classic Freedom and Necessity: An Introduction to the Study of Society.

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