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


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

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.


About pilkingtonphil

Philip Pilkington is a London-based economist and member of the Political Economy Research Group (PERG) at Kingston University. You can follow him on Twitter at @pilkingtonphil.
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7 Responses to Recollection and Repetition: Ergodic and Non-Ergodic Processes in the Sciences

  1. Lord Keynes says:

    This is great clarification.

    (1) I fully agree with this point:

    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.

    (2) A bit off the topic, but on determinism, and I know this is getting into esoteric aspects of philosophy of time/physics, but there is a widespread view in modern physics of “eternalism” or the “block universe.” That is, the whole present, past, and future of the universe already exists in a massive “block”. The future has already happened, and if one could look at the universe from “outside” (as it were), it would look like one huge, unchanging four-dimensional “block”.

    This should be examined by Post Keynesians, because, if this is true, it suggests that neoclassical economics might be right about uncertainty being only “epistemological” and the fixed future already existing.

    However, it looks like there are many reasons why the “block universe” is probably not true, as the cosmologist George Ellis notes. interestingly, one interesting alternative escape hatch is idealism, which I think you are sympathetic too?:

    • Yes, but look — and this really important — this is not a question of something being “true” or “false” from the point-of-view of science. The trick of probability theory is that, as I said, it buries questions that have been around since the Greeks (and exist in other cultures too) and pretends like it answers them. These are properly metaphysical questions — “metaphysics” being understood here as questions relating to the underlying structure of what we experience as reality.

      Now, stuff like physics and especially cosmological physics undertakes the same trick as probability theory but in a more sophisticated form. What the physicists do is they ask the same metaphysical questions but in the framework of what they currently (think they) know about what they call “the universe”. But they’re putting the cart before the horse here. It is — and this is simply due to the definition of the terms — metaphysics that underlies physics, not vice versa. So, logically you cannot answer metaphysical questions by examining the universe of physics. That is like trying to investigate the molecular structure of water by putting it in your mouth.

      This is the key point: it’s all in how you look at it. And that’s why the physicists have these mad debates about the underlying structure of the universe. It is not that one is right and one is wrong — in the sense that they can prove themselves right or wrong, as in falsifiable science. Instead it is a question of which viewpoint is more coherent and more useful.

      That raises an entirely different set of questions and I won’t even begin to dig at that here (although the above article lays out a pretty specific metaphysical structure…). But we must understand that even if these issues are given the veneer of mathematics (probability theory) or the veneer of science (advanced physics) its always the same metaphysical questions that lie beneath the surface. Repeating themselves in different contexts while slightly changing their meaning.

  2. Lord Keynes says:

    By an astonishing coincidence, there is an interesting article in the Guardian — a book review about a month ago — that makes a rather similar point to what you’ve said about:

    ” the reason physicists have come to reject the reality of time is that they have been bewitched by the beauty and success of the mathematical models they use into mistaking those models for reality. For timelessness, though not really a feature of our world, is a feature of mathematics. Two plus two equals four, but if we ask when or for how long the perplexing (though true) answer seems to be: “Well, always. It is an eternal truth. Time is irrelevant to it.” And thus we seem to be driven to accepting the thought that some truths, at least, are eternal. And, if we can have timeless truths in mathematics, why not in physics?”

    • Interesting. I will check that out.

      Although, while that is part of it, I think the problem in modern science runs deeper. You have to go back to the development of modern analytical philosophy — which, as you know, started just after Keynes stopped writing on these matters. There was this insane drive — it really began with the likes of Wittgenstein and Ramsay — to abolish metaphysics. Most of the establishment, like Russell, supported this. While only a few dissenters, like Whitehead, resisted (Wittgenstein, as is well known but firmly repressed and ignored, later repented and started doing metaphysical work again).

      But the view that metaphysics was irrelevant was accepted by the scientific establishment (at least in the Anglo-Saxon countries…). However, this was at a time when scientists were pretty self-content and thought that they had everything figured out — Einstein’s work hadn’t really sunk in yet (we’re talking in the post-WWI era). As relativity theory and other innovations in quantum physics began to sink in everything started getting crazy very quickly. But the scientists, who were taught to ignore metaphysical questions, could not contextualise what it was they were dealing with; which, as I’ve said, had to do with questions relating to the fundamental structure of reality (i.e. metaphysical questions).

      This has now been going on for nearly a century. And it’s generated some good sci-fi (the metaphysical novels of our time). But it is becoming absurd. Modern science rests on a massive repression and it is becoming grandiose to the point of self-parody. Neoclassical economics — the “science” of running society — is its most ugly form. But there are many others (you know what I think of Dawkins and his eugenicist friends…). The only current of thought that seriously challenges this is continental post-structuralism. But many of its practitioners (though not all) are not highly competent and the scientists are all smug after that highly dishonest Sokal incident (note that all the scientists that mock postmodernism rarely bring up a lesser known incident:

  3. Lord Keynes says:

    Sure, the extreme logicist program of early Analytic philosophy failed. E.g., Russell’s attempt in Principia Mathematica (with Whitehead though!) to set mathematics on firm logical basis failed, as Kurt Gödel’s incompleteness theorem supposedly shows.

    And logical positivism has a bad and extreme dead end (though I have a sneaking admiration for A. J. Ayer).

    But I think that some modern Analytic philosophers do realise that metaphysics is valid and important now.

    • Perhaps. I don’t follow it too closely. Although it strikes me as being similar to the neoclassicals “realising” that, for example, speculation can occur in financial markets or that stimulus is sometimes reasonable. Without a fundamental reorientation we’re just going to get more of the same.

      Closer to home, I submitted an article to an economic philosophy journal recently (no names!) running through some of these issues from a slightly different angle. I don’t think they even understood what I was talking about because they rejected it without peer review. When I pushed them for a reason they gave me an answer that made no sense at all — they didn’t seem to understand what the word “metaphysics” means because they told me that lots of people thinks that there is no metaphysics in economics… seriously! I am 90% sure these guys didn’t even have a reference point for what I was talking about because their training had not just evaded it but actively repressed it. Just like a training in neoclassical economics represses so many perspectives and ideas.

      When I pointed out that by definition of the word “metaphysics” economics must have a metaphysics if it claims to deal with reality they ignored me. This was NOT, by the way, a strictly neoclassical journal by any means. The sickness in philosophy — which has the same scientistic roots as the sickness in economics — has spread to heterodox work in the philosophy of economics. Of that, I’m pretty convinced.

  4. Lord Keynes says:

    Sorry you got such a negative response. And I do agree that metaphysics is important.

    And on this metaphysical note, I’ll just note all this has inspired me to a new post:

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