Tuesday, July 29, 2008

Is secular, liberal democracy a chaotic attractor?

In terms of mathematical physics, civilisation is a deterministic non-linear dynamical system far-from thermodynamic equilibrium, and human history is the study of one particular trajectory of that dynamical system. This means that there is a set of variables {Xi: i=1,...,n} whose values uniquely characterise the state of a civilisation at a moment in time. All other properties of a civilisation are functions of these state variables.

The evolution in time of a civilisation is then governed by a set of n coupled non-linear differential equations, which the state variables must satisfy:

dXi/dt = Fi(X1,...,Xn1,...,λm),      (i=1,...,n).

The m parameters define external constraints upon a civilisation, such as those determined by the geography, geology and meteorology of the planet on which the civilisation exists.

Unfortunately, unlike Hari Seldon in Isaac Asimov's Foundation books, we don't yet know what these equations are. We don't even know what the state variables are. One might, however, hypothesise the following candidates:

(i) Population size, and population rate of change.
(ii) Total amount of available free energy (i.e., energy resources), and rate of energy consumption (i.e., power output).
(iii) Amount of information stored, and amount of information processed.

Additional variables might then be required to characterise the hierarchies and organisations which define the political state of a civilisation. All economic variables, however, can be treated as functions of the variables in categories (i), (ii) and (iii).

Identifying the correct state variables, and the equations which govern the evolution of civilisations, is a task set for the reader. However, some progress towards understanding the dynamical processes in human history is being made by people such as Peter Turchin, who has launched his cliodynamics research programme, which aims to identify the mathematical patterns in human history. Turchin has identified, he claims:

...long-term cycles that, it turns out, characterize the dynamics of agrarian states and empires. When we consider the long course of history of Western Europe from the days of the Roman empire until the Industrial Revolution, we observe waves of internal instability (widespread rebellions, state collapse, and persistent civil war) that recur every two or three centuries. The internal warfare cycles appear to be dynamically linked with cycles of population increase and decline or stagnation: population peaks are followed, after a time lag, with peaks of instability. This empirical pattern suggests some kind of a Malthusian explanation. However, the American sociologist Jack Goldstone showed that population growth beyond the means of subsistence does not directly bring the onset of civil wars. Instead, its effect is indirect, mediated through the social and political structures (elite overproduction and state fiscal insolvency), which is why there is a time lag between population and instability peaks. This pattern of linked population and internal warfare oscillations is not limited to Europe. Recently two Russian historians, Sergey Nefedov and Andrey Korotayev, showed that the same relationship holds for China during its two thousand year imperial history, for Egypt (from the Hellenistic period to the nineteenth century), and for Russia. It is remarkable that such complex, and very different, societies would all show similar dynamical patterns.

Civilisation is a deterministic non-linear dynamical system, and it is also, presumably, one which exhibits sensitive dependence upon initial conditions: two different histories which begin in a very similar state can, one presumes, diverge from each other at an exponential rate. In terms of dynamical systems theory, such systems are said to be chaotic, hence civilisation is a chaotic dynamical system. Human history also appears to be an aperiodic trajectory in civilisation space, at least over the space of 10,000 years or so. A crucial question, however, is whether the laws of civilisation permit the exist of attractors.

An attractor is a subset of the set of all possible states of a dynamical system, which is such that once a trajectory of the system enters, it never leaves. This doesn't entail that the trajectories are doomed to become periodic once they enter the attractor; they can continue indefinitely, without repeating the same exact state. Whilst chaotic systems are defined by the sensitive dependence on initial conditions that they exhibit, they also tend to possess various chaotic attractors. Which begs the questions:

Is civilisation a chaotic system which possesses attractors, and if so, is human history converging to such an attractor?

The obvious candidate for such an attractor is secular, liberal, democratic, capitalist society. This is essentially the possibility Francis Fukuyama was raising in The End of History. Whilst the current state of the world might not currently reside inside this attractor, and perturbations like 9/11 might be capable of temporarily taking it further away from the attractor, perhaps the current state of the world lies inside the basin of attraction for global secular, liberal, democratic, capitalist society.


Jonathan said...

Alas I only did algebra to O-level standard, I found even that somewhat bewildering and impenetrable (though I ended up with an A grade in Maths, oddly enough). Still, it didn’t look as bewildering as that!:)

I wonder if whatever you expressed with your formlas could equally well, and as accurately, be expressed in words to a non-scientific layman – well, at least as far as such formulas impact upon our everyday human world. This is not a criticism or challenge to you personally, as a physist, please understand, for whom numerical formulae are, of course, your everyday tea and biscuits. I honestly defer, awed, to your grasp on these matters. I guess I just worry about others like me missing out –whose currency is words in the Humanities. We live in the same universe, after all, do we not? Moreover, I do believe and suppose that ideas are independent of their carriers, their means of expression, sufficiently that they can be, or should be able to be, expressed in varying ways…?

I like how you don’t see economics as fundamental, unlike Marx.

Sorry to be a pain, but can I ask you some questions? How do you know Civilisation is a “deterministic non-linear dynamical system”. Have you proved this in a lab? How could you know this? Do you live outside time, as I want to?:) Not sure what you mean by ‘deterministic’ here? Non-linear and dynamic, I have less of an issue with. What do you mean by ‘civilisation’?. Can your opening sentence be taken to suggest that human history is just one example of such a civilisation, or a subset of civilisation in general on a grander scale. Would this be civilisation as it existed before human history was recorded (if history be defined as that which we know about the past based on written records) – i.e Atlantis etc – or civilsations on other planets? How can we know about what we don’t know about?

Do we want Fukuyam’s own vision of such a society to be universal? Maybe it depends on who ‘we’ are. I don’t think many people in the world want it. Are they then inferior to us, in their ignorance, because they don’t know what’s best for them. Is this the new white man’s (ok, nowadays western man’s) burden talking?

Still, you speak of a ‘basin of attraction’. While I can’t pretend to undersatnd this in a scientific idiom, what I would think of by the phrase would be a broad catchment area of accommodation, whereby a certain wide variety of ideas could be acceptred into a ‘basin’ that was not so narrow and small that it would only accept them into it on a rigidly defined understanding, or through an exacting filter of acceptability. Or something like that.

Applied to liberal democracy, I suppose it could be that it does indeed possess certain qualities that attract universally (thinking off the top of my head these would be individual political freedom and the west’s freedom accorded to the life of the mind –those reasons why people from around the world want to study in the west (well, apart from the desire to make better money afterwards, of course). However, this need not mean that these non-western people will want it in its curent incarnation, with regard to all its specifics..especially its implied requirement that adherents stop taking metaphysics, tradition and history seriously and become as obsessed with decadent, consumerist materialism as we are.

Surely the atrractions can go in both directions, and we also can learn from the exotic regions of the world (without denying or abandoning our libertarian, individualistic idenity?)

Sorry if I bang on, or if my scientific ignorance lends my posts an inappropriateness. Just tell me to be quiet, and I’ll flee, but this is all very interesting to me.

Gordon McCabe said...

No problem Jonathan.

I would define a civilisation to be any post-agricultural revolution population of cognitive animals. And I do mean to say that human civilisation is just one example of such a civilisation.

By a deterministic system I mean that the specification of the state at a moment in time determines a unique future and past for that system.

The basin of attraction is a neighbourhood in state space of the attractor itself. You can be in the basin without being in the attractor, and being in the basin doesn't entail that you'll enter the attractor within a finite time, only that, at the very least, you will converge to the attractor.

If secular, liberal, capitalist democracy were an attractor for civilisation, then that wouldn't in itself entail that secular, liberal, capitalist democracy is a good thing.

And yes, I do live outside time!

Julien Frisch said...

What a nice little illusion trying to put civilisation into a formula...

If there could be such a formula, and the system would indeed be deterministic, than it should be able to predict the state of the civilisation tomorrow, next month, next year. Every social scientist knows that it is already difficult to construct general laws for micro-relations between human beings. Thus, predicting a whole civilisation would go beyond anything imaginable, whether with a hypothetical attractor or without.

Gordon McCabe said...

You're confusing a deterministic system with a predictable system, Julien.

A chaotic deterministic system is not predictable because the sensitive dependence upon initial conditions requires one to exactly know the initial state, and this generally isn't possible.

Julien Frisch said...

Which, however means that there would exist predictability if the initial status could be determined.

Deterministic, if I understand the term correctly, might not mean predictability, but it assumes a number of clear-cut laws that have to lead from a theoretically definable situation A to a definable situation B.

What I doubt that there are such laws existing in a social or political environments, but that social interaction already on a micro-level is non-deterministic.

(In social sciences, the term "deterministic" is also used as opposed to "probabilistic".)

Gordon McCabe said...

The absence of deterministic laws in the social sciences, attests to the difficulty in knowing them. It doesn't entail that they don't exist.

Julien Frisch said...

Yeah, that's like religion: That I don't see God doesn't mean he doesn't exist. You just have to believe... ;-)

Gordon McCabe said...

No, the very opposite of religion. Observation and experiment has verified that all the fundamental processes in the physical world satisfy deterministic equations, whether they be the Schrodinger equation, the Dirac equation, the Klein-Gordon equation, the Maxwell equations, the Einstein field equations, or the Yang-Mills equations. The physical world is built from nothing else other than entities and structures which satisfy deterministic equations, so the world will be deterministic on every level, irrespective of the level of complexity.

Jonathan said...

"The absence of deterministic laws in the social sciences, attests to the difficulty in knowing them. It doesn't entail that they don't exist."

Good point, but surely it doesn't entail that they do, either. And they may be hard to know because they are not there to know?

What does quantum physics have to say, though , about what you write in your last comment?

Doesn't it say that the world becomes significantly less-deterministic, when you look at it
..or is it look at it in a certain kind of way.

As I see it there are two problems regarding the scientific treatment of the God question:

a) to some people, what is taken to be God IS experienced, so involvement with God for them is not merely a 'belief' centred asssent to propositions in the dark. But he is not by others (for whatever reason).This seriously questions the universally verifiable principle.

and b)what is meant by God (if he exists or not) is a quality of being that is definied by self-autonomy, so incapable of possessing a deterministic, ontology - unlike the type of being which nature has, which science says will (or must?) conform to laws.

Gordon McCabe said...

The fundamental processes in quantum theory, as described by the Schrodinger equation, Dirac equation etc., are deterministic rather than stochastic. The main problem tackled by the interpretation of quantum theory is then to reconcile the probabilities in quantum theory with the fact that the fundamental processes are deterministic.

The probabilities arise, not from the fundamental processes, but from the introduction of measurement interactions, in which the results of microscopic events are amplified up to macroscopic scales. Whilst the inventors of quantum theory proposed the 'collapse of the wave-function' at this point, the general trend in the interpretation of quantum theory is now towards a no-collapse interpretation.

Julien Frisch said...

Yet, since you can only empirically prove a law by measurement, whether in quantum theory or in any social environment, there is always a measurement interference if you want to prove your hypotheses.

The concept of a law that cannot be observed makes it useless because it remains an unproved hypothesis about reality, not more and not less. A law that cannot be found because the chaotic initial conditions are too complex is useless for an application to reality.

As a consequence, trying to explain the rise and fall of civilisations with a formula of whatever quality is without any relevance because it can neither be verified nor, which is more important, falsified. And a hypothesis that can not be falsified is not of much scientific value.

Jonathan said...

"Stochastic" is a good word.

Interesting though, the popular perception of Quantum physics, or so it seems, as the intellectual justification for the ultimacy of creative chaos.


Jonathan said...

'And I do mean to say that human civilisation is just one example of such a civilisation.'

So you embrace purported civilisations on other planets? Or are you talking about 'animal civilisations'? I'm not sure what these could be meant to be exactly, though it's evident, if only looking at the formation of birds, that animals do organise themselves collectively, of course. But what makes these specifcally 'civilised' as we mean by the term - the conscious cultivation, refinement, restraint and channeling of innate animal impulses?

But how can animals be 'post-agricultural'?

'If secular, liberal, capitalist democracy were an attractor for civilisation, then that wouldn't in itself entail that secular, liberal, capitalist democracy is a good thing.'

Yes, I agree. So can we than mould and influence the force of this attractiveness, either to make it good, or change the attractor into something else wothout negating its inherent attractiveness?

'And yes, I do live outside time!'

I wonder what you mean by this? I only have a metaphorical, not a scintifically explicable, sense of what I mean. And to me it crucially implies the existence of God, in whose light (and eternity)one wants to live, etc.

Gordon McCabe said...

In terms of quantum theory, Julien, you produce a theoretical pair consisting of (i) a representation of the fundamental process, and (ii) a representation of the measurement process. In combination, these produce predictions, which are verified by measurement, and in so doing, you verify the theoretical pair. You certainly don't 'prove' a law, either here or elsewhere in science, given the underdetermination of theory by data.

In terms of verifying a chaotic deterministic theory, you derive from your underlying exact theory a coarse-grained theory, and you make observations and measurements which verify the coarse-grained predictions. In this respect, verifying a deterministic chaotic model of civilisation is no more problematic in principle than verifying Lorenz's non-linear equations for convection in fluids, or verifying meteorological models. Meteorology, in particular, demonstrates how one can derive, from the underlying chaotically deterministic theory, ensemble-simulation forecasts which predict the probability of various weather conditions. Such techniques are clearly falsifiable, and an extremely valuable application to reality.

Anonymous said...

By a deterministic system I mean that the specification of the state at a moment in time determines a unique future and past for that system.

A unique past? Really? A unique future makes sense, but surely multiple different trajectories might reach the same state? Is this not what you mean by convergence? (Or perhaps just the limit of convergence, I suppose.)

Thanks for the reference to cliodynamics - that looks fascinating. A sort of updated version of Arnold Toynbee...

Gordon McCabe said...

The attractor to which historical trajectories hypothetically converge is a subset of the state space, rather than a single point, so multiple different trajectories can converge to, and even belong to the same attractor, without ever intersecting.

Good luck with The Shires, Mr Turpin!

Gordon McCabe said...

Peter Turchin has made the following interesting point to me:

"I disagree with your formulation...of a completely deterministic system governing historical dynamics. I think that a better approach is to use a mixed stochastic/deterministic framework. Stochasticity may arise from true randomness (such as free will) or from lack of knowledge. In practice, it does not matter. In any case I think it is a better approach to include it explicitly, rather than write down a purely deterministic model."

My response is that lack of knowledge should, in principle, lead to a distinction between cliodynamics and statistical cliodynamics, in the same sense as the distinction between classical mechanics and classical statistical mechanics. Incomplete knowledge would be represented by a measure on cliodynamical phase space, and the evolution of the measure would be represented by a cliodynamical counterpart to the Liouville equation from classical statistical mechanics. Even if one could never pin down the precise cliodynamical state, there would be an underlying set of deterministic evolution equations, in the same way that Hamilton's equations of motion in classical mechanics underlie the Liouville equation.

Whether free will provides a source of stochasticity is an interesting question. Those who believe in the existence of free will tend to argue that it cannot be reduced to either randomness or determinism...

Unknown said...

I always thought the most interesting requirement of any mathematical treatment of social change would be that it be able to predict it's own emergence and effects. Sadly, my understanding of such a system is that it would be overwhelmed (for any practical purpose) by the computational complexity of calculating the effects of its emergence. I presume this is the reason that Asimov required a lack of knowledge of the principles of Psychohistory from the majority of those it predicted. This is still not sufficient if even a small portion have access to the knowledge and utilise it however, as the knowledge still becomes the source of change in the society that it must predict. Do you have any ideas on how to deal with this seeming paradox?