How much complexity and uncertainty?

Scales of complexity and uncertainty

We can think of Keynes, Whitehead etc as providing a scale for complexity and uncertainty. There are others: how do we choose one to use? A key factor is, what sort of complexity is there ‘out there’?

Looking for complexity

We might expect to find complexity in situations where our normal methods do not serve use well, and hence in situations of extreme competition, such as all-out conflict. But we might equally suppose that such situations simply reflect an irreconcilable difference of critical interests.

The key feature of Whitehead is the role of epochs. This corresponds to Clausewitz’s notion that while warfare had a general character, each war (and perhaps each battle) had its own ‘logic’. Given that western generals, and later Maoist fighters, have been brought up on such dictums, it is no surprise to find (as Montgomery notes) that warfare does indeed match the theory. Similarly, Keynes had a huge influence on economics for a period, so it is no surprise to find that during this period events match his theory. Warfare and economics are imprinted with the ideas of those involved (cf Turner). But what if we had different ideas?

The Cold War

Global deaths climbed steadily until the end of the Cold War, then fell steadily until 2005.

The end of the Cold War coincided with the end of an epoch.

During the Cold War the death rate got steadily worse, a situation that was plainly unsustainable. Looked at statistically, variations about the increasing average appeared random. Thus, while there was plenty of news the situation didn’t seem to change much, apart from getting steadily worse.

The end of the Cold War marked a sudden change to a period of gradual improvement, again unsustainable.

While this fits Whitehead’s model, it also fits simplistic models and extrapolations, apart from the end of the Cold War. Although the timing of the end caught many by surprise, the end was widely hoped for and the fact that it changed the rate of change of the death rate was expected. 


The Mathematics of War

An article in Nature has shown, firstly, how the casualty rates for insurgents in conflict approximate to ‘fat-tailed’ power-law distributions with characteristic exponents of about 2.5, making them very complex. (A smaller exponent is more random, while a lesser exponent is more structured.) An exact power-law distribution would be generated by groups fragmenting and re-forming randomly, but this does not seem very realistic.

The paper also gives a constructive model in which groups fragment  in conflict and re-group in-between, competing for media attention. This generates a fat-tail distribution, but with a reduction in the frequency of  large numbers of casualties compared with a power-law, which matches the actual data much better. The paper also notes a similarity between their model and statistics and financial market models.

The economic crash 2007/8

The economic crash was statistically like the end of the Cold War, but whereas some hoped that the Cold War would end, the assumption prior to the crash was that the great moderation would be an un-ending epoch. After the Crash, economists turned back to the insights of Keynes, and Brown has even evoked Whitehead.

The Balkans, 90s.

The Cold War was a bipolar world, relatively lacking in complexity and, like the great moderation,  people did well in the short run by ignoring uncertainty. The ‘unexpected’ end of the Cold War de-stabilised the Balkans, bringing back extreme complexity and uncertainty.

Statistics for confrontation and conflict, as for much else, typically identify a scale of interest and then divide the period for which data is available into epochs where the statistical properties seem stable. These epochs are then analysed, as in the ‘mathematics of war’ above. But these epochs are just what we are interested in. When we separate the data into epochs, it is the epochs that we want to see, as below.

The Balkans jumped between epochs of 'violent stability'.
KEDS data ( shows jumps between epochs

As we can see, after the Cold War, the situation did not change steadily (characteristic of common-sense evolution) but in jumps (or ‘saltations’), characteristic of complex evolution. If one tries to match a Markov model (i.e., standard probability) one inevitably ends up with a very improbable model, as if each epoch has its own model and there is a Markov model to explain the transitions between them. Such a thing begs an explanation. Looking at the dates, it can be seen that the transitions correspond to big events (such as atrocities or peace talks). More generally, sudden large scale casualties indicate either a break-through for one side or a disaster for the other. This:

  • has an impact on the relative strengths, and hence expectations
  • has an impact on perceptions of the capabilities of given sized forces of the other size
  • has psychological impacts.

Hence if the casualties are large enough it is reasonable that at least one side will change its expectations and strategies, hence changing ‘the rules of the game’. A big enough change will initiate a new epoch. Consequently one might expect big events to be suppressed with an epoch, as seen. Thus, following Whitehead we can see these big events as either deliberate decisions within a strategic game or a ‘fat-tail’ event which gets seized on and treated as a ‘game-changer’. We can also see some transient behaviour, in which it takes time for the new patterns to settle down. But typically, one has periods of conflict that are characterised by randomness, as in conventional combat models, separated by big game-changing events.

Complexity and uncertainty are important when one needs to think ahead across potential changes.


It would seem rash not to consider the possibility that radical complexity and uncertainty are factors in any large-scale system that involves a degree of adapting, learning or evolving. Thus, while we might go-along with Occam’s razor and pragmatism to the extent of seeking the simplest possible models for things, we should at the same time recognize the inevitable limits to such models and allow for the inevitable uncertainties about what they may be.

See Also

Reasoning in complex, dynamic, worlds , Complexity Physics


Dave Marsay


About Dave Marsay
Mathematician with an interest in 'good' reasoning.

4 Responses to How much complexity and uncertainty?

  1. Pingback: Complexity, uncertainty and heuristics | djmarsay

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