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MIT’s Technology Review reports a prediction by Didier Sornette and colleagues (Bastiaensen, Cauwels et al. 2009) that a Chinese stock market collapse is imminent–due before 27 July, in fact.

Crashes in stock markets represent cases of self-organised criticality (see, for example, Turcotte 1999): like avalanches, pressure builds in the system to the point where overloading triggers a collapse.  We cannot predict exactly when a collapse will occur, where, or how large the collapse will be, but collapses are inevitable–and sometimes small collapses trigger much larger cascades.  The behaviour of such systems over time follows a scale law: large collapses are few; small collapses are many.

Examples of self-organised criticality can be found in a wide range of natural and social systems, including finance and war (Turcotte and Rundle 2002).  Can we apply the same ideas to nuclear proliferation?

For example, we can substitute the idea of nuclear latency–the level of capability that would allow a swift transition to nuclear status, including through indigenous civilian programs–for load.  (The analogous component in other systems would be combustible material for forest fires, tectonic stress for earthquakes, and over-investment in financial systems.)    The load builds to a point where breakout is inevitable.   But the characteristics of criticality apply: we don’t know when, or where, such a breakout will occur, or how large the ‘avalanche’ will be–one or two nations, for example, or a cascade of proliferation.

What triggers collapse in such a system?  It cannot be capability alone.  But proliferation comprises a combination of material, expertise, infrastructure and intent.  As underlying capability–material, infrastructure and expertise–grows, then intent becomes increasingly important in assessing proliferation risks and behaviour.

And intent necessarily becomes a function of expectation: what are the expected consequences; and what are actors’ expectations of each other?   As in the market, we lack perfect information.  The differences between intent, expectation and surety generate instabilities, which as the load increases and system stress increases, increase the likelihood of collapse.

Moreover, the longer stresses in the system build, the more likely the collapse will be large, cascading as nations with high latency succumb to pressure generated by uncertainties of over others’ intent.

Can we adopt Sornette’s ideas for predicting collapse?  Sornette looks for bubbles in market data; no similar information is available–as far as I’m aware–on nuclear material, industry, or skills.  It’s not exactly the most open of industries–and even more so where there is a covert intent to proliferate.  And even in market data, finding bubble-like behaviour does not necessarily translate into collapses.

But then, Sornette et al do not rely on data alone, but seek to find drivers of such behaviour.  From the Technology Review piece again:

The telltale sign of a bubble, he says, is a faster than exponential growth rate caused by a positive feedback mechanism that generates this nonlinear growth.

Within nuclear proliferation, such drivers include

  • protective hedging against Western conventional dominance, and increasingly, against regional competitors; and
  • increased means of gaining the material, expertise and equipment needed for proliferation, including through sub-national means such as the AQ Khan network.

From a systems perspective there exist drivers trending towards proliferation. Taking the pressure out of the system requires adjusting or defusing the drivers, such as increased transparency of programs; redirecting intent, such as through cooperative security and international regimes; or some sort of as yet unknown technological solution.  The international community has tried a number of these, but given the increasing latency, new and different means may be needed: the barriers suitable for small avalanches, for example, are unlikely to be able to hold back large avalanches.  And therein lies a further problem for the international community: the more the system is held back, and pressure/latency allowed to build rather than being diffused or bled out, the greater the likelihood of a large, cascading breakout.


Bastiaensen, K., P. Cauwels, et al. (2009). “The Chinese Equity Bubble: Ready to Burst.” arXiv: 0907.1827.

Turcotte, D. L. (1999). “Self-organized criticality.” Reports on Progress in Physics 62(10): 1377-1429.

Turcotte, D. L. and J. B. Rundle (2002). “Self-organized complexity in the physical, biological, and social sciences.” Proceedings of the National Academy of Sciences of the United States of America 99: 2463-2465.

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