According to an interesting book called Deep Simplicity by John Gribbin, the frequency of earthquakes of different sizes follows what is called a ‘power law’. In other words for every 1000 quakes of magnitude 5 there are roughly 100 of magnitude 6 , 10 of magnitude 7 etc. While this is of course highly relevant if you live in San Francisco or Kobe, it has much wider implications. This law underpins the mathematics of fractals, so beloved of many computer users. Most importantly however it is scale independent – in other words large earthquakes are less likely than small ones, but do not require some unusual event to trigger them. After a large earthquake event it may be reassuring to think that it will be some time before the next one, but both statistics and the ‘power law’ say otherwise.
Looking at where the power law applies raises some interesting questions, which strike at the root of many of our cherished beliefs. As an example consider the traffic jam which occurs without any apparent cause on an otherwise free flowing road. Research at the University of Duisburg (p148) found that the number of jams of different sizes also follows a power law – in other words you don’t need a large event such as a crash to trigger a jam, it can be something as small as a car getting too close to the one in front and having to brake. Secondly however as the density of traffic increases traffic can be kept moving more smoothly by restricting the top speed, because this reduces the difference between the time to brake and the time to accelerate away again. This is the principle of the variable speed limits on the M25 and being tried elsewhere. So it really is true that if every one obeys the speed limit they get to their destination quicker.
This is interesting for other reasons too - the interaction of vehicles on the road is normally self-managing yet here is an instance where external intervention actually improves things – something likely to give libertarians apoplexy. After all - if libertarians can argue against traffic lights as an infringement of individual liberty, how will they view externally imposed speed limits?
The traffic signal was originally put up to replace the police officer on intersection duty. A police officer has the power to stop people for probable cause. If he stops someone without cause, he is abusing his power of office. Is the unnecessary delay at red lights on speculation that a driver will cause an accident an exercise of governmental power under color of law any less abusive than the action of a police officer who stops you on an unfounded suspicion that you are about to commit a crime? Traffic signal installation should not only be avoided because federal guidelines advise it and because of the damage it causes, but because the courts have ruled that the government, to protect constitutional rights, must show it uses the least restrictive means of furthering its goals. A control device that causes traffic jams is unlikely to qualify as a least restrictive means of achieving the goals the government claims to pursue.
In another example, Benoit Mandelbrot (he of fractal fame) found that the price fluctuations of commodities such as steel or cotton on the NY Stock Exchange also followed a power law. The implication of this is that large events, like for example the Stock Market crash of 1987, can happen as a result of a small trigger and don’t require an extraordinary event. More to the point the size of the outcome seems to be independent of the input. At first sight this seems to give support to those who argue against centralised economic planning since a given interest rate change can have wildly different outcomes. I assume this applies whether the rates are set by government or as now by the Monetary Policy Committee of an Independent bank of England.
This does not of course mean that human intervention cannot have an impact, only that it is unpredictable. The most important area here is probably climate change. It appears for example that species extinctions also follow a power law – meteor impacts may have triggered mass extinction for example at the time the K-T boundary was laid down, but equally large (or larger) impacts before and since have not triggered extinctions on the same scale.
If this argument holds up, it has huge implications for international policy. It would be impossible for example to predict with any certainty how effective the actions proposed in the Kyoto treaty might be, but equally we cannot predict with any certainty the impacts of what we are already doing. If ever there was a wicked problem then surely this is one.