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.
