Chaos Theory

Engineers have learned not to extrapolate curves, but it is still popular amongst politicians and journalists

The idea that analysis of stock market trends by solution of second order differential equations similar to those we use in vibration analysis (Ian Crossley's letter, PE April) is attractive but does not take account of the limitations by Chaos Theory. Chaos Theory proves that complex equations such as Navier Stokes are insoluble except in a few special cases. No matter how large the computer no solution will ever be possible.

Feed back and feed forward Control theory including Nyquist stability may be more relevant. It can give some useful qualitative predictions of the outcome of consumer demand (feed back) compared with government diktat, (feed forward) but mathematical analysis will still be limited by Chaos.

One branch of mathematics that definitely does not work in prediction of markets or economies is extrapolation of historical data. All engineers have learned not to extrapolate curves but it is still massively popular amongst our innumerate politicians and journalists.

Even our former Chancellor and Prime Minister Gordon Brown appears to believe in economic cycles and abolishing boom and bust. He seems to believe that once in a cycle the near future can be predicted. No surprise that he sold the national gold reserve at a bad time. It is even possible that the great international bodies such as the IMF base their growth forecasts on these extrapolations.

If mathematics has anything to teach us, it is Chaos Theory and its proof of limitation of computer analysis. At least a realisation that extrapolation or solution of equations cannot provide any form of prediction would reduce the risk of bad government and mad private investment strategies.

Terence Rook

Next letter: What is renewable energy?