Over the last century or so, science has made immense progress in understanding natural phenomena like the weather and social phenomena like markets and economics. Unfortunately, we still fall well short of being able to successfully predict their behaviour. In spite of the mindboggling leaps in knowledge and computing horsepower, systematically successful prediction continues to elude us. This is largely due to the difficulty in modelling complex systems in sufficient detail. An aspect of this problem, called “sensitive dependence on initial conditions” might well be altogether insurmountable.

In running computer models simulating systems like stock markets or hurricanes, very small differences in the values of initial variables can lead to very large variations in outcomes. The problem in modelling complex systems was discovered by MIT’s theoretical meteorologist Edward Lorenz in the early 1960s. Lorenz developed a relatively straightforward computer model simulating a weather system. One day in 1961, Lorenz resolved to rerun the results of one particular simulation, starting at the half-way point using the results he had for that particular point in his print-outs. The new simulation quickly started diverging from the original results and soon bore no resemblance to it. The ultimate explanation for this divergence had profound implications for science: while Lorenz’s program took its calculations to six decimal places, his print-outs only showed the values to three decimal places.

The minute difference between say, 1.234567 and 1.234 applied in the second simulation led to very large differences in the final results. Lorenz termed this phenomenon, “sensitive dependence on initial conditions.” We have every reason to expect that other complex systems will display a similar sensitivity, implying that the problem of accuracy of measurements poses quite a stumbling block in science’s attempt to get to the bottom of such systems. Indeed, accurate prediction will likely remain unattainable in spite of continued advances in all areas of research. As Bob Sheets, the former director of the National Hurricane Center in Miami put it, “The grid for the computer models does keep getting smaller and smaller, but we’re still taking in terms of miles, while the actual weather is taking place at the level of molecules.” [1]

[1] Sheets, Bob and Jack Williams. “Hurricane Watch.” New York: Vintage Books – 2001.

Alex Krainer is an author and hedge fund manager based in Monaco. Recently he has published the book “Mastering Uncertainty in Commodities Trading“.