A system of great complexity can be dramatically affected over time by small disturbances, as feedback loops plus second or higher-order effects combine to overwhelm expected behaviour. This is popularly known as the butterfly effect after the theory that a butterfly flapping its wings in the tropics can lead to storms elsewhere in the Globe. We’re not aware of any evidential proof for this effect, nor is there likely to be, however it does have parallels in model theory.
A mathematical model of a complex system can be hugely affected by small errors in the initial conditions fed into it. This can be demonstrated by re-running the model after introducing small changes at the start. Another interesting test is to take the outputs from a run and feed them as starting parameters to a re-run in reverse (backwards in time) to see how close to the original starting conditions it gets. This can starkly demonstrate the stability of the model faced with uncertain data.
It is very interesting that the Bank of England uses the idea of “uncertainty” in its economic forecasting models and attempts to quantify it by counting occurrences of the word itself in just four national newspapers: the Financial Times, The Times, The Guardian and The Independent. These are all strongly pro-Remain and keen to report on the doom facing Britain if it leaves the EU. It might have been better to have included some pro-Leave newspapers in the count, like The Telegraph, Express and Daily Mail which together have about three times more readers than the chosen ones.
Use of the ‘uncertainty factor’ reduces the Bank’s forecast for UK growth next year by 0.5%, down from a respectable 1.9% to a merely acceptable 1.4%.
The dubious ‘science’ behind this input to the Bank’s model is exposed by a senior member of the Bank itself: http://www.bankofengland.co.uk/publications/Documents/speeches/2016/speech942.pdf
(see also our previous post on The Truth, Plain and Simple)