How conkers created Israel, cats cause wars, and painkillers are bad for religion

November 22, 2010

I’ve recently been reading a book called Chaos, by James Gleick.  It is a nice, easy-to-read overview of chaos theory in all its forms.  Chaos theory is not really a proper mathematical field, more of an ideology, which has applications in all walks of life.   The phrase seems to be bandied about less these days, perhaps because the ideas have become so accepted that it is no longer considered a theory, but just “how things are”.  It takes the form of turbulence, entropy and unpredictability; it has great influence on the weather, the traffic, the stock markets…indeed it is hard to imagine how science worked before the notion of chaos.  As one physicist in the book puts it:

“Relativity eliminated the Newtonian illusion of absolute space and time; quantum theory eliminated the Newtonian dream of a controllable measurement process; and chaos eliminates the Laplacian fantasy of deterministic predicability”.

Poor physicists! Always having their work eliminated by something or other.  Luckily this doesn’t happen in mathematics.  Chaos in mathematics is studied in the form of dynamical systems,  in which small perturbations in initial conditions can have a dramatic long-term effect.  This sensitivity is known in popular culture as the “butterfly effect”, from a paper by Edward Lorenz – a pioneer of chaos theory – titled: Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?

Lorenz was  a meteorologist, and first noticed chaotic effects whilst running weather simulations.  Weather is notoriously chaotic (see, for example, long-term forecasts by the Met Office for evidence of this), and one day, whilst trying to restart a simulation where he had left off, he fed in data which had been output from the middle of a previous session.  He noticed that the outcome was wildly different from his previous results, a consequence of the computer having rounded his output to what he had thought was an insignificantly fewer number of decimal points.    Gleick goes into weather patterns in some depth, as well as delving into such interesting topics as the fractal – and by implication, infinite – nature of coastlines (the closer you get the more little “bays” there are), and the chaotic behaviour a human heart displays while fibrillating (basically what a defibrillator does is to reset a chaotic system with a massive jolt of electricity).*

But I am not actually going to talk about chaos theory today.  Well, not quite.  Instead I am going to share a few odd and interesting freakonomics-style chains of events I’ve learnt about recently.  They all involve seemingly insignificant things – conkers, diclofenac and a cat parasite, to be precise  – which have (arguably) had a huge impact on world events.   In that sense you could possibly claim that this was some kind of chaos in practice.  But that would be quite a tenuous way to try and link it with what I’ve written so far, so I won’t.

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All models are wrong (or: lies, damned lies and statistics)*

November 10, 2010

The statistician is seen with a certain amount of disdain (or possibly sympathy) by their pure mathematical brethren. And it is with that firmly in mind that I (as a fledgling statistician) take the reins of this worthy blog.

We have some idea of what mathematics is from Adam’s posts; but what is statistics?  Statistics is applied maths with uncertainty. In statistics mathematical techniques are used to model and quantify our uncertainty about reality. Modelling climate change, predicting the outcome of elections, wrecking the financial system and ensuring the casino always wins: statistics is everywhere. And uncertainty is the key to statistics.

In order to get across an understanding of what uncertainty is I will try to describe some of the different kinds we face and how statistics deals with them.  The five levels in the following taxonomy lie on a continuum running from complete certainty to complete uncertainty, and provide a means of measuring the range and limitations of statistics in different situations.** The further we go along this continuum the less effective statistics is at prediction and inference, and many problems in statistics and quantitative social sciences like economics come from not recognising just how far along the continuum we are.

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