The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner

The Unreasonable Effectiveness of Mathematics

The Unreasonable Effectiveness of Mathematics in the Natural Sciences is one of those pieces of writing whose title really sums up the whole thing – basically it does what it says on the tin.  It started life as a lecture and was subsequently published in the mathematical literature in 1960.  It is about something that a lot of people have noticed.  It is really quite surprising how often a mathematical idea developed for a particular purpose, or for no other purpose than simple pleasure in the exercise of the mind, turns out to be a useful tool later for something completely different.

The most surprised by this are those of us who have spent time in actual laboratories doing practical science.  Data in its raw form is rarely remotely reminiscent of mathematical purity.  The underlying trends are obscured by many factors.  There is the unavoidable variation in experimental observations.  There is usually a fair bit of variation that is avoidable but is introduced by the hamfistedness of the operators.  We are all human and mistakes get made.

The importance of the experimental design in generating useful data is rarely appreciated by non-scientists. Working out exactly how to control for all the factors that affect the results is a big part of making progress. Unfortunately this is often only appreciated by the scientists themselves when pondering the results they have generated, by which time it is usually too late to go back and do it properly.  Looked at in this context, the way that fitting the data to a mathematical model can bring order to chaos is not so much unreasonable as positively miraculous.

The example that shows this at its starkest is the remarkable achievement of Newton. He was able to infer the law of gravity from the very hazy set of data that was available to him in the seventeenth century.  Although we now know that his model of the universe wasn’t absolutely on the money, it was pretty damn near.  Near enough to be used to land a man on the Moon is near enough for most of us.  But this is just one of many examples in the physical sciences, particularly physics.   Chemists have a pretty well stocked mathematical toolkit as well.  Indeed there is a frame of mind that defines the rigour of the scientific discipline according to how mathematical it is.  The joke goes that physicists are failed mathematicians.  Chemists are failed physicists and biologists are failed chemists.  Everyone else is just a failure.  The Big Bang Theory comes up with a creative variation of this with the theoretical physicist Sheldon Cooper dismissing geology as not being a real science in the same way that the Kardashians aren’t real celebrities.

The trouble with this notion is that it isn’t really true.  While mathematics has been a hugely useful tool for scientists, it really isn’t the case that a mathematical description of something is better than a non-mathematical one in any meaningful way.  If you are dealing with gravity professionally you are going to need to understand calculus.   But it is perfectly possible to understand the underlying principle without recourse to maths, and most people manage it very well.  Biology uses maths when it needs it, but gets on very well as a perfectly rigorous scientific discipline most of the time without it.  In spite of the prejudice of some scientists towards the mathematical, nobody feels that biology needs more equations to be taken seriously.

But there is one academic discipline that does seem to feel the need to dress up its ideas in mathematical language.  Economists have always dabbled in numbers, and have become more and more enamoured of them as the years go by.  Economics as taught at university level is now full of differential equations and the like.  It’s become a really mathematical subject.

Black Scholes Equation

Black Scholes Equation

 

A good example is the Black Scholes equation.  This describes the behaviour of the put and call options on the European derivatives market.  If you have no idea of what a differential equation is, or what is meant by a put and call option, I suggest you don’t worry too much.  A company set up to exploit the profitable opportunities afforded by understanding these things called Long Term Capital Management lost so much money it threatened the stability of the world’s financial system for a while.  Knowledge with those kinds of consequences is the kind of knowledge you can live without.

This company was in the position to do this because of the credibility it gained from having one of the creators of the formula on the board.  He was a respected economist and even won a Nobel prize.  This prestige didn’t stop Long Term Capital Management proving to be a very short term exercise in capital mismanagement.  One might have thought that an experience like the inability of  a Nobel level economist to run an actual company in the real world ought to have chastened the economic profession somewhat.

But they seem to be carrying on regardless.  Major economic events like the 2007 liquidity crisis or the recent collapse in the price of oil continue to happen.  Economists routinely fail to predict them in advance or to explain them after they have happened.  That the media manage to find some economics prof somewhere who did simply underlines that economic predictions are all over the shop and that you might just as well consult the entrails of geese for all the good it is likely to do you.

Economics doesn’t need more equations.  It needs to be able to actually describe the real world effectively.  Plain language will do nicely if it works.  If it doesn’t, the maths just obscures things.  My proposal is that economics should simply be disbanded and its intellectual territory reallocated to a new branch of biology.  One of the rules of war is that you don’t reinforce failure, and economics has failed miserably.  We should stop pumping money, resources and faith into it.

The economics discipline does have some real world assets, which need to be disposed of.  Economics departments should be handed over to be run by the biologists.  Economists working in academia should be transported to camps for re-education.  Extant economics degrees should be declared void.

I do realise that this will cause some disruption to people’s day to day lives.  Not least, it will rob governments around the world of the justification for all those neoliberal policies that favour the rich over the poor.  I can live with that.

 

Reference

Wigner, E. P. (1960). “The unreasonable effectiveness of mathematics in the natural sciences. Richard Courant lecture in mathematical sciences delivered at New York University, May 11, 1959”.Communications on Pure and Applied Mathematics 13: 1–14.

Photo credit: Dzhus via photopin cc

 

2 Comments

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2 Responses to The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner

  1. Econobable

    Instead of sending economists off, what about requiring them to manage their own retirement investing (speclulating) where stock funds and indexes are not allowed. Thus if they do stocks they have to pick them them selves.

    Replace the economists in the media with accountants.

    Then after 10 years of the economists probable losses using their knowledge base, send them an accounting text book.

  2. J J Flattery

    Math won’t help if you don’t know the framework your operating within.

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