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Let R=Rigor Let M=Mathematics: R≠M

As Jim McClure points out in a Facebook comment, the editors of The Economist – in the July 21st introduction to that magazine’s recent series of six briefs of ‘big ideas’ in economics that economists should pay more attention to – wrote that

The job of economists is to impose mathematical rigour on intuitions about markets, economies and people. Maths was needed to formalise most of the ideas in our briefs.

I believe that this description of the job of economists is incorrect.  The job of economists is indeed, and emphatically, to impose rigor “on intuitions about markets, economies, and people” – and, I add, also on intuitions about government.  But it is a myth to suppose that mathematics is either necessary or sufficient to impose the necessary rigor.

I emphasize that I am not saying that mathematics is never helpful in imposing such rigor.  Instead, I am saying that – despite appearances to the contrary – the rigor that sound economics imposes on our intuitions not only does not require mathematics in most cases, in many cases the mathematics blinds its users to aspects of relevant reality.  If, for example, a mathematical model leaves out important margins of adjustment that are available to individuals in reality, then the mathematical model itself, despite its apparent rigor, will be a source of misguided analysis of reality.  And no amount of facility with mathematics reveals which avenues of action and response are open to individuals in reality.  Knowledge of reality, and wisdom about it, is necessary to have a good sense of which such avenues of action and response are available – and of which such avenues of action and response are more likely than others to be chosen.


Claims such as that made, above, by the editors of The Economist are standard fare when the discussion is of the science of economics.  Yet I wonder if biologists are subjected to the same sort of claim.  Do people regularly say that “The job of biologists is to impose mathematical rigour on intuitions about phenotypes, behaviors, and genetic mutations”?  Do biologists demand that an explanation of, say, how natural selection led to humans’ opposable thumbs or cheetahs’ hunting habits be expressed in equations before that explanation is regarded as scholarly enough to take seriously?

I’m no biologist, but having read some biology – my favorite works include Richard Dawkins’s The Selfish Gene and The Extended Phenotype, George Williams’s The Pony Fish’s Glow, and papers by Leda Cosmides and John Tooby – I don’t detect any demand, either by biologists themselves or by intellectuals who retail biologists’ findings to the general public, that explanations of observed phenotypes or of observed behaviors be expressed in mathematics in order to be regarded as sound.  (I might well be mistaken here.  I’ve read relatively very little biology scholarship that is addressed chiefly to professional biologists.  So I welcome correction or clarification.)

Surely we can understand, without mathematics, that if bearing and rearing offspring of a certain species to reproductive age demands more of the female’s resources and time than of the male’s resources and time, then that species’ females will be more sexually choosy than will that species’ males.  Surely when a biologist sees small sea creatures using mud on the sea floor to form protective dwellings for each of those creatures, the biologist asks “Why?  What purpose does that dwelling serve?  Does it control the creatures’ body temperature?  Is it for protection from predators?  Is it a display to attract mates?”  The biologist examines not only the creature’s observed behaviors and phenotype, but also its regular surroundings, in order to propose an explanation.  I don’t believe that the explanation must first be written in mathematical form in order for it to make sense or for it to be accepted as valid – or provisionally valid, until a better explanation comes along – by other biologists.


As it is (I suppose) with biologists, so it should be with economics.  Rigor is indeed called for; such rigorous thinking is what makes economics and biology scientific.  And this rigorous thinking does indeed demand that ‘things add up.’  For example, the economist who hears a politician screech about the trade deficit “costing jobs” points out (among other things) that the trade deficit is offset by capital inflows.  The economist who encounters a reporter’s prediction that the devastating hurricane will actually be good for the economy points out that the resources and labor used to rebuild that which the hurricane destroyed are thereby unavailable to build other goods and services that would otherwise have been made available.  But sound and rigorous economic explanations of many real-world phenomena – as with sound and rigorous biologists’ explanations of many real-world phenomena – do not necessarily require for their expression mathematics.

At the risk of being too repetitive, I repeat again: I do not oppose, as matter of methodological principle, the use of mathematics in economics.  What I oppose is the unthinking, if fine-sounding, assertion that solid economics must be done mathematically, or that it is always possible to improve an economic theory or explanation by putting it into mathematical form.