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Think Tank

You Are Not an Equation

What’s The Big Idea?

Math – and anything that sounds like math – is seductive, for two reasons. First, because it has the ring of immutable truth. Second, because it intimidates the vast majority of people into uncomprehending submission.

The more sophisticated our data-gathering and data-crunching tools become, the greater the temptation to rely on mathematical models to represent and reshape our society. From Wall Street to neuroimaging to data-driven school reform, we are becoming increasingly reliant on objective-looking formulae to explain the slippery complexity of human nature.

Emanuel Derman is a Quant, one of the shadowy legion of mathematicians on whose models Wall Street relies to make trading decisions. Overreliance on such models, which Derman and others have argued are insufficient to explain human financial behavior, played a major role in bringing about the 2008 crisis from which the world’s markets are still reeling.

In finance, people built models that use mathematics to describe markets and to describe people and the participants in the markets. And it becomes tempting for them to believe that the mathematics is a theory and forget that it’s actually an analogy [i.e. model] that only has limited extension.

It looks a lot like physics, but it doesn’t work anywhere near to the same effect at all. I mean, not even approximately. So I don’t know, I think the world’s still waiting for some good way to model human behavior which doesn’t rely on an analogy with physics.


Unlike most Quants, Derman started out as a promising theoretical physicist, earning his doctorate from Columbia in 1973. In physics, he says, mathematical theories (not models) are used to describe some aspect of the behavior of the universe. There is, for example, an inch-long equation that explains the behavior of an electron within an atom with dizzying accuracy.
Models, on the other hand, are a kind of mathematical metaphor. “The Efficient Market Model,” for example, hallowed on Wall Street before the collapse, “pretends, loosely speaking, that stock prices and security prices behave like smoke diffusing through a room when you give a puff on a cigarette.” As it happens, they don’t.  

While freely admitting that his Latin is stronger than his Greek, Derman has coined the term pragmamorphism to describe our tendency to define people in terms of inanimate things – IQ tests, magnetic brain scans, income. Pragmamorphic thinking, says Derman, is dangerous because it creates a one-or-two-dimensional representation of a multidimensional phenomenon – human behavior – and presents that as the whole story.

A few hours after the post went live, Emanuel Derman sent us this note: Just remembered something. The thing about being pragmamorphic is that the premise sort of destroys itself. This video by John Cleese is a favorite of mine and makes the same point with brilliant humor.

What’s the Significance?
 
Mathematical models themselves are not responsible for the financial meltdown. But our overreliance on them is, in large part. In every area of society – education, law, government, parenting – the “soft science” of mathematical modeling, coupled with our tendency to trust it as definitive, is exerting an increasing influence on how we tackle difficult questions. Just glance at any weekend Science section of any major newspaper for concrete, definitive parenting advice based upon one correlative study. 

A recent Big Think article addressed the “data-driven school reform” going on in New Jersey and elsewhere. Its proponents argue that a centralized database of student information based largely on test scores will give teachers and administrators a much clearer picture of what’s going on in classrooms, enabling them to make better teaching and hiring decisions. Its opponents (many of whom wrote to us eloquently in response to the article) argue that woefully imperfect tests and data will lead to the firing of good teachers and the misallocation of resources – that mathematical approaches will exacerbate the woes of public education rather than ending them.

Derman brings up a recent op-ed by Richard Dawkins, a public intellectual and evolutionary biologist:

He wrote saying that they should have kept Saddam Hussein around and not executed him, not out of kindness, but because it would have been so interesting to examine him and try to figure out what caused him to become the sort of monster that he was. And I think that’s kind of pragmamorphic in a way. You have to be kind of naive to imagine that questioning or
sending Hitler to a psychiatrist, even unwillingly, he’s going to let you discover how you should bring up your kids.

Derman's warning is powerfully relevant at this moment in history. Faced with the undeniable global and personal anxieties that characterize our age, we should be deeply skeptical of premature solutions based on science that cannot yet deliver what its sales representatives promise.


 

 


 

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