The failure of mathematics?
The failure of mathematics?
Monday, 07 September 2009
Mathematics has come in for criticism recently, that somehow it was the root cause of the credit crunch and the collapse of the world economy. That’s harsh. It was the misuse of mathematics, by bosses who didn’t understand it, that got us into the mire.
I am astonished that so many people boast of their mathematical inability. I think they think that this makes them more cultured than those they dismiss as “geeks”. I am more astonished that we allow these people to reach positions of leadership without possessing the basic mental tools for the job. Actually, they do possess the tools; they simply refuse to use them. And then we wonder when it goes wrong.
We humans have superb innate mathematical ability. Most of us can perform complicated ballistics calculations and position ourselves to catch a ball lobbed in the air. Or calculate the straight-line path to intercept a ball headed for the boundary. Contrast this with a dog, who will run straight at the ball and follow a nice curved path until he catches up with it. Or consider a scaffolder, who probably doesn’t give a monkey’s about Pythagoras, but who understands very well the significance of the 3–4–5 triangle to help him align horizontal and vertical.
The refusal to take mathematics seriously is the cause of all sorts of errors.
- We assume things are static when they are dynamic.
- We assume relationships between variables to be linear (and predictable) when they are not.
- We ignore ranges of possibility and use single-point average values instead—the flaw of averages.
- We assume that different uncertainties are independent, and get caught by surprise when we discover they are not.
- We confuse cause and symptom and treat the latter, and are surprised when the former does not go away.
- We assume that absence of evidence is evidence of absence.
- We let vanishingly small risks bias our perception of the world (and let unwarranted fear guide our behaviour), whilst ignoring the everyday risks that kill lots of us all the time.
The mathematics is sound. It’s the application that’s at fault. Bad decision makers make bad decisions because they refuse to accept what the mathematics could tell them. The failure of mathematicians—but not, I hope, this one—is to let them get away with it.
See also:
- The maths of the credit crunch, BBC presenter and economist Tim Harford tries to get to the bottom of the assertion that mathematics caused the credit crunch.
Update (22 February 2010):
- Today’s maths dunces revel in their ignorance, Justin King, CEO of J. Sainbury, offers up a lament in The Times.
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p.s. Mathematics partly involves an innate human understanding but is also counter-intuitive to humans at the same time. The brain has evolved to be an efficient processor for its owner - the human on earth. It uses non-linear, low level, massively parallel, processing with huge redundancy. This is at odds and contrary to the development of logistics and computation based on certain branches of mathematics (and not others). That's why there is a mismatch.