Thursday, March 18, 2010

The Single Number

Why is the human race so fascinated with single numbers for evaluating things?  The classic is "your IQ number" - a single number that's supposed to sum up "how intelligent you are."  Leaving out all the extended (and valid) criticisms that IQ tests are culturally biased, Stephen Jay Gould made it clear (in his book The Mismeasure of Man, 1981) that "your IQ number" is an artifact of the mathematical methods used to analyze the scores from IQ tests.  The researchers could have chosen to use a multivariate method that returned several scores - they chose to go with The Number.

Look at your credit score.  Whether you can get a loan or a new credit card depends on The Number, compiled from your financial history by Fair, Isaac & Co.  A whole industry of financial advice has grown up to teach people how to "tweak" their FICO scores, because of the influence of that Number.

Probably the most devastating Single Number we've had to deal with recently was the output of the Gaussian Copula formula developed by David X. Li (see Felix Salmon's Recipe for Disaster in Wired Magazine, 2/23/09, for a detailed analysis).  As the article will explain in probably more detail than most of you want to read (I still recommend it), Li's formula produced a single number that allowed traders to estimate the risk of default on extremely complex financial debt instruments.  It didn't, as it happened, account for all the possibilities - specifically a broad fall in overall house values.  But most of the people who used it to guide their day-to-day trading didn't understand it well enough to gauge its limitations.  It was quick and easy to use, and it gave them The Number.  And here we all are.

We do this all the time.  It's a regular habit.  I don't know if it's because we're intellectually lazy (most of us are, of course), or because we have a mystical faith that "the experts" must be right.  But we'd be much better off if we questioned these Numbers more closely, and perhaps didn't assume that they are an absolute guide to The Truth.  The idea that you can get The Truth from a single Number is just - too good to be true.


  1. Anonymous9:40 PM

    My Erdos Number is 5.

    And for the last word on numbers, see


  2. IQ tests are a fascinating subject.

    Certainly there is a scale--no matter how abstract--by which, theoretically, of course--it should be possible to map a given population of individuals according to their various lights. Some people ARE smarter than others, and it's a difference that's palpable. The problem, though, is in discovering a way by which to measure it.

    And there are many different kinds of "intelligence." We still don't know much about how the brain works. All our apparati for measuring are empirical--i.e., deductive from raw observation--a poor basis for mapping structure and performance. Rather like trying to find out how a computer works, if all you had were the sounds of the keyboard, or the level of light being given off by the screen. We can't "get inside" the workings of thought. Maybe we never will. It's so delicate and subtle and minute, that it's hard to imagine we ever will completely find out. Some people can memorize anything, while others can't. Some people can find their way out of mazes, while others get helplessly lost. Some people can read a complex narrative involving 30 characters, keeping them all straight; some can't. Some can work out complex chess problems; some can't. Why?

    Which may be just as well. Why would we want to know everything about thinking? It's almost like being able to predict the future. Do you want to KNOW, really, how you're going to die? I don't.

    All I know is that I've always had more luck writing paragraphs than solving equations. My aptitude's in that direction. I'd rather wonder about how beautiful a bridge is, than how likely it is to fail under stress.