Various signatures of William Shakespeare

The idea that people are underestimated has spurred the creation of Book of Odds and I explored this issue recently at the Boston Museum of Science. It is true that people make characteristic errors in judging large numbers and dealing with probability. These tendencies have been studied deeply by psychologists such as Daniel Kahneman and Amos Tversky. That real people do not behave in the way a game theory would suggest is optimal, or an econometric model would posit, has led to the rise of behavioral economics.

John Allen Paulos popularized Douglas Hofstadter’s term “ Innumeracy,” defined as a weakness in dealing with math and probability, analogous to illiteracy. The essence of the comparison is that as we do not expect ourselves or our children to be illiterate, we should no more expect them to be innumerate.

On our site, too, we often compare the odds a thing is feared with the likelihood of its occurrence, and it is clear that fear has roots other than calculated odds, or people are deeply irrational, or both.

I am fond of all these currents of thought, but I believe there is a counterpoint to be offered as well.

I had the chance to offer this counterpoint at two talks I gave recently at the Boston Museum of Science, and even ran a modest experiment with the crowd of roughly 200 who attended the two talks. A video of one of the talks, in two sections, accompanies this summary of its main argument.

The core of my argument is that people are capable of much more than they are credited with. I made this point by recalling skills we now take for granted which were once unmastered, even by the wisest. I also made the point with a little group exercise on pricing.

Take spelling, for example. Shakespeare spelled his name various ways. Between 1593 and 1616 literary references to the Bard of Avon include ten variants, from “Shake-speare” to “Shakspere,” according to David Kathman. Should we be surprised? After all, the most influential (though not the first) English dictionary, that of Dr. Johnson, would not be published until 1755. Standard spelling awaited the coming of dictionaries. If one inferred the human ability to spell from 17th century practice, one might have concluded that it was beyond us.

Or take simple arithmetic. Consider Samuel Pepys, for example. Famous for his fascinating diary, he was an administrator of the great British Navy and a Member of Parliament. In his diary he recounts how he learned his times-tables from an arithmetic tutor. Here was a leader of the most powerful Navy of its day, learning as an adult what our school children master in grade school! Again, if one were to have inferred numeracy from even the ruling elite of his day, the verdict would have been grim. Here is a postscript: Later in his life, Pepys would pester Sir Isaac Newton for the secrets of probability so he could do better at the gaming tables!

If skills we consider the normal attainments of school children eluded the wise and the great until lexicography and school primers came along, is it possible that the intuitive grasp of probability simply awaits its dictionary?

Part Two: A small experiment reveals a large capacity for numerical thinking.

But first here are the videos of the talk of January 16, 2010.

Click here for part two.