Math in Psychology

Since my Kindle got fixed mid last week, I've been reading a rather delightful book called Thinking, Fast and Slow. I've read books like this one before, on the clever psychological experiments that people have managed to design over the years and what they reveal about the human mind. But this book, in particular, pulls together a lot of interesting bits that I've either read or heard over the years and organizes them into one cohesive and surprisingly elegant theory. (I won't spoil the book for you here, but it's worth looking into. The theory is elegant and seemingly simple, but the details are very interesting and not always so predictable or obvious.)

I am also surprised by how mathematical the author is and how easily he ties abstract math ideas into concrete experiments. For this, I highly recommend the book to math teachers. For example, the author talks about how if you get one person to look at a jar of pennies to guess at how much money is inside, that person might over- or under- estimate by a lot. But then, if you repeat the experiment with a large number of people, their average errors will actually approach zero (in the absence of a systematic bias), and therefore if you average all of their guesses, that average is actually going to be quite accurate. This is a logical idea that kids can grasp, and it's a nice extension of the absolute-value error concept. By the same token, he ties this in general to public opinions. If you survey a large enough sample population on a certain issue, in the absence of a systematic bias, the average of their answers will represent the truth.

Another issue that the author addresses is basic numeracy when reading current event reports or statistics in the media. He illustrates with a simple picking-colored-balls-out-of-a-box example why, with small sample groups, we end up with more extreme values more often. And then he extends this to why when you poll different counties for health information, it's easy to see rural counties with more extreme health statistics. Again, it's not impressive math, but the ease with which he ties math to something real is delightful.

And, as an aside, try to answer this question:

"How many animals of each type did Moses bring into the ark?"*

If you're like me and (the author so says) most people, you let your mental image of the ark prevent you from noticing that Moses is the wrong biblical character here in this context. Our mind has the tendency to smooth over the little inconsistencies using preconstructed expectations, in order to make its job easier. And that's both advantageous and troublesome, depending on the context.

Anyway, so far, I thoroughly enjoy the book! :)

Addendum 12/07/11: I've reached a part of the book where the author talks about how we let our stereotypes affect our judgment of the likelihood of certain combined events. For example, after being exposed to a description to a liberal woman, people -- even those who are mathematically inclined -- would rank the probability of her being a "feminist banker" to be more likely than her being a banker, even though any added details should diminish the overall probability! --What an interesting intersection of math and psychology!!