Thursday, September 20, 2007

Test Your System 1 and System 2 Cognitive Processes

This is the shortest psych quiz for heuristics and bias, developed by Kahneman and Frederick:

1. A bat and a ball cost $1.10 in total. The bat cost $1.00 more than the ball. How much does the ball cost?

2. If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?

3. In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

Hightlight below for answers:

1. $0.05

2. 5 minutes

3. 47 days.

From Heuristics and Biases: The Psychology of Intuitive Judgment by Thomas Gilovich:

(describing the dual-process systems theory of cognition by Kahneman and Tversky):

"There is another set of dual-process models that do not conform to the cognitive miser perspective. These models, often referred to as "two systems" models, postulate the existence of two mental systems that operate in parallel. An associationist, parallel-processing system ("System 1") that renders quick, holistic judgments is always in operation--not just when motivation is low and judgments are made on the cheap. The assessments made by the associationist system are then supplemented--and sometimes overridden--by the output of a more deliberate, serial, and rule-based system ("System 2")."

If you got the wrong answers, you probably relied too much on System 1 cognition, which makes you more susceptible to errors of cognition, namely ones due to automatic, unconscious, low-effort, difficult to control heuristics and bias. System 2 cognition involves more cognitive effort and is more deliberate and logical, so you would have worked the problems out better and seen the tricks.

Don't worry. I missed #2, although I think it was because I freeze up with word problems, and forget that I actually rock logic. My dad told me all throughout my childhood that I was bad at math, because I was not as quick at it as my math-major siblings. He would test me by setting me up for embarassing failure at family gatherings, asking me to do poly multiplication, word problems, and long division in my head. One of my brothers is actually very good at these things. I am not.

I can, however, recite Shakespeare and recite up to five lines of poetry after reading it for just a few minutes. I actually have a fairly good memory, and some would say, immediate recall photographic memory. But did he ever test this? No. So I grew up thinking I was bad at math, and for a long while that was a self-fulfilling prophecy. I grew lazy with math, thinking that it wasn't worth the effort since I inherently sucked at it. To a certain degree, it does come harder to me than any other subject. I actually had to do the homework. I could breeze through literature, history, art, etc., but had to actually try with math, chemistry, and physics. I had to do every bit of homework, and then extra practice. So I just gave up, because I was lazy and it was easier to believe that I sucked at these subjects. Somehow though I made it through honors math classes all throughout high school with at least B+/B averages (and these were my only B's, so comparatively it did seem like I sucked when all my other grades were A's), and I went up to Calculus AP (but did not take the test). And I rocked statistics in college, and got A's. So I can't be that bad, I guess.

So I have to disabuse myself of other cognitive biases and heuristics, namely my latent resistance to math and numbers so I don't freak out and become stupid. Oddly enough, only the questions that remind me of word problems from high school do this to me. I am perfectly happy looking at p-values, T-tests, and correlation coefficients. Empirical legal studies does not scare me.

The joke is that every liberal arts/social science major went to law school because they couldn't do math, and that they fear math. This is by and large, a widespread joke that has some traction. But I wonder how much of it is really true (really? that much of the population responsible for our legal system and governance can barely add?) and how much of it is just an easy, lazy myth that is a self-fulfilling prophecy. Just a little bit of effort would do much to correct this serious cognitive error and bias.

Also, don't tell your kids they suck at something. If you do, they probably will just to spite you with their mediocre grades, and regret not having chosen economics as their major (rather than political science! arrrgh!).