Right Wing Nation

Bad Science has an excellent article up about how we are hardwired to find patterns:

But we have an innate human ability to make something out of nothing. We see shapes in the clouds and a man in the moon; gamblers are convinced that they have “runs of luck”; we can take a perfectly cheerful heavy metal record, play it backwards, and hear hidden messages about satan. Our ability to spot patterns is what allows us to make sense of the world but sometimes, in our eagerness, we can mistakenly spot patterns where none exist.

Back in grad school, this was a frequent topic of conversation among the cogsci crowd (specifically, the connectionists). Here’s an experiment you can do to demonstrate it to your class (particularly useful in a stats class, by the way).

Open up Excel. In cell AI, type “rand” and “Toss 1″ in cell B1. Click on B1, and drag the little rectangle in the lower right-hand corner through cells G1 (or type “Toss 2″ and so forth in the cells). In cell A2, under the “rand” label, enter =rand(). Grab the little rectangle in the lower-right corner of A2 and pull it down through A31. This will give you 30 random numbers.

In cell B2, under the “Toss 1″ label, type the following function:

=if($A2>0.5,”H”,”T”)

Grab the little rectangle in the lower right-hand corner of B2 and double-click it (it will fill in the function all the way down to the last random number). Grab the little rectangle in the lower right-hand corner of the selection, and drag it across to column G. Your results will look like this (I hid some rows to make it smaller and easier to see):

Now, select the range B2:G31, click Edit, Copy. Go to the next worksheet, and click in cell A1. Click Edit, Paste Special. Select the Values radio button, and press OK. You now have six series of thirty random coin tosses, more specifically, Bernoulli trials.

Here’s how the experiment works. Show students the trials on the second sheet, one column at a time. Ask students to look at the coin tosses and decide whether they are random or not. Give them a couple of minutes, then ask for a show of hands. At least nine-tenths of your students will say they are not random. Do this for each of the columns, then go back to the first worksheet and show the students how the data were created, and that they are, in fact, random.

Two related things are happening. First, the students’ brains are extracting patterns where there are none. Second, because we do this automatically, we don’t see “random” unless we see H T H T H T, where there is, ironically, a pattern.

If there is one fundamental concept about probability most people not only don’t understand, but have difficulty accepting, it is the independence of trials. This is a good way to get your students to get past their brains and understand that all coin tosses are independent of one another. You can appeal to their intellect by saying that the coin doesn’t “remember” how it came up the time before, but in my experience, that doesn’t overcome their natural tendency to see patterns where none exist.