It often pays to trust your instincts – but instincts aren’t always as trustworthy as they might seem.
In yesterday’s Part 1, I talked about how aesthetic and intuitive leanings based on real-world experiences often help guide our abstract reasoning. But on the other hand, our best guesses about many such concepts can be easily misled by flaws in our intuition.
I’ll start by telling a quick story. At this year’s World Science Festival, MIT’s Josh Tenenbaum started a panel on “Risk, Probability and Chance” by flipping a coin five times. Tenenbaum said – with tongue firmly in cheek – that he was telepathically broadcasting the results of each toss to the audience, and asked them to write down their “perceived” list of results.
Toward the panel’s conclusion, Tenenbaum read off his flip results, asking if anyone in the audience had written down identical answers. About a dozen people raised their hands – certainly not a majority, but still more than might be expected from sheer coincidence.
These audience members’ answers were identical to his – and to each other – Tenenbaum said, because human minds often have an excellent sense for what constitutes a “satisfyingly random” pattern.1 As this Ars Technica article puts it:
We’re unlikely to suggest a series of four heads followed by a tails. In the same way, we’re likely to end up choosing something like TTHTH. So likely, in fact, that if the coin flips do happen to produce one of these random looking patterns, it’ll be overrepresented in whatever crowd we’re testing. Instant psychic ability, with built in statistical significance.
Though this is sort of intuition about probability can help us reason more efficiently, it’s also vulnerable to mistakes. When it comes to guessing patterns about which we lack significant relevant data, the answer that makes the most intuitive sense isn’t always the right one.
To demonstrate this, Caltech physicist Leonard Mlodinow tried another test on the panel audience: he divided them into two groups, asking Group 1 if they thought there were more than 180 countries in Africa, and asking Group 2 if they thought there were more than five. He then reconvened the whole audience, and asked each of the groups to estimate the number of countries in Africa.
The actual answer is 52 – but members of Group 1 generally guessed much higher than this, and Group 2’s members guessed much lower. Members of both groups probably had the sense that their answers were near-random guesses, but Mlodinow’s “seed numbers” had sneaked a different unconscious bias into each group’s guess. As Ars Technica points out:
It’s easy to see how a similar effect could be generated accidentally, simply based on (for example) the order of questions in a survey.
This just goes to show that our intuitions and instincts are all ultimately based on experiences, whether we’re aware of which experiences are informing those intuitions or not. When we’re guessing solutions to equations, generating random numbers, or estimating answers to quiz questions, we always make those guesses for a reason. The more we complement our intuitions with an understanding of the reasons for them, the more accurate our instincts can become.
Tomorrow in Part 3, I’ll address one last point raised in the WSF panel – how linguistic phrasing often shapes our perceptions of mathematical probabilities – and I’ll explain how anyone can use Bayesian inference to develop more accurate intuition about complex probabilities.
1. Interestingly, Tenenbaum pointed out that audience members with math backgrounds tend to produce less “stereotypically random” patterns, because they understand that the probability of getting a head or tail always remains the same: 50 percent.