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**.

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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.

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