A few years ago, Tor Wager, a neuroscientist at Columbia University, wanted to figure out why placebos were so effective. His experiment was brutally straightforward: he gave college students electric shocks while they were stuck in an fMRI machine. (The subjects were well compensated, at least by undergraduate standards.)

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Unless you experience the unpleasant symptoms of being wrong, your brain will never revise its models. Before your neurons can succeed, they must repeatedly fail. There are no shortcuts for this painstaking process.

The advantage of knowing where insights come from is that it can make it easier to generate insights in the first place. When we’re struggling with seemingly impossible problems, it’s important to find time to unwind, to eavesdrop on all those remote associations coming from the right hemisphere. Instead of drinking another cup of coffee, indulge in a little daydreaming. Rather than relentlessly focusing, take a warm shower, or play some Ping-Pong, or walk on the beach.