, ,

Via Futility Closet:

One day in 1939, Berkeley doctoral candidate George Dantzig arrived late for a statistics class taught by Jerzy Neyman. He copied down the two problems on the blackboard and turned them in a few days later, apologizing for the delay — he’d found them unusually difficult. Distracted, Neyman told him to leave his homework on the desk.

On a Sunday morning six weeks later, Neyman banged on Dantzig’s door. The problems that Dantzig had assumed were homework were actually unproved statistical theorems that Neyman had been discussing with the class — and Dantzig had proved both of them. Both were eventually published, with Dantzig as coauthor.

“When I began to worry about a thesis topic,” he recalled later, “Neyman just shrugged and told me to wrap the two problems in a binder and he would accept them as my thesis.”

Dantzig, coincidently, served as the inspiration for the movie Good Will Hunting (at least as far as his mathematical skills are concerned).

The story got me thinking about how the framing of a problem can affect our ability to solve it.  More specifically, to what degree does the way in which we frame a problem as difficult or simple affect our ability to solve it?  Now obviously Dantzig was a world-class mathematical mind, but other world-class minds had wrestled with the very same problems and failed to find a solution.  I wonder to what extent his mental framing of the problems as routine homework assignments–problems that he should be able to solve rather easily–made it more likely that he would succeed.

We know that framing expectations has an impact on experience and decision. In Predictably Irrational, Dan Ariely spends an entire chapter discussing the various experiments he and his colleagues conducted in order to determine how people’s expectations influenced their experience of things like beer, music, and cars.  But what Ariely doesn’t examine is the extent to which framing a task as easy or hard affects the likelihood of success by participants.  The notion of positive thinking and reinforcement is not novel, but I am curious what scientific studies have say regarding it’s validity.

So how might the framing of difficulty affect performance?

My first guess is that the framing of difficulty might work via the same mechanism as “choking” or “the superstar effect”:

Recent research on what is known as the superstar effect demonstrates that such mental collapses aren’t limited to chess. While challenging competitions are supposed to bring out our best, these studies demonstrate that when people are forced to compete against a peer who seems far superior, they often don’t rise to the challenge. Instead, they give up.

The intense focus of competing against a star forces other competitors to over think the details of their performance, which leads to failure:

A little experience, however, changes everything. After golfers have learned how to putt—once they have memorized the necessary movements—analyzing the stroke is a dangerous waste of time. Ms. Beilock has found, for instance, that when experienced golfers are forced to think about their putts, they hit significantly worse shots.

This is what happens when people “choke.” Because the performers are nervous, they begin analyzing actions that are best performed on auto-pilot.

Just as competing against superior or more difficult to defeat opponents causes most to perform poorly it may be that competing against a difficult to solve problem has a similar effect.  Being freed from this frame and assuming the opponent/problem is easier to deal with might allow people to perform better by preventing a crippling focus on details.

Just a thought.