Einstellung

There's a scene in the 1995 movie, Die Hard with a Vengeance (the third installment in the "Die Hard" movie series starring the actor Bruce Willis) that most mathematics teachers love!  Apparently, there is an evil genius in this movie (played by the actor Jeremy Irons) who sends our hero, NYPD detective John McLane (played by Willis) and his new best buddie, Zeus Carver (played by the actor Samuel L. Jackson) out to solve a series of riddles and puzzles in order to stop the detonation of his bombs.  They end up in Central Park and have 30 minutes to solve a famous riddle (at least for mathematicians and cognitive psychologists) called simply, "the water jug problem" (see the scene from the movie here).

Here is the problem.  You have in front of you a 5-gallon water jug and a 3-gallon water jug.  You also have access to a water fountain, so you can fill up both water jugs as many times as you want.  Your job is to put 4 gallons of water exactly into one of the jugs.  In the movie, the bomb will only be defused when they place the 4 gallons of water on a scale - an ounce more or less will detonate the bomb.  How do you do it?

The solution to this puzzle is all over the Internet, so I won't spoil things if I tell you how John McLane (Willis) and Zeus Carver (Jackson) solved.  Mathematically, the puzzle can be solved if you remember the following:

5 - 3 = 2

5 - (3 - 2) = 4

Does that help?  Here is the step-by-step explanation:

• Fill the 5-gallon jug to the top (the 5-gallon jug has 5 gallons of water now)
• Pour water from the 5-gallon jug into the 3-gallon jug and fill it all the way up (the 5-gallon jug now has 2 gallons and the 3-gallon jug now has 3 gallons of water)
• Dump out the water from the 3-gallon jug (which now is empty)
• Pour the water (2 gallons) from the 5-gallon jug into the 3-gallon jug (the 3-gallon jug now has 2 gallons of water, and the 5-gallon jug is empty)
• Fill up the 5-gallon jug all the way (the 3-gallon jug still has 2 gallons, and the 5-gallon jug has 5 gallons)
• Pour water from the 5-gallon jug into the 3-gallon jug, filling up the 3-gallon jug (the 3-gallon jug now has 3 gallons and the 5-gallon jug now has 4 gallons!!)

Apparently this puzzle has been around for a long, long time.  There are of course different variations, some of which include three different water jugs, not two, as in the Die Hard movie.  The three water jug puzzle was used in a famous set of experiments that demonstrated the so-called Einstellung effect.  

The word "Einstellung" literally means "setting" or "installation" in German.  The Einstellung effect occurs when a person is presented with a problem that is similar to problems that he or she has successfully solved in the past.  The individual will model the solution on these past problems, often times giving the solution to the problem at hand very little thought.  Oftentimes, an easier or more appropriate solution to the problem is available, but due to the Einstellung effect, he or she discounts this alternative solution.  In other words, the Einstellung effect is a cognitive trap - in other words, a negative effect!  It blinds us to alternative and potentially better solutions.  For example, McLane and Carver could have used another method to solve their water jug puzzle in Die Hard.

We are all at risk of succumbing to the Einstellung effect.  So how do leaders prevent their teams from falling to this cognitive trap?  The blogger Tammy Lenski offers a few suggestions:

Remind yourself about the effect - as is the case with most cognitive biases and traps, simply acknowledging that they exist and thinking about them as you solve problems can help mitigate at least some of their effects.

Challenge yourself and others to push past the trap - I will bring in one of the principles from High Reliability Organization theory here - reluctance to simplify.  The simplest explanation is not always the only explanation.  After acknowledging a cognitive bias, be prepared to push past it.

Allow incubation time - take the time to think about the problem.  As Albert Einstein once said, "If I had an hour to solve a problem I'd spend 55 minutes thinking about the problem and five minutes thinking about solutions."

Practice boketto - Dr. Lenski says that boketto is the Japanese term for staring off into space without thinking.  Try giving your brain a break and let the creative juices flow.  In many cases, you will find a new way to think about a problem, which may offer some new and creative solutions.

Consciously adopt a beginner's mind - The expert has been here before and may be more prone to the Einstellung effect.  Think outside the box by thinking about the problem as if you were seeing it for the first time!

As I start to wind up this post, I am reminded of another mathematical puzzle that can only be solved when you "think outside the box."  Connect all of the dots below without lifting the pencil from the paper.  

Here is the answer:

Did you solve the puzzle?  Or were you stuck in the Einstellung effect?