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In 1942, an American psychologist called Abraham Luchins published a seminal experiment called the “Water Jug Problem” . In this experiment he investigated the cognitive asset of mental flexibility—the ability to be adaptable in the way you think and solve problems, as opposed to always thinking in the same, rigid way.
To do this he asked people to answer a series of 10 numerical problems. For each question the person had to propose a simple equation which allowed them to solve how the capacities of 3 different jugs could deliver a desired quantity. For example, if jug A could hold 21 units, jug 2 could hold 127 and jug 3 could hold 3 units, what equation was needed to compute the desired quantity of 100 units?
Here is a full list of the 10 problems he set them.
Source: Luchins, 1942All these problems (except number 8) could be solved using one particular formula B – 2C – A. For problems 1-5 this was the simplest solution. However for the subsequent problems (6-10) it was possible for the person to use a simpler equation (either A + C or A - C) to solve the problem. By designing the problems in this way Luchins was able to explore whether the person’s experience of solving the first five problems prevented them from realizing that the subsequent ones could be solved by this simpler solution. In other words, demonstrating whether their “familiar” routes of thinking and problem solving would inhibit their ability to use a novel, more efficient, approach to solve the problems.
Choosing the simplest solution?
Luchins gave the set of problems to two groups of people and recorded what equations they used to solve each of the 10 problems. In the first group, people answered all problems in order, while in the second group, they were only given the last 5 problems.
What he found was that in the first group, the majority of people used B – 2C – A on the later problems instead of choosing to use the simpler solution. In addition, 64% completely failed to solve problem 8 (compared to 5% in group 2), which could be solved by the relatively simple formula A – C, but not the familiar one. In contrast, almost everyone in the second group—who skipped the initial problems—arrived at the simplest answer for the later problems.
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So arose the idea of the “Einstellung Effect”—a mentally undesirable situation in which your familiar thoughts block or inhibit your ability to generate novel solutions and ideas. They introduce a degree of rigidity—where you steadfastly stand by what you know and think, often blind to other interesting possibilities or more efficient alternatives. And like many “biases” in your thinking, it all happens without you even realizing it.
This Einstellung effect, explored more recently by researchers such as Merim Bilalić from the University of Oxford [2,3], is one example where “forgetting” can actually be beneficial—something that has also been shown in other creative contexts. For example, researchers at the University of California showed that people who were better at “forgetting” recent distracting information (in this case, ideas provided by the experimenter), were actually able to generate more novel ideas on a creativity task .
Regretful thinking and fear inhibit flexibility
There are also other examples of how your inability to “let go of the past” prevents you from being flexible. Take the example of regret, a feeling that can prevent you from choosing the optimal action to take, causing you to “shut down"—paralyzed by the fear of making the wrong decision as you recollect the unpleasant outcomes of your past choices [5,6].
However, you also have inbuilt mechanisms to help you “extinguish” or re-program these unpleasant memories (a process called fear extinction), allowing you to flexibly update and adjust your thoughts and behavior in line with the ever-changing environment . The neural dynamics of this memory re-programming have even been shown using neuroimaging techniques such as electroencephalography (EEG). For example, researchers from Justus-Liebig University Giessen and Harvard Medical School measured EEG activity when people underwent a “fear extinction” task . They found that when people recalled memories of feared experiences, it was associated with changes in theta activity across anterior mid cingulate cortical sites. In contrast, when they recalled the “reprogrammed” memories where this fear had been extinguished, it was associated with changes in gamma activity across ventromedial prefrontal sites.
Mental flexibility is your ability to update, inhibit and overcome well-worn neural pathways to ensure that you are capable of adapting to your diverse and ever changing technological and social environment. It is the cognitive asset that has enabled humans to be so evolutionarily successful across a diverse range of experiences. Understanding the weaknesses in our mental flexibility, such as those illustrated by the Einstellung effect, and learningmore about how we can make it more efficient, is therefore key to creating human success stories across the globe.
I write articles based on my experience as a therapist or a training or conference attendee. Many of these articles are written by others who are experts in their field and I share their information as resources for others.