Mental Models: The Power of Reframing Problems Through Inversion

An approach to problem-solving that starts with imagining worst-case scenarios – and then using those scenarios as the basis for developing solutions.


How might this apply to great teams and cultures?
One of the methods used in creative ideation sessions is reverse thinking. Instead of following the ‘normal, logical’ direction of a challenge, you turn it around (or an important element in the challenge) and look for opposite ideas.

How might this apply to great products?
For instance,  when designing a chair, you can list the assumptions of a chair (it needs to have legs)  and think its opposite (no legs?!) to trigger additional ideas: what if chairs were hanging from the ceiling? or be built as part of the table? or….

taking a DEEPER LOOK

The concept of Inversion is often interpreted in two different ways, both are valuable to consider.

The first is the idea of considering the opposite. In particular, envision the negative things that could happen in life. The Stoic philosophers like Marcus Aurelius, Seneca, and Epictetus regularly conducted an exercise known as a premeditatio malorum, which translates to a “premeditation of evils.”

The second is the idea of working with the end in mind. German mathematician Carl Gustav Jacob Jacobi was famous for some work on elliptic functions that eludes me. Jacobi often solved difficult problems by following a simple strategy: “man muss immer umkehren” (or loosely translated, “invert, always invert.”).

Both approaches look at the end result uniquely. Considering an opposite asks you to hold your ideal result loosely, and to consider the opposite of your desired result. Working with the end in mind assumes you are keeping the same goal but approaching the solution from a different direction, by backing into it.

Very few problems can be solved directly. The most wicked, intractable problems must be dealt with indirectly. As such, the Inversion model is one of the most powerful mental models in our toolkit as human beings.

If you are always inverting a problem, like the way you play with a Rubik’s cube, you experience them from multiple perspectives. Multiple vantage points challenges your certainty. It can shake your beliefs.


Let’s take a look at some examples.

Let’s start with the positive-negative notion. When I coach clients, I get many people at major points of transition in their lives and careers. Some are facing big promotions, others are considering leaving their jobs for a second chapter.

Often I’ll ask: what is it you want? Seems like a simple enough question, but it’s really hard to answer. Specifically, what do you really want to happen?

Many people have a very hard time imagining the life, career, or outcome we want because we’ve been conditioned for such long periods of our life (at home, in school, at work) to think a certain way or to embrace a certain idea of success.

However, when asked to consider what would guarantee our unhappiness…and few are at a lack of words.

Let’s move on to the positive-negative notion. I teach an EMBA class called Managing Innovation. Most people take the class to learn how to improve and manage innovation in their organizations.

The course is guided by the central question: What can be done to foster innovation? The answers are pretty standard: engage small teams, enable autonomy, consider the tension of deliberate and emergent strategies, etc. And, by the way, implementing any one of those things in a culture that doesn’t naturally gravitate toward those qualities is really hard. 

But if we invert the problem to: How do we avoid becoming traditional or unoriginal? we consider all the things we can do to discourage innovation: reduce feedback loops, increase top-down decision making, enable homogeneous thinking, foster resistance to risk. Generally speaking, we would want to avoid these things, right?

And, it sounds so easy, doesn’t it? If we were to follow our own council we would have to take our own advice: “Just stop doing these things and do less of these other things instead.” Behavior change of any kind is no small thing.

Moving indirectly gains more ground than directly. 

Thinking forward/backward or negative/positive about a problem results in some action, you can also think of adding vs. subtracting.

Despite our best intentions, thinking forward increases the odds that you’ll cause harm (through unintended consequences). For example, drugs designed eradicate one disease might also have adverse effects, become harmful if overused, or cause antibiotic resistance in bacteria.

Thinking backward, call it subtractive avoidance or inversion, you are less likely to cause harm. Inverting the problem won’t always solve it, but it will help you avoid trouble and thinking through some of the undesirable and unintended consequences. You can think of it as the avoiding negativity filter. It’s not sexy but it’s a very easy way to improve.

So what does this mean in practice?

Thinking about what you don’t want isn’t necessarily inspiring, but it does bring clarity and can aid decision making to a problem or question that brings nothing but overwhelm. Many of the smartest people in history have done this naturally.

Inversion helps improve understanding of the problem on which you are focused. By using this method, you are forcing yourself toward doing the work of having an opinion that considers multiple perspectives.

The key takeaway: Spend less time trying seeking the right answer and more time avoiding the wrong answer. Avoiding loss is an easier starting point than seeking gain.