Don’t Try to Win: Using Inversion to Flip the Script on Your Trickiest Problems

“Look at me as an example of what not to do,” my father once told me.

As he is now serving a life sentence in prison, it was pretty solid life advice. It’s also an excellent example of a mental model called “inversion.”

Inversion is simply looking at the opposite of your problem to find an easier path to a solution.

This way of thinking is inspired by the 14th-century German mathematician Carl Gustav Jacob. Jacobi was famous for solving complex problems by following a simple strategy: loosely translated to “invert, always invert.” He believed that it was easier to restate tricky problems in the opposite form. He would write down the inverse of the problem he was trying to solve and found that the solution often came to him more easily. So instead of X + y = 10, he’d write x = 10 — y.

Looking at problems through this new lens can make new insights clear. It can be easier to see the mistakes and mental roadblocks that were not immediately clear. Instead of focusing on one side of the equation, flipping it can shed new light. Thinking about its opposite or how “not” to do something.

James Clear, the author of the best-selling book Atomic Habit, says, “Great thinkers, icons, and innovators think forward and backward. Occasionally, they drive their brain in reverse.”-James Clear.

• Getting rich is hard.
• Finding a great job is hard.
• Losing weight is hard.

These things lack clarity, and there are many routes to success — most of them challenging, time-consuming, and boring. The inverse of these problems, however, are much easier to solve.

It’s easier to avoid becoming poor than to become rich. Finding a not-bad job is more straightforward than finding a great job. Not gaining weight is more accessible than losing weight.

The road to success is ill-defined. The road to failure can be mapped with great clarity.

Charlie Munger, the business partner of Warren Buffett and Vice-Chairman of Berkshire Hathaway, is famous for saying, “All I want to know is where I’m going to die, so I’ll never go there.”

So how do you use this in real life?

Examples from History

A historical example of this comes from WW2. During World War II, the Allies studied Nazi damage to the airplanes that returned home. Their study resulted in this dotted illustration:

The scientists first thought was that they needed to reinforce the areas that were getting shot at. However, a statistician named Abraham Wald disagreed. Instead, he suggested that the airplanes should be reinforced where there were no indications of damage. He correctly thought that those areas that were damaged were in the aircraft that made it home; in other words, those red dots were where an airplane could be shot at in still made it home. If they had been able to study the aircraft that DIDN’T make it home, they probably would find the opposite shooting impact.

Or going back further, during World War I, the military forces increased the issuing of helmets for soldiers. They found that the number of wounded soldiers skyrocketed. This wasn’t because the helmets magically led to more injured soldiers but instead made sure fewer people died.

Examples of Personal Success

I work with many projects, and one thing I’ve started to do is a pre-mortem, sometimes known as “kill the project.” I won’t know how to make my project succeed. But I can think of 20 ways my project will go up in flames. With this map of “what-not-to-do” in place, it is easier to avoid the pitfalls than try to achieve success. And when something does fail, I have a new addition to that pitfall list.

Approaching tricky problems this way can also shed light on new ways of thinking. At my organization, we were puzzled by the number of men quitting. Our male turnover was a quarter higher than our female turnover so we asked the obvious question, “Why are men quitting at a much higher rate than women?”. We couldn’t find a clear answer until we looked at the problem differently.

Across the country, female turnover skyrocketed due to the pandemic knocking down the delicate house of cards of childcare. Our female turnover was nearly half the national average.

Reframing the question from “Why are men quitting at a much higher rate than women?” to “Why are women staying at a higher rate?” shifted the narrative. During the pandemic, our organization worked to provide remote and flexible options for as many people as possible. Leaders were encouraged to be lenient and flexible, and we transitioned many employees who needed remote work to new roles. Data shows this proactiveness worked as intended.

Instead of women being forced out of their jobs, we saw female turnover drop — unlike much of the country.

Using mental models like inversion allows you to look at problems through a new lens. By shifting the narrative, your brain is able to see a wider range of possibilities and solutions.

“It is remarkable how much long-term advantage people like us have gotten by trying to be consistently not stupid, instead of trying to be very intelligent.” said our old friend Charlie Munger.

Finding genius solutions is sexy; however, finding ways to be consistently not dumb is a much safer and easier strategy.