Inversion is a powerful concept that changes our perspective. From a different vantage point, we see things in a new light. Obstacles are removed from our path. It often doesn’t suffice to only think about complex problems in one way; instead, they require us to think about them both forwards and backwards. Carl Gustav Jacob Jacobi nailed it when he instructed, “Invert, always invert.”
As linear thinkers, we default to following a progression of steps towards solving a problem. This progression is often monodirectional, starting at the beginning and seeking the end. Our thought process includes questions like, “what should I do to achieve success?” and “what can I do to solve this problem?” While linear problem solving can be effective sometimes, there is a simple tool that has been implemented throughout the ages to great success: Inversion.
Indeed, many problems can’t be solved forward.
Charlie Munger
Inversion is the practice of approaching a problem from the opposite end of the natural starting point. By doing this, our viewpoint changes. Picture a problem as a house. Normally, we’d enter through the front door, but if we invert our approach, we’d instead enter through the back. Upon entering the house, we’d see a different setting than if we’d have entered through the front door.
Similarly, when we change our angle of attack on a problem, we see different things. Obstacles abate. Impasses become passable. Dots that originally seemed random can now be connected. Inversion simplifies the complex.
When we change the way we look at things, the things we look at change.
Dr. Wayne Dyer
Carl Gustav Jacob Jacobi
Carl Gustav Jacob Jacobi was a German mathematician who is famous in the academic world for his work in elliptical functions, differential equations, determinants, number theory, and more. He solved difficult problems by inverting them and starting at a different point. Jacobi believed that inverting known results can oftentimes open up new fields for research. While Jacobi primarily used inversion for academic purposes, this mental model is widely applicable in many different areas of life.
Man muss immer umkehren [Invert, always invert].
Carl Gustav Jacob Jacobi
Stoics and Inversion
Stoic philosophers made it a priority to practice an exercise referred to as premeditatio malorum, or “premeditation of evils.” They did this to strengthen their internal resolve. The stoics classified events as either internal or external: internal events are directly within our control, external events are not.
The purpose of the “premeditation of evils” exercise was to envision all the potentialities that could go wrong in life. What happens if you lose your wealth, your family, your reputation? While uncomfortable to contemplate, this exercise prepared the Stoics for worst-case scenarios so that they were not paralyzed when the suboptimal – and even tragic – happened.
Nothing happens to the wise man against his expectation. . . . nor do all things turn out for him as he wished but as he reckoned – and above all he reckoned that something could block his plans.
Seneca
In contrast to the stoics, how often today do we only focus on the best-case scenario? And how often do we scold those who contemplate the potential negatives as pessimists? What they are really doing is inverting the natural tendency to hope for – and look forward to – optimal outcomes. This form of inversion helps us stay grounded in reality and conceive backup plans when our hopes don’t pan out. Inversion mitigates the chances of getting blindsided.
Charlie Munger and Inversion
Charlie Munger is a master at inversion. And he’s clever about it. One of his mantras is that in order to succeed, we need to know what to avoid. He started using this principle early in his life as a meteorologist in World War II (Munger discusses this at the Daily Journal shareholder meeting in 2020). He asked himself, “Suppose I want to kill a lot of pilots. What would be the easiest way to do it?” He determined that he could accomplish this by 1) getting the planes into icing that they couldn’t handle, and 2) getting the pilots into a place where they’d run out of fuel before they could land. Knowing this, Munger made sure he stayed miles away from these scenarios. As a result, he kept pilots alive and became more valuable to the military.
This is very similar to the circle of competence mental model where we avoid what we don’t know. Inversion, on the other hand, identifies that which brings misery and failure. Once we know what yields poor outcomes, we know what to avoid.
A lot of success in life and success in business comes from knowing what you really want to avoid – like early death and a bad marriage.
Charlie Munger
In fact, Munger actually contemplates all the factors that would bring about poor outcomes. He asks, “What is it that I would need to do to have this bad outcome happen?” Then he outlines the actions that would achieve the negative event and refrains from them.
Munger does just this in a speech delivered to the Harvard-Westlake School in 1986 in which he expands upon late night television host Johnny Carson’s prescriptions to guarantee a life of misery. Through identification we can properly avoid the unwanted.
All I want to know is where I’m going to die, so I’ll never go there.
Charlie Munger
Sherlock Holmes and Inversion
One of fiction’s most famous problem solvers is Sherlock Holmes. And yes, Sir Arthur Conan Doyle wrote his protagonist with exceptional deduction skills, including inversion. Sherlock referred to his form of inversion as “reasoning backward”.
Most people, if you describe a train of events to them will tell you what the result will be. There will be few people, however, that if you told them a result, would be able to evolve from their own consciousness what the steps were that led to that result. This is what I mean when I talk about reasoning backward.
Sherlock Holmes in A Study in Scarlet, by Sir Arthur Conan Doyle
A particularly obvious use of inversion by Sherlock Holmes was in A Scandal in Bohemia. In this story, Sherlock is tasked with recovering incriminating photos of a royal family member. Irene Adler is the lady with these photos, and she’s keeping them for self-protection. Sherlock, instead of investigating where the photos are likely to be, creates a ruse where he gets invited into her house and forges a fake fire. In the initial moments of confusion, Adler glances at where she has the photos hidden. Sherlock used deduction to infer the photos were likely kept close to Adler, but rather than looking for them himself he used inversion to instead trick her into compromising their location.
Healthcare
The healthcare industry is incredibly important to the human species’ health and longevity. How do healthcare professionals achieve success at something so critical? Inversion. At first glance, the healthcare professional’s job is to help the patient. But overeagerness to help can sometimes be more detrimental than good.
Therefore, the healthcare industry has adopted a phrase to prevent unnecessary injury: “Primum non nocere (First, do no harm).” The greatest form of help is refraining from harm. Again, identification is key. Only once the subject to be avoided (harming the patient) is identified can it then effectively be avoided.
Games
In many games, there is a maniacal focus on winning. It’s glorified in the media. It’s easy to sell because it’s binary and emotional. But the professional games we watch are not the same as the games in which we usually participate. Professional sports are “Winner’s Games”; victory is due to the actions of the winner. Non-professional sports are “Loser’s Games”; defeat is determined by the actions of the loser. Charles Ellis elucidates this point with tennis in his 1975 essay, The Loser’s Game. He says:
The amatuer duffer seldom beats his opponent, but he beats himself all the time. The victor in this game of tennis gets a higher score than the opponent, but he gets that higher score because his opponent is losing even more points.
Similarly, golf is also about minimizing mistakes. Former professional golfer Tommy Armour wrote in his book How to Play Your Best Golf All The Time that, “the way to win is by making fewer bad shots.”
In situations where we can be our own greatest downfall, we need inversion. Instead of seeking more victories, we should instead invert our efforts to lose less. And to do that, we need to invert our strategy from trying to make incredible plays to avoiding mistakes. The desired outcome is the same, but it’s attacked from a different angle.
Business and Investing
Business and investing are like the Loser’s Games: our mistakes are more likely to be costly than our brilliance is to be successful. Therefore, inversion is a useful tool. Instead of seeking brilliance, avoid stupidity. Charlie Munger championed this idea in a letter to Wesco Shareholders when he was Chairman there.
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. There must be some wisdom in the folk saying, “It’s the strong swimmers who drown.”
Charlie Munger in Damn Right!: Behind the Scenes with Berkshire Hathaway Billionaire Charlie Munger, by Janet Lowe
Mark Sellers, a former hedge fund manager, followed the principles of inversion by focusing on the downside of an investment. In contrast, many financial decisions are presented in a frame where only the upside is emphasized, e.g. this stock could double in a year. In a Financial Times article, Sellers discusses his approach to achieving returns:
I’ll invest in a stock only when the potential upside (the ‘reward’) is at least three times larger than the potential downside (the ‘risk’). If I can’t find such a situation, I do nothing; I hold cash. I feel that if I take care of the downside, the upside will take care of itself.
Inversion in the world of business and investing mitigates the chance of loss.
War
War is the ultimate form of the Loser’s Game. As a result, mistakes must be avoided. Lives are in the balance. Ancient Chinese military general and strategist Sun Tzu documented the importance of using inversion to avoid mistakes in his foundational book The Art of War. He instructs that instead of pursuing dominance, participants in war should avoid failure.
He wins battles by making no mistakes. Making no mistakes is what establishes the certainty of victory, for it means conquering an enemy that is already defeated.
The Art of War, by Sun Tzu
Inversion is also used in deception. Not only is war the ultimate form of the Loser’s Game, it’s also the ultimate application of game theory. In game theory, participants strategize their best course of action based on what others do or are expected to do. Inverting that fact to ask, “What is it that my opponent expects me to do?” influences our behavior in the pursuit of getting the upper hand.
Appear weak when you are strong, and strong when you are weak.
The Art of War, by Sun Tzu
The Effects of Inversion on Our Latticework
Inversion is a powerful mental model on its own, but it impacts other parts of our latticework as well. Our ability to navigate and use our latticework strengthens from understanding these interdependencies.
Framing Effect
The framing effect is a bias that influences how we make decisions by presenting information in a particular way. Inversion combats the framing effect. When information is presented in one manner, flip it around and analyze it from that angle instead. For example, if a policy is presented as potentially saving 85 out of 100 lives, invert it so that instead the same policy potentially loses 15 out of 100 lives.
Hanlon’s Razor
Hanlon’s Razor is a mental model that reminds us that we do not know what the intent of others is. We assume it. Oftentimes, it is easy to get frustrated and assume someone acted out of malice when they mistreat us. To implement Hanlon’s Razor, we must invert our reaction of assuming the worst to instead entertain the idea that the other person was simply ignorant to how their actions impacted us. Without inversion, we couldn’t change our way of thinking.
Probabilistic Thinking
Probabilistic thinking is the practice of assigning likelihoods to various outcomes, reasons, and more. When we exercise our probabilistic thinking, we likely default to the commission; that is, we fixate on the likelihood of something being that way. However, we should also ascertain the likelihood of that same thing not being a certain way. In other words, we should invert. If we only look to the positive or negative, the picture is incomplete. Entertaining both the likelihood and unlikelihood of an event improves the holistic internalization of probability.
Rhetoric
Not only is inversion invaluable in combating our own biases, but it is also a powerful persuasion technique in the art of rhetoric. Specifically, when the other party tries to frame their argument in a certain way, invert it to show the audience what it looks like from the other perspective. If done correctly, inversion is highly effective in the art of persuasion.
Survivorship Bias
Inversion helps us avoid survivorship bias. Instead of looking at only the winners, inversion promotes the study of the losers. What did they do that caused them to fail? When we identify those causes, we know what to avoid to increase the odds of us being survivors.
Conclusion
The practical usage of inversion is broad. And while this mental model is simple to understand, altering our inherent behavior to implement inversion is not always easy. Inverting our thinking doesn’t come naturally to most people. We default to thinking about what we want, what we need to do to succeed. Sometimes that will work. But complex problems often need to be viewed from multiple angles. Inversion promotes viewing problems from various viewpoints.
To invert the idea of using inversion and contemplate the idea of not using it, we can more readily understand and accept the perils of its absence. First and foremost, we limit our understanding of a topic. If we look at something from only one vantage point, our understanding is limited to the information we reap from that vantage point. The more vantage points we pursue, the more data we collect, and the more holistic our understanding of that thing becomes.
Another issue of not using inversion is that we neglect future risks. That is, we only consider what we want to achieve. And what worked for others. We don’t consider patterns of failure that are worth avoiding. If we don’t know what to avoid, it’s much harder to stay clear of it.
The two points we can take away from inversion is the importance of increasing our number of vantage points and avoiding stupidity rather than seeking brilliance. In other words, seek diversity of thought and be vigilant in avoiding the downside. Do that and the upside will take care of itself.
