Mental Models

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