Inversion

Inversion is a powerful tool to improve your thinking because it helps you identify and remove obstacles to success. The root of inversion is “invert,” which means to upend or turn upside down. As a thinking tool it means approaching a situation from the opposite end of the natural starting point. Most of us tend to think one way about a problem: f

Inversion shows us that we don’t always need to be geniuses, nor do we need to limit its application to mathematical and scientific proofs. Simply invert, always invert, when you are stuck. If you take the results of your inversion seriously, you might make a great deal of progress on solving your problems.

There are two approaches to applying inversion in your life. Start by assuming that what you’re trying to prove is either true or false, then show what else would have to be true. Instead of aiming directly for your goal, think deeply about what you want to avoid and then see what options are left over.

The inversion happens between steps 3 and 4. Whatever angle you choose to approach your problem from, you need to then follow with consideration of the opposite angle. Think about not only what you could do to solve a problem, but what you could do to make it worse—and then avoid doing that, or eliminate the conditions that perpetuate it.

One useful mental model for thinking about this is the principle of inversion, popularized by German mathematician Carl Jacobi. He told his students to “invert, always invert,” encouraging them to approach difficult problems by inverting the equation to gain a new perspective.⁠1 We can also apply this principle to our lives. For example, instead of