Inversion

Their wordsWhat Carson did was to approach the study of how to create X by turning the question backward, that is, by studying how to create non-X. The great algebraist, Jacobi, had exactly the same approach as Carson and was known for his constant repetition of one phrase: “Invert, always invert.” It is in the nature of things, as Jacobi knew, that many hard problems are best solved only when they are addressed backward.

Their wordsThose of you who have mastered algebra know that inversion frequently will solve problems which nothing else will solve. And in life, unless you’re more gifted than Einstein, inversion will help you solve problems that you can’t solve in other ways.

Their wordsFirst, I had long looked for insight by inversion in the intense manner counseled by the great algebraist, Jacobi: “Invert, always invert.” I sought good judgment mostly by collecting instances of bad judgment, then pondering ways to avoid such outcomes.

Their wordsIt is not enough to think about difficult problems one way. You need to think about them forwards and backward.

Their wordsInversion often forces you to uncover hidden beliefs about the problem you are trying to solve.

Their wordsDespite our best intentions, thinking forward increases the odds that you’ll cause harm (iatrogenics). Thinking backward, call it subtractive avoidance or inversion, is less likely to cause harm.

Their wordsSpend less time trying to be brilliant and more time trying to avoid obvious stupidity. The kicker? Avoiding stupidity is easier than seeking brilliance.