“Invert, always invert.”
Leonardo Da Vinci’s “Vitruvian Man.” Source: Wikipedia
That’s what the 19th century German mathematician Carl Gustav Jacobi said when approaching particularly vexing problems. He made advances in elliptical algebra, number theory, and differential equations. The Jacobi identity and Jacobian sum are named after him. And mathematicians still use the Jacobi Inversion method.
Stated simply, inversion means to assume the opposite of the problem you’re trying to solve, and look at what goes into that answer set. For example, if you’re trying to foster innovation at your company, you could think of all the things you could do to be more innovative. But that’s a tough job: it’s hard to come up with creative ways to be more creative. But if you think of all the things you could do to discourage new ideas, it’s easy to generate a list: reinforce backbiting and sniping; allow meetings to be start late and be rushed, insist that new teammates “learn the ropes” before making suggestions, and so on.
Consider inversion backward reasoning: consider where you don’t want to be, and think backward from there. Most of the time we live moving forward, looking out the windshield far more often than in the rear view mirror. That’s why we have admonitions like the Hippocratic Oath’s dictum to “first do no harm”: we have a bias towards action. When faced with a competitive threat, we ask what we can do about it.
But sometimes the best thing to do is nothing. That was certainly true during the Global Financial Crisis. Folks who panicked and sold, say, after Lehman went bust would have had to get back into the market by the middle of 2009 – when many voices were calling for yet another downward thrust. If you want to avoid losing money, don’t panic when the market falls.
10-year S&P 500 weekly chart, log scale. Source: Bloomberg
Think of inversion thinking as an anti-stupidity tool. It helps us avoid self-inflicted errors. If we don’t want an unethical organization, we’ll inculcate moral factors in every decision we make. If we don’t want a conformist culture, we’ll encourage dissent and discussion at our meetings.
In art, a reflection can be more powerful than the original image. The notes around Leonardo Da Vinci’s famous “Vitruvian Man” illustration – and much of his other work — are in mirror writing. They’re only legible if you hold them it in front of a mirror. No one knows why Da Vinci did this. But sometimes the hardest problems can only be solved if you look at them backwards.
Douglas R. Tengdin, CFA