There's a German mathematician you've never heard of named Carl Jacobi, and he had one piece of advice for solving hard problems. Invert, always invert. When a problem refuses to crack head-on, flip it. Stop asking how to make it work and start asking how to make it fail.

It's one of the most useful thinking tools ever put into words, and Charlie Munger built a good chunk of a fortune on it.

His version was more blunt. "All I want to know is where I'm going to die, so I'll never go there." Morbid, sure. Useful, also yes.

Asking "how do I succeed at this" usually leads to many possible paths that seem equally likely. Success has a thousand possible ingredients, most of them uncertain, and you can't be sure which ones actually matter. It's a genuinely hard question.

Now ask "how would I absolutely guarantee failure here," and the answer arrives instantly, in vivid detail. You know exactly how to wreck the project, blow the relationship, or tank your health. The failure paths are obvious in a way the success paths never are.

Once you've named the surefire ways to fail, you have a checklist of things to avoid, and avoiding known disasters is far easier and more reliable than engineering brilliance. As Munger put it, it's remarkable how much advantage you get from simply trying to be consistently not stupid, instead of trying to be very smart.

Think about whatever thing you're trying to do well. Then ask: if I wanted to guarantee this goes terribly, what would I do? That’s your set of rules to avoid.

Watch how fast it works on real problems.

Want a project to succeed? Invert. How do I guarantee it fails? Vague scope, no owner, no deadline, no one telling me when it's off track. Now you know exactly what to lock down before you start.

Want to stay healthy? Invert. How do I guarantee decline? Sit all day, sleep badly, eat nothing but garbage, never lift anything heavy. Avoid those four and you're most of the way there without a fancy protocol.

Most self-improvement points you at what to add: the new habit, the new goal, the inspiring vision. Inversion does the opposite, and it's more honest about how things actually go wrong.

Failure is rarely caused by a missing stroke of genius. It's usually caused by a few obvious, avoidable mistakes that everyone could see coming and nobody avoided. Inversion drags those mistakes into the light before they happen, while you can still do something about them. It's a pre-mortem for any decision you face. Imagine it already failed, ask why, and then go prevent that.

You don't have to be brilliant to win at most things. You just have to avoid multiplying by zero.

Got a second? Give some feedback on today’s article so we can keep making improvements to The Manifold.

PS — If you read the newsletter from Monday as well, you’ll see a common theme between these ideas.