A German mathematician named Carl Jacobi, famous for his major contributions to elliptic functions, often solved difficult problems by following a simple strategy: inverted thinking. This is one of the best mental models for you to solve problems and improve your consulting business.
“Man muss immer umkehren” ("you should always invert"), Jacobi would say. What he meant was some questions are better solved when asked backward.
To be fair, this idea is much older than him. Stoic philosophers like Seneca and Marcus Aurelius already had an exercise that they performed regularly named premeditatio malorum. The goal was to imagine every kind of negative thing that could happen.
For example, Seneca would imagine how it would be like to become homeless, be publicly mocked and have his reputation ruined, or suffer from health issues. By imagining these worst-case scenarios in advance, they could not only overcome fears but also make good plans to prevent them from actually happening.
The Power Of Inversion
This counterintuitive approach of visualizing the negative and addressing problems backward was used by great thinkers in the past and remains a powerful tool to solve problems today.
Here are some practical examples:
- Leadership: "What does a horrible manager do every day?" Excellent leaders would likely avoid any of those things.
- Marketing: "What would damage our reputation among prospective buyers, or make us seen as non-credible, unreliable, and self-centered?" A strong marketing strategy should avoid any of these initiatives or mistakes.
- Sales: "You have a $1 million in qualified pipeline. Which kind of practices or interactions would ensure you lose all of those deals?" Use the answer to design or improve your sales process and learn any missing skills.
This practice is famous among project managers, who call this "failure premortem" or "kill the project" exercise. They imagine the project has failed - before even starting it - to list the main risks that need to be avoided.
Inverting the problem won't always solve it, but will certainly avoid a lot of trouble.
How To Use Inversion
Using this mental model is surprisingly easy. Here are the steps:
- Define one of your goals. "I want to increase my focus while working remotely."
- Invert that goal. "How do I get distracted when working remotely?"
- Brainstorm ideas to avoid the inverted situation becoming a reality. "I tend to browse social media, shift attention between tasks, and check for emails multiple times a day. These could be avoided by using apps to block my access to certain websites, break tasks into smaller activities, and set a policy to only open email on fixed times, twice a day."
Pick one of your main goals and perform this exercise today. You're likely to find more insights than you imagine.