Inversion – Invert, always invert!

Inversion is a mental model to look at a problem from a different angle ... backwards!

“Invert, always invert” . . . so said Carl Gustav Jacob Jacobi, the German mathematician. Though being German he probably said, ‘man muss immer umkehren’, in expressing his belief that the solution of many hard problems can be clarified by re-expressing them in inverse form.

Typically, we consider a problem in the same way that we phrase it in our mind or as it is written, then set out to solve it from there. This is referred to as the ‘forward way’. We have a problem or a task to resolve, and we naturally put into forward looking terms.

The ‘backward way’, with Inversion, is to look at the problem from a different perspective in order to help solve the problem. But this does not come so naturally to us.

The ‘backward way’ is complimentary to the ‘forward way’. Inversion helps us gain a better overall picture of the problem, simply by posing the problem in a different way.

Combining both forward and backward ways gives us a technique to help us unlock problems.

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

Charlie Munger from Bershire Hathaway has used Jacobi’s maxim over many years. And he did ok!

The simple technique is to insert words like NOT or DON’T or CAN’T, which inverts the phrase.

  • What career do I want to do? Becomes “What career don’t I want to do?”
  • What can I do …? Becomes “What can’t I do?”
  • Who can I trust? Becomes “Who can I not trust?”


A more complex approach to inversion is to ask the opposite of the original question, along the lines of what you do not want or what can stop you.

  • “How do I lose weight?” becomes, “What will stop me losing weight?”
  • “How can write more articles for my site?” becomes, “How can I prevent myself from writing 1 article a week?”


The answers to these questions will tell you what you don’t want. All that remains is for you to make a plan to avoid these things you don’t want.

The below video is a very good explainer from the Farnam Street blog about Mental Models.

Karen Holst from Start Within explains how Nirvana used inversion thinking to innovate and disrupt the music industry.

Some real world examples of this in action…


And finally, here is a perfect example of Inversion when investing your money . . . 

Rule No. 1: Never lose money
Rule No. 2: Never forget rule No. 1

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