- Leandro Herrero - https://leandroherrero.com -

‘Invert, always invert’: a fundamental, zero-cost, unstuck management technique

Carl Gustav Jacob Jacobi [1], a 19th century Swiss mathematician is remembered by many things in his scientific turf, but by one in particular outside the field: ‘Invert, always invert’. He used this phrase to suggest that hard mathematical problems could be addressed better, and eventually solved, by inverting the problem, articulating it in its inverse form, by working it backwards.

In recent years, the quote perhaps needed the visibility lent by Charles Munger [2], business partner of Warren Buffet. Munger is revered in many quarters as great thinker, and his pointing into directions, from general wisdom to investing wisdom, gets good highlights. He has referred to ‘Invert’ many times in his writings and interviews.

‘Invert, always invert’, is a very pragmatic and heuristic mental trick that we at The Chalfont Project [3] have long incorporated into our Critical Thinking [4] programme armamentarium. It is part of a broader set of ‘Reframing’ approaches. Reframing forces us to ask alternative questions to the question that seem to be obvious, or the given one.

For us in day to day management, a simple example of ‘invert, always invert’, is to invert the question. The question may be ‘how can we (succeed and) achieve X goal by Y time?’. This is a very standard question, but the problem may be complicated and people may get very stuck in the finding of the answer or answers.

Indeed, it may be that you find yourself already on the road with several brainstorming sessions and a few PowerPoint ‘summaries’ in your pocket, but you may feel that you are not getting closer to an answer or even a clear path towards it. And this may well be despite the overgrowing analysis of the issue.

Stop there. Invert! Reframe the issue as follows: ‘How can we completely and thoroughly screw up and fail miserably?’ Restart now. I can guarantee you that renewed energy will come to the collective brains, people close to falling asleep under the previous question will wake up, and, progressively, the dull infection of brainstorms will turn into speed recovery with exciting and creative exercises. Try it. Invert the problem.

Give to the inversion a serious change, not just a game or a mental trick. Apply the same brainstorm techniques that you use. Write down the principles of a Strategic Plan to Fail Miserably and Being Ashamed Fast.

At some point, when enough light has come up, you will invert again and will address the original question.

Reframe, always reframe.


Critical Thinking [4] Accelerator from The Chalfont Project:

Renew, transform, re-invent the way you do things. Organizations today need to look at better ways, alternative and innovative ways to change the status quo. It’s not about being radical for the sake of it. Only if you try radical ways will you be in a better position to find your ‘fit for purpose’ goals.

As Michelangelo said: ‘The greater danger for most of us lies not in setting our aim too high and falling short, but in setting our aim too low, and achieving our mark’. He was a radical in the way we talk about it.


At The Chalfont Project, we have crafted a short Accelerator on Critical Thinking [4]:

In this short intervention we teach you and your team Critical Thinking Methods and Questions that will help you focus your time on the things that matter, make good and fair decisions and escape the dangers of human biases. We will also help you apply these methods to your everyday challenges in your organization.

You will learn about Strategy Acid tests and many Mind Fallacies, including various biases, and the practical Critical Thinking methods that you can use to address these.

This high impact, short intervention will:

Contact us [5] to find out more information or discuss how we can support your business.