Inversion: Solving Problems by Thinking Backwards

Inversion illustrated by a thoughtful man standing at the edge of a dark reflecting pool at night, his golden reflection shown upside down in the water among a row of warm lanterns.
Inversion illustrated by a man looking at his upside-down, golden reflection in a dark pool: seeing the same problem from the opposite direction.


Inversion is a way of thinking where you approach a problem backwards. Instead of only asking “How do I achieve this?“, you also ask “What would guarantee that I fail?“, and then you avoid those things. It is one of the mental models I use the most, because it is simple, quick to apply and surprisingly powerful in health, career, investing and learning.

The essence of Inversion is that it is often much easier to see clearly what not to do than to find the perfect thing to do. By removing the obvious ways to fail, the path to success tends to reveal itself.


Origin: “Invert, Always Invert”

The idea is usually traced back to the German mathematician Carl Gustav Jacob Jacobi (1804–1851), known for his work on elliptic functions. Jacobi is said to have solved hard problems by following a simple rule: “man muss immer umkehren“, loosely translated as “invert, always invert“. He would restate a problem in its inverse form, which often made the solution much easier to find.

The approach was popularized far beyond mathematics by Charlie Munger, Warren Buffett’s long-time business partner and Vice Chairman of Berkshire Hathaway. Munger liked to quote the rustic who said: “All I want to know is where I’m going to die, so I’ll never go there.” In a 1986 commencement speech at the Harvard School in Los Angeles, he famously inverted the usual graduation advice: instead of telling the students how to be happy, he gave them his “prescriptions for guaranteed misery“, such as being unreliable, envious and resentful, and refusing to learn from the mistakes of others.


Avoiding Stupidity vs. Seeking Brilliance

One of my favorite quotes on this is also from Munger: “It is remarkable how much long-term advantage people like us have gotten by trying to be consistently not stupid, instead of trying to be very intelligent.“

Brilliance is rare, hard to plan for and difficult to repeat. Avoiding stupid mistakes, on the other hand, is something I can do every day. In many areas of life the results are driven less by a few brilliant moves and more by avoiding the big, unforced errors that wipe out everything else. Avoiding stupidity is easier and more straight-forward than seeking brilliance.


The Pre-Mortem: Inversion for Projects

A practical, team-friendly version of Inversion is the pre-mortem, described by psychologist Gary Klein in the Harvard Business Review article Performing a Project Premortem (2007). Before a project starts, the team imagines that it is a year later and the project has failed spectacularly. Everyone then writes down every reason they can think of for why it failed.

Klein points to research showing that this kind of “prospective hindsight“, imagining that an event has already happened, increases people’s ability to correctly identify reasons for future outcomes by 30%. It also makes it socially safe to voice doubts that would otherwise stay unspoken. I find it one of the cheapest ways to reduce the risk of a project.


Some Examples

  • Health
    Instead of searching for the perfect diet or supplement, I ask “What would reliably ruin my health?” The answers are obvious: poor sleep, smoking, excess alcohol, ultra-processed food, no exercise and chronic stress. Removing these usually does more than any optimization on top. See Healthy for more.

  • Career
    Rather than only asking how to get promoted, I ask “What would make me someone nobody wants to work with or promote?” Missing deadlines, not keeping promises, taking credit for others’ work and never asking for feedback. Avoiding these is a solid foundation for any career.

  • Investing
    Instead of hunting for the next big winner, I ask “How could I lose most of my money?” Using too much leverage, investing in things I don’t understand, not diversifying, chasing hype and selling in a panic. Avoiding permanent loss of capital is the first rule. See Wealthy for more.

  • Learning
    Instead of only asking how to learn faster, I ask “How could I guarantee that I forget everything I study?” Cramming, re-reading passively, never testing myself, sleeping too little and never applying what I learn. Doing the opposite (spaced repetition, active recall, good sleep and practice) is essentially how to accelerate learning. See Approaches to Accelerate Your Learning for more.


Applying Inversion

Applying Inversion does not mean replacing forward thinking. It means complementing it, so you look at the problem from both directions. This is the simple process I follow:

  1. Define the goal
    Clearly state what you want to achieve, e.g. “I want to be fit and healthy at 80” or “I want this product launch to succeed“.

  2. Invert the question
    Ask “What would guarantee the opposite?” or “If this failed, what would be the most likely reasons?“

  3. List the failure modes
    Write down every way it could go wrong, without filtering. Be honest, and include the uncomfortable ones that involve your own behavior.

  4. Prioritize
    Mark the failure modes that are most likely and those that would be most damaging or irreversible.

  5. Design your avoidance
    For each important failure mode, decide on a concrete rule, habit, checklist item or safeguard that prevents it.

  6. Think forward again and review
    Combine the list of things to avoid with your normal plan, and revisit it regularly as things change.


Limitations

  • Avoiding failure is not the same as achieving success. Inversion removes obstacles, but you still need a clear goal and a forward plan to make progress.

  • Taken too far, it can lead to excessive caution, negativity or analysis paralysis, where every idea is killed by a list of things that could go wrong.

  • It only finds the failure modes you can imagine. Truly unknown risks will still surprise you, which is why margins of safety matter.

  • It works best for problems where mistakes are clear and avoidable. For creative breakthroughs, it is a useful complement to tools such as First Principle Thinking, not a replacement.


Inversion is a simple habit with an outsized effect: by regularly asking what would make me fail and then avoiding it, I make fewer big mistakes and give the good decisions time to compound. As Jacobi put it, “invert, always invert“.



To learn more about scientific rational thinking, reasoning, epistemology and methods,
check out: Wise: How to Attain a Deep Understanding of the World, History, Our Place in It, and How to Live Well


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