Invert, always invert. - Carl Gustav Jacob Jacobi
Invert, always invert. This simple mental model can make hard problems easier to solve.
The essence of inverting is to flip a problem on its head. Instead of solving for X, solve for the opposite of X. By inverting the problem, the solution path often becomes clearer.
Why Does Invert Work?
Many systems in life are multiplicative. Small actions compound, leading to outsized results over time. Invert exposes the weak points in these systems.
For example, Charlie Munger applied invert to tackle a national development problem. When asked how to aid India’s development, Munger inverted the question. Instead of “how can I help India”, he asked “what is doing the worst damage in India?” This inversion revealed more potent points of intervention.
Invert transforms a pursuit of “goods” into an avoidance of “bads”. Multiplicative systems mean avoiding negatives has an outsized effect. Hence, inversion provides leverage.
Invert Unlocks Creativity
Claude Shannon, the father of information theory, frequently used inversion to solve problems. When stuck on a difficult mathematical proof, he would invert the givens and requirements. By flipping the problem around, the path to solution became clear.
Shannon found inversion helped break mental ruts. By viewing the problem from another angle, he sparked new creative insights.
Invert Powered a Chess Legend
How did chess grandmasters become elite players? They mastered the end game.
The end game is much simpler, with just a few pieces left. Grandmasters study end games deeply. When playing, they invert thinking from the current board to the end game possibilities. This inversion allows them to see many moves ahead.
Pre-Mortem: Invert to Avoid Disaster
A “pre-mortem” prevents disasters before they occur. When planning a major decision, imagine that the decision was already made and it resulted in failure. Then invert by asking: what caused the failure?
This inversion highlights risks not yet considered, allowing you to reduce chances of catastrophe.
Problem Solving with Invert
Invert is powerful for daily problem solving:
- Define your goal
- Invert it to find your non-goal
- Determine what causes the non-goal
- Invert again to avoid those causes
For example, if your goal is losing weight, invert it to not gaining weight. Overeating is a top cause of gaining weight. So, focus your efforts on strategies to prevent overeating.
When to Use Invert
Invert shines when solving:
- Complex multiplicative systems - it exposes break points
- Creative blocks - it provides an alternate viewpoint
- Difficult goals - it frames them as avoiding negatives
- Risk mitigation - it uncovers failure modes
By inverting, hard problems transform into easy ones. Like turning an equation upside down to simplify the solution.
So remember, when stuck on a hard problem, try inverting it. By flipping the problem on its head, the path forward often comes into view.