Two hundred years ago German mathematician Carl Gustav Jacob Jacobi said (or so the world is told): “Man muss immer umkehren.” — “Invert, always invert.” Devising the solution to a mathematical problem, Carl applied the method of inversion to the challenge at hand.
Inversion is a handy concept which has implications far beyond the world of mathematical theorems and numbers: When thinking about a problem, taking the inverse (opposite) perspective regularly unlocks new approaches, strategies and solutions.
Want to eat healthier? One approach is to put more vegetables on your plate. Apply inversion to the problem and you end up reducing the amount of unhealthy things you might eat. Same goal, different approach. Combining both will yield better results.
Investing money with a goal to make more money? Of course. But the inverse is something good money managers also take into account: Invest money from a perspective of not losing money. A good portfolio approach takes and applies both perspectives.
The next time you think about innovation (or, gasp!, disruption) I suggest you apply a healthy dose of Carl’s wisdom and invert the problem you are working on: In addition to only looking at the new-new, ask yourself what can be made better of the old.
Inverting regularly yields surprising insights, and at the very least will give you a much more holistic view of the challenge at hand.
Invert, always invert.