Inversion is great thinking tool which allows one, while thinking backwards, to come up with new perspectives to a problem. Consider the problem of losing weight, forward thinking would be: join a gym, run everyday, take up cycling etc. But using inversion we can start with a question: What can I do to increase my weight? The answer to this, essentially allows you to see the blockage to your final solution, and if you think about the blockage you will come up with new solutions to the problem, which in this case can be: have a healthy diet plan, avoid sitting long hours and take brisk walks etc.
John Kaufman, from his book The First 20 hours describes the inversion concept beautifully
By studying the opposite of what you want, you can identify important elements that aren’t immediately obvious. Take white-water kayaking. What would I need to know if I wanted to be able to kayak in a large, fast-moving, rock-strewn river?
Here’s the inversion: What would it look like if everything went wrong?
- I’d flip upside down underwater, and not be able to get back up.
- I’d flood my kayak, causing it to sink or swamp, resulting in a total loss of the kayak.
- I’d hit my head on a rock.
- I’d lose my paddle, eliminating my maneuverability.
- I’d eject from my kayak, get stuck in a hydraulic (a point in the river where the river flows back on itself, creating a loop like a washing machine) and not be able to get out.
If I managed to do all of these things at once in the middle of a raging river, I’d probably die — the worst-case scenario. This depressing line of thought is useful because it points to a few white-water kayaking skills that are probably very important:
- Learning to roll the kayak right side up if it flips, without ejecting.
- Learning how to prevent swamping the kayak if ejecting is necessary.
- Learning how to avoid losing my paddle in rough water.
- Learning and using safety precautions when rafting around large rocks.
- Scouting the river before the run to avoid dangerous river features entirely.
Inversion in mathematics
Carol Jacobi, 19th century mathematician, used to use inversion all the time. When faced with difficult axioms to prove, he might instead assume a property of the axiom was correct and then try to determine the consequences of this assumption. From that point, he could work out surprising, and at times counterintuitive, insights. His motto was: ‘Invert, always invert’
