Inversion is a mental model that helps us flip the problem and look at it backwards. Complex problems are difficult to figure out, so inverting helps us come up with new solutions.
For example, if you are trying to figure out ways to become more productive, you might invert the question and figure out all the things that are making you unproductive. The process of inversion helps look at the issue from a different perspective. Once you list all the things that are making you unproductive, you can start eliminating them one by one.
Tim Ferris used the process of inversion when embarking on difficult projects. In his Ted Talk, he talks about the process of fear setting, instead of goal setting. Before taking a leap on a project, Tim writes down all the ways the project might fail or how things might go wrong. He then takes each fear one by one and starts thinking about ways to mitigate or address them. By anticipating the failures, he is more prepared.
Inversion doesn't always help us solve to the problem but it helps us avoid trouble. By looking at the opposite of what we are trying to achieve, we figure out for things we need to avoid.
If you are trying to solve a difficult problem, try inverting and solving for the opposite.
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