One of the most exhilarating observations of physics and mathematics for me, comes from understanding the concept of nonlinearity. i.e. inputs don’t necessarily need to be proportionate to outputs. The understanding that in a non-linear system, increasing the “right inputs” are far more important than “increased average inputs”.
The notion of non-linearity is not a new observation, however what really fascinates me is the degree to which we don’t think in an non-linear fashion. The world around us is full of nonlinear relationships, however we tend to think and behave linearly. In a non-linear world doing the “right work” is what makes the difference. A nice truism that attests to this fact says “doing what is not important very well doesn’t make it important”.
I believe that the importance of understanding nonlinearity goes beyond our material success and up to the way we feel. One example that particularly makes me think about nonlinearity is the impostor syndrome. A lot of us have had accomplishments that we didn’t expect to have or we don’t feel we deserve. I believe that without understanding the concept of nonlinearity and the importance of the “right efforts” as opposed to “increased average effort”, we might experience the impostor syndrome in our accomplishments.