Yesterday I was explaining to my daughter the concept of things becoming smaller with distance. Some things become smaller in linear proportion, for example appearance. Others, like sound or light, become smaller as the inverse square of the distance. Which means that sounds get fainter very quickly as they move farther away.

Making the analogy to innovation: if the standard way of doing X is considered the point 0 in the axis, the farther away the innovation is from that point, the greater it has to be for the innovation to be taken up. This is because of the effort of moving: the farther the move, the more effort it requires. The innovation has to be perceived as considerably better to elicit a move.

I wonder if, for different arenas, these factors are sublinear, linear or exponential. In sublinear contexts, innovations should flow far more often and smoothly. In exponential contexts, innovations need to be overwhelmingly better, otherwise they will be ignored; but when they have a breakthrough, it’s revolutionary.

In any case, this distance from the center phenomenon is what injects antifragility in innovation. Overcoming the cost of moving from the center is what makes successful innovations so much better than what currently exists.

This argument completely ignores the possibility of trends and manias.