Darwin mentioned his concept of natural selection without mathematics at all, but it can describe why mathematics works for us. It has always seemed to me that evolutionary methods should choose for living forms that reply to nature’s real simplicities. Of course, it is difficult to know in common just what simple styles the universe has. In a sense, they may be like Plato’s ideal types, the geometrical designs such as the group and polygons. Apparently, we see their subjective perfection with our mind’s eye, but the real world only roughly understands them. Considering further in like fashion, we can sense easy, stylish ways to see dynamical systems. Here is why that matters.
Imagine a primate ancestor who saw the journey of a rock, tossed after fleeing prey, as a complex matter, difficult to estimate. It could try a tracking technique using rocks or even warrior spears, but with restricted success, because complex shapes are confusing. A relative who saw in the stone’s journey an easy and elegant parabola would have a better possibility of forecasting where it would drop. The cousin would eat more often and presumably recreate more as well. Sensory cabling could strengthen these actions by creating a feeling of authentic satisfaction at the vision of an artistic parabola.
There’s a further choice at work, too. To hit running prey, it’s no good to think about the issue for long. Rate forced selection: that primate had to see the beauty fast. This forced intellectual capabilities all the harder, plus, the satisfaction of a full tummy. We come down from that grateful cousin. Baseball outfielders learn to sense a ball’s diversions from its parabolic descent, due to air pressure and wind, because they are building on psychological handling equipment perfectly updated to the parabola issue. Other appreciations of natural geometrical ordering could appear from tracking techniques on smooth flatlands, from the brilliant design of simple resources, and the like. We all discuss an admiration for the appeal of convenience, a feeling growing from our roots. Simplicity is evolution’s way of saying, this works. Mathematics is simplicity at its finest.