Math and Occam’s Razor
In discussion with Ben about Zen and the Art of Motorcycle Maintenance, I concluded that the success of mathematical elegance in solutions is a physical manifestation of Occam’s Razor. Indeed, mathematical elegance is to be held above normal logic.
As an illustration of my point consider Quantum Mech. The math at that time was new and revolutionary. Not only was it elegant, but it actually predicted measurable results that other, more established theories could not. QM won out, and its math reshaped the logic through which we view the world.
Further, look at the Copernican model of the Solar System. It was more elegant than the epicycle system, and so was readily adopted. Again, this resulted in a paradigm shift of our world view.
A cumbersome theory can only survive for a limited time. Pirsig’s suggestion that the Scientific Method is invalid because it neglects the infinite multitude of explainations is based on an incomplete view. Explainations are valued first by their predictive power, and secondly by their elegance. In searching for a mathematical model, elegance is Occam’s Razor that whittles the plethora of possible explanations. Furthermore, one must never confuse a model with the thing it describes. Reality is too complicated for complete explaination.