Saturday, March 23, 2013
Organizing a Complex Argument So It Makes Sense and Seems Natural
The first chapter of Doing Physics, 1992, analogizes the work that walls, particles, and fields do to create the physical world, to the organization of a factory with its division of labor. Industrial engineers and physicists try to discern an organization that is efficient, divides the labor appropriately, etc. There may be many ways of organizing the production process, but only some work well. There are physical theories that only have particles or only fields, theories that are equally accurate, but it is often better to divide up the work so that the theory is easier to grasp and employ. By the way, don't take this to mean that theories are arbitrary. Rather, only some theoretical structures give you ways of thinking that are illuminating, even if you could calculate your answer in any one of the theoretical structures. In my Constitutions of Matter, 1996, and Doing Mathematics, 2003, I look at various ways of proving something or solving a problem, and show how each way illuminates something rather different, AND there is good reason to believe that the different ways of viewing can be connected more generically. It's one thing to show one theory is equivalent to another, but it is much more to show how each theoretical mode looks at the same thing but from different viewpoints, and those viewpoints are connected: you had better get the same result of a calculation, but it is even better to know why such disparate ways of thinking get hold of the same thing. This is the standard theme of phenomenology: a panoply of views of the same thing--how can it accommodate those various views.