Sunday, March 28, 2010

A hierarchy of concepts

Richard Feynman, in his Lectures on Physics, had a habit of discussing both the philosophical and practical issues of the science that he taught. One such issue was on the idea that waves could possess particle-like properties, such as momentum and position. As he notes in his Lectures, Vol. 3,

"Only measurable quantities are important to physics. This is false. We need to extend current concepts to unknown areas and then test these concepts. It was not wrong for classical physicists to extend their ideas of momentum and position to quantum particles. They were doing real science, so long as they then checked their assumptions."

What I believe is of value in this statement is the idea that understanding new phenomena is achieved by applying concepts from already well-understood processes and things. So what if a wave didn't traditionally possess momentum or a position? These two concepts (waves and particles) could at least be used to further our understanding of quantum entities, which possess both wave and particle-like properties but do not act entirely like one or the other of these classical constructs.

The same idea I think can be applied in teaching. First find a concept that students are familiar with, then show how this concept can be extended to describe a new phenomenon. However, to be self-consistent and complete, a discussion of how the concept fails to completely describe the phenomenon is required as well. Momentum and position obviously can't describe quantum interference of particles. In this manner, a knowledge of the world is built up of a patchwork of prior understanding.

I found this statement particularly enlightening:
"When a data set is mutilated (or, to use the common euphemism, ‘filtered’) by processing according to false assumptions, important information in it may be destroyed irreversibly. As some have recognized, this is happening constantly from orthodox methods of detrending or seasonal adjustment in econometrics. However, old data sets, if preserved unmutilated by old assumptions, may have a new lease on life when our prior information advances."