Thursday, October 12, 2017

Introduce Concepts in Historical Order?

Let me confess: I have read very few scientific classics in the original.

I haven't read the Principia, the Origin of Species, or the Elements.

I had not even read Einstein's 1905 classic on Brownian motion, until a few years ago, even though half of my research is directly or indirectly animated by it.

Ever since I saw this amazing series on complex numbers, I have been wondering whether presenting the historical progression of ideas might be "better" than the standard textbook introduction. Here are some of my observations.

The historical approach (HA) is inherently interesting, because it is about ideas and the people behind them. Stories of humans exploring and pushing boundaries, regardless of domain, are fascinating. These stories often have imperfect people grappling with new ideas, getting confused by their implications, arguing back and forth, improving, and gradually perfecting them over centuries. This happened with classical mechanics, evolution, complex numbers, quantum mechanics, etc.

The standard approach (SA), on the other hand, steers away from messy pasts, leaps of intuition that came seemingly from nowhere, the entertaining bickering, and the trials and errors. It trims away the excess fat of distractions, consolidates different viewpoints, and presents a sanitized account of an idea. It is, without question, the quickest and cleanest way to learn a new concept. This is an extremely desirable feature in university courses, which have a mandate to "cover" a set of concepts, often in limited time.

Perhaps, a good practical compromise is to start with an example rooted in the historical approach to motivate the topic,  and transition to the standard textbook approach to teach the meat of the topic. It might be interesting to conclude once again with a historical perspective, perhaps mixed with a discussion of the current state of art and open questions.