About Me

When not at work with students, I spend my time in my room either reading, calculating something using pen and paper, or using a computer. I read almost anything: from the pornographic to the profound, although my main interests are mathematics and physics. "When I get a little money I buy books; and if any is left I buy food and clothes." -Erasmus

Tuesday, September 6, 2011

How textbooks shape researchers, and mislead students

I downloaded a copy of Kuhn's The Structure of Scientific Revolutions because I couldn't find my hard copy. Sometimes finding a particular book in my collection is a problem because of the number I actually own. I'm not even sure if it's in one of the boxes, or in one of the shelves, or hidden under the stairs.

I was looking for a statement he made on textbooks-- and how unusual a textbook  that discusses alternative theories is. Although I would like to discuss historical issues in the development of physics, I don't have enough time in the classroom to do so. I find such issues fascinating, and you can sometimes use the confusion of the ancients to understand how difficult some of the concepts can be.

One of the books that I like is Arnold Aron's The Development of Concepts in Physics, which is unfortunately out-of-print. (I have to rely on a photocopy so that I could read it.) It  actually owes a lot to Gerald Holton's book (in fact, large areas were taken from it and reprinted with permission), and it helps me understand why older scientific beliefs, such as Aristotelian physics and impetus took hold in medieval minds. Another example is its development of the Bohr model, which follows Bohr's seminal paper.

Textbooks mislead. Let's again take the Bohr model as an example. If you follow the development in Young and Freedman's University Physics, what will be given is quantization of angular momentum as a postulate. This is in fact a major reversal of Bohr's paper. What Bohr actually did was to argue, from the Rydberg formula, and then argues that energy must be quantized. After that, he derives as a consequence, the quantization of angular momentum.

There are more examples of such reversals, which I will not multiply. The point is that textbooks will not present the historical development because it is too confusing, and distracts from the purpose of the textbook-- to display the current paradigm, give examples or models that serve as pieces that the scientist builds on when doing what Kuhn calls normal science.

(An aside: if you read older textbooks in general relativity, and compare them to each other, you will see examples of how the paradigms changed within the study of general relativity. The main problems in relativity during the early days was the study of small effects-- the deflection of light being the main example. It was only in the 1960's when strong gravitational fields, in the sense of great distortions of spacetime geometry from global Minkowski space, replaced weak effects as the main application of general relativity, as found in textbooks. An example of a text where this transition was incompletely done is Weinberg's Gravitation and Cosmology. Bergmann's, Moller's and Pauli's texts would represent the older the generation of textbooks, while Misner, Thorne and Wheeler's Gravitation, Hawking and Ellis's The Large Scale Structure of Spacetime, would be representative of the post-1960's paradigm shift.  

Another shift that I see is in the textbooks of today, which emphasizes the physics-first approach. When I first learned general relativity, I used Schutz's A First Course in General Relativity, which follows the math-first approach. The way it was developed put black holes near the end of the book, and I suppose that it took much stamina to be able to reach that point.

I think that the ordering it uses shapes the research of the people who use it. For example, since it places black holes at the end, its discussion of alternative coordinate systems is brief. This means the technique of choosing appropriate coordinate systems is under-emphasized, and it seems unlikely that a terminal user of Schutz's book will develop that skill. Or the technique of using orthonormal basis vectors. Compare this with the recent textbooks, such as Hartle's Gravity, or Taylor and Wheeler's Exploring Black Holes where these techniques are much used to answer basic questions.

Textbooks shape the research of the people who read them. The questions researchers ask are based on their choice of textbook, and someone who learned relativity from Schutz will ask different questions compared to someone who learned relativity from Hartle. )  

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