I find books about the history of science and particularly about the history of mathematics to be helpful to my teaching. The nineteenth century philosopher Herbert Spencer claimed that “If there be an order in which the human race has mastered its various kinds of knowledge, there will arise in every child an aptitude to acquire these kinds of knowledge in the same order.... Education is a repetition of civilization in little.” (Wikipedia) While I doubt that this is literally true, I have found that examining the long halting development of mathematical ideas by different cultures helps me understand the difficulty that students have in mastering them.
The first book from Steven Shapin’s list is The Measure of Reality: Quantification and Western Society, 1250 – 1600 by Alfred W. Crosby. This is one of those “big picture” books, like Guns, Germs and Steel that attempts (rather successfully) to explain the success of an entire civilization over a period of centuries.
The books’ argument is well described on the first page:
Western Europeans were among the first, if not the first, to invent mechanical clocks, geometrically precise maps, double-entry bookkeeping, exact algebraic and musical notations, and perspective painting. By the sixteenth century more people were thinking quantitatively in Western Europe than in any other part of the world. Thus, they became world leaders in science, technology, armaments, navigation, business practice, and bureaucracy, and created many of the greatest masterpieces of Western music and painting. [Emphasis added.]
The thesis of the book is contained in the word “thus”. That is, Crosby believes that the success of Western imperialism is due to the development of quantification. It would be pointless to argue whether this is true or not. Clearly, evidence can be found to either support or refute a thesis that is this broad. But what is fascinating to me are the examples that Crosby introduces, including a description of some of the high points of late medieval and renaissance culture: polyphony in music, perspective in art, the beginnings of modern physics and mathematics. I even gained an appreciation of the role of double-entry bookkeeping in enabling complex business arrangements.
What I found most interesting is trying to imagine the mentalité, or mind-set, of pre-quantitative people. How does one experience time, when one has never seen a clock? How does one picture a scene when viewing a picture of it that does not obey modern rules of perspective?
Despite its big picture, I found the most endearing feature of this book some of the details. For example, I have never realized that the invention of the staff to write music in the fourteenth century prefigured the Cartesian coordinate system. Note that the staff is a graph in which time is the horizontal axis and pitch the vertical. One wonders why it took centuries for the mathematicians to catch up.