How To Read A Book- A Classic Guide to Intelligent Reading - Mortimer J. Adler, Charles Van Doren [125]
Handl i ng the Mathematics in Scientific Books This digression on Euclid has led us a little out of our way. We were observing that the presence of mathematics in scientific books is one of the main obstacles to reading them.
There are a couple of things to say about that.
First, you can probably read at least elementary mathematics better than you think. We have already suggested that you should begin with Euclid, and we are confident that if you spent several evenings with the Elements you would overcome much of your fear of the subject. Having done some work on How to Read Science and Mathematics 265
Euclid, you might proceed to glance at the works of other classical Greek mathematicians-Archimedes, Apollonius, Nicomachus. They are not really very difficult, and besides, you can skip.
That leads to the second point we want to make. If your intention is to read a mathematical book in and for itself, you must read it, of course, from beginning to end-and with a pencil in your hand, for writing in the margins and even on a scratch pad is more necessary here than in the case of any other kinds of books. But your intention may not be that, but instead to read a scientific work that has mathematics in it. In this case, skipping is often the better part of valor.
Take Newton's Principia for an example. The book contains many propositions, both construction problems and theorems, but it is not necessary to read all of them in detail, especially the first time through. Read the statement of the proposition, and glance down the proof to get an idea of how it is done; read the statements of the so-called lemmas and corollaries; and read the so-called scholiums, which are essentially discussions of the relations between propositions and of their relations to the work as a whole. You will begin to see that whole if you do this, and so to discover how the system that Newton is constructing is built-what comes first and what second, and how the parts fit together. Go through the whole work in this way, avoiding the diagrams if they trouble you ( as they do many readers ), merely glancing at much of the interstitial matter, but being sure to find and read the passages where Newton is making his main points. One of these comes at the very end of the work, at the close of Book III, which is titled "The System of the World." This General Scholium, as Newton called it, not only sums up what has gone before but also states the great problem of almost all subsequent physics.
Newton's Optics is another scientific classic that you might want to try to read. There is actually very little mathematics in it, although at first glance that does not appear to be · so because the pages are sprinkled with diagrams. But these dia-266 HOW TO READ A BOOK
grams are merely illustrations describing Newton's experiments with holes for the sun to shine through into a dark room, with prisms to intercept the sunbeam, and with pieces of white paper placed so that the various colors of the beam can shine on them. You can quite easily repeat some of these experiments yourself, and this is fun to do, for the colors are beautiful, and the descriptions are eminently clear. You will want to read, in addition to the desc.riptions of the experiments, the statements of the various theorems or propositions, and the discussions that occur at the end of each of the three Books, where Newton sums up his discoveries and suggests their consequences. The end of Book Ill is famous, for it contains some statements by Newton about the scientific enterprise itself that are