How To Read A Book- A Classic Guide to Intelligent Reading - Mortimer J. Adler, Charles Van Doren [123]
This was exactly what Lavoisier did. He improved chemistry by improving its language, just as Newton, a century before, had improved physics by systematizing and ordering its language-in the process, as you may recall, developing the differential and integral calculus.
Mention of the calculus leads us to consider the second main difficulty in reading scientific books. And that is the problem of mathematics.
Facing the Problem of Mathematics
Many people are frightened of mathematics and think they cannot read it at all. No one is quite sure why this is so.
Some psychologists think there is such a thing as "symbol blindness"-the inability to set aside one's dependence on the concrete and to follow the controlled shifting of symbols. There may be something to this, except, of course, that words shift, too, and their shifts, being more or less uncontrolled, are perhaps even more difficult to follow. Others believe that the How to Read Science and Mathematics 261
trouble lies in the teaching of mathematics. If so, we can be gratified that much recent research has been devoted to the question of how to teach it better.
The problem is partly this. We are not told, or not told early enough so that it sinks in, that mathematics is a language, and that we can learn it like any other, including our own. We have to learn our own language twice, first when we learn to speak it, second when we learn to read it. Fortunately, mathematics has to be learned only once, since it is almost wholly a written language.
As we have already observed, learning a new written language always involves us in problems of elementary reading.
When we underwent our initial reading instruction in elementary school, our problem was to learn to recognize certain arbitrary symbols when they appeared on a page, and to memorize certain relations among these symbols. Even the best readers continue to read, at least occasionally, at the elementary level: for example, whenever we come upon a word that we do not know and have to look up in the dictionary. If we are puzzled by the syntax of a sentence, we are also working at the elementary level. Only when we have solved these problems can we go on to read at higher levels.
Since mathematics is a language, it has its own vocabulary, grammar, and syntax, and these have to be learned by the beginning reader. Certain symbols and relationships between symbols have to be memorized. The problem is different, because the language is different, but it is no more difficult, theoretically, than learning to read English or French or German. At the elementary level, in fact, it may even be easier.
Any language is a medium of communication among men on subjects that the communicants can mutually comprehend.
The subjects of ordinary discourse are mainly emotional facts and relations. Such subjects are not entirely comprehensible by any two different persons. But two different persons can comprehend a third thing that is outside of and emotionally separated from both of them, such as an electrical circuit, an 262 HOW TO READ A BOOK
isosceles triangle, or a syllogism. It is mainly when we invest these things with emotional connotations that we have trouble understanding them. Mathematics allows us to avoid this.
There are no emotional connotations of mathematical terms, propositions, and equations when these are properly used.
We are also not told, at least not early enough, how beautiful and how intellectually satisfying mathematics can be. It is probably not too late for anyone to see this if he will go to a little trouble. You might start with Euclid, whose Elements of Geometry is one of the most lucid and beautiful works of any kind that has ever been written.
Let us consider, for example, the first five propositions in Book I of the Elements. ( If a copy of the book is available, you should look at it. ) Propositions