Chapter 17 How to Read Science and Mathematics
This chapter discusses the reading of two primary types of books – the great classics of the science and mathematics traditions, and the modern popular science titles we see today.
Discuss how the major scientific books written before the end of the nineteenth century compare to modern scientific writing. (p. 249 – 250)
The major scientific books prior to the end of the nineteenth century were written for a lay audience. While specialists in their particular fields could read them, there was not an institutionalized specialization so much, so that well read persons tended to read scientific as well as history and philosophy books.
Adler and Van Doren mention that most modern scientists do not seem to care what lay readers think, and so tend to write for those in their respective fields. He extended this assessment to other fields as well. These modern writings are what we find in scientific journals and are not written with laypersons in mind.
The first rule of analytical reading – state as clearly as you can the problem that the author has tried to solve – is particularly relevant in the fields of science and mathematics. When reading classical scientific books – how can you carry out this first rule? (p. 251)
When we read classical scientific books, we are not reading to necessarily become knowledgeable in their subject matter, but rather to understand the history and philosophy of science. When reading, the reader should be aware of the the problems the scientists were trying to solve and the background of those problems. The reader is following the strands of scientific development and subsequently the activity of human reason. Reading classical scientific works will also serve to dispel to some degree the apparent unintelligibility of science.
What suggestions do the authors offer for the reading of classical scientific books? (p. 252 – 253)
Understanding what biases – in the form of initial presuppositions – the authors are working from, can involve distinguishing what the author assumes from what is established by their argument. The more objective scientific author will make clear what initial biases exist in their work.
The leading terms in scientific works are usually including uncommon or technical words, and can make identifying the author’s propositions easier to spot. Propositions tend to be general.
It is important to understand the difference between inductive and deductive arguments, and which are more often seen in scientific writing. Science arguments are primarily inductive, meaning that the primary arguments are those that establish a general proposition by referencing observable evidence, experimental data or investigations. Deductive arguments are those in which the proposition is proven by other established propositions. Adler points out that inductive argument is what is frequently observed in scientific writing.
Note – This is a key part of the scientific method – Inductive reasoning moves from specific observations to broader generalizations or theories, while deductive reasoning starts with general principles and applies them to specific situations to make predictions.
The authors discuss the difficulty that arises when trying to understand the inductive arguments in scientific works – meaning understanding the experimental work that has been done. Readers may need to go beyond what is available in the book, looking at hands-on demonstrations, museums for specimens or models.
Understanding the history of science requires the reader to become acquainted with the crucial experiments performed in that history. Scientific classics become better understood when the reader is able to see and understand the classical experiments that were instrumental.
In the absence of observing the experimental work done that has lead to scientific writing, much can still be gained. This is also true for scientific methods that are so dated so as to be unhelpful. These works can still be read and used to glean some understanding of the scientific reasoning of the time.
Why do the authors suppose that many people are afraid of mathematics, and what are some practical suggestions to make more intelligible? (p. 254 – 255, 258 – 260)
One possibility the authors mention is “symbol blindness” what psychologist describe as an inability to set aside the dependence on the concrete and follow shifting symbols, meaning that reading numbers and symbols in the text can be difficult for some readers to follow and understand.*
Additionally, readers are not always aware that mathematics is a language, and so learning to understand also involves the same stages in learning that readers go through. Elementary reading, such as learning to recognize symbols and words, syntax, grammar, relationships, etc. have an equivalent in learning mathematics. Math involves cumulative learning and prerequisites, just as any other language.
Adler and Van Doren propose an active approach: read with pencil in hand, restate every definition, work a simple example for each new concept, fill in skipped algebraic steps, and test understanding by reproducing a proof outline without looking. The progression is definitions, then propositions, then examples, then exercises. Mastery grows by doing, not by passive reading.
Practical suggestions on reading mathematics depends on what the reader hopes to get out of the book. If the intention is to read the mathematics book in and for itself (meaning the mathematics is what you are interested in specifically), plan to read the entire book, and with a pencil in hand to write notes in a notepad on in the margins.
If the reader’s intentions are to read a scientific book that happens to have mathematics, the authors state “ skipping is often the better part of valor.” Meaning, of course, that it is not always necessary to read through propositions, construction problems and theorems in detail. Reading statements and discussions but do not get overwhelmed in reading the mathematics – often the reader can gain understanding about the concepts without fully grasping the mathematics shown.
*Symbol blindness is also known as dyscalculia, which is a learning disability that affects the ability to understand and work with numbers and symbols, making it difficult to read, recognize, and differentiate them.
How do popular science books compare to classical science books, and what should the reader keep in mind about them being “easier” to read? (p. 260 – 262)
Science popularizations – also known as popular science or “pop sci” – are books and articles written for a wide audience, not specialists in the field. Two things that make popular science easier for lay readers are relatively few descriptions of experiments (focusing more on reporting results than the details of experiments) and relatively little mathematics (with the exception being popular books on mathematics).
While popular science books are easier to read than modern scientific writing (journals articles) and classical science books, popular science still requires active reading, more so than perhaps other types of reading.
** Note – assume much of the content following each discussion question is a paraphrase and comes from the book How to Read a Book.
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