Chapter 19 Chapter 17 How to Read Science and Math

The title of this chapter might mislead you.We are not going to give you advice about reading any kind of science or math.We limit ourselves to two forms of books: one, in our tradition, the great classics of science and mathematics.The other is modern popular science works.What we've said often applies to reading research papers on abstruse and specific topics, but we can't help you read them.There are two reasons, the first is very simple, we are not qualified to do so. The second is this: Until about the end of the nineteenth century, major scientific works were written for laymen.These writers—like Galileo, Newton, and Darwin—had no objection to being read by experts in their field, and, in fact, wished to reach such readers.But in that era, what Einstein called "the happy childhood of science," the institution of science majors had not yet been established.Intelligent and able readers read science as they read history or philosophy, with no gaps of difficulty, no speed, no insurmountable obstacles.Contemporary scientific writing makes no apparent attempt to ignore the general reader or the layman.But most modern scientific writing doesn't care about what a lay reader thinks, or even try to make it intelligible to such an reader.

Today, scientific papers have become something that experts write for experts.In the communication of a serious scientific topic, readers must also have relative professional knowledge. Usually, readers who are not in this field cannot read such articles at all.Such a tendency has the obvious advantage of making scientific progress more rapid.Experts exchange expertise with each other and quickly communicate with one another to get to the point—they quickly see where the problem lies and how to fix it.But the price to pay is also obvious.You—the average reader we're emphasizing in this book—wouldn't be able to read this kind of article.

In fact, this situation has also appeared in other fields, but the field of science is more serious.Today, philosophers no longer write for readers other than professional philosophers, economists only write for economists, and even historians have begun to write professional treatises.In the scientific world, it has long been a very important way for experts to communicate through professional papers. Compared with the traditional narrative writing method for all readers, this way is more convenient for mutual exchange of opinions. In such a situation, what should the average reader do?He cannot be an expert in any one field.He has to take a step back, which is to read popular science books.Some of them are good books and some of them are bad books.But we not only need to know the difference, the most important thing is to be able to achieve a full understanding when reading a good book.

※ Understand the industry of science The history of science is one of the fastest growing disciplines in the academic field.Over the past few years, we've seen the field change dramatically. It wasn't that long ago that "serious" scientists looked down on historians of science.In the past, historians of science were considered primarily historical because they were incapable of expanding the realm of true science.This attitude can be summed up by a famous quote from George Bernard Shaw: "He who can, do it. He who cannot, teach." Such attitudes are rarely described today.The Department of History of Science has become important, and eminent scientists study and write about the history of science.One example of this is Newton Industry.At present, many countries are doing intensive and massive research on Newton's theory and his unique personality.Six or seven related books have been published recently.The reason is that scientists care more about the science industry itself than before.

Therefore, we have no hesitation in recommending that you read at least some of the great scientific classics.In fact, you really have no excuse not to read a book like this.None of them are really difficult to read, and even Newton's Mathematical Principles of Natural Philosophy can be read if you really try hard. This is our most helpful advice for you.All you have to do is apply the rules of reading expository work and be very clear about the problem the author is trying to solve.This rule of analytical reading applies to any expository work, but especially to works of science and mathematics.

In other words, you are a layman, and you do not read the scientific classics to become an expert in a modern professional field.Instead, you read these books only to understand the history and philosophy of science.In fact, this is also a layman's due responsibility to science.Only when you notice what problem the great scientist is trying to solve—attention to the problem itself and the context of the problem—your responsibility ends. To keep up with the pace of scientific development, to find out the correlation between facts, assumptions, principles and evidence, is to participate in the activities of human reason, and that may be the most successful field of human beings.Perhaps, this alone can confirm the value of research on the history of science.In addition, such studies can go some way towards dispelling some of the fallacies of science.Above all, that is the mental activity that is fundamentally related to education, and from Socrates to us, has been regarded as the central goal, which is to release a free and open mind through the training of doubt.

※ Suggestions for reading scientific classics The so-called scientific works are research reports or conclusions written as a result of experiments or natural observations in a certain research field.The problem of describing science should always try to describe the correct phenomenon and find out the interactive relationship between different phenomena. Great scientific work, free from exaggeration or propaganda, despite the bias of the initial assumptions.You have to pay attention to the author's initial hypothesis, take it to heart, and then make a distinction between his hypothesis and the conclusion after the argument.A more "objective" scientific author will explicitly ask you to accept this and that assumption.The objectivity of science lies not in the absence of initial prejudices, but in the frank admission.

In scientific works, the main vocabulary is usually some unusual or technical terms.These terms are easy to find, and you can also find the main idea through these terms.The subject matter is usually very general.Science is not a chronicle. Scientists are just the opposite of historians. They want to get rid of the constraints of time and place.What he wanted to talk about were general phenomena, the general rules of how things change. There seem to be two main difficulties when reading scientific works.One is about discourse.Science is basically an induction method, and the basic discourse is a general rule established through research and verification—it may be a case created through experiments, or it may be a series of cases collected through long-term observation.There are other statements that use the deductive method to infer.Such a statement is inferred from other theories that have been proven.On the point of emphasizing evidence, science and philosophy are actually not very different.But induction is a characteristic of science.

The first difficulty arises because in order to understand an inductive argument in science, you have to understand the evidence that the scientist bases the theory on.Unfortunately, that's hard to do.You still know nothing but the book in your hand.If this book fails to inspire a person, the reader has only one solution, and that is to experience it for himself to gain the necessary special experience.He may have to see the experiment in action, or to observe the same experimental apparatus as mentioned in the operating book.He may also go to a museum to examine specimens and models. Anyone who wants to understand the history of science, in addition to reading classic works, should be able to do experiments by himself, so as to be familiar with the important experiments mentioned in the book.Classic experiments are just like classic works. If you can witness with your own eyes and do the experiments described by the great scientist, which is also the source of his inner insight, then you will have a deeper understanding of this classic scientific masterpiece. understand.

This is not to say that you have to complete all the experiments in order to start reading this book.In the case of Lavoisier's Elements of Chemistry, published in 1789, which is no longer considered a useful textbook in chemistry, a high school student who wants to pass Chemistry exam, and I will never be stupid to read this book.However, the method he proposed was still revolutionary at the time, and the chemical elements he conceived are largely still used today.So the point of reading this book is this: You don't have to read all the details to be inspired.For example, his preface emphasizes the importance of the scientific method, which is very enlightening.Lavoisier said:

Any branch of natural science consists of three parts: the successive facts in the subject of the science, the ideas in which those facts are presented, and the language in which those facts are expressed...for ideas are preserved and communicated by language, and if we cannot Improving science itself cannot promote the progress of scientific language.From another perspective, it is also impossible to improve the language or terminology of science without improving science itself.This is exactly what Lavoisier did.He advanced chemistry by improving the language of chemistry, just as Newton systematized and codified the language of physics a century ago to promote the progress of physics—in the process, you may recall, he developed the calculus study. The mention of calculus brings us to the second difficulty in reading scientific works, that of mathematics. ※ Facing math problems Many people are terrified of mathematics and think they are completely incapable of reading such a book.No one is sure why this is.Some psychologists see this as "Symbleblindness," the inability to let go of a reliance on entities to understand the controlled transformation of symbols.Maybe there's some truth to that, but the text also shifts, and how much is less controlled, and perhaps even harder to understand.Still others believe that the problem lies in the teaching of mathematics.If so, we can breathe a sigh of relief, because a lot of recent research has been devoted to how to teach mathematics well. Part of this is that no one told us, or didn't tell us sooner, so that we can understand that mathematics is actually a language, and we can learn it as we learn our own language.When we learn our own language, we learn it twice: the first time we learn how to speak it, and the second time we learn how to read it.Fortunately, mathematics only needs to be learned once, because it is entirely written language. We said earlier that learning a new written language involves basic reading.When we were first given reading instruction in elementary school, our problem was learning to recognize specific symbols that appeared on each page and remember the relationships between those symbols.Even those who later become masters of reading still need to read with basic reading once in a while.For example, when we see a word we don't know, we still have to look it up in the dictionary.If we are confused by the syntax of a sentence, we have to solve it at the basic level.Only when we solve these problems can our reading ability go to the next level. Since mathematics is a language, it has its own vocabulary, grammar and syntax (Syntax), beginners must learn these things.Specific symbols or relationships between symbols are noted.Because the language of mathematics is different from the language we usually use, the problems will be different, but in theory, it will not be difficult for us to learn English, French or German.In fact, from the level of basic reading, it may be a little simpler. Any language is a medium of communication through which people can understand each other about common themes.The general topic of everyday conversation is nothing more than about emotional matters or relationships.In fact, if it is two different people, they may not be able to fully communicate with each other on such a topic.But two different people, setting aside emotional topics, can jointly understand a third kind of event that has nothing to do with them, like an electric circuit, an isosceles triangle, or a syllogism.The reason is that when our topic involves emotions, it is difficult for us to read between the lines.Mathematics allows us to avoid such problems.As long as the mathematical consensus, themes and equations are properly used, there will be no problems with emotional overtones. In addition, no one told us, at least not earlier, how beautiful mathematics is and how satisfying a science of intelligence.If anyone is willing to take the trouble to read mathematics, it is never too late to appreciate the beauty of mathematics.You can start with Euclid, whose Principia is the clearest and most beautiful of all such works. Let us illustrate with the first five propositions of the first volume of "Principles of Geometry". (If you have this book handy, you should open it and read it.) There are two kinds of propositions in basic geometry: (1) Statements about construction problems. (2) Theorems concerning the relationship between geometric figures and their respective parts.The problem of drawing must be solved, and the problem of theorem must be proved.At the end of Euclid's construction problems, there will usually be the words QEF (Quod erat faciendum), which means "the drawing is finished", and at the end of theorems, you will see the words QED (Quod eratdemonstrandum), It means "The proof is complete,,. The first three propositions in the first volume of "Principles of Geometry" are all related to construction.why?One answer is that these graphs are used to prove theorems.We can't see it in the first four propositions, but we can see it in the fifth one, which is the part of the theorem.For example, the two base angles of an isosceles triangle (a triangle with two equal sides) are equal, which requires the use of "Proposition 3", the principle that a short line is taken from a long line.And "Proposition 3" is related to the drawing of "Proposition 2", and "Proposition 2" is related to the drawing of "Proposition 1", so in order to prove "Proposition 5", three pictures must be made first. We can also look at the problem of drawing from another purpose.Constructing is clearly similar to postulates, both claiming that geometric operations can be performed.In postulated cases, this possibility is assumed.In the case of propositions, that is to be proved.Of course, to prove this, we need to use postulates.So, for example, we might wonder whether there really is such a thing as an equilateral triangle as defined in "Definition 20".But we don't need to worry about the existence of these mathematical objects, at least we can see what "Proposition 1" says: Based on the assumption of these straight lines and circles, it can naturally lead to the existence of such things as equilateral triangles . Let's go back to "Proposition 5", the theorem about the same interior angle of an isosceles triangle.To reach this conclusion, many previous propositions and postulates are involved, and the proposition itself must be proved.So it can be seen that if one thing is true (that is, we have the hypothesis of an isosceles triangle), and if some other additional conditions are also true (definitions, postulates and other previous propositions), then another thing (that is, the conclusion) is also true.What the proposition emphasizes is the relationship of "if...then".What a proposition is to determine is not whether the hypothesis is true, nor whether the conclusion is true—except when the hypothesis is true.And unless the proposition is proven, we cannot confirm whether the relationship between the hypothesis and the conclusion is true.What the proposition proves is simply whether the relation is true.nothing else. Is it an exaggeration to say that such things are beautiful?We don't think so.What we are talking about here is only for a problem that is really limited in scope.Make a truly logical explanation.Among the qualities of clarity of explanation and limited scope of questions, there is a special appeal.In ordinary conversation, even very good philosophers cannot make things clear in this way.In philosophical problems, even using logical concepts, it is difficult to explain it clearly like this. Regarding the difference between the argument of "Proposition 5" listed above and the simplest syllogism, let us make some explanations.The so-called syllogism is: All animals are mortal; All men are animals; Therefore, all men are mortal. This inference does apply to some things, too.We can think of it as a mathematical inference.Suppose there are such things as animals and people, and suppose that animals are mortal.Then it can lead to the exact conclusion like the triangle mentioned above.But the problem here is that animals and people do exist, and we're assuming something in terms of something that actually exists.We must test our hypotheses in ways that are not mathematically necessary.Euclid's proposition does not worry about this.He didn't care whether there was such a thing as an isosceles triangle or not.What he said is that if there is an isosceles triangle, if it is defined in this way, it must be able to lead to the conclusion that the two base angles are the same.You really don't have to doubt it—never have to. ※ Master the mathematical problems in scientific works The topic of Euclid is already a bit off topic.What concerns us is that there is a fair amount of math in scientific writing, and that is a major dyslexia.There are a few things to say about this as follows. First, you can at least read some basic mathematics more clearly than you think.We've already suggested that you start with Euclid, and we're sure you'll be able to get over your fear of math in just a few evenings reading Principia Geometry.After reading Euclid, you can go further and look at the works of other classical Greek mathematics masters—Archimedes, Apollonius, Nicomachus.The books aren't really difficult, and you can skip and skim through them. This brings us to the second point we want to talk about.If you read mathematics with the intention of understanding mathematics itself, of course you will read mathematics from cover to cover—with a pen in your hand, and more than any other book, you will need to write some notes in the margins.But your intention may not be the case, but you just want to read a science book that includes mathematics, so it is smarter to skip and skim. Take Newton's "Mathematical Principles of Natural Philosophy" as an example. The book contains many propositions, including drawing problems and theorems.But you don't really have to read each of them carefully, especially if you're going through them for the first time.Look at the explanation of the theorem first, then look at the conclusion, and grasp how this is proved.Read the explanations of the lemmas and corollaries, and then the so-called scholiums (basically this discusses the relation between the proposition and the whole problem).In doing so, you'll see the whole book in its entirety, and you'll discover how Newton structured the system—what came first, and how the parts fit together.Read this book in this way, don't look at the diagrams if you find it difficult (many readers do this), just pick out the content that interests you, but make sure you don't miss the important points that Newton emphasized.One of the key points appears at the end of the third volume, the title is "Cosmic System", Newton called it a general marginal note, which not only summarizes the key points of the predecessors, but also proposes a great physics that almost all future generations will think about. question. Newton's Optics is another great science classic that you should try reading too.In fact, there is not much mathematics in the book, but you may not think so at first, because the book is full of diagrams.In fact, these charts are only used to illustrate Newton's experiment: let sunlight pass through a small hole, shoot into a dark room, intercept the light with a prism, put a piece of white paper under it, and you can see the various colors in the light. on the paper.You can easily repeat such an experiment yourself, and it is a lot of fun to do because the colors are beautiful and clearly drawn.Besides the description of the experiment, you will also want to read the notes on the various theorems or propositions, and the discussion at the end of each of the three volumes, where Newton summarizes his findings and points out their significance.The end of the third volume is especially famous, where Newton makes some remarks on the profession of science, which are well worth reading. Mathematics is often included in scientific works, mainly because of the precise, clear, and limited qualities of mathematics that we mentioned earlier.Sometimes you can read something, but you don't need to go deep into the field of mathematics, like Newton's book is an example.Odds are, even if math is terribly scary to you, no math at all can sometimes cause more trouble!For example, in Galileo's "Two New Sciences", which is a masterpiece of matter energy and motion, it is particularly difficult for modern readers because basically it is not a book of mathematics, but it is carried out in the form of dialogue.The form of dialogue is very suitable for stage or philosophical discussions by masters such as Plato, but not so suitable for scientific discussions.So it is actually very difficult to understand what Galileo was talking about.But if you try to read it, you will find him talking about some innovative ideas. Of course, not all scientific classics use mathematics, or must use mathematics.Like the Greek father of medicine, Hippocrates wrote without mathematics.You can easily read through this book and discover Hippocrates' view of medicine - the art of prevention is better than cure.Unfortunately, such an idea is out of fashion in modern times.William Harvey discussing the circulation of blood, or William Gilbert discussing magnetic fields, have nothing to do with mathematics.As long as you remember that your responsibility is not to become an expert on the subject, but to understand the relevant issues, reading will be much easier. ※ Important points about popular science books In one respect, we have nothing more to say about reading popular science books.By definition, these books—whether books or articles—are written for a broad audience, not just for specialists.So if you've read some of the great science classics, this type of popular book should be no problem for you.This is because these books, while relevant to science, have generally avoided two of the difficulties of reading an original scientific tome.First, they talk only a little about the relevant experiments (they only report the results of the experiments).Second, the content includes only a little math (unless it's a math-heavy bestseller). Popular science articles are usually easier to read than popular science books, but not always.Sometimes such articles are fine—like the monthly Scientific American or the more specialized weekly Science.Of course, no matter how good these publications are and how carefully and conscientiously their editors are, the problems discussed at the end of the previous chapter will still arise.When reading these articles, we are left to the journalists to filter the information for us.If they are good reporters, we are lucky.If not, we get nothing. Reading popular science books is definitely more difficult than reading story books.Even a three-page article about DNA with no lab report, no graphs, and no mathematical equations for the reader to calculate can be incomprehensible if you don't pay attention while reading it.Therefore, more initiative is required in reading this kind of work than in other books.To confirm the subject.To discover the relationship between the whole and the parts.To come to an agreement with the author.To find out the main idea and discussion.The book needs to be fully understood before the meaning can be assessed or measured.These rules should all be familiar to you by now.But it's more useful to use here. Essays are usually conveying information, and you don't need to think too much actively when you read them.All you have to do is to understand and understand what the author said, and most of the other cases don't need to spend too much effort.As for reading other excellent bestsellers like Whitehead's Introduction to Mathematics, Lincoln Barnett's The Universe and Dr. Einstein, Barry Commoner's Barry Commoner's "The Closing Circle" (The Closing Circle), etc., need more.This is especially true of Commoner's book, which deals with a subject—the environmental crisis—that is both interesting and important to us today.His writing is dense and demands constant attention.The whole book is a hint that the careful reader should not ignore.Although this is not a practical work, not the kind of work we talked about in chapter thirteen, the conclusions in the book have a major impact on our lives.The subject of the book—the environmental crisis—is about that.Environmental protection is our problem, and if there is a crisis, we have to pay attention.Even if the author doesn't say it -- and he does -- we're still in crisis.In the face of a crisis, there is (usually) a specific response, or a cessation of a response.So Commoner's book, although basically theoretical, has gone beyond theory and into the realm of practicality. This is not to say that Commoner's book is particularly important and that Whitehead's or Barnett's are not. After "The Universe and Dr. Einstein" was written, a theoretical book like this one written for general readers to study the history of the atom made everyone aware of the atomic bomb that was recently invented as the main representative, but not all. A serious crisis of physical nature.Therefore, theoretical books can bring practical results as well.Even if modern man does not pay attention to the looming atomic or nuclear war, there is still a practical need to read such books.For atomic or nuclear physics is the greatest achievement of our time, bringing us many wonderful promises, but also many great crises.A knowledgeable and caring reader should read as much as possible on this subject. In Whitehead's Mathematical Man, there is another important message that is a little different.Mathematics is one of the few great mysteries of the modern age.Perhaps, and the most indicative one, occupies the same place in our society as ancient religions did.If we want to understand the age in which we live, we should understand what mathematics is, how mathematicians use it, and how they think.Although Whitehead's work does not deal with this issue in depth, it has excellent insights into the principles of mathematics.If nothing else, this book will show the careful reader that mathematicians are not magicians but ordinary people.Such discoveries are especially important for a reader who wants to expand his field of thought and experience beyond the time and place.