Supplement 1WORDS AND IDEAS
The purpose of this book is to explain machines that think, without using technical words any more than necessary. This supplement is a digression. Its purposes are to consider how to explain in this way and to discuss the attempt made in this book to achieve simple explanation.
Words are the chief instruments we use for explaining. Of course, many other devices—pictures, numbers, charts, models, etc.—are also used; but words are the prime tools. We do most of our explaining with them.
Words, however, are not very good instruments. Like a stone arrow-head, a word is a clumsy weapon. In the first place, words mean different things on different occasions. The word “line,” for example, has more than fifty meanings listed in a big dictionary. How do we handle the puzzle of many meanings? As we grow older we gather experience and we develop a truly marvelous capacity to listen to a sentence and then fit the words together into a pattern that makes sense. Sometimes we notice the time lag while our brain hunts for the meaning of a word we have heard but not grasped. Then suddenly we guess the needed meaning, whereupon we grasp the meaning of the sentence as a whole in much the same way as the parts of a puzzle click into place when solved.
Another trouble with words is that often there is no good way to tell someone what a word means. Of course, if the word denotes a physical object, we can show several examples of the object and utter the word each time. In fact, several good illustrations of a word denoting a physical thing often tell most of its meaning. But the rest of its meaning we often do not learn for years, if ever. For instance, two people would more likely disagree than agree about what should becalled a “rock” and what should be called a “stone,” if we showed them two dozen examples.
In the case of words not denoting physical objects, like “and,” “heat,” “responsibility,” we are worse off. We cannot show something and say, “That is a ···.” The usual dictionary is of some help, but it has a tendency to tell us what some wordAmeans by using another wordB, and when we look up the other wordBwe find the wordAgiven as its meaning. Mainly, however, to determine the meanings of words, we gather experience: we soak up words in our brains and slowly establish their meanings. We seem to use an unconscious reasoning process: we notice how words are used together in patterns, and we conclude what they must mean. Clearly, then, words being clumsy instruments, the more experience we have had with a word, the more likely we are to be able to use it, work with it, and understand it. Therefore explanation should be based chiefly on words with which we have had the most experience. What words are these? They will be the well-known words. A great many of them will be short.
Now what is the set of all the words needed to explain simply a technical subject like machines that think? For we shall need more words than just the well-known and short ones. This question doubtless has many answers; but the answer used in this book was based on the following reasoning. In a book devoted to explanation, there will be a group of words (1) that are supposed to be known already or to be learned while reading, and (2) that are used as building blocks in later explanation and definitions. Suppose that we call these words thewords for explaining.There are at least three groups of such words:
Group 1.Words not specially defined that are so familiar that every reader will know all of them; for example, “is,” “much,” “tell.”Group 2.Words not specially defined that are familiar, but perhaps some reader may not know some of them; for example, “alternative,” “continuous,” “indicator.”Group 3.Words that are not familiar, that many readers are not expected to know, and that are specially defined and explained in the body of the book; for example, “abacus,” “trajectory,” “torque.”
Group 1.Words not specially defined that are so familiar that every reader will know all of them; for example, “is,” “much,” “tell.”
Group 2.Words not specially defined that are familiar, but perhaps some reader may not know some of them; for example, “alternative,” “continuous,” “indicator.”
Group 3.Words that are not familiar, that many readers are not expected to know, and that are specially defined and explained in the body of the book; for example, “abacus,” “trajectory,” “torque.”
In writing this book, it was not hard to keep track of the words in the third group. These words are now listed in the index, together with thepage where they are defined or explained. (The index, of course, also lists phrases that are specially defined.)
But what division should be made between the other two groups? A practical, easy, and conservative way to separate most words between the first and second groups seemed to be on the basis of number of syllables. All words of one syllable—if not specially defined—were put in Group 1. Also, if a word became two syllables only because of the addition of one of the endings “-es,” “-ed,” “-ing,” it was kept in Group 1, for these endings probably do not make a word any harder to understand. In addition, there were put into Group 1:
Of course, not all these words would be familiar to every reader (for example, “Maya”), but in the way they occur, they are usually not puzzling, for we can tell from the context just about what they must mean.
All remaining words for explaining—chiefly, words of two or more syllables and not specially defined—were put in Group 2 and were listed during the writing of this book. Many Group 2 words, of course, would be entirely familiar to every reader; but the list had several virtues. No hard words would suddenly be sprung like a trap. The same word would be used for the same idea. Every word of two or more syllables was continually checked: is it needed? can it be replaced by a shorter word? It is perhaps remarkable that there were fewer than 1800 different words allowed to stay in this list. This fact should be a comfort to a reader, as it was to the author.
Now there are more words in this book thanwords for explaining. So we shall do well to recognize:
Group 4.Words that do not need to be known or learned and that are not used in later explanation and definitions.
Group 4.Words that do not need to be known or learned and that are not used in later explanation and definitions.
These words occur in the book in such a way that understanding them, though helpful, is not essential. One subdivision of Group 4 are names that appear just once in the book, as a kind of side remark, for example, “a chemical, calledacetylcholine.” Such a name will also appear in the index, but it is not aword for explaining. Another subdivision of Group 4 are words occurring only in quotations. For example, in the quotation fromFrankensteinon page 198, a dozen words appear that occur nowhere else in the book, including “daemon,” “dissoluble,” “maw,” “satiate.” Clearly we would destroy the entire flavor of the quotation if we changed any of these words in any way. But only the general drift of the quotation is needed for understanding the book, and so these words are Group 4 words.
In this way the effort to achieve simple explanation in this book proceeded. But even supposing that we could reach the best set of words for explaining, there is more to be done. How do we go from simple explanation to understanding?
Understandingan idea is basically a standard process. First, we find the name of the idea, a word or phrase that identifies it. Then, we collect true statements about the idea. Finally, we practice using them. The more true statements we have gathered, and the more practice we have had in applying them, the more we understand the idea.
For example, do you understand zero? Here are some true statements about zero.
1. Zero is a number.2. It is the number that counts none or nothing.3. It is marked 0 in our usual numeral writing.4. The ancient Romans, however, had no numeral for it. Apparently, they did not think of zero as a number.5. 0 is what you get when you take away 17 from 17, or when you subtract any number from itself.6. If you add 0 to 23, you get 23; and if you add 0 to any number, you get that number unchanged.7. If you subtract 0 from 48, you get 48; and if you subtract 0 from any number, you get that number unchanged.8. If you multiply 0 by 71, you get 0; and if you multiply together 0 and any number, you get 0.9. Usually you are not allowed to divide by 0: that is against the rules of arithmetic.10. But if you do, and if you divide 12 by 0, for example—and there are times when this is not wrong—the result is calledinfinityand is marked∞, a sign that is like an 8 on its side.
1. Zero is a number.
2. It is the number that counts none or nothing.
3. It is marked 0 in our usual numeral writing.
4. The ancient Romans, however, had no numeral for it. Apparently, they did not think of zero as a number.
5. 0 is what you get when you take away 17 from 17, or when you subtract any number from itself.
6. If you add 0 to 23, you get 23; and if you add 0 to any number, you get that number unchanged.
7. If you subtract 0 from 48, you get 48; and if you subtract 0 from any number, you get that number unchanged.
8. If you multiply 0 by 71, you get 0; and if you multiply together 0 and any number, you get 0.
9. Usually you are not allowed to divide by 0: that is against the rules of arithmetic.
10. But if you do, and if you divide 12 by 0, for example—and there are times when this is not wrong—the result is calledinfinityand is marked∞, a sign that is like an 8 on its side.
This is not all the story of zero; it is one of the most important of numbers. But, if you know these statements about zero, and have had some practice in applying them, you have a goodunderstandingof zero. Incidentally, a mechanical brain knows all these statements about zero and a few more; they must be built into it.
For us to understand any idea, then, we pursue three aims:
We can do this about any idea. Therefore, we can understand any idea, and the degree of our understanding increases as the number of true statements mastered increases.
Perhaps this seems to be a rash claim. Of course, it may take a good deal of time to collect true statements about many ideas. In fact, a scientist may spend thirty years of his life trying to find out from experiment the truth or falsehood of one statement, though, when he has succeeded, the fact can be swiftly told to others. Also, we all vary in the speed, perseverance, skill, etc., with which we can collect true statements and apply them. Besides, some of us have not been taught well and have little faith in our ability to carry out this process: this is the greatest obstacle of all. But, there is in reality no idea in the field of existing science and knowledge which you or I cannot understand. The road to understanding lies clear before us.