A machinist, who was also a skilled mechanic, was compelled by circumstances to quit his trade and to accept a position as janitor. One day the pipe leading from the sink to the sewer was clogged. The teacher, in conjunction with a carpenter, worked a long time to fix it, but in vain. The janitor was called, who in a few moments overcame the difficulty by the application of a principle in natural philosophy on which the teacher could have talked learnedly, although he knew not how to apply it in the given case. The janitor related how the foreman in a foundry was baffled in the effort to bore a hole through a piece of iron until a workman, trained under a foreign master, suggested the purchase of two things at a drug-store by means of which the hole was easily bored. When the druggist asked about the use that was to be made of these chemicals, he was told that the use was one of the mysteries of the machinist’s trade.

Next, the carpenter fixed the mortise lock of a door which needed attention, and the others lauded the skill with which he handled his tools and applied his knowledge. Before the three separated, the janitor’s son came with a word which he could not find in his lexicon. With the aid of chalk and black-board and grammar, the teacher showed how to dig out the roots of a Greek verb and what beautiful changes occur in its conjugation. The turn had come for the tradesmen to admire the mysterious skill and power of the teacher.

In applying the principle of natural philosophy, the janitor made skilful use of one or two tools which the teacher and the carpenter had never seen. He could express thought through the tools of his own handicraft, in ways that they could not. Each one of the three men knew the tools and the mysteries of his own vocation. During the entire scene there was not a logical flaw in the thinking of any one of them. Probably there was little difference in their native ability; certainly none in the fundamental nature of their thought-processes. The practical difference resulted from the data at their command and from the tools they were using to express the thoughts peculiar to their several vocations.

The power to use tools, instruments, and machinery lifts man above the brute creation. There is labor-saving machinery in thinking as well as in manual labor. The more perfect the tools with which we work the greater the results we can achieve without waste of effort. In thinking as well as in working we must use the best tools in order to attain the greatest facility and efficiency. Yonder are two wheat-fields. In one of them a giant is wielding the sickle of our forefathers; in the other a youth, not yet out of his teens, is at work. At the close of the day the work of the giant will not bear comparison with that of the lad, because the latter was sitting upon a self-binder. They had the same material to work upon, yet, in spite of his superior strength, the giant could not cope with his weaker though better-equipped competitor. In like manner, the youth who has mastered the algebraic equation, or the symbols and formulas of chemistry, is in many respects the superior of a much brighter man who is not in possession of these tools or instruments of thought. A boy of average capacity who goes through a good high school thereby acquires certain fundamental ideas and the accompanying instruments of thought by which he is enabled to solve problems entirely beyond the power of a much brighter boy who never studies beyond the grammar grade.

The instruments of thought are generally spoken of as symbols, whilst the materials of thought are the things for which the symbols stand. In thinking, the mind may employ the ideas which correspond to the things in the external world; or it may employ the symbols by which science indicates things that have been definitely fixed or quantified. Failure to distinguish the sign from the thing signified, the symbol from its reality, leads to confusion in thought and to the most disastrous results in mental development. Loss of appetite for knowledge must inevitably result from methods of teaching by which the pupil is expected to learn the sounds of the letters from their names, or musical sounds from the notation on the staff, or the ideas of number from the arabic notation, or a knowledge of flowers from the technical terms of a text-book, or a knowledge of chemical elements and substances from the definitions, descriptions, and formulas of a scientific treatise. The symbol is indispensable in advanced thinking; but to expect the learner to get the fundamental ideas of a science from words, symbols, and definitions is evidence that the teacher does not understand the nature of thinking. It may, therefore, be helpful to set forth clearly the important distinction between thinking in things and thinking in symbols; to point out their relative value in mental development; and to fix their place in a rational system of education.

II

THINKING IN THINGS AND IN SYMBOLS

The rote system, like other systems of its age, made more of forms and symbols than of the things symbolized. To repeat the words correctly was everything, to understand the meaning nothing; and thus the spirit was sacrificed to the letter.

HERBERT SPENCER.

Words are men’s daughters, but God’s sons are things.

JOHNSON.

For words are wise men’s counters,—they do but reckon by them,—but they are the money of fools.

HOBBES.

It is only by the help of language (or some other equivalent set of signs) that we can think in the strict sense of the word; that is to say, consider things under their general or common aspects.

SULLY.

II

THINKING IN THINGS AND IN SYMBOLS

Within half a mile of the Susquehanna River a teacher was asking the class, “Of what is the earth’s surface composed?” “Of land and water,” was the reply. In answer to a question by the superintendent concerning the earth’s surface, one boy declared that he had never seen the earth. He had been acquiring words without the corresponding ideas. Turning to another boy, this official said, “Will you please show me water?” With a gleam of satisfaction on his face, the lad raised his atlas, pointed to the blue coloring around the map of North America, and said, “That is water.” “Will you please drink it?” The expression on the faces of teacher and pupils indicated that all felt as if some one had committed a blunder. Where did the blunder lie? Had the teacher taught what should not be learned? Surely, every child should learn how water is indicated on a map. Did the boy use language wrong in idiom? By no means; for, as every student who has handled a lexicon well knows, many words have both a literal and a tropical, or figurative, meaning. If, pointing to an object, the teacher says, “This is a desk,” he uses the word is in its literal sense. On the other hand, if he points to a division on the map of the United States, and says, “This is Pennsylvania,” he does not mean that the colored surface to which he is pointing is the real State of Pennsylvania (if it were, a political boss could pocket it, and carry it the rest of his days without further trouble). What is meant is, that a given space on the map indicates or represents Pennsylvania, the word is being used, in the latter instance, in a figurative sense. Whether the word is, in the expression, “This is my body,” should be understood in a literal or in a figurative sense has been discussed for ages in the Christian church. In the answer of the boy we strike a distinction in thought that lies at the basis of good teaching in all grades of schools, from the kindergarten to the university,—namely, the distinction between thinking in things and thinking in symbols. In one sense of the word, all thinking is symbolic; for the percepts, concepts, and images of external objects which the mind employs in the thinking process are symbolic of the things for which they stand. But in advanced thinking, and especially in scientific investigations, objective symbols, such as words, signs, letters, equations, formulas, technical terms and expressions, are utilized to facilitate the thinking process. Take the age questions in mental arithmetic that have been prematurely inflicted upon so many pupils in the public schools. So long as the mind consciously carries A’s age and the wife’s age, using the clumsy instruments of arithmetical analysis, the thinking is difficult indeed. As soon as x is made the symbol of A’s age, and y the symbol of the wife’s age, so that the conditions of the problem can be thrown into algebraic equations, the difficulty vanishes. In the algebraic solution the mind drops all thought of A’s age and the wife’s age while manipulating the signs and symbols of the equation, and restores the meaning of the symbols only when their value in figures has been found. The algebraic solution is a genuine specimen of thinking in symbols, and illustrates the labor-saving machinery which the human mind employs, more or less, in all the most difficult scientific investigations.

What is a symbol? It is a mark, sign, or visible representation of an idea. The mathematician uses the symbol to represent quantities, operations, and relations. The chemist uses the symbol to indicate elements and their groupings or combinations. The theologian applies the term symbol to creeds and abstract statements of doctrine. The grips, countersigns, and passwords of a secret society may be spoken of as symbols of the ideas, aims, and principles of the organization. Often the symbol is chosen on account of some supposed resemblance between it and that for which it stands, as when black is made the symbol of mourning, white of purity, the oak of strength, and the sword of slaughter. “A symbol,” says Kate Douglass Wiggin, “may be considered to be a sensuous object which suggests an idea, or it may be defined as the sign or representation of something moral or intellectual by the images or properties of natural things, as we commonly say, for instance, that the lion is the symbol of courage, the dove the symbol of gentleness. It need not be an object any more than an action or an event, for the emerging of the butterfly from the chrysalis may be a symbol of the resurrection of the body, or the silver lining of the cloud typify the joy that shines through adversity.” Frequently the symbol is chosen arbitrarily, or because it is the first letter of the word which denotes the quality, substance, thing, or idea for which the symbol stands. Generally the symbol is a visible representation, but it may also address the other senses, notably the ear and the sense of touch. The Standard Dictionary excludes the portrait from the extent or scope of the symbol, and confines it to the representation of that which is not capable of portraiture, as an idea, state, quality, or action. It is well to bear this limitation in mind during the present discussion.