V
THE INSTRUMENTS OF THOUGHT

Of the people who, though inheriting a rich vernacular like the English, spend their lives in the routine of a farm, a trade, or a store, very few have an adequate conception of the labor-saving instruments and appliances which modern civilization places at the disposal of the thinker. The machinery by which one man does as much as a thousand hands formerly did is not a whit more wonderful than the modern appliances for reaching results in the domain of thought. Reference might be made to the machines for adding used in counting-houses, to the tables of interest used by bankers, to the tables of logarithms by which it is as easy to find the one-hundredth power as the square of a number. The last named have, so to speak, multiplied the lives of astronomers by enabling them to make in a short time calculations that formerly occupied months, and even years. It is not necessary to discuss these; their value is apparent at a glance. But the value of a rich vocabulary, the function of the symbols and formulas of chemistry, physics, mathematics, and other sciences, and the advantages derived from the use of the technical terms peculiar to every domain of thought are not so easily seen. The teacher who fails at the right time to put the pupils in possession of these instruments of thought cripples their thinking, wastes their time and effort, and seriously mars their progress. Hence it is worth while to devote a chapter or two to the consideration of instruments of thought, for the purpose of showing how, by means of them, thinking is made easier and more effective. Let some one write the amounts in a ledger column by the Roman notation, then endeavor to add them without using any figures of the Arabic notation, either in his mind or in any other way, and he will soon realize what a labor-saving device our ten digits are. Then let him face the problem of squaring the circle as it confronted Archimedes, using the obvious truth that the perimeter of an inscribed polygon is less, while the perimeter of the circumscribed polygon is greater than the circumference of the circle, and long before his calculations reach the regular polygon of ninety-six sides (which is as far as Archimedes carried it), he will realize how the great Syracusan was hampered by the lack of the arithmetical notation now in use. Next, supposing himself in possession of the Arabic method of notation, let him conceive the labor of Rudolph von Ceulen, who, before logarithms were known, computed the ratio of the circumference to the diameter to thirty-five decimal places,—an achievement considered so great that the result was inscribed upon his tombstone,—and then, turning to the calculus, let him examine the formulas by which Clausen and Dase, of Germany, computing independently of each other, carried out the value to two hundred decimal places, their results agreeing to the last figure; this will give him a conception of the superior instruments of thought invented by those who developed the calculus. His idea of the labor-saving devices introduced by the calculus will be heightened still more on learning that Mr. Shanks, of Durham, England, carried the calculation to six hundred and seven decimal places,—a result so nearly accurate that if it were correctly used in calculating the circumference of the visible universe, the possible error would be inappreciable in the most powerful microscope. On further learning that in 1882 Lindeman, of KÖnigsberg, rigorously proved this ratio, commonly represented by the symbol p, to be incapable of representation as the root of any algebraic equation whatever with rational coefficients, he will not only refrain from joining the common herd of squarers of the circle, but no further argument will be needed to show the nature and value of the labor-saving devices introduced into the domain of thought by modern mathematics.

Since it is unreasonable to expect that every reader shall be familiar with higher mathematics, the duty of using simpler illustrations cannot be evaded. Fortunately for the purpose in hand, the book of experience furnishes these with an abundance that is almost bewildering.

A professor of chemistry was lecturing to an audience of teachers on agriculture. When he began to write upon the black-board they smiled at his spelling. Iron he wrote Fe. Water he spelled H2O. They soon saw that he was using the instruments of thought furnished by a science with which, unfortunately, few of them were familiar. He had found that the use of these chemical symbols made his thinking as much superior to that of the ordinary man as the work of the youth upon a self-binder is superior to that of the giant working with no better instrument than the sickle of our forefathers.

The school furnishes numerous examples to illustrate this point. When the teachers of a well-known city began the use of objects to impart the ideas of number and of the fundamental rules in arithmetic, the interest of the pupils and their facility in calculation grew wonderfully. The teaching was in accordance with the laws of mental growth. For fear the pupils would manipulate the Arabic figures without corresponding ideas, collections and equal parts of objects were drawn upon the slate to illustrate addition and subtraction of integers and fractions. The plan was followed for years and carried upward through the grades. Finally the pupils were examined for admission into the high school. A problem involving the four fundamental rules in combinations which could not be illustrated by pictures of objects, or the objects themselves, was set for solution. Out of fifty-nine applicants, only ten succeeded in giving the correct answer. The same kind of problem was given three times by three different persons, and with practically the same outcome. The teachers realized that they had kept up for too long a time the thinking in things, instead of drilling the pupils upon the process of thinking in the symbols of the Arabic notation. It is, of course, possible to think number without using the Arabic digits. The Romans did so by means of their counting-boards, and the Chinese do so by devices of their own. The characters which were brought into Western Europe through Arabic influences are derived, according to Max Mueller, from the first letters of the Sanskrit words for the first ten numerals. Their use facilitated calculation to such an extent that arithmetic gradually ceased to be the prerogative of slaves and ecclesiastics; its operations began to be understood by freemen and by the nobility. If children are denied the use of objects in their early lessons in number, they resort to counting on their fingers. If they are not led from this thinking on their fingers to thinking in figures, they will never become expert in arithmetic. Sometimes the fingers no longer move, but the mind conceives pictures of the hand, and the mind’s eye runs along the fingers of hands not visible to the corporeal eye. It is equally bad if the pupils never think number except by mental pictures of blocks, sticks, balls, and the like. When the pupil sees 7 × 9, he should not conceive seven heaps of nine shoe-pegs each, and then a rearrangement into six groups of ten shoe-pegs, and three stray ones alongside of these groups; but instantaneously the symbols 7 × 9 should suggest, with unerring accuracy, the result,—63.

In the schools of another district the principal proposed concrete work in fractions. The teachers and pupils began to divide things into halves, and thirds, and fourths, and sixths. They added and subtracted by subdividing these into fractions that denoted equal parts of a unit. Whilst the charm of novelty still clung to the process, a stranger who visited the schools asked one of the teachers how the pupils and parents liked the change. “Everybody is delighted,” was the exclamation. A year later the same teacher was asked by the visitor, “How are you succeeding with your concrete work in fractions?” With a dejected air she replied, “We are disappointed with the results.” “Just as I expected,” exclaimed the visitor; “for you were making the children think on the level of barbarism, instead of teaching them to use the tools and labor-saving machinery of modern civilization.”

Still another incident, taken from actual life, will serve to throw light upon the subject under discussion. In the booming days of the iron industry a laborer had saved and put out at interest twelve hundred dollars. The rate was six per cent., and no interest had been paid for one year and four months. Unable to reckon interest with figures, the toiler asked the principal of the schools to tell him the amount of interest due. Next day he greeted the principal by asking, “Did you not make a mistake in your calculation?” The reply was, “In my hurry to avoid being late at school I may have made a mistake.” He found that the man was right, and curiosity led him to ask how the error had been detected. “I reckoned it,” said the man. This aroused still greater curiosity; for the principal knew that, beyond the ability to count, the man had no knowledge of arithmetic. By agreement they met on Saturday afternoon, so that the man might show his method of reckoning interest. At the appointed hour the man laid six pennies on the floor to denote a year’s interest on one dollar, and then laid two pennies alongside of these as the additional interest on a dollar for four months. The supply of pennies being exhausted, he made strokes with chalk, and proceeded to do this twelve hundred times, and then to count them for the purpose of ascertaining the interest. It was thinking in things with a vengeance. And yet the making of strokes with chalk was a step in symbolic representation, and shows the innate tendency of the human mind to use symbols in thinking.

Even the words used in counting are symbols. In fact, every word that signifies anything is a symbol used by the mind to indicate an idea more or less complex, as well as the thing or things or relation of things in the external world which corresponds to the idea. In advanced thinking the words denote ideas more and more complex as the problems grow in difficulty or involve more of the abstract and general concepts under which the mind classifies the objects of which it takes cognizance. This is more largely true of the words in a developed language than it is of a dialect with little or no literature. A reference to the writer’s early home will be pardoned in this connection. His father, a plain farmer in Eastern Pennsylvania, sent four sons through college and gave each of them a professional or university education. When they gather under the parental roof they use the dialect of their early days in discussing life on the farm and in rehearsing the funny experiences of their boyhood; but when they discuss a question in science or mathematics, in law, medicine, or theology, they drop the dialect of their boyhood and use the instruments of thought furnished by languages having a literature. Some one has facetiously said of one town in the Lehigh Valley that the people pray in seven languages and swear in eight. It is a witty statement of an actual fact. The Welshman can pray as well as swear in his native tongue. The Pennsylvania German can vent his feelings fully in his own dialect when he grows profane. As soon as he says his prayers he reverts to the language of the pulpit and of Luther’s Bible because he there finds the words which express the deepest wants and emotions of the human soul.

When Melanchthon prepared the Saxony school plan he insisted that pupils should read Latin, write Latin, and speak Latin to the exclusion of the mother tongue. If an educator of to-day should advocate this policy in the fatherland, he would be banished. Melanchthon, surnamed preceptor GermaniÆ, knew what he was about. He taught at a time when teachers of the humanities lamented that children were born in the homes of parents speaking German. He lectured at a time when Luther and his colleagues were visiting market-places to talk with the peasants for the purpose of gathering words and phrases by which the New Testament might be adequately rendered in the vernacular of the common people. A development extending over one hundred and fifty years was required before the lecturers at the universities found in it enough words and phrases to serve as instruments of thought for purposes of advanced investigation and ratiocination. So rich and flexible has the German become that Voss succeeded in translating Homer into German, using the same metre, the same number of lines, without adding to or subtracting from the ideas of the original. Schlegel’s translation of Shakespeare is equally famous and equally successful. Both of these masterpieces show how essential a rich vocabulary is in rendering or in reproducing the best thoughts of the best minds; they show the importance of linguistic development and linguistic teaching. For purposes of thought and culture a rich mother tongue is of untold advantage. It is a great blessing to be born and raised in a home presided over by a well-educated mother. It is an invaluable help to be trained in schools whose teachers speak and write the languages which have felt the touch of the genius of Shakespeare and of Goethe. Next to furnishing ideas or something to think about, the thing of most importance in teaching a pupil to think is to enrich his vocabulary, to train him in language. Dr. Whewell has well remarked that “language is the atmosphere in which thought lives, for there is hardly a subject we can think about without the aid of language. Consequently, without knowledge of the language of a science all thinking with regard to that science is impossible; for although we conceive the world by means of our senses, we comprehend it only in and through the form of language.” In this connection one cannot do better than listen to the conclusions of men who have attained eminence as scholars, thinkers, and writers. Speaking from experience, they can throw light upon the art of correct and efficient thinking.

“Language, we must remember,” says Dr. Morrell, “is not constructed afresh by every individual mind which uses it. It is a world already created for us,—one into which we have simply to be introduced, and in which the process of human development, up to any given period, is more or less perfectly preserved and registered. Recollection, accordingly, by enabling us to appropriate to ourselves a whole system of signs, with the ideas attached to them, initiates us insensibly into the intellectual world of the present, puts us upon the vantage-ground of the latest degree of civilization, and enables us to grasp the ideas of the age without the labor of thinking them out consecutively by our own individual effort.”[11]

“Language,” says Dr. Whewell, “is often called an instrument of thought; but it is also the nutriment of thought; or, rather, it is the atmosphere in which thought lives; a medium essential to the activity of our speculative power, although invisible and imperceptible in its operation; and an element modifying, by its qualities and changes, the growth and complexion of the faculties which it feeds. In this way the influence of preceding discoveries upon subsequent ones, of the past upon the present, is most penetrating and universal, though most subtle and difficult to trace. The most familiar words and phrases are connected by imperceptible ties with the reasonings and discoveries of former men and most distant times. Their knowledge is an inseparable part of ours; the present generation inherits and uses the scientific wealth of all the past. And this is the fortune not only of the great and rich in the intellectual world, of those who have the key to the ancient storehouses and who have accumulated treasures of their own, but the humblest inquirer, while he puts his reasoning into words, benefits by the labors of the greatest discoverers. When he counts his little wealth, he finds he has in his hands coins which bear the image and superscription of ancient and modern intellectual dynasties; and that, in virtue of this possession, acquisitions are in his power, solid knowledge within his reach, which none could ever have attained to if it were not that the gold of truth, once dug out of the mine, circulates more and more widely among mankind.”[12]

“The word ‘vernacular,’” says Hinsdale, “is derived from vernaculus, which comes from verna, a slave born in his master’s house; and it means the speech to which one is born and in which he is reared,—the patrius sermo of the Roman, the Mutter-sprache of the German, the mother tongue of the Englishman. Command of a noble vernacular involves the most valuable discipline and culture that a man is capable of receiving. It conditions all other discipline and culture.... The greatest mental inheritance to which a German, a Frenchman, or an Englishman is born is his native tongue, rich in the knowledge and wisdom, the ideas and thoughts, the wit and fancy, the sentiment and feeling, of a thousand years. Nay, of more than a thousand years; for these languages, in their modern forms, were enriched by still earlier centuries. To come back to the old thought, such a speech as one of these only flows out from such a life as it expresses, and is in turn essential to the existence of that life.”[13]

Parents who wish their children to possess the best instruments of thought cannot be too careful in the selection of teachers for them. Children whose mother tongue is a dialect should be trained in one or more of the languages that have been enriched by centuries of development and literary culture. The best that the people of Pennsylvania-German extraction can do for future generations is to make the transition as speedily as possible from their vernacular—so poverty-stricken in its vocabulary—to the English, with its abundant vocabulary and its unsurpassed literary treasures. In the English they will find the instruments of thought fitted to develop native powers that have been inherited from an ancestry of sturdy husbandmen, and strengthened through heredity by centuries of contact with the soil, even as the giant AntÆus, in wrestling with Hercules, is fabled to have gained new strength as often as he came in contact with mother earth. The same advice will apply to the other nationalities who have come to live on American soil, even though they have brought with them a more developed vernacular. The English dictionary contains one hundred and twenty thousand words; but besides these words in common use, the dictionaries of the specialists contain several hundred thousand more, which may be called technical terms, and which serve as instruments of thought in scientific discussions and investigations. To these we next turn our attention.