Chapter III: Part 3

An adequate idea of the shape of the earth can be formed only by gradual development. The three kinds of roundness (dollar, pillar, ball) must be taught; then the various easily intelligible reasons for believing it to be round like a ball may follow in the elementary grade. As the pupil advances he may be told of the dispute between Newton and the French, the former affirming it to be round like an orange,—that is, flattened at the poles,—the latter asserting that it resembled a lemon with the polar axis longer than the equatorial diameter; and how, by measuring degrees of latitude and finding that their length increases as we approach the poles, the French mathematicians, in spite of their wishes to the contrary, proved Newton’s view to be correct. The same lesson might be taught by starting with the rotation of the earth, showing by experiment the tendency of revolving bodies to bulge out at the equator, and then drawing the inference that the degrees of latitude are shortest where the curvature is greatest, and that they are longest where the curvature is least. Either method is strictly logical; but the method which follows the order of discovery, whenever it is feasible, is calculated to arouse the greater interest in minds of average capacity. The teacher who is a master of his art will supplement the historical lesson by a lesson passing from cause to consequence, so as to fix and clarify the concept formed by passing from the ground of knowledge to the necessary inference. Finally, by drawing attention to the fact that the equatorial diameters are not all of the same length, he will build up in the pupil’s mind a concept of the real shape of the earth,—a shape unlike any mathematical figure treated of in the text-books on geometry. The attempt to give a complete idea of the shape of the earth in the first lessons on geography would have ended in confusion of thought; the wise teacher develops complex concepts gradually and not more rapidly than the learner is able to advance. This process may be called enriching the concept. The successive concepts, although only partial representations of what is to be known, are adequate for the thinking required at a given stage of development; the number of complete or exhaustive concepts in any department of knowledge is small indeed.

[Sidenote: The order of discovery and of instruction.]

Instructive as it often is to follow the order of discovery, it must not be inferred that this is invariably the best order of instruction. What teacher of astronomy would be so foolish as to lead a student through the nineteen imaginary paths which Kepler tried before he discovered that an elliptical orbit fitted the recorded observations of Tycho Brahe![6]

Much may be learned from the methods pursued by eminent teachers. It will abundantly pay any teacher of science to study Faraday’s lectures on the chemistry of a candle,—a series which for models of developing the fundamental concepts of chemistry is unsurpassed. The devices used by such teachers are often very suggestive. For instance, in teaching the concept of the new geography that the earth revolves not like a body with a liquid interior, but like a body with an interior as rigid as glass, Lord Kelvin suggests a comparison of the spinning of a hard-boiled egg and of an egg not boiled at all,—an experiment easily made in every school-room.

[Sidenote: Ideas of great distances.]

A few quotations from the astronomer Young will show how concepts of great distances can be developed so as to be more than a numeral with a row of ciphers annexed:

“If one were to try to walk such a distance, supposing that he
could walk four miles an hour, and keep it up for ten hours
every day, it would take sixty-eight and one-half years to make
a single million of miles, and more than sixty-three hundred
years to traverse the whole. If some celestial railway could
be imagined, the journey to the sun, even if our trains ran
sixty miles an hour, day and night, without a stop, would
require over one hundred and seventy-five years. To borrow
the curious illustration of Professor Mendenhall, if we could
imagine an infant’s arm long enough to enable him to touch
the sun and burn himself, he would die of old age before the
pain could reach him, since, according to the experiments of
Helmholtz and others, a nervous shock is communicated only
at the rate of one hundred feet per second, or one thousand
six hundred and thirty-seven miles a day, and would need more
than one hundred and fifty years to make the journey. Sound
would do it in about fourteen years if it could be transmitted
through celestial space, and a cannon-ball in about nine, if
it were to move uniformly with the same speed as when it left
the muzzle of the gun. If the earth could be suddenly stopped
in her orbit, and allowed to fall unobstructed towards the sun
under the accelerating influence of his attraction, she would
reach the centre in about two months. I have said if she could
be stopped, but such is the compass of her orbit that to make
its circuit in a year she has to move nearly nineteen miles
a second, or more than fifty times faster than the swiftest
rifle-ball; and in moving twenty miles her path deviates from
perfect straightness by less than one-eighth of an inch.”[7]

Professor Young uses a very suggestive device in his astronomy for showing the comparative sizes and distances of heavenly bodies:

“Representing the sun by a globe two feet in diameter, the
earth would be twenty-two-hundredths of an inch in diameter—the
size of a very small pea or a ‘twenty-two caliber round
pellet.’ Its distance from the sun on that scale would be just
two hundred and twenty feet, and _the nearest star_ (still on
the same scale) _would be eight thousand miles away at the
antipodes_.”[8]

Sometimes the employment of a new unit aids in realizing the idea of very great distances. The ordinary astronomical unit is the distance of the sun from the earth; it is not large enough to be convenient in expressing the distances of fixed stars. Hence astronomers have found it more satisfactory to take as a unit the distance light travels in a year, which is about sixty-three thousand times the distance of the sun from the earth. The tables of fixed stars give distances in terms of this unit from 3.5 upward. A glance at these figures fills the mind with an idea of the infinite grandeur of the universe and with feelings of awe and sublimity akin to those which must fill the soul on approaching the throne of Almighty God.

[Sidenote: Time of snap-shot.]

Scientists assert that the infinitely great is more easily conceived than the infinitely small; that quantities represented by billions and trillions are more easily grasped than fractions of a unit with a million in the denominator; that ages of time are more easily comprehended than fractions of a second. In a lecture delivered at the International Electrical Exhibition, Professor Charles F. Himes employed a very ingenious device for giving an idea of how a “snap-shot” may be made, or a photographic impression taken of an electric spark, or a flash of lightning. He exhibited a photograph of the sparks of a Holtz machine, which are of shorter duration than any instantaneous drop or slide could be made to give. “They impressed themselves upon an ordinary collodion plate as they passed. Suppose we assume one-twenty-thousandth of a second as the time, and we will be within bounds. That is a fraction difficult to comprehend. Our mental dividing engine fails as we work towards zero. The twenty-thousandth of a second is so small that it eludes our mental grasp.... Looking at it from another point of view, let us regard the effect as a space-effect instead of a time-effect. Light has a velocity, in round numbers, of one hundred and ninety thousand miles per second. That would be one hundred and ninety miles in one-thousandth of a second, nineteen in one-ten-thousandth, or, say, ten miles in our one-twenty-thousandth of a second. Ten miles of light drive in upon our plate in that time; or, if we held the corpuscular theory of Newton, a chain of these little pellets ten miles long would have delivered themselves upon the sensitive surfaces. Ten miles is comprehensible, one mile is, so that we could easily conceive of an effect in one-tenth of the time allowed to our electric sparks. But let us take another look at it. Light is not corpuscles, but undulations, tiny wavelets, ripplets of ether, eight hundred million million in a second for violet, a number we can easily understand, as Sir William Thomson[9] has told us. That would make eight hundred thousand million in one-thousandth, eight thousand million in one-ten-thousandth, or forty thousand million impulses striking our sensitive molecules in our one-twenty-thousandth of a second. Surely that number should produce an effect. We can readily conceive that one thousand million wavelets would produce an appreciable effect. They would represent one-eight-hundred-thousandth of a second, say one-millionth of a second. That would seem, then, to be ample time to produce a photographic effect.”[10]

[Sidenote: Idea of total depravity.]

Many teachers of science spend all their spare time in reading scientific literature and in posting themselves upon the latest achievements in their specialty. It might be to them a less delightful occupation if they traversed fields of investigation already well explored for the purpose of seeing how the student can be led over these most expeditiously and with minimum expenditure of time and effort. Thought bestowed upon the best way of imparting the elements of science would have a most beneficial effect upon their methods of instruction, and would greatly increase their skill in teaching. Many of the most abstruse and complex ideas can be resolved by analysis into their elements, and thereby be made intelligible to people of ordinary training. An eminent teacher of theology felt called upon to impart to a promiscuous audience an idea of the doctrine of total depravity as taught by the Church. He started by referring first to the popular mistake that the doctrine teaches the utter depravity of the human race, then to the ancient heresy that the depravity of human nature resides in the body, and not in the soul, and, finally, to the meaning of total as signifying not that man is as bad as he can become, but that he is depraved, or has a tendency towards sin not merely in his physical body, but in the totality of his being. Analysis prepared them to see that by total depravity is not meant that men are as bad as they can be, nor that they do not have in their natural condition certain amiable qualities or certain laudable virtues; that the doctrine means that depravity, or the sinful condition of man, infects the whole man,—intellect, feeling, heart, and will,—and that in each unrenewed person some lower affection, and not the love of God, is supreme. Such analysis of a complex concept into its elements, the explicit setting forth what it is and what it is not, followed by the synthesis of the parts into a thought-unit, is the plan pursued by the best teachers in teaching difficult subjects. By analysis we resolve complex concepts into their elements, which may be simple percepts or their relations. Things are separated in thought which go together in time, space, motion, force, or substance. Every essential attribute or constituent can then be viewed by itself until the mind has gone around it with the bounding line of thought, grasped its nature and essence, and explored it in its different aspects and relations. In this way the most abstruse subjects are shorn of their difficulties, the most complex problems are solved and elucidated.

[Sidenote: Value of analysis.]

The bearing of all this upon the art of teaching is easily shown. A teacher of geometry, whose mind was quite logical, failed, through lack of power, to make things plain. If the class did not grasp the demonstration of a theorem, he invariably started at the beginning, tried to throw light upon every link in the chain of proof, and by the time he reached the point of difficulty the members of the class were thinking of something else. A younger colleague pursued a different plan. Starting some pupil upon the demonstration, he detected the difficulty, and by a few words of explanation, or by a well-framed question, he focussed attention upon the simple elements, into which he resolved the difficulty, and frequently surprised the class by showing the simplicity of what had puzzled their minds. Under the clarifying light of analysis half the difficulties and half the sophistries of human thinking vanish like dew and mist before the morning sun.

[Sidenote: The moral nature.]

For the purpose of making an impression upon the moral nature word-painting is sometimes very helpful. All the text-books on physiology and hygiene intended for use in the public schools seek to teach the evils of strong drink by showing the effect of alcoholic stimulants upon different parts of the human system. Yet the most exhaustive lessons on how whiskey is made, and what are its exhilarating and its pernicious effects, cannot equal the effects of the word painting of Robert Ingersoll and the paraphrase by Dr. Buckley. In making a gift to a friend the former penned the following eulogy on whiskey:

“I send you some of the most wonderful whiskey that ever drove
the skeleton from the feast or painted landscapes in the brain
of man. It is the mingled souls of wheat and corn. In it you
will find the sunshine and the shadow that chased each other
over the billowy fields, the breath of June, the carol of the
lark, the dew of night, the wealth of summer, and autumn’s rich
content, all golden with imprisoned light. Drink it, and you
will hear the voice of men and maidens singing the ‘Harvest
Home,’ mingled with the laughter of children. Drink it, and
you will feel within your blood the starlit dawns, the dreamy,
tawny dusks of perfect days. For forty years this liquid joy
has been within the staves of oak, longing to touch the lips of
man.”

This was Dr. Buckley’s statement of the other side:

“I send you some of the most wonderful whiskey that ever
brought a skeleton into the closet, or painted scenes of lust
and bloodshed in the brain of man. It is the ghosts of wheat
and corn, crazed by the loss of their natural bodies. In it
you will find a transient sunshine chased by a shadow as cold
as an Arctic midnight, in which the breath of June grows icy
and the carol of the lark gives place to the foreboding cry
of the raven. Drink it, and you shall have ‘woe,’ ‘sorrow,’
‘babbling,’ and ‘wounds without cause.’ Your eyes shall
behold strange women, and ‘your heart shall utter perverse
things.’ Drink it deep, and you shall hear the voices of demons
shrieking, women wailing, and worse than orphaned children
mourning the loss of a father who yet lives. Drink it deep and
long, and serpents will hiss in your ears, coil themselves
about your neck, and seize you with their fangs; for at the
last it biteth like a serpent and stingeth like an adder. For
forty years this liquid death has been within staves of oak,
harmless there as purest water. I send it to you that you may
put an enemy in your mouth to steal away your brains, and yet I
call myself your friend.”

[Sidenote: The languages.]

There comes a stage of development of the learner at which the word itself becomes the object of thought. Words are then classified as parts of speech, and their function in sentences is studied. Their properties and endings must be learned and compared. There is abundant room for thought in the eleven hundred variations of the Greek verb. The variations of words by declension and conjugation can be made the material for thought, and as these are always at hand in the text-book, no excursions to the field being needed to secure specimens, and no preparation of difficult experiments being required on the part of the teacher, the ancient languages have held their own in the schools with most wonderful tenacity. The study of language has not merely the advantage of supplying material for thought in the words, grammatical forms, and sentences which are always at hand in the text, but through the classics it brings the learner into intellectual contact with the best thoughts of the best men in ancient and modern times. To translate an author like Virgil or Demosthenes is to think the thoughts of a master mind, to weigh words as in a most nicely adjusted balance, and finally to arrange them in sentences that shall adequately convey the meaning of the original text.

[Sidenote: Science.]

Science is, of course, a product of the human mind, quite as much as the so-called humanities, and answers the same purpose when studied as literature; but then it ceases to have the value of training the intellect in the rigid methods of original research and scientific investigation. Whilst it is the function of the laboratory to initiate the student into the mysteries of the methods by which new discoveries are made and verified, and thus to enable him to avail himself of the labors of others through their publications, it does not bring the student into living contact with human hopes, emotions, and aspirations as do the poems of Goethe, Schiller, and Shakespeare.

[Sidenote: History.]

History deals with what man has achieved. The materials for thought which it furnishes are mostly in the shape of the testimony of eye-witnesses and other original sources of information. The incidents, the achievements, the struggles, the victories and the defeats, the thoughts, feelings, and experiences of historic personages, are an inexhaustible supply of material from which authors, editors, and orators draw illustrations, figures of speech, and other matter for their thinking. Here is a field which must not be neglected by those who would influence their fellows or figure as leaders of men.

[Sidenote: Vigorous thinking.]

Some minds are slow at gathering materials; yet they think vigorously. They look at facts and ideas from every possible point of view, explore their nature and relations, their content and extent, and point out their bearing upon other things by the conclusions they reach. Sometimes they go astray because they do not have sufficient data to warrant a conclusion. Their condition resembles that of the King of Siam, who did not believe that water could become solid because he had been in the nine points of his kingdom and had not seen ice.

[Sidenote: Intellectual gluttony.]

Other men are intellectual gluttons. They keep pouring into themselves knowledge from every quarter, carry it in their minds as the overloaded stomach carries food, and end in mental dyspepsia. Better the man with few ideas, who can apply these in practical life, than the man of erudition who cannot apply his knowledge.

Too little food produces inanition and starvation; too much food brings on dyspepsia and a host of other ills and distempers. The haphazard selection of studies by inexperienced youth from the large list of electives offered by a great university is apt to result either in mental overfeeding or in intellectual starvation. The mind can be rightly formed only when it is rightly informed. To expect satisfactory thought-products when the mind lacks proper materials to act upon would be as irrational as to expect good grist from a flour-mill whose supply of grain is deficient in quality and quantity. In the process of making flour very much depends upon the instruments employed. The rude implements of antiquity, the buhr-stones of our fathers, and the improved machinery of the roller process make a difference in the product, even though the same quality of grain is used. In the elaboration of the thought-material the well-educated man uses instruments which may be likened to our modern inventions for saving labor in the domain of the mechanic arts. These instruments of thought will next claim our attention.

V

THE INSTRUMENTS OF THOUGHT

But words are things; and a small drop of ink
Falling, like dew, upon thought, produces
That which makes thousands, perhaps millions, think.

BYRON.

Constant thought will overflow in words unconsciously.

BYRON.

The great Lagrange specifies among the many advantages of
algebraic notation that it expresses truths more general than
those which were at first contemplated, so that by availing
ourselves of such extensions we may develop a multitude of
new truths from formulæ founded on limited truths. A glance
at the history of science will show this. For example, when
Kepler conceived the happy idea of infinitely great and
infinitely small quantities (an idea at which common sense
must have shaken its head pityingly), he devised an instrument
which in expert hands may be made to reach conclusions for
an infinite series of approximations without the infinite
labor of going successively through these. Again, when Napier
invented logarithms, even he had no suspicion of the value of
this instrument. He calculated the tables merely to facilitate
arithmetical computation, little dreaming that he was at the
same time constructing a scale whereon to measure the density
of the strata of the atmosphere, the height of the mountains,
the areas of innumerable curves, and the relation of stimuli to
sensations.

LEWES’S PROBLEMS OF LIFE AND MIND.

V

THE INSTRUMENTS OF THOUGHT

[Sidenote: Labor-saving in thinking.]

[Sidenote: Squaring the circle.]

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 π, 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.

[Sidenote: Chemistry.]

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.

[Sidenote: Arabic notation.]

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.

[Sidenote: Fractions.]

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.”

[Sidenote: Reckoning interest.]

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.

[Sidenote: Words.]

[Sidenote: Dialects.]

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.

[Sidenote: Melanchthon.]

[Sidenote: Growth of the German language.]

[Sidenote: Value of a rich vocabulary.]

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.

[Sidenote: Dr. Morrell.]

“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]

[Sidenote: Dr. Whewell.]

“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]

[Sidenote: Dr. Hinsdale.]

“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]

[Sidenote: English.]

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.

VI

TECHNICAL TERMS AS INSTRUMENTS OF THOUGHT

It is the power of thinking by means of symbols which
demarcates men from animals, and gives one man or nation the
superiority over others.

LEWES.

Hardly any original thoughts on mental or social subjects ever
make their way among mankind or assume their proper importance
in the minds even of their inventors until aptly selected words
or phrases have, as it were, nailed them down and held them
fast.

J. S. MILL.

Though most readers, probably, entertain, at first, a
persuasion that a writer ought to content himself with the use
of common words in their common sense, and feel a repugnance to
technical terms and arbitrary rules of phraseology, as pedantic
and troublesome, it is soon found by the student of any branch
of science that, without technical terms and fixed rules, there
can be no certain or progressive knowledge. The loose and
infantine grasp of common language cannot hold objects steadily
enough for scientific examination, or lift them from one stage
of generalization to another. They must be secured by the rigid
mechanism of a scientific phraseology. This necessity has been
felt in all the sciences, from the earliest periods of their
progress.

WHEWELL.

Ideas and existences are represented by terms and phrases;
and as terms and phrases are representative of thoughts and
things, and are the means which enable us to speak about them,
the definitions, descriptions, and explanations of terms form
a very necessary part of science; and he who would understand
science must learn the meaning of the special terms employed in
it.

GORE.

VI

TECHNICAL TERMS AS INSTRUMENTS OF THOUGHT

[Sidenote: Technical terms.]

[Sidenote: Their value.]

Some teachers are very much afraid of technical terms. They teach their pupils to say name-word instead of noun, action-word instead of verb, and bring over instead of transpose. There is no end to the phrases they invent for the sake of avoiding technical terms. Acting on the maxim that a pupil shall never be allowed to use a word without comprehending its meaning, they prefer to use compound words and phrases to denote the fundamental ideas of the various branches of study. This fear of technical terms is a natural result of the reaction against rote teaching. So much has been said and written against the teaching of mere words, especially big words, against parrot-like recitations of definitions, rules, principles, and forms of statement given in the text-book or wrought out by the teacher, that many people fail to see the value of technical terms as instruments of thought. A separate chapter is necessary to point out their function in scientific thinking and instruction. In common parlance the use of technical terms should be avoided. Do we say that Nebuchadnezzar had a long noun or a long name? Noun is a technical term; name is the word in ordinary use. Do we say that a man broke his femur or his leg? The doctors who set the limb will probably use the technical term in their conferences. In talking with the common people they use the common names, unless they wish to awe the multitudes by a show of learning. Often, indeed, men use big words to hide their ignorance. In physiology the investigations are carried as far as possible, and then a term is coined to cover the unknown. Often high-sounding words are strung together to cover a lack of ideas or to establish a reputation for erudition. These are tricks to which a genuine teacher has no occasion to resort. It is his duty to ascertain the educational value of the technical terms of science, and to use these terms for the purpose of fixing scientific ideas in the mind and of causing the pupil to think clearly and exactly.

[Sidenote: Basal concepts.]

At the basis of every science, as we have seen, there are certain ideas which cannot be conveyed to other minds by the use of the corresponding technical terms. These basal concepts must be built up in the learner’s mind by skilful teaching, sometimes by the very process by which the race acquired or discovered them. It may require a trip to the field, to the museum, or to the mine; or an experiment in the laboratory may be necessary. Perhaps a development lesson is needed to enable the pupil to grasp the idea clearly and fully. It is very certain that if the idea is hazy and ill-defined, the subsequent thinking will be loose, obscure, and unsatisfactory. The glib use of technical terms may often hide from the teacher the defects of the pupil’s thinking, and it may require an examination to reveal the points wherein the teacher has failed. Questions which require a pupil to look at his knowledge from a new point of view are helpful; an examination abounding in such questions may be an intellectual blessing to both teacher and pupil. The examiner should, of course, avoid puzzling catch-questions, for these are calculated to embarrass the pupil and confuse his thinking.

[Sidenote: Popular lectures.]

A clear thinker can always make his ideas intelligible to those who have acquired the basal concepts of the things, principles, and laws with which he deals. Lecturers on popular science avoid the abstruse questions of advanced science and the technical terms which do not convey a definite meaning to the average hearer. They select topics which can be discussed in the language of common life, and often state the results of scientific research without leading the audience through the successive steps by which these results are obtained. The popular lecture requires special gifts that are not in the possession of every scientist. Huxley was one of the most gifted men of the century; yet he says of himself,—

[Sidenote: Huxley.]

“I have not been one of those fortunate persons who are able to regard a popular lecture as a mere _hors d’œuvre_ unworthy of being ranked among the serious efforts of a philosopher, and who keep their fame as scientific hierophants unsullied by attempts—at least of the successful sort—to be understanded by the people. On the contrary, I have found that the task of putting the truths learned in the field, the laboratory, and the museum into language which, without bating a jot of scientific accuracy, shall be generally intelligible, taxed such scientific and literary faculty as I possessed to the uttermost; indeed, my experience has furnished me with no better corrective of the tendency to scholastic pedantry, which besets all those who are absorbed in pursuits remote from the common ways of men, and become habituated to think and speak in the technical dialect of their own little world, as if there were no other.”

[Sidenote: Exact thinking.]

There is an error, on the other hand, into which practical men fall when they object to the technical language of the scientist. There are many things in science which cannot be made plain to the non-scientific mind. The difficulty lies not in the terminology employed, but in the lack of the basal concepts necessary for the advanced thinking which must be employed. Says Robert Galloway, “Words when employed in science, unlike their employment in common use, have a meaning steadily fixed and precisely determined; this precision in the meaning of scientific terms necessarily requires on the part of those who can make proper use of them _accurate habits of thought_; this is an indispensable qualification for attainment in any science; there is no dispensing with it, consequently one who does not know the language of a science, and who has not been taught to think accurately with respect to it, cannot understand properly what may be told or shown him about the facts or principles of that science.”

[Sidenote: De Quincey.]

From this point of view it is easy to see the use which the teacher should make of technical terms. Circumlocutions and explanatory phrases may be helpful in developing fundamental ideas, but the corresponding technical terms should be associated with the ideas as soon as these assume clear, definite shape. Language is the atmosphere in which thinking lives; technical language is as necessary to the scientific thought as the air we breathe is to the physical life. In one of his letters to a young man whose education had been neglected, De Quincey renders an important service to the science of teaching. “In assigning to the complex notion X the name transcendental, Kant was not simply transferring a word which had previously been used by the school-men to a more useful office; he was bringing into the service of the intellect a new birth; that is, drawing into a synthesis, which had not existed before as a synthesis, parts or elements which exist and come forward hourly in every man’s mind. I urge this upon your attention, because you will often hear such challenges thrown out as this (or others involving the same error): ‘Now, if there be any sense in this Mr. Kant’s writings, let us have it in good old mother English.’ That is, in other words, transfer into the unscientific language of life scientific notions which it is not fitted to express. The challenger proceeds upon the common error of supposing all ideas fully developed to exist _in esse_ in all understandings, ergo, his own; and all that are in his own he thinks we can express in English. Thus the challenger, in his own notions, has you in a dilemma, at any rate; for, if you do not translate it, then it confirms his belief that the whole is jargon; if you do (as, doubtless, with the help of much periphrasis, that will be intelligible to a man who already understands the philosophy), then where was the use of the terminology? But the way to deal with this fellow is as follows: My good sir, I shall do what you ask; but before I do it I beg you will oblige me by (1) translating this mathematics into the language of chemistry; (2) translating this chemistry into the language of mathematics; (3) both into the language of cookery, and, finally, solve me the Cambridge problem, Given the captain’s name, the year of our Lord, to determine the longitude of the ship? This is the way to deal with such fellows.”

[Sidenote: Images.]

[Sidenote: Higher forms of thinking.]

Technical terms are very helpful in dealing with that which cannot be imaged or visualized. When Francis Galton began his inquiries into the power possessed by different minds to conceive the breakfast table, to recall vividly the various dishes and the way in which they are placed upon the table, many men of scientific habits of thought declared that there is no such human faculty. On the other hand, the educational reformer whose early training did not make him familiar with the thought-processes of higher mathematics may honestly declare that he cannot conceive an abstract number, and, as a matter of course, he can have no adequate conception of the value of the higher forms of thinking in symbols. Dr. W. T. Harris has well said that the mind can think ideas which cannot be pictorially conceived or made to stand before the mind in thought-images. In thinking this class of ideas, technical terms are indispensable as instruments of thought.

[Sidenote: Symbols classified.]

[Sidenote: Suggestive symbols.]

The value of technical terms as instruments of thought is seen in a still clearer light if we try to classify the various uses of the signs and symbols which are employed as aids in thinking. Many of these have no office beyond that of _suggesting_ the things or ideas for which they stand. To this class belong the marks which suggest to the tramp a cross dog or a good meal. As soon as he has seen them, they could be erased; the train of thought which they started in his mind can go on without them. Of a similar character are the devices by which the merchant marks the buying and the selling prices of goods, the red and blue lights used on railways and ocean steamers, the secret signs and signals employed by the signal corps of an army, and the steps, grips, signs, countersigns, and passwords employed by secret societies as a means of identification. Very many of the artificial devices used in systems of mnemonics have no higher function than that of suggesting what otherwise might be forgotten.

[Sidenote: Symbols as substitutes.]