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.