the earth is a top whirled about the sun, which speeds off with it into
infinite space; in finding that in the fixed stars the same elements
exist as on earth; in meeting everywhere the same processes of which the
life of man is merely a vanishingly small part--in such things, too, is
a widening of our view of the world, and edification, and poetry. There
are here perhaps grander and more significant facts than the bellowing
of the wounded Ares, or the charming island of Calypso, or the
ocean-stream engirdling the earth. He only should speak of the relative
value of these two domains of thought, of their poetry, who knows both.
The "utility" of physical science is, in a measure, only a _collateral_
product of that flight of the intellect which produced science. No one,
however, should underrate the utility of science who has shared in the
realisation by modern industrial art of the Oriental world of fables,
much less one upon whom those treasures have been poured, as it were,
from the fourth dimension, without his aid or understanding.
Nor may we believe that science is useful only to the practical man. Its
influence permeates all our affairs, our whole life; everywhere its
ideas are decisive. How differently does the jurist, the legislator, or
the political economist think, who knows, for example, that a square
mile of the most fertile soil can support with the solar heat annually
consumed only a definite number of human beings, which no art or science
can increase. Many economical theories, which open new air-paths of
progress, air-paths in the literal sense of the word, would be made
impossible by such knowledge.
* * * * *
The eulogists of classical education love to emphasise the cultivation
of taste which comes from employment with the ancient models. I candidly
confess that there is something absolutely revolting in this to me. To
form the taste, then, our youths must sacrifice ten years of their life!
Luxury takes precedence over necessity. Have the future generations, in
the face of the difficult problems, the great social questions, which
they must meet, and that with strengthened mind and heart, no more
important duties to fulfil than these?
But let us assume that this end were desirable. Can taste be formed by
rules and precepts? Do not ideals of beauty change? Is it not a
stupendous absurdity to force one's self artificially to admire things
which, with all their historical interest, with all their beauty in
individual points, are for the most part foreign to the rest of our
thoughts and feelings, provided we have such of _our own_. A nation that
is truly such, has its own taste and will not go to others for it. And
every individual perfect man has his own taste.[121]
And what, after all, does this cultivation of taste consist in? In the
acquisition of the personal literary style of a few select authors! What
should we think of a people that would force its youth a thousand years
from now, by years of practice, to master the tortuous or bombastic
style of some successful lawyer or politician of to-day? Should we not
justly accuse them of a woful lack of taste?
The evil effects of this imagined cultivation of the taste find
expression often enough. The young _savant_ who regards the composition
of a scientific essay as a rhetorical exercise instead of a simple and
unadorned presentation of the facts and the truth, still sits
unconsciously on the school-bench, and still unwittingly represents the
point of view of the Romans, by whom the elaboration of speeches was
regarded as a serious scientific (!) employment.
* * * * *
Far be it from me to underrate the value of the development of the
instinct of speech and of the increased comprehension of our own
language which comes from philological studies. By the study of a
foreign language, especially of one which differs widely from ours, the
signs and forms of words are first clearly distinguished from the
thoughts which they express. Words of the closest possible
correspondence in different languages never coincide absolutely with the
ideas they stand for, but place in relief slightly different aspects of
the same thing, and by the study of language the attention is directed
to these shades of difference. But it would be far from admissible to
contend that the study of Latin and Greek is the most fruitful and
natural, let alone the _only_, means of attaining this end. Any one who
will give himself the pleasure of a few hours' companionship with a
Chinese grammar; who will seek to make clear to himself the mode of
speech and thought of a people who never advanced as far as the analysis
of articulate sounds, but stopped at the analysis of syllables, to whom
our alphabetical characters, therefore, are an inexplicable puzzle, and
who express all their rich and profound thoughts by means of a few
syllables with variable emphasis and position,--such a person, perhaps,
will acquire new, and extremely elucidative ideas upon the relation of
language and thought. But should our children, therefore, study Chinese?
Certainly not. No more, then, should they be burdened with Latin, at
least in the measure they are.
It is a beautiful achievement to reproduce a Latin thought in a modern
language with the maximum fidelity of meaning and expression--for the
_translator_. Moreover, we shall be very grateful to the translator for
his performance. But to demand this feat of every educated man, without
consideration of the sacrifice of time and labor which it entails, is
unreasonable. And for this very reason, as classical teachers admit,
that ideal is never perfectly attained, except in rare cases with
scholars possessed of special talents and great industry. Without
slurring, therefore, the high importance of the study of the ancient
languages as a profession, we may yet feel sure that the instinct for
speech which is part of every liberal education can, and must, be
acquired in a different way. Should we, indeed, be forever lost if the
Greeks had not lived before us?
The fact is, we must carry our demands further than the representatives
of classical philology. We must ask of every educated man a fair
scientific conception of the nature and value of language, of the
formation of language, of the alteration of the meaning of roots, of the
degeneration of fixed forms of speech to grammatical forms, in brief, of
all the main results of modern comparative philology. We should judge
that this were attainable by a careful study of our mother tongue and of
the languages next allied to it, and subsequently of the more ancient
tongues from which the former are derived. If any one object that this
is too difficult and entails too much labor, I should advise such a
person to place side by side an English, a Dutch, a Danish, a Swedish,
and a German Bible, and to compare a few lines of them; he will be
amazed at the multitude of suggestions that offer themselves.[122] In
fact, I believe that a really progressive, fruitful, rational, and
instructive study of languages can be conducted only on this plan. Many
of my audience will remember, perhaps, the bright and encouraging
effect, like that of a ray of sunlight on a gloomy day, which the meagre
and furtive remarks on comparative philology in Curtius's Greek grammar
wrought in that barren and lifeless desert of verbal quibbles.
* * * * *
The principal result obtained by the present method of studying the
ancient languages is that which comes from the student's employment with
their complicated grammars. It consists in the sharpening of the
attention and in the exercise of the judgment by the practice of
subsuming special cases under general rules, and of distinguishing
between different cases. Obviously, the same result can be reached by
many other methods; for example, by difficult games of cards. Every
science, the mathematics and the physical sciences included, accomplish
as much, if not more, in this disciplining of the judgment. In addition,
the matter treated by those sciences has a much higher intrinsic
interest for young people, and so engages spontaneously their attention;
while on the other hand they are elucidative and useful in other
directions in which grammar can accomplish nothing.
Who cares, so far as the matter of it is concerned, whether we say
_hominum_ or _hominorum_ in the genitive plural, interesting as the fact
may be for the philologist? And who would dispute that the intellectual
need of causal insight is awakened not by grammar but by the natural
sciences?
It is not our intention, therefore, to gainsay in the least the good
influence which the study of Latin and Greek grammar _also_ exercises on
the sharpening of the judgment. In so far as the study of words as such
must greatly promote lucidity and accuracy of expression, in so far as
Latin and Greek are not yet wholly indispensable to many branches of
knowledge, we willingly concede to them a place in our schools, but
would demand that the disproportionate amount of time allotted to them,
wrongly withdrawn from other useful studies, should be considerably
curtailed. That in the end Latin and Greek will not be employed as the
universal means of education, we are fully convinced. They will be
relegated to the closet of the scholar or professional philologist, and
gradually make way for the modern languages and the modern science of
language.
Long ago Locke reduced to their proper limits the exaggerated notions
which obtained of the close connexion of thought and speech, of logic
and grammar, and recent investigators have established on still surer
foundations his views. How little a complicated grammar is necessary for
expressing delicate shades of thought is demonstrated by the Italians
and French, who, although they have almost totally discarded the
grammatical redundancies of the Romans, are yet not surpassed by the
latter in accuracy of thought, and whose poetical, but especially whose
scientific literature, as no one will dispute, can bear favorable
comparison with the Roman.
Reviewing again the arguments advanced in favor of the study of the
ancient languages, we are obliged to say that in the main and as
applied to the present, they are wholly devoid of force. In so far as
the aims which this study theoretically pursues are still worthy of
attainment, they appear to us as altogether too narrow, and are
surpassed in this only by the means employed. As almost the sole,
indisputable result of this study we must count the increase of the
student's skill and precision in expression. One inclined to be
uncharitable might say that our gymnasiums and classical academies turn
out men who can speak and write, but, unfortunately, have little to
write or speak about. Of that broad, liberal view, of that famed
universal culture, which the classical curriculum is supposed to yield,
serious words need not be lost. This culture might, perhaps, more
properly be termed the contracted or lopsided culture.
* * * * *
While considering the study of languages we threw a few side glances at
mathematics and the natural sciences. Let us now inquire whether these,
as branches of study, cannot accomplish much that is to be attained in
no other way. I shall meet with no contradiction when I say that without
at least an elementary mathematical and scientific education a man
remains a total stranger in the world in which he lives, a stranger in
the civilisation of the time that bears him. Whatever he meets in
nature, or in the industrial world, either does not appeal to him at
all, from his having neither eye nor ear for it, or it speaks to him in
a totally unintelligible language.
A real understanding of the world and its civilisation, however, is not
the only result of the study of mathematics and the physical sciences.
Much more essential for the preparatory school is the _formal_
cultivation which comes from these studies, the strengthening of the
reason and the judgment, the exercise of the imagination. Mathematics,
physics, chemistry, and the so-called descriptive sciences are so much
alike in this respect, that, apart from a few points, we need not
separate them in our discussion.
Logical sequence and continuity of ideas, so necessary for fruitful
thought, are _par excellence_ the results of mathematics; the ability to
follow facts with thoughts, that is, to observe or collect experiences,
is chiefly developed by the natural sciences. Whether we notice that the
sides and the angles of a triangle are connected in a definite way, that
an equilateral triangle possesses certain definite properties of
symmetry, or whether we notice the deflexion of a magnetic needle by an
electric current, the dissolution of zinc in diluted sulphuric acid,
whether we remark that the wings of a butterfly are slightly colored on
the under, and the fore-wings of the moth on the upper, surface:
indiscriminately here we proceed from _observations_, from individual
acts of immediate intuitive knowledge. The field of observation is more
restricted and lies closer at hand in mathematics; it is more varied and
broader but more difficult to compass in the natural sciences. The
essential thing, however, is for the student to learn to make
observations in all these fields. The philosophical question whether our
acts of knowledge in mathematics are of a special kind is here of no
importance for us. It is true, of course, that the observation can be
practised by languages also. But no one, surely, will deny, that the
concrete, living pictures presented in the fields just mentioned possess
different and more powerful attractions for the mind of the youth than
the abstract and hazy figures which language offers, and on which the
attention is certainly not so spontaneously bestowed, nor with such good
results.[123]
Observation having revealed the different properties of a given
geometrical or physical object, it is discovered that in many cases
these properties _depend_ in some way upon one another. This
interdependence of properties (say that of equal sides and equal angles
at the base of a triangle, the relation of pressure to motion,) is
nowhere so distinctly marked, nowhere is the necessity and permanency of
the interdependence so plainly noticeable, as in the fields mentioned.
Hence the continuity and logical consequence of the ideas which we
acquire in those fields. The relative simplicity and perspicuity of
geometrical and physical relations supply here the conditions of natural
and easy progress. Relations of equal simplicity are not met with in
the fields which the study of language opens up. Many of you, doubtless,
have often wondered at the little respect for the notions of cause and
effect and their connexion that is sometimes found among professed
representatives of the classical studies. The explanation is probably to
be sought in the fact that the analogous relation of motive and action
familiar to them from their studies, presents nothing like the clear
simplicity and determinateness that the relation of cause and effect
does.
That perfect mental grasp of all possible cases, that economical order
and organic union of the thoughts which comes from it, which has grown
for every one who has ever tasted it a permanent need which he seeks to
satisfy in every new province, can be developed only by employment with
the relative simplicity of mathematical and scientific investigations.
When a set of facts comes into apparent conflict with another set of
facts, and a problem is presented, its solution consists ordinarily in a
more refined distinction or in a more extended view of the facts, as may
be aptly illustrated by Newton's solution of the problem of dispersion.
When a new mathematical or scientific fact is _demonstrated_, or
_explained_, such demonstration also rests simply upon showing the
connexion of the new fact with the facts already known; for example,
that the radius of a circle can be laid off as chord exactly six times
in the circle is explained or proved by dividing the regular hexagon
inscribed in the circle into equilateral triangles. That the quantity of
heat developed in a second in a wire conveying an electric current is
quadrupled on the doubling of the strength of the current, we explain
from the doubling of the fall of the potential due to the doubling of
the current's intensity, as also from the doubling of the quantity
flowing through, in a word, from the quadrupling of the work done. In
point of principle, explanation and direct proof do not differ much.
He who solves scientifically a geometrical, physical, or technical
problem, easily remarks that his procedure is a _methodical_ mental
quest, rendered possible by the economical order of the province--a
simplified purposeful quest as contrasted with unmethodical,
unscientific guess-work. The geometer, for example, who has to construct
a circle touching two given straight lines, casts his eye over the
relations of symmetry of the desired construction, and seeks the centre
of his circle solely in the line of symmetry of the two straight lines.
The person who wants a triangle of which two angles and the sum of the
sides are given, grasps in his mind the determinateness of the form of
this triangle and restricts his search for it to a certain group of
triangles of the _same form_. Under very different circumstances,
therefore, the simplicity, the intellectual perviousness, of the
subject-matter of mathematics and natural science is felt, and promotes
both the discipline and the self-confidence of the reason.
Unquestionably, much more will be attained by instruction in the
mathematics and the natural sciences than now is, when more natural
methods are adopted. One point of importance here is that young students
should not be spoiled by premature abstraction, but should be made
acquainted with their material from living pictures of it before they
are made to work with it by purely ratiocinative methods. A good stock
of geometrical experience could be obtained, for example, from
geometrical drawing and from the practical construction of models. In
the place of the unfruitful method of Euclid, which is only fit for
special, restricted uses, a broader and more conscious method must be
adopted, as Hankel has pointed out.[124] Then, if, on reviewing
geometry, and after it presents no substantial difficulties, the more
general points of view, the principles of scientific method are placed
in relief and brought to consciousness, as Von Nagel,[125] J. K.
Becker,[126] Mann,[127] and others have well done, fruitful results will
be surely attained. In the same way, the subject-matter of the natural
sciences should be made familiar by pictures and experiment before a
profounder and reasoned grasp of these subjects is attempted. Here the
emphasis of the more general points of view is to be postponed.
Before my present audience it would be superfluous for me to contend
further that mathematics and natural science are justified constituents
of a sound education,--a claim that even philologists, after some
resistance, have conceded. Here I may count upon assent when I say that
mathematics and the natural sciences pursued alone as means of
instruction yield a richer education in matter and form, a more general
education, an education better adapted to the needs and spirit of the
time,--than the philological branches pursued alone would yield.
But how shall this idea be realised in the curricula of our intermediate
educational institutions? It is unquestionable in my mind that the
German _Realschulen_ and _Realgymnasien_, where the exclusive classical
course is for the most part replaced by mathematics, science, and modern
languages, give the _average_ man a more timely education than the
gymnasium proper, although they are not yet regarded as fit preparatory
schools for future theologians and professional philologists. The German
gymnasiums are too one-sided. With these the first changes are to be
made; of these alone we shall speak here. Possibly a _single_
preparatory school, suitably planned, might serve all purposes.
Shall we, then, in our gymnasiums fill out the hours of study which
stand at our disposal, or are still to be wrested from the classicists,
with as great and as varied a quantity of mathematical and scientific
matter as possible? Expect no such proposition from me. No one will
suggest such a course who has himself been actively engaged in
scientific thought. Thoughts can be awakened and fructified as a field
is fructified by sunshine and rain. But thoughts cannot be juggled out
and worried out by heaping up materials and the hours of instruction,
nor by any sort of precepts: they must grow naturally of their own free
accord. Furthermore, thoughts cannot be accumulated beyond a certain
limit in a single head, any more than the produce of a field can be
increased beyond certain limits.
I believe that the amount of matter necessary for a useful education,
such as should be offered to _all_ the pupils of a preparatory school,
is very small. If I had the requisite influence, I should, in all
composure, and fully convinced that I was doing what was best, first
greatly curtail in the lower classes the amount of matter in both the
classical and the scientific courses; I should cut down considerably the
number of the school hours and the work done outside the school. I am
not with many teachers of opinion that ten hours work a day for a child
is not too much. I am convinced that the mature men who offer this
advice so lightly are themselves unable to give their attention
successfully for as long a time to any subject that is new to them, (for
example, to elementary mathematics or physics,) and I would ask every
one who thinks the contrary to make the experiment upon himself.
Learning and teaching are not routine office-work that can be kept up
mechanically for long periods. But even such work tires in the end. If
our young men are not to enter the universities with blunted and
impoverished minds, if they are not to leave in the preparatory schools
their vital energy, which they should there gather, great changes must
be made. Waiving the injurious effects of overwork upon the body, the
consequences of it for the mind seem to me positively dreadful.
I know of nothing more terrible than the poor creatures who have learned
too much. Instead of that sound powerful judgment which would probably
have grown up if they had learned nothing, their thoughts creep timidly
and hypnotically after words, principles, and formulæ, constantly by the
same paths. What they have acquired is a spider's web of thoughts too
weak to furnish sure supports, but complicated enough to produce
confusion.
But how shall better methods of mathematical and scientific education be
combined with the decrease of the subject-matter of instruction? I
think, by abandoning systematic instruction altogether, at least in so
far as that is required of _all_ young pupils. I see no necessity
whatever that the graduates of our high schools and preparatory schools
should be little philologists, and at the same time little
mathematicians, physicists, and botanists; in fact, I do not see the
possibility of such a result. I see in the endeavor to attain this
result, in which every instructor seeks for his own branch a place apart
from the others, the main mistake of our whole system. I should be
satisfied if every young student could come into living contact with
and pursue to their ultimate logical consequences merely a _few_
mathematical or scientific discoveries. Such instruction would be mainly
and naturally associated with selections from the great scientific
classics. A few powerful and lucid ideas could thus be made to take root
in the mind and receive thorough elaboration. This accomplished, our
youth would make a different showing from what they do to-day.[128]