student with all the details of botany? The student who has botanised
under the guidance of a teacher finds on all hands, not indifferent
things, but known or unknown things, by which he is stimulated, and his
gain made permanent. I express here, not my own, but the opinion of a
friend, a practical teacher. Again, it is not at all necessary that all
the matter that is offered in the schools should be learned. The best
that we have learned, that which has remained with us for life, outlived
the test of examination. How can the mind thrive when matter is heaped
on matter, and new materials piled constantly on old, undigested
materials? The question here is not so much that of the accumulation of
positive knowledge as of intellectual discipline. It seems also
unnecessary that _all_ branches should be treated at school, and that
exactly the same studies should be pursued in all schools. A single
philological, a single historical, a single mathematical, a single
scientific branch, pursued as common subjects of instruction for all
pupils, are sufficient to accomplish all that is necessary for the
intellectual development. On the other hand, a wholesome mutual stimulus
would be produced by this greater variety in the positive culture of
men. Uniforms are excellent for soldiers, but they will not fit heads.
Charles V. learned this, and it should never be forgotten. On the
contrary, teachers and pupils both need considerable latitude, if they
are to yield good results.
With John Karl Becker I am of the opinion that the utility and amount
for individuals of every study should be precisely determined. All that
exceeds this amount should be unconditionally banished from the lower
classes. With respect to mathematics, Becker,[129] in my judgment, has
admirably solved this question.
With respect to the upper classes the demand assumes a different form.
Here also the amount of matter obligatory on all pupils ought not to
exceed a certain limit. But in the great mass of knowledge that a young
man must acquire to-day for his profession it is no longer just that ten
years of his youth should be wasted with mere preludes. The upper
classes should supply a truly useful preparation for the professions,
and should not be modelled upon the wants merely of future lawyers,
ministers, and philologists. Again, it would be both foolish and
impossible to attempt to prepare the same person properly for all the
different professions. In such case the function of the schools would
be, as Lichtenberg feared, simply to select the persons best fitted for
being drilled, whilst precisely the finest special talents, which do not
submit to indiscriminate discipline, would be excluded from the contest.
Hence, a certain amount of liberty in the choice of studies must be
introduced in the upper classes, by means of which it will be free for
every one who is clear about the choice of his profession to devote his
chief attention either to the study of the philologico-historical or to
that of the mathematico-scientific branches. Then the matter now treated
could be retained, and in some branches, perhaps, judiciously
extended,[130] without burdening the scholar with many branches or
increasing the number of the hours of study. With more homogeneous work
the student's capacity for work increases, one part of his labor
supporting the other instead of obstructing it. If, however, a young man
should subsequently choose a different profession, then it is _his_
business to make up what he has lost. No harm certainly will come to
society from this change, nor could it be regarded as a misfortune if
philologists and lawyers with mathematical educations or physical
scientists with classical educations should now and then appear.
* * * * *
The view is now wide-spread that a Latin and Greek education no longer
meets the general wants of the times, that a more opportune, a more
"liberal" education exists. The phrase, "a liberal education," has been
greatly misused. A truly liberal education is unquestionably very rare.
The _schools_ can hardly offer such; at best they can only bring home to
the student the necessity of it. It is, then, his business to acquire,
as best he can, a more or less liberal education. It would be very
difficult, too, at any one time to give a definition of a "liberal"
education which would satisfy every one, still more difficult to give
one which would hold good for a hundred years. The educational ideal, in
fact, varies much. To one, a knowledge of classical antiquity appears
not too dearly bought "with early death." We have no objection to this
person, or to those who think like him, pursuing their ideal after their
own fashion. But we may certainly protest strongly against the
realisation of such ideals on our own children. Another,--Plato, for
example,--puts men ignorant of geometry on a level with animals.[131]
If such narrow views had the magical powers of the sorceress Circe, many
a man who perhaps justly thought himself well educated would become
conscious of a not very flattering transformation of himself. Let us
seek, therefore, in our educational system to meet the wants of the
present, and not establish prejudices for the future.
But how does it come, we must ask, that institutions so antiquated as
the German gymnasiums could subsist so long in opposition to public
opinion? The answer is simple. The schools were first organised by the
Church; since the Reformation they have been in the hands of the State.
On so large a scale, the plan presents many advantages. Means can be
placed at the disposal of education such as no private source, at least
in Europe, could furnish. Work can be conducted upon the same plan in
many schools, and so experiments made of extensive scope which would be
otherwise impossible. A single man with influence and ideas can under
such circumstances do great things for the promotion of education.
But the matter has also its reverse aspect. The party in power works for
its own interests, uses the schools for its special purposes.
Educational competition is excluded, for all successful attempts at
improvement are impossible unless undertaken or permitted by the State.
By the uniformity of the people's education, a prejudice once in vogue
is permanently established. The highest intelligences, the strongest
wills cannot overthrow it suddenly. In fact, as everything is adapted to
the view in question, a sudden change would be physically impossible.
The two classes which virtually hold the reins of power in the State,
the jurists and theologians, know only the one-sided, predominantly
classical culture which they have acquired in the State schools, and
would have this culture alone valued. Others accept this opinion from
credulity; others, underestimating their true worth for society, bow
before the power of the prevalent opinion; others, again, affect the
opinion of the ruling classes even against their better judgment, so as
to abide on the same plane of respect with the latter. I will make no
charges, but I must confess that the deportment of medical men with
respect to the question of the qualification of graduates of your
_Realschulen_ has frequently made that impression upon me. Let us
remember, finally, that an influential statesman, even within the
boundaries which the law and public opinion set him, can do serious harm
to the cause of education by considering his own one-sided views
infallible, and in enforcing them recklessly and inconsiderately--which
not only _can_ happen, but has, repeatedly, happened.[132] The monopoly
of education by the State[133] thus assumes in our eyes a somewhat
different aspect. And to revert to the question above asked, there is
not the slightest doubt that the German gymnasiums in their present
form would have ceased to exist long ago if the State had not supported
them.
All this must be changed. But the change will not be made of itself, nor
without our energetic interference, and it will be made slowly. But the
path is marked out for us, the will of the people must acquire and exert
upon our school legislation a greater and more powerful influence.
Furthermore, the questions at issue must be publicly and candidly
discussed that the views of the people may be clarified. All who feel
the insufficiency of the existing _régime_ must combine into a powerful
organisation that their views may acquire impressiveness and the
opinions of the individual not die away unheard.
I recently read, gentlemen, in an excellent book of travels, that the
Chinese speak with unwillingness of politics. Conversations of this sort
are usually cut short with the remark that they may bother about such
things whose business it is and who are paid for it. Now it seems to me
that it is not only the business of the State, but a very serious
concern of all of us, how our children shall be educated in the public
schools at _our_ cost.
FOOTNOTES:
[Footnote 113: An address delivered before the Congress of Delegates
of the German Realschulmännerverein, at Dortmund, April 16, 1886.
The full title of the address reads: "On the Relative Educational
Value of the Classics and the Mathematico-Physical Sciences in
Colleges and High Schools."
Although substantially contained in an address which I was to have
made at the meeting of Natural Scientists at Salzburg in 1881
(deferred on account of the Paris Exposition), and in the
Introduction to a course of lectures on "Physical Instruction in
Preparatory Schools," which I delivered in 1883, the invitation of
the German Realschulmännerverein afforded me the first opportunity
of putting my views upon this subject before a large circle of
readers. Owing to the place and circumstances of delivery, my
remarks apply of course, primarily, only to German schools, but,
with slight modifications, made in this translation, are not without
force for the institutions of other countries. In giving here
expression to a strong personal conviction formed long ago, it is a
matter of deep satisfaction to me to find that they agree in many
points with the views recently advanced in independent form by
Paulsen (_Geschichte des gelehrten Unterrichts_, Leipsic, 1885) and
Frary (_La question du latin_, Paris, Cerf, 1885). It is not my
desire nor effort here to say much that is new, but merely to
contribute my mite towards bringing about the inevitable revolution
now preparing in the world of elementary instruction. In the opinion
of experienced educationists the first result of that revolution
will be to make Greek and mathematics alternately optional subjects
in the higher classes of the German Gymnasium and in the
corresponding institutions of other countries, as has been done in
the splendid system of instruction in Denmark. The gap between the
German classical Gymnasium and the German Realgymnasium, or between
classical and scientific schools generally, can thus be bridged
over, and the remaining inevitable transformations will then be
accomplished in relative peace and quiet. (Prague, May, 1886.)]
[Footnote 114: Maupertuis, _Oeuvres_, Dresden, 1752, p. 339.]
[Footnote 115: F. Paulsen, _Geschichte des gelehrten Unterrichts_,
Leipsic, 1885.]
[Footnote 116: There is a peculiar irony of fate in the fact that
while Leibnitz was casting about for a new vehicle of universal
linguistic intercourse, the Latin language which still subserved
this purpose the best of all, was dropping more and more out of use,
and that Leibnitz himself contributed not the least to this result.]
[Footnote 117: As a rule, the human brain is too much, and wrongly,
burdened with things which might be more conveniently and accurately
preserved in books where they could be found at a moment's notice.
In a recent letter to me from Düsseldorf, Judge Hartwich writes:
"A host of words exist which are out and out Latin or Greek, yet are
employed with perfect correctness by people of good education who
never had the good luck to be taught the ancient languages. For
example, words like 'dynasty.' ... The child learns such words as
parts of the common stock of speech, or even as parts of his
mother-tongue, just as he does the words 'father,' 'mother,'
'bread,' 'milk.' Does the ordinary mortal know the etymology of
these Saxon words? Did it not require the almost incredible industry
of the Grimms and other Teutonic philologists to throw the merest
glimmerings of light upon the origin and growth of our own
mother-tongue? Besides, do not thousands of people of so-called
classical education use every moment hosts of words of foreign
origin whose derivation they do not know? Very few of them think it
worth while to look up such words in the dictionaries, although they
love to maintain that people should study the ancient languages for
the sake of etymology alone."]
[Footnote 118: Standing remote from the legal profession I should
not have ventured to declare that the study of Greek was not
necessary for the jurists; yet this view was taken in the debate
that followed this lecture by professional jurists of high standing.
According to this opinion, the preparatory education obtained in the
German Realgymnasium would also be sufficient for the future jurists
and insufficient only for theologians and philologists. [In England
and America not only is Greek not necessary, but the law-Latin is so
peculiar that even persons of _good_ classical education cannot
understand it.--_Tr._]]
[Footnote 119: In emphasising here the weak sides of the writings of
Plato and Aristotle, forced on my attention while reading them in
German translations, I, of course, have no intention of underrating
the great merits and the high historical importance of these two
men. Their importance must not be measured by the fact that our
speculative philosophy still moves to a great extent in their paths
of thought. The more probable conclusion is that this branch has
made very little progress in the last two thousand years. Natural
science also was implicated for centuries in the meshes of the
Aristotelian thought, and owes its rise mainly to having thrown off
those fetters.]
[Footnote 120: I would not for a moment contend that we derive
exactly the same profit from reading a Greek author in a translation
as from reading him in the original; but the difference, the excess
of gain in the second case, appears to me, and probably will to most
men who are not professional philologists, to be too dearly bought
with the expenditure of eight years of valuable time.]
[Footnote 121: "The temptation," Judge Hartwich writes, "to regard
the 'taste' of the ancients as so lofty and unsurpassable appears to
me to have its chief origin in the fact that the ancients were
unexcelled in the representation of the nude. First, by their
unremitting care of the human body they produced splendid models;
and secondly, in their gymnasiums and in their athletic games they
had these models constantly before their eyes. No wonder, then, that
their statues still excite our admiration! For the form, the ideal
of the human body has not changed in the course of the centuries.
But with intellectual matters it is totally different; they change
from century to century, nay, from decennium to decennium. It is
very natural now, that people should unconsciously apply what is
thus so easily seen, namely, the works of sculpture, as a universal
criterion of the highly developed taste of the ancients--a fallacy
against which people cannot, in my judgment, be too strongly
warned."]
[Footnote 122: English: "In the beginning God created the heaven and
the earth. And the earth was without form and void; and darkness was
upon the face of the deep. And the spirit of God moved upon the face
of the waters."--Dutch: "In het begin schiep God den hemel en de
aarde. De aarde nu was woest en ledig, en duisternis was op den
afgrond; en de Geest Gods zwefde op de wateren."--Danish: "I
Begyndelsen skabte Gud Himmelen og Jorden. Og Jorden var ode og tom,
og der var morkt ovenover Afgrunden, og Guds Aand svoevede ovenover
Vandene."--Swedish: "I begynnelsen skapade Gud Himmel och Jord. Och
Jorden war öde och tom, och mörker war pä djupet, och Gods Ande
swäfde öfwer wattnet."--German: "Am Anfang schuf Gott Himmel und
Erde. Und die Erde war wüst und leer, und es war finster auf der
Tiefe; und der Geist Gottes schwebte auf dem Wasser."]
[Footnote 123: Compare Herzen's excellent remarks, _De
l'enseignement secondaire dans la Suisse romande_, Lausanne, 1886.]
[Footnote 124: _Geschichte der Mathematik_, Leipsic, 1874.]
[Footnote 125: _Geometrische Analyse_, Ulm, 1886.]
[Footnote 126: In his text-books of elementary mathematics]
[Footnote 127: _Abhandlungen aus dem Gebiete der Mathematik_,
Würzburg, 1883.]
[Footnote 128: My idea here is an appropriate selection of readings
from Galileo, Huygens, Newton, etc. The choice is so easily made
that there can be no question of difficulties. The contents would be
discussed with the students, and the original experiments performed
with them. Those scholars alone should receive this instruction in
the upper classes who did not look forward to systematical
instruction in the physical sciences. I do not make this proposition
of reform here for the first time. I have no doubt, moreover, that
such radical changes will only be slowly introduced.]
[Footnote 129: _Die Mathematik als Lehrgegenstand des Gymnasiums_,
Berlin, 1883.]
[Footnote 130: Wrong as it is to burden future physicians and
scientists with Greek for the sake of the theologians and
philologists, it would be just as wrong to compel theologians and
philologists, on account of the physicians, to study such subjects
as analytical geometry. Moreover, I cannot believe that ignorance of
analytical geometry would be a serious hindrance to a physician that
was otherwise well versed in quantitative thought. No special
advantage generally is observable in the graduates of the Austrian
gymnasiums, all of whom have studied analytical geometry. [Refers to
an assertion of Dubois-Reymond.]]
[Footnote 131: Compare M. Cantor, _Geschichte der Mathematik_,
Leipsic, 1880, Vol. I. p. 193.]
[Footnote 132: Compare Paulsen, _l. c._, pp. 607, 688.]
[Footnote 133: It is to be hoped that the Americans will jealously
guard their schools and universities against the influence of the
State.]
APPENDIX.
I.
A CONTRIBUTION TO THE HISTORY OF ACOUSTICS.[134]
While searching for papers by Amontons, several volumes of the Memoirs
of the Paris Academy for the first years of the eighteenth century, fell
into my hands. It is difficult to portray the delight which one
experiences in running over the leaves of these volumes. One sees as an
actual spectator almost the rise of the most important discoveries and
witnesses the progress of many fields of knowledge from almost total
ignorance to relatively perfect clearness.
I propose to discuss here the fundamental researches of Sauveur in
Acoustics. It is astonishing how extraordinarily near Sauveur was to the
view which Helmholtz was the first to adopt in its full extent a hundred
and fifty years later.
The _Histoire de l'Académie_ for 1700, p. 131, tells us that Sauveur had
succeeded in making music an object of scientific research, and that he
had invested the new science with the name of "acoustics." On five
successive pages a number of discoveries are recorded which are more
fully discussed in the volume for the year following.
Sauveur regards the _simplicity_ of the ratios obtaining between the
rates of vibration of consonances as something universally known.[135]
He is in hope, by further research, of determining the chief rules of
musical composition and of fathoming the "metaphysics of the agreeable,"
the main law of which he asserts to be the union of "simplicity with
multiplicity." Precisely as Euler[136] did a number of years later, he
regards a consonance as more perfect according as the ratio of its
vibrational rates is expressed in smaller whole numbers, because the
smaller these whole numbers are the oftener the vibrations of the two
tones coincide, and hence the more readily they are apprehended. As the
limit of consonance, he takes the ratio 5:6, although he does not
conceal the fact that practice, sharpened attention, habit, taste, and
even prejudice play collateral rôles in the matter, and that
consequently the question is not a purely scientific one.
Sauveur's ideas took their development from his having instituted at
all points more exact quantitative investigations than his predecessors.
He is first desirous of determining as the foundation of musical tuning
a fixed note of one hundred vibrations which can be reproduced at any
time; the fixing of the notes of musical instruments by the common
tuning pipes then in use with rates of vibration unknown, appearing to
him inadequate. According to Mersenne (_Harmonie Universelle_, 1636), a
given cord seventeen feet long and weighted with eight pounds executes
eight visible vibrations in a second. By diminishing its length then in
a given proportion we obtain a proportionately augmented rate of
vibration. But this procedure appears too uncertain to Sauveur, and he
employs for his purpose the beats (_battemens_), which were known to the
organ-makers of his day, and which he correctly explains as due to the
alternate coincidence and non-coincidence of the same vibrational phases
of differently pitched notes.[137] At every coincidence there is a
swelling of the sound, and hence the number of beats per second will be
equal to the difference of the rates of vibration. If we tune two of
three organ-pipes to the remaining one in the ratio of the minor and
major third, the mutual ratio of the rates of vibration of the first two
will be as 24: 25, that is to say, for every 24 vibrations to the lower
note there will be 25 to the higher, and one beat. If the two pipes give
together four beats in a second, then the higher has the fixed tone of
100 vibrations. The open pipe in question will consequently be five feet
in length. We also determine by this procedure the absolute rates of
vibration of all the other notes.
It follows at once that a pipe eight times as long or 40 feet in length
will yield a vibrational rate of 12½, which Sauveur ascribes to the
lowest audible tone, and further also that a pipe 64 times as small will
execute 6,400 vibrations, which Sauveur took for the highest audible
limit. The author's delight at his successful enumeration of the
"imperceptible vibrations" is unmistakably asserted here, and it is
justified when we reflect that to-day even Sauveur's principle, slightly
modified, constitutes the simplest and most delicate means we have for
exactly determining rates of vibration. Far more important still,
however, is a second observation which Sauveur made while studying
beats, and to which we shall revert later.
Strings whose lengths can be altered by movable bridges are much easier
to handle than pipes in such investigations, and it was natural that
Sauveur should soon resort to their use.