of _force_, in our phraseology _work_, appeared to him _a priori_
evident. "The creation or annihilation of a force," he says, "lies
without the province of human thought and power." Joule expressed
himself to a similar effect: "It is manifestly absurd to suppose that
the powers with which God has endowed matter can be destroyed." Strange
to say, on the basis of such utterances, not Joule, but Mayer, was
stamped as a metaphysician. We may be sure, however, that both men were
merely giving expression, and that half-unconsciously, to a powerful
_formal_ need of the new simple view, and that both would have been
extremely surprised if it had been proposed to them that their principle
should be submitted to a philosophical congress or ecclesiastical synod
for a decision upon its validity. But with all agreements, the attitude
of these two men, in other respects, was totally different. Whilst Mayer
represented this _formal_ need with all the stupendous instinctive force
of genius, we might say almost with the ardor of fanaticism, yet was
withal not wanting in the conceptive ability to compute, prior to all
other inquirers, the mechanical equivalent of heat from old physical
constants long known and at the disposal of all, and so to set up for
the new doctrine a programme embracing all physics and physiology;
Joule, on the other hand, applied himself to the exact verification of
the doctrine by beautifully conceived and masterfully executed
experiments, extending over all departments of physics. Soon Helmholtz
too attacked the problem, in a totally independent and characteristic
manner. After the professional virtuosity with which this physicist
grasped and disposed of all the points unsettled by Mayer's programme
and more besides, what especially strikes us is the consummate critical
lucidity of this young man of twenty-six years. In his exposition is
wanting that vehemence and impetuosity which marked Mayer's. The
principle of the conservation of energy is no self-evident or _a priori_
proposition for him. What follows, on the assumption that that
proposition obtains? In this hypothetical form, he subjugates his
matter.
I must confess, I have always marvelled at the æsthetic and ethical
taste of many of our contemporaries who have managed to fabricate out of
this relation of things, odious national and personal questions, instead
of praising the good fortune that made _several_ such men work together
and of rejoicing at the instructive diversity and idiosyncrasies of
great minds fraught with such rich consequences for us.
We know that still another theoretical conception played a part in the
development of the principle of energy, which Mayer held aloof from,
namely, the conception that heat, as also the other physical processes,
are due to motion. But once the principle of energy has been reached,
these auxiliary and transitional theories discharge no essential
function, and we may regard the principle, like that which Black gave,
as a contribution to the _direct description_ of a widely extended
domain of facts.
It would appear from such considerations not only advisable, but even
necessary, with all due recognition of the helpfulness of theoretic
ideas in research, yet gradually, as the new facts grow familiar, to
substitute for indirect description _direct_ description, which contains
nothing that is unessential and restricts itself absolutely to the
abstract apprehension of facts. We might almost say, that the
descriptive sciences, so called with a tincture of condescension, have,
in respect of scientific character, outstripped the physical expositions
lately in vogue. Of course, a virtue has been made of necessity here.
We must admit, that it is not in our power to describe directly every
fact, on the moment. Indeed, we should succumb in utter despair if the
whole wealth of facts which we come step by step to know, were presented
to us all at once. Happily, only detached and unusual features first
strike us, and such we bring nearer to ourselves by _comparison_ with
every-day events. Here the notions of the common speech are first
developed. The comparisons then grow more manifold and numerous, the
fields of facts compared more extensive, the concepts that make direct
description possible, proportionately more general and more abstract.
First we become familiar with the motion of freely falling bodies. The
concepts of force, mass, and work are then carried over, with
appropriate modifications, to the phenomena of electricity and
magnetism. A stream of water is said to have suggested to Fourier the
first distinct picture of currents of heat. A special case of vibrations
of strings investigated by Taylor, cleared up for him a special case of
the conduction of heat. Much in the same way that Daniel Bernoulli and
Euler constructed the most diverse forms of vibrations of strings from
Taylor's cases, so Fourier constructs out of simple cases of conduction
the most multifarious motions of heat; and that method has extended
itself over the whole of physics. Ohm forms his conception of the
electric current in imitation of Fourier's. The latter, also, adopts
Fick's theory of diffusion. In an analogous manner a conception of the
magnetic current is developed. All sorts of stationary currents are thus
made to exhibit common features, and even the condition of complete
equilibrium in an extended medium shares these features with the
dynamical condition of equilibrium of a stationary current. Things as
remote as the magnetic lines of force of an electric current and the
stream-lines of a frictionless liquid vortex enter in this way into a
peculiar relationship of similarity. The concept of potential,
originally enunciated for a restricted province, acquires a
wide-reaching applicability. Things as dissimilar as pressure,
temperature, and electromotive force, now show points of agreement in
relation to ideas derived by definite methods from that concept: viz.,
fall of pressure, fall of temperature, fall of potential, as also with
the further notions of liquid, thermal, and electric strength of
current. That relationship between systems of ideas in which the
dissimilarity of every two homologous concepts as well as the agreement
in logical relations of every two homologous pairs of concepts, is
clearly brought to light, is called an _analogy_. It is an effective
means of mastering heterogeneous fields of facts in unitary
comprehension. The path is plainly shown in which _a universal physical
phenomenology_ embracing all domains, will be developed.
In the process described we attain for the first time to what is
indispensable in the direct description of broad fields of fact--the
wide-reaching _abstract concept_. And now I must put a question smacking
of the school-master, but unavoidable: What is a concept? Is it a hazy
representation, admitting withal of mental visualisation? No. Mental
visualisation accompanies it only in the simplest cases, and then merely
as an adjunct. Think, for example, of the "coefficient of
self-induction," and seek for its visualised mental image. Or is,
perhaps, the concept a mere word? The adoption of this forlorn idea,
which has been actually proposed of late by a reputed mathematician
would only throw us back a thousand years into the deepest
scholasticism. We must, therefore, reject it.
The solution is not far to seek. We must not think that sensation, or
representation, is a purely passive process. The lowest organisms
respond to it with a simple reflex motion, by engulfing the prey which
approaches them. In higher organisms the centripetal stimulus encounters
in the nervous system obstacles and aids which modify the centrifugal
process. In still higher organisms, where prey is pursued and examined,
the process in question may go through extensive paths of circular
motions before it comes to relative rest. Our own life, too, is enacted
in such processes; all that we call science may be regarded as parts, or
middle terms, of such activities.
It will not surprise us now if I say: the definition of a concept, and,
when it is very familiar, even its name, is an _impulse_ to some
accurately determined, often complicated, critical, comparative, or
constructive _activity_, the usually sense-perceptive result of which is
a term or member of the concept's scope. It matters not whether the
concept draws the attention only to one certain sense (as sight) or to a
phase of a sense (as color, form), or is the starting-point of a
complicated action; nor whether the activity in question (chemical,
anatomical, and mathematical operations) is muscular or technical, or
performed wholly in the imagination, or only intimated. The concept is
to the physicist what a musical note is to a piano-player. A trained
physicist or mathematician reads a memoir like a musician reads a score.
But just as the piano-player must first learn to move his fingers singly
and collectively, before he can follow his notes without effort, so the
physicist or mathematician must go through a long apprenticeship before
he gains control, so to speak, of the manifold delicate innervations of
his muscles and imagination. Think of how frequently the beginner in
physics or mathematics performs more, or less, than is required, or of
how frequently he conceives things differently from what they are! But
if, after having had sufficient discipline, he lights upon the phrase
"coefficient of self-induction," he knows immediately what that term
requires of him. Long and thoroughly practised _actions_, which have
their origin in the necessity of comparing and representing facts by
other facts, are thus the very kernel of concepts. In fact, positive and
philosophical philology both claim to have established that all roots
represent concepts and stood originally for muscular activities alone.
The slow assent of physicists to Kirchhoff's dictum now becomes
intelligible. They best could feel the vast amount of individual labor,
theory, and skill required before the ideal of direct description could
be realised.
* * * * *
Suppose, now, the ideal of a given province of facts is reached. Does
description accomplish all that the inquirer can ask? In my opinion, it
does. Description is a building up of facts in thought, and this
building up is, in the experimental sciences, often the condition of
actual execution. For the physicist, to take a special case, the
metrical units are the building-stones, the concepts the directions for
building, and the facts the result of the building. Our mental imagery
is almost a complete substitute for the fact, and by means of it we can
ascertain all the fact's properties. We do not know that worst which we
ourselves have made.
People require of science that it should _prophesy_, and Hertz uses that
expression in his posthumous _Mechanics_. But, natural as it is, the
expression is too narrow. The geologist and the palæontologist, at times
the astronomer, and always the historian and the philologist, prophesy,
so to speak, _backwards_. The descriptive sciences, like geometry and
mathematics, prophesy neither forward or backwards, but seek from given
conditions the conditioned. Let us say rather: _Science completes in
thought facts that are only partly given_. This is rendered possible by
description, for description presupposes the interdependence of the
descriptive elements: otherwise nothing would be described.
It is said, description leaves the sense of causality unsatisfied. In
fact, many imagine they understand motions better when they picture to
themselves the pulling forces; and yet the _accelerations_, the facts,
accomplish more, without superfluous additions. I hope that the science
of the future will discard the idea of cause and effect, as being
formally obscure; and in my feeling that these ideas contain a strong
tincture of fetishism, I am certainly not alone. The more proper course
is, _to regard the abstract determinative elements of a fact as
interdependent_, in a purely logical way, as the mathematician or
geometer does. True, by comparison with the will, forces are brought
nearer to our feeling; but it may be that ultimately the will itself
will be made clearer by comparison with the accelerations of masses.
If we are asked, candidly, when is a fact _clear_ to us, we must say
"when we can reproduce it by very _simple_ and very familiar
intellectual operations, such as the construction of accelerations, or
the geometrical summation of accelerations, and so forth." The
requirement of _simplicity_ is of course to the expert a different
matter from what it is to the novice. For the first, description by a
system of differential equations is sufficient; for the second, a
gradual construction out of elementary laws is required. The first
discerns at once the connexion of the two expositions. Of course, it is
not disputed that the _artistic_ value of materially equivalent
descriptions may not be different.
Most difficult is it to persuade strangers that the grand universal laws
of physics, such as apply indiscriminately to material, electrical,
magnetic, and other systems, are not essentially different from
descriptions. As compared with many sciences, physics occupies in this
respect a position of vantage that is easily explained. Take, for
example, anatomy. As the anatomist in his quest for agreements and
differences in animals ascends to ever higher and higher
_classifications_, the individual facts that represent the ultimate
terms of the system, are still so different that they must be _singly_
noted. Think, for example, of the common marks of the Vertebrates, of
the class-characters of Mammals and Birds on the one hand and of Fishes
on the other, of the double circulation of the blood on the one hand and
of the single on the other. In the end, always _isolated_ facts remain,
which show only a _slight_ likeness to one another.
A science still more closely allied to physics, chemistry, is often in
the same strait. The abrupt change of the qualitative properties, in all
likelihood conditioned by the slight stability of the intermediate
states, the remote resemblance of the co-ordinated facts of chemistry
render the treatment of its data difficult. Pairs of bodies of different
qualitative properties unite in different mass-ratios; but no connexion
between the first and the last is to be noted, at first.
Physics, on the other hand, reveals to us wide domains of _qualitatively
homogeneous_ facts, differing from one another only in the number of
equal parts into which their characteristic marks are divisible, that
is, differing only _quantitatively_. Even where we have to deal with
qualities (colors and sounds), quantitative characters of those
qualities are at our disposal. Here the classification is so simple a
task that it rarely impresses us as such, whilst in infinitely fine
gradations, in a _continuum of facts_, our number-system is ready
beforehand to follow as far as we wish. The co-ordinated facts are here
extremely similar and very closely affined, as are also their
descriptions which consist in the determination of the numerical
measures of one given set of characters from those of a different set by
means of familiar mathematical operations--methods of derivation. Thus,
the common characteristics of all descriptions can be found here; and
with them a succinct, comprehensive description, or a rule for the
construction of all single descriptions, is assigned,--and this we call
_law_. Well-known examples are the formulæ for freely falling bodies,
for projectiles, for central motion, and so forth. If physics apparently
accomplishes more by its methods than other sciences, we must remember
that in a sense it has presented to it much simpler problems.
The remaining sciences, whose facts also present a physical side, need
not be envious of physics for this superiority; for all its acquisitions
ultimately redound to their benefit as well. But also in other ways this
mutual help shall and must change. Chemistry has advanced very far in
making the methods of physics her own. Apart from older attempts, the
periodical series of Lothar Meyer and Mendelejeff are a brilliant and
adequate means of producing an easily surveyed system of facts, which by
gradually becoming complete, will take the place almost of a continuum
of facts. Further, by the study of solutions, of dissociation, in fact
generally of phenomena which present a continuum of cases, the methods
of thermodynamics have found entrance into chemistry. Similarly we may
hope that, at some future day, a mathematician, letting the
fact-continuum of embryology play before his mind, which the
palæontologists of the future will supposedly have enriched with more
intermediate and derivative forms between Saurian and Bird than the
isolated Pterodactyl, Archæopteryx, Ichthyornis, and so forth, which we
now have--that such a mathematician shall transform, by the variation of
a few parameters, as in a dissolving view, one form into another, just
as we transform one conic section into another.
Reverting now to Kirchhoff's words, we can come to some agreement
regarding their import. Nothing can be built without building-stones,
mortar, scaffolding, and a builder's skill. Yet assuredly the wish is
well founded, that will show to posterity the complete structure in its
finished form, bereft of unsightly scaffolding. It is the pure logical
and æsthetic sense of the mathematician that speaks out of Kirchhoff's
words. Modern expositions of physics aspire after his ideal; that, too,
is intelligible. But it would be a poor didactic shift, for one whose
business it was to train architects, to say: "Here is a splendid
edifice; if thou wouldst really build, go thou and do likewise".
The barriers between the special sciences, which make division of work
and concentration possible, but which appear to us after all as cold and
conventional restrictions, will gradually disappear. Bridge upon bridge
is thrown over the gaps. Contents and methods, even of the remotest
branches, are compared. When the Congress of Natural Scientists shall
meet a hundred years hence, we may expect that they will represent a
unity in a higher sense than is possible to-day, not in sentiment and
aim alone, but in method also. In the meantime, this great change will
be helped by our keeping constantly before our minds the fact of the
intrinsic relationship of all research, which Kirchhoff characterised
with such classical simplicity.
FOOTNOTES:
[Footnote 80: An address delivered before the General Session of the
German Association of Naturalists and Physicians, at Vienna, Sept.
24, 1894.]
THE PART PLAYED BY ACCIDENT IN INVENTION AND DISCOVERY.[81]
It is characteristic of the naïve and sanguine beginnings of thought in
youthful men and nations, that all problems are held to be soluble and
fundamentally intelligible on the first appearance of success. The sage
of Miletus, on seeing plants take their rise from moisture, believed he
had comprehended the whole of nature, and he of Samos, on discovering
that definite numbers corresponded to the lengths of harmonic strings,
imagined he could exhaust the nature of the world by means of numbers.
Philosophy and science in such periods are blended. Wider experience,
however, speedily discloses the error of such a course, gives rise to
criticism, and leads to the division and ramification of the sciences.
At the same time, the necessity of a broad and general view of the world
remains; and to meet this need philosophy parts company with special
inquiry. It is true, the two are often found united in gigantic
personalities. But as a rule their ways diverge more and more widely
from each other. And if the estrangement of philosophy from science can
reach a point where data unworthy of the nursery are not deemed too
scanty as foundations of the world, on the other hand the thorough-paced
specialist may go to the extreme of rejecting point-blank the
possibility of a broader view, or at least of deeming it superfluous,
forgetful of Voltaire's apophthegm, nowhere more applicable than here,
_Le superflu--chose très nécessaire_.
It is true, the history of philosophy, owing to the insufficiency of its
constructive data, is and must be largely a history of error. But it
would be the height of ingratitude on our part to forget that the seeds
of thoughts which still fructify the soil of special research, such as
the theory of irrationals, the conceptions of conservation, the doctrine
of evolution, the idea of specific energies, and so forth, may be traced
back in distant ages to philosophical sources. Furthermore, to have
deferred or abandoned the attempt at a broad philosophical view of the
world from a full knowledge of the insufficiency of our materials, is
quite a different thing from never having undertaken it at all. The
revenge of its neglect, moreover, is constantly visited upon the
specialist by his committal of the very errors which philosophy long ago
exposed. As a fact, in physics and physiology, particularly during the
first half of this century, are to be met intellectual productions
which for naïve simplicity are not a jot inferior to those of the Ionian
school, or to the Platonic ideas, or to that much reviled ontological
proof.
Latterly, there has been evidence of a gradual change in the situation.
Recent philosophy has set itself more modest and more attainable ends;
it is no longer inimical to special inquiry; in fact, it is zealously
taking part in that inquiry. On the other hand, the special sciences,
mathematics and physics, no less than philology, have become eminently
philosophical. The material presented is no longer accepted
uncritically. The glance of the inquirer is bent upon neighboring
fields, whence that material has been derived. The different special
departments are striving for closer union, and gradually the conviction
is gaining ground that philosophy can consist only of mutual,
complemental criticism, interpenetration, and union of the special
sciences into a consolidated whole. As the blood in nourishing the body
separates into countless capillaries, only to be collected again and to
meet in the heart, so in the science of the future all the rills of
knowledge will gather more and more into a common and undivided stream.
It is this view--not an unfamiliar one to the present generation--that I
purpose to advocate. Entertain no hope, or rather fear, that I shall
construct systems for you. I shall remain a natural inquirer. Nor expect
that it is my intention to skirt all the fields of natural inquiry. I
can attempt to be your guide only in that branch which is familiar to
me, and even there I can assist in the furtherment of only a small
portion of the allotted task. If I shall succeed in rendering plain to
you the relations of physics, psychology, and the theory of knowledge,
so that you may draw from each profit and light, redounding to the
advantage of each, I shall regard my work as not having been in vain.
Therefore, to illustrate by an example how, consonantly with my powers
and views, I conceive such inquiries should be conducted, I shall treat
to-day, in the form of a brief sketch, of the following special and
limited subject--of _the part which accidental circumstances play in the
development of inventions and discoveries_.
* * * * *
When we Germans say of a man that he was not the inventor of
gunpowder,[82] we impliedly cast a grave suspicion on his abilities. But
the expression is not a felicitous one, as there is probably no
invention in which deliberate thought had a smaller, and pure luck a
larger, share than in this. It is well to ask, Are we justified in
placing a low estimate on the achievement of an inventor because
accident has assisted him in his work? Huygens, whose discoveries and
inventions are justly sufficient to entitle him to an opinion in such
matters, lays great emphasis on this factor. He asserts that a man
capable of inventing the telescope without the concurrence of accident
must have been gifted with superhuman genius.[83]
A man living in the midst of civilisation finds himself surrounded by a
host of marvellous inventions, considering none other than the means of
satisfying the needs of daily life. Picture such a man transported to
the epoch preceding the invention of these ingenious appliances, and
imagine him undertaking in a serious manner to comprehend their origin.
At first the intellectual power of the men capable of producing such
marvels will strike him as incredible, or, if we adopt the ancient view,
as divine. But his astonishment is considerably allayed by the
disenchanting yet elucidative revelations of the history of primitive
culture, which to a large extent prove that these inventions took their
rise very slowly and by imperceptible degrees.