devait au fond revenir a établir le mécanique entière sur une autre
base: car la demonstration d'une loi qui embrasse toute une science
ne peut être autre chose qua la reduction de cette science à une
autre loi aussi générale, mais évidente, ou du moins plus simple que
la première, et qui partant la rende inutile."]
[Footnote 51: _Traité de la lumière_, Leyden, 1690, p. 2.]
[Footnote 52: "L'on ne sçaurait douter que la lumière ne consiste
dans le _mouvement_ de certaine matière. Car soit qu'on regarde sa
production, on trouve qu'içy sur la terre c'est principalement le
feu et la flamme qui l'engendrent, lesquels contient sans doute des
corps qui sont dans un mouvement rapide, puis qu'ils dissolvent et
fondent plusieurs autres corps des plus solides: soit qu'on regarde
ses effets, on voit que quand la lumière est ramasseé, comme par des
miroires concaves, elle a la vertu de brûler comme le feu.
c-est-à-dire qu'elle desunit les parties des corps; ce qui marque
assurément du _mouvement_, au moins dans la _vraye Philosophie_,
dans laquelle on conçoit la cause de tous les effets naturels par
des raisons de _mechanique_. Ce qu'il faut faire à mon avis, ou bien
renoncer à tout espérance de jamais rien comprendre dans la
Physique."]
[Footnote 53: _Sur la puissance motrice du feu_. (Paris, 1824.)]
[Footnote 54: "On objectra peut-être ici que le mouvement perpétuel,
démontré impossible par les _seules actions mécaniques_, ne l'est
peut-être pas lorsqu'on emploie l'influence soit de la _chaleur_,
soit de l'électricité; mais pent-on concevoir les phénomènes de la
chaleur et de l'électricité comme dus à autre chose qu'à des
_mouvements quelconques des corps_ et comme tels ne doivent-ils pas
être soumis aux lois générales de la mécanique?"]
[Footnote 55: By this is meant the temperature of a Celsius scale,
the zero of which is 273° below the melting-point of ice.]
[Footnote 56: I first drew attention to this fact in my treatise
_Ueber die Erhaltung der Arbeit_, Prague, 1872. Before this, Zeuner
had pointed out the analogy between mechanical and thermal energy. I
have given a more extensive development of this idea in a
communication to the _Sitzungsberichte der Wiener_ _Akademie_,
December, 1892, entitled _Geschichte und Kritik des Carnot'schen
Wärmegesetzes_. Compare also the works of Popper (1884), Helm
(1887), Wronsky (1888), and Ostwald (1892).]
[Footnote 57: Sir William Thomson first consciously and
intentionally introduced (1848, 1851) a _mechanical_ measure of
temperature similar to the electric measure of potential.]
[Footnote 58: Compare my _Analysis of the Sensations_, Jena, 1886:
English translation, Chicago, 1897.]
[Footnote 59: A better terminology appears highly desirable in the
place of the usual misleading one. Sir William Thomson (1852)
appears to have felt this need, and it has been clearly expressed by
F. Wald (1889). We should call the work which corresponds to a
vanished quantity of heat its mechanical substitution-value; while
that work which can be _actually_ performed in the passage of a
thermal condition _A_ to a condition _B_, alone deserves the name of
the _energy-value_ of this change of condition. In this way the
_arbitrary_ substantial conception of the processes would be
preserved and misapprehensions forestalled.]
THE ECONOMICAL NATURE OF PHYSICAL INQUIRY.[60]
When the human mind, with its limited powers, attempts to mirror in
itself the rich life of the world, of which it is itself only a small
part, and which it can never hope to exhaust, it has every reason for
proceeding economically. Hence that tendency, expressed in the
philosophy of all times, to compass by a few organic thoughts the
fundamental features of reality. "Life understands not death, nor death
life." So spake an old Chinese philosopher. Yet in his unceasing desire
to diminish the boundaries of the incomprehensible, man has always been
engaged in attempts to understand death by life and life by death.
Among the ancient civilised peoples, nature was filled with demons and
spirits having the feelings and desires of men. In all essential
features, this animistic view of nature, as Tylor[61] has aptly termed
it, is shared in common by the fetish-worshipper of modern Africa and
the most advanced nations of antiquity. As a theory of the world it has
never completely disappeared. The monotheism of the Christians never
fully overcame it, no more than did that of the Jews. In the belief in
witchcraft and in the superstitions of the sixteenth and seventeenth
centuries, the centuries of the rise of natural science, it assumed
frightful pathological dimensions. Whilst Stevinus, Kepler, and Galileo
were slowly rearing the fabric of modern physical science, a cruel and
relentless war was waged with firebrand and rack against the devils that
glowered from every corner. To-day even, apart from all survivals of
that period, apart from the traces of fetishism which still inhere in
our physical concepts,[62] those very ideas still covertly lurk in the
practices of modern spiritualism.
By the side of this animistic conception of the world, we meet from time
to time, in different forms, from Democritus to the present day, another
view, which likewise claims exclusive competency to comprehend the
universe. This view may be characterised as the _physico-mechanical_
view of the world. To-day, that view holds, indisputably, the first
place in the thoughts of men, and determines the ideals and the
character of our times. The coming of the mind of man into the full
consciousness of its powers, in the eighteenth century, was a period of
genuine disillusionment. It produced the splendid precedent of a life
really worthy of man, competent to overcome the old barbarism in the
practical fields of life; it created the _Critique of Pure Reason_,
which banished into the realm of shadows the sham-ideas of the old
metaphysics; it pressed into the hands of the mechanical philosophy the
reins which it now holds.
The oft-quoted words of the great Laplace,[63] which I will now give,
have the ring of a jubilant toast to the scientific achievements of the
eighteenth century: "A mind to which were given for a single instant all
the forces of nature and the mutual positions of all its masses, if it
were otherwise powerful enough to subject these problems to analysis,
could grasp, with a single formula, the motions of the largest masses as
well as of the smallest atoms; nothing would be uncertain for it; the
future and the past would lie revealed before its eyes." In writing
these words, Laplace, as we know, had also in mind the atoms of the
brain. That idea has been expressed more forcibly still by some of his
followers, and it is not too much to say that Laplace's ideal is
substantially that of the great majority of modern scientists.
Gladly do we accord to the creator of the _Mécanique céleste_ the sense
of lofty pleasure awakened in him by the great success of the
Enlightenment, to which we too owe our intellectual freedom. But to-day,
with minds undisturbed and before _new_ tasks, it becomes physical
science to secure itself against self-deception by a careful study of
its character, so that it can pursue with greater sureness its true
objects. If I step, therefore, beyond the narrow precincts of my
specialty in this discussion, to trespass on friendly neighboring
domains, I may plead in my excuse that the subject-matter of knowledge
is common to all domains of research, and that fixed, sharp lines of
demarcation cannot be drawn.
The belief in occult magic powers of nature has gradually died away, but
in its place a new belief has arisen, the belief in the magical power of
science. Science throws her treasures, not like a capricious fairy into
the laps of a favored few, but into the laps of all humanity, with a
lavish extravagance that no legend ever dreamt of! Not without apparent
justice, therefore, do her distant admirers impute to her the power of
opening up unfathomable abysses of nature, to which the senses cannot
penetrate. Yet she who came to bring light into the world, can well
dispense with the darkness of mystery, and with pompous show, which she
needs neither for the justification of her aims nor for the adornment of
her plain achievements.
The homely beginnings of science will best reveal to us its simple,
unchangeable character. Man acquires his first knowledge of nature
half-consciously and automatically, from an instinctive habit of
mimicking and forecasting facts in thought, of supplementing sluggish
experience with the swift wings of thought, at first only for his
material welfare. When he hears a noise in the underbrush he constructs
there, just as the animal does, the enemy which he fears; when he sees a
certain rind he forms mentally the image of the fruit which he is in
search of; just as we mentally associate a certain kind of matter with a
certain line in the spectrum or an electric spark with the friction of a
piece of glass. A knowledge of causality in this form certainly reaches
far below the level of Schopenhauer's pet dog, to whom it was ascribed.
It probably exists in the whole animal world, and confirms that great
thinker's statement regarding the will which created the intellect for
its purposes. These primitive psychical functions are rooted in the
economy of our organism not less firmly than are motion and digestion.
Who would deny that we feel in them, too, the elemental power of a long
practised logical and physiological activity, bequeathed to us as an
heirloom from our forefathers?
Such primitive acts of knowledge constitute to-day the solidest
foundation of scientific thought. Our instinctive knowledge, as we shall
briefly call it, by virtue of the conviction that we have consciously
and intentionally contributed nothing to its formation, confronts us
with an authority and logical power which consciously acquired knowledge
even from familiar sources and of easily tested fallibility can never
possess. All so-called axioms are such instinctive knowledge. Not
consciously gained knowledge alone, but powerful intellectual instinct,
joined with vast conceptive powers, constitute the great inquirer. The
greatest advances of science have always consisted in some successful
formulation, in clear, abstract, and communicable terms, of what was
instinctively known long before, and of thus making it the permanent
property of humanity. By Newton's principle of the equality of pressure
and counterpressure, whose truth all before him had felt, but which no
predecessor had abstractly formulated, mechanics was placed by a single
stroke on a higher level. Our statement might also be historically
justified by examples from the scientific labors of Stevinus, S. Carnot,
Faraday, J. R. Mayer, and others.
All this, however, is merely the soil from which science starts. The
first real beginnings of science appear in society, particularly in the
manual arts, where the necessity for the communication of experience
arises. Here, where some new discovery is to be described and related,
the compulsion is first felt of clearly defining in consciousness the
important and essential features of that discovery, as many writers can
testify. The aim of instruction is simply the saving of experience; the
labor of one man is made to take the place of that of another.
The most wonderful economy of communication is found in language. Words
are comparable to type, which spare the repetition of written signs and
thus serve a multitude of purposes; or to the few sounds of which our
numberless different words are composed. Language, with its helpmate,
conceptual thought, by fixing the essential and rejecting the
unessential, constructs its rigid pictures of the fluid world on the
plan of a mosaic, at a sacrifice of exactness and fidelity but with a
saving of tools and labor. Like a piano-player with previously prepared
sounds, a speaker excites in his listener thoughts previously prepared,
but fitting many cases, which respond to the speaker's summons with
alacrity and little effort.
The principles which a prominent political economist, E. Hermann,[64]
has formulated for the economy of the industrial arts, are also
applicable to the ideas of common life and of science. The economy of
language is augmented, of course, in the terminology of science. With
respect to the economy of written intercourse there is scarcely a doubt
that science itself will realise that grand old dream of the
philosophers of a Universal Real Character. That time is not far
distant. Our numeral characters, the symbols of mathematical analysis,
chemical symbols, and musical notes, which might easily be supplemented
by a system of color-signs, together with some phonetic alphabets now in
use, are all beginnings in this direction. The logical extension of what
we have, joined with a use of the ideas which the Chinese ideography
furnishes us, will render the special invention and promulgation of a
Universal Character wholly superfluous.
The communication of scientific knowledge always involves description,
that is, a mimetic reproduction of facts in thought, the object of which
is to replace and save the trouble of new experience. Again, to save the
labor of instruction and of acquisition, concise, abridged description
is sought. This is really all that natural laws are. Knowing the value
of the acceleration of gravity, and Galileo's laws of descent, we
possess simple and compendious directions for reproducing in thought all
possible motions of falling bodies. A formula of this kind is a complete
substitute for a full table of motions of descent, because by means of
the formula the data of such a table can be easily constructed at a
moment's notice without the least burdening of the memory.
No human mind could comprehend all the individual cases of refraction.
But knowing the index of refraction for the two media presented, and the
familiar law of the sines, we can easily reproduce or fill out in
thought every conceivable case of refraction. The advantage here
consists in the disburdening of the memory; an end immensely furthered
by the written preservation of the natural constants. More than this
comprehensive and condensed report about facts is not contained in a
natural law of this sort. In reality, the law always contains less than
the fact itself, because it does not reproduce the fact as a whole but
only in that aspect of it which is important for us, the rest being
either intentionally or from necessity omitted. Natural laws may be
likened to intellectual type of a higher order, partly movable, partly
stereotyped, which last on new editions of experience may become
downright impediments.
When we look over a province of facts for the first time, it appears to
us diversified, irregular, confused, full of contradictions. We first
succeed in grasping only single facts, unrelated with the others. The
province, as we are wont to say, is not _clear_. By and by we discover
the simple, permanent elements of the mosaic, out of which we can
mentally construct the whole province. When we have reached a point
where we can discover everywhere the same facts, we no longer feel lost
in this province; we comprehend it without effort; it is _explained_ for
us.
Let me illustrate this by an example. As soon as we have grasped the
fact of the rectilinear propagation of light, the regular course of our
thoughts stumbles at the phenomena of refraction and diffraction. As
soon as we have cleared matters up by our index of refraction we
discover that a special index is necessary for each color. Soon after we
have accustomed ourselves to the fact that light added to light
increases its intensity, we suddenly come across a case of total
darkness produced by this cause. Ultimately, however, we see everywhere
in the overwhelming multifariousness of optical phenomena the fact of
the spatial and temporal periodicity of light, with its velocity of
propagation dependent on the medium and the period. This tendency of
obtaining a survey of a given province with the least expenditure of
thought, and of representing all its facts by some one single mental
process, may be justly termed an economical one.
The greatest perfection of mental economy is attained in that science
which has reached the highest formal development, and which is widely
employed in physical inquiry, namely, in mathematics. Strange as it
may sound, the power of mathematics rests upon its evasion of
all unnecessary thought and on its wonderful saving of mental
operations. Even those arrangement-signs which we call numbers are a
system of marvellous simplicity and economy. When we employ the
multiplication-table in multiplying numbers of several places, and so
use the results of old operations of counting instead of performing the
whole of each operation anew; when we consult our table of logarithms,
replacing and saving thus new calculations by old ones already
performed; when we employ determinants instead of always beginning
afresh the solution of a system of equations; when we resolve new
integral expressions into familiar old integrals; we see in this simply
a feeble reflexion of the intellectual activity of a Lagrange or a
Cauchy, who, with the keen discernment of a great military commander,
substituted for new operations whole hosts of old ones. No one will
dispute me when I say that the most elementary as well as the highest
mathematics are economically-ordered experiences of counting, put in
forms ready for use.
In algebra we perform, as far as possible, all numerical operations
which are identical in form once for all, so that only a remnant of work
is left for the individual case. The use of the signs of algebra and
analysis, which are merely symbols of operations to be performed, is due
to the observation that we can materially disburden the mind in this way
and spare its powers for more important and more difficult duties, by
imposing all mechanical operations upon the hand. One result of this
method, which attests its economical character, is the construction of
calculating machines. The mathematician Babbage, the inventor of the
difference-engine, was probably the first who clearly perceived this
fact, and he touched upon it, although only cursorily, in his work, _The
Economy of Manufactures and Machinery_.
The student of mathematics often finds it hard to throw off the
uncomfortable feeling that his science, in the person of his pencil,
surpasses him in intelligence,--an impression which the great Euler
confessed he often could not get rid of. This feeling finds a sort of
justification when we reflect that the majority of the ideas we deal
with were conceived by others, often centuries ago. In great measure it
is really the intelligence of other people that confronts us in science.
The moment we look at matters in this light, the uncanniness and magical
character of our impressions cease, especially when we remember that we
can think over again at will any one of those alien thoughts.
Physics is experience, arranged in economical order. By this order not
only is a broad and comprehensive view of what we have rendered
possible, but also the defects and the needful alterations are made
manifest, exactly as in a well-kept household. Physics shares with
mathematics the advantages of succinct description and of brief,
compendious definition, which precludes confusion, even in ideas where,
with no apparent burdening of the brain, hosts of others are contained.
Of these ideas the rich contents can be produced at any moment and
displayed in their full perceptual light. Think of the swarm of
well-ordered notions pent up in the idea of the potential. Is it
wonderful that ideas containing so much finished labor should be easy to
work with?
Our first knowledge, thus, is a product of the economy of
self-preservation. By communication, the experience of _many_ persons,
individually acquired at first, is collected in _one_. The communication
of knowledge and the necessity which every one feels of managing his
stock of experience with the least expenditure of thought, compel us to
put our knowledge in economical forms. But here we have a clue which
strips science of all its mystery, and shows us what its power really
is. With respect to specific results it yields us nothing that we could
not reach in a sufficiently long time without methods. There is no
problem in all mathematics that cannot be solved by direct counting. But
with the present implements of mathematics many operations of counting
can be performed in a few minutes which without mathematical methods
would take a lifetime. Just as a single human being, restricted wholly
to the fruits of his own labor, could never amass a fortune, but on the
contrary the accumulation of the labor of many men in the hands of one
is the foundation of wealth and power, so, also, no knowledge worthy of
the name can be gathered up in a single human mind limited to the span
of a human life and gifted only with finite powers, except by the most
exquisite economy of thought and by the careful amassment of the
economically ordered experience of thousands of co-workers. What strikes
us here as the fruits of sorcery are simply the rewards of excellent
housekeeping, as are the like results in civil life. But the business of
science has this advantage over every other enterprise, that from _its_
amassment of wealth no one suffers the least loss. This, too, is its
blessing, its freeing and saving power.
The recognition of the economical character of science will now help us,
perhaps, to understand better certain physical notions.
Those elements of an event which we call "cause and effect" are certain
salient features of it, which are important for its mental reproduction.
Their importance wanes and the attention is transferred to fresh
characters the moment the event or experience in question becomes
familiar. If the connexion of such features strikes us as a necessary
one, it is simply because the interpolation of certain intermediate
links with which we are very familiar, and which possess, therefore,
higher authority for us, is often attended with success in our
explanations. That _ready_ experience fixed in the mosaic of the mind
with which we meet new events, Kant calls an innate concept of the
understanding (_Verstandesbegriff_).
The grandest principles of physics, resolved into their elements, differ
in no wise from the descriptive principles of the natural historian. The
question, "Why?" which is always appropriate where the explanation of a
contradiction is concerned, like all proper habitudes of thought, can
overreach itself and be asked where nothing remains to be understood.
Suppose we were to attribute to nature the property of producing like
effects in like circumstances; just these like circumstances we should
not know how to find. Nature exists once only. Our schematic mental
imitation alone produces like events. Only in the mind, therefore, does
the mutual dependence of certain features exist.
All our efforts to mirror the world in thought would be futile if we
found nothing permanent in the varied changes of things. It is this that
impels us to form the notion of substance, the source of which is not
different from that of the modern ideas relative to the conservation of
energy. The history of physics furnishes numerous examples of this
impulse in almost all fields, and pretty examples of it may be traced
back to the nursery. "Where does the light go to when it is put out?"
asks the child. The sudden shrivelling up of a hydrogen balloon is
inexplicable to a child; it looks everywhere for the large body which
was just there but is now gone.
Where does heat come from? Where does heat go to? Such childish
questions in the mouths of mature men shape the character of a century.