light, designed to illuminate the paths of the will. But as delicate
reagents on our organic evolution our ideas are of paramount importance.
No theory can gainsay the vital transformation which we feel taking
place within us through their agency. Nor is it necessary that we should
have a proof of this process. We are immediately assured of it.
The transformation of ideas thus appears as a part of the general
evolution of life, as a part of its adaptation to a constantly widening
sphere of action. A granite boulder on a mountain-side tends towards the
earth below. It must abide in its resting-place for thousands of years
before its support gives way. The shrub that grows at its base is
farther advanced; it accommodates itself to summer and winter. The fox
which, overcoming the force of gravity, creeps to the summit where he
has scented his prey, is freer in his movements than either. The arm of
man reaches further still; and scarcely anything of note happens in
Africa or Asia that does not leave an imprint upon his life. What an
immense portion of the life of other men is reflected in ourselves;
their joys, their affections, their happiness and misery! And this too,
when we survey only our immediate surroundings, and confine our
attention to modern literature. How much more do we experience when we
travel through ancient Egypt with Herodotus, when we stroll through the
streets of Pompeii, when we carry ourselves back to the gloomy period of
the crusades or to the golden age of Italian art, now making the
acquaintance of a physician of Molière, and now that of a Diderot or of
a D'Alembert. What a great part of the life of others, of their
character and their purpose, do we not absorb through poetry and music!
And although they only gently touch the chords of our emotions, like the
memory of youth softly breathing upon the spirit of an aged man, we have
nevertheless lived them over again in part. How great and comprehensive
does self become in this conception; and how insignificant the person!
Egoistical systems both of optimism and pessimism perish with their
narrow standard of the import of intellectual life. We feel that the
real pearls of life lie in the ever changing contents of consciousness,
and that the person is merely an indifferent symbolical thread on which
they are strung.[78]
We are prepared, thus, to regard ourselves and every one of our ideas as
a product and a subject of universal evolution; and in this way we shall
advance sturdily and unimpeded along the paths which the future will
throw open to us.[79]
FOOTNOTES:
[Footnote 69: Inaugural Address, delivered on assuming the Rectorate
of the University of Prague, October 18, 1883.
The idea presented in this essay is neither new nor remote. I have
touched upon it myself on several occasions (first in 1867), but
have never made it the subject of a formal disquisition. Doubtless,
others, too, have treated it; it lies, so to speak, in the air.
However, as many of my illustrations were well received, although
known only in an imperfect form from the lecture itself and the
newspapers, I have, contrary to my original intention, decided to
publish it. It is not my intention to trespass here upon the domain
of biology. My statements are to be taken merely as the expression
of the fact that no one can escape the influence of a great and
far-reaching idea.]
[Footnote 70: At first sight an apparent contradiction arises from
the admission of both heredity and adaptation; and it is undoubtedly
true that a strong disposition to heredity precludes great
capability of adaptation. But imagine the organism to be a plastic
mass which retains the form transmitted to it by former influences
until new influences modify it; the _one_ property of _plasticity_
will then represent capability of adaptation as well as power of
heredity. Analogous to this is the case of a bar of magnetised steel
of high coercive force: the steel retains its magnetic properties
until a new force displaces them. Take also a body in motion: the
body retains the velocity acquired in (_inherited_ from) the
interval of time just preceding, except it be changed in the next
moment by an accelerating force. In the case of the body in motion
the _change_ of velocity (_Abänderung_) was looked upon as a matter
of course, while the discovery of the principle of _inertia_ (or
persistence) created surprise; in Darwin's case, on the contrary,
_heredity_ (or persistence) was taken for granted, while the
principle of _variation_ (_Abänderung_) appeared novel.
Fully adequate views are, of course, to be reached only by a study
of the original facts emphasised by Darwin, and not by these
analogies. The example referring to motion, if I am not mistaken, I
first heard, in conversation, from my friend J. Popper, Esq., of
Vienna.
Many inquirers look upon the stability of the species as something
settled, and oppose to it the Darwinian theory. But the stability of
the species is itself a "theory." The essential modifications which
Darwin's views also are undergoing will be seen from the works of
Wallace [and Weismann], but more especially from a book of W. H.
Rolph, _Biologische Probleme_, Leipsic, 1882. Unfortunately, this
last talented investigator is no longer numbered among the living.]
[Footnote 71: Written in 1883.]
[Footnote 72: See Pfaundler, _Pogg. Ann., Jubelband_, p. 182.]
[Footnote 73: See the beautiful discussions of this point in
Hering's _Memory as a General Function of Organised Matter_ (1870),
Chicago, The Open Court Publishing Co., 1887. Compare also Dubois,
_Ueber die Uebung_, Berlin, 1881.]
[Footnote 74: Spencer, _The Principles of Psychology_. London,
1872.]
[Footnote 75: See the article _The Velocity of Light_, page 63.]
[Footnote 76: I am well aware that the endeavor to confine oneself
in natural research to _facts_ is often censured as an exaggerated
fear of metaphysical spooks. But I would observe, that, judged by
the mischief which they have wrought, the metaphysical, of all
spooks, are the least fabulous. It is not to be denied that many
forms of thought were not originally acquired by the individual, but
were antecedently formed, or rather prepared for, in the development
of the species, in some such way as Spencer, Haeckel, Hering, and
others have supposed, and as I myself have hinted on various
occasions.]
[Footnote 77: Compare, for example, _Schiller, Zerstreute
Betrachtungen über verschiedene ästhetische Gegenstände_.]
[Footnote 78: We must not be deceived in imagining that the
happiness of other people is not a very considerable and essential
portion of our own. It is common capital, which cannot be created by
the individual, and which does not perish with him. The formal and
material limitation of the _ego_ is necessary and sufficient only
for the crudest practical objects, and cannot subsist in a broad
conception. Humanity in its entirety may be likened to a
polyp-plant. The material and organic bonds of individual union
have, indeed, been severed; they would only have impeded freedom of
movement and evolution. But the ultimate aim, the psychical
connexion of the whole, has been attained in a much higher degree
through the richer development thus made possible.]
[Footnote 79: C. E. von Baer, the subsequent opponent of Darwin and
Haeckel, has discussed in two beautiful addresses (_Das allgemeinste
Gesetz der Natur in aller Entwickelung_, and _Welche Auffassung der
lebenden Natur ist die richtige, und wie ist diese Auffassung auf
die Entomologie anzuwenden_?) the narrowness of the view which
regards an animal in its existing state as finished and complete,
instead of conceiving it as a phase in the series of evolutionary
forms and regarding the species itself as a phase of the development
of the animal world in general.]
ON THE PRINCIPLE OF COMPARISON IN PHYSICS.[80]
Twenty years ago when Kirchhoff defined the object of mechanics as the
"description, in complete and very simple terms, of the motions
occurring in nature," he produced by the statement a peculiar
impression. Fourteen years subsequently, Boltzmann, in the life-like
picture which he drew of the great inquirer, could still speak of the
universal astonishment at this novel method of treating mechanics, and
we meet with epistemological treatises to-day, which plainly show how
difficult is the acceptance of this point of view. A modest and small
band of inquirers there were, however, to whom Kirchhoff's few words
were tidings of a welcome and powerful ally in the epistemological
field.
Now, how does it happen that we yield our assent so reluctantly to the
philosophical opinion of an inquirer for whose scientific achievements
we have only words of praise? One reason probably is that few inquirers
can find time and leisure, amid the exacting employments demanded for
the acquisition of new knowledge, to inquire closely into that
tremendous psychical process by which science is formed. Further, it is
inevitable that much should be put into Kirchhoff's rigid words that
they were not originally intended to convey, and that much should be
found wanting in them that had always been regarded as an essential
element of scientific knowledge. What can mere description accomplish?
What has become of explanation, of our insight into the causal connexion
of things?
* * * * *
Permit me, for a moment, to contemplate not the results of science, but
the mode of its _growth_, in a frank and unbiassed manner. We know of
only _one_ source of _immediate revelation_ of scientific facts--_our
senses_. Restricted to this source alone, thrown wholly upon his own
resources, obliged to start always anew, what could the isolated
individual accomplish? Of a stock of knowledge so acquired the science
of a distant negro hamlet in darkest Africa could hardly give us a
sufficiently humiliating conception. For there that veritable miracle of
thought-transference has already begun its work, compared with which the
miracles of the spiritualists are rank monstrosities--_communication by
language_. Reflect, too, that by means of the magical characters which
our libraries contain we can raise the spirits of the "the sovereign
dead of old" from Faraday to Galileo and Archimedes, through ages of
time--spirits who do not dismiss us with ambiguous and derisive
oracles, but tell us the best they know; then shall we feel what a
stupendous and indispensable factor in the formation of science
_communication_ is. Not the dim, half-conscious _surmises_ of the acute
observer of nature or critic of humanity belong to science, but only
that which they possess clearly enough to _communicate_ to others.
But how, now, do we go about this communication of a newly acquired
experience, of a newly observed fact? As the different calls and
battle-cries of gregarious animals are unconsciously formed signs for a
common observation or action, irrespective of the causes which produce
such action--a fact that already involves the germ of the concept; so
also the words of human language, which is only more highly specialised,
are names or signs for universally known facts, which all can observe or
have observed. If the mental representation, accordingly, follows the
new fact at once and _passively_, then that new fact must, of itself,
immediately be constituted and represented in thought by facts already
universally known and commonly observed. Memory is always ready to put
forward for _comparison_ known facts which resemble the new event, or
agree with it in certain features, and so renders possible that
elementary internal judgment which the mature and definitively
formulated judgment soon follows.
Comparison, as the fundamental condition of communication, is the most
powerful inner vital element of science. The zoölogist sees in the
bones of the wing-membranes of bats, fingers; he compares the bones of
the cranium with the vertebræ, the embryos of different organisms with
one another, and the different stages of development of the same
organism with one another. The geographer sees in Lake Garda a fjord, in
the Sea of Aral a lake in process of drying up. The philologist compares
different languages with one another, and the formations of the same
language as well. If it is not customary to speak of comparative physics
in the same sense that we speak of comparative anatomy, the reason is
that in a science of such great experimental activity the attention is
turned away too much from the _contemplative_ element. But like all
other sciences, physics lives and grows by comparison.
* * * * *
The manner in which the result of the comparison finds expression in the
communication, varies of course very much. When we say that the colors
of the spectrum are red, yellow, green, blue, and violet, the
designations employed may possibly have been derived from the technology
of tattooing, or they may subsequently have acquired the significance of
standing for the colors of the rose, the lemon, the leaf, the
corn-flower, and the violet. From the frequent repetition of such
comparisons, however, made under the most manifold circumstances, the
inconstant features, as compared with the permanent congruent features,
get so obliterated that the latter acquire a fixed significance
independent of every object and connexion, or take on as we say an
_abstract_ or _conceptual_ import. No one thinks at the word "red" of
any other agreement with the rose than that of color, or at the word
"straight" of any other property of a stretched cord than the sameness
of direction. Just so, too, numbers, originally the names of the fingers
of the hands and feet, from being used as arrangement-signs for all
kinds of objects, were lifted to the plane of abstract concepts. A
verbal report (communication) of a fact that uses only these purely
abstract implements, we call a _direct description_.
The direct description of a fact of any great extent is an irksome task,
even where the requisite notions are already completely developed. What
a simplification it involves if we can say, the fact _A_ now considered
comports itself, not in _one_, but in _many_ or in _all_ its features,
like an old and well-known fact _B_. The moon comports itself as a heavy
body does with respect to the earth; light like a wave-motion or an
electric vibration; a magnet, as if it were laden with gravitating
fluids, and so on. We call such a description, in which we appeal, as it
were, to a description already and elsewhere formulated, or perhaps
still to be precisely formulated, an _indirect description_. We are at
liberty to supplement this description, gradually, by direct
description, to correct it, or to replace it altogether. We see, thus,
without difficulty, that what is called a _theory_ or a _theoretical
idea_, falls under the category of what is here termed indirect
description.
* * * * *
What, now, is a theoretical idea? Whence do we get it? What does it
accomplish for us? Why does it occupy a higher place in our judgment
than the mere holding fast to a fact or an observation? Here, too,
memory and comparison alone are in play. But instead of _a single_
feature of resemblance culled from memory, in this case _a great system_
of resemblances confronts us, a well-known physiognomy, by means of
which the new fact is immediately transformed into an old acquaintance.
Besides, it is in the power of the idea to offer us more than we
actually see in the new fact, at the first moment; it can extend the
fact, and enrich it with features which we are first induced to _seek_
from such suggestions, and which are often actually found. It is this
_rapidity_ in extending knowledge that gives to theory a preference over
simple observation. But that preference is wholly _quantitative_.
Qualitatively, and in real essential points, theory differs from
observation neither in the mode of its origin nor in its last results.
The adoption of a theory, however, always involves a danger. For a
theory puts in the place of a fact _A_ in thought, always a _different_,
but simpler and more familiar fact _B_, which in _some_ relations can
mentally represent _A_, but for the very reason that it is different, in
other relations cannot represent it. If now, as may readily happen,
sufficient care is not exercised, the most fruitful theory may, in
special circumstances, become a downright obstacle to inquiry. Thus, the
emission-theory of light, in accustoming the physicist to think of the
projectile path of the "light-particles" as an undifferentiated
straight-line, demonstrably impeded the discovery of the periodicity of
light. By putting in the place of light the more familiar phenomena of
sound, Huygens renders light in many of its features a familiar event,
but with respect to polarisation, which lacks the longitudinal waves
with which alone he was acquainted, it had for him a doubly strange
aspect. He is unable thus to grasp in abstract thought the fact of
polarisation, which is before his eyes, whilst Newton, merely by
adapting to the observation his thoughts, and putting this question,
"_Annon radiorum luminis diversa sunt latera?_" abstractly grasped
polarisation, that is, directly described it, a century before Malus. On
the other hand, if the agreement of the fact with the idea theoretically
representing it, extends further than its inventor originally
anticipated, then we may be led by it to unexpected discoveries, of
which conical refraction, circular polarisation by total reflexion,
Hertz's waves offer ready examples, in contrast to the illustrations
given above.
Our insight into the conditions indicated will be improved, perhaps, by
contemplating the development of some theory or other more in detail.
Let us consider a magnetised bar of steel by the side of a second
unmagnetised bar, in all other respects the same. The second bar gives
no indication of the presence of iron-filings; the first attracts them.
Also, when the iron-filings are absent, we must think of the magnetised
bar as in a different condition from that of the unmagnetised. For, that
the mere presence of the iron-filings does not induce the phenomenon of
attraction is proved by the second unmagnetised bar. The ingenuous man,
who finds in his will, as his most familiar source of power, the best
facilities for comparison, conceives a species of _spirit_ in the
magnet. The behavior of a warm body or of an _electrified_ body suggests
similar ideas. This is the point of view of the oldest theory,
_fetishism_, which the inquirers of the early Middle Ages had not yet
overcome, and which in its last vestiges, in the conception of forces,
still flourishes in modern physics. We see, thus, the _dramatic_ element
need no more be absent in a scientific description, than in a thrilling
novel.
If, on subsequent examination, it be observed that a cold body, in
contact with a hot body, warms itself, so to speak, _at the expense_ of
the hot body; further, that when the substances are the same, the cold
body, which, let us say, has twice the mass of the other, gains only
half the number of degrees of temperature that the other loses, a wholly
new impression arises. The demoniac character of the event vanishes, for
the supposed spirit acts not by caprice, but according to fixed laws. In
its place, however, _instinctively_ the notion of a _substance_ is
substituted, part of which flows over from the one body to the other,
but the total amount of which, representable by the sum of the products
of the masses into the respective changes of temperature, remains
constant. Black was the first to be _powerfully_ struck with this
resemblance of thermal processes to the motion of a substance, and under
its guidance discovered the specific heat, the heat of fusion, and the
heat of vaporisation of bodies. Gaining strength and fixity, however,
from these successes, this notion of substance subsequently stood in the
way of scientific advancement. It blinded the eyes of the successors of
Black, and prevented them from seeing the manifest fact, which every
savage knows, that heat is _produced_ by friction. Fruitful as that
notion was for Black, helpful as it still is to the learner to-day in
Black's special field, permanent and universal validity as a _theory_ it
could never maintain. But what is essential, conceptually, in it, viz.,
the constancy of the product-sum above mentioned, retains its value and
may be regarded as a _direct description_ of Black's facts.
It stands to reason that those theories which push themselves forward
unsought, instinctively, and wholly of their own accord, should have the
greatest power, should carry our thoughts most with them, and exhibit
the staunchest powers of self-preservation. On the other hand, it may
also be observed that when critically scrutinised such theories are
extremely apt to lose their cogency. We are constantly busied with
"substance," its modes of action have stamped themselves indelibly upon
our thoughts, our vividest and clearest reminiscences are associated
with it. It should cause us no surprise, therefore, that Robert Mayer
and Joule, who gave the final blow to Black's substantial conception of
heat, should have re-introduced the same notion of substance in a more
abstract and modified form, only applying to a much more extensive
field.
Here, too, the psychological circumstances which impart to the new
conception its power, lie clearly before us. By the unusual redness of
the venous blood in tropical climates Mayer's attention is directed to
the lessened expenditure of internal heat and to the proportionately
lessened _consumption of material_ by the human body in those climates.
But as every effort of the human organism, including its mechanical
work, is connected with the consumption of material, and as work by
friction can engender heat, therefore heat and work appear in kind
equivalent, and between them a proportional relation must subsist. Not
_every_ quantity, but the appropriately calculated _sum_ of the two, as
connected with a proportionate consumption of material, appears
_substantial_.
By exactly similar considerations, relative to the economy of the
galvanic element, Joule arrived at his view; he found experimentally
that the sum of the heat evolved in the circuit, of the heat consumed in
the combustion of the gas developed, of the electro-magnetic work of
the current, properly calculated,--in short, the sum of all the effects
of the battery,--is connected with a proportionate consumption of zinc.
Accordingly, this sum itself has a substantial character.