It was towards the close of the sixteenth century that Galileo with a superb indifference to the dialectic arts and sophistic subtleties of the Schoolmen of his time, turned the attention of his brilliant mind to nature. By nature his ideas were transformed and released from the fetters of inherited prejudice. At once the mighty revolution was felt, that was therewith effected in the realm of human thought—felt indeed in circles far remote and wholly unrelated to the sphere of science, felt in strata of society that hitherto had only indirectly recognised the influence of scientific thought.
And how great and how far-reaching that revolution was! From the beginning of the seventeenth century till its close we see arising, at least in embryo, almost all that plays a part in the natural and technical science of to-day, almost all that in the two centuries following so wonderfully transformed the facial appearance of the earth, and all that is moving onward in process of such mighty evolution to-day. And all this, the direct result of Galilean ideas, the direct outcome of that freshly awakened sense for the investigation of natural phenomena which taught the Tuscan philosopher to form the concept and the law of falling bodies from theobservationof a falling stone! Galileo began his investigations without an implement worthy of the name; he measured time in the most primitive way, by the efflux of water. Yet soon afterwards the telescope, the microscope, the barometer, the thermometer, the air-pump, the steam engine, the pendulum, and the electrical machine were invented in rapid succession. The fundamental theorems of dynamical science, of optics, of heat, and of electricity were all disclosed in the century that followed Galileo.
Of scarcely less importance, it seems, was that movement which was prepared for by the illustrious biologists of the hundred years just past, and formally begun by the late Mr. Darwin. Galileo quickened the sense for the simpler phenomena ofinorganicnature. And with the same simplicity and frankness that marked the efforts of Galileo, and without the aid oftechnical or scientific instruments, without physical or chemical experiment, but solely by the power of thought and observation, Darwin grasps a new property oforganicnature—which we may briefly call itsplasticity.[70]With the same directness of purpose, Darwin, too, pursues his way. With the same candor and love of truth, he points out the strength and the weakness of his demonstrations. With masterly equanimity he holds aloof from the discussion of irrelevant subjects and wins alike the admiration of his adherents and of his adversaries.
Scarcely thirty years have elapsed[71]since Darwin first propounded the principles of his theory of evolution.Yet, already we see his ideas firmly rooted in every branch of human thought, however remote. Everywhere, in history, in philosophy, even in the physical sciences, we hear the watchwords: heredity, adaptation, selection. We speak of the struggle for existence among the heavenly bodies and of the struggle for existence in the world of molecules.[72]
The impetus given by Galileo to scientific thought was marked in every direction; thus, his pupil, Borelli, founded the school of exact medicine, from whence proceeded even distinguished mathematicians. And now Darwinian ideas, in the same way, are animating all provinces of research. It is true, nature is not made up of two distinct parts, the inorganic and the organic; nor must these two divisions be treated perforce by totally distinct methods. Manysides, however, nature has. Nature is like a thread in an intricate tangle, which must be followed and traced, now from this point, now from that. But we must never imagine,—and this physicists have learned from Faraday and J. R. Mayer,—that progress along paths once entered upon is theonlymeans of reaching the truth.
It will devolve upon the specialists of the future to determine the relative tenability and fruitfulness of the Darwinian ideas in the different provinces. Here I wish simply to consider the growth of naturalknowledgein the light of the theory of evolution. For knowledge, too, is a product of organic nature. And althoughideas, as such, do not comport themselves in all respects like independent organic individuals, and although violent comparisons should be avoided, still, if Darwin reasoned rightly, the general imprint of evolution and transformation must be noticeable in ideas also.
I shall waive here the consideration of the fruitful topic of the transmission of ideas or rather of the transmission of the aptitude for certain ideas.[73]Nor would it come within my province to discuss psychical evolution in any form, as Spencer[74]and many other modern psychologists have done, with varying success. Neither shall I enter upon a discussion of the struggle for existence and of natural selection among scientific theories.[75]We shall consider here only such processes of transformation as every student can easily observe in his own mind.
The child of the forest picks out and pursues with marvellous acuteness the trails of animals. He outwits and overreaches his foes with surpassing cunning. He is perfectly at home in the sphere of his peculiar experience. But confront him with an unwonted phenomenon; place him face to face with a technical product of modern civilisation, and he will lapse into impotency and helplessness. Here are facts which he does not comprehend. If he endeavors to grasp their meaning, he misinterprets them. He fancies the moon, when eclipsed, to be tormented by an evil spirit. To his mind a puffing locomotive is a living monster. The letter accompanying a commission with which he is entrusted, having once revealed his thievishness, is in his imagination a conscious being, which he must hide beneath a stone, before venturing to commit a fresh trespass. Arithmetic to him is like the art of the geomancers in the Arabian Nights,—an art which is able to accomplish every imaginable impossibility. And, like Voltaire'singénu, when placed in our social world, he plays, as we think, the maddest pranks.
With the man who has made the achievements of modern science and civilisation his own, the case is quite different. He sees the moon pass temporarily into the shadow of the earth. He feels in his thoughts the water growing hot in the boiler of the locomotive; he feels also the increase of the tension which pushes the piston forward. Where he is not able to trace the direct relation of things he has recourse to his yard-stick and table of logarithms, which aid and facilitate his thought without predominating over it. Such opinions as he cannot concur in, are at least known to him, and he knows how to meet them in argument.
Now, wherein does the difference between these two men consist? The train of thought habitually employed by the first one does not correspond to the facts that he sees. He is surprised and nonplussed at every step. But the thoughts of the second man follow and anticipate events, his thoughts have become adapted or accommodated to the larger field of observation and activity in which he is located; he conceives things as they are. The Indian's sphere of experience, however, is quite different; his bodily organs of sense are in constant activity; he is ever intensely alert and on the watch for his foes; or, his entire attention and energy are engaged in procuring sustenance. Now, how can such a creature project his mind into futurity, foresee or prophesy? This is not possible until our fellow-beings have, in a measure, relieved us of our concern for existence. It is then that we acquire freedom for observation, and not infrequently too that narrowness of thought which society helps and teaches us to disregard.
If we move for a time within a fixed circle of phenomena which recur with unvarying uniformity, our thoughts gradually adapt themselves to our environment; our ideas reflect unconsciously our surroundings. The stone we hold in our hand, when dropped, not only falls to the ground in reality; it also falls in our thoughts. Iron-filings dart towards a magnet in imagination as well as in fact, and, when thrown into a fire, they grew hot in conception as well.
The impulse to complete mentally a phenomenon that has been only partially observed, has not its origin in the phenomenon itself; of this fact, we are fully sensible. And we well know that it does not lie within the sphere of our volition. It seems to confront us rather as a power and a law imposed from without and controlling both thought and facts.
The fact that we are able by the help of this law to prophesy and forecast, merely proves a sameness or uniformity of environment sufficient to effect a mental adaptation of this kind. A necessity of fulfilment, however, is not contained in this compulsory principle which controls our thoughts; nor is it in any way determined by the possibility of prediction. We are always obliged, in fact, to await the completion of what has been predicted. Errors and departures are constantly discernible, and are slight only in provinces of great rigid constancy, as in astronomy.
In cases where our thoughts follow the connexion of events with ease, and in instances where we positively forefeel the course of a phenomenon, it is natural to fancy that the latter is determined by and must conform to our thoughts. But the belief in that mysterious agency calledcausality, which holds thought and event in unison, is violently shaken when a person first enters a province of inquiry in which he has previously had no experience. Take for instance the strange interaction of electric currents and magnets, or the reciprocal action of currents, which seem to defy all the resources of mechanical science. Let him be confronted with such phenomena and he will immediately feel himself forsaken by his power of prediction; he will bring nothing with him into this strange field of events but the hope of soon being able to adapt his ideas to the new conditions there presented.
A person constructs from a bone the remaining anatomy of an animal; or from the visible part of a half-concealed wing of a butterfly he infers and reconstructs the part concealed. He does so with a feeling of highest confidence in the accuracy of his results; and in these processes we find nothing preternatural or transcendent. But when physicists adapt their thoughts to conform to the dynamical course of events in time, we invariably surround their investigations with a metaphysical halo; yet these latter adaptations bear quite the same character as the former, and our only reason for investing them with a metaphysical garb, perhaps, is their high practical value.[76]
Let us consider for a moment what takes place when the field of observation to which our ideas have been adapted and now conform, becomes enlarged. We had, let us say, always seen heavy bodies sink when their support was taken away; we had also seen, perhaps, that the sinking of heavier bodies forced lighter bodies upwards. But now we see a lever in action, and we are suddenly struck with the fact that a lighter body is lifting another of much greater weight. Our customary train of thought demands its rights; the new and unwonted event likewise demands its rights. From this conflict between thought and fact theproblemarises; out of this partial contrariety springs the question, "Why?" With the new adaptation to the enlarged field of observation, the problem disappears, or, in other words, is solved. In the instance cited, we must adopt the habit of always considering the mechanical work performed.
The child just awakening into consciousness of the world, knows no problem. The bright flower, the ringing bell, are all new to it; yet it is surprised at nothing. The out and out Philistine, whose only thoughts lie in the beaten path of his every-day pursuits, likewise has no problems. Everything goes its wonted course, and if perchance a thing go wrong at times, it is at most a mere object of curiosity and not worth serious consideration. In fact, the question "Why?" loses all warrant in relations where we are familiar with every aspect of events. But the capable and talented young man has his head full of problems; he has acquired, to a greater or less degree, certain habitudes of thought, and at the same time he is constantly observing what is new and unwonted, and in his case there is no end to the questions, "Why?"
Thus, the factor which most promotes scientific thought is the gradual widening of the field of experience. We scarcely notice events we are accustomed to; the latter do not really develop their intellectual significance until placed in contrast with something to which we are unaccustomed. Things that at home are passed by unnoticed, delight us when abroad, though they may appear in only slightly different forms. The sun shines with heightened radiance, the flowers bloom in brighter colors, our fellow-men accost us with lighter and happier looks. And, returning home, we find even the old familiar scenes more inspiring and suggestive than before.
Every motive that prompts and stimulates us to modify and transform our thoughts, proceeds from what is new, uncommon, and not understood. Novelty excites wonder in persons whose fixed habits of thought are shaken and disarranged by what they see. But the element of wonder never lies in the phenomenon or event observed; its place is in the person observing. People of more vigorous mental type aim at once at anadaptation of thoughtthat will conform to what they have observed. Thus does science eventually become the natural foe of the wonderful. The sources of the marvellous are unveiled, and surprise gives way to calm interpretation.
Let us consider such a mental transformative process in detail. The circumstance that heavy bodies fall to the earth appears perfectly natural and regular. But when a person observes that wood floats upon water, and that flames and smoke rise in the air, then the contrary of the first phenomenon is presented. An olden theory endeavors to explain these facts by imputing to substances the power of volition, as that attribute which is most familiar to man. It asserted that every substance seeks its proper place, heavy bodies tending downwards and light ones upwards. It soon turned out, however, that even smoke had weight, that it, too, sought its place below, and that it was forced upwards only because of the downward tendency of the air, as wood is forced to the surface of water because the water exerts the greater downward pressure.
Again, we see a body thrown into the air. It ascends. How is it that it does not seek its proper place? Why does the velocity of its "violent" motion decrease as it rises, while that of its "natural" fall increases as it descends. If we mark closely the relation between these two facts, the problem will solve itself. We shall see, as Galileo did, that the decrease of velocity in rising and the increase of velocity in falling are one and the same phenomenon, viz., an increase of velocity towards the earth. Accordingly, it is not a place that is assigned to the body, but an increase of velocity towards the earth.
By this idea the movements of heavy bodies are rendered perfectly familiar. Newton, now, firmly grasping this new way of thinking, sees the moon and the planets moving in their paths upon principles similar to those which determine the motion of a projectile thrown into the air. Yet the movements of the planets were marked by peculiarities which compelled him once more to modify slightly his customary mode of thought. The heavenly bodies, or rather the parts composing them, do not move with constant accelerations towards each other, but "attract each other," directly as the mass and inversely as the square of the distance.
This latter notion, which includes the one applying to terrestrial bodies as a special case, is, as we see, quite different from the conception from which we started. How limited in scope was the original idea and to what a multitude of phenomena is not the present one applicable! Yet there is a trace, after all, of the "search for place" in the expression "attraction." And it would be folly, indeed, for us to avoid, with punctilious dread, this conception of "attraction" as bearing marks of its pedigree. It is the historical base of the Newtonian conception and it still continues to direct our thoughts in the paths so long familiar to us. Thus, the happiest ideas do not fall from heaven, but spring from notions already existing.
Similarly, a ray of light was first regarded as a continuous and homogeneous straight line. It then became the path of projection for minute missiles; then an aggregate of the paths of countless different kinds of missiles. It became periodic; it acquired various sides; and ultimately it even lost its motion in a straight line.
The electric current was conceived originally as the flow of a hypothetical fluid. To this conception was soon added the notion of a chemical current, the notion of an electric, magnetic, and anisotropic optical field, intimately connected with the path of the current. And the richer a conception becomes in following and keeping pace with facts, the better adapted it is to anticipate them.
Adaptive processes of this kind have no assignable beginning, inasmuch as every problem that incites to new adaptation, presupposes a fixed habitude of thought. Moreover, they have no visible end; in so far as experience never ceases. Science, accordingly, stands midway in the evolutionary process; and science may advantageously direct and promote this process, but it can never take its place. That science is inconceivable the principles of which would enable a person with no experience to construct the world of experience, without a knowledge of it. One might just as well expect to become a great musician, solely by the aid of theory, and without musical experience; or to become a painter by following the directions of a text-book.
In glancing over the history of an idea with which we have become perfectly familiar, we are no longer able to appreciate the full significance of its growth. The deep and vital changes that have been effected in the course of its evolution, are recognisable only from the astounding narrowness of view with which great contemporary scientists have occasionally opposed each other. Huygens's wave-theory of light was incomprehensible to Newton, and Newton's idea of universal gravity was unintelligible to Huygens. But a century afterwards both notions were reconcilable, even in ordinary minds.
On the other hand, the original creations of pioneer intellects, unconsciously formed, do not assume a foreign garb; their form is their own. In them, childlike simplicity is joined to the maturity of manhood, and they are not to be compared with processes of thought in the average mind. The latter are carried on as are the acts of persons in the state of mesmerism, where actions involuntarily follow the images which the words of other persons suggest to their minds.
The ideas that have become most familiar through long experience, are the very ones that intrude themselves into the conception of every new fact observed. In every instance, thus, they become involved in a struggle for self-preservation, and it is just they that are seized by the inevitable process of transformation.
Upon this process rests substantially the method of explaining by hypothesis new and uncomprehended phenomena. Thus, instead of forming entirely new notions to explain the movements of the heavenly bodies and the phenomena of the tides, we imagine the material particles composing the bodies of the universe to possess weight or gravity with respect to one another. Similarly, we imagine electrified bodies to be freighted with fluids that attract and repel, or we conceive the space between them to be in a state of elastic tension. In so doing, we substitute for new ideas distinct and more familiar notions of old experience—notions which to a great extent run unimpeded in their courses, although they too must suffer partial transformation.
The animal cannot construct new members to perform every new function that circumstances and fate demand of it. On the contrary it is obliged to make use of those it already possesses. When a vertebrate animal chances into an environment where it must learn to fly or swim, an additional pair of extremities is not grown for the purpose. On the contrary, the animal must adapt and transform a pair that it already has.
The construction of hypotheses, therefore, is not the product of artificial scientific methods. This process is unconsciously carried on in the very infancy of science. Even later, hypotheses do not become detrimental and dangerous to progress except when more reliance is placed on them than on the facts themselves; when the contents of the former are more highly valued than the latter, and when, rigidly adhering to hypothetical notions, we overestimate the ideas we possess as compared with those we have to acquire.
The extension of our sphere of experience always involves a transformation of our ideas. It matters not whether the face of nature becomes actually altered, presenting new and strange phenomena, or whether these phenomena are brought to light by an intentional or accidental turn of observation. In fact, all the varied methods of scientific inquiry and of purposive mental adaptation enumerated by John Stuart Mill, those of observation as well as those of experiment, are ultimately recognisable as forms of one fundamental method, the method of change, or variation. It is through change of circumstances that the natural philosopher learns. This process, however, is by no means confined to the investigator of nature. The historian, the philosopher, the jurist, the mathematician, the artist, the æsthetician,[77]all illuminate and unfold their ideas by producing from the rich treasures of memory similar, but different, cases; thus, they observe and experiment in their thoughts. Even if all sense-experience should suddenly cease, the events of the days past would meet in different attitudes in the mind and the process of adaptation would still continue—a process which, in contradistinction to the adaptation of thoughts to facts in practical spheres, would be strictly theoretical, being an adaptation of thoughts to thoughts.
The method of change or variation brings before us like cases of phenomena, having partly the same and partly different elements. It is only by comparing different cases of refracted light at changing angles of incidence that the common factor, the constancy of the refractive index, is disclosed. And only by comparing the refractions of light of different colors, does the difference, the inequality of the indices of refraction, arrest the attention. Comparison based upon change leads the mind simultaneously to the highest abstractions and to the finest distinctions.
Undoubtedly, the animal also is able to distinguish between the similar and dissimilar of two cases. Its consciousness is aroused by a noise or a rustling, and its motor centre is put in readiness. The sight of the creature causing the disturbance, will, according to its size, provoke flight or prompt pursuit; and in the latter case, the more exact distinctions will determine the mode of attack. But man alone attains to the faculty of voluntary and conscious comparison. Man alone can, by his power of abstraction, rise, in one moment, to the comprehension of principles like the conservation of mass or the conservation of energy, and in the next observe and mark the arrangement of the iron lines in the spectrum. In thus dealing with the objects of his conceptual life, his ideas unfold and expand, like his nervous system, into a widely ramified and organically articulated tree, on which he may follow every limb to its farthermost branches, and, when occasion demands, return to the trunk from which he started.
The English philosopher Whewell has remarked that two things are requisite to the formation of science: facts and ideas. Ideas alone lead to empty speculation; mere facts can yield no organic knowledge. We see that all depends upon the capacity of adapting existing notions to fresh facts.
Over-readiness to yield to every new fact prevents fixed habits of thought from arising. Excessively rigid habits of thought impede freedom of observation. In the struggle, in the compromise between judgment and prejudgment (prejudice), if we may use the term, our understanding of things broadens.
Habitual judgment, applied to a new case without antecedent tests, we call prejudgment or prejudice. Who does not know its terrible power! But we think less often of the importance and utility of prejudice. Physically, no one could exist, if he had to guide and regulate the circulation, respiration, and digestion of his body by conscious and purposive acts. So, too, no one could exist intellectually if he had to form judgments on every passing experience, instead of allowing himself to be controlled by the judgments he has already formed. Prejudice is a sort of reflex motion in the province of intelligence.
On prejudices, that is, on habitual judgments not tested in every case to which they are applied, reposes a goodly portion of the thought and work of the natural scientist. On prejudices reposes most of the conduct of society. With the sudden disappearance of prejudice society would hopelessly dissolve. That prince displayed a deep insight into the power of intellectual habit, who quelled the loud menaces and demands of his body-guard for arrears of pay and compelled them to turn about and march, by simply pronouncing the regular word of command; he well knew that they would be unable to resist that.
Not until the discrepancy between habitual judgments and facts becomes great is the investigator implicated in appreciable illusion. Then tragic complications and catastrophes occur in the practical life of individuals and nations—crises where man, placing custom above life, instead of pressing it into the service of life, becomes the victim of his error. The very power which in intellectual life advances, fosters, and sustains us, may in other circumstances delude and destroy us.
Ideas are not all of life. They are only momentary efflorescences of 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]
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 exactingemployments 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 itsgrowth, in a frank and unbiassed manner. We know of onlyonesource ofimmediate revelationof 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 sciencecommunicationis. Not the dim, half-conscioussurmisesof the acute observer of nature or critic of humanity belong to science, but only that which they possess clearly enough tocommunicateto 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 andpassively, 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 forcomparisonknown 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 thecontemplativeelement. 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 anabstractorconceptualimport. 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 adirect 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 factAnow considered comports itself, not inone, but inmanyor inallits features, like an old and well-known factB. 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, anindirect 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 atheoryor atheoretical 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 ofa singlefeature of resemblance culled from memory, in this casea great systemof 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 toseekfrom such suggestions, and which are often actually found. It is thisrapidityin extending knowledge that gives to theory a preference over simple observation. But that preference is whollyquantitative. 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 factAin thought, always adifferent, but simpler and more familiar factB, which insomerelations can mentally representA, 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 ofspiritin the magnet. The behavior of a warm body or of anelectrifiedbody 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, thedramaticelement 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 expenseof 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,instinctivelythe notion of asubstanceis 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 bepowerfullystruck 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 isproducedby 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 atheoryit 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 adirect descriptionof 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 lessenedconsumption of materialby 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. Noteveryquantity, but the appropriately calculatedsumof the two, as connected with a proportionate consumption of material, appearssubstantial.
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.
Mayer was so absorbed with the view attained, that the indestructibility offorce, in our phraseologywork, appeared to hima priorievident. "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 powerfulformalneed 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 thisformalneed 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 ora prioriproposition 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 madeseveralsuch 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 thedirect descriptionof 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 descriptiondirectdescription, 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 bycomparisonwith 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 ananalogy. It is an effective means of mastering heterogeneous fields of facts in unitary comprehension. The path is plainly shown in whicha universal physical phenomenologyembracing 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-reachingabstract 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 animpulseto some accurately determined, often complicated, critical, comparative, or constructiveactivity, 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 practisedactions, 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 shouldprophesy, and Hertz uses that expression in his posthumousMechanics. 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 theaccelerations, 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 factclearto us, we must say "when we can reproduce it by verysimpleand very familiar intellectual operations, such as the construction of accelerations, or the geometrical summation of accelerations, and so forth." The requirement ofsimplicityis 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 theartisticvalue 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 higherclassifications, the individual facts that represent the ultimate terms of the system, are still so different that they must besinglynoted. 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, alwaysisolatedfacts remain, which show only aslightlikeness 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 ofqualitatively homogeneousfacts, differing from one another only in the number of equal parts into which their characteristic marks are divisible, that is, differing onlyquantitatively. 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 acontinuum 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 calllaw. 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.