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THE FOUNDATIONS OF THE NINETEENTH CENTURY -- VOLUMES 1 & 2 |
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2. SCIENCE (FROM ROGER BACON TO LAVOISIER) The difference between science and the raw material of knowledge, which is supplied by discovery, has already been pointed out, and I refer the reader to the discussion on p. 236; I also called attention to the boundary-line between science and philosophy. The fact that sharp distinguishing-lines can never be drawn without some arbitrary differentiation does not in any way invalidate the principle of separation. Even the sciences, that is, our new Teutonic scientific methods, have taught us another lesson. Leibniz might for all that again adopt the so-called law of continuity and carry it to its extreme consequences; in practice we dispense with metaphysical proof, for even experience shows us on all sides a gradual merging and blending. [1] But in order to build up science we must distinguish, and the correct differentiation is that which holds good in practice. Nature, of course, knows no such separation; that does not matter; nature knows no science either; it is differentiation in the material supplied by nature, followed by reuniting according to humanly comprehensible principles, that in general forms science.
That is why I appealed to Bichat at the beginning of this section. If the classification of tissues which he taught had been revealed by nature as classification, it would have been known from the earliest times; bl1t this is far from being the case, for the distinctions proposed by Bichat have been considerably modified since; as a matter of fact, we find everywhere transitional stages between the kinds of tissue, some of them perfectly obvious, others which reveal themselves only to minuter observation; and thus thoughtful investigators have been forced to experiment, till they were able to fix the exact point where the needs of the human intellect and respect for the facts of nature harmoniously counterbalance each other. This point can be determined -- not, it is true, at once, but by practical experience; for in its methods science is guided by two considerations, it has to store up as capital what is known, and it has to see that this capital bears interest in the form of new knowledge. It is by this standard that the work of a Bichat is measured; for here, as elsewhere, genius does not invent, it does not create out of nothing, but shapes what is present. As Horrier moulded the popular poetry, so Bichat gave shape to anatomy; and the same method is necessary in every department of knowledge. [3] This purely methodological remark, meant only to justify my own procedure, has obviously brought us to the heart of the subject; indeed I think we have already unwittingly laid our finger upon the central point. I have already pointed out that, while the Hellenes may be superior to us as theorists, they are certainly inferior as observers. Now theorising and systematising is nothing else than the shaping work of science. If we do not shape -- that is to say, if we do not theorise and systematise -- we can only assimilate a minimum of knowledge; it flows through our brain as through a sieve. However, the process of shaping is not without its drawbacks; for, as pointed out in Bichat's case; this shaping is essentially human, that is, in reference to nature it is a mere one-sided and inadequate beginning. The natural sciences [4] themselves reveal the nullity of the gross anthropomorphism of all the Hegels in the world. It is not true that the human intellect can adequately grasp phenomena; the sciences prove the contrary; everyone whose mind has been trained in the school of observation knows that. Even the much profounder conception of a Paracelsus, who called surrounding nature the "outer man," may, it is true, attract us from the point of view of philosophy, but it will be found to be, scientifically, of little use; for whenever I have to deal with empirical facts, my innermost heart is a muscle and my thought the function of a grey and white mass encased within a skull: so far as the life of my inner personality is concerned, this is all just as "external" as any of those stars, whose light, according to Wm. Herschel, requires two million years to reach my eye. If then nature is perhaps in a certain sense an "outer man," as Paracelsus and after him Goethe say, that; from the purely scientific point of view, brings her not one inch nearer to me and to my circumscribed and specifically human understanding; for man too is merely an "external."
Hence all scientific systematising and theorising is a fitting and adapting; of course it is as accurate as possible, but never quite free from error, and, above all, it is always a humanly tinted rendering, translating, interpreting. The Hellene did not know this. Unrivalled as a modeller, in science too he demanded the Faultless, the perfectly Rounded, and thus barred in his own face the door that led to knowledge of nature. True observation becomes impossible as soon as man marches forward with one-sided human demands; the example of the great Aristotle should warn us against that. Nothing will convince us more thoroughly on this point than the study of mathematics; here at once we observe what hampered the Hellenes and what has aided us. The achievements of the Hellenes in geometry are known to all; but it is very interesting to notice how the triumphant progress of their mathematical investigation encountered an insurmountable obstacle in its further development. Hoefer calls attention to the nature of this obstacle by pointing out that a Greek mathematician never tolerated an "approximately": for him the proof of the proposition had to be absolutely faultless or it was invalid; the conception that two magnitudes differing "infinitely" little can in practice be regarded as equal is something against which his whole nature would have revolted. [6] It is true that Archimedes in his investigations of the properties of the circle inevitably came upon results that could not be exactly expressed, but he then says simply, "greater than so much and less than so much"; and he expresses no opinion about the irrational roots, which he had to extract to get at his results. On the other hand, all modern mathematics with their almost incomprehensible achievements, are based, as we all know, upon calculations with" infinitely near," that is, therefore, approximate values. By this "Infinitesimal Calculus" the broad impenetrable forest of irrational numbers that blocked our way at every step has been felled; [7] for the great majority of roots and of so-called "functions" which occur in the measurement of angles and curves come under this head. But for this introduction of approximate values our whole astronomy, geodesy, physics, mechanics and very important parts of our industry would be impossible. And how was this revolution brought about? By boldly cutting a knot which is tied in the human brain alone. This knot could never have been untied. In this very province, that of mathematics, where everything seemed so transparent and free from contradiction, man had very soon reached the limit of his specific human possibilities; he saw quite well that nature does not trouble herself about what is humanly thinkable and unthinkable, and that the brain of the proud homo sapiens is inadequate to grasp and to express the very simplest thing -- the relation of magnitudes to one another; but what did it matter? As we have seen, the passion of the Teuton aimed rather at possession than at purely formal shaping; his shrewd observation of nature, his highly developed receptivity soon convinced him that the formal faultlessness of the image in the mind is absolutely no conditio sine qua non for its possession, that is, in this case, for an understanding which is as comprehensive as possible. The important thing with the Greek was the respect of man for himself and for his human nature; to cherish thoughts which were not thinkable in all parts seemed to him a crime against human nature: the Teuton, on the other hand, had a much more vivid reverence for nature (in contrast to man) than the Hellene, and moreover, like his Faust, he has never been afraid of contracts with the devil. And so he invented the imaginary magnitudes, that is, absolutely unthinkable quantities, the type of which is x = √-1 In handbooks they are usually defined as "magnitudes that exist only in the imagination;" it would be perhaps more correct to say, magnitudes which can occur anywhere except in the imagination, for man is incapable of conceiving them at all. Through this brilliant discovery of the Goths and Lombardians of the extreme north of Italy [8] calculation received an unsuspected elasticity: the absolutely unthinkable henceforth served to determine the relations of concrete facts, which otherwise could not have been tackled. The complementary step was soon taken: where one magnitude approaches "infinitely" near to another without ever reaching it, the gap was arbitrarily bridged, and over this bridge man marched from the sphere of the Impossible into the sphere of the Possible. Thus, for example, the insoluble problems of the circle were solved by regarding the latter as a polygon with an "infinite" number of sides, all therefore infinitely small. Pascal had already spoken of magnitudes which ate" smaller than any given magnitude" and had designated them quantites negligeables; [9] but Newton and Leibniz went much further, in that they systematically perfected calculation with these infinite series -- the infinitesimal calculation to which I have referred; The advance thus made was simply incalculable; for the first time only mathematics were redeemed from rigidity to life, for the first time they were enabled to analyse accurately not only motionless shape but also motion. Moreover, irrational numbers were now, in a way, done away with, since we can now, when necessary, avoid them. But this was not all, an idea -- the idea of the Infinite -- which had formerly been current only in philosophy, was henceforth extended to mathematics and acted like an elixir which gave them the strength to achieve unheard-of things. Just as it may happen that two magnitudes approach "infinitely" near to each other, so it may also happen that the one increases or decreases "infinitely," while the other remains constant: thus the infinitely great [10] and the infinitely small -- two absolutely inconceivable things -- may now also become workable components of our calculations: we cannot think them, but we can use them, and from their use we derive concrete, pre- minently practical results. Our knowledge of nature, our capacity even to approach many natural problems, rests to a very great extent upon this one daring, autocratic achievement. As Carnot says: "No other idea has supplied us with so simple and effectual means of acquiring an accurate knowledge of nature's laws." [11] The ancients had said, Non entis nulla sunt praedicata (Of things that are not nothing can be said); but that which is not within our head may well exist outside our head, and, vice versa, things which undoubtedly exist only in the human brain and are nevertheless recognised by us to be flagrantly "impossible" may as instruments do us very good service, enabling us defiantly to gain by roundabout ways a knowledge which is not directly available to human beings. The character of this work forbids me to pursue this mathematical discussion further, though I am glad to have found an opportunity in this section on Science to mention at the very beginning this chief organ of all systematic knowledge; we have seen that Leonardo even declared motion to be the cause of all life; he was soon followed by Descartes, who viewed matter itself as motion -- everywhere the mechanical interpretation of empirical facts, which was emphasised in the last section, asserts itself! But mechanics are an ocean over which the ship of mathematics alone can carry us. Only in so far as a science can be reduced to mathematical principles does it seem to us to be exact, and that because it is in so far strictly mechanical and consequently "navigable." "Nissuna humana investigatione si po dimandare vera scientia s'essa non passa per le mattematiche dimonstrationi," says Leonardo da Vinci; [12] and the voice of the Italian seer at the beginning of the sixteenth century is re-echoed by that of the German sage at the opening of the nineteenth: "I assert that in every special theory of nature there can only be so much real science as is vouched for by mathematics."[13] With these remarks, however, as I hinted at the very outset, I have been keeping a more general purpose in view; I wished to reveal the peculiar character not only of our mathematics but of our scientific method as a whole; I hope I have succeeded. I can best draw the moral of what has been said by quoting a remark of Leibniz: "Rest can be regarded as an infinitely slow speed or as an infinitely great retardation, so that in any case the law of rest is to be considered merely as a special case within the laws of motion. Similarly we can regard two perfectly equal magnitudes as unequal (if it serves our purpose), by looking upon the inequality as infinitely small," &c. [14] This statement expresses the fundamental principle of all Teutonic Science. Rest is, we must admit, not motion but its very opposite, just as equal magnitudes cannot be unequal: rather than have recourse to such hypotheses the Hellene would have dashed his head against the wall; but in this the Teuton has, quite unconsciously, revealed a deeper insight into the essence of man's relation to nature. He desired to know, not only that which was purely and exclusively Human (like a Homer and a Euclid), but on the contrary and above all that Nature which is external to man; [15] and here his passionate thirst for knowledge -- that is, the predominance of his longing to learn, not· of the need to shape -- has caused him to find paths which have led him very much farther than anyone of his predecessors. And these paths, as I remarked at the very beginning of this discussion, are those of shrewd adaptation to circumstances. Experience -- that is, exact, minute, indefatigable observation -- supplies the broad immovable foundation of Teutonic science, whether it be applied to philology, chemistry or anything else: the capacity of observation, the passionate enthusiasm, self-sacrifice and honesty with which it is pursued, are essential features of our race. Observation is the conscience of Teutonic science. Not only the professional natural scientist, not only the learned authority on language and the jurist investigate with painfully intent perception, eyen the Franciscan Roger Bacon spends his whole fortune in the cause of observation; Leonardo da Vinci preaches study of nature, observation, experiment and devotes years of his life to sketching accurately the invisible inner anatomy of the human body (especially the vascular system); Voltaire is an astronomer, Rousseau a botanist; Hume gives his chief work, which appeared a hundred and sixty years ago. the supplementary title, "An Attempt to introduce the Experimental Method into Philosophy"; Goethe's admirable and keen faculty of observation is well known, and Schiller begins his career with a treatise on "The Sensitiveness of Nerves and the Irritability of Muscle," and calls upon us to study more industriously the "mechanism of the body," if we wish to come to a better understanding of the "soul"! But that which has been experienced cannot faithfully be fashioned into Science, if man lays down the law instead of receiving it. The most daring capacities of his mind, its whole elasticity and the undaunted flight of fancy are pressed into the service of the Observed, in order that it may be classified as part of a human system of knowledge. Obedience on the one hand towards experienced nature; autocracy on the other in reference to the human intellect: these are the hall-mark of Teutonic Science. This then is the foundation upon which our theory and system are based; a brave building the chief character of which lies in the fact that we are rather engineers than architects. Builders, indeed, we are, but our object is not so much beauty of construction nor perfection of shape that will finally satisfy the human mind but the establishment of provisorium which enables us to gather new material for observation and to widen our knowledge. The work of an Aristotle acted like a brake upon science. Why was that? Because this Hellenic master-mind brooked no delay in attaining its object, because he knew no peace till he saw before his eyes a finished, symmetrical, absolutely rational and humanly plausible dogmatic system. In logic final results could be attained in this way, for there was a question of an exclusively human and exclusively formal science of universal validity within human limits; on the other hand, even his politics and theory of art are much less valid, because the law of the Hellenic intellect is here silently presupposed to be essentially the law of the human intellect, an idea which is contrary to experience; in natural science -- in spite of a wealth of facts which often astonishes us -- the absolutely predominating principle is, to draw the greatest number of hard and fast conclusions from the smallest number of observations. This is no question of idleness or of haste, still less of dilettantism, it is the presumption, first, that the organisation of man is quite adequate to grasp the organisation of nature, so that -- if I may so express it -- one single hint suffices to enable us to interpret and survey correctly a whole complex of phenomena; secondly, that the human mind is not only adequate but also equivalent (equal not only in compass but equal also in value) to the principle or law, or whatever it may be called, which reveals itself in nature as a whole. That is why the human mind is regarded without more ado as the central point from which we may not only with the greatest ease survey all nature, but also may trace all things from the cradle to the grave, that is to say, from their first causes to their supposed finality. This supposition is as erroneous as it is simple: our Teutonic science has from the first followed another course. Roger Bacon, though he valued Aristotle highly, was just as earnest in the thirteenth century in the warnings he addressed to scientists against Aristotle and the whole Hellenic method which he personified, as Francis Bacon was three centuries later; [16] in this connection, the Renaissance was fortunately only a passing sickness, and it was merely in the darkest shadows of the Church that the theology of the Stagirite henceforth continued to prolong a superfluous existence. To make the matter perfectly obvious, let me employ a mathematical comparison: the science of the Hellene was, so to speak, a circle in the centre of which he himself stood. Teutonic science, on the other hand, resembles an ellipse. At one of the two foci of the ellipse stands the human intellect, at the other an x of which we know nothing. If the human intellect succeeds in a definite case in bringing its own focus near to the other, human science approaches the form of a circle; [17] but the ellipse is generally a very extended one: on the one side understanding penetrates very far into the sum of the Known, on the other it lies almost at the periphery. Frequently man stands almost alone with his focus (his humble torch!); with all his groping he cannot find the connection with the second focus, and thus arises a mere parabola, the sides of which, it is true, seem to approach each other in the far distance, but without ever meeting, so that our theory gives us not a closed curve, but only the beginning of a curve, which is possible but in the meantime incapable of being completed. Our scientific procedure is obviously the negation of the Absolute. That was an acute and happy remark of Goethe's: "He who devotes himself to nature attempts to find the squaring of the circle." THE NATURE OF OUR SYSTEMATISING It is a matter of course that a mathematical procedure cannot be applied to other objects, especially to the sciences of observation; I scarcely think it necessary to defend myself or others against such a misconception. But if we know how we have proceeded in mathematics, we also know what is to be expected in other spheres of knowledge; for the same intellect will proceed, if not identically, since the subject renders this impossible, still analogously. Unconditional respect for nature (that is, for observation) and daring originality in the application of the means with which the human intellect provides us for interpretation and elaboration: these are the principles which we again encounter everywhere. Attend a course of lectures on systematic botany: the neophyte will be astonished to hear the lecturer talk of flowers that do not exist and to see "diagrams" of them on the blackboard; these are so-called types, purely "imaginary magnitudes," the assumption of which enables us to explain the structure of really existing flowers and to demonstrate the connection of the fundamental (from our human point of view mechanical) plan of structure in the special case with other related or divergent plans. Everyone, no matter how inexperienced in science, must at once be struck by the purely human element in such a procedure. But do not suppose that what is thus taught is an absolutely artificial and arbitrary system; the very opposite is the case. Man had proceeded artificially and thereby cut off every possibility of acquiring new knowledge, so long as he followed Aristotle in classifying plants according to the non-existent principle of a relative (so-called) "perfection," or according to the division, solely derived from human practice, into trees, shrubs, grasses and the like. On the other hand, our modern diagrams, our imaginary flower-forms, all the principles of our systematic botany, serve to bring home and to make clear to the human understanding true relations of nature at which we have arrived from thousands and thousands of faithful observations. The artificiality is conscious artificiality; as in mathematics, it is a question of "imaginary magnitudes," which help us, however, to approach nearer and nearer to the truth of nature, and to co-ordinate in our minds countless actual facts; this is the true function of science. With the Hellene, on the other hand, the foundation itself was thoroughly artificial, anthropomorphic, and it was this foundation which with simple unconsciousness was regarded as "nature." The rise of modern systematic botany provides indeed so excellent and intelligible an example of the Teutonic scientific method that I wish to give the reader a few more cardinal facts for his further consideration. Julius Sachs, the famous botanist, in describing the beginning of botanical science between the fourteenth and the seventeenth centuries, says that no progress could be made so long as Aristotle's influence predominated; it is to the unlearned plant-collectors alone that the awakening of genuine science is due. Whoever was learned enough to understand Aristotle "only worked mischief in the natural history of plants." On the other hand, the authors of the first books on herbs did not give this a further thought, but collected with the greatest possible accuracy hundreds and thousands of individual descriptions of plants. History shows how in this way, in the course of a few centuries, a new science arose, while the philosophical botany of Aristotle and Theophrastus led to no result worth mentioning. [18] The first learned systematiser of importance, Caspar Bauhin of Basle (second half of the sixteenth century), who frequently shows a lively appreciation of natural, that is structural, affinity, creates universal confusion once more, in that, under Aristotle's influence, he imagines himself to be bound to advance "from the most imperfect to the more and more perfect" -- as if man possessed an organ to measure relative "perfection" -- and also in that he naturally (after the example of Aristotle) considers the large trees as most perfect, the small grasses as most imperfect and more such anthropomorphic nonsense. [19] But the faithful collection of actual observations continued, and men at the same time endeavoured to systematise the enormously growing material in such a way as would adapt the system or classification to the needs of the human intellect and yet keep it as true to the facts of nature as possible. This is the salient point; thus arises the ellipse which is peculiar to us. The logical systematising comes last, not first, and we are ready at any moment to throw our system overboard as we did our gods of old, for in very truth its only significance for us is a "provisorium," a makeshift. The unlearned collectors and describers of herbs had discovered the natural affinities of plants by the trained eye, long before the learned proceeded to form systems. The reason is this: we base our science not on logic, which is human and therefore limited, but on intuitive perception, on what we see and divine, as it were, by affinity with nature; which moreover is the reason why our scientific systems are so true to nature. The Hellene thought only of the needs of the human intellect; we, however, wished to get at nature and felt vaguely that we could never fathom her mystery, never represent her own "system." Yet we were resolved to approximate as nearly as we could, and that by a path that would make ever greater proximity possible. That is why we rejected every purely artificial system, like that of Linnaeus; it contains much that is correct, but leads us no further. In the meantime there rose up men like Tournefort, John Ray, Bernard de Jussieu, Antoine Laurent de Jussieu, [20] and others who cannot be named here, and their work proved the absolute impossibility of constructing the classification of plants, as derived from observation of nature, upon one anatomical characteristic, a plea which the human passion for simplification and the logical mania wished to establish, and the best known and most successful example of which is the system of Linnaeus. On the contrary, it became apparent that for sub-orders of different grades different, and for special plant groups special, characteristics must be chosen. Moreover, there was brought to light a remarkable fact which was extremely important for the further development of science, viz., that, in reducing to a simple, logical, systematic principle the natural affinity of plants which is already recognised by quickened observation, the general external habit -- so sure an indication to the expert -- is of no use whatever, but that only characteristics from the secret interior of the structure, and in fact mostly such as are entirely invisible to the naked eye are of any service. In flowering plants we have to take into account especially relations of the embryo, then relations of the generative organs, connections between parts of the flower, &c. ; in non-flowering plants the most invisible and seemingly most unimportant things, such as the rings on the sporangia of ferns, the teeth round the spore-capsules of mosses, &c. In this way nature has provided us with a clue by means of which it is possible to penetrate far into her mystery. What happened here deserves our close attention, for it teaches us much concerning the historical development of our sciences. And so, even at the risk of repeating myself, I must direct the attention of the reader still more emphatically to what took place in systematic botany. By faithful and engrossing study of a very extensive material the eye of the observer had been quickened. and he was enabled to divine connections, to see them, as it were, with the eye, without, however, being able accurately to account for them and above all without being able to find a simple. so to speak" mechanical," visible and demonstrable characteristic by which he might finally and convincingly prove the truth of his observation. Every child, for example, can -- when its attention is aroused -- distinguish between monocotyledons and dicotyledons; but it cannot give a reason for it, cannot point to a definite, sure distinguishing-mark. Obviously here (as everywhere) intuition is at the bottom of the matter. Regarding John Ray, the real founder of modern systematic botany, his contemporary Antoine de Jussieu expressly tells us that he was engrossed in the external habit -- plantae facies exterior; [21] now it was this same John Ray who discovered the importance of the cotyledons for a natural system of flowering plants, and at the same time the simple and infallible anatomical characteristic to distinguish the monocotyledons from the dicotyledons. Hereby it was proved that a hidden, mostly microscopically small anatomical characteristic was the essential thing by which the needs of the human intellect could be brought into unison with the facts of nature. This led to further discoveries regarding the presence or absence of albumen in the seed, regarding the position of the germ in the albumen, &c. These are all systematic characteristics of fundamental importance. Thus observation, united to intuition, had first dimly suggested the right solution; but man had to grope long before he could draw his ellipse; for the other focus; the x, was altogether lacking. At last it was found (i.e., approximately found), but not where human reason would have sought it nor at the place which mere intuition would ever have reached: it was only after long searching, after indefatigable comparison, that man at last hit upon the series of anatomical characteristics which are the criterion of a system in consonance with nature. But note carefully what followed this discovery, for now and now only comes the decisive point, the point which reveals the incomparable value of our scientific method. Now that man had, so to speak, come upon the track of nature, and with her help had drawn an approximately correct ellipse, he discovered hundreds and thousands of new facts, which all the "unscientific" observation and all the intuition in the world would never have revealed to him. False analogies were seen to be false; unsuspected connections between things which appeared to be absolutely heterogeneous were irrefutably proved. In fact, man had now really created order. This order, it is true, was also artificial, at least it contained an artificial element, for man and nature are not synonymous; if we had the purely " natural" order before our eyes, we could do nothing with it, and Goethe's famous remark, "Natural system is a contradiction," expresses in a nut-shell all the objections that can here be raised; but this human-artificial order, in contrast to that of Aristotle, was one in which man had made himself as small as possible and retired into the background, while endeavouring to let nature speak, in so far as her voice can be understood. And this principle is one which ensures progress; for in this way we gradually learn to understand the language of nature better. Every purely logical-scientific and every philosophically dogmatic theory focus an obstacle to science, whereas every theory which has been drawn as accurately as possible from nature and is yet only accepted as provisional, contributes to the advance of both knowledge and science. This one example drawn from systematic botany must stand for many. It is a well-known fact that systematising as a necessary organ for shaping knowledge extends over all departments of knowledge; even religions are now classified in orders, species and categories. The victory of the method illustrated by botany forms in every sphere the backbone of the historical development of science between 1200 and 1800. In Physics, Chemistry, Physiology and in all related branches the same principles are at work. All knowledge must finally be systematised before it becomes science; that is why we encounter systematising everywhere and at all times. Bichat's theory of tissue -- which was the result of anatomical discoveries, and at the same time the source of new discoveries -- is an example, the exact analogy of which to John Ray's establishment of the so-called system of plants, and to the further history of this study, is at once apparent. Everywhere we see painfully exact observation, followed by daring, creative, but not dogmatic theorising. Before closing this section I should like to go a step farther, otherwise we should overlook an important point, one of those cardinal points which must serve to enable us to understand not only the history of our science, but also science itself as it exists in the nineteenth century. We must penetrate somewhat deeper into the nature and value of scientific theorising, and we can best do this by referring to that incomparable instrument of Teutonic science -- the experiment. But it is merely a parenthesis, for the experiment is peculiar only to some studies, while in this connection I must go down still deeper, in order to reveal certain cardinal principles of all more modern sciences. The experiment is, in the first place, merely "methodical" observation. But it is at the same time theoretical observation. [22] Hence its right application calls for philosophical reflection, otherwise it may easily happen that the result might be that the experiment rather than nature might speak. "An experiment which is not preceded by a theory, i.e., an idea, stands in the same relation to natural investigation as jingling with a child's rattle does to music," says Liebig, and in his brilliant fashion he compares the attempt to calculation; in both cases thoughts must precede. But bow much caution is necessary here! Aristotle had experimented with falling bodies; he certainly did not lack acumen; but the "preceding theory" made him observe falsely. And if we take up Galilei's Discorsi, the fictitious conversation between Simplicio, Sagredo and Salviati will convince us that in the discovery of the true law of gravity conscientious observation, burdened with as few prejudices as possible, had the lion's share in the work and that the real theories followed after rather than "preceded." We have here, I think, a confusion on the part of Liebig, and where so great a man, one who has deserved so well of science, is at fault, we may presume that true understanding can only be derived from the finest analysis. And such understanding is all the more essential, as it and it alone enables us to grasp the significance of genius for science and the history of science. That we shall now attempt to do. Liebig writes, "A theory, i.e., an idea"; he accordingly regards theory and idea as equivalents -- the first source of his error. The Greek word idea-which in its living significance has never been successfully translated into any modern language -- means exclusively something seen with the eyes, a phenomenon, a form; even Plato understands so fully by idea the quintessence of the Visible, that the single individual appears to him too pale to be regarded as more than the shadow of a true idea. [23] Theory, on the other hand, denoted even from the first not" looking at " but" looking on " (Watching) -- a very great difference, which continued to grow ever greater till the word theory had received the special meaning of an arbitrary, subjective view, an artificial arrangement. Theory and idea· are therefore not synonyms. When John Ray had by much observation attained so clear a picture of flowering plants as a whole that he distinctly perceived that they formed two great groups, he had an idea; when, however, he published in I703 his Methodus Plantarum, he propounded a theory, a theory far inferior to his idea; for though he had discovered the importance of the cotyledons as criteria for systematising, many other points (e.g., the importance of the parts of the flower) had escaped his notice, so that the man, who already correctly comprehended in its essential points the formation of the vegetable kingdom, nevertheless sketched an untenable system; in fact our knowledge at that time was not thorough enough for Ray's " idea" to be bodied forth adequately in a "theory." In the case of the idea man is still obviously a piece of nature; here speaks -- if I may venture to make the comparison -- that "voice of the blood" which forms the principal theme of the narratives of Cervantes; man perceives relations for which he cannot account, he has a presentiment of things which he could not prove. [23] That is not real knowledge; it is the reflection of a transcendent connection, and is, therefore, a direct, not a dialectical experience. The interpretation of such presentiments will always be uncertain ; neither they nor their interpretation can claim objective validity, their value is confined to the individual and depends absolutely on his individual importance. It is here that genius reveals its creative power. And while our whole Teutonic science is a science of faithful, painfully exact, absolutely prosaic observation, it is at the same time a science of genius. Everywhere "do ideas precede," here Liebig is perfectly right; we see it as clearly in the case of Galilei as of Ray, [25] in Bichat as well as Winckelmann, in Colebrooke as in Kant; but we must avoid the confusion of idea and theory; for these ideas of genius are far from being theories. The theory is the attempt so to organise a certain mass of experience -- often, perhaps always, collected with the aid of an idea -- that this artificial organism may serve the needs of the specific human intellect, without contradicting or arbitrarily treating the known facts. It is at once clear that the relative value of a theory will always stand in direct relation to the number of known facts, but this is by no means true of the idea, the value of which rather depends solely upon the greatness of the one personality. Leonardo da Vinci, for example, though his facts were very few, so correctly and accurately grasped the fundamental principles of geology, that not till the nineteenth century did we possess the necessary experience to demonstrate scientifically (and that means theoretically) the correctness of his intuition; again. he did not demonstrate the circulation of the blood (in some details he certainly did not even conceive it rightly or grasp it mechanically), but he guessed it, that is, he had the idea of circulation, not the theory. At a later point, and in another connection, I shall discuss the incomparable importance of genius for our whole culture; there is nothing to explain there; it is sufficient to point to the fact. [26] But here it is still necessary for the comprehension of our science to answer the one important question: How do theories arise? Here too, I hope, by criticising a well-known remark of Liebig, in which a widespread view is expressed, to point out the right path; and it will be seen that our great scientific theories are neither thinkable without genius nor, at the same time, indebted to genius alone for their shaping. The famous chemist writes, "Artistic ideas take root in fancy, scientific ideas in understanding." [26] This short sentence is full, if I am not mistaken, of psychological inaccuracies, but only one point interests us particularly at present; imagination is supposed to serve art alone, while science could get on without it; from this follows the further -- really monstrous -- assertion, that art "invents facts," science "explains facts." Science never explained anything! The word explain (erklaren) has no meaning for science, unless we take it to mean "to make more clearly visible." If my pen slips from my fingers, it falls to the ground; the law of gravitation is a theory which sets out in the very best way all the relations which are to be taken into account in this fall; but what does it explain? If I suggest the power of attraction, r arrive no further than the first chapter of Genesis, verse 1, that is to say, I put forward as an explanation a totally unthinkable and inexplicable entity. Oxygen and hydrogen unite to form water; good: what fact here explains and what fact is explained? Do oxygen and hydrogen explain water? Or are they explained by water? Obviously this word has not the shadow of a meaning. especially in science. It is true that in more complex phenomena this is not at once apparent, but the more thoroughly we analyse, the more does the delusion vanish, that explanation means an actual increase not only of knowledge but also of understanding. If the gardener, for example, says to me, "This plant turns towards the sun," I fancy in the first place, as he does, that I possess a perfectly valid "explanation." But if the physiologist says: strong light hinders growth, so that the plant grows more quickly on the shaded side and for that reason bends towards the sun -- if he shows me the influence of the capacity of extension on the part of the plant in question and of the differently refracted rays, &c., in short, if he reveals the mechanism of the process and unites all known facts to a theory of "heliotropism," I feel that I have learned a great deal more, but that the delusion of an "explanation" has considerably paled. The clearer the How, the more vague the Why. The fact that the plant "turns towards the sun" looked like a final explanation, for I myself, man, seek the sun; but when I hear that strong light hinders the separation of cells and consequently the lengthening of the stalk on the one side, and thus causes the plant to bend, this is a new fact, and that again impels me to seek explanation from still more remote causes, and so thoroughly dispels my original simple anthropomorphism that I begin to ask by what mechanical concatenation it happens that I am so fond of sunning myself. Here again Goethe is right: "Every solution of a problem is a new problem." [28] And if ever we should reach so far, that physical chemistry will take in hand the problem of heliotropism, and the whole become a calculation and finally an algebraical formula, then this question will have reached the same stage as gravitation, and everyone will recognise here, too, that science does not explain facts, put helps to discover and classify them -- with as much truth to nature and as much in the interest of man as possible. Now is this, the real work of science, possible, as Liebig says, without the co-operation of imagination? Does the creative faculty -- and that is what we call genius -- play no necessary part in the construction of our science? We need not enter into a theoretical discussion, for history proves the opposite. The more exact the science, the more need has it of imagination, and no science can altogether do without it. Where shall we find more daring creations of fancy than those atoms and molecules without which physics and chemistry would be impossible -- or than that "physical jack-of-all-trades and chimera," as Lichtenberg calls it, ether, which is indeed matter (otherwise it would be useless for our hypotheses) but to which the most essential characteristics of matter, as, for example, extension and impenetrability, must be denied (otherwise it Would be of equally little use), a true "Square root of minus one! it It would be hard to say where there is an Art so deeply "rooted in imagination." Liebig says that art invents facts." It never does! It has no need whatever to do that; moreover, we should not understand it if it did. It certainly condenses what lies apart, it unites what is only known to us as separate, and separates that part of the actual which stands in its way; in that way it gives shape to that which is beyond the sight of man, and distributes light and shade as it thinks fit: but it never crosses the boundary of what is familiar to conception and what is conceivably possible; for art is -- in direct contrast to science -- an activity of mind which confines itself solely to the purely human; from man it comes, to man it addresses itself, the Human alone is its field. [29] Science, as we have seen, is quite different; it is directed to the investigation of nature, and nature is not human. Indeed, would that it were so, as the Hellenes supposed I But experience has contradicted the supposition. In science, therefore, man attacks something which is, of course, not in- uman, for he himself belongs to it, but it is to a great extent super-and extra-human. As soon, therefore, as man has an earnest desire to understand nature, and not to be satisfied with dogmatising in usum Delphini, he is compelled, in science, and especially in natural science in the narrower sense of the word, to strain to the utmost the powers of his imagination, which must be infinitely inventive and pliable and elastic. know that such an assumption is contrary to the general acceptation; to me, however, it seems that science and philosophy make higher claims on the imagination than poetry. The purely creative element in men like Democritus and Kant is greater than in Homer and Shakespeare. That is the very reason why their works remain accessible to but few. This scientific imagination is rooted of course in facts, as all imagination is of necessity; [30] and scientific imagination is particularly rich for this reason, that it has at its disposal an enormous number of facts, and its store of facts is being continually increased by new discoveries. I have already briefly referred (p. 287) to the importance of new discoveries for nourishing and stimulating the imagination; this importance extends even to the highest of regions of culture, but it reveals itself to begin with and above all in science. The wonderful advance of science in the sixteenth century -- of which Goethe wrote: "The world will not soon see the like again" [31] -- is by no means due to the regeneration of foolish Hellenic dogmatics, as people would have us believe; this has rather had the effect of leading us astray -- as in systematic botany, so in every department of knowledge; on the contrary, this sudden advance was directly due to the stimulus of the new discoveries, which I discussed in the previous section, discoveries in the heavens, discoveries on earth. Read the letters in which Galilei, trembling with excitement, proclaims the discovery of the moons of Jupiter and of the ring round Saturn, thanking God for revealing to him "such never-dreamt-of wonders," and you will get an idea of the mighty influence which the new discoveries exercised upon the imagination, and how they at the same time impelled man to seek further and further, and to bring the object of search nearer to the understanding. When discussing mathematics, we saw to what glorious heights of extreme daring the human spirit allowed itself to be transported in the intoxicating atmosphere of a newly discovered super-human nature. But for the genuine idea of genius, which sprang from the imagination -- not from observation, nor, as Liebig says, from facts -- the higher mathematics together with our knowledge of the heavens, of light, of electricity, &c., would have been impossible. But the same holds good everywhere, and that for the simple reason adduced above, that we otherwise could not reach this world which is outside man The history of our sciences between 1200 and 1800 is an unbroken series of such magnificent workings of the imagination. That implies the predominant power of creative genius. AN EXAMPLE. Looking back, we now perceive that scientific chemistry was impossible so long as oxygen had not been discovered as an element; for this is the most important body of our planet, the body from which the organic as well as the inorganic phenomena of telluric nature derive their special colouring. In water, air and rocks, in all combustion (from the simple slow oxydising to flaming fire), in the breathing of all living creatures -- everywhere, in short, this element is at work. This is the very reason why it defied direct observation; for the outstanding characteristic of oxygen is the energy with which it unites with other elements, in other words, conceals from observation its existence as an independent body; even where it occurs not chemically united with other substances, but in a free state -- as, for example, in the air, where it only enters into a mechanical union with nitrogen -- it is impossible for the ignorant to observe oxygen; for not only is this element, under our conditions of temperature and pressure, a gas, it is, moreover, a colourless gas, without smell and without taste. The senses alone could not, therefore, discover it. Now in the second half of the seventeenth century there lived in England one of those genuine discoverers like Gilbert (see p. 269), namely, Robert Boyle, who by a treatise, Chemista scepticus, made an end of Aristotelian dialectics and alchemistic quackery in the field of chemistry, and at the same time set a twofold example: that of strict observation, and that of classifying and sifting the already much increased material of observation by the introduction of a creative idea. As a birthday gift he presented to chemistry, which was just arising in a genuine form, the new conception of elements, a more daring conception than the old one of Empedocles, one more after the spirit of Democritus. This idea was at that time based on no observation; it sprang from the imagination, but became henceforth the source of countless discoveries which have not yet reached the end of their course. Here we see what paths our science always follows. [32] But now for the example of which I am thinking. Boyle's idea had led to a rapid increase of knowledge, discovery had succeeded discovery, but the more numerous the facts became, the more confused was the total result; anyone who desires to know how impossible science is without theory, should study the state of chemistry at the beginning of the eighteenth century; he will find a Chinese chaos. If, as Liebig thinks, science can "explain" facts, if the unimaginative" understanding" is capable of such a task, why did it not prove so then? Were Boyle himself and Hooke and Becher and the many other capable collectors of facts of that age unintelligent persons? Certainly not; but understanding and observation alone are not sufficient, and the wish to "explain" is a delusion; what we call comprehension always presupposes a creative contribution from man. The important thing therefore was, to deduce from Boyle's brilliant idea the theoretical consequences, and this was done by a Franconian doctor, a man of "transcendentally speculative tendency of mind," [33] by the ever memorable Georg Ernst Stahl. He was not a professional chemist, but he saw what was lacking: an element! Could its existence be proved? Not at that time. But was a daring Teutonic mind to be disheartened by that? Fortunately not! So Stahl arbitrarily invented an imaginary element and called it phlogiston. At once in the escape of phlogiston, &c. Consequently, when Priestley and Scheele had at last separated oxygen from certain combinations, they firmly believed that they had within their grasp that famous phlogiston, which had been pursued ever since Stahl's time. But Lavoisier soon proved that the discovered element, far from possessing the qualities of the hypothetical phlogiston, revealed qualities of exactly the opposite kind! The oxygen thus discovered and rendered accessible to observation was in fact a different thing altogether from what the human imagination in its need had conceived. Without imagination man can establish no connection between phenomena, no theory, no science, but human imagination nevertheless always reveals itself as inadequate to and unlike nature, requiring to be corrected by empirical observation. That is also the reason why all theory is ever provisional, and science ceases as soon as dogmatism assumes the lead. The history of our science is the history of such phlogistons. Philology has its "Aryans," but for which its great achievements in the nineteenth century would have been inconceivable. [34] Goethe's theories of metamorphoses in the vegetable kingdom and the affinities of the bones of the skull and the vertebrae have exercised an enormous stimulus upon the increase and systematising of our knowledge, but Schiller was perfectly right when he shook his head and said: "That is not experience" (and he might have added, nor a theory); "that is an idea." [35] He was equally right when he added: "Your intellect works to a remarkable degree intuitively and all your thinking powers seem, as it were, to have committed themselves to the imagination, as to their common representative." [36] As Carnot says: "Mathematical analysis is full of enigmatical hypotheses and from these enigmas it draws its strength." [37] John Tyndall, a competent authority, says of physics: "The greatest of its instruments is the imagination." [38] In the sciences of life, to-day as well as yesterday. wherever we are endeavouring to open up new spheres for the understanding and to reduce to order facts that are in confusion, it is imaginative, creative men who take the lead. Haeckel's plastidules, Wiesner's plasoms, Weissmann's biophores, &c., spring from the same need as Stahl's masterly invention. The imagination of these men is, of course, nourished and stimulated by the wealth of exact observations; pure imagination, for which the theory of "signatures" may serve as an example, has for science the same significance as the picture painted by a man who does not know the technique of painting has for art; their hypothetical suppositions, however, are not observations, consequently not facts, but attempts to arrange facts and pave the way for new observations. The most salient phlogiston of the eighteenth century was really nothing less than Darwin's theory of natural selection. Perhaps I may be allowed, in summarising these results, to quote myself. I once had occasion to make a special and thorough study of a definite scientific subject, the rising sap of plants. On this occasion I was greatly interested in investigating the historical development of our knowledge of the question, and discovered that although there has been no lack of competent investigators, only three men, Hales (1727), Dutrochet (1826), and Hofmeister (1857) have really brought it one step farther. In these three exceptional men, though they differ absolutely in other respects, the concurrence of the following characteristics is very remarkable: they are all excellent observers, they are all men of wide outlook and of pre-eminently vivid, daring imagination, while all are, as theorists, somewhat one-sided and desultory. Highly gifted with imagination, they were in fact, like Goethe, inclined to ascribe too far-reaching significance to their creative ideas -- Hales to capillarity, Dutrochet to osmose, and Hofmeister to tension of tissue; the same power of imagination, which enabled these great men to enrich us, has therefore in a certain sense limited them: so that in this they have been forced to submit to correction from intellects which were their inferiors. Concerning them I wrote in my treatise: "To such men We owe all real progress of science; for whatever we may think of their theories, they have not only enriched our knowledge by the discovery of countless facts, but also our imagination by the promulgation of new ideas; theories come and go, but what the imagination once possesses, is eternal." But this investigation led me to a second discovery, one of still greater importance in principle: our imagination is very limited. If we trace the sciences back to antiquity, it is remarkable how few new conceptions the course of time has added to the very numerous old ones; this teaches us that it is solely and simply observation of nature that enriches our imagination, whereas all the thought in the world does not add one grain to its wealth. [39] Let me add one final word. Mathematicians -- never at a loss, as we have seen -- think it proper to say that a circle is an ellipse in which the two foci coincide. Will this coincidence of the foci ever be realised in our sciences? Is it to be supposed that human intuitive perception and nature will ever exactly coincide, that is, will our perception of things ever be absolute understanding? The preceding discussion shows how foolish such an assumption is; I am convinced that I may also assert that no single serious scientist of the present day, certainly no Teuton, believes it possible. [40] We find this conviction even where (as happens unfortunately very frequently to-day) the intellect is not adequately schooled by philosophy, and perhaps it is all the more impressive because it is expressed with perfect simplicity. Thus, for example, one of the admittedly most important investigators of the nineteenth century, Lord Kelvin, on celebrating in 1896 his jubilee as a Professor of fifty years standing, made the memorable confession: "One single word comprises the result of all that I have done towards the furthering of science during fifty-five years: this word is Failure. I know not one iota more to-day about electric or magnetic power, how ether, electricity and weighable matter stand to one another, or what chemical affinity means, than I did when I delivered my first lecture." These are the words of an honest, truthful, thorough Teuton, the man who seemed to have brought the hypothetical, unthinkable atoms so near to us, when in a happy hour he undertook to measure their length and breadth. Had he been in addition something of a philosopher, he would certainly not have needed to speak of failure in such a melancholy strain; for in that case he would not have assigned to science an absolutely unattainable goal, the ever impossible absolute knowledge, which may well be conceived in our inmost hearts but can never take the tangible form of an actual, empirical "knowledge"; he might then have unhesitatingly rejoiced over that brilliant, free, shaping power, which began to stir at the moment when the Teuton rebelled against the leaden might of the Chaos of Peoples, which since then has conferred on us so rich a blessing of civilisation, and in days to come is destined to attain still greater things. [41] I hope that with the remarks in this section I have contributed something to help us to understand the history of our Teutonic sciences and to form an exact estimate of the progress in the nineteenth century. We have seen that science -- according to our new and absolutely individual view -- is the human shaping of something extra-human; we have shown in the essential outlines and by the aid of individual examples how this shaping has hitherto been accomplished. Of a "makeshift bridge" more cannot be expected. _______________ Notes: 1. Naturally I am at this moment leaving the purely mathematical out of account: for in that sphere it was certainly a remarkable, epoch-making achievement, so to transform the idea of the Continuous and "to separate it from the geometrical conception, that we could use it for purposes of calculation" (Gerhardt: Geschichte der Mathematik in Deutschland, 1877, p. 144). 2. To comprehend the Infinite, you must distinguish and then unite. 3. See vol. i. p. 42 f. The suffix schaft in Wissenschaft (science) denotes to order, to form (Eng. shape); science, therefore, means the shaping of the Known. 4. I have already pointed out that all genuine science is natural science (p. 237 f.). 5. Nothing is within, nothing is without; for what is within is without. 6. Histoire des mathematiques, 4th ed. p. 206. There the reader will find an excellent example of how the Greek preferred the reductio ad absurdum, which was not directly convincing, because purely logical, rather than follow the path of evident, strictly mathematical proof, in which an "infinite approximation" is regarded as equality. 7. Irrational
numbers are such as can never be expressed quite accurately, that is to
say, in the language of arithmetic, such as contain an irrational
fraction; among them there is a large number of the most important
quantities that constantly occur in all calculations, e.g., the
square roots of most numbers, the relation of the diagonals to the side
of a square, of the diameter of a circle to its circumference, &c. The
latter quantity, the 8. Niccolo, called Tartaglia (i.e., the stutterer), of Brescia, and Cardanus of Milan; both flourished in the first half of the sixteenth century. But here, as in the case of the calculus, fluxions, &c., we can hardly name definite inventors, for the necessity of solving astronomical and physical problems (which the geographical discoveries had propounded) suggested similar thoughts to the most various individuals. 9. Saint-Beuve expresses the significant opinion that this daring man "formed in himself a second Frankish invasion of Gaul." In him the purely Teutonic spirit asserts itself once more against the Chaos of Peoples, that was flooding France, and its chief organ, the Order of the Jesuits. 10. The infinitely great is introduced into mathematics as unity divided by an infinitely small number. Concerning this supposition Berkeley remarks: "It is shocking to good sense": so it is, but it serves a practical purpose and that is the important thing. 11. Reflexions sur la melaphysque du calcul infinitesimal, 4th ed., 1860. This pamphlet of the famous mathematician is so perfectly clear that there is probably nothing quite like it on this subject, which, owing to the extremely contradictory nature of the matter, is not a little confused. As Carnot says, many mathematicians have worked with success in the field of infinitesimal calculation, without ever acquiring a clear conception of the thought which formed the basis of their operations. "Fortunately," he continues, "this has not detracted from the fruitfulness of the discovery: for there are certain fundamental ideas, which can never be grasped in all their clearness, and which nevertheless, as soon as ever some of their first results stand before us, open up to the human intellect a wide field, which it can investigate at leisure in all directions." 12. Libro di pittura i. 1 (in Heinrich Ludwig's edition). I should like to call special attention to one of the remarks of the great man which bear on this point. No. 1158 in the edition of his writings by J. P. Richter (ii. 289): "Nessuna certezza delle scientie e, dove non si pud applicare una delle scientie matematiche e che non sono unite con esse matematiche." 13. Kant, Metaphysische Anfangsgrunde der Naturwissenschaft, Preface. 14. Letter to Bayle, July 1687 (quoted from Hofer, i. c. p. 482). I do not know what Bayle's answer was. In his Dictionnaire I find under Zeno a violent attack upon all mathematics: "Mathematics have one fatal, immeasurable defect: they are in fact a mere chimera. The mathematical points, and consequently also the lines and surfaces of the geometricians, their spheres, axes, &c.. are all abstractions which have never possessed a trace of reality; that is why these phantasies are even of less importance than those of the poets, for the latter invented nothing which is intrinsically impossible. The the mathematicians." &c. This abuse has no special significance; but it calls our attention to the important fact that mathematics, not merely since Cardanus and Leibniz, but from all time, have drawn their strength from "imaginary" or, more properly speaking, absolutely inconceivable magnitudes. When we think of it, the point according to Euclid's definition is no less inconceivable than √-1. Obviously our "exact knowledge" is a peculiar thing. The keenest criticism of our higher mathematics is found in Berkeley's The Analyst and A Defence of Free-thinking in Mathematics. 15. He aimed so intently at this that when his study was applied to man (see Locke), he did his best to "objectivise" himself, that is. to creep out of his own skin and regard himself as a piece of "nature." 16. Francis Bacon's decisive remark is in the Preface to the Inslauratio Magna, and is as follows: "Scientias non per arrogantiam in humani ingenii cellulis, sed submisse in mundo majore quaerai." 17. An ellipse, the foci of which exactly coincide, is a circle. 18. Geschichte der Botanis, 1875, p. 18. 19. Sachs, as above, p. 38. 20. His fundamental work, Genera plantarum secundum ordines naturales disposita, appeared in 1774, just prior to the beginning of the nineteenth century. 21. From the quotation in Hooker's supplement to the English edition of Le Maout and Decaisne: System of Botany, 1873, p. 987. 22. Kant says regarding experiment: "Reason only perceives what she herself brings forth according to her own design, she must according to constant laws lead the way with principles of her own judgment and compel nature to answer her questions" (Preface to the second edition of the Critique of Pure Reason). 23. People imagine that Plato's ideas are abstractions; on the contrary, they are in his estimation the only concrete thing from which the phenomena of the empirical world are abstracted. It is the paradox of a mind longing for the most intense visualisation. 24. Kant has found a splendid expression for this and calls the idea, in the sense in which I use the word, eine inexponible Vorstsellung der Einbildungshraft (an inexpoundable conception of the Imagination); Kritik der Urteilskralt, § 57. note I. 25. Ray, who founded rational systematic botany, proved that in his case real genius predominated by the fact that he did exactly the same in the far removed and, previous to this time, hopelessly confused field of ichthyology. Power of Intuition is the divine gift here. 26. I merely wish to call the attention of those who are not very well read in philosophy to the fact that at the close of the epoch with which we are occupied in this chapter, the importance of genius was recognised and analysed with incomparable acumen: the great Kant has fixed upon the relative predominance of "nature" (i.e., what is, so to speak, outside and above man) in contrast to "reflection" (i.e., the circumscribed and logically Human) as the specific token of genius (see especially the Kritik der Urteilskraft). This does not mean that the genius is less "reflective," but rather that, in addition to a maximum of logical thinking power, something else is present; this addition is precisely the yeast which causes the dough of knowledge to rise. 27. Like the former quotation, this is from the speech on Francis Bacon in the year 1863. To obviate any misjudgment of Liebig, I beg the reader to read once more the totally different remark on p. 236. I am not exploiting the lapsus calami of the great investigator from any desire to put him right, but because this criticism helps to make my own thesis perfectly clear. 28. Gesprach mit Kanzler von Muller, June 8, 1821. 29. Landscape painting or animal painting is obviously never anything but a representation of landscapes or animals as they appear to man; the most daring caprice of a Turner or of one of the most modern impressionists can never be anything but an extravagant assertion of human autonomy. "When artists speak of nature, they always suppose the idea, without being clearly conscious of it" (Goethe). 30. See vol. i. pp. 177, 427; vol. ii. p. 273. 31. Geschichle der Farbenlehre, conclusion of the third part. An assertion which Liebig countersigns; "After this sixteenth century there is none which was richer in men of equal creative power" (Augsburger Allg. Zeitung, 1863, in the Reden und Abhandlungen, p. 272. 32. It deserves mention that Boyle's remarkable capacity for imaginative inventions found expression in theological writings from his pen, and was also noticed in his daily life. 33. I quote these words from Hirschel's Geschichte det Medizin, 2nd ed. p. 260. I possess a number of chemical books, but none of them mentions Stahl's intellectual gifts, their authors are much too prosaic and mechanical for that. 34. Cf. vol. i. p. 264, &c. 35. Goethe: Gluchliches Ereignis, sometimes printed as Annalen, 1794. Goethe himself, however, recognised this later and did not remain blind to the defects of his "idea," In the supplement to the Nachtrage zur Farbenlehre, under the heading Probleme, we find the remark, "The idea of metamorphosis is a most venerable but at the same time most dangerous gift from above. It leads to the Formless, destroys knowledge, disintegrates it." 36. Letter to Goethe, August 31, 1794. Schiller adds: "At bottom this is the highest point to which man can raise his powers, as soon as he succeeds in generalising his intuition and making his feeling lawgiver." 37. Loc. cit. p. 27. 38. On the Scientific Use of the Imagination, 1870. 39. Houston Stewart Chamberlain, Recherches sur la Seve ascendante, Neuchatel, 1897, p. 11. Locke, in his Human Understanding (iv. 3, 23), already points out that poverty of "ideas" (as he too calls them) is one of the chief primary causes of the limitation of our knowledge. 40. Our numerous excellent Jewish scholars may be in a different case, for when a people, without ever learning anything, has known everything for thousands of years, it is a bitter hardship to have to tread the painful but brilliant path of study and to be forced finally to confess that our knowledge is everlastingly and narrowly circumscribed by human nature. 41. In this connection I should like to draw the reader's attention to the change in men's views regarding the nature of life. At the beginning of the nineteenth century the gulf between the Organic and the Inorganic was thought to be, if not filled up, at least bridged over (vol, i. p. 43); at the close of the century that gulf, for all men of knowledge, is wider than ever. Far from being in a position to produce Homunculi chemically in our laboratories, we have learned first of all (through the researches of Pasteur, Tyndall, &c.), that there nowhere exists generatio spontanea, but that all life is produced solely by life; then minuter anatomy (Virchow) has taught us that every cell of a body can only arise from an already existing cell; now we know (Wiesner) that even the simplest organic structures of the cell arise not by the chemical activity of the contents of the cell, but only from similar organised structures, e.g. a chlorophyll granule only from an already existing chlorophyll granule. Form, not matter, is the fundamental principle of all life. And thus Herbert Spencer, who was formerly so daring, had lately, as an honest investigator, to confess that "the theory of a special vital principle is inadequate, the physico-chemical theory has, however, likewise failed: the corollary being that in its ultimate nature Life is incomprehensible," (Letter in Nature, vol, lviii. p. 593, October 12, 1898). Here too a little metaphysical thought would have saved him from a painful retreat. Taken in Spencer's sense, the whole empirical world too is incomprehensible. The mystery is preeminently striking in the case of life, because life is just the one thing which we ourselves know from direct experience. By virtue of life we attack the problem of life and must now confess that the cat may indeed bite the point of its tail (if the latter is long enough), but not more; it cannot swallow and digest itself. To what proud flights will our science rise on the day when it has discarded the last remnant of the Semitic delusion of understanding, and passes on to pure, intensive intuitive perception, united to free, consciously human shaping. Then in truth will "man by man have entered into the daylight of life!" (Cf. my Immanuel Kant, 5th lecture, "Plato.")
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of the
mathematicians, has already been calculated to two hundred decimal
places; we might calculate it to two millions. it would still be only an
approximation. This simple example will prove in a thoroughly tangible
manner the organic inadequacy of the human intellect, its incapacity to
express even quite simple relations. (See vol. i. p. 432 for the
contribution of the Indo-Aryans to the investigation of irrational
numbers.)