Chapter XI: Faustian and Apollinian Nature-Knowledge (3)

As late as 1629 the spirit of Renaissance physics appears in the theory of magnetism formulated by the Jesuit Nicolaus Cabeo. Conceived in the mould of an Aristotelian idea of the world, it was (like Palladio’s work on architecture) foredoomed to lead to nothing—not because it was “wrong” in itself but because it was in contradiction with the Faustian Nature-feeling which, freed from Magian leading-strings by the thinkers and researchers of the 14th Century, now required forms of its very own for the expression of its world-knowledge. Cabeo avoided the notions of force and mass and confined himself to the Classical concepts of form and substance—in other words, he went back from the architecture of Michelangelo’s last phase and of Vignola to that of Michelozzo and Raphael—and the system which he formed was complete and self-contained but without importance for the future. A magnetism conceived as a state of individual bodies and not as a force in unbounded space was incapable of symbolically satisfying the inner eye of Faustian man. What we need is a theory of the Far, not one of the Near. Newton’s mathematical- mechanical principles required to be made explicit as a dynamics pure and entire, and this another Jesuit, Boscovich,[520] was the first to achieve in 1758.

Even Galileo was still under the influence of the Renaissance feeling, to which the opposition of force and mass, that was to produce, in architecture and painting and music alike the element of grand movement, was something strange and uncomfortable. He therefore limited the idea of force to contact-force (impact) and his formulation did not go beyond conservation of momentum (quantity of motion). He held fast to mere moved-ness and fought shy of any passion of space, and it was left to Leibniz to develop—first in the course of controversy and then positively by the application of his mathematical discoveries—the idea of genuine _free and directional forces_ (living force, activum thema). The notion of conservation of momentum then gave way to that of conservation of living forces, as quantitative number gave way to functional number.

The concept of mass, too, did not become definite until somewhat later. In Galileo and Kepler its place is occupied by volume, and it was Newton who distinctly conceived it as _functional_—the world as function of God. That mass (defined nowadays as the constant relation between force and acceleration in respect of a system of material points) should have no proportionate relation whatever to volume was, in spite of the evidence of the planets, a conclusion inacceptable to Renaissance feeling.

But, even so, Galileo was forced to inquire into the _causes_ of motion. In a genuine Statics, working only with the notions of material and form, this question would have had no meaning. For Archimedes displacement was a matter of insignificance compared with form, which was the essence of all corporeal existence; for, if space be Nonent, what efficient can there be external to the body concerned? Things are not functions of motion, but they move themselves. Newton it was who first got completely away from Renaissance feeling and formed the notion of distant forces, the attraction and repulsion of bodies across space itself. Distance is already in itself a force. The very idea of it is so free from all sense-perceptible content that Newton himself felt uncomfortable with it—in fact it mastered him and not he it. It was the spirit of Baroque itself, with its bent towards infinite space, that had evoked this _contrapuntal and utterly un-plastic_ notion. And in it withal there was a contradiction. To this day no one has produced an adequate definition of these forces-at-a-distance. No one has ever yet understood what centrifugal force really is. Is the force of the earth rotating on its axis the cause of this motion or vice versa? Or are the two identical? Is such a cause, considered _per se_, a force or another motion? What is the difference between force and motion? Suppose the alterations in the planetary system to be workings of a centrifugal force; that being so, the bodies ought to be slung out of their path [tangentially], and as in fact they are not so, we must assume a centrifugal force as well. What do all these words mean? It is just the impossibility of arriving at order and clarity here that led Hertz to do away with the force-notion altogether and (by highly artificial assumptions of rigid couplings between positions and velocities) to reduce his system of mechanics to the principle of contact (impact). But this merely conceals and does not remove the perplexities, which are of intrinsically Faustian character and rooted in the very essence of dynamics. “Can we speak of forces which owe their origin to motion?” Certainly not; but can we get rid of _primary_ notions that are _inborn_ in the Western spirit though indefinable? Hertz himself made no attempt to apply his system practically.

This _symbolic_ difficulty of modern mechanics is in no way removed by the potential theory that was founded by Faraday when the centre of gravity of physical thought had passed from the dynamics of matter to the electrodynamics of the æther. The famous experimenter, who was a visionary through and through—alone amongst the modern masters of physics he was not a mathematician—observed in 1846: “I assume nothing to be true in any part of space (whether this be empty as is commonly said, or filled with matter) except forces and the lines in which they are exercised.” Here, plain enough, is the directional tendency with its intimately organic and historic content, the tendency in the knower to live the process of his knowing. Here Faraday is metaphysically at one with Newton, whose forces-at-a-distance point to a mythic background that the devout physicist declined to examine. The possible alternative way of reaching an unequivocal definition of force—viz., that which starts from World and not God, from the object and not the subject of natural motion-state—was leading at the very same time to the formulation of the concept of Energy. Now, this concept represents, as distinct from that of force, a quantum of directedness and not a direction, and is in so far akin to Leibniz’s conception of “living force” unalterable in quantity. It will not escape notice that essential features of the mass-concept have been taken over here; indeed, even the bizarre notion of an atomic structure of energy has been seriously discussed.

This rearrangement of the basic words has not, however, altered the feeling that a world-force with its substratum does exist. The motion- problem is as insoluble as ever. All that has happened on the way from Newton to Faraday—or from Berkeley to Mill—is that the religious deed- idea has been replaced by the irreligious work-idea.[521] In the Nature- picture of Bruno, Newton and Goethe something divine is working itself out in acts, in that of modern physics _Nature is doing work_; for every “process” within the meaning of the First Law of Thermodynamics is or should be measurable by the expenditure of energy to which a quantity of work corresponds in the form of “bound energy.”

Naturally, therefore, we find the decisive discovery of J. R. Mayer coinciding in time with the birth of the Socialist theory. Even economic systems wield the same concepts; the value-problem has been in relation with quantity of work[522]] ever since Adam Smith, who _vis-à-vis_ Quesney and Turgot marks the change from an organic to a mechanical structure of the economic field. The “work” which is the foundation of modern economic theory has purely dynamic meaning, and phrases could be found in the language of economists which correspond exactly to the physical propositions of conservation of energy, entropy and least action.

If, then, we review the successive stages through which the central idea of force has passed since its birth in the Baroque, and its intimate relations with the form-worlds of the great arts and of mathematics, we find that (1) in the 17th Century (Galileo, Newton, Leibniz) it is pictorially formed and in unison with the great art of oil-painting that died out about 1630; (2) in the 18th Century (the “classical” mechanics of Laplace and Lagrange) it acquires the abstract character of the fugue-style and is in unison with Bach; and (3) with the Culture at its end and the civilized intelligence victorious over the spiritual, it appears in the domain of pure analysis, and in particular in the theory of functions of several complex variables, without which it is, in its most modern form, scarcely understandable.

XIII

But with this, it cannot be denied, the Western physics is drawing near to the limit of its possibilities. At bottom, its mission as a historical phenomenon has been to transform the Faustian Nature-feeling into an intellectual knowledge, the faith-forms of springtime into the machine-forms of exact science. And, though for the time being it will continue to quarry more and more practical and even “purely theoretical” results, results as such, whatever their kind, belong to the superficial history of a science. To its deeps belong only the history of its symbolism and its style, and it is almost too evident to be worth the saying that in those deeps the essence and nucleus of our science is in rapid disintegration. Up to the end of the 19th Century every step was in the direction of an inward fulfilment, an increasing purity, rigour and fullness of the dynamic Nature-picture—and then, that which has brought it to an optimum of theoretical clarity, suddenly becomes a _solvent_. This is not happening intentionally—the high intelligences of modern physics are, in fact, unconscious that it is happening at all—but from an inherent historic necessity. Just so, at the same relative stage, the Classical science inwardly fulfilled itself about 200 B.C. Analysis reached its goal with Gauss, Cauchy and Riemann, and to-day it is only filling up the gaps in its structure.

This is the origin of the sudden and annihilating doubt that has arisen about things that even yesterday were the unchallenged foundation of physical theory, about the meaning of the energy-principle, the concepts of mass, space, absolute time, and causality-laws generally. This doubt is no longer the fruitful doubt of the Baroque, which brought the knower and the object of his knowledge together; it is a doubt affecting the very possibility of a Nature-science. To take one instance alone, what a depth of unconscious Skepsis there is in the rapidly-increasing use of enumerative and statistical methods, which aim only at _probability_ of results and forgo in advance the absolute scientific exactitude that was a creed to the hopeful earlier generations.

The moment is at hand now, when the possibility of a self-contained and self-consistent mechanics will be given up for good. Every physics, as I have shown, must break down over the motion-problem, in which the living person of the knower methodically intrudes into the inorganic form-world of the known. But to-day, not only is this dilemma still inherent in all the newest theories but three centuries of intellectual work have brought it so sharply to focus that there is no possibility more of ignoring it. The theory of gravitation, which since Newton has been an impregnable truth, has now been recognized as a temporally limited and shaky hypothesis. The principle of the Conservation of Energy has no meaning if energy is supposed to be infinite in an infinite space. The acceptance of the principle is incompatible with any three-dimensional structure of space, whether infinite or Euclidean or (as the Non- Euclidean geometries present it) spherical and of “finite, yet unbounded” volume. Its validity therefore is restricted to “a system of bodies self-contained and not externally influenced” and such a limitation does not and cannot exist in actuality. But symbolic infinity was just what the Faustian world-feeling had meant to express in this basic idea, which was simply _the mechanical and extensional re-ideation of the idea of immortality and world-soul_. In fact it was a feeling out of which knowledge could never succeed in forming a pure system. The luminiferous æther, again, was an ideal postulate of modern dynamics whereby every motion required a something-to-be-moved, but every conceivable hypothesis concerning the constitution of this æther has broken down under inner contradictions; more, Lord Kelvin has proved mathematically that there _can_ be no structure of this light- transmitter that is not open to objections. As, according to the interpretation of Fresnel’s experiments, the light-waves are transversal, the æther would have to be a rigid body (with truly quaint properties), but then the laws of elasticity would have to apply to it and in that case the waves would be longitudinal. The Maxwell-Hertz equations of the Electro-magnetic Theory of Light, which in fact are pure nameless numbers of indubitable validity, exclude the explanation of the æther by any mechanics whatsoever. Therefore, and having regard also to the consequences of the Relativity theory, physicists now regard the æther as pure vacuum. But that, after all, is not very different from demolishing the dynamic picture itself.

Since Newton, the assumption of constant mass—the counterpart of constant force—has had uncontested validity. But the Quantum theory of Planck, and the conclusions of Niels Bohr therefrom as to the fine structure of atoms, which experimental experience had rendered necessary, have destroyed this assumption. Every self-contained system possesses, besides kinetic energy, an energy of radiant heat which is inseparable from it and therefore cannot be represented purely by the concept of mass. For if mass is defined by living energy it is _ipso facto_ no longer constant with reference to thermodynamic state. Nevertheless, it is impossible to fit the theory of quanta into the group of hypotheses constituting the “classical” mechanics of the Baroque; moreover, along with the principle of causal continuity, the basis of the Infinitesimal Calculus founded by Newton and Leibniz is threatened.[523] But, if these are serious enough doubts, the ruthlessly cynical hypothesis of the Relativity theory strikes to the very heart of dynamics. Supported by the experiments of A. A. Michelson, which showed that the velocity of light remains unaffected by the motion of the medium, and prepared mathematically by Lorentz and Minkowski, its specific tendency is to _destroy the notion of absolute time_. Astronomical discoveries (and here present-day scientists are seriously deceiving themselves) can neither establish nor refute it. “Correct” and “incorrect” are not the criteria whereby such assumptions are to be tested; the question is whether, in the chaos of involved and artificial ideas that has been produced by the innumerable hypotheses of Radioactivity and Thermodynamics, it can hold its own as a _useable_ hypothesis or not. But however this may be, _it has abolished the constancy of those physical quantities into the definition of which time has entered_, and unlike the antique statics, the Western dynamics knows _only_ such quantities. Absolute measures of length and rigid bodies are no more. And with this the possibility of absolute quantitative delimitations and therefore the “classical” concept of mass as the constant ratio between force and acceleration fall to the ground—just after the quantum of action, a product of energy and time, had been set up as a new constant.

If we make it clear to ourselves that the atomic ideas of Rutherford and Bohr[524] signify nothing but this, that the numerical results of observations have suddenly been provided with a picture of a planetary world within the atom, instead of that of atom-swarms hitherto favoured; if we observe how rapidly card-houses of hypothesis are run up nowadays, every contradiction being immediately covered up by a new hurried hypothesis; if we reflect on how little heed is paid to the fact that these images contradict one another and the “classical” Baroque mechanics alike, we cannot but realize that the _great style of ideation is at an end_ and that, as in architecture and the arts of form, a sort of craft-art of hypothesis-building has taken its place. Only our extreme maestria in experimental technique—true child of its century— hides the collapse of the symbolism.

XIV

Amongst these symbols of decline, the most conspicuous is the notion of Entropy, which forms the subject of the Second Law of Thermodynamics. The first law, that of the conservation of energy, is the plain formulation of the essence of dynamics—not to say of the constitution of the West-European soul, to which Nature is necessarily visible only in the form of a contrapuntal-dynamic causality (as against the static- plastic causality of Aristotle). The basic element of the Faustian world-picture is not the Attitude but the Deed and, mechanically considered, the Process, and this law merely puts the mathematical character of these processes into form as variables and constants. But the Second Law goes deeper, and shows a _bias_ in Nature-happenings which is in no wise imposed _a priori_ by the conceptual fundamentals of dynamics.

Mathematically, Entropy is represented by a quantity which is fixed by the momentary state of a self-contained system of bodies and under all physical and chemical alterations can only increase, never diminish; in the most favourable conditions it remains unchanged. Entropy, like Force and Will, is something which (to anyone for whom this form-world is accessible at all) is inwardly clear and meaningful, but is formulated differently by every different authority and never satisfactorily by any. Here again, the intellect breaks down where the world-feeling demands expression.

Nature-processes in general have been classified as irreversible and reversible, according as entropy is increased or not. In any process of the first kind, free energy is converted into bound energy, and if this dead energy is to be turned once more into living, this can only occur through the simultaneous binding of a further quantum of living energy in some second process; the best-known example is the combustion of coal—that is, the conversion of the living energy stored up in it into heat bound by the gas form of the carbon dioxide, if the latent energy of water is to be translated into steam-pressure and thereafter into motion.[525] It follows that in the world as a whole entropy continually increases; that is, the dynamic system is manifestly approaching to some final state, whatever this may be. Examples of the irreversible processes are conduction of heat, diffusion, friction, emission of light and chemical reactions; of reversible, gravitation, electric oscillations, electromagnetic waves and sound-waves.

What has never hitherto been fully felt, and what leads me to regard the Entropy theory (1850) as the beginning of the destruction of that masterpiece of Western intelligence, the old dynamic physics, is the deep opposition of theory and actuality which is here for the first time introduced into theory itself. The First Law had drawn the strict picture of a causal Nature-happening, but the Second Law by introducing irreversibility has for the first time brought into the mechanical- logical domain a tendency belonging to immediate life and thus in fundamental contradiction with the very essence of that domain.

If the Entropy theory is followed out to its conclusion, it results, _firstly_, that in theory all processes must be reversible—which is one of the basic postulates of dynamics and is reasserted with all rigour in the law of the Conservation of Energy—but, _secondly_, that in actuality processes of Nature in their entirety are irreversible. Not even under the artificial conditions of laboratory experiment can the simplest process be exactly reversed, that is, a state once passed cannot be re- established. Nothing is more significant of the present condition of systematics than the introduction of the hypotheses of “elementary disorder” for the purpose of smoothing-out the contradiction between intellectual postulate and actual experience. The “smallest particles” of a body (an image, no more) throughout perform reversible processes, but in actual things the smallest particles are in disorder and mutually interfere; and so the irreversible process that alone is experienced by the observer is linked with increase of entropy by taking the mean probabilities of occurrences. And thus theory becomes a chapter of the Calculus of Probabilities, and in lieu of exact we have statistical methods.

Evidently, the significance of this has passed unnoticed. Statistics belong, like chronology, to the domain of the organic, to fluctuating Life, to Destiny and Incident and not to the world of laws and timeless causality. As everyone knows, statistics serve above all to characterize political and economic, that is, historical, developments. In the “classical” mechanics of Galileo and Newton there would have been no room for them. And if, now, suddenly the contents of that field are supposed to be understood and understandable only statistically and under the aspect of Probability—instead of under that of the _a priori_ exactitude which the Baroque thinkers unanimously demanded—what does it mean? It means that the object of understanding is ourselves. The Nature “known” in this wise is the Nature that we know by way of living experience, that we live in ourselves. What _theory_ asserts (and, being itself, must assert)—to wit, this ideal irreversibility that never happens in actuality—represents a relic of the old severe intellectual form, the great Baroque tradition that had contrapuntal music for twin sister. But the resort to statistics shows that the force that that tradition regulated and made effective is exhausted. Becoming and Become, Destiny and Causality, historical and natural-science elements are beginning to be confused. Formulæ of life, growth, age, direction and death are crowding up.

That is what, from this point of view, irreversibility in world- processes has to mean. It is the expression, no longer of the physical “t” but of genuine _historical_, inwardly-experienced Time, which is identical with Destiny.

Baroque physics was, root and branch, a _strict systematic_ and remained so for as long as its structure was not racked by theories like these, as long as its field was absolutely free from anything that expressed accident and mere probability. But directly these theories come up, it becomes _physiognomic_. “The course of the world” is followed out. The idea of the end of the world appears, under the veil of formulæ that are no longer in their essence formulæ at all. Something Goethian has entered into physics—and if we understand the deeper significance of Goethe’s passionate polemic against Newton in the “Farbenlehre”[526] we shall realize the full weight of what this means. For therein intuitive vision was arguing against reason, life against death, creative image against normative law. The critical form-world of Nature-_knowledge_ came out of Nature-_feeling_, God-feeling, as the evoked contrary. Here, at the end of the Late period, it has reached the maximal distance and is turning to come home.

So, once more, the imaging-power that is the efficient in dynamics conjures up the old great symbol of Faustian man’s historical passion, Care—the outlook into the farthest far of past and future, the back- looking study of history, the foreseeing state, the confessions and introspections, the bells that sounded over all our country-sides and measured the passing of Life. The ethos of the word Time, as we alone feel it, as instrumental music alone and no statue-plastic can carry it, is directed upon an _aim_. This aim has been figured in every life-image that the West has conceived—as the Third Kingdom, as the New Age, as the task of mankind, as the issue of evolution. And it is figured, as the destined end-state of all Faustian “Nature,” in Entropy.

Directional feeling, a relation of past and future, is implicit already in the mythic concept of force on which the whole of this dogmatic form- world rests, and in the description of natural processes it emerges distinct. It would not be too much, therefore, to say that entropy, as the intellectual form in which the infinite sum of nature-events is assembled as a _historical and physiognomic_ unit, tacitly underlay all physical concept-formation from the outset, so that when it came out (as one day it was bound to come out) it was as a “discovery” of scientific _induction_ claiming “support” from all the other theoretical elements of the system. The more dynamics exhausts its inner possibilities as it nears the goal, the more decidedly the historical characters in the picture come to the front and the more insistently the organic necessity of Destiny asserts itself side by side with the inorganic necessity of Causality, and Direction makes itself felt along with capacity and intensity, the factors of pure extension. The course of this process is marked by the appearance of whole series of daring hypotheses, all of like sort, which are only apparently demanded by experimental results and which in fact world-feeling and mythology imagined as long ago as the Gothic age.

Above all, this is manifested in the bizarre hypotheses of atomic disintegration which elucidate the phenomena of radioactivity, and according to which uranium atoms that have kept their essence unaltered, in spite of all external influences, for millions of years and then suddenly without assignable cause explode, scattering their smallest particles over space with velocities of thousands of kilometres per second. Only a few individuals in an aggregate of radioactive atoms are struck by Destiny thus, the neighbours being entirely unaffected. Here too, then, is a picture of history and not “Nature,” and although statistical methods here also prove to be necessary, one might almost say that in them mathematical number has been replaced by chronological.[527]

With ideas like these, the mythopoetic force of the Faustian soul is returning to its origins. It was at the outset of the Gothic, just at the time when the first mechanical clocks were being built, that the myth of the world’s end, Ragnarök, the Twilight of the Gods, arose. It may be that, like all the reputedly old-German myths Ragnarök (whether in the Völuspa form or as the Christian Muspilli) was modelled more or less on Classical and particularly Christian-Apocalyptic motives. Nevertheless, it is the expression and symbol of the Faustian and of no other soul. The Olympian college is historyless, it knows no becoming, no epochal moments, no aim. But the passionate thrust into distance is Faustian. Force, Will, has an aim, and where there is an aim there is for the inquiring eye an end. That which the perspective of oil-painting expressed by means of the vanishing point, the Baroque park by its _point de vue_, and analysis by the _n_th term of an infinite series—the conclusion, that is, of a willed directedness—assumes here the form of the concept. The Faust of the Second Part is dying, for he has reached his goal. What the myth of Götterdämmerung signified of old, the irreligious form of it, the theory of Entropy, signifies to-day—_world’s end as completion of an inwardly necessary evolution_.

XV

It remains now to sketch the last stage of Western science. From our standpoint of to-day, the gently-sloping route of decline is clearly visible.

This too, the power of looking ahead to inevitable Destiny, is part of the historical capacity that is the peculiar endowment of the Faustian. The Classical died, as we shall die, but it died unknowing. It believed in an eternal Being and to the last it lived its days with frank satisfaction, each day spent as a gift of the gods. But we know our history. Before us there stands a last spiritual crisis that will involve all Europe and America. What its course will be, Late Hellenism tells us. The tyranny of the Reason—of which we are not conscious, for we are ourselves its apex—is in every Culture an epoch between man and old-man, and no more. Its most distinct expression is the cult of exact sciences, of dialectic, of demonstration, of causality. Of old the Ionic, and in our case the Baroque were its rising limb, and now the question is what form will the down-curve assume?

In this very century, I prophesy, the century of scientific-critical Alexandrianism, of the great harvests, of the final formulations, a new element of inwardness will arise to overthrow the will-to-victory of science. Exact science must presently fall upon its own keen sword. First, in the 18th Century, its methods were tried out, then, in the 19th, its powers, and now its historical rôle is critically reviewed. But from Skepsis there is a path to “second religiousness,” which is the sequel and not the preface of the Culture. Men dispense with proof, desire only to believe and not to dissect.

The individual renounces by laying aside books. The Culture renounces by ceasing to manifest itself in high scientific intellects. But science exists only in the living thought of great savant-generations, and books are nothing if they are not living and effective in men worthy of them. Scientific results are merely items of an intellectual tradition. It constitutes the death of a science that no one any longer regards it as an event, and an orgy of two centuries of exact scientific-ness brings satiety. Not the individual, the soul of the Culture itself has had enough, and it expresses this by putting into the field of the day ever smaller, narrower and more unfruitful investigators. The great century of the Classical science was the third, after the death of Aristotle; when Archimedes died and the Romans came, it was already almost at its end. Our great century has been the 19th. Savants of the calibre of Gauss and Humboldt and Helmholtz were already no more by 1900. In physics as in chemistry, in biology as in mathematics, the great masters are dead, and we are now experiencing the _decrescendo_ of brilliant gleaners who arrange, collect and finish-off like the Alexandrian scholars of the Roman age. Everything that does not belong to the matter-of-fact side of life—to politics, technics or economics—exhibits the common symptom. After Lysippus no great sculptor, no artist as man- of-destiny, appears, and after the Impressionists no painter, and after Wagner no musician. The age of Cæsarism needed neither art nor philosophy. To Eratosthenes and Archimedes, true creators, succeed Posidonius and Pliny, collectors of taste, and finally Ptolemy and Galen, mere copyists. And, just as oil-painting and instrumental music ran through their possibilities in a few centuries, so also dynamics, which began to bud about 1600, is to-day in the grip of decay.

But before the curtain falls, there is one more task for the historical Faustian spirit, a task not yet specified, hitherto not even imagined as possible. There has still to be written a _morphology of the exact sciences_, which shall discover how all laws, concepts and theories inwardly hang together as forms and what they have meant as such in the life-course of the Faustian Culture. The re-treatment of theoretical physics, of chemistry, of mathematics as a sum of symbols—this will be the definitive conquest of the mechanical world-aspect by an intuitive, once more religious, world-outlook, a last master-effort of physiognomic to break down even systematic and to absorb it, as expression and symbol, into its own domain. One day we shall no longer ask, as the 19th Century asked, what are the valid laws underlying chemical affinity or diamagnetism—rather, we shall be amazed indeed that minds of the first order could ever have been completely preoccupied by questions such as these. We shall inquire whence came these forms that were prescribed for the Faustian spirit, why they had to come to our kind of humanity particularly and exclusively, and what deep meaning there is in the fact that the numbers that we have won became phenomenal in just this picture-like disguise. And, be it said, we have to-day hardly yet an inkling of how much in our reputedly objective values and experiences is only disguise, only image and expression.

The separate sciences—epistemology, physics, chemistry, mathematics, astronomy—are approaching one another with acceleration, converging towards a complete identity of results. The issue will be a fusion of the form-worlds, which will present on the one hand a system of numbers, functional in nature and reduced to a few ground-formulæ, and on the other a small group of theories, denominators to those numerators, which in the end will be seen to be myths of the springtime under modern veils, reducible therefore—and at once of necessity reduced—to picturable and physiognomically significant characters that are the fundamentals. This convergence has not yet been observed, for the reason that since Kant—indeed, since Leibniz—there has been no philosopher who commanded the problems of _all_ the exact sciences.

Even a century ago, physics and chemistry were foreign to one another, but to-day they cannot be handled separately—witness spectrum analysis, radioactivity, radiation of heat. Fifty years ago the essence of chemistry could still be described almost without mathematics, and to- day the chemical elements are in course of volatilizing themselves into the mathematical constants of variable relation-complexes, and with the sense-comprehensibility of the elements goes the last trace of magnitude as the term is Classically and plastically understood. Physiology is becoming a chapter of organic chemistry and is making use of the methods of the Infinitesimal Calculus. The branch of the older physics— distinguished, according to the bodily senses concerned in each, as acoustics, optics and heat—have melted into a dynamic of matter and a dynamic of the æther, and these again can no longer keep their frontiers mathematically clear. The last discussions of epistemology are now uniting with those of higher analysis and theoretical physics to occupy an almost inaccessible domain, the domain to which, for example, the theory of Relativity belongs or ought to belong. The sign-language in which the emanation-theory of radioactivity expresses itself is completely de-sensualized.

Chemistry, once concerned with defining as sharply as possible the qualities of elements, such as valency, weight, affinity and reactivity, is setting to work to get rid of these sensible traits. The elements are held to differ in character according to their derivation from this or that compound. They are represented to be complexes of different units which indeed behave (“actually”) as units of a higher order and are not practically separable but show deep differences in point of radioactivity. Through the emanation of radiant energy degradation is always going on, so that we can speak of the _lifetime_ of an element, in formal contradiction with the original concept of the element and the spirit of modern chemistry as created by Lavoisier. All these tendencies are bringing the ideas of chemistry very close to the theory of Entropy, with its suggestive opposition of causality and destiny, Nature and History. And they indicate the paths that our science is pursuing—on the one hand, towards the discovery that its logical and numerical results are identical with the structure of the reason itself, and, on the other, towards the revelation that the whole theory which clothes these numbers merely represents the symbolic expression of Faustian life.

And here, as our study draws to its conclusion, we must mention the truly Faustian theory of “aggregates,” one of the weightiest in all this form-world of our science. In sharpest antithesis to the older mathematic, it deals, not with singular quantities but with the aggregates constituted by all quantities [or objects] having this or that specified morphological similarity—for instance all square numbers or all differential equations of a given type. Such an aggregate it conceives as a new unit, a new _number of higher order_, and subjecting it to criteria of new and hitherto quite unsuspected kinds such as “potency,” “order,” “equivalence,” “countableness,” and devising laws and operative methods for it in respect of these criteria. Thus is being actualized a last extension of the function-theory.[528] Little by little this absorbed the whole of our mathematic, and now it is dealing with variables by the principles of the Theory of Groups in respect of the character of the function and by those of the Theory of Aggregates in respect of the values of the variables. Mathematical philosophy is well aware that these ultimate meditations on the nature of number are fusing with those upon pure logic, and an algebra of logic is talked of. The study of geometrical axioms has become a chapter of epistemology.

The aim to which all this is striving, and which in particular every Nature-researcher feels in himself as an impulse, is the achievement of a pure numerical transcendence, the complete and inclusive conquest of the visibly apparent and its replacement by a language of imagery unintelligible to the layman and impossible of sensuous realization—but a language that the great Faustian symbol of Infinite space endows with the dignity of inward necessity. The deep scepticism of these final judgments links the soul anew to the forms of early Gothic religiousness. The inorganic, known and dissected world-around, the World as Nature and System, has deepened itself until it is a pure sphere of functional numbers. But, as we have seen, number is one of the most primary symbols in every Culture; and consequently the way to pure number is the return of the waking consciousness to its own secret, the revelation of its own formal necessity. The goal reached, the vast and ever more meaningless and threadbare fabric woven around natural science falls apart. It was, after all, nothing but the inner structure of the “Reason,” the grammar by which it believed it could overcome the Visible and extract therefrom the True. But what appears under the fabric is once again the earliest and deepest, the Myth, the immediate Becoming, Life itself. The less anthropomorphic science believes itself to be, the more anthropomorphic it is. One by one it gets rid of the _separate_ human traits in the Nature-picture, only to find at the end that the supposed pure Nature which it holds in its hand is—humanity itself, pure and complete. Out of the Gothic soul grew up, till it overshadowed the religious world-picture, the spirit of the City, the alter ego of irreligious Nature-science. But now, in the sunset of the scientific epoch and the rise of victorious Skepsis, the clouds dissolve and the quiet landscape of the morning reappears in all distinctness.

The final issue to which the Faustian wisdom tends—though it is only in the highest moments that it has seen it—is the dissolution of all knowledge into a vast system of morphological relationships. Dynamics and Analysis are in respect of meaning, form-language and substance, identical with Romanesque ornament, Gothic cathedrals, Christian-German dogma and the dynastic state. One and the same world-feeling speaks in all of them. They were born with, and they aged with, the Faustian Culture, and they present that Culture in the world of day and space as a historical drama. The uniting of the several scientific aspects into one will bear all the marks of the great art of counterpoint. _An infinitesimal music of the boundless world-space_—that is the deep unresting longing of this soul, as the orderly statuesque and Euclidean Cosmos was the satisfaction of the Classical. That—formulated by a logical necessity of Faustian reason as a dynamic-imperative causality, then developed into a dictatorial, hard-working, world-transforming science—is the grand legacy of the Faustian soul to the souls of Cultures yet to be, a bequest of immensely transcendent forms that the heirs will possibly ignore. And then, weary after its striving, the Western science returns to its spiritual home.

-----

Footnote 369:

See pp. 55 et seq.

Footnote 370:

See p. 126.

Footnote 371:

Primitive languages afford no foundations for abstract ordered
thought. But at the beginning of every Culture an inner change takes
place in the language that makes it adequate for carrying the highest
symbolic tasks of the ensuing cultural development. Thus it was
_simultaneously with the Romanesque style_ that English and German
arose out of the Teutonic languages of the Frankish period, and
French, Italian and Spanish out of the “lingua rustica” of the old
Roman provinces—languages of _identical_ metaphysical content though
so dissimilar in origin.

Footnote 372:

See p. 262.

Footnote 373:

See p. 172.

Footnote 374:

That is, discussion of the doctrines of the Eleatic school regarding
unity and plurality, the Ent and Nonent, focussed themselves, in Zeno,
down to the famous paradoxes concerning the nature of motion (such as
“Achilles and the Tortoise”) which within the Greek discipline were
unanswerable. Their general effect was to show that motion depended
upon the existence of an indefinitely great plurality, that is, of
infinitely small subdivisions as well as infinitely great quantities,
and, the denial of this plurality being the essential feature of the
Eleatic philosophy, its application to motion was bound to produce
“paradoxes.”

The enunciations, with a brief but close critique, will be found in
the Ency. Brit., XI ed., Article _Zeno of Elea_. Here it suffices to
draw attention to the difficulties that are caused by the absence (or
unwelcome presence) of time and direction elements, not only in the
treatment of plurality itself (which is conceived of indifferently as
an augmentation or as a subdivision of the finite magnitude) but
especially in the conclusion of the “arrow” paradox and in the very
obscure enunciation of Paradox 8.—_Tr._

Footnote 375:

See Vol. II, pp. 296 et seq.

Footnote 376:

De Boer, _Gesch. d. Philos. im Islam_ (1901), pp. 93, 108.

Footnote 377:

A detailed summary will be found in Ency. Brit., XI ed., article
_Kabbalah_, by Dr. Ginsburg and Dr. Cook.—_Tr._

Footnote 378:

See Windelband, _Gesch. d. neueren Philosophie_ (1919), I, 208; also
Hinnebert, _Kultur der Gegenwart_, I, V (1913), p. 484.

Footnote 379:

See Ency. Brit., XI ed., article _Cartesianism_ (V, 421).—_Tr._

Footnote 380:

See Vol. II, p. 296.

Footnote 381:

When, therefore, in the present work also, precedence is consistently
given to Time, Direction and Destiny over Space and Causality, this
must not be supposed to be the result of reasoned proofs. It is the
outcome of (quite unconscious) tendencies of life-feeling—the only
mode of origin of philosophic ideas.

Footnote 382:

See p. 201.

Footnote 383:

See Vol. II, p. 363.

Footnote 384:

In the German, “Vor allem aber sein eignes Ich.” (But in Luther’s
Bible, characteristically, “Auch dazu sein eigen Leben.”)—_Tr._

Footnote 385:

_Barnasha._ The underlying idea is not the filial relation, but an
impersonal coming-up in the field of mankind.

Footnote 386:

ἐθέλω and βούλομαι imply, to have the intention, or wish, or
inclination (βουλή means counsel, council, plan, and ἐθέλω has no
equivalent noun). _Voluntas_ is not a psychological concept but, like
_potestas_ and _virtus_, a thoroughly Roman and matter-of-fact
designation for a practical, visible and outward asset—substantially,
the _mass_ of an individual’s being. In like case, we use the word
energy. The “will” of Napoleon is something very different from the
energy of Napoleon, being, as it were, lift in contrast to weight. We
must not confuse the outward-directed intelligence, which
distinguishes the Romans as civilized men from the Greeks as cultured
men, with “will” as understood here. Cæsar is _not_ a man of will in
the Napoleonic sense. The idioms of Roman law, which represent the
root-feeling of the Roman soul far better than those of poetry, are
significant in this regard. Intention in the legal sense is _animus_
(_animus occidendi_); the wish, directed to some criminal end, is
_dolus_ as distinct from the unintended wrongdoing (_culpa_).
_Voluntas_ is nowhere used as a technical term.

Footnote 387:

The Chinese soul “wanders” in its world. This is the meaning of the
East-Asiatic perspective, which places the vanishing point in the
_middle_ of the picture instead of in the depth as we do. The function
of perspective is to subject things to the “I,” which in ordering
comprehends them; and it is a further indication that “will”—the claim
to command the world—is absent from the Classical make-up that its
painting denies the perspective background. In Chinese perspective as
in Chinese technique (see Vol. II, p. 627), _directional_ energy is
wanting, and it would not be illegitimate to call East-Asiatic
perspective, in contrast with the powerful thrust into depth of _our_
landscape-painting, a perspective of “Tao”; for the world-feeling
indicated by that word is unmistakably the operative element in the
picture.

Footnote 388:

Obviously, atheism is no exception to this. When a Materialist or
Darwinian speaks of a “Nature” that orders everything, that effects
selections, that produces and destroys anything, he differs only to
the extent of one word from the 18th-Century Deist. The _world-
feeling_ has undergone no change.

Footnote 389:

Lines 525-534:

ΧΟ. τούτων ἄρα Ζεύς ἐστιν ἀσθενέστερος;
ΠΡ. οὔκουν ἂν ἐκφύγοι γε τὴν πεπρωμένην, etc.—_Tr._

Footnote 390:

Iliad, XXII, 208-215.—_Tr._

Footnote 391:

The great part played by learned Jesuits in the development of
theoretical physics must not be overlooked. Father Boscovich, with his
system of atomic forces (1759), made the first serious advance beyond
Newton. The idea of the equivalence of God and pure space is even more
evident in Jesuit work than it is in that of the Jansenists of Port
Royal with whom Descartes and Pascal were associated.

(Boscovich’s atomic theory is discussed by James Clerk Maxwell in
Ency. Brit., XI ed., XVIII, 655—a reference that, for more general
reasons, no student of the Faustian-as-scientist should fail to follow
up.—_Tr._)

Footnote 392:

Luther placed practical activity (the day’s demands, as Goethe said)
at the very centre of morale, and that is one of the main reasons why
it was to the deeper natures that Protestantism appealed most
cogently. Works of piety devoid of directional energy (in the sense
that we give the words here) fell at once from the high esteem in
which they had been sustained (as the Renaissance was sustained) by a
relic of _Southern_ feeling. On ethical grounds monasticism
thenceforth falls into ever-increasing disrepute. In the Gothic Age
entry into the cloister, the renunciation of care, deed and will, had
been an act of the loftiest ethical character—the highest sacrifice
that it was possible to imagine, that of _life_. But in the Baroque
even Roman Catholics no longer felt thus about it. And the
institutions, no longer of renunciation but merely of inactive
comfort, went down before the spirit of the Enlightenment.

Footnote 393:

προσῶπον meant in the older Greek “visage,” and later, in Athens,
“mask.” As late as Aristotle the word is not yet in use for person.
“Persona,” originally also a theatre-mask, came to have a juristic
application, and in Roman Imperial times the pregnant Roman sense of
this word affected the Greek προσῶπον also. See R. Hirzel, _Die
Person_ (1914), pp. 40 et seq.

Footnote 394:

See pp. 127 et seq.

Footnote 395:

W. Creizenach, _Gesch. d. neueren Dramas_ (1918), II, 346 et seq.

Footnote 396:

See p. 265.

Footnote 397:

We too have our anecdote, but it is of our own type and diametrically
opposed to the Classical. It is the “short story” (_Novelle_)—the
story of Cervantes, Kleist, Hoffmann and Storm—and we admire it in
proportion as we are made to feel that its motive is _possible only
this once, at this time and with these people_, whereas the mythic
type of anecdote, the Fable, is judged by precisely opposite criteria.

Footnote 398:

See pp. 143 et seq.

Footnote 399:

The Fates of the Greeks are represented as spinning, measuring out and
cutting the thread of a man’s destiny, but not as weaving it _into the
web_ of his life. It is a mere dimension.—_Tr._

Footnote 400:

See p. 129.

Footnote 401:

The evolution of meaning in the Classical words _pathos_ and _passico_
corresponds with this. The second was formed from the first only in
the Imperial period, and carried its original sense in the “Passion”
of Christ. It was in the early Gothic times, and particularly in the
language of the Franciscan “Zealots” and the disciples of Joachim of
Floris, that its meaning underwent the decisive reversal. Expressing
thenceforward a condition of profound excitement which strained to
discharge itself, it became finally a generic name for all spiritual
dynamic; in this sense of strong will and directional energy it was
brought into German as _Leidenschaft_ by Zesen in 1647.

Footnote 402:

The Eleusinian mysteries contained no secrets at all. Everyone knew
what went on. But upon the believers they exercised a strange and
overpowering effect, and the “betrayal” consisted in profaning them by
imitating their holy forms outside the temple-precinct. See, further,
A. Dieterich, _Kleine Schriften_ (1911), pp. 414 et seq.

Footnote 403:

See Vol. II, pp. 345 et seq.

Footnote 404:

The dancers were goats, Silenus as leader of the dance wore a
horsetail, but Aristophanes’s “Birds,” “Frogs” and “Wasps” suggest
that there were still other animal disguises.

Footnote 405:

See pp. 283 et seq.

Footnote 406:

As the student of cultural history to-day is not necessarily familiar
with technical Greek, it may be helpful to reproduce from Cornish’s
edition of Smith’s “Greek and Roman Antiquities,” s.v. “Tragoedia,”
the following paragraph, as clear as it is succinct:

“Tragedy is described by Aristotle (_Poet._, VI, 2) as effecting by
means of pity and terror that purgation [of the soul] (κάθαρσις) which
belongs to [is proper for] such feelings.”... Tragedy excites pity and
terror by presenting to the mind things which are truly pitiable and
terrible. When pity and terror are moved, as tragedy moves them, by a
worthy cause, then the mind experiences that sense of relief which
comes from finding an outlet for a natural energy. And thus the
impressions made by Tragedy leave behind them in the spectator a
temperate and harmonious state of the soul. Similarly Aristotle speaks
of the enthusiastic worshippers of Dionysus as obtaining a κάθαρσις, a
healthful relief, by the “lyric utterance of their sacred frenzy.”—
_Tr._

Footnote 407:

The evolution of ideals of stage-presentation in the minds of
Æschylus, Sophocles and Euripides successively is perhaps comparable
with that of sculptural style which we see in the pediments of Ægina,
of Olympia and of the Parthenon.

Footnote 408:

It must be repeated that the Hellenistic shadow-painting of Zeuxis and
Apollodorus is a modelling of the individual body for the purpose of
producing the plastic effect on the eye. There was no idea of
rendering space by means of light and shade. The body is “shaded” but
it _casts no shadow_.

(Contrast with this Dante’s exact and careful specification of the
time-of-day in every episode of the _Purgatorio_ and the _Paradiso_,
sublimely imaginative as these poems are.—_Tr._)

Footnote 409:

The great mass of Socialists would cease to be Socialists if they
could understand the Socialism of the nine or ten men who to-day grasp
it with the full historical consequences that it involves.

Footnote 410:

See p. 239 et seq.

Footnote 411:

See p. 68.

Footnote 412:

See Vol. II, p. 363, note.

Footnote 413:

As we increase the powers of the telescope we find that the number of
newly appearing stars falls off rapidly towards the edges of the
field.

Footnote 414:

The thrill of big figures is a feeling peculiar to Western mankind. In
the Civilization of to-day this significant passion for gigantic sums,
for indefinitely big and indefinitely minute measurements, for
“records” and statistics, is playing a conspicuous part.

(Our very notation of number is ceasing to rest on sense-standards.
Science has carried number, as ordinarily written, so high and so low
that it now uses a _movable base_ for its numerical statements. For
example, a number in astronomy is written, not as 3,450,000,000 but as
3.45 × 10^9, one relating to ordinary experience as 3.45 (i.e., 3.45 ×
10^0) and one in electromagnetic theory, not as 0.00000345 but as 3.45
× 10^{-6}. Under this system the conceptual unit may be as large or as
small, compared with the unit of daily experience, as the region of
thought in which the calculation is taking place requires. And
different conceptual worlds can be connected as to number [say, a
number of kilometres brought into an order of thought that deals with
millimetres] by simply changing the ten-power.—_Tr._)

Footnote 415:

In stellar calculations even the mean radius of the earth’s orbit
(1.493 × 10^{13} cm.) hardly suffices as unit, as the distance of a
star of one second parallax is already 206,265 such units away from
us; star-distances are reckoned therefore either in light-years or in
terms of the unit distance of a star of this standard parallax.—_Tr._

Footnote 416:

As early as the second millennium before Christ they worked from
Iceland and the North Sea past Finisterre to the Canaries and West
Africa. An echo of these voyagings lingers in the Atlantis-saga of the
Greeks. The realm of Tartessus (at the mouth of the Guadalquivir)
appears to have been a centre of these movements (see Leo Frobenius,
_Das unbekannte Afrika_, p. 139). Some sort of relation, too, there
must have been between them and the movements of the “sea peoples,”
Viking swarms which after long land-wanderings from North to South
built themselves ships again on the Black Sea or the Ægean and burst
out against Egypt from the time of Rameses II (1292-1225). The
Egyptian reliefs show their ship-types to have been quite different
from the native and the Phœnician; but they may well have been similar
to those that Cæsar found afterwards among the Veneti of Brittany. A
later example of such outbursts is afforded by the Varyags or
Varangians in Russia and at Constantinople. No doubt more light will
shortly be thrown on the courses of these movement-streams.

Footnote 417:

Here there is no need to postulate firearms (as distinct from
gunpowder used in fireworks) in the Chinese Culture. The archery of
the Chinese and Japanese was such as only the British 14th-century
archery could match in the Western and nothing in the Classical.

It should be noted also that it was in our 14th Century that—quite
independently of gunpowder—archery and the construction of siege-
engines reached their zenith in the West. The “English” bow had long
been used by the Welsh, but it was left to Edward I and Edward III to
make it the tactical weapon par excellence.—_Tr._

Footnote 418:

See Vol. II, pp. 626 et seq.

Footnote 419:

Half as long again as Nelson’s _Victory_ and about the same length as
the last wooden steam three-deckers (e.g., _Duke of Wellington_) of
the mid-19th Century.—_Tr._

Footnote 420: