CHAPTER XI

FAUSTIAN AND APOLLINIAN NATURE-KNOWLEDGE

I

Helmholtz observed, in a lecture of 1869 that has become famous, that “the final aim of Natural Science is to discover the motions underlying all alteration, and the motive forces thereof; that is, to resolve itself into Mechanics.” What this resolution into mechanics means is the reference of all qualitative impressions to fixed quantitative base- values, that is, to the _extended_ and to _change of place_ therein. It means, further—if we bear in mind the opposition of becoming and become, form and law, image and notion—the referring of the seen Nature-picture to the imagined picture of a single numerically and structurally measurable Order. The specific tendency of all Western mechanics is towards an intellectual _conquest by measurement_, and it is therefore obliged to look for the essence of the phenomenon in a system of constant elements that are susceptible of full and inclusive appreciation by measurement, of which Helmholtz distinguishes _motion_ (using the word in its everyday sense) as the most important.

To the physicist this definition appears unambiguous and exhaustive, but to the sceptic who has followed out the history of this scientific conviction, it is very far from being either. To the physicist, present- day mechanics is a logical system of clear, uniquely-significant concepts and of simple, necessary relations; while to the other it is a _picture_ distinctive of the structure of the West-European spirit, though he admits that the picture is consistent in the highest degree and most impressively convincing. It is self-evident that no _practical_ results and discoveries can prove anything as to the “truth” of the _theory_, the _picture_.[463] For most people, indeed, “mechanics” appears as the self-evident synthesis of Nature-impressions. But it merely appears to be so. For what is motion? Is not the postulate that everything qualitative is reducible to the motion of unalterably-alike mass-points, essentially Faustian and not common to humanity? Archimedes, for example, did not feel himself obliged to transpose the mechanics that he saw into a mental picture of motions. Is motion generally a purely mechanical quantity? Is it a word for a visual experience or is it a notion derived from that experience? Is it the number that is found by measurement of experimentally-produced facts, or the picture that is subjected to that number, that is signified by it? And if one day physics should really succeed in reaching its supposed aim, in devising a system of law-governed “motions” and of efficient forces behind them into which everything whatsoever appreciable by the senses could be fitted—would it thereby have achieved “knowledge” of that which occurs, or even made one step towards this achievement? Yet is the form-language of mechanics one whit the less dogmatic on that account? Is it not, on the contrary, a vessel of the myth like the root- words, not proceeding from experience but shaping it and, in this case, shaping it with all possible rigour? What is force? What is a cause? What is a process? Nay, even on the basis of its own definitions, has physics a specific problem at all? Has it an object that counts as such for all the centuries? Has it even one unimpeachable imagination-unit, with reference to which it may express its results?

The answer may be anticipated. Modern physics, as a science, is an immense system of _indices_ in the form of names and numbers whereby we are enabled to work with Nature as with a machine.[464] As such, it may have an exactly-definable end. But as a piece of _history_, all made up of destinies and incidents in the lives of the men who have worked in it and in the course of research itself, physics is, in point of object, methods and results alike an expression and actualization of a Culture, an organic and evolving element in the essence of that Culture, and every one of its results is a symbol. That which physics—which exists only in the waking-consciousness of the Culture-man—thinks it finds in its methods and in its results was already there, underlying and implicit in, the choice and manner of its search. Its discoveries, in virtue of their imagined content (as distinguished from their printable formulæ), have been of a purely mythic nature, even in minds so prudent as those of J. B. Mayer, Faraday and Hertz. In every Nature-law, physically exact as it may be, we are called upon to distinguish between the nameless number and the naming of it, between the plain fixation of limits[465] and their theoretical interpretation. The formulæ represent general logical values, pure numbers—that is to say, objective space—and boundary-elements. But formulæ are dumb. The expression _s_ = ½_gt_² means nothing at all unless one is able mentally to connect the letters with particular words and their symbolism. But the moment we clothe the dead signs in such words, give them flesh, body and life, and, in sum, a perceptible significance in the world, we have overstepped the limits of a mere _order_. θεωρία means image, vision, and it is this that makes a Nature-law out of a figure-and-letter formula. Everything exact is in itself _meaningless_, and every physical observation is so constituted that it _proves the basis of a certain number of imaged presuppositions_; and the effect of its successful issue is to make these presuppositions more convincing than ever. Apart from these, the result consists merely of empty figures. But in fact we do not and cannot get apart from them. Even if an investigator puts on one side every hypothesis that he knows as such, as soon as he sets his _thought_ to work on the supposedly clear task, he is not controlling but being controlled by the unconscious form of it, for in living activity he is always a man of his Culture, of his age, of his school and of his tradition. Faith and “knowledge” are only two species of inner certitude, but of the two faith is the older and it dominates all the conditions of knowing, be they never so exact. And thus it is theories and not pure numbers that are the support of all natural science. The unconscious longing for that genuine science which (be it repeated) is peculiar to the spirit of Culture-man sets itself to apprehend, to penetrate, and to comprise within its grasp the world-image of Nature. Mere industrious measuring for measuring’s sake is not and never has been more than a delight for little minds. Numbers may only be the key of the secret, no more. No significant man would ever have spent himself on them for their own sake.

Kant, it is true, says in a well-known passage: “I maintain that in each and every discipline of natural philosophy it is only possible to find as much of true science as is to be found of mathematics therein.” What Kant has in mind here is pure delimitation in the field of the become, so far as law and formula, number and system can (at any particular stage) be seen in that field. But a law without words, a law, consisting merely of a series of figures read off an instrument, cannot even as an intellectual operation be completely effective in this pure state. Every savant’s experiment, be it what it may, is at the same time an instance of the _kind_ of symbolism that rules in the savant’s ideation. All Laws formulated in words are Orders that have been activated and vitalized, filled with the very essence of the one—and only the one—Culture. As to the “necessity” which is a postulate in all exact research, here too we have to consider two kinds of necessity, viz., a necessity within the spiritual and living (for it is Destiny that the history of every individual research-act takes its course when, where and how it does) and a necessity within the known (for which the current Western name is Causality). If the pure numbers of a physical formula represent a causal necessity, the existence, the birth and the life-duration of a theory are a Destiny.

Every fact, even the simplest, contains _ab initio_ a theory. A fact is a uniquely-occurring impression upon a waking being, and everything depends on whether that being, the being for whom it occurs or did occur, is or was Classical or Western, Gothic or Baroque. Compare the effect produced by a flash of lightning on a sparrow and on an alert physical investigator, and think how much more is contained in the observer’s “fact” than in the sparrow’s. The modern physicist is too ready to forget that even words like quantity, position, process, change of state and body represent specifically Western images. These words excite and these images mirror a feeling of significances, too subtle for verbal description, incommunicable to Classical or to Magian or to other mankind as like subtleties of their thought and feeling are incommunicable to us. And the character of scientific facts as such—that is, the mode of their becoming known—is completely governed by this feeling; and if so, then also _a fortiori_ such intricate intellectual notions as work, tension, quantity of energy, quantity of heat, probability,[466] every one of which contains a veritable scientific myth of its own. We think of such conceptual images as ensuing from quite unprejudiced research and, subject to certain conditions, definitively valid. But a first-rate scientist of the time of Archimedes would have declared himself, after a thorough study of our modern theoretical physics, quite unable to comprehend how anyone could assert such arbitrary, grotesque and involved notions to be Science, still less how they could be claimed as necessary consequences from actual facts. “The scientifically-justified conclusions,” he would have said, “are really so-and-so”; and thereupon he would have evolved, on the basis of the same elements made “facts” by _his_ eyes and _his_ mind, theories that our physicists would listen to with amazed ridicule.

For what, after all, are the basic notions that have been evolved with inward certainty of logic in the field of our physics? Polarized light- rays, errant ions, flying and colliding gas-particles, magnetic fields, electric currents and waves—are they not one and all Faustian visions, closely akin to Romanesque ornamentation, the upthrust of Gothic architecture, the Viking’s voyaging into unknown seas, the longings of Columbus and Copernicus? Did not this world of forms and pictures grow up in perfect tune with the contemporary arts of perspective oil- painting and instrumental music? Are they not, in short, our passionate directedness, our passion of the third dimension, coming to symbolic expression in the imagined Nature-picture as in the soul-image?

II

It follows then that all “knowing” of Nature, even the exactest, is based on a religious faith. The pure mechanics that the physicist has set before himself as the end-form to which it is his task (and the purpose of all this imagination-machinery) to reduce Nature, presupposes a _dogma_—namely, the religious world-picture of the Gothic centuries. For it is from this world-picture that the physics peculiar to the Western intellect is derived. There is no science that is without unconscious presuppositions of this kind, over which the researcher has no control and which can be traced back to the earliest days of the awakening Culture. _There is no Natural science without a precedent Religion._ In this point there is no distinction between the Catholic and the Materialistic views of the world—both say the same thing in different words. Even atheistic science has religion; modern mechanics exactly reproduces the contemplativeness of Faith.

When the Ionic reaches its height in Thales or the Baroque in Bacon, and man has come to the urban stage of his career, his self-assurance begins to look upon critical science, in contrast to the more primitive religion of the countryside, as the superior attitude towards things, and, holding as he thinks the only key to real knowledge, to explain religion itself empirically and psychologically—in other words, to “conquer” it with the rest. Now, the history of the higher Cultures shows that “science” is a transitory spectacle,[467] belonging only to the autumn and winter of their life-course, and that in the cases of the Classical, the Indian, the Chinese and the Arabian thought alike a few centuries suffice for the complete exhaustion of its possibilities. Classical science faded out between the battle of Cannæ and that of

## Actium and made way for the world-outlook of the “second

religiousness.”[468] And from this it is possible to foresee a date at which our Western scientific thought shall have reached the limit of its evolution.

There is no justification for assigning to this intellectual form-world the primacy over others. Every critical science, like every myth and every religious belief, rests upon an inner certitude. Various as the creatures of this certitude may be, both in structure and in sound, they are not different in basic principle. Any reproach, therefore, levelled by Natural science at Religion is a boomerang. We are presumptuous and no less in supposing that we can ever set up “The Truth” in the place of “anthropomorphic” conceptions, for no other conceptions but these exist at all. Every idea that is possible at all is a mirror of the being of its author. The statement that “man created God in his own image,” valid for every historical religion, is not less valid for every physical theory, however firm its reputed basis of fact. Classical scientists conceived of light as consisting in corporeal particles proceeding from the source of light to the eye of the beholder. For the Arabian thought, even at the stage of the Jewish-Persian academies of Edessa, Resaïna and Pombaditha (and for Porphyry too), the colours and forms of things were evidenced without the intervention of a medium, being brought in a magic and “spiritual” way to the seeing-power which was conceived as substantial and resident in the eyeball. This was the doctrine[469] taught by Ibn-al-Haitan, by Avicenna and by the “Brothers of Sincerity.”[470] And the idea of light as a force, an _impetus_, was current even from about 1300 amongst the Paris Occamists who centred on Albert of Saxony, Buridan and Oresme the discoverer of co-ordinate geometry. Each Culture has made its own set of images of processes, which are true only for itself and only alive while it is itself alive and actualizing its possibilities. When a Culture is at its end and the creative element—the imaginative power, the symbolism—is extinct, there are left “empty” formulæ, skeletons of dead systems, which men of another Culture read literally, feel to be without meaning or value and either mechanically store up or else despise and forget. Numbers, formulæ, laws _mean_ nothing and _are_ nothing. They must have a body, and only a _living_ mankind—projecting its livingness into them and through them, expressing itself by them, inwardly making them its own— can endow them with that. And thus there is no absolute science of physics, but only individual sciences that come, flourish and go within the individual Cultures.

The “Nature” of Classical man found its highest artistic emblem in the nude statue, and out of it logically there grew up a _static of bodies, a physics of the near_. The Arabian Culture owned the arabesque and the cavern-vaulting of the mosque, and out of this world-feeling there issued _Alchemy_ with its ideas of mysterious efficient substantialities like the “philosophical mercury,” which is neither a material nor a property but some thing that underlies the coloured existence of metals and can transmute one metal into another.[471] And the outcome of Faustian man’s Nature idea was _a dynamic of unlimited span, a physics of the distant_. To the Classical therefore belong the conceptions of _matter and form_, to the Arabian (quite Spinozistically) the idea of _substances_ with visible or secret _attributes_,[472] and to the Faustian the idea of _force and mass_. Apollinian theory is a quiet meditation, Magian a silent knowledge of Alchemy the means of Grace (even here the religious source of mechanics is to be discerned), and the Faustian is from the very outset a _working hypothesis_.[473] The Greek asked, what is the essence of visible being? We ask, what possibility is there of mastering the invisible motive-forces of becoming? For them, contented absorption in the visible; for us, masterful questioning of Nature and methodical experiment.

As with the formulation of problems and the methods of dealing with them, so also with the basic concepts. They are symbols in each case of the one and only the one Culture. The Classical root-words ἄπειρον, ἀρχή, μορφή, ὕλη, are not translatable into our speech. To render ἀρχή by “prime-stuff” is to eliminate its Apollinian connotation, to make the hollow shell of the word sound an alien note. That which Classical man saw before him as “motion” in space, he understood as ἀλλοίωσις, change of position of bodies; we, from the way in which we experience motion, have deduced the concept of a _process_, a “going forward,” thereby expressing and emphasizing that element of directional energy which our thought necessarily predicates in the courses of Nature. The Classical critic of Nature took the visible juxtaposition of states as the original diversity, and specified the famous four elements of Empedocles—namely, earth as the rigid-corporeal, water as the non-rigid- corporeal and air as the incorporeal, together with fire, which is so much the strongest of all optical impressions that the Classical spirit could have no doubt of its bodiliness. The Arabian “elements,” on the contrary, are ideal and implicit in the secret constitutions and constellations which define the phenomenon of things for the eye. If we try to get a little nearer to this feeling, we shall find that the opposition of rigid and fluid means something quite different for the Syrian from what it means for the Aristotelian Greek, the latter seeing in it different degrees of bodiliness and the former different magic attributes. With the former therefore arises the image of the _chemical_ element as a sort of magic substance that a secret causality makes to appear out of things (and to vanish into them again) and which is subject even to the influence of the stars. In Alchemy there is deep scientific doubt as to the plastic actuality of things—of the “somata” of Greek mathematicians, physicists and poets—and it dissolves and destroys the soma in the hope of finding its essence. It is an iconoclastic movement just as truly as those of Islam and the Byzantine Bogomils were so. It reveals a deep disbelief in the tangible figure of phenomenal Nature, the figure of her that to the Greek was sacrosanct. The conflict concerning the person of Christ which manifested itself in all the early Councils and led to the Nestorian and Monophysite secessions is an _alchemistic_ problem.[474] It would never have occurred to a Classical physicist to investigate things while at the same time denying or annihilating their perceivable form. And for that very reason there was no Classical chemistry, any more than there was any theorizing on the substance as against the manifestations of Apollo.

The rise of a chemical method of the Arabian style betokens a new world- consciousness. The discovery of it, which at one blow made an end of Apollinian natural science, of mechanical statics, is linked with the enigmatic name of Hermes Trismegistus,[475] who is supposed to have lived in Alexandria _at the same time as Plotinus and Diophantus_. Similarly it was just at the time of the definite emancipation of the Western mathematic by Newton and Leibniz that the Western chemistry[476] was freed from Arabic form by Stahl (1660-1734) and his Phlogiston theory. Chemistry and mathematic alike became pure analysis. Already Paracelsus (1493-1541) had transformed the Magian effort to make gold into a pharmaceutical science—a transformation in which one cannot but surmise an altered world-feeling. Then Robert Boyle (1626-1691) devised the analytical method and _with it the Western conception of the Element_. But the ensuing changes must not be misinterpreted. That which is called the founding of modern chemistry and has Stahl and Lavoisier at its turning-points is anything but a building-up of “chemical” ideas, in so far as chemistry implies the alchemistic outlook on Nature. It is in fact the _end_ of genuine chemistry, its dissolution into the comprehensive system of pure dynamic, its assimilation into the mechanical outlook which the Baroque age had established through Galileo and Newton. The elements of Empedocles designate states of bodiliness (bezeichnen ein körperliches Sichverhalten) but the elements of Lavoisier, whose combustion-theory followed promptly upon the isolation of oxygen in 1771, designate energy-systems accessible to human will, “rigid” and “fluid” becoming mere terms to describe tension-relations between molecules. By our analysis and synthesis, Nature is not merely asked or persuaded but forced. The modern chemistry is a chapter of the modern physics of Deed.

What we call Statics, Chemistry and Dynamics—words that as used in modern science are merely traditional distinctions without deeper meaning—are really the _respective physical systems of the Apollinian, Magian and Faustian souls_, each of which grew up in its own Culture and was limited as to validity to the same. Corresponding to these sciences, each to each, we have the mathematics of Euclidean geometry, Algebra and Higher Analysis, and the arts of statue, arabesque and fugue. We may differentiate these three kinds of physics (bearing in mind of course that other Cultures may and in fact do give rise to other kinds) by their standpoints towards the problem of motion, and call them mechanical orderings of states, secret forces and processes respectively.

III

Now, the tendency of human thought (which is always causally disposed) to reduce the image of Nature to the simplest possible quantitative form-units that can be got by causal reasoning, measuring and counting— in a word, by mechanical differentiation—leads necessarily in Classical, Western and every other possible physics, to an atomic theory. Of Indian and Chinese science we know hardly more than the fact they once existed, and the Arabian is so complicated that even now it seems to defy presentation. But we do know our own and the Apollinian sciences well enough to observe, here too, a deeply symbolical opposition.

The Classical atoms are _miniature forms_, the Western _minimal quanta_, and quanta, too, of energy. On the one hand perceptibility, sensuous nearness, and on the other, abstractness are the basic conditions of the idea. The atomistic notions of modern physics—which include not only the Daltonian or “chemical” atom but also the electrons[477] and the quanta of thermodynamics—make more and more demands upon that truly Faustian power of _inner vision_ which many branches of higher mathematics (such as the Non-Euclidean geometries and the Theory of Groups) postulate, and which is not at the disposal of laymen. A quantum of action is an extension-element conceived without regard to sensible quality of any kind, which eludes all relation with sight and touch, for which the expression “shape” has no meaning whatever—something therefore which would be utterly inconceivable to a Classical researcher. Such, already, were Leibniz’s “Monads”[478] and such, superlatively, are the constituents of Rutherford’s picture of the atom as positively-charged nucleus with planetary negative electrons, and of the picture that Niels Bohr has imagined by working these in with the “quanta” of Planck.[479] The atoms of Leucippus and Democritus were different in form and magnitude, that is to say, they were purely plastic units, “indivisible,” as their name asserts, but only plastically indivisible. The atoms of Western physics, for which “indivisibility” has quite another meaning, resemble the figures and themes of music; their being or essence consisting in vibration and radiation, and their relation to the processes of Nature being that of the “motive” to the “movement.”[480] Classical physics examines the aspect, Western the working, of these ultimate elements in the picture of the Become; in the one, the basic notions are notions of stuff and form, in the other they are notions of capacity and intensity.

_There is a Stoicism and there is a Socialism of the atom_, the words describing the static-plastic and the dynamic-contrapuntal ideas of it respectively. The relations of these ideas to the images of the corresponding ethics is such that every law and every definition takes these into account. On the one hand—Democritus’s multitude of confused atoms, put there, patient, knocked about by the blind chance that he as well as Sophocles called ἀνάγκη, hunted like Œdipus. On the other hand— systems of abstract force-points working in unison, aggressive, energetically dominating space (as “field”), overcoming resistances like Macbeth. The opposition of basic feelings makes that of the mechanical Nature-pictures. According to Leucippus the atoms fly about in the void “of themselves”; Democritus merely regards shock and countershock as a form of change of place. Aristotle explains individual movements as accidental, Empedocles speaks of love and hate, Anaxagoras of meetings and partings. All these are elements also of Classical tragedy; the figures on the Attic stage are related to one another just so. Further, and logically, they are the elements of Classical politics. There we have minute cities, political atoms ranged along coasts and on islands, each jealously standing for itself, yet ever needing support, shut-in and shy to the point of absurdity, buffeted hither and thither by the planless orderless happenings of Classical history, rising to-day and ruined to-morrow. And in contrast—the dynastic states of our 17th and 18th Centuries, political fields of force, with cabinets and great diplomats as effective centres of purposeful direction and comprehensive vision. The spirit of Classical history and the spirit of Western history can only be really understood by considering the two souls as an opposition. And we can say the same of the atom-idea, regarded as the basis of the respective physics. Galileo who created the concept of force and the Milesians who created that of ἀρχή, Democritus and Leibniz, Archimedes and Helmholtz, are “contemporaries,” members of the same intellectual phases of quite different Cultures.

But the inner relationship between atom-theory and ethic goes further. It has been shown how the Faustian soul—whose being consists in the overcoming of presence, whose feeling is loneliness and whose yearning is infinity—puts its need of solitude, distance and abstraction into all its actualities, into its public life, its spiritual and its artistic form-worlds alike. This pathos of distance (to use Nietzsche’s expression) is peculiarly alien to the Classical, in which everything human demanded nearness, support and community. It is this that distinguishes the spirit of the Baroque from that of the Ionic, the culture of the Ancien Régime from that of Periclean Athens. And this pathos, which distinguishes the heroic doer from the heroic sufferer, appears also in the picture of Western physics as _tension_. It is tension that is missing in the science of Democritus; for in the principle of shock and countershock it is denied by implication that there is a force commanding space and identical with space. And, correspondingly, the element of Will is absent from the Classical soul- image. Between Classical men, or states, or views of the world, there was—for all the quarrelling and envy and hatred—no inner tension, no deep and urging need of distance, solitude, ascendancy; and consequently there was none between the atoms of the Cosmos either. The principle of tension (developed in the potential theory), which is wholly untranslatable into Classical tongues and incommunicable to Classical minds, has become for Western physics fundamental. Its content follows from the notion of energy, _the Will-to-Power in Nature_, and therefore it is for us just as necessary as for the Classical thought it is impossible.

IV

_Every atomic theory, therefore, is a myth and not an experience._ In it the Culture, through the contemplative-creative power of its great physicists, reveals its inmost essence and very self. It is only a preconceived idea of criticism that extension exists in itself and independently of the form-feeling and world-feeling of the knower. The thinker, in imagining that he can cut out the factor of Life, forgets that knowing is related to the known as direction is to extension and that it is only through the living quality of direction that what is felt extends into distance and depth and becomes space. The cognized structure of the extended is a projection of the cognizing being.

We have already[481] shown the decisive importance of the _depth- experience_, which is identical with the awakening of a soul and therefore with the creation of the outer world belonging to that soul. The mere sense-impression contains only length and breadth, and it is the living and necessary act of interpretation—which, like everything else living, possesses direction, motion and irreversibility (the qualities that our consciousness synthesizes in the word Time)—that _adds_ depth and thereby fashions actuality and world. Life itself enters into the experiences as third dimension. The double meaning of the word “far,” which refers both to future and to horizon, betrays the deeper meaning of this dimension, through which extension as such is evoked. The Becoming stiffens and passes and is at once the Become; Life stiffens and passes and is at once the three-dimensional Space of the known. It is common ground for Descartes and Parmenides that thinking and being, i.e., imagined and extended, are identical. “Cogito, ergo sum” is simply the formulation of the depth-experience—I cognize, and therefore I am in space. But in the style of this cognizing, and therefore of the cognition-product, the prime-symbol of the particular Culture comes into play. The perfected extension of the Classical consciousness is one of sensuous and bodily presence. The Western consciousness achieves extension, after its own fashion, as transcendental space, and as it thinks its space more and more transcendentally it develops by degrees the abstract polarity of Capacity and Intensity that so completely contrasts with the Classical visual polarity of Matter and Form.

But it follows from this that in the known there can be no reappearance of living time. For this has already passed into the known, into constant “existence,” as Depth, and hence duration (i.e., timelessness) and extension are identical. Only the knowing possesses the mark of direction. The application of the word “time” to the imaginary and measurable time-dimension of physics is a mistake. The only question is whether it is possible or not to avoid the mistake. If one substitutes the word “Destiny” for “time” in any physical enunciation, one feels at once that pure Nature does not contain Time. The form-world of physics extends just as far as the cognate form-world of number and notion extend, and we have seen that (notwithstanding Kant) there is not and cannot be the slightest relation of any sort between mathematical number and Time. And yet this is controverted _by the fact of motion_ in the picture of the world-around. It is the unsolved and unsolvable problem of the Eleatics—being (or thinking) and motion are incompatible; motion “is” not (is only “apparent”).

And here, for the second time, Natural science becomes dogmatic and mythological. The words Time and Destiny, for anyone who uses them instinctively, touch Life itself in its deepest depths—life as a whole, which is not to be separated from lived-experience. Physics, on the other hand—i.e., the observing Reason—_must_ separate them. The livingly-experienced “in-itself,” mentally emancipated from the act of the observer and become object, dead, inorganic, rigid, is now “Nature,” something open to exhaustive mathematical treatment. In this sense the knowledge of Nature is an activity of _measurement_. All the same, we live even when we are observing and therefore the thing we are observing _lives with us_. The element in the Nature-picture in virtue of which it not merely from moment to moment _is_, but in a continuous flow with and around us _becomes_, is the copula of the waking-consciousness and its world. This element is _called_ movement, and it contradicts Nature as a picture, but it represents the _history_ of this picture. And therefore, as precisely as Understanding is abstracted (by means of words) from feeling and mathematical space from light-resistances (“things”[482]), so also physical “time” is abstracted from the impression of motion.

Physics investigates Nature, and consequently it knows time only as a length. But the physicist _lives_ in the midst of the _history_ of this Nature, and therefore he is forced to conceive motion as a mathematically determinable magnitude, as a concretion of the pure numbers obtained in the experiment and written down in formulæ. “Physics,” says Kirchhoff, “is the complete and simple description of motions.” That indeed has always been its object. But the question is one not of motions _in_ the picture but of motions _of_ the picture. Motion, in the Nature of physics, is nothing else but that _metaphysical_ something which gives rise to the consciousness of a succession. The known is timeless and alien to motion; its state of becomeness implies this. It is the _organic sequence_ of knowns that gives the impression of a motion. The physicist receives the word as an impression not upon “reason” but upon the whole man, and the function of that man is not “Nature” only but the whole world. And that is the world-as-history. “Nature,” then, is an expression of the Culture in each instance.[483] All physics is treatment of the motion-problem—in which the life-problem itself is implicit—not as though it could one day be solved, _but in spite of, nay because of, the fact that it is insoluble_. The secret of motion awakens in man the apprehension of death.[484]

If, then, Nature-knowledge is a subtle kind of self-knowledge—Nature understood as picture, as mirror of man—the attempt to solve the motion- problem is an attempt of knowledge to get on the track of its own secret, its own Destiny.

V

Only physiognomic tact can, if creative, succeed in this, and in fact it has done so from time immemorial in the arts, particularly tragic poetry. It is the thinking man who is perplexed by movement; for the contemplative it is self-evident. And however completely the former can reduce his perplexities to system, the result is systematic and not physiognomic, pure extension logically and numerically ordered, nothing living but something become and dead.

It is this that led Goethe, who was a poet and not a computer, to observe that “Nature has no system. It has Life, it is Life and succession from an unknown centre to an unknowable bourne.” For one who does not live it but knows it, Nature has a system. But it is only a system and nothing more, and motion is a contradiction in it. The contradiction may be covered up by adroit formulation, _but it lives on in the fundamental concepts_. The shock and countershock of Democritus, the entelechy of Aristotle, the notions of force from the “impetus” of 14th-Century Occamists to the quantum-theory of radiation, all contain it. Let the reader conceive of the motion _within_ a physical system as the _ageing_ of that system (as in fact it is, as lived-experience of the observer), and he will feel at once and distinctly the fatefulness immanent in, the unconquerably organic content of, the word “motion” and all its derivative ideas. But Mechanics, having nothing to do with ageing, should have nothing to do with motion either, and consequently, since no scientific system is conceivable without a motion-problem in it, a complete and self-contained mechanics is an impossibility. Somewhere or other there is always an organic starting-point in the system where immediate Life enters it—an umbilical cord that connects the mind-child with the life-mother, the thought with the thinker.

This puts the fundamentals of Faustian and Apollinian Nature-science in quite another light. No “Nature” is pure—there is always something of history in it. If the man is ahistorical, like the Greek, so that the totality of his impressions of the world is absorbed in a pure point- formed present, his Nature-image is static, self-contained (that is, walled against past and future) in every individual moment. Time as magnitude figures in Greek physics as little as it does in Aristotle’s entelechy-idea. If, on the other hand, the Man is historically constituted, the image formed is dynamic. Number, the definitive evaluation of the become, is in the case of ahistoric man Measure, and in that of the historical man Function. One measures only what is present and one follows up only what has a past and a future, a course. And the effect of this difference is that the inner inconsistencies of the motion-problem are covered up in Classical theories and forced into the foreground in Western.

History is eternal becoming and therefore eternal future; Nature is become and therefore eternally past.[485] And here a strange inversion seems to have taken place—the Becoming has lost its priority over the Become. When the intellect looks back from _its_ sphere, the Become, the aspect of life is reversed, the idea of Destiny which carries aim and future in it having turned into the mechanical principle of cause-and- effect of which the centre of gravity lies in the past. The spatially- experienced is promoted to rank above the temporal living, and time is replaced by a length in a spatial world-system. And, since in the creative experience extension follows from direction, the spatial from life, the human understanding imports life _as a process_ into the inorganic space of its imagination. While life looks on space as something functionally belonging to itself, intellect looks upon life as something _in_ space. Destiny asks: “Whither?”, Causality asks: “Whence?” To establish scientifically means, starting from the become and actualized, to search for “causes” by going back along a mechanically-conceived course, that is to say, by treating becoming as a length. But it is not possible to live backwards, only to think backwards. Not Time and Destiny are reversible, but only that which the physicist calls “time” and admits into his formulæ as divisible, and preferably as negative or imaginary quantities.

The perplexity is always there, though it has rarely been seen to be originally and necessarily inherent. In the Classical science the Eleatics, declining to admit the necessity of thinking of Nature as in motion, set up against it the logical view that thinking is a being, with the corollary that known and extended are identical and knowledge and becoming therefore irreconcilable. Their criticisms have not been, and cannot be, refuted. But they did not hinder the evolution of Classical physics, which was a necessary expression of the Apollinian soul and as such superior to logical difficulties. In the “classical” mechanics so-called of the Baroque, founded by Galileo and Newton, an irreproachable solution of the motion-problem on dynamic lines has been sought again and again. The history of the concept of force, which has been stated and restated with all the tireless passion of a thought that feels its own self endangered by a difficulty, is nothing but the history of endeavours to find a form that is unimpeachable, mathematically and conceptually, for motion. The last serious attempt— which failed like the rest, and of necessity—was Hertz’s.

Without discovering the true source of all perplexities (no physicist as yet has done that), Hertz tried to eliminate the notion of force entirely—rightly feeling that error in all mechanical systems has to be looked for in one or another of the basic concepts—and to build up the whole picture of physics on the quantities of time, space and mass. But he did not observe that it is Time itself (which as direction-factor is present in the force-concept) that is the organic element without which a dynamic theory cannot be expressed and with which a clean solution cannot be got. Moreover, quite apart from this, the concepts force, mass and motion constitute a dogmatic unit. They so condition one another that the application of one of them tacitly involves both the others from the outset. The whole Apollinian conception of the motion-problem is implicit in the root-word ἀρχή, the whole Western conception of it in the force-idea. The notion of mass is only the complement of that of force. Newton, a deeply religious nature, was only bringing the Faustian world-feeling to expression when, to elucidate the words “force” and “motion,” he said that masses are points of attack for force and carriers for motion. So the 13th-Century Mystics had conceived of God and his relation to world. Newton no doubt rejected the metaphysical element in his famous saying “hypotheses non fingo,” but all the same he was metaphysical through and through in the founding of his mechanics. _Force is the mechanical Nature-picture of western man; what Will is to his soul-picture and infinite Godhead in his world-picture._ The primary ideas of this physics stood firm long before the first physicist was born, for they lay in the earliest religious world-consciousness of our Culture.

VI

With this it becomes manifest that the physical notion of Necessity, too, has a religious origin. It must not be forgotten that the mechanical necessity that rules in what our intellects comprehend as Nature is founded upon another necessity which is organic and fateful in Life itself. The latter creates, the former restricts. One follows from inward certitude, the other from demonstration; that is the distinction between tragic and technical, historical and physical logic.

There are, further, differences within the necessity postulated and assumed by science (that of cause-and-effect) which have so far eluded the keenest sight. We are confronted here with a question at once of very great difficulty and of superlative importance. A Nature-knowledge is (however philosophy may express the relation) a function of knowing, which is in each case knowing in a particular style. A scientific necessity therefore has the style of _the appropriate intellect_, and this brings morphological differences into the field at once. It is possible to see a strict necessity in Nature even where it may be impossible to express it in natural laws. In fact natural laws, which for us are self-evidently the proper expression-form in science, are not by any means so for the men of other Cultures. They presuppose a quite special form, the distinctively Faustian form, of understanding and therefore of Nature-knowing. There is nothing inherently absurd in the conception of a mechanical necessity wherein each individual case is morphologically self-contained and never exactly reproduced, in which therefore the acquisitions of knowledge cannot be put into consistently- valid formulæ. In such a case Nature would appear (to put it metaphorically) as an unending decimal that was also non-recurring, destitute of periodicity. And so, undoubtedly, it was conceived by Classical minds—the feeling of it manifestly underlies their primary physical concepts. For example, the proper motion of Democritus’s atoms is such as to exclude any possibility of calculating motions in advance.

Nature-laws are forms of the known in which an aggregate of individual cases are brought together as a unit of higher degree. Living Time is ignored—that is, it does not matter whether, when or how often the case arises, for the question is not of chronological sequence but of mathematical consequence.[486] But in the consciousness that no power in the world can shake this calculation lies our will to command over Nature. That is Faustian. It is only from this standpoint that miracles appear as breaches of the laws of Nature. Magian man saw in them merely the exercise of a power that was not common to all, not in any way a contradiction of the laws of Nature. And Classical man, according to Protagoras, was only the measure and not the creator of things—a view that unconsciously forgoes all conquest of Nature through the discovery and application of laws.

We see, then, that the causality-principle, in the form in which it is self-evidently necessary for us—the agreed basis of truth for our mathematics, physics and philosophy—is a Western and, more strictly speaking, a Baroque phenomenon. It cannot be proved, for every proof set forth in a Western language and every experiment conducted by a Western mind presupposes itself. In every problem, the enunciation contains the proof in germ. The method of a science is the science itself. Beyond question, the notion of laws of Nature and the conception of physics as “scientia experimentalis,”[487] which has held ever since Roger Bacon, contains _a priori_ this specific kind of necessity. The Classical mode of regarding Nature—the alter ego of the Classical mode of being—on the contrary, does _not_ contain it, and yet it does not appear that the scientific position is weakened in logic thereby. If we work carefully through the utterances of Democritus, Anaxagoras, and Aristotle (in whom is contained the whole sum of Classical Nature-speculation), and, above all, if we examine the connotations of key-terms like ἀλλοίωσις, ἀνάγκη, ἐντελέχεια, we look with astonishment into a world-image totally unlike our own. This world-image is self-sufficing and therefore, for this definite sort of mankind, unconditionally true. And causality in our sense plays no part therein.

The alchemist or philosopher of the Arabian Culture, too, assumes a necessity within his world-cavern that is utterly and completely different from the necessity of dynamics. There is no causal nexus of law-form but only _one_ cause, God, immediately underlying _every_ effect. To believe in Nature-laws would, from this standpoint, be to doubt the almightiness of God. If a rule seems to emerge, it is because it pleases God so; but to suppose that this rule was a necessity would be to yield to a temptation of the Devil. This was the attitude also of Carneades, Plotinus and the Neo-Pythagoreans.[488] _This_ necessity underlies the Gospels as it does the Talmud and the Avesta, and upon it rests the technique of alchemy.

The conception of number as function is related to the dynamic principle of cause-and-effect. Both are creations of the same intellect, expression-forms of the same spirituality, formative principles of the same objectivized and “become” Nature. In fact the physics of Democritus differs from the physics of Newton in that the chosen starting-point of the one is the optically-given while that of the other is abstract relations that have been deduced from it. The “facts” of Apollinian Nature-knowledge are things, and they lie on the surface of the known, but the facts of Faustian science are relations, which in general are invisible to lay eyes, which have to be mastered intellectually, which require for their communication a code-language that only the expert researcher can fully understand. The Classical, static, necessity is immediately evident in the changing phenomena, while the dynamic causation-principle prevails beyond things and its tendency is to weaken, or to abolish even, their sensible actuality. Consider, for example, the world of significance that is connected, under present-day hypotheses, with the expression “a magnet.”

The principle of the Conservation of Energy, which since its enunciation by J. R. Mayer has been regarded in all seriousness as a plain conceptual necessity, is in fact a redescription of the _dynamic_ principle of causality by means of the physical concept of force. The appeal to “experience,” and the controversy as to whether judgment is necessary or empirical—i.e., in the language of Kant (who greatly deceived himself about the highly-fluid boundaries between the two), whether it is _a priori_ or _a posteriori_ certain—are characteristically Western. Nothing seems to us more self-evident and unambiguous than “experience” as the source of exact science. The Faustian experiment, based on working hypotheses and employing the methods of measurement, is nothing but the systematic and exhaustive exploitation of this “experience.” But no one has noticed that a whole world-view is implicit in such a concept of “experience” with its aggressive dynamic connotation, and that there is not and cannot be “experience” in this pregnant sense for men of other Cultures. When we decline to recognize the scientific results of Anaxagoras or Democritus as experiential results, it does not mean that these Classical thinkers were incapable of interpreting and merely threw off fancies, but that we miss in their generalizations that causal element which for us _constitutes_ experience in our sense of the word. Manifestly, we have never yet given adequate thought to the _singularity_ of this, the pure Faustian, conception of experience. The contrast between it and faith is obvious—and entirely superficial. For indeed exact sensuous-intellectual experience is in point of structure completely congruent with that heart-experience (as we may well call it), that illumination which deep religious natures of the West (Pascal, for instance, whom one and the same necessity made mathematician and Jansenist) have known in the significant moments of their being. Experience means to us an _activity_ of the intellect, which does not resignedly confine itself to receiving, acknowledging and arranging momentary and purely present impressions, but seeks them out and calls them up in order to overcome them in their sensuous presence and to bring them into an unbounded unity in which their sensuous discreteness is dissolved. Experience in our sense possesses the tendency _from particular to infinite_. And for that very reason it is in contradiction with the feeling of Classical science. What for us is the way to acquire experience is for the Greek the way to lose it. And therefore he kept away from the drastic method of experiment; therefore his physics, instead of being a mighty system of worked-out laws and formulæ that strong-handedly override the sense-present (“only knowledge is power”), is an aggregate of impressions—well ordered, intensified by sensuous imagery, clean-edged—which leaves Nature intact in its self-completeness. Our exact Natural science is imperative, the Classical is θεωρία in the literal sense, the result of passive contemplativeness.

VII

We can now say without any hesitation that the form-world of a Natural science corresponds to those of the appropriate mathematic, the appropriate religion, the appropriate art. A deep mathematician—by which is meant not a master-computer but a man, any man, who feels the spirit of numbers living within him—realizes that through it he “knows God.” Pythagoras and Plato knew this as well as Pascal and Leibniz did so. Terentius Varro, in his examination of the old Roman religion (dedicated to Julius Cæsar), distinguished with Roman seriousness between the _theologia civilis_, the sum of officially-recognized belief, the _theologia mythica_, the imagination-world of poets and artists, and the _theologia physica_ of philosophical speculation. Applying this to the Faustian Culture, that which Thomas Aquinas and Luther, Calvin and Loyola taught belongs to the first category, Dante and Goethe belong to the second; and to the third belongs scientific physics, inasmuch as behind its formulæ there are images.

Not only primitive man and the child, but also the higher animals spontaneously evolve from the small everyday experiences an image of Nature which contains the sum of technical indications observed as recurrent. The eagle “knows” the moment at which to swoop down on the prey; the singing-bird sitting on the eggs “knows” the approach of the marten; the deer “finds” the place where there is food. In man, this experience of all the senses has narrowed and deepened itself into experience of the eye. But, as the habit of verbal speech has now been superadded, understanding comes to be abstracted from seeing, and thenceforward develops independently as reasoning; to the instantly- comprehending _technique_ is added the reflective _theory_. Technique applies itself to visible near things and plain needs, theory to the distance and the terrors of the invisible. By the side of the petty knowledge of everyday life it sets up belief. And still they evolve, there is a new knowledge and a new and higher technique, and to the myth there is added the cult. The one teaches how to know the “numina,” the other how to conquer them. For theory in the eminent sense is religious through and through. It is only in quite late states that scientific theory evolves out of religious, _through men having become aware of methods_. Apart from this there is little alteration. The image-world of physics remains mythic, its procedure remains a cult of conjuring the powers in things, and the images that it forms and the methods that it uses remain generically dependent upon those of the appropriate religion.[489]

From the later days of the Renaissance onward, the notion of God has steadily approximated, in the spirit of every man of high significance, to the idea of pure endless Space. The God of Ignatius Loyola’s _exercitia spiritualis_ is the God also of Luther’s “ein’ feste Burg,” of the Improperia of Palestrina and the Cantatas of Bach. He is no longer the Father of St. Francis of Assisi and the high-vaulted cathedrals, the personally-present, caring and mild God felt by Gothic painters like Giotto and Stephen Lochner, but an impersonal principle; unimaginable, intangible, working mysteriously in the Infinite. Every relic of personality dissolves into insensible abstraction, such a divinity as only instrumental music of the grand style is capable of representing, a divinity before which painting breaks down and drops into the background. This God-feeling it was that formed the scientific world-image of the West, its “Nature,” its “experience” and therefore its theories and its methods, in direct contradiction to those of the Classical. The force which moves the mass—that is what Michelangelo painted in the Sistine Chapel; that is what we feel growing more and more intense from the archetype of Il Gesù to the climax in the cathedral façades of Della Porta and Maderna, and from Heinrich Schütz to the transcendent tone-worlds of 18th-Century church music; that is what in Shakespearian tragedy fills with world-becoming scenes widened to infinity. And that is what Galileo and Newton captured in formulæ and concepts.

The word “God” rings otherwise under the vaulting of Gothic cathedrals or in the cloisters of Maulbronn and St. Gallen than in the basilicas of Syria and the temples of Republican Rome. The character of the Faustian cathedral is that of the _forest_. The mighty elevation of the nave above the flanking aisles, in contrast to the flat roof of the basilica; the transformation of the columns, which with base and capital had been set as self-contained individuals in space, into pillars and clustered- pillars that grow up out of the earth and spread on high into an infinite subdivision and interlacing of lines and branches; the giant windows by which the wall is dissolved and the interior filled with mysterious light—these are the architectural actualizing of a world- feeling that had found the first of all its symbols in the high forest of the Northern plains, the deciduous forest with its mysterious tracery, its whispering of ever-mobile foliage over men’s heads, its branches straining through the trunks to be free of earth. Think of Romanesque ornamentation and its deep affinity to the sense of the woods. The endless, lonely, twilight wood became and remained the secret wistfulness in all Western building-forms, so that when the form-energy of the style died down—in late Gothic as in closing Baroque—the controlled abstract line-language resolved itself immediately into naturalistic branches, shoots, twigs and leaves.

Cypresses and pines, with their corporeal and Euclidean effect, could never have become symbols of unending space. But the oaks, beeches and lindens with the fitful light-flecks playing in their shadow-filled volume are felt as bodiless, boundless, spiritual. The stem of the cypress finds conclusive fulfilment of its vertical tendency in the defined columniation of its cone-masses, but that of an oak seems, ever restless and unsatisfied, to strain beyond its summit. In the ash, the victory of the upstriving branches over the unity of the crown seems actually to be won. Its aspect is of something dissolving, something expanding into space, and it was for this probably that the World-Ash Yggdrasil became a symbol in the Northern mythology. The rustle of the woods, a charm that no Classical poet ever felt—for it lies beyond the possibilities of Apollinian Nature-feeling—stands with its secret questions “whence? whither?” its merging of presence into eternity, in a deep relation with Destiny, with the feeling of History and Duration, with the quality of Direction that impels the anxious, caring, Faustian soul towards infinitely-distant Future. And for that reason the organ, that roars deep and high through our churches in tones which, compared with the plain solid notes of aulos and cithara, seem to know neither limit nor restraint, is the instrument of instruments in Western devotions. Cathedral and organ form a symbolic unity like temple and statue. The history of organ-building, one of the most profound and moving chapters of our musical history, is a history of a longing for the forest, a longing to speak in the language of that true temple of Western God-fearing. From the verse of Wolfram von Eschenbach to the music of “Tristan” this longing has borne fruit unceasingly. Orchestra- tone strove tirelessly in the 18th Century towards a nearer kinship with the organ-tone. The word “schwebend”—meaningless as applied to Classical things—is important alike in the theory of music, in oil-painting, in architecture and in the dynamic physics of the Baroque. Stand in a high wood of mighty stems while the storm is tearing above, and you will comprehend instantly the full meaning of the concept of a force which moves mass.

Out of such a primary feeling in the existence that has become thoughtful there arises, then, an idea of the Divine immanent in the world-around, and this idea becomes steadily more definite. The thoughtful percipient takes in the impression of motion in outer Nature. He feels about him an almost indescribable _alien life_ of unknown powers, and traces the origin of these effects to “numina,” to The Other, inasmuch as this Other also possesses Life. Astonishment at _alien motion_ is the source of religion and of physics both; respectively, they are the elucidations of Nature (world-around) by the soul and by the reason. The “powers” are the first object both of fearful or loving reverence and of critical investigation. There is a religious experience _and_ a scientific experience.

Now it is important to observe how the consciousness of the Culture intellectually concretes its primary “numina.” It imposes significant words—_names_—on them and there conjures (seizes or bounds) them. By virtue of the Name they are subject to the intellectual power of the man who possesses the Name, and (as has been shown already) the whole of philosophy, the whole of science, and everything that is related in any way to “knowing” is at the very bottom nothing but an infinitely-refined mode of _applying the name-magic of the primitive to the “alien.”_ The pronouncement of the right name (in physics, the right concept) is an incantation. Deities and basic notions of science alike come into being first as vocable names, with which is linked an idea that tends to become more and more sensuously definite. The outcome of a _Numen_ is a _Deus_, the outcome of a notion is an idea. In the mere naming of “thing-in-itself,” “atom,” “energy,” “gravitation,” “cause,” “evolution” and the like is for most learned men the same sense of deliverance as there was for the peasant of Latium in the words “Ceres,” “Consus,” “Janus,” “Vesta.”[490]

For the Classical world-feeling, conformably to the Apollinian depth- experience and its symbolism, the individual body was “Being.” Logically therefore the form of this body, as it presented itself in the light, was felt as its essence, as the true purport of the word “being.” What has not shape, what is not a shape, is not at all. On the basis of this feeling (which was of an intensity that we can hardly imagine) the Classical spirit created as counter-concept[491] to the form of “The Other” _Non-Form_ viz., stuff, ἀρχή, ὕλη, that which in itself possesses no being and is merely complement to the actual “Ent,” representing a secondary and corollary necessity. In these conditions, it is easy to see how the Classical pantheon inevitably shaped itself, as a higher mankind side by side with the common mankind, as a set of perfectly- formed bodies, of high possibilities incarnate and present, but in the unessential of stuff not distinguished and therefore subject to the same cosmic and tragic necessity.

It is otherwise that the Faustian world-feeling experiences depth. Here the sum of true Being appears as pure efficient Space, which _is_ being. And therefore what is sensuously felt, what is very significantly designated the plenum (das Raumerfüllende), is felt as a fact of the second order, as something questionable or specious, as a resistance that must be overcome by philosopher or physicist before the true content of Being can be discovered. Western scepticism has never been directed against Space, always against tangible things only. Space is the _higher_ idea—force is only a less abstract expression for it—and it is only as a counter-concept to space that mass arises. For mass is what is _in_ space and is logically and physically dependent upon space. From the assumption of a wave-motion of light, which underlies the conception of light as a form of energy, the assumption of a corresponding mass, the “luminiferous æther” necessarily followed. A definition of mass and ascription of properties to mass follows from the definition of force (and not vice versa) with all the necessity of a symbol. All Classical notions of substantiality, however they differed amongst themselves as realist or idealist, distinguish a “to-be-formed,” that is, a Nonent, which only receives closer definition from the basic concept of form, whatever this form may be in the particular philosophical system. All Western notions of substantiality distinguish a “to-be-moved,” which also is a negative, no doubt, but one polar to a different positive. _Form and non-form, force and non-force_—these words render as clearly as may be the polarities that in the two Cultures underlie the world- impression and contain all its modes. That which comparative philosophy has hitherto rendered inaccurately and misleadingly by the one word “matter” signifies in the one case the substratum of shape, in the other the substratum of force. No two notions could differ more completely. For here it is the feeling of God, a _sense of values_, that is speaking. The Classical deity is superlative shape, the Faustian superlative force. The “Other” is the Ungodly to which the spirit will not accord the dignity of Being; to the Apollinian world-feeling this ungodly “other” is substance without shape, to the Faustian it is substance without force.

VIII

Scientists are wont to assume that myths and God-ideas are creations of primitive man, and that as spiritual culture “advances,” this myth- forming power is shed. In reality it is the exact opposite, and had not the morphology of history remained to this day an almost unexplored field, the supposedly universal mythopoetic power would long ago have been found to be limited to particular periods. It would have been realized that this ability of a soul to fill its world with shapes, traits and symbols—like and consistent amongst themselves—belongs most decidedly not to the world-age of the primitives but exclusively to the springtimes of _great_ Cultures.[492] Every myth of the great style stands at the beginning of an awakening spirituality. It is the first formative act of that spirituality. Nowhere else is it to be found. There—it _must_ be.

I make the assumption that that which a primitive folk—like the Egyptians of Thinite times, the Jews and Persians before Cyrus,[493] the heroes of the Mycenæan burghs and the Germans of the Migrations— possesses in the way of religious ideas is not yet myth in the higher sense. It may well be a sum of scattered and irregular traits, of cults adhering to names, fragmentary saga-pictures, but it is not yet a divine order, a mythic organism, and I no more regard this as myth than I regard the ornament of that stage as art. And, be it said, the greatest caution is necessary in dealing with the symbols and sagas current to- day, or even those current centuries ago, amongst ostensibly primitive peoples, for in those thousands of years every country in the world has been more or less affected by some high Culture alien to it.

There are, therefore, as many form-worlds of great myth as there are Cultures and early architectures. The antecedents—that chaos of undeveloped imagery in which modern folk-lore research, for want of a guiding principle, loses itself—do not, on this hypothesis, concern us; but we _are_ concerned, on the other hand, with certain cultural manifestations that have never yet been thought of as belonging to this category. It was in the Homeric age (1100-800 B.C.) and in the corresponding knightly age of Teutonism (900-1200 A.D.), that is, the _epic_ ages, and neither before nor after them, that the great world- image of a new religion came into being. The corresponding ages in India and Egypt are the Vedic and the Pyramid periods; one day it will be discovered that Egyptian mythology did in fact ripen into _depth_ during the Third and Fourth Dynasties.

Only in this way can we understand the immense wealth of religious- intuitive creations that fills the three centuries of the Imperial Age in Germany. What came into existence then was _the Faustian mythology_. Hitherto, owing to religious and learned preconceptions, either the Catholic element has been treated to the exclusion of the Northern- Heathen or vice versa, and consequently we have been blind to the breadth and the unity of this form-world. In reality there is no such difference. The deep change of meaning in the Christian circle of ideas is identical, as a creative act, with the consolidation of the old heathen cults of the Migrations. It was in this age that the folk-lore of Western Europe became an entirety; if the bulk of its material was far older, and if, far later again, it came to be linked with new outer experiences and enriched by more conscious treatment, yet it was then and neither earlier nor later that it was vitalized with its symbolic meaning. To this lore belong the great God-legends of the Edda and many motives in the gospel-poetry of learned monks; the German hero-tales of Siegfried and Gudrun, Dietrich and Wayland; the vast wealth of chivalry- tales, derived from ancient Celtic fables, that was simultaneously coming to harvest on French soil, concerning King Arthur and the Round Table, the Holy Grail, Tristan, Percival and Roland. And with these are to be counted—beside the spiritual transvaluation, unremarked but all the deeper for that, of the Passion-Story—the Catholic hagiology of which the richest floraison was in the 10th and 11th Centuries and which produced the Lives of the Virgin and the histories of SS. Roch, Sebald, Severin, Francis, Bernard, Odilia. The _Legenda Aurea_ was composed about 1250—this was the blossoming-time of courtly epic and Icelandic skald-poetry alike. The great Valhalla Gods of the North and the mythic group of the “Fourteen Helpers” in South Germany are contemporary, and by the side of Ragnarök, the Twilight of the Gods, in the Völuspa we have a Christian form in the South German Muspilli. This great myth develops, like heroic poetry, at the _climax_ of the early Culture. They both belong to the two primary estates, priesthood and nobility; they are at home in the cathedral and the castle and not in the village below, where amongst the people the simple saga-world lives on for centuries, called “fairy-tale,” “popular beliefs” or “superstition” and yet inseparable from the world of high centemplation.[494]

Nowhere is the final meaning of these religious creations more clearly indicated than in the history of Valhalla. It was not an original German idea, and even the tribes of the Migrations were totally without it. It took shape just at _this_ time, instantly and as an inward necessity, in the consciousness of the peoples newly-arisen on the soil of the West. Thus it is “contemporary” with Olympus, which we know from the Homeric epos and which is as little Mycenæan as Valhalla is German in origin. Moreover, it is only for the two higher estates that Valhalla emerges from the notion of Hel; in the beliefs of the people Hel remained the realm of the dead.[495]

The deep inward unity of this Faustian world of myth and saga and the complete congruence of its expression-symbolism has never hitherto been realized, and yet Siegfried, Baldur, Roland, Christ the King in the “Heliand,” are different names for one and the same figure. Valhalla and Avalon, the Round Table and the communion of the Grail-templars, Mary, Frigga and Frau Holle mean the same. On the other hand, the external provenance of the material motives and elements, on which mythological research has wasted an excessive zeal, is a matter of which the importance does not go deeper than the surface. As to the meaning of a myth, its provenance proves _nothing_. The “numen” itself, the primary form of the world-feeling, is a pure, necessary and unconscious creation, and it is not transferable. What one people takes over from another—in “conversion” or in admiring imitation—is a name, dress and mask for its own feeling, never the feeling of that other. The old Celtic and old Germanic myth-motives have to be treated, like the repertory of Classical forms possessed by the learned monk, and like the entire body of Christian-Eastern faith taken over by the Western Church, simply as the material out of which the Faustian soul in these centuries created a mythic architecture of its own. It mattered little whether the persons through whose minds and mouths the myth came to life were individual skalds, missionaries, priests or “the people,” nor did the circumstance that the Christian ideas dictated its forms affect the inward independence of that which had come to life.

In the Classical, Arabian and Western Cultures, the myth of the springtime is in each case that which we should expect; in the first static, in the second Magian, in the third dynamic. Examine every detail of form, and see how in the Classical it is an attitude and in the West a deed, there a being and here a will that underlies them; how in the Classical the bodily and tangible, the sensuously-saturated, prevails and how therefore in the mode of worshipping the centre of gravity lies in the sense-impressive _cult_, whereas in the North it is space, force and therefore a religiousness that is predominantly dogmatic in colouring that rule. These very earliest creations of the young soul tell us that there is relationship between the Olympian figures, the statue and the corporeal Doric temple; between the domical basilica, the “Spirit” of God and the arabesque; between Valhalla and the Mary myth, the soaring nave and instrumental music.

The Arabian soul built up its myth in the centuries between Cæsar and Constantine—that fantastic mass of cults, visions and legends that to- day we can hardly even survey,[496] syncretic cults like that of the Syrian Baal and of Isis and Mithras not only transported to but transformed in Syrian soil; Gospels, Acts of Apostles and Apocalypses in astonishing profusion; Christian, Persian, Jewish, Neoplatonist and Manichæan legends, and the heavenly hierarchy of angels and spirits of the Fathers and the Gnostics. In the suffering-story of the Gospels, _the very epic of the Christian nation_, set between the story of Jesus’s childhood and the Acts of the Apostles, and in the Zoroaster- legend that is contemporary with it, we are looking upon the hero- figures of Early Arabian epic as we see Achilles in the Classical and Siegfried and Percival in the Faustian. The scenes of Gethsemane and Golgotha stand beside the noblest pictures of Greek and Germanic saga. These Magian visions, almost without exception, grew up under the pressure of the dying Classical which, in the nature of things unable to communicate its spirit, the more insistently lent its forms. It is almost impossible now to estimate the extent to which given Apollinian elements had to be accepted and transvalued before the old Christian myth assumed the firmness that it possessed in the time of Augustine.

IX

The Classical polytheism, consequently, has a style of its own which puts it in a different category from the conceptions of any other world- feelings, whatever the superficial affinities may be. This mode of possessing gods without godhead has only existed once, and it was in the one Culture that made the statue of naked Man the whole sum of its art.

Nature, as Classical man felt and knew it about him, viz., a sum of well-formed bodily things, could not be deified in any other form but this. The Roman felt that the claim of Yahweh to be recognized as sole God had something atheistic in it. One God, for him, was no God, and to this may be ascribed the strong dislike of popular feeling, both Greek and Roman, for the philosophers in so far as they were pantheists and godless. Gods are bodies, σώματα of the perfectest kind, and plurality was an attribute of bodies alike for mathematicians, lawyers and poets. The concept of ζῷον πολιτικόν was valid for gods as well as for men; nothing was more alien to them than oneness, solitariness and self- adequacy; and no existence therefore was possible to them save under the aspect of eternal propinquity. It is a deeply significant fact that in Hellas of all countries star-gods, the numina of the Far, are wanting. Helios was worshipped only in half-Oriental Rhodes and Selene had no cult at all. Both are merely artistic modes of expression (it is as such only that they figure in the courtly epos of Homer), elements that Varro would class in the _genus mythicum_ and not in the _genus civile_. The old Roman religion, in which the Classical world-feeling was expressed with special purity, knew neither sun nor moon, neither storm nor cloud as deities. The forest stirrings and the forest solitude, the tempest and the surf, which completely dominated the Nature of Faustian man (even that of pre-Faustian Celts and Teutons) and imparted to their mythology its peculiar character, left Classical man unmoved. Only concretes—hearth and door, the coppice and the plot-field, this

## particular river and that particular hill—condensed into Being for him.

We observe that everything that has farness, everything that contains a suggestion of unbounded and unbodied in it and might thereby bring space as Ent and divine into the felt Nature, is excluded and remains excluded from Classical myth; how should it surprise, then, if clouds and horizons, that are the very meaning and soul of Baroque landscapes, are totally wanting in the Classical backgroundless frescoes? The unlimited multitude of antique gods—every tree, every spring, every house, nay every part of a house is a god—means that every tangible thing is an _independent_ existence, and therefore that none is functionally subordinate to any other.

The bases of the Apollinian and the Faustian Nature-images respectively are in all contexts the two opposite symbols of _individual thing_ and _unitary space_. Olympus and Hades are perfectly sense-definite places, while the kingdom of the dwarfs, elves and goblins, and Valhalla and Niflheim are all somewhere or other in the universe of space. In the old Roman religion “Tellus Mater” is not the all-mother but the visible ploughable field itself. Faunus _is_ the wood and Vulturnus _is_ the river, the name of the seed _is_ Ceres and that of the harvest _is_ Consus. Horace is a true Roman when he speaks of “sub Jove frigido,” under the cold sky. In these cases there is not even the attempt to reproduce the God in any sort of image at the places of worship, for that would be tantamount to duplicating him. Even in very late times the instinct not only of the Romans but of the Greeks also is opposed to idols, as is shown by the fact that plastic art, as it became more and more profane, came into conflict more and more with popular beliefs and the devout philosophy.[497] In the house, Janus is the door as god, Vesta the hearth as goddess, the two functions of the house are objectivized and deified at once. A Hellenic river-god (like Acheloüs, who appears as a bull,) is definitely understood as being the river and not as, so to say, dwelling in the river. The Pans[498] and Satyrs are the fields and meadows as noon defines them, well bounded and, as having figure, having also existence. Dryads and Hamadrayads _are_ trees; in many places, indeed, individual trees of great stature were honoured with garlands and votive offerings without even the formality of a name. On the contrary, not a trace of this localized materiality clings to the elves, dwarfs, witches, Valkyries and their kindred the armies of departed souls that sweep round o’nights. Whereas Naiads _are_ sources, nixies and hags, and tree-spirits and brownies are souls that are only bound to sources, trees and houses, from which they long to be released into the freedom of roaming. This is the very opposite of the plastic Nature-feeling, for here things are experienced merely as spaces of another kind. A nymph—a spring, that is—assumes human form when she would visit a handsome shepherd, but a nixy is an enchanted princess with nenuphars in her hair who comes up at midnight from the depths of the pool wherein she dwells. Kaiser Barbarossa sits in the Kyffhäuser cavern and Frau Venus in the Hörselberg. It is as though the Faustian universe abhorred anything material and impenetrable. In things, we suspect other worlds. Their hardness and thickness is merely appearance, and—a trait that would be impossible in Classical myth, because fatal to it—some favoured mortals are accorded the power to see through cliffs and crags into the depths. But is not just this the secret intent of our physical theories, of each new hypothesis? No other Culture knows so many fables of treasures lying in mountains and pools, of secret subterranean realms, palaces, gardens wherein other beings dwell. The whole substantiality of the visible world is denied by the Faustian Nature-feeling, for which in the end nothing is of earth and the only actual is Space. The fairy-tale dissolves the matter of Nature as the Gothic style dissolves the stone-mass of our cathedrals, into a ghostly wealth of forms and lines that have shed all weight and acknowledge no bounds.

The ever-increasing emphasis with which Classical polytheism somatically individualized its deities is peculiarly evident in its attitude to “strange gods.” For Classical man the gods of the Egyptians, the Phœnicians and the Germans, in so far as they could be imagined as figures, were as real as his own gods. Within his world-feeling the statement that such other gods “do not exist” would have no meaning. When he came into contact with the countries of these deities he did them reverence. The gods were, like a statue or a polis, Euclidean bodies having locality. They were beings of the near and not the general space. If a man were sojourning in Babylon, for instance, and Zeus and Apollo were far away, all the more reason for _particularly_ honouring the local gods. This is the meaning of the altars dedicated “to the unknown gods,” such as that which Paul so significantly misunderstood in a Magian monotheistic sense at Athens.[499] These were gods not known by name to the Greek but worshipped by the foreigners of the great seaports (Piræus, Corinth or other) and therefore entitled to their due of respect from him. Rome expressed this with Classical clearness in her religious law and in carefully-preserved formulæ like, for example, the _generalis invocatio_.[500] As the universe is the sum of things, and as gods are things, recognition had to be accorded even to those gods with whom the Roman had not yet practically and historically come into relations. He did not know them, or he knew them as the gods of his enemies, but they _were_ gods, for it was impossible for him to conceive the opposite. This is the meaning of the sacral phrase in Livy, VIII, 9, 6: “di quibus est potestas nostrorum hostiumque.” The Roman people admits that the circle of its own gods is only momentarily bounded, and after reciting these by name it ends the prayer thus so as not to infringe the rights of others. According to its sacral law, the annexation of foreign territory involves the transfer to Urbs Roma of all the religious obligations pertaining to this territory and its gods— which of course logically follows from the _additive_ god-feeling of the Classical. Recognition of a deity was very far from being the same as acceptance of the forms of its cult; thus in the Second Punic War the Great Mother of Pessinus[501] was received in Rome as the Sibyl commanded, but the priests who had come in with her cult, which was of a highly un-Classical complexion, practised under strict police supervision, and not only Roman citizens but even their slaves were forbidden under penalty to enter this priesthood. The reception of the goddess gave satisfaction to the Classical world-feeling, but the personal performance of her despised ritual would have infringed it. The attitude of the Senate in such cases is unmistakable, though the people, with its ever-increasing admixture of Eastern elements, had a liking for these cults and in Imperial times the army became in virtue of its composition a vehicle (and even the chief vehicle) of the Magian world- feeling.

This makes it the easier to understand how the cult of deified men could become a _necessary_ element in this religious form-world. But here it is necessary to distinguish sharply between Classical phenomena and Oriental phenomena that have a superficial similarity thereto. Roman emperor-worship—i.e., the reverence of the “genius” of the living Princes and that of the dead predecessors as “Divi”—has hitherto been confused with the ceremonial reverence of the Ruler which was customary in Asia Minor (and, above all, in Persia,)[502] and also with the later and quite differently meant Caliph-deification which is seen in full process of formation in Diocletian and Constantine. Actually, these are all very unlike things. However intimately these symbolic forms were interfused in the East of the Empire, in Rome itself the Classical type was actualized unequivocally and without adulteration. Long before this certain Greeks (e.g., Sophocles, Lysander and, above all, Alexander) had been not merely hailed as gods by their flatterers but felt as gods in a perfectly definite sense by the people. It is only a step, after all, from the deification of a thing—such as a copse or a well or, in the limit, a statue which represented a god—to the deification of an outstanding man who became first hero and then god. In this case as in the rest, what was reverenced was the perfect shape in which the world- stuff, the un-divine, had actualized itself. In Rome the consul on the day of his triumph wore the armour of Jupiter Capitolinus, and in early days his face and arms were even painted red, in order to enhance his similarity to the terra-cotta statue of the God whose “numen” he for the time being incorporated.

X

In the first generations of the Imperial age, the antique polytheism gradually dissolved, often without any alteration of outward ritual and mythic form, into the Magian monotheism.[503] A new soul had come up, and it lived the old forms in a new mode. The names continued, but they covered other numina.

In all Late-Classical cults, those of Isis and Cybele, of Mithras and Sol and Serapis, the divinity is no longer felt as a localized and formable being. In old times, Hermes Propylæus had been worshipped at the entrance of the Acropolis of Athens, while a few yards away, at the point where later the Erechtheum was built, was the cult-site of Hermes as the husband of Aglaure. At the South extremity of the Roman Capitol, close to the sanctuary of Juppiter Feretrius (which contained, not a statue of the god, but a holy stone, _silex_[504]) was that of Juppiter Optimus Maximus, and when Augustus was laying down the huge temple of the latter he was careful to avoid the ground to which the numen of the former adhered.[505] But in Early Christian times Juppiter Dolichenus or Sol Invictus[506] could be worshipped “wheresoever two or three were gathered together in his name.” All these deities more and more came to be felt as a single numen, though the adherents of a particular cult would believe that they in particular knew the numen in its true shape. Hence it is that Isis could be spoken of as the “million-named.” Hitherto, names had been the designations of so many gods different in body and locality, now they are _titles_ of the One whom every man has in mind.

This Magian monotheism reveals itself in all the religious creations that flooded the Empire from the East—the Alexandrian Isis, the Sun-god favoured by Aurelian (the Baal of Palmyra), the Mithras protected by Diocletian (whose Persian form had been completely recast in Syria), the Baalath of Carthage (Tanit, Dea Cælestis[507]) honoured by Septimius Severus. The importation of these figures no longer increases as in Classical times the number of concrete gods. On the contrary, they absorb the old gods into themselves, and do so in such a way as to deprive them more and more of picturable shape. Alchemy is replacing statics. Correspondingly, instead of the image we more and more find symbols—e.g., the Bull, the Lamb, the Fish, the Triangle, the Cross— coming to the front. In Constantine’s “in hoc signo vinces” scarcely an echo of the Classical remains. Already there is setting in that aversion to human representation that ended in the Islamic and Byzantine prohibitions of images.

Right down to Trajan—long after the last trait of Apollinian world- feeling had departed from the soil of Greece—the Roman state-worship had strength enough to hold to the Euclidean tendency and to _augment_ its world of deities. The gods of the subject lands and peoples were accorded recognized places of worship, with priesthood and ritual, in Rome, and were themselves associated as perfectly definite individuals with the older gods. But from that point the Magian spirit began to gain ground even here, in spite of an honourable resistance which centred in a few of the very oldest patrician families.[508] The god-figures as such, as bodies, vanished from the consciousness of men, to make way for a transcendental god-feeling which no longer depended on sense- evidences; and the usages, festivals and legends melted into one another. When in 217 Caracalla put an end to all sacral-legal distinctions between Roman and foreign deities and Isis, absorbing all older female numina, became actually the first goddess of Rome[509] (and thereby the most dangerous opponent of Christianity and the most obnoxious target for the hatred of the Fathers), then Rome became a piece of the East, a religious diocese of Syria. Then the Baals of Doliche, Petra, Palmyra and Edessa began to melt into the monotheism of Sol, who became and remained (till his representative Licinius fell before Constantine) God of the Empire. By now, the question was not between Classical and Magian—Christianity was in so little danger from the old gods that it could offer them a sort of sympathy—but it was, which of the Magian religions should dictate religious form to the world of the Classical Empire? The decline of the old plastic feeling is very clearly discernible in the stages through which Emperor-worship passed— first, the dead emperor taken into the circle of State gods by resolution of the Senate (Divus Julius, 42 B.C.), a priesthood provided for him and his image removed from amongst the ancestor-images that were carried in purely domestic celebrations; then, from Marcus Aurelius, no further consecrations of priests (and, presently, no further building of temples) for the service of deified emperors, for the reason that religious sentiment was now satisfied by a general “templum divorum”; finally, the epithet Divus used simply as a _title_ of members of the Imperial family. This end to the evolution marks the victory of the Magian feeling. It will be found that multiple names in the inscriptions (such as Isis-Magna Mater-Juno-Astarte-Bellona, or Mithras-Sol Invictus- Helios) come to signify titles of one sole existent Godhead.[510]

XI

Atheism is a subject that the psychologist and the student of religion have hitherto regarded as scarcely worth careful investigation. Much has been written and argued about it, and very roundly, by the free-thought martyr on the one hand and the religious zealot on the other. But no one has had anything to say about the _species_ of atheism; or has treated it analytically as an _individual and definite_ phenomenon, positive and necessary and intensely symbolic; or has realized how it is limited in time.

Is “Atheism” the _a priori_ constitution of a certain world- consciousness or is it a voluntary self-expression? Is one born with it or converted to it? Does the unconscious feeling that the cosmos has become godless bring in its train the consciousness that it is so, the realization that "Great Pan is dead"? Are there early atheists, for example in the Doric or the Gothic ages? Has this thinker or that been denounced as atheist with injustice as well as with passion? And can there be civilized men who are _not_ wholly or at any rate partially atheist?

It is not in dispute (the word itself shows it in all languages) that atheism is essentially a negation, that it signifies the foregoing of a spiritual idea and therefore the precedence of such an idea, and that it is not the creative act of an unimpaired formative power. But what is it that it denies? In what way? And who is the denier?

Atheism, rightly understood, is the necessary expression of a spirituality that has accomplished itself and exhausted its religious possibilities, and is declining into the inorganic. It is entirely compatible with a living wistful desire for real religiousness[511]— therein resembling Romanticism, which likewise would recall that which has irrevocably gone, namely, the Culture—and it may quite well be in a man as a creation of his feeling without his being aware of it, without its ever interfering with the habits of his thought or challenging his convictions. We can understand this if we can see what it was that made the devout Haydn call Beethoven an atheist after he had heard some of his music. Atheism comes not with the evening of the Culture but with the dawn of the Civilization. It belongs to the great city, to the “educated man” of the great city who acquires mechanistically what his forefathers the creators of the Culture had lived organically. In respect of the Classical feeling of God, Aristotle is an atheist unawares. The Hellenistic-Roman Stoicism is atheistic like the Socialism of Western and the Buddhism of Indian modernity, reverently though they may and do use the word “God.”

But, if this late form of world-feeling and world-image which preludes our “second religiousness” is universally a negation of the religious in us, the structure of it is different in each of the Civilizations. There is no religiousness that is without an atheistic opposition belonging uniquely to itself and directed uniquely against itself. Men continue to experience the outer world that extends around them as a cosmos of well- ordered bodies or a world-cavern or efficient space, as the case may be, but they no longer livingly experience the sacred causality in it. They only learn to know it in a profane causality that is, or is desired to be, inclusively mechanical.[512] There are atheisms of Classical, Arabian and Western kinds and these differ from one another in meaning and in matter. Nietzsche formulated the dynamic atheism on the basis that “God is dead,” and a Classical philosopher would have expressed the static and Euclidean by saying that the “gods who dwell in the holy places are dead,” the one indicating that boundless space has, the other that countless bodies have, become godless. But _dead_ space and _dead_ things are the “facts” of physics. The atheist is unable to experience any difference between the Nature-picture of physics and that of religion. Language, with a fine feeling, distinguishes wisdom and intelligence—the early and the late, the rural and the megalopolitan conditions of the soul. Intelligence even sounds atheistic. No one would describe Heraclitus or Meister Eckart as an intelligence, but Socrates and Rousseau were intelligent and not “wise” men. There is something root-less in the word. It is only from the standpoint of the Stoic and of the Socialist, of the typical irreligious man, that want of intelligence is a matter for contempt.

The spiritual in every living Culture is religious, has religion, whether it be conscious of it or not. That it exists, becomes, develops, fulfils itself, _is_ its religion. It is not open to a spirituality to be irreligious; at most it can play with the idea of irreligion as Medicean Florentines did. But the megalopolitan _is_ irreligious; this is part of his being, a mark of his historical position. Bitterly as he may feel the inner emptiness and poverty, earnestly as he may long to be religious, it is out of his power to be so. All religiousness in the Megalopolis rests upon self-deception. The degree of piety of which a period is capable is revealed in its attitude towards toleration. One tolerates, either because the form-language appears to be expressing something of that which in one’s own lived experience is felt as divine, or else because that experience no longer contains _anything_ so felt.

What we moderns have called “Toleration” in the Classical world[513] is an expression of the _contrary_ of atheism. Plurality of numina and cults is inherent in the conception of Classical religion, and it was not toleration but the self-evident expression of antique piety that allowed validity to them all. Conversely, anyone who demanded exceptions showed himself _ipso facto_ as godless. Christians and Jews counted, and necessarily counted, as atheists in the eyes of anyone whose world- picture was an aggregate of individual bodies; and when in Imperial times they ceased to be regarded in this light, the old Classical god- feeling had itself come to an end. On the other hand, respect for the form of the local cult whatever this might be, for images of the gods, for sacrifices and festivals was always expected, and anyone who mocked or profaned them very soon learned the limits of Classical toleration— witness the scandal of the Mutilation of the Hermae at Athens and trials for the desecration of the Eleusinian mysteries, that is, impious travestying of the sensuous element. But to the Faustian soul (again we see opposition of space and body, of conquest and acceptance of presence) _dogma_ and not visible ritual constitutes the essence. What is regarded as godless is opposition to doctrine. Here begins the spatial-spiritual conception of heresy. A Faustian religion by its very nature cannot allow any freedom of conscience; it would be in contradiction with its space-invasive dynamic. Even free thinking itself is no exception to the rule. After the stake, the guillotine; after the burning of the books, their suppression; after the power of the pulpit, the power of the Press. Amongst us there is no faith without leanings to an Inquisition of some sort. Expressed in _appropriate_ electrodynamic imagery, the field of force of a conviction adjusts all the minds within it according to its own intensity. Failure to do so means absence of conviction—in ecclesiastical language, ungodliness. For the Apollinian soul, on the contrary, it was contempt of the cult—ἀσέβεια in the literal sense—that was ungodly, and here its religion admitted no freedom of _attitude_. In both cases there was a line drawn between the toleration demanded by the god-feeling and that forbidden by it.

Now, here the Late-Classical philosophy of Sophist-Stoic speculation (as distinct from the general Stoic disposition) was in opposition to religious feeling. And accordingly we find the people of Athens—that Athens which could build altars to “unknown gods”—persecuting as pitilessly as the Spanish Inquisition. We have only to review the list of Classical thinkers and historical personages who were sacrificed to the integrity of the cult. Socrates and Diagoras were executed for ἀσέβεια; Anaxagoras, Protagoras, Aristotle, Alcibiades only saved themselves by flight. The number of executions for cult-impiety, in Athens alone and during the few decades of the Peloponnesian War, ran into hundreds. After the condemnation of Protagoras, a house-to-house search was made for the destruction of his writings. In Rome, acts of this sort began (so far as history enables us to trace them) in 181 B.C. when the Senate ordered the public burning of the Pythagorean “Books of Numa.”[514] This was followed by an uninterrupted series of expulsions, both of individual philosophers and of whole schools, and later by executions and by public burnings of books regarded as subversive of religion. For instance, in the time of Cæsar alone, the places of worship of Isis were five times destroyed by order of the Consuls, and Tiberius had her image thrown into the Tiber. The refusal to perform sacrifice before the image of the Emperor was made a penal offence. All these were measures against “atheism,” in the _Classical_ sense of the word, manifested in theoretical or practical contempt of the visible cult. Unless we can put our Western feeling of these matters out of

## action we shall never penetrate into the essence of the world-image that

underlay the Classical attitude to them. Poets and philosophers might spin myths and transform god-figures as much as they pleased. The dogmatic interpretation of the sensuous data was everyone’s liberty. The _histories_ of the gods could be made fun of in Satyric drama and comedy—even that did not impugn their Euclidean existence. But the statue of the god, the cult, the plastic embodiment of piety—it was not permitted to any man to touch these. It was not out of hypocrisy that the fine minds of the earlier Empire, who had ceased to take a myth of any kind seriously, punctiliously conformed to the public cults and, above all, to the cult—deeply real for all classes—of the Emperor. And, on the other hand, the poets and thinkers of the mature Faustian Culture were at liberty “not to go to Church,” to avoid Confession, to stay at home on procession-days and (in Protestant surroundings) to live without any relations with the church whatever. But they were not free to touch points of dogma, for that would have been dangerous within any confession and any sect, including, once more and expressly, free- thought. The Roman Stoic, who without faith in the mythology piously observed the ritual forms, has his counterpart in those men of the Age of Enlightenment, like Lessing and Goethe, who disregarded the rites of the Church but never doubted the “fundamental truths of faith.”

XII

If we turn back from Nature-feeling become form to Nature-knowledge become system, we know God or the gods as the origin of the images by which the intellect seeks to make the world-around comprehensible to itself. Goethe once remarked (to Riemer): “The Reason is as old as the World; even the child has reason. But it is not applied in all times in the same way or to the same objects. The earlier centuries had their ideas in intuitions of the fancy, but ours bring them into notions. _The great views of Life were brought into shapes, into Gods; to-day they are brought into notions._ Then the productive force was greater, now the destructive force or art of separation.” The strong religiousness of Newton’s mechanics[515] and the almost complete atheism of the formulations of modern dynamics are of like colour, positive and negative of the same primary feeling. A physical system of necessity has all the characters of the soul to whose world-form it belongs. The Deism of the Baroque belongs with its dynamics and its analytical geometry; its three basic principles, God, Freedom and Immortality, are in the language of mechanics the principles of inertia (Galileo), least action (D’Alembert) and the conservation of energy (J. R. Mayer).

That which nowadays we call quite generally physics is in reality an artifact of the Baroque. At this stage the reader will not feel it as paradoxical to associate the mode of representation which rests on the assumption of distant forces and the (wholly un-Classical and anything but naïve) idea of action-at-a-distance, attraction and repulsion of masses, specially with the Jesuit style of architecture founded by Vignola, and to call it accordingly the Jesuit style of physics; and I would likewise call the Infinitesimal Calculus, which of necessity came into being just when and where it did, the Jesuit style of mathematic. Within this style, a working hypothesis that deepens the technique of experimentation is “correct”; for Loyola’s concern, like Newton’s, was not description of Nature but _method_.

Western physics is by its inward form dogmatic and not ritualistic (kultisch). Its content is the _dogma of Force_ as identical with space and distance, the theory of the mechanical Act (as against the mechanical Posture) in space. Consequently its tendency is persistently to overcome the apparent. Beginning with a still quite Apollinian- sensuous classification of physics into the physics of the eye (optics), of the ear (acoustics) and of the skin-sense (heat), it by degrees eliminated all sense-impressions and replaced them by abstract systems of relations; thus, under the influence of ideas concerning dynamical motion in an æther, radiant heat is nowadays dealt with under the heading of “optics,” a word which has ceased to have anything to do with the eye.

“Force” is a mythical quantity, which does not arise out of scientific experimentation but, on the contrary, defines the structure thereof _a priori_. It is only the Faustian conception of Nature that instead of a magnet thinks of a magnetism whose field of force includes a piece of iron, and instead of luminous bodies thinks of radiant energy, and that imagines personifications like “electricity,” “temperature” and “radioactivity.”[516]

That this “force” or “energy” is really a numen stiffened into a concept (and in nowise the result of scientific experience) is shown by the often overlooked fact that the basic principle known as the First Law of Thermodynamics[517] says nothing whatever about the nature of energy, and it is properly speaking an incorrect (though psychologically most significant) assumption that the idea of the “Conservation of Energy” is fixed in it. Experimental measurement can in the nature of things only establish a _number_, which number we have (significantly, again) named _work_. But the dynamical cast of our thought demanded that this should be conceived as a _difference_ of energy, although the absolute value of energy is only a figment and can never be rendered by a definite number. There always remains, therefore, an undefined additive constant, as we call it; in other words, we always strive to maintain the image of an energy that our inner eye has formed, although actual scientific practice is not concerned with it.

This being the provenance of the force-concept, it follows that we can no more define it than we can define those other un-Classical words Will and Space. There remains always a felt and intuitively-perceived remainder which makes every personal definition an almost religious _creed_ of its author. Every Baroque scientist in this matter has his personal inner experience which he is trying to clothe in words. Goethe, for instance, could never have defined his idea of a world-force, but to himself it was a certainty. Kant called force the phenomenon of an ent- in-itself: “we know substance in space, the body, only through forces.” Laplace called it an unknown of which the workings are all that we know, and Newton imagined immaterial forces at a distance. Leibniz spoke of _Vis viva_ as a quantum which together with matter formed the unit that he called the monad, and Descartes, with certain thinkers of the 18th Century, was equally unwilling to draw fundamental distinctions between motion and the moved. Beside _potentia_, _virtus_, _impetus_ we find even in Gothic times peri-phrases such as _conatus_ and _nisus_, in which the force and the releasing cause are obviously not separated. We can, indeed, quite well differentiate between Catholic, Protestant and Atheistic notions of force. But Spinoza, a Jew and therefore, spiritually, a member of the Magian Culture, could not absorb the Faustian force-concept at all, and it has no place in his system.[518] And it is an astounding proof of the secret power of root-ideas that Heinrich Hertz, the only Jew amongst the great physicists of the recent past, was also the only one of them who tried to resolve the dilemma of mechanics by _eliminating_ the idea of force.

The force-dogma is the one and only theme of Faustian physics. That branch of science which under the name of Statics has been passed from system to system and century to century is a fiction. “Modern Statics” is in the same position as “arithmetic” and “geometry,” which, if the literal and original senses of the words be kept to, are void of meaning in modern analysis, empty names bequeathed by Classical science and only preserved because our reverence for all things Classical has hitherto debarred us from getting rid of them or even recognizing their hollowness. There _is_ no Western statics—that is, no interpretation of mechanical facts that is natural to the Western spirit bases itself on the ideas of form and substance, or even, for that matter, on the ideas of space and mass otherwise than in connexion with those of time and force.[519] The reader can test this in any department that he pleases. Even “temperature,” which of all our physical magnitudes has the most plausible look of being static, Classical and passive, only falls into its place in our system when it is brought into a force-picture, viz., the picture of a quantity of heat made up of ultra-swift subtle irregular motions of the atoms of a body, with temperature as the _mean vis viva_ of these atoms.

The Late Renaissance imagined that it had revived the Archimedean physics just as it believed that it was continuing the Classical sculpture. But in the one case as in the other it was merely preparing for the forms of the Baroque, and doing so out of the spirit of the Gothic. To this Statics belongs the picture-subject as it is in Mantegna’s work and also in that of Signorelli, whose line and attitude later generations regarded as stiff and cold. With Leonardo, dynamics begins and in Rubens the movement of swelling bodies is already at a maximum.

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:

See Vol. II, pp. 207 et seq., and