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 Chapter IV B.

Footnote 421:

See Vol. II, p. 80.

Footnote 422:

I.e., adherents of the various syncretic cults. Sec Vol. II, pp. 212

et seq.

Footnote 423:

This applies even more forcibly to the other “long-range” episode,

that of the Ten Thousand (Xenophon, _Anabasis_ I).—_Tr._

Footnote 424:

In this place it is exclusively with the conscious, religio-

philosophical morale—the morale which can be known and taught and

followed—that we are concerned, and not with the racial rhythm of

Life, the habit, Sitte, ἦθος, that is unconsciously present. The

morale with which we are dealing turns upon _intellectual_ concepts of

Virtue and Vice, good and bad; the other, upon ideals in the _blood_

such as honour, loyalty, bravery, the feeling that attributes nobility

and vulgarity. See Vol. II, 421 et seq.

Footnote 425:

The original is here expanded a little for the sake of clarity.—_Tr._

Footnote 426:

After what has been said above regarding the absence of pregnant words

for “will” and “space” in the Classical tongues, the reader will not

be surprised to hear that neither Greek nor Latin affords exact

equivalents for these words action and activity.

Footnote 427:

See Vol. II, pp. 293 et seq.

Footnote 428:

“He who hath ears to hear, let him hear”—there is no claim to power in

these words. But the Western Church never conceived its mission thus.

The “Glad Tidings” of Jesus, like those of Zoroaster, of Mani, of

Mahomet, of the Neo-Platonists and of all the cognate Magian religions

were mystic benefits _displayed_ but in nowise imposed. Youthful

Christianity, when it had flowed into the Western world, merely

imitated the missionarism of the later Stoa, itself by that time

thoroughly Magian. Paul may be thought of as urgent; the itinerant

preachers of the Stoa were certainly so, as we know from our

authorities. But _commanding_ they were not. To illustrate by a

somewhat farfetched parallel—in direct contrast to the physicians of

the Magian stamp who merely proclaimed the virtues of their mysterious

arcana, the medical men of the West seek to obtain for their knowledge

the _force of civil law_, as for instance in the matter of vaccination

or the inspection of pork for trichina.

Footnote 429:

For the Buddhist Four Truths see Ency. Brit., XI ed., Vol. IV, p. 742.

English translation of Kant’s _Kritik der praktischen Vernunft_ by T.

K. Abbott.—_Tr._

Footnote 430:

See p. 201.

Footnote 431:

See p. 205 and 222 et seq.

Footnote 432:

See Vol. II, p. 334.

Footnote 433:

The philosophy and dogma of charity and almsgiving—a subject that

English research seems generally to have ignored—is dealt with at

length in Dr. C. S. Loch’s article _Charity and Charities_, Ency.

Brit., XI ed.—_Tr._

Footnote 434:

Not only as local sovereigns enforcing order, like the good Bishop

Wazo of Liége who fought down his castled robber-barons one by one in

the middle of the 11th Century, but even as high commanders for the

Emperor in distant Italy. The battle of Tusculum in 1167 was won by

the Archbishops of Köln and Mainz. English history, too, contains the

figures of warlike prelates—not only leaders of national movements

like Stephen Langton but strong-handed administrators and fighters.

The great Scots invasion of 1346 was met and defeated by the

Archbishop of York. The Bishops of Durham were for centuries

“palatines”; we find one of them serving _on pay_ in the King’s army

in France, 1348. The line of these warlike Bishops in our history

extends from Odo the brother of William the Conqueror to Scrope,

archbishop and rebel in Henry IV’s time.—_Tr._

Footnote 435:

A paraphrase of the opening of “John Tanner’s Revolutionist’s

Handbook,” Ch. V.—_Tr._

Footnote 436:

See Vol. II, pp. 116 et seq.

Footnote 437:

Rousseau’s _Contrat Social_ is paralleled by exactly equivalent

productions of Aristotle’s time.

Footnote 438:

The first on the atheistical system of Sankhya, the second (through

Socrates) on the Sophists, the third on English sensualism.

Footnote 439:

See Vol. II, pp. 441 et seq.

Footnote 440:

It was many centuries later that the Buddhist ethic of life gave rise

to a religion for simple peasantry, and it was only enabled to do so

by reaching back to the long-stiffened theology of Brahmanism and,

further back still, to very ancient popular cults. See Vol. II, pp.

378, 285.

Footnote 441:

The articles _Buddha_ and _Buddhism_ in the Ency. Brit., XI ed., by T.

W. Rhys Davids, may be studied in this connexion.—_Tr._

Footnote 442:

See “The Questions of King Milinda,” ed. Rhys Davids.—_Tr._

Footnote 443:

Of course, each Culture naturally has its own kind of materialism,

conditioned in every detail by its general world-feeling.

Footnote 444:

To begin with, it would be necessary to specify _what_ Christianity

was being compared with it—that of the Fathers or that of the

Crusades. For these are two different religions in the same clothing

of dogma and cult. The same want of psychological _flair_ is evident

in the parallel that is so fashionable to-day between Socialism and

early Christianity.

Footnote 445:

The term must not be confused with _anti_-religious.

Footnote 446:

Note the striking similarity of many Roman portrait-busts to the

matter-of-fact modern heads of the American style, and also (though

this is not so distinct) to many of the portrait-heads of the Egyptian

New Empire.

Footnote 447:

See Vol. II, pp. 122 et seq.

Footnote 448:

The original is here very obscure; it reads: “... es ist der

‘Gebildete,’ jener Anhänger eines Kultus des geistigen Mittelmasses

und der Offentlichkeit als Kultstätte.”—_Tr._

Footnote 449:

See P. Wendland, _Die hellenist.-röm. Kultur_ (1912), pp. 75 et seq.

Footnote 450:

See Vol. II, pp. 318 et seq.

Footnote 451:

See Vol. II, pp. 269 et seq.

Footnote 452:

Compare my _Preussentum und Sozialismus_, pp. 22 et seq.

Footnote 453:

See Vol. II, pp. 324 et seq., 368 et seq.

Footnote 454:

See Vol. II, p. 345. It is possible that the peculiar style of

Heraclitus, who came of a priestly family of the temple of Ephesus, is

an example of the form in which the old Orphic wisdom was orally

transmitted.

Footnote 455:

See Vol. II, p. 307.

Footnote 456:

Here we are considering only the scholastic side. The mystic side,

from which Pythagoras and Leibniz were not very far, reached its

culminations in Plato and Goethe, and in our own case it has been

extended beyond Goethe by the Romantics, Hegel and Nietzsche, whereas

Scholasticism exhausted itself with Kant—and Aristotle—and degenerated

thereafter into a routine-profession.

Footnote 457:

Zeno the Stoic, not to be confused with Zeno of Elea, whose

mathematical fineness has already been alluded to.—_Tr._

Footnote 458:

_Neue Paralipomena_, § 656.

Footnote 459:

Even the modern idea that unconscious and impulsive acts of life are

completely efficient, while intellect can only bungle, is to be found

in Schopenhauer (Vol. II, cap. 30).

Footnote 460:

In the chapter “Zur Metaphysik der Geschlechtsliebe” (II, 44) the idea

of natural selection for the preservation of the genus is anticipated

in full.

Footnote 461:

See Vol. II, pp. 36 et seq.

Footnote 462:

This began to appear in 1867. But the preliminary work _Zur Kritik der

politischen Ökonomie_ came out in the same year as Darwin’s

masterpiece.

Footnote 463:

Vol. II, p. 625. See, for example, Leonard, _Relativitäts-Prinzip,

Aether, Gravitation_ (1920), pp. 20 et seq.

Footnote 464:

See Vol. II, pp. 369 et seq., 624 et seq.

Footnote 465:

See p. 57.

Footnote 466:

E.g., in Boltzmann’s formulation of the Second Law of Thermodynamics:

“the logarithm of the probability of a state is proportional to the

entropy of that state.” Every word in this contains an entire

scientific concept, capable only of being sensed and not described.

Footnote 467:

See Vol. II, p. 369.

Footnote 468:

See Vol. II, pp. 382 et seq.

Footnote 469:

E. Wiedermann, _Die Naturwissensch. bei den Arabern_ (1890). F.

Struntz, _Gesch. d. Naturwissensch. im Mittelalter_ (1910), p. 58.

Footnote 470:

An order of encyclopædists and philosophers; see Ency. Brit., XI ed.,

Vol. II, p. 278a.—_Tr._

Footnote 471:

M. P. E. Berthelot, _Die Chemie im Altertum u. Mittelalter_ (1909),

pp. 64 et seq. (The reference is evidently to a German version;

Berthelot published several works on the subject, viz., _Les origines

de l’Alchémie_ [1885]; _Introduction à l’étude de la chimie des

anciens et du moyen âge_ [1889]; _Collection des anciens alchimistes

grecs_ [1887, translations of texts]; _La chimie au moyen âge_

[1893].—_Tr._

Footnote 472:

For the metals, “mercury” is the principle of substantial character

(lustre, tensility, fusibility), “sulphur” that of the attributive

generation (e.g., combustion, transmutation). See Struntz, _Gesch. d.

Naturwissensch. im Mittelalter_ (1910), pp. 73 et seq.

(It seems desirable to supplement this a little for the non-technical

reader, by stating, however roughly and generally, the principle and

process of transmutation as the alchemist saw them. All metals consist

of mercury and sulphur. Remove “materiality” from common mercury (or

from the mercury-content of the metal under treatment) by depriving it

(or the metal) of “earthness,” “liquidness” and “airiness” (i.e.,

volatility) and we have a prime, substantial (though not material) and

stable thing. Similarly, remove materiality from sulphur (or the

sulphur-content of the metal treated) and it becomes an elixir,

efficient for generating attributes. Then, the prime matter and the

elixir react upon one another so that the product on reassuming

materiality is a different metal, or rather a “metallicity” endowed

with different characters and attributes. The production of one metal

from another thus depends merely on the modalities of working

processes.—_Tr._)

Footnote 473:

See Vol. II, pp. 370, 627.

Footnote 474:

See Vol. II, pp. 314 et seq.

Footnote 475:

See the article under this heading, and also that under _Alchemy_,

Ency. Brit., XI ed.—_Tr._

Footnote 476:

During the Gothic age, in spite of the Spanish Dominican Arnold of

Villanova (d. 1311), chemistry had had no sort of creative importance

in comparison with the mathematical-physical research of that age.

Footnote 477:

For even Helmholtz had sought to account for the phenomena of

electrolysis by the assumption of an atomic structure of electricity.

Footnote 478:

Which in their physical aspect are individual centres of force,

without parts or extension or figure. (For their metaphysical aspect,

see Ency. Brit., XI edition. Article _Leibniz_, especially pp. 387-8.—

_Tr._)

Footnote 479:

M. Born, _Aufbau der Materie_ (1920), p. 27.

(So many books and papers—strict, semi-popular and frankly popular—

have been published in the last few years that references may seem

superfluous, the more so as the formulation of this central theory of

present-day physics. The article _Matter_ by Rutherford in the Ency.

Brit., XIIth edition (1922), and Bertrand Russell, _The A.B.C. of

Atoms_, are perhaps the clearest elementary accounts that are

possible, having regard to the scientist’s necessary reservations of

judgment.—_Tr._

Footnote 480:

See p. 231.

Footnote 481:

See p. 172.

Footnote 482:

See p. 121 and Vol. II, pp. 11 et seq.

Footnote 483:

See p. 169.

Footnote 484:

See p. 166 and Vol. II, p. 18.

Footnote 485:

See p. 152.

Footnote 486:

See p. 116 et seq., pp. 151 et seq.

Footnote 487:

See Vol. II, pp. 369 et seq.

Footnote 488:

J. Goldziher, _Die islam. und jüd. Philosophie_ (“Kultur der

Gegenwart,” I, V, 1913), pp. 306 et seq.

Footnote 489:

See Vol. II, pp. 27 et seq., 427 et seq.

Footnote 490:

And it may be asserted that the downright faith that Haeckel, for

example, pins to the names atom, matter, energy, is not essentially

different from the fetishism of Neanderthal Man.

Footnote 491:

See p. 126.

Footnote 492:

Compare Vol. II, pp. 38 et seq.

Footnote 493:

See Vol. II, p. 305.

Footnote 494:

See Vol. II, pp. 343 et seq., and p. 346.

Footnote 495:

E. Mogk, _Germ. Mythol._, Grundr. d. Germ. Philos., III (1900), p.

340.

Footnote 496:

See Vol. II, p. 241 et seq., 306 et seq.

Footnote 497:

See p. 268.

Footnote 498:

The pantheistic idea of Pan, familiar in European poetry, is a

conception of later Classical ages, acquired in principle from Egypt.—

_Tr._

Footnote 499:

Few passages in the Acts of the Apostles have obtained a stronger hold

on _our_ imagination than Paul’s meeting with the altar of “the

Unknown God” at Phalerum (Acts XVII, 23). And yet we have perfectly

definite evidence, later than Paul’s time, of the plurality of the

gods to whom this altar was dedicated. Pausanias in his guide-book (I,

24) says: “here there are ... altars of the gods styled Unknowns, of

heroes, etc.” (βωμοί δε θεῶν τε ὀνομαζομένων Ἀγνώστων καὶ ἡρῴων ...

κ.τ.λ.). Such, however, is the force of our fixed idea that even Sir

J. G. Frazer, in his “Pausanias and Other Studies,” speaks of “The

Altar to the Unknown God which St. Paul, and Pausanias after him,

saw.” More, he follows this up with a description of a dialogue

“attributed to Lucian” (2nd Cent. A.D.) in which the Unknown God of

Athens figures in a Christian discussion; but this dialogue (the

Philopatris) is almost universally regarded as a much later work,

dating at earliest from Julian’s time (mid-4th Cent.) and probably

from that of Nicephorus Phocas (10th Cent.).—_Tr._

Footnote 500:

Wissowa, _Religion und Kultus der Römer_ (1912), p. 38.

Footnote 501:

See Ency. Brit., XI ed., article _Great Mother of the Gods_.—_Tr._

Footnote 502:

In Egypt Ptolemy Philadelphus was the first to introduce a ruler-cult.

The reverence that had been paid to the Pharaohs was of quite other

significance.

Footnote 503:

See Vol. II, pp. 241 et seq.

Footnote 504:

Significantly enough, the formula of the oath sworn by this stone was

not “per Jovis lapidem” but “per Jovem lapidem.”—_Tr._

Footnote 505:

The Erechtheum, similarly, was a group of cult-sites, each refraining

from interference with the others.—_Tr._

Footnote 506:

Juppiter Dolichenus was a local deity of Doliche in Commagene, whose

worship was spread over all parts of the Empire by soldiers recruited

from that region; the tablet dedicated to him which is in the British

Museum was found, for example, near Frankfurt-on-Main.

Sol Invictus is the Roman official form of Mithras. Troop-movements

and trade spread his worship, like that of Juppiter Dolichenus, over

the Empire.—_Tr._

Footnote 507:

To whom the inhabitants of “Roman” Carthage managed to attach even

Dido.—_Tr._

Footnote 508:

Wissowa, _Kult. und. Relig. d. Römer_ (1912), pp. 98 et seq.

Footnote 509:

Wissowa, _Relig. u. Kult. der Römer_ (1912), p. 355.

Footnote 510:

The symbolic importance of the Title, and its relation to the concept

and idea of the Person, cannot here be dealt with. It must suffice to

draw attention to the fact that the Classical is the only Culture in

which the Title is unknown. It would have been in contradiction with

the strictly somatic character of their names. Apart from personal and

family names, only the technical names of offices actually exercised

were in use. “Augustus” became at once a personal name, “Cæsar” very

soon a designation of office. The advance of the Magian feeling can be

seen in the way in which courtesy-expressions of the Late-Roman

bureaucracy, like “Vir clarissimus,” became permanent titles of honour

which could be conferred and cancelled. In just the same way, the

names of old and foreign deities became titles of the recognized

Godhead; e.g., Saviour and Healer (Asklepios) and Good Shepherd

(Orpheus) are titles of Christ. In the Classical, on the contrary, we

find the secondary names of Roman deities evolving into independent

and separate gods.

Footnote 511:

Diagoras, who was condemned to death by the Athenians for his

“godless” writings, left behind him deeply pious dithyrambs. Read,

too, Hebbel’s diaries and his letters to Elise. He “did not believe in

God,” but he prayed.

Footnote 512:

See Vol. II, p. 376.

Footnote 513:

See Vol. II, p. 244.

Footnote 514:

Livy XL, 29.—_Tr._

Footnote 515:

In the famous conclusion of his “Optics” (1706) which made a powerful

impression and became the starting-point of quite new enunciations of

theological problems, Newton limits the domain of mechanical causes as

against the Divine First Cause, whose perception-organ is necessarily

infinite space itself.

Footnote 516:

As has been shown already, the dynamic structure of our thought was

manifested first of all when Western languages changed “feci” to “ego

habeo factum,” and thereafter we have increasingly emphasized the

dynamic in the phrases with which we fix our phenomena. We say, for

instance, that industry “finds outlets for itself” and that

Rationalism “has come into power.” No Classical language allows of

such expressions. No Greek would have spoken of Stoicism, but only of

the Stoics. There is an essential difference, too, between the imagery

of Classical and that of Western poetry in this respect.

Footnote 517:

The law of the equivalence of heat and work.—_Tr._

Footnote 518:

See p. 307.

Footnote 519:

Original: “Keine dem abendländischen Geist natürliche Art der Deutung

mechanischer Tatsachen, welche die Begriffe Gestalt und Substanz

(allenfalls Raum und Masse) statt Raum, Zeit, Masse, und Kraft

zugrunde liegt.”

Footnote 520:

See foot-note, p. 314.—_Tr._

Footnote 521:

See p. 355.

Footnote 522:

See Vol. II, p. 618.

Footnote 523:

See M. Planck, _Entstehung und bisherige Entwicklung der

Quantentheorie_ (1920), pp. 17-25.

Footnote 524:

Which in many cases have led to the supposition that the “actual

existence” of atoms has now at last been proved—a singular throw-back

to the materialism of the preceding generation.

Footnote 525:

This sentence follows the original word for word and phrase for

phrase. Its significance depends wholly on the precise meaning to be

attached to such words as “dead,” “free,” “latent,” and to attempt any

sharper formulation of the processes in English would require not only

the definition of these (or other) basic terms but also extended

description of what they imply.

The Second Law of Thermodynamics is something which is _absorbed by_,

rather than specified for, the student. Elsewhere in this English

edition, indications have been frequently given to enable the ordinary

student to follow up matters referred to more allusively in the text.

But in this difficult domain such minor aids would be worthless. All

that is possible is to recommend such students to make a very careful

study of some plain statement of the subject like Professor Soddy’s

“Matter and Energy” (especially chapters 4 and 5) and to follow this

up—to the extent that his mathematical knowledge permits—in the

articles _Energy_, _Energetics_ and _Thermodynamics_ in the Ency.

Brit., XI ed.—_Tr._

Footnote 526:

See foot-note, p. 157.

Footnote 527:

The application of the idea of “lifetime” to elements has in fact

produced the conception of “half-transformation times” [such as 3.85

days for Radium Emanation.—_Tr._].

Footnote 528:

The text of this paragraph has been slightly condensed, as in such a

field as this of philosophical mathematics partial indications would

serve no useful purpose. The mathematical reader may refer to the

articles _Function_, _Number_, and _Groups_ in the Ency. Brit., XI

ed.—_Tr._

INDEX

Prepared by DAVID Μ. MATTESON

Aachen Minster, and style, 200

Abaca, Evaristo F. dall’, sonatas, 283

Abel, Niels H., mathematic problem, 85

Absolutism, contemporary periods, table iii

Abydos, 58_n._;

contemporaries, table ii

Abyssinia, cult-buildings, 209

Academy, contemporaries, table i

Acanthus motive, history, 215

Acheloüs, as god, 403

Achilles, archetype, 203, 402

Acre, battle, 150

Acropolis, contemporaries, table ii. _See also_ Parthenon

Act, and portrait, 262, 266, 270

Action, in Western morale, 342

Actium, battle, 381

Activity, as Western trait, 315, 320;

as quality of Socialism, 362-364

Actuality, as test of philosophy, 41;

significance, 164

Adam de la Hale. _See_ La Hale

Addison, Joseph, type, 254

Adolescence, initiation-rites as symbol, 174_n._

Adrastos, cult, 33_n._

Ægina temple, sculpture, 226, 244

Æschines, portrait statue, 270

Æschylus, tragic form and method, 129, 320, 321;

and architecture, 206;

and motherhood, 268;

and deity, 313;

morale, 355

Æsthetics, and genius in art, 128

Æther, contradictory theories, 418

Agamemnon, contemporaries, table iii

Aggregates, theory, 426

Aglaure, cult, 406

Ahmes, arithmetic, 58

Ahriman, Persian Devil, 312

Aim, and direction, 361;

nebulousness, 363

Aksakov, Sergei, and Europe, 16_n._

Albani, Francesco, linear perspective, 240;

colour, 246

Albani villa, garden, 240

Albert of Saxony, Occamist, 381

Alberti, Leone B., gardening, 240

Alcamenes, contemporary mathematic, 78;

period, 284

Alchemy, as symbol, 248;

as Arabian physics, 382, 383;

process of transmutation, 382_n._;

and substance, 383;

and mechanical necessity, 393

Alcibiades, and Napoleon, 4;

and Classical morale, 351;

condemnation, 411

Alcman, music, 223

Alembert, Jean B. le R. d’, mathematic, 66, 78;

and time, 126;

mechanics and deism, 412

Alexander the Great, analogies, 4;

and Dionysus legend, 8;

romantic, 38;

and economic organization, 138;

expedition as episode, 147;

himself as epoch, 149;

as conqueror, 336;

morale, 349;

as paradox, 363;

deification, 405;

contemporaries, table iii

Alexander I of Russia, and Napoleon, 150

Alexandria, as a cultural left-over, 33, 73_n._, 79;

contemporaries, 112;

collections of University, 136_n._;

as irreligious, 358

Alfarabi, and extension, 178;

and dualism, 306;

contemporaries, table i

Algebra, defined, significance of letter-notation, 71;

Diophantus and Arabian Culture, 71-73;

Western liberation, 86;

contemporaries, table i.

_See also_ Mathematics

Algiers, origin of French war, 144_n._

Alhambra, courtyard, 235

Alien, and “proper”, 53

Alkabi, and extension, 178

Alkarchi, contemporaries, table i

Al-Khwarizmi, mathematic, 72;

contemporaries, table i

Alkindi, and dualism, 307;

contemporaries, table i

Allegory, motive and word, 219_n._

Almighty, philosophical attitude toward, 123. _See also_ Religion

Alphabet, and historical consciousness, 12_n._ _See also_ Language

Alsidzshi, mathematic, 72

Altar of the Unknown God, Paul’s error, 404

Amarna art, contemporaries, table ii

Ambrosian chants, and Jewish psalmody, 228

Amenemhet III, pyramid, 13;

portrait, 108, 262

Amida, and Arabian art, 209

Analogies, superficial and real historical, 4, 6, 27, 38, 39;

necessity of technique, 5

Analysis, and Classical mathematic, 69;

in Western mathematic, 74, 75;

inadequacy as term, 81;

and earlier mathematics, 84;

contemporaries, table i.

_See also_ Mathematics

Anamnesis, and comprehension of depth, 174

Ananke, and Tyche, 146

Anarchism, basis, 367, 373

Anatomy, in Classical and Western art, 264;

Michelangelo and Leonardo, 277

Anaxagoras, and ego, 311;

on atoms, 386;

and mechanical necessity, 392, 394;

condemnation, 411

Anaximander, and chaos, 64;

popularity, 327

Ancestral worship, cultural basis, 134, 135_n._

Ancient History, as term, 16

Anecdote, and Classical tragedy, 318;

Western, 318_n._

Angelico, Fra, and the antique, 275

Anthesteria, 135_n._

Antigone, and Kriemhild, 268

Antiphons, and Jewish psalmody, 228

Antisthenes, character of Nihilism, 357;

and diet, 361

Antonello da Messina, Dutch influence, 236

Apelles, contemporaries, table ii

Aphrodisias Temple in Caria, as pseudomorphic, 210

Aphrodite, as goddess, 268;

in Classical art, 268

Apocalypses, and world-history, 18_n._;

contemporaries, table i

Apollinian soul, explained, 183. _See also_ Classical Culture

Apollo Didymæus Temple, form-type, 204

Apollo of Tenea, contemporaries, table ii

Apollodorus of Athens, unpopularity, 35;

painting, 283, 325_n._

Apollodorus of Damascus, Roman architecture, 211

Apollonius Pergæus, and infinity, 69;

mathematic, 90

Appius Claudius, contemporaries, table iii

Arabesque, algebraic analogy, 72;

period, 108;

spun surface, 196;

character, 203, 212;

as symbol, 215, 248;

end-art, 223;

contemporaries, table ii

Arabian Culture, and polar idea of history, 18;

mathematic, significance of algebra, 63, 71-73;

expressions, 72;

and Late-Classical, 73, 209, 212, 214;

and Marycult, 137;

prime symbol, cavern, 174, 209, 215;

soul and dualism, 183, 305-307, 363;

“inside” architectural expression, 184, 199, 200, 224;

religious expression, 187, 188, 312, 401;

and Russian art, 201;

autumn of style, 207;

art as single phenomenon, 207-209;

art research, 209;

dome space-symbolism, 210-212;

ornamentation, 212;

fetters, 212;

emancipation, hurry, 213;

and mosaic, 214;

arch-column, 214;

Acanthus motive, 215;

and portraiture, 223, 262;

architecture in Italy, 235;

music, 228;

and Renaissance, 235;

gold as symbol, 247;

political concept, 335;

will-lessness, 309, 311;

art and spectator, 329;

and world-history, 363;

nature idea, chemistry, 382-384, 393;

religion in Late-Classical, 407;

spiritual epochs, table i;

art epochs, table ii

Arabian Nights, as symbol, 248

Arbela, battle, 151

Arcadians, provided history, 11

Arch, and column, 214, 236

Archæology, and historical repetition, 4;

cultural attitude, 14, 132, 254;

significance, 134.

Archery, Eastern and Western, 333_n._

Archimedes, style, 59;

and infinity, 69;

mathematical limitation, 84, 90;

contemporaries, 112, 386;

and metaphysics, 366;

and motion, 377;

as creator, 425

Architecture, ahistoric symbolism of Classical, 9, 12_n._;

symbolism of Egyptian, 69, 189, 202;

transition to and from Arabian, 72, 73;

Rococo as music, 87, 231, 285;

as early art of a Culture, mother-art, 128, 224;

undurable basis of Classical, 132, 198;

column, and arch, 166, 184, 204, 214, 236, 260_n._, 345;

dimension and direction, cultural relation, 169_n._, 177, 184, 205,

224;

symbolism in Chinese, 190, 196;

imitation and ornament, becoming and become, 194-198, 202;

history of techniques and ideas, 195;

of Civilization period, 197;

stage of Russian, 201;

Classical, feeble development of style, 204;

pseudomorphic Late-Classical, basilica, 209, 212, 214;

Arabian, dome type, 208, 210-212;

Western façade and visage, 224;

cathedral and infinite space, forest character, 198-200, 224, 396;

Arabian in Italy, 235;

place of Renaissance, 235;

Michelangelo and Baroque, 277;

and cultural morale, 345;

contemporary cultural epochs, table ii.

_See also_ Art; Baroque; Egyptian Culture; Doric; Gothic; Romanesque

Archytas, irrational numbers and fate, 65_n._;

and higher powers, 66;

contemporaries, 78, 90, 112, table i;

and metaphysics, 366

Arezzo, school of art, 268

Aristarchus of Samos, and Eastern thought, 9;

and heliocentric system, 68, 69, 139

Aristogiton, statue, 269_n._

Aristophanes, and burlesque, 30, 320_n._

Aristotle, ahistoric consciousness, 9;

entelechy, 15;

contemporaries, 17, table i;

and philosophy of being, 49_n._;

mechanistic world-conception, 99, 392;

and deity, 124, 313;

tabulation of categories, 125;

as collector, 136_n._;

as Plato’s opposite, 159;

on tragedy, 203, 318, 320, 321, 351;

on body and soul, 259;

on Zeuxis, 284;

and inward life, 317;

and philanthropy, 351;

and Civilization, 352;

and diet, 361;

culmination of Classical philosophy, 365, 366;

and mathematics, 366;

on atoms, 386;

as atheist, 409;

condemnation, 411

Arithmetic, Kant’s error, 6_n._;

and time, 125, 126.

_See also_ Mathematics

Army, Roman notion, 335

Arnold of Villanova, and chemistry, 384_n._

Art and arts, irrational polar idea, 20;

as sport, 35;

and future of Western Culture, 40;

as mathematical expression, 57, 58, 61, 62, 70;

Arabian, relation to algebra, 72;

and vision, 96;

causal and destiny sides, 127, 128;

Western, and “memory,” 132_n._;

mortality, 167;

religious character of early periods, 185;

lack of early Chinese survivals, 190_n._;

as expression-language, 191;

and witnesses, 191;

imitation and ornament, 191-194;

their opposition, becoming and become, 194-196;

typism, 193;

so-called, of Civilization, copyists, 197, 293-295;

meaning of style, 200, 201;

forms and cultural spirituality, 214-216;

as symbolic expression of Culture, 219, 259;

expression-methods of wordless, 219_n._;

sense-impression and classification, 220, 221;

historical boundaries, organism, 221;

species within a Culture, no rebirths, 222-224;

early period architecture as mother, 224;

Western philosophical association, 229;

secularization of Western, 230;

dominance of Western music, 231;

outward forms and cultural meaning, 238;

and popularity, 242;

space and philosophy, 243;

cultural basis of composition, 243;

symptom of decline, striving, 291, 292;

trained instinct and minor artists, 292, 293;

cultural association with morale, 344;

contemporary cultural epochs, table ii.

_See also_ Imitation; Ornament; Science; Style; arts by name

Aryan hero-tales, contemporaries, table i

Asklepios, as Christian title, 408_n._

Astrology, cultural attitude, 132, 147

Astronomy, Classical Culture and, 9;

heliocentric system, 68, 139;

dimensional figures, 83;

cultural significance, 330-332

Ataraxia, Stoic ideal, 343, 347, 352, 361

Atheism, and “God”, 312_n._;

as definite phenomenon, position, 408, 409;

cultural basis of structure, 409;

and toleration, 410, 411

Athene, as goddess, 268

Athens, and Paris, 27;

culture city, 32;

as religious, 358

Athtar, temples, 210

Atlantis, and voyages of Northmen, 332_n._

Atmosphere, in painting, 287

Atomic theories, Boscovich’s, 314_n._;

cultural basis, 384-387, 419;

disintegration hypotheses, 423

Augustan Age, Atticism, 28_n._

Augustine, Saint, and time, 124, 140;

and Jesus, 347;

contemporaries, table i

Augustus, as epoch, 140;

statue, 295

Aurelian, favourite god, 406;

contemporaries, table iii

Avalon, and Valhalla, 401

Avesta. _See_ Zend Avesta

Aviation, Leonardo’s interest, 279

Avicenna, on light, 381;

contemporaries, table i

Axum, empire, and world-history, 16, 208, 209_n._, 223