{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_12648/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_12648","id":"gutenberg_12648","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/12648","summary":null,"tags":["Architecture","Category: Architecture","Category: Art","Category: Essays, Letters & Speeches","Category: Philosophy & Ethics","Racism","Theosophy"],"text":"THE BEAUTIFUL NECESSITY\n\nSeven Essays on Theosophy and Architecture\n\nby CLAUDE BRAGDON, F.A.I.A.\n\nMCMXXII\n\n\n\n\n\n\n\n  \"Let us build altars to the Beautiful Necessity\"\n                                                --EMERSON\n\n\n\nBy the Same Author:\n  Episodes From An Unwritten History\n  The Golden Person In The Heart\n  Architecture And Democracy\n  A Primer Of Higher Space\n  Four Dimensional Vistas\n  Projective Ornament\n  Oracle\n\n\n\n\nCONTENTS\n\n  I    THE ART OF ARCHITECTURE\n\n  II   UNITY AND POLARITY\n\n  III  CHANGELESS CHANGE\n\n  IV   THE BODILY TEMPLE\n\n  V    LATENT GEOMETRY\n\n  VI   THE ARITHMETIC OF BEAUTY\n\n  VII  FROZEN MUSIC\n\n       CONCLUSION\n\n\n\n\nPREFACE TO THE SECOND EDITION\n\n\n_The Beautiful Necessity_ was first published in 1910. Save for a slim\nvolume of privately printed verse it was my first book. I worked hard\non it. Fifteen years elapsed between its beginning and completion;\nit was twice published serially--written, rewritten and\ntre-written--before it reached its ultimate incarnation in book form.\n\nConfronted now with the opportunity to revise the text again, I find\nmyself in the position of a surgeon who feels that the operation he\nis called upon to perform may perhaps harm more than it can help.\nPrudence therefore prevails over my passion for dissection: warned by\neminent examples, I fear that any injection of my more mature and less\ncocksure consciousness into this book might impair its unity--that I\n\"never could recapture the first fine careless rapture.\"\n\nThe text stands therefore as originally published save for a few\nverbal changes, and whatever reservations I have about it shall\nbe stated in this preface. These are not many nor important: _The\nBeautiful Necessity_ contains nothing that I need repudiate or care to\ncontradict.\n\nIts thesis, briefly stated, is that art in all its manifestations is\nan expression of the cosmic life, and that its symbols constitute a\nlanguage by means of which this life is published and represented. Art\nis at all times subject to the _Beautiful Necessity_ of proclaiming\nthe _world order_.\n\nIn attempting to develop this thesis it was not necessary (nor as\nI now think, desirable) to link it up in so definite a manner with\ntheosophy. The individual consciousness is colored by the particular\nmedium through which it receives truth, and for me that medium was\ntheosophy. Though the book might gain a more unprejudiced hearing,\nand from a larger audience, by the removal of the theosophic\n\"color-screen,\" it shall remain, for its removal now might seem to\nimply a loss of faith in the fundamental tenets of theosophy, and such\nan implication would not be true.\n\nThe ideas in regard to time and space are those commonly current\nin the world until the advent of the Theory of Relativity. To a\ngeneration brought up on Einstein and Ouspensky they are bound to\nappear \"lower dimensional.\" Merely to state this fact is to deal\nwith it to the extent it needs to be dealt with. The integrity of my\nargument is not impaired by these new views.\n\nThe one important influence that has operated to modify my opinions\nconcerning the mathematical basis of the arts of space has been the\ndiscoveries of Mr. Jay Hambidge with regard to the practice of the\nGreeks in these matters, as exemplified in their temples and their\nceramics, and named by him _Dynamic Symmetry_.\n\nIn tracing everything back to the logarithmic spiral (which embodies\nthe principle of extreme and mean ratios) I consider that Mr. Hambidge\nhas made one of those generalizations which reorganizes the old\nknowledge and organizes the new. It would be only natural if in his\nimmersion in his idea he overworks it, but Mr. Hambidge is a man of\nsuch intellectual integrity and thoroughness of method that he may be\ntrusted not to warp the facts to fit his theories. The truth of the\nmatter is that the entire field of research into the mathematics of\nBeauty is of such richness that wherever a man plants his metaphysical\nspade he is sure to come upon \"pay dirt.\" _The_ _Beautiful Necessity_\nrepresents the result of my own prospecting; _Dynamic Symmetry_\nrepresents the result of his. If at any point our findings appear to\nconflict, it is less likely that one or the other of us is mistaken\nthan that each is right from his own point of view. Be that as it may,\nI should be the last man in the world to differ from Mr. Hambidge,\nfor if he convicted me of every conceivable error his work would still\nremain the greatest justification and confirmation of my fundamental\ncontention--that art is an expression of the _world order_ and\nis therefore orderly, organic; subject to mathematical law, and\nsusceptible of mathematical analysis.\n\nCLAUDE BRAGDON\n\nRochester, N.Y.\n\nApril, 1922\n\n\n\n\nI\n\nTHE ART OF ARCHITECTURE\n\n\nOne of the advantages of a thorough assimilation of what may be called\nthe theosophic idea is that it can be applied with advantage to every\ndepartment of knowledge and of human activity: like the key to a\ncryptogram it renders clear and simple that which before seemed\nintricate and obscure. Let us apply this key to the subject of art,\nand to the art of architecture in particular, and see if by so\ndoing we may not learn more of art than we knew before, and more of\ntheosophy too.\n\nThe theosophic idea is that everything is an expression of the\nSelf--or whatever other name one may choose to give to that immanent\nunknown reality which forever hides behind all phenomenal life--but\nbecause, immersed as we are in materiality, our chief avenue of\nknowledge is sense perception, a more exact expression of the\ntheosophic idea would be: Everything is the expression of the Self\nin terms of sense. Art, accordingly, is the expression of the Self in\nterms of sense. Now though the Self is _one_, sense is not one, but\nmanifold: and therefore there are _arts_, each addressed to some\nparticular faculty or group of faculties, and each expressing some\nparticular quality or group of qualities of the Self. The white light\nof Truth is thus broken up into a rainbow-tinted spectrum of Beauty,\nin which the various arts are colors, each distinct, yet merging one\ninto another--poetry into music; painting into decoration; decoration\nbecoming sculpture; sculpture--architecture, and so on.\n\nIn such a spectrum of the arts each one occupies a definite place, and\nall together form a series of which music and architecture are the two\nextremes. That such is their relative position may be demonstrated in\nvarious ways. The theosophic explanation involving the familiar idea\nof the \"pairs of opposites\" would be something as follows. According\nto the Hindu-Aryan theory, Brahma, that the world might be born, fell\nasunder into man and wife--became in other words _name and form_[A]\nThe two universal aspects of name and form are what philosophers call\nthe two \"modes of consciousness,\" one of time, and the other of space.\nThese are the two gates through which ideas enter phenomenal life; the\ntwo boxes, as it were, that contain all the toys with which we play.\nEverything, were we only keen enough to perceive it, bears the mark of\none or the other of them, and may be classified accordingly. In such a\nclassification music is seen to be allied to time, and architecture to\nspace, because music is successive in its mode of manifestation, and\nin time alone everything would occur successively, one thing following\nanother; while architecture, on the other hand, impresses itself upon\nthe beholder all at once, and in space alone all things would exist\nsimultaneously. Music, which is in time alone, without any relation to\nspace; and architecture, which is in space alone, without any relation\nto time, are thus seen to stand at opposite ends of the art spectrum,\nand to be, in a sense, the only \"pure\" arts, because in all the others\nthe elements of both time and space enter in varying proportion,\neither actually or by implication. Poetry and the drama are allied to\nmusic inasmuch as the ideas and images of which they are made up are\npresented successively, yet these images are for the most part\nforms of space. Sculpture on the other hand is clearly allied to\narchitecture, and so to space, but the element of _action_, suspended\nthough it be, affiliates it with the opposite or time pole. Painting\noccupies a middle position, since in it space instead of being\nactual has become ideal--three dimensions being expressed through\nthe mediumship of two--and time enters into it more largely than into\nsculpture by reason of the greater ease with which complicated action\ncan be indicated: a picture being nearly always time arrested in\nmidcourse as it were--a moment transfixed.\n\nIn order to form a just conception of the relation between music and\narchitecture it is necessary that the two should be conceived of not\nas standing at opposite ends of a series represented by a straight\nline, but rather in juxtaposition, as in the ancient Egyptian symbol\nof a serpent holding its tail in its mouth, the head in this case\ncorresponding to music, and the tail to architecture; in other words,\nthough in one sense they are the most-widely separated of the arts, in\nanother they are the most closely related.\n\nMusic being purely in time and architecture being purely in space,\neach is, in a manner and to a degree not possible with any of\nthe other arts, convertible into the other, by reason of the\ncorrespondence subsisting between intervals of time and intervals of\nspace. A perception of this may have inspired the famous saying\nthat architecture is _frozen music_, a poetical statement of a\nphilosophical truth, since that which in music is expressed by means\nof harmonious intervals of time and pitch, successively, after the\nmanner of time, may be translated into corresponding intervals of\narchitectural void and solid, height and width.\n\nIn another sense music and architecture are allied. They alone of\nall the arts are purely creative, since in them is presented, not\na likeness of some known idea, but _a thing-in-itself_ brought to\na distinct and complete expression of its nature. Neither a musical\ncomposition nor a work of architecture depends for its effectiveness\nupon resemblances to natural sounds in the one case, or to natural\nforms in the other. Of none of the other arts is this to such a degree\ntrue: they are not so much creative as re-creative, for in them all\nthe artist takes his subject ready made from nature and presents it\nanew according to the dictates of his genius.\n\nThe characteristic differences between music and architecture are the\nsame as those which subsist between time and space. Now time and space\nare such abstract ideas that they can be dealt with best through\ntheir corresponding correlatives in the natural world, for it is a\nfundamental theosophic tenet that nature everywhere abounds in such\ncorrespondences; that nature, in its myriad forms, is indeed the\nconcrete presentment of abstract unities. The energy which everywhere\nanimates form is a type of time within space; the mind working in\nand through the body is another expression of the same thing.\nCorrespondingly, music is dynamic, subjective, mental, of one\ndimension; while architecture is static, objective, physical, of three\ndimensions; sustaining the same relation to music and the other\narts as does the human body to the various organs which compose, and\nconsciousnesses which animate it (it being the reservatory of these\norgans and the vehicle of these consciousnesses); and a work of\narchitecture in like manner may and sometimes does include all of the\nother arts within itself. Sculpture accentuates and enriches, painting\nadorns, works of literature are stored within it, poetry and the drama\nawake its echoes, while music thrills to its uttermost recesses, like\nthe very spirit of life tingling through the body's fibres.\n\nSuch being the relation between them, the difference in the nature of\nthe ideas bodied forth in music and in architecture becomes apparent.\nMusic is interior, abstract, subjective, speaking directly to the soul\nin a simple and universal language whose meaning is made personal and\nparticular in the breast of each listener: \"Music alone of all the\narts,\" says Balzac, \"has power to make us live within ourselves.\"\nA work of architecture is the exact opposite of this: existing\nprincipally and primarily for the uses of the body, it is like the\nbody a concrete organism, attaining to esthetic expression only in\nthe reconciliation and fulfilment of many conflicting practical\nrequirements. Music is pure beauty, the voice of the unfettered\nand perpetually vanishing soul of things; architecture is that soul\nimprisoned in a form, become subject to the law of causality, beaten\nupon by the elements, at war with gravity, the slave of man. One is\nthe Ariel of the arts; the other, Caliban.\n\nComing now to the consideration of architecture in its historical\nrather than its philosophical aspect, it will be shown how certain\ntheosophical concepts are applicable here. Of these none is more\nfamiliar and none more fundamental than the idea of reincarnation. By\nreincarnation more than mere physical re-birth is meant, for physical\nre-birth is but a single manifestation of that universal law of\nalternation of state, of animation of vehicles, and progression\nthrough related planes, in accordance with which all things move,\nand as it were make music--each cycle complete, yet part of a larger\ncycle, the incarnate monad passing through correlated changes,\ncarrying along and bringing into manifestation in each successive arc\nof the spiral the experience accumulated in all preceding states,\nand at the same time unfolding that power of the Self peculiar to the\nplane in which it is momentarily manifesting.\n\nThis law finds exemplification in the history of architecture in the\norderly flow of the building impulse from one nation and one country\nto a different nation and a different country: its new vehicle of\nmanifestation; also in the continuity and increasing complexity of\nthe development of that impulse in manifestation; each \"incarnation\"\nsummarizing all those which have gone before, and adding some new\nfactor peculiar to itself alone; each being a growth, a life, with\nperiods corresponding to childhood, youth, maturity and decadence;\neach also typifying in its entirety some single one of these\nlife-periods, and revealing some special aspect or power of the Self.\n\nFor the sake of clearness and brevity the consideration of only one\nof several architectural evolutions will be attempted: that which,\narising in the north of Africa, spread to southern Europe, thence to\nthe northwest of Europe and to England--the architecture, in short, of\nthe so-called civilized world.\n\nThis architecture, anterior to the Christian era, may be broadly\ndivided into three great periods, during which it was successively\npracticed by three peoples: the Egyptians, the Greeks and the Romans.\nThen intervened the Dark Ages, and a new art arose, the Gothic, which\nwas a flowering out in stone of the spirit of Christianity. This was\nin turn succeeded by the Renaissance, the impulse of which remains\nto-day unexhausted. In each of these architectures the peculiar genius\nof a people and of a period attained to a beautiful, complete and\ncoherent utterance, and notwithstanding the considerable intervals\nof time which sometimes separated them they succeeded one another\nlogically and inevitably, and each was related to the one which\npreceded and which followed it in a particular and intimate manner.\n\nThe power and wisdom of ancient Egypt was vested in its priesthood,\nwhich was composed of individuals exceptionally qualified by birth\nand training for their high office, tried by the severest ordeals\nand bound by the most solemn oaths. The priests were honored and\nprivileged above all other men, and spent their lives dwelling\napart from the multitude in vast and magnificent temples, dedicating\nthemselves to the study and practice of religion, philosophy, science\nand art--subjects then intimately related, not widely separated as\nthey are now. These men were the architects of ancient Egypt: theirs\nthe minds which directed the hands that built those time-defying\nmonuments.\n\nThe rites that the priests practiced centered about what are known\nas the Lesser and the Greater Mysteries. These consisted of\nrepresentations by means of symbol and allegory, under conditions\nand amid surroundings the most awe-inspiring, of those great truths\nconcerning man's nature, origin and destiny of which the priests--in\nreality a brotherhood of initiates and their pupils--were the\ncustodians. These ceremonies were made the occasion for the initiation\nof neophytes into the order, and the advancement of the already\ninitiated into its successive degrees. For the practice of such rites,\nand others designed to impress not the elect but the multitude, the\ngreat temples of Egypt were constructed. Everything about them was\ncalculated to induce a deep seriousness of mind, and to inspire\nfeelings of awe, dread and even terror, so as to test the candidate's\nfortitude of soul to the utmost.\n\nThe avenue of approach to an Egyptian temple was flanked on both\nsides, sometimes for a mile or more, with great stone sphinxes--that\nemblem of man's dual nature, the god emerging from the beast. The\nentrance was through a single high doorway between two towering\npylons, presenting a vast surface sculptured and painted over with\nmany strange and enigmatic figures, and flanked by aspiring obelisks\nand seated colossi with faces austere and calm. The large court thus\nentered was surrounded by high walls and colonnades, but was open\nto the sky. Opposite the first doorway was another, admitting to a\nsomewhat smaller enclosure, a forest of enormous carved and painted\ncolumns supporting a roof through the apertures of which sunshine\ngleamed or dim light filtered down. Beyond this in turn were other\ncourts and apartments culminating in some inmost sacred sanctuary.\n\nNot alone in their temples, but in their tombs and pyramids and\nall the sculptured monuments of the Egyptians, there is the same\ninsistence upon the sublimity, mystery and awefulness of life,\nwhich they seem to have felt so profoundly. But more than this, the\nconscious thought of the masters who conceived them, the buildings of\nEgypt give utterance also to the toil and suffering of the thousands\nof slaves and captives which hewed the stones out of the heart of the\nrock, dragged them long distances and placed them one upon another, so\nthat these buildings oppress while they inspire, for there is in them\nno freedom, no spontaneity, no individuality, but everywhere the felt\npresence of an iron conventionality, of a stern immutable law.\n\nIn Egyptian architecture is symbolized the condition of the human soul\nawakened from its long sleep in nature, and become conscious at once\nof its divine source and of the leaden burden of its fleshy envelope.\nEgypt is humanity new-born, bound still with an umbilical cord to\nnature, and strong not so much with its own strength as with the\nstrength of its mother. This idea is aptly symbolized in those\ngigantic colossi flanking the entrance to some rock-cut temple, which\nthough entire are yet part of the living cliff out of which they were\nfashioned.\n\nIn the architecture of Greece the note of dread and mystery yields to\none of pure joyousness and freedom. The terrors of childhood have been\noutgrown, and man revels in the indulgence of his unjaded appetites\nand in the exercise of his awakened reasoning faculties. In Greek art\nis preserved that evanescent beauty of youth which, coming but once\nand continuing but for a short interval in every human life, is yet\nthat for which all antecedent states seem a preparation, and of\nwhich all subsequent ones are in some sort an effect. Greece typifies\nadolescence, the love age, and so throughout the centuries humanity\nhas turned to the contemplation of her, just as a man all his life\nlong secretly cherishes the memory of his first love.\n\nAn impassioned sense of beauty and an enlightened reason characterize\nthe productions of Greek architecture during its best period. The\nperfection then attained was possible only in a nation whereof the\ncitizens were themselves critics and amateurs of art, one wherein\nthe artist was honored and his work appreciated in all its beauty\nand subtlety. The Greek architect was less bound by tradition and\nprecedent than was the Egyptian, and he worked unhampered by any\nrestrictions save such as, like the laws of harmony in music, helped\nrather than hindered his genius to express itself--restrictions\nfounded on sound reason, the value of which had been proved by\nexperience.\n\nThe Doric order was employed for all large temples, since it possessed\nin fullest measure the qualities of simplicity and dignity, the\nattributes appropriate to greatness. Quite properly also its formulas\nwere more fixed than those of any other style. The Ionic order,\nthe feminine of which the Doric may be considered the corresponding\nmasculine, was employed for smaller temples; like a woman it was more\nsupple and adaptable than the Doric, its proportions were more slender\nand graceful, its lines more flowing, and its ornament more delicate\nand profuse. A freer and more elaborate style than either of these,\ninfinitely various, seeming to obey no law save that of beauty, was\nused sometimes for small monuments and temples, such as the Tower of\nthe Winds, and the monument of Lysicrates at Athens.\n\n[Illustration 1]\n\nBecause the Greek architect was at liberty to improve upon the work of\nhis predecessors if he could, no temple was just like any other,\nand they form an ascending scale of excellence, culminating in the\nAcropolis group. Every detail was considered not only with relation\nto its position and function, but in regard to its intrinsic beauty as\nwell, so that the merest fragment, detached from the building of which\nit formed a part, is found worthy of being treasured in our museums\nfor its own sake.\n\nJust as every detail of a Greek temple was adjusted to its position\nand expressed its office, so the building itself was made to fit\nits site and to show forth its purpose, forming with the surrounding\nbuildings a unit of a larger whole. The Athenian Acropolis is an\nillustration of this: it is an irregular fortified hill, bearing\ndiverse monuments in various styles, at unequal levels and at\ndifferent angles with one another, yet the whole arrangement seems as\norganic and inevitable as the disposition of the features of a face.\nThe Acropolis is an example of the ideal architectural republic\nwherein each individual contributes to the welfare of all, and at the\nsame time enjoys the utmost personal liberty (Illustration 1).\n\nVery different is the spirit bodied forth in the architecture of\nImperial Rome. The iron hand of its sovereignty encased within the\nsilken glove of its luxury finds its prototype in buildings which were\nstupendous crude brute masses of brick and concrete, hidden within a\ncovering of rich marbles and mosaics, wrought in beautiful but often\nmeaningless forms by clever degenerate Greeks. The genius of Rome\nfinds its most characteristic expression, not in temples to the high\ngods, but rather in those vast and complicated structures--basilicas,\namphitheatres, baths--built for the amusement and purely temporal\nneeds of the people.\n\nIf Egypt typifies the childhood of the race and Greece its beautiful\nyouth, Republican Rome represents its strong manhood--a soldier filled\nwith the lust of war and the love of glory--and Imperial Rome its\ndegeneracy: that soldier become conqueror, decked out in plundered\nfinery and sunk in sensuality, tolerant of all who minister to his\npleasures but terrible to all who interfere with them.\n\nThe fall of Rome marked the end of the ancient Pagan world. Above\nits ruin Christian civilization in the course of time arose. Gothic\narchitecture is an expression of the Christian spirit; in it is\nmanifest the reaction from licentiousness to asceticism. Man's\nspiritual nature, awakening in a body worn and weakened by\ndebaucheries, longs ardently and tries vainly to escape. Of some such\nmood a Gothic cathedral is the expression: its vaulting, marvelously\nsupported upon slender shafts by reason of a nicely adjusted\nequilibrium of forces; its restless, upward-reaching pinnacles and\nspires; its ornament, intricate and enigmatic--all these suggest the\nover-strained organism of an ascetic; while its vast shadowy interior\nlit by marvelously traceried and jeweled windows, which hold the eyes\nin a hypnotic thrall, is like his soul: filled with world sadness,\ndead to the bright brief joys of sense, seeing only heavenly visions,\nknowing none but mystic raptures.\n\nThus it is that the history of architecture illustrates and enforces\nthe theosophical teaching that everything of man's creating is made in\nhis own image. Architecture mirrors the life of the individual and of\nthe race, which is the life of the individual written large in time\nand space. The terrors of childhood; the keen interests and appetites\nof youth; the strong stern joy of conflict which comes with manhood;\nthe lust, the greed, the cruelty of a materialized old age--all these\nserve but as a preparation for the life of the spirit, in which the\nman becomes again as a little child, going over the whole round, but\non a higher arc of the spiral.\n\nThe final, or fourth state being only in some sort a repetition of\nthe first, it would be reasonable to look for a certain correspondence\nbetween Egyptian and Gothic architecture, and such a correspondence\nthere is, though it is more easily divined than demonstrated. In\nboth there is the same deeply religious spirit; both convey, in some\nobscure yet potent manner, a sense of the soul being near the surface\nof life. There is the same love of mystery and of symbolism; and in\nboth may be observed the tendency to create strange composite figures\nto typify transcendental ideas, the sphinx seeming a blood-brother to\nthe gargoyle. The conditions under which each architecture flourished\nwere not dissimilar, for each was formulated and controlled by small\nwell-organized bodies of sincerely religious and highly enlightened\nmen--the priesthood in the one case, the masonic guilds in the\nother--working together toward the consummation of great undertakings\namid a populace for the most part oblivious of the profound and subtle\nmeanings of which their work was full. In Medi\u00e6val Europe, as in\nancient Egypt, fragments of the Ancient Wisdom--transmitted in the\nsymbols and secrets of the cathedral builders--determined much of\nGothic architecture.\n\nThe architecture of the Renaissance period, which succeeded the\nGothic, corresponds again, in the spirit which animates it, to Greek\narchitecture, which succeeded the Egyptian, for the Renaissance as\nthe name implies was nothing other than an attempt to revive Classical\nantiquity. Scholars writing in what they conceived to be a Classical\nstyle, sculptors modeling Pagan deities, and architects building\naccording to their understanding of Vitruvian methods succeeded\nin producing works like, yet different from the originals they\nfollowed--different because, animated by a spirit unknown to the\nancients, they embodied a new ideal.\n\nIn all the productions of the early Renaissance, \"that first\ntranscendent springtide of the modern world,\" there is the evanescent\ngrace and beauty of youth which was seen to have pervaded Greek art,\nbut it is a grace and beauty of a different sort. The Greek artist\nsought to attain to a certain abstract perfection of type; to build\na temple which should combine all the excellencies of every similar\ntemple, to carve a figure, impersonal in the highest sense, which\nshould embody every beauty. The artist of the Renaissance on the other\nhand delighted not so much in the type as in the variation from it.\nPreoccupied with the unique mystery of the individual soul--a sense of\nwhich was Christianity's gift to Christendom--he endeavored to portray\nthat wherein a particular person is unique and singular. Acutely\nconscious also of his own individuality, instead of effacing it he\nmade his work the vehicle and expression of that individuality. The\nhistory of Renaissance architecture, as Symonds has pointed out,\nis the history of a few eminent individuals, each one moulding and\nmodifying the style in a manner peculiar to himself alone. In the\nhands of Brunelleschi it was stern and powerful; Bramante made\nit chaste, elegant and graceful; Palladio made it formal, cold,\nsymmetrical; while with Sansovino and Sammichele it became sumptuous\nand bombastic.\n\nAs the Renaissance ripened to decay its architecture assumed more and\nmore the characteristics which distinguished that of Rome during the\ndecadence. In both there is the same lack of simplicity and sincerity,\nthe same profusion of debased and meaningless ornament, and there is\nan increasing disposition to conceal and falsify the construction by\nsurface decoration.\n\nThe final part of this second or modern architectural cycle lies still\nin the future. It is not unreasonable to believe that the movement\ntoward mysticism, of which modern theosophy is a phase and the\nspiritualization of science an episode, will flower out into an\narchitecture which will be in some sort a reincarnation of and a\nreturn to the Gothic spirit, employing new materials, new methods,\nand developing new forms to show forth the spirit of the modern world,\nwithout violating ancient verities.\n\nIn studying these crucial periods in the history of European\narchitecture it is possible to trace a gradual growth or unfolding\nas of a plant. It is a fact fairly well established that the Greeks\nderived their architecture and ornament from Egypt; the Romans in\nturn borrowed from the Greeks; while a Gothic cathedral is a lineal\ndescendant from a Roman basilica.\n\n[Illustration 2]\n\n[Illustration 3]\n\nThe Egyptians in their constructions did little more than to place\nenormous stones on end, and pile one huge block upon another. They\nused many columns placed close together: the spaces which they spanned\nwere inconsiderable. The upright or supporting member may be said to\nhave been in Egyptian architecture the predominant one. A vertical\nline therefore may be taken as the simplest and most abstract symbol\nof Egyptian architecture (Illustration 2). It remained for the Greeks\nfully to develop the lintel. In their architecture the vertical\nmember, or column, existed solely for the sake of the horizontal\nmember, or lintel; it rarely stood alone as in the case of an Egyptian\nobelisk. The columns of the Greek temples were reduced to those\nproportions most consistent with strength and beauty, and the\nintercolumnations were relatively greater than in Egyptian examples.\nIt may truly be said that Greek architecture exhibits the perfect\nequality and equipoise of vertical and horizontal elements and these\nonly, no other factor entering in. Its graphic symbol would therefore\nbe composed of a vertical and a horizontal line (Illustration 3). The\nRomans, while retaining the column and lintel of the Greeks, deprived\nthem of their structural significance and subordinated them to the\nsemicircular arch and the semi-cylindrical and hemispherical vault,\nthe truly characteristic and determining forms of Roman architecture.\nOur symbol grows therefore by the addition of the arc of a circle\n(Illustration 4). In Gothic architecture column, lintel, arch and\nvault are all retained in changed form, but that which more than\nanything else differentiates Gothic architecture from any style which\npreceded it is the introduction of the principle of an equilibrium of\nforces, of a state of balance rather than a state of rest, arrived at\nby the opposition of one thrust with another contrary to it. This fact\ncan be indicated graphically by two opposing inclined lines, and\nthese united to the preceding symbol yield an accurate abstract of the\nelements of Gothic architecture (Illustration 5).\n\n[Illustration 4]\n\n[Illustration 5]\n\nAll this is but an unusual application of a familiar theosophic\nteaching, namely, that it is the method of nature on every plane and\nin every department not to omit anything that has gone before, but to\nstore it up and carry it along and bring it into manifestation later.\nNature everywhere proceeds like the jingle of _The House that Jack\nBuilt_: she repeats each time all she has learned, and adds another\nline for subsequent repetition.\n\n[Footnote A: The quaint Oriental imagery here employed should not\nblind the reader to the precise scientific accuracy of the idea of\nwhich this imagery is the vehicle. Schopenhauer says: \"Polarity, or\nthe sundering of a force into two quantitively different and opposed\nactivities striving after re-union,... is a fundamental type of almost\nall the phenomena of nature, from the magnet and the crystal to man\nhimself.\"]\n\n\n\n\nII\n\nUNITY AND POLARITY\n\n\nTheosophy, both as a philosophy, or system of thought, which discovers\ncorrelations between things apparently unrelated, and as a life,\nor system of training whereby it is possible to gain the power to\nperceive and use these correlations for worthy ends, is of great value\nto the creative artist, whose success depends on the extent to which\nhe works organically, conforming to the cosmic pattern, proceeding\nrationally and rhythmically to some predetermined end. It is of value\nno less to the layman, the critic, the art amateur--to anyone in\nfact who would come to an accurate and intimate understanding and\nappreciation of every variety of esthetic endeavor. For the benefit of\nsuch I shall try to trace some of those correlations which theosophy\naffirms, and indicate their bearing upon art, and upon the art of\narchitecture in particular.\n\nOne of the things which theosophy teaches is that those transcendent\nglimpses of a divine order and harmony throughout the universe\nvouchsafed the poet and the mystic in their moments of vision are not\nthe paradoxes--the paronomasia as it were--of an intoxicated state of\nconsciousness, but glimpses of reality. We are all of us participators\nin a world of concrete music, geometry and number--a world of\nsounds, odors, forms, motions, colors, so mathematically related and\ncoordinated that our pigmy bodies, equally with the farthest star,\nvibrate to the music of the spheres. There is a _Beautiful Necessity_\nwhich rules the world, which is a law of nature and equally a law of\nart, for art is idealized creation: nature carried to a higher power\nby reason of its passage through a human consciousness. Thought and\nemotion tend to crystallize into forms of beauty as inevitably as does\nthe frost on a window pane. Art therefore in one of its aspects is the\nweaving of a pattern, the communication of an order and a method to\nthe material or medium employed. Although no masterpiece was ever\ncreated by the conscious following to set rules, for the true artist\nworks unconsciously, instinctively, as the bird sings or as the bee\nbuilds its honey-cell, yet an analysis of any masterpiece reveals the\nfact that its author (like the bird and the bee) has \"followed the\nrules without knowing them.\"\n\nHelmholtz says, \"No doubt is now entertained that beauty is subject\nto laws and rules dependent on the nature of human intelligence. The\ndifficulty consists in the fact that these laws and rules, on whose\nfulfilment beauty depends, are not consciously present in the mind of\nthe artist who creates the work, or of the observer who contemplates\nit.\" Nevertheless they are discoverable, and can be formulated,\nafter a fashion. We have only to read aright the lessons everywhere\nportrayed in the vast picture-books of nature and of art.\n\nThe first truth therein published is the law of _Unity_--oneness; for\nthere is one Self, one Life, which, myriad in manifestation, is yet\nin essence ever _one_. Atom and universe, man and the world--each is\na unit, an organic and coherent whole. The application of this law to\nart is so obvious as to be almost unnecessary of elucidation, for to\nsay that a work of art must possess unity, must seem to proceed from a\nsingle impulse and be the embodiment of one dominant idea, is to state\na truism. In a work of architecture the co\u00f6rdination of its various\nparts with one another is almost the measure of its success. We\nremember any masterpiece--the cathedral of Paris no less than the\npyramids of Egypt--by the singleness of its appeal; complex it may be,\nbut it is a coordinated complexity; variety it may possess, but it is\na variety in an all-embracing unity.\n\nThe second law, not contradicting but supplementing the first is the\nlaw of _Polarity_, i.e., duality. All things have sex, are either\nmasculine or feminine. This too is the reflection on a lower plane\nof one of those transcendental truths taught by the Ancient Wisdom,\nnamely that the Logos, in his voluntarily circumscribing his infinite\nlife in order that he may manifest, encloses himself within his\nlimiting veil, _maya_, and that his life appears as spirit (male), and\nhis _maya_ as matter (female), the two being never disjoined during\nmanifestation. The two terms of this polarity are endlessly repeated\nthroughout nature: in sun and moon, day and night, fire and water, man\nand woman--and so on. A close inter-relation is always seen to subsist\nbetween corresponding members of such pairs of opposites: sun, day,\nfire, man express and embody the primal and active aspect of the\nmanifesting deity; moon, night, water, woman, its secondary and\npassive aspect. Moreover, each implies or brings to mind the others\nof its class: man, like the sun, is lord of day; he is like fire, a\ndevastating force; woman is subject to the lunar rhythm; like water,\nshe is soft, sinuous, fecund.\n\nThe part which this polarity plays in the arts is important, and the\nconstant and characteristic distinction between the two terms is a\nthing far beyond mere contrast.\n\nIn music they are the major and minor modes: the typical, or\nrepresentative chords of the dominant seventh, and of the tonic (the\ntwo chords into which Schopenhauer says all music can be resolved): a\npartial dissonance, and a consonance: a chord of suspense, and a chord\nof satisfaction. In speech the two are vowel, and consonant sounds:\nthe type of the first being _a_, a sound of suspense, made with the\nmouth open; and of the second _m_, a sound of satisfaction, made by\nclosing the mouth; their combination forms the sacred syllable Om\n(_Aum_). In painting they are warm colors, and cold: the pole of\nthe first being in red, the color of fire, which excites; and of the\nsecond in blue, the color of water, which calms; in the Arts of design\nthey are lines straight (like fire), and flowing (like water); masses\nlight (like the day), and dark (like night). In architecture they are\nthe column, or vertical member, which resists the force of gravity;\nand the lintel, or horizontal member, which succumbs to it; they are\nvertical lines, which are aspiring, effortful; and horizontal lines,\nwhich are restful to the eye and mind.\n\nIt is desirable to have an instant and keen realization of this sex\nquality, and to make this easier some sort of classification and\nanalysis must be attempted. Those things which are allied to and\npartake of the nature of _time_ are masculine, and those which are\nallied to and partake of the nature of _space_ are feminine: as\nmotion, and matter; mind, and body; etc. The English words \"masculine\"\nand \"feminine\" are too intimately associated with the idea of physical\nsex properly to designate the terms of this polarity. In Japanese\nphilosophy and art (derived from the Chinese) the two are called _In_\nand _Yo_ (In, feminine; Yo, masculine); and these little words, being\nfree from the limitations of their English correlatives, will be found\nconvenient, Yo to designate that which is simple, direct, primary,\nactive, positive; and In, that which is complex, indirect, derivative,\npassive, negative. Things hard, straight, fixed, vertical, are Yo;\nthings soft, curved, horizontal, fluctuating, are In--and so on.\n\n[Illustration 6: WILD CHERRY; MAPLE LEAF]\n\n[Illustration 7: CALLAS IN YO]\n\nIn passing it may be said that the superiority of the line, mass, and\ncolor composition of Japanese prints and kakemonos to that exhibited\nin the vastly more pretentious easel pictures of modern Occidental\nartists--a superiority now generally acknowledged by connoisseurs--is\nlargely due to the conscious following, on the part of the Japanese,\nof this principle of sex-complementaries.\n\nNowhere are In and Yo more simply and adequately imaged than in the\nvegetable kingdom. The trunk of a tree is Yo, its foliage, In; and\nin each stem and leaf the two are repeated. A calla, consisting of\na single straight and rigid spadix embraced by a soft and tenderly\ncurved spathe, affords an almost perfect expression of the\ncharacteristic differences between Yo and In and their reciprocal\nrelation to each other. The two are not often combined in such\nsimplicity and perfection in a single form. The straight, vertical\nreeds which so often grow in still, shallow water, find their\ncomplement in the curved lily-pads which lie horizontally on its\nsurface. Trees such as pine and hemlock, which are excurrent--those in\nwhich the branches start successively (i.e., after the manner of time)\nfrom a straight and vertical central stem--are Yo; trees such as\nthe elm and willow, which are deliquescent--those in which the trunk\ndissolves as it were simultaneously (after the manner of space) into\nits branches--are In. All tree forms lie in or between these two\nextremes, and leaves are susceptible of a similar classification. It\nwill be seen to be a classification according to time and space,\nfor the characteristic of time is _succession_, and of space,\n_simultaneousness_: the first is expressed symbolically by elements\narranged with relation to axial lines; the second, by elements\narranged with relation to focal points (Illustrations 6,7).\n\nThe student should train himself to recognize In and Yo in all\ntheir Protean presentments throughout nature--in the cloud upon the\nmountain, the wave against the cliff, in the tracery of trees against\nthe sky--that he may the more readily recognize them in his chosen\nart, whatever that art may be. If it happens to be painting, he will\nendeavor to discern this law of duality in the composition of every\nmasterpiece, recognizing an instinctive obedience to it in that\nfavorite device of the great Renaissance masters of making an\narchitectural setting for their groups of figures, and he will\ndelight to trace the law in all its ramifications of contrast between\ncomplementaries in line, color, and mass (Illustration 8).\n\n[Illustration 8: THE LAW OF POLARITY CLEOPATRA MELTING THE PEARL. BY\nTIEPOLO]\n\nWith reference to architecture, it is true, generally speaking,\nthat architectural forms have been developed through necessity, the\nfunction seeking and finding its appropriate form. For example, the\nbuttress of a Gothic cathedral was developed by the necessity of\nresisting the thrust of the interior vaulting without encroaching upon\nthe nave; the main lines of a buttress conform to the direction of the\nthrust, and the pinnacle with which it terminates is a logical shape\nfor the masonry necessary to hold the top in position (Illustration\n9). Research along these lines is interesting and fruitful of result,\nbut there remains a certain number of architectural forms whose origin\ncannot be explained in any such manner. The secret of their undying\ncharm lies in the fact that in them In and Yo stand symbolized and\ncontrasted. They no longer obey a law of utility, but an abstract\nlaw of beauty, for in becoming sexually expressive as it were, the\nconstruction itself is sometimes weakened or falsified. The familiar\nclassic console or modillion is an example: although in general\ncontour it is well adapted to its function as a supporting bracket,\nembedded in, and projecting from a wall, yet the scroll-like ornament\nwith which its sides are embellished gives it the appearance of\nnot entering the wall at all, but of being stuck against it in some\nmiraculous manner. This defect in functional expressiveness is\nmore than compensated for by the perfection with which feminine\nand masculine characteristics are expressed and contrasted in the\nexquisite double spiral, opposed to the straight lines of the moulding\nwhich it subtends (Illustration 10). Again, by fluting the shaft of a\ncolumn its area of cross-section is diminished but the appearance of\nstrength is enhanced because its masculine character--as a supporting\nmember resisting the force of gravity--is emphasized.\n\n[Illustration 9: CROSS SECTION OF BUTTRESS.]\n\nThe importance of the so-called \"orders\" lies in the fact that they\nare architecture epitomized as it were. A building consists of a wall\nupholding a roof: support and weight. The type of the first is the\ncolumn, which may be conceived of as a condensed section of wall; and\nof the second, the lintel, which may be conceived of as a condensed\nsection of roof. The column, being vertical, is Yo; the lintel, being\nhorizontal, is In. To mark an entablature with horizontal lines in the\nform of mouldings, and the columns with vertical lines in the form\nof flutes, as is done in all the \"classic orders,\" is a gain\nin functional and sex expressiveness, and consequently in art\n(Illustration 11).\n\n[Illustration 10: CORINTHIAN MODILLION; CLASSIC CONSOLE; IONIC CAP]\n\nThe column is again divided into the shaft, which is Yo; and the\ncapital, which is In. The capital is itself twofold, consisting of a\ncurved member and an angular member. These two appear in their utmost\nsimplicity in the _echinus_ (In) and the _abacus_ (Yo) of a\nGreek Doric cap. The former was adorned with painted leaf forms,\ncharacteristically feminine, and the latter with the angular fret\nand meander (Illustration 12). The Ionic capital, belonging to a more\nfeminine style, exhibits the abacus subordinated to that beautiful\ncushion-shaped member with its two spirally marked volutes. This,\nthough a less rational and expressive form for its particular office\nthan is the echinus of the Doric cap, is a far more perfect symbol of\nthe feminine element in nature. There is an essential identity between\nthe Ionic cap and the classic console before referred to--although\nsuperficially the two do not resemble each other--for a straight line\nand a double spiral are elements common to both (Illustration 10).\nThe Corinthian capital consists of an ordered mass of delicately\nsculptured leaf and scroll forms sustaining an abacus which though\nrelatively masculine is yet more curved and feminine than that of any\nother style. In the caulicole of a Corinthian cap In and Yo are again\ncontrasted. In the unique and exquisite capital from the Tower of the\nWinds at Athens, the two are well suggested in the simple, erect, and\npointed leaf forms of the upper part, contrasted with the complex,\ndeliquescent, rounded ones from which they spring. The essential\nidentity of principle subsisting between this cap and the Renaissance\nbaluster by San Gallo is easily seen (Illustration 13).\n\n[Illustration 11]\n\n[Illustration 12]\n\nThis law of sex-expressiveness is of such universality that it can\nbe made the basis of an analysis of the architectural ornament of any\nstyle or period. It is more than mere opposition and contrast. The egg\nand tongue motif, which has persisted throughout so many centuries and\nsurvived so many styles, exhibits an alternation of forms resembling\nphallic emblems. Yo and In are well suggested in the channeled\ntriglyphs and the sculptured metopes of a Doric frieze, in the\nstraight and vertical mullions and the flowing tracery of Gothic\nwindows, in the banded torus, the bead and reel, and other familiar\nornamented mouldings (Illustrations 14, 15, 16).\n\nThere are indications that at some time during the development\nof Gothic architecture in France, this sex-distinction became a\nrecognized principle, moulding and modifying the design of a cathedral\nin much the same way that sex modifies bodily structure. The masonic\nguilds of the Middle Ages were custodians of the esoteric--which is\nthe theosophic--side of the Christian faith, and every student of\nesotericism knows how fundamental and how far-reaching is this idea of\nsex.\n\n[Illustration 13: CAPITAL FROM THE TOWER OF THE WINDS, ATHENS;\nCORINTHIAN CAP FROM HADRIAN BUILDINGS, ATHENS; ROSETTE FROM TEMPLE OF\nMARS, ROME; CAULICULUS OF CORINTHIAN CAP; BULUSTER BY SAN GALLO]\n\n[Illustration 14: EGG AND TONGUE; BEAD AND REEL; BANDED TORUS]\n\nThe entire cathedral symbolized the crucified body of Christ; its two\ntowers, man and woman--that Adam and that Eve for whose redemption\naccording to current teaching Christ suffered and was crucified. The\nnorth or right-hand tower (\"the man's side\") was called the sacred\nmale pillar, Jachin; and the south, or left-hand tower (\"the woman's\nside\"), the sacred female pillar, Boaz, from the two columns flanking\nthe gate to Solomon's Temple--itself an allegory to the bodily temple.\nIn only a few of the French cathedrals is this distinction clearly\nand consistently maintained, and of these Tours forms perhaps the most\nremarkable example, for in its flamboyant fa\u00e7ade, over and above the\ndifference in actual breadth and apparent sturdiness of the two towers\n(the south being the more slender and delicate), there is a clearly\nmarked distinction in the character of the ornamentation, that of the\nnorth tower being more salient, angular, radial--more masculine in\npoint of fact (Illustration 17). In Notre Dame, the cathedral of\nParis, as in the cathedral of Tours, the north tower is perceptibly\nbroader than the south. The only other important difference appears to\nbe in the angular label-mould above the north entrance: whatever may\nhave been its original function or significance, it serves to define\nthe tower sexually, so to speak, as effectively as does the beard on\na man's face. In Amiens the north tower is taller than the south, and\nmore massive in its upper stages. The only traceable indication of\nsex in the ornamentation occurs in the spandrels at the sides of the\nentrance arches: those of the north tower containing single circles,\nand those of the south tower containing two in one. This difference,\nsmall as it may seem, is significant, for in Europe during the Middle\nAges, just as anciently in Egypt and again in Greece--in fact wherever\nand whenever the Secret Doctrine was known--sex was attributed to\nnumbers, odd numbers being conceived of as masculine, and even, as\nfeminine. Two, the first feminine number, thus became a symbol of\nfemininity, accepted as such so universally at the time the cathedrals\nwere built, that two strokes of a bell announced the death of a woman,\nthree, the death of a man.\n\n[Illustration 15: FRIEZE OF THE FARNESE PALACE; ROMAN CONSOLE. VATICAN\nMUSEUM; FRIEZE IN THE EMPIRE STYLE BY PERCIER AND FONTAINE.\nFRIEZE FROM THE TEMPLE OF VESTA AT TIVOLI. (ROMAN); ROMAN DORIC\nFRIEZE--VIGNOLE]\n\n[Illustration 16]\n\n[Illustration 17]\n\nThe vital, organic quality so conspicuous in the best Gothic\narchitecture has been attributed to the fact that necessity determined\nits characteristic forms. Professor Goodyear has demonstrated that\nit may be due also in part to certain subtle vertical leans and\nhorizontal bends; and to nicely calculated variations from strict\nuniformity, which find their analogue in nature, where structure is\nseldom rigidly geometrical. The author hazards the theory that still\nanother reason why a Gothic cathedral seems so living a thing is\nbecause it abounds in contrasts between what, for lack of more\ndescriptive adjectives, he is forced to call masculine and feminine\nforms.\n\n[Illustration 18]\n\n[Illustration 19]\n\nRuskin says, in _Stones of Venice_, \"All good Gothic is nothing more\nthan the development, in various ways, and on every conceivable scale,\nof the group formed by the pointed arch for the bearing line below,\nand the gable for the protecting line above, and from the huge, gray,\nshaly slope of the cathedral roof, with its elastic pointed vaults\nbeneath, to the crown-like points that enrich the smallest niche of\nits doorway, one law and one expression will be found in all. The\nmodes of support and of decoration are infinitely various, but the\nreal character of the building, in all good Gothic, depends on the\nsingle lines of the gable over the pointed arch endlessly rearranged\nand repeated.\" These two, an angular and a curved form, like the\neverywhere recurring column and lintel of classic architecture,\nare but presentments of Yo and In (Illustration 18). Every Gothic\ntraceried window, with straight and vertical mullions in the\nrectangle, losing themselves in the intricate foliations of the arch,\ncelebrates the marriage of this ever diverse pair. The circle and the\ntriangle are the In and Yo of Gothic tracery, its Eve and Adam, as\nit were, for from their union springs that progeny of trefoil,\nquatrefoil, cinquefoil, of shapes flowing like water, and shapes\ndarting like flame, which makes such visible music to the entranced\near.\n\n[Illustration 20: SAN GIMIGNANO S. JACOPO.]\n\nBy seeking to discover In and Yo in their myriad manifestations, by\nlearning to discriminate between them, and by attempting to express\ntheir characteristic qualities in new forms of beauty--from\nthe disposition of a fa\u00e7ade to the shaping of a moulding--the\narchitectural designer will charge his work with that esoteric\nsignificance, that excess of beauty, by which architecture rises\nto the dignity of a \"fine\" art (Illustrations 19, 20). In so doing,\nhowever, he should never forget, and the layman also should ever\nremember, that the supreme architectural excellence is fitness,\nappropriateness, the perfect adaptation of means to ends, and the\nadequate expression of both means and ends. These two aims, the one\nabstract and universal, the other concrete and individual, can always\nbe combined, just as in every human countenance are combined a type,\nwhich is universal, and a character, which is individual.\n\n\n\n\nIII\n\nCHANGELESS CHANGE\n\nTRINITY, CONSONANCE, DIVERSITY IN MONOTONY, BALANCE, RHYTHMIC CHANGE,\nRADIATION\n\n\nThe preceding essay was devoted for the most part to that \"inevitable\nduality\" which finds concrete expression in countless pairs of\nopposites, such as day and night, fire and water, man and woman;\nin the art of music by two chords, one of suspense and the other of\nfulfilment; in speech by vowel and consonant sounds, epitomized in _a_\nand in _m_; in painting by warm colors and cold, epitomized in red\nand blue; in architecture by the vertical column and the horizontal\nlintel, by void and solid--and so on.\n\n\nTRINITY\n\nThis concept should now be modified by another, namely, that in every\nduality a third is latent; that two implies three, for each sex so\nto speak is in process of becoming the other, and this alternation\nengenders and is accomplished by means of a third term or neuter,\nwhich is like neither of the original two but partakes of the nature\nof them both, just as a child may resemble both its parents. Twilight\ncomes between day and night; earth is the child of fire and water;\nin music, besides the chord of longing and striving, and the chord of\nrest and satisfaction (the dominant seventh and the tonic), there is\na third or resolving chord in which the two are reconciled. In the\nsacred syllable Om (_Aum_), which epitomizes all speech, the _u_ sound\neffects a transition between the _a_ sound and the _m_; among the\nso-called primary colors yellow comes between red and blue; and in\narchitecture the arch, which is both weight and support, which is\nneither vertical nor horizontal, may be considered the neuter of the\ngroup of which the column and the lintel are respectively masculine\nand feminine. \"These are the three,\" says Mr. Louis Sullivan, \"the\nonly three letters from which has been expanded the architectural art,\nas a great and superb language wherewith man has expressed, through\nthe generations, the changing drift of his thoughts.\"\n\n[Illustration 21: THE LAW OF TRINITY. A ROMAN IONIC ARCADE, BY\nVIGNOLE.--THE COLUMN, THE ENTABLATURE, AND THE ARCH CORRESPOND TO LINES\nVERTICAL, HORIZONTAL AND CURVED.]\n\nIt would be supererogatory to dwell at any length on this \"trinity\nof manifestation\" as the concrete expression of that unmanifest and\nmystical trinity, that _three-in-one_ which under various names occurs\nin every world-religion, where, defying definition, it was wont\nto find expression symbolically in some combination of vertical,\nhorizontal and curved lines. The anstated cross of the Egyptians\nis such a symbol, the Buddhist wheel, and the fylfot or swastika\ninscribed within a circle, also those numerous Christian symbols\ncombining the circle and the cross. Such ideographs have spelled\nprofound meaning to the thinkers of past ages. We of to-day are not\ngiven to discovering anything wonderful in three strokes of a pen,\nbut every artist in the weaving of his pattern must needs employ these\nmystic symbols in one form or another, and if he employs them with\na full sense of their hidden meaning his work will be apt to gain\nin originality and beauty--for originality is a new and personal\nperception of beauty, and beauty is the name we give to truth we\ncannot understand.\n\nIn architecture, this trinity of vertical, horizontal and curved\nlines finds admirable illustration in the application of columns and\nentablature to an arch and impost construction, so common in Roman and\nRenaissance work. This is a redundancy, and finds no justification in\nreason, because the weight is sustained by the arch, and the \"order\"\nis an appendage merely; yet the combination, illogical as it is,\nsatisfies the sense of beauty because the arch effects a transition\nbetween the columns and the entablature, and completes the trinity\nof vertical, horizontal and curved lines (Illustration 21). In the\nentrances to many of the Gothic cathedrals and churches the same\nelements are better because more logically disposed. Here the\nhorizontal lintel and its vertical supports are not decorative merely,\nbut really perform their proper functions, while the arch, too, has\na raison d'\u00eatre in that it serves to relieve the lintel of the\nsuperincumbent weight of masonry. The same arrangement sometimes\noccurs in classic architecture also, as when an opening spanned by a\nsingle arch is subdivided by means of an order (Illustration 22).\n\nThree is pre-eminently the number of architecture, because it is the\nnumber of space, which for us is three-dimensional, and of all the\narts architecture is most concerned with the expression of spatial\nrelations. The division of a composition into three related parts is\nso universal that it would seem to be the result of an instinctive\naction of the human mind. The twin pylons of an Egyptian temple with\nits entrance between, for a third division, has its correspondence in\nthe two towers of a Gothic cathedral and the intervening screen\nwall of the nave. In the palaces of the Renaissance a threefold\ndivision--vertically by means of quoins or pilasters, and horizontally\nby means of cornices or string courses--was common, as was also the\ndivision into a principal and two subordinate masses (Illustration\n23).\n\n[Illustration 22: THE LAW OF TRINITY. THE TRINITY OF HORIZONTAL VERTICAL\nAND CURVED LINES.]\n\nThe architectural \"orders\" are divided threefold into pedestal or\nstylobate, column and entablature; and each of these is again divided\nthreefold: the first into plinth, die and cornice; the second into\nbase, shaft and capital; the third into architrave, frieze and\ncornice. In many cases these again lend themselves to a threefold\nsubdivision. A more detailed analysis of the capitals already shown to\nbe twofold reveals a third member: in the Greek Doric this consists\nof the annulets immediately below the abacus; in the other orders, the\nnecking which divides the shaft from the cap.\n\n\nCONSONANCE\n\n\"As is the small, so is the great\" is a perpetually recurring phrase\nin the literature of theosophy, and naturally so, for it is a succinct\nstatement of a fundamental and far-reaching truth. The scientist\nrecognizes it now and then and here and there, but the occultist\ntrusts it always and utterly. To him the microcosm and the macrocosm\nare one and the same in essence, and the forth-going impulse\nwhich calls a universe into being and the indrawing impulse which\nextinguishes it again, each lasting millions of years, are echoed and\nrepeated in the inflow and outflow of the breath through the nostrils,\nin nutrition and excretion, in daily activity and nightly rest, in\nthat longer day which we name a lifetime, and that longer rest in\n_Devachan_--and so on until time itself is transcended.\n\n[Illustration 23]\n\nIn the same way, in nature, a thing is echoed and repeated throughout\nits parts. Each leaf on a tree is itself a tree in miniature, each\nblossom a modified leaf; every vertebrate animal is a complicated\nsystem of spines; the ripple is the wave of a larger wave, and that\nlarger wave is a part of the ebbing and flowing tide. In music this\nlaw is illustrated in the return of the tonic to itself in the octave,\nand its partial return in the dominant; also in a more extended sense\nin the repetition of a major theme in the minor, or in the treble and\nagain in the bass, with modifications perhaps of time and key. In\nthe art of painting the law is exemplified in the repetition with\nvariation of certain colors and combinations of lines in different\nparts of the same picture, so disposed as to lead the eye to some\nfocal point. Every painter knows that any important color in his\npicture must be echoed, as it were, in different places, for harmony\nof the whole.\n\n[Illustration 24]\n\nIn the drama the repetition of a speech or of an entire scene, but\nunder circumstances which give it a different meaning, is often most\neffective, as when Gratiano, in the trial scene of _The Merchant\nof Venice_ taunts Shylock with his own words, \"A Daniel come to\njudgment!\" or, as when in one of the later scenes of _As You Like It_\nan earlier scene is repeated, but with Rosalind speaking in her proper\nperson and no longer as the boy Ganymede.\n\nThese recurrences, these inner consonances, these repetitions with\nvariations are common in architecture also. The channeled triglyphs of\na Greek Doric frieze echo the fluted columns below (Illustration 24).\nThe balustrade which crowns a colonnade is a repetition, in some sort,\nof the colonnade itself. The modillions of a Corinthian cornice are\nbut elaborated and embellished dentils. Each pinnacle of a Gothic\ncathedral is a little tower with its spire. As Ruskin has pointed out,\nthe great vault of the cathedral nave, together with the pointed roof\nabove it, is repeated in the entrance arch with its gable, and the\nsame two elements appear in every statue-enshrining niche of the\ndoorway. In classic architecture, as has been shown, instead of the\narch and gable, the column and entablature everywhere recur under\ndifferent forms. The minor domes which flank the great dome of the\ncathedral of Florence enhance and reinforce the latter, and prepare\nthe eye for a climax which would otherwise be too abrupt. The central\npavilion of the Ch\u00e2teau Maintenon, with its two turrets, echoes the\nentire fa\u00e7ade with its two towers. Like the overture to an opera, it\nintroduces themes which find a more extended development elsewhere\n(Illustration 26).\n\n[Illustration 25]\n\n[Illustration 26]\n\n[Illustration 27]\n\nThis law of Consonance is operative in architecture more obscurely\nin the form of recurring numerical ratios, identical geometrical\ndetermining figures, parallel diagonals and the like, which will be\ndiscussed in a subsequent essay. It has also to do with style and\nscale, the adherence to substantially one method of construction and\nmanner of ornament, just as in music the key, or chosen series of\nnotes, may not be departed from except through proper modulations, or\nin a specific manner.\n\nThus it is seen that in a work of art, as in a piece of tapestry,\nthe same thread runs through the web, but goes to make up different\nfigures. The idea is deeply theosophic: one life, many manifestations;\nhence, inevitably, echoes, resemblances--_Consonance_.\n\n\nDIVERSITY IN MONOTONY\n\nAnother principle of natural beauty, closely allied to the foregoing,\nits complement as it were, is that of _Diversity in Monotony_--not\nidentity, but difference. It shows itself for the most part as a\nperceptible and piquant variation between individual units belonging\nto the same class, type, or species.\n\nNo two trees put forth their branches in just the same manner, and no\ntwo leaves from the same tree exactly correspond; no two persons\nlook alike, though they have similiar members and features; even the\nmarkings on the skin of the thumb are different in every human hand.\nBrowning says,\n\n  \"As like as a hand to another hand!\n  Whoever said that foolish thing,\n  Could not have studied to understand--\"\n\nNow every principle of natural beauty is but the presentment of some\noccult law, some theosophical truth; and this law of Diversity in\nMonotony is the presentment of the truth that identity does not\nexclude difference. The law is binding, yet the will is free: all men\nare brothers united by the ties of brotherhood, yet each is unique, a\nfree agent, and never so free as when most bound by the Good Law. This\ntruth nature beautifully proclaims, and art also. In architecture it\nis admirably exemplified in the metopes of the Parthenon frieze: seen\nat a distance these must have presented a scarcely distinguishable\ntexture of sunlit marble and cool shadow, yet in reality each is\na separate work of art. So with the capitals of the columns of the\nwonderful sea-arcade of the Venetian Ducal palace: alike in general\ncontour they differ widely in detail, and unfold a Bible story.\nIn Gothic cathedrals, in Romanesque monastery cloisters, a teeming\nvariety of invention is hidden beneath apparent uniformity. The\ngargoyles of Notre Dame make similiar silhouettes against the sky,\nbut seen near at hand what a menagerie of monsters! The same spirit of\ncontrolled individuality, of liberty subservient to the law of all, is\nexemplified in the bases of the columns of the temple of Apollo near\nMiletus--each one a separate masterpiece of various ornamentation\nadorning an established architectural form (Illustration 28).\n\n[Illustration 28]\n\n[Illustration 29]\n\nThe builders of the early Italian churches, instinctively obeying this\nlaw of Diversity in Monotony, varied the size of the arches in the\nsame arcade (Illustration 29), and that this was an effect of art and\nnot of accident or carelessness Ruskin long ago discovered, and the\nBrooklyn Institute surveys have amply confirmed his view. Although\nby these means the builders of that day produced effects of deceptive\nperspective, of subtle concord and contrast, their sheer hatred of\nmonotony and meaningless repetition may have led them to diversify\ntheir arcades in the manner described, for a rigidly equal and regular\ndivision lacks interest and vitality.\n\n\nBALANCE\n\nIf one were to establish an axial plane vertically through the center\nof a tree, in most cases it would be found that the masses of foliage,\nhowever irregularly shaped on either side of such an axis, just about\nbalanced each other. Similarly, in all our bodily movements, for every\nchange of equilibrium there occurs an opposition and adjustment of\nmembers of such a nature that an axial plane through the center of\ngravity would divide the body into two substantially equal masses,\nas in the case of the tree. This physical plane law of Balance\nshows itself for the most part on the human plane as the law of\nCompensation, whereby, to the vision of the occultist, all accounts\nare \"squared,\" so to speak. It is in effect the law of Justice, aptly\nsymbolized by the scales.\n\nThe law of Balance finds abundant illustration in art: in music by\nthe opposition, the answering, of one phrase by another of the same\nelements and the same length, but involving a different sequence of\nintervals; in painting by the disposition of masses in such a way that\nthey about equalize one another, so that there is no sense of \"strain\"\nin the composition.\n\nIn architecture the common and obvious recognition of the law of\nBalance is in the symmetrical disposition of the elements, whether of\nplan or of elevation, on either side of axial lines. A far more subtle\nand vital illustration of the law occurs when the opposed elements do\nnot exactly match, but differ from each other, as in the case of the\ntwo towers of Amiens, for example. This sort of balance may be said to\nbe characteristic of Gothic, as symmetry is characteristic of Classic,\narchitecture.\n\n\nRHYTHMIC CHANGE\n\nThere is in nature a universal tendency toward refinement and\ncompactness of form in space, or contrariwise, toward increment\nand diffusion; and this manifests itself in time as acceleration or\nretardation. It is governed, in either case, by an exact mathematical\nlaw, like the law of falling bodies. It shows itself in the widening\ncircles which appear when one drops a stone into still water, in the\nconvolutions of shells, in the branching of trees and the veining\nof leaves; the diminution in the size of the pipes of an organ\nillustrates it, and the spacing of the frets of a guitar. More and\nmore science is coming to recognize, what theosophy affirms, that the\nspiral vortex, which so beautifully illustrates this law, both in its\ntime and its space aspects is the universal archetype, the pattern of\nall that is, has been, or will be, since it is the form assumed by the\nultimate physical atom, and the ultimate physical atom is the physical\ncosmos in miniature.\n\nThis Rhythmic Diminution is everywhere: it is in the eye itself, for\nany series of mathematically equal units, such for example as the\ncolumns and intercolumnations of a colonnade, become when seen\nin perspective rhythmically unequal, diminishing according to the\nuniversal law. The entasis of a Classic column is determined by this\nlaw, the spirals of the Ionic volute, the annulets of the Parthenon\ncap, obey it (Illustration 30).\n\nIn recognition of the same principle of Rhythmic Diminution a building\nis often made to grow, or appear to grow lighter, more intricate,\nfiner, from the ground upward, an end attained by various devices,\none of the most common being the employment of the more attenuated\nand highly ornamented orders above the simpler and sturdier, as in the\nRoman Colosseum, or in the Palazzo Uguccioni, in Florence--to mention\nonly two examples out of a great number. In the Riccardi Palace\nan effect of increasing refinement is obtained by diminishing the\nboldness of the rustication of the ashlar in successive stories; in\nthe Farnese, by the gradual reduction of the size of the angle quoins\n(Illustration 30). In an Egyptian pylon it is achieved most simply by\nbattering the wall; in a Gothic cathedral most elaborately by a\nkind of segregation, or breaking up, analogous to that which a tree\nundergoes--the strong, relatively unbroken base corresponding to\nthe trunk, the diminishing buttresses to the tapering limbs, and\nthe multitude of delicate pinnacles and crockets, to the outermost\nbranches and twigs, seen against the sky.\n\n\nRADIATION\n\nThe final principle of natural beauty to which the author would call\nattention is the law of _Radiation_, which is in a manner a return\nto the first, the law of _Unity_. The various parts of any organism\nradiate from, or otherwise refer back to common centers, or foci,\nand these to centers of their own. The law is represented in its\nsimplicity in the star-fish, in its complexity in the body of man; a\ntree springs from a seed, the solar system centers in the sun.\n\nThe idea here expressed by the term \"radiation\" is a familiar one\nto all students of theosophy. The Logos radiates his life and light\nthroughout his universe, bringing into activity a host of entities\nwhich become themselves radial centers; these generate still others,\nand so on endlessly. This principle, like every other, patiently\npublishes itself to us, unheeding, everywhere in nature, and in\nall great art as well; it is a law of optics, for example, that all\nstraight lines having a common direction if sufficiently prolonged\nappear to meet in a point, i.e., radiate from it (Illustration 31).\nLeonardo da Vinci employed this principle of perspective in his Last\nSupper to draw the spectator's eye to the picture's central figure,\nthe point of sight toward which the lines of the walls and ceiling\nconverge centering in the head of Christ. Puvis de Chavannes, in his\nBoston Library decoration, leads the eye by a system of triangulation\nto the small figure of the Genius of Enlightenment above the central\ndoor (Illustration 32); and Ruskin, in his _Elements of Drawing_, has\nshown how artfully Turner arranged some of his compositions to attract\nattention to a focal point.\n\nThis law of Radiation enters largely into architecture. The Colosseum,\nbased upon the ellipse, a figure generated from two points or foci,\nand the Pantheon, based upon the circle, a figure generated from a\ncentral point, are familiar examples. The distinctive characteristic\nof Gothic construction, the concentration or focalization of the\nweight of the vaults and arches at certain points, is another\nillustration of the same principle applied to architecture,\nbeautifully exemplified in the semicircular apse of a cathedral, where\nthe lines of the plan converge to a common center, and the ribs of the\nvaulting meet upon the capitals of the piers and columns, seeming\nto radiate thence to still other centers in the loftier vaults which\nfinally meet in a center common to all.\n\n[Illustration 30]\n\n[Illustration 31]\n\n[Illustration 32]\n\nThe tracery of the great roses, high up in the fa\u00e7ades of the\ncathedrals of Paris and of Amiens, illustrate Radiation, in the one\ncase masculine: straight, angular, direct; in the feminine: curved,\nflowing, sinuous. The same _Beautiful Necessity_ determined the\ncharacteristics of much of the ornament of widely separated styles\nand periods: the Egyptian lotus, the Greek honeysuckle, the Roman\nacanthus, Gothic leaf work--to snatch at random four blossoms from\nthe sheaf of time. The radial principle still inherent in the debased\nornament of the late Renaissance gives that ornament a unity, a\ncoherence, and a kind of beauty all its own (Illustration 35).\n\n[Illustration 33]\n\n[Illustration 34]\n\nSuch are a few of the more obvious laws of natural beauty and their\napplication to the art of architecture. The list is by no means\nexhausted, but it is not the multiplicity and diversity of these laws\nwhich is important to keep in mind, so much as their relatedness and\nco\u00f6rdination, for they are but different aspects of the One Law, that\nwhereby the Logos manifests in time and space. A brief recapitulation\nwill serve to make this correlation plain, and at the same time fix\nwhat has been written more firmly in the reader's mind.\n\n[Illustration 35]\n\n[Illustration 36]\n\nFirst comes the law of _Unity_; then, since every unit is in its\nessence twofold, there is the law of _Polarity_; but this duality is\nnot static but dynamic, the two parts acting and reacting upon one\nanother to produce a third--hence the law of _Trinity_. Given this\nthird term, and the innumerable combinations made possible by\nits relations to and reactions upon the original pair, the law\nof _Multiplicity in Unity_ naturally follows, as does the law\nof _Consonance_, or repetition, since the primal process of\ndifferentiation tends to repeat itself, and the original combinations\nto reappear--but to reappear in changed form, hence the law of\n_Diversity in Monotony_. The law of _Balance_ is seen to be but a\nmodification of the law of Polarity, and since all things are waxing\nand waning, there is the law whereby they wax and wane, that of\n_Rhythmic Change_. _Radiation_ rediscovers and reaffirms, even in the\nutmost complexity, that essential and fundamental unity from which\ncomplexity was wrought.\n\nEverything, beautiful or ugly, obeys and illustrates one or another of\nthese laws, so universal are they, so inseparably attendant upon every\nkind of manifestation in time and space. It is the number of them\nwhich finds illustration within small compass, and the aptness and\ncompleteness of such illustration, which makes for beauty, because\nbeauty is the fine flower of a sort of sublime ingenuity. A work of\nart is nothing if not _artful_: like an acrostic, the more different\nways it can be read--up, down, across, from right to left and from\nleft to right--the better it is, other things being equal. This\nstatement, of course, may be construed in such a way as to appear\nabsurd; what is meant is simply that the more a work of art is\nfreighted and fraught with meaning beyond meaning, the more secure its\nimmortality, the more powerful its appeal. For enjoyment, it is not\nnecessary that all these meanings should be fathomed, it is only\nnecessary that they should be felt.\n\nConsider for a moment the manner in which Leonardo da Vinci's Last\nSupper, an acknowledged masterpiece, conforms to everyone of the laws\nof beauty enumerated above (Illustration 32). It illustrates the law\nof Unity in that it movingly portrays a single significant episode in\nthe life of Christ. The eye is led to dwell upon the central personage\nof this drama by many artful expedients: the visible part of the\nfigure of Christ conforms to the lines of an equilateral triangle\nplaced exactly in the center of the picture; the figure is separated\nby a considerable space from the groups of the disciples on either\nhand, and stands relieved against the largest parallelogram of light,\nand the vanishing point of the perspective is in the head of Christ,\nat the apex, therefore, of the triangle. The law of Polarity finds\nfulfilment in the complex and flowing lines of the draped figures\ncontrasted with the simple parallelogram of the cloth-covered table,\nand the severe architecture of the room. The law of Trinity is\nexemplified in the three windows, and in the subdivision of the twelve\nfigures of the disciples into four groups of three figures each. The\nlaw of Consonance appears in the repetition of the horizontal lines\nof the table in the ceiling above; and in the central triangle before\nreferred to, continued and echoed, as it were, in the triangular\nsupports of the table visible underneath the cloth. The law of\nDiversity in Monotony is illustrated in the varying disposition of the\nheads of the figures in the four groups of three; the law of Balance\nin the essential symmetry of the entire composition; the law of\nRhythmic Change in the diminishing of the wall and ceiling spaces; and\nthe law of Radiation in the convergence of all the perspective lines\nto a single significant point.\n\nTo illustrate further the universality of these laws, consider now\ntheir application to a single work of architecture: the Taj Mahal, one\nof the most beautiful buildings of the world (Illustration 36). It is\na unit, but twofold, for it consists of a curved part and an angular\npart, roughly figured as an inverted cup upon a cube; each of these\n(seen in parallel perspective, at the end of the principal vista) is\nthreefold, for there are two sides and a central parallelogram, and\ntwo lesser domes flank the great dome. The composition is rich in\nconsonances, for the side arches echo the central one, the subordinate\ndomes the great dome, and the lanterns of the outstanding minarets\nrepeat the principal motif. Diversity in Monotony appears abundantly\nin the ornament, which is intricate and infinitely various; the law of\nBalance is everywhere operative in the symmetry of the entire design.\nRhythmic Change appears in the tapering of the minarets, the outlines\nof the domes and their mass relations to one another; and finally,\nthe whole effect is of radiation from a central point, of elements\ndisposed on radial lines.\n\nIt would be fatuous to contend that the prime object of a work of\narchitecture is to obey and illustrate these laws. The prime object of\na work of architecture is to fulfill certain definite conditions in a\npractical, economical, and admirable way, and in fulfilling to express\nas far as possible these conditions, making the form express the\nfunction. The architect who is also an artist however will do this\nand something beyond: working for the most part unconsciously,\nharmoniously, joyously, his building will obey and illustrate natural\nlaws--these laws of beauty--and to the extent it does so it will be a\nwork of art; for art is the method of nature carried into those higher\nregions of thought and feeling which man alone inhabits: regions which\nit is one of the purposes of theosophy to explore.\n\n\n\n\nIV\n\nTHE BODILY TEMPLE\n\n\nCarlyle says: \"There is but one temple in the world, and that is the\nbody of man.\" If the body is, as he declares, a temple, it is not less\ntrue that a temple or any work of architectural art is a larger body\nwhich man has created for his uses, just as the individual self is\nhoused within its stronghold of flesh and bones. Architectural beauty\nlike human beauty depends upon the proper subordination of parts\nto the whole, the harmonious interrelation between these parts, the\nexpressiveness of each of its function or functions, and when these\nare many and diverse, their reconcilement one with another. This being\nso, a study of the human figure with a view to analyzing the sources\nof its beauty cannot fail to be profitable. Pursued intelligently,\nsuch a study will stimulate the mind to a perception of those simple\nyet subtle laws according to which nature everywhere works, and\nit will educate the eye in the finest known school of proportion,\ntraining it to distinguish minute differences, in the same way that\nthe hearing of good music cultivates the ear.\n\nThose principles of natural beauty which formed the subject of the\ntwo preceding essays are all exemplified in the ideally perfect human\nfigure. Though essentially a unit, there is a well marked division\ninto right and left--\"Hands to hands, and feet to feet, in one body\ngrooms and brides.\" There are two arms, two legs, two ears, two eyes,\nand two lids to each eye; the nose has two nostrils, the mouth has\ntwo lips. Moreover, the terms of such pairs are masculine and feminine\nwith respect to each other, one being active and the other passive.\nOwing to the great size and one-sided position of the liver, the right\nhalf of the body is heavier than the left; the right arm is usually\nlonger and more muscular than the left; the right eye is slightly\nhigher than its fellow. In speaking and eating the lower jaw and under\nlip are active and mobile with relation to the upper; in winking it is\nthe upper eyelid which is the more active. That \"inevitable duality\"\nwhich is exhibited in the form of the body characterizes its motions\nalso. In the act of walking for example, a forward movement is\nattained by means of a forward and a backward movement of the thighs\non the axis of the hips; this leg movement becomes twofold again below\nthe knee, and the feet move up and down independently on the axis of\nthe ankle. A similar progression is followed in raising the arm and\nhand: motion is communicated first to the larger parts, through them\nto the smaller and thence to the extremities, becoming more rapid and\ncomplex as it progresses, so that all free and natural movements of\nthe limbs describe invisible lines of beauty in the air. Coexistent\nwith this pervasive duality there is a threefold division of the\nfigure into trunk, head and limbs: a superior trinity of head and\narms, and an inferior trinity of trunk and legs. The limbs are divided\nthreefold into upper-arm, forearm and hand; thigh, leg and foot. The\nhand flowers out into fingers and the foot into toes, each with a\nthreefold articulation; and in this way is effected that transition\nfrom unity to multiplicity, from simplicity to complexity, which\nappears to be so universal throughout nature, and of which a tree is\nthe perfect symbol.\n\n[Illustration 37: THE LAW OF RHYTHMIC DIMINUTION ILLUSTRATED IN THE\nTAPERING BODY, LIMBS, FINGERS & TOES.]\n\n[Illustration 38]\n\n[Illustration 39]\n\nThe body is rich in veiled repetitions, echoes, _consonances_. The\nhead and arms are in a sense a refinement upon the trunk and legs,\nthere being a clearly traceable correspondence between their various\nparts. The hand is the body in little--_\"Your soft hand is a woman of\nitself\"_--the palm, the trunk; the four fingers, the four limbs; and\nthe thumb, the head;-each finger is a little arm, each finger tip a\nlittle palm. The lips are the lids of the mouth, the lids are the\nlips of the eyes--and so on. The law of _Rhythmic Diminution_ is\nillustrated in the tapering of the entire body and of the limbs, in\nthe graduated sizes and lengths of the palm and the toes, and in\nthe successively decreasing length of the palm and the joints of the\nfingers, so that in closing the hand the fingers describe natural\nspirals (Illustrations 37, 38). Finally, the limbs radiate as it were\nfrom the trunk, the fingers from a point in the wrist, the toes from\na point in the ankle. The ribs radiate from the spinal column like the\nveins of a leaf from its midrib (Illustration 39).\n\n[Illustration 40]\n\nThe relation of these laws of beauty to the art of architecture has\nbeen shown already. They are reiterated here only to show that man is\nindeed the microcosm--a little world fashioned from the same elements\nand in accordance with the same _Beautiful Necessity_ as is the\ngreater world in which he dwells. When he builds a house or temple he\nbuilds it not literally in his own image, but according to the laws of\nhis own being, and there are correspondences not altogether fanciful\nbetween the animate body of flesh and the inanimate body of stone. Do\nwe not all of us, consciously or unconsciously, recognize the fact\nof character and physiognomy in buildings? Are they not, to our\nimagination, masculine or feminine, winning or forbidding--_human_,\nin point of fact--to a greater degree than anything else of man's\ncreating? They are this certainly to a true lover and student of\narchitecture. Seen from a distance the great French cathedrals appear\nlike crouching monsters, half beast, half human: the two towers stand\nlike a man and a woman, mysterious and gigantic, looking out over city\nand plain. The campaniles of Italy rise above the churches and houses\nlike the sentinels of a sleeping camp--nor is their strangely human\naspect wholly imaginary: these giants of mountain and campagna have\neyes and brazen tongues; rising four square, story above story, with\na belfry or lookout, like a head, atop, their likeness to a man is not\ninfrequently enhanced by a certain identity of proportion--of ratio,\nthat is, of height to width: Giotto's beautiful tower is an example.\nThe caryatid is a supporting member in the form of a woman; in the\nIonic column we discern her stiffened, like Lot's wife, into a pillar,\nwith nothing to show her feminine but the spirals of her beautiful\nhair. The columns which uphold the pediment of the Parthenon are\nunmistakably masculine: the ratio of their breadth to their height is\nthe ratio of the breadth to the height of a man (Illustration 40).\n\n[Illustration 41: THE BODY THE ARCHETYPE OF SACRED EDIFICES.]\n\n[Illustration 42: THE VESICA PISCIS AND THE PLAN OF CHARTRES.]\n\nAt certain periods of the world's history, periods of mystical\nenlightenment, men have been wont to use the human figure, the soul's\ntemple, as a sort of archetype for sacred edifices (Illustration 41).\nThe colossi, with calm inscrutable faces, which flank the entrance to\nEgyptian temples; the great bronze Buddha of Japan, with its dreaming\neyes; the little known colossal figures of India and China--all these\nbelong scarcely less to the domain of architecture than of sculpture.\nThe relation above referred to however is a matter more subtle and\noccult than mere obvious imitation on a large scale, being based upon\nsome correspondence of parts, or similarity of proportions, or both.\nThe correspondence between the innermost sanctuary or shrine of a\ntemple and the heart of a man, and between the gates of that temple\nand the organs of sense is sufficiently obvious, and a relation once\nestablished, the idea is susceptible of almost infinite development.\nThat the ancients proportioned their temples from the human figure\nis no new idea, nor is it at all surprising. The sculpture of the\nEgyptians and the Greeks reveals the fact that they studied the body\nabstractly, in its exterior presentment. It is clear that the rules\nof its proportions must have been established for sculpture, and it is\nnot unreasonable to suppose that they became canonical in architecture\nalso. Vitruvius and Alberti both lay stress on the fact that all\nsacred buildings should be founded on the proportions of the human\nbody.\n\n[Illustration 43: A GOTHIC CATHEDRAL THE SYMBOL OF THE BODY OF JESUS\nCHRIST]\n\n[Illustration 44: THE SYMBOLISM OF A GOTHIC CATHEDRAL FROM THE\nROSICRUCIANS: HARGRAVE JENNINGS]\n\nIn France, during the Middle Ages, a Gothic cathedral became, at the\nhands of the secret masonic guilds, a glorified symbol of the body\nof Christ. To practical-minded students of architectural history,\nfamiliar with the slow and halting evolution of a Gothic cathedral\nfrom a Roman basilica, such an idea may seem to be only the\nmaunderings of a mystical imagination, a theory evolved from the inner\nconsciousness, entitled to no more consideration than the familiar\nfallacy that vaulted nave of a Gothic church was an attempt to imitate\nthe green aisles of a forest. It should be remembered however that the\nhabit of the thought of that time was mystical, as that of our own age\nis utilitarian and scientific; and the chosen language of mysticism is\nalways an elaborate and involved symbolism. What could be more natural\nthan that a building devoted to the worship of a crucified Savior\nshould be made a symbol, not of the cross only, but of the body\ncrucified?\n\n[Illustration 45: THE GEOMETRICAL BASIS OF THE HUMAN FIGURE]\n\n[Illustration 46]\n\nThe _vesica piscis_ (a figure formed by the developing arcs of two\nequilateral triangles having a common side) which in so many cases\nseems to have determined the main proportion of a cathedral plan--the\ninterior length and width across the transepts--appears as an aureole\naround the figure of Christ in early representations, a fact which\ncertainly points to a relation between the two (Illustrations 42,\n43). A curious little book, _The Rosicrucians_, by Hargrave Jennings,\ncontains an interesting diagram which well illustrates this conception\nof the symbolism of a cathedral. A copy of it is here given. The apse\nis seen to correspond to the head of Christ, the north transept to his\nright hand, the south transept to the left hand, the nave to the body,\nand the north and south towers to the right and left feet respectively\n(Illustration 44).\n\n[Illustration 47]\n\nThe cathedral builders excelled all others in the artfulness with\nwhich they established and maintained a relation between their\narchitecture and the stature of a man. This is perhaps one reason why\nthe French and English cathedrals, even those of moderate dimensions\nare more truly impressive than even the largest of the great\nRenaissance structures, such as St. Peter's in Rome. A gigantic order\nfurnishes no true measure for the eye: its vastness is revealed\nonly by the accident of some human presence which forms a basis\nof comparison. That architecture is not necessarily the most\nawe-inspiring which gives the impression of having been built by\ngiants for the abode of pigmies; like the other arts, architecture is\nhighest when it is most human. The medi\u00e6val builders, true to this\ndictum, employed stones of a size proportionate to the strength of\na man working without unusual mechanical aids; the great piers and\ncolumns, built up of many such stones, were commonly subdivided\ninto clusters, and the circumference of each shaft of such a cluster\napproximated the girth of a man; by this device the moulding of the\nbase and the foliation of the caps were easily kept in scale. Wherever\na balustrade occurred it was proportioned not with relation to the\nheight of the wall or the column below, as in classic architecture,\nbut with relation to a man's stature.\n\n[Illustration 48: FIGURE DIVIDED ACCORDING TO THE EGYPTIAN CANON]\n\nIt may be stated as a general rule that every work of architecture,\nof whatever style, should have somewhere about it something fixed and\nenduring to relate it to the human figure, if it be only a flight of\nsteps in which each one is the measure of a stride. In the Farnese,\nthe Riccardi, the Strozzi, and many another Italian palace, the stone\nseat about the base gives scale to the building because the beholder\nknows instinctively that the height of such a seat must have some\nrelation to the length of a man's leg. In the Pitti palace the\nbalustrade which crowns each story answers a similar purpose: it\nstands in no intimate relation to the gigantic arches below, but is\nof a height convenient for lounging elbows. The door to Giotto's\ncampanile reveals the true size of the tower as nothing else could,\nbecause it is so evidently related to the human figure and not to the\ngreat windows higher up in the shaft.\n\n[Illustration 49: THE MEDI\u00c6VAL METHOD OF DRAWING THE FIGURE]\n\nThe geometrical plane figures which play the most important part in\narchitectural proportion are the square, the circle and the triangle;\nand the human figure is intimately related to these elementary forms.\nIf a man stand with heels together, and arms outstretched horizontally\nin opposite directions, he will be inscribed, as it were, within a\nsquare; and his arms will mark, with fair accuracy, the base of an\ninverted equilateral triangle, the apex of which will touch the ground\nat his feet. If the arms be extended upward at an angle, and the\nlegs correspondingly separated, the extremities will touch\nthe circumferences of a circle having its center in the navel\n(Illustrations 45, 46).\n\n[Illustration 50]\n\nThe figure has been variously analyzed with a view to establishing\nnumerical ratios between its parts (Illustrations 47, 48, 49). Some\nof these are so simple and easily remembered that they have obtained\na certain popular currency; such as that the length of the hand equals\nthe length of the face; that the span of the horizontally extended\narms equals the height; and the well known rule that twice around\nthe wrist is once around the neck, and twice around the neck is once\naround the waist. The Roman architect Vitruvius, writing in the age of\nAugustus C\u00e6sar, formulated the important proportions of the statues\nof classical antiquity, and except that he makes the head smaller than\nthe normal (as it should be in heroic statuary), the ratios which\nhe gives are those to which the ideally perfect male figure should\nconform. Among the ancients the foot was probably the standard of all\nlarge measurements, being a more determinate length than that of the\nhead or face, and the height was six lengths of the foot. If the head\nbe taken as a unit, the ratio becomes 1:8, and if the face--1:10.\n\nDoctor Rimmer, in his _Art Anatomy_, divides the figure into four\nparts, three of which are equal, and correspond to the lengths of\nthe leg, the thigh and the trunk; while the fourth part, which is\ntwo-thirds of one of these thirds, extends from the sternum to the\ncrown of the head. One excellence of such a division aside from its\nsimplicity, consists in the fact that it may be applied to the face as\nwell. The lowest of the three major divisions extends from the tip of\nthe chin to the base of the nose, the next coincides with the height\nof the nose (its top being level with the eyebrows), and the last with\nthe height of the forehead, while the remaining two-thirds of one of\nthese thirds represents the horizontal projection from the beginning\nof the hair on the forehead to the crown of the head. The middle of\nthe three larger divisions locates the ears, which are the same height\nas the nose (Illustrations 45, 47).\n\nSuch analyses of the figure, however conducted, reveals an\nall-pervasive harmony of parts, between which definite numerical\nrelations are traceable, and an apprehension of these should assist\nthe architectural designer to arrive at beauty of proportion by\nmethods of his own, not perhaps in the shape of rigid formul\u00e6, but\npresent in the consciousness as a restraining influence, acting and\nreacting upon the mind with a conscious intention toward rhythm and\nharmony. By means of such exercises, he will approach nearer to an\nunderstanding of that great mystery, the beauty and significance of\nnumbers, of which mystery music, architecture, and the human figure\nare equally presentments--considered, that is, from the standpoint of\nthe occultist.\n\n\n\n\nV\n\nLATENT GEOMETRY\n\n\n[Illustration 51: THE HEXAGRAM AND EQUILATERAL TRIANGLE IN NATURE]\n\nIt is a well known fact that in the microscopically minute of nature,\nunits everywhere tend to arrange themselves with relation to certain\nsimple geometrical solids, among which are the tetrahedron, the cube,\nand the sphere. This process gives rise to harmony, which may be\ndefined as the relation between parts and unity, the simplicity latent\nin the infinitely complex, the potential complexity of that which is\nsimple. Proceeding to things visible and tangible, this indwelling\nharmony, rhythm, proportion, which has its basis in geometry and\nnumber, is seen to exist in crystals, flower forms, leaf groups, and\nthe like, where it is obvious; and in the more highly organized world\nof the animal kingdom also; though here the geometry is latent rather\nthan patent, eluding though not quite defying analysis, and thus\naugmenting beauty, which like a woman is alluring in proportion as she\neludes (Illustrations 51, 52, 53).\n\n[Illustration 52: PROPORTIONS OF THE HORSE]\n\n[Illustration 53]\n\nBy the true artist, in the crystal mirror of whose mind the universal\nharmony is focused and reflected, this secret of the cause and source\nof rhythm--that it dwells in a correlation of parts based on an\nultimate simplicity--is instinctively apprehended. A knowledge of it\nformed part of the equipment of the painters who made glorious the\ngolden noon of pictorial art in Italy during the Renaissance. The\nproblem which preoccupied them was, as Symonds says of Leonardo,\n\"to submit the freest play of form to simple figures of geometry in\ngrouping.\" Alberti held that the painter should above all things have\nmastered geometry, and it is known that the study of perspective and\nkindred subjects was widespread and popular.\n\n[Illustration 54]\n\nThe first painter who deliberately rather than instinctively based\nhis compositions on geometrical principles seems to have been Fra\nBartolommeo, in his Last Judgment, in the church of St. Maria Nuova,\nin Florence. Symonds says of this picture, \"Simple figures--the\npyramid and triangle, upright, inverted, and interwoven like the\nrhymes of a sonnet--form the basis of the composition. This system was\nadhered to by the Fratre in all his subsequent works\" (Illustration\n54). Raphael, with that power of assimilation which distinguishes\nhim among men of genius, learned from Fra Bartolommeo this method\nof disposing figures and combining them in masses with almost\nmathematical precision. It would have been indeed surprising if\nLeonardo da Vinci, in whom the artist and the man of science were\nso wonderfully united, had not been greatly preoccupied with the\nmathematics of the art of painting. His Madonna of the Rocks, and\nVirgin on the Lap of Saint Anne, in the Louvre, exhibit the very\nperfection of pyramidal composition. It is however in his masterpiece,\nThe Last Supper, that he combines geometrical symmetry and precision\nwith perfect naturalness and freedom in the grouping of individually\ninteresting and dramatic figures. Michael Angelo, Andrea del Sarto,\nand the great Venetians, in whose work the art of painting may be said\nto have culminated, recognized and obeyed those mathematical laws of\ncomposition known to their immediate predecessors, and the decadence\nof the art in the ensuing period may be traced not alone to the false\nsentiment and affectation of the times, but also in the abandonment by\nthe artists of those obscurely geometrical arrangements and groupings\nwhich in the works of the greatest masters so satisfy the eye and\nhaunt the memory of the beholder (Illustrations 55, 56).\n\n[Illustration 55: THE EMPLOYMENT OF THE EQUILATERAL TRIANGLE IN\nRENAISSANCE PAINTING]\n\n[Illustration 56: GEOMETRICAL BASIS OF THE SISTINE CEILING PAINTINGS]\n\n[Illustration 57: ASSYRIAN; GREEK]\n\n[Illustration 58: THE GEOMETRICAL BASIS OF THE PLAN IN ARCHITECTURAL\nDESIGN]\n\n[Illustration 59]\n\nSculpture, even more than painting, is based on geometry. The colossi\nof Egypt, the bas-reliefs of Assyria, the figured pediments and\nmetopes of the temples of Greece, the carved tombs of Revenna,\nthe Della Robbia lunettes, the sculptured tympani of Gothic church\nportals, all alike lend themselves in greater or less degree to a\ngeometrical synopsis (Illustration 57). Whenever sculpture suffered\ndivorce from architecture the geometrical element became less\nprominent, doubtless because of all the arts architecture is the most\nclearly and closely related to geometry. Indeed, it may be said that\narchitecture is geometry made visible, in the same sense that music\nis number made audible. A building is an aggregation of the commonest\ngeometrical forms: parallelograms, prisms, pyramids and cones--the\ncylinder appearing in the column, and the hemisphere in the dome.\nThe plans likewise of the world's famous buildings reduced to their\nsimplest expression are discovered to resolve themselves into a few\nsimple geometrical figures. (Illustration 58). This is the \"bed rock\"\nof all excellent design.\n\n[Illustration 60: EGYPTIAN; GREEK; ROMAN; MEDI\u00c6VAL]\n\n[Illustration 61: JEFFERSON'S PEN SKETCH FOR THE ROTUNDA OF THE\nUNIVERSITY OF VIRGINIA]\n\n[Illustration 62: APPLICATION OF THE EQUILATERAL TRIANGLE TO THE\nERECHTHEUM AT ATHENS]\n\n[Illustration 63]\n\n[Illustration 64: THE EQUILATERAL TRIANGLE IN ROMAN ARCHITECTURE]\n\nBut architecture is geometrical in another and a higher sense than\nthis. Emerson says: \"The pleasure a palace or a temple gives the eye\nis that an order and a method has been communicated to stones, so that\nthey speak and geometrize, become tender or sublime with expression.\"\nAll truly great and beautiful works of architecture from the Egyptian\npyramids to the cathedrals of Ile-de-France--are harmoniously\nproportioned, their principal and subsidiary masses being related,\nsometimes obviously, more often obscurely, to certain symmetrical\nfigures of geometry, which though invisible to the sight and not\nconsciously present in the mind of the beholder, yet perform the\nimportant function of co\u00f6rdinating the entire fabric into one easily\nremembered whole. Upon some such principle is surely founded what\nSymonds calls \"that severe and lofty art of composition which seeks\nthe highest beauty of design in architectural harmony supreme, above\nthe melodies of gracefulness of detail.\"\n\n[Illustration 65: THE EQUILATERAL TRIANGLE IN ITALIAN ARCHITECTURE]\n\n[Illustration 66: THE HEXAGRAM IN GOTHIC ARCHITECTURE]\n\nThere is abundant evidence in support of the theory that the\nbuilders of antiquity, the masonic guilds of the Middle Ages, and\nthe architects of the Italian Renaissance, knew and followed certain\nrules, but though this theory be denied or even disproved--if after\nall these men obtained their results unconsciously--their creations\nso lend themselves to a geometrical analysis that the claim for the\nexistence of certain canons of proportion, based on geometry, remains\nunimpeached.\n\n[Illustration 67]\n\n[Illustration 68]\n\nThe plane figures principally employed in determining architectural\nproportion are the circle, the equilateral triangle, and the\nsquare--which also yields the right angled isosceles triangle. It\nwill be noted that these are the two dimensional correlatives of the\nsphere, the tetrahedron and the cube, mentioned as being among the\ndetermining forms in molecular structure. The question naturally\narises, why the circle, the equilateral triangle and the square?\nBecause, aside from the fact that they are of all plane figures the\nmost elementary, they are intimately related to the body of man, as\nhas been shown (Illustration 45), and the body of man is as it were\nthe architectural archetype. But this simply removes the inquiry to\na different field, it is not an answer. Why is the body of man so\nconstructed and related? This leads us, as does every question, to\nthe threshold of a mystery upon which theosophy alone is able to throw\nlight. Any extended elucidation would be out of place here: it is\nsufficient to remind the reader that the circle is the symbol of the\nuniverse; the equilateral triangle, of the higher trinity (_atma,\nbuddhi, manas_); and the square, of the lower quaternary of man's\nsevenfold nature.\n\n[Illustration 69]\n\n[Illustration 70]\n\nThe square is principally used in preliminary plotting: it is the\ndetermining figure in many of the palaces of the Italian Renaissance;\nthe Arc de Triomphe, in Paris is a modern example of its use\n(Illustrations 59, 60). The circle is often employed in conjunction\nwith the square and the triangle. In Thomas Jefferson's Rotunda for\nthe University of Virginia, a single great circle was the determining\nfigure, as his original pen sketch of the building shows (Illustration\n61). Some of the best Roman triumphal arches submit themselves to a\ncircular synopsis, and a system of double intersecting circles has\nbeen applied, with interesting results, to fa\u00e7ades as widely different\nas those of the Parthenon and the Farnese Palace in Rome, though\nit would be fatuous to claim that these figures determined the\nproportions of the fa\u00e7ades.\n\nBy far the most important figure in architectural proportion,\nconsidered from the standpoint of geometry, is the equilateral\ntriangle. It would seem that the eye has an especial fondness for\nthis figure, just as the ear has for certain related sounds. Indeed it\nmight not be too fanciful to assert that the common chord of any key\n(the tonic with its third and fifth) is the musical equivalent of\nthe equilateral triangle. It is scarcely necessary to dwell upon\nthe properties and unique perfection of this figure. Of all regular\npolygons it is the simplest: its three equal sides subtend equal\nangles, each of 60 degrees; it trisects the circumference of a circle;\nit is the graphic symbol of the number three, and hence of every\nthreefold thing; doubled, its generating arcs form the _vesica\npiscis_, of so frequent occurrence in early Christian art; two\nsymmetrically intersecting equilateral triangles yield the figure\nknown as \"Solomon's Seal,\" or the \"Shield of David,\" to which mystic\nproperties have always been ascribed.\n\nIt may be stated as a general rule that whenever three important\npoints in any architectural composition coincide (approximately or\nexactly) with the three extremities of an equilateral triangle, it\nmakes for beauty of proportion. An ancient and notable example occurs\nin the pyramids of Egypt, the sides of which, in their original\ncondition, are believed to have been equilateral triangles. It is a\ndemonstrable fact that certain geometrical intersections yield the\nimportant proportions of Greek architecture. The perfect little\nErechtheum would seem to have been proportioned by means of the\nequilateral triangle and the angle of 60 degrees, both in general and\nin detail (Illustration 62). The same angle, erected from the central\naxis of a column at the point where it intersects the architrave,\ndetermines both the projection of the cornice and the height of\nthe architrave in many of the finest Greek and Roman temples\n(Illustrations 67-70). The equilateral triangle used in conjunction\nwith the circle and the square was employed by the Romans in\ndetermining the proportions of triumphal arches, basilicas and\nbaths. That the same figure was a factor in the designing of Gothic\ncathedrals is sufficiently indicated in the accompanying facsimile\nreproductions of an illustration from the Como Vitruvius, published in\nMilan in 1521, which shows a vertical section of the Milan cathedral\nand the system of equilateral triangles which determined its various\nparts (Illustration 71). The _vesica piscis_ was often used to\nestablish the two main internal dimensions of the cathedral plan: the\ngreatest diameter of the figure corresponding with the width across\nthe transepts, the upper apex marking the limit of the apse, and the\nlower, the termination of the nave. Such a proportion is seen to be\nboth subtle and simple, and possesses the advantage of being easily\nlaid out. The architects of the Italian Renaissance doubtless\ninherited certain of the Roman canons of architectural proportion,\nfor they seem very generally to have recognized them as an essential\nprinciple of design.\n\n[Illustration 71]\n\nNevertheless, when all is said, it is easy to exaggerate the\nimportance of this matter of geometrical proportion. The designer\nwho seeks the ultimate secret of architectural harmony in mathematics\nrather than in the trained eye, is following the wrong road to\nsuccess. A happy inspiration is worth all the formul\u00e6 in the world--if\nit be really happy, the artist will probably find that he has\n\"followed the rules without knowing them.\" Even while formulating\nconcepts of art, the author must reiterate Schopenhauer's dictum\nthat the _concept_ is unfruitful in art. The mathematical analysis\nof spatial beauty is an interesting study, and a useful one to the\nartist; but it can never take the place of the creative faculty, it\ncan only supplement, restrain, direct it. The study of proportion is\nto the architect what the study of harmony is to a musician--it helps\nhis genius adequately to express itself.\n\n\n\n\nVI\n\nTHE ARITHMETIC OF BEAUTY\n\n\nAlthough architecture is based primarily upon geometry, it is possible\nto express all spatial relations numerically: for arithmetic, not\ngeometry, is the universal science of quantity. The relation of masses\none to another--of voids to solids, and of heights and lengths to\nwidths--forms ratios; and when such ratios are simple and harmonious,\narchitecture may be said, in Walter Pater's famous phrase, to\n\"aspire towards the condition of music.\" The trained eye, and not an\narithmetical formula, determines what is, and what is not, beautiful\nproportion. Nevertheless the fact that the eye instinctively rejects\ncertain proportions as unpleasing, and accepts others as satisfactory,\nis an indication of the existence of laws of space, based upon number,\nnot unlike those which govern musical harmony. The secret of the deep\nreasonableness of such selection by the senses lies hidden in the very\nnature of number itself, for number is the invisible thread on which\nthe worlds are strung--the universe abstractly symbolized.\n\nNumber is the within of all things--the \"first form of Brahman.\" It\nis the measure of time and space; it lurks in the heart-beat and is\nblazoned upon the starred canopy of night. Substance, in a state of\nvibration, in other words conditioned by number, ceaselessly undergoes\nthe myriad transmutations which produce phenomenal life. Elements\nseparate and combine chemically according to numerical ratios:\n\"Moon, plant, gas, crystal, are concrete geometry and number.\" By\nthe Pythagoreans and by the ancient Egyptians sex was attributed to\nnumbers, odd numbers being conceived of as masculine or generating,\nand even numbers as feminine or parturitive, on account of their\ninfinite divisibility. Harmonious combinations were those\ninvolving the marriage of a masculine and a feminine--an odd and an\neven--number.\n\n[Illustration 72: A GRAPHIC SYSTEM OF NOTATION]\n\nNumbers progress from unity to infinity, and return again to unity as\nthe soul, defined by Pythagoras as a self-moving number, goes forth\nfrom, and returns to God. These two acts, one of projection and the\nother of recall; these two forces, centrifugal and centripetal, are\nsymbolized in the operations of addition and subtraction. Within them\nis embraced the whole of computation; but because every number, every\naggregation of units, is also a new unit capable of being added\nor subtracted, there are also the operations of multiplication and\ndivision, which consists in one case of the addition of several equal\nnumbers together, and in the other, of the subtraction of several\nequal numbers from a greater until that is exhausted. In order to\nthink correctly it is necessary to consider the whole of numeration,\ncomputation, and all mathematical processes whatsoever as _the\ndivision of the unit_ into its component parts and the establishment\nof relations between these parts.\n\n[Illustration 73]\n\n[Illustration 74]\n\nThe progression and retrogression of numbers in groups expressed by\nthe multiplication table gives rise to what may be termed \"numerical\nconjunctions.\" These are analogous to astronomical conjunctions: the\nplanets, revolving around the sun at different rates of speed, and\nin widely separated orbits, at certain times come into line with one\nanother and with the sun. They are then said to be in conjunction.\nSimilarly, numbers, advancing toward infinity singly and in groups\n(expressed by the multiplication table), at certain stages of their\nprogression come into relation with one another. For example, an\nimportant conjunction occurs in 12, for of a series of twos it is\nthe sixth, of threes the fourth, of fours the third, and of sixes the\nsecond. It stands to 8 in the ratio of 3:2, and to 9, of 4:3. It is\nrelated to 7 through being the product of 3 and 4, of which numbers 7\nis the sum. The numbers 11 and 13 are not conjunctive; 14 is so in\nthe series of twos, and sevens; 15 is so in the series of fives and\nthrees. The next conjunction after 12, of 3 and 4 and their first\nmultiples, is in 24, and the next following is in 36, which numbers\nare respectively the two and three of a series of twelves, each end\nbeing but a new beginning.\n\n[Illustration 75]\n\nIt will be seen that this discovery of numerical conjunctions consists\nmerely of resolving numbers into their prime factors, and that a\nconjunctive number is a common multiple; but by naming it so, to\ndismiss the entire subject as known and exhausted, is to miss a\nsense of the wonder, beauty and rhythm of it all: a mental impression\nanalogous to that made upon the eye by the swift-glancing balls of a\njuggler, the evolutions of drilling troops, or the intricate figures\nof a dance; for these things are number concrete and animate in time\nand space.\n\n[Illustration 76]\n\nThe truths of number are of all truths the most interior, abstract\nand difficult of apprehension, and since knowledge becomes clear and\ndefinite to the extent that it can be made to enter the mind through\nthe channels of physical sense, it is well to accustom oneself to\nconceiving of number graphically, by means of geometrical symbols\n(Illustration 72), rather than in terms of the familiar arabic\nnotation which though admirable for purposes of computation, is of\ntoo condensed and arbitrary a character to reveal the properties of\nindividual numbers. To state, for example, that 4 is the first square,\nand 8 the first cube, conveys but a vague idea to most persons, but if\n4 be represented as a square enclosing four smaller squares, and 8\nas a cube containing eight smaller cubes, the idea is apprehended\nimmediately and without effort. The number 3 is of course the\ntriangle; the irregular and vital beauty of the number 5 appears\nclearly in the heptalpha, or five-pointed star; the faultless symmetry\nof 6, its relation to 3 and 2, and its regular division of the circle,\nare portrayed in the familiar hexagram known as the Shield of David.\nSeven, when represented as a compact group of circles reveals itself\nas a number of singular beauty and perfection, worthy of the important\nplace accorded to it in all mystical philosophy (Illustration 73). It\nis a curious fact that when asked to think of any number less than 10,\nmost persons will choose 7.\n\n[Illustration 77]\n\nEvery form of art, though primarily a vehicle for the expression and\ntransmission of particular ideas and emotions, has subsidiary offices,\njust as a musical tone has harmonics which render it more sweet.\nPainting reveals the nature of color; music, of sound--in wood,\nin brass, and in stretched strings; architecture shows forth the\nqualities of light, and the strength and beauty of materials. All\nof the arts, and particularly music and architecture, portray in\ndifferent manners and degrees the truths of number. Architecture does\nthis in two ways: esoterically as it were in the form of harmonic\nproportions; and exoterically in the form of symbols which represent\nnumbers and groups of numbers. The fact that a series of threes and\na series of fours mutually conjoin in 12, finds an architectural\nexpression in the Tuscan, the Doric, and the Ionic orders according to\nVignole, for in them all the stylobate is four parts, the entablature\n3, and the intermediate column 12 (Illustration 74). The affinity\nbetween 4 and 7, revealed in the fact that they express (very nearly)\nthe ratio between the base and the altitude of the right-angled\ntriangle which forms half of an equilateral, and the musical interval\nof the diminished seventh, is architecturally suggested in the Palazzo\nGiraud, which is four stories in height with seven openings in each\nstory (Illustration 75).\n\n[Illustration 78]\n\n[Illustration 79]\n\n[Illustration 80]\n\n[Illustration 81]\n\nEvery building is a symbol of some number or group of numbers, and\nother things being equal the more perfect the numbers involved the\nmore beautiful will be the building (Illustrations 76-82). The numbers\n5 and 7--those which occur oftenest--are the most satisfactory because\nbeing of small quantity, they are easily grasped by the eye, and being\nodd, they yield a center or axis, so necessary in every architectural\ncomposition. Next in value are the lowest multiples of these numbers\nand the least common multiples of any two of them, because the\neye, with a little assistance, is able to resolve them into their\nconstituent factors. It is part of the art of architecture to\nrender such assistance, for the eye counts always, consciously or\nunconsciously, and when it is confronted with a number of units\ngreater than it can readily resolve, it is refreshed and rested if\nthese units are so grouped and arranged that they reveal themselves as\nfactors of some higher quantity.\n\n[Illustration 82]\n\n[Illustration 83: A NUMERICAL ANALYSIS OF GOTHIC TRACERY]\n\nThere is a raison d'\u00eatre for string courses other than to mark the\nposition of a floor on the interior of a building, and for quoins and\npilasters other than to indicate the presence of a transverse wall.\nThese sometimes serve the useful purpose of so subdividing a fa\u00e7ade\nthat the eye estimates the number of its openings without conscious\neffort and consequent fatigue (Illustration 82). The tracery of Gothic\nwindows forms perhaps the highest and finest architectural expression\nof number (Illustration 83). Just as thirst makes water more sweet, so\ndoes Gothic tracery confuse the eye with its complexity only the more\ngreatly to gratify the sight by revealing the inherent simplicity in\nwhich this complexity has its root. Sometimes, as in the case of\nthe Venetian Ducal Palace, the numbers involved are too great for\ncounting, but other and different arithmetical truths are portrayed;\nfor example, the multiplication of the first arcade by 2 in\nthe second, and this by 3 in the cusped arches, and by 4 in the\nquatrefoils immediately above.\n\n[Illustration 84: NUMERATION IN GROUPS EXPRESSED ARCHITECTURALLY]\n\n[Illustration 85: ARCHITECTURAL ORNAMENT CONSIDERED AS THE\nOBJECTIFICATION OF NUMBER. MULTIPLICATION IN GROUPS OF FIVE; TWO;\nTHREE; ALTERNATION OF THREE AND SEVEN]\n\n[Illustration 86]\n\nSeven is proverbially the perfect number. It is of a quantity\nsufficiently complex to stimulate the eye to resolve it, and yet so\nsimple that it can be analyzed at a glance; as a center with two equal\nsides, it is possessed of symmetry, and as the sum of an odd and even\nnumber (3 and 4) it has vitality and variety. All these properties a\nwork of architecture can variously reveal (Illustration 77). Fifteen,\nalso, is a number of great perfection. It is possible to arrange the\nfirst 9 numbers in the form of a \"magic\" square so that the sum of\neach line, read vertically, horizontally or diagonally, will be 15.\nThus:\n\n     4    9    2   =  15\n     3    5    7   =  15\n     8    1    6   =  15\n    --   --   --\n    15   15   15\n\nIts beauty is portrayed geometrically in the accompanying figure which\nexpresses it, being 15 triangles in three groups of 5 (Illustration\n86). Few arrangements of openings in a fa\u00e7ade better satisfy the eye\nthan three superimposed groups of five (Illustrations 76-80). May not\none source of this satisfaction dwell in the intrinsic beauty of the\nnumber 15?\n\nIn conclusion, it is perhaps well that the reader be again reminded\nthat these are the by-ways, and not the highways of architecture: that\nthe highest beauty comes always, not from beautiful numbers, nor\nfrom likenesses to Nature's eternal patterns of the world, but from\nutility, fitness, economy, and the perfect adaptation of means to\nends. But along with this truth there goes another: that in every\nexcellent work of architecture, in addition to its obvious and\nindividual beauty, there dwells an esoteric and universal beauty,\nfollowing as it does the archetypal pattern laid down by the Great\nArchitect for the building of that temple which is the world wherein\nwe dwell.\n\n\n\n\nVII\n\nFROZEN MUSIC\n\n\nIn the series of essays of which this is the final one, the author has\nundertaken to enforce the truth that evolution on any plane and on\nany scale proceeds according to certain laws which are in reality only\nramifications of one ubiquitous and ever operative law; that this law\nregisters itself in the thing evolved, leaving stamped thereon as it\nwere fossil footprints by means of which it may be known. In the arts\nthe creative spirit of man is at its freest and finest, and nowhere\namong the arts is it so free and so fine as in music. In music\naccordingly the universal law of becoming finds instant, direct\nand perfect self-expression; music voices the inner nature of the\n_will-to-live_ in all its moods and moments; in it form, content,\nmeans and end are perfectly fused. It is this fact which gives\nvalidity to the before quoted saying that all of the arts \"aspire\ntoward the condition of music.\" All aspire to express the law, but\nmusic, being least encumbered by the leaden burden of materiality,\nexpresses it most easily and adequately. This being so there is\nnothing unreasonable in attempting to apply the known facts of musical\nharmony and rhythm to any other art, and since these essays concern\nthemselves primarily with architecture, the final aspect in which\nthat art will be presented here is as \"frozen music\"--ponderable form\ngoverned by musical law.\n\nMusic depends primarily upon the equal and regular division of time\ninto beats, and of these beats into measures. Over this soundless and\ninvisible warp is woven an infinitely various melodic pattern, made\nup of tones of different pitch and duration arithmetically related\nand combined according to the laws of harmony. Architecture,\ncorrespondingly, implies the rhythmical division of space, and\nobedience to laws numerical and geometrical. A certain identity\ntherefore exists between simple harmony in music, and simple\nproportion in architecture. By translating the consonant\ntone-intervals into number, the common denominator, as it were, of\nboth arts, it is possible to give these intervals a spatial, and\nhence an architectural, expression. Such expression, considered as\nproportion only and divorced from ornament, will prove pleasing to\nthe eye in the same way that its correlative is pleasing to the ear,\nbecause in either case it is not alone the special organ of sense\nwhich is gratified, but the inner Self, in which all senses are one.\nContaining within itself the mystery of number, it thrills responsive\nto every audible or visible presentment of that mystery.\n\n[Illustration 87]\n\nIf a vibrating string yielding a certain musical note be stopped in\nits center, that is, divided by half, it will then sound the octave\nof that note. The numerical ratio which expresses the interval of\nthe octave is therefore 1:2. If one-third instead of one-half of the\nstring be stopped, and the remaining two-thirds struck, it will yield\nthe musical fifth of the original note, which thus corresponds to the\nratio 2:3. The length represented by 3:4 yields the fourth; 4:5 the\nmajor third; and 5:6 the minor third. These comprise the principal\nconsonant intervals within the range of one octave. The ratios of\ninverted intervals, so called, are found by doubling the smaller\nnumber of the original interval as given above: 2:3, the fifth, gives\n3:4, the fourth; 4:5, the major third, gives 5:8, the minor sixth;\n5:6, the minor third, gives 6:10, or 3:5, the major sixth.\n\n[Illustration 88: ARCHITECTURE AS HARMONY]\n\nOf these various consonant intervals the octave, fifth, and major\nthird are the most important, in the sense of being the most perfect,\nand they are expressed by numbers of the smallest quantity, an odd\nnumber and an even. It will be noted that all the intervals above\ngiven are expressed by the numbers 1, 2, 3, 4, 5 and 6, except the\nminor sixth (5:8), and this is the most imperfect of all consonant\nintervals. The sub-minor seventh, expressed by the ratio 4:7 though\nincluded among the dissonances, forms, according to Helmholtz, a more\nperfect consonance with the tonic than does the minor sixth.\n\nA natural deduction from these facts is that relations of\narchitectural length and breadth, height and width, to be \"musical\"\nshould be capable of being expressed by ratios of quantitively small\nnumbers, preferably an odd number and an even. Although generally\nspeaking the simpler the numerical ratio the more perfect the\nconsonance, yet the intervals of the fifth and major third (2:3 and\n4:5), are considered to be more pleasing than the octave (1:2), which\nis too obviously a repetition of the original note. From this it is\nreasonable to assume (and the assumption is borne out by experience),\nthat proportions, the numerical ratios of which the eye resolves too\nreadily, become at last wearisome. The relation should be felt rather\nthan fathomed. There should be a perception of identity, and also\nof difference. As in music, where dissonances are introduced to give\nvalue to consonances which follow them, so in architecture simple\nratios should be employed in connection with those more complex.\n\n[Illustration 89]\n\nHarmonics are those tones which sound with, and reinforce any musical\nnote when it is sounded. The distinguishable harmonics of the tonic\nyield the ratios 1:2, 2:3, 3:4, 4:5, and 4:7. A note and its harmonics\nform a natural chord. They may be compared to the widening circles\nwhich appear in still water when a stone is dropped into it, for when\na musical sound disturbs the quietude of that pool of silence which\nwe call the air, it ripples into overtones, which becoming fainter\nand fainter, die away into silence. It would seem reasonable to assume\nthat the combination of numbers which express these overtones, if\ntranslated into terms of space, would yield proportions agreeable\nto the eye, and such is the fact, as the accompanying examples\nsufficiently indicate (Illustrations 87-90).\n\nThe interval of the sub-minor seventh (4:7), used in this way, in\nconnection with the simpler intervals of the octave (1:2), and the\nfifth (2:3), is particularly pleasing because it is neither too\nobvious nor too subtle. This ratio of 4:7 is important for the reason\nthat it expresses the angle of sixty degrees, that is, the numbers 4\nand 7 represent (very nearly) the ratio between one-half the base and\nthe altitude of an equilateral triangle: also because they form part\nof the numerical series 1, 4, 7, 10, etc. Both are \"mystic\" numbers,\nand in Gothic architecture particularly, proportions were frequently\ndetermined by numbers to which a mystic meaning was attached.\nAccording to Gwilt, the Gothic chapels of Windsor and Oxford are\ndivided longitudinally by four, and transversely by seven equal parts.\nThe arcade above the roses in the fa\u00e7ade of the cathedral of Tours\nshows seven principal units across the front of the nave, and four in\neach of the towers.\n\nA distinguishing characteristic of the series of ratios which\nrepresent the consonant intervals within the compass of an octave is\nthat it advances by the addition of 1 to both terms: 1:2, 2:3,\n3:4, 4:5, and 5:6. Such a series always approaches unity, just as,\nrepresented graphically by means of parallelograms, it tends toward a\nsquare. Alberti in his book presents a design for a tower showing his\nidea for its general proportions. It consists of six stories, in a\nsequence of orders. The lowest story is a perfect cube and each of the\nother stories is 11-12ths of the story below, diminishing practically\nin the proportion of 8, 7, 6, 5, 4, 3, allowing in each case for the\namount hidden by the projection of the cornice below; each order being\naccurate as regards column, entablature, etc. It is of interest to\ncompare this with Ruskin's idea in his _Seven Lamps_, where he takes\nthe case of a plant called Alisma Plantago, in which the various\nbranches diminish in the proportion of 7, 6, 5, 4, 3, respectively,\nand so carry out the same idea; on which Ruskin observes that\ndiminution in a building should be after the manner of Nature.\n\n[Illustration 90: ARCADE OF THE CANCELLERIA]\n\nIt would be a profitless task to formulate exact rules of\narchitectural proportion based upon the laws of musical harmony. The\ntwo arts are too different from each other for that, and moreover\nthe last appeal must always be to the eye, and not to a mathematical\nformula, just as in music the last appeal is to the ear. Laws there\nare, but they discover themselves to the artist as he proceeds, and\nare for the most part incommunicable. Rules and formul\u00e6 are useful and\nvaluable not as a substitute for inspiration, but as a guide: not as\nwings, but as a tail. In this connection perhaps all that is necessary\nfor the architectural designer to bear in mind is that important\nratios of length and breadth, height and width, to be \"musical\" should\nbe expressed by quantitively small numbers, and that if possible they\nshould obey some simple law of numerical progression. From this basic\nsimplicity complexity will follow, but it will be an ordered and\nharmonious complexity, like that of a tree, or of a symphony.\n\n[Illustration 91: THE PALAZZO VERZI AT VERONA (LOWER PORTION ONLY).\nA COMPOSITION FOUNDED ON THE EQUAL AND REGULAR DIVISION OF SPACE, AS\nMUSIC IS FOUNDED ON THE EQUAL AND REGULAR DIVISION OF TIME.]\n\n[Illustration 92: ARCHITECTURE AS RHYTHM. A DIVISION OF SPACE\nCORRESPONDING TO 3/4 AND 4/4 TIME.]\n\nIn the same way that a musical composition implies the division of\ntime into equal and regular beats, so a work of architecture should\nhave for its basis some unit of space. This unit should be nowhere too\nobvious and may be varied within certain limits, just as musical time\nis retarded or accelerated. The underlying rhythm and symmetry will\nthus give value and distinction to such variation. Vasari tells how\nBrunelleschi. Bramante and Leonardo da Vinci used to work on paper\nruled in squares, describing it as a \"truly ingenious thing, and of\ngreat utility in the work of design.\" By this means they developed\nproportions according to a definite scheme. They set to work with a\ndivision of space analogous to the musician's division of time.\nThe examples given herewith indicate how close a parallel may exist\nbetween music and architecture in this matter of rhythm (Illustrations\n91-93).\n\n[Illustration 93]\n\nIt is a demonstrable fact that musical sounds weave invisible patterns\nin the air. Architecture, correspondingly, in one of its aspects,\nis geometric pattern made fixed and enduring. What could be more\nessentially musical for example than the sea arcade of the Venetian\nDucal Palace? The sand forms traced by sound-waves on a musically\nvibrating steel plate might easily suggest architectural ornament did\nnot the differences of scale and of material tend to confuse the mind.\nThe architect should occupy himself with identities, not differences.\nIf he will but bear in mind that architecture is pattern in space,\njust as music is pattern in time, he will come to perceive the\nessential identity between, say, a Greek rosette and a Gothic\nrose-window; an arcade and an egg and dart moulding (Illustration 94).\nAll architectural forms and arrangements which give enduring pleasure\nare in their essence musical. Every well composed fa\u00e7ade makes harmony\nin three dimensions; every good roof-line sings a melody against the\nsky.\n\n[Illustration 94: ARCHITECTURE AS PATTERN]\n\n\n\n\nCONCLUSION\n\n\nIn taking leave of the reader at the end of this excursion together\namong the by-ways of a beautiful art, the author must needs add a\nfinal word or two touching upon the purpose and scope of these essays.\nArchitecture (like everything else) has two aspects: it may be viewed\nfrom the standpoint of utility, that is, as construction; or from the\nstandpoint of expressiveness, that is, as decoration. No attempt has\nbeen made here to deal with its first aspect, and of the second\n(which is again twofold), only the universal, not the particular\nexpressiveness has been sought. The literature of architecture is rich\nin works dealing with the utilitarian and constructive side of the\nart: indeed, it may be said that to this side that literature is\nalmost exclusively devoted. This being so, it has seemed worth while\nto attempt to show the reverse of the medal, even though it be \"tails\"\ninstead of \"heads.\"\n\nIt will be noted that the inductive method has not, in these pages,\nbeen honored by a due observance. It would have been easy to\nhave treated the subject inductively, amassing facts and drawing\nconclusions, but to have done so the author would have been false\nto the very principle about which the work came into being. With the\nacceptance of the Ancient Wisdom, the inductive method becomes\nno longer necessary. Facts are not useful in order to establish a\nhypothesis, they are used rather to elucidate a known and accepted\ntruth. When theosophical ideas shall have permeated the thought of\nmankind, this work, if it survives at all, will be chiefly--perhaps\nsolely--remarkable by reason of the fact that it was among the\nfirst in which the attempt was made again to unify science, art and\nreligion, as they were unified in those ancient times and among those\nancient peoples when the Wisdom swayed the hearts and minds of men.","title":"The Beautiful Necessity: Seven Essays on Theosophy and Architecture","tradition":"philosophy-ethics","translated_text":null,"word_count":22321}