Chapter II: The Fourth Dimension (1)

The subject of the fourth dimension is not an easy one to understand. Fortunately the artist in design does not need to penetrate far into these fascinating halls of thought in order to reap the advantage which he seeks. Nevertheless an intention of mind upon this "fairy-tale of mathematics" cannot fail to enlarge his intellectual and spiritual horizons, and develop his imagination--that finest instrument in all his chest of tools.

By way of introduction to the subject Prof. James Byrnie Shaw, in an article in the _Scientific Monthly_, has this to say:

Up to the period of the Reformation algebraic equations of
more than the third degree were frowned upon as having no
real meaning, since there is no fourth power or dimension.
But about one hundred years ago this chimera became an actual
existence, and today it is furnishing a new world to physics,
in which mechanics may become geometry, time be co-ordinated
with space, and every geometric theorem in the world is a
physical theorem in the experimental world in study in the
laboratory. Startling indeed it is to the scientist to be told
that an artificial dream-world of the mathematician is
more real than that he sees with his galvanometers,
ultra-microscopes, and spectroscopes. It matters little that
he replies, "Your four-dimensional world is only an analytic
explanation of my phenomena," for the fact remains a fact,
that in the mathematician's four-dimensional space there is
a space not derived in any sense of the term as a residue of
experience, however powerful a distillation of sensations or
perceptions be resorted to, for it is not contained at all in
the fluid that experience furnishes. It is a product of the
creative power of the mathematical mind, and its objects are
real in exactly the same way that the cube, the square, the
circle, the sphere or the straight line. We are enabled to see
with the penetrating vision of the mathematical insight that
no less real and no more real are these fantastic forms of the
world of relativity than those supposed to be uncreatable or
indestructible in the play of the forces of nature.

These "fantastic forms" alone need concern the artist. If by some potent magic he can precipitate them into the world of sensuous images so that they make music to the eye, he need not even enter into the question of their reality, but in order to achieve this transmutation he should know something, at least, of the strange laws of their being, should lend ear to a fairy-tale in which each theorem is a paradox, and each paradox a mathematical fact.

He must conceive of a space of four mutually independent directions; a space, that is, having a direction at right angles to every direction that we know. We cannot point to this, we cannot picture it, but we can reason about it with a precision that is all but absolute. In such a space it would of course be possible to establish four axial lines, all intersecting at a point, and all mutually at right angles with one another. Every hyper-solid of four-dimensional space has these four axes.

The regular hyper-solids (analogous to the Platonic solids of three-dimensional space) are the "fantastic forms" which will prove useful to the artist. He should learn to lure them forth along them axis lines. That is, let him build up his figures, space by space, developing them from lower spaces to higher. But since he cannot enter the fourth dimension, and build them there, nor even the third--if he confines himself to a sheet of paper--he must seek out some form of _representation_ of the higher in the lower. This is a process with which he is already acquainted, for he employs it every time he makes a perspective drawing, which is the representation of a solid on a plane. All that is required is an extension of the method: a hyper-solid can be represented in a figure of three dimensions, and this in turn can be projected on a plane. The achieved result will constitute a perspective of a perspective--the representation of a representation.

This may sound obscure to the uninitiated, and it is true that the plane projection of some of the regular hyper-solids are staggeringly intricate affairs, but the author is so sure that this matter lies so well within the compass of the average non-mathematical mind that he is willing to put his confidence to a practical test.

It is proposed to develop a representation of the tesseract or hyper-cube on the paper of this page, that is, on a space of two dimensions. Let us start as far back as we can: with a point. This point, a, [Figure 14] is conceived to move in a direction w, developing the line a b. This line next moves in a direction at right angles to w, namely, x, a distance equal to its length, forming the square a b c d. Now for the square to develop into a cube by a movement into the third dimension it would have to move in a direction at right angles to both w and x, that is, out of the plane of the paper--away from it altogether, either up or down. This is not possible, of course, but the third direction can be _represented_ on the plane of the paper.

Let us represent it as diagonally downward toward the right, namely, y. In the y direction, then, and at a distance equal to the length of one of the sides of the square, another square is drawn, a'b'c'd', representing the original square at the end of its movement into the third dimension; and because in that movement the bounding points of the square have traced out lines (edges), it is necessary to connect the corresponding corners of the two squares by means of lines. This completes the figure and achieves the representation of a cube on a plane by a perfectly simple and familiar process. Its six faces are easily identified by the eye, though only two of them appear as squares owing to the exigencies of representation.

Now for a leap into the abyss, which won't be so terrifying, since it involves no change of method. The cube must move into the fourth dimension, developing there a hyper-cube. This is impossible, for the reason the cube would have to move out of our space altogether--three-dimensional space will not contain a hyper-cube. But neither is the cube itself contained within the plane of the paper; it is only there _represented_. The y direction had to be imagined and then arbitrarily established; we can arbitrarily establish the fourth direction in the same way. As this is at right angles to y, its indication may be diagonally downward and to the left--the direction z. As y is known to be at right angles both to w and to x, z is at right angles to all three, and we have thus established the four mutually perpendicular axes necessary to complete the figure.

The cube must now move in the z direction (the fourth dimension) a distance equal to the length of one of its sides. Just as we did previously in the case of the square, we draw the cube in its new position (ABB'D'C'C) and also as before we connect each apex of the first cube with the corresponding apex of the other, because each of these points generates a line (an edge), each line a plane, and each plane a solid. This is the tesseract or hyper-cube in plane projection. It has the 16 points, 32 lines, and 8 cubes known to compose the figure. These cubes occur in pairs, and may be readily identified.[1]

The tesseract as portrayed in A, Figure 14, is shown according to the conventions of oblique, or two-point perspective; it can equally be represented in a manner correspondent to parallel perspective. The parallel perspective of a cube appears as a square inside another square, with lines connecting the four vertices of the one with those of the other. The third dimension (the one beyond the plane of the paper) is here conceived of as being not beyond the boundaries of the first square, but _within_ them. We may with equal propriety conceive of the fourth dimension as a "beyond which is within." In that case we would have a rendering of the tesseract as shown in B, Figure 14: a cube within a cube, the space between the two being occupied by six truncated pyramids, each representing a cube. The large outside cube represents the original generating cube at the beginning of its motion into the fourth dimension, and the small inside cube represents it at the end of that motion.

These two projections of the tesseract upon plane space are not the only ones possible, but they are typical. Some idea of the variety of aspects may be gained by imagining how a nest of inter-related cubes (made of wire, so as to interpenetrate), combined into a single symmetrical figure of three-dimensional space, would appear from several different directions. Each view would yield new space-subdivisions, and all would be rhythmical--susceptible, therefore, of translation into ornament. C and D represent such translations of A and B.

In order to fix these unfamiliar ideas more firmly in the reader's mind, let him submit himself to one more exercise of the creative imagination, and construct, by a slightly different method, a representation of a hexadecahedroid, or 16-hedroid, on a plane. This regular solid of four-dimensional space consists of sixteen cells, each a regular tetrahedron, thirty-two triangular faces, twenty-four edges and eight vertices. It is the correlative of the octahedron of three-dimensional space.

First it is necessary to establish our four axes, all mutually at right angles. If we draw three lines intersecting at a point, subtending angles of 60 degrees each, it is not difficult to conceive of these lines as being at right angles with one another in three-dimensional space. The fourth axis we will assume to pass vertically through the point of intersection of the three lines, so that we see it only in cross-section, that is, as a point. It is important to remember that all of the angles made by the four axes are right angles--a thing possible only in a space of four dimensions. Because the 16-hedroid is a symmetrical hyper-solid all of its eight apexes will be equidistant from the centre of a containing hyper-sphere, whose "surface" these will intersect at symmetrically disposed points. These apexes are established in our representation by describing a circle--the plane projection of the hyper-sphere--about the central point of intersection of the axes. (Figure 15, left.) Where each of these intersects the circle an apex of the 16-hedroid will be established. From each apex it is now necessary to draw straight lines to every other, each line representing one edge of the sixteen tetrahedral cells. But because the two ends of the fourth axis are directly opposite one another, and opposite the point of sight, all of these lines fail to appear in the left hand diagram. It therefore becomes necessary to _tilt_ the figure slightly, bringing into view the fourth axis, much foreshortened, and with it, all of the lines which make up the figure. The result is that projection of the 16-hedroid shown at the right of Figure 15.[2] Here is no fortuitous arrangement of lines and areas, but the "shadow" cast by an archetypal, figure of higher space upon the plane of our materiality. It is a wonder, a mystery, staggering to the imagination, contradictory to experience, but as well entitled to a place at the high court of reason as are any of the more familiar figures with which geometry deals. Translated into ornament it produces such an all-over pattern as is shown in Figure 16 and the design which adorns the curtains at right and left of pl. XIII. There are also other interesting projections of the 16-hedroid which need not be gone into here.

For if the author has been successful in his exposition up to this point, it should be sufficiently plain that the geometry of four-dimensions is capable of yielding fresh and interesting ornamental motifs. In carrying his demonstration farther, and in multiplying illustrations, he would only be going over ground already covered in his book _Projective Ornament_ and in his second Scammon lecture.

Of course this elaborate mechanism for producing quite obvious and even ordinary decorative motifs may appear to some readers like Goldberg's nightmare mechanics, wherein the most absurd and intricate devices are made to accomplish the most simple ends. The author is undisturbed by such criticisms. If the designs dealt with in this chapter are "obvious and even ordinary" they are so for the reason that they were chosen less with an eye to their interest and beauty than as lending themselves to development and demonstration by an orderly process which should not put too great a tax upon the patience and intelligence of the reader. Four-dimensional geometry yields numberless other patterns whose beauty and interest could not possibly be impeached--patterns beyond the compass of the cleverest designer unacquainted with projective geometry.

The great need of the ornamentalist is this or some other solid foundation. Lacking it, he has been forced to build either on the shifting sands of his own fancy, or on the wrecks and sediment of the past. Geometry provides this sure foundation. We may have to work hard and dig deep, but the results will be worth the effort, for only on such a foundation can arise a temple which is beautiful and strong.

In confirmation of his general contention that the basis of all effective decoration is geometry and number, the author, in closing, desires to direct the reader's attention to Figure 17 a slightly modified rendering of the famous zodiacal ceiling of the Temple of Denderah, in Egypt. A sun and its corona have been substituted for the zodiacal signs and symbols which fill the centre of the original, for except to an Egyptologist these are meaningless. In all essentials the drawing faithfully follows the original--was traced, indeed, from a measured drawing.

Here is one of the most magnificent decorative schemes in the whole world, arranged with a feeling for balance and rhythm exceeding the power of the modern artist, and executed with a mastery beyond the compass of a modern craftsman. The fact that first forces itself upon the beholder is that the thing is so obviously mathematical in its rhythms, that to reduce it to terms of geometry and number is a matter of small difficulty. Compare the frozen music of these rhymed and linked figures with the herded, confused, and cluttered compositions of even our best decorative artists, and argument becomes unnecessary--the fact stands forth that we have lost something precious and vital out of art of which the ancients possessed the secret.

It is for the restoration of these ancient verities and the discovery of new spatial rhythms--made possible by the advance of mathematical science--that the author pleads. Artists, architects, designers, instead of chewing the cud of current fashion, come into these pastures new!

[Footnote 1: The eight cubes in A, Figure 14, are as follows: abb'd'c'c; ABB'D'C'C; abdDCA; a'b'd'D'C'A'; abb'B'A'A; cdd'D'C'C; bb'd'D'DB; aa'c'C'CA.]

[Footnote 2: The sixteen cells of the hexadehahedroid are as follows: ABCD: A'B'C'D': AB'C'D': A'BCD: AB'CD: A'BC'D: ABC'D: A'B'CD': ABCD': A'B'C'D: ABC'D': A'B'CD: A'BC'D: AB'CD': A'BCD': AB'C'D.]

HARNESSING THE RAINBOW

Reference was made in an antecedent essay to an art of light--of mobile color--an abstract language of thought and emotion which should speak to consciousness through the eye, as music speaks through the ear. This is an art unborn, though quickening in the womb of the future. The things that reflect light have been organized æsthetically into the arts of architecture, painting, and sculpture, but light itself has never been thus organized.

And yet the scientific development and control of light has reached a stage which makes this new art possible. It awaits only the advent of the creative artist. The manipulation of light is now in the hands of the illuminating engineers and its exploitation (in other than necessary ways) in the hands of the advertisers.

Some results of their collaboration are seen in the sky signs of upper Broadway, in New York, and of the lake front, in Chicago. A carnival of contending vulgarities, showing no artistry other than the most puerile, these displays nevertheless yield an effect of amazing beauty. This is on account of an occult property inherent in the nature of light--_it cannot be vulgarized_. If the manipulation of light were delivered into the hands of the artist, and dedicated to noble ends, it is impossible to overestimate the augmentation of beauty that would ensue.

For light is a far more potent medium than sound. The sphere of sound is the earth-sphere; the little limits of our atmosphere mark the uttermost boundaries to which sound, even the most strident can possibly prevail. But the medium of light is the ether, which links us with the most distant stars. May not this serve as a symbol of the potency of light to usher the human spirit into realms of being at the doors of which music itself shall beat in vain? Or if we compare the universe accessible to sight with that accessible to sound--the plight of the blind in contrast to that of the deaf--there is the same discrepancy; the field of the eye is immensely richer, more various and more interesting than that of the ear.

The difficulty appears to consist in the inferior impressionability of the eye to its particular order of beauty. To the average man color--as color--has nothing significant to say: to him grass is green, snow is white, the sky blue; and to have his attention drawn to the fact that sometimes grass is yellow, snow blue, and the sky green, is disconcerting rather than illuminating. It is only when his retina is assaulted by some splendid sunset or sky-encircling rainbow that he is able to disassociate the idea of color from that of form and substance. Even the artist is at a disadvantage in this respect, when compared with the musician. Nothing in color knowledge and analysis analogous to the established laws of musical harmony is part of the equipment of the average artist; he plays, as it were, by ear. The scientist, on the other hand, though he may know the spectrum from end to end, and its innumerable modifications, values this "rainbow promise of the Lord" not for its own beautiful sake but as a means to other ends than those of beauty. But just as the art of music has developed the ear into a fine and sensitive instrument of appreciation, so an analogous art of light would educate the eye to nuances of color to which it is now blind.

It is interesting to speculate as to the particular form in which this new art will manifest itself. The question is perhaps already answered in the "color organ," the earliest of which was Bambridge Bishop's, exhibited at the old Barnum's Museum--before the days of electric light--and the latest A.W. Rimington's. Both of these instruments were built upon a supposed correspondence between a given scale of colors, and the musical chromatic scale; they were played from a musical score upon an organ keyboard. This is sufficiently easy and sufficiently obvious, and has been done, with varying success in one way or another, time and again, but its very ease and obviousness should give us pause.

It may well be questioned whether any arbitrary and literal translation, even though practicable, of a highly complex, intensely mobile art, unfolding in time, as does music, into a correspondent light and color expression, is the best approach to a new art of mobile color. There is a deep and abiding conviction, justified by the history of æsthetics, that each art-form must progress from its own beginnings and unfold in its own unique and characteristic way. Correspondences between the arts--such a correspondence, for example, as inspired the famous saying that architecture is frozen music--reveal themselves usually only after the sister arts have attained an independent maturity. They owe their origin to that underlying unity upon which our various modes of sensuous perception act as a refracting medium, and must therefore be taken for granted. Each art, like each individual, is unique and singular; in this singularity dwells its most thrilling appeal. We are likely to miss light's crowning glory, and the rainbow's most moving message to the soul if we preoccupy ourselves too exclusively with the identities existing between music and color; it is rather their points of difference which should first be dwelt upon.

Let us accordingly consider the characteristic differences between the two sense-categories to which sound and light--music and color--respectively belong. This resolves itself into a comparison between time and space. The characteristic thing about time is succession--hence the very idea of music, which is in time, involves perpetual change. The characteristic of space, on the other hand, is simultaneousness--in space alone perpetual immobility would reign. That is why architecture, which is pre-eminently the art of space, is of all the arts the most static. Light and color are essentially of space, and therefore an art of mobile colour should never lack a certain serenity and repose. A "tune" played on a color organ is only distressing. If there is a workable correspondence between the musical art and an art of mobile color, it will be found in the domain of harmony which involves the idea of simultaneity, rather than in melody, which is pure succession. This fundamental difference between time and space cannot be over-emphasized. A musical note prolonged, becomes at last scarcely tolerable; while a beautiful color, like the blue of the sky, we can enjoy all day and every day. The changing hues of a sunset, are _andante_ if referred to a musical standard, but to the eye they are _allegretto_--we would have them pass less swiftly than they do. The winking, chasing, changing lights of illuminated sky-signs are only annoying, and for the same reason. The eye longs for repose in some serene radiance or stately sequence, while the ear delights in contrast and continual change. It may be that as the eye becomes more educated it will demand more movement and complexity, but a certain stillness and serenity are of the very nature of light, as movement and passion are of the very nature of sound. Music is a seeking--"love in search of a word"; light is a finding--a "divine covenant."

With attention still focussed on the differences rather than the similarities between the musical art and a new art of mobile color, we come next to the consideration of the matter of form. Now form is essentially of space: we speak about the "form" of a musical composition, but it is in a more or less figurative and metaphysical sense, not as a thing concrete and palpable, like the forms of space. It would be foolish to forego the advantage of linking up form with colour, as there is opportunity to do. Here is another golden ball to juggle with, one which no art purely in time affords. Of course it is known that musical sounds weave invisible patterns in the air, and to render these patterns perceptible to the eye may be one of the more remote and recondite achievements of our uncreated art. Meantime, though we have the whole treasury of natural forms to draw from, of these we can only properly employ such as are _abstract_. The reason for this is clear to any one who conceives of an art of mobile color, not as a moving picture show--a thing of quick-passing concrete images, to shock, to startle, or to charm--but as a rich and various language in which light, proverbially the symbol of the spirit, is made to speak, through the senses, some healing message to the soul. For such a consummation, "devoutly to be wished," natural forms--forms abounding in every kind of association with that world of materiality from which we would escape--are out of place; recourse must be had rather to abstract forms, that is, geometrical figures. And because the more remote these are from the things of sense, from knowledge and experience, the projected figures of four-dimensional geometry would lend themselves to these uses with an especial grace. Color without form is as a soul without a body; yet the body of light must be without any taint of materiality. Four-dimensional forms are as immaterial as anything that could be imagined and they could be made to serve the useful purpose of separating colors one from another, as lead lines do in old cathedral windows, than which nothing more beautiful has ever been devised.

Coming now to the consideration, not of differences, but similarities, it is clear that a correspondence can be established between the colors of the spectrum and the notes of a musical scale. That is, the spectrum, considered as the analogue of a musical octave can be subdivided into twelve colors which may be representative of the musical chromatic scale of twelve semi-tones: the very word, _chromatic_, being suggestive of such a correspondence between sound and light. The red end of the spectrum would naturally relate to the low notes of the musical scale, and the violet end to the high, by reason of the relative rapidity of vibration in each case; for the octave of a musical note sets the air vibrating twice as rapidly as does the note itself, and roughly speaking, the same is true of the end colors of the spectrum with relation to the ether.

But assuming that a color scale can be established which would yield a color correlative to any musical note or chord, there still remains the matter of _values_ to be dealt with. In the musical scale there is a practical equality of values: one note is as potent as another. In a color scale, on the other hand, each note (taken at its greatest intensity) has a positive value of its own, and they are all different. These values have no musical correlatives, they belong to color _per se_. Every colorist knows that the whole secret of beauty and brilliance dwells in a proper understanding and adjustment of values, and music is powerless to help him here. Let us therefore defer the discussion of this musical parallel, which is full of pitfalls, until we have made some examination into such simple emotional reactions as color can be discovered to yield. The musical art began from the emotional response to certain simple tones and combinations, and the delight of the ear in their repetition and variation.

On account of our undeveloped sensitivity, the emotional reactions to color are found to be largely personal and whimsical: one person "loves" pink, another purple, or green. Color therapeutics is too new a thing to be relied upon for data, for even though colors are susceptible of classification as sedative, recuperative and stimulating, no two classifications arrived at independently would be likely to correspond. Most people appear to prefer bright, pure colors when presented to them in small areas, red and blue being the favourites. Certain data have been accumulated regarding the physiological effect and psychological value of different colors, but this order of research is in its infancy, and we shall have recourse, therefore, to theory, in the absence of any safer guide.

One of the theories which may be said to have justified itself in practice in a different field is that upon which is based Delsarte's famous art of expression. It has schooled some of the finest actors in the world, and raised others from mediocrity to distinction. The Delsarte system is founded upon the idea that man is a triplicity of physical, emotional, and intellectual qualities or attributes, and that the entire body and every part thereof conforms to, and expresses this triplicity. The generative and digestive region corresponds with the physical nature, the breast with the emotional, and the head with the intellectual; "below" represents the nadir of ignorance and dejection, "above" the zenith of wisdom and spiritual power. This seems a natural, and not an arbitrary classification, having interesting confirmations and correspondencies, both in the outer world of form, and in the inner world of consciousness. Moreover, it is in accord with that theosophic scheme derived from the ancient and august wisdom of the East, which longer and better than any other has withstood the obliterating action of slow time, and is even now renascent. Let us therefore attempt to classify the colors of the spectrum according to this theory, and discover if we can how nearly such a classification is conformable to reason and experience.

The red end of the spectrum, being lowest in vibratory rate, would correspond to the physical nature, proverbially more sluggish than the emotional and mental. The phrase "like a red rag to a bull," suggests a relation between the color red and the animal consciousness established by observation. The "low-brow" is the dear lover of the red necktie; the "high-brow" is he who sees violet shadows on the snow. We "see red" when we are dominated by ignoble passion. Though the color green is associated with the idea of jealousy, it is associated also with the idea of sympathy, and jealousy in the last analysis is the fear of the loss of sympathy; it belongs, at all events to the mediant, or emotional group of colors; while blue and violet are proverbially intellectual and spiritual colors, and their place in the spectrum therefore conforms to the demands of our theoretical division. Here, then, is something reasonably certain, certainly reasonable, and may serve as an hypothesis to be confirmed or confuted by subsequent research. Coming now finally to the consideration of the musical parallel, let us divide a color scale of twelve steps or semi-tones into three groups; each group, graphically portrayed, subtending one-third of the arc of a circle. The first or red group will be related to the physical nature, and will consist of purple-red, red, red-orange, and orange. The second, or green group will be related to the emotional nature, and will consist of yellow, yellow-green, green, and green-blue. The third, or blue group will be related to the intellectual and spiritual nature, and will consist of blue, blue-violet, violet and purple. The merging of purple into purple-red will then correspond to the meeting place of the highest with the lowest, "spirit" and "matter." We conceive of this meeting-place symbolically as the "heart"--the vital centre. Now "sanguine" is the appropriate name associated with the color of the blood--a color between purple and purple-red. It is logical, therefore, to regard this point in our color-scale as its tonic--"middle C"--though each color, just as in music each note, is itself the tonic of a scale of its own.

Mr. Louis Wilson--the author of the above "ophthalmic color scale" makes the same affiliation between sanguine, or blood color, and middle C, led thereto by scientific reasons entirely unassociated with symbolism. He has omitted orange-yellow and violet-purple; this makes the scale conform more exactly with the diatonic scale of two tetra-chords; it also gives a greater range of purples, a color indispensable to the artist. Moreover, in the scale as it stands, each color is exactly opposite its true spectral complementary.

The color scale being thus established and broadly divided, the next step is to find how well it justifies itself in practice. The most direct way would be to translate the musical chords recognized and dealt with in the science of harmony into their corresponding color combinations.

For the benefit of such readers as have no knowledge of musical harmony it should be said that the entire science of harmony is based upon the _triad_, or chord of three notes, and that there are various kinds of triads: the major, the minor, the augmented, the diminished, and the altered. The major triad consists of the first note of the diatonic scale, or tonic; its third, and its fifth. The minor triad differs from the major only in that the second member is lowered a semi-tone. The augmented triad differs from the major only in that the third member is raised a semi-tone. The diminished triad differs from the minor only in that the third member is lowered a semi-tone. The altered triad is a chord different by a semi-tone from any of the above.

The major triad in color is formed by taking any one of the twelve color-centers of the ophthalmic color scale as the first member of the triad; and, reading up the scale, the fifth step (each step representing a semi-tone) determines the second member, while the third member is found in the eighth step. The minor triad in color is formed by lowering the second member of the major triad one step; the augmented triad by raising the third member of the major triad one step, and the diminished triad by lowering the third member of the minor triad one step.

These various triads are shown graphically in Figure 18 as triangles within a circle divided into twelve equal parts, each part representing a semi-tone of the chromatic scale. It is seen at a glance that in every case each triad has one of its notes (an apex) in or immediately adjacent to a different one of the grand divisions of the colour scale hereinbefore established and described, and that the same thing would be true in any "key": that is, by any variation of the point of departure.

This certainly satisfies the mind in that it suggests variety in unity, balance, completeness, and in the actual portrayal, in color, of these chords in any "key" this judgment is confirmed by the eye, provided that the colors have been thrown into proper _harmonic suppression_. By this is meant such an adjustment of relative values, or such an establishment of relative proportions as will produce the maximum of beauty of which any given combination is capable. This matter imperatively demands an æsthetic sense the most sensitive.

So this "musical parallel," interesting and reasonable as it is, will not carry the color harmonist very far, and if followed too literally it is even likely to hamper him in the higher reaches of his art, for some of the musical dissonances are of great beauty in color translation. All that can safely be said in regard to the musical parallel in its present stage of development is that it simplifies and systematizes color knowledge and experiment and to a beginner it is highly educational.

If we are to have color symphonies, the best are not likely to be those based on a literal translation of some musical masterpiece into color according to this or any theory, but those created by persons who are emotionally reactive to this medium, able to imagine in color, and to treat it imaginatively. The most beautiful mobile color effects yet witnessed by the author were produced on a field only five inches square, by an eminent painter quite ignorant of music; while some of the most unimpressive have been the result of a rigid adherence to the musical parallel by persons intent on cutting, with this sword, this Gordian knot.

Into the subject of means and methods it is not proposed to enter, nor to attempt to answer such questions as to whether the light shall be direct or projected; whether the spectator, wrapped in darkness, shall watch the music unfold at the end of some mysterious vista, or whether his whole organism shall be played upon by powerful waves of multi-coloured light. These coupled alternatives are not mutually exclusive, any more than the idea of an orchestra is exclusive of that of a single human voice.

In imagining an art of mobile color unconditioned by considerations of mechanical difficulty or of expense, ideas multiply in truly bewildering profusion. Sunsets, solar coronas, star spectra, auroras such as were never seen on sea or land; rainbows, bubbles, rippling water; flaming volcanoes, lava streams of living light--these and a hundred other enthralling and perfectly realizable effects suggest themselves. What Israfil of the future will pour on mortals this new "music of the spheres"?

LOUIS SULLIVAN

PROPHET OF DEMOCRACY

Due tribute has been paid to Mr. Louis Sullivan as an architect in the first essay of this volume. That aspect of his genius has been critically dealt with by many, but as an author he is scarcely known. Yet there are Sibylline leaves of his, still let us hope in circulation, which have wielded a potent influence on the minds of a generation of men now passing to maturity. It is in the hope that his message may not be lost to the youth of today and of tomorrow that the present author now undertakes to summarize and interpret that message to a public to which Mr. Sullivan is indeed a name, but not a voice.

That he is not a voice can be attributed neither to his lack of eloquence--for he is eloquent--nor to the indifference of the younger generation of architects which has grown up since he has ceased, in any public way, to speak. It is due rather to a curious fatality whereby his memorabilia have been confined to sheets which the winds of time have scattered--pamphlets, ephemeral magazines, trade journals--never the bound volume which alone guards the sacred flame from the gusts of evil chance.

And Mr. Sullivan's is a "sacred flame," because it was kindled solely with the idea of service--a beacon to keep young men from shipwreck traversing those straits made dangerous by the Scylla of Conventionality, and the Charybdis of License. The labour his writing cost him was enormous. "I shall never again make so great a sacrifice for the younger generation," he says in a letter, "I am amazed to note how insignificant, how almost nil is the effect produced, in comparison to the cost, in vitality to me. Or perhaps it is I who am in error. Perhaps one must have reached middle age, or the Indian Summer of life, must have seen much, heard much, felt and produced much and been much in solitude to receive in reading what I gave in writing 'with hands overfull.'"

This was written with reference to _Kindergarten Chats. A sketch Analysis of Contemporaneous American Architecture_, which constitutes Mr. Sullivan's most extended and characteristic preachment to the young men of his day. It appeared in 1901, in fifty-two consecutive numbers of _The Interstate Architect and Builder_, a magazine now no longer published. In it the author, as mentor, leads an imaginary disciple up and down the land, pointing out to him the "bold, upholsterrific blunders" to be found in the architecture of the day, and commenting on them in a caustic, colloquial style--large, loose, discursive--a blend of Ruskin, Carlyle and Whitman, yet all Mr. Sullivan's own. He descends, at times, almost to ribaldry, at others he rises to poetic and prophetic heights. This is all a part of his method alternately to shame and inspire his pupil to some sort of creative activity. The syllabus of Mr. Sullivan's scheme, as it existed in his mind during the writing of _Kindergarten Chats_, and outlined by him in a letter to the author is such a torch of illumination that it is quoted here entire.

A young man who has "finished his education" at the
architectural schools comes to me for a post-graduate
course--hence a free form of dialogue.

I proceed with his education rather by indirection and
suggestion than by direct precept. I subject him to certain
experiences and allow the impressions they make on him to
infiltrate, and, as I note the effect, I gradually use a
guiding hand. I supply the yeast, so to speak, and allow the
ferment to work in him.

This is the gist of the whole scheme. It remains then to
determine, carefully, the kind of experiences to which I shall
subject the lad, and in what order, or logical (and especially
psychological) sequence. I begin, then, with aspects that
are literal, objective, more or less cynical, and brutal, and
philistine. A little at a time I introduce the subjective,
the refined, the altruistic; and, by a to-and-fro increasingly
intense rhythm of these two opposing themes, worked so to
speak in counterpoint, I reach a preliminary climax: of
brutality tempered by a longing for nobler, purer things.

Hence arise a purblind revulsion and yearning in the lad's
soul; the psychological moment has arrived, and I take him
at once into the _country_--(Summer: The Storm). This is the
first of the four out-of-door scenes, and the lad's first
real experience with nature. It impresses him crudely but
violently; and in the tense excitement of the tempest he is
inspired to temporary eloquence; and at the close is much
softened. He feels in a way but does not know that he has been
a participant in one of Nature's superb dramas. (Thus do
I insidiously prepare the way for the notion that creative
architecture is in essence a dramatic art, and an art of
eloquence; of subtle rhythmic beauty, power, and tenderness).

Left alone in the country the lad becomes maudlin--a callow
lover of nature--and makes feeble attempts at verse. Returning
to the city he melts and unbosoms--the tender shaft of the
unknowable Eros has penetrated to his heart--Nature's subtle
spell is on him, to disappear and reappear. Then follow
discussions, more or less didactic, leading to the second
out-of-door scene (Autumn Glory). Here the lad does most of
the talking and shows a certain lucidity and calm of mind. The
discussion of Responsibility, Democracy, Education, etc., has
inevitably detached the lurking spirit of pessimism. It has
to be:--Into the depths and darkness we descend, and the
work reaches the tragic climax in the third out-of-door
scene--Winter.

Now that the forces have been gathered and marshalled the
true, sane movement of the work is entered upon and pushed
at high tension, and with swift, copious modulations to its
foreordained climax and optimistic peroration in the fourth
and last out-of-door scene as portrayed in the Spring Song.
The _locale_ of this closing number is the beautiful spot in
the woods, on the shore of Biloxi Bay:--where I am writing
this.

I would suggest in passing that a considerable part of the
K.C. is in rhythmic prose--some of it declamatory. I have
endeavoured throughout this work to represent, or reproduce
to the mind and heart of the reader the spoken word and
intonation--not written language. It really should be read
aloud, especially the descriptive and exalted passages.

There was a movement once on the part of Mr. Sullivan's admirers to issue _Kindergarten Chats_ in book form, but he was asked to tone it down and expurgate it, a thing which he very naturally refused to do. Mr. Sullivan has always been completely alive to our cowardice when it comes to hearing the truth about ourselves, and alive to the danger which this cowardice entails, for to his imaginary pupil he says,

If you wish to read the current architecture of your country,
you must go at it courageously, and not pick out merely the
little bits that please you. I am going to soak you with it
until you are absolutely nauseated, and your faculties turn
in rebellion. I may be a hard taskmaster, but I strive to be
a good one. When I am through with you, you will know
architecture from the ground up. You will know its virtuous
reality and you will know the fake and the fraud and the
humbug. I will spare nothing--for your sake. I will stir up
the cesspool to its utmost depths of stench, and also the
pious, hypocritical virtues of our so-called architecture--the
nice, good, mealy-mouthed, suave, dexterous, diplomatic
architecture, I will show you also the kind of architecture
our "cultured" people believe in. And why do they believe in
it? Because they do not believe in themselves.

_Kindergarten Chats_ is even more pertinent and pointed today than it was some twenty years ago, when it was written. Speech that is full of truth is timeless, and therefore prophetic. Mr. Sullivan forecast some of the very evils by which we have been overtaken. He was able to do this on account of the fundamental soundness of his point of view, which finds expression in the following words: "Once you learn to look upon architecture not merely as an art more or less well, or more or less badly done, but as a _social manifestation_, the critical eye becomes clairvoyant, and obscure, unnoted phenomena become illumined."

Looking, from this point of view, at the office buildings that the then newly-realized possibilities of steel construction were sending skyward along lower Broadway, in New York, Mr. Sullivan reads in them a denial of democracy. To him they signify much more than they seem to, or mean to; they are more than the betrayal of architectural ignorance and mendacity, they are symptomatic of forces undermining American life.

These buildings, as they increase in number, make this city
poorer, morally and spiritually; they drag it down and down
into the mire. This is not American civilization; it is the
rottenness of Gomorrah. This is not Democracy--it is savagery.
It shows the glutton hunt for the Dollar with no thought for
aught else under the sun or over the earth. It is decadence of
the spirit in its most revolting form; it is rottenness of
the heart and corruption of the mind. So truly does this
architecture reflect the causes which have brought it into
being. Such structures are _profoundly anti-social_, and as
such, they must be reckoned with. These buildings are not
architecture, but outlawry, and their authors criminals in the
true sense of the word. And such is the architecture of lower
New York--hopeless, degraded, and putrid in its pessimistic
denial of our art, and of our growing civilization--its
cynical contempt for all those qualities that real humans
value.

We have always been very glib about democracy; we have assumed that this country was a democracy because we named it so. But now that we are called upon to die for the idea, we find that we have never realized it anywhere except perhaps in our secret hearts. In the life of Abraham Lincoln, in the poetry of Walt Whitman, in the architecture of Louis Sullivan, the spirit of democracy found utterance, and to the extent that we ourselves partake of that spirit, it will find utterance also in us. Mr. Sullivan is a "prophet of democracy" not alone in his buildings but in his writings, and the prophetic note is sounded even more clearly in his _What is Architecture? A Study in the American People of Today_, than in _Kindergarten Chats_.

This essay was first printed in _The American Contractor_ of January 6, 1906, and afterwards issued in brochure form. The author starts by tracing architecture to its root in the human mind: this physical thing is the manifestation of a psychological state. As a man thinks, so he is; he acts according to his thought, and if that act takes the form of a building it is an emanation of his inmost life, and reveals it.

Everything is there for us to read, to interpret; and this
we may do at our leisure. The building has not means of
locomotion, it cannot hide itself, it cannot get away. There
it is, and there it will stay--telling more truths about him
who made it, than he in his fatuity imagines; revealing his
mind and his heart exactly for what they are worth, not a whit
more, not a whit less; telling plainly the lies he thinks;
telling with almost cruel truthfulness his bad faith, his
feeble, wabbly mind, his impudence, his selfish egoism, his
mental irresponsibility, his apathy, his disdain for real
things--until at last the building says to us: "I am no more a
real building than the thing that made me is a real man!"

Language like this stings and burns, but it is just such as is needful to shame us out of our comfortable apathy, to arouse us to new responsibilities, new opportunities. Mr. Sullivan, awake among the sleepers, drenches us with bucketfuls of cold, tonic, energizing truth. The poppy and mandragora of the past, of Europe, poisons us, but in this, our hour of battle, we must not be permitted to dream on. He saw, from far back, that "we, as a people, not only have betrayed each other, but have failed in that trust which the world spirit of democracy placed in our hands, as we, a new people, emerged to fill a new and spacious land." It has taken a world war to make us see the situation as he saw it, and it is to us, a militant nation, and not to the slothful civilians a decade ago, that Mr. Sullivan's stirring message seems to be addressed.

The following quotation is his first crack of the whip at the architectural schools. The problem of education is to him of all things the most vital; in this essay he returns to it again and again, while of _Kindergarten Chats_ it is the very _raison d'être_.

I trust that a long disquisition is not necessary in order to
show that the attempt at imitation, by us, of this day, of the
by-gone forms of building, is a procedure unworthy of a free
people; and that the dictum of the schools, that Architecture
is finished and done, is a suggestion humiliating to every
active brain, and therefore, in fact, a puerility and a
falsehood when weighed in the scales of truly democratic
thought. Such dictum gives the lie in arrogant fashion, to
healthful human experience. It says, in a word: the American
people are not fit for democracy.

He finds the schools saturated with superstitions which are the survivals of the scholasticism of past centuries--feudal institutions, in effect, inimical to his idea of the true spirit of democratic education. This he conceives of as a searching-out, liberating, and developing the splendid but obscured powers of the average man, and particularly those of children. "It is disquieting to note," he says, "that the system of education on which we lavish funds with such generous, even prodigal, hand, falls short of fulfilling its true democratic function; and that particularly in the so-called higher branches its tendency appears daily more reactionary, more feudal. It is not an agreeable reflection that so many of our university graduates lack the trained ability to see clearly, and to think clearly, concisely, constructively; that there is perhaps more showing of cynicism than good faith, seemingly more distrust of men than confidence in them, and, withal, no consummate ability to interpret things."

In contrast to the schoolman he sketches the psychology of the active-minded but "uneducated" man, with sympathy and understanding, the man who is courageously seeking a way with little to guide and help him.

Is it not the part of wisdom to cheer, to encourage such a
mind, rather than dishearten it with ridicule? To say to it:
Learn that the mind works best when allowed to work naturally;
learn to do what your problem suggests when you have reduced
it to its simplest terms; you will thus find that all
problems, however complex, take on a simplicity you had
not dreamed of; accept this simplicity boldly, and with
confidence, do not lose your nerve and run away from it, or
you are lost, for you are here at the point men so heedlessly
call genius--as though it were necessarily rare; for you are
here at the point no living brain can surpass in essence,
the point all truly great minds seek--the point of vital
simplicity--the point of view which so illuminates the mind
that the art of expression becomes spontaneous, powerful, and
unerring, and achievement a certainty. So, if you seek and
express the best that is in yourself, you must search out the
best that is in your people; for they are your problem, and
you are indissolubly a part of them. It is for you to affirm
that which they really wish to affirm, namely, the best that
is in them, and they as truly wish you to express the best
that is in yourself. If the people seem to have but little
faith it is because they have been tricked so long; they are
weary of dishonesty, more weary than they know, much more
weary than you know, and in their hearts they seek honest and
fearless men, men simple and clear in mind, loyal to their own
manhood and to the people. The American people are now in a
stupor; be on hand at the awakening.

Next he pays his respects to current architectural criticism--a straining at gnats and a swallowing of camels, by minds "benumbed by culture," and hearts made faint by the tyranny of precedent. He complains that they make no distinction between _was_ and _is_, too readily assuming that all that is left us moderns is the humble privilege to select, copy and adapt.