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Architecture and Democracy by Claude Fayette Bragdon

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ARCHITECTURE AND DEMOCRACY

BY

CLAUDE BRAGDON
F.A.I.A.

1918

[Illustration: PLATE I. THE WOOLWORTH BUILDING, NEW YORK]

PREFACE

This book can lay no claim to unity of theme, since its subjects range
from skyscrapers to symbols and soul states; but the author claims for
it nevertheless a unity of point of view, and one (correct or not) so
comprehensive as to include in one synthesis every subject dealt
with. For according to that point of view, a skyscraper is only a
symbol--and of what? A condition of consciousness, that is, a state of
the soul. Democracy even, we are beginning to discover, is a condition
of consciousness too.

Our only hope of understanding the welter of life in which we are
immersed, as in a swift and muddy river, is in ascending as near
to its pure source as we can. That source is in consciousness and
consciousness is in ourselves. This is the point of view from which
each problem dealt with has been attacked; but lest the author be at
once set down as an impracticable dreamer, dwelling aloof in an ivory
tower, the reader should know that his book has been written in
the scant intervals afforded by the practice of the profession of
architecture, so broadened as to include the study of abstract form,
the creation of ornament, experiments with color and light, and such
occasional educational activities as from time to time he has been
called upon to perform at one or another architectural school.

The three essays included under the general heading of "Democracy
and Architecture" were prepared at the request of the editor of _The
Architectural Record_, and were published in that journal. The two
following, on "Ornament from Mathematics," represent a recasting and
a rewriting of articles which have appeared in _The Architectural
Review, The Architectural Forum_, and _The American Architect_.
"Harnessing the Rainbow" is an address delivered before the Ad. Club
of Cleveland, and the Rochester Rotary Club, and afterwards made into
an essay and published in _The American Architect_ under a different
title. The appreciation of Louis Sullivan as a writer appears here for
the first time, the author having previously paid his respects to Mr.
Sullivan's strictly architectural genius in an essay in _House and
Garden_. "Color and Ceramics" was delivered on the occasion of the
dedication of the Ceramic Building of the University of Illinois,
and afterwards published in _The Architectural Forum_. "Symbols and
Sacraments" was printed in the English Quarterly _Orpheus_. "Self
Education" was delivered before the Boston Architectural Club, and
afterwards published in a number of architectural journals.

Acknowledgment is hereby tendered by the author to the editors of
these various magazines for their consent to republication, together
with thanks, however belated, for their unfailing hospitality to the
children of his brain.

CLAUDE BRAGDON.

_August 1, 1918_.

CONTENTS

ARCHITECTURE AND DEMOCRACY

I. Before the War

II. During the War

III. After the War

ORNAMENT FROM MATHEMATICS

I. The World Order

II. The Fourth Dimension

HARNESSING THE RAINBOW

LOUIS SULLIVAN, PROPHET OF DEMOCRACY

COLOR AND CERAMICS

SYMBOLS AND SACRAMENTS

SELF-EDUCATION

LIST OF FULL PAGE ILLUSTRATIONS

Plate I. The Woolworth Building, New York

Plate II. The New York Public Library

Plate III. The Prudential Building, Buffalo, N.Y.

Plate IV. The Erie County Savings Bank, Buffalo, N.Y.

Plate V. The New York Central Terminal

Plate VI. Plan of the Red Cross Community Club House,
Camp Sherman, Ohio

Plate VII. Interior View of the Camp Sherman Community House

Plate VIII. Imaginative Sketch by Henry P. Kirby

Plate IX. Architectural Sketch by Otto Rieth

Plate X. 200 West 57th Street, New York

Plate XI. Imaginary Composition: The Portal

Plate XII. Imaginary Composition: The Balcony

Plate XIII. Imaginary Composition: The Audience Chamber

Plate XIV. Song and Light: An Approach toward "Color Music"

Plate XV. Symbol of Resurrection

Every form of government, every social institution, every
undertaking, however great, however small, every symbol of
enlightenment or degradation, each and all have sprung and are still
springing from the life of the people, and have ever formed and are
now as surely forming images of their thought. Slowly by centuries,
generations, years, days, hours, the thought of the people has
changed; so with precision have their acts responsively changed; thus
thoughts and acts have flowed and are flowing ever onward, unceasingly
onward, involved within the impelling power of Life. Throughout this
stream of human life, and thought, and activity, men have ever felt
the need to build; and from the need arose the power to build. So,
as they thought, they built; for, strange as it may seem, they could
build in no other way. As they built, they made, used, and left behind
them records of their thinking. Then, as through the years new men
came with changed thoughts, so arose new buildings in consonance
with the change of thought--the building always the expression of
the thinking. Whatever the character of the thinking, just so was the
character of the building.

What is Architecture? A Study in the American People of Today, by
LOUIS SULLIVAN.

Architecture and Democracy

I

BEFORE THE WAR

The world war represents not the triumph, but the birth of democracy.
The true ideal of democracy--the rule of a people by the _demos_, or
group soul--is a thing unrealized. How then is it possible to consider
or discuss an architecture of democracy--the shadow of a shade? It is
not possible to do so with any degree of finality, but by an intention
of consciousness upon this juxtaposition of ideas--architecture and
democracy--signs of the times may yield new meanings, relations may
emerge between things apparently unrelated, and the future, always
existent in every present moment, may be evoked by that strange magic
which resides in the human mind.

Architecture, at its worst as at its best, reflects always a true
image of the thing that produced it; a building is revealing even
though it is false, just as the face of a liar tells the thing
his words endeavor to conceal. This being so, let us make such
architecture as is ours declare to us our true estate.

The architecture of the United States, from the period of the Civil
War, up to the beginning of the present crisis, everywhere reflects a
struggle to be free of a vicious and depraved form of feudalism,
grown strong under the very aegis of democracy. The qualities that made
feudalism endeared and enduring; qualities written in beauty on
the cathedral cities of mediaeval Europe--faith, worship,
loyalty, magnanimity--were either vanished or banished from this
pseudo-democratic, aridly scientific feudalism, leaving an inheritance
of strife and tyranny--a strife grown mean, a tyranny grown prudent,
but full of sinister power the weight of which we have by no means
ceased to feel.

Power, strangely mingled with timidity; ingenuity, frequently
misdirected; ugliness, the result of a false ideal of beauty--these
in general characterize the architecture of our immediate past; an
architecture "without ancestry or hope of posterity," an architecture
devoid of coherence or conviction; willing to lie, willing to steal.
What impression such a city as Chicago or Pittsburgh might have made
upon some denizen of those cathedral-crowned feudal cities of the
past we do not know. He would certainly have been amazed at its giant
energy, and probably revolted at its grimy dreariness. We are wont
to pity the mediaeval man for the dirt he lived in, even while smoke
greys our sky and dirt permeates the very air we breathe: we think of
castles as grim and cathedrals as dim, but they were beautiful and gay
with color compared with the grim, dim canyons of our city streets.

Lafcadio Hearn, in _A Conservative_, has sketched for us, with a
sympathy truly clairvoyant, the impression made by the cities of the
West upon the consciousness of a young Japanese samurai educated under
a feudalism not unlike that of the Middle Ages, wherein was worship,
reverence, poetry, loyalty--however strangely compounded with the more
sinister products of the feudal state.

Larger than all anticipation the West appeared to him,--a
world of giants; and that which depresses even the boldest
Occidental who finds himself, without means or friends, alone
in a great city, must often have depressed the Oriental exile:
that vague uneasiness aroused by the sense of being invisible
to hurrying millions; by the ceaseless roar of traffic
drowning voices; by monstrosities of architecture without a
soul; by the dynamic display of wealth forcing mind and
hand, as mere cheap machinery, to the uttermost limits of
the possible. Perhaps he saw such cities as Dore saw London:
sullen majesty of arched glooms, and granite deeps opening
into granite deeps beyond range of vision, and mountains
of masonry with seas of labor in turmoil at their base, and
monumental spaces displaying the grimness of ordered power
slow-gathering through centuries. Of beauty there was nothing
to make appeal to him between those endless cliffs of stone
which walled out the sunrise and the sunset, the sky and the
wind.

The view of our pre-war architecture thus sketchily presented is sure
to be sharply challenged in certain quarters, but unfortunately for
us all this is no mere matter of opinion, it is a matter of fact. The
buildings are there, open to observation; rooted to the spot, they
cannot run away. Like criminals "caught with the goods" they stand,
self-convicted, dirty with the soot of a thousand chimneys, heavy with
the spoils of vanished civilizations; graft and greed stare at us out
of their glazed windows--eyes behind which no soul can be discerned.
There are doubtless extenuating circumstances; they want to be clean,
they want to be honest, these "monsters of the mere market," but they
are nevertheless the unconscious victims of evils inherent in our
transitional social state.

Let us examine these strange creatures, doomed, it is hoped, to
extinction in favor of more intelligent and gracious forms of
life. They are big, powerful, "necessitous," and have therefore an
impressiveness, even an aesthetic appeal, not to be denied. So subtle
and sensitive an old-world consciousness as that of M. Paul Bourget
was set vibrating by them like a violin to the concussion of a
trip-hammer, and to the following tune:

The portals of the basements, usually arched as if crushed
beneath the weight of the mountains which they support, look
like dens of a primitive race, continually receiving and
pouring forth a stream of people. You lift your eyes, and you
feel that up there behind the perpendicular wall, with
its innumerable windows, is a multitude coming and
going,--crowding the offices that perforate these cliffs of
brick and iron, dizzied with the speed of the elevators.
You divine, you feel the hot breath of speculation quivering
behind these windows. This it is which has fecundated these
thousands of square feet of earth, in order that from them may
spring up this appalling growth of business palaces, that hide
the sun from you and almost shut out the light of day.

"The simple power of necessity is to a certain degree a principle of
beauty," says M. Bourget, and to these structures this order of beauty
cannot be denied, but even this is vitiated by a failure to press the
advantage home: the ornate facades are notably less impressive
than those whose grim and stark geometry is unmitigated by the
grave-clothes of dead styles. Instances there are of strivings toward
a beauty that is fresh and living, but they are so unsuccessful and
infrequent as to be negligible. However impressive these buildings may
be by reason of their ordered geometry, their weight and magnitude,
and as a manifestation of irrepressible power, they have the
unloveliness of things ignoble being the product neither of praise,
nor joy, nor worship, but enclosures for the transaction of sharp
bargains--gold bringing jinn of our modern Aladdins, who love them not
but only use them. That is the reason they are ugly; no one has loved
them for themselves alone.

For beauty is ever the very face of love. From the architecture of
a true democracy, founded on love and mutual service, beauty would
inevitably shine forth; its absence convicts us of a maladjustment in
our social and economic life. A skyscraper shouldering itself aloft at
the expense of its more humble neighbors, stealing their air and
their sunlight, is a symbol, written large against the sky, of
the will-to-power of a man or a group of men--of that ruthless and
tireless aggression on the part of the cunning and the strong so
characteristic of the period which produced the skyscraper. One of
our streets made up of buildings of diverse styles and shapes and
sizes--like a jaw with some teeth whole, some broken, some rotten,
and some gone--is a symbol of our unkempt individualism, now happily
becoming curbed and chastened by a common danger, a common devotion.

Some people hold the view that our insensitiveness to formal beauty is
no disgrace. Such argue that our accomplishments and our interests are
in other fields, where we more than match the accomplishments of older
civilizations. They forget that every achievement not registered in
terms of beauty has failed of its final and enduring transmutation. It
is because the achievements of older civilizations attained to their
apotheoses in art that they interest us, and unless we are able
to effect a corresponding transmutation we are destined to perish
unhonoured on our rubbish heap. That we shall effect it, through
knowledge and suffering, is certain, but before attempting the
more genial and rewarding task of tracing, in our life and in our
architecture, those forces and powers which make for righteousness,
for beauty, let us look our failures squarely in the face, and
discover if we can why they are failures.

Confining this examination to the particular matter under discussion,
the neo-feudal architecture of our city streets, we find it to lack
unity, and the reason for this lack of unity dwells in a _divided
consciousness_. The tall office building is the product of many
forces, or perhaps we should say one force, that of necessity; but its
concrete embodiment is the result of two different orders of talent,
that of the structural engineer and of the architectural designer.
These are usually incarnate in two different individuals, working
more or less at cross purposes. It is the business of the engineer
to preoccupy himself solely with ideas of efficiency and economy,
and over his efficient and economical structure the designer smears
a frosting of beauty in the form of architectural style, in the
archaeological sense. This is a foolish practice, and cannot but result
in failure. In the case of a Greek temple or a mediaeval cathedral
structure and style were not twain, but one; the structure determined
the style, the style expressed the structure; but with us so divorced
have the two things become that in a case known to the author, the
structural framework of a great office building was determined and
fabricated and then architects were invited to "submit designs"
for the exterior. This is of course an extreme example and does not
represent the usual practice, but it brings sharply to consciousness
the well known fact that for these buildings we have substantially one
method of construction--that of the vertical strut, and the horizontal
"fill"--while in style they appear as Grecian, Roman, Renaissance,
Gothic, Modern French and what not, according to the whim of the
designer.

[Illustration: PLATE II. THE NEW YORK PUBLIC LIBRARY]

With the modern tendency toward specialization, the natural outgrowth
of necessity, there is no inherent reason why the bones of a building
should not be devised by one man and its fleshly clothing by another,
so long as they understand one another, and are in ideal agreement,
but there is in general all too little understanding, and a
confusion of ideas and aims. To the average structural engineer the
architectural designer is a mere milliner in stone, informed in those
prevailing architectural fashions of which he himself knows little and
cares less. Preoccupied as he is with the building's strength, safety,
economy; solving new and staggeringly difficult problems with address
and daring, he has scant sympathy with such inconsequent matters as
the stylistic purity of a facade, or the profile of a moulding. To the
designer, on the other hand, the engineer appears in the light of a
subordinate to be used for the promotion of his own ends, or an evil
to be endured as an interference with those ends.

As a result of this lack of sympathy and co-ordination, success crowns
only those efforts in which, on the one hand, the stylist has been
completely subordinated to engineering necessity, as in the case of
the East River bridges, where the architect was called upon only to
add a final grace to the strictly structural towers; or on the other
hand, in which the structure is of the old-fashioned masonry sort, and
faced with a familiar problem the architect has found it easy to be
frank; as in the case of the Manhattan Storage Warehouse, on 42nd
Street, New York, or in the Bryant Park facade on the New York
Library. The Woolworth building is a notable example of the complete
co-ordination between the structural framework and its envelope, and
falls short of ideal success only in the employment of an archaic and
alien ornamental language, used, however, let it be said, with a fine
understanding of the function of ornament.

For the most part though, there is a difference of intention between
the engineer and the designer; they look two ways, and the result of
their collaboration is a flat and confused image of the thing that
should be, not such as is produced by truly binocular vision. This
difference of aim is largely the result of a difference of education.
Engineering science of the sort which the use of steel has required is
a thing unprecedented; the engineer cannot hark back to the past for
help, even if he would. The case is different with the architectural
designer; he is taught that all of the best songs have been sung, all
of the true words spoken. The Glory that was Greece, and the Grandeur
that was Rome, the romantic exuberance of Gothic, and the ordered
restraint of Renaissance are so drummed into him during his years of
training, and exercise so tyrannical a spell over his imagination that
he loses the power of clear and logical thought, and never becomes
truly creative. Free of this incubus the engineer has succeeded in
being straightforward and sensible, to say the least; subject to it
the man with a so-called architectural education is too often tortuous
and absurd.

The architect without any training in the essentials of design
produces horrors as a matter of course, for the reason that sin is the
result of ignorance; the architect trained in the false manner of the
current schools becomes a reconstructive archaeologist, handicapped by
conditions with which he can deal only imperfectly, and imperfectly
control. Once in a blue moon a man arises who, with all the advantages
inherent in education, pierces through the past to the present, and
is able to use his brain as the architects of the past used theirs--to
deal simply and directly with his immediate problem.

Such a man is Louis Sullivan, though it must be admitted that not
always has he achieved success. That success was so marked, however,
in his treatment of the problem of the tall building, and exercised
subconsciously such a spell upon the minds even of his critics and
detractors, that it resulted in the emancipation of this type of
building from an absurd and impossible convention--the practice,
common before his time, of piling order upon order, like a house
of cards, or by a succession of strongly marked string courses
emphasizing the horizontal dimension of a vertical edifice, thus
vitiating the finest effect of which such a building is capable.

The problem of the tall building, with which his predecessors dealt
always with trepidation and equivocation, Mr. Sullivan approached
with confidence and joy. "What," he asked himself, "is the chief
characteristic of the tall office building? It is lofty. This
loftiness is to the artist-nature its thrilling aspect. It must be
tall. The force of altitude must be in it. It must be every inch a
proud and soaring thing, rising in sheer exultation that from bottom
to top it is a unit without a dissenting line." The Prudential
(Guaranty) building in Buffalo represents the finest concrete
embodiment of his idea achieved by Mr. Sullivan. It marks his
emancipation from what he calls his "masonry" period, during which
he tried, like so many other architects before and since, to make a
steel-framed structure look as though it were nothing but a masonry
wall perforated with openings--openings too many and too great not
to endanger its stability. The keen blade of Mr. Sullivan's mind cut
through this contradiction, and in the Prudential building he carried
out the idea of a _protective casing_ so successfully that Montgomery
Schuyler said of it, "I know of no steel framed building in which the
metallic construction is more palpably felt through the envelope of
baked clay."

[Illustration: PLATE III. THE PRUDENTIAL BUILDING, BUFFALO N.Y.]

The present author can speak with all humbleness of the general
failure, on the part of the architectural profession, to appreciate
the importance of this achievement, for he pleads guilty of day after
day having passed the Prudential building, then fresh in the majesty
of its soaring lines, and in the wonder of its fire-wrought casing,
with eyes and admiration only for the false romanticism of the Erie
County Savings Bank, and the empty bombast of the gigantic Ellicott
Square. He had not at that period of his life succeeded in living down
his architectural training, and as a result the most ignorant layman
was in a better position to appraise the relative merits of these
three so different incarnations of the building impulse than was he.

Since the Prudential building there have been other tall office
buildings, by other hands, truthful in the main, less rigid, less
monotonous, more superficially pleasing, yet they somehow fail to
impart the feeling of utter sincerity and fresh originality inspired
by this building. One feels that here democracy has at last found
utterance in beauty; the American spirit speaks, the spirit of the
Long Denied. This rude, rectangular bulk is uncompromisingly practical
and utilitarian; these rows on rows of windows, regularly spaced, and
all of the same size, suggest the equality and monotony of obscure,
laborious lives; the upspringing shafts of the vertical piers stand
for their hopes and aspirations, and the unobtrusive, delicate
ornament which covers the whole with a garment of fresh beauty is like
the very texture of their dreams. The building is able to speak
thus powerfully to the imagination because its creator is a poet
and prophet of democracy. In his own chosen language he declares, as
Whitman did in verse, his faith in the people of "these states"--"A
Nation announcing itself." Others will doubtless follow who will make
a richer music, commensurate with the future's richer life, but such
democracy as is ours stands here proclaimed, just as such feudalism
as is still ours stands proclaimed in the Erie County Bank just across
the way. The massive rough stone walls of this building, its pointed
towers and many dormered chateau-like roof unconsciously symbolize the
attempt to impose upon the living present a moribund and alien
order. Democracy is thus afflicted, and the fact must needs find
architectural expression.

In the field of domestic architecture these dramatic contrasts are
less evident, less sharply marked. Domestic life varies little from
age to age; a cottage is a cottage the world over, and some manorial
mansion on the James River, built in Colonial days, remains a fitting
habitation (assuming the addition of electric lights and sanitary
plumbing) for one of our Captains of Industry, however little an
ancient tobacco warehouse would serve him as a place of business.
This fact is so well recognized that the finest type of modern country
house follows, in general, this or some other equally admirable model,
though it is amusing to note the millionaire's preference for a feudal
castle, a French chateau, or an Italian villa of the decadence.

The "man of moderate means," so called, provides himself with
no difficulty with a comfortable house, undistinguished but
unpretentious, which fits him like a glove. There is a piazza towards
the street, a bay-window in the living room, a sleeping-porch for the
children, and a box of a garage for the flivver in the bit of a back
yard.

For the wage earner the housing problem is not so easily nor
so successfully solved. He is usually between the devil of the
speculative builder and the deep sea of the predatory landlord, each
intent upon taking from him the limit that the law allows and giving
him as little as possible for his money. Going down the scale of
indigence we find an itinerancy amounting almost to homelessness, or
houses so abject that they are an insult to the very name of home.

[Illustration: PLATE IV: THE ERIE COUNTY SAVINGS BANK, BUFFALO, N.Y.]

It is an eloquent commentary upon our national attitude toward a most
vital matter that in this feverish hustle to produce ships, airplanes,
clothing and munitions on a vast scale, the housing of the workers was
either overlooked entirely, or received eleventh-hour consideration,
and only now, after a year of participation in the war, is it
beginning to be adequately and officially dealt with--how efficiently
and intelligently remains to be seen. The housing of the soldiers was
another matter: that necessity was plain and urgent, and the miracle
has been accomplished, but except by indirection it has contributed
nothing to the permanent housing problem.

Other aspects of our life which have found architectural expression
fall neither in the commercial nor in the domestic category--the great
hotels, for example, which partake of the nature of both, and our
passenger railway terminals, which partake of the nature of neither.
These latter deserve especial consideration in this connection, by
reason of their important function. The railway is of the very essence
of the modern, even though (with what sublime unreason) Imperial Rome
is written large over New York's most magnificent portal.

Think not that in an age of unfaith mankind gives up the building
of temples. Temples inevitably arise where the tide of life flows
strongest; for there God manifests, in however strange a guise. That
tide is nowhere stronger than in the railroad, which is the arterial
system of our civilization. All arteries lead to and from the heart,
and thus the railroad terminus becomes the beating heart at the center
of modern life. It is a true instinct therefore which prompts to
the making of the terminal building a very temple, a monument to
the conquest of space through the harnessing of the giant horses of
electricity and steam. This conquest must be celebrated on a scale
commensurate with its importance, and in obedience to this necessity
the Pennsylvania station raised its proud head amid the push-cart
architecture of that portion of New York in which it stands. It is not
therefore open to the criticism often passed upon it, that it is too
grand, but it is the wrong kind of grandeur. If there be truth in the
contention that the living needs of today cannot be grafted upon the
dead stump of any ancient grandeur, the futility of every attempt to
accomplish this impossible will somehow, somewhere, reveal itself to
the discerning eye. Let us seek out, in this building, the place of
this betrayal.

It is not necessarily in the main facade, though this is not a face,
but a mask--and a mask can, after its kind, always be made beautiful;
it is not in the nobly vaulted corridor, lined with shops--for all we
know the arcades of Imperial Rome were similarly lined; nor is it in
the splendid vestibule, leading into the magnificent waiting room, in
which a subject of the Caesars would have felt more perfectly at home,
perhaps, than do we. But beyond this passenger concourse, where the
elevators and stairways descend to the tracks, necessity demanded the
construction of a great enclosure, supported only on slender columns
and far-flung trusses roofed with glass. Now latticed columns, steel
trusses, and wire glass are inventions of the modern world too useful
to be dispensed with. Rome could not help the architect here. The mode
to which he was inexorably self-committed in the rest of the building
demanded massive masonry, cornices, mouldings; a tribute to Caesar
which could be paid everywhere but in this place. The architect's
problem then became to reconcile two diametrically different systems.
But between the west wall of the ancient Roman baths and the modern
skeleton construction of the roof of the human greenhouse there is
no attempt at fusion. The slender latticed columns cut unpleasantly
through the granite cornices and mouldings; the first century A.D. and
the twentieth are here in incongruous juxtaposition--a little thing,
easily overlooked, yet how revealing! How reassuring of the fact "God
is not mocked!"

The New York Central terminal speaks to the eye in a modern tongue,
with however French an accent. Its facade suggests a portal, reminding
the beholder that a railway station is in a very literal sense a city
gate placed just as appropriately in the center of the municipality as
in ancient times it was placed in the circuit of the outer walls.

Neither edifice will stand the acid test of Mr. Sullivan's formula,
that a building is an organism and should follow the law of organisms,
which decrees that the form must everywhere follow and express the
function, the function determining and creating its appropriate form.
Here are two eminent examples of "arranged" architecture. Before
organic architecture can come into being our inchoate national life
must itself become organic. Arranged architecture, of the sort we
see everywhere, despite its falsity, is a true expression of the
conditions which gave it birth.

[Illustration: PLATE V. THE NEW YORK CENTRAL TERMINAL]

The grandeur of Rome, the splendour of Paris--what just and adequate
expression do they give of modern American life? Then shall we find in
our great hotels, say, such expression? Truly they represent, in the
phrase of Henry James, "a realized ideal" and a study of them should
reveal that ideal. From such a study we can only conclude that it
is life without effort or responsibility, with every physical need
luxuriously gratified. But these hotels nevertheless represent
democracy, it may be urged, for the reason that every one may there
buy board and lodging and mercenary service if he has the price. The
exceeding greatness of that price, however, makes of it a badge
of nobility which converts these democratic hostelries into feudal
castles, more inaccessible to the Long Denied than as though entered
by a drawbridge and surrounded by a moat.

We need not even glance at the churches, for the tides of our
spiritual life flow no longer in full volume through their portals;
neither may the colleges long detain us, for architecturally
considered they give forth a confusion of tongues which has its
analogue in the confusion of ideas in the collective academic head.

Is our search for some sign of democracy ended, and is it vain? No,
democracy exists in the secret heart of the people, all the people,
but it is a thing so new, so strange, so secret and sacred--the ideal
of brotherhood--that it is unmanifest yet in time and space. It is
a thing born not with the Declaration of Independence, but only
yesterday, with the call to a new crusade. The National Army is its
cradle, and it is nurtured wherever communities unite to serve the
sacred cause. Although menaced by the bloody sword of Imperialism in
Europe, it perhaps stands in no less danger from the secret poison
of graft and greed and treachery here at home. But it is a spiritual
birth, and therefore it cannot perish, but will live to write itself
on space in terms of beauty such as the world has never known.

II

DURING THE WAR

The best thing that can be said about our immediate architectural
past is that it is past, for it has contributed little of value to an
architecture of democracy. During that neo-feudal period the architect
prospered, having his place at the baronial table; but now poor Tom's
a-cold on a war-swept heath, with food only for reflection. This
is but natural; the architect, in so far as he is an artist, is a
purveyor of beauty; and the abnormal conditions inevitable to a state
of war are devastating to so feminine and tender a thing, even though
war be the very soil from which new beauty springs. With Mars in
mid-heaven how afflicted is the horoscope of all artists! The skilled
hand of the musician is put to coarser uses; the eye that learned
its lessons from the sunset must learn the trick of making invisible
warships and great guns. Let the architect serve the war-god likewise,
in any capacity that offers, confident that this troubling of the
waters will bring about a new precipitation; that once the war is
over, men will turn from those "old, unhappy, far-off things" to
pastures beautiful and new.

In whatever way the war may complicate the architect's personal
problem, it should simplify and clarify his attitude toward his art.
With no matter what seriousness and sincerity he may have undertaken
his personal search for truth and beauty, he will come to question,
as never before, both its direction and its results. He is bound to
perceive, if he does not perceive already, that the war's arrestment
of architecture (in all but its most utilitarian and ephemeral phases)
is no great loss to the world for the reason that our architecture was
uninspired, unoriginal, done without joy, without reverence, without
conviction: a thing which any wind of a new spirit was bound to make
appear foolish to a generation with sight rendered clairvoyant through
its dedication to great and regenerative ends.

He will come to perceive that between the Civil War and the crusade
that is now upon us, we were under the evil spell of materialism. Now
materialism is the very negation of democracy, which is a government
by the _demos_, or over-soul; it is equally the negation of joy, the
negation of reverence, and it is without conviction because it cannot
believe even in itself. Reflecting thus, he can scarcely fail to
realize that materialism, everywhere entrenched, was entrenched
strongest in the camps of the rich---not the idle rich, for
materialism is so terrible a taskmaster that it makes its votaries its
slaves. These slaves, in turn, made a slave of the artist, a minister
to their pride and pretence. His art thus lacked that "sad sincerity"
which alone might have saved it in a crisis. When the storm broke
militant democracy turned to the engineer, who produced buildings at
record speed, by the mile, with only such architectural assistance as
could be first and easiest fished up from the dragnet of the draft.

In one direction only does there appear to be open water. Toward the
general housing problem the architectural profession has been spurred
into activity by reason of the war, and to its credit be it said, it
is now thoroughly aroused. The American Institute of Architects sent a
commissioner to England to study housing in its latest manifestations,
and some of the ablest and most influential members of that
organization have placed their services at the disposal of the
government. Moreover, there is a manifest disposition, on the part of
architects everywhere, to help in this matter all they can. The danger
dwells in the possibility that their advice will not be heeded, their
services not be fully utilized, but through chicanery, ignorance,
or inanition, we will relapse into the tentative, "expensively
provisional" methods which have governed the housing of workers
hitherto. Even so, architects will doubtless recapture, and more
than recapture, their imperiled prestige, but under what changed
conditions, and with what an altered attitude toward their art and
their craft!

They will find that they must unlearn certain things the schools had
taught them: preoccupation with the relative merits of Gothic and
Classic--tweedledum and tweedledee. Furthermore, they must learn
certain neglected lessons from the engineer, lessons that they will
be able immeasurably to better, for although the engineer is a very
monster of competence and efficiency within his limits, these are
sharply marked, and to any detailed knowledge of that "beautiful
necessity" which determines spatial rhythm and counterpoint he is a
stranger. The ideal relation between architect and engineer is that of
a happily wedded pair--strength married to beauty; in the period just
passed or passing they have been as disgruntled divorces.

[Illustration: PLATE VI. PLAN OF THE RED CROSS COMMUNITY CLUB HOUSE,
CAMP SHERMAN, OHIO]

The author has in mind one child of such a happy union brought about
by the war; the building is the Red Cross Community Club House at Camp
Sherman, which, in the pursuit of his destiny, and for the furtherance
of his education, he inhabited for two memorable weeks. He learned
there more lessons than a few, and encountered more tangled skeins of
destiny than he is ever likely to unravel. The matter has so direct a
bearing, both on the subject of architecture and of democracy, that it
is worth discussing at some length.

This club house stands, surrounded by its tributary dormitories, on a
government reservation, immediately adjacent to the camp itself,
the whole constituting what is known as the Community Center. By the
payment of a dollar any soldier is free to entertain his relatives
and friends there, and it is open to all the soldiers at all times.
Because the iron discipline of the army is relaxed as soon as the
limits of the camp are overpassed, the atmosphere is favourable to
social life.

The building occupies its acre of ground invitingly, though exteriorly
of no particular distinction. It is the interior that entitles it to
consideration as a contribution to an architecture of that new-born
democracy of which our army camps have been the cradle. The plan of
this interior is cruciform, two hundred feet in each dimension. Built
by the Red Cross of the state of Ohio, and dedicated to the larger
uses of that organization, the symbolic appropriateness of this
particular geometrical figure should not pass unremarked. The cross
is divided into side aisles, nave, and crossing, with galleries and
mezzanines so arranged as to shorten the arms of the cross in its
upper stages, leaving the clear-story surrounding the crossing
unimpeded and well defined. The light comes for the most part from
high windows, filtering down, in tempered brightness to the floor. The
bones of the structure are everywhere in evidence, and an element of
its beauty, by reason of the admirably direct and logical
arrangement of posts and trusses. The vertical walls are covered with
plaster-board of a light buff color, converted into good sized
panels by means of wooden strips finished with a thin grey stain. The
structural wood work is stained in similar fashion, the iron rods,
straps, and bolts being painted black. This color scheme is
completed and a little enlivened by red stripes and crosses placed at
appropriate intervals in the general design.

The building attained its final synthesis through the collaboration of
a Cleveland architect and a National Army captain of engineers. It is
so single in its appeal that one does not care to inquire too closely
into the part of each in the performance; both are in evidence, for
an architect seldom succeeds in being so direct and simple, while an
engineer seldom succeeds in being so gracious and altogether suave.

Entirely aside from its aesthetic interest--based as this is on beauty
of organism almost alone--the building is notable for the success with
which it fulfils and co-ordinates its manifold functions: those of a
dormitory, a restaurant, a ballroom, a theatre, and a lounge. The
arm of the cross containing the principal entrance accommodates the
office, coat room, telephones, news and cigar stand, while leaving
the central nave unimpeded, so that from the door one gets the unusual
effect of an interior vista two hundred feet long. The restaurant
occupies the entire left transept, with a great brick fireplace at the
far end. There is another fireplace in the centre of the side of
the arm beyond the crossing; that part which would correspond in a
cathedral to the choir and apse being given over to the uses of a
reading and writing room. The right transept forms a theatre, on
occasion, terminating as it does with a stage. The central floor
spaces are kept everywhere free except in the restaurant, the sides
and angles being filled in with leather-covered sofas, wicker and
wooden chairs and tables, arranged in groups favourable to comfort and
conversation. Two stairways, at the right and left of the restaurant,
give access to the ample balcony and to the bedrooms, which occupy
three of the four ends of the arms of the cross at this level.

The appearance and atmosphere of this great interior is inspiring;
particularly of an evening, when it is thronged with soldiers, and
civilian guests. The strains of music, the hum of many voices, the
rhythmic shuffle on the waxed floor of the feet of the dancers--these
eminently social sounds mingle and lose themselves in the spaces of
the roof, like the voice of many waters. Tobacco smoke ascends like
incense, blue above the prevailing green-brown of the crowd, shot here
and there with brighter colors from the women's hats and dresses, in
the kaleidoscopic shifting of the dance. Long parallel rows of orange
lights, grouped low down on the lofty pillars, reflect themselves
on the polished floor, and like the patina of time on painted canvas
impart to the entire animated picture an incomparable tone. For the
lighting, either by accident or by inspiration, is an achievement
of the happiest, an example of the friendliness of fate to him who
attempts a free solution of his problem. The brackets consist merely
of a cruciform arrangement of planed pine boards about each column,
with the end grain painted red. On the under side of each arm of the
cross is a single electric bulb enclosed within an orange-coloured
shade to kill the glare. The light makes the bare wood of the fixture
appear incandescent, defining its geometry in rose colour with the
most beautiful effect.

The club house is the centre of the social and ceremonial life of the
camp, for balls, dinners, receptions, conferences, concerts without
number; and it has been the scene of a military wedding--the daughter
of a major-general to the grandson of an ex-president. To these events
the unassuming, but pervasive beauty of the place lends a dignity new
to our social life. In our army camps social life is truly democratic,
as any one who has experienced it does not need to be told. Not alone
have the conditions of conscription conspired to make it so, but there
is a manifest _will-to-democracy_--the growing of a new flower of
the spirit, sown in a community of sacrifice, to reach its maturity,
perhaps, only in a community of suffering.

The author may seem to have over-praised this Community Club House;
with the whole country to draw from for examples it may well appear
fatuous to concentrate the reader's attention, for so long, on a
building in a remote part of the Middle West: cheap, temporary,
and requiring only twenty-one days for its erection. But of the
transvaluation of values brought about by the war, this building is
an eminent example: it stands in symbolic relation to the times; it
represents what may be called the architecture of Service; it is among
the first of the new temples of the new democracy, dedicated to the
uses of simple, rational social life. Notwithstanding that it fills a
felt need, common to every community, there is nothing like it in
any of our towns and cities; there are only such poor and partial
substitutes as the hotel, the saloon, the dance hall, the lodge room
and the club. It is scarcely conceivable that the men and women who
have experienced its benefits and its beauty should not demand and
have similar buildings in their own home towns.

[Illustration: PLATE VII. INTERIOR OF THE CAMP SHERMAN COMMUNITY
HOUSE]

Beyond the oasis of the Community Club House at Camp Sherman stretch
the cantonments--a Euclidian nightmare of bare boards, black roofs
and ditches, making grim vistas of straight lines. This is the
architecture of Need in contradistinction to the architecture of
Greed, symbolized in the shop-window prettiness of those sanitary
suburbs of our cities created by the real estate agent and the
speculative builder. Neither contain any enduring element of beauty.

But the love of beauty in one form or another exists in every human
heart, and if too long or too rigorously denied it finds its own
channels of fulfilment. This desire for self-expression through beauty
is an important, though little remarked phenomenon of these mid-war
times. At the camps it shows itself in the efforts of men of
specialized tastes and talents to get together and form dramatic
organizations, glee clubs, and orchestras; and more generally by the
disposition of the soldiers to sing together at work and play and on
the march. The renascence of poetry can be interpreted as a revulsion
against the prevailing prosiness; the amateur theatre is equally a
protest against the inanity and conventionality of the commercial
stage; while the Community Chorus movement is an evidence of a desire
to escape a narrow professionalism in music. A similar situation
has arisen in the field of domestic architecture, in the form of
an unorganized, but wide-spread reaction against the cheap and ugly
commercialism which has dominated house construction and decoration of
the more unpretentious class. This became articulate a few years ago
in the large number of books and magazines devoted to house-planning,
construction, decoration, furnishing, and garden-craft. The success
which has attended these publications, and their marked influence,
give some measure of the magnitude of this revolt.

But now attention must be called to a significant, and somewhat
sinister fact. The professional in these various fields of aesthetic
endeavour, has shown either indifference or active hostility toward
all manner of amateur efforts at self-expression. Free verse aroused
the ridicule of the professors of metrics; the Little Theatre movement
was solemnly banned by such pundits as Belasco and Mrs. Fiske; the
Community Chorus movement has invariably met with opposition and
misunderstanding from professional musicians; and with few exceptions
the more influential architects have remained aloof from the effort
to give skilled architectural assistance to those who cannot afford to
pay them ten per cent.

Thus everywhere do we discover a deadening hand laid upon the
self-expression of the democratic spirit through beauty. Its enemies
are of its own household; those who by nature and training should
be its helpers hinder it instead. Why do they do this? Because their
fastidious, aesthetic natures are outraged by a crudeness which they
themselves could easily refine away if they chose; because also they
recoil at a lack of conformity to existing conventions--conventions
so hampering to the inner spirit of the Newness, that in order to
incarnate at all it must of necessity sweep them aside.

But in every field of aesthetic endeavour appears here and there a
man or a woman with unclouded vision, who is able to see in the
flounderings of untrained amateurs the stirrings of _demos_ from his
age-long sleep. These, often forsaking paths more profitable, lend
their skilled assistance, not seeking to impose the ancient outworn
forms upon the Newness, but by a transfusion of consciousness
permitting it to create forms of its own. Such a one, in architecture,
Louis Sullivan has proved himself; in music Harry Barnhart, who evokes
the very spirit of song from any random crowd. The _demos_ found voice
first in the poetry of Walt Whitman who has a successor in Vachel
Lindsay, the man who walked through Kansas, trading poetry for food
and lodging, teaching the farmers' sons and daughters to intone
his stirring odes to Pocahontas, General Booth, and Old John Brown.
Isadora Duncan, Gordon Craig, Maeterlinck, Scriabine are perhaps
too remote from the spirit of democracy, too tinged with old-world
aestheticism, to be included in this particular category, but all
are image-breakers, liberators, and have played their part in the
preparation of the field for an art of democracy.

To the architect falls the task, in the new dispensation, of providing
the appropriate material environment for its new life. If he holds the
old ideas and cherishes the old convictions current before the war
he can do nothing but reproduce their forms and fashions; for
architecture, in the last analysis, is only the handwriting of
consciousness on space, and materialism has written there already all
that it has to tell of its failure to satisfy the mind and heart of
man. However beautiful old forms may seem to him they will declare
their inadequacy to generations free of that mist of familiarity which
now makes life obscure. If, on the other hand, submitting himself
to the inspiration of the _demos_ he experiences a change of
consciousness, he will become truly and newly creative.

His problem, in other words, is not to interpret democracy in terms
of existing idioms, be they classic or romantic, but to experience
democracy in his heart and let it create and determine its new forms
through him. It is not for him to _impose_, it is for him to be
_imposed upon_.

"The passive Master lent his hand
To the vast soul that o'er him planned"

says Emerson in _The Problem_, a poem, which seems particularly
addressed to architects, and which every one of them would do well to
learn by heart.

If he is at a loss to know where to go and what to do in order to be
played upon by these great forces let him direct his attention to
the army and the army camps. Here the spirit of democracy is
already incarnate. These soldiers, violently shaken free from their
environment, stripped of all but the elemental necessities of life;
facing a sinister destiny beyond a human-shark-infested ocean,
are today the fortunate of earth by reason of their realization of
brotherhood, not as a beautiful theory, but as a blessed fact of
experience. They will come back with ideas that they cannot utter,
with memories that they cannot describe; they will have dreamed dreams
and seen visions, and their hearts will stir to potencies for which
materialism has not even a name.

The future of the country will be in their young hands. Will they
re-create, from its ruins, the faithless and loveless feudalism
from which the war set them free? No, they will seek only for
self-expression, the expression of that aroused and indwelling spirit
which shall create the new, the true democracy. And because it is a
spiritual thing it will come clothed in beauty; that is, it will find
its supreme expression through the forms of art. The architect who
assists in the emprise of weaving this garment will be supremely
blessed, but only he who has kept the vigil with prayer and fasting
will be supremely qualified.

III

AFTER THE WAR

"When the old world is sterile
And the ages are effete,
He will from wrecks and sediment
The fairer world complete."

_The World Soul_. Emerson.

He whom the World Soul "forbids to despair" cannot but hope; and he
who hopes tries ever to imagine that "fairer world" yearning for birth
beyond this interval of blood and tears. Prophecy, to all but the
anointed, is dangerous and uncertain, but even so, the author cannot
forbear attempting to prevision the architecture likely to arise from
the wrecks and sediment left by the war. As a basis for this forecast
it is necessary first of all briefly to classify the expression of the
building impulse from what may be called the psychological point of
view.

Broadly speaking, there are not five orders of architecture--nor
fifty--but only two: _Arranged_ and _Organic_. These correspond to the
two terms of that "inevitable duality" which bisects life. Talent and
genius, reason and intuition, bromide and sulphite are some of the
names we know them by.

Arranged architecture is reasoned and artificial; produced by talent,
governed by taste. Organic architecture, on the other hand, is the
product of some obscure inner necessity for self-expression which
is sub-conscious. It is as though Nature herself, through some human
organ of her activity, had addressed herself to the service of the
sons and daughters of men.

Arranged architecture in its finest manifestations is the product of
a pride, a knowledge, a competence, a confidence staggering to behold.
It seems to say of the works of Nature, "I'll show you a trick worth
two of that." For the subtlety of Nature's geometry, and for her
infinite variety and unexpectedness, Arranged architecture substitutes
a Euclidian system of straight lines and (for the most part) circular
curves, assembled and arranged according to a definite logic of
its own. It is created but not creative; it is imagined but not
imaginative. Organic architecture is both creative and imaginative. It
is non-Euclidian in the sense that it is higher-dimensional--that is,
it suggests extension in directions and into regions where the spirit
finds itself at home, but of which the senses give no report to the
brain.

[Illustration: PLATE VIII. IMAGINATIVE SKETCH BY HENRY P. KIRBY]

To make the whole thing clearer it may be said that Arranged and
Organic architecture bear much the same relation to one another that
a piano bears to a violin. A piano is an instrument that does not give
forth discords if one follows the rules. A violin requires absolutely
an ear--an inner rectitude. It has a way of betraying the man of
talent and glorifying the genius, becoming one with his body and his
soul.

Of course it stands to reason that there is not always a hard and fast
differentiation between these two orders of architecture, but there
is one sure way by which each may be recognized and known. If the
function appears to have created the form, and if everywhere the
form follows the function, changing as that changes, the building is
Organic; if on the contrary, "the house confines the spirit," if the
building presents not a face but however beautiful a mask, it is an
example of Arranged architecture.

The Gothic cathedrals of the "Heart of Europe"--now the place of
Armageddon--represent the most perfect and powerful incarnation of
the Organic spirit in architecture. After the decadence of mediaeval
feudalism--synchronous with that of monasticism--the Arranged
architecture of the Renaissance acquired the ascendant; this was
coincident with the rise of humanism, when life became increasingly
secular. During the post-Renaissance, or scientific period, of which
the war probably marks the close, there has been a confusion of
tongues; architecture has spoken only alien or dead languages, learned
by rote.

But in so far as it is anything at all, aesthetically, our architecture
is Arranged, so if only by the operation of the law of opposites, or
alternation, we might reasonably expect the next manifestation to
be Organic. There are other and better reasons, however, for such
expectancy.

Organic architecture is ever a flower of the religious spirit. When
the soul draws near to the surface of life, as it did in the two
mystic centuries of the Middle Ages, it _organizes_ life; and
architecture, along, with the other arts becomes truly creative. The
informing force comes not so much _from_ man as _through_ him. After
the war that spirit of brotherhood, born in the camps--as Christ was
born in a manger--and bred on the battlefields and in the trenches of
Europe, is likely to take on all the attributes of a new religion of
humanity, prompting men to such heroisms and renunciations, exciting
in them such psychic sublimations, as have characterized the great
religious renewals of time past.

If this happens it is bound to write itself on space in an
architecture beautiful and new; one which "takes its shape and
sun-color" not from the niggardly mind, but from the opulent heart.
This architecture will of necessity be organic, the product not of
self-assertive personalities, but the work of the "Patient Daemon"
organizing the nation into a spiritual democracy.

The author is aware that in this point of view there is little of
the "scientific spirit"; but science fails to reckon with the soul.
Science advances facing backward, so what prevision can it have of a
miraculous and divinely inspired future--or for the matter of that,
of any future at all? The old methods and categories will no longer
answer; the orderly course of evolution has been violently interrupted
by the earthquake of the war; igneous action has superseded aqueous
action. The casements of the human mind look out no longer upon
familiar hills and valleys, but on a stark, strange, devastated
landscape, the ploughed land of some future harvest of the years.
It is the end of the Age, the _Kali Yuga_--the completion of a major
cycle; but all cycles follow the same sequence: after winter, Spring;
and after the Iron Age, the Golden.

The specific features of this organic, divinely inspired architecture
of the Golden Age cannot of course be discerned by any one, any more
than the manner in which the Great Mystery will present itself anew to
consciousness. The most imaginative artist can imagine only in
terms of the already-existent; he can speak only the language he has
learned. If that language has been derived from mediaevalism, he
will let his fancy soar after the manner of Henry Kirby, in his
_Imaginative Sketches_; if on the contrary he has learned to think in
terms of the classic vernacular, Otto Rieth's _Architectur-Skizzen_
will suggest the sort of thing that he is likely to produce. Both
results will be as remote as possible from future reality, for the
reason that they are so near to present reality. And yet some germs of
the future must be enfolded even in the present moment. The course
of wisdom is to seek them neither in the old romance nor in the new
rationalism, but in the subtle and ever-changing spirit of the times.

[Illustration: PLATE IX. ARCHITECTURAL SKETCH BY OTTO RIETH]

The most modern note yet sounded in business, in diplomacy, in social
life, is expressed by the phrase, "Live openly!" From every quarter,
in regard to every manner of human activity, has come the cry, "Let
in the light!" By a physical correspondence not the result of
coincidence, but of the operation of an occult law, we have, in a very
real sense, let in the light. In buildings of the latest type devoted
to large uses, there has been a general abandonment of that "cellular
system" of many partitions which produced the pepper-box exterior, in
favour of great rooms serving diverse functions lit by vast areas of
glass. Although an increase of efficiency has dictated and determined
these changes, this breaking down of barriers between human beings
and their common sharing of the light of day in fuller measure, is a
symbol of the growth of brotherhood, and the search, by the soul, for
spiritual light.

Now if this fellowship and this quest gain volume and intensity, its
physical symbols are bound to multiply and find ever more perfect
forms of manifestation. So both as a practical necessity and as a
symbol the most pregnant and profound, we are likely to witness in
architecture the development of the House of Light, particularly as
human ingenuity has made this increasingly practicable.

Glass is a product still undergoing development, as are also those
devices of metal for holding it in position and making the joints
weather tight. The accident and fire hazard has been largely overcome
by protecting the structural parts, by the use of wire glass, and
by other ingenious devices. The author has been informed on good
authority that shortly before the outbreak of the war a glass had been
invented abroad, and made commercially practicable, which shut out
the heat rays, but admitted the light. The use of this glass would
overcome the last difficulty--the equalization of temperatures--and
might easily result in buildings of an entirely novel type, the
approach to which is seen in the "pier and grill" style of exterior.
This is being adopted not only for commercial buildings, but for
others of widely different function, on account of its manifest
advantages. Cass Gilbert's admirable studio apartment at 200 West
Fifty-Seventh Street, New York, is a building of this type.

In this seeking for sunlight in our cities, we will come to live on
the roofs more and more--in summer in the free air, in winter under
variformed shelters of glass. This tendency is already manifesting
itself in those newest hotels whose roofs are gardens, convertible
into skating ponds, with glazed belvideres for eating in all weathers.
Nothing but ignorance and inanition stand in the way of utilization of
waste roof spaces. People have lived on the roofs in the past, often
enough, and will again.

[Illustration: PLATE X. RODIN STUDIOS, 200 WEST 57TH STREET, NEW YORK]

By shouldering ever upward for air and light, we have too often
made of the "downtown" districts cliff-bound canyons--"granite deeps
opening into granite deeps." This has been the result of no inherent
necessity, but of that competitive greed whose nemesis is ever to
miss the very thing it seeks. By intelligent co-operation, backed
by legislation, the roads and sidewalks might be made to share the
sunlight with the roofs.

This could be achieved in two ways: by stepping back the facades
in successive stages--giving top lighting, terraces, and wonderful
incidental effects of light and shade--or by adjusting the height of
the buildings to the width of their interspaces, making rows of tall
buildings alternate with rows of low ones, with occasional fully
isolated "skyscrapers" giving variety to the sky-line.

These and similar problems of city planning have been worked out
theoretically with much minuteness of detail, and are known to every
student of the science of cities, but very little of it all has been
realized in a practical way--certainly not on this side of the water,
where individual rights are held so sacred that a property owner may
commit any kind of an architectural nuisance so long as he confines
it to his own front yard. The strength of IS, the weakness of _should
be_, conflicting interests and legislative cowardice are responsible
for the highly irrational manner in which our cities have grown great.

The search for spiritual light in the midst of materialism finds
unconscious symbolization in a way other than this seeking for the
sun. It is in the amazing development of artificial illumination. From
a purely utilitarian standpoint there is almost nothing that cannot
now be accomplished with light, short of making the ether itself
luminiferous. The aesthetic development of this field, however, can be
said to have scarcely begun. The so recent San Francisco Exposition
witnessed the first successful effort of any importance to enhance the
effect of architecture by artificial illumination, and to use colored
light with a view to its purely pictorial value. Though certain
buildings have since been illuminated with excellent effect, it
remains true that the corset, chewing-gum, beer and automobile
sky signs of our Great White Ways indicate the height to which our
imagination has risen in utilizing this Promethean gift in any but
necessary ways. Interior lighting, except negatively, has not been
dealt with from the standpoint of beauty, but of efficiency; the
engineer has preempted this field to the exclusion of the artist.

All this is the result of the atrophy of that faculty to worship and
wonder which alone induces the mood from which the creation of beauty
springs. Light we regard only as a convenience "to see things by"
instead of as the power and glory that it inherently is. Its intense
and potent vibrations and the rainbow glory of its colour beat at the
door of consciousness in vain. When we awaken to these things we shall
organize light into a language of spontaneous emotion, just as from
sound music was organized.

It is beside the purpose of this essay to attempt to trace the
evolution of this new art form, made possible by modern invention, to
indicate what phases it is likely to pass through on the way to what
perfections, but that it is bound to add a new glory to architecture
is sure. This will come about in two ways: directly, by giving color,
quality, subtlety to outdoor and indoor lighting, and indirectly by
educating the eye to color values, as the ear has been educated by
music; thus creating a need for more color everywhere.

As light is the visible symbol of an inner radiance, so is color the
sign manual of happiness, of joy. Our cities are so dun and drab in
their outward aspects, by reason of the weight of care that burdens
us down. We decry the happy irresponsibility of the savage, and the
patient contentment of the Oriental with his lot, but both are able
to achieve marvels of color in their environment beyond the compass
of civilized man. The glory of mediaeval cathedral windows is a still
living confutation of the belief that in those far-off times the human
heart was sad. Architecture is the index of the inner life of those
who produced it, and whenever it is colorful that inner life contains
an inner joy.

In the coming Golden Age life will be joyous, and if it is joyous,
colour will come into architecture again. Our psychological state even
now, alone prevents it, for we are rich in materials and methods to
make such polychromy possible. In an article in a recent number
of _The Architectural Record_, Mr. Leon V. Solon, writing from an
entirely different point of view, divines this tendency, and expresses
the opinion that color is again renascent. This tendency is so marked,
and this opinion is so shared that we may look with confidence toward
a color-evolution in architectural art.

The question of the character of what may be called the ornamental
mode of the architecture of the New Age is of all questions the most
obscure. Evolution along the lines of the already existent does not
help us here, for we are utterly without any ornamental mode from
which a new and better might conceivably evolve. Nothing so betrays
the spiritual bankruptcy of the end of the Iron Age as this.

The only light on this problem which we shall find, dwells in the
realm of metaphysics rather than in the world of material reality.
Ornament, more than any other element of architecture, is deeply
psychological, it is an externalization of an inner life. This is
so true that any time-worn fragment out of the past when art was
a language can usually be assigned to its place and its period, so
eloquent is it of a particular people and a particular time. Could we
therefore detect and understand the obscure movement of consciousness
in the modern world, we might gain some clue to the language it would
later find.

It is clear that consciousness is moving away from its absorption in
materiality because it is losing faith in materialism. Clairvoyance,
psychism, the recrudescence of mysticism, of occultism--these signs
of the times are straws which show which way the wind now sets, and
indicate that the modern mind is beginning to find itself at home in
what is called _the fourth dimension_. The phrase is used here in
a different sense from that in which the mathematician uses it, but
oddly enough four-dimensional geometry provides the symbols by
which some of these occult and mystical ideas may be realized by the
rational mind. One of the most engaging and inspiring of these
ideas is that the personal self is a _projection_ on the plane of
materiality of a metaphysical self, or soul, to which the personal
self is related as is the shadow of an object to the object
itself. Now this coincides remarkably with the idea implicit in all
higher-space speculation, that the figures of solid geometry
are projections on a space of three dimensions, of corresponding
four-dimensional forms.

All ornament is in its last analysis geometrical--sometimes directly
so, as in the system developed by the Moors. Will the psychology
of the new dispensation find expression through some adaptation of
four-dimensional geometry? The idea is far from absurd, by reason of
the decorative quality inherent in many of the regular hypersolids of
four-dimensional space when projected upon solid and plane space.

If this suggestion seems too fanciful, there is still recourse to the
law of analogy in finding the thing we seek. Every fresh religious
impulse has always developed a symbology through which its truths are
expressed and handed down. These symbols, woven into the very texture
of the life of the people, are embodied by them in their ornamental
mode. The sculpture of a Greek temple is a picture-book of Greek
religion; the ornamentation of a Gothic cathedral is a veritable bible
of the Christian faith. Almost all of the most beautiful and enduring
ornaments have first been sacred symbols; the swastika, the "Eye of
Buddha," the "Shield of David," the wheel, the lotus, and the cross.

Now that "twilight of the world" following the war perhaps will
witness an _Avatara_--the coming of a World-Teacher who will rebuild
on the one broad and ancient foundation that temple of Truth which
the folly and ignorance of man is ever tearing down. A material
counterpart of that temple will in that case afterward arise. Thus
will be born the architecture of the future; and the ornament of that
architecture will tell, in a new set of symbols, the story of the
rejuvenation of the world.

In this previsioning of architecture after the war, the author
must not be understood to mean that these things will be realized
_directly_ after. Architecture, from its very nature, is the most
sluggish of all the arts to respond to the natural magic of the
quick-moving mind--it is Caliban, not Ariel. Following the war the
nation will be for a time depleted of man-power, burdened with
debt, prostrate, exhausted. But in that time of reckoning will come
reflection, penitence.

"And I'll be wise hereafter,
And seek for grace. What a thrice-double ass
Was I, to take this drunkard for a god,
And worship this dull fool."

With some such epilogue the curtain will descend on the great drama
now approaching a close. It will be for the younger generations, the
reincarnate souls of those who fell in battle, to inaugurate the work
of giving expression, in deathless forms of art, to the vision of that
"fairer world" glimpsed now only as by lightning, in a dream.

[Illustration]

ESSAYS

ORNAMENT FROM MATHEMATICS

I

THE WORLD ORDER

No fact is better established than that we live in an _orderly_
universe. The truth of this the world-war may for the moment, and to
the near and narrow view appear to contradict, but the sweep of human
history, and the stars in their courses, show an orderliness which
cannot be gainsaid.

Now of that order, _number_--that is, mathematics--is the more than
symbol, it is the very thing itself. Whence this weltering tide of
life arose, and whither it flows, we know not; but that it is governed
by mathematical law all of our knowledge in every field confirms. Were
it not so, knowledge itself would be impossible. It is because man is
a counting animal that he is master over all the beasts of the earth.

Number is the tune to which all things move, and as it were make
music; it is in the pulses of the blood no less than in the starred
curtain of the sky. It is a necessary concomitant alike of the sharp
bargain, the chemical experiment, and the fine frenzy of the poet.
Music is number made audible; architecture is number made visible;
nature geometrizes not alone in her crystals, but in her most
intricate arabesques.

If number be indeed the universal solvent of all forms, sounds,
motions, may we not make of it the basis of a new aesthetic--a loom on
which to weave patterns the like of which the world has never seen? To
attempt such a thing--to base art on mathematics--argues (some one
is sure to say) an entire misconception of the nature and function of
art. "Art is a fountain of spontaneous emotion"--what, therefore,
can it have in common with the proverbially driest, least spontaneous
preoccupation of the human mind? But the above definition concludes
with the assertion that this emotion reaches the soul "through various
channels." The transit can be effected only through some sensuous
element, some language (in the largest sense), and into this the
element of number and form must inevitably enter--mathematics is
"there" and cannot be thought or argued away.

[Illustration: PLATE XI. IMAGINARY COMPOSITION: THE PORTAL]

But to make mathematics, and not the emotion which it expresses, the
important thing, is not this to fall into the time-worn heresy of
art for art's sake, that is, art for form's sake--art for the sake of
mathematics? To this objection there is an answer, and as this answer
contains the crux of the whole matter, embraces the proposition by
which this thesis must stand or fall, it must be full and clear.

What is it, in the last analysis, that all art which is not
purely personal and episodical strives to express? Is it not the
_world-order_?--the very thing that religion, philosophy, science,
strive according to their different natures and methods to express?
The perception of the world-order by the artist arouses an emotion to
which he can give vent only in terms of number; but number is itself
the most abstract expression of the world order. The form and content
of art are therefore not different, but the same. A deep sense of this
probably inspired Pater's famous saying that all art aspires toward
the condition of music; for music, from its very nature, is the
world-order uttered in terms of number, in a sense and to a degree not
attained by any other art.

This is not mere verbal juggling. We have suffered so long from an
art-phase which exalts the personal, as opposed to the cosmic, that
we have lost sight of the fact that the great arts of antiquity,
preceding the Renaissance, insisted on the cosmic, or impersonal
aspect, and on this alone, just as does Oriental art, even today.
The secret essence, the archetypal idea of the subject is the
preoccupation of the Oriental artist, as it was of the Egyptian,
and of the Greek. We of the West today seek as eagerly to fix the
accidental and ephemeral aspect--the shadow of a particular cloud upon
a particular landscape; the smile on the face of a specific person, in
a recognizable room, at a particular moment of time. Of symbolic art,
of universal emotion expressing itself in terms which are universal,
we have very little to show.

The reason for this is first, our love for, and understanding of,
the concrete and personal: it is the _world-aspect_ and not the
_world-order_ which interests us; and second, the inadequacies of
current forms of art expression to render our sense of the eternal
secret heart of things as it presents itself to our young eyes.
Confronted with this difficulty, we have shirked it, and our ambition
has shrunk to the portrayal of those aspects which shuffle our poverty
out of sight. It is not a poverty of technique--we are dexterous
enough; nor is it a poverty of invention--we are clever enough; it is
the poverty of the spiritual bankrupt trying to divert attention by a
prodigal display of the smallest of small change.

Reference is made here only to the arts of space; the arts of
time--music, poetry, and the (written) drama--employing vehicles more
flexible, have been more fortunate, though they too suffer in some
degree from worshipping, instead of the god of order, the god of
chance.

The corrective of this is a return to first principles: principles so
fundamental that they suffer no change, however new and various their
illustrations. These principles are embodied in number, and one might
almost say nowhere else in such perfection. Mathematics is not the
dry and deadly thing that our teaching of it and the uses we put it
to have made it seem. Mathematics is the handwriting on the human
consciousness of the very Spirit of Life itself. Others before
Pythagoras discovered this, and it is the discovery which awaits us
too.

To indicate the way in which mathematics might be made to yield the
elements of a new aesthetic is beyond the province of this essay, being
beyond the compass of its author, but he makes bold to take a single
phase: ornament, and to deal with it from this point of view.

The ornament now in common use has been gathered from the dust-bin
of the ages. What ornamental _motif_ of any universality, worth, or
importance is less than a hundred years old? We continue to use the
honeysuckle, the acanthus, the fret, the egg and dart, not because
they are appropriate to any use we put them to, but because they are
beautiful _per se_. Why are they beautiful? It is not because they
are highly conventionalized representations of natural forms which
are themselves beautiful, but because they express cosmic truths. The
honeysuckle and the acanthus leaf, for example, express the idea
of successive impulses, mounting, attaining a maximum, and
descending--expanding from some focus of force in the manner universal
throughout nature. Science recognizes in the spiral an archetypal
form, whether found in a whirlpool or in a nebula. A fret is a series
of highly conventionalized spirals: translate it from angular to
curved and we have the wave-band; isolate it and we have the volute.
Egg and dart are phallic emblems, female and male; or, if you prefer,
as ellipse and straight line, they are symbols of finite existence
contrasted with infinity. [Figure 1.]

[Illustration: Figure 1.]

Suppose that we determine to divest ourselves of these and other
precious inheritances, not because they have lost their beauty and
meaning, but rather on account of their manifold associations with a
past which the war makes suddenly more remote than slow centuries have
done; suppose that we determine to supplant these symbols with others
no less charged with beauty and meaning, but more directly drawn from
the inexhaustible well of mathematical truth--how shall we set to
work?

We need not _set_ to work, because we have done that already, we are
always doing it, unknowingly, and without knowing the reason why. All
ornamentalists are subjective mathematicians--an amazing statement,
perhaps, but one susceptible of confirmation in countless amusing
ways, of which two will be shown.

[Illustration: Figure 2.]

Consider first your calendar--your calendar whose commonplace face,
having yielded you information as to pay day, due day, and holiday,
you obliterate at the end of each month without a qualm, oblivious to
the fact that were your interests less sordid and personal it would
speak to you of that order which pervades the universe; would make you
realize something of the music of the spheres. For on that familiar
checkerboard of the days are numerical arrangements which are
mysterious, "magical"; each separate number is as a spider at the
center of an amazing mathematical web. That is to say, every number
is discovered to be half of the sum of the pairs of numbers which
surround it, vertically, horizontally, and diagonally: all of the
pairs add to the same sum, and the central number divides this sum by
two. A graphic indication of this fact on the calendar face by means
of a system of intersecting lines yields that form of classic grille
dear to the heart of every tyro draughtsman. [Figure 2.] Here is
an evident relation between mathematical fact and ornamental mode,
whether the result of accident, or by reason of some subconscious
connection between the creative and the reasoning part of the mind.

To show, by means of an example other than this acrostic of the days,
how the pattern-making instinct follows unconsciously in the groove
traced out for it by mathematics, the attention of the reader is
directed to the design of the old Colonial bed-spread shown in Figure
3. Adjacent to this, in the upper right hand corner, is a magic
square of four. That is, all of the columns of figures of which it is
composed: vertical, horizontal and diagonal add to the same sum: 34.
An analysis of this square reveals the fact that it is made up of
the figures of two different orders of counting: the ordinary order,
beginning at the left hand upper corner and reading across and down in
the usual way, and the reverse-ordinary, beginning at the lower right
hand corner and reading across and up. The figures in the four central
cells and in the four outside corner cells are discovered to belong
in the first category, and the remaining figures in the second. Now
if the ordinary order cells be represented by white, and the reverse
ordinary by black, just such a pattern has been created as forms the
decorative motif of the quilt.

It may be claimed that these two examples of a relation between
ornament and mathematics are accidental and therefore prove nothing,
but they at least furnish a clue which the artist would be foolish not
to follow up. Let him attack his problem this time directly, and
see if number may not be made to yield the thing he seeks: namely,
space-rhythms which are beautiful and new.

We know that there is a beauty inherent in _order_, that necessity of
one sort or another is the parent of beauty. Beauty in architecture
is largely the result of structural necessity; beauty in ornament
may spring from a necessity which is numerical. It is clear that the
arrangement of numbers in a magic square is necessitous--they must be
placed in a certain way in order that the summation of every column
shall be the same. The problem then becomes to make that necessity
reveal itself to the eye. Now most magic squares contain a _magic
path_, discovered by following the numbers from cell to cell in
their natural order. Because this is a necessitous line it should not
surprise us that it is frequently beautiful as well.

[Illustration: Figure 3.]

The left hand drawing in Figure 4 represents the smallest aggregation
of numbers that is capable of magic square arrangement. Each vertical,
horizontal, and corner diagonal column adds up to 15, and the sum of
any two opposite numbers is 10, which is twice the center number. The
magic path is the endless line developed by following, free hand, the
numbers in their natural order, from 1 to 9 and back to 1 again. The
drawing at the right of Figure 4 is this same line translated into
ornament by making an interlace of it, and filling in the larger
interstices with simple floral forms. This has been executed in white
plaster and made to perform the function of a ventilating grille.

Now the number of magic squares is practically limitless, and while
all of them do not yield magic lines of the beauty of this one, some
contain even richer decorative possibilities. But there are also other
ways of deriving ornament from magic squares, already hinted at in the
discussion of the Colonial quilt.

[Illustration: Figure 4.]

[Illustration: Figure 5.]

Magic squares of an even number of cells are found sometimes to
consist of numbers arranged not only in combinations of the ordinary
and the reverse ordinary orders of counting, but involving two others
as well: the reverse of the ordinary (beginning at the upper right
hand, across, and down) and the reversed inverse, (beginning at the
lower left hand, across, and up). If, in such a magic square, a simple
graphic symbol be substituted for the numbers belonging to each order,
pattern spontaneously springs to life. Figures 5 and 6 exemplify the
method, and Figures 7 and 8 the translation of some of these squares
into richer patterns by elaborating the symbols while respecting their
arrangement. By only a slight stretch of the imagination the beautiful
pierced stone screen from Ravenna shown in Figure 9 might be conceived
of as having been developed according to this method, although of
course it was not so in fact. Some of the arrangements shown in Figure
6 are closely paralleled in the acoustic figures made by means of
musical tones with sand, on a sheet of metal or glass.

[Illustration: Figure 6.]

[Illustration: Figure 7.]

The celebrated Franklin square of 16 cells can be made to yield a
beautiful pattern by designating some of the lines which give the
summation of 2056 by different symbols, as shown in Figure 10. A free
translation of this design into pattern brickwork is indicated in
Figure 11.

If these processes seem unduly involved and elaborate for the
achievement of a simple result--like burning the house down in
order to get roast pig--there are other more simple ways of deriving
ornament from mathematics, for the truths of number find direct and
perfect expression in the figures of geometry. The squaring of
a number--the raising of it to its second power--finds graphic
expression in the plane figure of the square; and the cubing of a
number--the raising of it to its third power--in the solid figure
of the cube. Now squares and cubes have been recognized from time
immemorial as useful ornamental motifs. Other elementary geometrical
figures, making concrete to the eye the truths of abstract number, may
be dealt with by the designer in such a manner as to produce ornament
the most varied and profuse. Moorish ceilings, Gothic window tracery,
Grolier bindings, all indicate the richness of the field.

[Illustration: Figure 8.]

[Illustration: PLATE XII. IMAGINARY COMPOSITION. THE BALCONY]

[Illustration: Figure 9.]

Suppose, for example, that we attempt to deal decoratively which such
simple figures as the three lowest Platonic solids--the tetrahedron,
the hexahedron, and the octahedron. [Figure 12.] Their projection on a
plane yields a rhythmical division of space, because of their inherent
symmetry. These projections would correspond to the network of lines
seen in looking through a glass paperweight of the given shape, the
lines being formed by the joining of the several faces. Figure 13
represents ornamental bands developed in this manner. The dodecahedron
and icosahedron, having more faces, yield more intricate patterns, and
there is no limit to the variety of interesting designs obtainable by
these direct and simple means.

[Illustration: Figure 10.]

If the author has been successful thus far in his exposition, it
should be sufficiently plain that from the inexhaustible well of
mathematics fresh beauty may be drawn. But what of its significance?
Ornament must _mean something_; it must have some relation to the
dominant ideation of the day; it must express the psychological mood.

What is the psychological mood? Ours is an age of transition; we live
in a changing world. On the one hand we witness the breaking up of
many an old thought crystal, on the other we feel the pressure of
those forces which shall create the new. What is nature's first
visible creative act? The formation of a geometrical crystal. The
artist should take this hint, and organize geometry into a new
ornamental mode; by so doing he will prove himself to be in relation
to the _anima mundi_. It is only by the establishment of such a
relation that new beauty comes to birth in the world.

[Illustration: Figure 11.]

Ornament in its primitive manifestations is geometrical rather than
naturalistic. This is in a manner strange, that the abstract and
metaphysical thing should precede the concrete and sensuous. It would
be natural to suppose that man would first imitate the things which
surround him, but the most cursory acquaintance with primitive art
shows that he is much more apt to crudely geometrize. Now it is
not necessary to assume that we are to revert to the conditions of
savagery in order to believe that in this matter of a sound aesthetic
we must begin where art has always begun--with number and geometry.
Nevertheless there is a subtly ironic view which one is justified in
holding in regard to quite obvious aspects of American life, in the
light of which that life appears to have rather more in common with
savagery than with culture.

[Illustration: Figure 12.]

[Illustration: Figure 13.]

The submersion of scholarship by athletics in our colleges is a case
in point, the contest of muscles exciting much more interest and
enthusiasm than any contest of wits. We persist in the savage habit of
devouring the corpses of slain animals long after the necessity for it
is past, and some even murder innocent wild creatures, giving to their
ferocity the name of sport. Our women bedeck themselves with furs and
feathers, the fruit of mercenary and systematic slaughter; we perform
orgiastic dances to the music of horns and drums and cymbals--in
short, we have the savage psychology without its vital religious
instinct and its sure decorative sense for color and form.

But this is of course true only of the surface and sunlit shadows of
the great democratic tide. Its depths conceal every kind of subtlety
and sophistication, high endeavour, and a response to beauty and
wisdom of a sort far removed from the amoeba stage of development
above sketched. Of this latter stage the simple figures of Euclidian
plane and solid geometry--figures which any child can understand--are
the appropriate symbols, but for that other more developed state of
consciousness--less apparent but more important--these will not do.
Something more sophisticated and recondite must be sought for if we
are to have an ornamental mode capable of expressing not only the
simplicity but the complexity of present-day psychology. This need not
be sought for outside the field of geometry, but within it, and by
an extension of the methods already described. There is an altogether
modern development of the science of mathematics: the geometry of
four dimensions. This represents the emancipation of the mind from
the tyranny of mere appearances; the turning of consciousness in a
new direction. It has therefore a high symbolical significance as
typifying that movement away from materialism which is so marked a
phenomenon of the times.

Of course to those whose notion of the fourth dimension is akin to
that of a friend of the author who described it as "a wagon-load
of bung-holes," the idea of getting from it any practical advantage
cannot seem anything but absurd. There is something about this form
of words "the fourth dimension" which seems to produce a sort of
mental-phobia in certain minds, rendering them incapable of perception
or reason. Such people, because they cannot stick their cane into it
contend that the fourth dimension has no mathematical or philosophical
validity. As ignorance on this subject is very general, the following
essay will be devoted to a consideration of the fourth dimension and
its relation to a new ornamental mode.

[Illustration]

II

THE FOURTH DIMENSION

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.

[Illustration: Figure 14. TWO PROJECTIONS OF THE HYPERCUBE OR
TESSERACT, AND THEIR TRANSLATION INTO ORNAMENT.]

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.

[Illustration: PLATE XIII. IMAGINARY COMPOSITION: THE AUDIENCE
CHAMBER]

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.

[Illustration: Figure 15. DIRECT VIEW AXES SHOWN BY HEAVY LINES TILTED
VIEW APEXES SHOWN BY CIRCLES THE 16-HEDROID IN PLANE PROJECTION]

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.

[Illustration: Figure 16.]

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.

[Illustration: Figure 17. CEILING DECORATION FROM THE TEMPLE OF
DENDERAH]

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!

[Illustration]

[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

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