FINE ARTS LIBRARY
FL 1494 -
PROJECTIVE
ORNAMENT
331



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Danman Rocs
Claude
Bragden
al des
Sept
1016





PROJECTIVES
ORNAMENTO
Claude Bragdon
ROCHESTERNY
THE MANAS PRESS
4191504


DEDICATED TO E. B.



THE NEED OF A NEW FORM
LANGUAGE
We are without a form language suitable to the needs of today. Archi-
tecture and ornament constitute such a language. Structural necessity
may be depended upon to evolve fit and expressive architectural forms,
but the same thing is not true of ornament. This necessary element
might be supplied by an individual genius, it might be derived from
the conventionalization of natural forms, or lastly it might be devel-
oped from geometry. The geometric source is richest in promise.
ARCHITECTURE AND ORNAMENT
IN contemplating the surviving relics of any period
1 in which the soul of a people achieved aesthetic
utterance through the arts of space, it is clear that
in their architecture and in their ornament they had
a form language as distinctive and adequate as any
spoken language. Today we have no such language.
This is equivalent to saying that we have not at-
tained to aesthetic utterance through the arts of
space. That we shall attain to it, that we shall
develop a new form language, it is impossible to
doubt; but not until after we realize our need, and
set about supplying it.


PROJECTIVE OR N A MENT
Consider the present status of architecture,
which is preëminently the art of space. Modern
architecture, except on its en-
gineering side, has not yet
found itself: the style of a
building is determined, not
by necessity, but by the whim
of the designer; it is made up
of borrowings and survivals.
So urgent is the need of more
appropriate and indigenous
architectural forms with
which to clothe the steel
framework for which some
sort of protective covering is
of first importance, that some
architects have ceased search-
ing in the cemetery of a too
Pentahedroids
sacredly cherished past. They
are seeking to solve their
problems rather by a process of elimination, using
the most elementary forms and the materials readiest
to hand. In thus facing their difficulty they are re-
creating their chosen art, and not abrogating it.
The development of new architectural forms
appropriate to the new structural methods is already
under way, and its successful issue may safely be
left to necessity and to time; but the no less urgent
need of fresh motifs in ornament has not yet even
begun to be met. So far as architecture is con-
cerned, the need is acute only for those who are
determined to be modern. Having perforce abandon-
ed the structural methods of the past, and the forms

CV


PROJECTIVE OR N A M E N T
associated with these methods, they nevertheless
continue to use the ornament associated with what
they have abandoned: the clothes are new, but not
the collar and necktie. The reason for this failure
of invention is that while common sense, and a
feeling for fitness and proportion, serve to produce
the clothing of a building, the faculty for originating
appropriate and beautiful ornament is one of the
rarest in the whole range of art. Those arts of space
which involve the element of decoration suffer
from the same lack, and for a similar reason.
Three possible sources of supply suggest them-
selves for this needed element in a new form language.
Ornament might be the single-handed creation of an
original genius in this partic-
ular field; it might be de-
rived from the conventional-
ization of native flora, as it
was in the past; or it might
be developed from geometry.
Let us examine each of these
possibilities in turn.
The first we must reject.
Even supposing that this art
saviour should appear as some
rarely gifted and resourceful
creator of ornament, it would
be calamitous to impose the
idiosyncratic space rhythm of
a single individual upon an
entire architecture. Fortu Tesseracts: Cubes
nately such a thing is impossible. In Mr. Louis
Sullivan, for example, we have an ornamentalist


PROJECTIVE OR N A MENT
GEOMETRY
. There remains at least one other possibility, and
it is that upon which we shall now concentrate all
our attention, for it seems indeed an open door.
Geometry and number are at the root of every kind
of formal beauty. That the tapestry of nature is
woven on a mathematical framework is known to
every sincere student. As Emerson says, “Nature
geometrizes ... moon, plant, gas, crystal, are con-
crete geometry and number.”
Art is nature selected, ar-
ranged, sublimated, triply re-
fined, but still nature, how-
ever refracted in and by con-
sciousness. If art is a higher
power of nature, the former
must needs submit itself to
mathematical analysis too.
The larger aspect of this whole
matter — the various vistas
that the application of geom-
etry to design opens up—has
been treated by the author in
a previous volume*. Narrow-
ed down to the subject of
ornament, our question is,
Tesseract
what promise does geometry
hold of a new ornamental mode?
In the past, geometry has given birth to many
characteristic and consistent systems of ornamenta-
tion, and from its very nature is capable of giving
*The Beautiful Necessity.


PROJECTIVE ORNAMENT
birth to many more. Much of Hindu, Chinese, and
Japanese ornament was derived from geometry, yet
these all differ from one another, and from Moorish
ornament, which owes its origin to the same source.
Gothic tracery, from Perpendicular to Flamboyant,
is nothing but a system of straight lines, circles,
and the intersecting arcs of circles, variously ar-
ranged and combined. The interesting development
of ornament in Germany which has taken place of
late years, contains few elements other than the
square and the circle, the parallelogram and the
ellipse. It is a remarkable fact that ornamentation,
in its primitive manifestations, is geometrical rather
than naturalistic, though the geometrical source is
the more abstract and purely intellectual of the two.
Is not this a point in its favor? The great war
undoubtedly ends an era:“the old order changeth.”
Our task is to create the art of the future: let us
then draw our inspiration from the deepest, purest
well.
Geometry is an inexhaustible well of formal
beauty from which to fill our bucket; but before the
draught is fit for use it should be examined, analyzed,
and filtered through the consciousness of the artist.
If with the zeal of the convert we set at once to
work with T square and compass to devise a new
system of ornament from geometry, we shall proba-
bly end where we began. Let us, therefore, by a
purely intellectual process of analysis and selection,
try to discover some system of geometrical forms
and configurations which shall yield that new orna-
mental mode of which we are in search.
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0
0


II
ORNAMENT AND PSYCHOLOGY
*..
Ornament is the outgrowth of no practical necessity, but of a striving
toward beauty. Our zeal for efficiency has resulted in a corresponding
aesthetic infertility. Signs are not lacking that consciousness is now
looking in a new direction-away from the contemplation of the facts
of materiality towards the mysteries of the supersensuous life. This
transfer of attention should give birth to a new aesthetic, expres-
sive of the changing psychological mood. The new direction of con-
sciousness is well suggested in the phrase, The Fourth Dimension of
Space, and the decorative motifs of the new aesthetic may appropri-
ately be sought in four-dimensional geometry.
.---
THE ORNAMENTAL MODE AND THE PSYCHOLOGICAL
MOOD
ARCHITECTURAL forms and features, such as
11 the column, the lintel, the arch, the vault, are
the outgrowth of structural necessity, but this is not
true of ornament. Ornament develops not from the
need and the power to build, but from the need and
the power to beautify. Arising from a psychological
impulse rather than from a physical necessity, it re-
flects the national and racial consciousness. To such
a degree is this true that any mutilated and time-
worn fragment out of the great past when art was a
language can without difficulty be assigned its place
and period. Granted a dependence of the ornamental
mode upon the psychological mood, our first business
is to discover what that mood may be.
A great change has come over the collective
consciousness: we are turning from the accumula-


PROJECT I V E O RN A M E N T
A Primer of Higher Space may be found useful, and
there is besides a literature upon the subject.
If after reviewing this literature the reader is
disposed to regard the fourth dimension as a mere
mathematical convention, it matters not in the
least, so long as he is able to make practical use of it.
He may likewise, with equal justice, question the
existence of minus quantities, for example, but they
produce practical results.
With this brief explanation the author now turns
up his shovelful, leaving it to the discerning to
determine whether it contains any gold.


PROTECTIVE ORN A M E N T
If we have really achieved the plane representa-
tion of a pentahedroid, it should be easy to identify
the projections of the five tetrahedral cells or bound-
ing tetrahedrons, just as we are able to identify the
four equilateral sides of the tetrahedron in plane pro-
jection. We find that it is possible to do this. For
convenience of identification, these are separately
shown. By dint of continued gazing at this pentagon
circumscribing a five-pointed star, and by trying to
recognize all its intricate inter-relations, we may come
finally to the feeling that it is not merely a figure on a
plane, but that it represents a hypersolid of hyper-
space, related to the tetrahedron as that is related
to the triangle.
THE CORRESPONDING HIGHER DEVELOPMENTS OF THE
SQUARE
Let us next consider the series beginning with the
square. The cube may be conceived of as developed
by the movement of a
TESSERACT GENERATION AND square in a direction at
PLANE PROJECTION
right angles to its two
dimensions, a distance
equal to the length of
SQUARE
one of its sides. The
direction of this move-
TESSERACT or HYPERCUBE)
ment can be represented
JCUDE
on a plane anywhere
we wish. Suppose we
2
establish it as diagonal-
ly downward and to the right. The resultant figure is
a cube in isometric perspective, for each of the four
18


PROJECTIVE OR N A MENT
sions; the plane representations of the tetrahedron
and the cube portray certain relations in solid space,
while those of the pentahedroid and the tesseract
portray relations peculiar to four-dimensional space.
It will be observed that the
decorative value of the figures
increases as they proceed from
space to space: the higher-
dimensional developments are
more beautiful and carry a
greater weight of meaning.
dictum, “Beauty is Truth;
Truth, Beauty.”
The above exercises consti-
tute the only clue needed to
understand the system of orna-
bibilibisinibinizibile
Sigisisisi liigi
symmetrical plane figure has
its three-dimensional correla-
tive, to which it is related as Tetrahedrons: Prisms
a boundary or a cross-section.
These solids may in turn be conceived of as boundaries
or cross-sections of corresponding figures in four-
dimensional space. The plane projections of these
hypersolids are the motifs mainly used in Projective
Ornament.


PROJECTIVE ORN A MENT
THE DECORATIVE VALUE OF THESE FIGURES
M
1
*
cise his skill.
As this is a handbook for artists and not a geome-
trical treatise, the description of regular polyhedroids
need not be carried further than this. The reader
who is ambitious to continue, from the 24-hedroid
even unto the 600-hedroid, is referred to the geo-
metry of four dimensions; upon this he can exer-
cise his mind and experience for himself the stern
joy of the conquest of new spaces. But the designer
has already, in the penta-
hedroid, the hypercube, and
THE HEXADEKAHE DROID
the hexadekahedroid, ample
AXES
material on which to exer-
cise his skill. It should be
remembered that just as in
plane geometry a regular
polygon can always be in-
scribed in a circle, and in
geometry of three dimen-
sions a regular polyhedron
can always be inscribed in
a sphere, so in four-dimensional geometry every
regular polyhedroid can be inscribed in a hyper-
sphere. In plane projection this hypersphere would
be represented by a circle circumscribing the plane
figure representing the polyhedroid.
Almost any random arrangement on the page of
these three hypersolids in plane projection will
serve to indicate what largess of beauty is here-
they are like cut jewels, like flowers, and like frost.
Combined symmetrically they form patterns of
endless variety.
13





PROJECTIVE OR N A MENT
It is a simple feat of
PATTERN FROM MAGIC SQUARES
mnemonics. The per-
former must remember
64 numbers in their or-
der, the sequence which
yields the magic line in
MAGIC LINE FROM MAGIC LINE OF 3
the magic square of 8.
ASQUALE OFS TAKEN FOUR TIMES The plotting of this line
is shown in Figure 23;
its decorative applica-
tion in the binding of
The Beautiful Necessity.
Euler, the great mathe-
matician, constructed
knight's move squares
PATH TRACED BY THE KNIGHT IN MAKING
WHAT IS KNOWN AS THE KNIGHT'S TOUR of 5 and of 6, having
peculiar properties. In
one diagram of Figure
28 the natural numbers
show the path of a knight moving in such a manner
that the sum of the pairs of numbers opposite to
and equidistant from the middle figure is its double.
In the other diagram the knight returns to its
starting cell in such a manner that
the difference between the pairs of
numbers opposite to and equidis-
tant from the middle point is 18.
26

W
MAGIC LINE OF 7
INTERLACES
Figure 28 shows interlaces derived
from these two magic squares.
They so resemble the braided bands
found on Celtic crosses that one
21
52


PROJECTIVE OR N A M E N T
1 to 16, they will be found to fall magically into the
same places they occupy in the magic square of 4.
Because all magic lines in magic squares have, in
their corresponding cubes, this three-dimensional ex-
tension, the patterns derived from magic squares
come properly under the head of Projective Orna-
ment.

BINDING THE MAGIC LINE OF 3. A TESSERACT





PROJECTIVE ORNAMENT
SPACE AND TIME: THE FIELD AND THE FRAME
Now the characteristic of time is succession; in time
alone one thing follows another in endless sequence.
The unique characteristic of space is simultaneity,
for in space alone everything exists at once. In
classifying the arts, for example, music would go
into the time box, for it is in time alone, being
successive; architecture, on the other hand, would
go into the space box. Yet because nothing is pure,
so to speak, architecture has something of the ele-
ment of succession, and music of simultaneousness.
An arcade or a colonnade may be spoken of as
successive; while a musical chord, consisting of
several notes sounded together, is simultaneous.
The same thing holds true throughout nature.
The time element and the space element everywhere
appear, either explicitly or implicitly, the first as
succession, the second as simultaneity.
In ornament we have the field and the frame,
and the unfolding of living forms in space within
some fixed time cycle may be thought of as symbo-
lized by a foliated field and a geometrical frame or
border. In the field, the units will be disposed with
relation to points and radiating lines, implying the
simultaneity of space, and in the border they will
be arranged sequentially, implying the succession of
time (Figure 31). Seeking greater interest, subtlety,
and variety, we have, in the projected plane re-
presentations of symmetrical three-fold and four-
fold solids, a frame rhythmically subdivided. These
subdivisions of a frame may be taken to represent
lesser time cycles within a greater, and the arabesque
with which these spaces can be filled may be felt to
66


PROJECTIVE OR N A MENT
symbolize the growth of
a plant through succes-
siveseasons, or the
development of an indi-
vidual in different incar-
nations.
TIME AND SPACE SYMBOL-
IZED IN ORNAMENTAS
SUCCESSIVE ( 9)
SIMULTANEOUS
TDI
A BOOK ALL BONES AND
NO FLESH
SIMULTANEOUS
It is by artifices such as
these that the world
order gets itself external-
ized in forms and ar-
SUCCESSIVE
rangements which ex-
press “the life movement
of the spirit through
the rhythm of things.” This is the very essence
of art: first to perceive, and then to publish
news from that nowhere of the world from which all
things flow and to which all things return. It will
be evident to the discerning reader from what has
been said regarding the symbolic value of the straight
line and the curve (the frame and the arabesque)
that the whole subject of foliated or free-spreading
ornament has received scant attention from the
author. This intentional concentration upon the
straight line explains the poverty and hard monotony
of many of the diagrams here presented. They are
not so much ornament as the osseous framework of
ornament. But by reason of our superficial manner
of observing nature, our preoccupation with mere
externals, we have lost our perception of her beauti-
68



Conwy
AUSZUB
IKKAA





PROJECTIVE OR N A MENT
into curves; and by subjecting them to these modi-
fications their beauty is often augmented. Yet if
their geometrical truth and integrity be too much
tampered with, they will be found to have lost a
certain precious quality. It would seem as though
they were beautiful to the eye in proportion as they

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