Selected Quotes from 
The Fourth Dimension and Non-Euclidean Geometry in Modern Art, 
see Bibliography at end of list.

p 29. Hinton, A New Era of Thought, 1888.
..I shall bring forward a complete system of four dimensional thought -
mechanics, science, and art. The necessary condition is, that the mind acquire
the power of using four-dimensional space as it now does three dimensional.
And there is a condition which is no less important. We can never see, for
instance, four dimensional pictures with our bodily eyes, but we can with our
mental and inner eye.



p 33. H.G. Wells, The Time Machine
Clearly,. . .  any real body must have extension in four directions: it must
have Length, Breadth, Thickness, and - Duration.



p53 Pawlowski 
The vocabulary of our language is in fact conceived according to the given
facts of three dimensional space. Words do not exist which are capable of
defining exactly the strange, new sensations that are experienced when one
raises himself forever above the vulgar world.
..
When one reaches the country of the fourth dimension when one is freed forever
from the notions of space and time, it is with this intelligence that one
thinks and reflects. Thanks to it, one finds himself blended with the entire
universe, with so called future events, as with so called past events.



p. 73 Jouffret
For our part, we have already stated our opinion. It is that the reader should
not hope to objectify, as does the blindfold chess player with the pieces on
his mental chessboard, either the 4 dimensional beings which are the object
of this study, or the movements that we impart to them; he would exhaust his
intelligence in vain efforts seeking to break through the infinitely thin
plane which extends between those beings and himself. If there are really four
dimensions, our mind is confined in the first three.



p. 76 Apollinaire, La peinture Nouvelle
..I would say that in the plastic arts, the forth dimension is engendered by
the three known dimensions; it represents the immensity of space eternalising
itself in all directions at any given moment.
.. The art of the new painters takes the infinite universe as its ideal, and
it is to the fourth dimension alone that we owe this new norm of the perfect,
which permits the artist to proportion objects in accordance with the degree
of plasticity he desires them to have.



p77 Gleizes and Metzinger, Du Cubisme
There is nothing real outside ourselves, there is nothing real except the
coincidence of sensation and an individual mental direction.



p80 Picasso I paint objects as I think them, not as I see them.



p82 Poincare
But apart from the data of sight and touch.. they accompany all our movements,
the muscular sensations. From this point of view, motor space would have as
many dimensions as we have muscles.


p110 Boccioni
It seems clear to me that this succession is not to be found in repetition of
legs, arms and faces,.. it is achieved through the intuitive search for the
unique form which gives continuity in space. Dynamic form is a species of
fourth dimension.

The Plastic Analogies of Dynamism, Futurist Manifesto. 1913.
We must forget exterior reality and our knowledge of it in order to create the
new dimensions.



Duchamp, Salt Seller 1973, re the Bride of the large glass
The shadow cast by a 4 diml figure on our space is a 3diml shadow (see
Jouffret). 



Bragdon 1915, Projective ornament
Art must attune itself to this new 4D keyhole of the modern world,
consciousness is moving towards the conquest of a new space. Ornament must
indicate this move.

Are we at the point of discovering that the only reality is thought -
consciousness?
If so by a long detour, Western Science arrives at the same conclusion as
Eastern mysticism: that reality is only maya, illusion - the mirror of
consciousness.



Francis Picabia
Art can express the 4d of the soul but not the 3d of actuality. It cannot
legitimately portray objects which exist in space and so involve the 3rd
dimension. There should be no perspective in painting.



1924 paper Lissitsky: Proun advances toward the construction of a new space and by dividing it into
the elements of its first second and third dimensions passing through time it, the proun, constructs a many sided but unified image of nature agreed with van doesburg the relativity theory the absolute of a all measures and standards has been destroyed.



Severini 
the 4d is finally only the identification of object and subject time and space matter and energy



Theo Von Doesburg, What is Dada, 1923
Dada completely negates the generally acknowledged duality of matter and mind,
woman and man, and in doing so creates the point of indifference, a point
beyond mans understanding of time and space - in this connection Dada is one
of the strongest manifestations of the 4d.



Eiseinstein 1929
Einstein assured us The non mathematician is seized by a mysterious shuddering
when he learns of 4d things, by a feeling not unlike that awakened by thoughts
of the occult. And yet there is no more commonplace statement that the world
in which we live in is a 4d space time continuum.
Possessing such as excellent medium as the cinema we should soon learn a
concrete orientation in this 4d s t continuum and feel as much at home in it
as our house slippers and we'll soon be posing the question of a fifth
dimension.



Charles Sirato, 1936 The Manifeste Dimensioniste Revue N+1 

Animated by a new conception of the world, the arts in a collective
fermentation (interpenetration of the arts) have begun to stir. 
And Each of them has involved with a new dimension, objectifying the weighty spiritual
consequences of this fundamental change. Thus the constructivist tendency
compels:

1 Literature to depart from the line and move in the plane

2 Painting to leave the plane and occupy space: Painting in space,
constructivism, multimedia compositions.

3 Sculpture to abandon the closed immobile and dead space, that is to say the
3d space of Euclid, in order to conquer for artistic expression the four
dimensional space of Minkowsky.



Then must come the creation of an absolutely new art: cosmic art (vaporisation
of sculpture), syno-sense theatre. The total conquest of the art of 4d space
(a Vacuum artis until now) Rigid material is abolished and replaced by gaseous
materials.



signed: Ben Nicholson, Alexander Calder, Vincent Huidobro, Kakabdze, Kobro,
Joan Miro, Moholy Nagy, Antonio Pedro, Arp, PA Birot, Camille Bryen, Robert
Delauney, Cesar Doemla, Marcel Duchamp, Kandinsky, Fred Karm, Kotchar, Nina
Negri, Mario Nissim, F Picabia, Prampolini, Prinner, Rathamann, Ch. Siarto,
Sonia Delauney, Sophie Tauber Arp.




Bibliography



The Fourth Dimension and Non-Euclidean Geometry in Modern Art,
Linda Dalrymple Henderson, Princeton University Press, 1983.



Flatland: A Romance of Many Dimensions by a Square, Edwin Abbott Abott,
Seeley & co., 1884.



The Fourth Dimension, toward a geometry of higher reality, Rudy Rucker,
Houghton Mifflin, 1984.



Art and the Electronic Age, Frank Popper, Thames & Hudson, 1993.



Constructivism, origins and evolution, George Rickey, Studio Vista, 1967.



Marcel Duchamp, Eros c'est la vie, Alice Goldfarb Marquis, Whitson, 1981.