Art in the Fourth Dimension:

Art in the Fourth Dimension:
Giving Form to Form – The Abstract Paintings of Piet Mondrian


Runette Kruger
Tshwane University of Technology, South Africa


Citation: Runette Kruger, “Art in the Fourth Dimension: Giving Form to Form – The Abstract Paintings of Piet
Mondrian”, Spaces of Utopia: An Electronic Journal, nr. 5, Summer 2007, pp. 23-35 <http://ler.letras.up.pt > ISSN
1646-4729.



The aim of this paper is to explore the art and utopian ideology of early-twentieth-
century Dutch artist Piet Mondrian. As an idealist, Mondrian believed that his art
would be instrumental in establishing the utopia he conceived of, and his writings
and art are the painstaking and eloquent manifestations of his efforts in this regard.
Mondrian is a key figure in Modernist art, as co-founder, with Theo van
Doesburg, of the Dutch De Stijl movement (1917-1924), and as a pioneer in the
development of twentieth-century abstraction – it was Mondrian who took non-
representation further than even the revolutionary Picasso, with his cubist
compositions, had.
The background against which Mondrian formulated his notions on utopia is
markedly dystopian. The turn of the twentieth century was a time in which the gap
left by loss of faith in the Church could be only partially filled by a belief in
positivism. The result was a fin de siècle characterised by a pervasive nihilism
(Tuchman 1986: 19). This ideological impasse was exacerbated by the outbreak of
the First World War. The turmoil and cruelty engendered by this event created a

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fertile basis for the development of new and radical ideologies (Long 1986: 206).
Critic Mathew Shadbolt notes: “[M]any artists attempted ways in which to remove
themselves from wartime activities [but] [t]he notion of transcending world disorder
... was arguably no better explored in these [inter-war] years than in the work of ...
Piet Mondrian” (Shadbolt 1996: §7, 9). Mondrian’s thought and art were created in
reaction to a world he found both brutal and brutalising – a pro-active attempt to
establish a utopia on earth.
Mondrian named his ideology, and abstract style of painting, Neoplasticism
(Nieuwe Beelding). An analysis of Neoplastic theory reveals a non-material,
universalist utopia based on the balancing of archetypal opposites. In his writings
Mondrian borrowed from theosophy, Hegel, and Plato, as well as mystical notions
of a transcendent fourth dimension. It is, furthermore, possible to show that
Mondrian’s conception of utopia shares aspects of Hindu, Buddhist and Daoist
thought.
Mondrian dwells on the notion of the universal, and for him Neoplasticism is
“the most direct aesthetic manifestation of the universal possible” (Mondrian
1918a: 51, artist’s own emphasis). In order to do justice to the universal, Mondrian
felt it necessary to reduce natural appearance, in visual terms, to its essential
constituents. Hence, Mondrian’s pure abstract compositions consist of straight,
black lines placed perpendicularly to each other, delineating flatly painted
rectangles of primary colour interspersed with white planes. In his attempt to
discover and give form to the invisible elements which underlie everyday
appearance, Mondrian is a Platonist. For Plato, as for Mondrian, these essences

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(or Forms) are more real than the material world, and are the source of that which
we perceive in our daily lives. The eighteenth-century German philosopher
Immanuel Kant’s conception of the noumena seems very close to Plato’s Forms.
The noumena, or ‘things-in-themselves’, are unfathomable, “the external source of
experience … [but] not themselves knowable” (Flew 1984: 251). Similarly, in the
Dao de jing, the Dao is described as follows: “We look at it, and we do not see it ...
We listen to it and we do not hear it ... it cannot be made the subject of description
... this is called the Form of the Formless” (Lao Tzu 1997: 11).
Mondrian equates the universal and non-material with the spiritual. In a
letter written in 1909, Mondrian states: “In order to approach the spiritual in art, one
employs reality as little as possible … This explains logically why primary forms are
employed … Art must transcend [physical] reality … Otherwise it would be of no
value to man” (Holtzman / James 1986: 17).
In Mondrian’s writings the Platonic essences converge with the Hegelian
concept of the whole. For Hegel, “nothing can be really true unless it is about
Reality as a whole” (Russell 1985: 703, emphasis added). The absolute, or whole,
is the logical conclusion of the dialectical process, whereby the thesis is replaced
by its antithesis, and where, subsequently, both are united and superseded in their
synthesis. The dialectic is, by its nature, ever-widening, leading to the final
conflation of everything into one, ultimate synthesis: the absolute. In this regard
Bertrand Russell states: “[S]ince everything, except the Whole, has relations to
outside things, it follows that nothing quite true can be said of separate things, and
that in fact, only the Whole is real” (ibidem). Thus, the notion (and appearance) of

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the world as constituted of separate and discrete elements is an illusion, and the
reality of separate things consists solely in their relation to the whole. Mondrian’s
mature paintings, where the coloured planes are cropped off and the black lines
seem to extend beyond the picture plane, are not meant to function as “objects in
themselves”, autonomously asserting only their material, delimited existence.
Rather, they encourage thoughtfulness about their role as part of an infinite spatial
continuum. This spatial continuum, as a manifestation of the absolute, can be
related to Dao. Lao Tzu states:

There was something undefined and complete, coming into existence before Heaven and
Earth. How still it was and formless, standing alone ... reaching everywhere and in no danger
of being exhausted ... All pervading is the Great Tâo! It may be found on the left hand and on
the right. (Lao Tzu 1997: 21, 30)

What these systems of thought, namely Platonism, the Kantian noumena, Hegel’s
absolute, and the oriental conception of Dao, have in common is a belief in the
trans-personal, as well as the conviction that to focus solely on the material is to be
misled. (The Buddhist notion of the physical world as an illusion, and the Hindu
goddess Maya who weaves a spell of illusion in the form of the physical world, also
clearly pertain). For Mondrian, “deception follows … [when] reckon[ing] only with
the senses” (Mondrian [S.a.]: 382).
Mondrian’s search for a utopian construct (predicated thus far on the non-
material and universal) furthermore led him to assimilate theosophical ideas as well
as mystical thought relating to the fourth dimension. From theosophy, notably H. P.
Blavatsky’s Isis Unveiled (1877) and The Secret Doctrine (1888),1 Mondrian
adopted the notion of universal harmony as the balance of archetypal opposites.

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Blavatsky traces the notion of the dual nature of the universe back to Phoenician
thought, where the cosmos manifests itself as male Essence, or Wisdom, and
where primitive Matter, or chaos, is defined as female (Blavatsky 1893: 61).
Similarly, the Swiss philosopher Paracelsus states: “Everything is double in nature;
magnetism is … active and passive, male and female … equilibrium is the resultant
of two opposing forces eternally reacting upon each other” (apud Blavatsky 1893:
xxvi). In Hindu philosophy, too, the union of Shiva, the male element, and Shakti,
the female element, constitutes enlightenment, or “an actual resolution of the
duality that constitutes the phenomenal world” (Cross 1994: 113).
Mondrian, seeking for a way in which to give form to balanced primordial
opposites, lighted on the representation of the vertical and the horizontal meeting
at a ninety-degree angle. Mondrian states: “[N]ature ... is governed by one
relationship above all others: … by duality of position, the perpendicular. This
relationship ... expresses ... complete harmony” (Mondrian 1918c: 38). For
Mondrian, the vertical line represents the male, mental/spiritual principle, whereas
the horizontal, aligned as it is with the earth, represents the female, material
principle. The correspondence with ideas noted in Blavatsky’s writings is clear.
The question arises as to how the concept of the dual nature of the universe
may be reconciled with Mondrian’s preoccupation with the ‘whole’, or the universe
as radically integrated. One solution is to consider dualism and monism as part of
the same system, a notion found in Western mysticism as well as in Daoism.

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Seventeenth century German mystic Jakob Böhme2, describes the creative
principle of dualism as follows: “The being of all being is but a single being, yet in
giving birth to itself, it divides itself into two principles … and out of these two
eternal beginnings into a third beginning, into the Creation itself as its own love-
play” (apud Watts 1986: 245). Similarly, the Dao de jing reads: “Dao gives rise to
one, one to two, two to three, and three to the myriad of things. The myriad of
things shoulder yin and embrace yang, and mix the qi to achieve harmony”
(Henricks / Lock 1998: 15). Thus, the absolute, or monist whole, comes to self-
awareness through the dynamic of duality by means of which all phenomena are
created. Mondrian echoes this precisely: “Unity, in its most profound essence,
radiates: it is. The radiation of unity’s being wrecks itself upon the physical – and
thus gives rise to life and art” (Mondrian 1918b: 90 n5).
In this way, Mondrian, in search of the primordial, universal paradigm, based
his formulation of abstract painting and the conceptual basis of Neoplasticism on
the notion of balanced duality – a duality which nevertheless forms part of an
holistically integrated absolute.
The last school of thought pertaining to Mondrian’s notion of utopia relates
to mystical explications of the fourth dimension, or so-called “hyperspace
philosophy”,3 as formulated by early twentieth century philosopher Peter
Demianovich Ouspensky. The nature of an inscrutable fourth dimension was a
prominent theme of discussion in artistic circles in early-twentieth-century Europe,
and Mondrian was quick to respond to the non-materialist implications of a “higher”
dimension.

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Ouspensky’s Tertium Organum (1911) is the summation of his thought on
hyperspace. Here Ouspensky attempts to explain the fourth dimension as a spatial
phenomenon, and, in order to achieve this, explores the relations between the
three dimensions with which we are familiar as well as the relation between three-
and four-dimensional forms. In this way, Ouspensky points out that a line consists
of an infinite number of points, that a plane consists of an infinite number of lines,
and that a solid consists of an infinite number of planes. By implication, a four
dimensional body consists of an infinite number of three-dimensional bodies.
Continuing his analogy, Ouspensky establishes that a line is the trace of the
movement of a point, and a plane is the trace of the movement of a line. A three-
dimensional solid is the trace of the movement of a plane, and by analogy, a four-
dimensional form is the trace of the movement of a three-dimensional form
(Ouspensky 1981: 22). The question arises: in which direction does the three-
dimensional form move to leave an impression of itself as the trace of a four-
dimensional body?
It is useful to keep in mind that a line moves in a direction perpendicular to
itself in order to form a plane. Similarly, a plane moves in a direction perpendicular
to itself, and at the same time not parallel to the first line, in order to form a cube.
Hence, in a three-dimensional cube there is ‘movement’ in three directions, each
direction perpendicular to each other direction and none of the directions parallel to
one another. By implication, a four-dimensional body is a three-dimensional body
which moves in a direction perpendicular to itself, and at the same time in a
direction not parallel to its height, width or depth – in effect, the three-dimensional

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solid moves “away from itself”. The answer to the question of which direction this
could be, lies in visualising time as space (idem, 54).
In our common perception of time, what we experience as phenomena well
up from nowhere (the future) and immediately disappear into oblivion (the past),
never to be encountered again – non-existent (idem, 25). Contrary to this
perception, Ouspensky states: “Reality is continuous and constant”, despite the
fact that we represent it to ourselves as an endless series of separate moments,
“as through a narrow slit” (idem, 26).
Based on the hypothesis that reality is continuous and constant, it would be
more logical to assume that events do not come from and disappear into nowhere.
Rather, everything, the past, present and future, exists as it is, in a continuous
present, which we are inadequately equipped to see in its entirety. Our erroneous
perception of time causes us to experience it as a series of segments of a line,
rather than as a whole. In light of this, Ouspensky urges us to rise above this “line”,
and to perceive time as a plane (idem, 28). On this plane the events of eternity
coexist simultaneously, arranged serenely and motionlessly next to each other.
Upon seeing time as a plane, our “time-sense” is transformed into “space-
sense”. The “now” which we experience as fleeting, expands into the ever-existing
infinity referred to in oriental philosophy as the “Eternal Now”, “a universe in which
there [is] no before and no after, but only the present, known or unknown” (idem,
95).
Ouspensky argues that this Eternal Now is the fourth dimension, but how is
this explanation of time as space to be related to three-dimensional bodies existing

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as traces of the movement of four-dimensional bodies? The direction, not
contained in itself, in which a three-dimensional body must move in order to leave
its trace as a four-dimensional body in space, is a direction perpendicular to our
line of time. This means that four-dimensional bodies are the manifestation of
three-dimensional bodies in their entirety, existing in perpetual time. We are
(ordinarily) unable to experience phenomena (three-dimensional bodies) in their
entirety, as four-dimensional bodies, and as we travel “through” four-dimensional
bodies (on our time line), we experience only their three-dimensional section, as
finite phenomena that come into and fade out of existence. It is also in this way
that, according to Ouspensky, a four-dimensional body is made up of an infinite
number of three-dimensional bodies.4

Ouspensky argues that these four-dimensional bodies are the Forms
described by Plato, and the noumena addressed by Kant. Yet whereas, according
to Kant, we can never experience things-in-themselves, Ouspensky posits ways in
which we can, notably by means of artistic sensibility and mystic insight, but
emphasises that positivist science and logic can not assist us in this regard. For
Ouspensky, a positivist is like a savage for whom a book is a “thing”, and who will
forever interpret it by carefully taking measurements of its appearance (1981: 117).
Whilst contemplating the outer representation of the book, the positivist savage will
never fathom its content, or noumena, nor even acknowledge that this content
exists. Conceding that positivism was refreshing and progressive in its time,
Ouspensky regrets the fact that it inevitably led to materialism, and feels that

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positivism has become conservative and reactionary, arresting rather than
benefiting thought (idem, 290). Ouspensky states:

[W]e do not realise that we rob ourselves … of all beauty, all mystery, all meaning, and then
wonder why we are so bored and disgusted … we do not see that we understand nothing
around us; that brute force or deceit and falsification always win, and we have nothing with
which to oppose them. THE METHOD IS NO GOOD … positivism wears a uniform … It rules
over thought … and struggle against it is already declared a crime. (ibidem)

By the same token, logic, as first devised by Aristotle, proves obfuscating when it
comes to the fourth dimension. Aristotle’s laws of logical inference read as follows:
A is A; A is not not-A; Everything is either A or not-A. Ouspensky remarks that this
formula is “simply deduced from observation”, and, given the conditioned nature of
our perception, brings us nowhere as regards the fourth dimension. Perception,
after all, proves misleading even within the realm of the three-dimensional world
(Ouspensky 1981: 74).5
As a counter system, Ouspensky envisages transcendental logic, or logic of
infinity and intuition, its axioms reading as follows: “A is both A and not A, or
Everything is both A and not A, or Everything is All” (idem, 221). These axioms,
Ouspensky points out, correlate with the central teaching of the Upanishads,
namely Tat tvam asi, or “Thou art That” (idem, 229). Thus, in the fourth dimension,
where “Everything is All”, opposition is resolved in a mystical union of opposites, in
accordance with Mondrian’s conception of utopia.
In Mondrian’s utopia, material reality is not the bedrock of existence. Rather,
it is the non-material, the diaphanous, the eternal and invisible that constitutes true
reality. In this non-material utopia conflict is resolved in the balancing, or ultimately
the union of, all oppositional elements. Mondrian chose to believe that humankind

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