Thinking Space - José Jiménez

in Conceptes de l'espai Catalogue of the exhibition, Fundación Joan Miró, Barcelona, March 14 - May 12, 2002, p. 82-6.

THINKING SPACE

José Jiménez.-

1. Space is an abstraction

At first glance, space is transparent, invisible: we see the things, the persons and the objects, but not space itself. Perceiving space involves a whole process of abstraction. It is in space that geometry originates, based on an abstract vision of nature and the forms found in nature. On this point, as on so many others in our cultural tradition, the conception of space is a product of the Greek mind.

It is a well-known fact that the Greeks’ knowledge of astronomy was no more advanced than that of neighbouring civilisations, particularly the Babylonians. And yet, by developing a rational focus, by going beyond mythological or astrological thought, the Greeks founded cosmology and astronomy, the disciplines concerned with the scientific study of the universe.

This rational conception of knowledge, which has its basis in what the Greeks called logos, thought-language, involves the replacement of a symbolic system of representation by a numerical, mathematical, geometrical system. For example, whereas in the Ancient Greek cosmogonies, the Earth was conceived as being set on roots that descended down into infinity, or placed inside a large receptacle, for Anaximander (c. 618-c. 548 B.C.), the philosopher from Miletus, the Earth was a truncated column situated in the middle of the cosmos. Comparing these two representations, the Hellenist Jean-Pierre Vernant (1973, p 187) writes: “We see the birth of a new space, which is no longer the mythical space with its roots or its receptacle but a geometrical type of space. It is of course a space essentially defined by distance and position, a space that allows the stability of the Earth to be founded on the geometrical definition of the centre in relation to the circumference.”

It was in fact the Ancient Greeks who, going beyond the mythical notions of place (topos) and of home – the human home (first a palace, then a hero’s mansion and finally a family residence) and the home of the gods (the temple) – established the idea of space, which was to become one of the most important and significant categories in Western thought.

The idea of space requires the configurating, operational activity of a rational, mathematical mind. Only on this basis do the literary, artistic or musical – i.e. aesthetic – uses of it become possible afterwards, in a “cultural” afterwards conceived as anthropological tradition.

The concept appears in the process of creation of science-philosophy in Greece, and probably for the first time with Pythagoras (570-497 b.c.), which in itself is relevant, given the central role of numbers and of mathematics in his thinking. It later occupied the attention of Zeno of Elea (490 B.C.), in his well-known logical paradoxes on movement. And it received a precise formulation as a category in one of the last, and in time most influential, of Plato’s dialogues – Timaeus, probably written in the second half of the fourth century B.C.

How did the creation of the world occur? It is in this cosmological context that Plato establishes a precise categorial use of the term space (jora) when he states that “being and space and generation, these three, existed in their three ways before the world was born” (Timaeus, 52d). In Plato, the being corresponds to the “exemplary Forms” or “Ideas”, which he characterises as “the same, uncreated, indestructible being”, and also as “invisible and imperceptible by any sense”. On the other hand, creation is “perceived by sense, created, always in motion” (Timaeus, 52a).

Between these two opposite poles – Ideas-Forms, which are “beyond” the world, and creation, which relates to the world of the senses – there is also, according to Plato, “a third nature, which is space, and is eternal, and does not admit of destruction and provides a home for all created things, and is apprehended without the help of sense, by a kind of spurious reason; which we beholding as in a dream, say of all existence that it must of necessity be in some place and occupy a space, but that what is neither in heaven nor on earth has no existence.” (Timaeus, 52b).

The Platonic conception of space not only makes it a kind of “intermediary” between the essential fixedness of being and the changing creation of what is perceptible to the senses, but in addition its eternal, indestructible nature provides a home to everything that has an origin; in other words, it acts as a receptacle or container, in which all things and beings are situated and have their place. It can only be apprehended “by a kind of spurious reason”, and in this it is distinguished from the Forms that can only be reached through “true reason”, through the strict use of reason; but “without the help of sense”, which also implies that it is different from creation, apprehended by the senses and not by reason. Thus in the final instance, in a situation midway between reason and the senses, while at the same time outside both planes, space is such an abstract idea that, as Plato himself admits, it is difficult to credit.

Certainly, this abstract idea of space can only be sustained in the framework of a cosmological reflection, and can only be apprehended by a type of reasoning that is eminently numerical and formal – the reasoning of mathematics, of geometry. But precisely because it lacks “figure”, lacks form, space acts categorially as the conceptual framework of possibility in order to distinguish and demarcate every form or figure; and also as the territory that enables us to make distinctions between what is empty and what is filled, which were central aspects of Greek cosmological thinking prior to Plato, particularly in Parmenides and Democritus.

It is obvious, moreover, that this abstract category is formulated on the basis of the experience and the impulse provided by forms of construction, by architecture. In all human societies, from the most ancient and remote times, the solution to the problem of shelter or habitat has been a fundamental question. The notion of “home” that covers both domestic use and the different ritual uses (in religion, power, etc.) involves changing from a more or less prepared “natural” space to an “artificial” space constructed according to the material determinations of the ecosystem and the use to which it is put.

However, what is interesting in the Greek case is that the different forms of construction (house, temple and city) form a unit together, a “visual unit”, that derives precisely from the existence of an organic system of structuring space: “The only common factor whose essence is not susceptible to material alteration or practical change is the system of structuring space that lies behind all the manifestations of architecture in Greece” (Martienssen, 1956, p 145). The construction variables derive from the requirements of the specific purpose, whereas the elements of the measurement and organisation of space appear as constants, which shows “the subtle gradation of the abstract as a constituent element of Greek architecture” (Martienssen, 1956, p 146).

Measurement and organisation, or measure and order, are precisely two of the aesthetic categories that are central not only to Greek culture but also to the Roman and Hellenistic world. But they in themselves appear in the constructive process as procedures for defining an abstract premise that acts as a substrate or foundation. In other words, measure and order are ways of making space visible, of demarcating it in a specific human use.

2. Visual space

The Greek conception of space as an abstract entity not only permits a mathematical, geometrical foundation for the theories of the universe but also confers a unity on the visual forms of representation. It is not only architecture, but statuary and painting too are involved in placing it on an abstract plane of experience that makes its autonomy and development possible.

But there is a great difference between the geometric and cosmological version of space and its visual version. Visual space is conceived as an image of cosmic and geometrical space, which it presupposes, though situated in a different order of thought and existence. The visual (and literary and musical) version of space in the Ancient Greek world was established within the framework of perceptible representation, as one more aspect of mimesis, that skill or talent for producing images that, with time, has become central to our idea of art.

The artist (sculptor, painter and to some extent architect) makes a cut, a caesura, in the abstract substrate that we conceive as a receptacle for all forms and things, thus making it visible: by giving it a perceptible support, by demarcating its form, the work of art becomes a kind of echo, a materialisation, of that abstract idea that enables us to think scientifically of the development of the cosmos.

The classical order of representation, which in Greece and the ancient world in general already had as one of its principal objectives the achievement of figurative illusion, was finally to be structured in the Quattrocento – thanks to the perfecting of geometrical perspective – as an artistic universe whose figures looked more lifelike on account of the illusion of spatial framing that was then perfectly possible. Nearness and distance became elements in a process that gave priority to the fixed, stable nature of the visual space, which in turn determined the strict position of the viewpoint, the observer.

Although geometrical perspective is a visual and symbolic convention (cf. Erwin Panofsky’s classical study, 1927), it was eventually to become the sole and exclusive criterion for the representation of space in the Western artistic tradition until the eclipse of Classicism in the last quarter of the nineteenth century and the early twentieth century.

It is perhaps not too hazardous to establish a relationship between this tendency to fix as an absolute in art what must have always been considered as one option among many others, and the similarly exclusive nature of Euclidean geometry, which served as the scientific basis for it. The question is of even more concern when, in the process of development of modern science, Isaac Newton (1687, p 33) formulated what is known as his theory of “absolute space”: “Absolute space, in its own nature, without relation to anything external, remains always similar and immovable”.

This idea of space is, as already mentioned, the counterpart in physics to Euclidean space in mathematics. Cosmic space becomes a kind of large “stage”: according to Gray (1992, p 244), it can be conceived as an immense stage on which occur the events that constitute the universe: eternal stars, small particles, ourselves. In fact, we are not far from the Platonic concept of space as an eternal receptacle, but of course with Newton we have a mathematical and cosmological foundation for his theories that had not yet been possible in the Greek world.

These questions serve to reveal an interesting parallel in the field of art. If in Newton’s physics space and time are conceived as “absolute” magnitudes, in one of the high spots of the theory of the arts of the Classical period, in Laocoon (Lessing, 1766), the notions of space and time are the reference points that enable a semiotic difference to be established also in “absolute” terms between the visual arts on the one hand and literature and music on the other.

It is well known that at the core of Lessing’s book is the need to establish a rigorous critique of the humanist formulations of the identical nature of the arts. To fix with precision the limits of the different artistic “languages” or genres is certainly fundamental to the stability of the Classical aesthetic order. In this context and based on Aristotle, Lessing magisterially formulates a semiotic rather than a normative theory of the difference between the visual arts (“painting”, he says metonymically) and literature (“poetry” in its equally metonymic formulation).

Painting and poetry, according to Lessing (1766, p 106), use entirely different media or signs in order to imitate reality. Whereas painting uses “figures and colours arranged in space”, poetry uses “articulated sounds that succeed each other over a space of time”. Hence, too, he says, the representation of “the bodies” is the object of painting, whereas, since the successive objects or their successive parts are generally called “actions”, it is these that constitute the object of poetry.

Lessing (1766, pp 106-107) nevertheless concedes a degree of “crossing-over” between the objects of poetry and of painting. This is because, as the actions have no independent existence but are performed by specific beings, and to the extent that these beings are bodies, poetry “also represents bodies, but only in an allusive way, through actions”. This merely allusive representation of the body involves a choice, since, as a temporal art, poetry “can only use a single quality of bodies; hence the fact that it has to choose the one that brings to the mind a more visual image of the body from the viewpoint that this art requires for its own purposes”.

In the same way that bodies exist not only in space but also in time, painting for its part “can also imitate actions”, although again “only in an allusive way, through bodies”. In the same way as what happened with poetry, the characteristics of the signs it employs mean that painting, when representing actions, can only use “a single moment of the action”; so it has to select the most pregnant of all these moments, the one most able to take over the preceding moment and the following moment”.

Although in Laocoon itself there are certain lines of perspective that afford a glimpse of the then imminent crisis in Classicism and the beginning of the Romantic revolution, particularly through the central role that Lessing (1766, p. 53) attributes to the imagination in the perception of beauty, nonetheless the structural frontier between “spatial” arts and “temporal” arts is too rigid. He also ignores the fact that the mixture of supports and forms of expression in a single aesthetic proposal have been a constant factor throughout the history of perceptible representation in our cultural tradition, as occurs, for example, in the case of drama, or in the inclusion of song, music and gesture in the most ancient forms of Greek poetry.

3. Space is indissociable from time

Already in our era, with the development of modern technology, and in the specific field of the arts, with the invention of motion pictures, which epitomised the combining of the dimensions of space and time in a single expressive universe, the aesthetic, semiotic separation between the representation of space and of time increasingly came to be seen as somewhat inadequate. In this new cultural climate, the artistic avant-gardes also rejected the Classical idea of the frontiers between the different artistic genres or languages, precisely seeking in the violation of these boundaries a new aesthetic ideal – that of the convergence of all types of processes and materials in the unity of the work of art. This was an idea already anticipated by Richard Wagner, in his theory of the “musical drama” and his formulation of the category of the “total work of art” (Gesamtkunstwerk), as the maximum expression of the desire to transgress the classical limits and merge all kinds of materials and processes in the unity of the work.

Paul Klee (1920, p 4), for example, who in his youth had been an enthusiastic reader of Laocoon, expresses quite clearly Lessing’s rejection of any distinction: “In Lessing’s Laocoon, much noise is made about the difference between temporal art and spatial art. And this, contemplated with greater precision, is no more than erudite delirium. Because space too is a temporal concept.” Klee considers movement as the basis of all creation, and this means seeing the temporal dimension in the creation of space. Obviously, Klee is referring to visual space rather than to that abstract space, conceived as a receptacle of creation, that Plato had characterised as “eternal”.

It should be noted also that, since Antiquity and even in the ordinary sense, space and time had been considered as related entities. The Latin expression spatium temporis (space of time) is a good example of this. Succession can also be perceived as extension. Only the abstract, cosmological formulations of Newtonian physics, with its ideas of “absolute” time and space, considered as independent magnitudes, could conceptually justify such an absolute separation between the two categories.

But the development in the nineteenth century of non-Euclidean geometries and the appearance later on of new theories of physics, such as undulatory mechanics or the theory of relativity – significantly in the same period as the emergence of the artistic avant-gardes – was to lead to a profound questioning of the absolute conceptions of space and time, and to different cosmological formulations all based on the idea of the space-time continuum.

The resistance to the abandonment of the postulations of Newtonian physics in the scientific community itself is well documented. As Gray (1992) explains, what shocked most people was the complete abandonment of absolute space. The existence of an external world independent from the observer had been associated with the belief in the absolute properties of objects in space. The objects move, therefore the objects are there, whether we like it or not. Despite this, and in principle for philosophical and aesthetic reasons (“their elegance and beauty”, a decisive aspect in the acceptance of scientific theories), the formulations of the new physics were forging a path: Einstein showed, however, that the description we offer depends on what we are doing and where we are in a way that is more subtle than any other we would have expected, and more subtle that what many people were prepared to accept (Gray, 1992, p 254).

The questions raised by the great mathematician Hermann Minkowski, at a lecture given in 1905, clearly and precisely establish the new use of the categories of space and time in contemporary physics: “Space and time must be lost in the shadows and only a world in itself will exist.” And again: “Nobody has yet observed any place other than in a time, nor has anybody observed any time other than in a place” (quoted in Gray, 1992, p 255). Although it should be taken into account that the notion of time-space prevalent in physics, and especially in the generalised theory of relativity, formulated by Einstein in 1916, must not be confused with an intuitive image of a “reality” or parameter in which time is “blended” with space, there is no doubt that the abolition of the conception of absolute space and time in the framework of contemporary scientific knowledge was to have a notable repercussion in the field of artistic practice and theory as well as in matters of common sense, gradually accustomed to confronting more or less successful film or literary “versions” of the paradoxes of Einstein’s relativity, today so familiar to us all.

4. From the representation of space to the construction of space

The art of our time gradually took a revolutionary turn that hinged on the idea of the transition from the visual representation of space to the construction of space. It was a step that was strongly influenced by the new sensibility that had made the development of technology possible. New viewing mechanisms provided by high precision machines, and in particular photography and films, liberated the visual arts from the commitment to figuration and illusion that had marked their fate since Classical Antiquity.

The visual idea of space, the artist’s work of perceptibly demarcating the image, was thus released from a conventional representation and gave way to the fully autonomous possibility of spatial structuring, or construction of the visual space, conceived as an entirely independent, perceptible, intellectual entity.

The “emblem” that marked this new horizon in the arts was Picasso’s Les demoiselles d’Avignon (1907), with its deconstruction of classical representation and the inclusion of different representational conventions in a single painting. After this would come Cubism and the various Constructivist proposals, whose developments were to cover the entire twentieth century down to the present day.

This, as I mentioned above, is the context of Paul Klee’s ideas (1920, p 4) as expressed in his “Creative confession” on the integration of space and time in the work of art: “When a point becomes movement and line, it requires time. The same happens when a line moves to become a surface. In the same way the movement of surfaces creates spaces.”

These ideas are clearly echoed in Point and line to plane (1926), one of the most important theoretical texts written by Wassily Kandinsky, who had joined Klee at the Bauhaus in 1922. What is notable, in particular, is the counterpoint that Kandinsky (1926, pp 109-110) establishes between artistic work and technical work, and his call for a “pure art”: “The Constructivist works of recent years are in a large part, especially in their primitive form, ‘pure’ or abstract construction in space, without any practical purpose, which distinguishes them from works of engineering and forces us to place them in the category of ‘pure art’.”

Something had changed, radically and irreversibly, in the world of art, and the newly emerging conception of visual space played a fundamental role in that change. When Kandinsky spoke of “pure or abstract construction in space” he was fixing with precision the new horizon of the plastic arts, finally freed from the mere reproduction of a “fragment” of space. The art of our time had entered a territory that was entirely different from any previous references – that of the dynamic construction in time of a fully autonomous space. Instead of reproduction, construction. This is what Paul Klee (1920, p 2) had also expressed in different terms in the first sentence of his “Creative confession”: “Art does not reproduce the invisible, but makes something visible.”

All the rest was to follow along at its own pace. With Brancusi, sculpture was to begin a process of emancipation from the pedestal and of formal, staged expansion that has continued down to the present day. And at least after El Lissitzsky, with his constructions that he called “Proun” (an acronym for “Project in affirmation of the new”) in the early twenties, art appeared as the global articulation of a set of diverse elements.

The concept of “installation” derives from all this, from that Constructivist core that finally freed the work of art from any subjection to representation, steering it towards the production of a space – a space that can contain the traditional supports and media of the visual arts (drawing, painting, sculpture, etc.), but also the “new” media – from photography and film to video and digital supports – and, more importantly, the supports and media that are “non-visual” (?) according to the classical mentality: language, sound, gesture, setting, etc.

Art opens up a process of generation of autonomous universes, each with its own time and space, breaking away from the everyday experience or the practical uses of technology. Worlds apart. In them, we seem to hear an echo of what Hermann Minkowski, as I mentioned above, formulated in the field of the theory of physics: “Space and Time must lose themselves in the shadows and only a world in itself will exist.”

R e f e r e n c e s

Jeremy Gray (1992): [Ideas of Space] Ideas de espacio. Spanish translation by F. Romero, revised by J. Ferreirós; Mondadori, Madrid, 1992.

Vasily Kandinsky (1926): [Punkt und Linie zu Fläche] Punto y línea sobre el plano. Contribución al análisis de los elementos pictóricos. Spanish translation by R. Echavarren; Barral, Barcelona, 1971.

Paul Klee (1920): [Schöpferische Konfession] “Confesión creadora”. Spanish translation [there are many other versions] from the catalogue Klee. Óleos, acuarelas y dibujos; Fundación Juan March, Madrid, 1981, pp 2-7.

Gotthold Ephraim Lessing (1766): [Laokoon: oder über die Grenzen der Malerei und Poesie] Laocoonte. Introduction and Spanish translation by Eustaquio Barjau; Tecnos, Madrid, 1990.

R. D. Martienssen (1956): [The Idea of Space in Greek Architekture] La idea del espacio en la arquitectura griega. Spanish translation by E. Loedel; Nueva Visión, Buenos Aires, 1980.

Isaac Newton (1687): [Philosophiae Naturalis Principia Mathematica] Principios matemáticos de la filosofía natural. Spanish translation and notes by Antonio Escohotado; Tecnos, Madrid, 1987.

E. Panofsky (1927): [Die Perspektive als "symbolische Form"] La perspectiva como forma simbólica. Spanish translation by V. Careaga; Tusquets, Barcelona, 1973.

Jean-Pierre Vernant (1973): Mito y pensamiento en la Grecia antigua; Ariel, Barcelona. Spanish translation by J. D. López Bonillo from the corrected version of Mythe et pensée chez les Grecs; F. Maspero, Paris, 1965.