3rd Lecture — Abstract

Logical variables

About space


Architectural space is a phenomenon dependent on perception, it is a formation that follows from the relations between bodies and their constitutive pictorial elements – qualities.

It is defined by the dimension of bodies and the distance between them. The size and shape of the bodies and the distances between them constitute (establish) the space, while the qualities of the bodies (colour, texture, optical tightness, etc.) perceptually realise the space. The relations (connections) between bodies represent space as a given, and the relations between humans and bodies represent the relationship of humans to space, which is conditioned by the place of observation.

Starting point

The moment we demand of a painting or a sculpture that it must be given to live in, to work in, to dwell in, to hold inventory in, we get architecture. Then we put to the painting or sculpture the question of construction, technique and economy. But today architecture is losing its place in the group of artistic creativity because the majority understands construction as a purely architectural-technical element, which is pure degradation. Construction is at the same time a spatial, plastic and, through colour and other surface qualities, a pictorial element. Therefore, the architectural-technical basis must be identical with the sense of the artistic idea. At the same time, the artistic elements already contain technically rational spatial regulations. The surface must not be an isolated sphere of action. It must be part of the space; it can create a room, a sculpture or a painting (figure 1).

Fig. 1: A canvas should not be an isolated sphere of action. It must be part of a space; it can create a room, a sculpture or a painting. The Hundertwasser House in Vienna is shown here as an extreme example; a house designed by the Austrian painter Hundertwasswer.

On the other hand, architecture can also appear to us as a surface element and as a sculpture (Figure 2). What is special about architecture is the space in which we can physically move, and this is what gives it its mutability. As we move, we experience new views. We perceive space as a whole and as a fine spatial image at the same time. The images jump from one format to another, the area of space expands to the next, and one creates an idea of space by means of memory. Space itself is a cubic concept, but it is the movement of the human being itself that raises it to the level of the fourth dimension.

Fig. 2: Architecture can appear to us as a planar element. In this case, the planarity is mainly the result of the particular lighting conditions and the orthogonal view of the façade. Algarve, Spain

When we talk about what we design, we are not talking about hierarchy, but about the convergent presence of painting, sculpture and architecture. It is a unified art world. The Gothic cathedrals are the most perfect examples of the unity of the whole and the detail, i.e. the unity of these three spheres of artistic creativity.


Thirty crossings converge in a fist,
in the empty space between them is the essence of the chariot.
They knead the clay to make it into a vessel,
the hollowness in them makes the essence of the vessels.
windows and doors pierce the walls,
the essence of the house is made of the voids themselves.
So then:
the benefit is in the material,
the essence is in the substancelessness.

(Lao Zi: Dao de jing, 11)

Space is the relationship between the positions of bodies and volumes.

(Laszlo Moholy-Nagy)

Space is a system of relations between things.

(O. F. Bollnow)

As we can see, definitions of space are derived from the relations between bodies. This means that the relations between bodies are the fundamental properties that we rely on when we talk about space.

We can define space as absolute emptiness, but we cannot imagine it, nor can we perceive it. At most, it can be detected by diffuse light reflections. In our representation, a void is a plane without bodies, which can also be a blank sheet of paper. A void is therefore something that does not contain that by which it can be perceived in itself. The imaginable or perceptible void is always a relative void.

The term architectural space is mainly used to describe everything that is surrounded by walls and floors. Whether or not there is a ceiling or a roof, we also roughly distinguish between external and internal space (the ceiling is not a necessary distinction). In addition to the term architectural space, there are many other notions of space. In his classification analysis, Hartmann makes a meaningful distinction between ideal, real and perceptual (visible) space.

Ideal space (also geometric space) is a pure dimensional system. It is homogeneous, continuous and unbounded. Mathematically, it is defined as a space with n dimensions. Three-dimensional, i.e. Euclidean, space is just a special case of such a space.

Real space is the space where things exist, where form and type are determined by the outside world. It is the space in which we live; it is the earthly space (world space) – the space where man works and manages.

Perceptual space is not visible in itself. It is only the form of visible content. In it we see the exterior of objects. Only objects in their corporeality are visible, i.e. optically perceptible. This is determined by its three-dimensional dimension. Perceptual space is only perceived through the distances that bodies have between them. These distances are also “that between bodies” which we perceive as space. We therefore define (describe) perceptual space in terms of dimension and distance.

Visible space can be perceived, pictorially experienced and represented. Here Hartmann distinguishes between perceptual space, the space of performance (representation) and the space we experience. Here the latter is closely related to the other two.

Among these forms, the visual space is not homogeneous, because the observer judges the relations between bodies differently depending on his position. Visible space is therefore a system of arrangement in which not all stand-points (all points) are equal (organisational-topological hierarchy).

The three basic types of space are not clearly distinguished from each other. Certain determinants of one form often meet with others. Thus, visible space, with its three-dimensionality, also has the characteristics of Euclidean space and can be realistically described.

What characterises architectural space as a form of visible space? Visible space can be evaluated in terms of its meaningful connections (between bodies) and in terms of its semantic content. Each space of a specific meaningful relationship is characterised by its structure, function and meaning. However, since these features are only perceived through bodies, it is bodies that constitute architectural space. They constitute it in an architectural way, i.e. according to the way in which they surround it.

Therefore, in our case, it makes sense to consider as space only the formations that follow directly from the relations between bodies. We call everything that we describe as “that between bodies” space.

We proceed from the following:

Take a pair of bodies. The two bodies stand at a distance from each other. This means not only that they are separated from each other, that is, that they occupy different positions, but that they are connected in the sense of creating “that in-between” (Figure 3). The observer, observing and judging the ‘in-between’, i.e. the relationship of the pillars to each other, can tell by the magnitude of the distance between them that they stand close together or far apart (remembering that the judgement of ‘close or far’ depends on the height or dimension of the bodies). Accordingly, he judges that the relationship is strong or weak. The judgement of the intensity of the relationship, based on perception, is therefore formed according to the magnitude of the distance. In addition, we also know that the observer of the column is making a judgement in relation to himself. In particular, the size of the distance between him and the two pillars is important. From the point of view of the whole space, this means that the characteristics of the observer’s relationship to the space are already determined by the place of observation.

Fig. 3: The bodies create the “in-between” that we know as space. The example in the picture shows an industrial object (a gas storage tank), as depicted photographically by the Becher couple.

We attach new bodies to a pair of columns. The area is captured as a space formed by several bodies. If only the corner “pillars” are left standing, the area of the inner space is preserved. The interrelation of the bodies becomes the perimeter of the defined area. This means that the area formed by the bodies is space. Its dimension is determined by the relations between these bodies.

It is clear from what has been shown why only the formations which follow directly from the relations between the bodies can be regarded as space. It should be noted here that the perception of space is linked to the three-dimensional dimension of the field. It is also important in what relation (relationship) the horizontal and vertical dimensions are. It is very difficult to call an area defined by a pair of very slender pillars a space. Space is not perceptible at all if it is not defined by the horizontal dimension of the bodies. It is only the larger horizontal dimension, or the relation of the two pillars to the third, that we perceive as space.

Fig. 4: Space is not perceived unless it is defined by the horizontal dimension of the bodies. The picture shows La defence in Paris by architect Von Speckelsen. We can see that although the front and back walls are missing, we can clearly see the interior space

Cognising the space

The basic experience of space is of boundedness (Figure 5). This experience can be modified in many ways: by changing the shape of the space and its proportions, by the character of the perimeter walls or bodies in the space, by the position of the observer… The observer can be low down, high up… The space can be narrow or wide, its boundaries can be clear or less clear. The view may open forward or to the side.

Fig. 5: The basic experience of space is one of confinement. Pictured.

Constraint is the relationship between the observer and the wider surroundings, the feeling the observer has when “measuring” an empty space. The observer perceives space by identifying the interrelationships between bodies; we say that bodies classify each other.

The dimension of a body and the distances to other bodies or to the observer are perceived as a ratio of size. We speak of the size of a body, its shape and its distance. These concepts are used to describe the geometrical properties of bodies. They are how space is created. Qualities such as colour, texture, optical tightness (and meaning…) make space visually real. All these concepts together describe (define) the singularity (particularity) of the body and therefore of space.

To make things clearer, let us say this: it is certain that we do not get the same results by measuring as by perceiving. When we speak of distance or proximity, this judgment depends, on the one hand, on the distance between the bodies, and, on the other hand, on what the bodies are like; whether they are of an intense colour or not, whether one can see through them well or badly, and so on.

Size and distance

There is an optimum viewing distance depending on the amount of detail desired. The optimal distance in a theatre determines the price of individual tickets. In a film, we see a dramatic story by the small distance between the actor and the camera. Depending on what we want to say, we choose between close-ups and long focal lengths. The same applies to the design of a room, where “everything” depends on the distance from one’s current position in the room.
Size is inversely proportional to distance. The farther away a body is, the smaller it appears to us (Figure 6). However, we should know that distance only becomes separated from size as a person moves through space, when the distance between him and the bodies is constantly changing. As long as we do not move through space, our judgement of it is more or less flat (for more on this, see Milan Butina’s book The Elements of Art Practice). Movement is therefore very important for the perception and understanding of space (and reality). Motor interaction with the environment is essential for the normal development of perception and thinking in general, because bodily movement provides us with feedback and information about those parts of space that we cannot grasp with a single glance.

Fig. 6: Size is inversely proportional to distance. The further away a body is, the smaller it appears to us. It is quite clear that the skyscrapers in the background, although appearing smaller, are in fact larger than the houses in the foreground. Mexico is pictured.

Thinking is similar to moving (motion). When we move and when we think, we move from less perfect knowledge to more perfect knowledge. By moving and thinking, we make up for missing information. More information – better thinking – more appropriate actions.

Moving adds a time dimension to the three spatial dimensions. In reality, we don’t see what is happening, but changes in things. Movement is also a change in the relationship between the observer and bodies (the observer can only perceive it in relation to other bodies in space), and time is a dimension of this change (it helps us to describe the changes, and does not exist without them). So movement (motion) and space are linked in an inseparable whole, a time-space continuum.

Lighting – colour, texture, optical tightness (transparency)

A spatial image is created by many elements. The floor and the sky (ceiling) fill most of the field of vision. The details that are close to us are very important: surface textures, rhythms and surface changes. The quality of the light directly determines the intensity of seeing colour, texture, movement, contours… Looking towards the sun emphasises the silhouettes and is completely different from the sun shining from the side; then textures and details become visible. Artificial light can be used to direct attention, to change the apparent shape of a space. Light alone can be used to create spatial images. At night, otherwise important spatial accents and events can disappear; the whole is given an appearance of soothing unity. Or even a whole new world of light can be created.

It is well known that panels of certain colours appear closer to the observer than panels of other colours, even though they are in fact all equidistant. For example, a glowing red plane appears closer than a light blue plane. Colours therefore affect the optical perception of distance in such a way that the result of the perception is not the same as the result of the measurement.
Just as colour influences the determination of distance, it also influences the determination of the size of a plane. We know, for example, that the colour black or white apparently makes a surface appear smaller or larger according to its measured size. However, this phenomenon is due not only to the colour itself, but also to the brightness obtained through the incident light. In strong light the colour appears brighter than in weak light. In addition, the colour of the incident light affects the colour tone of the coloured surface. Since colour (or rather colour perception) is as much related to light as light is to colour, we perceive the colour of the surface at the same time as the light. Colour and light are therefore inextricably linked. We therefore speak of the power and colour of the light itself together with the colour of the surface.

Patterns on the surface, for example, raster and graininess of different sizes, cause apparent changes in size and distance to the surfaces, just as colour does. Thus, a surface with a finer texture appears farther away from the observer than one with a coarser texture at the same measured distance. On the other hand, a finely textured surface appears larger than a more coarsely textured surface. This is actually a paradoxical phenomenon, where the surface is seemingly both getting further away and bigger (instead of smaller).

In reality, it is even more complicated. The above is true when we pay attention to the centre, the interior of the surface. But when we pay attention to the edges of the surface, the opposite is true.

We have a colourless, perfectly flat, polished glass surface with no reflections. Ideally, we do not detect it. But if there is even a very thin layer of paint or dust on the glass, that is enough to be able to detect it optically, while still being able to see through it. The denser the coating, i.e. the more resistance the surface offers to vision, the harder it will be to see through it.

We know from experience that the lower the optical tightness of a surface (for example, glass or a wall made of transparent material), the lower the perimeter and therefore the lower the space-forming effect. The less the boundaries are perceived, the “bigger” the space looks.


It is also necessary to include those components of the environment that cannot be expressed by the visible surroundings alone. They are called forth, however, by our general ability to complete each partial perception or cognition into a whole when we recall the missing ones from memory. Man wants to find meanings in the things he sees; he wants to connect the visible bodies with the behaviour and meanings in his mind. Tourists see their surroundings with fresh eyes and do not overly associate them with personal feelings and meanings because they are busy orienting themselves. The everyday traveller, on the other hand, is not so attentive to the wider environment (space) because he is already familiar with it. His or her gaze only takes in the narrow angle straight ahead and is focused mainly on the events on the route itself. We have already established that architectural space is defined by the bodies of architectural types. Therefore, bodies of this type are probably of primary importance in the evaluation of architectural space, while bodies of a different type are of lesser importance.

In the evaluation of an urban space, such as a square, the buildings (bodies of an architectural type) are of primary importance, while the trees standing in the square (bodies that cannot be classified with certainty as architectural types) are generally seen as elements that co-determine the square. Parked cars should not play any role in the evaluation (Figure 7).

Fig. 7: Buildings (bodies of an architectural type) are of primary importance in the evaluation of architectural space, while parked cars (bodies that cannot be classified with certainty as an architectural type) should play no role in the evaluation. An example from Sicily.

Bodies are therefore seen in a certain order (rank) according to their type. However, bodies of architectural type alone can have different meanings, depending on the perspective from which the space is being evaluated. For example, the interior space of a church can be seen in its entirety, where the individual parts of the perimeter of the space have (roughly) the same meaning. It can also be seen in terms of the rhythm created by the sequence of columns and arches. In this sense, the columns, pilasters, niches, etc. are more important in relation to the other elements of the space. It is always the primarily observed bodies that are more important. So the perceived is not only determined by the size, distance, position and material properties of the bodies, but also by the importance or significance that these elements have in relation to the architectural whole (composition).

From what has been said so far, we can clearly see that architectural space is a phenomenon that depends primarily on perception. We have learned that we capture space by perceiving the relations between the bodies that fill it. These relations, in turn, derive from a classification of bodies that does not depend so much on the will, but is carried out mainly spontaneously in the flow of perception. Moreover, the perception or evaluation of the relations depends on the attention of the observer.

As a rule, we cannot capture a space with a single glance. With single glances, we see only snippets, spatial segments, which we associate with changes in the direction of gaze. Therefore, perceiving and judging space from a particular place (the place of observation) is only possible mentally, after we have perceived it in parts.

It is important to stress, however, that each topos of space has an “objective” (independent of us) content, since it causes its own sensations in the human body (e.g. below, above, deep, upright, in front, in the middle, etc.). Of course, these elementary sensations can be evaluated differently in personal experience. Areas of space do not have quite the same values (meanings) as they are given by each individual in the space.

In the artistic-architectural activity in space, man is concerned with the size, shape, relative position, direction, etc. of spatial bodies, which have certain properties. With concepts such as size, position and distance between the bodies, he describes how space is constituted (each shape has an abstract value: it is a circle, a square, a triangle, etc.), and with concepts of quality, he describes how space is perceptually realised (each shape has its own visual content: it has a colour, a brightness, a texture, etc.) The artist describes how space is perceptually realised (each shape has its own visual content: it has a colour, a brightness, a texture, etc.). All these concepts together speak of the singularity (particularity) of the body (each form has a relative value (context) that derives from its relationship to the space and forms that surround and influence it). The history of architectural space is, in fact, only the history of “great” architectural spaces. We are mainly talking only about city centres, church spaces and, to some extent, castles. We do not talk about other architectures, which are in the majority, because there is no real data (remains). Thus, a historical overview of the development of the space is necessarily very limited and questionable from this point of view.

Romanesque architecture began where it developed most, in southern Europe, where the tradition of antiquity was strongly felt. This was a time when ancient knowledge was being adapted to the church, which was the vehicle of development. In the main, the Romanesque expressed itself only in cool and warm colours. Thus, the emotional component was almost exclusively represented, and it was also very much emphasised. The rooms were therefore more low and small, and the paintings were more non-objective. So the sense of confinement was very strong. It was as if God suspected every living thing and condemned it in advance as guilty. The Last Judgement was often depicted above the portals.

Romanesque was the first international style (fig. 8).

Fig. 8: The Romanesque was mainly expressed only by warm-cold contrast. Thus, the emotional component was very much emphasised. The rooms were more low and tight. The cathedral in Modena.

Gothic architecture began in the north of Europe. Although the church was still the vehicle of culture, the developing bourgeoisie, which was stronger in the north, brought a mental quality to architecture that overrode the emotional. The result or harbinger of the mental was the phenomenon of volume, and the main means of artistic expression was the shadow. Space often took the place of mass. Hence in sculpture the drapery – under which there can be no body because it is too deep – and in architecture the struts. This means that the technology of building has also been adapted to a different mentality. They started to consciously deal with space (the void), making it taller and airier. The paintings were more object-oriented.

Gothic was the second International Style and represents the opposite of Romanesque (Fig. 9).

Fig. 9: The burgeoning bourgeoisie brought a cerebral quality to architecture. The result or harbinger of the mental was the phenomenon of volume and the main means of artistic expression was the shadow. Space often came first. Palazzo Publico, Piazza del Campo, Siena.

In the Renaissance, the bourgeoisie was the vehicle of development. As it was not progressive, architecture rebelled against antiquity. The new way of designing space intertwined a mental and an emotional component. The beyond was imagined as a world of the totally real, moving into the real. Man became the new (basic) value, part of nature and discovering its laws. Every artist was a scientist because he had to discover the laws of nature, technology and art. Art was a social activity and subject to the laws of nature. Some conceived of art as a pure mirror of nature (Leonardo – the mental category); others argued that the artist could transcend it (Michelangelo – the emotional category) (Figure 10).

Fig. 10: In the Renaissance, architecture reacted to antiquity, but it also boldly built on it – reinterpreted it. The staircase in the Biblioteca Laurenziana by the genius of Michelangelo Buonarotti

In the Baroque, architecture once again helped the church to get what it once had. In the Middle Ages, it was the material that mattered, but in the Baroque it was only the appearance that mattered. They tried to create spaces that were larger than they were. That is why ceilings were opened up to give a new space above the real – illusionism. The mental and spatial orientation was upwards – man was in the real world and in the sky at the same time. It was as if he had moved into the upper cube (the opposite orientation to the Renaissance). As height increased, density decreased, because gravity and tectonics were respected. They were very concerned with light, which they led through lines in very thick walls into the interior of the churches. This is how they got directional light. It all expressed a very strong mental component.

In the Rococo, man was depicted in the unearthly, and in the upper cuboid he was becoming more and more insubstantial. In fact, he was returning to the lower cube, that is to say, the orientation was turning downwards again, to the real, and the sky was emptying, which nevertheless gave a certain brightness. What was most important was the unity of place, time and action, and form, which was a reflection of cosmopolitan nobility. The creators were looking for pride, clarity, sublime style, noble expression. They imitated the visual and used strictly defined forms.

In Romanticism, there was a space of the real and the living on the one hand, and next to it (in parallel) there was a space of the unreal and the immaterial. Both existed in parallel and there was no superior-subordinate relation. The horizontal orientation prevailed. Thus the inanimate was equivalent to the concept of the animate. Therefore, in architecture, the object and the non-object existed simultaneously.

In realism and later, architecture was transferred to the level of class opposites. In Europe, the development of the classical came to an end. Until modernity, architecture followed social needs, but with modernity it began to rush ahead of its time. Becoming famous after death was very much in vogue. That is why science also developed rapidly. America joined the European architectural currents and often became decisive. Modernity was above all sensitive and of the moment.

Throughout Europe, architecture did not develop at the same pace because of its uneven development. Until modernity, styles were tied to a particular social class. International architecture was a reflection mainly of the highly developed countries. Architecture became a co-creator and a reflection of social aspirations. It stopped coquettishly flirting with society and looking to it for a protector. It showed its contradictions. This had already begun during the Impressionist period. The development of society and science demanded objectivity. The architect was proving himself through technique. Architects “technicians” created buildings that were primarily constructions (Figure 11).

Fig. 11: In modernity, the architect proved himself through technique. The “technician” architects created buildings that were primarily structures. Fiat factory in Lingotto, Turin, Italy


Nicolai Hartmann: Kategorialanalyse des Raumes; in: Philosophie der Natur; Berlin, 1950.

Donald Appleyard, Kevin Lynch, John R. Myer: The View from the Road; MIT Press, Cambridge, Massachusetts, 1964.

Milan Butina: Prvine likovne prakse; Debora, Ljubljana, 1997.

Milan Butina: Slikarsko mišljenje; Cankarjeva založba, Ljubljana, 1995.