The dialectic of form as such, in itself, is outlined by the antithesis "sphericity – cubicity". The next point of logically consistent thinking of a form should be its correlation with space, and this correlation is when we are also interested in the form itself. This point is revealed by the antithesis "massiveness – transparency".
And here we find three fundamental relations of form and space – their identity, their difference, and, finally, synthesis.
What is the identity of form and space? This means that space and form communicate and mutually penetrate each other completely unhindered. Space encompasses the form and enters into it, and the form stays in space and encompasses it. This is possible only if the form is thought of as loose and unsaturated, absolutely transparent and permeable. But this means that the form is represented only by its outlines, borders, and edges. It is a form built exclusively of edges, filled with nothing but space, elaborate and open to external and internal penetrations.
Even earlier than N. Ladovsky, who said his famous aphorism52, the sage Lao Tzu emphasized that the importance of a building is in the space for life and filling it. Space was the dominant element of ancient Japanese and Chinese architecture, as N. Brunov writes in detail53. Thus, the Japanese and Chinese pavilion houses organize a gradual transition from the mass of the building to the space of nature, as opposed to the sharp contrast of surroundings and architecture originating from Renaissance palaces.
In modern architecture, the fusion of form and space is achieved by means of form perforation and the widespread use of glass. Transparent glass is the only material that allows spaces and objects to be considered identical while maintaining minimal differences. Glass with mirror properties already visually prevents the environment from entering from the outside, but allows houses to dissolve into each other. The environment loses its clear boundaries, and its image is doubled and repeated tenfold by multiple reflections. Such interpenetration and mutual dissolution of objects in each other creates the illusion of overcoming the gravity and immobility of matter. It is a shimmering, pulsating medium where shapes blend and color each other.
The second type of relationship between form and space is a difference. Taken to its utmost extent, it will give a form that is fenced off from the outside space, self-contained, closed, and possibly opposing itself to the environment. Here, first of all, one remembers the thicknesses of the Egyptian pyramids and the walls of Romanesque castles. It's a massive form.
Finally, a synthetic way of relating form and space will be a form that is both massive and elaborate at the same time. It is both open to space and has isolated areas within it. In the history of architecture, there are examples of such solutions that have demonstrated the power of the combination of opposites.
The antithesis of "massiveness – transparency" correlates with the antithesis of relationship with the landscape. The openness of the form can mean a connection not only with an empty space, but also with a space filled with natural forms.
Let's recall the Mortuary Temple of Queen Hatshepsut in Deir el-Bahari. The powerful dynamic ramps of the building are energetically turning into ledges of natural rocks. The temple is clearly distinguished from its surroundings by the measured rhythm of the pillars of the porticos, and at the same time merged with it – to the point of literally cutting into the rock.
An example of the new architecture is the Sainsbury Center in Norwich designed by N. Foster (1977). Among other advantages of the project, one is interesting for our topic: "from the sidewalls, one can look through the huge building, as though merging with nature. From other points of view, the laconic outline opposes it. The huge portals of the ends of this supershed, framed by trusses, are literally open to nature. They serve as a kind of frame, the backdrop of beautiful landscape paintings, and the external space rushes through the giant structure with a roar, imparting unexpected dynamism to its statics."54
Jean Nouvel demonstrated unexpected identifications and syntheses of the massive and transparent, architectural and natural in a number of his works. In the Soho Hotel in New York's Broadway (2003), "transparent, semi- and not at all transparent give rise to "transit effects", the transition of one into another, as a result, the building seems massive or permeable depending on the time of day, the weather … – the impression of instant dematerialization, the appearance and disappearance of matter.
A more sophisticated stage is the dissolution into the landscape, nature… The Museum of Ancient Cultures on the Quai Branly in Paris (2001) is fused with an exotic natural environment, you forget about its man-made nature… At the Guggenheim Museum in Tokyo (2001), architecture in general seems to be absorbed by nature – a hill in flowering trees, and the exhibition spaces inside, stained glass windows are masked in the folds of the relief… The seemingly fantastic formula has been realized: the invisible architecture turns out to be the most impressive.55"
The two antitheses of developed by us, sphericity vs. cubicity and massiveness vs. transparency, mutually intersect in a broader antithesis of architectural form versus natural form. The history of architecture has witnessed two opposing trends. One tries to connect architecture with landscape. The synthesis model was developed by the same Japanese and Chinese architecture, which organizes a complex spatial proportion: the main room of the building correlates with the surrounding bypass connecting it to the outside space, just as the whole building correlates with the garden connecting the house and nature. Both the architecture and the garden are dominated by a curved line.
The opposite concept to this approach is the contrast of form and environment. It was followed, for example, by Ivan Leonidov, who believed that the new city (Magnitogorsk) should cut into a green massif, contrasting with the surrounding nature by the geometricity of its layout and the rhythmic row of glass crystals of multi-storey residential buildings dominating other buildings forming a rationally organized network of servicing institutions56.
Architecture in this concept is opposed to nature as something rational and orderly to irrational and chaotic. In this contrast, a side of the essence of architecture is expressed. Man strives to overcome the chaos of natural forces, to crystallize and strengthen a certain stronghold in the sea of circulation and spreading of natural phenomena. "The city becomes an image of … a world completely created by man, a world more rational than the natural one… The rational is thought of as "anti-natural."57 The image of St. Petersburg is illustrative in this regard. "If we take old Petersburg, then the cultural image of the military capital city, the utopian city, which is supposed to demonstrate the power of the state mind and its victory over the elemental forces of nature, will be expressed in the myth of stone and water, firmament and mud (water, swamp), will and resistance.58" This understanding of architecture was very characteristic of the Renaissance and utopias.
Architecture is the design of oneself, one's own physicality, and the surrounding space. Architecture is the self-organization of society, it is the desire to get used to the natural world, make it your own, organize yourself in it and organize it according to yourself.
The moment of confrontation with nature is also associated with another one, the opposite, which consists not in conquering, but in the peaceful development of nature. The task of architecture, Hegel argues, as a "symbolic" art, is "to work out the external inorganic nature in such a way that it becomes related to the spirit as an artistically appropriate external world.59" The task of architecture is to overcome the conflict between nature and man, making nature related to man and man related to nature, and removing the opposition between them. The purpose of architecture is to make nature dear, kindred, close, instead of hostile and threatening, to humanize it.
First of all, let's notice the connection between the categories of rhythm and meter with the previous antithesis. The meter is a symmetry expanded into a spatial series, and the rhythm is an expanded ordered asymmetry. From this we can immediately conclude that rhythm and meter are opposites, like movement and rest.
What are rhythm and meter?
Rhythm and meter are, first of all, a certain separation, discontinuity. However, discontinuity alone as a complete isolation of moments is unthinkable. Rhythm is precisely such a discontinuity and such a set of isolated elements, which, without ceasing to be itself, is and is perceived as continuity, integrity. Rhythm is the organization of discontinuity as integrity. How does this happen? If the rhythm (meter) is originally a separation, then it has no reason for continuity in itself. What makes the rhythm be exactly series, and not a chaotic set, is the extra-rhythmic principle of integrity, in which isolated elements merge. This is a regular pattern. A regular pattern is an arrangement of separate parts in which they, while remaining isolated, merge into one whole. This means that it is possible to logically, regularly, and not randomly or arbitrarily, move from any element of the series to the adjacent, next or previous one.
The metro-rhythmic series consists of elements and inter-element intervals. Either one or the other can be rhythmized (then we have peculiar syntheses of meter and rhythm), or both parameters together (this is pure rhythm). The meter is obtained if both elements and intervals are unchanged. Rhythmization, that is, the organization of disparate parts into a logical sequence, occurs due to the principle of regular patterns, which consists in the fact that each subsequent element or interval of a series is modified by a certain constant coefficient (constant). Arithmetic and geometric progressions may serve as an example.
By itself, that is, objectively, the rhythm is given entirely and immediately, since spatially it exists at each of its points simultaneously, no element is either earlier or later than the other. But for the perceiving subject, the rhythm is given at some discrete point, and for its perception it presupposes the movement of the subject in time with a consistent coverage of the rhythmic series.
Let's summarize the definitions. Rhythm is the determinism of the constant formation of elements and inter-element relationships, presented in an orderly series, given in itself as an actual thing that has become and as a potential becoming perception of the subject. In the rhythm, the same eidos hypostatizes differently each time, but the steps of its hypostatization form a regular pattern. Rhythm is the ordering of unequal elements of the actual set of a single eidos, functioning in this set as a difference in both space and time, and each time with a different degree of intensity, which either decreases (slowing rhythm) or increases (accelerating rhythm).
Meter and rhythm together – metrorhythm – are ways of regularly organizing elements and relationships. There are other unifying means that allow to avoid chaos and preserve the integrity of the form with an arbitrary combination of its parts60.
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