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Every liberating action depends on recognition, which is best performed by scientific methods,so science becomes the most important instrument for the improvement of our life.
Rudolf Carnap, Intellectual Autobiography

Sir Karl Popper describes the experiment as an essential part of a four-figure scheme. In this scheme, he designs a general model for recognition:

01] The elder problem;
02] Theories as a first trial (= models);
03] Attempt of elimination of models throughout criticism, experimental proof included;
04] New problems, deriving from the critical discussion of our
theories (1).

One can assume that this four-figure scheme is valid for architecture, as a human product, as well. Therefore every new building design forms an experimental solution towards a specific problem, probably with a long history of its own.

To grasp a problem, today we design models or formal systems. There are many abstract models in architecture: on the one hand we have functional typologies, describing specific relations of functional areas. On the other hand there are formal typologies for the composition of various building components. Probably, and not at last, there is a manifold of constructive solutions and systems. Successful models are improved, less successful models are critically questioned, adapted or finally removed.

Important Dialectics

What is a formal system and which fascination is it all about this abstract models?

Carnap defines a constitution system as a "...stepwise order..." of objects, "...so, that the objects of every level can be constituted form the objects of a lower level. Because of the transitivity of the reductivity, all objects are constituted from the primary objects of the first level. These primary objects form the basis of the whole system... The term "object" is used in a wider sense, for everything which can be described in a statement" (3). Beside these elements, Carnap describes three more parts of a constitution system. The description of the quality of elements, the description of the relation of elements and the description of the structure of the system (4).

Franz Pichler mentions another essential characteristic. He describes formal systems as "a construct, which is able to perform a special behavior in an abstract way" (5). With this statement, he confirms the important assumption of a separated existence of reality and controlled model. By 500 BC, the Greek poet and singer Xenophanes wrote:

Certain truth no man ever will discern
About the gods and all things, I talk about.
Should ever one man proclaim perfect truth?
How could he know: everything is filled with suspicion. (6)

In this sense, all our models and theories are based on more or less reasonable assumptions and rational construction.

Systems and Isomorphisms

- - p - - - g - - - - -
as 2 plus 3 equal 5

so we discover an isomorphism, between the derived set of a formal system and a part of our own reality. Hofstadter says:

This is our first example of the case, that a formal system covers a part of our reality and seems to reproduce it perfectly, as all sets are isomorphic to the related part in reality. In spite of that reality and formal system are independent to each other (8).

As an interesting personal gain Hofstadter describes the discovery of the isomorphism between reality and the set of a formal system. He mentions this moment as:

...a reason to rejoice. It appears as a lightning from clear skies and is a source of amazement. The discovery of an isomorphism between two well known structures means a big heap in knowledge - and I claim, that these discoveries of isomorphism create meaning in the human brain (9).

An isomorphism can explain a certain case in reality and give way to successful predictions. Maybe we will discover more sets in the same system, which might give no sense at all, or have not been confirmed by evidence yet. These apparently senseless or unconfirmed sets form a valuable potential for the experimental research and the architectural experiment.

Autocatalytic Dwellings

Peter Weibel describes the common use of formal systems in arts and science.

The use of mathematics and logic models in arts, especially in the analytic and conceptual art forms, is just one example for the astonishing convergence of science and art (10).

Furthermore Weibel mentions the influence of abstract models towards modern art, "... far beyond the golden section...", "...on the way towards abstraction..." (11).

One of the most popular examples for an ideal formal system, is the algorithmic concept for the Wittgensteinhaus in Vienna, designed by the philosopher Ludwig Wittgenstein and the architect Paul Engelmann.

As a design problem Wittgenstein chose the confrontation with an symmetric outward appearance of all rooms. The self-made simple algorithm "Design all visible surfaces due to an axis based symmetry" led to a constructive and technological very complex result, submitting the reasonable architectural syntax for the finish of the surface.

Jan Turnovskı describes in, to my mind, one of the best works on this theme, "Die Poetik eines Mauervorsprunges" (12), the everlasting problem between a complex result and a very simple and clear procedure in architecture. This example not only shows the immense interconnection of architectural reflexivity between construction, function and form, but belongs to the most fascinating works of the early 20th century.

There is no more handwriting of the architect as an individual signature, no use for the fulfillment of an aim, no preformed functions as metaphors of technologies. We have overcome the long-term dominance of form, object and material; Architecture is no longer a carrier of meaning; parted from retrospection, free from habits, personal desire and projections, it is no more an instrument of the powerful. Architecture is no longer derivative, architecture will be autocatalytic (13).

 

In a simple polyhedron, the sum from the amount of corners and surfaces is equal 2 + the amount of all edges (14)

N corners + N surfaces - N edges = 2

Probably the architect develops a condition for balance between the corners, edges and surfaces and defines the new outline of her building. In this case the object is just one of all possible forms, with an equal amount of surfaces, edges and corners.

This self-reflexive interconnection is made visible by an optical design concept. Mirrors in the central area give always a view of a strolling visitor throughout the whole building, and even towards the outside.

The basic room is being wrapped from the other rooms and wraps the other rooms in itself (15).

4-D Variations

Have we been confronted with positive and negative form, functional areas or constructive components as elements in various formal systems, Wittgenstein chose a self-reflexive geometry as a constituent of his composition. Pieces of waste are the elements of the design generator, a defined amount of site-conditions form the basis of the autocatalytic design of Ernst J. Fuchs, a simple mathematics theorem forms a variety of possible geometries in the nested cube project of Hideyuki Yamashita.

"How free is freedom", Otl Aicher asked himself and described the delicate relations between the improbable freedom in the possibilities of a soccer match and the systematic order of the necessary rules.

Freedom presupposes the order, they are related to each other, one is founded on the other (16).

In any of the projects mentioned, there emerges an enormous amount of variations in a rigid framework of conditions. Some of the variations might be useful in handling a topical problem, others might be less useful, some complete senseless, but still possible.

These enormous possibilities will always be in the center of a sensible application, as operable tools in the computer aided design process and the experimental design, with surprising results and a fantastic potential of surrealistic interpretations.

4-D, Buckminster Fuller named a series of designs in the time about 1928. It stood for "four-dimensional thinking - thinking in time instead of only in space, thinking of consequences for humanity instead of only immediate personal gain" (17). In this way, he defines design as a necessary and contemporary solution for the improvement of our circumstances.

The computer aided design process today, opens a broad field of possibilities in the application and the automation of self-generating algorithms. Just in this point formal systems stay commonly understandable and open for a surprising architectural and cultural experiment.

Most interesting will be an integral solution towards architectural design problems, not only oriented at the final form of a building, but respecting all necessary data.

(1) Karl R. Popper, "Alles Leben ist Problemlösen", München 1997, p. 32.
(2) Ole Bouman, "Quick Space in Real Time", Part 3, in "Archis", 6, 1998, p. 72.
(3) Rudolf Carnap, "Der logische Aufbau der Welt", Hamburg 1979, p. 1.
(4) Rudolf Carnap, 1979.
(5) Franz Pichler, "Mathematische Systemtheorie", Berlin 1975, p. 13.
(6) Karl R. Popper, "Auf der Suche nach einer besseren Welt", München 1987, p. 50.
(7) Douglas R. Hofstadter, "Gödel, Escher e Bach", Stuttgart 1985, p. 37.
(8) Douglas R. Hofstadter, 1985, p. 58.
(9) Douglas R. Hofstadter, 1985, p. 54.
(10) Peter Weibel, "Analyse des Realen", in "Jenseits von Kunst", Neue Galerie Graz 1998, p. 48.
(11) Peter Weibel, 1998.
(12) Jan Turnovskı, "Die Poetik eines Mauervorsprunges", Braunschweig 1999.
(13) Manfred Wolff-Plottegg, "Architektur Algorithmen", in Peter Weibel, "Jenseits von Kunst", Wien 1997, p. 704.
(14) Karl Kreutzer, "Mathematik", München 1969, p. 198.
(15) "Die Schrift des Raumes", Kunsthalle Wien 1996, p. 82.
(16) Otl Aicher, "Typografie", Lüdenscheid 1992, p. 15.
(17) Martin Pawley, "Buckminster Fuller", New York 1990, p. 39.

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