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INVARIANTS

Remembering Martin Luther King, I had a dream. I dreamt that the two worlds of the so called humanities and of technology had indissolubly melted into a common culture and that scientific rigour had entered full sail into the extraordinary world of creativity giving it a much more fascinating connotation of rigour.
When I say that the field of creativity is much more contiguous to the scientific rigour than you can imagine, I think the reactions among professionals, be they creative people (artists, if we use a term now close to obsolescence) or experts in creativity, are equal to a wall rather than to a door willingly opened. The old all in division into two cultures is hard to die. I speak here of a way of conceiving architecture that can bring this category of human activities nearer to the field of science and, consequentially, to the field of logic. Everything begins with the quite obvious finding that in the course of architectural design, at any time and anywhere in the world, architects during the various stages of the design itself, have faced, are facing and will face a myriad of different problems. These problems, once somehow solved, will produce an object which sometimes belongs to architecture, while in most cases simply to construction. If we try to analyse this large and often confusing set of problems and needs more carefully and with stricter sequencing we will come across a very interesting fact, that, in my opinion, deserves to be investigated by all the people involved in teaching architecture, by all those experts who give aesthetic judgements - sometimes wholesale and usually retail - on architecture itself and all those who of architecture make it their job. I should add that the argument I am about to expose is fine not only for architects, but also for people working in the field of the genesis of form and of its manipulation.
I will start therefore with the statement number 1: in the course of design, the architect or anyone interested in producing forms of all kinds, evidently addressing many situations to be solved, is however and always faced with some problems, that, whatever the subject of the same design, are always the same, at any time, in any space, and in any cultural environment.
It is therefore reasonable to say that these issues, for the fact of always recurring, represent a constant factor easily traceable in the design of any object of any kind. The indisputable presence of constant situations/moments in any evolutionary process entitles us to assume that we are dealing with a category that could be fairly contiguous to a minimum of scientific rigour.
This contiguity to that field in which the presence of constant factors, axioms and everything that is constantly repeated in time and space without change of any kind, suggests that we are moving in a dimension which is strictly related to scientific thought. I will begin, therefore, to organize a more rigorous and more logical analysis of some phenomena that have their full citizenship in the field of creativity.
So what are those cases, those design situations, which, at any time, on any point on the face of the earth, in any cultural circumstance continuously arise for those who have to do with design?
In the field of architectural practice I have identified some situations, which I will define invariants, because they come up so implacably invariant for the designer.

FOREWORD

Of all the ideas current in the various Architecture faculties in Italian universities on how to teach planning, the most deep-rooted and widespread is the belief that almost everything can be taught except design itself.
It is not, however, my intention, in this paper, to try to discover why this idea is so common (to the extent that it becomes a pseudo-intellectual screen to hide behind).
It is worth remembering briefly that, while reams of papers have been published on the above impossibility, discussions on other subjects have often, inexplicably, stood still. I shall not speak here of architects who have founded their literary forces on the strength of reasoning; my point of departure in what follows is the correct, and above all, logical use of what has been done up to now, and will continue to be done, in architecture.


INITIAL CONSIDERATIONS

We shall start from two established facts:

The existence on the face of the Earth of a myriad of objects conceived and constructed by man, many of which are firmly "anchored" to the ground and therefore unlikely to be moved onto the architect's drawing table or that of the student architect.
The existence also of an enormous number of publications on Architecture including drawings, photographs and an immense amount of words organised in various different ways.

There are, therefore, two artificial universes:

Architectural constructions.
Architecture which has been drawn or written about, or history of architecture.


ENUNCIATION OF THE PROBLEM


I ask myself:
how it is possible, if it is possible, using these two universes, to create a way of starting to:
Talk Architecture.
Talk about Architecture ?


PRESENTATION OF THE PROBLEM

It must be considered that, despite temporal and cultural changes, and although affected by varied forms of conditioning and evolution, the architect, in certain parts of the designing process has always been faced by certain situations which have never changed trough the years.
I shall explain myself better: the design of any objects (no matter what its dimensions may be) can be compared to the articulate organisation of material and forms.
Within this organisation, however complex, there are situations which are always unchanged, as follows:

The putting together of different materials which are on the same plane but have different directions.
The change of plane of two different materials.
The change of plane of a single material.
The confines of any material.
The treatment of spaces with the same material around them.

At this point we have two terms on our drawing board:

An organisation which is always complex.
The five unchanging situations.

Let us now consider the above mentioned complex organisation as a set and the unchanging situations as a few elements of the set.

Since we have introduced two terms taken from mathematical terminology, that is set and elements of the set, the transfer of the problem from a conceptual area to an area belonging to mathematical logic seems inevitable. The term inevitable has been used in the light of the following considerations:

1st consideration: "If any discourse is presented in such a way that it consists of symbols and precise rules on the operation of these symbols, which are only subject to the condition of having an internal coherence, that discourse is mathematical." C. Boyer, demonstrating this important concept expressed in "The Mathematical Analysis of Logic" by George Boole (1847).

2nd consideration: "Mathematics can be compared to an exquisitely made mill which grinds materials of any grade of fineness; but, nevertheless, what comes out depends on what goes in; and just as the greatest mill in the world will not extract flour from pea pods, so pages and pages of formulae will not produce precise results from incoherent data!" T.H. Huxley (1825 - 1895).

3rd consideration: In 1872 George Cantor defined a set as " The joining in a whole of objects of our intuition or of our thoughts, which are well defined and different each from the other."

4th consideration: "Pure mathematics is the class of all the propositions which have the form "p implies q" where "p" and "q" are propositions containing one or more variables, which are the same in each proposition, and neither "p" nor "q" contains a single constant except the logical constants." Bertrand Russel "The Principles of Mathematics" 1903.

5th consideration: In the 1939 first edition of "Théorie des Ensembles", Nicolas Bourbaki wrote: "A set is made up of elements which have certain properties and which have a certain relationship with each other and with elements of other sets".

6th consideration: In 1950, N. Bourbaki wrote in "The Architecture of Mathematics", American Mathematical Monthly: "From the axiomatic point of view, mathematics is presented as a storehouse of abstract forms: mathematical structures; and it happens that, without us knowing why, certain aspects of empirical reality adapt themselves to these forms, almost through a sort of predisposition."

7th consideration: In 1950 André Weil wrote in "The future of Mathematics", American Mathematical Monthly: "It is through unexpected combinations……that the mathematician of the future will lay out in a
new way and resolve the problems that we have left him to inherit."








FINAL NOTES

From a didactic point of view, and to make things clearer for the reader, it is worth remembering that the five unchanging situations can be rewritten in the following way, with the addition of useful comments:

Study how the problem: when two different materials, having the same planes and different directions, are in contact with each other has been resolved structurally and/or formally or how it can be resolved.

Study how the problem: when two different materials, having two different planes and joining at the same point, are in contact with each other has been resolved structurally and/or formally or how it can be resolved.


Study how the problem: when a single material changes plane has been resolved structurally and/or formally or how it can be resolved.

Study how the problem: when a material ends has been resolved structurally and/or formally or how it can be resolved.

Study how the problem: when two different materials ends, a space begins and the same material begins again has been resolved structurally and/or formally or how it can be resolved.


Any correspondence should be addressed to:
prof. arch. Franz Falanga
via Campaner 1
31034 CAVASO (TV)
ITALIEN