| STUDY THE WORKS OF PETER EISENMAN? WHY?! |
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Department of "Cultura del progetto"
II University of Naples, Faculty of Architecture , Aversa, Italy
INTRODUCTION
The ancient Greeks knew that reasoning
is a structured process governed, at least partially, by a system
of explainable rules. Aristotele codified syllogisms; Euclide
formulated geometric theorems; Vitruvius defined the criterion
and referential key so that every architectural element could
be proportioned according to an ideal model, symbolizing the
aspirations and aptitudes of that particular civil society.
In these forms of reasoning it is possible to distinguish
contingent aspects with regard to the role which the use of a
method and the application of a procedure play within any conceptual
process: communicable by virtue of the codes and the prescribed
norms, comparable in every time and place by virtue of the reproducibility
of the procedures.
Euclidian logic begins with
the inductive definition of very simple concepts and gradually
constructs a vast body of results, organised in such a way so
that each concept depends on the previous. Thus, a strong and
rigorous construction is derived that makes all operations perceptible,
comprehensible and intelligible. But, unlike processes that are
physically constructed, Euclidian reasoning does not materially
crumble if its structural elements, that is, its demonstrations,
are not coherent with the reality of the empirical world. This
explains why deductive-inductive logic, subtended by the philosophical-scientific
thought of classical culture, has unconditionally influenced
almost all fields of knowledge for almost two thousand years.
Physical-mathematical knowledge was the first to understand the
conventional character that is typical of axiomatic reasoning:
".. which firstly, and in the most rigorous manner, became
conscious of the symbolic character of its fundamental instruments"
[Cassirer, 1929]. The attempt to render Euclid's works without
contradictions has caused a review of the form in which scientific
work is carried out [Saccheri, 1733]. The verification of the
existence of many types of points and lineshas sanctioned the
distinction, even in the field of knowledge, between common language
and technical language, clarifying once and for all that it is
the the type of link established between the symbol and the meaning
that provides the symbol with its significance.
Already in antiquity, the criticism raised by the sophists against
the use of a ‘common' language had established the premises
for the definition of a technical, or pseudo-technical, language,
which would be later adopted by Euclid in his Elements.
Here, the first twenty-eight propositions, thanks to the uniqueness
of the relations that link human intuitions to the properties
of geometric entities, define absolute geometry; geometry, that
is, which doesn't necessitate any preformulated theorem for its
enunciation. In contrast, the other propositions, formulated
with the aid of the fifth postulate, have demonstrated the impossibility
of any axiomatic system whatever being always coherent with the
reality of the natural world. This is why nineteenth century
mathematicians and humanists disputed even the most concrete
of the mathematical sciences, namely the arithmetic. The ‘demonstrability'
was actually a notion weaker than the truth.
THE LOGIC OF FORMAL SYSTEMS WITHIN ARCHITECTURAL
RESEARCH
The
problems of interpretation, description, prediction and synthesis,
and therefore the operative choices, are in fact resolved by
the perceptive capacity of the intelligence. The procedures linked
to the concept of "variable linguistic" [Chomsky, 1966;
Zadeh, 1978] or of "calculation with words" [Zadeh,
1965] have proved themselves more adapted to describing choices
of everyday life. It is, therefore, no wonder that in every field
of knowledge deductive-inductive logic gives way to other types
of logic considered more fluid.
Euclidian logic is founded on the possibility of always deducing
new theorems. Instead, propositional logic is founded on the
possibilities of always constructing new strings of solutions
free from any theorem but founded on the correct use of the few
but immutable rules with which to relate symbols without ‘active'
meanings. This doesn't prevent any theorem of empirical experience
from being inserted into the "rules of imaginations"
[Hofstadter, 1979] which preside over the chosen formal system.
When this happens, between one system and the other are established
isomorphisms [Hofstadter, 1979] capable of revealing portions
of truth that are coherent with the natural world. The result
is not predictable, but is the outcome of a formative process
which, by virtue of its actualizing modality, can overcome the
limits of human comprehension.
Each architectural work can be considered a living organism:
its life includes the definition of the idea, the law that governs
it and the formative process which is realised in the material
it forms [Vattimo, 1976]. The finished work is not the result
of a linear process as much as the outcome of a formative process
whose fluid dynamics derives only minimally from the precision
of deductive-inductive logic.
"FUZZY"
LOGIC IN THE PROJECTS OF PETER
EISENMAN
In
architecture it is possible to demonstrate, as Peter Eisenman
states, "...all the changes can in some way refer to cultural
changes... the most tangible changes... were determinated by
technological progress, by the development of new conditions
of use and by the change in meaning of certain rituals and their
field of representation" [Eisenman, 1989]. Thus in the simple
use of geometric solids, he limits himself to the promotion of
a language orientated with a correspondent systematic order.
In the spatial manipulations of plans and sections,
Eisenman experiments with the "laws of thought" (1854)
put in place in the nineteenth century by George Boole and Augustus
De Morgan. In the same way that the two English logicians brought
to extreme consequences the Aristotelian syllogisms which prelude
to mechanised reasoning, Peter Eisenman manipulates an idea,
submitting it to a sort of propositional calculation. Through
probings and attempts which follow each other in a sequence of
approximations made possible by a new conception of notation
and representation, and beginning with elementary solids or simple
internal relations, architectural space takes shape. Every element
is charged with "active" meaning since it doesn't have
any reference or architectural content, but lives only in relation
to intrinsic order which impress energy on the formative process;
this justifies the relation of one part to the other in an organic
whole. The process that sustains the final construction is similar
to that which regulates the axial growth of crystals. The form
of the crystal, like the architectural one, is the fulfilment
of an organic movement which configures the form as much in the
visible structure as in the substantial structure [Zodiac, 1969].
Answering the question What would happen if?, the fluid
laws that lie at the base of the planning process inflect solutions
that, if "isomorphic" to spatial necessities, can reveal
themselves as architectural hypotheses, calculated but extremely
free. Thus, if the first projects of Eisenman illustrate the
internal virtualities of a rigorously closed, rigid cube, the
following plans show the virtualities of the same shape subjected
to the internal laws of deformation.
THE CARNEGIE MELLON RESEARCH INSTITUTE
(CMRI)
The plan
for the CMRI (Pittsburgh, Pennsylvania, 1987-88) is an emblematic
example of a process of deformation (Figure
1). "The fundamental element
of this architectonic elaboration is the Boolian cube, a geometric
model relative to the function of computers" [Oechlin, 1991].
The vertexes of the tridimensional cube, considered as solid
shapes or transparent frames, represent all the possible terns
of 0,1 by which to organise orderly strings. The organisation
of the place takes shape in the mathematical functions which
regulate the procedures of conjunction, separation, deformation.
The process, in its becoming, makes the results as well as the
objectives mutable. Once defined the interval of the space and
its mathematical progression, in asintotic curves differently
directed are placed as cubes at 4-N, repeated for a certain number
of times. Every building is constructed from the matching of
a couple of cubes. Every couple contains two solid cubes (visible
shapes) and two cubic frames (internal structures) of 12 and
14 meters corresponding to the dimensions of the module that
defines the architectural space destined to receive the offices
and the laboratories of the CMRI. Every couple can be seen as
a projection of the other, inverting the rapport between solid
and frame (Figure
2). The wealth and the complexity
of the formal result of the project derive from these simple
operations. [Oechlin, 1991] (Figure
3).
THE ARONOFF CENTER AT THE COLLEGE OF DESIGN,
ARCHITECTURE, ART AND PLANNING
Whatever the subject, in
the era of information dominated by the media, teaching has a
moral obligation to describe how and why it works. Convinced
of this, Eisenman makes the plan for the Aronoff Center at the
College of Design, Architecture, Art and Planning (University
of Cincinnati, Cincinnati, Ohio, 1988-1983) a sort of manifesto
of the education imparted by the University of Cincinnati [Ciorra,
1993] (Figure 4). Here, the structures that already existed
are related to the orthography of the place: a double curve,
deviated, redoubled and deformed with the help of computer simulation,
is transferred into tridimensional space (Figure
5). The configuration that descends
from it contains within itself the figurative force structuring
the compositive solution. The procedure reminds one the traditional
cut of precious stones or the formal reasoning applied by Lewis
Carroll to the studies of Hilbert [Hilbert and Cohn-Vossen, 1932]
. The finished work is an unconventional image that pushed the
architect himself to define his project as "a weak configuration"
calculated but aesthetically free [Vattimo, 1976].
A REPRESENTATION OF THE WORKS OF PETER
EISENMAN
Eisenman
shows how it is possible to proceed from an abstract idea to
a concept that is anything but abstract, to show how the generative
dynamic of all his plans can be described or, if necessary, rebuilt
in every minimal detail. The study induces, therefore, a reflection
on the possibilities but also on the limits that characterise
the uncertain logic of formal systems applied to the new knowledge
of notation and architectural representation.
The
space of architecture can be declined at different scales of
reading and intervention, permitting a gamut of representations
that ranges from maximum abstraction with respect of the concrete
space, to maximum detail. Each path allows for the rediscussion
of the outcome of a formative process which orientates solutions
and objectives. The result reflects Colin Rowe's [Rowe, 1984]
teaching of Chomsky [Ciorra, 1993] or the mathematical logic
laying at the base of the "variable linguistic" or
of the ‘calculation with words' conceived by Zadeh [Zadeh,
1978].
The use of a method and the application
of a process as "the art of thought" remind one also
of the geometric experiments of Francesco Borromini or of his
greatest admirer Guarino Guarini. Borromini chooses a geometrical
figure, an equilateral triangle, to demonstrate how the unconventional
use of this shape-structure could become the matrix of new architectural
conceptions. The church of S. Carlo alle Quattro Fontane (1637-41)
or the church of S. Ivo alla Sapienza (1643-60) show how the
geometric-mathematical language is able to drive the formative
intentionality over the conventional aspects. In the same way
the process of geometrical deformation, brought to a head by
Guarino Guarini treating the section
of a cylinder, reveals how geometrical language can be a ‘weak'
structure of thought able to investigate : "...against the
certainty of reason... an anguished passion and working thought...
suspended in time" [Griseri, 1967] (Figure
6).
In our century
Jacques Derrida has clarified better
than any other intellectual how the lay-out of geometric research,
in grasping the original sense of the constituent act, can succeed
in expressing a new image of the world [Derrida, 1962].
In the architecture of Peter Eisenman, but also in
that of Borromini or of Guarini, almost nothing remains of the
hermetic exactness of geometric reasoning, but much of the geometric
language shines through.
IN CONCLUSION, A QUESTION MARK
No design reproduces
the reality, but rather builds up a logical model in order to
organize a system of relations that are either observed, hypothesized
or planned. The consequent schema re-presents, according to an
intentional design for its reading, the set of characteristics
that are, time and time again, selected and destined to become
a sign [De Rubertis, 1994]. Let us quote the following superb
motivations that are basic for the theory of description and
meaning inside the theory of fuzzy sets:
An exact description of any real physical situation is virtually impossible. This is a fact we have had to accept and adjust to. As a result, one of the major problems in description (essential to communication,decision making, and, in a broader sense, to any human activity) is to reduce the necessary imprecision to a level of relative unimportance. We must balance the needs for exactness and simplicity, and reduce complexity without oversimplification in order to match the level of detail at each step with the problem we face.
The inexactness of the description is not a liability; òn the contrary, it is a blessing in the sufficient information can be conveyed with less effort. The vague description is also easier to remember. That is, inexactness makes for grater efficiency. [Goguen, 1969]
Finally, let us mention the so called principle of incompatibility.
The essence of this principle is that as the complexity of a
system increases, our ability to make precise and yet significant
statements about its behaviour diminishes until a threshold is
reached beyond which precision and significance (or relevance)
become almost mutually exclusive characteristics. It is in this
sense that precise quantitative analyses of the behaviour of
humanistic systems are not likely to have much relevance to the
real-world societal, political, economic, and other types of
problems which involve humans either as individuals or in groups
[Zadeh, 1973].
It isn't difficult to intuit how
the limits and complexity of our present culture tend to displace
our attention from the conceptual area of production to that
of transformation. Design, as much in the overall specifications
for a project as in the design of the details, presents itself
with reference to knowing displacements, that is, the conveying
of multiplicities, contradictions and differences to temporary
equilibriums. Actual realizations and designs on papers are the
place where reflections consist; the reflections matured in several
technological ambits appear in terms of sums of experiences and
solutions "shifted" from their own place of origin
to the detailed synthesis that rules the assembling. [De Rubertis,
1994].
We pose the final question: how can fuzzy
logic, which finds its reason for existence in the interpretation
of the reality and exalts the "shifts", point towards
the architectural process?
ACKNOWLEDGMENT
This paper was first published in New Trends in
Fuzzy Systems, (Proceedings of the International Joint Conference
on current Issues on Fuzzy Technologies, Methods and Environments
for Planning and Programming, Aversa and Naples, 10-11 October
1996) Dario Mancini, Massimo Squillante and Aldo Ventre, editors
(Singapore:World Scientific Publishing Company, 1997). It is
republished in the Nexus Network Journal by the gracious
permission of the World Scientific Publishing.
BIBLIOGRAPHY
G. Bachelard, La formation de l'esprit scientifique
(Paris: Gallimard, 1986).
R. Bellman and M. Giertz, "On the analytic formalism of the theory of Fuzzy Sets", Information Sciences, 5 (1973), 149-157.
W. Blackwell, Geometry in Architecture (New York: Wiley, 1984). To order this book from Amazon.com, click here.
R. Briggs, Geometry of Meaning (A.M. Young, 1984). To order this book from Amazon.com, click here.
E. Cassirer, Philosophie der symbolischen Formen, vol. IV (Berlin: 1923-1929).
M. Chaouli, "La formula magica dell'innovazione", Management, 2 (1991), 92.
M. Chomsky, Linguistic variable (NewYork, 1966).
P. Ciorra, Peter Eisenman, opere e progetti (Milan: Electa,1993).
E. B. Condillac, Essai sur l'origine des connaissances humainés (Paris: 1746).
R. De Rubertis, Il Disegno dell'architettura (Rome: NIS, 1994).
J. Derrida, L'origine de la géométrie (Paris: Presses Univérsitaires de France, 1962).
P. Eisenman, "Oltre lo sguardo: l'architettura nell'epoca dei media elettronici", Domus 734 (1992), 17-24.
P. Eisenman, "La maison dom-ino e il segno autoreferenziale", Sulle tracce di Le Corbusier, C. Palazzolo and R. Vio, eds. (Venice: Arsenale, 1989), 12-35.
P. Eisenman, "The end of the Classical", Perspectiva 21 (1984), 154-172.
C. Frommel, "Il disegno di architettura nel rinascimento italiano", Domus 759 [1994], 41-46.
V. Gheorghiu and V. Dragomir, Geometry of Structural Forms (Elsevier, 1978). To order this book from Amazon.com, click here.
J. Goguen, "The logic of Inexact Concepts", Synthese, 19 (1969), 325-373.
W. Grace, Geometry for Architects (Stipes Dover, 1975). To order this book from Amazon.com, click here.
B. Gravagnuolo, "I tracciati dell'armonia. Tra storia mito e progetto", Quaderni Di 8 [1989], 83-95.
M. Griseri, La metamorfosi del barocco (Torino: 1967).
D. Hilbert and S. Cohn-Vossen, Anschauliche Geometrie (Berlin: Springer, 1932).
D. R. Hofstadter, Fluid Concepts and Creative Analogies (New York: Harper Collins, 1995). To order this book from Amazon.com, click here.
D. R. Hofstadter, Gödel, Escher, Bach: an Eternal Golden Braid (Basic books, 1979). To order this book from Amazon.com, click here.
M. Kemp, Geometrical Perspective from Brunelleschi to Desargues: a Pictorial Means or an Intellectual End? (Longwood Publishing Group, 1986).
L. Kollar and Hegedus, Analysis and Design of Space frames by the Continuum Methods (Elsevier, 1985).
M. A. Laugier, Essai sur l'architecture (Paris, 1753-55).
V. Mancini and W. Bandler, "A database theory of truth", Fuzzy sets and Systems 25 (1988), 369-379.
W. Oechlin, "Peter Eisenman: The Cube and its Deviations", Daidalos 35 (1991), 46- 52.
L. Pareyson, Estetica (Milan: Bompiani, 1988).
F. Purini, "Ed infine un classico ...", Casabella (1987).
F. Purini, "La forma storica della decostruzione nell'architettura italiana", Decostruzione in architettura e filosofia (Milan: Città Studi, 1992), 45-56.
C. Rowe, "Neoclassicism and Modern Architecture", The Mathematics of Ideal Villa and Other Essays, (Cambridge,Massachusetts: 1984). To order this book from Amazon.com, click here.
G. Saccheri, Euclides ab omni naevo vindicatus (Milan, 1733).
G. Vattimo, ed., Saggi e Discorsi (Milan: Mursia, 1976).
Zodiac 19 (1969).
L. A. Zadeh, "Fuzzy Sets as a Basis for the Theory of Possibility", Fuzzy Sets and Systems, 1 (1978), 3-28.
L. A. Zadeh, "Fuzzy Sets and Systems", Information and Control, 8 (1965), 338-353.
L. A. Zadeh, "Outline of a New Approach to the Analysis of Complex Systems and Decision Processes", IEEE Transactions ou Systems Man and Cybernetics, 3 (1973), 28-44.
FUZZY LOGIC
What is fuzzy logic?Fuzzy logic Pilot and Demonstration Workshop
PETER EISENMAN
Peter Eisenman biographyPeter Eisenman at Stanford University
The Carnegie Mellon Research Institute
The Aronoff Center under construction (photos)
JACQUES DERRIDA
Introduction to Jacques DerridaJacques Derrida at Stanford University
On Grammatology by Jacques Derrida
GUARINO GUARINI
History of Guarino Guarini
|
Adriana Rossi "Study the Works of Peter Eisenman? Why?", Nexus Network Journal, vol. 1 ( 1999), pp. 65-74. http://www.nexusjournal.com/Rossi_eng.html |
Copyright ©1999 Kim Williams