Poincaré defined topology as the science that introduces us to the qualitative
properties of the geometric figures not only in ordinary space but also in more than 3-
dimensional space.Thus topology is the study of the properties of geometric figures
that, undergoing intense distortions which cause them to lose all of their metric and
projective qualities, for example shape and size, are still invariant. In other words, the
geometrical figures maintain their qualitative properties. We can consider figures that
are made of materials that can be arbitrarily deformed, that cannot be lacerated or
welded: there are properties that these figures conserve even when they are
deformed.
In 1858 the German mathematician and astronomer August Ferdinand Moebius
described for the first time in a work presented to the Academy of Sciences in Paris
a new surface of three-dimensional space, a surface that is known today as the
Moebius Strip. In his work Moebius described how to build (quite simply) the surface
that bears his name. Among other things, the Moebius Strip is the first example of a
non-orientable surface – it is impossible to distinguish between two faces.
Artists and architects sensed some of the topological ideas in the past decades, first
by artists, then much later by architects. These shapes, that so interested Max Bill in
the 1930s [4], could not go unnoticed in architecture, although it took some time: until
the diffusion of computer graphics, which allows the visualization of the mathematical
objects discussed, thus giving concrete support to the intuition which otherwise, for
the non-mathematician, is hard to grasp.
These are the words of Martin Kemp, an art historian specialized in the relationship
between art and science, published in Focus ([5], one of the volumes that make up
the catalogue of the 2004 Venice International Architecture Exhibition.
In his article Kemp writes mainly about architecture. The image accompanying
Kemp's article is a project by Frank O. Gehry, an architect who obviously cannot be
overlooked when discussing modern architecture, continuous transformation,
unfinished architecture, and infinite architecture.
In november 2009 a new space for contemporary art and architecture was opened
in Rome, the MAXXI. A project of the architect Zara Hadid
Fluidity is one key word in contemporary architecture. And without topology, the
science of continuous transformations, these new forms would have been difficult to
imagine.
“Van Berkel's house, inspired by the Moebius Strip (Moebius House), was designed
as a programmatically continuous structure, that combines the continuous mutation
of the dialectic sliding couples that flow into each other, from the interior to the
exterior, from the activity of work to that of free time, from the fundamental to the
non-fundamental structure."
During the same period Peiter Eisenman was designing the Max Reinhardt Haus in
Berlin [12].
Ben van Berkel and Caroline Bos
“The building, composed of arches, made up of intersecting and overlapping forms,
presents a unified structure that separates, that compresses, transforms and finally
comes back together on the horizontal plane at the height of the attic. The origin of
the form is represented in the Moebius Strip. Just as the Moebius Strip folds two
sides into one surface by folding on itself, the Max Reinhardt Haus denies the
dialectic tradition between internal and external and confuses the distinction between
public and private."[11]
Topological architecture means that dynamic variation of form, facilitated by
information technology, by computer-assisted design, by animation software. The
topologification of architectonic forms according to dynamic and complex
configurations leads architectural design to a new and often spectacular plasticity, in
the footsteps of the Baroque or organic Expressionism."
Stephen Perrella, one of the most interesting virtual architects, describes
Architectural Topology as follows: [14]
“Architectural topology is the mutation of form, structure, context and programme
into interwoven patterns and complex dynamics. Over the past several years, a
design sensibility has unfolded whereby architectural surfaces and the topologising
of form are being systematically explored and unfolded into various architectural
programmes. Topological “space" differs from Cartesian space in that it imbricates
temporal events-within form. Space then, is no longer a vacuum within which
subjects and objects are contained, space is instead transformed into an
interconnected, dense web of particularities and singularities better understood as
substance or filled space.
This nexus also entails more specifically the pervasive deployment of teletechnology
within praxis, leading to an usurping of the real (material) and an unintentional
dependency on simulation." Observations in which ideas about geometry, topology,
computer graphics, and space-time merge. Over the years the cultural nexus has
been successful: new words, new meanings, new connections.
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