of a conceptual space:
relationship between form and function, programme and context, and structure and
meaning is continuously and rapidly changing.
Ruptures occur within an old fabric, which is
constantly dismantled and dislocated, leading to new concepts or structures. The
traditional opposition between use and architectural form is rejected in favour
of a superimposition or juxtaposition of two terms that can be independently and
similarly subjected to identical methods of architectural analysis. The rift
between form and function, and between space and action within architectural
parameters is ever expanding. Today, we are a part of the dislocation of these
terms, bringing attention to the disappearance of functionalist theories, but
perhaps also to the normative function of architecture itself.
methods we use to communicate our perception2
of objects are influenced by the human mind engaging with an ever-expanding
objective world (constantly redefined through research). This provides a
systematic structure and representation with which to experience that world
whilst questioning the responsive manner in which dimensions evolve alongside
objects and concepts to be considered real, the mind, which has an active role
in the construction of their reality, provides the framework into which
perception and thought are choreographed in order to be represented. This
structure includes space, time and causation3,
space being a precondition of perception rather than an idea formed in the mind
because we are capable of perceiving objects in three dimensions.
Natural fractals and complex geometries
simulated complex geometry
Our knowledge is constrained to mathematics and the science of the natural, empirical world. The reason that knowledge has these constraints, Immanuel Kant4 argues, is that the mind plays an active role in constituting the features of experience and limiting the mind's access to the empirical realm of space and time.
Things that we perceive are apparently unknowable, as they themselves are
mere concepts; yet without concept, intuition is nondescript; without intuition,
concept is meaningless. If this is to be reasoned, then the identity of
dimension needs to be addressed. One explanation of space is that it is part of
the fundamental structure of the universe, a set of dimensions
in which objects are separated and located, have
size and shape, and through which they can move.
dimensions/divination and dimension:
space, on the other hand, is not based upon architectural forms or
landscapes but is concerned with the notion of information and cognitive space.
Conceptual space is the virtual space with which we are most familiar, hence the
This virtual space may be the clouds of data that travel and reside on the
network or the interface-space. Though there may be a lack of buildings or doors
in conceptual space, we are nevertheless encountering space (Second Life7
further pushes the boundaries of conceptual virtual space, events and
dimensions). The interface acts as a locale at which further experiences and
dimensions of virtual space are revealed.
have a hard time visualizing fractional dimensions or more than three, because
our imagination limits us, even though many of our speculated theories can be
formulated in any number of them. Some theories are only mathematically
consistent if space has a certain number of dimensions. For example,
super-string theory needs nine spatial dimensions. Judging from this, it seems
plausible that there are extra dimensions of space we simply do not observe
them in everyday life because they are small which brings me to the fractal
dimension and its part in the design criteria for the Tower project in
separate discipline defines space using its own relevant dimensions, whereby
specific contexts in which dimensions as descriptive parameters are addressed.
In popular usage, a dimension (Latin
"measured out") is a parameter or measurement that defines the characteristics of an object, most
height, size and shape. In mathematics,
dimensions are required to describe the position
and relevant characteristics of any object within conceptual space. Locating a city on a
map of the earth, for
example, requires two parameters latitude
The corresponding space therefore has two dimensions. Locating the exact
position of an aircraft in flight
requires another dimension altitude and hence the position of the aircraft can be
rendered in three-dimensional space. Adding the three Euler
angles, for a total of six dimensions, allows the current degrees of freedom, orientation
of the aircraft to be known. We then include time, the more abstract dimension,
for the fundamental parameters of simulation and dynamics. Theoretical
physicists often experiment with dimensions, adding more or changing their
properties in order to describe unusual conceptual models of space, such as
quantum mechanics, also known as the "physics beneath the visible physical
world", or a speculative abstract dimension.
believed that space and time exist at one level of reality but not at another,
whereby the axioms of geometry are not self-evident or true in any logically
necessary way. Instead, these axioms are thought of as logically
"synthetic", meaning that they may be denied without contradiction.
This claim stresses that consistent non-Euclidean8
geometries are possible. Nevertheless, Kant believed that the axioms of geometry
are known to be true prior to all experience, because Euclidean axioms depend on
our "pure intuition" of space, namely actual space, because we are
able to visualize imaginatively. Only if non-Euclidean space could be visualized
would Kant be wrong.
is no model or projection of curved space that does not distort shapes and
sizes. The best model of a curved Riemannian9
space (the two-dimensional surface of a sphere) only has lines that are
intuitively curved in the third dimension. The surface cannot be
visualized without that third dimension. This is why spherical trigonometry
existed for centuries without anyone thinking of it as a non-Euclidean geometry.
The fascination with complex geometry10
highlights the awareness that dimension is limited through our perception of
Euclidean geometry because the possibilities are confined within our mind's eye
hence their dimensions are negated and contrived along with our ability to
envisage these complex geometries or to justify their precedence within the real
world. This is why the knowledge that we are able to hold expands with our
relationship to the real world.
While parametric design can involve light-level adaptation, structural
load resistance and aesthetic principles, its main references are to Cartesian
geometry. Because of its ability to modify by means other than erasure and
recomposition, parametric design is known as associative geometry. This
complexity of proportionate dimensions and their continuous cross-model
amendments are specific auxiliary tools to design processes: the antithesis of
intuitive, accidental and adaptive design criteria.
replace predictable appropriation
It is important to stress that dimensions are not
simply descriptions of objects in existing space; any space that can be
conceived has an associated characteristic number its dimension. By
employing time-sequence simulation and metamorphosis11
to describe and evolve physical space (animation lends the capability of change
in location, through time, while metamorphosis is change in form, through time
or space), we can then bring the notion of dimension into the intuitive realm,
whereby the ever-changing framework with which our mind identifies and relates
to also contributes to the changing dimensions of the experiential world. Thus,
this framework replaces expectation and the predictable with a plundered
intuitive dimension that, because it can be imagined,
can therefore be made real. Dimension can be regarded as the degrees
of freedom (of both movement and knowledge) available within space.
The following project looks at light-level parameters as a way of influencing
and altering our perception of static surface dimensions in an attempt to make
parametric design less formulaic and more intuitive. This is achieved by using
perception and the mind's eye to re-appropriate the individual's relationship to
space and his/her use of that space.
Gallery Tower digital plan
Tower viewing pod
Tower sits on the edge of a pier in Manhattan's Battery Park. It screens,
reflects and alters the urban fabric. The building programme consists of an
ever-increasing gallery space that sits within the suspended surface, which
envelops it. Its plans do not dictate the Tower's perceived presence, because
its pattern iterations are distorted by reflecting geometries (dislocating
physical from perceived), which affect the manner in which the individual
appropriates and engages with this space. Both fractal reflections and physical
hyperbolic geometries simulate an illusion of the Tower project.
describe the physical world, and parameters within those dimensions, such as
light levels, alter our perceptions and in turn our relationship with these
descriptions. This allows for an adaptation of Cartesian geometry and Gestalt
psychology to address the non-Euclidean within our
surroundings. With regard to the Tower, the imagined/subjectively perceived
space is translated and continually morphed as a result of the surface
renderings and reflections, whose boundaries and physical transitions are
non-static, thus creating a dynamic series of dimensions. The reflecting
surfaces have a Hausdorff dimension12
greater than its topological dimension, with the aim of presenting an infinite
number of geometric iterations of an infinite length while the area remains finite.
viewing pod. Reflected, collage views
The surface reflections, however, are too
irregular to be easily described using a traditional Euclidean geometric
language. Both these criteria are characteristics of
fractal as a geometric
Julia fractal configuration, non-specific scale
distorts surface iterations
Looking up at towers fractal surface viewing pod
complex dimensions before the invention of computers. A fractal is neither one
or two-dimensional; rather it is of a fractional dimension, because its complex
geometry suggests its surface. No single, small piece of it is line-like, but
neither does it describe a plane. It is too big to be thought of as a
one-dimensional object, but too thin to be of two dimensions. Its dimension
is most accurately described by a number between one and two. Fractal dimensions
reserve self-similarity across scales, only being restricted through context. Scale invariance is an exact form of
self-similarity where at any magnification there is a smaller piece of the
object that is similar
to the whole. The reason I use this as a tool for the Tower's design criteria is
to separate the perception and appropriation of Euclidean geometry and space
from the constraints of expectation and as an analogy to its vertical gallery
and exhibition typology.
Tower project therefore attempts to present a projected physicality, reiterating
that the tangibility of architectural dimension is expanding along with our
objective world. What can be imagined can be communicated using a lexicon of
2 Perception, in philosophy, is the process of apprehending objects by means of the senses. Causal theory of perception, one perceives and object if and only if one has a sensory experience as of it, the object is there, and the object causes ones sensory experience of it.
3 Causation, certain events cause, or bring about others. An event of one kind is said to cause an event of another just if all the events of the first kind are constantly conjoined with events of the second.
D. Owens, Causes and Coincidences; R. Sosa(ed)
4 Immanuel Kant, Critique of Pure Reason.
5 A priori knowledge applies to a priori judgments, which are arrived at independently of experience and hold universally.
6 The term Cyberspace, was coined by cyberpunk writer William Gibson, Gibson was influenced by American counterculture author William S. Burroughs.
Gibson, William. Neuromancer:20th Anniversary Edition. New York:Ace Books, 2004
8 Non-Euclidean geometry, in mathematics, describes hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. The essential difference between Euclidean and non-Euclidean geometry is the characteristics of parallel lines
10 Complex geometry cross-references algebraic and differential geometry. A tool used by theoretical physicists working on super string theory.
11 Metamorphosis, Michael Benedikt, Steps in Cyberspace, 1994.
12 The Hausdorff dimension is one measure of the dimension of an arbitrary metric space; this includes complicated spaces such as fractals.