Architecture and Contemporary Physics: Possibility of High-Dimensional Spaces
Note: This is a philosophical inquiry and author is not a physicist. Please report, should you discover any inconsistency in the theories.
The 21st Century as the era Information Age rapidly adopts an operational system based on knowledge. Architecture in the Information Age as the next evolutionary step of the art of space enclosure is a conjuncture of spatial and temporal processes directly linked to development in technology, science and culture. The role of information in the digital era sets the ground for a new philosophy and methods of conceptualization of space and multiple possibilities of its operating.
Contemporary physics currently offers theories on mathematical spacetime of movement, topology and dimension. An algorithmic analogy between String Theory, M-theory and architecture can be used in to create new thinking about the informational transition of the structural elements of design, its morphology and thus a possibility of higher-dimensional forms of space.
On Spacetime
The philosophical stance of architecture and the spatial expression of it marks the transitional process of information transference into spatial structures. The alignment of all operational levels — physical, functional, technical, social, cultural, economic, political or aesthetic represents a correlation of abstract connections that are organized into a concept. A concept is usually created by analyzing the existing restrictions of the current situation and drawing limitations as to what is possible, what is not, and what are the approaches to fit the design result into the current state of space, time and culture. These make the process non-accidental, resulting in a spatialized artifact of an abstract concept. A particular set of methodologies is used to repetitively (re)define the positioning of multitude of elements and adjustments of their connections. There is a standard routine of this methodology established in the practice, yet it is and should be expandable. Indirect analogies from modern physics are a source of new perspectives on the interconnectedness, organization and possibilities of redefinition of the context that bind physical structures into space and time.
Ilya Prigogine, physical chemist and Nobel laureate known for his work on complex systems, dissipative structures and irreversibility, referred to the organization of embryo: „How can an inert Newtonian mass animated by the forces of gravitational interaction, be the starting point of organized active local structures?“ [1] The act of processing organization can be truly mysterious, bringing a philosophical paradox into science. The question above can be just as well as be asked in relation to architecture, as the spatialized form of design as an active structure also has a starting point generated by forces of interaction. The design is not a product coming from the mass of the structure. It comes from a specific organization of pure states of information about the relations of individual elements of the structure. Therefore the origin of any design is a systemic configuration of information and its interpretation. That itself is not a subject of science, it is a subject of philosophy [2]. Information transitions linking particular facts configured by systems are the subject of science. The frameworks of diversity tendencies about how these two relate are the new patterns of possible derivates creating organizational structures.
Contemporary comprehension of architecture is marked by its rapid alteration by technology and science. These alterations are observable in design processes and typologies, inevitably influencing the culture. The substantial growth of diversification of everyday activities related to technological progress has turned space into a multi-layered machine of constant alteration and never-ending accumulation of information. Space of the 21st Century seeks a new language of organization of the design elements due to changed philosophical meaning of the role of architecture. Seeking new ways of translating the spatial and temporal information has become a quest and a call for shift towards new frameworks of relating science and technology with philosophy and culture. One way is to explore the algorithmic analogy derived from the spacetime framework in physics with a possibility of transference into design methods and thus morphology. The concept of movement, topology and dimension described in String Theory and M-theory is a particular way of transformation of information related to space in terms of: (a) providing a new conceptual ground for causality (cause and effect) of design structure and (b) the possibility of form emergence. Despite this being an indirect analogy, it represents one of the many ways of possible operation of complex dynamic systems.
The basis of this analysis dwells on scientific attempts to join two theories — Theory of Quantum Mechanics and the Theory of General Relativity into Unified field theory or the Theory of Everything (TOE). The ground principle is that particles, which in classical physics are considered point-like, are in reality minute strings vibrating in a sub-quantum (mathematical multi-dimensional spaces) resulting in production of properties of bigger particles. M-theory, superseding String Theory, describes strings as surpassing the sub-atomic dimension where they form large membranes resulting in collision and production of multitude of universes. This radically obscure and highly controversial theory cannot (yet) be proven by experiment as it goes beyond our current comprehension of the physical world as well as the established scientific framework. Even though this is not directly applicable to the design process, the inner logic of organizing spatial and temporal elements could be applied to design as a way of offering challenging connections among the concepts of movement, topology and dimension. It is a new way of understanding of the mathematical structure and connections of spatial and temporal information. In architecture, this would mean not only emergence of new morphologies, but predominantly new contexts — new algorithms of informational patterns changing the space-time variables of objects. The sole influence would not lie in transformations of the objects. The contextual change would resonate through the environment onto other subjects and therefore achieve new variables and thus diversification of spatial and temporal events.
On Movement
The wild vibrations of different strings [3] differing from ordinary vibrations due to quantum fluctuations of that scale could be considered as a form of time alteration under the condition that we accept time without being able to take its measure in the quantum. In classical physics, there is a distinguishable difference among elementary particles resulting from the difference in vibrations of the strings in multi-dimensional spaces. Such framework of space-time represents not only a repetition of movement and energy exchange, but also allows the movement to serve as a pathway of informational transition. To bring the concept of movement into architecture, we should examine both aspects: (a) the dynamic possibilities of design elements and (b) the possibility of tracing motion of static form. In the first case would indicate the movement as a tool of informational transformation about space and time in designed object while the second implies an imposition of a form onto it.
The movement in n-dimensions as a tool of organization could be applied to designing objects to impose a particular structure to the connectivity. The new organizational structure would inevitably mean creation of a new frame of information organization. This would also bring an opportunity in a form of new awareness for designers in how objects and subjects communicate among each other. For example, a transition from three-dimensional to a four-dimensional way of designing is to introduce articulation of design elements that are changing in time. The dynamic aspects of an architectural object would reflect the changing properties of its immediate environment (and thus communicate the consequential changes in spatial and temporal information) such as changing light, wind or water shown in sensitive, reflective and flexible materials. In a way, it is an attempt of object animation performed by introducing movement into traditionally static elements and thus assigning new identification to the object. Such architectural object should then be able to respond to the constant and changing informational flows and communicate the ‚cause and effect‘ in the organization of design.
If we consider the classical understanding of the three-dimensional nature of architecture, adding dimensions (not literally) represents additional states of information incorporated into the spatial form. If adding the next, fourth dimension to three-dimensional state means introduction of the dynamic into the static, there could be potentially infinite number of dimensions added as possible information flows, if these are found in the fabric of the operational network in the environment. The imposition of the dynamic vectoral orientations onto space would investigate the movement in n-dimensional space-time in terms of dynamic organization of static objects. The multidimensionality in this case lies in connecting the static and dynamic states.
According to Terzidis [4], the form itself does not involve time. In a traditional sense, it can only capture the change of time as depicting the consequences of the movement through time and space in a form of spatial configurations. Yet multidimensionality does not always have to require dynamic animation of the object in time. Animation can also be achieved by violating the integrity of space by communicating the notion of movement and leaving geometrical traces of rotation, mirroring, duplication or cutting — i.e. translating the information about movement. When an object is being ‘animated’ in a sense of leaving traces of geometrical projections, it articulates the final form as a result. Therefore the spatial memory of the multiple projections of certain movements in spacetime creates a memory storage. This has a potential to form as a consequence of n-dimensional movement and provide the flux of informational transitions in space and time. So the new designer will eventually be able create an architectural body changing its shape in real time [5].
On Dimension
Dimension is defined by the measure of the information on the location of elements in the space-time. Therefore, an element in the systemic structure of design in the four-dimensional paradigm with relevance to the classical understanding of our physical reality is identified in spacetime by three spatial measures and one temporal. String Theory and M- theory recognizes ten and eleven dimensions of the physical reality. This implies more complex informational structures and connections among the elements identified in these theories. If, according to our current practice, we work with only three (or four) dimensions, we should consider the existence of high-dimensional spaces comprising more information about objects, more relations and more contexts all connected in an intriguing manner. The significance of these theories for architectural methodology is in the mathematical meaning of dimension. They are not isolated, but woven into the structure of spacetime while the particular dimensional realms operate within specific conditions and vibrational patterns [6]. For architects and for many others I presume, it is difficult to imagine more than three dimensions.
How is it relevant to design process? By altering the concept of dimension, what they represent and what is possible to do within them, we disturb the tools and the continuity of the design process. We disturb the dynamics of the form, the connectivity of the information represented by the design structure and provide an additional mode of framing information into space. Since the primary way to experience the form is the visual processing, manipulation of appearance of multi-dimensional projections can also generate form as successive models of projections of fourth-dimensional space leading to a vision of the fourth dimension [7]. Such projections could be considered to be form-generative for example on urban level, yet it would differ from the traditional urban morphology by being visually appreciated as an experience of the spatial n-dimensionality.
Since n-dimensionality represents an increased level of structural connectivity and informational transitions, it also represents a different vibrational pattern (as is string’s mass and charge determining the properties of the particles) in a form of technical geometrical projections. This context has been tested in the study of the hyperspace [8] attempting to build richer informational transitions, where hypersurfaces are rendered by more complex spacetime information that those that are mathematically defined. The abstractness of the higher (mathematical) dimensions are still in a process of shifting into our lived reality [9]. Another interpretation, not as a tool of systemic organization of elements, is to apply the concept of dimension onto topology. The difference between hyperspace and hypersurface of the hyperspace of n-dimensions is a submanifold of (n-1) dimensions. That means that the hypersurface of a hyperspace of four spatial dimensions is a space of three dimensions produced by a projection, screenshot or a section [10].
On Topology
Topology, widely utilized in the architectural practice, has undergone a test of topological structures and how they relate to the morphology of architecture. Affected by the programmatic, economic, aesthetic, social, political, structural and contextual influences [11], it has been used to navigate the flexibility and the continuum of the form. The mathematical approach taken from String Theory and M-theory applying the concept of topology and n-dimensionality suggests, yet again, the relation between topology, movement and dimension. These relations provide various algorithmic organizations of structures that assigns the form a unique spatial character with temporal features of their structures.
The string vibrating in the sub-quantum, in the six-dimensional mathematical spaces (Calabi-Yau manifolds) form the properties of particles. The vibrational patterns of the strings influenced by the twists in geometry of the six dimensions [12] create a set-up for an interconnected and self-regulatory system given that topological control of the deformations of the form — twisting, stretching, scaling and folding, all preserve the integrity of the form. Such form subjected to topological deformations would reveal particular properties and allow the imprints of time on form and be an ‚object in disguise‘ because it would combine the topology of one object and the geometry of another object. It implies that topology would be in control of the very design mechanism as well as organization of their unity. Deformations (transformations) of an object by twisting, stretching, scaling or folding would open up the range of possibilities for contextual and morphological manipulation as well as re-organization of relations between objects and subjects. Topology is therefore a powerful instrument for data transformation, breaking the restrictions of spatial and temporal structures and boundaries of conditions, setting up to create new multi-scalar categories of identities. It would introduce a causal framework for dealing with multitude of objects and subjects at once and introduce them as a unit of a single topological structure overlooking the complexity due to continuous behavior governing all finite elements and their generalized behavior. Finite elements cannot be regarded as arbitrary units, but rather as localized samples [13].
The Transience of Frameworks
The discoveries that we make and the frameworks we use to make an understanding of what we are discovering, are of transient nature. Due to expansive nature of our reality, we can say that mathematics and physics of ‚our time‘ offers a temporary foundation as the structure of already acquired knowledge that is defining the limits of the current momentum within a continuous unfolding of the infinite amount of what there is to know. After forming a hypothesis or making a discovery, we might find that at different times we accept different answers to our questions and our framework of understanding is undergoing expansive change. According to our way of thinking — regardless of our occupation as philosophers, scientists or artists — we organize known information to achieve a better interconnectedness of the information structure, which is a subject to our discovery.
This article presents a new approach towards framing architectural methodology and theory in a form of reflection and indirect analogies of a scientific analysis. It investigates possible interpretations of String Theory and M-theory, using them towards developing new methods of structural organization of the algorithmic order in the design process. Examination of topology, movement and dimension reveals the importance of the space-time framework, because it is a tool for dealing with complex dynamic systems (such as architecture). One day, perhaps, these theories might be proven wrong. And even if they will, it would not deprive of value any of the designs that arose from the attempts to animate a multi-dimensional space-time form. Moreover, it would be a way to exercise one way from the infinite set of variables representing a particular point of space and time.
References
[1], [2] Prigogine, I.; Stegners, I. (1984) Order Out of Chaos: Man’s New Dialogue with Nature. Boulder: New Science Library.
[3], [6], [12] Greene, B. (2004) The Fabric of the Cosmos. New York: Alfred A. Knopf.
[4], [11], [13] Terzidis, K. (2003) Expressive Form. A Conceptual Approach to Computational Design, 2003:33.
[5] Oosterhuis, K. (2002) Hyperbodies: Towards an E-motive Architecture. Basel: Birkhäuser, 2002b:30.
[7] Robbin, Tony (1997) Quasicrystal Architecture: The Space of Experience. pp. 434-435 in Beyond the Cube. The Architecture of Space Frames and Polyhedra , J. Francois Gabriel, ed. New York: John Wiley & Sons.
[8] Architect Stephen Perrella on Systems of Exchange and Hypersurfaces.
[9] Emmer, M. (2004) Mathland: From Flatland to Hypersurfaces. Basel: Birkhäuser, 2004:57.
[10] Novak, M. (1998) Transarchitecture and Hypersurfaces: Operations of Transmodernity, Novak 1998:85.