"While motion implies movement and action, animation implies the evolution of a form and its shping forces; it suggests animalism, animism, growth, actuation, vitality and virtuality." (9)

"Form can be shaped by the collaboration between an enveloppe and the active context in which it is situated. While physical form can be defined in terms of static coordinats, the virtual force of the environement in which it is designed contributes to its shape. (...) In this way, topology allows for not just the incorporation of a single moment but rather a multiplicity of vectors and therefore a multiplicity of times in a single continuous surface. (...) Actual movement often involves a mechanical paradigm of multiple discrete positions, whereas virtual movement allows form to occupy a multiplicity of possible positions contimuously with the same form." (10)

"An object defined as a vector whose trajectory is relative to other objects, forces, fields and flows, defines form with an active space of force and motion. This shift from a passive space of static coordinates to an active space of intractions implies a move from autonomous purity to contextual specificity. (...) Animate design is defined by the co=presence of motion and force at the moment of formal conception. Force is an initial condition, th cause of both motion and the particular inflection of a form." (11)

"The intervals between the moments that are superimposed generte irresolute conditions which are exploited for their destabilizing effect on the present. (...) Statics becomes the condition of matter without fore and dynamics becomes the condition of matter acted on by force. Both positions assume that force is something which can be added or subtracted from matter." (13)

"Independent interacting variables can be linked to influence one another through logical expressions defining the size, position, rotation, direction or speed of an object by looking to other objects for their characteristics. This concept of an envelope of potential from which either a single or aseries of instances can be taken, is radically different from the idea of a fixed prototype that can be varied. " (14)

"A reconceptualization of ground and verticality in light of complex vctors and movements might not change the expediency and need for level floors, but it would open up possibilities for structure and support that take into account orientations other than the simply vertical."(14)

"Stasis is the ordering system through the unchanging constant force of a ground point. (...) Stability is the ordering of motion into rhythmic phases." (14)

"Once design is posed within a Leibnizian monadological space, architecture may embrace a sensibility of micro and macro contextual specificity as a logic that can not be idealized in an abstract space of fixed coordinates. In such an abstract active space, the statics of fixed points in neutral space is replaced by the stability of vectors that balance one another in a phase space." (15)

"The present limits of connectionism are staggeringly complex and the directness with which multiple entities can be related challenges human sensibility. (...) but the failures of A.I. suggest a need to developp a systematic human intuition about the connective medium, rather than atempting to build critically into the machine." (19)

"The formal organizations that result from the sequential mathematical calculation of differential equations are irreducibly open in terms of their shape. They are often interpreted as organic because of the inability to reduce these shapes to an ideal form. In contrast, the reducible, fixed forms of simple mathematics -- such as spheres, cubes, pyramids, cones and cylinders -- have a simplicity and purity that allows them to transcend their formal particularities." (19)

"There is a critical difference between the discrete geometry of baroque space -- a geometry with multiple points, and the continuity of topology -- a multiplicity without points. (...) Instead of being defined by points and centers, topolgy is characterized by flexible surfaces composed of splines." (20)

"A change in any pont distributes an inflection acros regions of these entities. Because splines are vectorial flows through sequences of points they are by definition continuous multiplicities rather than discrete entities. A multiplicity is a collection of compoents tha is neither reducible to a single entity nor to acollection of multiple entities. A multiplicity is neither one nor many, but a continuous assemblage of heterogenous singularities that exhibits both collective qualities of continuity and local qualities of heterogeneity. (...) Because topological entities are based on vectors, they are capable of sysematically incorporating time and motion into their shape as inflection. Inflection, or continuous curvature is the graphical and mathematical model for the imbrication of multiple forces in time. (...) Curvilinearity is a more sophisticated and complex form of organization than linearity in two regards: (1) it integrates multiple rather than single entities, and (2) it is capable of expressing vectorial attributes, and therefore time and motion. Curvature in a tempral environment is the method by which the interaction of multiple forces can be structured, analyzed and expressed." (23)

"Multiplicities are constructed of interacting entities exerting a differential influence on one another. Curvature is a mode of integrating complex interacting entities into a continuous form." (24)

"The linkages between these characteristics of time, topology, and parameters combine to establish the virtual possibilities for designing in an animate rather than static space." (25)

"deformation, inflection and curvature (...) all involve the registration of force on form. Rather than thinking of deformation as a subset of the pure, the term deformation can be understood as a system of regulation and order that proceeds through the intergration and resolution of multiple interacting forces and fields." (26)

## Thursday, August 23, 2007

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## 2 comments:

Well said.

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