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A MATHEMATICAL VISION Naomi Scully: Architectural Geometry Language of Diagram and Representation Original article: https://soilandbody.wordpress.com/2020/06/16/futurist-geomtry-para-tale/ Peter Burgess COMMENTARY Naomi Scully sent me this a couple of years back (around 2019, I think). As a student at school, I thought of myself as being good at mathematics, but at university and in my adult life I learned that while I was good at 'arithmetic' I could not conceptualise sufficiently to be good at mathematics. This paper seems to be conceptual thinking on steroids! Peter Burgess | ||
The periodic table of art and soil.
GIVE THANKS; RESEARCH: TEST : ACT : RELY : DRAW: REGENERATE : HYPOTHESIZEFuturist Geometry : Para-tale ... urbanpassages Architecture and Theory ... June 16, 2020 Architectural Geometry ... Language of Diagram and Representation ... 5/1/2010 Southern California Institute of Architecture Graduate Program ... Abstracted Language, Diagrams, and Mathematics all have assumptions; Representation cannot be absolute, and continues to be generative. Table of Contents
This paper contains intrinsic organizations based on the information gathered by the author. From the research, overlapping terms such as manifold and homogeneous, emerged allowing the paper to grow out of itself. The Section, Hegira, initially gives the impression of a narrative, but it is the story; Hegira means migration and opposes the Exodus of departing; and although they are different, they each can exist as their opposite-depending on context. The characters are adopted from Rem Koolhaas’ Exodus. The two towers are two aspects of an object; idea and form. The towers are introduced and the paper itself extrapolates the narrative, referencing mathematical equations that define moments of change in a hypothetical system. It provides insight on human-computer relationships and resembles a transformation of geometric evolution. It introduces new metaphors for complex relationships between geometry and form explained in later chapters, including; Hyperreality, Fossils, Geometry Matters, Broken Butterflies, and Aether. Geometry is traced as both a mathematical and an architectural concept. The computer transformed geometry’s function proving that numbers and vectors also describe Architecture. ‘Form finding’ explains the internal specifics of the programmatic language used to create the software. Information systems reference the initial narrative. The dichotomy of mind and matter reveals itself as linguistically and mathematically linked and it makes bold statements about how this paper and other literature can be used as a generative tool through the misappropriation of language. .be gun .1. HEGIRA: Consequential Reciprocity Deep in Exodus, among The Voluntary Prisoners of Architecture, within The Park of Aggression stand two towers, “one is infinite, a continuous spiral; the other, consisting of 42 platforms has a familiar architectural system. Magnetic fields between these towers create a tension that mirrors the psychological motivations of their users.” This setting provides insight into the potential contemporary state of affairs concerning computational geometry. The hostility in the park is due to the field interference. The computer acts as a referential stage toward the reconciliation of the conceptual world and the built environment of architecture. The spiral tower is congruent with the potentials beyond perception into infinitum and within its set lies ideas including those of the digital world. The systematic tower relates to the temporal sameness of the historically fossilized. The number 42 results from no golden ratios, series, nor factorial; its invariant ratio is 2:3:7. The sequence of prime numbers resulting in the product of 42 skips over 5, making the hand just short of a primary straight. This evidently amplifies the towers frustrated relationship, which despite their obvious differences, any proximity change will dramatically affect their magnetic field. Superficially, the towers stand tall, juxtaposed and different, discrete. The ground suddenly drops out from under them, absorbed by the annihilation of the two frequencies. They are thrown downward by their own weight ostensibly inevitably convergent, and just as they are about to collide, they “swerve ever so little from their course, just so much that you would call it a change in direction.” Re-materialization of the World commences immediately. A human emerges alone, with a normalized magnitude, among the ‘real’ World, where there exists two governing equations of space: Let: The Ring R = This World, and I = All scientific and mathematical assumptions of R. Where, The Quotient Ring -> Quotient World which represents all that is the digital space ( R)/I. QRing = ( R)/I = [(chora)/2]^2 As with the chora there is an ‘Ideal Amplitudinal Summation’ within the synaptic networks contextualizing the individual’s relationships to the world. Number 2 may vary. The digital now seeks to unite space, theory, and form. The ultimate architectural geometry developed and inspired by external disciplines will synthesize back into those fields as an exchange, or feedback loop. The quotient, or projective, chora ‘screen’ is a dimensional projection of the chora ‘mirror’ where the perception of the world changes based on the optics and parameters of this reality. The warping of the vector forces applied during the towers’ transitional state correspond to the formula inserted into the software that will ultimately define the manifold space. The resultant morphogenic geometries output by the computer exemplify the tower’s psychologically desired, perpetual, and illusionary convergence. The projective chora exists as a shadow exploration of chora, where there are subtle particle jumps on the quantum level. The screen exists as an intersection of two curved solids, an ellipsoidal solid and a sphere of a larger radius. Behind the screen, the electrically charged hairy group is composed of long cellular strands that flow like hair under water. They originate from a Riemann center. Their sense has a slight curvature relative to the ellipsoidal solid controlled by the size of the luner screen. The system undulates as three dimensional striations. Each hair is a discontinuous vessel within a homogeneous transformation group. When the electrically charged strands reach an asymptotic distance from the screen, the two bodies exchange energy as a synaptic jump from the hair to the screen. The electric phase exchange results in energy absorbed by the screen and completely dissipated from a single portion of the hair. The length of the dead end is determined by the length to the first discontinuous point. This portion of the cell drops, as if due to ‘gravity’, toward the bottom of the ovular solid. It falls until it drops a distance equal to its dead end length, at which point it switches its continuity and electricity pulses back into it. The exchange of energy releases an optical, audio or vibrational reaction on the screen relative to the amplitude, wavelength and position of the action. The user cannot feel the overall field, only the representational instantaneous morphisms mapped onto the screen, however, when they enter into the proximally pulsed electric field that is embedded within the screen, the polarity of the field tests their conceptual strength. Depending on the strength of their molecular bonds, the user may resist the charge or become polarized externally. Potentially, their internal axis realigns with the field creating an oriented domain. When the user exits the field, their new intrinsic symmetry causes them to react to the world in a new way. The dimensional projection has optically convinced the user of a physical relationship to it, despite the fact that the electric pulses present the object, resting at equilibrium in isomorphic digital space, offers no affordance associated with its conceptual projection. .2. HYPERREALITY: Dimension Shadows The digital space described in Hegira, where the computer takes on our assumption based reality obviously interfaces with the mathematical number system. Baudrillard’s model helps explain our perceptions of volume/space even further, “today, abstraction is no longer that of the map, the double, the mirror, or the concept. Simulation is no longer that of a territory, a referential being, or a substance. It is the generation by models of a real without origin or reality: a hyperreal. The territory no longer precedes the map, nor does it survive it. It is nevertheless the map that precedes the territory – precession of simulacra.” The simulations that occur in digital space today can extend beyond the dimensions that we perceive, although abstracted, the conceptual arithmetic allows for the production of geometric organizational systems that result from the projections from nth dimensional models. The computer takes the conceptualization of geometry to another level, allowing theoretical experiments like that of Penrose’s Geometry, programmed by Nicolaas de Bruijn, to define a territory which then generates a geometrical map- the geometry becomes an aftermath. Bruijn’s model uses “projection from a higher dimension down to our more familiar two or three-dimensional space.” The form, then establishes itself through quantum mechanics as a “hyper-dimensional object whose shadow exists in our reality,” If architectural or geometric practice becomes redundant, Pluto suggests becoming purposefully distracted by exploring a problem or invariant. Plato lists four but the specifics are no longer relevant, however, the idea of an invariant promotes growth. It can be described as normalizing and also pertains to the relationship of sets in mathematics; in biology, it describes health and natural occurance; in psychology, it relates to a normal[sane] person; in chemistry, it is equal parts with water, having to do with neutral salts, or having to do with aliphatic hydrocarbon chain; and finally, in language, it represents a common standard for establishing something natural. Math describes both natural and unnatural forms. The relevance of their existence branches into two trajectories for architectural potentials, neither completely worthless, in fact, our population has divided so many times, that logistically we may have reached the threshold of variance inside of invariance. Ironically, the methods we use to arrive at variance use invariance to describe them. An algorithm provides ‘multitudes of variables,’ but the abstract digital space relies on mathematics based in homeomorphic space. The variation does not exist within the surface or spatial mathematic qualities, but on the geometric volumes produced. One of his invariants, dubbed the anharmonic invariant, more popularly known as projective geometry remains relevant to the exploration of geometry into multiple dimensions of space-time. Renaissance architects from Brunelleschi to Guarini and Desargues, contrived the theory of projective geometry. Later, Michel Chasles shows that “projective transformation does not maintain lengths—the ratio of lengths—but rather bi-ratios which are ratios of ratios—the so called anharmonic ratio,” causing the subject to ‘warp’ and ‘stretch.’ Today, Plato would even add chaos to his list of invariants. Architecture, music and design, in general, reference its unpredictability beginning around when John Cage correlated the natural sounds of the city to ‘music.’ It is also reminiscent to the exploration of the ‘ugly.’ If Plato were to describe the wrong way to approach digital architecture, he would deem the one who chooses to construct architecture only in the vacuum of computational space, completely distracted by its invariance and overwhelmed by the analysis of realizing the geometries in real space, neoteric simulacra. Another way to be distracted exists with “scripting” without an effort to infuse human nature into its perfection. Scripting will effectively “produce differentiated repetition in digital modeling that would otherwise require a great deal of time and effort,” but it produces superficially good-looking images because they “appear full” as well as “coherent and cohesive due to the finely calibrated change in each repeated form.” This fails to be a strong design tool because it does not create enough differentiation to be natural, however, in combination with other techniques, it could follow the contemporary goal of difference, rather than simulation. Geometry’s evolution parallels that of mathematics, physics, and architecture as digits become numbers and translate equations and vectors. Historically speaking, as seen in “Derrida’s seminal text on Husserl’s Origin of Geometry,” there is no linear origin; instead, geometry moves toward its origin, or perhaps, toward the geometric description of space, or potentially chora. In the Elements, “even the integers themselves are represented by segments of lines.” Numbers remained discrete, but the associated world of magnitudes existed “apart from number and had to be treated through geometric method. It seemed to be geometry, not number that ruled the world.” The idea of the vector preceded the number itself. Numbers, existing only to describe form and magnitude, suggests that the vector is the simplest form of a geometric idea. They further develop into much more complex systems such as parametric, differential equations, fluid dynamics, and quantum mechanics. Each intrinsically hold axial and spatial relationships whose representation feeds the growth of formal practice in geometry and architecture. .3. FOSSILS: Formations We live in a complex world invariably relating and disseminating scientific, aesthetic, geometric, geological, social and linguistic constructs deciphering between pyramids of “accumulations hardened by history.” People communicate through languages, which are structure. Languages describe ideas expressed as descriptors, such as words, and forms, which are projected words. Forms are generated through tools. People then relate perceptively and physically with the tools establishing more ideas and forms. To fully analyze and asses architectural geometry today, we must understand what it is, and how it has changed over time emphasizing its relationship with the architecture world. Science and math use assumption to isolate systems in order to understand them more fully. Geometric concepts can be isolated and purified as through Derrida’s “’Cartesian Intellectualism,’ which necessarily suppresses certain questions of ‘imagination’ and ‘sensibility,’” The Languages that have emerged from this couple both drive and describe form. We interact with the fossilized structures of our past, unavoidably and systematically. Everything overlaps at illusive convergences like the one between the towers of Hegira. Here, their exchange potentials become possibilities, where “synergistic combinations, whether of human origin or not, become the raw material for further mixtures.” De Landa describes a feedback-loop, where the output becomes the input in the process of creation and explains “how the population of structures inhabiting our planet has acquired its rich variety, as the entry of novel materials into the mix triggers wild proliferations of new forms.” [Note: he specifically mentions naturally occurring invariant variance.] The dichotomy of geometry’s identity pertains to that of architecture. Theoretically, Stereometry, emphasized early by Plato, explains that volumes do “not refer to the visible figures that are drawn but to the absolute ideas that they represent.” Absolute ideas include all of the intellectual interactions between human and volumetric geometry, including; the plans, predictions, goals and retrospective reactions of volume on the human. He went on to explain what he described as the two main forms of geometry, “the form itself defined by numbers and the sense that the shape radiates, – technique and computation.” The terms technique and computation have been redefined because of the computer. There are no singular terms to fully explain concept and form, but computation became a new form of creation, where the computer mediates the input and the output. Plato’s computation became conception and technique became formation of volumes. Later, In The Mathematics of the Ideal Villa, Rowe justifies the duality of the “absolute and the contingent, the abstract and the natural; and the gap between the ideal world and the too human exigencies of realization.” Later, A phase transition occurred between geometry and architecture, when the Eisenman asks does “the diagram- the primitive configuration of geometry” become architecture? Literature and architecture express themselves best when simplified to the furthest extent, without the loss of that feeling, similar to the diagram. The diagram in question contains geometric constructions which are ideas themselves describing some potential form acting, according to Rowe, as a transitory element, “between form and word.” Eisenman defined architecture as the “intrinsic aspect of any space,” equaconsistant to the Platonian geometry’s absolute ideas and therefore the terminology became synonymous, where architecture became a study of geometric volumes. In Perfect acts of architecture, Kipnis announces that “the architectural drawing as end work can function in any of three ways: as an innovative design tool, as the articulation of a new direction, or as a creation of consummate artistic merit.” Eisenman’s diagrammatic architecture not only remained true to the three allowable built drawings, he also “reconceptualized architectural drawing itself; the axonometric, for example, was no longer understood as a representation of spatial relations but as a syntax for semantic elements. ‘Building’ became a matter of enlarging and rendering certain drawings.” The architecture of diagrams provide an acceptance of the inability to actualize more complex digital models, yet allowing them to be ‘buildings’. JP This type of modeling became “the first generation of indexing,” despite Eisenman’s distaste for computer arithmetic. Indexing describes two systems “generating an organization by playing one system off of another. A simple example in nature would be a seedpod; the bulging skin of the pod serves as an index of the pressure exerted by the seeds within.” Geometry begins pick up descriptors for indexing and set the stage for the transition from Delouzian’s emerging digital idioms of ‘rhizome’ or ‘folding’ and others played out as a conceptually experimental architecture. The words themselves, rooted in botany and geology, philosophically apply first to organizations of literature and then later become diagrammatic and thus a descriptor in the history of geometry. “Accumulation of linguistic replicators” like these continues to stochastically feed the linguistic boundaries of diagrammatic geometric architecture. To operate in today’s digital diagrammatic dilemma, “it is necessary to acquire a geometric vocabulary that operates between oblique and curved forms and the economically determined mechanical constraints of building assembly. This vocabulary, derived from projective and topological geometry, constitutes an auxiliary system of order, one which can ultimately serve to discretize curved surfaces into flat units, and thus translate complex surfaces into forms constructible at an architectural scale. Such an application of geometry produces a continually expanding repertoire of three-dimensional architectural form.” Exploring representation fuels the descriptive vocabularies of form. Drawing always contains abstraction that compares to a visual conversation between the optic qualities of the constructed drawing and the idea of the drawing itself. The architect’s “field of visibility” is affected by the act of drawing. It uses the same sort of limiting assumption based system as math making some things clearer, while suppressing others. Consequentially, within the ‘field of visibility’, an architect can begin to make conceptual connections allowing changes like coordinate space initially used “for the purpose of invariant communication,” like those of “plan, section and elevation [which] were originally formulated as a system for measuring archeological ruins; only later did they get turned into projective instruments.” Both literal communications and figurative potentials result from these types of drawings. The exchange between the literal and the figurative world allow perspective and projection geometry drawing to share a pedagogical boundary with mathematics and art. Projective geometry virtually throws a descriptor from one dimension to another or from one perspective to another. Throwing is the term used to describe the action; the object through a vanishing line to a plane or through a vanishing plane into axonometric space. The Taylorian Method of projective geometry produces “orthographic projections from perspective” and is useful for architects like Preston Scott Cohen to construct The Tubular Embrasure of San Carlo ai Catinari from two-dimensional imagery. Exploration of design is not linear; it uses cycles of techniques, a feedback loop “like working drawings following creative sketches, there must be reciprocity between the two.” Innovations in projective and “pictorial technique have transcended the problem of representation and proved to be effective design tools.” The resulting graphic appeal of their rigor and complexity has added “tang to the resulting buildings” because ”oblique and elliptical lines are dynamic by their very nature and have an emotive power a thousand times greater than that of perpendicular and horizontal lines…And dynamic architecture is impossible without them.” Techniques of representation and abstraction stay relevant longer than the conceptions because they are generative in the feedback loop of innovation. .4. GEOMETRY MATTERS: Digital Transformations Formal explorations of computer generated forms started as “early as the 1980’s with the appropriation of animation software from the entertainment world.” The Illusion between user and interface exists, because “the computer is a finite machine. Finite memory, finite clock ticks per second, and every number represented on a very fine, but finite grid. A very high resolution, but definitely finite, ‘pixel’ grid.” The totality of digital geometry confuses our eyes because “in the end everything must be reduced to the fundamental units of ones and zeros at the bottom of the hierarchy of computational representation,” and the trigonometric equations like sine and log have to be approximated. Still, the computer holds a conception of a “perfect open-ended automatism, a nonstop variability untainted by false consciousness, with the machine pumping out endless versions, and continuous surprises.” Empirical computation holds the dream of infinitum with the potential to surpass the unreliability of the human. The two interests, who have reoccurring dualities similar to those from Exodus, became “reconciled in scripted parametric indexicality, which serves the ambition of non-arbitrariness at the micro-scale where each point along the curve may be understood to stand for something, and the desire for surprise at the larger scale, where the overall shape of the curve remains unpredictable.” Often, the user ignores the computations of the programming language, forcing a blind disconnect between the idea and understanding of the output geometries. At the same time, however, the computer allows us to ‘find form’ outside of our desires, reaching deeper into both the subconscious and the world of assumption mathematics as in the transformation expressed in Hegira. The application of conceptual matter to geometry redefines ‘finding form.’ For instance, Jason Payne uses ‘matter as organizer: matter first, organization second” in his work, where “points, lines, and planes come laden with distinct qualities in measurable quantities such as density, pull, drag, tension, compression, acceleration, and porosity.“ Applying theses forces to geometry allow characteristics to become “behavioral and active rather than representational and passive.” Active geometry results from the territory and transcends the etymological definition of construction where computational construction of the formal digital idea sits as an intermittent step between the idea and the output, expressing a similar syntactic potential as the diagram. Out of matter, “the designer no longer develops geometry for what it draws but for what it does.” These geometries generally use parametric equations, more than one equality describing a form; “in practical terms, dimension and form are now fluid,” such that their abstraction is no longer only projected and two dimensionally drawn. Instead, they represent three dimensional objects whose forms remain “malleable, deformable, transformable, blended, morphed, and animated rather than ideals that can be eidetically deduced as underlying a design.” In Complex relevant membrane surfaces defined by partial differential equations, for example, their form emerges from the theoretical applications of forces to manipulate mathematically. Greg Lynn uses an example of wire mesh dipped in soap film. In order to compute something similar to soap film we consider surface tension of the film acting on the frame; it relaxes “the surface into a shape which minimizes its area while spanning the given (boundary) frame. This can be capture mathematically by describing an energy, here the surface area, and searching for that surface S which minimizes this energy. “ Harmonics were the first wavelength influence applied to geometry outside of form. Now, digital/parametric and spatial design morphologies derive from “Postmodern reworking of ancient patterns (like waves) or new ones (like DNA) found or simulated with new and emerging visualization and design technologies. Among these we find patterns of soap bubbles, Fibonacci series, hydrological and vascular systems, Protein Folds, cellular automata, attractors, force fields, Sierpinski Cubes, skins, mire, knots messes, fractals, networks, swarms/flocks, atoms and molecular structures in quasi crystals. Fluid and gas/smoke/meteorological forms and dynamics, architextile, viruses, and microorganisms, blocks, Voronoi Cells, Lindenmeyer Systems, light, fire, landscapes, geology, rhizomes, and various hybrids and permutations of these.” Computational Spring systems work in a similar way, where the ‘forces’ used in the software follow Hook’s Law. Two particles represent mass and forces acting in two directions on the two particles; one in compression and one in tension relative to the displacement. The resulting “topology is a user-defined condition and is no positional.” Algorithms of dynamic relaxation determine the geometric form and vector forces find equilibrium through oscillations between springs. The process converts the network topology into geometric form.” The fascination with forces in programming output geometries remains a form of abstraction based on input parameters and isometric illusionary space. Working matter describes a conscience relationship of the formal derivation of computer languages and decisive control of the applications of active geometry. Animation tools are “not in the service of simulations of growth or time-lapse design; instead, it is a means to shape, form, and configure spaces using incremental inflections, transformations, and deformations.” These programs, like Maya, generally configured by polygon mesh formations, are rooted in Discrete Differential Geometry. Here, Subdividing, or ‘corner cutting,’ a curve to infinitum will yield a smooth curve. A “smooth surface only exists as the idealized limit of an infinite process of repeated mesh refinement” but can be simulated by computer programmed optics. Despite the illusionary ideal produced by the computer screen, it is important to understand computational linguistics to provide a clear “relationship between the surface and its controls.” The interface is far more complex than we can grasp because, “not everything is easily quantifiable not all relationships are geometric and not all are to be coordinated into a smooth relationship.” .5. BROKEN BUTTERFLIES: Locale Relativity “Purely mathematical tools provide a new vocabulary for creation.” “According to the mathematical definition, topology is a study of intrinsic, qualitative properties of geometric forms that are not normally affected by changes in size or shape, i.e. which remain invariant through continuous one to one transformations or elastic deformations, such as stretching or twisting. “ The surface adopts properties like isomorphism, rooted in abstract algebra, which is a bijective map, where both it and its inverse are homomorphisms. A homomorphism preserves the structure of the map. Bijective functions are one to one and must be both an interjection and a surjection where no two values on the map are the same and it must be possible to map from every element from the domain to the co-domain. The digital space is a manifold space, or quotient-chora, which is locally Euclidean, and homeomorphic to an open set. Homeomorphic topology is best recognized through the example of the exchange from the donut to the coffee mug. Topology studies the forces that act on the donut’s metamorphosis within the consistancies defining it. By switching on calculations for a local domain, the computer processes the math at “a reasonable rate and complex non-Euclidean geometric formations, like hyperbolic space, are locally disconnected and calculated as a constant relative curvature.” “The result is a large range from “simple, topologically invariant transformations, such as twisting and bending,” to much more complicated variations, like the morphing temporal modeling technique, “ in which dissimilar forms blend to produce a range of hybrid forms that combine form attributes of the ‘base’ and ‘target’ objects.“ Virtual design “begins with some primitive geometric figure that is both proto-typological within the discipline of architecture and proto-spatial at its appropriate scale. As all of these geometries are defined as topological surfaces or polygon meshes, the medium requires some convolution or envagination of a surface to form an enclosure, or, more importantly, and interior.” In La geometry, Descartes ascertained that “Geometry should not include lines (or curves) that are like strings… sometimes straight and sometimes curves.” The computer’s abstract interface allows geometry to accept splines, because it rationalizes them in parts. Nurbs provide “efficient data representation of geometric forms, using a minimum amount of data.” The mathematical program language of NURBS, “Non-Uniform Rational B-Splines,” is distinguishable from other programs because “parametric are not forms but simply relations between forms.” NURBS “provided a departure from the Euclidean geometry of discrete volumes represented in Cartesian space and made possible the present use of ‘topological,’ ‘rubber-sheet’ geometry of continuous curves and surfaces that feature prominently in contemporary architecture.” A NURBS curve with “varying continuity is referred to as multiplicity.” .6. ÆTHER: Silent Voices Deleuze, who is known for codifying, mutating and universally applying linguistic forces to semantic structures into, but not limited to, architectural ideas that are now programmed into the computer database also uses the term multiplicity. For instance, in Geology of Morals, he describes the world as a sum of shifting and porous boundaries- a computation of ideas. The degrees of order are of “a particular multiplicity in the milieu, and as a function of a particular variation in the milieu.” The significance of adding function to the vocabulary, for example, of the locale helped to conceptualize the orders of the programming hierarchy. Our conceptual geometric world has expanded beyond one-sided “topological structures such as the mobius strip and Klein bottle” which hold a specific architectural implication of blurred interior and exterior, “an architecture that avoids the normative distinctions of ‘inside’ and ‘outside’.” These mathematical concepts produce multiple meanings and allow architecture, as well as other explorations, to misinterpret languages and transform them into visual cues. The chora exists as the idea of a mobius strip; the dividing line between the proverbial inside and outside; where they illusively appear as “the fleeting shadow of some other, must be inferred to be in another…[and] maintains that while two things are different they cannot exist one of them in the other and so be one and two at the same time.” Chora, here is the bounding line of all mathematical and theoretical symmetries that organize all of our computer and mathematic realities; the basis for all assumptions. According to De Landa, M.L. Samuels describes language evolution through the terms of distance and isolation, although these concepts also relate to the previously described programmatic discontinuity, it does not describe the potentials for intentional misreading of syntax. It does, however describe a “dialectic continuum… show[ing] only slight differences, whereas the whole continuum, may show a large degree of total variation.” This relates both to architecture’s disciplinary subcultures and their pedagogical separations over time and the introduction of complex vector analysis from disciplines into the geometric articulation of architectural computation. Deleuze’s abstract machine has also linguistically informed architectural geometric transformations using descriptors like the referential, “homogeneous reality.” De Landa’s explanation of the abstract machine helps to further break it down for geometric interpretations for manifold space, where the abstract machine of language is no longer “seen as an automatic mechanism embodied in individual brains but as a diagram governing the dynamics of collective human interaction.” Here, the diagram is bound by forces, magnitudes, directions, and shapes of language, but if misinterpreted, they become geometric and their conceptual framework compares to Eisenman’s. Architecture’s diagrams will begin to emerge as a form of literature, mixing the conceptual framework and words to merge the illustration with the text and will transform our books toward a universal visual linguistic asymptote. One future of spatial and computational geometries lies in abstract frequency domains which analyze mathematical functions or signals with respect to frequency, rather than time. A side effect of this universal frequency system creates one more visual language overlapping various proximal relationships. New geometry will emerge from this underlying law, relating light to sound and magnetic fields, etc. Overlapping the cues may expand our awareness and inter-sensory relationship to the limits of perception, representation and architecture. For instance, The Aegis is interactive architecture that exists as a reconfigurable screen where the “calculating speed of the computer is deployed to a matrix of actuators which derive a ‘deep’ elastic surface.” It would need this type of technology to fully actualize the “implicit suggestion” to become “a physically-responsive architecture where the building develops an electronic central nervous system, the surfaces responding instinctively to any digital input” including sound, movement and the internet. These three things can be described by wavelength and frequency but in different units. The translation of the information from one sense to the next builds a neoteric sensory relationship between the perceptive frequency domains in alternative sensory organs that will push the limits of architectural constructions. .7. END: Gifted Invariance Minkowski, during a discussion of the existence of illusionary objecthood, describes his version of space-time with the following property: “Henceforth space by itself, and time by itself are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.” Silagadze retorts, “because even if space and time are really illusions they proved to be very useful concepts.” All of our realities are configured by the qualitative nature of our brain systems, conceptually powerful. “Geometry lies at the crossroads of a physics problem and an affair of the State.” Px 2010 @rhoxrose Rx .8. Bibliography
| The text being discussed is available at | https://soilandbody.wordpress.com/2020/06/16/futurist-geomtry-para-tale/ and |