Exploring Labyrinths of Architecture by ciro podany

Wandering through Knowledge, Perception, and Existence: NYPL Book-stacks Extension Ciro Podany

Ciro Podany

Wandering through Knowledge, Perception, and Existence: NYPL Book-stacks Extension

COME WANDER IN YOUR LABYRINTH… “For happiness, how little suffices for happiness!…the least thing precisely, the gentles thing, the lightest thing, a lizard’s rustling, a breath, a wink, an eye glance— little maketh up the best happiness.(…) Be

still.”

Nietzsche

For the duration of this semester and maybe for the rest of my life, I will be writing lyrical labyrinths of analogy, reflection, lies, truths, lives, deaths, and other topics that become us as we wander our path in search for meaning and self worth. These will be written and numbered in sequences that can be read either direction or, if you prefer, in any order. Not unlike both the game and the book called “Hopscotch”. The hope is to continue evoking the very interesting dialogue that has begun to murmur between my peers, friends, teachers, and loved ones…maintaining horizontality, everyones voice is encouraged to bring awareness to awareness itself. It begins and ends with 1 every time…

SECONDARY ADVISOR Professor Weldon Pries

Endless Space The mind, like space, designed in ceaseless flux, of ceaseless weaving and meaning. Endless speculative activity catalyzes the disclosure of space to the infinite; a flow seemingly contradicting even the possibility of applying measure to its architecture. Light reveals new interests, and casts inner shadows many times before materializing.

Table of Contents Discovery

Innate Structures

Spatial Keywords

Research Essay: Natureâ&#x20AC;&#x2122;s Intuitive Mathematical Structures 17-31 Discovery Hypothesis

Research Graphics

35-47

Frames/Probes

49-79

Conclusion

Un-Doings

Translation

Wandering Through Architecture of Human Knowledge

Abstract

Labyrinths

91-129

Genesis|Exodus

131-135

Final Graphics

137-149

Final Reflection

151

Appendix

153-155

Discovering the Geometric Labyrinth of Architectural Knowledge: Fractal Space Mind Worlds Within the passage of the speculation cloud, fantastic ideas can bloom and suddenly flow from the mind inspiring and creating space for dialogue. Outlining an overarching question, critical perspective, or insane image. Thought Structure The invisible structure of thought itself. Beginning, with a spontaneous preoccupation; each thought offers a way out and a way in. Once sure of the path desired, the mind must sift through unrelated scenarios and events until an understanding can provide the structure for the ideaâ&#x20AC;&#x2122;s sustenance. Limbo Can it truly be that ninety-nine percent of everything that effects our life cannot be detected by the human senses? Does this make our world, (especially the physically constructed world of architecture) more invisible than anything? We cannot see space so how do we know that it exists?

Innate Structures

Spatial Keywords

Euclidean Geometry: Based on the axioms of Euclid the Greek Mathematician who is credited with the establishment of threedimensional geometry and the box that withholds possibilities of fractal nature. Synonym: The Grid Mastery of Nature: The strong assumption that humankind can, and should, control natures systems, arguably leading to the destruction of both meaningful city form and human-nature interconnectivity. Synonym: Human Coherence: All spatial components or fragments, clearly manifest a framework of order and organization to ensure intrinsic relations with other organisms. Synonym: Environment Legibility: Way-finding of complex space and the ability to physically orient and navigate. Synonym: Perception Harmony: A combination of spatial conditions that compliment each other, resounding a seamless chord of invigoration. Synonym: Interdependency Complexity Captures spatial detail to physically and psychologically excite the user, while invigorating components of exploration within the site environment. Synonym: Diversity Recursive An intuitive sequence of spatial growth, results networks of spaces generating other spaces creating a process loop and creating a self-conscience space enabling itself to reflect on itself . Synonym: Reproduction: Self-Similar: Repetitive self-copying patterns that grow or diminish in scale (inhalation/exhalation) creating solid correlations between major structural elements and tiny details. Synonym: Breath Fractal Space: A composition of complex space, formed through the process of a recursive loop that self-similarly iterates different dimension of detail. The design language of, trees, clouds, crystals, and mountains is borrowed and translated to express coherence, legibility and harmony with all possible entities. Synonym: The Organism

Nature’s Intuitive Mathematical Structures The application of mathematics to nature explains the humans desire to “Understand his environment, to give play to his artistic instincts, to engage in absorbing intellectual activity,”1 in addition to describes the relationship between humans and nature that reflect recent research of fractal geometry and biophilia. Mathematics, beginning “In pre-historic times, struggled to exist for thousands of years,”2 due to human fear of the natural world forces. It was the Classical Greek (500-336 BCE) atmosphere of reason that truly recognized the potential power of mathematics to conceptually grasp the workings of the universe. Greeks applied mathematics to nature in order to comprehend their environment “Because they enjoyed reasoning and because nature presented the most imposing challenge to their minds.”3 Abstract theories of nature allowed the Greeks to realize that all things encountered by the human senses worked by patterns discernible through numbers. Pythagoras and his followers asserted that, “nature is built in accordance with mathematical principles, and that number relationships reveal the order in nature.”4 The theories and axioms developed by the Greeks culminate humans curiosity, respect, and awe of nature and it is at this point of departure where most mathematics grows from. After the Greeks, the development of new societies in Europe transforms mathematics role to assist in the “mastery of nature.”5 The important English thinker Francis Bacon (1562-1662) makes this perspective clear by criticizing the Greeks, claiming, “Interrogation of nature should be pursued not to delight scholars, but to relieve suffering, to better the mode of life, and to increase happiness.”6 Rene Descartes (1596-1650), the French philosopher, adds that “Knowing the force and action of all bodies that environ us, we can thus render ourselves the masters and possessors of nature.”7 Differing completely from the Greeks in motive, these ideas still recognized the natural environment as the powerful life force that must be understood to better life and sought the application of trades and arts to do so. It has taken humankind until recently to look at its relation with nature scientifically and critically. The Biophilia Hypothesis (1993) embodies the intersection between the Greeks love of nature and subsequent civilizations love of human life with the aim to “probe what an affinity to life can mean for all of us.” 8

1 Kline, Morris., Mathematics for the Nonmathematician. (New York: Dover, 1985,1967.)Page 27. 2 Ibid. Page 14. 3 Ibid. Page 16. 4 Ibid. Page 189. 5 Ibid, Page 23. 6 Ibid. Page 280. 7 Ibid. Page 280. 8 Kellert, Stephen R., and Edward O. Wilson. The Biophilia hypothesis. Washington, D.C.: Island Press, 1993. Page 17.

Fractal Space: Mandelbrot establishes fractal geometry and publishes Fractal Geometry of Nature (1982) to initiate discussion around emerging definitions and concepts. The content of Morris Kline’s Mathematic for the Nonmathematician (1985) provides a brief but necessary historical backdrop to Mandelbrot’s innovation, and crystallizes the connection between man, nature and mathematics. Rhonda Roland Shearer, in her article “Chaos Theory and Fractal Geometry: Their Potential Impact on the Future of Art” (1992) investigates the role of human perception to distinguish the conceivable benefits of fractal space. Holmes Rolston III breaks the concept of sexual reproduction down into pieces that can instill the continuous diversity of an artificial human environment section titled “Biophilia, Selfish Genes, Shared Values,” (1993) and depict plausible reasoning for humans innate comprehension of natural space. Michael Batty and Paul Longley’s Fractal Cities (1994) addresses modern urban design criticism by proposing fractal space as a meaningful closeness of parts that are perceptually pleasing and architecturally legible. Ron Eglash’s book, African Fractals: Modern Computing and Indigenous design (1999) analyzes vast cultural applications of fractal geometry drawing intriguing results from keywords that capture the true to life behavior of fractals and the complex spaces they can generate. Stephen Kellert’s, Building for Life: Designing and Understanding the Human-Nature Connection (2010) revisits spatial design theories, and attempts to further develop and define these components into contemporary design methodologies. A chapter titled “super organisms” within Tim Flannery’s book Here on Earth, (2010) compiles research on the incredible effectiveness of super organisms through their interconnected existence.

Claim: Fractal space embodies elements of life with enough conviction to anticipate the psychological and physical progression of human consciousness. Complexity: The birth of fractal theory The discovery of fractal geometry by the mathematician Benoit Mandelbrot describes the systematic design of both humans and nature; therefore describing the mathematical components of human’s love of life. Abstract qualities found in fractals are best explained through natural elements. This is mainly because once a fractal seed shape is planted ,it functions and grows as a living entity. Mandelbrot uses this truth to reinforce the fractals ability to describe what Euclidean geometry cannot, including, clouds, mountains, coastlines, plants, and snowflakes. Mandelbrot tests fractals ability to define natural elements

by computer generating fictional landscapes from the number sets, (fig. 1). A

Peano curve, (fig.2) also exemplifies certain geometric conditions of nature, such

as “rivers, watersheds, botanical trees, and human vascular systems,” The Koch 9

curve, (fig. 3) which begins as a triangle connected to a line must be thought of as a living organism according as it iterates itself continuously, “It would not be possible to do away with it without destroying it altogether, for it would rise again and again from the depths of its triangles, as life does in the universe.”10 Recursion:

Ron Eglash’s discovery of African villages designed with fractal methods builds

upon Mandelbrot’s theories. Eglash studies the psychological, social, and physical interconnection these African’s have with their natural environment. Two examples of fractal shapes established by Mandelbrot contain the overarching themes of: scaling, and self-similarity employed by Africans in their use of fractals. Similar to the Peano curve, it has been found that the paths through certain African settlements are “like the bronchial passages that oxygenate the round alveoli of the lungs, the routes that

nourish circular settlements often take branching form.”11 It is not only the African settlements that take on fractal concepts and forms, Eglash points to “traditional hairstyling, textiles, (fig. 4), and sculptures, in painting carvings, metalwork, in religion, games, (fig. 5), and practical craft, in quantitative techniques, and symbolic systems, Africans have used the patterns and abstract concepts of Fractal geometry. “12 A distinction noted by Eglash between African Fractals and The Fractal Geometry of Nature is the concept of “recursion”13 which is not recognized once in Mandelbrot’s text. This is the understanding that fractals are created “by a circular process, a loop in which the

output at one stage becomes the input for

9 Mandelbrot, Benoit B. The Fractal Geometry of Nature. San Francisco: W.H. Freeman, 1982. 10 Ibid. Page 43. 11 Eglash, Ron. African fractals: modern computing and indigenous design. New Brunswick, N.J.: Rutgers University Press, 1999. Page 34. 12 Ibid. Page 7. 13 Ibid. Page 109.

the next,”14 just as biological and geological change occurs. This concept also captures how a physical object can be fractal only a limited range of scales. The recursive properties of a particular

village allowed for women to express “social control” by implementing the next iteration, of space by building an addition to a current living space. Social power can potential empower women through difficulties like divorce or a changing family structure.15 Dr. David Hughes, an architect and professor, notes the African settlements to be environmentally harmonious as well as the product of intentional design and semiotics, in contrast to a vernacular approach “unconsciously”16 adapting to its environment. Another example of fractal scaling occurs along a royal passage where as the spaces scale smaller you go up in social ranking and must act more formal, until you reach the room of leader and must take your shoes off and speak with complete formalities, (fig 6.) Eglash attributes the recursive, self-similar, scaling properties of indigenous African design to an open perception of sexual reproduction, a close relationship to agricultural cycles, and the belief in sand divination techniques, maintaining theory that recursion holds “some kind of universal ethical or social value.”17 Similar patterns to fractals can be found in the “grand masters paintings and beaux arts architecture,” because of the implementation of many scales of length and self-similarity, (fig 7). Algorithmic games, traditions, and artwork leads to the conception of spaces using similar recursive methods, interconnecting notions of culture with architectural space.

Reproduction: Research shows evidence that humans are stimulated by nature because of an innate biological dependence on it. The artist Rhonda Roland Shearer explains that the, “Visual experience of plants exists somewhere between direct perception (subjective) and memory (universal).”18 Experiencing plants is distinct from unnatural pattern perception because it

connects humans to the larger context of life systems on Earth. The understanding of collective origin and time “universal” is juxtaposed with singular emotions, and reactions to the “universal”. Shearer references experts like neurologist Antonio Damasio who supports “that the brain perceives human-made objects and natural objects

14 Ibid. Page 17. 15 Ibid. Page 195. 16 Ibid. Page 218. 17 Ibid. Page 192. 18 Rhonda Roland, Shearer,. “Chaos Theory and Fractal Geometry: Their Potential Impact on the Future of Art.” Leonardo 25 (1992): Page 148.

using distinctly different processing.”19 Perceptual distinction touches on the trans-formative spatial implications plant geometry, or fractals, hold in the world of art and architecture. Conditions of visual interest occur at every scale due to growth. Human perception of this particular aspect provides assimilation of different stages of life within a larger cycle demonstrating the self-similar “relatedness”20 of the parts to the whole, (fig. 8).

Human’s awareness of sexual reproduction, portrays the vital effects of plant perception.

Holmes

Rolston III’s article Biophilia, Selfish Genes, Shared Values describes the arrival of an organism “In the world as a beneficiary of past variation, and it inhabits a natural system in which it can cope only if it can make variant copies of itself.”21 Humans recognize the existence of fractals in the patterns of variant recursive copies in plants and in this subtle exchange a deeper understanding of place is possible. Potentially, the forms of plants stimulate in order to facilitate the interaction of organisms. The human Importance of interconnectedness is exhibited well by superorganisms Tim Flannery’s Here on Earth identifies how super organisms are “Emblematic of the co-evolutionary capacity to create an entity that is more competent and productive than the sum of its parts.”22 The coordination of systematic groups of people, exhibit some of humankinds greatest achievements. Construction of a building requires an extensive coordination and human power possible only through the strength of systematized groups. Human’s love and desire connection to systematized groups of people because chances of survival and evolution increase drastically. This behavioral pattern draws directly from the theory that “every creature, is in some sense, is connected to and dependent upon the rest. “23 Humans make up a network of genetic copies and compose a groups inherently strengthened by their interconnection. Each reproduction of a fractal pattern can establish individual spatial relationships

while simultaneously strengthening the whole system, (fig. 9). The Grid:

Research at the scale of city, has reinforced the value of fractals inherent form that describes the

geometric essence of life and nature. Cities reflect the human desire for a survival through interconnection, and require opportunities for diverse form in order to maintain longevity. The two main approaches to city design 19 Ibid., 148. 20 Ibid., 151. 21 Kellert, Stephen R., and Edward O. Wilson. The Biophilia hypothesis. Washington, D.C.: Island Press, 1993. Page 391. 22 Tim Flannery,. Here on earth: a natural history of the planet. (New York: Atlantic Monthly Press :, 2010.) 23 Ibid., 55.

extend tensions between nature’s organic growth and modern cities artificial harshness. Michael Batty and Paul Longley’s Fractal Cities considers the mastery of nature as a point of departure, joining an ongoing critique of artificial geometry’s role in urban design theory. Ideas of the journalist, activist, and architectural critic Jane Jacobs, borrowed by Batty and Longley, illustrate the “destruction of visual order and harmony,”24 inflicted by gridded cities .25 One possible attribute to this argument is the generic aspect of scale immediate established by a cities size.

10 Coherence, Legibility, and Self-Similarity:

Older cities, like London, and Paris, (fig. 10) according to Batty and Longley encapsulate a greater level of spatial awareness . Without the goal of controlling the entirety of a cities visual form, each portion of the city can complete another portions imbalance or create contrast in order to instill coherence. Looking at An issue underlying the origins of human’s inclination to master nature is the inability to properly comprehend the complexity of a natural environment at the scale of a planned city condition. The feasibility to construct larger cities spurred humans to introduce simpler geometries than urban models like citadels, fortresses, and castles had previously called for. At a larger scale, an immediate way to understand built form can be efficiently executed by forcing geometric order upon an environment. Fractal’s self-similar scaling can possibly resolve the scalar issues of the grid largeness due to diversity of scales accommodation of growth and decay. Generating spatial richness of scale, connecting to the surrounding environment and its conditions, suggests an architectural methodology beginning to, “identify, understand, and treat cities as problems of organized complexity,”26 and legibility.

Closeness of Parts and Adaptation: When looking at more complexly composed cities, the opportunity to understand a higher dimension of the living components through “spatial hierarchies and successive scaling, where elements of the urban structure are repeated in diverse ways.”27 When the emphasis of space forming challenges the notion of simplification and focuses on adaptation, site is realized as a geometric model from which fractal growth of space 24 Batty, Michael, and Paul Longley. Fractal cities: a geometry of form and function. London: Academic Press, 1994. Page 7. 25 Ibid., 7. 26 Ibid., 7. 27 Ibid., 47.

appropriates the built form with true meaning. Historic cities and towns depended on geometries growing from the site for survival and longevity, (fig 11). In the classic style of fortification, repetitive angular displacements of the main outer wall “increase wall space available for their defense and as such represent a kind of space filling phenomenon reminiscent of the regular fractal called the Koch curve.”28 Cities built with this attentiveness to existing natural geometries successfully transfer local interests into clarity of human’s dimensional relationships to their landscape. The interconnected development of urban spaces supports self-affinity through closeness of parts and their ability to adapt.

The over-simplification of unnatural geometry represents an overarching trend of disengagement with the natural environment as a whole. Stephen Kellert’s Building for Life considers the psychological, and physical consequences disconnection from nature has on humans. Many of the theories are based on research done by experts like Nobel Prize Biologist Rene Dubos who affirms, “The functioning and maturing of the human body, mind, and spirit depend on the quality of people’s ongoing experience of nature.”29 Among many of the inherent benefits discussed, problem solving, intellectual performance, social ties, and relationships, highlight the difference between fractal space and typical green architecture, that fails to recognizes geometry as a key tool of integration. Green architecture instead focuses on applicatory methods of green walls, solar panels, and gray water systems. These elements lower the energy consumption of a building, the form is largely incongruent with fostering a cultural “recognition of symmetry and harmony.”30 Distillation of natures conditions into language applicable to design bridges the gap between both the natural and built environment . According to Rachel and Stephen Kaplan , a more meaningful geometry embodies, coherence, mystery, complexity, and legibility. Coherence presences the human mind. Understanding time and place, coherence “discerns order and organization in nature. “Mystery suspends normal interest. It motivates care, development, growth, and knowledge. Mystery enables “investigation and examination of the complexities in nature.” Complexity describes not only nature’s mathematical form, but where it is oriented in time and place because of the laws of growth and interdependence. For humans it is the “ability to identify and respond to diversity and variability in the natural world.” Legibility is visual clarity and “reflects the human capacity to orient and navigate natural

28 Ibid., 22. 29 Dubos, quoted in, Kellert, Building for life designing and understanding the human-nature connection. (Washington, DC: Island Press, 2005.) Page 11. 30

Ibid., 15.

settings.”31 The applicability to design through a language of geometries from the psychological properties of nature can be appropriate because it seeks not to make an exact copy of nature but to extract conditions that convey the essence of nature. In the language of architecture, form and space epitomize the main tools that must relate to the “archetypal image of the natural world.”32 Frank Lloyd Wright began to architecturally employ spatial theories intuitively from an understanding of natural conditions. He designed “visual connections between interior rooms, with outside views and few closed interior spaces as a way to “destroy the box,” of artificial space. Due to the recent understanding of fractal geometry, the design of architectural space has the potential to revolutionize humans understanding of the built environment on the same level that nature can scientifically be understood. Harmony: Seeking to control nature by imposing simple geometry misunderstands science and a falsely assumes the assurance of progression. The negative impact of built environment, suggests that “if we do not strive to love our planet as much as we love ourselves, then no further human progress is possible here on Earth.”33 The state of the urban gridded environment, doesn’t successfully extend beyond the limits of it sets upon itself. The capability to transcend conceptual and physical gridded boundaries intersects “the heart of mathematical, computational, limits of our subjective experience of consciousness.”34 With a desire to recursively love and grow instead of control and dictate there are opportunities to strengthen the interconnected environment of humans. Discovery of fractal geometries represents deeper self-reflection of humans and the “revelation that beyond the three-dimensional space of Euclid, new spaces are possible.”35 Through the implementation of complex geometric spaces, playfulness, discovery, and appreciation brings humans closer to harmony

within vastness of life connecting all environments and living creatures, (fig 12). Beginning as a simple shape, a fractal iterates itself, growing out “into the community it inhabits, until the self has come to focus on not-self, but on other selves.”36 Fractals form and structure natural elements existing in a multiplicity of complex environments, channeling power through architectural space and envisioning human life in a truly congruent harmonious interplay with its world. 31

Ibid., 15.

Ibid., 127.

33 Griffith, as quoted in, Flannery, Tim F.. Here on earth: a natural history of the planet. New York: Atlantic Monthly Press :, 2010. Page 47. 34 Eglash, Ron. African fractals: modern computing and indigenous design. New Brunswick, N.J.: Rutgers University Press, 1999. Page 219. 35 Shearer, Rhonda Roland . “Chaos Theory and Fractal Geometry: Their Potential Impact on the Future of Art .” Leonardo 25 (1992): Page 151. 36 Rolston III , as quoted in, Kellert, Stephen R., and Edward O. Wilson. The Biophilia hypothesis. Washington, D.C.: Island Press, 1993. Page 17.

Hypothesis

If a fractal space is planted in the interstitial space of oversimplified Euclidean geometry, than it will catalyze a harmonious coherent and complex architectural organism, continually strengthened by its interconnected relation to its host.

Research Questions

geometry infinite irregularity small and large details the same endless non-integer dimension describes form of nature algorithm equation measurment organization computable

evolution reproduction naturally occurring affinity super-organism genetic biology fear/pleasure naturalistic vernacular adaptation life/death survival origin instinct

Venn Blending

Chaos and The Cave

Process of Iteration Methodology, transformation, described through the lens of nature and the computer. Where do they meet?

Mind Map 1

Inhabitation How can we inhabit something that we canâ&#x20AC;&#x2122;t hear, touch, taste, or smell? Space can only be thought of as awareness itself. Because architecture, in its bodiless state is free of sensual perception it is potentially quite purely derived fromâ&#x20AC;Ś

World of complexity: Fractal

World of action:

Program is growth, discovery, and intersection.

Positive and negative extractions of a leafâ&#x20AC;&#x2122;s fractal geometry.

The forms are pulled apart and joined at structural overlaps abstracting the spatial qualities within the leafs geometry.

Building in an iterative process, the largest triangleâ&#x20AC;&#x2122;s dimension was continually divided to intuitively grow structure,

The resulting form brings forth an idea of section multiplicity that could portray a alteration and iteration through time, as well as self-similarity and recursion.

The Koch Snowflake Curve was used to generate the exterior and interior tectonic study. The exterior of the module is on iteration 1 while the inside is on iteration 3, illustrating Solid folding planes embody density at the top and bottom of the models interior. Members of structure give the feeling of openness and perforation.

Recursions of triangles grows from the ground plane and uproots the simplicity of a three dimensional, Euclidean rectangle.

Though the iterations of triangles are smaller in size and built with lighter structural pieces, the interconnection of them transforms a simple space and potential establishes a setting of spatial harmony.

Shatter, a series of charcoal explorations capture swift and momentous shifts in energy through the fragmentation of geometry. While certain spaces and forms grow from within, adjacent forces decay the essence of what space and form once was. Each illustration captures a different moment of time in the life and death of converging energies. Process sketches and paintings explore the human form intertwined with recursive geometric proportions, epitomizing the spatial inhabitation, life, and connection. The subsequent expressions of charcoal extract the emotional psychological weight of modification and transience The juxtaposition of forms, spaces, and lines, echoes through the process of making. To grasp the solidity and structure of energy, paper pyramid like models construct an abstraction of force vectors colliding. These models become a layer of solid force that becomes flattened and compacted through the fine charcoal dust. Memories and movement remain suspended in their charcoal atmosphere. The next layer of force is generated from hard lines of willow charcoal sticks, stretching the mediums potential between two states of viscosity. Finally, the human hand blurs boundaries, darkens connections, and de-constructs movement. Volatile movements and explosive trajectories tenuously balance between the imprint life and death after its physical embodiments shatter.

Conclusions: Discovery

Process Evaluation Research began with an interest in biophilia, humans natural love of nature, but transformed into an exploration of fractal geometry and space. This transformation occurred when it was realized that fractal geometry constructs spaces naturally interesting to humans... Critiquing the role of geometric space in architecture is no small or simple task. That fact considered, this research topic has sustained the great challenge it poses because of its exciting spatial implications. Due to the vastness and complexity of fractal geometry, process has focused on gaining an understanding of what a fractal is , how it relates to humans, and its influence on the space occupied by humans. The inherent difficulty to encapsulate this complex relationship calls for mitigation by extracting certain characteristics of fractal geometry that can inform an architectural space. For the purpose of direction and =clarity, conditions of recursion, self-similarity, and scaling have been selected for further focused investigation. With the knowledge of fractal geometries basic components of behavior, research has begun to evolve towards connecting its properties to architectural spatial theories. Program Program was abstractly based on Bernard Tschumiâ&#x20AC;&#x2122;s La Villette principle where he overlays (and equates) ideas of activity, movement, and appropriation with the architectural elements of points, lines, and spaces. The axon in frame 1 translated this approach by using the architectural line as a fractal path to collide with cubes symbolizing space that create a tension and release of activity and movement. Site The question of site requires the critic of pre-existing spatial elements both of interior and exterior nature. For an alternate theory of space to be tested, it must be in the context it seeks to transform and enhance. These parameters resulted in the investigation of abandoned sites of dead space in New York. Each site desperately needs revitalization and exists as a shell of emptiness and nothingness. The dead architectural space within each of these sites could be enlivened and transformed by introducing a fractal form that grows from the interior to the exterior. Re-integration to the surrounding context would be possible as well with the intervention of fractal spaces that stem from the original growth within the dead space. Tectonics Models have contributed valuable information concerning translatable tectonic design elements. De-constructing the fractal patterns of a leaf, lead to investigation of structural implications and focused the project on an urban context epitomized by its euclidean form. The most important discovery thus far has been the iteration and sequence of growth in the design probe model. The method of bifurcating a triangle transforms the three-dimensional euclidean framework into a composition of fractal spaces. The result uproots the original structure and envisions a diverse interconnected network of spaces blurring interior and exterior boundaries. Architectural tectonics holds the consequential elements and characteristics of a fractal space because it must structurally conceptualize space and convey ideas of construction and assembly. A fractal space is defined by growth and evolution, architecturally providing the understanding of space constructing itself and other spaces through the use of a spatial tectonic. A method of generating and designing architecture of fractal space requires a set of rules to accommodate the needs of site program and user. An algorithm must be developed to establish clarity of process, cohesion of concept, and comprehension of tectonic fractal space.

Un-Doings

When we touch the invisible walls of its limits than we know more about what is contained within them. The space which thought and inspiration are conceived of, is vastly larger and more complex than that which we inhabit. Limits can mediate between the translation from the world of intangible conjectures into the physical realm of facts, true and false.

Transition:Translation:Transcendance

After a full semester of studying “fractal space” and the properties of complex geometry, I was left uncertain where in the vast world of architecture to apply these architectural ideas. I stepped back from the impulse to continue forcing my abstracted ideas about design potentials, and began reading and learning site. This method completely reversed the projects trajectory and was both scary and liberating at the same time. That this thesis could potentially not utilize an entire semester of work that I had put so much of myself into allowed me to open my mind to any and all possibilities while maintaining faith that what I had learned would somehow benefit my new focus: Bryant Park New York City. I quickly learned that this was of immense importance to NYC and in many ways epitomizes Rem Koolhaas’ concept of “manhattanism” in his manifesto Delirious New York. Screen Shot 2014-01-15 at 12.18.59 PM Structures like the (New York) Crystal Palace and Latting Observatory of Bryant Park in 1853 completely transformed people’s idea of architecture and deployed structurally innovative methods of construction. Each structure directly relates to the awareness of the user in opposite ways. The Latting Observatory, a 350 foot tower with one of the first elevators ever used brought people up to 3 levels of platforms where telescopes allowed for the full extent of manhattan to be viewed, a projection of exterior awareness. The New York Crystal palace housed thousands of inventions, machines, technology, and culture, from all over the world, a reflection of internal awareness. Currently the New York Public Library’s Schwarzman building sits at the 5th avenue side of the park and houses around 15 million items. It represents the central largest contained system of public knowledge in New York and one of the largest in the entire world. What quickly became interesting to me is the What is the form of knowledge? How and why do humans seek to categorize knowledge within an architectural form? What is the nature of this form and how do we reflect or project our awareness through engaging with the fruit of knowledge it contains? Most importantly, how does a systematic catalogue of knowledge reflect the larger system of the city within it resides? Self-similarity, recursion, holism, structure, organizational depth, dimension, generative quality, all relate to many areas of design but have a specific affinity to the ideas of reflecting and projecting awareness and the questions about the form of a knowledge system. These are the properties of fractal geometries that occur in nature. It is the way that a plant organizes itself to collect the proper amount of sunlight and water as well as maintain a strong structure. New York, as a gridded city denies the importance of natures form and is a very efficient machine as a result. The power of this machine also allows for anomalies to occur in the many disconnected abstract worlds of the rectangular city block. It is the convergence of these interests that has led this architectural thesis project to pursue the idea of seeking a form of knowledge that exhibits an awareness of projection and reflection interconnected to the genius loci of Bryant Park and the Manhattan Machine.

Wandering through Knowledge, Perception, and Existence: NYPL Book-stacks Extension

Architecture is of another world. It is the imposition of structures it never asked for and that existed previously only as clouds of conjectures in the minds of their creators. The transformation of the speculative into the “undeniably there.” Raising the question, is architecture’s substance, within its physical matter.

Or is it, an immeasurable collection of philosophies, expanding in-definitely towards heaven? Each imaginary block’s proximity and juxtaposition reinforcing separate meanings. A theory that works, a mania that sticks, a lie that has become a truth. A dream from which there is no waking up.

Wandering through Knowledge, Perception, and Existence: Abstract

“thus surrounded, this monster bookcase becomes, architecturally, the heart of the whole structure, the treasure for whose protection this marble palace is built” -Times, 1905 How can architecture manifest a direct (physical/metaphysical) relationship between humans and knowledge? A plan of destroying the 107 year old “heart” of the NYPL in Bryant Park, threatens to comprise the integrity of the Libraries fundamental meaning as a machine for exploring and acquiring knowledge. Physically and intellectually sustaining by its essential nature, the architecture of knowledge questions its limited capacity inquiring a transcendence of its current metaphysical reality: A three-dimensional gridded container of human knowledge interconnected with the architectural DNA of Manhattan. The stacks “marble palace” sets limitations on the potential of its architectures undying and unfulfilled desire for knowledge. Reading the NYPL’s meaning above its appearance allows for the stacks to deliberately ignore its marble costume and become the heart of its own architecture, mediating a new set of limitations in a transformative but familiar context. Now a truly open and public network, the stacks begin to reveal a critical mapping of the spatial/structural (solid/ void) conditions of knowledge. Architecture of knowledge utilizes an method of self-referencing assembly drawings, demonstrative of the actions (verbs) of a human pursuit of meaningful existence.

Choices in the Labyrinth of Architectural Knowledge The labyrinth represents the never ending search for the one book that will decode one’s “self.” Statistically speaking this has a 0% chance of happening according to the unknown narrator of the story. The book is told from the point of view of a nearly blind elderly man who has always lived in this library or universe. The man explains the inner workings of the library. He describes his younger years and the quest for finding the book of his self. Now he is just waiting to die and be thrown into a fall of infinite time and depth where his body will decompose and turn to dust. “At that same period there was also hope that the fundamental mysteries of mankind - the origin of the library and of time - might be revealed. In all likelihood those profound mysteries can indeed be explained in words; if the language of the philosophers is not sufficient, then the multiform Library must surely have produced the extraordinary language that is required, together with the words and grammar of that language.” (26) Borges, Library of Babel. So many questions arise from Borges concepts that I wouldn’t even know where to start. I am interested in looking at some of his poetry and other ideas. The fantastical allegory of The Library of Babel encompasses what I would hope for my thesis project, in that it completely conveys complex theories of reality into an amazing story that provokes thought and the desire to understand more. It seems as though the library is inherently at a level of complexity that no human could ever attain. The exploration of the space and form of knowledge could seemingly take many forms so maybe confining it to one building/form/shelf is an oversimplification.

Dreamtigers: human desires, architectural conjectures

And so, as I sleep, some dream beguiles me, and suddenly I know I am dreaming. Then I think: This is a dream, a pure diversion of my will; and now that I have unlimited power, I am going to cause a tiger. Oh, incompetence! Never can my dreams engender the wild beast I long for. The tiger indeed appears, but stuffed or flimsy, or with impure variations of shape, or of an implausible size, or all too fleeting, or with a touch of the dog or the bird. -Jorge Luis Borges, Excerpt from Dreamtigers.

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Open Heart Surgery

Excerpt from New York Times 1905... â&#x20AC;&#x153; ...In the New York Public Library. Here it stands, one huge square, in a chamber 78 feet by 297 feet, rising in seven tiers of 7 1/2 feet each tier. Above it will be placed the spacious reading room of the library, on either side the various halls, offices, and exhibition rooms. thus surrounded, this monster bookcase becomes, architecturally, the heart of the whole structure, the treasure for whose protection this marble palace is built.â&#x20AC;?

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Time ..May 20th For it is only habit and memory that dull the physical passion...Without memory, each night is the first night, each morning is the first morning, each kiss and touch are the first . . . In order to know himself, each person carries his own book of life, which is filled with the history of his life . . . Without his book of life, a person is a snapshot, a two-dimensional image, a ghost . . . Some have stopped reading altogether. They have abandoned the past, They have decided that it matters not if yesterday they were rich or poor, educated or ignorant, proud or humble, in love or empty hearted----no more than it matters how a soft wind gets into their hair: Such people look you directly in the eye and grip you hand firmly. Such people have learned to live in a world without memory... 25 June 1905 There is an infinite number of melodies and thought. And this one hour, while the young men play their violins, is not one hour but many hours. For time is like the light between two mirrors. Time bounces back and forth, producing an infinite number of images, of melodies, of thoughts. It is a world of countless copies . . . His music floats and fills the room, and when the hour passes that was countless hours, he remembers only music. 22 June 1905 He almost permits himself a smile, so pleased is he at his decision. He breathes the moist air and feels oddly free to do as he pleases, free in a world without freedom. Interlude He wants to tell Besso about his dreams, but he cannot bring himself to do it. 17 June 1905 So tiny are the disconnection in time that a single second would have to be magnified and dissected into one thousand parts before a single missing part of time could be spotted. So tiny are the disconnections in time that the gaps between segments are practically imperceptible. After each restart of time, the new world looks just like the old. 28 June 1905 In truth, these birds are rarely caught. The children, who alone have the speed to catch the birds, have no desire to stop time. For the children, time moves too slowly already. May 1.5 1905 There is nothing there but what you manifest, watch the birds flutter with the breeze, close times eyes and let songs of mysticism fill your awe of existence. All excerpts from Alan Lightmanâ&#x20AC;&#x2122;s Einsteinâ&#x20AC;&#x2122;s Dreams.

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Multiplicity/Pluralism

The very nature is there to be in... within in between interstitially situated tensioned balance between many mirrored references oscillated inquiry demonic presencing the fight accept loss enjoy pain rejoice with misery we are here no matter what.

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Belief in Architecture of Knowledge

And do you believe? Is there hesitation in your being? subconscious missed understandings over shooting powerful meanings to fragile minds trying to hard trying at all is never successful if you are trying you are not arriving when each moment is perfect just how it is why not let why not every conscious step listened observed learneDimensions glass onion truths

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Space

Take a breath, did you listen to it? did you feel it? the rib cage expanding the air filling the void the air filling the void cyclical organized perfect in its simplicity Refreshing and cool to the touch the room around me stops moving and I am I Am here for now and forever in this void of moving solid particles that flow waterâ&#x20AC;&#x2122;s life through the cavernous realms of incessant ...Existence

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Steps Drawings Days Moments Plains Realizations Manifestations Designs People Lives Architectures Ideas Realities Times Lines Lives Deaths

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Born

Deep breaths lead to steep treads up and down the smoke of consciousness reflective crystal caverns of knowledge un-needed not wanted spite ed by those that want all and see none

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Genesis...-I-...Exodus

Birth unto me Freedoms Speak through me truth Winds Steps from single cells prison rails untouched nudes until openings cracks revelation illumination between creation and freedom wont we realize that each mirrors to the other? ...DEATH=REBIRTH=FREEDOM=LIFE=FREEDOM=REBIRTH=DEATH...

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Live

Evil

Tree 1,000 faces Wisdom beyond my story gnarled mouths transport I in land of terror Kindness, wrinkled faces the bringing, meadows bliss-full carpets dark green moss, Serene caressing twistedly Bark hard un-controllable scarring f u r i e s . . . Birth unto me freedoms Speak through me truth Winds Steps , from single cells prison rails untouched nudes until openings c r a c k s r e v e l a t i o n i l l u m i n a t i o n between creation and freedom wont we realize! . . . that each m i r r o r s to the other? . . . curtains part excitedly obsessively with Vital existence l i f e sweeping colors warmth of Knowing sheen truth alighting gently as though the bird of time froze in flight, on skies pure white, positioned right intrinsic sight

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Reflection on the Journey: Concluding Thoughts The architecture of human knowledge takes many forms in the physical and non-physical environment around us. Beginning with fractals and ending with an architectural reality where time, space, situation, and atmosphere re-write there very limits, was not a planned route of educational research. It just happened. It was the result of a rigorous process with which I fell in love with. Not the resulting work, but a love for the work. I simply put my heart and soul into every action, every word read, every line drawn. Each step was calculated, I never took short cuts, easy ways out, and never did I settle for work which I felt didn’t capture the idea of intent. This led to a process of discovery where architecture, for me, became whole. It became one environment of changeful multiplicity where I couldn’t see one side of the coin without understanding the other. The idea of “Illumination” brought to me the knowledge that, without darkness, light doesn’t matter. Without massive and violent possibilities or acts of destruction, construction has no weight, no meaning, no reality. The final drawings, I can confidently say, actually hold all work that I have done for this entire year. The graphics, (for me again) successfully convey an architectural world where each buildings reflection is as real as the physical object. The ideas are equally important as the physical environment. The shadows as spectacular as the light. The labyrinths within the books spill into the built environment mirroring, human constructs (metaphysical or physical) upon human constructs. Translation in this world brings its architecture incremental steps away from its fundamental beginnings. Bedrock and sky frame a volatile Manhattan, set into never ending motion by its inhabitants quest for knowledge, money, success, understanding, fulfillment. The heart of this non-satisfiable desire is the NYPL book stacks, soon to be ripped out of their home of 107 years resulting in the displacement of 3.5 million books. The intent of this “final” book, is to illuminate the process by which I came to the graphical representations of architectural realities that emanate from my personal experience of human knowledge and how it might both shroud and reveal our true selves through the built environment.

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Appendix

1. Benoit B. Mandelbrot, The Fractal Geometry of Nature (San Francisco: W.H. Freeman, 1982). Benoit B Mandelbrot’s book The Fractal Geometry of Nature (1982) explains and demonstrates a plethora of fractal number sets that describe the form and function of elements found in nature. Mandelbrot applies fractals to snowflake’s, rivers, clouds, plants, and mountains. He also uses human’s lungs and vascular system as fractal examples. His main claim is that fractals can define a more complex dimension of form that includes characteristics of growth, decay, and reproduction. Mandelbrot’s The Fractal Geometry of Nature is important for this thesis because it provides concrete evidence, formulas, and data, of the inherent connection nature’s form has with fractals. 2. Morris Kline, Mathematics for the Nonmathematician, (New York: Dover, 1985). Morris Kline’s book Mathematics for the Nonmathematician (1985) supports the claim that mathematics is essential for understanding the natural systems of the world and human’s relation to these systems. The book reveals a dichotomy between mathematics applied for the understanding of nature and mathematics applied for the mastery of nature. By revealing this tension, the book affirms inherent connections between man, nature, and mathematics. Kline’s book imparts upon this thesis precedents of mathematics use for humans to better assimilate their environment. 3. Rhonda Roland Shearer, “Chaos Theory and Fractal Geometry: Their Potential Impact on the Future of Art ,” Leonardo 25 (1992): 143-152. The article, “Chaos Theory The article, “Chaos Theory and Fractal Geometry: Their Potential Impact on the Future of Art” (1992) by Rhonda Roland Shearer makes the claim that the next major innovation in art (comparable to the Renaissance, and Modern Art) can happen through the use of fractal geometry. Shearer borrows examples from architecture and urbanism to critique simplified geometries and uses examples from nature to reinforce the value of complex fractal geometries. Shearer references the discoveries of new geometries in history as the key to human comprehension of space. The article looks at the psychological properties of fractal geometry and the opportunity it poses to see the world from a different perspective. Shearer’s article holds the spirit and direction of this thesis with its goal of capturing the exciting complexity fractal space has for humans. As an artist who investigates the potential of fractal geometry, Shearer provides creative methods for further investigating questions of fractal space. 4. Stephen R. Kellert and Edward O. Wilson, The Biophilia Hypothesis. (Washington, D.C. Island Press, 1993). Stephen R. Kellert and Edward O. Wilson’s edited book The Biophilia Hypothesis (1993) compiles the voices of expert scientists from different fields to examine what a human affinity to nature means for the world. The book claims that humans are connected to nature on a deep, “aesthetic, intellectual, and spiritual” level that extends from humans physical dependence on their natural environment. The research complied in The Biophilia Hypothesis informs this thesis of the human love of nature and how natures form and growth can act as a model for the design and implementation of fractal space. 5. Michael Batty, and Paul Longley. Fractal cities: a geometry of form and function, (London: Academic Press, 1994). The book Fractal Cities: A Geometry of form and function (1994) by Michael Batty and Paul Longley, researches the connection between cities complex form and fractal geometry. It theorizes that cities can be better organized, understood, and designed through the usage of fractal geometry. Batty and Longley claim their results to overlap with urban design theory and use the critical voice of Jane Jacobs to guide their research. Most importantly, this source offers a scope and method of applying fractal geometry to urban design. The methodology of this thesis can be approached with rules and constraints appropriated from Batty and Longley’s research. 6. Ron Eglash, African Fractals: Modern Computing and Indigenous Design (New Brunswick, N.J. : Rutgers University Press, 1999). Ron Eglash’s book African Fractals: Modern Computing and Indigenous Design (1999) makes the claim that fractal patterns are very similar to African designs and African knowledge systems. Eglash unpacks these similarities through his research while living in African fractal villages and speaking with the people who build

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using fractal patterns. An overarching aspect of importance is the usage of algorithms in culture, as a way to organize the space of people physically, psychologically, socially and spiritually. This source provides architectural fractal examples and real world design techniques that are of great use for the research for this thesis. 7. Stephen R. Kellert, Building for life designing and understanding the human-nature connection. (Washington, DC: Island Press, 2005). Stephen R. Kellert’s book Building for Life: Designing and Understanding the Human-Nature Connection, studies architecture’s ability to “restore the basis for a more compatible and even harmonious relationship with nature.”(3) The discipline of building and design should surpass typical constraints according to the theories of Kellert’s book, and must capture conditions found in a natural environment. Kellert translates characteristics of nature that benefit humans into a language that can bridge the gap between design and biophilia. The design language explored in Building for Life contributes a taxonomy of biophilic design conditions that overlap with the spatial concepts of fractal geometry. 8. Tim F Flannery, Here on earth: a natural history of the planet, (New York: Atlantic Monthly Press, 2010). Here on Earth: A Natural History of the Planet (2010) by Tim F. Flannery claims that humans progress isn’t possible without love and understanding of the planet we live on. Here on Earth studies a variety of animals that bring unique elements into the architecture of our natural environments form and function. Super organisms are studied in a chapter dedicated to better understand the interconnected qualities of nature. The concept of the super organism is of interest to this thesis because it embodies the interdependency a fractal has between the different iterations of its self.

More Readings Alan Lightman, Einstein’s Dreams. (New York, Vintage, 2004). Bruno Ernst The Magic Mirror of M.C. Escher. (Cologne: Taschen; 25th edition 2007). Doug Darden, Condemned Building. (New Jersey: Princeton Architectural Press 1993). Erwin Panofsky, Studies in Iconology: Humanistic Themes in the Art of the Renaissance. (Boulder: Westview Press, 1972). Jorge Luis Borges, Dreamtigers. (Austin: University of Texas Press; Reprint edition, 1985). Jorge Luis Borges, Labyrinths. (New York: New Directions Pub. Corp; [Augmented ed edition, 1964). Jorge Luis Borges, Library of Babel. (Boston: David R. Godine Publisher, 2000). Jose Ortega Y Gasset The Dehuminization of Art, and Other Essays on Art, Culture, and Literature. (New Jersey, Princeton University Press, 1968). Rem Koolhaas, Delirious New York. (New York: The Monacelli Press, 1997) Walter Isaacson, Einstein: His Life and Universe. (New York: Simon and Schuster 2008).