Embed Size (px)
DESCRIPTION
A year long endeavor of passionate work that holds a lot of meaning for me today. I hope you come and wander around a bit in your own labyrinths via materials/ideas/evocations found here.
Citation preview
Wandering through Knowledge, Perception, and Existence: NYPL Book-stacks Extension
Ciro Podany
2
SECONDARY ADVISOR Professor Weldon Pries
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 numberedin 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…
Wandering through Knowledge, Perception, and Existence: NYPL Book-stacks Extension
Ciro Podany
4
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.
6
8
Table of Contents
Discovery
Innate Structures
Spatial Keywords
Research Essay: Nature’s Intuitive Mathematical Structures
Discovery Hypothesis
Research Graphics
Frames/Probes
Conclusion
Un-Doings
Translation
Wandering Through Architecture of Human Knowledge
Abstract
Labyrinths
Genesis|Exodus
Final Graphics
Final Reflection
Appendix
11
13
15
17-31
33
35-47
49-79
81
83
85
87
89
91-129
131-135
137-149
151
153-155
10
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 StructureThe 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 idea’s sustenance.
Limbo Can it truly be that ninety-nine percent of everything that effects our life cannot be detect-ed 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?
12
Innate Structures
14
Spatial Keywords
Euclidean Geometry:Based on the axioms of Euclid the Greek Mathematician who is credited with the establishment of three-dimensional 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
ComplexityCaptures 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
16
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.
18
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 1
20
Peano curve, (fig.2) also exemplifies certain geometric conditions of nature, such
as “rivers, watersheds, botanical trees, and human vascular systems,”9 The Koch
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.
2
3
4
5
22
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.
6
7
24
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.
8
9
26
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.
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.
10
28
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.
11
30
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. 32 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. Washing-ton, D.C.: Island Press, 1993. Page 17.
12
32
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.
Hypothesis
34
Research Questions
36
Venn Blending
geom
etry
infin
ite ir
regu
larit
ysm
all a
nd la
rge
deta
ils th
e sa
me
endl
ess
non-
inte
ger d
imen
sion
desc
ribes
form
of n
atur
eal
gorit
hmeq
uatio
nm
easu
rmen
t or
gani
zatio
nco
mpu
tabl
e
evol
utio
nre
prod
uctio
nna
tura
lly o
ccur
ring
affini
tysu
per-o
rgan
ism
gene
ticbi
olog
yfe
ar/p
leas
ure
natu
ralis
ticve
rnac
ular
adap
tatio
nlif
e/de
ath
surv
ival
orig
inin
stin
ct
38
Chaos and The Cave
40
42
Methodology, transformation, described through the lens of nature and the computer. Where do they meet?
Process of Iteration
44
Mind Map 1
46
48
50
How can we inhabit something that we can’t hear, touch, taste, or smell? Space can only be thought of as awareness itself. Because architecture, in its bodiless state is free of sen-sual perception it is potentially quite purely derived from…
Inhabitation
52
Wor
ld o
f act
ion:
3d
Wor
ld o
f com
plex
ity:
Fra
ctal
Prog
ram
is g
row
th,
disc
over
y, a
nd in
ters
ectio
n.
54
Posi
tive
and
nega
tive
extr
actio
ns o
f a
leaf
’s fr
acta
l ge
omet
ry.
The
form
s ar
e pu
lled
apar
t and
jo
ined
at s
truc
-tu
ral o
verla
ps
abst
ract
ing
the
spat
ial q
ualit
ies
with
in th
e le
afs
geom
etry
.
56
Build
ing
in
an it
erat
ive
proc
ess,
the
larg
est t
riang
le’s
di
men
sion
was
co
ntin
ually
di
vide
d to
in
tuiti
vely
gro
w
stru
ctur
e,
The
resu
lting
fo
rm b
rings
fo
rth
an id
ea
of s
ectio
n m
ultip
licity
that
co
uld
port
ray
a al
tera
tion
and
itera
tion
thro
ugh
time,
as
wel
l as
self-
sim
ilarit
y an
d re
curs
ion.
58
The
Koch
Sn
owfla
ke
Curv
e w
as u
sed
to g
ener
ate
the
exte
rior
and
inte
rior
tect
onic
stu
dy.
The
exte
rior o
f th
e m
odul
e is
on
iter
atio
n 1
whi
le th
e in
side
is
on
itera
tion
3, il
lust
ratin
g
Solid
fold
ing
plan
es
embo
dy
dens
ity a
t th
e to
p an
d bo
ttom
of
the
mod
els
inte
rior.
M
embe
rs o
f st
ruct
ure
give
th
e fe
elin
g of
op
enne
ss a
nd
perf
orat
ion.
60
Recu
rsio
ns o
f tr
iang
les
grow
s fr
om t
he g
roun
d pl
ane
and
upro
ots
the
sim
plic
ity o
f a
thre
e di
men
sion
al,
Eucl
idea
n re
ctan
gle.
Thou
gh th
e ite
ratio
ns o
f tr
iang
les
are
smal
ler i
n si
ze
and
built
with
lig
hter
str
uctu
ral
piec
es, t
he
inte
rcon
nect
ion
of th
em
tran
sfor
ms
a si
mpl
e sp
ace
and
pote
ntia
l es
tabl
ishe
s a
sett
ing
of s
patia
l ha
rmon
y.
62
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 char-coal 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 mod-els 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 char-coal sticks, stretching the mediums potential between two states of viscosity. Fi-nally, 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.
64
66
68
70
72
74
76
78
80
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.
ProgramProgram was abstractly based on Bernard Tschumi’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.
SiteThe 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. TectonicsModels 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.
Conclusions: Discovery
82
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 con-ceived 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.
Un-Doings
84
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 po-tentials, 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 poten-tially 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 op-posite 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 build-ing 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 knowl-edge? 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 qual-ity, 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 struc-ture. 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 ge-nius loci of Bryant Park and the Manhattan Machine.
Transition:Translation:Transcendance
86
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, expand-ing 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 be-come a truth. A dream from which there is no waking up.
88
“thus surrounded, this monster bookcase becomes, architecturally, the heart of the whole structure, the treasure for whose protection this marble palace is built” -Times, 1905How 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.
Wandering through Knowledge, Perception, and Existence: Abstract
90
92
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 myster-ies 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 com-pletely 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 com-plexity that no human could ever attain. The exploration of the space and form of knowl-edge could seemingly take many forms so maybe confining it to one building/form/shelf is an oversimplification.
94
96
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.
98
100
Open Heart Surgery
Excerpt from New York Times 1905...
“ ...In the New York Public Library. Here it stands, one huge square, in a cham-ber 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 be-comes, architecturally, the heart of the whole structure, the treasure for whose protection this marble palace is built.”
102
104
Time..May 20thFor 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 1905There 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.
InterludeHe 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 dis-sected 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 Lightman’s Einstein’s Dreams.
106
108
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.
110
112
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
114
116
118
120
122
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 water’s life through the cavernous realms of incessant
...Existence
Space
124
Steps
Drawings
Days
Moments
Plains
Realizations
Manifestations
Designs
People
Lives
Architectures
Ideas
Realities
Times
Lines
Lives
Deaths
7
126
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
Born
128
130
132
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...
Genesis...-I-...Exodus
134
136
Live On nO Evil
Tree 1,000 facesWisdom beyond my story gnarled mouths transport I in land of terrorKindness, wrinkled facesthe bringing, meadows bliss-full carpetsdark green moss, Serenecaressing twistedlyBark hardun-controllable scarringf u r i e s. . .Birth unto me free-doms Speak through metruth WindsSteps , from single cells prison railsuntouched nudesuntil openingsc r a c k sr e v e l a t i o n i l l u m i n a t i o nbetween creation and freedom wont werealize! . . . that eachm i r r o r sto the other?. . .curtains part excitedly obsessively with Vital existencel i f esweeping colorswarmth of Knowingsheen truthalighting gently as though the bird of timefroze in flight, on skies pure white, positioned rightintrinsic sight
138
140
142
144
146
148
150
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 hap-pened.
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 archi-tectural 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 envi-ronment 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 Man-hattan, 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.
152
Appendix1. 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 pleth-ora 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 mathemat-ics 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 ap-plied 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 (com-parable 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
154
Appendixusing 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 architec-tural 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. (Washing-ton, DC: Island Press, 2005). Stephen R. Kellert’s book Building for Life: Designing and Understanding the Human-Nature Connec-tion, 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).
