The Triangle of Sierpinski Variation

What I am showing here is my artistic variation of the Sierpinski Fractal.

The Sierpinski triangle, also called Sierpinski gasket or the Sierpinski Sieve is an autosimilar fractal of a mathematically generated pattern with (but not necessarily) an equilateral triangle. The midpoints of each side are connected to form four separate triangles. This operation forms the triangle in the center. The same operation has to be iterated infinitely inside each remaining triangle. The pattern, per its property of autosimilarity can be reproducible at any magnification or reduction.

The generation of this fractal with non deterministic algorithm, has very interesting results.

Poster SI DIPRO Morfología Urbana y Diseño Fractal Sept.2009

Poster on fractal Urban Morphology by Myriam Mahiques. Exhibited at SI DIPRO, FADU, XXIV Jornadas de Investigación: Didáctica del Proyecto / SI+DIPRO y VI Encuentro Regional de Investigación September 10-11 2009.

This is the poster that represented the research of Fractal Urban Morphology in the Laboratory of Mathematics and Design of Faculty of Architecture, Design and Urbanism of Buenos Aires. The abstract is posted below in the original Spanish. I am willing to provide a translation in English if required.

Desde que los diseñadores urbanos analizaron a la ciudad organizada como un organismo biológico que podía ser interpretada con nuevas herramientas conceptuales, una nueva teoría dentro del fisicalismo epistemológico y el organicismo fue desarrollada dentro de la teorías de sistemas complejos y caos, cuya resultante geométrica son los fractales aplicados en la creación de modelos matemáticos. Nuestra polifacética disciplina, nos permite tomar de otras disciplinas aquellos conceptos que nos ayuden a investigar en pro de un diseño urbano adecuado.

Bajo estos conceptos teóricos, presentamos nuestro avance en la línea de investigación Morfología Urbana y Diseño Fractal, dentro del Laboratorio de Matemática y Diseño de la FADU dirigido por la dra. Vera de Spinadel.

El modelo matemático es una representación de los aspectos esenciales de un sistema, de un hecho o fenómeno del mundo real. El objetivo del modelo es entender ampliamente el fenómeno, analizarlo, y en base a los resultados arrojados por los softwares predecir su comportamiento futuro. Nuestra investigación comenzó con modelos matemáticos aplicados a morfologías urbanas en el barrio de la Boca, con la expectativa de analizar cómo los inmigrantes italianos, según su cultura y necesidades le habían dado forma.

La investigación siguió desarrollándose y aplicándose en barrios latinos del Sur de California, de los que contamos con un extenso material de primera mano. Los pasos a seguir para elaborar el modelo propuesto son los siguientes:

1) Tomar una problemática en el mundo real

2) Aplicar nuestra experiencia en el momento de realizar evaluaciones

3) Aplicar softwares

4) Seleccionar el modelo adecuado

5) Establecer comparaciones con otros modelos

6) Comparar los datos y arribar a conclusiones.

7) Considerar posibles predicciones de forma urbana
Los tipos de modelos matemáticos pueden variar y nosotros hemos propuesto superponerlos para lograr involucrar una variedad de estructuras abstractas que servirán a los fines de proponer futuros diseños urbanos. Durante la experimentación, hemos aplicado softwares como DLA, Cellullar Automata, caminos de percolación, y otros basados específicamente en modelación de fractales artificiales, a fines de evaluar las formas urbanas originadas por la comunidad y su evolución en el tiempo.

Labyrinths Concepts

Sun and the Petroglyph. Digital collage by Myriam B. Mahiques. Here, my interpretation of the built labyrinth in the analogy of the stone plus the oniric space in the attractor. 2009.

Labyrinths have been built in several cultures in all continents, archaeologists have traced them back some 4000 years ago; there is also speculation that this symbol dates back to the Paleolithic period (20000 BC) in prehistoric rock art. It is sustained in a universal pattern of disorientation, with a psycho-somatic quality that triggers our experience. Its meaning is expressed in both conscious (architecture) and unconscious levels (memory and experience). Bernard Tschumi appropriates the figure of labyrinth to explain that it concentrates on the senses, on the experience of space, as well as the relationship between space and practice; the morphological opposite is the pyramid, with its shape variations implies the dematerialization of architecture.

The labyrinth or maze is a good analogy to describe some cities with morphologies of fractal patterns. More than the geometrical pattern itself, city is a labyrinth only to the activity of unwitting users. Some cities are the realization of this ancient human dream in the impossibility to conceptualize and experience space at the same time; though sensations and feelings are enhanced, there is no way to know how to get out of them. In ancient cities, the analogy is seen in the network of paths and corridors of its tangible construction, but in modern city, it refers to the attraction and fear that they transmit. In both cases, the same psychological state is produced: confusion, disorientation. In this sense, as stated by Walter Benjamin, the modern citizen becomes a Theseus inside the Minotaur’s labyrinth.

Bartolomo Veneto, "The Man and the Labyrinth" http://www.endicott-studio.com/rdrm/rrLabyrinths.html

The most known labyrinth is the seven circuit type. The author of “Through the labyrinths”, Herman Kern, speculates that it has been originated in the Neolithic period, in celestial observation rituals where the psychic structure created a disposition towards dancing and movement to a central point; or possibly in cave cults in which the winding natural caverns symbolized the bowels of Mother Earth. Nevertheless, Henri Lefebvre, states that the labyrinth was originally a military and political structure designed to trap enemies inextricably in a maze; it served too as a palace, fortification, refuge and shelter before coming to stand for the womb (Lefebvre, p. 233). Movement has to be considered independently of the graphical motif. Kern suggests that the path consisting in seven circuits has a cultural and anthropological connection; the inner path, then the outward circuit with a central point to be reached and departed from, has an implicit metaphor in the path through life to death to rebirth; the circle is an universal symbol representing the wholeness.

Greek myth of Perseus and the Minotaur [Medieval rendition] web.rollins.edu/~jsiry/healthofPlace.html

This is a true Theseus’ labyrinth of a single path, with no dead ends to deceive the explorer, it leads directly to the center, then from the center, one makes its way to the exit. The point is to have the Minotaur at the Center and “the terror comes in because you don’t not know where you will come out and see what the Minotaur will do….Then there is the mannerist labyrinth. If you unravel it, you find in your hands a kind of tree, a root-like structure with many dead ends. There is only one exit, but you can get it wrong. You need an Ariadne's thread to keep from getting lost. This labyrinth is the model of the trial-and-error process. Finally, there is the network, the structure that Deleuze and Guattari call a rhizome. The rhizome is set up that each path connects to every other one. It has no center, no periphery, and no exit, because it is potentially infinite.” (Umberto Eco). In botany, rhizome is a subterranean horizontal stem of a plant sending out roots and shoots from its nodes. In philosophy, Gilles Deleuze and Felix Guattari used the term “rhizome” to describe the theory that allows multiple, non hierarchical entry and exit points in data representation and interpretation. It is very difficult to see the extinction of a rhizome, as a new one is always emerging. It would be a maze, instead of a labyrinth, the maze is more complex, it presents choices among alternative routes, some of them are deliberate dead-ends.

Piranesi's drawing. http://www.blogger.com/feeds/4854605417962288462/posts/default

Labyrinth in a garden.goldenagegardens.blogspot.com/2008_09_01_arch...

In landscape, the labyrinth means an intricate network of pathways, usually enclosed by tiny bushes, in which it is not possible to visualize the center. Nowadays, this design has experienced a revival of the old geometrical style of gardening, as a “healing walk” that helps in humans emotional stability; the person needs to walk, to immerse in it and search for the center, because it is impossible to grasp its whole entirety in just one look.

Currently, there are labyrinths in prisons, drug rehabilitation centers, medical facilities and of course in domestic gardens. Once inside them, rational conscious orientation is disturbed, the initiate temporarily loses his way in confusion to enter in the Nature dimension.

Ideas for the experience of the labyrinth in an outdoor environment are: approach and curiosity of enter; path in an uni-cursal way; interruption for meditation; final destination; return that evokes memory and sense. (Hollis Vellenga, Amber.2001)

Considering labyrinths are intermediaries between reality and oniric fields, and they are so close to the idea of motion and universality, I will end with a beautiful example in an excerpt of Invisible Cities, by Italo Calvino:

“after six days and seven nights, you arrive at Zobeide…with streets wound about themselves as in a skein. They tell this tale of its foundation: men of various nations had an identical dream. They saw a woman running at night through an unknown city; she was seen from behind, with long hair, and she was naked. They dreamed of pursuing her. As they twisted and turned, each of them lost her. After the dream they set out in search of that city; they never found it, but they found one another; they decided to build a city like the one in the dream. In laying out the streets, each followed the course of his pursuit; at the spot where they had lost the fugitive’s trail, they arranged spaces and walls differently from the dream, so she would be unable to escape again. This was the city of Zobeide, where they settled, waiting for that scene to be repeated one night.”

An aerial view of the urban fabric in Fez (Morocco), Tamentit (Algeria) and a village in Saudi Arabia. www.palgrave-journals.com/.../udi20097f1.html

Further readings:

S. McCaffery, S. “To lose one’s way” ,2003
http://74.125.155.132/search?q=cache:7Zhit2OvRwcJ:college.holycross.edu/interfaces/vol2122_articles/to_lose_ones_way.pdf+bernard+tschumi%2Blabyrinths&cd=5&hl=en&ct=clnk&gl=us
http://www.labyrinthos.net/labyrinthstory.html
Hollis Vellenga, Amber. Taking the First Step: The Labyrinth and The World of Landscape Architecture Virginia Polytechnic and State University. Department of Landscape Architecture.2 001
http://scholar.lib.vt.edu/theses/available/etd05302001160852/unrestricted/thesisav.pdf
Lefebvre, Henri. The Production of Space. Massachusetts. U.S.A. 1999

Urban consequences of the 1924 plague in Los Angeles

Los Angeles city dump, 1924. Online archive of California

The plague is an infectious disease of animals and humans caused by a bacterium named Yersinia pestis. People usually get plague from being bitten by a rodent flea that is carrying the plague bacterium or by handling an infected animal. (CDC Plague home page). Three clinical forms of human plague exist: bubonic, pneumonic, and septicemic.

About 10 to 15 people per year contract the disease in the US, usually in rural places, according to the US Centers for Disease Control and Prevention, but now is rarely fatal. Plague was first recognized in the United States in San Francisco in 1900, and appeared in Los Angeles County in 1908. The disease was likely introduced to western United States ports via infected rats and humans who traveled on ships from Asia. In the United States, the last urban plague epidemic occurred in Los Angeles in 1924-25.

By that time, nineteen percent of the residents in Los Angeles were foreign born. There were approximately 2,000 Chinese, 12,000 Japanese, and 22,000, each group settling in different locations. (A.J. Viseltear,1974)

This plague had ethnic connotations. The plague was to be controlled together with immigrants, in a clear form of segregation that was unquestionably understood.

Though historical pictures show many buildings in very precarious conditions, including the public ones, the city health department ordered a quarantine of the “Mexican District”, a downtown section of small homes and industrial sites around Macy Street and near the river.(Deverell, 2005). Many of the structures pictured in 1924 are shacks and other low income residences. Captions identify a "Mexican Village," "Chinatown," and "negro dwellings" in various locations.

Immigrants shacks, Los Angeles 1924. Online archive of California

Mexican shacks, Los Angeles 1924. Online archive of California

“The quarantine, which lasted two weeks, would eventually stretch to include five urban districts. There can be little doubt, given the way in which these neighborhoods were described, by language and by perimeter, that officials perceived an overlap between ethnicity and disease.” (Deverell, 2005). Mexican areas had to be condemned and destroyed, all of them, though the verifiable cases of plague were concentrated in a couple of blocks. The plague had been peculiarly Mexicanized overseeing the rest of inhabitants.

Urban fabric of Los Angeles changed drastically, by plague-fighting design. Poor properties –approximately 2500 units- were demolished or burnt without compensation. The overall plan was a combination of slash and burn destruction and a campaign to lift structures off the ground with blocks, so cats and dogs would be free to hunt the rats under the buildings.

“The men, it was later reported, had to destroy a large part of Los Angeles”. (Deverell, 2005). Buildings were not replaced, so the dispossessed scattered to other parts of the city and county, many of them into other quarters that were unfit for home habitation. It would affect the existing neighborhoods for long years.

Burning of a Mexican Village, Los Angeles, 1924. Online Archive of California

Wrecking of China Town in Los Angeles, 1924. Online Archive of California

Wrecking shacks in Los Angeles, 1924. Online Archive of California.

One contemporary report read, Mexicans, unlike Orientals, did not attempt to hide their dead. When seriously ill, they called a priest and were prompt in securing medical aid. What proved to be lucky for health authorities, as they knew about the death toll from the beginning. The irony in the report is that the mere Mexican practices, would help the disease transfer, what was also reinforced by cultural habits as to visit relatives and friends during their illness.

Health authorities also agreed that Mexicans should not be permitted to live next to food industries, even though they were the ones doing the work in these industries.

The description of Mexican districts were no more than captions on the pictures. It became obvious that immigration was increasing with the logical consequences of overcrowded rooming houses and shacks construction at the backyards.

This terrible malady is expressed as a social and cultural phenomenon; it is related with the organization, way of life and configuration of the urban space. Its ecological impact generates adaptive strategies in the inhabitants and community organizations, new immigrants displacements, and reviews of religions beliefs that justify these changes.

Further readings:
Online Archive of California
http://www.oac.cdlib.org/ark:/13030/tf8n39p67d/?brand=oac4
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2595158/pdf/yjbm00152-0044.pdf
Deverell, William. Whitewashed Adobe. The rise of Los Angeles and the remaking of its Mexican past. University of California Press, 2005.

González, Andrea S. “El impacto de la enfermedad en la organización social y el espacio urbano El caso de la epidemia de fiebre amarilla en la Ciudad de Buenos Aires en 1871” en Revista Medicina y Sociedad.No2-2001. También on line, 2001

http://www.medicinaysociedad.org.ar/publicaciones/publicaciones2001/ElimpactodelaenfermenlaorgsocialRev2de2001.doc

Evolution or Regression (?) of Organic Architecture

This picture belongs to a competition I participated with my partner arch. Luis Makianich, " Proyecto Utopia", in 1989. It is an Utopian city, where the buildings grow as organisms. They were feeded by a cyclotron. We had a second award. Personal files.

There could be a dialogue between past and present architectures. This dialectic exists in particular situations in history.

Frank Lloyd Wright introduced the word “organic” in 1908, as part of the philosophy of architecture. Organicism was an interpretation of Nature, a guide for the design process, by looking at Nature’s principles, harmony between human constructions and Nature would be promoted. It was an answer to industrialized cultures, a resistance to science and technology but not a rejection to them. Buildings were considered as organisms in themselves. The organism would include urban planning, the building, furniture and surroundings. It is important to point out that this philosophy does not mean imitation of Nature, forms would never copy the morphologies found in it. Organic architecture was an element of social reform that involved concepts of organic society and organic economic systems: the universe as a whole organism.

Overtaken beliefs of inhibited tradition of decades of '20s to '50s, where architectural demonstrations had components of a mystical fundamentalism to dominate the masses, we face the new theories of the 60s, where most of the studies were not based on history, although they considered the existence and distribution of historic buildings; architects shared with Le Corbusier's the idea that architecture could socially transform to men and should reflect some ordering principles of nature. This idea of considering the architecture underlying a cosmic scale, is expressed as "metaphysical school" and its leader, Louis Kahn, in 1960 defined what "the building should be": The order is intangible, while organic architecture was a total break from the association of order and geometry. The most prominent critics of this position were Kevin Lynch, Christopher Alexander and Jane Jacobs, who urged a more humane approach to urban planning, based on information of what happens in cities. Alexander was the first one to incorporate mathematical concepts in his studies, realizing that the city was a complex organized in the manner of a biological organism.

Over the last three decades there has been new developments in organic architecture. Though it is difficult to recognize where the organicism lies…

The organic analogy is not based on biological science, but rather in the shapes, the metaphores and the ecological analogy, it means the adaptation of the building to its environment. We find zoological and botanical allusions; there is a “zoomorfic” architecture, a botanical architecture assisted by softwares that mimic the biological evolutions, we also find organicing principles in Nature, as the Fibonacci series and the spiral habits of shells (P. Steadman, 2008), or fractal patterns. In general, these designs are connected to green (environmental) architecture. The main critic for botanical and zoological mimic is that these buildings are ruled by the form, but do not work as full organisms do.

Nautilus by Senosiain architects. http://unusuallife.com/category/outrageous-architecture/

Plantis. By Elena Pavlidou. 2007. From worldarchitecture.org.

The design process follow six tendencies:

1) Composition that works from inside-out. The designer takes into account the user’s needs, the program. The organic form grows and develops out of the material. Forms is not imposed a priori, it is discovered by the future users’ goals and the environment. The client is usually involved in the process, even in construction.

2) A more universal tendency is the rejection of the Euclidian forms by accepting curvilinear and “organic” shapes. This is the reverse of the composition from inside-out. The architecture is originated in the form, function follows it. The designer refers explicitly not only to the shapes in nature, he also incorporates the local terrain. There is a desire for continuity, rooms have no boundaries and spaces are overlapped. (Biodynamism).

3) An intermediate option is organic but not essencialy an anti-functionalist one. The analysis of the users’ program and the properties of materials result in non orthogonal shapes, for example when using branches, stones, bamboo. Though, bricks can also be used, hanging from a steel frame. If steels usurped the forms produced by bricks, the product would be a conceptual hybrid.

4) Designs that reflect the desire to live in a rural way of life, in harmony and contact with Nature, as a rejection to global cities. House and landscape interpenetrate, boundaries between them become indistinct. (P. Steadman, 2008). Rocks, water an trees could be incorporated inside the structures.

Window looking like an eye. www.simondale.net/house/intview.htm

5) Biomimetic technology. Designs where Nature is implicit, but only in the substance of their component materials. For instance, goats raised by Nexia Biotechnologies in Montreal, have a spider gene that produces the protein of spider silk, developed in their milk. This protein is being used in a new fiber that is five times stronger than steel. It would apply in sutures and then in the construction industry. (National Geographic, January 2003) “Life has had millions of years to finely-tune mechanisms and structures (such as photosynthesis, or spider’s silk) that work better than current technologies, require less energy and produce no life-unfriendly waste. The emulation of this technology is the goal of biomimicry, the art of innovation inspired by nature.” (Holverstott, Brett. What Can Architecture Learn From Nature. GreenBizSite. September 7, 2008).

6) Organic architecture that embodies the human spirit, it goes beyond the minimum shelter, it has to be something that enhances human lives. It is the theoritical idea of the seed, landscape and spirit. And it reminds me the whale bones dwellings in the Artic, all of them embeded with religion and symbolism. It is like returning to the origins. The result produces original forms. In this sense, there is a close connection between the new organic architecture, land art and Natural architecture.

Land art, Earthworks, or Earth art is an art movement which emerged in the United States in the late 1960s and early 1970s, in which landscape and the work of art are inextricably linked. Sculptures are not placed in the landscape; rather the landscape is the very means of their creation. (wikipedia.org). Land art is a different appreciation of Nature, to be understood as a protest against the austerity of the gallery and commercialization of art. Now, it is also focusing on “environmental” art, in order to offer a new understanding of the place in which we live. And Natural architecture is an emerging movement that is exploring man’s desire to reconnect to the earth, through the built environment. It is a link between man and nature, a new appreciation of Nature that combines Art and architectural design, by means of activism but no protests. The results, often resemble Indigenous architecture, though without the primigenius symbolism.

Natural Art-architecture. 'weidendom' by sanfte strukturen, 2001 http://www.designboom.com/contemporary/naturalarchitecture.html

Natural Art-architecture. 'toad hall' by patrick dougherty, 2004 http://www.designboom.com/contemporary/naturalarchitecture.html

Ideas seem to be the same at this point, but, after all, primitive huts made by whale and mammoth bones and-or trees were built with cosmological principles and cultural ideologies that have played an important role in primitive dwellings patterns, as they show traditions and myths. Maybe instead of evolution of organicism, architects and artists have a regression to the primitive roots. There is too much we can learn from Nature: systems, materials, processes, structures and aesthetics. It is a matter of choice.

Further readings
http://sensingarchitecture.com/1374/biomimicry-architecture-inspired-by-nature/http://www.designboom.com/contemporary/naturalarchitecture.html

Frank Lloyd Wright and the Principles of Organic Architecture. By Kimberly Elman
http://www.pbs.org/flw/legacy/essay1.html
Holverstott, Brett. What Can Architecture Learn From Nature. GreenBizSite. September 7, 2008
B. L. Powel http://etd.lib.ttu.edu/theses/available/etd-08252008-31295012212030/unrestricted/31295012212030.pdf
Steadman, Philip. The evolution of designs: biological analogy in architecture and the applied arts. New York, 2008

Urban Image Analysis through Perception

Facades in La Boca, Buenos Aires. See the cables, wires, hanging clothes. Personal archives.

A lot has been advanced in the possible representations of a city, and the most significant changes have arisen in the abstraction of images that represent the complex urban phenomena with a simple reading: the development of Google Earth of public and free access, improved satelital images, digital images in general. The whole access to information that we are allowed, added to the multiple digital tools, makes us reconsider which is the best visual way of analyzing the city.

Although the urban image is fundamentally built with elements studied as objective realities where the researcher supposes the urban fabric as the only geometric constituent of form, we intend to speak of sensitive experimentation, keeping in mind all the senses. The tact, related with the vision, the sounds and aromas, contribute to the apprehension of the materiality, its distances and depth, everything possible thanks to the cooperation of the haptic memory.

¨Perceptions are framed by experience and motives, and therefore images and symbols play an important role in sharing thought and action. It would be foolish to claim that all studies of ¨objective¨ morphology ignore human agency, but such studies certainly have tended to leave human action implicit in the results…¨. (M. Conzen, p.10, 2001)

An authentic experience of the city consists then, in the approach and confrontation of the building; in the act of enter and look through a window more than the window in itself; to occupy the space of cold-heat, instead of examining objects that produce it. The lived space always transcends the geometry and mensurability (J. Pallasmaa), and the understanding that the space outside the building is used differently from the interior space, will conform a transition area that is a representation of the dependence among internal and external areas.

Humans take the information of the built environment and understand it according to their own cognitive capacity and their point of view of models of interactions in the real world. Therefore, the resultant is IMAGE PLUS BEHAVIOR. What suggests that the urban images we analize, will include a logic of image with all its plastic-geometric attributes and a social intrinsic behavior that responds to the social group.

In facades, it is recommendable to utilize pictures that reflect the user's real perception, not by means of individual elements, but as a systems of configurations of great richness of shapes. The researcher-designer will also contribute his knowledge to interpret what is visually significant for the user; the elements that the users have incorporated along the history, should be considered like inseparable part of the building to analyze.

So, we are joining here the concepts of OBSERVATION AND PERCEPTION.

This is an interior patio of a "conventillo" in La Boca, Buenos Aires. Notice again, the repetitive elements: wires, water pipes exposed, clothes. Personal archives. 

This is the Fourier transform corresponding to the patio above. The Fourier transform application has the quality of showing hidden patterns. Notice the repetitive elements are clearly exposed in the Fourier analysis. Personal archives

It might be questionable then, if we speak of perception, how many elements we will include in our image cutting. In my work on La Boca immigrant neighborhood, Buenos Aires, I have proceeded to analyze pictures of the area through the years. The pictures from the museums and those of conventillos interiors published in "Todo es Historia" (Everything is History) by Félix Luna, show the same domestic praxis until the present time, to hang clothes crossing the patios; addition of strings or wires to cables of illumination, exposed water pipes, etc. This demonstrates the users's intentions that have taken root in the time and were included in my considerations.

Overpopulation in cities: John Calhoun´s experiment with rats

That´s terrible overcrowding in India. apublicdefender.com/.../page/2/

Asian overcrowding. nerdnirvana.org/tag/building/

Overpopulation is a term that refers to conditions by which the population density enlarges to a limit that provokes the environment deterioration, a remarkable decline in the quality of life or a population collapse. (Nasif Nahle, 2003). It has a detrimental effect on people; it is the cause of the destruction of natural habitats of many animal and vegetal; people die more and more from illnesses associated to organic and inorganic wastes; water, will be desperately needed….

Some social and psychological consequences are: tendency to dominate spaces; violence; depression, anxiety, emotional stress, quarrels in families and among neighbors; early marriage and divorce; incest, school drop outs.

Many years ago, I have seen an impressive documentary film about rats and overcrowding in comparison with humans –laboratory animals are a good substitute for humans in hazardous environments-; the documentary was based in the ecologist John B. Calhoun´s experiment with Norway rats. And, to my surprise, I found its complete explanation in Edward T. Hall´s book ¨The Hidden Dimension¨. This is the experiment, and conclusions for urban overpopulation are obvious.

A funny (?) overcrowding cartoon. www.wfsd.k12.ny.us/.../Page651.htm

The research began at Johns Hopkins in 1946 and continued through the '60s, when Calhoun, then a research psychologist, initiated his studies of population dynamics under natural conditions, in a disused land in Towson, Maryland, by introducing five pregnant Norway rats in a quarter acre outdoor enclosure with plenty of food and no predation issues. He observed them for 28 months. The population expanded to conform a ¨rat city¨, it never exceeded 200 individuals and at last stabilized at 150, as social fights were so disruptive to normal maternal care, that only a few of the young survived. The point is that female rats, in a natural environment could have produced 50000 progeny in 28 months, but available space could not have accommodated this number.

Rat´s pen.nihrecord.od.nih.gov/.../07_25_2008/story1.htm

Calhoun´s behavioural sink, 1970. Wikipedia.org

These animals grew up in confinement, for generations, without the ability of escape or migrate to a frontier. They developed social pathologies similar to humans in overcrowded cities or settlements (let us think about slums). Behavioral disturbances reached the levels of deadly fights, sexual deviation and cannibalism.

In response to invasion and the large number of males, females became aggressive and this attitude generalized to their baby rats. And so became the beginning of mortality. Overcrowding produced dramatic results ranging from aggression to many forms of abnormal behaviour, to mass die off.

Calhoun's goals are unusual because psychologists conducting this type of research, mostly apply to individuals and not social groups. Calhoun´s work remains unfinished; they should continue to produce new insights. His experiments could include a frontier or many frontiers, as this is the case of refugees and immigrants in real life.

References.
All this text is based on chapter III of The Hidden Dimension by Edward T. Hall, including some sentences.

Further reading:
Winn, Larry. Universe 25. September 1998
http://www.suite101.com/article.cfm/frontier_theory/10037
Nahle, Nasif. Overpopulation. Published on 10 November 2003 by Biology Cabinet Organization. http://biocab.org/Overpopulation.html.

Architectural Space in the Gothic Novel

Castel of Otranto.www.tate.org.uk/.../heimozobernig/exguide8.shtm

YOU, WHO are blessed with shade as well as light, you, who are gifted with two eyes, endowed with a knowledge of perspective, and charmed with the enjoyment of various colours, you, who can actually see an angle, and contemplate the complete circumference of a Circle in the happy region of the Three Dimensions - how shall I make clear to you the extreme difficulty which we in Flatland experience in recognizing one another's configuration?(Abbot, Edwin A., Flatland. 1884)

The interest of the authors of Gothic novels about the symbolic or allegorical space was founded in Christian roots that sustained that the spirit prevailed on the matter. In theory, they were seeking for physical, moral, and spiritual analogies. However, the analogy was not already between God and the Nature, but the man and the Nature. In this process, the objects represent psychic questions and moral problems.

It is therefore explained that in the atmosphere of the Gothic novel, the man is connected to the space atmosphere, immersed in the psychic or moral conflict developed along the text. From my point of view, the most explicit exhibitor of these concepts is Edgar Allan Poe.

It is important to highlight that the Gothic architecture arose before the homonymous literature. Horace Walpole was the first one in combining both in his book ¨The Castle of Otranto¨ that takes the subtitle ¨A gothic story¨, where two interdependent speeches, that of the literature and the architecture, take place.

Starting from the book of Walpole, the space of the Gothic fiction has been represented with castles, monasteries, convents, prisons, often in ruins, in a dark landscape.

The materialization of the atmosphere takes advantage of the size of these buildings, so overpowering for the human scale, the interiors are shown dark, cavernous, labyrinthine, invoking feelings of fear, surprise, confinement. And beyond these characterizations, the building is physically alive - still more than its inhabitants -.

Roger Corman, director and producer of ¨The Tomb of Ligeia¨ recalls that in a meeting with the producers Nicholson and Sam Arkoff, while they discussed the project of 'The fall of the house Usher', Arkoff asked him:

- "But, and the monster? ".

- "The monster is the house", he responded. (from ¨El Mundo.es¨. Cultura. On line).

The internal conflicts are transferred to the spaces and the objects, they are incorporated to them, and at the same time, in a continuous cycle, the space materialization generates the psychological conflicts of the characters.

The interest in the non rational experience, was a Romantic reaction against the hard rationalism of the SXVIII that evolved in two ways, one in the search of the spiritual reality, and the other one in the personal and social exploration of the personal subconscious of the characters, hopelessly attached to the world of the memory and dreams, many times induced by the opium.

The symbolic character is shaped in the psychology and the reader's imagination, who is submitted to the ¨first person¨ narration; then, metaphors are apprehended and transformed in symbolism.

In his Philosophy of Composition, Edgard Allan Poe provides a reason for this attitude, when explaining the main character's location with the crow, not in the forest (that would be a more natural suggestion), but in a chamber:

"that a close circumscription of space is absolutely necessary to the effect of insulated incident: -- it has the force of a frame to a picture. It has an indisputable moral power in keeping concentrated the attention, and, of course, must not be confounded with mere unity of place.

I determined, then, to place the lover in his chamber — in a chamber rendered sacred to him by memories of her who had frequented it. The room is represented as richly furnished —"

Notice the importance that has been given to the incorporation of furniture whose form, color, magnitude, are expressive in themselves. They can force the atmosphere so that it seems strange or normal, threatening, familiar. The pure ornament becomes in a new dramatic form; the interior space is emphasized in disregard of the exterior. The sounds, the movements, the lights and shades supplement the creation of the disturbing atmosphere; the optic games are caused by the decoration, to such a point that is difficult to separate the illusions of the hallucinations.

Shot of the movie ¨The Tomb of Ligeia¨, 1964. Representation of the threatening, tenebrous atmosphere, through the color and the objects. Web download.

We, architects, use different representations to communicate an idea, a design, a description. Among them, descriptive memoirs, perspectives, sketches, drawings. In general, the visual aspects are shown, but it is very difficult to transmit the phenomenological effects of the architecture previously described.

To express the concepts of the Gothic architectural space better, I have selected the movie ¨The Tomb of Ligeia¨ that was filmed for the first time in 1964, performed by Vincent Price, directed and produced by Roger Corman, as the last of a saga of low budget movies based on stories of Edgard Allan Poe. Although Corman shows a technical advance in ¨The Tomb of Liegia¨, since he also uses shots in the exterior, the scenarios were basic, they were adapted for several movies and the fog used to cover the similarity among scenarios of the saga .

Picture of the preliminary images in the movie ¨The Tomb of Ligeia¨, 1964. It belongs to Castle Acre Priory Ruins. http://farm4.static.flickr.com/3215/2895421716_91dc090f66.jpg?v=0

In his book "Vincent Price: The Art of Fear¨, Denis Meikle quotes the actor, who took some of the credits of the unusual film set: “The Tomb of Ligeia was vaguely based on an idea that Roger and I had once. I had said I had always wanted to do a picture in a ruin, but actually using the ruin as an actual place, with real furniture in it and the ruin around it, which I thought would be very effective¨. (TMC Archives. http://www.tcm.com/tcmdb/index.jsp.) The movie was filmed at an Abbey in Norfolk, England. Perhaps Vincent Price has captured the atmosphere of the architectural space of the story, I understand his proposal of set, like a coalition among the place in ruins and the furniture, where the furniture is indispensable part of the architecture of the pentagonal tower, it transforms it, giving it the final character and form.

A shot of the movie ¨The Tomb of Ligeia¨. Vincent Price and Elizabeth Shepherd. 1964. Notice the decorative elements of the set, behind them. http://movies.sky.com/review/the-tomb-of-ligeia

The ornament of arabesque in the curtains and covers was another device to relate the Nature with the geometric abstraction.The structure of arabesque consists basically on a stylized leaf with its petiole, to which it is inexorably tied. In the Gothic novel, the petiole forks ad infinitum. In this respect, let us notice that Poe mentions the Greek philosopher Democritus (460-370 BC) who speculated that the whole matter of the Universe consists on atoms (indivisible matter) that move everywhere. The allusion of Poe is a clear reference to the expansion to infinite.

Once the ornamental outline of the furniture is exceeded, we focus on the small scale, that not for being small is innocent, but rather it expresses the summum of the anguish and the terror, since the decoration becomes indivisible part of the oniric images and hallucinations. With these methods, it is achieved an intensification and dramatization of interpersonal relationships, between the man and the architecture (or rather space) that surrounds him.

In the symbolic space of Gothic novels, the aesthetics of the Renaissance perfection, that of the normative speculation and the symmetrical resultant, -banner of classic beauty-, is left aside . It faces the concept of ¨without geometry there is no truth¨, because in fact, there is geometry, but a different geometry, that is not summarized in the anatomy and the focal perspective, but has other more complicated and darker roads. And, perhaps Poe is correct when quoting Bacon: ¨There is no excellent beauty that hath not some strangeness in the proportion¨

REFERENCES
- Abbot, Edwin. Flatland, a Romance of Many Dimension.
- Gordon, Rae Beth. Poe: Optics, Hysteria and Aesthetic Theory
http://www.cercles.com/n1/gordon.pdf
- Hoffmann, Gerhard. " Space and Symbol in the Tales of Edgar Allan Poe," from Poe Studies, vol. XII, no. 1, Washington State University. June 1979 http://www.eapoe.org/pstudies/PS1970/P1979101.HTM
- Poe, Edgar Allan. The Philosophy of Composition. 1846
http://www.eapoe.org/works/ESSAYS/PHILCOMP.HTM
- Stamps III, Arthur E.; Krishnan V. V. Spaciosness and Boundary Roughness.
- Stein, Mandy. The Use of the Arabesque in Edgar Allen Poe’s Short Stories “Ligeia “and “The Visionary“ Scholarly Paper, 2007
http://www.grin.com/e-book/119284/the-use-of-the-arabesque-in-edgar-allen-poe-s-short-stories-ligeia-and