Is the set of Mandelbrot discovered or invented?

Set of Mandelbrot

As you can see in my CV, my line of research is Fractal Urban Morphology. That´s why I´m so interested in fractals. I´m still reading Pi in the Sky, by John D. Barrow and I´ve already ordered The Artful Universe, same author, it seems promising to me.

Well, in Chapter ¨Footsteps through Plato´s footnotes¨ Barrow says that Pythagoreans began to see things solely as numbers, that are immanent property of things; that is numbers are ¨in¨ things and cannot be separated or distinguished from them in any way. As  a contrary point of view, I read that Plato maintained that we discover the truths and theorems of mathematics: we do not simply invent them; for him, mathematics is an  (wonderful) example of a particular form of knowledge that owed nothing to the process of human recognition.

Then, in chapter ¨The Platonic world of mathematics¨ (p. 261), Barrow says that the most famous exponent of Platonism was undoubtedly Kurt Gödel. And, what ´s more important for me ¨Most recently, the belief in ¨Pi in the sky¨ Platonism in mathematics has  been forcefully restated by Roger Penrose who uses the example of the intricacy of structure displayed by fractals like the Mandelbrot set, which he claims ¨is not an invention of the human mind: it was a discovery. Like Mount Everest,... it is just there¨, to argue that this bottomless structure is not invented by the mind, rather,

though defined in an entirely abstract mathematical way, nevertheless (it has) a reality about it that seems to go beyond any particular mathematician´s conceptions and beyond the technology of any particular computer... it seems clearly to be ¨there¨, somewhere, quite independently of us or our machines.¨ (P.262)

Above, the set of Mandelbrot and three variations. All fractals generated by arq. Myriam Mahiques

Vertical gardens in Mexico

I remember many years ago, when the newspapers published that Mexican women traveled to the country to give birth to their babies, because of the terrible pollution in the City.

At least, some effort is shown to find a solution. From New York Times, by Damien Cave:

 “We must cultivate our garden,” Voltaire famously wrote at the end of “Candide,” but even he could not have imagined this: a towering arch of 50,000 plants rising over a traffic-clogged avenue in a metropolis once called “Mexsicko City” because of its pollution.

The vertical garden aims to scrub away both the filth and the image. One of three eco-sculptures installed across the city by a nonprofit called VerdMX, the arch is both art and oxygenator. It catches the eye. And it also helps clean the air.

“The main priority for vertical gardens is to transform the city,” said Fernando Ortiz Monasterio, 30, the architect who designed the sculptures. “It’s a way to intervene in the environment.”(.....)

“Both L.A. and Mexico City have improved but in Mexico City, the change has been a lot more,” said Luisa Molina, a research scientist with the Massachusetts Institute of Technology, who has done extensive pollution comparisons. Mexico “is very advanced not just in terms of Latin America, but around the world. When I go to China, they all want to hear the story of Mexico.”

Partly, it is policy. Starting in the 1980s, Mexico’s government created mandates that reformulated gasoline, closed or moved toxic factories, and banned most drivers from using their cars one day a week. More recently, Mexico City added a popular free bicycle loan program and expanded public transportation systems.

The Eco sculpture. Photo by Rodrigo Cruz

Picture from verdmx. com

http://www.nytimes.com/2012/04/10/world/americas/vertical-gardens-in-mexico-a-symbol-of-progress.html?_r=3&partner=rss&emc=rss

Toronto, the first city in North America to require the installation of green roofs

Today I´m sharing an interesting article by Kaid Benfield, published at theatlanticcities.com:

In January of 2010, Toronto became the first city in North America to require the installation of green roofs on new commercial, institutional, and multifamily residential developments across the city. Next week, the requirement will expand to apply to new industrial development as well. Simply put, a green roof is a rooftop that is vegetated. Green roofs produce multiple environmental benefits by reducing the urban heat island effect and associated energy demand, absorbing rainwater before it becomes runoff, improving air quality, and bringing nature and natural diversity into urban environments. In many cases, green roofs can also be enjoyed by the public much as a park can be. Toronto’s requirements are embodied in a municipal bylaw that includes standards for when a green roof is required and what elements are required in the design. Generally speaking, smaller residential and commercial buildings (such as apartment buildings less than six stories tall) are exempt; from there, the larger the building, the larger the vegetated portion of the roof must be. For the largest buildings, 60 percent of available space on the roof must be vegetated. (...) 

The triptych image above was developed by students at the University of Toronto to illustrate changes that could ensue from ten years of progress under the city’s requirements. Prior to the bylaw, Toronto was second among North American cities (after Chicago) in its total amount of green roof coverage.

READ IT IN FULL:

http://www.theatlanticcities.com/design/2012/04/what-cities-can-learn-torontos-green-roof-policy/1846/

The end of ¨New Towns¨ projects in Seoul

This picture by Jo Yong hak of a new town in Seoul looks scary. Even worst it is to know that approximately 48000 houses were demolished in Seoul for redevelopment and only 22000 new units were built.

From The Atlantic Cities.com:

After 10 years, a Korean program that actively tore down older, low-density neighborhoods and replaced them with high-density “new towns” is coming to an end. Seoul Mayor Park Won-soon announced the end of the program, which was intended to help provide housing for the rapidly growing South Korean capital, last week. The "new towns" were initially heralded as a success but quickly fell victim to the global economic downturn. Thousands of Seoul residents have been caught in the crash.(...)

The new towns seemed like a good idea during the real estate boom, with locals in “old towns” clamoring for the redevelopment projects that would grandly increase their property values. But now, most residents in areas that had been slated for redevelopment as new towns would prefer to stick with the old as the financial benefits of redevelopment have disappeared. Indeed, 85 percent of the proposed new town developments haven’t broken ground. Property values, though, are not the only reason the citizens of Seoul have turned against new towns. Many of the new towns have been built so far out into the periphery that it takes hours to commute to the city, where jobs are. And many residents have been priced out of the marketplace, taking buyouts for their demolished homes that don’t come close to paying for new ones in the city.

Keep on reading Nate Berg´s article:

http://www.theatlanticcities.com/housing/2012/02/seoul-ends-failed-new-towns-project/1149/

Urbes opulentas y guetos miseria. De Héctor Pavón

Ciudad artificial en Dubai. Imagen que acompaña al artículo de Pavón

El porvenir urbano ya está escrito, proyectado y construido. Hacia el año 2050, un 70% de la población mundial vivirá en ciudades: un diagnóstico opuesto al que se presentaba cien años antes (1950) cuando sólo el 30% de los habitantes vivía en zonas urbanas. La proyección es del Instituto de Análisis de Mercado Emergente de Credit Suisse. 2009 fue el año en que se cruzó el umbral del 50% y en el que por primera vez hubo más personas viviendo en la ciudad que en el campo. Para 2025 sólo dos de las que serán las 15 mayores ciudades del mundo están en el Primer Mundo: Tokio y Nueva York. En Africa e India se producirán las mayores tasas de crecimiento de la población urbana. 

 “Las ciudades siempre tienen que ver con la tensión y la diferencia. Siempre tienen que ver con el cambio y nunca son estáticas, explica el geógrafo marxista David Harvey, autor de Urbanismo y desigualdad social . El fenómeno de las urbes superpobladas está cruzado por las ciudades dentro de las ciudades. Las que vendrán sólo tendrán variantes visuales y estéticas en torno de un trazado que no se modifica: inmensos barrios pauperizados conviven con fortificaciones herméticamente cerradas. Pobres y ricos de un lado y otro de los muros. La tendencia que comenzó a percibirse en los 70, a concretarse en los 80 y masificarse a partir de los años 90 hizo un corte transversal y global donde no importa la pobreza o riqueza de las naciones. “Cercas, rejas y muros son esenciales en la ciudad hoy en día, no sólo para su seguridad y la segregación, sino también por razones estéticas y de estatus. Todos los elementos asociados con la seguridad se vuelven parte de un nuevo código de expresión de distinción que yo llamo ‘estética de la seguridad’. Este código encapsula elementos de seguridad en un discurso de gusto y los transforma en símbolos de estatus” escribió la antropóloga urbana brasileña Teresa Caldeira en su libro Espacio, segregación y arte urbano en el Brasil . Según Zygmunt Bauman: “En las grandes ciudades, el espacio se divide en “comunidades cerradas” (guetos voluntarios) y “barrios miserables” (guetos involuntarios).

 El resto de la población lleva una incómoda existencia entre esos dos extremos, soñando con acceder a los guetos voluntarios y temiendo caer en los involuntarios”. Del otro lado se hallan las megafortalezas que partieron de barrios cerrados, desarrollaron pueblos privados y que hoy encuentran su clímax en el emprendimiento artificial llamado The world sobre el mar de Dubai. Un conjunto de islas privadas y erigidas sobre el agua que representan territorios del globo. La toma de una imagen aérea da la idea de mapamundi. En Territorio, autoridad y derechos , la urbanista Saskia Sassen observa que hay nuevas ciudades compuestas por enormes territorios que atraviesan el espacio geográfico. “¿Cómo etiquetar hechos como los que ocurren en Africa cuando Arabia Saudita planta ‘su’ arroz en Etiopía o cuando empresarios chinos compran 2,9 millones de hectáreas en el Congo...?” De ese modo, explica Sassen, se generan “territorialidades elementales”, “inserciones” como ocurría en el Medioevo cuando los comerciantes atravesaban los campos de la aristocracia, de la Iglesia para ir de ciudad en ciudad construyendo nuevos espacios geográficos. Richard Sennett está trabajando en el tercer tomo de su tríptico sobre cultura material donde aborda, entre otras cosas, el futuro de las ciudades desde el hombre; analiza las habilidades necesarias para producir y habitar entornos sostenibles. Algo que ya había esbozado en El artesano . Las soluciones urbanas van muy por detrás de los problemas. De todos modos, en la búsqueda perpetua por recuperar el humanismo, se sueña con la ciudad inteligente, descontaminada y al servicio del hombre.

http://www.revistaenie.clarin.com/literatura/Urbes-opulentas-guetos-miseria_0_686331371.html

Renzo Piano´s addition to Ronchamp´s site

Notre Dame du Haut. The new visitors´ center and the nuns convent, designed by Renzo Piano. Photo by Iwan Baan

I´m happy that I had the opportunity to see the work on Renzo Piano in San Francisco, and also, I´ve been at the exhibition of his work at LACMA, the Museum of Art of Los Angeles.

Though, I don´t like his proposal for the City of Los Angeles, in the area surrounding the Museum  -it is said that Piano won the competition because he respected the sponsors´ buildings- :( , I think he has always respected the environment and the landscape. As Michael Kimmelman says in the New York Times article, ¨Quiet Additions to a Modernist Masterpiece¨, humility is a virtue. 

Ronchamp. Grand Opening. Photo by Michel Denancé, Architectural Record

 RONCHAMP, France — Completed in 1955, Le Corbusier’s hilltop chapel of Notre Dame du Haut in this hardscrabble patch of eastern France attracts some 100,000 supplicants each year, architectural and religious. If critics still sometimes blame Le Corbusier for inspiring generations of soulless, cookie-cutter housing projects and office parks, he remains the high priest of Modernism for singular works like this. So it was predictable that a firestorm broke several years ago after plans circulated for a convent and new visitors’ center at the site of the chapel. Renzo Piano was the designer. Big-name colleagues like Richard Meier, Rafael Moneo and Cesar Pelli signed an online petition denouncing the $16 million project. The Fondation Le Corbusier, keeper of the architect’s flame, fumed. Now the buildings have opened, with some landscaping (by Atelier Corajoud, a Paris firm) and a bit of tinkering yet to come. I took a train from Paris recently and found the chapel empty on a bright, crisp spring morning (a godsend), then visited the nuns. They are not quite a dozen elderly Poor Clares, lately moved from their home of 800 years at Besançon, 60 miles to the south, which they had sold to help pay for the new place. Cheerful in their light gray habits, the sisters were finishing lunch in the refectory around a handsome glazed courtyard open to a cloudless sky. A few minor acoustic problems with the nuns’ concrete quarters aside, Mr. Piano and his team (Paul Vincent was the partner in charge at Renzo Piano Building Workshop) have created remarkably light and peaceful spaces that are virtually invisible from the chapel and gracefully connected to nature. Competing with Le Corbusier’s masterwork would have been a fool’s game and an affront, Mr. Piano clearly realized; spoiling it, a cinch. Doing neither, the additions insert new life onto the hill, and in the process remove a despised 1960s gatehouse that had obscured sight of the chapel from the town below. Humility is a virtue. That’s the obvious lesson, but doing anything, even constructing a few self-effacing buildings at Ronchamp, is a big deal. Mr. Piano solved the riddle of adding to a site without appearing conspicuously to do so by burrowing into the brow of the hill, below the chapel, and inserting the convent and visitors’ center into the cuts, half buried, with zinc-and-glass facades to let in light. He placed the visitors’ center beside the old pilgrims’ path, which winds through woods from the valley all the way up the hill, and adjacent to a parking lot, which has been usefully trimmed.

Keep on reading:

http://www.nytimes.com/2012/04/18/arts/design/renzo-pianos-demure-additions-to-le-corbusiers-chapel.html?_r=2&pagewanted=1&hp

Read the on line petition:

http://www.ipetitions.com/petition/ronchamp/

In Memoriam. Arquitecto Néstor Pablo Doval

Este post es en homenaje a mi colega y ex compañero de estudios, arquitecto Néstor Pablo Doval, quien falleciera el 30 de Septiembre de 2011 a los 49 años de edad. Me acabo de enterar.

Pablo residía en Key Biscayne, Florida. Estudió en la Facultad de Arquitectura, Diseño y Urbanismo de Buenos Aires y alcanzó su Master degree en Harvard.

Con Pablo habíamos cursado en la FADU y estudiado juntos para exámenes de Sistemas Constructivos, materia que no era de su agrado, su gran preferida, al menos en ese momento, era el diseño arquitectónico.

Nos vimos por última vez de casualidad, esperando mi esposo y yo para cruzar una de las vías del Barrio de Belgrano R, Buenos Aires. Nos intercambiamos noticias, ambos ya estábamos casados y con hijos.

Lamento mucho su deceso; la noticia me causó gran pesar.

Para conocer los proyectos del arq. Néstor Pablo Doval:

http://www.pablodoval.com/

Which cities are the richest ones?

According to the 2012 Wealth Report released by real estate firm Knight Frank and Citi Private Bank. The report is based on detailed data on the number, distribution, and preferred locations of high net-worth individuals (defined as households with more than $100 million in assets). This is the globe-straddling capitalist over-class that Cynthia Freeland has dubbed the "new global elite," or what the report itself labels the global economic "plutonomy" of the "richest 1%."

1. London
2. New York
3. Hong Kong
4. Paris
5. Singapore
6. Miami
7. Geneva
8. Shanghai
9. Beijing
10. Berlin

The report also asked respondents to predict the most important cities in 10 years. The projected key cities of 2022 include:

1. London
2. New York
3. Beijing
4. Shanghai
5. Singapore
6. Hong Kong
7. Paris
8. São Paulo
9. Geneva
10. Berlin

Reference:

http://www.theatlanticcities.com/jobs-and-economy/2012/04/where-global-1-live-now/1668/