Después de Einstein: una arquitectura para una teoría

En 1905, aparecen en la revista "Annalen der physik" tres artículos que revolucionarán las ciencias físicas y pondrán en jaque los asentados conceptos newtonianos de Espacio y Tiempo. La formulación de la Teoría de la Relatividad por Albert Einstein pone en crisis el valor absoluto de estos conceptos, y permite proponer nuevas reflexiones a propósito de su concepción dentro del campo de la física. Esta revolución ¿podría extrapolarse al campo de la arquitectura, donde Espacio y Tiempo tienen un papel protagonista? Hay que entender la complejidad del hecho arquitectónico y las innumerables variables que participan de su definición. Se estudia en esta Tesis Doctoral un aspecto muy concreto: cómo un paradigma (la Teoría de la Relatividad) puede intervenir y modificar, o no, la Arquitectura. Se plantea para ello ir al origen; desentrañar el momento de interacción entre la Teoría de la Relatividad y la Teoría de la Arquitectura, que permita determinar si aquella influyó sobre ésta en los escritos teóricos de las vanguardias aplicados a la Arquitectura. “Después de Einstein. Una arquitectura para una teoría” buscará los puntos de conexión de la Teoría de la Relatividad con la teoría arquitectónica de las vanguardias de principio del siglo XX, su influencia, la contaminación entre una y otra, con posibles resultados arquitectónicos a partir de esta interacción, capaz de definir nuevos argumentos formales para un nuevo lenguaje enArquitectura. Annalen der physik Después de Einstein. Una arquitectura para una teoría Para ello la Tesis se estructura en cuatro capítulos. El primero expone el ámbito geográfico y cronológico donde se desarrolla la Teoría de la Relatividad con la repercusión teórica que tiene para el arte, en función de una nueva definición de espacio vinculado al tiempo, como evento que se desarrolla en un ámbito cuatridimensional; la indeterminación de las medidas de espacio y de las medidas de tiempo, y la importancia de entender la materia como energía. El segundo capítulo estudia los movimientos de vanguardia coetáneos a la eclosión de la Relatividad, enmarcados en su ámbito geográfico más próximo. El cubismo se muestra como movimiento que participa ocasionalmente de las matemáticas y la geometría, bajo el influjo del científico Henri Poincaré y las geometrías no euclidianas. El futurismo indaga en los avances de la ciencia desde una cierta lejanía, cierta falta de rigor o profundidad científica para extraer las leyes de su nuevo idealismo plástico constructivo, definiendo e interpretando su Universo a partir de los avances de la ciencia, en respuesta a la crisis del espacio y del tiempo newtonianos. El lenguaje científico se encuentra presente en conceptos como "simultaneidad" (Boccioni), "expansión esférica de la luz en el espacio" (Severini y Carrá), "cuatridimensionalidad", "espacio-tiempo", "aire-luz-fuerza", "materia y energía" que paralelamente conforman el cuerpo operacional de la teoría de Einstein. Si bien no es posible atribuir a la Teoría de la Relatividad un papel protagonista como referente para el pensamiento artístico, en 1936, con la aparición del manifiesto Dimensionista, se atribuyen explícitamente a las teorías de Einstein las nuevas ideas de espacio-tiempo del espíritu europeo seguido por cubistas y futuristas. El tercer capítulo describe cómo la Teoría de la Relatividad llegó a ser fuente de inspiración para la Teoría de la Arquitectura. Estructurado en tres subcapítulos, se estudia el autor principal que aportó para la Arquitectura conceptos e ideas extrapoladas de la Teoría de la Relatividad después de su estudio e interpretación (Van Doesburg), dónde se produjeron las influencias y puntos de contacto (Lissitzky, Eggeling, Moholy-Nagy) y cómo fueron difundidas a través de la arquitectura (Einsteinturm de Mendelsohn) y de las revistas especializadas. El cuarto capítulo extrae las conclusiones del estudio realizado en esta Tesis, que bien pudiera resumir MoholyNagy en su texto "Vision inmotion" (1946) al comentar: "Ya que el "espacio-tiempo" puede ser un término engañoso, tiene que hacerse especialmente hincapié en que los problemas de espacio-tiempo en el arte no están necesariamente basados en la Teoría de la Relatividad de Einstein. Esto no tiene intención de descartar la relevancia de su teoría para las artes. Pero los artistas y los laicos rara vez tienen el conocimiento matemático para visualizar en fórmulas científicas las analogías con su propio trabajo. La terminología de Einstein del "espacio-tiempo" y la "relatividad" ha sido absorbida por nuestro lenguaje diario." ABSTRACT. "AFTER EINSTEIN:ANARCHITECTUREFORATHEORY." In 1905, three articles were published in the journal "Annalen der Physik ". They revolutionized physical sciences and threw into crisis the newtonian concepts of Space and Time. The formulation of the Theory of Relativity by Albert Einstein put a strain on the absolute value of these concepts, and proposed new reflections about them in the field of Physics. Could this revolution be extrapolated to the field of Architecture, where Space and Time have a main role? It is necessary to understand the complexity of architecture and the countless variables involved in its definition. For this reason, in this PhD. Thesis, we study a specific aspect: how a paradigm (Theory of Relativity) can intervene and modify -or not- Architecture. It is proposed to go back to the origin; to unravel the moment in which the interaction between the Theory of Relativity and the Theory of Architecture takes place, to determine whether the Theory of Relativity influenced on the theoretical avant-garde writings applied to Architecture. "After Einstein.An architecture for a theory " will search the connection points between the Theory of Relativity and architectural avant-garde theory of the early twentieth century, the influence and contamination between them, giving rise to new architectures that define new formal arguments for a new architectural language. Annalen der Physik This thesis is divided into four chapters. The first one describes the geographical and chronological scope in which the Theory of Relativity is developed showing its theoretical implications in the field of art, according to a new definition of Space linked to Time, as an event that takes place in a fourdimensional space; the indetermination of the measurement of space and time, and the importance of understanding "matter" as "energy". The second chapter examines the avant-garde movements contemporary to the theory of relativity. Cubism is shown as an artist movement that occasionally participates in mathematics and geometry, under the influence of Henri Poincaré and non-Euclidean geometries. Futurism explores the advances of science at a certain distance, with lack of scientific rigor to extract the laws of their new plastic constructive idealism. Scientific language is present in concepts like "simultaneity" (Boccioni), "expanding light in space" (Severini and Carra), "four-dimensional space", "space-time", "light-air-force," "matter and energy" similar to the operational concepts of Einstein´s theory. While it is not possible to attribute a leading role to the Theory of Relativity, as a benchmark for artistic laws, in 1936, with the publication of the Dimensionist manifest, the new ideas of space-time followed by cubist and futurist were attributed to the Einstein's theory. The third chapter describes how the Theory of Relativity became an inspiration for the architectural theory. Structured into three subsections, we study the main author who studied the theory of relativity and ,as a consequence, contributed with some concepts and ideas to the theory of architecture (Van Doesburg), where influences and contact points took place (Lissitzky, Eggeling, Moholy-Nagy) and how were disseminated throughArchitecture (Einsteinturm, by Mendelsohn) and journals. The fourth chapter draws the conclusions of this PhD. Thesis, which could be well summarized by Moholy Nagy in his text "Vision in Motion" (1946): vi Since "space-time" can be a misleading term, it especially has to be emphasized that the space-time problems in the arts are not necessarily based upon Einstein´s Theory of Relativity. This is not meant to discount the relevance of his theory to the arts. But artists and laymen seldom have the mathematical knowledge to visualize in scientific formulae the analogies to their own work. Einstein's terminology of "space-time" and "relativity" has been absorbed by our daily language.

Una casa para Einstein: Konrad Wachsmann y la evolucion de un modelo prefabricado desde las casas "Christoph & Unmack A.G." al "General Panel System"

Este artículo estudia la evolución de un modelo de vivienda prefabricada en madera, ejemplificada en la casita de verano que construye Konrad Wachsmann para Albert Einstein en 1929 en Caputh, cerca de Potsdam. El físico deseaba construirse un "lugar de descanso", eligiendo la construcción en madera por su facilidad y rapidez de montaje, adaptabilidad, calidez y para que armonizara mejor con el medio ambiente en el paraje donde se insertaba. Konrad Wachsmann, que trabajaba para la firma de viviendas prefabricadas en madera "Christoph&Unmack A.G." le presentará un modelo prefabricado moderno. Esta tipología, que había evolucionado desde los diseños iniciales "nórdico escandinavos", pasando por el "jugendstil", hasta introducir un nuevo lenguaje de líneas puras, cubierta plana, y grandes ventanales iniciado por Poelzig, será ligeramente modificada por Einstein, que finalmente adjudica el encargo. Ayudado por Einstein a trasladarse a EEUU, Konrad Wachsmann continuará allí la labor de investigación sobre vivienda prefabricada junto con Walter Gropius, que dará como resultado el "General Panel System" y sus conocidas "Packaged Houses". A HOUSE FOR EINSTEIN: KONRAD WACHSMANN AND THE EVOLUTION OF A PREFABRICATED WOODEN HOUSING MODEL FROM " CHRISTOPH & UNMACK A.G." TO "GENERAL PANEL SYSTEM". This article studies the evolution of a prefabricated wooden housing model, exemplified in the summer house built by Konrad Wachsmann for Albert Einstein in 1929, in Caputh, near Potsdam. The Physician wanted to build a "resting house", choosing a wood construction because of its easy and fast assembly, adaptability, warmth and harmony with the environment where it would be inserted. Konrad Wachsmann, who worked for the wooden prefabricated houses firm "Christoph & Unmack AG", proposed Einstein a modern prefabricated wood model. This typology, which had evolved from the initial "Nordic Scandinavian" and "Jugendstil" designs to a new modern language initiated by Poelzig (with clean lines, flat roof, and large windows) will be slightly modified by Einstein, that finally hired the construction of the house. Aided by Einstein to move to USA, Konrad Wachsmann continued there his research work about prefabricated houses with Walter Gropius, giving as a results the "General Panel System" and the popular "Packaged Houses".

Einstein-like geometric structures on surfaces

An AH (affine hypersurface) structure is a pair comprising a projective equivalence class of torsion-free connections and a conformal structure satisfying a compatibility condition which is automatic in two dimensions. They generalize Weyl structures, and a pair of AH structures is induced on a co-oriented non-degenerate immersed hypersurface in flat affine space. The author has defined for AH structures Einstein equations, which specialize on the one hand to the usual Einstein Weyl equations and, on the other hand, to the equations for affine hyperspheres. Here these equations are solved for Riemannian signature AH structures on compact orientable surfaces, the deformation spaces of solutions are described, and some aspects of the geometry of these structures are related. Every such structure is either Einstein Weyl (in the sense defined for surfaces by Calderbank) or is determined by a pair comprising a conformal structure and a cubic holomorphic differential, and so by a convex flat real projective structure. In the latter case it can be identified with a solution of the Abelian vortex equations on an appropriate power of the canonical bundle. On the cone over a surface of genus at least two carrying an Einstein AH structure there are Monge-Amp`ere metrics of Lorentzian and Riemannian signature and a Riemannian Einstein K"ahler affine metric. A mean curvature zero spacelike immersed Lagrangian submanifold of a para-K"ahler four-manifold with constant para-holomorphic sectional curvature inherits an Einstein AH structure, and this is used to deduce some restrictions on such immersions.

Una casa para Einstein: Konrad Wachsmann y la evolución de un modelo prefabricado desde las casas "Christoph & Unmack A. G." al "General Panel System"

Este artículo estudia la evolución del modelo de vivienda prefabricada en madera que construye Konrad Wachsmann para Einstein en 1929 en Caputh, cerca de Potsdam. El físico deseaba construirse un "lugar de descanso", eligiendo la construcción en madera por su facilidad y rapidez de montaje, adaptabilidad, calidez y para que armonizara mejor con el medio ambiente. Wachsmann, que trabajaba para la firma "Christoph & Unmack A.G." le presentará un modelo prefabricado moderno. Esta tipología, evolucionada desde los diseños "nórdico-escandinavo" y "jugendstil", hasta introducir un nuevo lenguaje de líneas puras, cubierta plana, y grandes ventanales, será ligeramente modificada por Einstein, que finalmente adjudica el encargo. Wachsmann continuará la labor de investigación sobre vivienda prefabricada junto con Gropius en EEUU, que dará como resultado el "General Panel System" y sus conocidas "Packaged Houses".

Ricci flows on surfaces related to the Einstein weyl and Abelian vortex equations

There are described equations for a pair comprising a Riemannian metric and a Killing field on a surface that contain as special cases the Einstein Weyl equations (in the sense of D. Calderbank) and a real version of a special case of the Abelian vortex equations, and it is shown that the property that a metric solve these equations is preserved by the Ricci flow. The equations are solved explicitly, and among the metrics obtained are all steady gradient Ricci solitons (e.g. the cigar soliton) and the sausage metric; there are found other examples of eternal, ancient, and immortal Ricci flows, as well as some Ricci flows with conical singularities.

First-order equivalent to Einstein-Hilbert Lagrangian

A first-order Lagrangian L ∇ variationally equivalent to the second-order Einstein- Hilbert Lagrangian is introduced. Such a Lagrangian depends on a symmetric linear connection, but the dependence is covariant under diffeomorphisms. The variational problem defined by L ∇ is proved to be regular and its Hamiltonian formulation is studied, including its covariant Hamiltonian attached to ∇ .

Phosphorylation of histone H3 at serine 10 is correlated with chromosome condensation during mitosis and meiosis in Tetrahymena

H3 phosphorylation has been correlated with mitosis temporally in mammalian cells and spatially in ciliated protozoa. In logarithmically growing Tetrahymena thermophila cells, for example, H3 phosphorylation can be detected in germline micronuclei that divide mitotically but not in somatic macronuclei that divide amitotically. Here, we demonstrate that micronuclear H3 phosphorylation occurs at a single site (Ser-10) in the amino-terminal domain of histone H3, the same site phosphorylated during mitosis in mammalian cells. Using an antibody specific for Ser-10 phosphorylated H3, we show that, in Tetrahymena, this modification is correlated with mitotic and meiotic divisions of micronuclei in a fashion that closely coincides with chromosome condensation. Our data suggest that H3 phosphorylation at Ser-10 is a highly conserved event among eukaryotes and is likely involved in both mitotic and meiotic chromosome condensation.

Resistance to DNA fragmentation and chromatin condensation in mice lacking the DNA fragmentation factor 45

The DNA fragmentation factor 45 (DFF45) is a subunit of a heterodimeric nuclease complex critical for the induction of DNA fragmentation in vitro. To understand the in vivo role of DFF45 in programmed cell death, we generated DFF45 mutant mice. DNA fragmentation activity is completely abolished in cell extracts from DFF45 mutant tissues. In response to apoptotic stimuli, splenocytes, thymocytes, and granulocytes from DFF45 mutant mice are resistant to DNA fragmentation, and splenocytes and thymocytes are also resistant to chromatin condensation. Nevertheless, development of the immune system in the DFF45 mutant mice is normal. These results demonstrate that DFF45 is critical for the induction of DNA fragmentation and chromatin condensation in vivo, but is not required for normal immune system development.

The Role of Topoisomerase II in Meiotic Chromosome Condensation and Segregation in Schizosaccharomyces pombe

Topoisomerase II is able to break and rejoin double-strand DNA. It controls the topological state and forms and resolves knots and catenanes. Not much is known about the relation between the chromosome segregation and condensation defects as found in yeast top2 mutants and the role of topoisomerase II in meiosis. We studied meiosis in a heat-sensitive top2 mutant of Schizosaccharomyces pombe. Topoisomerase II is not required until shortly before meiosis I. The enzyme is necessary for condensation shortly before the first meiotic division but not for early meiotic prophase condensation. DNA replication, prophase morphology, and dynamics of the linear elements are normal in the top2 mutant. The top2 cells are not able to perform meiosis I. Arrested cells have four spindle pole bodies and two spindles but only one nucleus, suggesting that the arrest is nonregulatory. Finally, we show that the arrest is partly solved in a top2 rec7 double mutant, indicating that topoisomerase II functions in the segregation of recombined chromosomes. We suggest that the inability to decatenate the replicated DNA is the primary defect in top2. This leads to a loss of chromatin condensation shortly before meiosis I, failure of sister chromatid separation, and a nonregulatory arrest.

Molecular mechanism for silencing virally transduced genes involves histone deacetylation and chromatin condensation

Virally transduced genes are often silenced after integration into the host genome. Chromatin immunoprecipitation and nuclease sensitivity experiments now demonstrate that silencing of the transgene is characterized by deacetylation of histone H4 lysines and chromatin condensation. Trichostatin A treatment results in dramatic reactivation of gene expression that is preceded by histone acetylation and chromatin decondensation. Analysis of individual histone H4 lysines demonstrate that chromatin domain opening is coincident with rapid acetylation of histone H4 K5, K12, and K16 and that maintenance of the open domain is correlated with acetylation of histone H4 K8. Removal of trichostatin A results in rapid deacetylation of histone H4 K8, chromatin condensation, and transcription silencing. The results suggest that deacetylation of histone H4 lysines and coincident chromatin condensation are critically involved in the silencing of virally transduced genes.

The reversible condensation and expansion of the rotavirus genome

Understanding the structural organization of the genome is particularly relevant in segmented double-stranded RNA viruses, which exhibit endogenous transcription activity. These viruses are molecular machines capable of repeated cycles of transcription within the intact capsid. Rotavirus, a major cause of infantile gastroenteritis, is a prototypical segmented double-stranded RNA virus. From our three-dimensional structural analyses of rotavirus examined under various chemical conditions using electron cryomicroscopy, we show here that the viral genome exhibits a remarkable conformational flexibility by reversibly changing its packaging density. In the presence of ammonium ions at high pH, the genome condenses to a radius of ≈180 Å from ≈220 Å. Upon returning to physiological conditions, the genome re-expands and fully maintains its transcriptional properties. These studies provide further insights into the genome organization and suggest that the observed isometric and concentric nature of the condensation is due to strong interactions between the genome core and the transcription enzymes anchored to the capsid inner surface. The ability of the genome to condense beyond what is normally observed in the native virus indicates that the negative charges on the RNA in the native state may be only partially neutralized. Partial neutralization may be required to maintain appropriate interstrand spacing for templates to move around the enzyme complexes during transcription. Genome condensation was not observed either with increased cation concentrations at normal pH or at high pH without ammonium ions. This finding indicates that the observed genome condensation is a synergistic effect of hydroxyl and ammonium ions involving disruption of protein–RNA interactions that perhaps facilitate further charge neutralization and consequent reduction in the interstrand spacing.