The Bunker on the Shore

<p>This thesis seeks to investigate the role of architecture in distilling of ephemerality within a fixed geometry; using the variables of light, texture, context and atmospheric conditions as experimental catalysts. Consequently, this research explores the notion that a rigid architecture can play a central role in the creation of temporal atmosphere. It investigates this proposition by developing a method to represent ephemerality through architectural form and medium with an iterative design process as the overarching methodology. The design research begins with establishing the literary and physical context of projective geometries, abstraction of ‘place’ and atmospheric manipulation. This follows onto a three-part design-led exploration, with each test increasing in scale and architectural complexity. These include a site less installation, a gallery and a rehabilitation centre site on the rugged South Brighton coastline. This series explores the relationship between the temporary and the constant, with lessons learnt from each previous experiment translated into the later. These develop a range of architectural techniques for distilling ephemerality within fixed geometries with social response and programmatic factors being supplementary factors.The research recognises the already well established study into the ephemerality of spatial conditions within the architectural discourse and seeks to build on this through abstraction of place and site specific design responses.</p>

The Bunker on the Shore

<p>This thesis seeks to investigate the role of architecture in distilling of ephemerality within a fixed geometry; using the variables of light, texture, context and atmospheric conditions as experimental catalysts. Consequently, this research explores the notion that a rigid architecture can play a central role in the creation of temporal atmosphere. It investigates this proposition by developing a method to represent ephemerality through architectural form and medium with an iterative design process as the overarching methodology. The design research begins with establishing the literary and physical context of projective geometries, abstraction of ‘place’ and atmospheric manipulation. This follows onto a three-part design-led exploration, with each test increasing in scale and architectural complexity. These include a site less installation, a gallery and a rehabilitation centre site on the rugged South Brighton coastline. This series explores the relationship between the temporary and the constant, with lessons learnt from each previous experiment translated into the later. These develop a range of architectural techniques for distilling ephemerality within fixed geometries with social response and programmatic factors being supplementary factors.The research recognises the already well established study into the ephemerality of spatial conditions within the architectural discourse and seeks to build on this through abstraction of place and site specific design responses.</p>

Symmetries and Geometries of Qubits, and Their Uses

The symmetry SU(2) and its geometric Bloch Sphere rendering have been successfully applied to the study of a single qubit (spin-1/2); however, the extension of such symmetries and geometries to multiple qubits—even just two—has been investigated far less, despite the centrality of such systems for quantum information processes. In the last two decades, two different approaches, with independent starting points and motivations, have been combined for this purpose. One approach has been to develop the unitary time evolution of two or more qubits in order to study quantum correlations; by exploiting the relevant Lie algebras and, especially, sub-algebras of the Hamiltonians involved, researchers have arrived at connections to finite projective geometries and combinatorial designs. Independently, geometers, by studying projective ring lines and associated finite geometries, have come to parallel conclusions. This review brings together the Lie-algebraic/group-representation perspective of quantum physics and the geometric–algebraic one, as well as their connections to complex quaternions. Altogether, this may be seen as further development of Felix Klein’s Erlangen Program for symmetries and geometries. In particular, the fifteen generators of the continuous SU(4) Lie group for two qubits can be placed in one-to-one correspondence with finite projective geometries, combinatorial Steiner designs, and finite quaternionic groups. The very different perspectives that we consider may provide further insight into quantum information problems. Extensions are considered for multiple qubits, as well as higher-spin or higher-dimensional qudits.

Random inscribed polytopes in projective geometries

We establish central limit theorems for natural volumes of random inscribed polytopes in projective Riemannian or Finsler geometries. In addition, normal approximation of dual volumes and the mean width of random polyhedral sets are obtained. We deduce these results by proving a general central limit theorem for the weighted volume of the convex hull of random points chosen from the boundary of a smooth convex body according to a positive and continuous density in Euclidean space. In the background are geometric estimates for weighted surface bodies and a Berry–Esseen bound for functionals of independent random variables.

Combining Methods of Euclidean, Affine, and Projective Geometries in Solving Geometric Problems

The aim of the paper is to demonstrate how the techniques of one of the geometries indicated in the title can be used for solving problems formulated in the framework of one of the other geometries. In particular, it is shown how problems formulated in the framework of affine or projective geometry can be solved with an appropriate choice of Euclidean scalar product.

The Smallest Matroids with no Large Independent Flat

We show that a simple rank-$r$ matroid with no $(t+1)$-element independent flat has at least as many elements as the matroid $M_{r,t}$ defined to be the direct sum of $t$ binary projective geometries whose ranks pairwise differ by at most $1$. We also show for $r \geqslant 2t$ that $M_{r,t}$ is the unique example for which equality holds.

Sympathetic World-making: Drawing-out Ecological-Empathy

This article reflects on an experiment in drawing, titled Surrogate Drawing, in which an assemblage of people, materials and artefacts engaged in a live, improvisational process of co-production. The group was interested in how empathy might be cultivated through architectural drawing. The article develops an argument across three main parts. The first part offers a brief overview of the drawing experiment, situated relative to some key assumptions and conventions of architectural drawing, via the work of Robin Evans and others. In particular, this involved unsettling the idea of translation and its underlying premise of projection—a premise that resonates with the concept of empathy. The second part moves into a series of first-person accounts, one from each author. This experiential access reveals degrees of complexity that question the model of projection as a primary operative principle for either drawing or empathy, calling for an alternative conceptual framework. The third part offers such an alternative, via Jakob von Uexküll’s work concerning the Umwelt, or perceptual life-worlds. Via Uexküll we come to better understand drawing as less of a process of translation or transmission, and more of a process of creative world-making. Through Uexküll’s depiction of the Umwelt as a ‘bubble,’ the paper offers an alternative diagrammatic to that of projective geometries: that of a foaming. The manifestly collective world-making inherent in this drawing experiment leads us to conclude by opening up something we discuss as ‘ecological empathy’—or sympathy. It is proposed that drawing, if conceptually liberated from projective models, may be an important technique to cultivate ecological-empathy, or sympathy. This points toward a way that architecture might be reoriented toward sympathetic world-making.