A year later, together with his partner Patrick Beauce, he founded the company Objectile, in order to conceive and manufacture non-standard architecture components. right: The photo features Swiss steel fabricator Simon Veglio, artist Bruce McLean and designer Mark Boyce. Secondly he conducts collaborative research with leading universities and companies. Trained as both an architect and mathematician, he was previously a director at the practice’s Paris office where he consulted on parametric design, geometric approaches and new technologies for clients including Gehry Partners, Ateliers Jean Nouvel, UNStudio and Coop Himmelb(l)au. Similarly, the algebraic complexity of finite element analysis (FEA) has got a whole lot more interesting since it became a visual medium with a high-speed turnaround structural – optimisation rendered immediately in colour – coded stress. Will McLean is the joint coordinator of technical studies teaching in the Department of Architecture at the University of Westminster. He has taught parametric and computational design at the University of Pennsylvania and the Architectural Association (AA) in London, and has been a tutor and organiser for SmartGeometry workshops and symposia in Delft and Barcelona. Alternatively, why not engage in a thought experiment and thoroughly immerse ourselves in the elegant complexity of the Navier – Stokes equations where the mathematics of flows will not discriminate between air, water, blood or smoke. He has published numerous books and articles mostly dealing with the complementary histories of architecture and technology. analysis and algorithmic compilation used to predict which queue we choose to join, what music we buy and the general evolution of our purchasing habits. Is architecture heading for a ‘procedural mathematic cul-de-sac’? Such paradoxes are mathematical fertile ground and present a more aberrant and less algorithmic precision than the well-defined certainty of parametricism; this year’s answer to everything. Or what about Karl Sims’s Virtual Creatures,9 where he developed virtual creatures from simple digitally modelled blocks and then articulated and animated these forms through virtual muscles. Daniel Bosia, an experienced structural designer with a masters in architecture and engineering, is an expert in complex geometries and computation. And while we go about digitising the physical world and its behaviour, we should also revisit Craig Reynolds’s work on simulating human and animal behaviour, notably his ‘Boids’ project from 1986,8 which neatly modelled the group flocking and schooling behaviour of birds and fish. After graduating from the Architectural Association (AA) with honours in 2008, he worked as an associate at IJP Corporation. Firstly, he conducts project-driven R&D, for which he has worked on over 100 projects and competitions, including the SwissRe HQin London and the new Airport for the Beijing Olympics. He is also a PhD candidate at the Archives Henri Poincare, Department of Philosophy and History of Science. Edwin Abbott’s elegant paean to dimensionality, Flatland: A Romance of Many Dimensions,6 takes us cumulatively through the non-dimensional pointland, lineland, flatland and three-dimensional spaceland, and Thomas F Banchoff takes us Beyond The Third Dimension7 into a world of four, five or six mathematical dimensions. He is a member of the Advisory Board of Gehry Technologies in Los Angeles and was a member of the Australian Research Council College of Experts from 2003 to 2007. From 2002 until 2006 he studied the use of artificial-life methods in architectural construction as a member of Ludger Hovestadt’s CAAD group at the ETH Zurich and managed to transfer the results to a number of collaborative projects between architects, engineers and fabrication experts. In 2006 he was awarded the Australian Research Council’s most prestigious funding award, a Federation Fellowship, for five years. Mathematics, David Bergamini’s excellent popular science survey of the subject from the late 1960s,4 reads like a manual of proto-architectural projects, which includes the topological problem of the seven bridges of Konigsberg (neatly solved by Leonhard Euler), conic sections, statistical chicanery, Boolean logic and any amount of relations between number and human endeavour. I am not specifically talking of GA shape optimisation, which in application to turbine blade design seems useful, but its application to the crudely conceived programmatic congruence of a building might be less relevant. He is currently dedicated to fundamental research both on antiquity and new CAD/CAM software in collaboration with Missler Software Corporation, where he teaches teams of software developers to read century-old treatises of geometry. She is also a tutor at the Bartlett, teaching programming to graduate students. From 2000 she turned her attention to the modelling of complex systems, and has since directed numerous doctoral theses on issues of climate change considered in scientific, societal and political terms. She is currently working as a research scientist at the Singapore University of Technology and Massachusetts Institute of Technology (MIT). Michalatos received a masters of science from the art and technology programme jointly organised by Chalmers and IT-Universitet in Gothenburg, Sweden. His most recent book, Digital Culture in Architecture (Birkhauser, 2010), proposes a comprehensive interpretation of the changes brought by the computer to the design professions. 1

Francis Aish is a Partner in Foster + Partners’ Specialist Modelling Group, where his role is the research and development of systems to model and solve complex, multi-disciplinary design problems. — Simon Singh, ‘Packing Them In’, New Scientist, 28 June 1997, pp 20-11
The realisation that the pre-‘scientific calculator’ logarithmic table books that I used at school were in any way related to specific curves was a kind of minor revelation. In 2008 he established Bibliotheque McLean, an independent publisher of art and architecture books. In 1995 he introduced the concept of non-standard architecture in his MIT Press book Earth Moves, a concept given the name ‘Objectile’ by Gilles Deleuze in his own book The Fold: Leibniz and the Baroque in 1992. He studied at the Escuela Tecnica Superior de Arquitectura de Madrid (ETSAM), where he was a Marcelino Botin Fellow. He has written extensively about the consequences of technological phenomena on global disurbanism as well as on our most recent technological and economical shifts. Fabian Scheurer is a founding partner of designtoproduction and leads the company’s office in Zurich. In addition he holds a research position at the Ecole Nationale des Ponts et Chaussees. Architects and designers should learn to enjoy more mathematical delights, which might suggest organisational nomenclature as well as the visual treat. Will McLean and Bruce McLean, School as a Rule, 1998
Proposal for a self-measuring linear sculpture at Lawthorn Primary School in North Ayrshire. Why, as designers, is our interest in mathematics strictly limited to its artefacts and not its use as a genuinely generative tool? Architects might spend less time parametrically polishing the proverbial and usefully employing the rubric of mathematics for the positive production of new alternatives, employing simple rule-based techniques such as John Horton Conway’s cellular automata or the predictive statistical

Bruce McLean and Will McLean, Abacus, Dalry Primary School, North Ayrshire, 2007
One of the artworks that were specially designed for each classroom space of Dalry Primary School, fabricated by Simon Veglio. There is a model from the 1970s in London’s Science Museum of the UK’s economy rendered in plastic tubes, and using water and controllable valves for computation and statistical analysis of such data as our gross domestic product (GDP). In the last 15 years in practice, he has worked in a series of high-profile collaborations with architects such as Daniel Libeskind, Toyo Ito, Enric Miralles and Nicholas Grimshaw. The answer is perhaps more complex than one might imagine and it is indeed possible to create darkness (or not to fully extend illumination) through a specific geometric disposition. More recently he has supported emerging practices such as BIG and LAVA, and collaborated with artists including Anish Kapoor and Matthew Ritchie. He studied architecture at the AA from 1982 to 1988 and has taught at the AA School of Architecture since 1989 in a range of positions from workshop tutor, intermediate and then diploma unit master, master of technical studies through to academic head. It seems unfortunate that architects are generally so easily satiated with such deterministic procedural numericism that would not seem to enjoy the full potential of mathematical exploration. Architects seem to get unnecessarily stuck on a superficial mathematics of pattern, which is the kind of maths which can be printed, etched or cast into some willing substrate or crudely abstracted into some planned urban metropolis, its edges denoted variously in a keenly deployed chamfered-edge building, the hard landscaping of angular anti-skate bench/ bollard ensembles and the interminable layouts of the non-deciduous anti-personnel shrub. Mathematics to the non-mathematician but interested observer is a world of infinite possibilities, which are elegantly posed in a mathematical problem discussed by Ian Stewart.3 In a column for Scientific American magazine, Stewart tries to solve a problem first posed by Victor Klee in 1969, which is, if you lit a match somewhere in a totally reflective room, no matter what shape the room was, would you see the light from the match anywhere in that room? He also studied architecture and engineering at the NTUA in Athens. Will McLean, Senior Lecturer at the University of Westminster, urges designers to open themselves up to the wider delights of mathematics and the full range of possibilities that the discipline has to offer. This role takes two forms. Gordon Pask, Random Number Machine, c 1963
The Random Number Machine, designed by Gordon Pask for the office of Cedric Price, and now housed in the Cedric Price Archive, Canadian Centre for Architecture (CCA), Montreal. Test assembly of the Pythagorean School, in South Acton, in 1999. lustrisim Senyor by the Reial Academia Catalana de Belles Arts de Sant Jordi in recognition of his contribution. He has taught widely in Europe and America, most recently holding a visiting chair at the Politecnico di Torino. Her first book (with Jeanne Peiffer), History ofMathematics: Highways and Byways was translated into English and published in 2010 by the Washington-based Mathematical Association of America. Max Kahlen works as an architect in London and Germany. Over the last decade his published work has arisen from research into the dynamics, forms and energy transactions of natural systems, and the application of the mathematics and processes of emergence to cities, to groups of buildings within cities and to individual buildings. Their consultancywork and applied research is focused on complex form and its structural implications. The useful generalism and eclecticism of the architect should employ the full range of mathematical possibilities and engage in a more thorough exploration of the world of mathematical models. As a recipient of a La Caixa Fellowship, he earned his masters of architecture with distinction from Harvard GSD. He is a lecturer in architecture and engineering schools, and now an associate director at Expedition Engineering after leading the Advanced Geometry Unit (AGU) at Arup for many years, with realised projects including the Pedro and Ines Bridge and the Weave Bridge. Mark Burry is Professor of Innovation (Spatial Information Architecture) and director of the Spatial Information Architecture Laboratory (SIAL) at RMIT University. He is currently researching machine perception as part of the Virtual Environments, Imaging and Visualisation programme at University College London. We might ask:
Bruce McLean, Will McLean and Mel Gooding, The Pythagorean School, 2000
left: A mathematically imperfect model for a school. randomly.’10 As interesting (in architectural history terms) as the hyperbolic paraboloid frozen music of the Philips Pavilion (Brussels, 1958) might be, it is surely the subsequent stochastic and granular synthesis compositional experiments of Iannis Xenakis that are of greater ‘mathematic’ interest.11 A composer of international renown is surely how Xenakis is remembered and not as the truculent job architect for a trade-sponsored Expo goody by Le Corbusier. Are architects just too ready to settle for the ‘well-defined certainty of parametricism’, having got stuck on a mathematics of pattern? She taught mathematics at university level until 1983 and has held prestigious appointments in the history of science at the Paris-based Ecole Polytechnique, the Ecole des Hautes Etudes, the Free University of Brussels and France’s Centre national de la recherche scientifique (CNRS). The first publication was Quik Build: Adam Kalkin’s ABC of Container Architecture (2008), and forthcoming publications include Sabbioneta: Cryptic City by James Madge (2011) and Accelerating Architecture by Professor John Frazer (2011). She is the author of four books and numerous papers. We can all enjoy the sequential niceties of the Fibonacci sequence without mindlessly rendering it in double-curved steel sections and top-of-the – line curtain walling. He has published and lectured widely, and taught seminar courses, studios and workshops on these topics at many other schools of architecture in Europe, including Brighton, Delft, Rome, Barcelona, Vienna and in Stuttgart; and in the US at Yale and Rice. That the 19th-century mechanical calculators of computer pioneer (and scourge of street performers) Charles Babbage2 were developed to compute and print these tables was yet another. He is currently working as a lecturer at Harvard University Graduate School of Design. She holds a BA in environmental information, majoring in media design from Keio University, Japan. He is a co-founder of the online platform RhinoScript. Since 2009 he has been a visiting professor at the Architectural Association’s EmTech programme in London. AndrewJ Witt is Director of Research at Gehry Technologies. With increasingly serious computational processing power available to anyone with a computer, we might begin to ask more pertinent questions as to the nature of what the designer does and could do, and spend our processing power on causation (new possibilities) and not on images of saleable iterations and no ideas at all. The mathematics of computational fluid dynamics (CFD) is not only scaleable and non-discriminatory in its viscous medium; it also produces a wonderfully interactive graphic interface making visible the not always visible eddies and turbulence of fluid dynamics. She graduated from the Escuela Tecnica Superior de Arquitectura de Madrid (ETSAM) and completed an exchange programme at the Ecole Polytechnique Federale de Lausanne (EPFL) in Switzerland in 2003. He has co-authored two books with Pete Silver and is currently working on a third with both Pete Silver and Peter Evans, entitled Structures in Action: Structural Engineering for Architects., to be published by Laurence King in 2012. He has published a number of papers on design and simulation systems, and lectured on the same subject in Europe and North America. The Masterwork (programmed as the ‘definitive work in mediocrity’) was subtitled An Award Winning Fishknife and was a highly choreographed scabrous tale about an architect whose major coup de grace was the development of some stonkingly good tableware. He worked as a web technologist for Internet and open-source software companies before attending the University of Pennsylvania School of Design, where he received Master of Architecture and Master of Landscape Architecture degrees. The drawing was etched onto bronze plate and exhibited as a part of the exhibition ‘Bruce McLean, Works 1969-1999’ at the Talbot Rice Gallery, Edinburgh, in January 2000. He has taught at the Architectural Association (AA) and was the organiser and curator of the exhibition ‘Architecture Beyond Forms: The Computational Turn’ at the Maison de l’Architecture et de la Ville PACA in Marseille (spring 2007). A registered architect in Greece and the UK, she has worked for various architectural and engineering firms. Michael Weinstock is an architect, and currently Director of Research and Development and Director of the Emergent Technologies and Design programme at the Architectural Association (AA) in London. Cedric Price observed: ‘It is surprisingly difficult to randomise with one’s own brain – try and think of 45 random numbers… Prior to joining Foster + Partners, he spent two years in the Advanced Technology division of Nortel Networks. Francis received his undergraduate degree in Aerospace Systems Engineering from the University of Southampton in 1996, and is currently undertaking an Engineering Doctorate at University College London. He is also founding director of RMIT’s Design Research Institute which brings together investigators from a range of design disciplines and harnesses their collective expertise to address major social and environmental dilemmas. He received an MArch and an MDes from Harvard GSD. org and has given RhinoScript classes. In November 1979 artists Bruce McLean and Paul Richards staged and performed The Masterwork,12 a kind of multi-headed performance artwork at Riverside Studios in London. Architects, generally gifted with little humour or self-doubt, are only too willing to redesign dead ends for any number of despicable clients and are currently indulging in a kind of procedural mathematical cul-de-sac while presumably the world awaits another masterwork.

Updated: 31.10.2014 — 16:56