While mathematics in architecture has historically referenced notions of order, proportion, and ideal form, the discipline of mathematics itself has shifted to encompass uncertainty, incompleteness, relativity, and chaos towards a situation in which truth itself is elusive. This move stems in part from an engagement with real phenomena, in which natural systems were shown to behave non-linearly and unpredictably. In architecture, while computational developments enabling dynamic and variable modeling have been subsumed into our culture of design and production, a new kind of idealism has emerged. Formally prolific and inherently multiplicitous, this book proposes algorithmic truth and statistical outcomes over predetermined objectives; it signifies a retreat away from reality and back towards abstraction and simulation in the smooth space of possibility. Meanwhile, the consequences of uncertainty have pervaded our culture to its core. Recovering from the initial high of fractal and random geometrical proficiency, architecture is just beginning to re-embrace the underlying issues embedded within this contemporary mathematics: uncertainty, unpredict-ability, chance, recursion, wildness, and informality. Contributors: Cecil Balmond, Mario Carpo, Lily Chi + Adrian Lewis, Dana Cupkova + Kevin Pratt, Tom Fecht, Francois Roche, Jenny Sabin, Anthony Vidler and others.

Earth Moves, Bernard Cache's first major work, conceptualizes a series of architectural images as vehicles for two important developments. First, he offers a new understanding of the architectural image itself. Following Gilles Deleuze and Henri Bergson, he develops an account of the image that is nonrepresentational and constructive - images as constituents of a primary, image world, of which subjectivity itself is a special kind of image. Second, Cache redefines architecture as the art of the frame, extending architecture beyond building proper to include cinematic, pictorial, and other framings. Complementary to this classification, Cache offers what is to date the only Deleuzean architectural development of the "fold", a form and concept that has become important over the last few years. For Cache, as for Deleuze, what is significant about the fold is that it provides a way to rethink the relationship between interior and exterior, between past and present, and between architecture and the urban.