This book questions the relevance of computation to the physical universe. Our theories deliver computational descriptions, but the gaps and discontinuities in our grasp suggest a need for continued discourse between researchers from different disciplines, and this book is unique in its focus on the mathematical theory of incomputability and its relevance for the real world. The core of the book consists of thirteen chapters in five parts on extended models of computation; the search for natural examples of incomputable objects; mind, matter, and computation; the nature of information, complexity, and randomness; and the mathematics of emergence and morphogenesis. This book will be of interest to researchers in the areas of theoretical computer science, mathematical logic, and philosophy.

A journey through the uncomputable remains of computer history Narrating some lesser known episodes from the deep history of digital machines, Alexander R. Galloway explains the technology that drives the world today, and the fascinating people who brought these machines to life. With an eye to both the computable and the uncomputable, Galloway shows how computation emerges or fails to emerge, how the digital thrives but also atrophies, how networks interconnect while also fray and fall apart. By re-building obsolete technology using today's software, the past comes to light in new ways, from intricate algebraic patterns woven on a hand loom, to striking artificial-life simulations, to war games and back boxes. A description of the past, this book is also an assessment of all that remains uncomputable as we continue to live in the aftermath of the long digital age.

In Contingent Computation, M. Beatrice Fazi offers a new theoretical perspective through which we can engage philosophically with computing. The book proves that aesthetics is a viable mode of investigating contemporary computational systems. It does so by advancing an original conception of computational aesthetics that does not just concern art made by or with computers, but rather the modes of being and becoming of computational processes. Contingent Computation mobilises the philosophies of Gilles Deleuze and Alfred North Whitehead in order to address aesthetics as an ontological study of the generative potential of reality. Through a novel philosophical reading of Gödel’s incompleteness theorems and of Turing’s notion of incomputability, Fazi finds this potential at the formal heart of computational systems, and argues that computation is a process of determining indeterminacy. This indeterminacy, which is central to computational systems, does not contradict their functionality. Instead, it drives their very operation, albeit in a manner that might not always fit with the instrumental, representational and cognitivist purposes that we have assigned to computing.

Non-representational theory is one of the contemporary moment’s most influential theoretical perspectives within social and cultural theory. It is now widely considered to be the logical successor of postmodern theory, the logical development of post-structuralist thought, and the most notable intellectual force behind the turn across the social and cultural sciences away from cognition, meaning, and textuality. And yet, it is often poorly understood. This is in part because of its complexity, but also because of its limited treatment in the few volumes chiefly dedicated to it. Theories must be useful to researchers keen on utilizing concepts and analytical frames for their personal interpretive purposes. How useful non-representational theory is, in this sense, is yet to be understood. This book outlines a variety of ways in which non-representational ideas can influence the research process, the very value of empirical research, the nature of data, the political value of data and evidence, the methods of research, the very notion of method, and the styles, genres, and media of research.

Arturo Carsetti According to molecular Biology, true invariance (life) can exist only within the framework of ongoing autonomous morphogenesis and vice versa. With respect to this secret dialectics, life and cognition appear as indissolubly interlinked. In this sense, for instance, the inner articulation of conceptual spaces appears to be linked to an inner functional development based on a continuous activity of selection and “anchorage” realised on semantic grounds. It is the work of “invention” and g- eration (in invariance), linked with the “rooting” of meaning, which determines the evolution, the leaps and punctuated equilibria, the conditions related to the unfo- ing of new modalities of invariance, an invariance which is never simple repetition and which springs on each occasion through deep-level processes of renewal and recovery. The selection perpetrated by meaning reveals its autonomy aboveall in its underpinning, in an objective way, the ongoing choice of these new modalities. As such it is not, then, concerned only with the game of “possibles”, offering itself as a simple channel for pure chance, but with providing a channel for the articulation of the “ le” in the humus of a semantic (and embodied) net in order to prepare the necessary conditionsfor a continuousrenewal and recoveryof original creativity. In effect, it is this autonomy in inventing new possible modules of incompressibility whichdeterminestheactualemergenceofnew(andtrue)creativity,whichalsotakes place through the “narration” of the effected construction.

A proposal that algorithms are not simply instructions to be performed but thinking entities that construct digital spatio-temporalities. In Contagious Architecture, Luciana Parisi offers a philosophical inquiry into the status of the algorithm in architectural and interaction design. Her thesis is that algorithmic computation is not simply an abstract mathematical tool but constitutes a mode of thought in its own right, in that its operation extends into forms of abstraction that lie beyond direct human cognition and control. These include modes of infinity, contingency, and indeterminacy, as well as incomputable quantities underlying the iterative process of algorithmic processing. The main philosophical source for the project is Alfred North Whitehead, whose process philosophy is specifically designed to provide a vocabulary for “modes of thought” exhibiting various degrees of autonomy from human agency even as they are mobilized by it. Because algorithmic processing lies at the heart of the design practices now reshaping our world—from the physical spaces of our built environment to the networked spaces of digital culture—the nature of algorithmic thought is a topic of pressing importance that reraises questions of control and, ultimately, power. Contagious Architecture revisits cybernetic theories of control and information theory's notion of the incomputable in light of this rethinking of the role of algorithmic thought. Informed by recent debates in political and cultural theory around the changing landscape of power, it links the nature of abstraction to a new theory of power adequate to the complexities of the digital world.

Data has emerged as a key component that determines how interactions across the world are structured, mediated and represented. This book examines these new data publics and the areas in which they become operative, via analysis of politics, geographies, environments and social media platforms. By claiming to offer a mechanism to translate every conceivable occurrence into an abstract code that can be endlessly manipulated, digitally processed data has caused conventional reference systems which hinge on our ability to mark points of origin, to rapidly implode. Authors from a range of disciplines provide insights into such a political economy of data capitalism; the political possibilities of techno-logics beyond data appropriation and data refusal; questions of visual, spatial and geographical organization; emergent ways of life and the environments that sustain them; and the current challenges of data publics, which is explored via case studies of three of the most influential platforms in the social media economy today: Facebook, Instagram and Whatsapp. Data Publics will be of great interest to academics and students in the fields of computer science, philosophy, sociology, media and communication studies, architecture, visual culture, art and design, and urban and cultural studies.