This book deals with the development of thinking under different cultural conditions, focusing on the evolution of mathematical thinking in the history of science and education. Starting from Piaget's genetic epistemology, it provides a conceptual framework for describing and explaining the development of cognition by reflective abstractions from systems of actions.

An illuminating exploration of the meaning of abstract art by acclaimed art historian Kirk Varnedoe "What is abstract art good for? What's the use—for us as individuals, or for any society—of pictures of nothing, of paintings and sculptures or prints or drawings that do not seem to show anything except themselves?" In this invigorating account of abstract art since Jackson Pollock, eminent art historian Kirk Varnedoe, the former chief curator of painting and sculpture at the Museum of Modern Art, asks these and other questions as he frankly confronts the uncertainties we may have about the nonrepresentational art produced in the past five decades. He makes a compelling argument for its history and value, much as E. H. Gombrich tackled representation fifty years ago in Art and Illusion, another landmark A. W. Mellon Lectures volume. Realizing that these lectures might be his final work, Varnedoe conceived of them as a statement of his faith in modern art and as the culminating example of his lucidly pragmatic and philosophical approach to art history. He delivered the lectures, edited and reproduced here with their illustrations, to overflowing crowds at the National Gallery of Art in Washington in the spring of 2003, just months before his death. With brilliance, passion, and humor, Varnedoe addresses the skeptical attitudes and misunderstandings that we often bring to our experience of abstract art. Resisting grand generalizations, he makes a deliberate and scholarly case for abstraction—showing us that more than just pure looking is necessary to understand the self-made symbolic language of abstract art. Proceeding decade by decade, he brings alive the history and biography that inform the art while also challenging the received wisdom about distinctions between abstraction and representation, modernism and postmodernism, and minimalism and pop. The result is a fascinating and ultimately moving tour through a half century of abstract art, concluding with an unforgettable description of one of Varnedoe's favorite works. Please note: All images in this ebook are presented in black and white and have been reduced in size.

Computer Science: Reflections on the Field, Reflections from the Field provides a concise characterization of key ideas that lie at the core of computer science (CS) research. The book offers a description of CS research recognizing the richness and diversity of the field. It brings together two dozen essays on diverse aspects of CS research, their motivation and results. By describing in accessible form computer science's intellectual character, and by conveying a sense of its vibrancy through a set of examples, the book aims to prepare readers for what the future might hold and help to inspire CS researchers in its creation.

"This book explores the relation of abstract art to nature. Traditional picturing and sculpture are based on conventions of resemblance between the work and that which it is a representation "of". Abstract works, in contrast, adopt alternative modes of visual representation, or break down and reconfigure the mimetic conventions of pictorial art and sculpture. Obviously this means that abstract art takes many different forms. However, this diversity should not mask some key structural features; these center on two basic relations to nature (understanding nature in the broadest sense to comprise the world of recognisable objects, creatures, organisms, processes, and states of affairs). The first involves abstracting from nature, to give selected aspects of it a new and extremely unfamiliar appearance. The second involves abstract art as the affirmation of a relatively unconstrained natural creativity that issues in new, autonomous forms that are not constrained by mimetic conventions. (Such creativity is often attributed to the power of the unconscious.)The book contains three categories of essays: 1) those on classical modernism (Mondrian, Malevich, Kandinsky, Arp, early American abstraction), 2) those on post-war abstraction (Pollock, Still, Newman, Smithson, Noguchi, Arte Povera, Michaux, postmodern developments), and 3) those of a broader art historical and philosophical scope"--Provided by publisher.

How the formal ingenuity of abstract art has been cross-fertilized by creative discrepancies—a cross-cultural voyage stretching from Hong Kong and Islamic regions to Canada, Australia, Europe, and the United States. For anyone who thinks the question of abstract art is settled, this book will come as a surprise. Discrepant abstraction is hybrid and partial, elusive and repetitive, obstinate and strange. It includes almost everything that does not neatly fit into the institutional narrative of abstract art as a monolithic quest for artistic purity. Exploring cross-cultural scenarios in twentieth-century art, this second volume in the Annotating Art's Histories series alters our understanding of abstract art as a signifier of modernity by revealing the multiple directions it has taken in wide-ranging international contexts.Impure, imperfect, and incomplete, the version of abstraction that emerges from this global journey—from Hong Kong and Islamic regions to Canada, Australia, Europe, and the United States—shows how the formal ingenuity of abstract art has been cross-fertilized, from abstract expressionism onwards, by creative discrepancies that arise when disparate visual languages are brought into dialogue. Discrepant Abstraction is essential reading for students, practitioners and anyone curious about cross-cultural interaction in the visual arts. Copublished with inIVA/Institute of International Visual Arts, London