Felix Klein, one of the great nineteenth-century geometers, rediscovered in mathematics an idea from Eastern philosophy: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeated reflections and was led to forms with multiple co-existing symmetries. For a century these ideas barely existed outside the imagination of mathematicians. However in the 1980s the authors embarked on the first computer exploration of Klein's vision, and in doing so found many further extraordinary images. Join the authors on the path from basic mathematical ideas to the simple algorithms that create the delicate fractal filigrees, most of which have never appeared in print before. Beginners can follow the step-by-step instructions for writing programs that generate the images. Others can see how the images relate to ideas at the forefront of research.

Hua-yen is regarded as the highest form of Buddhism by most modern Japanese and Chinese scholars. This book is a description and analysis of the Chinese form of Buddhism called Hua-yen (or Hwa-yea), Flower Ornament, based largely on one of the more systematic treatises of its third patriarch. Hua-yen Buddhism strongly resembles Whitehead's process philosophy, and has strong implications for modern philosophy and religion. Hua-yen Buddhism explores the philosophical system of Hua-yen in greater detail than does Garma C.C. Chang's The Buddhist Teaching of Totality (Penn State, 1971). An additional value is the development of the questions of ethics and history. Thus, Professor Cook presents a valuable sequel to Professor Chang's pioneering work. The Flower Ornament School was developed in China in the late 7th and early 8th centuries as an innovative interpretation of Indian Buddhist doctrines in the light of indigenous Chinese presuppositions, chiefly Taoist. Hua-yen is a cosmic ecology, which views all existence as an organic unity, so it has an obvious appeal to the modern individual, both students and layman.

A masterful translation of one of the most influential Buddhist sutras—the Avatamsaka Sutra—by one of the greatest translators of Buddhist texts of our time Known in Chinese as Hua-yen and in Japanese as Kegon-kyo, the Avatamsaka Sutra, or Flower Ornament Scripture, is held in the highest regard and studied by Buddhists of all traditions. Through its structure and symbolism, as well as through its concisely stated principles, it conveys a vast range of Buddhist teachings. This one-volume edition contains Thomas Cleary’s definitive translation of all thirty-nine books of the sutra, along with an introduction, a glossary, and Cleary’s translation of Li Tongxuan’s seventh-century guide to the final book, the Gandavyuha, “Entry into the Realm of Reality.”

Originating in the Atharva Veda, the concept of Indra's Net is a powerful metaphor for interconnectedness. It was transmitted via Buddhism's Avatamsaka Sutra into Western thought, where it now resides at the heart of post-modern discourse. According to this metaphor, nothing ultimately exists separately by itself and all boundaries can be deconstructed. This book invokes Indra's Net to articulate the open architecture, unity and continuity of Hinduism. Seen from this perspective, Hinduism defies pigeonholing into the traditional, modern and post-modern categories by which the West defines itself; rather, it becomes evident that Hinduism has always spanned all three categories simultaneously and without contradiction.It is fashionable among intellectuals to assert that dharma traditions lacked any semblance of unity before the British period, and that the contours of contemporary Hinduism were bequeathed to us by our colonial masters. Such arguments routinely target Swami Vivekananda, a key interlocutor who shattered many deeply rooted prejudices against Indian civilization. They accuse him of having camouflaged various alleged 'contradictions' within traditional Hinduism, and charge him with having appropriated the principles of Western religion to 'manufacture' a coherent and unified worldview and set of practices known today as Hinduism.Indra's Net: Defending Hinduism's Philosophical Unity provides a foundation for theories that slander contemporary Hinduism as illegitimate, ascribing sinister motives to its existence, and characterizing its fabric as oppressive. Rajiv Malhotra offers a detailed, systematic rejoinder to such views, and articulates the multidimensional, holographic understanding of reality that grounds Hindu dharma. He also argues that Vivekananda's creative interpretations of Hindu dharma informed and influenced many Western intellectual movements of the post-modern era. Indeed, as he cites with many insightful examples, appropriations from Hinduism have provided a foundation for cutting-edge discoveries in several fields, including cognitive science and neuroscience.

Hymn to Tripurasundarī (Hindu deity).

The long-awaited new edition of a groundbreaking work on the impact of alternative concepts of space on modern art. In this groundbreaking study, first published in 1983 and unavailable for over a decade, Linda Dalrymple Henderson demonstrates that two concepts of space beyond immediate perception—the curved spaces of non-Euclidean geometry and, most important, a higher, fourth dimension of space—were central to the development of modern art. The possibility of a spatial fourth dimension suggested that our world might be merely a shadow or section of a higher dimensional existence. That iconoclastic idea encouraged radical innovation by a variety of early twentieth-century artists, ranging from French Cubists, Italian Futurists, and Marcel Duchamp, to Max Weber, Kazimir Malevich, and the artists of De Stijl and Surrealism. In an extensive new Reintroduction, Henderson surveys the impact of interest in higher dimensions of space in art and culture from the 1950s to 2000. Although largely eclipsed by relativity theory beginning in the 1920s, the spatial fourth dimension experienced a resurgence during the later 1950s and 1960s. In a remarkable turn of events, it has returned as an important theme in contemporary culture in the wake of the emergence in the 1980s of both string theory in physics (with its ten- or eleven-dimensional universes) and computer graphics. Henderson demonstrates the importance of this new conception of space for figures ranging from Buckminster Fuller, Robert Smithson, and the Park Place Gallery group in the 1960s to Tony Robbin and digital architect Marcos Novak.

The roots between the Hindu religion and the wider culture are deep and uniquely complex. No study of either ancient or contemporary Indian culture can be undertaken without a clear understanding of Hindu visual arts and their sources in religious belief and practice. Defining what is meant by religion - no such term exists in Sanskrit - and what is understood by Hindu ideals of beauty, Heather Elgood provides the best synthesis and critical study of recent scholarship on the topic. In addition, this book offers critical background information for anyone interested in the social and anthropological roots of artistic creativity, as well as the rites, practices and beliefs of the hundreds of millions of Hindus in the world today.

Originally written in the First Century, A.D. by Asvaghosha. This may be the oldest known story of the complete life of Buddha, having been written in the first century AD. The author was an educated ecclesiastic Buddhist who traveled throughout India collecting stories and traditions relating to the Buddhas life. He was a famous preacher and musician who then wove them into a Sanskrit poem which he performed musically during his travels. The people of India delighted in this magical tale whenever it was performed with the choir of musicians who traveled with him. It holds many facts that other biographies or stories of the Buddha dont have, which makes this work so important. The entire epic is preserved in this rare book, long out of print, which may have otherwise been lost to the western world.