In the past four decades, the notion of quantum polynomial-time computability has been mathematically modeled by quantum Turing machines as well as quantum circuits. This paper seeks the third model, which is a quantum analogue of the schematic definition of recursive functions. For quantum functions mapping finite-dimensional Hilbert spaces to themselves, we present such a schematic definition, composed of a small set of initial quantum functions and a few construction rules that dictate how to build a new quantum function from (...) the existing ones. We prove that our schematic definition precisely characterizes all functions that can be computable with high success probabilities on well-formed quantum Turing machines in polynomial time, or equivalently uniform families of polynomial-size quantum circuits. Our new, schematic definition is quite simple and intuitive and, more importantly, it avoids the cumbersome introduction of the well-formedness condition imposed on a quantum Turing machine model as well as of the uniformity condition necessary for a quantum circuit model. Our new approach can further open a door to the descriptional complexity of quantum functions, to the theory of higher-type quantum functionals, to the development of new first-order theories for quantum computing, and to the designing of programming languages for real-life quantum computer. (shrink)

Two-player, zero-sum, non-cooperative, blindfold games in extensive form with incomplete information are considered in this paper. Any information about past moves which players played is stored in a database, and each player can access the database. A polynomial game is a game in which, at each step, all players withdraw at most a polynomial amount of previous information from the database. We show resource-bounded determinacy of some kinds of finite, zero-sum, polynomial games whose pay-off sets are computable by non-deterministic polynomial-time (...) function-oracle Turing machines. We call a pay-off set -determined if, for any polynomial game G associated with the given pay-off set, either player has a winning strategy which is in for any subgames of G. We show that there exists an FP-strongly-determined pay-off set which is computed by an exponential-time oracle Turing machine, where FP is the set of polynomial-time computable functions. We also discuss several relationships between the determinacy of polynomial games and recursion-theoretic properties for the classes co-NP and co-NEXP. We show that the polynomial version of the axiom of choice holds under some assumption of polynomial determinacy for a pay-off set which is polynomial-time computable with parallel queries. This principle of choice implies that co-NP has the separation property. (shrink)

When Sasaki Sokei-an founded his First Zen Institute of North America in 1930 he suggested that bringing Zen Buddhism to America was like "holding a lotus against a rock and waiting for it to set down roots." Today, Buddhism is part of the cultural and religious mainstream. Flowers on the Rock examines the dramatic growth of Buddhism in Canada and questions some of the underlying assumptions about how this tradition has changed in the West. Using historical, ethnographic, and biographical approaches, (...) contributors illuminate local expressions of Buddhism found throughout Canada and relate the growth of Buddhism in Canada to global networks. A global perspective allows the volume to overcome the stereotype that Asia and the West are in opposition to each other and recognizes the continuities between Buddhist movements in Asia and the West that are shaped by the same influences of modernity and globalization. Flowers on the Rock studies the fascinating and ingenious changes, inflections, and adaptations that Buddhists make when they set down roots in a local culture. It is essential reading for anyone interested in Buddhism, religious life in Canada, and the broader issues of multiculturalism and immigration. Contributors include Michihiro Ama, D. Mitra Barua, Paul Crowe, Melissa Anne-Marie Curley, Mavis Fenn, Kory Goldberg, Sarah F. Haynes, Jackie Larm, Paul McIvor, James Placzek, and Angela Sumegi. (shrink)

Introduction to zen training" is a translation of "Sanzen nyumon", a text for beginning students by Omori Sogen, one of the foremost Zen masters of the twentieth century. Providing a solid grounding in the physical nature of Zen meditation, this book discusses brreathing, posture, physiology, drowsiness, pain, how to find a teacher, and the differences between the two main schools of Zen.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Zen War StoriesSteven HeineZen War Stories. By Brian Daizen Victoria. London and New York: Routledge-Curzon, 2003. Pp. xviii + 268. Hardcover $124.95. Paper $34.95.Brian Daizen Victoria's Zen War Stories, following his highly acclaimed but also highly provocative Zen at War (Weatherhill, 1997), continues his withering attack on the embracing of wartime ideology by leading Zen masters and practitioners in Japan. Victoria seeks to show that the attitude characteristic (...) of numerous examples of prominent Zen monks and scholars was not simply a matter of benignly resisting, or even passively accepting, the rhetoric of Imperial Way Buddhism by clergy who were under pressure and powerless to stand up to the authorities. Nor was it an example of innocently recognizing historical and ideological affinities between Zen monastic discipline and military training.On the contrary, the Zen masters discussed here eagerly and enthusiastically endorsed some of the most excessive and reprehensible aspects of imperial ideology in the name of a corrupted vision of spiritual realization as a tool to spread the doctrine of the Greater East Asia Co-prosperity Sphere. They also used Zen wedded to hyper-nationalism and imperialism as a tool to misread the historical records of their own tradition and to help transport Japanese supremacy to China and Korea, while refusing to acknowledge or repent for their actions with the defeat of Japan. This outlook also infected numerous politicians and military figures, who turned to Buddhism as a way of explaining away or masking their roles leading up to, as well as during and after, World War II.In part 1 of Zen War Stories Victoria documents several masters who have become icons in the West for their apparent adherence to a Zen tradition linked with an ability to address contemporary culture. After showing in chapter 4 that Ōmori [End Page 345] Sōgen, praised for his prowess in swordsmanship and other arts, had a fascistic, "Mr. Hyde" side as manifested in the founding in 1932 of the Kinnō Ishin Dōmei (League for Loyalty to the Emperor and the Restoration), Victoria turns to the case of Yasutani Haku'un. In chapter 5, "Zen Master Dōgen Goes to War," we find that Yasutani, known as the teacher of Philip Kapleau and the inspiration for The Three Pillars of Zen, wanted to smash all universities for being traitors. He was a fanatical militarist who "transformed the life and thought of Zen Master Dōgen (1200-1253), the thirteenth-century founder of the Sōtō Zen sect in Japan, into a propaganda tool for Japanese militarism" (p. 68).In particular, Yasutani tried to argue that Dōgen's famed pilgrimage to Song China in 1223 was triggered not by a longing for the Buddhist Dharma but by a disgust with the new shogunate and an infatuation with preserving the Imperial House. According to Victoria, Yasutani's corrupted spirituality did not end with a support for militarism. He was also even more "ethnic chauvinist, sexist, and anti-Semitic" (p. 68) than his teacher Harada Daiun Sōgaku, whose "most memorable wartime quote is: '[If ordered to] march: tramp, tramp, or shoot: bang, bang. This is the manifestation of the highest Wisdom [of enlightenment]"' (pp. 66-67).After discussing in chapter 7, "Zen 'Selflessness' in Japanese Militarism," how Zen's historical relation to the samurai was misinterpreted to support the imperial ideology concerning the acceptance of death by D. T. Suzuki and other prominent representatives of Zen, including former Eiheiji temple abbot Kumazawa Taizen, part 2 takes up examples of the involvement with Buddhist thought by military and political leaders. While this section is less devastating as a critique of Zen than of Japanese Buddhism and society in general, Victoria explains in chapter 10, "Buddhism-The Last Refuge of War Criminals," how easily the moral basis of religion can be distorted and subverted. For example, as recollected by Buddhist studies scholar Hanayama Shinshō, seven Class A war criminals who had been condemned to death continued, while on death row, to cling hypocritically to Buddhism to find some feeling of solace. For instance, Hirota Kōki never abandoned his attachment to Zen and the warrior class and... (shrink)

This is a book review of the book Frontiers of Japanese Philosophy 2: Neglected Themes and Hidden Variations edited by Victor Sōgen Hori and Melissa Anne-Marie Curley, published in 2008 by the Nanzan Institute for Religion and Culture, Nagoya, Japan.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Zen War StoriesSteven HeineZen War Stories. By Brian Daizen Victoria. London and New York: Routledge-Curzon, 2003. Pp. xviii + 268. Hardcover $124.95. Paper $34.95.Brian Daizen Victoria's Zen War Stories, following his highly acclaimed but also highly provocative Zen at War (Weatherhill, 1997), continues his withering attack on the embracing of wartime ideology by leading Zen masters and practitioners in Japan. Victoria seeks to show that the attitude characteristic (...) of numerous examples of prominent Zen monks and scholars was not simply a matter of benignly resisting, or even passively accepting, the rhetoric of Imperial Way Buddhism by clergy who were under pressure and powerless to stand up to the authorities. Nor was it an example of innocently recognizing historical and ideological affinities between Zen monastic discipline and military training.On the contrary, the Zen masters discussed here eagerly and enthusiastically endorsed some of the most excessive and reprehensible aspects of imperial ideology in the name of a corrupted vision of spiritual realization as a tool to spread the doctrine of the Greater East Asia Co-prosperity Sphere. They also used Zen wedded to hyper-nationalism and imperialism as a tool to misread the historical records of their own tradition and to help transport Japanese supremacy to China and Korea, while refusing to acknowledge or repent for their actions with the defeat of Japan. This outlook also infected numerous politicians and military figures, who turned to Buddhism as a way of explaining away or masking their roles leading up to, as well as during and after, World War II.In part 1 of Zen War Stories Victoria documents several masters who have become icons in the West for their apparent adherence to a Zen tradition linked with an ability to address contemporary culture. After showing in chapter 4 that Ōmori [End Page 345] Sōgen, praised for his prowess in swordsmanship and other arts, had a fascistic, "Mr. Hyde" side as manifested in the founding in 1932 of the Kinnō Ishin Dōmei (League for Loyalty to the Emperor and the Restoration), Victoria turns to the case of Yasutani Haku'un. In chapter 5, "Zen Master Dōgen Goes to War," we find that Yasutani, known as the teacher of Philip Kapleau and the inspiration for The Three Pillars of Zen, wanted to smash all universities for being traitors. He was a fanatical militarist who "transformed the life and thought of Zen Master Dōgen (1200-1253), the thirteenth-century founder of the Sōtō Zen sect in Japan, into a propaganda tool for Japanese militarism" (p. 68).In particular, Yasutani tried to argue that Dōgen's famed pilgrimage to Song China in 1223 was triggered not by a longing for the Buddhist Dharma but by a disgust with the new shogunate and an infatuation with preserving the Imperial House. According to Victoria, Yasutani's corrupted spirituality did not end with a support for militarism. He was also even more "ethnic chauvinist, sexist, and anti-Semitic" (p. 68) than his teacher Harada Daiun Sōgaku, whose "most memorable wartime quote is: '[If ordered to] march: tramp, tramp, or shoot: bang, bang. This is the manifestation of the highest Wisdom [of enlightenment]"' (pp. 66-67).After discussing in chapter 7, "Zen 'Selflessness' in Japanese Militarism," how Zen's historical relation to the samurai was misinterpreted to support the imperial ideology concerning the acceptance of death by D. T. Suzuki and other prominent representatives of Zen, including former Eiheiji temple abbot Kumazawa Taizen, part 2 takes up examples of the involvement with Buddhist thought by military and political leaders. While this section is less devastating as a critique of Zen than of Japanese Buddhism and society in general, Victoria explains in chapter 10, "Buddhism-The Last Refuge of War Criminals," how easily the moral basis of religion can be distorted and subverted. For example, as recollected by Buddhist studies scholar Hanayama Shinshō, seven Class A war criminals who had been condemned to death continued, while on death row, to cling hypocritically to Buddhism to find some feeling of solace. For instance, Hirota Kōki never abandoned his attachment to Zen and the warrior class and... (shrink)