The late tenth century siddha and scholar Ratnākaraśānti, also known as the Mahāsiddha Śāntipa, was renowned as the author of both philosophical śāstras and commentaries on tantra. Typically, these are considered separate spheres of activity. However, Ratnākaraśānti’s approach, building on the tradition of scholarship associated with the Mahāvairocanābhisaṃbodhitantra and the Guhyasamājatantra, as well as on Yogācāra analysis and Buddhist pramāṇa theory, is highly syncretic. This paper is a study of Ratnākaraśānti’s commentaries that highlights his synthesis of the exoteric and esoteric (...) streams of Buddhist discourse, with particular emphasis on the nondual nature of reflexive awareness (svasaṃvitti, rang rig), or 'luminosity' (prakāśa, gsal ba), which serves as the conceptual bridge between sūtra and tantra. (shrink)

The Yang-Mills mass gap problem has stood as one of the most profound unresolved questions in theoretical physics for nearly half a century. Despite extensive efforts, a rigorous mathematical proof of the mass gap's existence in Yang-Mills theory has remained elusive—until now. -/- The proof presented in this work represents not merely a technical achievement, but a fundamental paradigm shift in our understanding of the mathematical structures underlying physical reality. By rigorously demonstrating that the mass gap arises as a direct (...) consequence of the gauge-invariant constraint structure of Yang-Mills theory, we overturn decades of conventional assumptions and reveal a startling truth: what we perceive as physical laws are in fact mathematically unavoidable necessities emerging from the very consistency conditions required for a well-defined quantum field theory. (shrink)

This dissertation examines the theory of perceptual cognition laid out by the 7th century Buddhist scholar, Dharmakīrti, in his magnum opus, the Pramāṇavārttika. Like most theories of perception, both ancient and modern, the sensory cognition of ordinary objects is a topic of primary concern. Unlike other theorists, however, Dharmakīrti advances a technical definition of “perception” as a cognition which is both nonconceptual and non-erroneous. Dharmakīrti’s definition of perception is thereby deliberately inclusive of three additional types of “perceptual” cognition, in addition (...) to veridical sensory awareness: the nonconceptual mental apprehension of an immediately-preceding cognition (“mental perception”), the vivid appearance of soteriologically efficacious objects of contemplative practice (“yogic perception”), and the sheer unmediated presence of the contents of cognition—whatever these might be—to the cognizing mind (“reflexive awareness”). Through the logical examination of what it means to be aware of an object, Dharmakīrti demonstrates that the awareness of an object is just the awareness of a phenomenal form or cognitive image produced by that object. Pursuing this analysis further, however, Dharmakīrti argues that the very notion of an object of cognition that exists “externally” or outside the mind is incoherent. Additionally, Dharmakīrti maintains that the phenomenological structure of subject and object—that is, the “first-personal” sense of one’s own cognitions as pertaining to oneself (“for-me-ness”), together with the inseparably concomitant sense that the objects of cognition exist “out there” in an extramental world—is strictly a form of cognitive error. Therefore, because ordinary sensory cognition is inherently structured by this subject-object duality, ordinary sensory cognition must in the final analysis be understood as erroneous. According to Dharmakīrti, in other words, ultimately only the nondual “luminosity” of reflexive awareness is genuinely perceptual, because only reflexive awareness is undistorted by nature. In this way, Dharmakīrti’s epistemology provides a theoretical foundation for the advanced nondual contemplative practices of Indian and Tibetan Buddhism, particularly Mahāmudrā and rDzogs chen. (shrink)