We investigate whether small perturbations can cause relaxation to quantum equilibrium over very long timescales. We consider in particular a two-dimensional harmonic oscillator, which can serve as a model of a field mode on expanding space. We assume an initial wave function with small perturbations to the ground state. We present evidence that the trajectories are highly confined so as to preclude relaxation to equilibrium even over very long timescales. Cosmological implications are briefly discussed.

Study of inference in Jaina and Buddhist logic.

On Jainism and its history, philosophy, culture and literature.

There are good reasons to think that Vāsudeva, Saṃkarṣaṇa, Pradyumna and Aniruddha already form a sort of implicit tetrad in the HV. The aim of this paper is to draw attention to often overlooked data related to this tetrad. (1) Upon first reading, the sequence of the HV episodes appears to be somewhat disconnected, and might lead one to conclude that no such grouping of these figures had as of yet taken place. Nevertheless, a closer look at the structure (...) of the text makes it clear that these four characters are one of the main focuses of the narrator’s interest. (2) The relationships of these four heroes to one another and to other deities will be examined. In addition to their close kinship, these heroes with the exception of Aniruddha, are also said to be incarnations of other entities; thus the logic underpinning this grouping must be located at this other level. (3) Considered against the backdrop of the entire HV, one realizes that a basic pattern is established in which the presence of the goddess, under various names and functions, is required not only to facilitate Saṃkarṣaṇa’s and Kr̥ṣṇa’s births and actions on earth, but also the actions of Pradyumna and Aniruddha. In fact, neither Kr̥ṣṇa Vāsudeva, nor Saṃkarṣaṇa, nor Pradyumna nor Aniruddha can act entirely independently of her assistance. (4) The HV does not employ the word vyūha in connection with the group of Vāsudeva, Saṃkarṣaṇa, Pradyumna and Aniruddha. Nevertheless, during the battle waged to deliver Aniruddha, the idea of vyūha is present even if the word itself is not. HV 110.47–49 describes a true trivyūha composed of three fighters (Vāsudeva, Saṃkarṣaṇa and Pradyumna), who are arranged in such a way as to protect one another. The episode of Aniruddha’s liberation appears to be the missing link, showing clearly that at least Kr̥ṣṇa, Saṃkarṣaṇa and Pradyumna are capable of assuming a vyūha as they fight the Rudraic forces. (shrink)