Related papers: Arp's Indomitable Universe
We introduce an expressive probabilistic temporal epistemic logic PTEL suitable to reason about uncertain knowledge of a non-rigid set of agents that can be changed during time. We define semantics for PTEL as Kripke models with epistemic…
Basic problems of complex systems are outlined with an emphasis on irreducibility and dynamic many-to-many correspondences. We discuss the importance of a constructive approach to artificial reality and the significance of an internal…
Discussion of ``The William Kruskal Legacy: 1919--2005'' by Stephen E. Fienberg, Stephen M. Stigler and Judith M. Tanur [arXiv:0710.5063]
A homage to the life and mathematics of John K. S. McKay. Obituary for the Bulletin of the London Mathematical Society.
We develop a new approach for the p-adic Simpson correspondence, closely related to the original approach of Faltings, but also inspired by the work of Ogus and Vologodsky on an analogue in characteristic p>0. This second article is devoted…
The observable universe is fundamentally inhomogeneous and anisotropic. Quantum description of the generation of these inhomogeneities and anisotropies is ill-understood and unsatisfactory. After providing a brief account of the standard…
The long story of the oscillatory approach to the initial cosmological singularity and its more recent incarnation in multidimensional universe models is told.
Three illustrated lectures given by Stephen Hawking as part of a series of six lectures with Roger Penrose on the nature of space and time sponsored by Princeton University Press.
A brief review of Heisenberg's life and work: participating in the youth movement in the aftermath of World War I, creating quantum mechanics, conflict with "deutsche Physik", involvement in "Hitler's Uranium Project", last illusions.…
We give a Hopf-algebraic formulation of the $R^*$-operation, which is a canonical way to render UV and IR divergent Euclidean Feynman diagrams finite. Our analysis uncovers a close connection to Brown's Hopf algebra of motic graphs. Using…
Doob's essential contributions to Probability theory are discussed; this includes the main early results on martingale theory, Doob's $h$-transform, as well as a summary of Doob's three books. Finally, Doob's `stochastic triangle' is viewed…
Conceptual problems regarding the arrow of time in classical physics, quantum physics, cosmology, and quantum gravity are discussed. Particular attention is paid to the dynamical role of the quantum indeterminism, and to various concepts of…
This work introduces a novel framework of uniform realizability that unifies and generalizes various realizability interpretations of logic, particularly focussing on the treatment of atomic formulas and quantifiers. Traditional…
We investigate properties of the ineffability and the Ramsey operator, and a common generalization of those that was introduced by the second author, with respect to higher indescribability, as introduced by the first author. This extends…
The Hubble Space Telescope (HST), in its thirteen years of operation, has allowed us to observe properties of the universe humans have been able, until very recently, to probe only with their thoughts. This review presents a brief summary…
Several chapters in this book present various aspects of Michel Henon's scientific acheivements that spread over a large range of subjects, and yet managed to make deep contributions to most of them. The authors of these chapters make a…
Identifying literary, scientific, and technical works of enduring interest is challenging. Few are able to name significant works across more than a handful of domains or languages. This paper introduces an automatic method for identifying…
This paper explores the fundamental causal limits on how much of the universe we can observe or affect. It distinguishes four principal regions: the affectable universe, the observable universe, the eventually observable universe, and the…
The article surveys a little of the history of the technology, sets out the main current theoretical approaches in brief, and discusses the on-going opposition between theoretical and empirical approaches. It illustrates the situation with…
This text tries to give an elementary introduction to the mathematical properties of infinite sets. The aim is to keep the approach as simple as possible. Advanced knowledge of mathematics is not necessary for a proper understanding, and…