相关论文: Geometry of Psychological Time

Recent developments in extreme value statistics have established the so-called geometric approach as a powerful modelling tool for multivariate extremes. We tailor these methods to the case of spatial modelling and examine their efficacy at…

Probabilistic mental simulation is thought to play a key role in human reasoning, planning, and prediction, yet the demands of simulation in complex environments exceed realistic human capacity limits. A theory with growing evidence is that…

Some new aspects of axially symmetric spacetimes are discussed. These results open the door for future interplay between analytical and numerical studies. The new developments are based on the role of the total mass in axial symmetry.…

Optics of metamaterials is shown to provide interesting table top models of many non-trivial space-time metrics. The range of possibilities is broader than the one allowed in classical general relativity. For example, extraordinary waves in…

Certain geometric properties of submanifolds of configuration space are numerically investigated for classical lattice phi^4 models in one and two dimensions. Peculiar behaviors of the computed geometric quantities are found only in the…

The formulation of gravity theory is considered where space-time is a 4-dimensional surface in flat ten-dimensional space. The possibility of using the "external" time (the time of ambient space) in this approach is investigated. The…

I argue that consistent geometrical descriptions of the universe are far from unique even as low-energy limits and that an abstract "atomic" description of spacetime and gauge-theoretic geometry in terms of K-theories of algebraic and…

We explore the properties of physical theories in space-times with two time dimensions. We show that the common arguments used to rule such theories out do not apply if the dynamics associated with the additional time dimension is thermal…

This paper presents an alternative approach of analyzing possibly multitype point patterns in space and space-time that occur on network structures, and introduces several different graph-related intensity measures. The proposed formalism…

In this paper we introduce a definition of time that emerges in terms of the geometry of the configuration space of a dynamical system. We illustrate this, using the Hamilton-Jacobi equation, in various examples: particle mechanics on a…

A particular science is not only defined by its object of study, but also by the point of view and method under which it considers that same object. Taking space and time as an illustrative example, our main aim here is to bring out an…

A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.

The existence of a global time is often taken for granted but should instead be considered as a matter of investigation. By using the tools of global Lorentzian geometry I show that, under physically reasonable conditions, the impossibility…

The paper presents several quantum models constructed with the formalism of algebraic geometry. The Universe is presented as a presheaf on the "space of ultimation" (i.e. the branching future) with values in certain category which enhances…

This essay is a tour around many of the lesser known pregeometric models of physics, as well as the mainstream approaches to quantum gravity, in search of common themes which may provide a glimpse of the final theory which must lie behind…

An enquiry into the physical nature of time and space and into the ontology of quantum mechanics from a metageometric perspective, resulting from the belief that geometric thought and language are powerless to farther understanding of these…

We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class $\operatorname{PTIME}$ of languages computable in polynomial time in terms of differential…

This is a brief review, in relatively non-technical terms, of recent advances in the theory of random field geometry. These advances have provided a collection of explicit new formulae describing mean values of a variety of geometric…

A theoretical analysis of the earthquake prediction problem in space-time is presented. We find an explicit structure of the optimal strategy and its relation to the generalized error diagram. This study is a generalization of the…

We introduce a novel technique to find the asymptotic time behaviour of deterministic systems exhibiting anomalous diffusion. The procedure is tested for various classes of simple but physically relevant 1-D maps and possible relevance of…