Related papers: Geometry of Psychological Time
A sketch of three senses of emergence and a suggestive view on the emergence of time and the direction of time is presented. After trying to identify which issues philosophers interested in emergent phenomena in physics view as important I…
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.
In this survey I should like to introduce some concepts of algebraic geometry and try to demonstrate the fruitful interaction between algebraic geometry and computer algebra and, more generally, between mathematics and computer science. One…
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…
Dynamics, the study of change, is normally the subject of mechanics. Whether the chosen mechanics is ``fundamental'' and deterministic or ``phenomenological'' and stochastic, all changes are described relative to an external time. Here we…
In this contribution, we suggest the approach that geometric concepts ought to be defined in terms of physical operations involving quantum matter. In this way it is expected that some (presumably nocive) idealizations lying deep within the…
We describe the algebraic relations satisfied by the harmonic and anti-harmonic moments of simply connected, but not necessarily convex planar polygons with a given number of vertices.
Information geometry has offered a way to formally study the efficacy of scientific models by quantifying the impact of model parameters on the predicted effects. However, there has been little formal investigation of causation in this…
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…
We gather material from many sources about the quantum potential and its geometric nature. The presentation is primarily expository but some new observations relating Q, V, and psi are indicated.
We study geometric data structures for sets of point-based temporal events, answering time-windowed queries, i.e., given a contiguous time interval we answer common geometric queries about the point events with time stamps in this interval.…
The issue of whether some manifestations of gravitation in the quantum domain, are indicative or not of a non-geometrical aspect in gravitation is discussed. We examine some examples that have been considered in this context, providing a…
We discuss the possibility that spacetime geometry may be an emergent phenomenon. This idea has been motivated by the Analogue Gravity programme. These are systems where the kinematics of small perturbations are dominated by an effective…
Some notions of algebraic geometry can be defined for arbitrary varieties of algebras. This leads to universal algebraic geometry. The main idea of the presented theory is to consider interactions between algebra, logic and geometry in…
We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the…
It is proposed that the mathematical formalism that is most appropriate for the study of spatially non-integrable cosmological models is the transverse geometry of a one-dimensional foliation (congruence) defined by a physical observer. By…
A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…
This paper investigates the mathematical representation of time in physics. In existing theories time is represented by the real numbers, hence their formal properties represent properties of time: these are surveyed. The central question…
Discussion of some aspects of the concept of time for a general audience: nature of time, A- and B-series, time in physics, the "now", measurement of time, definition of time units, time's arrow, relativity of time, relativity of…