Related papers: Space as relation
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The aim of the present paper is to investigate the half-spaces in the convexity structure of all quasiorders on a given set and to use them in an alternative approach to classical order dimension. The main result states that linear orders…
The human mind is endowed with innate primordial perceptions such as space, distance, motion, change, flow of time, matter. The field of cognitive science argues that the abstract concepts of mathematics are not Platonic, but are built in…
In this paper we will give two different natural generalizations of compact spaces and connected spaces simultaneously. We will show that these generalizations coincide for the subspaces of the real line and that they differ for subspaces…
We are going to introduce a new algebraic, analytic structure that is a kind of generalization of the Hausdorff dimension and measure. We give many examples and study the basic properties and relations of such systems.
We introduce a new form of logical relation which, in the spirit of metric relations, allows us to assign each pair of programs a quantity measuring their distance, rather than a boolean value standing for their being equivalent. The…
Relational particle dynamics include the dynamics of pure shape and cases in which absolute scale or absolute rotation are additionally meaningful. These are interesting as regards the absolute versus relative motion debate as well as…
We discuss the possibility of making the {\it initial} definitions of mutually different (possibly interacting, or even entangled) systems in the context of decoherence theory. We point out relativity of the concept of elementary physical…
We propose that the effective dimensionality of the space we live in depends on the length scale we are probing. As the length scale increases, new dimensions open up. At short scales the space is lower dimensional; at the intermediate…
This paper introduces a model that identifies spatial relationships for a structural analysis based on the concept of simplicial complex. The spatial relationships are identified through overlapping two map layers, namely a primary layer…
A qualitatively new, much more liberal and efficient organisation of science is proposed and justified, in connection with growing debate about further role and development of fundamental science. Although the key ideas can be explained…
We define the time travel paradox in physical terms and prove its existence by constructing an explicit example. We argue further that in theories -- such as general relativity -- where the spacetime geometry is subject to nothing but…
We consider the possibility that the basic space of physics is not spacetime, but configuration space. We illustrate this on the example with a system of gravitationally interacting point particles. It turns out that such system can be…
Distance Geometry is based on the inverse problem that asks to find the positions of points, in a Euclidean space of given dimension, that are compatible with a given set of distances. We briefly introduce the field, and discuss some open…
The current debate about a possible change of paradigm from a single universe to a multiverse scenario could have deep implications on our view of cosmology and of science in general. These implications therefore deserve to be analyzed from…
A physical theory of the world is presented under the unifying principle that all of nature is laid out before us and experienced through the passage of time. The one-dimensional progression in time is opened out into a multi-dimensional…
The concept of the space-time as emerging in the world phase transition, vs. a priori existing, is put forward. The theory of gravity with two basic symmetries, the global affine one and the general covariance, is developed. Implications…
This article explores the overall geometric manner in which human beings make sense of the world around them by means of their physical theories; in particular, in what are nowadays called pregeometric pictures of Nature. In these, the…
We argue that whether the universe is infinite or finite is less crucial than usually supposed. Paradoxes of repeating behaviour in the infinite, or eternal inflationary, universe can be alleviated by a realistic definition of differing…
In the field theories in physics, any particular region of the presumed space-time continuum and all interactions between elementary objects therein can be objectively measured and/or accounted for mathematically. Since this does not apply…