Related papers: A Constructive Definition of Space via Dynamical E…
A new dynamical paradigm merging quantum dynamics with cosmology is discussed. Time evolution involves a genuine passage of time, which distinguishes the formalism from those where dynamics in space is equivalent to statics in space-time.…
We prove that, under suitable assumptions, operationally motivated data completely determine a space-time in which the quantum systems can be interpreted as evolving. At the same time, the dynamics of the quantum system is also determined.…
In line with the sensorimotor contingency theory, we investigate the problem of the perception of space from a fundamental sensorimotor perspective. Despite its pervasive nature in our perception of the world, the origin of the concept of…
This paper concerns the intersection of natural language and the physical space around us in which we live, that we observe and/or imagine things within. Many important features of language have spatial connotations, for example, many…
We investigate structure that describes physical data in gravitational systems that is, to one degree or another, independent of the metric and affine structure. We dub such structure surplus structure and seek to incorporate it into our…
Dynamical systems are abstract models of interaction between space and time. They are often used in fields such as physics and engineering to understand complex processes, but due to their general nature, they have found applications for…
The personal spatial structure of an observer is introduced as a central element in the positioning of objects in space. The link between a reference frame used by an observer and his personal spatial structure is discussed. Research on…
This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a…
Evolutionary dynamics is often viewed as a subtle process of change accumulation that causes a divergence among organisms and their genomes. However, this interpretation is an inheritance of a gradualistic view that has been challenged at…
Establishing the emergence of evolutionary behavior as a defining characteristic of 'life' is a major step in the Artificial life (ALife) studies. We present here an abstract formal framework for this aim based upon the notion of high-level…
Exploration is one of the most important tasks in Reinforcement Learning, but it is not well-defined beyond finite problems in the Dynamic Programming paradigm (see Subsection 2.4). We provide a reinterpretation of exploration which can be…
We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator $\mathbf{T}$ with a suitable real-valued function $T$ on the space of physical states. The proper…
The discussion is limited to first-class parametrized systems, where the definition of time evolution and observables is not trivial, and to finite dimensional systems in order that technicalities do not obscure the conceptual framework.…
In this paper, we present a constructive generalization of metric and uniform spaces by introducing a new class of spaces, called cover spaces. These spaces form a topological concrete category with a full reflective subcategory of complete…
In this work, we propose the concept of Construction Defining Functionality (CDF), which characterizes functions by the structural spaces they generate through iteration,recursion, and logical application. By viewing functions as generators…
Universe structure emerges in the unreduced, complex-dynamic interaction process with the simplest initial configuration (two attracting homogeneous fields, quant-ph/9902015). The unreduced interaction analysis gives intrinsically creative…
In the mathematical tradition, reversibility requires that the evolution of a dynamical system be a bijective function. In the context of graph rewriting, however, the evolution is not even a function, because it is not even deterministic…
We explore the notion of spatial extent and structure, already alluded to in earlier literature, within the formulation of quantum mechanics on the noncommutative plane. Introducing the notion of average position and its measurement, we…
To analyze the evolutionary emergence of structural complexity in physical processes we introduce a general, but tractable, model of objects that interact to produce new objects. Since the objects--\emph{$epsilon$-machines}--have well…
Time is, figuratively and literally, becoming the new dimension for crystalline matter. As such, rapid recent progress on time-varying media gave rise to the notion of temporal and spatiotemporal crystals. Fundamentally rethinking the role…