相关论文: Geometry of Psychological Time
The paper presents, to our knowledge, a first fairly comprehensive and mathematically well-underpinned classification of the psychopathology of time (and space). After reviewing the most illustrative first-person accounts of…
One of the most distinguished features of our algebraic geometrical, pencil concept of space-time is the fact that spatial dimensions and time stand, as far as their intrinsic structure is concerned, on completely different footings: the…
We briefly review two concepts of time - the usual time associated with "being" and more recent ideas, answering to the description of "becoming". The approximation involved in the former is examined. Finally we argue that it is…
We summarize the arguments that space and time are likely to be emergent notions; i.e. they are not present in the fundamental formulation of the theory, but appear as approximate macroscopic concepts. Along the way we briefly review…
Experience of time is one of the primordial human experiences which is deeply tied to human consciousness. But despite this intimate relation of time with human conscious experience, time has proved to be very elusive. Particularly in…
Some ideas aimed to understand that time is one-dimensional are briefly reviewed. Some attempts to construct theories in varieties with more spatial and temporal components are presented. It is discussed, from the epistemological point of…
This is a survey paper about a selection of results in complex algebraic geometry that appeared in the recent and less recent litterature, and in which rational homogeneous spaces play a prominent r{\^o}le. This selection is largely…
This paper presents a geometric approach to the problem of modelling the relationship between words and concepts, focusing in particular on analogical phenomena in language and cognition. Grounded in recent theories regarding geometric…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
We distinguish two different concepts of time that play a role in physics: \textit{geometric time} and \textit{creative time}. The former is the time of deterministic physics and merely parametrizes a given evolution. The latter is instead…
Granular space-time posits that everything can be expressed as a function of space-time and matter. And this includes the quantum wave function {\Psi} . To give a geometric interpretation of {\Psi} , we first need to examine time. The fact…
Mathematical theory of an observer is elaborated upon the basis of A.Poincare's ideas on the nature of geometry and the role of observer's perceptive space. The said theory is generalizing reference frames theory in GR. Physical structure…
The advantages to consider the ordinary space-time as the symplectic rather than pseudo-orthogonal one are indicated, and the consequences of extending this view to extra space/time dimensions are discussed.
Psychometrics and quantitative psychology rely strongly on statistical models to measure psychological processes. As a branch of mathematics, geometry is inherently connected to measurement and focuses on properties such as distance and…
Confusion and disagreement around the notion of time is due to the fact that we often fail to recognize that we call 'time' a variety of distinct notions, only partially related to one another. Many apparently obvious properties of time are…
This paper proposes an abstract mathematical frame for describing some features of biological time. The key point is that usual physical (linear) representation of time is insufficient, in our view, for the understanding key phenomena of…
An algebraic scheme is suggested in which discretized spacetime turns out to be a quantum observable. As an example, a toy model producing spacetimes of four points with different topologies is presented. The possibility of incorporating…
Space-Time in general relativity is a dynamical entity because it is subject to the Einstein field equations. The space-time metric provides different geometrical structures: conformal, volume, projective and linear connection. A deep…
We review some modern theories about the structure of space and time, in particular those related to discrete space and time. Following an epistemological method we start from theories which discuss discrete space and time as a mathematical…
A simple visual representation of Minkowski spacetime appropriate for a student with a background in geometry and algebra is presented. Minkowski spacetime can be modeled with a Euclidean 4-space to yield accurate visualizations as…