Related papers: Geography as a Science of the Earth's Surface Foun…
Astrobiology is usually defined as the study of the origin, evolution, distribution, and future of life in the universe. As such it is inherently interdisciplinary and cannot help but engender a worldview infused by cosmic and evolutionary…
We view difference algebra as the study of algebraic objects in the topos of difference sets. The methods of topos theory and categorical logic enable us to develop difference homological algebra, identify a solid foundation for difference…
The notion that the geometry of our space-time is not only a static background but can be physically dynamic is well established in general relativity. Geometry can be described as shaped by the presence of matter, where such shaping…
Based on the cosmological principle only, the method of describing the evolution of the Universe, called cosmography, is in fact a kinematics of cosmological expansion. The effectiveness of cosmography lies in the fact that it allows, based…
In living systems, we often see the emergence of the ingredients necessary for computation -- the capacity for information transmission, storage, and modification -- begging the question of how we may exploit or imitate such biological…
The theory uses methods and language of linear algebra to study nonlinear spaces. These techniques can be used particularly to describe analytic geometry of non-linear elliptic, hyperbolic, De Sitter and Anti de Sitter spaces. The main…
Geographical phenomena fall into two categories: scaleful phenomena and scale-free phenomena. The former bears characteristic scales, and the latter has no characteristic scale. The conventional quantitative and mathematical methods can…
The recognition that the cosmological constant may be non-zero forces us to re-evaluate standard notions about the connection between geometry and the fate of our Universe. An open Universe can recollapse, and a closed Universe can expand…
A physical applicability of normed split-algebras, such as hyperbolic numbers, split-quaternions and split-octonions is considered. We argue that the observable geometry can be described by the algebra of split-octonions. In such a picture…
A new mathematical theory, non-associative geometry, providing a unified algebraic description of continuous and discrete spacetime, is introduced.
The question of the nature of space around us has occupied thinkers since the dawn of humanity, with scientists and philosophers today implicitly assuming that space is something that exists objectively. Here we show that this does not have…
In the era of foundation models and Large Language Models (LLMs), Euclidean space has been the de facto geometric setting for machine learning architectures. However, recent literature has demonstrated that this choice comes with…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
What is the best way to divide a rugged landscape? Since ancient times, watersheds separating adjacent water systems that flow, for example, toward different seas, have been used to delimit boundaries. Interestingly, serious and even tense…
Earth is the only planet known to harbor life and, as a result, the search for habitable and inhabited planets beyond the Solar System commonly focuses on analogs to our planet. However, Earth's atmosphere and surface environment have…
The astrobiology is an interdisciplinary science, combining the methods and the means of physics, biology, chemistry and astronomy. Its main purpose is to find out if the exoplanets are habitable and if so, to confirm life on them. The…
The proper Euclidean geometry is considered to be metric space and described in terms of only metric and finite metric subspaces (sigma-immanent description). Constructing the geometry, one does not use topology and topological properties.…
Seen from a satellite, observing land use in the daytime or at night, most cities have circular shapes, organised around a city centre. A radial analysis of artificial land use growth is conducted in order to understand what the recent…
Cosmology is built on a relativistic understanding of gravity, where the geometry of the Universe is dynamically determined by matter and energy. In the cosmological concordance model, gravity is described by General Relativity, and it is…
Life can be viewed as a localized chemical system that sits on, or in the basin of attraction of, a metastable dynamical attractor state that remains out of equilibrium with the environment. Such a view of life allows that new living states…