Related papers: Gods as Topological Invariants
This article looks at philosophical aspects and questions that modern astrophysical research gives rise to. Other than cosmology, astrophysics particularly deals with understanding phenomena and processes operating at "intermediate" cosmic…
The aim of homotopy theory in topology is to simplify, after continuous deformation, continuous maps between topological spaces. What prevents this from happening are homotopy invariants. This raises quantitative questions: $\bullet$ Is the…
For digital images, there is an established homotopy equivalence relation which parallels that of classical topology. Many classical homotopy equivalence invariants, such as the Euler characteristic and the homology groups, do not remain…
Cosmology contributes a good deal to the investigation of variation of fundamental physical constants. High resolution data is available and allows for detailed analysis over cosmological distances and a multitude of methods were developed.…
Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories. In this article, we give a brief introduction to this approach, emphasising the logical aspects. Each topos serves…
We introduce a new concept, `(topological) (vacuum) parallel world, ' which is a new tool to research submanifolds. Roughly speaking, `Observables in (T)QFT' is equal to `a (topological) modification of space-time.' In other words, we give…
A quantum theory of the universe consists of a theory of its quantum dynamics and a theory of its quantum state The theory predicts quantum multiverses in the form of decoherent sets of alternative histories describing the evolution of the…
We introduce the notion of \emph{topo-symmetric extensions} of topological groups, a new generalization of classical group extensions that incorporates both topological and symmetry constraints. We define morphisms between such extensions,…
Topological descriptors, such as the Euler characteristic function and the persistence diagram, have grown increasingly popular for representing complex data. Recent work showed that a carefully chosen set of these descriptors encodes all…
A basic problem in smooth dynamics is determining if a system can be distinguished from its inverse, i.e., whether a smooth diffeomorphism $T$ is isomorphic to $T^{-1}$. We show that this problem is sufficiently general that asking it for…
Theoretical physics is the search for simple and universal mathematical descriptions of the natural world. In contrast, much of modern biology is an exploration of the complexity and diversity of life. For many, this contrast is prima facie…
Cosmological observations are beginning to reach a level of precision that allow us to test some of the most fundamental assumptions in our working model of the Universe. One such an assumption is that gravity is governed by the General…
In this paper, the theoretical terms of contemporary cosmology are examined as intellectual artefacts. An ontology and methodology are introduced for this purpose, which includes defining the concept of a hypothetical object. Introducing a…
During the last three decades, there has been a growing realization among physicists and cosmologists that the relation between particle physics and cosmology may constitute yet another successful example of the unity of science. However,…
I make the case that the Universe according to unitary (no-collapse) quantum theory has a branching structure, and so can literally be regarded as a "many-worlds" theory. These worlds are not part of the fundamental ontology of quantum…
Fundamental duality is a concept which refers to two irreducible, heterogeneous principles which are in opposite and complementary of each other. The complementary principle in quantum mechanics is also praised by Bohr. This important…
The scientific method is often presented, e.g. to children, as a linear process, starting by a question and ending by the elaboration of a theory, with a few experiments in-between. The reality of the building of science is much more…
A description of physical reality in which wholeness is the foundation is discussed along with the motivation for such an attempt. As a possible mathematical framework within which a physical theory based on wholeness may be expressed,…
From classical mechanics to quantum field theory, the physical facts at one point in space are held to be independent of those at other points in space. I propose that we can usefully challenge this orthodoxy in order to explain otherwise…
During the last centuries of human history, many questions was repeated in connection with the great problems of the existence and origin of human beings, and also of the Universe. The old questions of common sense and philosophy have not…