Related papers: The Origin of a Metric
The problem of enumerating meanders -- pairs of simple plane curves with transverse intersections -- was formulated about forty years ago and is still far from solved. Recently, it was discovered that meanders admit a factorization into…
We propose a new constructive model of the real continuum based on the notion of fractal definability. Rather than assuming the continuum as a completed uncountable totality, we view it as the cumulative result of a vast space of stratified…
The measurement conundrum seems to have plagued quantum mechanics for so long that impressions of an inconsistency amongst its axioms have spawned. A demonstration that such purported inconsistency is fictitious may then be in order and is…
Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data and with compositional data, like percentages and the like. If the natural measure of difference is not the absolute…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
The general concept of symmetry is realized in manifold ways in different realms of reality, such as plants, animals, minerals, mathematical objects or human artefacts in literature, fine arts and society. In order to arrive at a common…
In 1984, K. Mahler asked how well elements in the Cantor middle third set can be approximated by rational numbers from that set, and by rational numbers outside of that set. We consider more general missing digit sets $C$ and construct…
Singularities appear in numerous important mathematical models used in Physics. And in most of such cases singularities are involved in essentially nonlinear contexts. For more than four decades, general enough nonlinear theories of…
Quantum transients are temporary features of matter waves before they reach a stationary regime. Transients may arise after the preparation of an unstable initial state or due to a sudden interaction or a change in the boundary conditions.…
We show that products of sufficiently thick Cantor sets generate trees in the plane with constant distance between adjacent vertices. Moreover, we prove that the set of choices for this distance has non-empty interior. We allow our trees to…
The concepts of the perfect system and degeneracy are introduced. A special symmetry is found which is related to the entropy invariant. The inversion relation of system is obtained which is used to give the oppsite direction of time to…
In view of experimentally obtainable resolutions, equal to the Compton wavelength of an electron, the conventional interpretation of quantum mechanics no longer seems to provide a sufficiently subtle tool. Based on the intrinsic properties…
A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This approach concludes finally the problem of the…
In these lectures we look for parallels between symmetry breaking in the early universe and condensed matter systems, and discuss experiments that display these.
Drawing from the theory of optimal transport we propose a rigorous notion of a causal relation for Borel probability measures on a given spacetime. To prepare the ground, we explore the borderland between causality, topology and measure…
Tetraquarks are studied with an approximation which reduces the in- ternal degrees of freedom of the system, using both finite differences and scattering theory. The existence of bound states and resonances is inspected and the masses and…
Motivated by ideas from the model theory of metric structures, we introduce a metric set theory, $\mathsf{MSE}$, which takes bounded quantification as primitive and consists of a natural metric extensionality axiom (the distance between two…
In these lectures I describe some of the open questions in the standard model relating to the nature and origin of mass, forces and matter and discuss some of the speculative theoretical ideas put forth in this regard. Some of the topics…
In a purely relational theory there exists a tension between the relational character of the theory and the existence of quantities like distance and duration. We review this issue in the context of the Leibniz-Clarke correspondence. We…
Complex spatiotemporal patterns in nature significantly challenge reductionism-based modern science. The lack of a paradigm beyond reductionism hinders our understanding of the emergence of complexity. The diversity of countless patterns…