Related papers: On the Philosophy of Higher Structures
Structuring theories is one of the main approaches to reduce the combinatorial explosion associated with reasoning and exploring large theories. In the past we developed the notion of development graphs as a means to represent and maintain…
I summarize here the logic that leads us to a program for the Theory of the Total Field in Einstein's sense. The purpose is to show that this theory is a logical culmination of the developments of (fundamental) physical concepts and, hence,…
We introduce and analyze a new geometric structure on topological surfaces generalizing the complex structure. To define this so called higher complex structure we use the punctual Hilbert scheme of the plane. The moduli space of higher…
In earlier work, my colleagues and I developed a formalism for using information theory to understand scales of organization and structure in multi-component systems. One prominent theme of that work was that the structure of a system…
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
Hypercomputational formal theories will, clearly, be both structurally and foundationally different from the formal theories underpinning computational theories. However, many of the maps that might guide us into this strange realm have…
We address a recent proposal concerning 'surplus structure' due to Nguyen et al. ['Why Surplus Structure is Not Superfluous.' Br. J. Phi. Sci. Forthcoming.] We argue that the sense of 'surplus structure' captured by their formal criterion…
This article is dedicated to the investigation of difficulties involved in the understanding of the homomorphism concept. It doesn't restrict to group-theory but on the contrary raises the issue of developing teaching strategies aiming at…
The literature in persistent homology often refers to a "structure theorem for finitely generated graded modules over a graded principal ideal domain". We clarify the nature of this structure theorem in this context.
To present a survey on known results from the theory of transposed Poisson algebras, as well as to establish new results on this subject, are the main aims of the present paper. Furthermore, a list of open questions for future research is…
There has been a great deal of research on graphs defined on algebraic structures in the last two decades. In this paper we begin an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this…
The outline of a programme for restructuring mathematical logic. We explain what we mean by "restructuring" and carry out exemplary parts of the programme.
This is the first of a series of papers that we intend to publish about the epistemology of fundamental physics in its current state. One of the main objectives of these papers is to improve our understanding of fundamental physics (and…
We impose a rather unknown algebraic structure called a `hyperstructure' to the underlying space of an affine algebraic group scheme. This algebraic structure generalizes the classical group structure and is canonically defined by the…
The objective of this paper is to explain the principles of the design of a coarse space in a simplified way and by pictures. The focus is on ideas rather than on a more historically complete presentation. Also, space limitation does not…
The article provides a new approach to creating hierarchical structure of file system. First, it gives overview of the existing ways of storing files in current operating systems. Second, it describes the new way of building structures of a…
In these lectures we review the motivation, principles of and (circumstantial) evidence for the program of unification of the fundamental forces. In an appendix, we review the group theory pertinent to the program.
We think about what the subscheme of the formal scheme is. Differently form the ordinary scheme, the formal scheme has different notions of ``subscheme''. We lay a foundation for these notions and compare them. We also relate them to…
The purpose of this note is to start the systematic analysis of cofinal types of topological groups.
A set of general physical principles is proposed as the structural basis for the theory of complex systems. First the concept of harmony is analyzed and its different aspects are uncovered. Then the concept of reflection is defined and…