Related papers: It From Bit and The Unsmooth Reality
The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order to better understand where the structure…
We continue to explore, in the context of a toy model, the hypothesis that the interacting universe we see around us could result from single particle (undergraduate) quantum mechanics via a novel spontaneous symmetry breaking (SSB) acting…
Rough set theory is a new mathematical approach to imperfect knowledge. The notion of rough sets is generalized by using an arbitrary binary relation on attribute values in information systems, instead of the trivial equality relation. The…
We give an overview of the constrained Willmore problem and address some conjectures arising from partial results and numerical experiments. Ramifications of these conjectures would lead to a deeper understanding of the Willmore functional…
We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.
Let L be the zero set of a nonconstant monic polynomial with complex coefficients. In the context of constructive mathematics without countable choice, it may not be possible to construct an element of L. In this paper we introduce a notion…
To unite quantum theory and general relativity, in a new access it is shown that from a theory of an abstract quantum information - called Protyposis - the theory of general relativity can be deduced by means of few and physically good…
The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that…
We provide new simple proofs of the Kolmogorov extension theorem and Prokhorovs' theorem. The proof of the Kolmogorov extension theorem is based on the simple observation that $\mathbb{R}$ and the product measurable space…
We give a framework to produce constructible functions from natural functors between categories, without need of a morphism of moduli spaces to model the functor. We show using the Riemann-Hilbert correspondence that any natural (derived)…
We study totally bounded subsets in weighted variable exponent amalgam and Sobolev spaces. Moreover, this paper includes several detailed generalized results of some compactness criterions in these spaces.
This article explains basic constructions and results on group algebras and their cohomology, starting from the point of view of commutative algebra. It provides the background necessary for a novice in this subject to begin reading Dave…
This paper links the conjecture that the physical world is a virtual reality to the findings of modern physics. What is usually the subject of science fiction is here proposed as a scientific theory open to empirical evaluation. We know…
Here we will embark on a journey starting with some ostensibly inauspicious boxes. Carefully stacking them in different ways yields amazing identities. From humble beginnings at the integer version: `how many steps does it take to get from…
We show the existence of rigid combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, $t$-designs, and $t$-wise…
Due to M\"{u}ller's theorem, the Kolmogorov complexity of a string was shown to be equal to its quantum Kolmogorov complexity. Thus there are no benefits to using quantum mechanics to compress classical information. The quantitative amount…
We call for a theory of the particle-scale structure of materials that is based on the general notion of information rather than its special case of symmetry. An inherent limitation to the symmetry-based understanding of structure is…
We survey the logical structure of constructive set theories and point towards directions for future research. Moreover, we analyse the consequences of being extensible for the logical structure of a given constructive set theory. We…
The paper considers a non-reductionist theory of consciousness, which is not reducible to theories of reality and to physiological or psychological theories. Following D.I.Dubrovsky's "informational approach" to the "Mind-Brain Problem", we…
We introduce the theory of div point sets, which aims to provide a framework to study the combinatoric nature of any set of points in general position on an Euclidean plane. We then show that proving the unsatisfiability of some first-order…