Related papers: Symmetry and Contextuality
Reciprocity is a fundamental symmetry present in many natural phenomena and engineered systems. Distinct situations where this symmetry is broken are typically grouped under the umbrella term "nonreciprocity", colloquially defined by: the…
Correctly capturing the symmetry transformations of data can lead to efficient models with strong generalization capabilities, though methods incorporating symmetries often require prior knowledge. While recent advancements have been made…
If a concept is not well defined, there are grounds for its abuse. This is particularly true of complexity, an inherently interdisciplinary concept that has penetrated very different fields of intellectual activity from physics to…
The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical…
Standard quantum mechanics undeniably violates the notion of separability that classical physics accustomed us to consider as valid. By relating the phenomenon of quantum nonseparability to the all-important concept of potentiality, we…
Symmetry Theories (SymThs) provide a flexible framework for analyzing the global categorical symmetries of a $D$-dimensional QFT$_{D}$ in terms of a $(D+1)$-dimensional bulk system SymTh$_{D+1}$. In QFTs realized via local string…
There are two very important subjects in physics: Symmetry of dynamical models and nonlinearity. All really fundamental models are invariant under some particular symmetry groups. There is also no true physics, no our Universe and life at…
We define the concept of self-similarity of an object by considering endomorphisms of the object as `similarity' maps. A variety of interesting examples of self-similar objects in geometry, algebra and arithmetic are introduced.…
Modern deep learning models are highly overparameterized, resulting in large sets of parameter configurations that yield the same outputs. A significant portion of this redundancy is explained by symmetries in the parameter…
We review the current status of dimensions, as the result of a long and controversial history that includes input from philosophy and physics. Our conclusion is that they are subjective but essential concepts which provide a kind of…
The view of nature we adopt in the natural attitude is determined by common sense, without which we could not survive. Classical physics is modelled on this common-sense view of nature, and uses mathematics to formalise our natural…
Symmetry is a powerful tool for understanding phases of matter in equilibrium. Quantum circuits with measurements have recently emerged as a platform for novel states of matter intrinsically out of equilibrium. Can symmetry be used as an…
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…
Symmetries play a central role in physics, organizing dynamics, constraining interactions, and determining the effective number of physical degrees of freedom. In parallel, modern artificial intelligence methods have demonstrated a…
The treatment of the principle of general covariance based on coordinate systems, i.e., on classical tensor analysis suffers from an ambiguity. A more preferable formulation of the principle is based on modern differential geometry: the…
We outline a general strategy developed for the analysis of critical models, which we apply to obtain a heuristic classification of all universality classes with up to three field-theoretical scalar order parameters in $d=6-\epsilon$…
A general, incomplete and partisan overview of various areas of the theoretical investigation is presented. Most of this activity stems from the search for physics beyond quantum field theory and general relativity, a titanic struggle that,…
Any system based on axioms is incomplete because the axioms cannot be proven from the system, just believed. But one system can be less-incomplete than other. Neutrosophy is less-incomplete than many other systems because it contains them.…
We argue that symmetry and unification can emerge as byproducts of certain physical constraints on dynamical scattering. To accomplish this we parameterize a general Lorentz invariant, four-dimensional theory of massless and massive scalar…
We present a computational model for the semantic interpretation of symmetry in naturalistic scenes. Key features include a human-centred representation, and a declarative, explainable interpretation model supporting deep semantic…