Related papers: On a categoriacal theory for emergence
As far as human perceptions and rational thinking are concerned, contradictions constitute a non negligible part of our reality. We often refer to these phenomena, in a more informal way, as the chicken or the egg causality dilemma.…
Optics, aka functional references, are classes of tools that allow composable access into compound data structures. Usually defined as programming language libraries, they provide combinators to manipulate different shapes of data such as…
We study the central objects of symbolic dynamics, that is, subshifts and block maps, from the perspective of basic category theory, and present several natural categories with subshifts as objects and block maps as morphisms. Our main…
Evolutionary game theory has been successfully used to investigate the dynamics of systems, in which many entities have competitive interactions. From a physics point of view, it is interesting to study conditions under which a coordination…
The primordial confrontation underlying the existence of our universe can be conceived as the battle between entropy and complexity. The law of ever-increasing entropy (Boltzmann H-theorem) evokes an irreversible, one-directional evolution…
For classical dynamical systems, the polynomial entropy serves as a refined invariant of the topological entropy. In the setting of categorical dynamical systems, that is, triangulated categories endowed with an endofunctor, we develop the…
Two different conceptions of emergence are reconciled as two instances of the phenomenon of detection. In the process of comparing these two conceptions, we find that the notions of complexity and detection allow us to form a unified…
The present article is the first of a series whose goal is to define a logical formalism in which it is possible to reason about genetics. In this paper, we introduce the main concepts of our language whose domain of discourse consists of a…
The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…
When we think of model ensembling or ensemble modeling, there are many possibilities that come to mind in different disciplines. For example, one might think of a set of descriptions of a phenomenon in the world, perhaps a time series or a…
The past decade has witnessed a surge of interest in exploring emergent particles in condensed matter systems. Novel particles, emerged as excitations around exotic band degeneracy points, continue to be reported in real materials and…
A sketch of three senses of emergence and a suggestive view on the emergence of time and the direction of time is presented. After trying to identify which issues philosophers interested in emergent phenomena in physics view as important I…
As early indicated by Charles Darwin, languages behave and change very much like living species. They display high diversity, differentiate in space and time, emerge and disappear. A large body of literature has explored the role of…
We prove coherence theorems for bicategories, pseudofunctors and pseudonatural transformations. These theorems boil down to proving the coherence of some free $(4,2)$-categories. In the case of bicategories and pseudofunctors, existing…
Information theory is a mathematical theory of learning with deep connections with topics as diverse as artificial intelligence, statistical physics, and biological evolution. Many primers on information theory paint a broad picture with…
This is a largely expository paper about how groups arise or are of interest in model theory. Included are the following topics: classifying groups definable in specific structures or theories and the relation to algebraic groups, groups…
We consider biological individuality in terms of information theoretic and graphical principles. Our purpose is to extract through an algorithmic decomposition system-environment boundaries supporting individuality. We infer or detect…
We propose Universal Causality, an overarching framework based on category theory that defines the universal property that underlies causal inference independent of the underlying representational formalism used. More formally, universal…
In another paper (Butterfield 2011), one of us argued that emergence and reduction are compatible, and presented four examples illustrating both. The main purpose of this paper is to develop this position for the example of phase…
A general theory of innovation and progress in human society is outlined, based on the combat between two opposite forces (conservatism/inertia and speculative herding "bubble" behavior). We contend that human affairs are characterized by…