Shannon information theory provides various measures of so-called syntactic information, which reflect the amount of statistical correlation between systems. By contrast, the concept of ‘semantic information’ refers to those correlations which carry significance or ‘meaning’ for a given system. Semantic information plays an important role in many fields, including biology, cognitive science and philosophy, and there has been a long-standing interest in formulating a broadly applicable and formal theory of semantic information. In this paper, we introduce such a theory. We define semantic information as the syntactic information that a physical system has about its environment which is causally necessary for the system to maintain its own existence. ‘Causal necessity’ is defined in terms of counter-factual interventions which scramble correlations between the system and its environment, while ‘maintaining existence’ is defined in terms of the system’s ability to keep itself in a low entropy state. We also use recent results in non-equilibrium statistical physics to analyse semantic information from a thermodynamic point of view. Our framework is grounded in the intrinsic dynamics of a system coupled to an environment, and is applicable to any physical system, living or otherwise. It leads to formal definitions of several concepts that have been intuitively understood to be related to semantic information, including ‘value of information’, ‘semantic content’ and ‘agency’.
Semantic information, autonomous agency and non-equilibrium statistical physics
Artemy Kolchinsky, David H. Wolpert
Published 19 October 2018.DOI: 10.1098/rsfs.2018.0041
Network Science In Education
Transformational Approaches in Teaching and Learning
Catherine B. Cramer, Mason A. Porter, Hiroki Sayama, Lori Sheetz, Stephen Miles Uzzo
Self-organisation lies at the core of fundamental but still unresolved scientific questions, and holds the promise of de-centralised paradigms crucial for future technological developments. While self-organising processes have been traditionally explained by the tendency of dynamical systems to evolve towards specific configurations, or attractors, we see self-organisation as a consequence of the interdependencies that those attractors induce. Building on this intuition, in this work we develop a theoretical framework for understanding and quantifying self-organisation based on coupled dynamical systems and multivariate information theory. We propose a metric of global structural strength that identifies when self-organisation appears, and a multi-layered decomposition that explains the emergent structure in terms of redundant and synergistic interdependencies. We illustrate our framework on elementary cellular automata, showing how it can detect and characterise the emergence of complex structures.
An Information-Theoretic Approach to Self-Organisation: Emergence of Complex Interdependencies in Coupled Dynamical Systems
Fernando Rosas, Pedro A.M. Mediano, Martín Ugarte and Henrik J. Jensen
Entropy 2018, 20(10), 793; https://doi.org/10.3390/e20100793
Urban transformations within large and growing metropolitan areas often generate critical dynamics affecting social interactions, transport connectivity and income flow distribution. We develop a statistical–mechanical model of urban transformations, exemplified for Greater Sydney, and derive a thermodynamic description highlighting critical regimes. We consider urban dynamics at two time scales: fast dynamics for the distribution of population and income, modelled via the maximum entropy principle, and slower dynamics evolving the urban structure under spatially distributed competition. We identify phase transitions between dispersed and polycentric phases, induced by varying the social disposition—a factor balancing the suburbs’ attractiveness—in contrast with the travel impedance. Using the Fisher information, we identify critical thresholds and quantify the thermodynamic cost of urban transformation, as the minimal work required to vary the underlying parameter. Finally, we introduce the notion of thermodynamic efficiency of urban transformation, as the ratio of the order gained during a change to the amount of required work, showing that this measure is maximized at criticality.
On critical dynamics and thermodynamic efficiency of urban transformations
Emanuele Crosato, Ramil Nigmatullin, Mikhail Prokopenko
Published 17 October 2018.DOI: 10.1098/rsos.180863