Next Article in Journal
A Class of Association Measures for Categorical Variables Based on Weighted Minkowski Distance
Previous Article in Journal
Combination of Active Learning and Semi-Supervised Learning under a Self-Training Scheme
Previous Article in Special Issue
Criticality as a Determinant of Integrated Information Φ in Human Brain Networks
Open AccessArticle

Causal Composition: Structural Differences among Dynamically Equivalent Systems

Department of Psychiatry, Wisconsin Institute for Sleep and Consciousness, University of Wisconsin-Madison, Madison, WI 53719, USA
*
Authors to whom correspondence should be addressed.
Entropy 2019, 21(10), 989; https://doi.org/10.3390/e21100989
Received: 11 September 2019 / Revised: 30 September 2019 / Accepted: 9 October 2019 / Published: 11 October 2019
(This article belongs to the Special Issue Integrated Information Theory)
The dynamical evolution of a system of interacting elements can be predicted in terms of its elementary constituents and their interactions, or in terms of the system’s global state transitions. For this reason, systems with equivalent global dynamics are often taken to be equivalent for all relevant purposes. Nevertheless, such systems may still vary in their causal composition—the way mechanisms within the system specify causes and effects over different subsets of system elements. We demonstrate this point based on a set of small discrete dynamical systems with reversible dynamics that cycle through all their possible states. Our analysis elucidates the role of composition within the formal framework of integrated information theory. We show that the global dynamical and information-theoretic capacities of reversible systems can be maximal even though they may differ, quantitatively and qualitatively, in the information that their various subsets specify about each other (intrinsic information). This can be the case even for a system and its time-reversed equivalent. Due to differences in their causal composition, two systems with equivalent global dynamics may still differ in their capacity for autonomy, agency, and phenomenology. View Full-Text
Keywords: integrated information; causation; graphical models; organizational structure; multivariate interaction; agency integrated information; causation; graphical models; organizational structure; multivariate interaction; agency
Show Figures

Figure 1

MDPI and ACS Style

Albantakis, L.; Tononi, G. Causal Composition: Structural Differences among Dynamically Equivalent Systems. Entropy 2019, 21, 989.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop