Short-term survival and an exuberant plunge into building our future are generating a new kind of unintended consequence -- hidden fragility. This is a direct effect of the sophistication and structural complexity of the socio-technical systems humans create. It is inevitable. And so the challenge is, How much can we understand and predict about these systems and about the social dynamics that lead to their construction?

Computing power and sophisticated data acquisition mask the fact that, in many sciences and engineering, the balance between theory and experiment is getting increasingly out of whack. The imbalance becomes an even greater concern in light of the increasingly complex natural systems science now confronts and the increasingly complex and interdependent sociotechnical systems modern engineering allows us to construct. Given its critical role in understanding such complex systems, Big Theory deserves a place alongside Big Data and Big Iron, says Jim Crutchfield. © 2014 Wiley Periodicals, Inc.

The principle goal of computational mechanics is to define pattern and structure so that the organization of complex systems can be detected and quantified. Computational mechanics developed from efforts in the 1970s and early 1980s to identify strange attractors as the mechanism driving weak fluid turbulence via the method of reconstructing attractor geometry from measurement time series and in the mid-1980s to estimate equations of motion directly from complex time series. In providing a mathematical and operational definition of structure it addressed weaknesses of these early approaches to discovering patterns in natural systems. Since then, computational mechanics has led to a range of results from theoretical physics and nonlinear mathematics to diverse applications---from closed-form analysis of Markov and non-Markov stochastic processes that are ergodic or nonergodic and their measures of information and intrinsic computation to complex materials and deterministic chaos and intelligence in Maxwellian demons to quantum compression of classical processes and the evolution of computation and language. This brief review clarifies several misunderstandings and addresses concerns recently raised regarding early works in the field (1980s). We show that misguided evaluations of the contributions of computational mechanics are groundless and stem from a lack of familiarity with its basic goals and from a failure to consider its historical context. For all practical purposes, its modern methods and results largely supersede the early works. This not only renders recent criticism moot and shows the solid ground on which computational mechanics stands but, most importantly, shows the significant progress achieved over three decades and points to the many intriguing and outstanding challenges in understanding the computational nature of complex dynamic systems.

Accumulating observational evidence suggests an intimate connection between rapidly expanding insect populations, deforestation, and global climate change. We review the evidence, emphasizing the vulnerability of key planetary carbon pools, especially the Earth's forests that link the micro-ecology of insect infestation to climate. We survey current research regimes and insect control strategies, concluding that at present they are insufficient to cope with the problem's present regional scale and its likely future global scale. We propose novel bioacoustic interactions between insects and trees as key drivers of infestation population dynamics and the resulting wide-scale deforestation. The bioacoustic mechanisms suggest new, nontoxic control interventions and detection strategies.

Coherent structures form spontaneously in nonlinear spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary climate dynamics. Phenomenologically, they appear as key components that organize the macroscopic behaviors in such systems. Despite a century of effort, they have eluded rigorous analysis and empirical prediction, with progress being made only recently. As a step in this, we present a formal theory of coherent structures in fully discrete dynamical field theories. It builds on the notion of structure introduced by computational mechanics, generalizing it to a local spatiotemporal setting. The analysis' main tool employs the local causal states, which are used to uncover a system's hidden spatiotemporal symmetries and which identify coherent structures as spatially localized deviations from those symmetries. The approach is behavior-driven in the sense that it does not rely on directly analyzing spatiotemporal equations of motion, rather it considers only the spatiotemporal fields a system generates. As such, it offers an unsupervised approach to discover and describe coherent structures. We illustrate the approach by analyzing coherent structures generated by elementary cellular automata, comparing the results with an earlier, dynamic-invariant-set approach that decomposes fields into domains, particles, and particle interactions.

In quantum mechanics, states are described by density matrices. Though their probabilistic interpretation is rooted in ensemble theory, density matrices embody a known shortcoming. They do not completely express the physical realization of an ensemble. Conveniently, the outcome statistics of projective and positive operator-valued measurements do not depend on the ensemble realization, only on the density matrix. Here, we show how the geometric approach to quantum mechanics tracks ensemble realizations. We do so in two concrete cases of a finite-dimensional quantum system interacting with another one with (i) finite-dimensional Hilbert space, relevant for quantum thermodynamics, and (ii) infinite-dimensional Hilbert space, relevant for state-manipulation protocols.

Building on parallels between geometric quantum mechanics and classical mechanics, we explore an alternative basis for quantum thermodynamics that exploits the differential geometry of the underlying state space. We focus on microcanonical and canonical ensembles, looking at the geometric counterpart of Gibbs ensembles for distributions on the space of quantum states. We show that one can define quantum heat and work in an intrinsic way, including single-trajectory work. We reformulate thermodynamic entropy in a way that accords with classical, quantum, and information-theoretic entropies. We give both the first and second laws of thermodynamics and Jarzynki's fluctuation theorem. Overall, this results in a more transparent physics than conventionally available. The mathematical structure and physical intuitions underlying classical and quantum dynamics are seen to be closely aligned. The experimental relevance is brought out via a stochastic model for chiral molecules (in the two-state approximation) and Josephson junctions. Numerically, we demonstrate this invariably leads to the emergence of the geometric canonical ensemble.

Computational mechanics quantifies structure in a stochastic process via its causal states, leading to the process’s minimal, optimal predictor—the (Formula presented.)-machine. We extend computational mechanics to communication channels coupling two processes, obtaining an analogous optimal model—the (Formula presented.)-transducer—of the stochastic mapping between them. Here, we lay the foundation of a structural analysis of communication channels, treating joint processes and processes with input. The result is a principled structural analysis of mechanisms that support information flow between processes. It is the first in a series on the structural information theory of memoryful channels, channel composition, and allied conditional information measures.

Computational mechanics quantifies structure in a stochastic process via its causal states, leading to the process's minimal, optimal predictor---the $\epsilon$-machine. We extend computational mechanics to communication channels between two processes, obtaining an analogous optimal model---the $\epsilon$-transducer---of the stochastic mapping between them. Here, we lay the foundation of a structural analysis of communication channels, treating joint processes and processes with input. The result is a principled structural analysis of mechanisms that support information flow between processes. It is the first in a series on the structural information theory of memoryful channels, channel composition, and allied conditional information measures.