Idea engines: Unifying innovation & obsolescence from markets & genetic evolution to science.

Innovation and obsolescence describe dynamics of ever-churning and adapting social and biological systems, concepts that encompass field-specific formulations. We formalize the connection with a reduced model of the dynamics of the "space of the possible" (e.g., technologies, mutations, theories) to which agents (e.g., firms, organisms, scientists) couple as they grow, die, and replicate. We predict three regimes: The space is finite, ever growing, or a Schumpeterian dystopia in which obsolescence drives the system to collapse. We reveal a critical boundary at which the space of the possible fluctuates dramatically in size, displaying recurrent periods of minimal and of veritable diversity. When the space is finite, corresponding to physically realizable systems, we find surprising structure. This structure predicts a taxonomy for the density of agents near and away from the innovative frontier that we compare with distributions of firm productivity, COVID diversity, and citation rates for scientific publications. Our minimal model derived from first principles aligns with empirical examples, implying a follow-the-leader dynamic in firm cost efficiency and biological evolution, whereas scientific progress reflects consensus that waits on old ideas to go obsolete. Our theory introduces a fresh and empirically testable framework for unifying innovation and obsolescence across fields.

Valence and interactions in judicial voting.

The collective statistics of voting on judicial courts present hints about their inner workings. Many approaches for studying these statistics, however, assume that judges' decisions are conditionally independent: a judge reaches a decision based on the case at hand and his or her personal views. In reality, judges interact. We develop a minimal model that accounts for judge bias, depending on the context of the case, and peer interaction. We apply the model to voting data from the US Supreme Court. We find strong evidence that interaction is an important factor across natural courts from 1946 to 2021. We also find that, after accounting for interaction, the recovered biases differ from highly cited ideological scores. Our method exemplifies how physics and complexity-inspired modelling can drive the development of theoretical models and improved measures for political voting. This article is part of the theme issue 'A complexity science approach to law and governance'.

Growth, death, and resource competition in sessile organisms.

Population-level scaling in ecological systems arises from individual growth and death with competitive constraints. We build on a minimal dynamical model of metabolic growth where the tension between individual growth and mortality determines population size distribution. We then separately include resource competition based on shared capture area. By varying rates of growth, death, and competitive attrition, we connect regular and random spatial patterns across sessile organisms from forests to ants, termites, and fairy circles. Then, we consider transient temporal dynamics in the context of asymmetric competition, such as canopy shading or large colony dominance, whose effects primarily weaken the smaller of two competitors. When such competition couples slow timescales of growth to fast competitive death, it generates population shocks and demographic oscillations similar to those observed in forest data. Our minimal quantitative theory unifies spatiotemporal patterns across sessile organisms through local competition mediated by the laws of metabolic growth, which in turn, are the result of long-term evolutionary dynamics.

Discovering sparse control strategies in neural activity.

Biological circuits such as neural or gene regulation networks use internal states to map sensory input to an adaptive repertoire of behavior. Characterizing this mapping is a major challenge for systems biology. Though experiments that probe internal states are developing rapidly, organismal complexity presents a fundamental obstacle given the many possible ways internal states could map to behavior. Using C. elegans as an example, we propose a protocol for systematic perturbation of neural states that limits experimental complexity and could eventually help characterize collective aspects of the neural-behavioral map. We consider experimentally motivated small perturbations-ones that are most likely to preserve natural dynamics and are closer to internal control mechanisms-to neural states and their impact on collective neural activity. Then, we connect such perturbations to the local information geometry of collective statistics, which can be fully characterized using pairwise perturbations. Applying the protocol to a minimal model of C. elegans neural activity, we find that collective neural statistics are most sensitive to a few principal perturbative modes. Dominant eigenvalues decay initially as a power law, unveiling a hierarchy that arises from variation in individual neural activity and pairwise interactions. Highest-ranking modes tend to be dominated by a few, "pivotal" neurons that account for most of the system's sensitivity, suggesting a sparse mechanism of collective control.

Discovering the mesoscale for chains of conflict.

Conflicts, like many social processes, are related events that span multiple scales in time, from the instantaneous to multi-year development, and in space, from one neighborhood to continents. Yet, there is little systematic work on connecting the multiple scales, formal treatment of causality between events, and measures of uncertainty for how events are related to one another. We develop a method for extracting causally related chains of events that addresses these limitations with armed conflict. Our method explicitly accounts for an adjustable spatial and temporal scale of interaction for clustering individual events from a detailed data set, the Armed Conflict Event & Location Data Project. With it, we discover a mesoscale ranging from a week to a few months and tens to hundreds of kilometers, where long-range correlations and nontrivial dynamics relating conflict events emerge. Importantly, clusters in the mesoscale, while extracted from conflict statistics, are identifiable with mechanism cited in field studies. We leverage our technique to identify zones of causal interaction around conflict hotspots that naturally incorporate uncertainties. Thus, we show how a systematic, data-driven, and scalable procedure extracts social objects for study, providing a scope for scrutinizing and predicting conflict and other processes.

Sensitivity of collective outcomes identifies pivotal components.

A social system is susceptible to perturbation when its collective properties depend sensitively on a few pivotal components. Using the information geometry of minimal models from statistical physics, we develop an approach to identify pivotal components to which coarse-grained, or aggregate, properties are sensitive. As an example, we introduce our approach on a reduced toy model with a median voter who always votes in the majority. The sensitivity of majority-minority divisions to changing voter behaviour pinpoints the unique role of the median. More generally, the sensitivity identifies pivotal components that precisely determine collective outcomes generated by a complex network of interactions. Using perturbations to target pivotal components in the models, we analyse datasets from political voting, finance and Twitter. Across these systems, we find remarkable variety, from systems dominated by a median-like component to those whose components behave more equally. In the context of political institutions such as courts or legislatures, our methodology can help describe how changes in voters map to new collective voting outcomes. For economic indices, differing system response reflects varying fiscal conditions across time. Thus, our information-geometric approach provides a principled, quantitative framework that may help assess the robustness of collective outcomes to targeted perturbation and compare social institutions, or even biological networks, with one another and across time.

Scaling theory of armed-conflict avalanches.

Armed conflict data display features consistent with scaling and universal dynamics in both social and physical properties like fatalities and geographic extent. We propose a randomly branching armed conflict model to relate the multiple properties to one another. The model incorporates a fractal lattice on which conflict spreads, uniform dynamics driving conflict growth, and regional virulence that modulates local conflict intensity. The quantitative constraints on scaling and universal dynamics we use to develop our minimal model serve more generally as a set of constraints for other models for armed conflict dynamics. We show how this approach akin to thermodynamics imparts mechanistic intuition and unifies multiple conflict properties, giving insight into causation, prediction, and intervention timing.

Audio cues enhance mirroring of arm motion when visual cues are scarce.

Swing in a crew boat, a good jazz riff, a fluid conversation: these tasks require extracting sensory information about how others flow in order to mimic and respond. To determine what factors influence coordination, we build an environment to manipulate incoming sensory information by combining virtual reality and motion capture. We study how people mirror the motion of a human avatar's arm as we occlude the avatar. We efficiently map the transition from successful mirroring to failure using Gaussian process regression. Then, we determine the change in behaviour when we introduce audio cues with a frequency proportional to the speed of the avatar's hand or train individuals with a practice session. Remarkably, audio cues extend the range of successful mirroring to regimes where visual information is sparse. Such cues could facilitate joint coordination when navigating visually occluded environments, improve reaction speed in human-computer interfaces or measure altered physiological states and disease.

Collective memory in primate conflict implied by temporal scaling collapse.

In biological systems, prolonged conflict is costly, whereas contained conflict permits strategic innovation and refinement. Causes of variation in conflict size and duration are not well understood. We use a well-studied primate society model system to study how conflicts grow. We find conflict duration is a 'first to fight' growth process that scales superlinearly, with the number of possible pairwise interactions. This is in contrast with a 'first to fail' process that characterizes peaceful durations. Rescaling conflict distributions reveals a universal curve, showing that the typical time scale of correlated interactions exceeds nearly all individual fights. This temporal correlation implies collective memory across pairwise interactions beyond those assumed in standard models of contagion growth or iterated evolutionary games. By accounting for memory, we make quantitative predictions for interventions that mitigate or enhance the spread of conflict. Managing conflict involves balancing the efficient use of limited resources with an intervention strategy that allows for conflict while keeping it contained and controlled.