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Recently, we proposed polycontextural networks as a model of evolving systems of interacting beliefs. Here, we present an analysis of the phase transition as well as the scaling properties. The model contains interacting agents that strive for consensus, each with only subjective perception. Depending on a parameter that governs how responsive the agents are to changing their belief systems the model exhibits a phase transition that mediates between an active phase where the agents constantly change their beliefs and a frozen phase, where almost no changes appear. We observe the build-up of convention-aligned clusters only in the intermediate regime of diverging susceptibility. Here, we analyze in detail the behavior of polycontextural networks close to this transition. We provide an analytical estimate of the critical point and show that the scaling properties and the space-time structure of these clusters show self-similar behavior. Our results not only contribute to a better understanding of the emergence of consensus in systems of distributed beliefs but also show that polycontextural networks are models, motivated by social systems, where susceptibility -- the sensitivity to change own beliefs -- drives the growth of consensus clusters.

The collective coordination of distributed tasks in a complex system can be represented as decision dynamics on a graph. This abstract representation allows studying the performance of local decision heuristics as a function of task complexity and network architecture. Here we identify hard-to-solve and easy-to-solve networks in a social differentiation task within the basic model of small-world graphs. We show that, depending on the details of the decision heuristic as well as the length of the added links, shortcuts can serve as structural promotors, which speed up convergence towards a solution, but also as structural insulators, which make the network more difficult to solve. Our findings have implications for situations where, in distributed decision systems, regional solutions emerge, which are globally incompatible as for example during the emergence of technological standards.

The rich body of physical theories defines the foundation of our understanding of the world. Its mathematical formulation is based on classical Aristotelian (binary) logic. In the philosophy of science the ambiguities, paradoxes, and the possibility of subjective interpretations of facts have challenged binary logic, leading, among other developments, to Gotthard G\"unther's theory of polycontexturality (often also termed 'transclassical logic'). G\"unther's theory explains how observers with subjective perception can become aware of their own subjectivity and provides means to describe contradicting or even paradox observations in a logically sound formalism. Here we summarize the formalism behind G\"unther's theory and apply it to two well-known examples from physics where different observers operate in distinct and only locally valid logical systems. Using polycontextural logic we show how the emerging awareness of these limitations of logical systems entails the design of mathematical transformations, which then become an integral part of the theory. In our view, this approach offers a novel perspective on the structure of physical theories and, at the same time, emphasizes the relevance of the theory of polycontexturality in modern sciences., Comment: This is a preprint of an article published in Foundations of Science (2021). The final authenticated version is available online at: https://doi.org/10.1007/s10699-021-09814-0

Collective phenomena in systems of interacting agents have helped us understand diverse social, ecological and biological observations. The corresponding explanations are challenged by incorrect information processing. In particular, the models typically assume a shared understanding of signals or a common truth or value system, i.e., an agreement of whether the measurement or perception of information is `right' or `wrong'. It is an open question whether a collective consensus can emerge without these conditions. Here we introduce a model of interacting agents that strive for consensus, however, each with only a subjective perception of the world. Our communication model does not presuppose a definition of right or wrong and the actors can hence not distinguish between correct and incorrect observations. Depending on a single parameter that governs how responsive the agents are to changing their world-view we observe a transition between an unordered phase of individuals that are not able to communicate with each other and a phase of an emerging shared signalling framework. We find that there are two types of convention-aligned clusters: one, where all social actors in the cluster have the same set of conventions, and one, where neighbouring actors have different but compatible conventions (`stable misunderstandings')., Comment: This is a preprint of an article published in Scientific Reports. The final authenticated version is available online at: https://doi.org/10.1038/s41598-022-06880-7