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arXiv · 2510.02649

Engineering Emergence

Abel Jansma·Erik Hoel
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Abstract

A defining property of complex systems is that they have multiscale structure. How does this multiscale structure come about? We argue that within systems there emerges a hierarchy of scales that contribute to a system's causal workings. An intuitive example is how a computer can be described at the level of its hardware circuitry (its microscale) but also its machine code (a mesoscale) and all the way up at its operating system (its macroscale). Here we show that even simple systems possess this kind of emergent hierarchy, which usually forms over only a small subset of the super-exponentially many possible scales of description. To capture this formally, we extend the theory of causal emergence (version 2.0) so as to analyze how causal contributions span the full multiscale structure of a system. Our analysis reveals that systems can be classified along a taxonomy of emergence, such as being either top-heavy or bottom-heavy in their causal workings. From this new taxonomy of emergence, we derive a measure of complexity based on a literal notion of scale-freeness (here, when causation is spread equally across the scales of a system) and compare this to the standard network science definition of scale-freeness based on degree distribution, showing the two are closely related. Finally, we demonstrate the ability to engineer not just the degree of emergence in a system, but to control it with pinpoint precision.

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Abel Jansma, Erik Hoel. 2025-10-14. Engineering Emergence. https://arxiv.org/abs/2510.02649

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