Recently Philip Ball collaborator of Quanta Magazine in an article entitled “The New Math of How Large-Scale Order Emerges“, discussed some research advances around the question of how emergence emerge in complex systems? He focuses on the work of Fernando Rosas and six other researchers entitled “Software in the natural world: A computational approach to emergence in complex multi-level systems”, which presents a mathematical framework based on computational mechanics to better understand the phenomenon of emergence.
According to the researchers, by organizing systems such as economic, urban or even biological systems into hierarchies of levels, it is possible to find in each of them properties that allow each level to operate independently of the others, just as software does in a computer, each software works independently the computation mechanism of the hardware circuits. This means that emergent phenomena are governed by macroscale rules that appear to be self-contained, regardless of what the components or entities of other hierarchies do.
In general, the approach of Rosas et al. (2024) characterizes the interdependence between micro and macro levels by combining principles of computational mechanics with fluid dynamics and dynamical systems theory, which are widely used in continuous systems. This contribution to bridging the gap between emergence and complex systems is guided by previous research by Barnett & Seth (2023), which proposes a system in which a dynamically macro level is conditional on its own history and independent of the history of the micros process. Both studies turn around systems whose macro levels have a degree of causal ‘self-containment’ with respect to their micro processes, which could be understood as a kind of emergence.
To access the Quanta Magazine article, use this link:
https://www.quantamagazine.org/the-new-math-of-how-large-scale-order-emerges-20240610
For the Rosas et al. (2024) paper:
https://arxiv.org/abs/2402.09090v2
And for the paper by Barnett & Seth (2023):
https://arxiv.org/pdf/2106.06511
Made in Adobe Firefly AI, prompt: Jorge Salgado.
References:
Barnett, L. and Seth A. K. 2023. “Dynamical independence: discovering emergent macroscopic processes in complex dynamical systems,” Physical Review E, vol. 108, no. 1, p. 014304.
Rosas, F. E., Geiger, B. C., Luppi, A. I., Seth, A. K., Polani, D., Gastpar, M., & Mediano, P. A. M. (2024). Software in the natural world: A computational approach to hierarchical emergence. arXiv.
