Bruce M. Boghosian in the November 2019 issue of Scientific American (p. 73) writes about wealth distribution. Using math and physics, it seems that a slight perturbation to a symmetric or isotropic starting point can result in inequality. Slight inequality results in increasing inequality (anisotropy) over time. These issues are also canvassed in the Growth of Oligarchy in a Yard-Sale Model of Asset Exchange by Bruce M. Boghosian, Adrian Devitt-Lee, and Hongyan Wang, arxiv 2016 and in The Affine Wealth Model by Jie Li, Bruce M. Boghosian, and Chengli Lion, arxiv 2018.
Ehud Meron in Physics Today November 2019 issue writes about Vegetation Pattern Formation (p. 31). While water distribution for a given topography may initially be isotropic, vegetation can distribute in anisotropic patterns.
Are these two instances of initial isotropic distribution leading to anisotropic patterns connected by the same physics? If so, what is the physics?
The 'physics' you refer to is more like the 'maths' of the issue. Surely in a field of some property P, the result of any local deformation must depend critically on P, and whether any restoring force is either positive, zero, or negative. In the case of money, the restoring force is invariably negative so that local increases lead to further increases, like the accretion of mass due to relativistic (gravitational) effects. With a monetary field, it's properties have been defined socio economically so that a similar effect occurs - otherwise why have the field at all if its inventors cannot 'profit' by it? It would be straightforward to have a monetary field with a positive restoring force - but you would find it incredibly difficullt to get rich in such an environment. Which is why it was never invented.
The common properties of the systems described in the question are the complexity, the multi-scale nature and the self-similarity of the governing laws with respect to scaling. The concept of complexity used here is very general and indicates that the system is composed of a large number of interacting parts and has a marked tendency to self-organization (emergence of macroscopic structures).
Multiscale complex systems are described by a non-Gaussian statistical distribution. They also exhibit the self-organized criticality observed in phenomena ranging from earthquakes and landslides to undesirable stock market behavior.
In examining the problem from the historical point of view, it is worth mentioning that the non-Gaussian statistical distribution was identified in 1892 by Wilfredo Pareto after a survey of the income distribution. Asymmetrical distributions, similar to those studied by Pareto, have also been observed in the natural sciences.
This fact led to the creation of a physical economy based on the methods developed in statistical physics. This new disciplines shows significant predictive skill with respect to the forecasting of general trends.
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