Emerging social brain: A collective self-motivated Boltzmann machine

Boltzmann machines are unsupervised-learning neural networks, which have contributed to the opening of the field of deep learning architectures. Here we show that, using the modern theory of economic growth, when the number of agents in a free-market society with equal opportunity exceeds a threshold value, a Boltzmann-like income distribution emerges, where the entropy plays the role of swarm intelligence in humans and quantifies its cumulative technological progress. Theoretically, we further show that the emergence of a Boltzmann-like income distribution in a society of optimizing agents reflects the spontaneous organization of a human society to form a Boltzmann machine in which each person plays a role analogous to that of a neuron within a brain-like architecture. This Boltzmann machine exhibits three essential brain-like features, namely the McCulloch-Pitts learning rule, unsupervised-learning, and self-motivation, and satisfies in addition the minimum free-energy principle of the brain theory. Empirically, we investigate the household income data from 66 free-market countries and Hong Kong SAR, and find that, for all of the countries, the income structure for low and middle classes (about 95% of populations) is accurately described by a Boltzmann-like distribution. We suggest that this is a statistical signature that our social networks are going through a critical evolution in the form of a kind of brain-like structure.