Self-referential Boltzmann machine

Yong Tao

Physica A: Statistical Mechanics and its Applications, 2020, vol. 545, issue C

Abstract: We recently reported that the income structure for low and middle classes (about 95% of populations) in a well-functioning free-market country would follow a Boltzmann-like distribution that has a self-referential entropy (Tao, 2018). The empirical evidences cover 66 free-market countries and the Hong Kong SAR. By contrast, the entropy of a physical system is not self-referential. This finding implies that the self-reference may be a potential difference between biological and lifeless-physical systems. In this paper, we argue that if a human society obeys such a Boltzmann-like income distribution, it will spontaneously form a self-referential Boltzmann machine (SRBM), where each person plays the role of a neuron. Because of the self-reference of the entropy, we show that the SRBM always has a positive energy even if all neurons are inactive. This implies the presence of a kind of positive zero-point energy. Based on such a positive zero-point energy, we further show that the SRBM may be a self-motivated system with a biological sense. Our finding supports that a human society functions like a kind of complex system (or organism) with potential self-motivations, just as motivated by an “invisible hand” coined by Adam Smith. As a simple application, we apply the self-motive of the SRBM to perform the task of searching images.

Keywords: Boltzmann machine; Self-reference; Self-motive; Self-awareness; Gibbs term (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119321028

DOI: 10.1016/j.physa.2019.123775

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