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Self-referential Boltzmann machine

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  • Tao, Yong

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.

Suggested Citation

  • Tao, Yong, 2020. "Self-referential Boltzmann machine," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119321028
    DOI: 10.1016/j.physa.2019.123775
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    References listed on IDEAS

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    1. Stanley, H.E. & Afanasyev, V. & Amaral, L.A.N. & Buldyrev, S.V. & Goldberger, A.L. & Havlin, S. & Leschhorn, H. & Maass, P. & Mantegna, R.N. & Peng, C.-K. & Prince, P.A. & Salinger, M.A. & Stanley, M., 1996. "Anomalous fluctuations in the dynamics of complex systems: from DNA and physiology to econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 224(1), pages 302-321.
    2. Yong Tao, 2015. "Universal Laws of Human Society's Income Distribution," Papers 1506.05418, arXiv.org.
    3. Yong Tao & Xiangjun Wu & Tao Zhou & Weibo Yan & Yanyuxiang Huang & Han Yu & Benedict Mondal & Victor M. Yakovenko, 2019. "Exponential structure of income inequality: evidence from 67 countries," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(2), pages 345-376, June.
    4. Yong Tao, 2010. "Competitive market for multiple firms and economic crisis," Papers 1010.1413, arXiv.org.
    5. Tao, Yong, 2018. "Swarm intelligence in humans: A perspective of emergent evolution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 436-446.
    6. Tao, Yong, 2015. "Universal laws of human society’s income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 435(C), pages 89-94.
    7. Yong Tao, 2016. "Spontaneous economic order," Journal of Evolutionary Economics, Springer, vol. 26(3), pages 467-500, July.
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    Cited by:

    1. Li, Hanwen & Shang, Qiuyan & Deng, Yong, 2021. "A generalized gravity model for influential spreaders identification in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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    3. Belieres, Simon & Hewitt, Mike & Jozefowiez, Nicolas & Semet, Frédéric, 2021. "A time-expanded network reduction matheuristic for the logistics service network design problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 147(C).
    4. Tao, Yong & Sornette, Didier & Lin, Li, 2021. "Emerging social brain: A collective self-motivated Boltzmann machine," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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