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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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Yong Tao, 2015. "Universal Laws of Human Society's Income Distribution," Papers 1506.05418, arXiv.org.
    6. Yong Tao, 2010. "Competitive market for multiple firms and economic crisis," Papers 1010.1413, arXiv.org.
    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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