In physics,the energy conservation and least action principle are of universal effectiveness. Fermat proposed that the ray of light has the least time for path traverse through different media based on the proof by simple geometry. In social structure people will choose different understanding and reaction to a same event depending on their states. How can people choose the least resistance approved by behavior from different states,different classes and different layers (equale-vant to different media) may be considered as the attempt of applying the Fermat's principle of least action to find the social optimal organization. That is also an important content for explaining social phenomena and giving the universal answer by socio-physics. Based on the fundamental thinking of least action principle, the paper tries to find the existence of least action in every layer of society,furthermore to link the global optimization of n layers in society,and thus to find the exact analysis of the theory of social optimal management in some extents.%在物理学中,能量守恒与最小作用原理具有普遍有效性.费马以简单几何学的证明提出了光在不同介质中传递路径的最小性.在社会结构中,对于同一事件的理解和反应,常因所处状态的不同而有不同的选择.如何能从不同状态、不同等级、不同层级(相当于物理学中的不同介质)中,寻求行为认同的最小阻力,可以考虑应用费马最小作用原理进行寻求社会组织优化的尝试,这也是社会物理学企图定量解释社会现象并给予普遍性回答的一项重要内容.本文从费马最小作用原理的基本思路出发,在社会的每一层级中揭示最小作用的存在性,并进而联系到社会n层级的整体优化,从而为社会优化管理理论寻求某种精确化的解析.
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