West Bruce J
Office of the Director Army Research, Research Triangle Park, NC 27709, USA.
Entropy (Basel). 2020 Oct 25;22(11):1204. doi: 10.3390/e22111204.
The theme of this essay is that the time of dominance of Newton's world view in science is drawing to a close. The harbinger of its demise was the work of Poincaré on the three-body problem and its culmination into what is now called chaos theory. The signature of chaos is the sensitive dependence on initial conditions resulting in the unpredictability of single particle trajectories. Classical determinism has become increasingly rare with the advent of chaos, being replaced by erratic stochastic processes. However, even the probability calculus could not withstand the non-Newtonian assault from the social and life sciences. The ordinary partial differential equations that traditionally determined the evolution of probability density functions (PDFs) in phase space are replaced with their fractional counterparts. Allometry relation is proven to result from a system's complexity using exact solutions for the PDF of the Fractional Kinetic Theory (FKT). Complexity theory is shown to be incompatible with Newton's unquestioning reliance on an absolute space and time upon which he built his discrete calculus.
本文的主题是，牛顿世界观在科学领域占据主导地位的时代即将结束。其衰落的先兆是庞加莱关于三体问题的研究，以及该研究最终发展成为如今所谓的混沌理论。混沌的特征是对初始条件的敏感依赖，这导致单个粒子轨迹的不可预测性。随着混沌的出现，经典决定论已越来越罕见，取而代之的是不稳定的随机过程。然而，即使是概率演算也无法抵挡来自社会科学和生命科学的非牛顿式冲击。传统上用于确定相空间中概率密度函数（PDF）演化的普通偏微分方程，已被其分数阶对应方程所取代。利用分数动力学理论（FKT）的PDF精确解，证明了异速生长关系源于系统的复杂性。复杂性理论表明，牛顿毫无质疑地依赖他构建离散微积分所依据的绝对空间和时间是不相容的。
