Sir Isaac Newton Stranger in a Strange Land

Entropy

BruceJ. West¹ 

[1] Office of the Director Army Research Office, Research Triangle Park, NC 27709, USA;

关键词: complexity;    chaos;    fractional calculus;    subordination;   

DOI  :  10.3390/e22111204

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown