总结1:今天,我们不再把决定论看成是单个路径的演变而是看成一个群体的整体的发展。轨迹对于初始条件的敏感性,似乎被某种统计上的稳定性所抵消。
总结2: 洛伦的贡献不仅仅是告诉我们:“未来很大程度上取决于现在”(蝴蝶效应,现在状态微小的不同,会对未来产生巨大的影响)。他通过洛伦吸引子,还告诉了我们非常重要的一个道理:通过重新聚焦于统计问题,科学仍然可以对未来做出预测!
By refocusing on statistical issues, science can still make predictions!
记录几个定义帮助理解:
”Chaos(混乱): When the present determines the future, but the approximate present does not approximately determine the future.“
--Edward Lorenz
ps:混沌:轨迹对于初始条件的极大的敏感性
In mathematics, a dynamical system(动力系统) is a system in which a function describes the timedependence of a point in a geometrical space.
--Wikipedia
Ergodic theory(遍历论) is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics.
--Wikipedia
Sinai-Ruelle-Bowen (SRB) measure: The concept of SRB measure is a rigorous formulation of what it means for an invariant measure to be “physically meaningful.” An SRB measure attracts a large set of orbits into its support, and its statistical features are reflected in the behavior of these attracted orbits.
--AMIE WILKINSON "SMOOTH ERGODIC THEORY"