As science probes the nature of life, society, and technology ever more closely, what it finds there is complexity. The sophisticated group behavior of social insects, the unexpected intricacies of the genome, the dynamics of population growth, and the self-organized structure of the World Wide Web - these are just a few examples of complex systems that still elude scientific understanding. Comprehending such systems seems to require a wholly new approach, one that goes beyond traditional scientific reductionism and that re-maps long-standing disciplinary boundaries. This remarkably accessible and companionable book, written by a leading complex systems scientist, provides an intimate, detailed tour of the sciences of complexity, a broad set of efforts that seek to explain how large-scale complex, organized, and adaptive behavior can emerge from simple interactions among myriad individuals. In this richly illustrated work, Melanie Mitchell describes in equal parts the history of ideas underlying complex systems science, the current research at the forefront of this field, and the prospects for the field's contribution to solving some of the most important scientific questions of our current century.
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Melanie Mitchell is a professor of computer science at Portland State University. She has worked at the Santa Fe Institute and Los Alamos National Laboratory. Her major work has been in the areas of analogical reasoning, complex systems, genetic algorithms and cellular automata, and her publications in those fields are frequently cited
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当然,在通用图灵机U中,将M的代码置于U的带子的“程序”部分,将M置于带子的“输入”部分,U就能在M上运行M。
·看似混沌的行为有可能来自确定性系统,无须外部的随机源 ·一些简单的确定性系统的长期变化,由于对初始条件的敏感依赖性,即使在原则上也无法预测。 ·虽然混沌系统的具体变化无法预测,在大量混沌系统的普适共性中确有一些“混沌中的秩序”,例如通往混沌的倍周期之路,以及费根鲍姆常数。因此虽然在细节上“预测变得不可能”,但在更高的层面上混沌系统确实可以预测的。
混沌指的是一些系统——混沌系统——对于其初始位置和动量的测量如果有极其微小的不精确,也会导致对其的常期预测产生巨大的误差。也就是常说的“对初始条件的敏感依赖性”。
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