In a rented convent in Santa Fe, a revolution has been brewing. The activists are not anarchists, but rather Nobel Laureates in physics and economics such as Murray Gell-Mann and Kenneth Arrow, and pony-tailed graduate students, mathematicians, and computer scientists down from Los Alamos. They've formed an iconoclastic think tank called the Santa Fe Institute, and their radical idea is to create a new science called complexity. These mavericks from academe share a deep impatience with the kind of linear, reductionist thinking that has dominated science since the time of Newton. Instead, they are gathering novel ideas about interconnectedness, coevolution, chaos, structure, and order - and they're forging them into an entirely new, unified way of thinking about nature, human social behavior, life, and the universe itself. They want to know how a primordial soup of simple molecules managed to turn itself into the first living cell - and what the origin of life some four billion years ago can tell us about the process of technological innovation today. They want to know why ancient ecosystems often remained stable for millions of years, only to vanish in a geological instant - and what such events have to do with the sudden collapse of Soviet communism in the late 1980s. They want to know why the economy can behave in unpredictable ways that economists can't explain - and how the random process of Darwinian natural selection managed to produce such wonderfully intricate structures as the eye and the kidney. Above all, they want to know how the universe manages to bring forth complex structures such as galaxies, stars, planets, bacteria, plants, animals, and brains. There are commonthreads in all of these queries, and these Santa Fe scientists seek to understand them. Complexity is their story: the messy, funny, human story of how science really happens. Here is the tale of Brian Arthur, the Belfast-born economist who stubbornly pushed his theories of economic ch
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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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