1701069421
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[88]这被称为事物的算法信息量”:对柯尔莫哥洛夫、查汀和索罗蒙洛夫的思想的详细论述,参见Li, M.&Vitanyi, P.,An Introduction to Kolmogorov Complexity and Its Applications,2nd Edition.New York:Springer-Verlag,1997。
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[89]“盖尔曼提出了一种称为‘有效复杂性’的相关度量”:Gell-Mann, M.What is complexity?Complexity,1(1),1995,pp.16—19。
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[90]“这个定义中的主观性也有待解决”:参见,Mc Allister, J.W.,Effective complexity as a measure of information content.Philosophy of Science70,2003,pp.302—307。
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[91]“有逻辑深度的事物”:Bennett, C.H.,How to define complexity in physics, and why.收录在W.H.Zurek(编辑),Complexity, Entropy, and the Physics of Information,Reading, MA:Addison-Wesley,1990,p.142。
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[92]“用最合理的方法生成某个事物时需要处理的信息量”:Lloyd, S.,The calculus of intricacy.The Sciences,30,1990,p.42。
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[93]“劳埃德和裴杰斯提出了一种新的复杂性度量”:Lloyd, S.&Pagels, H.,Complexity as thermodynamic depth.Annals of Physics,188,1988,pp.186—213。
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[94]“产生出这个事物最科学合理的确定事件序列”和“物理构造过程所需的热力源和信息源的总量”:Lloyd, S.,The calculus of intricacy.The Sciences,30,1990,p.42。
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[95]“也有批评意见指出”:Crutchfield, J.P.&Shalizi, C.R.,Thermodynamic depth of causal states:When paddling around in Occam’s pool shallowness is a virtue.Physical Review E,59(1),1999,pp.275—283。
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[96]“像物理学家沃尔夫勒姆就提出”:Wolfram, S.,Universality and complexity in cellular automata.PhysicaD,10,1984,pp.1—35。
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[97]“不过,班尼特等人则认为”:例如,参见Bennett, C.H.,Dissipation, information, computational complexity and the definition of organization.收录在D.Pines(编辑),Emerging Synthesesin Science.Redwood City, CA:Addison-Wesley,1985,pp.215—233。
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1701069442
[98]“统计复杂性”:Crutchfield, J.P.&Young, K.,Inferring statistical complexity,Physics Review Letters63,1989,pp.105—108。
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1701069444
[99]“复杂晶体的原子结构”:Varn, D.P.,Canright, G.S.,&Crutchfield, J.P.,Discovering planar disorder in close-packed structures from X-ray diffraction:Beyond the fault model.Physical ReviewB,66,2002,pp.174110-1-174110-4。
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[100]“神经元的激发模式”:Haslinger, R.,Klinkner, K.L.&Shalizi, C.R.,The computational structure of spike trains.未发表手稿,2007。
1701069447
1701069448
[101]“宇宙也是分形的”:Mandelbrot, B.B.,The Fractal Geometry of Nature.New York:W.H.Freeman,1977。
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[102]“一般来说分形指的是‘在任何尺度上都有微细结构’的几何形状”:Strogatz, S.,Nonlinear Dynamics and Chaos.Reading, MA:Addison-Wesley,1994。
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[103]“这里我们直接给出结果”:对于科赫曲线,3 维数 =4。为了得出维数,将两边取对数(基可为任意数):log(3 维数 )=维数×log(3)=log(4)从而维数=log(4)/log(3)≈1.26
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[104]“分形维数”:对分形和分形维数概念的精彩阐述参见曼德布罗特的书——The Fractal Geometry of Nature.New York:W.H.Freeman,1977。
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[105]“细节的瀑流”:Bovill, C.,Fractal Geometry in Architecture and Design.Birkhäuser Boston,1996,p.4。
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[106]“《复杂性的结构》”:Simon, H.A.,The architecture of complexity.Proceedingsofthe American Philosophical Society,106(96),1962,pp.467—482。
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[107]“复杂系统由子系统组成”:同上,p.468。
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[108]“麦克西……提出了一种层次标度”:Mc Shea, D.W.,The hierarchical structure of organisms:A scale and documentation of a trend in the maximum.Paleobiology,27(2),2001,pp.405—423。
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[109]“大自然逐渐将无生命的东西”:引自Grene, M.&Depew, D.,The Philosophy of Biology:An Episodic History.Cambridge University Press,2004,p.14。
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[110]“我们都本能地知道生命是什么”:Lovelock, J.E,The Agesof Gaia.New York:W.W.Norton,1988,p.16。
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[111]“自我复制的计算机程序”:这一章部分是来自Mitchell, M.,Life and evolution in computers.History and Philosophy of the Life Sciences,23,2001,pp.361—383。
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[112]“……有一些让人着迷的研究”:参见,Luisi, P.L.,The Emergenceof Life:From Chemical Origins to Synthetic Biology.Cambridge:Cambridge University Press,2006;或Fry, I.,The Emergence of Life on Earth:A Historical and Scientific Overview.Piscataway, NJ:Rutgers University Press,2000。
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