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Self-organisation in dynamical systems: a limiting result

机译：动力系统中的自组织：一个有限的结果

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There is presently considerable interest in the phenomenon of “self-organisation” in dynamical systems. The rough idea of self-organisation is that a structure appears “by itself” in a dynamical system, with reasonably high probability, in a reasonably short time, with no help from a special initial state, or interaction with an external system. What is often missed, however, is that the standard evolutionary account of the origin of multi-cellular life fits this definition, so that higher living organisms are also products of self-organisation. Very few kinds of object can self-organise, and the question of what such objects are like is a suitable mathematical problem. Extending the familiar notion of algorithmic complexity into the context of dynamical systems, we obtain a notion of “dynamical complexity”. A simple theorem then shows that only objects of very low dynamical complexity can self organise, so that living organisms must be of low dynamical complexity. On the other hand, symmetry considerations suggest that living organisms are highly complex, relative to the dynamical laws, due to their large size and high degree of irregularity. In particular, it is shown that since dynamical laws operate locally, and do not vary across space and time, they cannot produce any specific large and irregular structure with high probability in a short time. These arguments suggest that standard evolutionary theories of the origin of higher organisms are incomplete.
机译：当前，人们对动力系统中的“自组织”现象非常感兴趣。自组织的粗略想法是，结构在动态系统中“以其自身”出现，在相当短的时间内，在没有特殊初始状态的帮助下或与外部系统交互作用下，以相当高的概率出现。然而，经常被遗忘的是，关于多细胞生命起源的标准进化论符合这一定义，因此高等生物也是自组织的产物。很少种类的对象可以自组织，而这些对象是什么样的问题是一个合适的数学问题。将熟悉的算法复杂性概念扩展到动态系统的上下文中，我们得到了“动态复杂性”的概念。然后，一个简单的定理表明，只有动态复杂度很低的对象才能自我组织，因此活生物体必须具有较低的动态复杂度。另一方面，出于对对称性的考虑，相对于动力学定律，由于生物体的大小和高度的不规则性，它们是高度复杂的。特别地，显示出，由于动力定律在局部起作用，并且不随时间和空间变化，因此它们不能在短时间内高概率地产生任何特定的大型和不规则结构。这些论点表明，高级生物起源的标准进化论是不完整的。

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