Spontaneous self-organisation: A limiting result

The term “spontaneous self-organisation” (SSO for short) is used to describe the emergence of an object or structure “by itself” within a dynamical system. While usage of the term will no doubt vary somewhat, in this paper I will take it to have three key features: 1. The appearance of the object does not require a special, “fine-tuned” initial state. 2. There is no need for interaction with an external system. 3. The object is likely to appear in a reasonably short time. The first two conditions say that the object arises from the dynamics of the system alone, without any help. The third condition says that, for an object s to appear by spontaneous self-organisation, its appearance should not just a matter of dumb luck (e.g. a monkey with a typewriter just happening to produce Hamlet), nor just from waiting long enough (e.g. a monkey typing for long enough that Hamlet was likely to appear), or any combination of the two. What is “reasonably short” in this context? The time needed for spontaneous self-organisation should be much shorter than the expected time required to assemble the object purely at random from its components. Note that, for very large and intricate systems, the random-assembly time will be unimaginably vast, so that the appearance of such objects in merely billions of years will count as spontaneous self-organisation.
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