Heraclitus and Bounded Chaos

We perceive nature as change and if change  is extremely slow it is regarded as constant. In other words constancy is an extremely slow change. This insight is summarized by Heraclitus’ statement: “Nothing endures but change”

Heraclitus (535 - 475 BC), know as “The Obscure” created some profound metaphors which are relevant  even  today. Stated in a modern way he  regards  nature as a complex process and says: ”The sun is new every day.”  Since the sun changes extremely  slowly it  appears invariant. However the sun is a process which burns itself to death and from our viewpoint is rejuvenated  every morning. Note how poetic this metaphor  is. The sun-process is not at all a random birth-death process, since randomness does not exist in nature .The sun is a  bounded chaotic process. It is like a river which flows and does not stand still.

Since “nothing endures but change” , and  “everything flows, nothing stands still”, “you could not step twice into the same river; for other waters are ever flowing on to you.” The last  metaphor is known as “panta rhe” .(All streams). It  implies the modern notion of Chaos. Scientists at UC Santa Cruz found chaos in a dripping water faucet. Unfortunately they did not bother to establish chaos in the Santa Cruz river which would convince them  that one cannot experience twice the same chaos.

The river metaphor implies also that despite being chaotic you still recognize the Santa Cruz  river as a river, since its chaos is bounded by the river bed. Bounded chaos is illustrated by an interesting CA experiment. 

However since “nothing endures but change” the river bed is also chaotic, and  we are fortunate that its chaos changes very slowly. Like the newborn sun.

In another  fragment Heraclitus adds to the river metaphor: “No man ever steps in the same river twice, for it's not the same river and he's not the same man.” Processes in our organism continually stream, and  we are bounded chaotic. Therefore one never meets the same individual twice.
Heraclitus’ river has neither a source nor a sink.

The  spring might be regarded as  source of the river and the sea as its sink but they are in some remote regions.  The river is neither flowing in nor out. We can appreciate only the change of its structure, which we interpret as flowing. It has never been turned on  since the river is nourished by rain which started pouring on the primordial soup eons ago. The river is a metaphor for a process. All processes in our organism are interconnected. They neither have a source nor a sink and we can’t determine the direction of their flow, which to my understanding is irrelevant.

CA are discrete and I apply them to illustrate the above features of  an interconnected complex system. Click on the proliferon and watch it evolve. It may change its position in space, however its structure does not reveal where it is flowing to.  Its previous states seem to flow backward however if you reduce the CA to one state its past memory will vanish.

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