11 Apr 2009

Ancient Chaos: Ch 2.1 of Mainzer, Thinking in Complexity: The Computational Dynamics of Matter, Mind, and Mankind

by Corry Shores
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Klaus Mainzer

Thinking in Complexity:
The Computational Dynamics
of Matter, Mind, and Mankind

2 Complex Systems and the Evolution of Matter

Matter comes in complex, irregular, and chaotic states. Order arises from it. How?

2.1 Aristotle's Cosmos and the Logos of Heraclitus

Many presocratic philosophers traced the complexity of nature back to the order of "first principles." Thales asserts that the wet is the original cause of all things.

Anaximander says it is "a boundlessly indeterminable" original matter. Out of it arises all oppositional forms of matter, such as heat & cold, and wet & dry. (18bc) Thus everything begins in a completely heterogeneous and symmetrical state. The symmetry becomes broken. Then opposites and tensions emerge. The new material states are determined and ordered.

Anaximines held that change results from the condensation and rarefaction of air.

For Heraclitus, the original matter is change. It is fire.
The ray of lightning (i.e., fire) guides the All. This world order which is the same for all was created neither by one of the gods nor by one of the humans, but it was always, and is, and will be eternally living fire, glimmering and extinguishing according to measures. (qt. 10bc)
In the 20th century, physicists would say something similar, except speak of energy rather than fire.

But Heraclitus did not mean all was chaos. The material world "consists of opposite conditions and tendencies which, nevertheless, are held in unity by hidden harmony," which is logos. (19d, emphasis mine)

Parmenides conceived the world as being motionless, homogeneous, and timeless. (20b)

Empedocles argued that four elements "arose from nature and chance." Changes result from their intermixing. Love/attraction and hatred/repulsion are the basic forces.

Anaxagoras replaces Empedocles' four elements with an unlimited number of substances composed of seed particles. Matter is infinitely divisible, so they were unlimited in their number and smallness. Everything is contained in everything else. There is black in snow, but too little to discern. Anaxagoras also said that the cosmos proceeds from a homogeneous mixture of matter. An immaterial original spirit force "set this mixture into a whirling motion which brought about a separation of the various things depending on the speed of each of them." (21c)

Democritus posited atoms. There is full. And there is empty. Full are the atoms. Empty are the spaces between. "Atoms differ in the form (morphe), the position (thesis), and their diverse configurations (taxis) in material combinations." (21d) The atoms "move according to necessity in a constant whirl." (22a)

Plato gives a mathematical model for atomism in his Timaeus. The geometrical shapes of the basic material parts determine how they combine, and the sorts of matter that their combinations make-up. (22b-c)

For Aristotle, the most perfect motion was circular. It can go without end. (25c) The cosmos' motion is based on the circular movement of the spheres.

Taoism considers nature to be "a great organism governed by cyclical motions and rhythms." (30cd) All things are interrelated. "Rhythms follow upon each other like waves in the water." There are two opposite forces: yin and yang. (30d) Energies return to their origins. Chinese philosophy had no notions of atomistic particles. So they never developed mathematical mechanics.
Instead, at its center there was a harmonious model of nature with rhythmic waves and fields that cause everything to be connected to everything. (31b)
In this way, the Taoists resemble the Stoics.
Here too the discussion centers on effects that spread out in a great continuum like waves on water. This continuum is the Stoics' pneuma, whose tensions and vibrations are said to determine the various states of nature. The multifarious forms of nature are only transitory patterns that are formed by varied tensions of the pneuma. (31c, emphasis mine)
But the Taoist and Stoic ideas did not lead directly to the sort of wave and field sciences of today. For them,
the emergence of order from complex, irregular, and chaotic states of matter was only qualitatively described, using different models for earth and for heaven. (31c)

Mainzer, Klaus. Thinking in Complexity: The Computational Dynamics of Matter, Mind, and Mankind. Berlin: Springer, 2004.

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