Chaos Sensitive Dependence

Something about initial condition. I'm not a mathemagician.

Chaos in Greek mythology and cosmology refers to a gap or abyss at the beginning of the world, or more generally the initial, formless state of the universe.

Later uses of the term by philosophers varies over time. In modern English, the word is used in classical studies with the original meaning; in mathematics and science to refer to a very specific kind of unpredictability; and informally to mean a state of confusion. In philosophy, and in popular culture, the word can occur with all three meanings.

Chaos in mythology, philosophy, literature, and religionEdit

Plato said:

As I said at first, when all things were in disorder God created in each thing in relation to itself, and in all things in relation to each other, all the measures and harmonies which they could possibly receive. For in those days nothing had any proportion except by accident; nor did any of the things which now have names deserve to be named at all — as, for example, fire, water, and the rest of the elements. All these the creator first set in order, and out of them he constructed the universe.

Plato acknowledges a debt to Hesiod in this dialogue, but Hesiod's concept of Chaos has been altered somewhat here,and begins to approach the informal sense of chaos as disorder, both within the constituents of matter, as well in their random distribution.

For Aristotle, chaos simply referred to empty space. Thomas Aquinas, in his Summa Theologica, takes chaos to mean "confusion," and discusses whether primordial chaos is compatible with Christian theology.

The LogrusEdit

See the Logrus.

Free WillEdit

The chaos argument is a philosophical argument. It argues that determinism is an idealistic mathematical construction whose mapping onto reality is untestable in the real world, and that this is an essential precondition for the existence of free will.

The chaos argument asserts that given any description of position and momentum (of all particles in the universe) approaching completeness, long-term prediction is impossible, because variances from completeness multiply over even short periods of time.

Due to the uncertainty principle of quantum mechanics, we as observers can never have access to a complete description and therefore can never close the debate on free will versus determinism.

Also, the electrodynamics of the human brain are chaotic in nature; accordingly there is also no way to prove, in the event that free will does exist in the universe, whether the human has none.

One common objection to drawing conclusions about free will from the chaos argument is that it seems unclear how quantum uncertainty, whether reducible or irreducible, could provide a basis for any kind of free will. The philosopher J. J. C. Smart observed, "Indeterminism does not confer freedom on us: I would feel that my freedom was impaired if I thought that a quantum mechanical trigger in my brain might cause me to leap into the garden and eat a slug".

Scientific and mathematical chaosEdit

Chaos theory is a field of study in mathematics, physics, economics, and philosophy studying the behavior of dynamic systems that are highly sensitive to initial conditions. This sensitivity is popularly referred to as the butterfly effect. Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for chaotic systems, rendering long-term prediction impossible in general. This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved. This behavior is known as deterministic chaos, or simply chaos.

Chaotic behavior can be observed in many natural systems, such as the weather. Explanation of such behavior may be sought through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincaré maps.

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