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WD_436/ 2008
(  Satoshi Kinoshita )
| Series: | Works on paper: Drawings 5 | | Medium: | oilstick on paper | | Size (inches): | 40.2 x 25.2 | | Size (mm): | 1020 x 640 | | Catalog #: | WD_0436 | | Description: | Signed, date and copyright in pencil on the reverse.
Edward Norton Lorenz -
Edward Norton Lorenz (May 23, 1917 – April 16, 2008) was an American mathematician and meteorologist, and an early pioneer of the chaos theory. He discovered the strange attractor notion and coined the term butterfly effect.
Selected publications:
* 1955 Available potential energy and the maintenance of the general circulation. Tellus. Vol.7
* 1963 Deterministic nonperiodic flow. Journal of Atmospheric Sciences. Vol.20 : 130—141
* 1967 The nature and theory of the general circulation of atmosphere. World Meteorological Organization. No.218
* 1969 Three approaches to atmospheric predictability. American Meteorological Society. Vol.50
* 1976 Nondeterministic theories of climate change. Quaternary Research. Vol.6
* 1990 Can chaos and intransitivity lead to interannual variability? Tellus. Vol.42A
* 2005 Designing Chaotic Models. Journal of the Atmospheric Sciences: Vol. 62, No. 5, pp. 1574–1587.
-en.wikipedia.org/wiki/Edward_Lorenz
Chaos theory -
In mathematics and physics, chaos theory describes the behavior of certain nonlinear dynamical systems that may exhibit dynamics that are highly sensitive to initial conditions (popularly referred to as the butterfly effect). As a result of this sensitivity, which manifests itself as an exponential growth of perturbations in the initial conditions, the behavior of chaotic systems appears to be random. This happens even though these systems are deterministic, meaning that their future dynamics are fully defined by their initial conditions, with no random elements involved. This behavior is known as deterministic chaos, or simply chaos.
-en.wikipedia.org/wiki/Chaos_theory
Strange attractor -
An attractor is informally described as strange if it has non-integer dimension or if the dynamics on it are chaotic. The term was coined by David Ruelle and Floris Takens to describe the attractor that resulted from a series of bifurcations of a system describing fluid flow. Strange attractors are often differentiable in a few directions, but some are like a Cantor dust, and therefore not differentiable.
Examples of strange attractors include the Hénon attractor, Rössler attractor, Lorenz attractor, Tamari attractor.
-en.wikipedia.org/wiki/Strange_attractor#Strange_attractor
Butterfly effect -
The butterfly effect is a phrase which encapsulates the more technical notion of sensitive dependence on initial conditions in chaos theory. Small variations of the initial condition of a nonlinear dynamical system may produce large variations in the long term behavior of the system. So this is sometimes presented as esoteric behavior, but can be exhibited by very simple systems: for example, a ball placed at the crest of a hill might roll into any of several valleys depending on slight differences in initial position.
The phrase refers to the idea that a butterfly's wings might create tiny changes in the atmosphere that ultimately cause a tornado to appear (or prevent a tornado from appearing). The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale phenomena. Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different.
Recurrence, the approximate return of a system towards its initial conditions, together with sensitive dependence on initial conditions are the two main ingredients for chaotic motion. They have the practical consequence of making complex systems, such as the weather, difficult to predict past a certain time range (approximately a week in the case of weather).
-en.wikipedia.org/wiki/Butterfly_effect
Deterministic system (philosophy) -
A deterministic system is a conceptual model of the philosophical doctrine of determinism applied to a system for understanding everything that has and will occur in the system, based on the physical outcomes of causality. In a deterministic system, every action, or cause, produces a reaction, or effect, and every reaction, in turn, becomes the cause of subsequent reactions. The totality of these cascading events can theoretically show exactly how the system will exist at any moment in time.
An example system:
To understand this concept, start with a fairly small everyday system. Visualize a set of three dominoes lined up in a row with each domino less than a domino's length away from its neighbors, impervious to external environment influences. Once the first domino has toppled, the third domino will topple because the second will topple upon being contacted by the first domino. This could feasibly be shown by a scientist using a computer model front-loaded with the ability to correctly apply physics.
Small deterministic systems are easy to visualize, but are necessarily linked to the rest of reality by an initial cause and/or final effect. To go back to the dominoes, something outside the system has to cause the first domino to topple. The last domino falling might cause something else outside the system to happen. And the system itself must be considered in isolation--if external forces such as hurricanes, earthquakes or the hands of nearby people were taken into consideration, the final domino toppling might not be a predetermined outcome. Complete isolation of a system is unrealistic, but useful for understanding what would normally happen to a system when the possibility of external influences is negligible. Complex physical systems are necessarily built using simpler ones, and using isolated systems as a starting model can help bridge the gap and aid in understanding. The domino example is developed in the Petri net computational model.
This example assumes that dominoes toppling into each other behave deterministically. Even the above-mentioned external forces which might interrupt the system are causes which the system did not consider, but which could be explained by cause and effect in a larger deterministic system.
Or otherwise stated : A system in which the later states of the system follow from, or are determined by, the earlier ones. Such a system contrasts with a stochastic or random system in which future states are not determined from previous ones. An example of a stochastic system would be the sequence of heads or tails of an unbiased coin, or radioactive decay. If a system is deterministic, this doesn’t necessarily imply that later states of the system are predictable from a knowledge of the earlier ones. In this way, chaos is similar to a random system. For example, chaos has been termed "deterministic chaos" since, although it is determined by simple rules, its property of sensitive dependence on initial conditions makes a chaotic system, in practice, largely unpredictable.
Some deterministic systems:
* Classical physics is the deterministic system assumed in the domino example which scientists can use to describe all events which take place on a scale larger than individual atoms. Classical physics includes Newton's laws of motion, Classical electrodynamics, thermodynamics, the Special theory of relativity, the General theory of relativity, chaos theory and nonlinear dynamics. Some of these systems are complex, and events may be difficult to predict in practice, but if the starting conditions were known in enough detail, the outcomes of events in such systems could be predicted.
* Nearly all electronic computers in use today are based on theoretical von Neumann computers or Turing machines, i.e.: they are devices that perform one small, deterministic step at a time. If all inputs are specified, the computer will always produce a particular output which is calculated deterministically. Computer scientists also study other models of computation including parallel computers (more than one deterministic step at a time), and quantum computers (which are based on non-deterministic quantum mechanical models).
* Some schools of Islamic thought dictate that the world is predetermined in Hadith. "If the whole community gathered to help you, they could only help you with what God has already prescribed for you. If the whole community gathered to harm you, they could only harm you with what God has already prescribed for you. The pens have been lifted, the pages, dried." Other schools of Islamic thought describe a less restricted view, indeed the Quran itself describes the actions of people to undetermined and that actions proceed from volition conveyed through the agency of the soul.
* Behaviorism, an approach to psychology based on the proposition that behavior can be researched scientifically without recourse to inner mental states, is usually considered to be deterministic and opposed to free will.
Non-deterministic systems:
Events without natural causes cannot be part of a deterministic system. Whether such events actually occur is a matter of philosophical and scientific debate - however, possible uncaused events include:
* Random Quantum events
Quantum physics holds that certain events such as radioactive decay and movement of particles are completely random when taken at the level of single atoms or smaller. Schrödinger's cat is a famous thought experiment in which a cat's survival cannot be determined theoretically before the experiment is done. For almost all everyday non-microscopic occurrences, however, the probability of such random events is extremely close to zero, and can be approximated to almost certainty with statistics using the correspondence principle. The philosophical consequences of quantum physics were once considered by many (including Albert Einstein) to be a major problem for the scientific method which traditionally used a strong version of scientific determinism (see Philosophy of science).
Systems with controversial classification:
Some systems are particularly difficult to classify as deterministic or not, and have generated much philosophical debate. The major example would be human minds, and possibly animal minds too. Can people have free will if their minds are truly deterministic? Conversely, when deterministic computers are said to exhibit artificial intelligence, how are their minds similar to ours?
The entire universe:
The larger the deterministic system, the longer the necessary chain of cause and effect. The entire universe may be considered as such a system, which creates its own philosophical questions (see Determinism).
See also:
* Chaos theory
* Classical mechanics
* Classical physics
* Philosophy of science
* Quantum indeterminacy
* Quantum mechanics
* Quantum mind
* Scientific determinism
* Social cycle theory of Sarkar
* Uncertainty principle
* Indeterminacy
-en.wikipedia.org/wiki/Deterministic_system_%28philosophy%29
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