Topic: chaotic behavior

topics > Group: mathematics


limitations of formalism
Kolmorgorov and algorithmic complexity

Subtopic: variety up

Quote: there is tremendous variety of behavior from the equations for viscous fluid flow with just one parameter; how much more is possible with more complex equations! [»feynRP_1964]
Quote: the complexities of things can easily and dramatically escape the simplicity of the equations which describe them

Subtopic: unpredictable chaos up

Quote: science needs more than finite description; must address the unformalizable, catastrophes
Quote: many scientists believe the world is governed by simple mathematical laws; but in practice, all consequences can not be predicted [»hoarCA8_1986]
Quote: the first step in understanding the unformalizable is dynamical models that are compatible with a given morphology [»thomR_1975]
Quote: phenomena can either be unstable or more or less deterministic; determinism isn't an issue [»thomR_1975]
Quote: gives an erratic recursion, i.e., chaos can be produced by an orderly statement [»hofsDR_1979]
Quote: while a chain will break at its weakest link, it is difficult to predict the link [»bateG_1979]
Quote: convergent sequences are predictable because they concern immense crowds or classes of individuals [»bateG_1979]
Quote: divergent sequences are unpredictable because they concern individuals [»bateG_1979]

Subtopic: randomness up

Quote: maybe pure mathematics is random; e.g., distribution of the primes; there's nothing there to prove [»chaiGJ_2001]

Subtopic: catastrophe theory up

Quote: catastrophe theory describes the shapes of equilibrium surfaces; for at most 4 factors, there are 7 elementary catastrophes [»zeemEC4_1976]
Quote: catastrophe or bifurcation points are those points with some discontinuity in every neighborhood; defines morphology [»thomR_1975]
Quote: the butterfly catastrophe occurs from trimodal behavior; allows a stable, compromise position [»zeemEC4_1976]
Quote: the butterfly factor creates three cusps with a triangular pocket supporting stable behavior [»zeemEC4_1976]

Subtopic: cusp catastrophe up

Quote: the cusp catastrophe is the most productive of catastrophe theory
Quote: in a cusp catastrophe, the behavior surface has two sheets of possible behaviors and an intermediate sheet of inaccessible behavior [»zeemEC4_1976]
Quote: a pleated behavioral surface represents the cusp catastrophe; the fold curve appears as a cusp [»zeemEC4_1976]
Quote: the behavioral surface for a dog under rage and fear contains a pleat of unlikely behavior that narrows to a point [»zeemEC4_1976]
Quote: model a dog's performance under rage and fear by a behavioral surface with a cusp catastrophe [»zeemEC4_1976]
Quote: if a process is governed by only two control factors, then its behavior surface can only have folds and cusps; e.g., a cusp catastrophe [»zeemEC4_1976]
Quote: divergent behavior at the singularity of a cusp catastrophe; behavior depends critically on conditions [»zeemEC4_1976]
Quote: the fold curve in catastrophe theory marks the edges of the pleat [»zeemEC4_1976]

Subtopic: attractors up

Quote: the attractor of a system is a stable cycle of states; e.g., the base note of a bowed violin string [»zeemEC4_1976]
Quote: bifurcation forms lie at the threshold between two or more basins of attraction; their appearance oscillates between the attractors [»thomR_1975]

Subtopic: universe is not chaotic up

Quote: our universe is not chaos; we perceive and name beings and objects that have stable structures [»thomR_1975]
Quote: scientific experimentation is only possible if the process is structurally stable w.r.t. the initial state and environmental interactions

Related Topics up

Group: science   (45 topics, 1960 quotes)

Topic: change (28 items)
Topic: entropy (14 items)
Topic: limitations of formalism (93 items)
Topic: Kolmorgorov and algorithmic complexity (10 items)
Topic: randomness
(20 items)

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