chaos theory
Sensitivity breeds unpredictability
Chaos theory is a branch of mathematics studying systems highly sensitive to initial conditions—where tiny differences produce vastly different outcomes.
The classic illustration is the butterfly effect: a butterfly's wings might set off atmospheric changes culminating in a distant tornado.
Despite the name, chaos theory doesn't mean randomness; these systems follow deterministic rules but remain practically unpredictable.
Chaos theory explains why weather forecasts become unreliable beyond a few days.
Small inputs, disproportionate results
- sensitivityResponsiveness to stimuli
- initial conditionsState at time zero
- unpredictabilityState resisting forecasts
- nonlinearityDisproportionate cause and effect
feedback loops · turbulence · emergence · perturbation · self-organization · entropy · complexity · tipping point
Fractal pattern in chaos
- bifurcationDivision into two branches
- Lyapunov exponentRate of orbital separation
- iterationRepeated procedural pass
- deterministicCompletely caused by prior conditions
Identical at every magnification
- space-fillingUsing all available room
- scalingClimbing or resizing
- recursiveDefined in terms of itself
- dimensionMeasurable extent or scope
iteration · geometry · pattern · tessellation
butterfly effect
Small inputs, disproportionate results
- sensitivityResponsiveness to stimuli
- initial conditionsState at time zero
- unpredictabilityState resisting forecasts
nonlinearity · feedback loops · turbulence · emergence · perturbation · self-organization · entropy · complexity · tipping point · cascade
strange attractor
Fractal pattern in chaos
- bifurcationDivision into two branches
- Lyapunov exponentRate of orbital separation
- iterationRepeated procedural pass
self-similarity
Identical at every magnification
- space-fillingUsing all available room
- scalingClimbing or resizing
- recursiveDefined in terms of itself
dimension · iteration · geometry · pattern · tessellation
- simulation modelspredictive models, Monte Carlo, climate models, growth models, carrying capacity
- academic fieldsmathematics, biology, chemistry, physics, history
- scientific theoriesevolution, general relativity, relativity, plate tectonics, special relativity
- theoretical sciencephysics, mathematics, quantum mechanics, relativity, cosmology
- theories
- theoryhypothesis, theorem, axiom, postulate, conjecture
chaos theoryclockwork universe
Reality as divine machinery
Newtonian mechanics · classical mechanics · determinism · predictability · regularity
chaos theorylinear equations
Algebraic statements without powers
reductionism · stable equilibrium · two-body problem · order
chaos theorycosmic order
Universe's fundamental organizing principle
teleology · mechanism · clockwork universe · predictability · fatalism