Topic: chaotic behavior
Topic: handling complexity
Topic: Kolmorgorov and algorithmic complexity
Topic: limitations of formalism
Topic: probabilistic and randomized algorithms
Topic: probability
Topic: probability assessment
Topic: quantum mechanics
Topic: random number generation
Topic: statistics
Topic: statistical mechanics
 
Summary
Something is random if it does not follow a pattern. Randomness is measured by comparing a sequence of selections from a set. When selecting a sequence of ones and zeros, does prior or future choices allow one to predict the current choice?
Algorithmic or Kolmorgorov complexity measures randomness by the shortest, generating program. For example, the sequence 010101... has a short description.
What is the role of randomness in the world? Is the world driven by random events? Randomness is an important part of the physical world of atoms, molecules, photons, and energy. (cbb 6/06)
Subtopic: is the world random?
Quote: Euripidesdoes random careless chance and change, alone control the world? [»euri_425]
 Quote: the elements are not ordered by their intellect; by trial and error they fell into their present form [»lucr_55]
 Quote: this world is the product of Nature, the seeds of things colliding into each other by pure chance [»lucr_55]
 Quote: a single molecule of water receives 10^14 collisions per second; over a hundredth of a second the collisions are effectively random [»feynRP_1963]
 Quote: software must have internal regularies which can be found by random search
 Subtopic: is math random?
Quote: maybe pure mathematics is random; e.g., distribution of the primes; there's nothing there to prove [»chaiGJ_2001]
 Quote: the halting probability is a welldefined real number with no mathematical structure; the bits are random [»chaiGJ_2001]
 Subtopic: deviation towards the mean
Quote: chance is commonly viewed as a selfcorrecting process. In fact, deviations are merely diluted [»tverA9_1974]
 Quote: deviation towards the mean: consider variables X and Y with the same distribution; the extremes of X will be less extreme in Y [»tverA9_1974]
 Subtopic: probabilistic predicates
Quote: while a deterministic, prime number predicate is probably exponential, a probabilistic predicate is linear [»carbJG3_1978]
 Subtopic: distributed algorithms
Quote: rumor mongering  mail updates until they're old news at multiple sites [»demeA8_1987]
 Quote: antientropy compares databases at random  is much slower than direct mail [»demeA8_1987]
 Subtopic: randomness
Quote: TDGammon is successful because of the randomness of backgammon and a fairly smooth outcome function [»tesaG3_1995]
 Subtopic: algorithmic complexity
Quote: random elements as defined by Kolmogorov possess all conceivable statistical properties of randomness; equivalent to a universal stochasticity test [»martP12_1966]
 Quote: almost all infinite binary sequences are random [»martP12_1966]
 Quote: something is random iff it is incompressible [»chaiGJ_2001]
 Quote: a random, finite binary sequence is one that requires a program at least as long as for any other sequence of the same length [»chaiGJ_1966]
 Quote: random sequences are those that require the longest programs; not random if generated by a short program [»chaiGJ_1970]
 Quote: to prove that a particular series of digits is random must prove that there is no small program for it; probably impossible [»chaiGJ5_1975]
 Quote: protein is incompressible; prior context does not improve compression; perhaps due to random mutation or compact representation

Related Topics
Topic: chaotic behavior (27 items)
Topic: handling complexity (60 items)
Topic: Kolmorgorov and algorithmic complexity (10 items)
Topic: limitations of formalism (93 items)
Topic: probabilistic and randomized algorithms (11 items)
Topic: probability (21 items)
Topic: probability assessment (26 items)
Topic: quantum mechanics (103 items)
Topic: random number generation (29 items)
Topic: statistics (12 items)
Topic: statistical mechanics (22 items)
