Randomnicity: Rules and Randomness in the Realm of the InfiniteThis unique book explores the definition, sources and role of randomness. A joyful discussion with many non-mathematical and mathematical examples leads to the identification of three sources of randomness: randomness due to irreversibility which inhibits us from extracting whatever rules may underlie a process, randomness due to our inability to have infinite power (chaos), and randomness due to many interacting systems. Here, all sources are found to have something in common: infinity. The discussion then moves to the physical system (our universe). Through the quantum mechanical character of small scales, the second law of thermodynamics and chaos, randomness is shown to be an intrinsic property of nature ? this is consistent with the three sources of randomness identified above. Finally, an explanation is given as to why rules and randomness cannot exist by themselves, but instead have to coexist. Many examples are presented, ranging from pure mathematical to natural and social processes, that clearly demonstrate how the combination of rules and randomness produces the world we live in. |
Other editions - View all
Randomnicity: Rules and Randomness in the Realm of the Infinite Anastasios A Tsonis Limited preview - 2008 |
Randomnicity: Rules and Randomness in the Realm of the Infinite Anastasios A. Tsonis Limited preview - 2008 |
Common terms and phrases
argue Aristotle assume attractor automata ball behavior cell cellular automaton chaos Chapter complete consider corresponding described deterministic digits dynamics electron energy entropy Epimenides equilibrium Escher evolution example follows G¨odel geometry Gödel grid happen infinite number infinity initial condition integers intentionally left blank interacting interference pattern irrational numbers irreversible iteration Koch curve Koch island languages lightning logarithms logistic equation M. C. Escher mathematical mathematical system molecules motion natural networks nodes object observed operation O2 outcome particles pendulum physical positive integers possible power law predict previous step probability procedure produce properties quantum mechanics random numbers random sequences rational number real numbers result rules and randomness scales second law self-organization simple rules simulated slit small-world network snowflake solution speed stepped leader stochastic straight line strange loop structure temperature theorem trajectory universe unpredictable variable wavelength waves Wolfram Research words zero