Randomnicity : rules and randomness in the realm of the infinite /
Tsonis, Anastasios A.
Randomnicity : rules and randomness in the realm of the infinite / Anastasios A. Tsonis. - London : Singapore : Imperial College Press ; Distributed by World Scientific Pub. Co., ©2008. - 1 online resource (xii, 191 pages) : illustrations (some color)
Includes bibliographical references (pages 175-187) and index.
pt. I. 1. The three parts of everything. 2. Gödel visits Escher's studio. Gödel's theorem. 3. Slippery road. 4. Fuller than full. 5. Cantor would have been pleased -- pt. II. Sources of randomness. 6. A private lesson a long, long time ago. 7. The five faces of order. 8. Randomness of the first kind. 9. Randomness of the second kind. 10. Randomness of the third kind -- pt. III. Randomness in the universe. 11. From Aristotle to Einstein. 12. The world according to an electron. 13. Chaos. 14. The supreme law. 15. Randomness of the fourth kind? 16. Connections. 17. Allowed behaviors -- Part IV. The emergence of the real world. 18. The fractal character of nature. 19. Physics plus randomness. 20. Stochastic processes. 21. Self-organization. 22. The blueprint of life. 23. Human products and social phenomena. 24. The principle of minimum energy consumption -- pt. V. The role of randomness. 25. Efficiency, paradoxes and beauty.
This 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.
9781848161986 (electronic bk.) 1848161980 (electronic bk.) 1848162057 (pbk.) 1848161972 9781848161979 9781848162051 (pbk.)
Chaotic behavior in systems.
Stochastic processes.
Infinite.
Chaos.
Processus stochastiques.
Infini.
infinity.
MATHEMATICS--Probability & Statistics--General.
Chaotic behavior in systems.
Infinite.
Stochastic processes.
Electronic books.
Electronic books.
Q172.5.C45
519.2
Randomnicity : rules and randomness in the realm of the infinite / Anastasios A. Tsonis. - London : Singapore : Imperial College Press ; Distributed by World Scientific Pub. Co., ©2008. - 1 online resource (xii, 191 pages) : illustrations (some color)
Includes bibliographical references (pages 175-187) and index.
pt. I. 1. The three parts of everything. 2. Gödel visits Escher's studio. Gödel's theorem. 3. Slippery road. 4. Fuller than full. 5. Cantor would have been pleased -- pt. II. Sources of randomness. 6. A private lesson a long, long time ago. 7. The five faces of order. 8. Randomness of the first kind. 9. Randomness of the second kind. 10. Randomness of the third kind -- pt. III. Randomness in the universe. 11. From Aristotle to Einstein. 12. The world according to an electron. 13. Chaos. 14. The supreme law. 15. Randomness of the fourth kind? 16. Connections. 17. Allowed behaviors -- Part IV. The emergence of the real world. 18. The fractal character of nature. 19. Physics plus randomness. 20. Stochastic processes. 21. Self-organization. 22. The blueprint of life. 23. Human products and social phenomena. 24. The principle of minimum energy consumption -- pt. V. The role of randomness. 25. Efficiency, paradoxes and beauty.
This 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.
9781848161986 (electronic bk.) 1848161980 (electronic bk.) 1848162057 (pbk.) 1848161972 9781848161979 9781848162051 (pbk.)
Chaotic behavior in systems.
Stochastic processes.
Infinite.
Chaos.
Processus stochastiques.
Infini.
infinity.
MATHEMATICS--Probability & Statistics--General.
Chaotic behavior in systems.
Infinite.
Stochastic processes.
Electronic books.
Electronic books.
Q172.5.C45
519.2