ISBN:
9780080257969
Language:
English
Pages:
Online-Ressource (195 p)
Edition:
Online-Ausg.
Series Statement:
Foundations and philosophy of science and technology series
Parallel Title:
Print version Mathematics as a Cultural System
DDC:
303.4/83
Keywords:
Electronic books
Abstract:
Mathematics as a Cultural System discusses the relationship between mathematics and culture. The book is comprised of eight chapters discussing topics that support the concept of mathematics as a cultural system. Chapter I deals with the nature of culture and cultural systems, while Chapter 2 provides examples of cultural patterns observable in the evolution of mechanics. Chapter III treats historical episodes as a laboratory for the illustration of patterns and forces that have been operative in cultural change. Chapter IV covers hereditary stress, and Chapter V discusses consolidation as a f
Description / Table of Contents:
Front Cover; Mathematics as a Cultural System; Copyright Page; Inroductory Note; Table of Contents; Chapter I. The nature of Culture and Cultural Systems; 1. Evolution of a cultural artifact; 2. The things that make up a culture; 3. Culture as a collection of elements in a communications network; 4. Mathematics as a cultural system; 5. Cultural and conceptual evolution; Chapter II. Examples of Cultural Patterns Observable in the Evolution of Mathematics; 1. Multiples; 2. ""Clustering of genius""; 3. The ""before his time"" phenomenon; 4. The operation of cultural lag in mathematics
Description / Table of Contents:
5. Patterns of thought. Mathematical reality and mathematical existence6. Evolution of greater abstraction; 7. Forced origins of new concepts; 8. Selection in mathematics; 9. The effect of the occurrence of paradox, or the discovery of inconsistency; 10. The relativity of mathematical rigor; 11. Growth patterns of fields of mathematics; 12. A problem; Chapter III. Historical Episodes; a Laboratory for the Study of Cultural Change; 1. The great diffusions; 2. Symbolic achievements; 3. Pressure from the environment; environmental stress; 4. Motivation for multiple invention
Description / Table of Contents:
exceptions to the rule5. The great consolidations; 6. Leaps in abstraction; 7. Great generalizations; Chapter IV. Potential of a Theory or Field; Hereditary Stress; 1. Hereditary stress; 2. Components of hereditary stress; 3. General remarks; Chapter V. Consolidation: Force and Process; Part I. General theory; Part II. The consolidation process in mathematics; Part III. Concluding remarks; Chapter VI. The Exceptional Individual; Singularities in the Evolution of Mathematics; 1. General remarks. Mendel, Bolzano, Desargues; 2. Historical background of Desargues' work
Description / Table of Contents:
3. Why was PG17 not developed into a field?4. Avenues of possible survival; 5. The success of projective geometry in the 19th century; 6. General characteristics of the ""before-his-time"" phenomenon; 7. Comment; Chapter VII. ""Laws"" Governing the Evolution of Mathematics; 1. Law governing multiple discovery; 2. Law re. acceptance of a new concept; 3. Law re. evolution of new concepts; 4. Law re. the status of creator of a new concept; 5. Law re. continued importance of a concept; 6. Law re. the solution of an important problem; 7. Law re. the occurrence of consolidation
Description / Table of Contents:
8. Law re. interpretation of ""unreal"" concepts9. Law re. the cultural intuition; 10. Law re. diffusion; 11. Law re. environmental stresses; 12. Law re. great advances or breakthroughs; 13. Law re. inadequacies of a conceptual structure; 14. Law re. revolutions in mathematics; 15. Law re. mathematical rigor; 16. Law re. evolution of a mathematical system; 17. Law re. the individual and mathematics; 18. Law re. mathematics becoming ""worked out""; 19. Law re. beginnings; 20. Law re. ultimate foundation of mathematics; 21. Law re. hidden assumptions
Description / Table of Contents:
22. Law re. emergence of periods of great activity
Note:
Description based upon print version of record
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