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  1. The Nature of Scientific Change Lyndsi Monjon-November 8, 2007

  2. Quotes • “The simplest schoolboy is now familiar with truths for which Archimedes would have sacrificed his life.” -Ernest Renan, 1883 • “Science is the great antidote to the position of enthusiasm and superstition.” –Adam Smith, 1776

  3. Scientific Revolutions • Periods of Revolutions • Share some features of political revolutions • More like a formal, ongoing dialogue between opposing parties

  4. More on Scientific Revolutions • Loyalty oaths uncommon • Rarely appeal to arms • Usually the result of informal alliances with an occasional ‘set price’ in the form of a review, program or manifesto designed to sharpen the awareness of the professionals in a particular area

  5. Dialogues of Scientific Revolution • Take the form of reasoned argument • Have few threats • Moderate language used by all

  6. The Hemholtz-Brücke Pact • 1840s • Intended as anti-Müller, anti-vitalist manifesto • Put together by Müller’s brightest students

  7. Who was Müller? • Leading exponent of the vitalist doctrine • “Life on earth could not have originated from chemical and physical forces alone” • Believes it was triggered by some external, “vitalizing” principle

  8. The Process of Change • Have been several attempts to explain the origins and process of social revolution • Conflict of interest between two groups or social classes over the division of social resources

  9. The Ruling Group • Monopoly of violence due to control of resources • Uses those resources to suppress opposition

  10. Revolutions usually begin from the perception that the existing body of knowledge is flawed.

  11. Scientific Research • Humdrum, routine tasks • Humdrum-dull • Some form of measurement • Checking and rechecking of facts

  12. Normal science • Carried out within a theoretical framework of assumptions • In-depth understandings of specialized subject area • The frame of reference within which science is developed

  13. Paradigmatic Shifts • Resulted from abandoning religious explanations of the creation of the universe • Some resulted of more practical, specialized work

  14. Paradigmatic Shifts in Science

  15. Spheres of Influence • Strong states overwhelm weaker ones • Vulnerable nations form alliances against a common enemy • Some nations dominate, others are subservient

  16. Who really gets the credit? • Omar Khayyam (and others): arithmetic triangle: credited to Pascal • Ruffino’s method of solving equations of high degree was know to the ancient Chinese

  17. Credit? Leibniz did not discover the differential calculus (Newton did) Nor did Leibniz invent the binary system (the Chinese did) Leibniz’s basic philosophy (Monadology) was “borrowed” from Lady Anne Conway

  18. Credit? • 3 people believed the discovered non-Euclidean geometry but Euler gets the credit

  19. History of Science • Post-1789 idea of nation state is too narrow of a concept • Spheres of Influence have had an effect on scientist

  20. Sphere of Influence with Math • Neolithic, pre-literate European and North American • Sumerian, Babylonian, Akkadian, Chaldean, Phoenician • Egyptian • Greek/Roman- first Pax Romana • Chinese, Japanese, Korean

  21. Cont. 6. Arab, Indian, Syrian- first Scientific Revolution 7. Roman Catholic, Mediaeval European- Second Pax Romana 8. Renaissance, Christian, European (especially Italian) 9. Western Europe (especially British, French, and German)- second Scientific Revolution 10. Old European science and mathematics; world science

  22. The Future of Mathematics • Due to the invention of the electric computer, soon we will not be able to talk about numbers in the old-fashioned way • Students will have a different sense of values • Key process is liberation from the domination of age-old traditions

  23. More of the Future • The method of teaching math will change • Most prosperous countries: • Japan • USA • Germany

  24. Any Questions???

  25. Resources • Websites • http://www.jiskha.com/images/subjects/mathematics/mathematics_cover.gif • http://upload.wikimedia.org/wikipedia/commons/0/0a/AdamSmith.jpg • http://content.answers.com/main/content/wp/en/e/e3/Renan.jpg • http://www.bluefield.edu/clientimages/30250/academics/mathlogo.gif • http://britton.disted.camosun.bc.ca/tnpascal.gif • http://www.spsu.edu/math/edwards/2253/leibniz.jpg • http://www.crossingwallstreet.com/euler-1000.png • http://www.math.msu.edu/~mshapiro/kidmath_files/mathematics.jpg • Books • The Story of Numbers