That's So Second Millennium

Ep 132 – The Long Road to Mathematical Physics

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A solo episode from Paul today inspired by the content of Wyoming Catholic College’s Deductive Reasoning in Science course (SCI 301).

  1. Greek arithmetic and the Pythagoreans
  • The crisis of incommensurables (irrational numbers)
  • The triumph of geometry over arithmetic
  • Emphasis on axiomatic systems and proofs: Euclid
  • Archimedes: physics within the Euclidean paradigm
  • Aristotle and the medieval: qualitative and categorical accounts of motion
  • The long reach of ancient methods and paradigms
  • Galileo and his big ideas, shaky proofs, and tedious Euclidean methodology
  • 16th century algebra and the need for negative numbers to simplify the cubic equation
  • Galileo’s multiple cases of proportions of times, spaces, speeds in the Euclidean paradigm
  • Overturns in algebraic notation and the advent of analytical geometry in the 17th century
  • The looming role of calculus in Galileo’s attempts to argue by means of infinite parallels
  • Imaginary and complex numbers in the solution of cubic equations with real roots, real physical problems
    • ...more
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    That's So Second MillenniumBy Paul Giesting, William Schmitt
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