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