Category Archives: Euclid

Frank Wilczek’s “We’re All Still Living in Euclid’s World”

The Weekend Wall Street Journal,  2/5-6/2022, featured Frank Wilczek’s (MIT) column entitled “We’re All Still Living in Euclid’s World.”  The article prompts further thinking about how space, space-time, and generalized coordinates underly Bernard Lonergan’s pretio-quantital Functional Macroeconomic Dynamics, AKA Macroeconomic Field Theory. (continue reading)

Scientific Generalization by Functional Analysis of the Network of Interdependent Rates

The non-Euclideans moved geometry back to premises more remote than Euclid’s axioms, they developed methods of their own quite unlike Euclid’s, and though they did not impugn Euclid’s theorems, neither were they very interested in them; casually and incidentally they turn them up as particular cases in an enlarged and radically different field. Continue reading

Theoretical Breakthroughs of Euclid, Newton, Hilbert, Einstein, and Lonergan

To help the reader gain an appreciation of Lonergan’s achievement of Modern Macroeconomic Field Theory we will, in each section, print leading excerpts, then highlight the key concepts of those excerpts. We will comment on the historically-significant advances in geometry of Euclid and Hilbert, in physics of Newton and Einstein, and in macroeconomics of Lonergan.

  • Euclid’s great achievement was his rigorous deduction of geometry.
  • Hilbert’s great achievement was his employment of implicit definition to reorder Euclid’s geometry.
  • Newton’s two great achievements were unifying the isolated insights of Galileo and Kepler into a unified system of mechanics and his invention of the calculus.
  • One of the great achievements of Einstein was the invention of the field theories of Special Relativity, General Relativity, and Gravitation.
  • One of Lonergan’s several great achievements was his systematization of macroeconomic phenomena in his Modern Macroeconomic Field Theory. He combined the technique of implicit definition introduced by Hilbert and the concept of a field theory developed by Faraday and Einstein; and he developed an explanatory macroeconomics, which is general, invariant, and relevant in any instance. (Continue reading)