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)

# Category Archives: Mathematics and Isomorphism

# Functions Are Not Seen, But Must Be Understood

Functions are

not seen, but must beunderstood. (Catherine Blanche King, private communication)A systematic explanation, then, requires a normative theoretical framework. The basic terms and relations of such a framework would specify the distinctions and correlations that articulate the causes, which are

not necessarily visible, of events that are apparent to all. (CWL 15, Editors’ Introduction, lv) (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)**

# Why Economists Haven’t Yet Flocked to Functional Macroeconomic Dynamics

**Economists don’t have the methodological and conceptual toolkit needed for appreciation of FMD’s scientific and historical significance.**

- They don’t know what they don’t know.
- They’re not methodologists and don’t know what constitutes good theory.
**They never read CWL 3, pages 3-172 and 490-97**and, thus, they never studied the**canons of empirical method**, especially the**Canon of Parsimony**and the**Canon of Complete Explanation;**they have no idea of the deficiencies of their method.

- Thus, they lack a purely
**scientific and explanatory heuristic**.- They do not adequately distinguish
**description vs. explanation**. - They do not know the type of answer they’re seeking, i.e. their known unknown.
- They do not put questions in the right order to discover basic terms of
**scientific significance.** - They are mired in muddy premises and disorienting assumptions.
- They are unable to employ a
**scientific, dynamic heuristic**adequate for analysis of a**current**,**purely dynamic process.** - They don’t understand what constitutes the normative system’s requirement for
**concomitance, continuity, and equilibrium of flows.**

- They do not adequately distinguish
- They lack a
**background in theoretical physics**. They don’t understand the principles and abstract laws of**hydrodynamics, electric circuits, or field theory**. Nor do they understand adequately the idea of**continuity**and the**conditions of equilibrium in macroeconomic dynamics**. They are unaware of analogies from physics applicable on the basis of**isomorphism**to the phenomena of Functional Macroeconomic Dynamics. (Continue reading.)