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.

The minds of inquisitive economists cannot help but roam beyond the immanent intelligibilities of macroeconomics to the intelligibilities treated by Lonergan in CWL 3, Insight: A Study of Human Understanding.

List of intelligibilities treated in CWL 3::

  • The abstract and the concrete intelligibility of space and time
  • Hilbert’s sublation of Euclid by implicit definition
  • Einstein’s space-time sublation of Newton and the non-Euclidean geometers
  • intuitive spatial-image geometry vs. Cartesian algebra;
  • being
  • Lonergan’s positions and counter-positions re the real, re knowing, and re objectivity
  • truth and verification
  • generalization of coordinates and Lonergan’s substitution of factors of production for units of extension in space
  • Lonergan’s article “A Note on Geometric Possibility” in  [CWL 4, Collection,  1967] 

Before we quote F, Wilczek and offer comments, we ask the reader to keep constantly in mind two key issues:

1) Euclid’s and the pre-Faraday-Maxwell-Einstein physicists’ space and time are not external containers, rather they are intellectually contained and to be explained as determinations within all-inclusive being.  There is a big shift and a complete role reversal.  The supposed container becomes the really contained.  Space and time are not absolutes, rather they are explained in the light of their being relativistic determinations within all-inclusive being; and instead of there being space and time, we have space-time.  

2) In his generalized coordinate system, Lonergan substitutes  velocitously-applied units of factors of production for units of spatial extension. Thus units of factors of production, analytically distinguished by their point-to-point (“basic”) and point-to-line (“surplus”) functional correspondences, become fundamental vectoral dimensional units. Along with money, they constitute interdependent explanatory monetary flows; and thus, they are explained in the light of those flows. The so-constituted “pretio-quantital” flows are intelligible; they explain the deduced superstructure constituting a “system”; they, constituted by their price and quantity components, are determinations within all-inclusive being.

More fully for clarification:

This reversal of roles in which the sensible container becomes the intellectually contained has already been noted. ‘To be’ cannot mean ‘to be in space’ or ‘to be in time’.  If that were so, and space is or time is, then space would be in space and time would be in time.  The further space and time, if real, would also be, and so would demand  a still further space and time.  The argument would be repeated indefinitely to yield an infinity of spaces and times.  ‘To be’ then is just ‘to be’.  Space and time, if real, are determinations within being; and if they are determinations within being, then they are not containers but the contained.  To put the issue more concretely, there are extensions, durations, juxtapositions and successions.  Still such affirmations are descriptive.  They have to be transposed into explanatory statements before one may ask legitimately for their metaphysical equivalents; and when that transposition takes place, then from the general nature of explanation it follows that the metaphysical equivalents will be the conjugate potencies, forms, and acts that ground the truth of spatio-temporal laws and frequencies.  So it comes about that the extroverted subject (sensibly) visualizingextension and (sensibly) experiencing duration gives place to the subject oriented to the objective of the unrestricted desire to know and affirm beings differentiated by certain conjugate potencies, forms, and acts grounding certain laws and frequencies.  It is this shift that gives rise to the antithesis of positions and counter-positions.  It is through its acknowledgment of the fact of this shift that a philosophy or metaphysics is critical.  It  is only by a rigorous confinement of the metaphysician to the intellectual pattern of experience and of metaphysical objects to the universe of being as explained, that this basic enterprise of human intelligence can free itself from the morass of pseudo-problems that otherwise beset it. (CWL 3, 513-4/)

… first we must establish that as a matter of fact we know and that as a matter of fact there is some reality proportionate to our knowing.  For only after the facts are known can we entertain any hope of reaching an explanation of the possibility of a correspondence between our inquiry and understanding, our reflection and judgment, and on the other hand the real as it really is. … As has been seen, our own unrestricted desire to know defines for us what we must mean when we speak of being; in the light of that notion we can settle by intelligent grasp and reasonable affirmation what in fact is and what in fact is not;  and while this procedure des not explain why every possible and actual reality must be intelligible, it does settle what in fact already is known to be true and, at the same time, it gives rise to the further question that asks for complete explanation and complete intelligibility. (CWL 3, 678-9/701)

Let us quote Professor Wilczek, then follow with our own Comments on his affirmations and on the possible relevance to macroeconomics of the topics in the list above.

Wilczek 1: “The ‘Elements’ deduces abundant, surprising and powerful consequences from a few clearly stated, “self-evident” assumptions, or axioms.”

Comment 1.1: Euclid used a few clearly stated, fundamental “self-evident” assumptions or axioms defining point, line, and plane.

… a science emerges when thinking in a given field moves to the level of system. Prior to Euclid there were many geometrical theorems that had been established.  The most notable example is Pythagoras’ theorem on the hypotenuse of the right-angled triangle, which occurs at the end of  book 1 of Euclid’s Elements.  Euclid’s achievement was to bring together all these scattered theorems by setting up a unitary basis that would handle all of them and a great number of others as well. (Method, 241-2)

in contrast to Euclid, Lonergan’s most basic propositions are precise, Porphyrean, analytic distinctions between a) the first-order algebraic relation of determinate-point-to-determinate-point, and b) determinate-point-to-indeterminate-line correspondences constituting basic foundational  ‘forms’ in the productive process.  From these axiomatic distinctions he constructs a visual model representing, and conceptually isomorphic with, the correlations constituting and explaining the fundamental workings of the economic process.  Then, from this base he deduces a superstructure of classical abstract laws constituting a complete field-theoretic explanation of the always-current, concrete, pretio-quantital, purely dynamic, economic process.  The process is a concrete dynamic process of production and sale, whose explanation has two components: a primary classical abstract formulation to be applied to secondary boundary values, and statistical laws or ideal frequencies of secondary pretty-quantital events from which relative actual frequencies of prices and quantities in the non-systematic manifold of human decisions do not systematically diverge.

… real analysis (is) identifying money with what money buys. … If you want to treat money that doesn’t make a difference, you can have a beautiful liberal monetary theory.  But it doesn’t say the way the thing works. [CWL 21, Editors’ Introduction, xxviii  quoting Lonergan]

… The analysis that insists on the indeterminacy (of the point-to-indeterminate-line) is the analysis that insists on the present fact: estimates and expectations are proofs of the present indeterminacy and attempts to get round it; and, to come to the main point, an analysis based on such estimates and expectations can never arrive at a criticism of them; it would move in a vicious circle.  It is to avoid that circle that we have divided the (primary productive) process in terms of determinate point-to-point, point-to- indeterminate-line and point-to-indeterminate-surface and higher correspondences. [CWL 15, 28]

Scientific thought involves a more exact anticipation.  What is to be known inasmuch as data are understood is some correlation or function that states universally the relations of things … to one another.  Hence the scientific anticipation is of some unspecified correlation to be specified, some indeterminate function to be determined; and now the task of specifying or determining is carried out by measuring, by tabulating measurements, by reaching an insight into the tabulated measurements, and by expressing the insight through some general correlation or function that, if verified, will define a limit on which converge the relations between all subsequent appropriate measurements.  [CWL 3, 44/68]

… verified correlations necessarily involve the verification of terms implicitly defined by the correlations; …what is verified accurately is not this or that particular proposition but the general and abstract proposition on which ranges of ranges of particular propositions converge. … there is a fundamental heuristic structure that leads to the determination of conjugates, that is, of terms defined implicitly by their empirically-verified, explanatory relations.  Such terms as related are known by understanding, and so they are forms. Let us name them conjugate forms.[quoted more fully below from CWL 3, 435/460]

Wilczek 2: Isaac Newton’s system of classical mechanics and James Clerk Maxwell’s system of electromagnetism were built upon the foundation of Euclidean geometry. They added particles, fields and forces, but the space in which those things lived was Euclid’s.

Comment 2.1: Space is a determination within being.  It was never a property owned by Euclid.  It preceded Euclid and he did not buy it.  He might have been the first to posit its intelligibility, but it had “been for all ages. Also, “Space is not a container in which things live.  Rather space and time are determinations within all-inclusive being and are to be understood and explained by forms of differential and statistical laws.

‘To be’ then is just ‘to be’.  Space and time, if real, are determinations within being; and if they are determinations within being, then they are not containers but the contained.  To put the issue more concretely, there are extensions, durations, juxtapositions and successions.  Still such affirmations are descriptive.  They have to be transposed into explanatory statements … (CWL 3, 513-4/)

Comment 2.2: Lagrange introduced generalized coordinates.  One’s axes of algebraic explanation need not always be axes of spatial extensions.  Axes of algebraic explanation may be in a Cartesian coordinate system but represent other units than units of extension.

… , goods and services are in a point-to-point correspondence with elements in the standard of living when they are some determinate, though not immutable or unvarying, algebraic function of the first degree with respect to elements in the standard of living.  Finally, just as the aggregate of rates constituting the emergent standard of living is an aggregate of instances of ‘so much every so often,’ so also is the aggregate of rates of production in the basic stage of the process; and again, as the emergent standard of living, so also the basic stage of the process is an aggregate of rates that are qualitatively and quantitatively variable with respect to successive intervals of time. (CWL 15, 29)

(The Diagram’s) basic terms are (implicitly) defined by their functional relations.  The maintaining of a standard of living (distinct process 1) is attributed to a basic process, an ongoing sequence of instances of so much every so often.  The maintenance and acceleration (distinct process 2) of this basic process is brought about by a sequence of surplus stages, in which each lower stage is maintained and accelerated by the next higher.  Finally, transactions that do no more than transfer titles to ownership (distinct process 3) are concentrated in a redistributive function, whence may be derived changes in the stock  of money dictated by the acceleration (positive or negative) in the basic and surplus stages of the process. ¶So there is to be discerned a threefold process in which a basic stage is maintained and accelerated by a series of surplus stages, while the needed additions to or subtractions from the stock of money in these processes is derived from the redistributive area. A first task thereafter will be to correlate the need for more or less money in the productive process with the magnitudes and frequencies of their turnovers.  On that basis it will be possible to distinguish stable and unstable combinations and sequences of rates in the three main areas and so gain some insight into the long-standing recurrence of crises in the modern expanding economy. [CWL 15, 53-4 and 177]

Comment 2.3: Lonergan’s “space” is the space of units of applications of factors of the productive process.  The “absolute” and measurable, experiential, spatial manifold of Euclid is replaced by the determinately measurable concrete manifold of velocitous application of factors of production.

qi = ΣΣqijk  (for context see CWL 15, 30)

The final product, qi, is composed of a double summation: a summation of rates of application of factors of production, k, across a summation of units of enterprise, j. Look at that Nestle’s Crunch bar in your hand and understand it as a set of ingredients (including overhead contributions) applied at rates or velocities by compensated humans.  It emerges as a final for-sale product from a process.

Comment 2.4: Euclid’s geometric space was 3-dimensional; thus the physicists could speak of velocity as 3-D measurable extension per 1-dimensional measurable temporal interval. Lonergan, on the other hand, replaces measurable units of extension with distinct and measurable factoral units of production. The factors are applied at (or so to speak, “move at”) velocities and accelerations in a Galilean temporal interval; i.e. productive components implemented per interval of time rather than physical mechanics’ mere lengths per interval of Galilean time.  In Functional Macroeconomic Dynamics, “Space” is not extension ordered by a totality of inches or centimeters along axes; rather it has become a vector field ordered by axes representing units of production factors.  We have a new coordinate system indexed by fundamental units of production.  Euclid’s intuited form and Descartes’ coordinates remain, but have been generalized in a new coordinate system.

In Lonergan’s Circulation Analysis, the basic terms are rates – rates of productive activities and rates of payments.  The objective of the analysis is to discover the underlying intelligible and dynamic (accelerative) network of functional, mutually conditioning, and interdependent relationships of these rates to one another.  [CWL 15  26-27  ftnt 27]

… just as the aggregate of rates constituting the emergent standard of living is an aggregate of instances of ‘so much every so often,’ so also is the aggregate of rates of production in the basic stage of the process; and again, as the emergent standard of living, so also the basic stage of the process is an aggregate of rates that are qualitativelyand quantitatively variable with respect to successive intervals of time. (CWL 15, 29)

Lonergan built a model of pretio-quantital flows (price times quantity) called the Diagram of Rates of Flow.  It is a model of interdependent, mutually-defining, functional, monetary flows, or circulations, associated with production and sale.  The model itself sits still as nothing but a mark on a page of paper, but the observer will imagine and interpret the arrows as channels-alive-with-flows of internally-, externally-  and rhythmically-conditioned monetary Outlays-Incomes and Expenditures-Receipts.

(Again here,) (The Diagram’s) basic terms are (implicitly) defined by their functional relations.  The maintaining of a standard of living (distinct process 1) is attributed to a basic process, an ongoing sequence of instances of so much every so often.  The maintenance and acceleration (distinct process 2) of this basic process is brought about by a sequence of surplus stages, in which each lower stage is maintained and accelerated by the next higher.  Finally, transactions that do no more than transfer titles to ownership (distinct process 3) are concentrated in a redistributive function, whence may be derived changes in the stock  of money dictated by the acceleration (positive or negative) in the basic and surplus stages of the process. … So there is to be discerned a threefold process in which a basic stage is maintained and accelerated by a series of surplus stages, while the needed additions to or subtractions from the stock of money in these processes is derived from the redistributive area. … it will be possible to distinguish stable and unstable combinations and sequences of rates in the three main areas and so gain some insight into the long-standing recurrence of crises in the modern expanding economy. [CWL 15, 53-4 and 177]

 Again, more fully for emphasis:

… , goods and services are in a point-to-point correspondence with elements in the standard of living when they are some determinate, though not immutable or unvarying, algebraic function of the first degree with respect to elements in the standard of living.  Finally, just as the aggregate of rates constituting the emergent standard of living is an aggregate of instances of ‘so much every so often,’ so also is the aggregate of rates of production in the basic stage of the process; and again, as the emergent standard of living, so also the basic stage of the process is an aggregate of rates that are qualitatively and quantitatively variable with respect to successive intervals of time. (CWL 15, 29)

Comment 2.5: Lonergan understood production and sale as primary and he understood money as a “dummy” in the pretio-quantital (price times quantity) system of monetary flows.

Money is an instrument invented to fulfill a definite task; it is not the ultimate master of the situation.  One has to place first human society which is served by the economic process, and second the economic process which is to be served by money.  Accordingly money has to conform to the objective exigencies of the economic process, and not vice versa. (CWL 21, 101)

These differences and correlations (of the productive process of a hierarchical, advanced economy) have now to be projected into their monetary correlates to set up classes of payments.  Thus a restrictive supposition is introduced into the argument.  The productive process is now envisaged as occurring in an exchange economy.  It will be supposed to be an economy of notable size, complexity, and development, with property, exchange, prices, supply and demand, money.  [CWL 15, 39]

Now if the gold-standard (or ideas analogous to it) has no validity, “What is needed,” Lonergan tells us, “is a frank avowal that money is simply a system of public bookkeeping, and then a coherent and thorough transformation of all monetary practice with the fundamental fact.” Otherwise, “the whole economy comes to be regulated not by the social good, not by the objective exigencies of the economy itself, but by the money invented to serve the objective process and the social good.”38 (CWL 15, 105) [Fred Lawrence; “Money, Institutions, and The Human Good,” in Liddy, 2010, 185]

Comment 2.6: Lonergan was clear on inflation as a dedensification or dilution of the purchasing power of money.  And he debunked Marx’s simpliste labor-theory of value.

It is now necessary to state the necessary and sufficient condition of constancy or variation in the exchange value of the dummy.  To this end we compare two flows of the circulation: the real flow of property, goods, and services, and the dummy flow being given and taken in exchange for the real flow….Accordingly, the necessary and sufficient condition of constant value in the dummy lies in its concomitant variation with the real flow. (CWL 21, 38-39)

Comment 2.7: Like the physicists, Lonergan employs velocity vectors; he expresses velocitous production quantities in terms of velocity vectors; and he expresses the price-cost of a correlated Outlay-Income payments as a vector; thus a pretio-quantital, velocitous flow of price-times-quantity payments is expressed as the vector dot product of the price and the quantity vectors.

Z = Σ piqi  = PQ = PQ cos A (See CWL 15, 108-9)

Comment 2.8: Like electromagnetics and special relativity, Functional Macroeconomic Dynamics is a field theory of the relations of explanatory conjugates among themselves.  Lonergan distinguishes between efficient, exemplary, final and field-theoretic formal cause.

 In some concrete instance, a community may be divided by a river and see in a bridge the solution to many of its problems; an engineer will examine the site and design an appropriate structure, finally, contractors will assemble labourers and materials to build it.  The final cause in this case will be the use to which the bridge is put by the community; the efficient cause will be the work of building it; the exemplary cause will be the design grasped and conceived by the engineer. (CWL 3, 651-2/)

The formal cause is the immanent intelligibility of the process.

Ought there not to be introduced a technical term to denote this type of intelligibility?  … The intelligibility that is neither final nor material nor instrumental nor efficient causality is, of course, formal causality…What we have called the intelligibility immanent in sensible data and residing in the relations of things to one anothermight be named more briefly formal causality … [CWL  3, 78/101-102]

… again, as to the notion of cause, Newton conceived of his forces as efficient causes, and the modern mechanics drops the notion of force; it gets along perfectly well without it.  It thinks in terms of a field theory, the set of relationships between n objects.  The field theory is a set of intelligible relations linking what is implicitly defined by the relations themselves; it is a set of relational forms.  The form of any element is known through its relations to all other elements.  What is a mass?  A mass is anything that satisfies the fundamental equations that regard masses.  Consequently, when you add a new fundamental equation about mass, as Einstein did when he equated mass with energy, you get a new idea of mass.  Field theory is a matter of the immanent intelligibility of the object. (CWL 10, 154)

The point I wish to make is that modern science is not simply an addition to what was known before.  It is the perfecting of the very notion of science itself, of knowing things by their causes, by analysis and synthesis.  What are the causes?  The field of intelligible relations that implicitly define the objects.  The objects with which a science deals are whatever is defined by its field of intelligible relations, whatever falls into that field.  The causes are formal causes; it is only applied science that is concerned with agents and ends. (CWL 10, 155)

Comment 2.9:  The overall functional economic process has an external, as it were, motive power in the person of productive human participants applying factors of production at rates.  The participants may be viewed as outside the process which, as outside, they understand, and so effect by their compensated contribution. Also, they are not to be ignorant; they should understand the norms and precepts yielded by their understanding; and they must seek to abide by and to efficiently implement these norms and precepts in the personal conduct of their economic involvements.

 From the viewpoint of intelligence, the satisfactions allotted to individuals are to be measured by the ingenuity and diligence of each in contributing to the satisfactions of all; from the same high viewpoint the desires of each are to be regarded quite coolly as the motive power that keeps the social system functioning. [CWL 3, “The Tension of Community” 214-16/239-42]

However, the formal cause is the immanent intelligibility of the process grounded in the precise analytic distinctions and the idea of money as a dummy.

Comment 2.10: Like Faraday and Clerk-Maxwell, Lonergan developed a field theory of terms implicitly defined by their purely functional relations among themselves.  Thus, unlike in the textbooks’ unexplained, externally-causal prices and quantities, in FMD prices and quantities are understood in the light of the interdependence of the pretio-quantital explanatory flows modeled in the diagram.

Wilczek 3: Albert Einstein’s 1905 special theory of relativity inspired one of his teachers, Hermann Minkowski, to propose another generalization of Euclidean geometry. Ending his 1908 lecture “Space and Time,” he proclaimed, “Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.”  Yet Minkowski’s space-time is still rooted in Euclid.  It incorporates a generalization of the parallel postulate and its “space” part, at any fixed time, is pure Euclid.

 Comment 3.1: The reader should focus on Minkowski’s expression “union of the two will preserve an independent reality.”  Minkowski spoke of space and time becoming space-time.  Lonergan’s Functional Macroeconomic dynamics accepts Galilean time but employs reasoning similar to Einstein’s with respect to price and quantity in the a) technique of implicit definition, b) relativity of left side and right side,and c) battles and compromises between pricing and quantity in FMD’s key equations to satisfy the necessary equality. (CWL 15, 156-60)

P’Q’ = p’a’q’ + p”a”q”

P/p = a’ + a”R

J = a’ + a”R

dJ = da’ + a”dR + R da”

There is a sense in which one may speak of the fraction of basic outlay that moves to basic income as the “costs” of basic production.  It is true that that sense is not at all an accountant’s sense of costs; … But however remote from the accountant’s meaning of the term “costs,” it remains that there is an aggregate and functional sense in which the fraction… is an index of costs.  For the greater the fraction that basic income is of total income (or total outlay), the less the remainder which constitutes the aggregate possibility of profit.  But what limits profit may be termed costs.  Hence we propose ….to speak of (c’O’  = p’a’Q’) and (c”O” = p”a”Q”) as costs of production, having warned the reader that the costs in question are aggregate and functional costs…. [CWL 15, 156-57]

 Lonergan unifies the ideas of

  • Factor as a fundamental quantum (CWL 15, 30)
  • the lagged technical accelerator (CWL 15, 37)
  • expansion in phases (CWL 15, 113 ff.)
  • crossover equilibria and disequilibria (CWL 15, 50-1)

to explain a) the pure cycle of expansion, and b) the implicit relativity of prices and quantities in their determination of one another both normatively and in the case of correction of a trade cycle of excesses and deficiencies.

Comment 3.2: Lonergan also spoke of a generalization of the isolated and limited insights of previous economists.  As Einstein generalized the non-Euclideans, and the non-Euclideans generalized Newton,, and Newton generalized Kepler and Copernicus, Lonergan generalized the isolated insights of Adam Smith, Karl Marx, Walras, Ricardo, Pareto, S. M. Longfield , John Rae, Nassau Senior, Eugen von Bohm-Bawerk, Piero Sraffa, et al. into a Macroeconomic Field Theory, a new, purely-relational, scientific system.

It is, we believe, a scientific generalization of the old political economy and of modern economics that will yield the new political economy which we need. … Plainly the way out is through a more general field. [CWL 21, 6-7]

Lonergan pointed out that this differentiation of economic activities … is discussed by traditional economists such as S. M. Longfield (1802-1884), John Rae (1796-1872), Nassau Senior (1790-1864), Eugen von Bohm-Bawerk (1851-1914), and in the heavily disputed “Ricardo effect.” But Lonergan credits Piero Sraffa (1898-1983) as having clarified it most thoroughly in his famous essay, “Production of Commodities by Means of Commodities” (1960).  Yet even Sraffa does not use his sophisticated explanation of the “Ricardo effect” and the “roundabout” or “concertina”-like phenomena associated with it in the way Lonergan does. Lonergan is alone in using this difference in economic activities to specify the significant variables in his dynamic analysis… no one else considers the functional distinctions between different kinds of productive rhythms prior to, and more fundamental than, wealth, value, supply and demand, price levels and patterns, capital and labor, interest and profits, wages, and so forth….only Lonergan analyzes booms and slumps in terms of how their (explanatory) velocities, accelerations, and decelerations are or are not equilibrated in relation to the events, movements, and changes in two distinct monetary circuits of production and exchange as considered both in themselves (with circulatory, sequential dependence) and in relation to each other by means of crossover payments. [CWL 15, Editors’ Introduction, lxii]

As there exists such a thing as absolute value, there can be relative value by which “excellence may belong to an object in its relativity, its utility, its aptitude to excel in serving ulterior purposes … only some of them relative to man.”  Economic value is the human relative value that regards abundance or scarcity.  Economic value is specified by both the proportion of a product relative to the effort of producing it, and by the exchange value that results from any decision to strive for an object, even when the decision is independent of either the striving or the effort involved in producing it.  Adam Smith and all the proponents of the “labor” theory of value were never able to clarify the relationship between exchange value and “toil and trouble” as the measure of value.  Lonergan shifted the issue entirely by explaining that an “economic value relates an object to human effort, but an exchange value relates objects among themselves.”31 (CWL 21, 31) [Fred Lawrence; “Money, Institutions, and The Human Good,” in Liddy, 2010, 183-84]

However, like Smith, Locke, Ricardo, and Marx later on, Aristotle did not seem to understand money in terms of exchange value, and therefore as relating objects among themselves in relation to the concomitance or lack of concomitance between “the real flow of property, goods, and services and the dummy flow being given and taken in exchange for the real flow.”39 CWL 21, 40 Still less did they grasp that in an advanced industrial society, the real flow and the money flow are channeled within two separate circuits of production and circulation functionally distinguished into producer goods and consumer goods, and operating in real time in accord with distinct phases of expansion.  Besides misunderstanding money of account, they misunderstood the relationship of money to time. [Fred Lawrence; “Money, Institutions, and The Human Good,” in Liddy, 2010, 186]

More fully re Lonergan’s search for generalization,

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. … Einstein went beyond Newton by employing the new geometries to make time an independent variable (sic?); and as Newton transformed the formulation and interpretation of Kepler’s laws, so Einsteintransforms the Newtonian laws of motion. … It is, we believe, a scientific generalization of the old political economy and of modern economics that will yield the new political economy which we need. … Plainly the way out is through a more general field. [CWL 21, 6-7]

… again, as to the notion of cause, Newton conceived of his forces as efficient causes, and the modern mechanics drops the notion of force; it gets along perfectly well without it.  It thinks in terms of a field theory, the set of relationships between n objects.  The field theory is a set of intelligible relations linking what is implicitly defined by the relations themselves; it is a set of relational forms.  The form of any element is known through its relations to all other elements.  What is a mass?  A mass is anything that satisfies the fundamental equations that regard masses.  Consequently, when you add a new fundamental equation about mass, as Einstein did when he equated mass with energy, you get a new idea of mass.  Field theory is a matter of the immanent intelligibility of the object. (CWL 10, 154)

The point I wish to make is that modern science is not simply an addition to what was known before.  It is the perfecting of the very notion of science itself, of knowing things by their causes, by analysis and synthesis.  What are the causes?  The field of intelligible relations that implicitly define the objects.  The objects with which a science deals are whatever is defined by its field of intelligible relations, whatever falls into that field.  The causes are formal causes; it is only applied science that is concerned with (external) agents and ends. (CWL 10, 155)

… a science emerges when thinking in a given field moves to the level of system. Prior to Euclid there were many geometrical theorems that had been established.  The most notable example is Pythagoras’ theorem on the hypotenuse of the right-angled triangle, which occurs at the end of  book 1 of Euclid’s Elements.  Euclid’s achievement was to bring together all these scattered theorems by setting up a unitary basis that would handle all of them and a great number of others as well. … Similarly, mechanics became a system with Newton.  Prior to Newton, Galileo’s law of the free fall and Kepler’s three laws of planetary motion were known.  But these were isolated laws.  Galileo’s prescription was that the system was to be a geometry; so there was something functioning as a system.  But the system really emerged with Newton.  This is what gave Newton his tremendous influence upon the enlightenment. He laid down a set of basic, definitions, and axioms, and proceeded to demonstrate and conclude from general principles and laws that had been established empirically by his predecessors.  Mechanics became a science in the full sense at that point where it became an organized system. … Again, a great deal of chemistry was known prior to Mendeleev.  But his discovery of the periodic table selected a set of basic chemical elements and selected them in such a way that further additions could be made to the basic elements.  Since that time chemistry has been one single organized subject with a basic set of elements accounting for incredibly vast numbers of compounds.  In other words, there is a point in the history of any science when it comes of age, when it has a determinate systematic structure to which corresponds a determinate field. [Method, 241-42]

Newton set down laws of motion and proceeded to demonstrate that if a body moves in a field of central force, its trajectory is a conic section.  He set out with a minimal cluster of insights, definitions, postulates, axioms and proceeded to account for the laws that had previously been empirically established, bringing them into a single explanatory unity.  ¶A single insight yields a conception, a definition, an object of thought; but from a cluster of insights, you build up a system of definitions, axioms, postulates, and deductions.  We have to note that a system is quite an achievement; systems are not numerous. There are Euclid’s geometry and subsequent developments in geometry, Newton’s mechanics and dynamics and the building upon Newton, and the Mendeleev table in chemistry.  System, then, is the expression of a cluster of insights. [CWL 5, 52]

McShane, the editor of CWL 21, For a New Political Economy, states in the Introduction to the Index:

Part Two (of CWL 21), entitled Fragments, belongs almost entirely in what I call the Einsteinian context of Part Three, in contrast to the Newtonian achievement of Part One; (however, that Fragments section) is still somewhat transitional in system and expression.  So, for example, to take the central character in the drama, pure surplus income is there named systematic profits.  In Part One it is named net surplus or even surplus. [CWL 21, 325]

[Paraphrase of CWL 10, 154]: again, as to the notion of cause, Walras and Keynes conceived of external and internal elements and events as forces and as efficient causes; however, Functional Macroeconomic Dynamics drops the notion of force.  It thinks in terms of a field theory, the set of relationships between n objects.  Macroeconomic field theory is a set of intelligible relations linking economic functions which are implicitly defined by the functional relations among themselves; it is a set of relational forms.  The form of any element is known through its relations to all other elements.  What is a point-to-point activity?  A point-to-point function is any production activity whose constituent elements relate to elements exiting the process in the first-order mathematical expression that defines the point-to-point relation.  Consequently, when you add a newfundamental equation defining a purely relational function, as Einstein did when he equated mass with energy, you get a new idea of the dynamics of the macroeconomic process.  Macroeconomic field theory is a matter of the immanent intelligibility in the field of velocitous interdependent, mutually defining functionings.

 F. Wilczek 4 (a repeat): Ending his 1908 lecture “Space and Time,” (Minkowski) proclaimed, “Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.”Yet Minkowski’s space-time is still rooted in Euclid.

Comment 4.1: Price and quantity changes within and between explanatory flows are to be interpreted in the light of the imperious equals sign of the equations explaining the dynamic process.

Lonergan agreed with Schumpeter on the importance of a systematic or analytic framework in order to explain, rather than merely record or describe, the aggregate phenomena of macroeconomics; he agreed with Schumpeter that to be able to explain the booms, slumps, and crashes of the trade or business cycles the economist’s analysis had to be as dynamic as the subject matter under investigation; and he agreed that the economist had to know what are the significant variables in the light of which price changes are to be interpreted.  According to Lonergan, standard economic theory had successfully achieved none of these desiderata. [CWL 15, Editors’ Introduction liii]

F. Wilczek 5: “It was left to Einstein, in his 1915 general theory of relativity, to do for Minkowski what Reimann had done for Euclid, that is, to bring in space-time curvature.”

Comment 5.1: Re curvature between one stationary (flat) state and a higher, more abundant, stationary (flat) state

once long-term acceleration is underway, rates of production increase increasingly; their graphs are concave upward; but the curvature moves from being flatter to being rounder as the acceleration is generalized from one section to another throughout the productive process.  During this period of generalization, rates of production are not merely increasing in geometrical progression but moving from less to more rapid geometrical progressions. … This situation, however, is bound to be temporary; its existence is the lag between the generalized long-term acceleration of the surplus stage and that of the basic stage.  When that is overcome, dQ’/Q’ moves again to a peak and remains there; and by the same token, dQ”/Q” will begin to decline. CWL 15, 126

Einstein’s special relativity is a transposition of that Newtonian idea from mechanics to electromagnetics, and from a (efficient-) causal theory to a (immanent intelligibility, formal-cause) field theory.  What is occurring in special relativity is a new way of determining the level of what one abstracts from. (CWL 10, 125)

 F. Wilczek 6: … our Standard Model of fundamental interactions still has Euclid under the hood. Its relativistic quantum fields still live in Euclid’s continuum – or more precisely, in Einstein’s update.

 Comment 6.1:  Functional Macroeconomic Dynamic, AKA Macroeconomic Field Theory constitutes a new Standard Model in macroeconomics.  Its relativistic macroeconomic field theory stand beside other field theories in the realms of mechanics, thermodynamics, and electromagnetics in physics.

 F. Wilczek 7: “To me, this is the most striking example of what Eugene Wigner called “the unreasonable effectiveness of mathematics in the natural sciences.”

 Comment 7.1: Lonergan identifies the effectiveness as grounded in accurate isomorphisms.

Again, to take perhaps a simpler and more familiar example, if someone is doing physics and you open his book, what do you find?  You find just mathematical equations.  He is solving problems, and what is it?  It is more mathematics. Why do you say he is doing physics?  He seems to be doing mathematics all the time.  It is because there are regions of mathematics that are isomorphic with physical reality.  There is the same relational structure between a given mathematical theory or system as there is between events that can be observed.   This is another case, a big case, of isomorphism: on the one hand, mathematical expressions, and on the other hand, physical events.  There is the same relational structure.  But in the mathematical case, the relational structure links symbolic expressions, or mathematical concepts, with one another, while in the physical case what are related are concrete physical events, wave lengths that you observe through a machine and so on.  ¶ So there is an isomorphism of geometry, algebra, physics; the same relational structure can be found in all three.  Consequently, one’ symbolism can be given a geometrical interpretation, or an algebraic interpretation, or a physical interpretation. [CWL 18, 32-33]

In the following we have paraphrased, and we have substituted “macroeconomics” and “economics” for “physics” and “macroeconomic” and “economic” for “physical.”  We thereby gain a good idea of Lonergan’s dynamic heuristic.

… if someone is doing macroeconomics and you open his book, what do you find?  You find just mathematical equations.  He is solving problems, and what is it?  It is more mathematics.  Why do you say he is doing macroeconomics?  He seems to be doing mathematics all the time.  It is because there are regions of mathematics that are isomorphic with macrodynamic reality.  There is the same relational structure between a given mathematical theory or system as there is between macroeconomic functionings that can be observed.   This is another case, a big case, of isomorphism: on the one hand, mathematical expressions, and on the other hand, macroeconomic functionings.  There is the same relational structure.  But in the mathematical case, the relational structure links symbolic expressions, or mathematical concepts, with one another, while in the economics case what are related are concrete macroeconomic dynamic functionings.  ¶ So there is an isomorphism [Paraphrase of CWL 18, 32-33]

… just as a mathematical equation may be said to be the most adequate expression of purely intelligible relations among explanatory termsin certain instances – for example, Einstein’s gravitational field tensor equations – something closely akin to Lonergan’s diagram (and the equations it represents) seems necessary for the realm of dynamic economic functioning.  So, for example, the existence and manner of dynamic mutual interdependence of the two circuits of payment, basic and surplus, is not adequately expressed either by descriptive terms (since this pattern does not directly relate to the senses of anyone operating in a common-sense way in a concretely functioning economy) nor by the series of (simultaneous) equations that do not explicitly manifest the interchanging of ‘flows.’ [CWL 15, 179]

F. Wilczek 8 (repeat quote): “Isaac Newton’s system of classical mechanics and James Clerk Maxwell’s system of electromagnetism were built upon the foundation of Euclidean geometry. They added particles, fields and forces, but the space in which those things lived was Euclid’s.”

 Comment 8.1: Again, the quantities and pretio-quantital flows do not live in a container.  They are determinations within being.  They simply are; and they constitute an intelligibility of the process, which is Lonergan’s double-circuited, credit-centered Macroeconomic Flow Field in which Newton’s “space” is redefined as a vector field of velocities of application of factors of production realizing the potential of the process.

The coefficients gμν are for the time being any functions whatever of the coordinates x1 to x4, and the structure of space is not really determined until these functions gμν are really known.  It is only determined more closely by specifying laws which the metrical field of the gμν satisfy. Einstein, Essays, p. 73

If one would understand, not men’s notions of Space and Time, but the intelligibility  immanent in Space and Time, then one must advance from reference frames to the geometrical principles and laws whose expression is invariant under transformations.  Moreover, the geometry to be reached will coincide with the geometry determined by physicists in securing invariant expression for physical principles and laws. (CWL 3, 171/)

The concrete intelligibility of Space is that it grounds the possibility of those simultaneous multiplicities named situations.  The concrete intelligibility of Time is that it grounds the possibility of successive realizations in accord with the probabilities.  In other words, concrete extensions and concrete durations are the field or matter or potency in which emergent probability is the immanent form or intelligibility. (CWL 3, 171-2/)

… unlike his predecessors, (the contemporary scientist) has to think of knowledge, not as taking a look, but as experiencing, understanding and judging; he has to think of objectivity, not as mere extroversion, but as experiential, normative, and tending towards an absolute; he has to think of the real, not as a part of the ‘already out there now’, but as the verifiable.  Clearly, the imagined as imagined can be verified only by actually seeing, and so there is no verifiable image of the elements of the mechanism.  Moreover, what science does verify, does not lie in any particular affirmations, which are never more than approximate; what science verifies is to be found ingeneral affirmations, on which ranges of ranges of particular affirmations converge with an accuracy that increases with the precision of measurements and with the elimination of probable errors. (CWL 3, 424-25/449-50)

… first we must establish that as a matter of fact we know and that as a matter of fact there is some realityproportionate to our knowing.  For only after the facts are known can we entertain any hope of reaching an explanation of the possibility of a correspondence between our inquiry and understanding, our reflection and judgment, and on the other hand the real as it really is. … As has been seen, our own unrestricted desire to know defines for us what we must mean when we speak of being; in the light of that notion we can settle by intelligent grasp and reasonable affirmation what in fact is and what in fact is not;  and while this procedure des not explain why every possible and actual reality must be intelligible, it does settle what in fact already is known to be true and, at the same time, it gives rise to the further question that asks for complete explanation and complete intelligibility. (CWL 3, 678-9/701)

 Finally, in the light of what has been said above, the reader may appreciate why we often intimate that graduate students with a solid background in theoretical physics are the best candidates for the mastery and appreciation of Lonergan’s Macroeconomic Field Theory.