Field Theory in Physics and Macroeconomics

CONTENTS:

  • .I. INTRODUCTORY (1)
  • .II. HISTORICAL DEVELOPMENTS (5)
    • .II.1. Historical Phases of Fields (5)
      • .II.1.1 Phases in Physical Mechanics – Phases 1-3 (5)
      • .II.1.2 Phases in Macroeconomics – Phases and Isms 1-3 (5)
  •  .III.  THE CONCEPT OF A “FIELD” (6)
  •  .IV. ABSTRACTION, INSIGHT, IMPLICIT DEFINITION AND PRINCIPLES FOR INVARIANCE 
  • .V STAND TO’S
  • .VI.PRE-FIELD THEORY IN PHYSICS AND MACROECONOMICS (15)
    • .VI.1. Pre-Field Physics (Newton Et alii) (16)
    • .VI.2. Pre-Field Macroeconomics (Walras et alii) (16)
  •  .VII. EARLY FIELD THEORY – the concept of force is retained
    • .VII.1.  Early Force-Field Theory in Physics (16)
      • .VII.1.1.  The Early Gravitational Field (16)
      • .VII.1.2.  The Early Electric Field (Faraday) (17)
      • .VII.1.3.  The Early Magnetostatic Field (17)
    • .VII.2.  The Early and Keynesian Macroeconomic Field (18)
  •  .VIII. MODERN FIELD THEORY – the concept of force is dropped (20)
    • .VIII.1. Modern Field Theory in Physics (20)
      • .VIII.1.1.  The Modern Field CalledThe Special Theory of Relativity (20)
      • .VIII.1.2.  The Modern Field Called The General Theory of Relativity (21)
      • .VIII.1.3  Other Fields and Formulations (22)
    • .VIII.2. Modern Field-Theoretic Macroeconomics (22)

.I. INTRODUCTORY

We hope to inspire serious graduate students of economics a) to seek and achieve an understanding of  “Macroeconomic Field Theory,” b) to verify empirically Lonergan’s field relations,  and c) to use the explanatory field relations as the basis of influential scholarly papers.

We trace developments

  • in physics from Newtonian mechanics to modern field theory, and
  • in economics from Walrasian supply-demand economics to purely relational, Modern Macroeconomic Field Theory.

Key ideas include a) abstraction and implicit definition as the basis and ground of invariance in both physics and macroeconomics, b) the concept of a purely relational field, c) immanent intelligibility and formal causality, and d) the canons of parsimony and of complete explanation. We highlight some key ideas:

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 formsThe 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]

Special Relativity is primarily a field theory, that is, it is concerned not with efficient, instrumentalmaterial, or final causes of events, but with the intelligibility immanent in data; but Newtonian dynamics seems primarily a theory of efficient causes, of forces, their action, and the reaction evoked by action. … Special Relativity is stated as a methodological doctrine that regards the mathematical expression of physical principles and laws, but Newtonian dynamics is stated as a doctrine about the objects subject to laws.  [3, 43/67]

Maxwell, at first, did not adopt the modern concept of a field as a fundamental quantity that could independently exist. … the situation was resolved by the introduction of the Special Theory of Relativity by Albert Einstein in 1905.  This theory changed the way the viewpoints of modern observers were related to each other.  They became related to each other in such a way that velocity of electromagnetic waves in Maxwell’s theory would be the same for all observers.  By doing away with the need for a background medium, this development opened the way for physicists to start thinking about fields as truly independent entities. [Wikipedia (3), Field (Physics), page 3 of 11]

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]

(Lonergan) approaches the focus armed with precise analytic distinctions between basic and surplus activities, outlays, incomes, etc. [CWL 21, xxvi]

…  the productive process (is) a purely dynamic entity, … It is to be shown that the correspondence between elements in the productive process and elements in the standard of living may be a point-to-point, or a point-to-line, or a point-to-surface, or even a higher correspondence. (CWL 15, 23)

All science begins from particular correlations, but the key discovery is the interdependence of the whole.  (CWL 15, 53 and 177)

(the) whole structure (of Functional Macroeconomic Dynamics) is purely relational.  A macroeconomic functioning is not a compilation or aggregation of particular income statement categories, such as wages or interest expense.  A macroeconomic functioning is implicitly defined by its functional relation to other functionings. The whole structure is purely relational.  “Lonergan’s analysis is concrete but heuristic.  It focuses on functionalrelations intrinsic to the productive process to reach eventually a general theory of dynamic equilibria and disequilibria.” [McShane 1980, 117]

“Functional” is for Lonergan a technical term pertaining to the realm of explanation, analysis, theory;  … Lonergan (identified) the contemporary notion of a function as one of the most basic kinds of explanatory, implicit definition – one that specifies “things in their relations to one another” … [CWL 15, 26-27  ftnt 27]

Lonergan … was seeking the explanatory intelligibility underlying the ever-fluctuating rhythms of economic functioning.  To that end he worked out a set of terms and relations that ‘implicitly defined’ that intelligible pattern.  When all was said and done the relations, and the terms they implicitly defined, were markedly different from either the terms of ordinary business parlance or the terms of neoclassical and Keynesian economic theory.  Moreover, not only did Lonergan’s terms differ, but he also indicated that these aforementioned terms (of neoclassical and Keynesian economic theory) were permeated, as were the terms of Newton’s theory of gravitation, with descriptive, nonexplanatory residues.  Hence, just as a mathematical equation may be said to be the most adequate expression of purely intelligible relations among explanatory terms in 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]

Lonergan’s critique (shows that) by using the technique of implicit definition, the emphasis shifts from trying to define the relevant variables to searching heuristically for the maximum extent of interconnections and interdependence; and that the variables discovered in this way might not resemble very much the objects (or the aggregates) which, in the first instance, one was thinking about.  [Gibbons, 1987]

Inversely, because science seeks knowledge of the things as related among themselves, because such relations lie outside our immediate experience, because the ultimates in such relations are to be reached only when ultimate explanation is reached, each great forward step of scientific knowledge involves a more or less profound revision of its fundamental terms.  Again, because science is analytic and abstractive, its terms are exact; because its correlations purport to be generally valid, they must be determined with utmost precision; because its terms are exact and its correlations general, it must be ready to bear the weight of a vast superstructure of logical deductions in which each conclusion must be equally exact and valid generally. [CWL 3, 296/321]

The productive process is, then, the (current) aggregate of activities proceeding from the potentialities of nature and terminating in a standard of living.  Always it is the current process, and so it is distinguished both from the natural resources, which it presupposes, and from the durable effects of past production. [CWL 15, 20]

There is no doubt that the solar system, even macrodynamically speaking, involves an aggregate of bodies.  Was, then, the solution of the two-body problem irrelevant?  Again, there is no doubt that tidal waves are not sinusoidal.  Should we then drop the dynamic question and settle for some equivalent of photography and comparative statics?  Or should we not make sense of elementary rhythms, momenta, etc., acknowledging that we are only paving the way for such developments as Fourier analysis? [#71] [McShane, 1980,  104-106, and118-119]

.II. HISTORICAL DEVELOPMENTS

 .II.1. HISTORICAL PHASES OF “FIELDS”

We wish to provide a brief outline of how physics and economics have advanced to modern field theory.  The categories and boundaries of time periods in the advances are not as neat as one would like, and there is some unavoidable overlap of periods and contents; but the reader will get clearly the general ideas of the significant revolutionary developments leading up to and culminating in modern field theory.

.II.1.1. PHASES IN PHYSICAL MECHANICS – PHASES 1-3:

  1. Newtonian phase, in which a body at rest or in uniform motion stays such unless acted upon by an external force; “force” is conceived as an external, efficient cause; there is action at a distance; and F = ma. Notable contributors include Newton, Laplace, Ampere, and Coulomb.

The uniform velocity takes care of itself without introducing causes.  You come to something that demands an intelligible cause when you come to acceleration. [CWL 18, 61]

  1. Early “field theory” in which a) the notion of force is retained, and b) a field is characterized in general as an object every point of which has a value such as a scalar, a vector, etc.  Early fields include Faraday’s lines of force, elasticity of materials, fluid dynamics, Maxwell’s equations, and a reformulation of Newtonian gravitation, F = -Gm1m2/d2.  Notable contributors were Faraday, Minkowski, Lorentz, Clerk-Maxwell, Lagrange and Hamilton. [Wikipedia (3), Field (Physics), page 3 of 11],
  2. Modern field theory, exemplified by a) Einstein’s Special Relativity, General Relativity, and Generalized Theory of Gravitation, in which the “absolute containers” – space and time – were redefined as a 4-dimensional spatio-temporal manifold and tensors were invoked for invariance of expression in the case of continuous transformations, and b) quantum mechanics, characterized by the pure relations among quanta of subatomic particles.  Notable contributors include Legendre, Mach, Riemann, Ricci, Planck, Bohr, Jordan, Wigner, Dirac, Heisenberg, Schroedinger, and Feynman.

 .II.1.2.  PHASES IN MACROECONOMICS – PHASES AND ISMS 1-3:

Macroeconomics has also gone through what we might roughly categorize as three phases, not to be strictly correlated with the periods of physics:

  1. The classical Walrasian development of the supply-demand statics between efficient-causal (i.e. force-ful) firms and households. These statics feature a confusion of external and internal efficient causes, such as supposedly-exogenously determined interest rates, prices, and shocks of all kinds, and the series of internal efficient causations which follow.
  2. The neoclassical, Keynesian, and new Keynesian phase in which a somewhat mysterious – postulated, but not dynamically explained – inadequate demand is to be efficiently cured by price adjustments or by false-third-party government borrowing and spending – with distinction between short-run and long-run effects.
  3. The field-theoretic phase in which the wholly unitary economic process is conceived as the always current, purely dynamic process of production and exchange, and the neoclassical and Keynesian confusion of “external and internal efficient causes” is replaced by the abstract, unitary, invariant immanent intelligibility or “formal cause”, i.e. the primary, immanent, intelligible relations among themselves of interdependent constituent functionings.

In brief Lonergan is looking for an explanation in which the terms are defined by the relations in which they stand, that is, by a process of implicit definition. … No doubt Keynes was an economist first and a methodologist second … Lonergan, for his part, is perhaps a methodologist first and an economist second, but he was able to push his economic reflections further than Keynes because he had a firmer grasp of the essentials of an effective theory.  … Lonergan’s critique (shows that) … the emphasis shifts … to searching heuristically for the maximum extent of (functional) interconnections and interdependence; and that the variables (of the mechanism) discovered in this way might not resemble very much the objects (or the aggregates) (such as coincidental prices) which, in the first instance, (the non-methodologist) was thinking about.   [Gibbons, 1987]

Lonergan discovers two sets of abstract primary relativities in the always current, purely dynamic economic process.  These primary relativities may be applied in any instance to the secondary, non-systematic determinations of quantity and price in a non-systematic manifold to reach the concrete relations of the objective economic process.

.III. THE CONCEPT OF A “FIELD”

We begin with a sort of walk through a series of excerpts providing a summary of ideas which will be relevant to the distinction between a “force field” and the more recent and modern “purely relational field”.

Field theory itself is a set of intelligible relations linking terms that are 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.  [CWL 10, 154] Again,

Re fields in physics:

… , 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 formsThe 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]

Special Relativity is primarily a (modern) field theory, that is, it is concerned not with efficient, instrumentalmaterial, or final causes of events, but with the intelligibility immanent in data; but Newtonian dynamics seems primarily a theory of efficient causes, of forces, their action, and the reaction evoked by action. … Special Relativity is stated as a methodological doctrine that regards the mathematical expression of physical principles and laws, but Newtonian dynamics is stated as a doctrine about the objects subject to laws.  [3, 43/67]

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]

Field:  The concept of a field is that there is associated with each point of the “space” under consideration a scalar, a velocity vector, an acceleration vector, a tensor, etc.  Meteorologists, for example, identify on a map of some weather region a (scalar) temperature field, a wind velocity field, etc. [Lindsay and Margenau, 1957]  Stewart??

Scalar field: In general, a scalar field is a function whose domain is all points in Region2 (or Region3) and whose range is a set of scalars at all points in V2 (or (V3). [Stewart, 2008, 1028]

We have seen that a field is characterized by the values associated with certain physical quantities at every point and every instant of timeThere are several types of fields, depending on the nature of these quantities.  A physical quantity which has a numerical value at every point in a region independent of direction is a scalar quantity, and a field characterized by such is a scalar field.  The gravitational potential is a scalar, for its value at any point has no direction associated with it.  …  In so far as the gravitational field is characterized by the potential, it is a scalar field.  In similar fashion the velocity potential which characterizes a fluid medium under certain conditions (irrotational motion) is a scalar, and the fluid under these conditions and to this extent may be considered a scalar field.  Other illustrations of scalars and scalar fields are provided by density and temperature. [Lindsay and Margenau, 1957, 287]

Vector field:  In general, a vector field is a function whose domain is all points in Region2 (or Region3) and whose range is a set of vectors at all points in V2 (or (V3). [Stewart, 2008, 1028]

… the concept of continuum is capable of more extensive application… .  Curiously enough, it also proves possible to use this concept to advantage in the study of particle motion, …Here the continuum enters in the guise of field. [Lindsay and Margenau, 1957, 283]

Re fields in macroeconomics:

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

Part Two, 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]: … , 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 formsThe form of any functional element is known through its functional relations to all other elements.  What is a point-to-point activity?  A point-to-point function is any production activity whose constituent factors relate to the integral of factors exiting the process in the first-order mathematical expression that defines the point-to-point relation.  Consequently, when you make new precise analytical distinctions and discover new functional relations, as Lonergan did when he distinguished point-to-point (basic) and point-to-line (surplus) relations and their significant scientific implications, you get a new idea of the dynamics of the macroeconomic processMacroeconomic field theory is a matter of the immanent intelligibility of the field of interdependent, mutually defining functional relations.

Macroeconomic science is abstract; it advances from familiar experiential conjugates and reconciles them as explanatory conjugates; its significant explanatory variables are abstract point-to-point and point-to-line functions; and it prescinds from human psychology.  Therefore, abstraction from our sensitive experience provides the grounds of invariant expression of macroeconomic principles and laws; and because Functional Macroeconomic Dynamics is abstract, it is not contaminated by the analyst’s psychological utilities and preferences, egoistic bias, group bias, or political, cultural, standpoint (as in so-called Modern Monetary Theory).

Invariant expression in functional macroeconomics, which, because macroeconomic science is independent of the egoistic bias, group bias, and political, cultural, technological, spatio-temporal standpoint of particular thinkers, is a property of abstract propositions.  It is a set of abstract relations of terms among themselves rather than a manifesto wittingly or unwittingly contaminated by psychological propositions.

And macroeconomic field theory is not a recitation of statistics or of accountant’s aggregates.  It is explanatory science.

 Today, for instance, I heard Paul Krugman speak of Picketty … as giving rise to a “unified field theory.”  A video recording is available on You Tube at https://www.youtube.com/watch?v=heOVJM2JZxI Wow! LOL: as I listened, I could not but think of what I had written below, on the next page here: “their efforts do not escape the category of statistically-infested journalism.” [McShane, Philip, Picketty’s Plight 65 ftnt 99]

.IV. ABSTRACTION, INSIGHT, IMPLICIT DEFINITION, AND PRINCIPLES FOR INVARIANCE

Note:  the reader is advised in advance that this subsection IV, though very important, is lengthy and sometimes repetitive.  It is strategically placed here in the presentation, and it should be read carefully.  But in the interest of time, the reader may want to skip and circle back later to get the full context of what follows this section.

(Lonergan) worked out a set of terms and relations that ‘implicitly defined’ the intelligible pattern underlying the ever-fluctuating rhythms of economic functioning. (CWL 15, 179)

invariant mathematical expression (results) from the abstractness of principles and laws, (CWL 3, 42/66)

Einstein’s position …  follows quite plausibly from the premise that empirical science seeks not the relations of things to our senses but their relations to one another. (CWL 3, 41/65)

principles and laws are the same for all observers because they lie simply outside the range of observational activities. [CWL 3, 41/65]

physicists surmount their peculiar difficulty (of having to use reference frames) by expressing their principles and laws in mathematical equations that remain invariant under transformations of frames of reference. [CWL 3, 40/64]

Also see An Adequate Level of Abstraction and Generalization; a Deeper Explanatory  Unity

In general:

Implicit definition is the mutual definition of terms according to their relations to one another.  And, since science is explanation in the form of terms related to one another, the technique of abstract implicit definition is used to yield general, universally-relevant, purely-relational terms of scientific and explanatory significance.  Implicit definition is constitutive of

  • Hilbert’s geometry – two points and a line are mutually definitive by the relation between them
  • Newtonian mechanics – F = Gm1m2/d2 ; (a relational definition of mass)
  • Early gravitational field theory – g = F/m = d2R/dt2 = -(GM/R2) Ř = − Del ϕ [Wikipedia (1), Gravitational Field, page 1 of 4]
  • Modern field theory –
    • Special Relativity:

Δt = Δt0/√1 – v2/c2 ;;  (in Special Relativity Δt0 is the interval of time experienced by an observer at rest with respect to the motion of light; Δt is the interval of time experienced by an observer in uniform motion with respect to the motion of light; v is the velocity of the uniform motion; and c is the speed of light in all inertial reference frames.)

Special Relativity is primarily a field theory, that is, it is concerned not with efficient, instrumentalmaterial, or final causes of events, but with the intelligibility immanent in data;  … Special Relativity is stated as a methodological doctrine that regards the mathematical expression of physical principles and laws, …  [3, 43/67]

As pure conjugates, extension and duration are defined implicitly by the postulate that the principles and laws of physics are invariant under inertial or, generally, under continuous transformations. [CWL 3, 84/108]

    • General Relativity:

Gab = 8πTab ; (Einstein’s tensor of the curvature of space equals 8π times the stress-energy tensor)

  • Functional Macroeconomic Dynamics

The abstract acceleration vectors, d²/dt², at every point in the modern economic field may be functionally defined as a) the curvatures of the ideal pure cycle consisting of two equilibrated, interacting circuits and b) the systematic corrective curvatures necessitated by variations from the ideal pure cycle. “By this cyclic variation within the exchange equilibria there is effected the “curvature” of the exchange equations.” (CWL 21, 51-52)

M. Leon Walras developed the conception of the markets as exchange equilibria. Concentrate all markets into a single hall. Place entrepreneurs behind a central counter.  Let all agents of supply offer their services, and the same individuals, as purchasers, state their demands.  Then the function of the entrepreneur is to find the equilibrium between these demands and potential supply. … The conception is exact, but it is not complete.  It follows from the idea of exchange, but it does not take into account the phases of the productive rhythms. As has been shown, economic activity moves through a series of transformations and exploitations; and this series generates the succession of (surplus, basic, cultural, and static phases.)  Now each phase in the exchange economy will have its exchange equilibrium, but the equilibria of the different phases differ radically from one another.  By this cyclic variation within the exchange equilibria there is effected the “curvature” of the exchange equations. (CWL 21, 51-52)

Macroeconomic “costs” and “basic expenditures” receive new abstract, purely-relational meanings and implicitly define each other; they are mutually defining, supporting and constraining functional elements in an abstract, explanatory, monetary circuit. The equals sign constitutes an identity by the principle of concomitance. The equation may be read from left to right or from right to left.

P’Q’ = p’a’Q’ + p”a”Q”, or,

P’Q’  is implicitly defined as  p’a’Q’ + p”a”Q” . [CWL 15, 157-58]

Thus, 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’ and c”O” as costs of production, having warned the reader that the costs in question are aggregate and functional costs… . [CWL 15 156-57]

Thus, there is a sense in which supply always equals demand.  A good or service is under process until it is actually and finally sold, at which moment it is concomitantly supplied rather than merely under process or sitting in finished-goods inventory.  And a good or service is actually demanded at the moment when it is actually and finally purchased, so as to exit the process and no longer be under process.  Actual (in contrast to potential) supply and demand occur at the same moment. They are simultaneous and concomitant.

Similarly, macroeconomic outlays for purely expansionary products and purely surplus expansionary expenditures are concomitant.  They are mutually defining, supporting and constraining functional elements in an abstract, explanatory, surplus monetary circuit.  Pure surplus income is the monetary correlate of expansionary investment.

At the root of the depression lies a misinterpretation of the significance of pure surplus income. In fact it is the monetary equivalent of the new fixed investment of an expansion…..our culture can not be accused of mistaken ideas on pure surplus income as it has been defined…; for on that precise topic it has no ideas whatever………However the phenomena referred to by …”pure surplus income” are well known.  Entrepreneurs are quite aware that there are times of prosperity in which even a fool can make a profit and other mysterious times in which the brilliant and the prudent may be driven to the wall……….Thus pure surplus income may be identified best by calling it net aggregate savings and viewing them as functionally related to the rate of new fixed investment. [CWL 15 152-53]

(the) whole structure (of Functional Macroeconomic Dynamics) is purely relational.  A macroeconomic functioning is not a compilation or aggregation of particular income statement categories, such as wages or interest expense.  A macroeconomic functioning is implicitly defined by its functional relation to other functionings.  The whole structure is purely relational. [McShane 1980, 117]

“Lonergan’s analysis is concrete but heuristic.  It focuses on functional relations intrinsic to the productive process to reach eventually a general theory of dynamic equilibria and disequilibria.” [McShane 1980, 117]

Lonergan … was seeking the explanatory intelligibility underlying the ever-fluctuating rhythms of economic functioning.  To that end he worked out a set of terms and relations that ‘implicitly defined’ that intelligible pattern.  When all was said and done the relations, and the terms they implicitly defined, were markedly different from either the terms of ordinary business parlance or the terms of neoclassical and Keynesian economic theory.  Moreover, not only did Lonergan’s terms differ, but he also indicated that these aforementioned terms (of neoclassical and Keynesian economic theory) were permeated, as were the terms of Newton’s theory of gravitation, with descriptive, nonexplanatory residues.  Hence, just as a mathematical equation may be said to be the most adequate expression of purely intelligible relations among explanatory terms in 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]

Abstract, implicit definition yields abstract terms related to one another rather than commonsense terms defined by their relations to us in our everyday experience of getting and spending.

Lonergan’s critique (shows that) by using the technique of implicit definition, the emphasis shifts from trying to define the relevant variables to searching heuristically for the maximum extent of interconnections and interdependence; and that the variables discovered in this way might not resemble very much the objects (or the aggregates) which, in the first instance, one was thinking about.  [Gibbons, 1987]

A distinction has been drawn between description and explanation.  Description deals with things as related to us.  Explanation deals with the same things as related among themselves.  The two are not totally independent, for they deal with the same things and, as we have seen, description supplies, as it were, the tweezers by which we hold things while explanations are being discovered or verified, applied or revised. … [CWL 3, 291/316]

the scientist is seeking … an intelligibility that can be expressed mathematically. … The first basic assumption is that the purpose of science is the search for an intelligibility that can be expressed mathematically. [CWL 10, 139]

The true aim of science is verification of understanding.

For Lonergan, prediction and control are not legitimate ends of science because they are not the same as verified understanding, which is the true aim of science.  [CWL 15, Editors’ Introduction, ftnt 32, xxxvii]

analysis may attain its goal without being able to predict, … [CWL 15, 11]

physicists surmount their peculiar difficulty (of having to use reference frames) by expressing their principles and laws in mathematical equations that remain invariant under transformations of frames of reference. [CWL 3, 40/64]

Anticipations and expectations of invariance in physics and macroeconomics:

invariant mathematical expression (such as Lonergan’s  two sets of primary relativities) (results) from the abstractness of principles and laws, (CWL 3, 42/66)

However, to determine under which group of transformations invariance is to be achieved, some further principle has to be invoked and, in fact, in different scientific theories different principles are invoked.  Of these the most general is the principle of equivalence which asserts that physical principles and laws are the same for all observers … [CWL 3, 40/64-65]

Einstein’s position …  follows quite plausibly from the premise that empirical science seeks not the relations of things to our senses but their relations to one another.  For, as has been remarked, observations give way to measurements; measurements relate things to one another rather than to our senses; and it is only the more remote relations of measurements to one another that lead to empirical correlations, functions, laws.  [CWL 3, 41/65]

Now clearly if laws are reached by eliminating the relations of things to the senses of observers and by arriving at relations between the measured relations of things to one another, then there exists an extremely solid foundation for the affirmation that principles and laws are the same for all observers because they lie simply outside the range of observational activities. [CWL 3, 41/65]

The broad invariance that we have described has to be conceived precisely in terms of tensors.  Secondly, appropriate empirical hypotheses have to be formulated and verified.  But by those steps there are reached the General Theory of Relativity and the Generalized Theory of Gravitation and incidentally it may not be amiss to note that our remote anticipation offers a simple explanation for certain aspects of those theories.  For what was anticipated was a non-relatedness of abstract laws to observers. [CWL 3, 41-42/65-66]

An abstract further principle and appropriate abstract empirical hypotheses must be invoked in the particular field:

A less general anticipation of invariance is contained in the basic postulate of Special Relativity. … On the present analysis then, the difference between the anticipations represented respectively by General and by Special Relativity is that, while both expect invariant mathematical expression to result from the abstractness of principles and laws, General Relativity implements this expectation by invoking a direct insight into the significance of measurements but Special Relativity implements it by invoking an inverse insight into the insignificance of constant velocity. [CWL 3, 42/66]

The explanation of data consists in a process from experiential conjugates towards pure conjugates.  Therefore, from extensions and durations as experienced, there must be a process to extensions and durations as implicitly defined by empirically established laws. [CWL 3, 85/108]

Paraphrasing:  The explanation of data consists in a process from experiential conjugates towards pure conjugates. Therefore, from quantities and prices as experienced in everyday life in a non-systematic manifold, there must be a process to quantities and prices as ultimately implicitly defined and interpreted as probabilistically relative  – price to price, quantity to quantity, and velocitous flow to velocitous flow – in their constituting or being the velocitous and accelerative flows of scientific and explanatory significance by empirically established laws. [CWL 3, 85/108]

As pure conjugates, extension and duration are defined implicitly (in relativity physics) by the postulate that the principles and laws of physics are invariant under inertial or, generally, under continuous transformations. [CWL 3, 84/108]

[Paraphrasing] As pure conjugates, pretty-quantital flows are defined implicitly by the postulate that the principles and laws of macroeconomics are invariant under transformations between states of a) technological and cultural advance, b) fiscal organization and act, c) monetary organization and act, d) executive or judicial institutions, and political systems.

And so – unlike as in IS-LM, AD-AS, and philips curve analytics – contingent prices are not the given absolute basis of explanation; they are not the given from which all explanation of aggregate supply and aggregate demand emanate.  Contingent prices are to be understood in the light of the significant interdependent variables, which are the interdependent and mutually-definitive accelerator flows and accelerated flows of pretio-quantital basic and surplus outlays, expenditures, borrowing, and reverse-borrowing.

… conjugate forms are defined implicitly by their explanatory and empirically verified relations to one another.  Still, such relations are general laws; they hold in any number of instances; they admit application to the concrete only through the addition of further determinations, and such further determinations pertain to a non-systematic manifold.  There is then, a primary relativity that is contained in the general law; it is inseparable from its base in the conjugate form which implicitly it defines; and to reach the concrete relation that holds at a given place and time, it is not enough to think about the general law; one has to add further determinations that are contingent from the very fact that they have to be obtained from a non-systematic manifold. [CWL 3, 492/516]  (In addition, read in the entirety CWL 3, 491-6/514-520)

Applying the above to macroeconomic dynamics:

conjugate forms such as basic income velocity, ordinary surplus income velocity, and pure surplus income velocity are defined implicitly by their explanatory and empirically verified relations to one another.  Still, such relations are general laws; they hold in any number of instances; they admit application to the concrete only through the addition of further determinations such as the pretio-quantital magnitudes of the velocities of explanatory flows; and such further determinations pertain to a non-systematic manifold.  There is then, a primary relativity that is contained in the general law relating explanatory conjugates; it is inseparable from its base in the conjugate form which implicitly it defines; and to reach the concrete relation that holds at a given place and time, it is not enough to think about the general law; one has to add further determinations that are contingent from the very fact that they have to be obtained from a non-systematic manifold. [CWL 3, 492/516]  (In addition, read in the entirety CWL 3, 491-6/514-520)

The immanent intelligibility is intrinsically immanent and purely relational.  And this immanent intelligibility is not the external efficient cause; nor is it the material, instrumental, or final cause; this immanent intelligibility is the “formal cause.”

The whole structure is relational: one cannot conceive the terms without the relations nor the relations without the terms.  Both terms and relations constitute a basic framework to be filled out, first by the advance of the sciences and, secondly, by full information on concrete situations. [CWL 3, 492/516]  (In addition, read in the entirety CWL 3, 491-6/514-520)

And, returning for emphasis to an excerpt above:

A distinction has been drawn between description and explanation.  Description deals with things as related to us.  Explanation deals with the same things as related among themselves.  The two are not totally independent, for they deal with the same things and, as we have seen, description supplies, as it were, the tweezers by which we hold things while explanations are being discovered or verified, applied or revised. … [CWL 3, 291/316]

Paraphrasing:  A distinction has been drawn between description and explanation.  Description deals with things as related to us.  Explanation deals with the same things as related among themselves.  The two are not totally independent, for they deal with the same things and, as we have seen, description (of prices, quantities, or pretio-quantital flows supplies, as it were, the tweezers by which we hold things while explanations among functional flows and their component prices and quantities are being discovered or verified, applied or revised. … [CWL 3, 291/316]

.V. “STAND TO”S

There is an analytic process from sensitive experience to abstract explanation.  Note the boldface “stand to‘s in the excerpts below.

… on our analysis, the (abstract, purely intelligible, and explanatory) space-time (concept) of Relativity stands to the (purely experiential) extensions and durations of (everyday sensation and perception) in exactly the same explanatory vs. descriptive relations as wave-lengths of light stand to experience of colour, as longitudinal waves in air stand to experience of sound, as the type of energy defined by the first law of thermodynamics stands to experiences of heat, etc. [CWL 3, 84-5/108]

(Our) immediate task is to work out the correlations that exist between the velocity and accelerator rhythms of production and the corresponding rhythms of income and expenditure.  The set of such correlations constitutes the mechanical structure, a pattern of laws that stand to (purely experiential) economic activity as the laws of mechanics to buildings and machines. [CWL 21, 43]

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.  The framework would thus stand to the ordinary apprehension of the booms and slumps of the trade cycle in much the same way that the explanatory grasp of acceleration as the second derivative of a continuous function of distance and time stands to the ordinary, commonsense grasp of what it is to be going faster.  CWL 15,  lv

… the heart of the normative theoretical framework that can actually explain business and trade cycles is what (Lonergan) calls the ‘pure cycle.’  This cycle generalizes into clearly articulated relationships the ideal phases characteristic of major economic transformations as they depart from a stationary phase and move through phases first of surplus expansion and then of basic expansion, only to return to a new stationary phase.  this pure cycle stands to our ordinary apprehension of economic booms and slumps as the explanatory conception of acceleration stands to our ordinary apprehension of going faster or slower.  It sheds ‘new light on equilibrium’ that Schumpeter was seeking.  the meaning of pure cycle is fully revealed in the course of the Essay.  Here we offer only two brief illustrations of the implications of that model. (CWL 15, Editor’s Introduction, lxiii) (Also see CWL 15, Sections 10, 24, and Additional Note to Section 24: the Pure Cycle, p.120 ff.)

.VI. PRE-FIELD THEORY IN PHYSICS AND MACROECONOMICS

Relevant to what is to come, we print as a preliminary item the following footnote.

Footnote 1:  Lonergan taught physics and knew his physics well; he distinguished Newtonian mechanics from modern field theory.
Now the principles and laws of a geometry are abstract and generally valid propositions.  It follows that the mathematical expression of the principles and laws of a geometry will be invariant under the permissible transformations of that geometry. … Such is the general principle and it admits at least two applications.  In the first application one specifies successive sets of transformation equations, determines the mathematical expressions invariant under those transformations, and concludes that the successive sets of invariants represent the principles and laws of successive geometries.  In this fashion one may differentiate Euclidean, affine, projective and topological geometries. … A second, slightly different application of the general principle occurs in the theory of Riemannian manifolds.  The one basic law governing all such manifolds is given by the equation for the infinitesimal interval, namely,
ds2= Σgijdxidxj           [i, j = 1,2…n]
where dx1dx2… are differentials of the coordinates, and where in general there are n2 products under the summation. Since this equation defines the infinitesimal interval, it must be invariant under all permissible transformations. However, instead of working out successive sets of transformations, one considers any transformations to be permissible and effects the differentiation of different manifolds by imposing restrictions upon the coefficients.  This is done by appealing to the tensor calculus.  For tensors are defined by their transformation properties and it can be shown that, in the present case, if the coefficients gij are any instance of a covariant tensor of the second degree, then the expression for the interval will be invariant under arbitrary transformations.  It follows that there are as many instances of the Riemannian manifold and so as many distinct geometries, as there are instances of covariant tensors of the second degree employed to specify the coefficients gij. Thus in the familiar Euclidean instance, gij is unity when i equals j; it is zero when i does not equal j; and there are three dimensions.  In Minkowski space, the gij is unity or zero as before, but there are four dimensions, and x4equals ict.  In the General Theory of Relativity, the coefficients are symmetrical, so that gij equals gji; and in the Generalized Theory of Gravitation, the coefficients are anti-symmetrical.   [CWL 3, 146 -147/170-71] [14]

.VI.1. PRE-FIELD THEORY IN PHYSICS

In pre-field theory the concept of force is conceived and formulated as an external efficient cause.  There are levers, catapults, and throwing arms.  The particular force of gravity is an instance of action at a distance.

Newtonian dynamics seems primarily a theory of efficient causes, of forces, their action, and the reaction evoked by action. … [3, 43/67]

… , as to the notion of cause, Newton conceived of his forces as efficient causes, … [CWL 10, 154]

Newton’s laws of motion:

  1. A body at rest or in uniform motion stays such unless acted upon by an external force
  2. F = ma
  3. For every action there is an equal and opposite reaction.

Newton’s implicit definition of mass: F = Gm1m2/d2

.VI.2. PRE-FIELD THEORY IN MACROECONOMICS:

In macroeconomics, pre-field theory is any theory not stated as a field theory.  That includes all theories from before Adam Smith right up to the neoclassicism and New Keynesianism of today – no matter how high their renown in textbooks or the frequency of their wide, but faulty, application by government.

.VII. EARLY FIELD THEORY – the concept of force is retained

.VII.1. EARLY FORCE-FIELD THEORY IN PHYSICS:

In early field theory in physics the concept of force remains;  it is conceived as an external efficient cause, but formulations are in terms of a force-field rather than action at a distance.

.VII.1.1 THE EARLY GRAVITATIONAL FIELD

Though Newton thought in terms of action at a distance, his gravitation may be reconceived in terms of a field. Newton’s gravitational field is constituted by the force of gravity at all points in the force’s region or field.   [Wikipedia (1), Gravitational Field, page 1 of 4]:

In this early field theory, a gravitational field is a physical quantity. … The magnitude of the field at every point is calculated applying the universal law, and represents the force per unit mass on any object at that point in space. … because the force field is conservative, there is a scalar potential energy per unit mass, ϕ, at each point in space associated with the force fields; this is called the gravitational potential. 6 The gravitational field equation is 7

g = F/m = d2R/dt2 = -(GM/R2)Ř = −Del ϕ [Wikipedia (1), Gravitational Field page 1 of 4]

(We are forced by lack of symbols and compatibility of fonts to use Ř to represent the unit tangent, using Δ to represent the Del operator, and noting that Rin the denominator R2 should have absolute value indication)

And in Riemannian transformation notation: (See Footnote 1 above)

  • … in the familiar Euclidean instance,  gij is unity when equals j; it is zero when does not equal j; and there are three dimensions.   [CWL 3, 146 -147/170-71] See Footnote 1 below.

.VII.1.2  THE EARLY ELECTRIC FIELD (FARADAY)

The electric field is constituted by the force of the electron’s charge (Q).  Coulomb’s law reminds us of Newton’s definition of mass.:

F = kQ1Q2/r2  (Coulomb’s law)

or

F = (1/4πε)(Q1Q2/r2) (ε is  ) (whose law?)

.VII.1.3 THE EARLY MAGNETOSTATIC FIELD

Michael Faraday first realized the importance of a field as a physical quantity, during his investigations into magnetism.  He realized that electric and magnetic fields are not only fields of force which dictate the motion of particles, but also have independent physical reality because they carry energy. ¶ These ideas eventually led to the creation, by James Clerk Maxwell, of the first unified field theory in physics with the introduction of equations for the electromagnetic field.  The modern version of these equations is simply referred to as Maxwell’s equations. [Wikipedia (3), Field (Physics), page 4 of 11]

In Clerk Maxwell’s electromagnetic equations, the electric intensity and the magnetic intensity are implicitly defined by an intelligible pattern of relationships among themselves, not by verbal description.  And the pattern of relationships constituting the field is explanatory and of scientific significance. (We invert the delta to represent the del operators: Δ, ğ, and Δ×)

  • Δ X E = (-1/c)H’
  • Δ X H = (+1/c)E’
  • Δ Ÿ H = 0
  • Δ Ÿ E = 0

.VII.2 EARLY MACROECONOMIC FIELDS 

In its early and Keynesian phase, the macroeconomic field retains the notion of force and external efficient cause.  And, still to this day, classical, neoclassical, Keynesian, and new Keynesian macroeconomics and the method of Dynamic Stochastic General Equilibrium conceive of pricing, interest rates, supply shocks, demand shocks, and monetary shocks as exogenously-determined forces determining a set of stresses in the economic process; i.e. as efficient causes.

Without these shocks, the economy would evolve along a perfectly predictable path, with neither booms nor recessions. [Sbordone, Tambalotti, Rao, Walsh, 2010, 26]

The process is not viewed and understood as a nuanced and naturally innovative unitary process of surges and taperings, having throughout the surges and tapering, an abstract invariant theory conceived as a field.  To be sure, surprises occur and adjustments may be needed, but the macroeconomic field remains a field of values at every point. Any of the rates of flow may begin to vary independently of the others, and adjustment of the others may lag.  But any systematic divergence[1] brings automatic sectoral correctives to work in the vector field of accelerations.

Now it is important to distinguish two different aspects of equations (39) and (42) (CWL 21, 141)  Under a certain aspect these equations express a truism: if entrepreneurial receipts and payments equate, then they equate not only among entrepreneurs but also between entrepreneurs and the third party, demand.  But under another aspect the same equations, so far from expressing an necessary truth, express an almost unattainable ideal, namely a dynamic equilibrium to which any actual process continually attempts to approximate by varying prices and changing quantities of supply.  To study the truism is to study bookkeeping, to study the art of double entry, and to learn the magic of the variable items, profit and loss, which perforce make the books balance.  To study the ideal is to study equilibrium analysis.  The bookkeepers are wise after the event.  But if the entrepreneurs are to be wise, they have to be wise before the event, for their payments precede their receipts, and the receipts may equal the payments but they may also be greater or less, to give the entrepreneur a windfall profit or loss.  Such justification or condemnation of payments by receipts the bookkeeper records but the entrepreneur has to anticipate, and the grounds of his anticipations, their effects upon his decisions, and the interaction of all decisions form the staple topic of equilibrium analysis.  Now the viewpoint of the present discussion is neither that of the bookkeeper nor that of the equilibrium analyst.  Equations (39) to (42) are regarded not as a set of facts recorded by bookkeepers, nor as an ideal which entrepreneurs strive yet fail to attain, but as a first approximation to the law of circulation in the basic circuit.  The first approximation to the law of projectiles is the parabola: one might, if one chose, consider the projectiles as aiming at or tending towards the ideal of the parabola yet ever being frustrated by wind resistance; one might elaborately describe the trajectory of the projectile as an indefinite series of parabolas, each one in succession the goal of its tendency only to be deserted because adverse circumstance set it on another track.  In such a description of trajectories there is to be found at least a superficial resemblance with the statement that an economy is tending towards equilibrium at every instant, though towards a different equilibrium at every successive instant.  But whatever the resemblance, and however deep and significant the difference, we here propose to take a circuit and examine first the implications of this law and then the second approximations that are relevant to our inquiry.  [CWL 21, 142-43]

A condition of circuit acceleration was seen … to include the keeping in step of basic outlay, basic income, and basic expenditure, and on the other hand, the keeping in step of surplus outlay, surplus income, and surplus expenditure.  Any of these rates may begin to vary independently of the others, and adjustment of the others may lag.  But any systematic divergence[1] brings automatic correctives to work.  The concomitance of outlay and expenditure follows from the interaction of supply and demand.  The concomitance of income with outlay and expenditure is identical with the adjustment of the rate of saving to the requirements of the productive process. [CWL 15, 144]

Rather, still to this day the economic process is conceived less as the always current, purely dynamic process with an exigence for a normative pure cycle and more as a happenstantial past and future series of reactions to external, Newtonianlike, force-ful shocks.  The process is not understood as always the current, purely relative, purely dynamic, unitary process whose primary, explanatory, immanent relativities are general, and thus relevant in any and every instance.  In the simplistic IS-LM macrostatic model, the supposedly exogenously-determined interest rate is the external force efficient-causing the momentary levels of investing vs. consuming, and saving vs. spending.  In the simplistic AD-AS macrostatic model, prices are the exogenously-determined efficient cause of the momentary level of demand and the momentary level of supply. In the Phillips Curve scheme, economists attempt, with notable difficulty, to correlate interest rates – the rental price of money – and the level of unemployment as mutual conditions and causes of one another.

Without these shocks, the economy would evolve along a perfectly predictable path, with neither booms nor recessions. [Sbordone, Tambalotti, Rao, Walsh, 2010, 26]

Footnote:

Re the Bureau of Economic Analysis’s Gross Domestic Product:  This is merely a tally of the recent aggregates deemed useful by corporate accountants and managers and National Income accountants to determine a) net income (The Statement of Income), b) net wealth (Balance sheet  assets minus liabilities), c) change in cash and liquid assets (cash outflow minus cash inflows) (or vice versa), d) product produced (Gross domestic Product), e) value added by industry.  These data may be analyzed with respect to change and ratio to get a sense of trend, but they do not constitute explanatory conjugates which provide understanding of relations among the functional explanatory aggregates.  Does the velocity of aggregate wages-and-salaries explain the velocity of advertising costs?  Does the rate of investment bear any determinable relation to the rate of current heat-and-light expenses?

.VIII. MODERN FIELD THEORY – THE CONCEPT OF FORCE IS DROPPED

.VIII.1. MODERN FIELD THEORY IN PHYSICS

In its explanatory form, modern field theory drops the whole notion of force as an external efficient cause and, therefore, the notion of external efficient cause.  Modern field theory is purely relational.  The “causes” are the set of relationships between n objects constituting the field itself.  “Forces can be ignored.”

May it not be that all forces can be “transformed away” in a similar manner  The answer given by Einstein in his general theory of relativity is in the affirmative, at least as regards gravitational forces which are proportional to masses.  His stand is that there is some reference system, or in more technical language, some space in which forces can be ignored.  Their occurrence in our physical experience is due only to our failure to use the correct system of reference, i.e. the correct space. [Lindsay and Margenau, 1957, 358]

 .VIII.1.1.  THE MODERN FIELD CALLED THE SPECIAL THEORY OF RELATIVITY

Special Relativity is primarily a field theory; it is concerned with the intelligibility immanent in data, not with efficient, instrumentalmaterial, or final causes of events.

…  observations give way to measurements; measurements relate things to one another rather than to our senses; and it is only the more remote relations of measurements to one another that lead to empirical correlations, functions, laws.  [CWL 3, 41/  ]

Special Relativity is primarily a field theory, that is, it is concerned not with efficient, instrumentalmaterial, or final causes of events, but with the intelligibility immanent in data; but Newtonian dynamics seems primarily a theory of efficient causes, of forces, their action, and the reaction evoked by action. … Special Relativity is stated as a methodological doctrine that regards the mathematical expression of physical principles and laws, but Newtonian dynamics is stated as a doctrine about the objects subject to laws.  [3, 43/67]

Δt = Δt0/√1 – v2/c2

Special Relativity is a field theory in the form of terms are related to one another.  In Special Relativity Δt0 is the interval of time experienced by an observer at rest with respect to the motion of light; Δt is the interval of time experienced by an observer in uniform motion with respect to the motion of light; v is the velocity of the uniform motion; and c is the speed of light in all inertial reference frames.

For an observer in motion with respect to a light pulse and viewing it as occurring at different distances, time dilates, lengths contract, his/her velocity is different from that of an observer at rest with the light pulse. Newton’s 3-D space and 1-D time are redefined by Einstein as 4-D spacetime.  Space and time are no longer external, separate and unrelated, given absolute containers.  They are remotely implicitly defined as a 4-dimensional spacetime by the constancy of the speed of light. They are purely relational, not isolated alsolutes.

All the results of special relativity can be obtained by recasting physical equations in such a manner that they represent relations between 4-vectors or tensors in a space in which the element of a world line is given by eq. (7.3.28) [L&M 356]

The infinitesimal interval of the Riemannian manifold is,

ds2= Σgijdxidxj           [i, j = 1,2…n]

where, in Special Relativity, the gij  is unity or zero …, but there are four dimensions, and x4  equals ict. [CWL 3, 146 -147/170-71]

.VIII.1.2.  THE MODERN FIELD THEORY CALLED THE GENERAL THEORY OF RELATIVITY

In the General Theory of Relativity we shall free ourselves from the restriction to this particular space, previously called Minkowski space, and require general invariance. [Lindsay and Margenau, 1957, 356]

In general relativity’s (generalized theory of gravitation), the Christoffel symbols [d’inverno, 1992, 83] play the role of the gravitational force field and the metric tensor plays the role of the gravitational potential. ¶ In general relativity, the gravitational field is determined by solving the Einstein field equations 10  where the metric tensor is gab, T is the stress-energy tensor, G is the Einstein tensor, and c is the speed of light. [Wikipedia (1), Gravitational Field page 2 of 4]

  • Gab = 8πTab  (where G/c4 = 1) [d’inverno, 1992,143]

    In the infinitesimal interval of the Riemannian manifold, the transformation equations in the geometry of Generalized Theory of Gravitation are, again:

    ds2=Σgijdxidxj           [i, j = 1,2…n]

    and the coefficients of the metric tensor are anti-symmetrical.   [CWL 3, 146 -147/170-71]

    This equation, with ds interpreted as an element of 4-space in which the gij are in some manner related to what we ordinarily term forces, is the fundamental equation of general relativity.  Since our endeavor is to explain the motion of particles in a gravitational field, the gij must depend on the gravitational masses present in the universe.  They must reduce to the form (5) for space free from gravitating matter. [Lindsay and Margenau, 1957, 362]

The curvature of space, due to the existence of matter, and the energy-momentum tensor implicitly define and implicitly determine one another by their functional relations to one another.

.VIII.1.3.  OTHER FIELDS AND FORMULATIONS

There are also formalisms of general relativity based upon Lagrange’s variational principle or Hamilton’s variational principle in terms of kinetic energy, T, and potential energy, V.

  • L = T – V      Lagrange
  • L = T + V      Hamilton

.VIII.2.  MODERN FIELD-THEORETIC MACROECNONOMICS

Field theory is a matter of the immanent intelligibility of the object. [CWL 10, 154]

The form of any inner functioning is known through its relations to all other inner functionings, rather than being known through its relation to an external efficient cause.

the terms are defined by the relations in which they stand, that is, by a process of implicit definition. [Gibbons 1987, 313]

Let’s get our bearings and gather our wits.  We have characterized modern field theory (MFT) as follows:

  • MFT does not require (the notion of) an external influence as an efficient cause
  • It explains the field by the immanent relations among the n objects the fall within the field
  • It is a set of intelligible relations linking that which is implicitly defined by the relations themselves
  • Thus it is the theory of what may be called the formal cause, or immanent intelligibility among n objects in a unitary system
  • The formal cause is distinct from the efficient, material, instrumental, or final causes which would be of interest to applied science as distinct from abstract theoretic science
  • The field is a “region” at every point of which there is a value – whether scalar, and/or vector, and/or tensor
  • Three examples of modern field theory are Einstein’s Special Relativity, General Relativity, and Generalized Theory of Gravitation.

… 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 formsThe 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]

our inquiry differs radically from traditional economics, in which the ultimate premises are not production and exchange but rather exchange and self-interest, or later, exchange and a vaguely defined psychological situation.  Our aim is to prescind from human psychology (so) that, in the first place, we may define the objective situation with which man has to deal, and, in the second place, define the psychological attitude that has to be adopted if man is to deal successfully with economic problems.  Thus something of a Copernican revolution is attempted: instead of taking man as he is or as he may be thought to be and from that deducing what economic phenomena are going to be, we take the exchange process in its greatest generality and attempt to deduce the human adaptations necessary for survival. [CWL 21,42- 43]

It is the viewpoint of the present inquiry that, besides the pricing system, there exists another economic mechanism, that relative to this system man is not an internal factor but an external agent, and that the present economic problems are peculiarly baffling because man as external agent has not the systematic guidance he needs to operate successfully the machine he controls. [CWL 21, 109]

As to the notion of cause, macroeconomists in academia, at the Bureau of Economic analysis, and at the Federal Reserve Board mistakenly base explanation of the objective economic process upon psychic elements – such as utility, time preference, expectations, hunches about interest rates, which are, as it were, external to the immanent intelligibility of the objective process as a point-to-point and point-to-line unitary system of production and exchange.  The psyche of the human driver is not the immanent intelligibility of the car; the psyche of the switcher is not the immanent intelligibility of the the electric circuit.  The psyche of the operator is not the immanent intelligibility of the objective process.  However, Functional Macroeconomic Dynamics drops the notion of psychic motive and cause; it gets along perfectly well without it.  It thinks in terms of a field theory, the set of internal relationships among the n interdependent, implicitly-defined, objective functionings which constitute the process.  The field theory of Functional Macroeconomic Dynamics explains the objective process.  Functional Macroeconomic Dynamics is a set of intelligible functional relations linking functionings which are implicitly defined by the functional relations of immanent functioning among themselves; it is a set of relational forms.  The form of any inner functioning is known through its relations to all other inner functionings, rather than being known through its relation to an external efficient cause.  ….  The field theory of macroeconomics is a matter of the immanent intelligibility of the objective, dynamic functional process.

An abstract objective theory, which has laws of its own which must be respected by agents, yields premises and framework for criticisms of agents.  The participant-agents are, as it were, outside the process.

Consider the immanent intelligibility of the automobile apart from the performance of the driver.

A study of the mechanics of motor-cars yields premises for a criticism of drivers, precisely because the motor-cars, as distinct from the drivers, have laws of their own which drivers must respect.  But if the mechanics of motors included, in a single piece, the anthropology of drivers, criticism could be no more than haphazard. [CWL 21, 109]

Also, since the economic process is dynamic, the abstract immanent intelligibility of the economic field must be in the form of a dynamics at an adequate level of abstraction.

Those familiar with elementary statics and dynamics will appreciate the shift in thinking involved in passing from (static) equilibrium analysis … to an analysis where attention is focused on second-order differential equations, on d2θ/dt2, d2x/dt2, d2y/dt2, on the primary relativities … .  Particular secondary boundary conditions, past and future pricings and quantities, are relatively insignificant for the analysis of the primary relativity immanent in, and applicable to, every instance of the process.  What is significant is the Leibnitz-Newtonian shift of context. [McShane, 1980, 127]

Frish’s failure to develop a significant theory typifies the failure of economists who search for a dynamic heuristic.  As well as a fundamental disorientation of approach there is also a tendency to shift to an inadequate level of abstraction with a premature introduction of boundary conditions in a determinate set of differential and difference equations. [McShane, 1980, 114]

The explanation requires abstract implicit definition.

In brief, Lonergan is looking for an explanation in which the terms are defined by the relations in which they stand, that is, by a process of implicit definition.  This technique (implicit definition) has been used to great effect by David Hilbert in his Foundations of Geometry in which, for example, the meaning of a point and a straight line is fixed by the relation that two, and only two points, determine a line.  “The significance of implicit definition is its complete generality.  The omission of nominal definition is the omission of a restriction to objects which, in the first instance, one happens to be thinking about.  The exclusive use of explanatory or postulational elements concentrates attention upon the set of relationships in which the whole scientific significance is contained.”  [Gibbons, 1987, 313]

We must bring macroeconomic process into the two-thousand twenties.  We seek a modern field theory of the concrete economic process.  This process is a part of world process; there are a) two sets of abstract primary relativities among velocitous and accelerative functionings which generally explain the process, and b) a set of secondary concrete determinations of contingent price and quantity variables happening in the non-systematic manifold; to these contingent, happenstantial, price and quantity variables the primary relativities are universally relevant and applicable in any instance.  Functional Macroeconomic Dynamics specifies two sets of abstract primary relativities: first, the primary relativities, represented in the Diagram of Rates of Flow, constituting the general and always currently relevant interrelations of functional flows of products and payments, and, second, the normative general laws governing the phases of any and every particular pure cycle of expansion.

The primary relativities are abstract.  They are relations of abstract conjugates among themselves, not experiential conjugates of our sentient experience of producing and buying.  These abstract primary relativities constitute the process’s immanent intelligibility, its normative “mechanics,” and such is identified as the modern field theory of the process.  The concrete secondary determinations – quantities and prices – occurring in the non-systematic manifold (including the price called the interest rate) are supplied as boundary values by the non-systematic, concrete, pricing system, which determines Who, among millions of persons, does What, among millions of tasks, in return for Which, among millions of rewards.

The first set of primary functional relations will now be listed, with source pages included in parentheses for reference by the serious reader.  Its first equation is called the lagged technical accelerator of the productive process.  It deals only in the primary productive process, to which the dummy money of the monetary order is correlated.

kn[f’n(t-a)-Bn] = f”n-1(t) – An-1    (CWL 15, 37)

The lagged technical accelerator distinguishes “surplus” accelerative point-to-line relations from “basic” accelerated point-to-point relations.  It allows for depreciation and R&M; it allows for slack; and it provides the  internal relations of these two aggregate functionings in action with each other.  No “forces” or external efficient causes are needed or admitted!  It is a general and abstract statement of internal relations and immanent intelligibility of the rhythm of the productive process. It covers

  • point-to-point and point-to-line circuits and their relations
  • temporalities
  • velocities
  • accelerations
  • accelerative multiplier

Based upon this general theory of the productive process – the process of producing what money buys – classes of payments then get mapped out from, and thus correlated to, the first-order and second-order flowings of the double-circuited productive process, so as to reveal a unitary system of rhythmic and correlated production and payments; the first-order and second-order monetary circulations of dummy money meet the two-leveled, double-circuited first-order and second-order flowings of the process of production and exchange.

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]Diagram of Rates of Flow 2

Since we are delineating a “field theory”, let us, at least temporarily, change the title of the above diagram to “The Diagram of Macroeconomic Field Theory.”

The rest of the first set of equations (below) define the purely functional interrelations in the circulation of money.  Round and round the old and new money go.  One of the monetary relations in this set,

G = c”O” –i’O’ = 0     the condition of dynamic equilibrium of flows   (CWL 16, 50),

specifies the condition of dynamic equilibrium of flows, so that we could also call our image the Diagram of Field-Theoretic Equilibrium.  Dynamic equilibrium – not microstatic or macrostatic equilibrium – is a constant requirement throughout the time-consuming process of a long-run economic expansion.

Also, note that, the upper-case flows and their interrelations are symbolized in algebraic functions.  Still, the symbols represent interdependent magnitudes of flows, i.e. a dynamic so much or so many every so often, d/dt and Δ/Δt, and the mathematical operators represent their relations.

The flows are implicitly-defined among themselves.  And, as an important exercise, those should be traced  by the reader, pencil in hand, in “The Diagram of Macroeconomic Field Theory.” Note that there is neither representation nor even mention of external efficient causes such as neoclassical, Keynesian, DSGE’s “generative force” of exogenously determined prices.  Macroeconomic Field theory is an immanentism of a unitary system.

Footnote:  Rates or flows are generally designated by upper-case letters (primed or unprimed), and upper-case letters (primed or unprimed) always designate rates or flows, unless otherwise specifically noted. Quantities are generally designated by lower-case letters (primed or unprimed), using the same letter as for the rate or flow, where pertinent.  At times lower-case letters are also used, following Lonergan’s own practice, to designate fractions; but these and other exceptions to the scheme will be specifically noted. (CWL 15, 30, ftnt. 29)

Diagram of Rates of Flow 2

  1. R’ = E’     (CWL 15, 54)
  2. R” = E”      (CWL 15, 54)
  3. I’ = O’ +M’      (CWL 15, 54)
  4. I” = O” +M”     (CWL 15, 54)
  5. G = c”O” –i’O’   (CWL 15, 54)
  6. G = c”O” –i’O’ = 0     the condition of dynamic equilibrium   (CWL 16, 50)
  7. M’ = (S’ – s’O’) + (D’ – s’I’) + G   (CWL 15, 54)
  8. M” = (S” – s”O”) + (D” – s”I”) – G   (CWL 15, 54)
  9. (S’-s’O’) = ΔT’ + (O’ – R’) + ΔR’   (CWL 16, 67)
  10. (S”- s”O”) = ΔT” + (O” – R”) + ΔR”   (CWL 16, 67)

Thus for example, assuming G = 0, and in keeping with both the principle of concomitance (flows keeping pace) and the functional role of credit to bridge brief time gaps, we have for  the relations of functional flows among themselves in the basic circuit:

  1. R’ = E’ = I’ = O’ +M’
  2. Thus, per 7 above, R’ = E’ = I’ = O’ +[S’ – s’O’] + [D’ – s’I’]
  3. Thus, per 9 above and 2 immediately above, R’ = E’ = I’ = O’ + [ΔT’ + (O’ – R’) + ΔR’] + [D’ – s’I’]

One can develop parallel equations for the surplus circuit, and then combine both circuits to calculate Gross Domestic Functional Flows, GDFF, to replace the BEA’s Gross Domestic Product, GDP, and to supplement the FRB’s Z.1 matrix as the primary reference for false-third-party government’s management of the economy.

Again, Those familiar with elementary statics and dynamics will appreciate the shift in thinking involved in passing from (static) equilibrium analysis … to an analysis where attention is focused on second-order differential equations, on d2θ/dt2, d2x/dt2, d2y/dt2, on the primary relativities … .  Particular secondary boundary conditions, past and future pricings and quantities, are relatively insignificant for the analysis of the primary relativity immanent in, and applicable to, every instance of the process.  What is significant is the Leibnitz-Newtonian shift of context. [McShane, 1980, 127]

A second set of primary relativities providing the intelligibility of how the process should normatively play out over phases in the long run is provided in CWL 15, sections 26-28, which treat the long-term cycles of

  • basic income,
  • pure surplus income,
  • the aggregate basic price-spread.

These sections, 26-28, explain both the normative equilibria and the violative disequilibria in the phases of the evolutionary process as it expands over time to the tune of the lagged technical accelerator.

kn[f’n(t-a)-Bn] = f”n-1(t) – An-1  (CWL 15, 37),

per the possibilities of a) the Table of Possibilities on CWL 15, 114, b) Figure 24-7, p. 125 and c) the equations of pages 107-113.

The differentials (in bold) of the long-run expansionary economic cycle:

  • dI’Σ(widni+ nidwi+dnidwi)yi       [CWL 15, 134]
  • df = vdw + wdv       [CWL 15, 148-49]
  • P’Q’ = p’a’Q’ + p”a”Q’      [CWL 15, 156-58]
  • P’/p’ = a’ + a”(p”Q”)/(p’Q’)      [CWL 15, 156-58] , or
  • J = a’ + a”R       [CWL 15, 156-58]
  • d(P’/p’) = dJ = da’ + a”dR + Rda”       [CWL 15, 158]

The pattern of an ideal long-term pure cycle would have an exigence for a keeping pace of circuit elements with one another and in particular for a normative balance of crossovers (G = c”O” –i’O’ = 0) between circuits.  And, as exemplified by  Burley’s and Csapo’s Characteristic Equations, and their root solutions, the pure cycle would exhibit a) normative relative intensities of analytically distinct productive activities, and b) normative relative pricing of analytically distinct product groups.  And, per the lagged technical accelerator, the pure cycle would properly implement the magnitude of coefficient k, and the timing indicated by t, t-a, t-b, etc, in that lagged technical accelerator.  Neither too fast nor too slow, neither excessive nor deficient, and dependent upon the state of technology, culture, and institutions.

An image of possible different normative logistic growth processes demonstrates the possible different ideal pure cycles of expansion, depending upon the particular variables of the lagged technical accelerator in the particular case.  In any instance, what is the particular value of k, t, t-a, t-b, B, A etc?

In Stewart , 2008. p. 594,substituting the symbol Q for Stewart’s P,  the logistic differential equation of growth, with Q as quantity, k as the constant of proportionality, and K being the maximum carrying value of quantity, is

dQ/dt = kQ(1-Q/K)

The solution of the differential equation is

Q(t) = K/(1+Aε –kt)

where

A = (K-Q0)/Q0

The reader can apply boundary values to verify that, at first, “the graph of P is concave upward and the growth curve appears to be almost exponential, but then it becomes concave downward and approaches the limiting population K.”[1]  This path resembles, though with a slight difference, the path described by Lonergan for Q” in the surplus expansion and for Q’ in the subsequent basic expansion.

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 (of the capital sector) 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

 

 

There would be different potentials of different “revolutions.”: train, automobile, applied science, hardware-software computations and control revolution.  But, though all differ, each would have an ideal pure cycle.  In the case of logistic growth, the S-curve might be shorter or taller.  But each revolution would proceed through phases with changing values of surplus  dQ”/Q” and basic dQ’/Q’.

As for value at every point of the field:  Given a particular ideal pure cycle and random divergence of flows from their norms, there would be a corrective acceleration vector at every point of the macroeconomic region with its own magnitude and direction.

A condition of circuit acceleration was seen … to include the keeping in step of basic outlay, basic income, and basic expenditure, and on the other hand, the keeping in step of surplus outlay, surplus income, and surplus expenditure.  Any of these rates may begin to vary independently of the others, and adjustment of the others may lag.  But any systematic divergence[1] brings automatic correctives to work.  The concomitance of outlay and expenditure follows from the interaction of supply and demand.  The concomitance of income with outlay and expenditure is identical with the adjustment of the rate of saving to the requirements of the productive process. [CWL 15, 144]

Independent variations may be productive or monetary, minor or major, supply or demand, in basic or surplus circuits. But the primary relativities of the Diagram of Macroeconomic Field Theory remain applicable and relevant in any instance.

Now it is important to distinguish two different aspects of equations (39) and (42).  Under a certain aspect these equations express a truism: if entrepreneurial receipts and payments equate, then they equate not only among entrepreneurs but also between entrepreneurs and the third party, demand.  But under another aspect the same equations, so far from expressing an necessary truth, express an almost unattainable ideal, namely a dynamic equilibrium to which any actual process continually attempts to approximate by varying prices and changing quantities of supply.  To study the truism is to study bookkeeping, to study the art of double entry, and to learn the magic of the variable items, profit and loss, which perforce make the books balance.  To study the ideal is to study equilibrium analysis.  The bookkeepers are wise after the event.  But if the entrepreneurs are to be wise, they have to be wise before the event, for their payments precede their receipts, and the receipts may equal the payments but they may also be greater or less, to give the entrepreneur a windfall profit or loss.  Such justification or condemnation of payments by receipts the bookkeeper records but the entrepreneur has to anticipate, and the grounds of his anticipations, their effects upon his decisions, and the interaction of all decisions form the staple topic of equilibrium analysis.  Now the viewpoint of the present discussion is neither that of the bookkeeper nor that of the equilibrium analyst.  Equations (39) to (42) are regarded not as a set of facts recorded by bookkeepers, nor as an ideal which entrepreneurs strive yet fail to attain, but as a first approximation to the law of circulation in the basic circuit.  The first approximation to the law of projectiles is the parabola: one might, if one chose, consider the projectiles as aiming at or tending towards the ideal of the parabola yet ever being frustrated by wind resistance; one might elaborately describe the trajectory of the projectile as an indefinite series of parabolas, each one in succession the goal of its tendency only to be deserted because adverse circumstance set it on another track.  In such a description of trajectories there is to be found at least a superficial resemblance with the statement that an economy is tending towards equilibrium at every instant, though towards a different equilibrium at every successive instant.  But whatever the resemblance, and however deep and significant the difference, we here propose to take a circuit and examine first the implications of this law and then the second approximations that are relevant to our inquiry.  CWL 21, 142-43

Functional Macroeconomic Field theory proposes explanation by immanent intelligibility and recognizes possible independent variation of flows from their norms requiring systematic correction.  The pre-field-theory-macrostatics economists analyze from the outside in; field theory economists analyze the immanent normative dynamics and errant disequilibria  The macrostatics outside-in groups stumble their way from the momentary external to the intrinsically unpredictable, whereas inside-in Functional Macroeconomic Field Theory moves from the immanent intrinsic intelligibility to the complete explanation of equilibria and disequilibria.

Functional Macroeconomic Dynamics, like modern field theory in physics, seeks prior and more fundamental explanation; it drops the notion of external efficient-causal forces as a mistaken basis of prediction.  FMD is concerned with field-theoretic immanent explanatory intelligibility, i.e. the notion of the immanent interdependencies, interconnections, and interrelations among the flow velocities which constitute the objective economic process.  These flows of so much or so many per interval are velocities subject to change.  And these interdependent, mutually defining, and mutually-conditioning, velocitous functionings prove to be the basic terms of scientific and explanatory significance for explaining the economic process.

To be sure, efficient causation does exist.  Human participants are efficient causes.  they operate the machine.  They drive the car.  But humans must adapt to objective exigencies in order to survive.

Our aim is to prescind from human psychology (so) that, in the first place, we may define the objective situation with which man has to deal, and, in the second place, define the psychological attitude that has to be adopted if man is to deal successfully with economic problems.  Thus something of a Copernican revolution is attempted: instead of taking man as he is or as he may be thought to be and from that deducing what economic phenomena are going to be, we take the exchange process in its greatest generality and attempt to deduce the human adaptations necessary for survival. [CWL 21,42- 43]It is the viewpoint of the present inquiry that, besides the pricing system, there exists another economic mechanism, that relative to this system man is not an internal factor but an external agent, and that the present economic problems are peculiarly baffling because man as external agent has not the systematic guidance he needs to operate successfully the machine he controls. [CWL 21, 109]

Lonergan’s intention was ‘to formulate the laws of an economic mechanism more remote and, in a sense, more fundamental than the pricing system…laws which men themselves administrate in the personal conduct of their lives. In 1978 he began to refer to Nicholas Kaldor in support of his judgment that the significance traditionally accorded to price theory by conventional economics since Adam Smith’s Wealth of Nations (1776) amounted to a virtual derailment of economic theory. [CWL 15, Editors’ Introduction xlv]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 another might be named more briefly formal causality … [CWL  3, 78/101-102]

Biased and self-defensive academic macroeconomists tend to look down upon a section of the Baseball Diamond and exclaim, “No kidding, Sherlock. Duh!”  But the yoke (sic) is on them.  They fail to grasp that the Diamond represents a unitary and complete explanation of functional relations; it constitutes an intelligibility prior to, more fundamental, and more useful in practice than the reports of the BEA and FRB.  The academics are at once both Doctor Watson, who cannot solve a mystery, and Professor Moriarty, who has become the perpetrator of error.

Functional Macroeconomic Dynamics is prior to and more fundamental than neoclassical pricing analysis and Keynesian supply-demand analysis

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, … price levels and patterns, … interest and profits, 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]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; and as Newton transformed the formulation and interpretation of Kepler’s laws, so Einstein transforms 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]

The “cause” in modern field-theoretic macroeconomics is what is named the formal cause – the field of intelligible relations that implicitly define the objects.  Note that in the conception of field theory the objects of analysis don’t define the field, rather the prior intelligibility of the field of relations itself defines the objects that fall into it.  The field itself is constituted by intelligible relations and, in this macroeconomic case, it can be filled by a macroeconomic scheme isomorphic with the scheme of the field.  And, thus, elements such as happenstantial prices and quantities can only be interpreted in the light of the patterns of the significant variables in their relations within the field.  Happenstantial, secondary prices and quantities in the non-systematic manifold “fall into that field” and are understood in the light of the significant variables of that field.

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]The whole structure is relational: one cannot conceive the terms without the relations nor the relations without the terms.  Both terms and relations constitute a basic framework to be filled out, first, by the advance of the sciences and, secondly, by full information on concrete situations. [CWL 3, 492/516]…  observations give way to measurements; measurements relate things to one another rather than to our senses; and it is only the more remote relations of measurements to one another that lead to empirical correlations, functions, laws.  [CWL 3, 41/  ]Einstein’s position …  follows quite plausibly from the premise that empirical science seeks not the relations of things to our senses but their relations to one another.  For, as has been remarked, observations give way to measurements; measurements relate things to one another rather than to our senses; and it is only the more remote relations of measurements to one another that lead to empirical correlations, functions, laws.  [CWL 3, 41/  ]

Paraphrasing: modern scientific macroeconomics is not simply a horizontal and statistical refining of what was claimed before by neoclassical and New Keynesian analytics.  It is the perfecting of the very notion of macroeconomic science itself, of discovering explanatory elements by their causes, … .  What are the causes?  The field of intelligible relations that implicitly define the fundamental terms and relations.  The objects with which Functional Macroeconomic Dynamics 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 macroeconomics that is concerned with efficient agents such as firms and households and their utilities, preferences, and goals.

In the doing of macroeconomics the purpose is to discover the explanatory field relations of constituent interdependent, mutually-defining, functionings; scientific macroeconomics seeks the immanent intelligibility of this object-field.  Just as in Hilbert’s geometry the conceptions called a) two points, and b) a line are mutually defined by the relation between them, so, the concepts of scientific and explanatory significance in macroeconomic field theory, called velocitous functionings are known by their relations in their field. The relation defines the function, and the function defines the relation.  The search is a search for interdependencies and interrelations in a field.  And the whole unitary macroeconomic process of interdependent functionings has a unitary, general, and completely explanatory set of primary relativities, which are completely general, universally relevant, and applicable in any instance, and completely explanatory.

At the end of “A Note on Geometric Possibility,” Lonergan encouraged others to complete and perfect his treatment.  Let me say the same:

As a final word, may I say that I suspect there exist in this paper a number of failures to hit things off with complete accuracy; I present it in the hope that I have noted some worthwhile points and that others will be moved to complete and perfect my treatment. [Collection  1967, 113]

Thank you.

For further treatment of aspects of macroeconomic modern field theory –  prescinding from human psychology – please refer to the Table of Topics and the series of blogs.