Contents

.I. Relations and Relativity in General

.II. Einstein’s Special Relativity and General Relativity

.III Lonergan’s Double-Circuited, Pretio-Quantital Relativity Theory

.IV. The Basic Price Spread; The Co-ordinated Relativity of Three Major Pretio-Quantital Flows and the Co-operative Relations Within Each Major Flow

.V. The Macroeconomic Field Theory Equations

.VI. Concerning Verification

.VII. Miscellaneous Selections

.VIII. Conclusion

  

.I. Relations and Relativity in General

Terminology:

relative: that which has an order to another being (CWL 12, 713)

absolute: opposite of relative (CWL 12, 713)

‘relation’ is an order of one to another, and is opposed to the absolute. … an absolute is anything defined through itself.  Something that functions as a principle, then would be an absolute if there is a definition of its reality that is through itself. (CWL 12, 357, ftnt 48)

In his Editor’s Introduction to For a New Political Economy (CWL 21), P. McShane stated

Part Two (of CWL 21), entitled Fragments, belongs almost entirely in what I call the Einsteinian context of Part Three, in contrast to the Newtonian achievement of Part One; … [CWL 21, Index, 325]

Einstein’s Special Relativity states as a methodological doctrine that a) no inertial framework is to be considered a preferential framework; b) the speed of light is the same constant in every inertial reference frame.  Thus, space and time must be redefined as a four-dimensional unity within being rather each being an absolute container, and b) length, time, momentum, and kinetic energy are spatio-temporal and relative to different observers.

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]

We shall be comparing  features of Einstein’s General Relativity with Lonergan’s purely-relational equation of aggregate revenues equaling aggregate costs.  Both expressions may be read from right to left, left to right, or back and forth.

P’Q’ = p’a’Q’ + p”a”Q”  (CWL 15, 157-8)

The formulation of the full field equations of General Realtivity is dense with ten equations connecting twenty quantities:

(d.Inverno) Before attempting to solve the field equations we shall consider some of their important physical and mathematical properties ….  The full field equations (in relativistic units) are

G_ab= 8πT_ab

1. 1. The field equations are differential equations for determining the metric tensorg_ab from a given energy-momentum tensor T_ab. Here we are reading the equations from right to left.  … one specifies a matter distribution and then solves the equations to ascertain the resulting geometry.
   2. The field equations are equations from which the energy-momentum tensor, T_ab, can be read off corresponding to a given metric tensor g_ab. Here we are reading the equations from left to right.
   3. The field equations consist of ten equations connecting twenty quantities, namely, the ten components of g_ab and the ten components of T_ab. Hence, from this point of view, the field equations are to be viewed as constraints on the simultaneous choice of  g_ab and T_ab.  This approach is used when one can partly specify the geometry and the energy-momentum tensor from physical considerations and then the equations are used to try and determine both quantities completely. [d’Inverno, 1992, 169]

But Special Relativity and General Relativity are not the only relativities.  The equals sign, the greater-than sign, and the less-than sign express relations.  That is, they express relativities.

In his treatment of world process, Lonergan speaks of the classical formulations of the primary relativities of schemes of recurrence and the secondary components comprising the actual boundary values from the non-systematic manifold events.

Seventh-grade algebra deals with relations, and the person in the street casually proclaims that everything is relative.

We understand, or at least have heard about, several brilliant relativities: Newton’s law of mass and his laws of motion, Clerk-Maxwell’s electromagnetic equations, Hamilton’s canonical equations, Kirchhoff’s laws of junctions and currents, Schroedinger’s wave equation, Gell-Mann’s eightfold way, Feynman’s electrodynamics.

.II. Einstein’s Special Relativity and General Relativity

Terminology

field theory: an intelligibility of objects according to their relations among themselves

In his Special Theory of Relativity Einstein expresses one precise type of field-theoretic relativity.  Lonergan, in order to distinguish immanent formal cause from external efficient cause, contrasts Einstein’s Special Relativity with Newton’s mechanics; and he distinguishes a field theory of objects related among themselves from a theory of objects subject to laws.

… Special Relativity is primarily a field theory, that is, it is concerned not with efficient, instrumental, material, 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]

Further, Lonergan treats the redefinition of space and time to spacetime and, thus, the need for a critical gnoseology.

This reversal of roles in which the sensible container becomes the intellectually contained has already been noted. ‘To be’ cannot mean ‘to be in space’ or ‘to be in time’.  If that were so, and space is or time is, then space would be in space and time would be in time.  The further space and time, if real, would also be, and so would demand  a still further space and time.  The argument would be repeated indefinitely to yield an infinity of spaces and times.  ‘To be’ then is just ‘to be’.  Space and time, if real, are determinations within being; and if they are determinations within being, then they are not containers but the contained.  To put the issue more concretely, there are extensions, durations, juxtapositions and successions.  Still such affirmations are descriptive.  They have to be transposed into explanatory statements before one may ask legitimately for their metaphysical equivalents; and when that transposition takes place, then from the general nature of explanation it follows that the metaphysical equivalents will be the conjugate potencies, forms, and acts that ground the truth of spatio-temporal laws and frequencies.  So it comes about that the extroverted subject (sensibly) visualizingextension and (sensibly) experiencing duration gives place to the subject oriented to the objective of the unrestricted desire to know and affirm beings differentiated by certain conjugate potencies, forms, and acts grounding certain laws and frequencies.  It is this shift that gives rise to the antithesis of positions and counter-positions.  It is through its acknowledgment of the fact of this shift that a philosophy or metaphysics is critical.  It  is only by a rigorous confinement of the metaphysician to the intellectual pattern of experience and of metaphysical objects to the universe of being as explained, that this basic enterprise of human intelligence can free itself from the morass of pseudo-problems that otherwise beset it. (CWL 3, 513-4/537)

Einstein’s General Relativity [d’Inverno, 1992, 169]

G_ab= 8πT_ab     

expresses in tensor form the curvature of space [determined by the distribution of matter in the metric tensor (g_ab) and Einsteinian tensor (G_ab)] and the energy-momentum tensor (T_ab) as reciprocally determinative and mutually definitive.

While Special Relativity is sparse with basically Pythagorean geometric relations, General Relativity is dense with ten equations connecting twenty quantities.

Classical and relativistic formulations of Special Relativity [Cutnell & Johnson 2004, 858] include

Time dilation (1)

Length contraction (2)

Momentum (3) 

Kinetic energy (4)

Addition of Velocities (5)

The full field equations of General Relativity consist of ten equations connecting twenty quantities.  Again:

Before attempting to solve the field equations we shall consider some of their important physical and mathematical properties ….  The full field equations (in relativistic units) are

G_ab= 8πT_ab

1. 1. The field equations are differential equations for determining the metric tensor g_ab from a given energy-momentum tensor T_ab. Here we are reading the equations from right to left.  … one specifies a matter distribution and then solves the equations to ascertain the resulting geometry.
   2. The field equations are equations from which the energy-momentum tensor can be read off corresponding to a given metric tensor g_ab. Here we are reading the equations from left to right.
   3. The field equations consist of ten equations connecting twenty quantities, namely, the ten components of g_ab and the ten components of T_ab. Hence, from this point of view, the field equations are to be viewed as constraints on the simultaneous choice of  g_ab and T_ab.  This approach is used when one can partly specify the geometry and the energy-momentum tensor from physical considerations and then the equations are used to try and determine both quantities completely. [d’Inverno, 1992, 169]

.III Lonergan’s Double-Circuited, Pretio-Quantital Relativity Theory

Note: This Section III and the next Section IV are introductory to displaying Lonergan’s Field-Theory equations in Section V.  Readers may want to, first, leap ahead and preview that Section V, then return to this Section III with a good sense of where they are heading.

What are the unique relativities in Macroeconomic Relativity Theory (MRT)  that are such as to constitute a “relativity theory”; is not every simple, explicit or implicit equation of economics a “relativity”?  What’s the big deal? Why the new designation?  Are we overcomplexifying what is a simple differential calculus?

First, the historical significance is that MRT is a recent revolutionary explanation of a process that has puzzled economists for hundreds of years. MRT must be recognized as a newly systematized field theory.  Second, the theoretic significance is that MRT explains – by relations resembling the full field of General Relativity – the immanent intelligibility or “formal cause” of what always is the current, purely dynamic, double-circuited, lagged and phased economic process.  It recognizes but gets along well  without the notions of efficient causes – such as external unexplained price shocks or quantity shocks –  nor does it find adequate explanation of a dynamic multi-level process in momentary intersections of  supply and demand curves at a price level.  MRT is not a macrostatics, nor does it consist of a single undifferentiated circuit of production and exchange or an undifferentiated simultaneity of explanatory functional flows.  MRT is a field theory of the relations of interdependence of velocitous economic functionings among themselves.  MRT is a dynamical field theory.  And its full set of relations constitute a unique, unified, scientific, explanatory intelligibility.  MRT deals with a particular, special, sui-generis field.

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

The relations among “significant variables,” i.e. scientific, explanatory variables, replace the castle in the air called “price theory” – whether the prices be the prices of goods and services or the rental price of money (the interest rate).

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

 Lonergan agreed with Schumpeter that the economist had to know what are the significant variables in the light of which price changes are to be interpreted.  According to Lonergan, standard economic theory had successfully achieved none of these desiderata. [CWL 15, Editors’ Introduction liii]

The question of prices, though first in the IS-LM and AD-AS models, is last in Lonergan’s analysis.  Price changes must be interpreted in the light of the significant explanatory relations among interdependent, implicitly-defined, concomitant functional flows.

The question of prices, then, last in Lonergan’s analysis of the closed economy, is faced within the developed dynamic perspective. (McShane, 1980, ?)

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

Pretio-quantitality bears some relation to space-time.

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

Paraphrasing:

If one would understand, not men’s notions of single-circuited Production-and-Exchange and Time, but rather the intelligibility immanent in double-circuited Production-and-Exchange and Time; then one must advance from Walrasian reference frames to the structural principles and laws of that fundamental double-circuited, lagged, functional, productive process whose intellibibility is universal and invariant under transformations between large and small economies, greater or lesser monetary scaling factors, and free or totalitarian political systems.  Moreover, the universally-applicable, invariant field-theoretic relations will be mathematized so as to be a) isomorphic with the structural dynamics of the concrete process, and b) verifiable by econometricians. (paraphrase of CWL 3, 171/)

MRT is a theory of functional relations.  Its diagrams do not represent static  accumulations; they represent functional velocities.  Q’ and Q” represent velocities.  (In Lonergan’s symbolization, they have the same meaning as dQ’/dt and dQ”/dt in an alternate symbolization.)

“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 is alone;”  … “only Lonergan”:

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

Again, here,

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

Lonergan’s Diagram of Rates of Flow is a brilliant representation of interdependent flows.

There is the tremendous simplification (a diagram) effects the aims and limitations of macroeconomics make the use of a diagram particularly helpful, …  For its basic terms are defined by their functional relations.  The maintaining of a standard of living (distinct process 1) is attributed to a basic process, an ongoing sequence of instances of so much every so often.  The maintenance and acceleration (distinct process 2) of this basic process is brought about by a sequence of surplus stages, in which each lower stage is maintained and accelerated by the next higher.  Finally, transactions that do no more than transfer titles to ownership (distinct process 3) are concentrated in a redistributive function, whence may be derived changes in the stock of money dictated by the acceleration (positive or negative) in the basic and surplus stages of the process. (CWL 15, 54) More positively, the channels account for booms and slumps, for inflation and deflation, for changed rates of profit, for the attraction found in a favorable balance of trade, the relief given by deficit spending, and the variant provided by multinational corporations and their opposition to the welfare state. [CWL 15, 17]

… positive or negative transfers to basic demand (D’-s”I’) and consequent similar transfers to surplus demand (D”-s”I”) belong to the theory of booms and slumps.  They involve changes in (aggregate basic or aggregate surplus) demand, with entrepreneurs receiving back more (or less) than they paid out in outlay (which includes profits of all kinds).  The immediate effect (of these aberrational monetary transfers) is on the price levels at the final markets, and to these changes (in price), enterprise as a whole responds to release an upward (or downward)  movement of the whole economy.  But the initial increased transfers to demand [that is, excess transfers along (D’-s’I’)  and (D”-s”I”) ] are not simply to be supposed.  For that would be postulating without explaining the boom or slump. [CWL 15, 64]

Macroeconomic Relativity Theory is a radically different “modern field theory.”  It acknowledges the efficient cause of participants – who may suffer from egoistic, group or commonsense bias ((CWL 3, 218-45/244-67) and may be knowledgable or innocently ignorant, malicious or kind, weak or powerful, influential or unnoticed, etc. – but it drops the notion of external shock-force and explains the immanent intelligibility of the process.  And this explanation yields norms for adaptation by psychological participants. Thus, MRT deals with a particular special field.  In tensor analysis there exist scalar fields, vector fields, tensor fields, and the Special Relativity field; and then there exists the Macroeconomic Relativity field.  This MRT field of production and exchange is a vector-velocity and vector-acceleration field. Its explanation bears little resemblance to the external, efficient-cause theories of Newton and of Establishment Macrostatics, but it resembles rather the formal-cause, immanent intelligibility-theory of Faraday and Clerk Maxwell’s electromagnetics.  It has a set of primary internal relativities:

• A relation of composition of a product q_i = q_ijk in the productive process
• A distinction between point-to-point activities and point-to-indeterminate-line activities, which distinction implies two or more circuits and lagged acceleration
• A relation of lagged acceleration of the basic process by the pure surplus accelerator, k_n [f’_n(t-a)-B_n] = f”_n-1(t) – A_{n-1 (CWL 15, 37)}
• Relations of correspondence between factors currently in process and factors currently exiting the process
• The relations of production and exchange keeping pace with one another
• A dummy money, and the congruence of payments with the proprietary network of the system
• A correlation of the magnitudes and frequencies of payments to the magnitudes and frequencies of production turnovers
• Relations of concomitance of elements constituting the monetary flows in each and every circuit, i.e. A relation of equality (by the principle of normative concomitance) between Expenditures and Outlays
• Relations of the monetary flows between analytically distinct circuits
• A relational condition of equilibrium for the monetary flows between circuits; G = c”O” – i’O’ = 0
• A relation between rates of Incomes for rates of consuming and rates of Incomes for rates of investing
• A relation of analytically distinct pure surplus income to the process of expansionary investment
• A relation of phases identified by a relational comparison of the acceleration ratio of point-to-point production to the acceleration ratio of point-to-line production
• A relation of collision or clash between the systematic rise and fall of pure surplus income and the criterion of ever increasing pure surplus income as the only acceptable evidence of successful management
• A relation between the monetary values of imports and exports
• A normative relation of balance between government monetary inflows and outflows
• Ideal frequencies of occurrences
• Non-systemtic divergences of actual relative frequencies from ideal frequencies

MRT is, broadly speaking, a theory constituted by explanatory relations; and, narrowly speaking, it is the modern relativistic field theory which explains, rather than describes, the objective, purely dynamic economic process.

More positively, the channels account for booms and slumps, for inflation and deflation, for changed rates of profit, for the attraction found in a favorable balance of trade, the relief given by deficit spending, and the variant provided by multinational corporations and their opposition to the welfare state. [CWL 15, 17]

It is a normative theory in which new money should enter through the Supply Functions (through (S’ – s’O’) and (S” – s”O”).

… positive or negative transfers to basic demand (D’-s”I’) and consequent similar transfers to surplus demand (D”-s”I”) belong to the theory of booms and slumps.  They involve changes in (aggregate basic or aggregate surplus) demand, with entrepreneurs receiving back more (or less) than they paid out in outlay (which includes profits of all kinds).  The immediate effect (of these aberrational monetary transfers) is on the price levels at the final markets, and to these changes (in price), enterprise as a whole responds to release an upward (or downward)  movement of the whole economy.  But the initial increased transfers to demand [that is, excess transfers along (D’-s’I’)  and (D”-s”I”) ] are not simply to be supposed.  For that would be postulating without explaining the boom or slump. [CWL 15, 64]

Lonergan discovered the invariant laws of the interdependence among normative monetary flows a) within each monetary circuit, b) in the crossovers between two monetary circuits during a pure cycle of expansion, and c) in the changing ratio of basic income to surplus income as the pure cycle of expansion proceeds through its phases.  Again,

More positively, the channels account for booms and slumps, for inflation and deflation, for changed rates of profit, for the attraction found in a favorable balance of trade, the relief given by deficit spending, and the variant provided by multinational corporations and their opposition to the welfare state. [CWL 15, 17]

 Lonergan agreed with Schumpeter that the economist had to know what are the significant variables in the light of which price changes are to be interpreted.  According to Lonergan, standard economic theory had successfully achieved none of these desiderata. [CWL 15, Editors’ Introduction liii]

The ground of the intelligibility of the economic process is the intelligibility of the structure of the dynamic process of production and exchange.

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

The process is intrinsically a process of value.

(Payments) stand in a network that is congruent with the technical network of the productive process. …above all, their connection with production is immediate: they …  are, so to speak, the immanent manifestation of the productive process as a process of value. [CWL 21, 114]

MRT’s explanatory superstructure is grounded in precise analytic distinctions.  New foundational distinctions, definitions, and equations serve to ground the rigorously-deduced superstructure comprising a complete new theory.

…, when you add a new fundamental equation in macroeconomics defining a purely relational function, as Einstein did when he equated mass with energy, you get a new idea of the dynamics of the macroeconomic process.  Macroeconomic field theory is a matter of the immanent intelligibility in the field of velocitous interdependent, mutually defining functionings. [Paraphrase of CWL 10, 154]

Again, re price theory: University Economics’ price theory, isolated from any consideration of an intelligibility of pretio-quantitality, is disorienting.  Nicholas Kaldor said that the isolated price theory of University Economics amounts to “a virtual derailment of economic theory.”  The process of production and sale is intrinsically a process of the flow of valued items.  That is, price and quantity are not isolated silos having their own isolated intelligibility; they are understood as pretio-quantital velocitous unities; and the pretio-quantitalities circulate as flows of valued products in abstract explanatory channels.

the lack of ultimacy that Lonergan ascribes to prices and price theory can scarcely be overemphasized. (CWL 15, Editors’ Introduction, xlvi-xlvi)

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……….Lonergan’s interest in Kaldor’s sweeping statement was to emphasize that prices and their changes are not explanatory but accountants’ entities.  For a first approximation of what Lonergan means here, let us draw an analogy to empirical scientific inquiry.  The physicist’s antecedent job of measuring and plotting measurements on graphs in physical science might be compared to tracing movements of prices as the exchange economy ebbs and flows.  What Lonergan has called ‘grasping in the scattered points the possibility of a smooth curve,’ or determining an indeterminate function in physics, would then be comparable to working out an economic theory that specifies the channels through which money circulates. Lonergan insists that the mechanism of the pricing system does not furnish economists with distinctions among significant variables of aggregate surplus (or producer-goods) and basic (or consumer-goods) supply and demand with their determinate yet flexible velocities and accelerations, any more than Galileo Galilei’s discrete measurements of distances and times at the Tower of Pisa of themselves provided the law of the acceleration of falling bodies…….the lack of ultimacy that Lonergan ascribes to prices and price theory can scarcely be overemphasized. (CWL 15, Editors’ Introduction, xlvi-xlvi)

Establishment University Macroeconomics tends to regard price changes as external shocks rather than inner constituents.  But price changes are to be understood and interpreted in the light of the significant internal flows which constitute the dynamic economic process.  These flows are dynamical pretio-quantital flows of valued products where P represents so many units of value and Q represents a velocitous flow of factors having relativistic, price-quantity values.  Thus, the economist has to know what are the significant variables in the light of which price changes are to be interpreted relativistically.

Once again, more fully,

Lonergan agreed with Schumpeter on the importance of a systematic or analytic framework in order to explain, rather than merely record or describe, the aggregate phenomena of macroeconomics; he agreed with Schumpeter that to be able to explain the booms, slumps, and crashes of the trade or business cycles the economist’s analysis had to be as dynamic as the subject matter under investigation; and he agreed l

.IV. The Basic Price Spread Explaining the Co-ordinated Relativity of Three Major Terms and the Co-operative Relativity of Price and Quantity Within Each Major Term

 

Keeping in mind D. Hilbert’s method of implicit definition and focusing on one of Lonergan’s implicit equations, let us explore the idea of price and quantity as relativistic price-quantity explaining the economic process.  Though “price” and “quantity” are everyday, commonsense, concrete, descriptive terms, they take on new meaning by being redefined so as to function as general and abstract, technical and explanatory terms.  They are redefined according to the general and abstract functional relations in which they stand relative to one another in explanatory flows.  And these functional relations are grounded in the very structure of the velocitous productive process of making and exchanging.

A key relation embedded in the Diagram of Rates of Flow (above) found on p. 55 is the Basic Price-Spread Ratio, treated on pages 156-62.  Its interpretation shines a bright light on all that Lonergan has said, especially regarding prices, on pages prior to page 156.

The question of prices, though first in the IS-LM and AD-AS models, is last in Lonergan’s analysis.  Price changes must be interpreted in the light of the significant explanatory relations among interdependent, implicitly-defined, concomitant functional flows.

The question of prices, then, last in Lonergan’s analysis of the closed economy, is faced within the developed dynamic perspective. (McShane 1980, ?)

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

Consider:

• P’Q’ = p’a’Q’ + p”a”Q”   (See all of CWL 15, 157-78)
• Value = value + value  (intrinsically a process of values)

derivatively, dividing by p’Q’

P’/p’ = a’ + a”(p”Q”)/(p’Q’)      [CWL 15, 156-58] ,

or in conveniently simple symbols,

J = a’ + a”R       [CWL 15, 156-58]

and differentiating,

d(P’/p’) = dJ = da’ + a”dR + Rda”       [CWL 15, 158]

A heuristic analysis of dJ/dt over the phases of the an economic expansion reveals cyclic fluctuations on the basic price spread … [McShane, 1980, 127-128]

We may read this field-theoretic, macroeconomic-identity equation

P’Q’ = p’a’Q’ + p”a”Q”   (CWL 15, 157-78)

from left to right, right to left, or back and forth between right and left.  The equals sign is imperious.  Though there is flexibility and variability in price and quantity on both sides, by the principles of continuity, concomitance, and solidarity, each side implicitly defines and continuously determines the other.  From left to right, Expenditures-Receipts for basic products, P’Q’, define  and determine the sum of concomitant “macroeconomic costs”, (c’O’ = p’a’Q’) and( c”O” = p”a”Q”), as they are defined.  From right to left, basic and surplus Outlays-Costs constitute the left-side Incomes which define and determine what is concomitantly Expenditures-Receipts for basic products.  Travelling back and forth between left and right, the equals sign mandates the reciprocal constraining or expansive influence on one another of pretio-quantial Expenditures-Receipts constituting cash revenues and pretio-quantital Outlays-Incomes constituting basic cash incomes.

We thus suggest for the Basic Price-Spread Ratio what R. d’Inverno suggests with respect to general relativity,

G_ab= 8πT_ab

1. 1. The field equations are differential equations for determining the metric tensor g_ab from a given energy-momentum tensor T_ab. Here we are reading the equations from right to left.  … one specifies a matter distribution and then solves the equations to ascertain the resulting geometry.
   2. The field equations are equations from which the energy-momentum tensor can be read off corresponding to a given metric tensor g_ab. Here we are reading the equations from left to right.
   3. The field equations consist of ten equations connecting twenty quantities, namely, the ten components of g_ab and the ten components of T_ab. Hence, from this point of view, the field equations are to be viewed as constraints on the simultaneous choice of  g_ab and T_ab.  This approach is used when one can partly specify the geometry and the energy-momentum tensor from physical considerations and then the equations are used to try and determine both quantities completely. [d’Inverno, 1992, 169]

The determinations of either side can be used by the scientist to solve the other side.  The analyst may measure some key explanatory price-quantity flows to deduce the pretio-quantital unities of other explanatory price-quantity flows.  Any discrepancies may be understood as credit in its abstract meaning of bridging the gap between payments made and payments received.  Thus, the scientific explanatory significance of credit.

Again, in Lonergan’s implicit field equation, P’Q’ = p’a’Q’ + p”a”Q”  [CWL 15,156-62], the three major terms are implicitly defined by the relations in which they stand with one another .  We may read from left to right, right to left, or back and forth between right and left.

Further, “coincidental” prices and quantities (determinations within being – Reference) must be understood in the light of the three major price-quantity terms.  Prices are not external givens; and their changes are not to be interpreted non-scientifically as external shocks.  Prices and their changes are to be “interpreted in the light of the three major significant explanatory flows” of which they are co-operating constituents  Once again,

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

.V. The Macroeconomic Field Theory Equations

• R’ = E’     (CWL 15, 54)
• R” = E”      (CWL 15, 54)
• I’ = O’ +M’      (CWL 15, 54)
• I” = O” +M”     (CWL 15, 54)
• G = c”O” –i’O’   (CWL 15, 54)
• G = c”O” –i’O’ = 0     the condition of dynamic equilibrium   (CWL 16, 50)
• M’ = (S’ – s’O’) + (D’ – s’I’) + G   (CWL 15, 54)
• M” = (S” – s”O”) + (D” – s”I”) – G   (CWL 15, 54)
• (S’-s’O’) = ΔT’ + (O’ – R’) + ΔR’   (CWL 16, 67)
• (S”- s”O”) = ΔT” + (O” – R”) + ΔR”   (CWL 16, 67)

Thus for example, assuming G = 0, and by the principle of concomitance and by the functional role of credit to bridge time gaps, we have for the basic circuit the relations of functional flows among themselves:

• R’ = E’ = I’ = O’ +M’
• R’ = E’ = I’ = O’ +[S’ – s’O’] + [D’ – s’I’]
• 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.  The Bureau of Economic Analysis and The Federal Reserve – even if it makes them unpopular – can use these to a) replace Gross domestic Product, GDP, as the primary reference for management of the economy, b) assess current operations, and c) advise the Executive and Legislative Branches and the commercial banking system.

Banks are not there to “force their money upon people,”⁴ nor “do they congratulate themselves if they are loanedup.”⁵  A banking committee is not “an automaton” but understanding and attentive to purpose and situation, “ judging chances of success of each purpose and, as means to this end, the kind of man the borrower is, watching him as he proceeds …”⁶  “It should be observed how important it is for the system of which we are trying to construct a model, that the banker should know, and be able to judge, what his credit is for and that he should be an independent agent.  To realize this is to understand what banking means.”⁷  “the banker’s function is essentially a critical, checking, admonitory one.  Alike in this respect to economists, bankers are worth their salt only if they make themselves thoroughly unpopular with governments, politicians and the public.  This does not matter in times of intact capitalism.  In the times of decadent capitalism, this piece of machinery is likely to be put out of gear by legislation.”⁸  McShane, Philip (quoting Joseph Schumpeter’s Business Cycles I and II) Implementing Lonergan’s Economics, in The Lonergan Review, Culture Science and Economics, Vol. III, No 1, Spring 2011, Seton Hall University, pp. 196-204

The analysis has become an analysis of the intellibibility of pretio-quantital monetary flows – P’ times Q’, p’ times a’Q’, and p” times a”Q”.  It has become “circulation analysis,” and thus the subtitle of CWL 15, “An Essay in Circulation Analysis.”  

See Lonergan’s “macroeconomic field Theory” (MFT), AKA “Functional Macroeconomic Dynamics” (FMD)

See Explanation By Gross domestic functional Flows to Supplement description By Gross Domestic Product.

.VI. Concerning Verification

Initially the explanatory theory would be considered a hypothesis to be verified by empirical tests.  The hypothesis would be the immanent intelligibility in the correlations among the data of the empirical tests.

… clearly, if the law of falling bodies is verified, it is not experienced.  All that is experienced is a large aggregate of contents of acts of observing.  It is not experience but understanding that unifies the aggregate by referring them to a hypothetical law of falling bodies.  It is not experience but critical reflection that asks whether the data correspond to the law and whether the correspondence suffices for an affirmatiom of the law.  It is not experience but a reflective grasp of the fulfillment of conditions for a probable affirmation that constitutes the only act of verifying that exists for the law of falling bodies; and similarly it is a reflective grasp of the unconditioned that grounds every other judgment. (CWL 3, 671/694)

There is a virtually unconditioned that has its conditions fulfilled solely by acts of defining and postulating; such is the analytic proposition.  To this virtually unconditioned there can accrue a further fulfillment inasmuch as what it defines and what it postulates also prove to be virtually unconditioned; such is the analytic principle.  This further fulfillment arises in concrete judgments of fact, such as occur in the process of verification; and so our position resembles that of the logical positivists.  But resemblance need not be identity.  For unlike the logical positivists, we are completely disillusioned of the notion that knowing is somehow looking at what is already out there now.  Unlike them, we have much to say about the unconditioned and, indeed it is in the unconditionedthat we place the whole meaning and force of verification.  (CWL 3, 671-72/694)

.VII. Miscellaneous Selections

We list below a few excerpts buttressing what we have said above implying that, as Einstein redefined commonsense notions of space and time as 4-d spacetime, so Lonergan redefines price and quantity as relativisticprice-quantity or pretio-quantitality.  A circulatory flow of, say, $100.00 may be comprised of 5 units times $20.00 each, or 25 units times $4.00 each.  The quantities and prices are co-operative and relative to one another; so to speak, entrepreneurs make them contend with one another inside the three major implicit price-quantity flows. Consumers may use their incomes of $100.00 to purchase as much of whatever they want with as much income as they have.  And units of enterprise may direct their Outlays – which become Incomes – to different combinations of inputs.  And, since goods and services are each theoretically indistinct point-to-point in the basic circuit, any distinction between goods and services is non-explanatory and specious. Pointing the reader to further appreciation of the relativistic character of prices and quantities.

Previously I have suggested a lack of adaptation in the free economies to the requirements of the pure cycle.  What that lack is can now be stated.  It is an inability to distinguish between the significance of a relative and an absolute rise or fall of monetary prices.  A relative (i.e. “real”) rise or fall (in prices between and among products) is, indeed, a signal for a relatively increased or reduced production (of one product relative to another)………(much)……..Inversely, the rising prices of the surplus expansion are not real and relative but only monetary and absolute rising prices (resulting from an increase of p”Q”/p’Q’); to allow them to stimulate production (beyond the bounds determined by technical coefficients) is to convert the surplus expansion into a (substantially artificial) boom (which must be followed out of systematic necessity by a corrective and devastating slump-recession-depression).  This I believe is the fundamental lack of adaptation to the productive cycle that our economies have to overcome.  The problem, however, has many ramifications of which the most important is the relativity of the significance of profits.  To this we now turn.  (CWL15, 139-140)

(JMC Insert something re I”/ (I’ + I”))

Insert reference to the road up and down are the same

The principles and laws of macroeconomics are invariant; they are general and universally applicable in any political system at any stage of advancement.

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]

 Paraphrasing:

As pure conjugates, quantities and prices are remotely defined implicitly by the postulate that the principles and laws of macroeconomic dynamics are invariant generally, under expansions and contractions of production, and continuous transformations of the money scale factor. And basic quantities and prices are proximately defined implicitly by P’Q’ = p’a’Q’ + p”a”Q” of the turnovers in the interval (roughly the money supply; think of the transformations of the money scale factor effected by Quantitative Easing’s (D – s’I)) or invention, innovation, proportionate expansion, surplus expansion, basic expansion in a long-term pure cycle of expansion. [CWL 3, 84/108]

In General Relativity, the gravitational field is determined by solving the Einstein field equations ¹⁰  where the metric tensor is g_ab, 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]

• G = (8πG/c⁴)T
• or
• G_ab = 8πT_ab  (where G/c4 = 1)

In macroeconomics, the (“gravitational”) exigence pulling the process in towards equilibrium (G = c”O” – I’O’ = 0) is determined by solving, measuring and applying Lonergan’s field equations .  (See  [Burley, 1992-2])

A condition of circuit acceleration was seen in section 15 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 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]

 Minkowski provided another interpretation of extensions and durations:

A third interpretation (of extensions and durations) is in terms of Minkowski space.  It asserts that, within the context of Special Relativity, it is a blunder to suppose that a difference of position is a merely spatial entity or that a difference of time is a merely temporal entity.  Hence, a standard rod is spatio-temporal: it is not merely a distance between two positions; it is a difference between a position , x₁, at a time, t₁,  and a position, x₂, at a time t₂.  Similarly, a standard clock is spatio-temporal: it does not assign merely temporal differences; it assigns a difference between a time, t₁, at a position, x₁, and a time, t₂, at a position x₂.  Moreover a unit on any standard rod determines one and the same invariant spatio–temporal interval for all frames of reference, namely, unity; and a unit on any standard clock determines one and the same invariant spatio-temporal interval for all frames of reference, namely, ic.  However, while standard rods and clocks determine the same spatio-temporal intervals for all frames of reference, still these invariant intervals divide differently into spatial and temporal components in different frames of reference. [CWL 3, 163-64/186-7]

Paraphrasing:

… it is a blunder to suppose that a difference of price is a merely pretial or that a difference of quantity is merely quantital.  Hence, by the necessity implicit in and constituted by P’Q’ = p’a’Q’ + p”a”Q”, a change in price is relativistically pretio-quantital: it is not merely a change between two prices; it is a difference between a quantity , q₁, at a price, p₁,  at t₁, and a quantity, q₂, at a price, p₂, at t₂.  Similarly, a circulatory flow is pretio-quantital: it does not assign merely temporal differences; it assigns a difference between a quantity, q₁, at a price, p₁, at a time, t₁, and a quantity, q₂, and price, p₂, at time, t₂. [CWL 3, 163-64/186-7]

(JMC shorten the next 2 paragraphs and incorporate in previous “gravitational exigence”)

In macroeconomics’ relativistic field theory, (generalized theory of macroeconomics), the concomitant flows of the diagram and the condition of equilibrium play the role of the quasi-gravitational attraction for which the process has an exigence; and the lagged technical accelerator, k_n [f’_n(t-a)-B_n] = f”_n-1(t) – A_{n-1  (CWL 15, 37)}, plays the role of the system’s non-conservative potential. In Macroeconomic Field Theory, the purely relational theory expressing an idel p[ure cycle and a condition of equilibrium is determined in any particular case by measuring explanatory flows and by solving the macroeconomic field equations.

The curvature of space, G_ab, due to the existence of matter, and the energy-momentum tensor, T_ab, implicitly define and implicitly determine one another by their functional relations to one another.  Similarly, in the double-circuited, credit-centered, concrete economic process, the condition of equilibrium and the immanent form called the lagged technical accelerator implicitly determine one another by their functional conditioning of one another.

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= Σg_ijdx_idx_j           [i, j = 1,2…n]

where dx₁, dx₂… are differentials of the coordinates, and where in general there are n²products 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. …  Thus in the familiar Euclidean instance, g_ij is unity when i equals j; it is zero when i does not equal j; and there are three dimensions.  In Minkowski space, the g_ij is unity or zero as before, but there are four dimensions, and x₄ equals ict. In the General Theory of Relativity, the coefficients are symmetrical, so that g_ij equals g_ji; and in the Generalized Theory of Gravitation, the coefficients are anti-symmetrical.   [CWL 3, 146 -147/170-71] [#41]

.VIII. Conclusion

To conclude: Macroeconomic analysis is no longer the simple graphing of snapshots of external price levels or interest-rate levels and their supposed determination of momentary interactions of supply and demand.  It has become an analysis of the relativistic relations among circulatory pretio-quantital monetary flows – P’ times Q’, p’times a’Q’, and p” times a”Q”.  It has become “relativistic circulation analysis,” and, thus, the subtitle of CWL 15, “An Essay in Circulation Analysis.”  Further, prices and quantities must each be understood only in the context of a) the interdependent flows within and between major circuits.  As Einstein redefined space and time as relativistic space-time, rather than as two separate absolute containers, so Lonergan redefines price and quantity as the relativistic price-quantity constituting explanatory flows, rather than as externally given separate and absolute containers.

Macroeconomic Field Theory explains a dynamic process. It is not a theoryof efficient cause, rather it is a theory of “immanent intelligibility” or “formal cause.” Macroeconomic field Theory involves a) a principle of concomitance of certain flows with one another, b) a theorem of continuity, c) a condition of equilibrium and solidarity among flows, d) a theorem of phased expansion, and e) an invariant set of equations isomorphic with the relativistic structure of the double-circuited, credit-centered process of expansionary production and exchange.