Insight Into The “Baseball Diamond”: Discovery For Implementation

As both Aristotle and Lonergan acknowledged, forms are grasped by mind in images.

τα μεν ουν ειδη το νοητικον εν τοις φαντασμασι νοει

[Aristotle, De Anima, III, 7, 431b 2] and [CWL 3, title page]

Forms are grasped by mind in images  [CWL 3, 677]

Under Key Notions we have treated The Necessity of a Diagram .

Thus, if we want to have a comprehensive grasp of everything in a unified whole, we shall have to construct a diagram in which are symbolically represented all the various elements along with all the connections between them. [McShane 2014, 11 (quoting CWL 7, 151)]

Further below we will list thirty-one insights the reader should have to fully appreciate all that is contained in the Diagram of Rates of Flow.

Diagram of Rates of Flow 2

Insight into image yields understanding.  The reader must have his own insight into the Baseball Diamond and into other key images of Functional Macroeconomic Dynamics.  No one can do it for him.  The act of understanding yielding interrelated terms must be achieved by the student.  Our primary purpose is not simply to “talk about” insight and “talk about” the Baseball Diamond; rather it is to cajole the reader to strain for his own insight into that and other images and, thereby, to grasp and possess in his habitual mentality the full and enriching intelligibility of Functional Macroeconomic Dynamics; and further, to put his understanding to effective use in the world in which he lives.

A picture is worth a thousand words.  A single formula is worth a ton of prose.  Three foundational equations in particular virtually contain 176 pages of instruction.  The formulation of the composition of a product by compensated factors of production

qi= Σqijk  [CWL 15, 30]

plus the formulation of basic expenditures implicitly defining “macroeconomic costs”

P’Q’ = p’a’Q’ + p”a”Q” [CWL 15, 158]

plus the lagged technical accelerator

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

compactly contain 176 pages of laborious instruction in CWL 15. The reader must stop, stay, review, and start over until he understands the full foundational significance of the equations.

The images in CWL 15 are of heuristic and explanatory significance. All the various velocitous flows, interdependencies, and connections constituting the understanding of the economic process are symbolically represented in these images.

The aim of discursive reason is to understand; and it arrives at understanding not only by grasping how each conclusion follows from premises, but also by comprehending in a unified whole all the conclusions intelligibly contained in those very principles. … Thus, if we want to have a comprehensive grasp of everything in a unified whole, we shall have to construct a diagram in which are symbolically represented all the various elements (of the current dynamic process) along with all the connections between them. [McShane 2014 11 (quoting CWL 7, 151)]

For the human mind is such that it does not wonder about things just individually but, understanding individual elements, goes on to ask how they are connected with one another. [CWL 12, 17]

All science begins from particular correlations, but the key discovery is the interdependence of the whole. … the diagram (of a few precise aggregates) has compensating features that Quesnay’s system of simultaneous equations may imply but does not manifest. [CWL 15, 53 and 177]

The reader must distinguish between the image and the insight.  An image is an organized diagram or chart.  An insight is an act of understanding.  It is the insight into a representative image, symbolizing all the elements of explanation, which yields terms related to one another, and thus, terms of explanatory and scientific significance.  In the act of understanding all the concepts tumble out together.  The critical understanding is suggested by, but not constituted by the image; the critical understanding is in the insight into the image; for the insight constitutes the act of understanding.

Let us say, then, that for every basic insight there is a circle of terms and relations, such that the terms fix the relations, the relations fix the terms, and the insight fixes both.  If one grasps the necessary and sufficient conditions for the perfect roundness of this imagined plane curve, then one grasps not only the circle but also the point, the line, the circumference, the radii, the plane, and equality.  All the concepts tumble out together, because all are needed to express adequately a single insight.  All are coherent, for coherence basically means that all hang together from a single insight.  [CWL 3, 12/36]

… how is one to recognize some formalizations as mathematical and others as not mathematical? … the material element is what we have named the empirical residue.  There are aspects of data from which understanding always abstracts.  Such have been seen to be the individual (of pt-to-pt and pt-to-line), the continuum (of exchanges), particular places and times, and the nonsystematic divergence of actual frequency from probable expectations. … the formal element may be designated by abstraction as enriching. It has been seen that insight goes beyond images and data by adding intelligible unities and correlations and frequencies, which, indeed, contain a reference to images or data but, none the less, add a component to knowledge that does not exist actually on the level of sense or imagination. … finally, the actual element lies in the conjunction of the material and formal elements. [CWL 3, 311/  ]

To have a comprehensive insight into the Baseball Diamond is to then understand in a unified whole all the concepts implicitly or explicitly symbolized in that arrangement of interrelated elements.  It is to grasp in a single view how they fit together and implicitly determine one another.  It is to grasp the explanation of the entire closed economic process in a unified whole.

Depending on one’s momentary interest and point of view, the Baseball Diamond can be called by several names, each representing one or more of the intelligible elements of the unified whole represented in the diagram:

  • The Diagram of Two Operative Circuits Connected by Operative Crossovers
  • The Diagram of Functional Monetary Interdependencies
  • The Diagram of the Relations of Monetary Functions Among Themselves
  • The Configuration of Monetary Conditions
  • The Diagram of Operative Functional Flows of Products, Payments, and Financings
  • The Diagram of Monetary Channels
  • The Diagram of Monetary Transfers
  • The Diagram of the Monetary Correlates of the Hierarchical and Lagged, Concrete Productive Process
  • The Diagram of Interdependent, Implicitly-Defining, Mutually-Conditioning Velocitous Functional Flows
  • The Diagram of Explanatory Interconnections
  • The Double-Circuited, Credit-Centered Diagram which Sublates, Supervenes, and Replaces the Single-Circuit, Credit-Centered Diagram of Macroeconomics Textbooks
  • The Functional Framework
  • (Colloquially) The Way the Process Works
  • (Colloquially, because of its shape) Lonergan’s Baseball Diamond

The Baseball Diamond shown above reveals a normative circuitry and circulation; it prescinds from non-normative a) trade imbalances, b) government surpluses and deficits, and c) other collective surpluses and deficits, each of which can be imaged and explained by a superposed circuit lacking vital c’O’ and c”O” flows.

Let us first simply catalog, supplemental to the list of possible titles above, what we find contained in the double-circuited, credit-centered Baseball Diagram.  In so doing we shall notice that the diagram is soundly embedded in the ideas of Lonergan’s Insight, A Study of Human Understanding [CWL 3].

  • The diagram represents a current, concrete, purely dynamic process.
  • The diagonal arrows represent functional flows of money within and between operative circuits.Thus the arrows may be envisaged as channels or pipes or wires through which payments pass.
  • The flows are of so much per period; i.e. they must be represented mathematically as velocities, rather than static accumulations..
  • Because they are connected in a definite directional scheme, the arrowheaded arrows indicate the requirements of certain intracircuit flows and crossover flows keeping pace with other certain flows for continuity and for dynamic equilibrium.
  • Thus, the connections indicate interdependencies, mutual conditionings, and mutual definings.The aggregate functional flows are implicitly defined by the functional relations in which they stand with one another.
  • The terms which identify the operative functional flows of the operative circuits, such as basic and surplus incomes, macroeconomic costs and macroeconomic profits, are implicitly defined by the functional relations in which the flows stand in interdependence with one another.
  • Because science is explanation by terms related to one another, implicit definition of representative terms by the functional relations in which they stand with one another yields terms of scientific and explanatory significance.
  • Because the arrows “contain” flows of products and money, they have functional resemblance to fluid channels or electric wires; so, the reader may consult texts of Physics 101 regarding fluid dynamics or electric currents and circuits to broaden and deepen his general understanding of flows and, by understanding that the arrows signify motion, thus make the diagram “come alive” as a circulatory system, in which things are flowing according to the laws of the process’ normative explanatory intelligibility.
  • The entire diagram represents interrelated elements of Gross Domestic Functional Flows, a name we have given to an explanatory arrangement of the National Income and Product Accounts.
  • Per the lagged technical accelerator, kn[f’n(t-a)-Bn] = f”n-1(t) – An-1 , [CWL 15, 37] the surplus process in the diagram’s surplus circuit is the accelerator of the accelerated basic process in the basic circuit.  Thus in an expansion, flows in the surplus process will accelerate before flows in the basic process accelerate.
  • By imposing an expansion of the process, one may generate a “motion picture” of swelling in the surplus circuit during the surplus-expansion phase followed by a swelling in the basic circuit representing the implementation of the basic expansion.
  • Insight into the pattern of interconnected velocities yields an explanatory formulation of the interdependent velocities of the dynamic process rather than a descriptive snapshot of the process, as does Gross Domestic Product.
  • Horizontal and vertical arrows represent dealings with commercial banks, the Central Bank, and other institutions in the Redistributive Function.They represent credit (+) “into” the operative circuits and savings (-) “out of” the operative circuits.
  • Any gap of time between initial outlays and final receipts within the process involves a flow of credit.
  • These gaps include the significant gaps in a vast and complex long-term expansion and the gaps (even in a static economy) in normal turnover times symbolized in CWL 21 by Σsij =  Σvirij (See Appendix including spreadsheet)
  • Additions to the money supply necessary to enable expansion of transactions in an expanding economy emanate from the Central Banking system symbolically located in the Redistributive Function.
  • Transfers of credit to or from supply, (S’ – s’O’) and (S” – s”O”), tend to equal the sum of the increments of aggregate turnover dollar magnitudes in final payments and transitional payments. Of these, two, the increment in transitional payments will be the larger, since for each sale at the final market there commonly is a sale at a number of transitional markets.  [CWL 15, 67]
  • The conditions of dynamic equilibrium are that a) flows in circular dependence keep pace, or be concomitant, b) flows in crossover dependence balance, or be concomitant, and c) activity neither exceeds nor falls short of normative technical or technological limits.
  • The immanent intelligibility of the process represented by the diagram “alive” with flows, is to be grasped all at once, in a single sweeping insight, in which all the flows fit together in a whole characterized by concomitance within an overall unity.
  • The diagram is an image of the immanent classic intelligibility or formal cause of the process.
  • The formal cause of the process – the normative scheme of interdependent functional flows – is the primary relativity, i.e. the ideal pure cycle or central tendency, to which may be applied the coincidental secondary values of the significant variables in the non-systematic manifold – prices and quantities.
  • Activities are classified by their functional characteristics.The few functional explanatory aggregates contain the millions of productive activities and payments in the schemes of recurrence developed by human ingenuity and related to seasons, life events, etc.
  • The process is a mechanism in the sense that it has normative and internal laws of operation. Analogous to, say, the coiled spring, its intelligibility includes a central tendency and corrective mechanism.
  • The macroeconomic mechanism supersedes the microeconomic pricing mechanism which operates within the channels.
  • The economic process, given the state of culture, technology, and institutions, has the aforementioned general ideal pure cycle and a central tendency; but the process is fraught with indeterminacy.  Due to ignorance, malice, mistake or happenstance, the flow in any channel may vary independently, thus diverging from the ideal pure cycle’s central tendency and necessitating a systematic correction.
  • The monetary correlates (payments flows)of production and sale are congruent with the technical network of the process.
  • The diagram is an aid to insightful explanation in terms of flows rather than nominal descriptions. Thus a boom is explained as flows of products and prices exceeding normative technical constraints in one or both circuits. And stagflation is explained as excessive (inflationary) monetary demand in the basic circuit simultaneous with lack of adequate investment in the surplus circuit.  Thus, a boom or a slump or stagflation is not merely named or postulated with appropriate regret and handwringing, it is formally explained.  And mystery is removed.
  • Imbalances of foreign trade and government operations may be easily explained by superposed circuits lacking vital c’O’and c”O” components. Expenditures are not predicated on productive outlays that become domestic incomes. [CWL 15, 162-76]
  • The quantity of goods under process and the frequency of their turnover is mated with the dollar magnitude of payments and the frequency of payments to give a new and determinate theory of the velocity of money.
  • The “voltage” or “electromotive force” driving the mechanism is human desires motivating human work.That is, human desires and activities are the efficient cause of the process rather than the formal cause of the objective functional interdependencies.
  • But these human desires are, as it were, outside the process. The immanent intelligibility of the process is constituted by laws of operation to which human psychology must adapt.

Analysis begins from matters of fact.  Questions must be put in the right order.

… analysis begins from matters of fact, say, the conspicuous recurrence of changes in plant and equipment and the concomitance of such changes with the business cycle. Next analysis turns from such instances of concomitance to lists of successful and unsuccessful changes. Finally, from a study of such instances, by a process of trial and error, analysis aims to arrive at an ever fuller understanding of business cycles. [CWL 15, 9]

Questions cannot be put in any order whatsoever. Some questions simply cannot be answered until others have been resolved.  And sometimes the answers to one question immediately provide the answers to others. [CWL 12, 23]

… putting things in their right order is the special talent of the wise person, and so the wise person will start with the problem that is first in the sense (1) that its solution does not presuppose the solution to other problems, (2) that solving it will expedite solving a second problem, (3) that solving the first and second problems will lead right away to solving a third, and so on through all consequent connected problems. [CWL 12, 23]

Next, understanding is about principles.  A principle is defined as what is first in some order.  Therefore, it belongs to understanding to grasp the solution of that problem that is first in the order proposed by wisdom.  Since this order is such that solving the first means that the others are expeditiously solved, the understanding should be such as virtually to contain in itself the answers to the rest of the questions. [CWL 12, 23]

… the questions are put in such an order that, once the first is solved, the solutions to the others follow with almost no difficulty.  Therefore, because the later solutions are connected to the first as conclusions are connected to some principle, all solutions after the first seem to be the proper province of knowledge. [CWL 12, 25]

The matters of fact are tabulated and symbolized as elements of a diagram.

Lonergan held the diagram to have both explanatory and heuristic significance.  First, then, the later versions of the Essay in Circulation Analysis text draw ever-greater attention to the fact that 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. [CWL 15, 179-80]

The two circuits of the Baseball Diamond are in dynamic mutual dependence.  They explicitly manifest the interchanging of ‘flows.’

the existence and manner of dynamic mutual interdependence of the two circuits of payment, basic and surplus, is (purely relational and) 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, 179-80]

The Baseball Diagram aids understanding.

Forms are grasped by mind in images. (Aristotle)

… the diagram can be said to have a heuristic significance.  …Thus the diagram as itself a visual image can facilitate the occurrence of insights. For example, while the text of Section 13 works out in great detail sets of relations among terms, the diagram makes it easy to understand that the exchange economy consists of two circuits of payments, basic and surplus; that these circuits are mutually and dynamically interdependent (because of the crossovers); and that these circuits are dependent upon the activities of the redistributive function. [CWL 15, 180]

The human mind seeks understanding of the whole.

For the human mind is such that it does not wonder about things just individually but, understanding individual elements, goes on to ask how they are connected with one another. [CWL 12, 17]

Money is to buy goods and services.  Payments of money are correlated with the flows of goods and services; payments are congruent with the network of the production and provision of goods and services. The structural nature of the production of goods and services is prior in the order of understanding to the correlated payments for goods and services. Therefore, the intellectually-prior structure of the current, purely dynamic, productive process – as to factoral makeup, functional interdependencies, flow quantities, and timing – sets the pattern for the pattern of monetary flows.  The structure of the productive process is conceptually prior to, and really determinate of, the normative structure of flowings of money in the Baseball Diamond.

real analysis (is) identifying money with what money buys. … And that is the source of the problem in real analysis.  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, xxviii]

The Baseball Diamond is an aid to reaching the act of understanding of the existence and manner of dynamic mutual interdependence of the two circuits of payment, basic and surplus.

When (Lonergan’s) analysis 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 (purely relational) mathematical equation (devoid of descriptive, nonexplanatory residues) 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 (purely relational) diagram 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 (purely relational and) 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, 179-80]

The Baseball-Diamond is radically different from the single-circuit diagram found in all textbooks. How did Lonergan come up with it? Let us attempt, first,  to communicate Lonergan’s orientation and scientific heuristic, based upon his understanding of mathematics and scientific method,  second, to trace his progress to the supervening explanatory insight represented by the Baseball Diamond, and, third, to point out the usefulness of the diagram in the analysis of the economic process.

First: Lonergan’s orientation and scientific heuristic

In 1957 Lonergan published his monumental work, Insight, A Study of Human Understanding.  His understanding of scientific method and of the insights of mathematicians and scientists paved the way for his discoveries in economics.  So, it will be helpful for us to go on a brief excursion through key passages of Insight to gain an understanding of his orientation and goals in the study of macroeconomics.

Lonergan sought explanation.

Already a distinction has been drawn between description and explanation.  Description deals with things as related to us.  Explanation deals with the same things related among themselves.  The two are not totally independent, for they deal with the same thing 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.  But despite their intimate connection, it remains that description and explanation envisage things in fundamentally different manners.  The relations of things among themselves are, in general, a different field from the relations of things to us. Insight p. 291

Insight mediates between the concrete and the abstract; in science it leads to explanatory formulations of concrete processes. Insight is the mediator, the hinge, the pivot.

Because insights arise with reference to the concrete, mathematicians need pen and paper, teachers need blackboards, pupils have to perform experiments for themselves, doctors have to see patients, trouble-shooters have to travel to the spot, people with a mechanical bent take things apart to see how they work.  But because the significance and relevance of insight goes beyond any concrete problem or application, men formulate abstract sciences with their numbers and symbols, their technical terms and formulae, their definitions, postulates, and deductions.  Thus, by its very nature, insight is the mediator, the hinge, the pivot.  It is insight into the concrete world of sense and imagination.  Yet what is known by insight, what insight adds to sensible and imagined presentations, finds its adequate expression only in the abstract and recondite formulations of the sciences. [CWL 3, 6/30]

Forms are grasped by mind in images.  Forms are grasped by insight into images.  The image is necessary for the insight.

(An) image is necessary for the insight. … Points and lines cannot be imagined.  But neither can necessity or impossibility be imagined.  Yet in approaching the definition of the circle, there occurred some apprehension of necessity and of impossibility.  As we remarked, if all the radii are equal, the curve must be perfectly round; and if any radii are unequal, the curve cannot avoid bumps or dents. … Further, the necessity in question was not necessity in general but a necessity of roundness from these equal radii.  Similarly, the impossibility in question was not impossibility in the abstract but an impossibility of roundness resulting from these unequal radii.  Eliminate the image of the centre, the radii, the curve, and by the same stroke there vanishes all grasp of necessary or of impossible roundness. … But it is that grasp that constitutes the insight. It is the occurrence of that grasp that makes the difference between repeating the definition of a circle, as a parrot might, and uttering it intelligently, uttering it with the ability to make up a new definition for oneself. … It follows that the image is necessary for the insight.  Inversely, it follows that the insight is the act of catching on to a connection between imagined equal radii and, on the other hand, a curve that is bound to look perfectly round.  [CWL 3, 9/33]

The analyst works through thought experiments.  He tries in trials.  He adjusts.  The image strains.  Differences are noticed and taken into account.  On and on the analyst struggles for fully explanatory insights.

By their cooperation, by successive adjustments, question and insight, image and concept, present a solid front.  The answer is a patterned set of concepts. The image strains to approximate the concepts.  The concepts, by added conceptual determinations, can express their differences from the merely approximate image.  The pivot between images and concepts is the insight.  [CWL 3, 10/34-35]

In order to explain in a purely relational scheme rather than to describe, and in order to discover the immanent intelligibility and reason Why,  Lonergan employed the technique of implicit definition, of terms defining each other by their relations.  Implicit definition, wherein terms define one another by their relation, confers upon the terms a scientific significance. It carries one beyond the “objects which, in the first instance, one happens to see and be thinking about” to a deeper level of abstraction and formal understanding. In economics, it frees one from thinking only about the first-instance objects that occupy one’s mind every day such as wages, wealth, interest, etc., and it pushes one towards theory and explanatory science.

Hilbert has worked out Foundations of Geometry that satisfy contemporary logicians. One of his important devices is known as implicit definition. Thus the meaning of both point and straight line is fixed by the relation that two and only two points determine a straight line.  In terms of the foregoing analysis, one may say that implicit definition consists in explanatory definition without nominal definition. It consists in explanatory definition, for the relation … is a postulational element such as the equality of all radii in a circle.  (Implicit definition) omits nominal definition, for one cannot restrict Hilbert’s point to the Euclidean meaning of position without magnitude. … The significance of implicit definition is its complete generality (and potential applicability).  The omission of nominal definition is the omission of a restriction to objects which, in the first instance, one happens to be merely thinking about.  The exclusive use of explanatory or postulational elements concentrates attention upon the set of pure relationships in which the whole scientific significance is contained. [CWL 3, 12/36]

The scientist – in economics or physics – must go beyond “classification based on sensible similarity” or “objects which, in the first instance, one happens to be thinking about” to some set of relationships which explain the system.

Galileo inaugurated modern science by insisting that the nature of weight was not enough; from sensible similarity, which resides in the relations of things to our senses, one must proceed to relations that hold directly between things themselves.  [CWL 3, 38/62]

By his orientation to explanatory science and by using the technique of implicit definition, rather than merely nominal definition, Lonergan set out to discover principles and laws of economics which are the same for all observers in all cases, be they liberal or conservative, libertarian or socialist, rich or poor, republican or democrat, operating in a system of free enterprise or centralist bureaucracy, just as the laws of physics are the same for all observers regardless of their frame of reference.  These principles and laws would apply to all economies regardless of the citizenry’s dominant psychological bent or the particular system of government.

Mathematics is concerned with pure relation; and science, be it physics or economics, employs the pure relationships in mathematical forms to express the relations yielded by insight into the tabulated measurements of concrete data.

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

The theorist in mathematics or physics or, in our case, macroeconomics is creative, constructive, and intellectually proactive, anticipating the ideal or pure or typical or limiting case.  With this orientation, Lonergan discovered the “pure cycle” symbolized and imaged in part in the Baseball Diagram and in Figures 24-4, 24-6, and 24-7 and symbolized and formulated mathematically in the basic formalisms on pages 30, 37, and 48-54 for which the entire economic process has an exigence.

While practical people wait for concrete situations to arise before attempting to work out their consequences, theoretical minds are given to anticipating ideal or typical cases and to determining how a deduction could be carried out in each case. [CWL 3, 46/70]

Now in these anticipatory concrete inferences a different type of insight comes into play.  For in the practical inference the situation determines the relevant insight and the insight determines the selection, combination, and particularization of laws.  But in the anticipatory inference insight is creative and constructive.  It is not hampered by any given situation.  Rather it tends to be free exploration of the potentialities of known laws, and its principal fruit is the formulation of ideal or typical processes that are dominated throughout by human intelligence. [CWL 3, 47/70-71]

In the end, the economic scientist reaches a supervening insight in which all tabulated data are explained by a single perspective and form.  In the case at hand, the image of functional interdependencies into which the scientist has insight happens to resemble a baseball infield, which represents the functional interconnections of velocitous and accelerative monetary flows. The relating of terms purely among themselves is what confers upon the result the significance of science.

Moreover, once initial difficulties are overcome and basic insights are reached, the investigation approaches a supreme moment when all data suddenly fall into a single perspective, …[CWL 3, 47/71]

How did Lonergan come up with the Baseball Diamond?

Lonergan brought the orientation of a mathematician and scientist to the study of economics.  He successively adjusted question and insight, image and concept.  He tweaked the image; tried different arrangements; his image strained to approximate the concepts by added conceptual determinations and expressed their differences from the merely approximate images.  His insight pivoted between the images and the concepts, until Eureka!, the Baseball Diamond.  And this orientation coupled with a lot of reading and the light of genius carried him beyond all previous work in economics to an adequate level of abstraction and a scientific understanding of the objective economic process.  And this understanding can now supply an heuristic guide to any analysis of historical and current data.

While analysis begins from matters of fact,

… analysis begins from matters of fact, say, the conspicuous recurrence of changes in plant and equipment and the concomitance of such changes with the business cycle. Next analysis turns from such instances of concomitance to lists of successful and unsuccessful changes. Finally, from a study of such instances, by a process of trial and error, analysis aims to arrive at an ever fuller understanding of business cycles. [CWL 15, 9]

Lonergan gives credit to and quotes Schumpeter regarding the advantages of a diagram, particularly in the understanding of macroeconomics:

it will be well at once to draw attention to J.A. Schumpeter’s insistence on the merits of the diagram as a tool. (Schumpeter,History 240-43, on the Cantillon-Quesnay tableau.) … First, there is the tremendous simplification it effects.  From millions of exchanges one advances to precise aggregates, relatively few in number, and hence easy to follow up and handle. … Francois Quesnay’s tableau economique. … was the first to make explicit the concept of economic equilibrium.  All science begins from particular correlations, but the key discovery is the interdependence of the whole. … the diagram (of a few precise aggregates) has compensating features that Quesnay’s system of simultaneous equations may imply but does not manifest. [CWL 15, 53 and 177]

Lonergan’s explanatory insight reveals a threefold process which effects its expansions in phases over the full ideal pure cycle.

… In figure 14-1 the reader will notice five circles representing the monetary functions. … I would add that the aims and limitations of macroeconomics (that is, the circulation analysis presented here) 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 is attributed to a basic process, an ongoing sequence of instances of so much every so often.  The maintenance and acceleration (positive or negative) 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 are concentrated in a redistributive function, whence may be derived changes in the stock of money dictated by the acceleration (positive or negative) in the basic and surplus stages of the process. … So there is to be discerned a threefold process in which a basic stage is maintained and accelerated by a series of surplus stages, while the needed additions to or subtractions from the stock of money in these processes is derived from the redistributive area. … it will be possible to distinguish stable and unstable combinations and sequences of rates in the three main areas and so gain some insight into the long-standing recurrence of crises in the modern expanding economy. [CWL 15, 53-54]

Having constructed a diagram of the functions and their interrelations, and having analyzed the structure of the productive process, and having preliminarily discerned and described five monetary functionings, or functions, in a threefold process with interdependencies, Lonergan was able to relate these purely dynamic functionings or functions to one another in his Diagram of Rates of Flow.

Other images and attendant insights which are essential to Functional Macroeconomic Dynamics are, in CWL 15, Figures 24-4, 24-6, 24-7, and 27-1, plus the basic formalisms:

qi= Σqijk  [CWL 15, 30]

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

P’Q’ = p’a’Q’ + p”a”Q”  [CWL 15, 302]

Σsij  =  Σvirij   [CWL 21, 170]

I’ = Σwiniyi   [CWL 15, 134]

f = vw   [CWL 15, 148]

J = a’ + a”R   [CWl 15, 158]

How do we put our understanding to good use in the world?

Now, how do we all put our understanding to use?  How do we implement Functional Macroeconomic Dynamics?