The Necessity of a Diagram

Lonergan brought knowledge from several other fields which was foundational to his work on Functional Macroeconomic Dynamics.  During our writing of these pages, two different ideas frequently occurred to the authors: 1) it was important to communicate the key background that Lonergan brought to Functional Macroeconomic Dynamics from mathematics and the sciences, and 2) perhaps specialists in pure and applied mathematics and physics, rather than economists, might be better candidates for understanding and appreciating Lonergan’s work.  If the readers themselves had backgrounds adequate to appreciate the full context of Functional  Macroeconomic Dynamics, they would be more intrigued and interested.  How could the person who authored Insight not be innovative, perhaps revolutionary, when he sought to discover a scientific macroeconomics?  So, we say some background things about a) insight into diagrams and images, b) the importance of images to Einstein and other physicists, and c) the theoretical breakthrough represented by the particular diagram entitled Diagram of Rates of Flow.

In large and complex questions of natural science, macroeconomics, and other subjects, comprehension of everything in a unified whole cannot be achieved without the aid of a diagram-image-phantasm which represents the relations.[1]

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.  [CWL 15, 54]

This comprehending of everything in a unified whole can either be formal or virtual.  It is virtual when one is habitually able to answer readily and without difficulty, or at least ‘without tears,’ a whole series of questions right up to the last ‘why?’  Formal comprehension, however cannot take place without a turning to phantasm; but in larger and more complex questions it is impossible to have a suitable phantasm unless the imagination is aided by some sort of diagram.  Thus, if we want 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 question along with all the connections between them. [CWL 7, 151]

We show several diagrams.  In particular,  we show Lonergan’s Diagram of Rates of Flow in several sections of this website.  The image provides part of the framework for all of Functional Macroeconomic Dynamics.

Depending on one’s momentary interest and point of view, the Baseball Diamond can be called by several names, each indicative of an important intelligibility and the inner richness of the diagram:

  • The Diagram of Two Operative Circuits Connected by Operative Crossovers
  • The Diagram of Functional Monetary Interdependencies
  • The Diagram of Operative Functional Flows of Products, Payments, and Financings
  • The Diagram of Monetary Transfers
  • The Diagram of Monetary Channels
  • The Diagram of the Monetary Correlates of the Productive Process
  • The Diagram of Interdependent, Implicitly-Defining, Mutually-Conditioning Velocitous Functionings
  • The Diagram which Sublates, Supervenes, and Replaces the Single-Circuit Diagram of Macroeconomics Textbooks
  • The Functional Framework
  • (Colloquially, because of its shape) Lonergan’s Baseball Diamond

The diagram prescinds from trade imbalances and government surpluses and deficits and other collective surpluses and deficits, which can be imaged by superposed circuits lacking vital c’O’ and c”O” flows.  These superposed circuits are usually not noticed, much less understood.

The Diagram of Rates of flow is an image into which one can have an insight so as to understand Functional Macroeconomic Dynamics in a unified whole.  In one’s complete appreciation of this diagram, all the concepts such as basic, surplus, costs, pure surplus income, velocities, accelerations, interdependencies, mutual conditionings, operative circuits, credit, savings, and non-operative exchanges tumble out together.  While other diagrams are needed to comprehend everything in a unified whole, this diagram is key.

Please read carefully the narrative beneath the image.

In Insight, A Study of Human Understanding, as an indication of the importance of the image to the insight in the doing of science, Lonergan chose for the epigraph Aristotle’s statement, in translation, “ …forms are grasped by mind in images.” [2]

In the Preface to CWL 3, Lonergan introduces his study of the phenomenon called insight:

(Insight is) a quite distinct activity of organizing intelligence that places the full set of clues in a unique explanatory perspective. [CWL 3, ix/3-4]

Insight …  is the supervening act of understanding. [CWL 3, ix/3]

… the aim of the work is to convey an insight into insight. [CWL 3, ix/4]

… inasmuch as (insight) is the act of organizing intelligence, insight is an apprehension of relations. [CWL 3, x/4]

…(insight) adds to the merely given an explanatory unification or organization. [CWL 3, x/5]

In a particular illustration of an insight into an image, Lonergan invoked the image of a cartwheel with its hub and spokes.

The third observation is that the 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. … 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, 8-9/31-2]

All the concepts yielded by the insight into the image (in this case the plane curve) tumble out together, satisfying both the epistemological principle and the canon of complete explanation that a complete explanation forms a closed system, i.e. a coherent aggregate of functional relations.[3]

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]

In one’s grasp of a circle, all concepts tumble out together: point, line, circumference, radii, the plane, and equality.  In like manner, in one’s grasp of the intelligibility immanent in the Diagram of Rates of Flow, all the concepts tumble out together.  In one’s grasp of the functionings constituting the schematic image, one grasps simultaneously the following concepts: rates of flow, basic goods, surplus maintenance goods, surplus expansionary goods, costs, pure surplus income, the supply functions, the demand functions, the operative circuits, the crossovers between operative circuits, interdependence, circular conditioning, crossover conditioning, and the finance function.  In a complete understanding of scientific Functional Macroeconomic Dynamics, all the interrelated concepts tumble out together.  “All are coherent, for coherence basically means that all hang together from a single insight.”  They are all contained in the single sweeping insight into the diagram. This sweeping insight is a complete apprehending of relations…

 (insight) adds to the merely given an explanatory unification or organization. [CWL 3, x/5]

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]

… the diagram can be said to have a heuristic significance.  In Lonergan’s usage, ‘heuristic’ denoted the sorts of innovations that expedite the occurrence of certain acts of consciousness, particularly insights. 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 (diagrammed as the crossovers) ; and that these circuits are dependent upon the activities of the redistributive function (preferably dispensing or contracting “good credit” rather than “bad credit”). [CWL 15, 179]

The Baseball Diagram is a diagram of interdependent, implicitly and mutually defined and mutually defining, functional flows

the diagram is an aid to separating and understanding functions.  The circles are not places, nor are they, say, groups of capitalists, workers, bankers, exporters. … The diagram represents the functional journeys. [McShane, 1995, 79]

The flowings within the channels are normatively to be equilibrated so that, in general, conditions are satisfied as flows in circular condition keep pace, flows in crossover condition balance, magnitudes and frequencies are in accord with potentials and limiting constraints of the process, and the money supply is proper for the volume of transactions, given the current state of culture, technology, and institutions.  But norms can be violated.  Flows can become disequilibrated; and the several arrows show how many possible different flows can become disequilibrated.

The absence of the normative concomitance required in the channels explains booms and slumps, stagflation, and economic crises of any sort. Because they explain, the confusion of professional academics vanishes.

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. [CWL15, 17]

This particular diagram helped Lonergan discover an explanation when Schumpeter was stumped.

Lonergan was grateful for the way Schumpeter had shown slumps and crises were related to contraction of plant and equipment, and that there were ‘a hundred theories’ on why – so that in Schumpeter’s estimation there really existed no solid explanation.  Lonergan claimed: ‘I have an explanation on that.’  In addition he said he was grateful to Schumpeter for elucidating the virtualities of Francois Quesnay’s (1694-1774) tableau economique (MD:ECA 53).  Lonergan appreciated the way the tableau(1) allowed the theorist (a) to correlate many things all at once, and not just one at a time, piecemeal; (b) to assign numbers arithmetically to the variables involved; (2) permitted insight into phantasm instead of mere speculation detached from the facts.  See Joseph A. Schumpeter, History of Economic Analysis 222-23, 241-43.  Lonergan’s own use of his five-point diagram indicates just how seriously he took the need for adequate diagrams.  See ‘Appendix History of the diagram, 1944-1998’ below, pp 177-202 [CWL 15, Editors’ Introduction, ftnt 86, liii]

Lonergan’s diagram of two circuits connected by crossovers replaces the conventional single-circuit diagram of all macroeconomic textbooks.[4] His channels of circulation (of monetary aggregates) replace the overall dominance claimed for general equilibrium theory, but they reveal the condition under which partial equilibrium can exist. … More positively, the channels account for (explain) 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]

Fully:

I have spoken of the analysis revealing channels and bringing to light an undertow.  My meaning may become clearer by referring to the distinction sometimes made between general equilibrium (Walras, Wicksell) and partial equilibrium (Marshall).  The channels of circulation (of monetary aggregates) replace the overall dominance claimed for general equilibrium theory, but they reveal the condition under which partial equilibrium can exist. … More positively, the channels account for (i.e. they explain) 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]

Again, Lonergan’s two-circuit diagram represents a theoretical breakthrough.  It replaces the single-circuit diagram of the textbooks.

Lonergan started with a dominant one-flow economic analysis –  think in terms of the household-firm diagram  –  and separated it into two flows “to form a more basic concept and develop a more general theory.” 21  [McShane, 2017, viii] … much …The distinction was never built scientifically (by other economists) into a systematics of dynamic economics [McShane, 2017, viii; ftnt 22]

Academic economists have missed it.

The entire tradition slipped past Lonergan’s simple move.  I describe the move as paralleling Newton’s move. Newton started within an old culture of two flows: an earthly flow and, to recall ancient searchings, a quintessential flow.  Newton went from two to one.  Lonergan started with a dominant one-flow economic analysis  –  think in terms of the household-firm diagram  –  and separated it into two flows “to form a more basic concept and develop a more general theory.” 21  [McShane 2017, viii]; also see CWL 21, 11]

[1] re phantasm (φαντασμα, ατος, το):  A diagram is a visual image.  In past times, a simple mental representation of a real or supposed object could be called a phantasm.  There might be no necessary association with fantasy, ghosts, or delusions.  It meant simply an image.  So, please be tolerant of our occasional retention of the word phantasm.  It is used in the following excerpt.  Though somewhat archaic, it is occasionally useful.[1]

Lonergan was grateful for the way Schumpeter had shown slumps and crises were related to contraction of plant and equipment, and that there were ‘a hundred theories’ on why – so that in Schumpeter’s estimation there really existed no solid explanation.  Lonergan claimed: ‘I have an explanation on that.’  In addition he said he was grateful to Schumpeter for elucidating the virtualities of Francois Quesnay’s (1694-1774) tableau economique (MD:ECA 53).  Lonergan appreciated the way the tableau(1) allowed the theorist (a) to correlate many things all at once, and not just one at a time, piecemeal; (b) to assign numbers arithmetically to the variables involved; (2) permitted insight into phantasm instead of mere speculation detached from the facts. See Joseph A. Schumpeter, History of Economic Analysis 222-23, 241-43. Lonergan’s own use of his five-point diagram indicates just how seriously he took the need for adequate diagrams.  See ‘Appendix History of the diagram, 1944-1998’ below, pp 177-202 [CWL 15, Editors’ Introduction, ftnt 86, liii]

[2]CWL 3, 677/699-700

[3]CWL 3, 583/

[4]See this website’s image of the double-circuited flows replacing the textbooks single-circuit flows.