Formal Similarities of Space-Time in Physics and Pretio-Quantitality in Functional Macroeconomics

The basic postulate of Special Relativity is that the mathematical expression of physical principles and laws is the same for all observers under inertial transformations. Similarly, in Functional Macroeconomic Dynamics, the mathematical expression of macroeconomic principles and laws is the same for all observers regardless of their frame of reference being psychological, psychopolitical, producer-analytic, or consumer-analytic.

Hence, if physical principles and laws are independent of any movement of observers, they should be equally independent of any similar movement of reference frames. But observers may be moving with any linear or angular velocity provided the motion is continuous and provided it involves no excursions into the imaginary sections of a manifold constructed by introducing complex numbers.  It follows that physical principles and laws should be independent of similar movements of reference frames.  Accordingly, by the principle of equivalence the mathematical expression of physical principles and laws is to be expected to be invariant as long as transformation equations are functions of real variables. … To implement this conclusion, which is no more than a general anticipation based on cognitional theory, two further steps are required. [CWL 3, 41/65]

(First,) the broad invariance that we have described has to be conceived precisely in terms of tensors.  Secondly, appropriate empirical hypotheses (for the geometries of different phenomena such as gravity, electromagnetism, and heat) have to be formulated and verified. But by those steps there are reached the General Theory of Relativity and the Generalized Theory of Gravitation and incidentally it may not be amiss to note that our remote anticipation offers a simple explanation for certain aspects of those theories.  For what was anticipated was a non-relatedness of abstract laws to observers. [CWL 3, 41-42/65-6]

Paraphrasing:

The broad invariance of economics’ principles and laws that we have described has to be conceived precisely in terms of tensors for their transformation properties. Secondly, appropriate empirical hypotheses (for the geometries of different fluxes such as domestic private-flows of productive activities and monetary activities, foreign flows, and government flows) have to be formulated and verified.  But by those steps there are reached the General Theory of Economic Relativity, and incidentally it may not be amiss to note that our remote anticipation (based on cognitional theory and the abstractness of classical laws) offers a simple explanation for certain aspects of those theories.  For what was anticipated was a non-relatedness of the abstract laws of the concrete process in any standpoint.

In physics, General Relativity of  is a generalization of Special Relativity: the mutual definition of the curvature of space and the energy-momentum contains Special Relativity’s constant velocity and relegates it to an uninteresting special case. Special Relativity’s empirical hypothesis of constant velocity necessitating the relativity of extensions and durations under inertial transformations is superseded.  In macroeconomics, its General Relativity of valued flows of Exit Expenditures

( e.g. P’Q’) equaling the valued flows of Entrance Outlays (e.g. p’a’Q’ + p”a”Q”) contains and supersedes its Special Relativity of a given flow being divisible into the relativity to one another of pricings and factoral quantities.

On the one hand, it does not prevent Special Relativity from being regarded as a particular case of General Relativity, for General Relativity does not attribute any significance to constant velocity, and Special Relativity primarily regards laws reached by relating measurements to one another. … [CWL 3, 42/66]

Generalization comes with Newton, who attacked the general theory of motion, laid down its pure theory, identified Kepler’s and Galileo’s laws by inventing the calculus, and so found himself in a position to account for any corporeal motion known.  Aristotle, Ptolemy, Copernicus, Galilei, and Kepler had all been busy with particular classes of moving bodies.  Newton dealt in the same way with all.  He did so by turning to a field of greater generality, the laws of motion, and by finding a deeper unity in the apparent disparateness of Kepler’s ellipse and Galilei’s time squared. … Similarly the non-Euclidean geometers and Einstein went beyond Euclid and Newton. … The non-Euclideans moved geometry back to premises more remote than Euclid’s axioms, they developed methods of their own quite unlike Euclid’s, and though they did not impugn Euclid’s theorems, neither were they very interested in them; casually and incidentally they turn them up as particular cases in an enlarged and radically different field. … Einstein went beyond Newton by employing the new geometries to make time an independent variable; and as Newton transformed the formulation and interpretation of Kepler’s laws, so Einstein transforms the Newtonian laws of motion. … It is, , a scientific generalization of the old political economy and of modern economics that will yield the new political economy which we need. … Plainly the way out is through a more general field. [CWL 21, 6-7]

In physics, the negation of intelligibility in constant velocity has two manifestations: first, in the Einsteinian context an affirmation of invariance of principles and laws despite inertial transformations; second, in the Newtonian context, an affirmation of invariance of uniform motion in a straight line despite the absence of external forces.

… what Einstein stated for physics in terms of the transformation properties of the mathematical expression of principles and laws, Newton stated for mechanics in terms of the forces that move bodies.  In both cases what is stated is a negation of intelligibility in constant velocity. But the Einsteinian context makes the statement an affirmation of invariance despite inertial transformations, while the Newtonian context makes the statement an affirmation of continued uniform motion in a straight line despite the absence of external forces. [CWL 3, 43/67]

As pure conjugates, extension and duration are defined implicitly by the postulate that the principles and laws of physics are invariant under inertial or, generally, under continuous transformations. [CWL 3, 84-5/108]

Paraphrasing:

As pure explanatory conjugates in macroeconomics, price and quantity are defined implicitly by the postulate that the principles and laws of interconnected flows are invariant regardless of observer’s frame of reference as psychological, psychopolitical, producer analytic or consumer analytic.  Thus, the immanent intelligibility of interconnected flows is that it is always, in General, the case that  P’Q’ = p’a’Q’+p”a”Q”,dJ = a’ +a”R (See CWL 15, 158-60),Π”Κ”= π”α”Κ”Purely expansionary+ π”α”Κ”R&M to self, and in the Special case that any definite flow is fixed regardless of the self-interested participant’s obsession with prices or quantities and regardless of the pretio-quantital composition of the flow.

Also,

(in physics,) though there is a difference in the spatio-temporal standpoint from which thedata are considered, still there is no difference in the act of understanding the data, no difference in the general intelligibility grasped in the data, and no difference in the form of the mathematical expression of the intelligibility. [CWL 3, 23/48]

Paraphrasing, (replacing n-dimensional space with 2-dimensional monetary price-quantity flows)

though there may be a difference in the sensitive, perceptive, psychological, psychopolitical, self-interested, pretio-quantital standpoint from which different economic monetary price-quantity flows are viewed and considered, still there is no difference in the act of objective understanding of the equivalencies and identities in the general intelligibility of the data, and no difference in the form of the mathematical expression of the intelligibility of the equivalencies and identities in the data.

Also,

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

Paraphrasing:

In the analytics of FMD, the purely intellectual, relativistic pretio-quantital (concept of) Special flows stand to the exorbitant or giveaway prices and quantities of experience in exactly the same relations as the space-time of Relativity stands to the extensions and durations of experience, as wave-lengths of light stand to experience of colour, as longitudinal waves in air stand to experience of sound, as the type of energy defined by the first law of thermodynamics stand to experiences of heat, etc.

The learner’s understanding of both extensions and durations in physics and prices and quantities in economics advances from experiential conjugates to pure conjugates.  The learner advances from the purely experiential to the purely intellectual.

… as extensions and durations, so also local movement has a preliminary definition in terms of experiential conjugates and an explanatory definition in terms of pure conjugates.  It was obvious and excusable for Galileo and Kepler and Newton to conceive local movement in the two steps of determining a path or trajectory and then correlating points on the path with instants of time. … this account of local movement can be no more than preliminary for, throughout, it is in terms of movement as related to us, as in terms of experiential conjugates.  What movement is, when movements are defined in terms of their relations to one another, is another question.  The answer to it will depend upon the answer that determines extensions and durations as pure conjugates; and so it is that Relativity mechanics conceives a velocity, not as a function of three dimensions with time as a parameter, but as a function of four dimensions, of which three are spatial and the fourth temporal. [CWL 3, 85/108-9]

Paraphrasing:

 … as compositions of prices and quantities, so also price-quantity flow has a preliminary definition in terms of experiential conjugates and an explanatory definition in terms of pure conjugates.  It was obvious and excusable for classical, neo-classical, and Keynesian economists to understand price and quantity within a subjective framework of utility or time-preference and then correlating these with an imagined supply curve, demand curve, or indifference curve. … this account of economic movement can be no more than preliminary for, throughout, it is cast in terms as related sensitively and perceptively to us, as in terms of subjective experiential utilities and preferences.  What valued functional flowings are, when valued functional flowings are defined in terms of their relations to one another, is another question.  The answer to it will depend upon the answer that determines interdependent, velocitous functionings as pure conjugates; and so it is that macroeconomics conceives an interdependent functional flow, not as a function of experiential elements, but in its functional relation to other functional flows and as a relativistic composition function of three pure conjugates, of which two are the pretio-quantital price and the pretio-quantital quantity and the third is the classic Newtonian interval.

The economy is fluxo-temporal, with the flow being a price-quantity-time object and and the general intelligibility being a tensor in three-space, though the time dimension is uncomplicated.

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:

(Our) interpretation is in terms of 3-space.  It asserts that, within the context of Special Macroeconomic Dynamics, it is a blunder to suppose that a difference of price is a merely pricing entity or that a difference of quantity is a merely quantital entity.  Hence, a standard price is pretio-quantital: it is not merely a difference between two prices; it is a difference between a price , p1, at a quantity, q1, and a price, p2, at a quantity, q2.  Similarly, a standard quantity is pretio-quantital: it does not assign merely quantitative differences; it assigns a difference between a quantity, q1, at a price, p1, and a quantity, q2, at a price p2.  Moreover a unit on any standard price scale determines one and the same invariant pretio-quantital unit for all frames of reference, namely, unity; and a unit of any standard quantity determines one and the same invariant pretio-quantital unit for all frames of reference, namely, the standard quantital factor.  However, while standard prices and factors would determine the same pretio-quantital flows for any frames of reference, still these flows could divide differently into price and factoral components in different flows in different frames of reference.

Whether doing physics or macroeconomics, one should seek the immanent, deepest explanatory intelligibility of the data being investigated.  And one should discover and construct a complete explanation by an analytic process, that first, digs down to precise analytical definitions of functional terms of scientific significance, upon which one can construct a superstructure of a complete and unified theory.

What Einstein did was to show that what holds for the secondary qualities also holds for the primary qualities.  Extensions and durations, just as color, sound, feeling, weight, pressure, and so on, are to be reduced to their immanent intelligibility.  The canon of complete explanation demands that the scientific world, which expresses the relations of things to one another, be constructed completely.  It is not a world of common sense. [CWL 10, 144]