Though mathematics constitute much of the language by which economic ideas are communicated, little import attaches to whether or not these putative ‘systems’ are mathematically determinant.
This is barbaric: mathematicians are clever people; and they have refined their notions of mathematical determinacy to a point where we can be all but certain that an indeterminate system has no possibility of objective embodiment. If a formal macroeconomic ‘system’ cannot be objectively solved to emulate some theory of the mutual causality between prices and the distribution of assets over time, then its existence is limited to whatever hallucinations it might generate within the human cortex.
Economics’ studied disregard for the determinacy of its formal systems is one of those bold facts of which we do not speak. It is, rather, concealed in economists’ mere disdain for having their systems examined in terms of their mathematical integrity — a sentiment celebrated at all points on the doctrinal spectrum:
Joan Robinson, self-proclaimed heir to Keynes, was famous for her many intonations to the effect that I do not know math, so I am obliged to think; and
Bryan Caplan, self-proclaimed leading interpreter of modern neoclassicism, speaks derisively of the large deadweight cost of mathematics to economics.1Mathematics are anything but deadweight cost when they are the determinant expression of a prospective analog to some objective phenomena. Mathematically determinant analogs exhibit their intrinsic behaviors in the same dimensions of time and space as the phenomena they represent. This gives students a baseline of confidence in the reality of scientific principles, as well as constructing a objective picture of the principles’ operation for the students’ consideration.
The impression of dynamism is, after all, conveyed in a fundamentally different manner than that which conveys the impression of stasis. Where algebra is sufficient for a description of space-without-time, dynamic generalities often require explication in terms of a fable, e.g.: Lucy, Charlie Brown, and the football; the impossibility of explaining water to a fish; boiling a frog; the tragedy of the commons, etc. Any of these familiar homilies could provide an exercise by which the student is introduced to dynamic modeling; but stasis expressed through analytic geometry provides no inadequate path to the moral of any of these stories.
Should economic science be content to proclaim the arrival of steady states upheld by, say, general optima? Where this state is presented as actual it is because, insofar as optimality does not prevail, there would be unrealized profits to be had in bringing it about. But any static view is limited because it only asserts that the forces upholding an economic state have achieved balance. It allows us to suppose whatever we will about what forces are opposed in that balance, how their prior imbalances maneuvered the system into its current state, when the steady-state was achieved, or most anything else likely to satisfy our curiosity about causality in material affairs.
Given the relentless dynamics of their subject, economists’ habitual tethering of their perceptions to equilibrium will always prohibit any valid mathematical expression of economic activity. Valid ideas about economic causation must at some point convey the subject’s dynamics, which can only interact with equilibrium references to create a self-contradictory system. Until the equilibrium idea is overthrown, economic ‘science’ cannot become determinant, and ‘economics’ will certainly remain just what the economist wishes to talk about and nothing more.