From Cambridge to Eternity: “Dimension Algebra”

 

There are two factions of Three R’s, conservative and progressive: the former are Reading, Writing and Arithmetic; the latter Recycle, Reuse and Reduce. We call as Algebra the plain or plane (L²) extension of Arithmetic of the former.   .   

            In measurement of performance to be accounted for, we need before anything else a clearly defined metric of dimensions and scales. Virtually no one, a macroeconomist or otherwise, has difficulty recognizing such different scales, for instance, of length (L in dimension): millimeter, meter, inch, yard, mile, and all the way to light-year. Unfortunately, we except for physical scientists have difficulty figuring out the dimensions and as a result conveniently choose to neglect them.

            Traditionally, we have three dimensions, viz., space, time (T for time duration) and mass (“M” for mass as opposed to M for money), which interact so as to create force, power and energy. The space is usually sub-classified into length (L¹, L for length), area (L²) and volume (L³). The English economist and logician William Stanley Jevons suggested in 19^th century the 6^th dimension of value (U for value of Utility). The value dimension is private home but public in the sovereign currency unit from the market to the economy.

            Thanks to Jevons as well as physical scientists, we can now have the demand and the supply curves for a given product in the beginning of a certain period which is defined for the sake of accounting convenience. Blessed, we can name at the end of the period the quantity traded as well as the price of “market average” aka “equilibrium.”    

            Ever since before the time began, there has been the “nature” on Earth. All different creatures with the mandate of survival have come into being subject to a definitely limited temporal span (T), together with limited yet indefinitely diverse kinds of spaces (L³) and masses (M). So, the time has become the most basic unit of account, or “currency”: homogenous, with minimal cost of carrying around, and beyond control of individuals.  

            On the other hand, competition is inevitable in Here because time, spaces ant masses are limited. On the flipside of competition, wants for goods and services are insatiable partly because of the survival mandate and partly due to agnosticism of the individual life span. According to an Eastern saying, after all, “The wealthier the being is, the more graceful the ending will be.”

            The first rule in competition is of course, “survival of the fittest.” How do creatures tell “fitness”? The answer is “via periodical accounting of performance in each creature’s way of convenience.” The reverse: a lack of accounting leads to little fit performance to few chances of survival.

            Domestic accounting is private. Public accounting must be according to GAAP which is popularly known to the public. Scales of real quantities such as millimeters to light-years are household knowledge as well. Practically saying, on the other hand, dimensions are out of question on the condition that most everyone unwittingly takes dimensions as a matter of course; for instance, few would add the driving distance to the driving peed. In no race, either, the distance of running would be the performance to be crowned.  

            A problem, great or trivial, of macroeconomics as a discipline: Wrongful algebra of dimensions. For example, a stock (M∙T⁰, that is, “LM”) and a flow (M∙T^-1, “IS”) coexist peacefully resting on the same plane (L²) of IS-LM.