From Cambridge to Eternity: “Nominalism of Mathematics”

 

To survive, we need to account for performance of the past period, the short run (read: the current period) and the long run (so many coming periods) under the Earth standard. As such, performance as in Here shalt not be as at moments, with dots, or in the “thin air” to vacuum to Eternity. In other words, we in the first place of accounting must define the boundary conditions in definitive metrics. “Indefiniteness” thereof renders nothing.

             Mathematics is invented largely for the sake of convenience  in  accounting. On the other hand, no two things in the reality are perfectly equal so as to get mathematical operation precisely true; for example, every natural unit of apple is different from all else. If so, the simplest equation of all, 1+ 1= 2, is not quite “real” but rather “nominal.”

             With the above said, we might well be careful in mobilizing mathematics of imagination to account for economic activities of reality.

             Take the demand "function" in economics of mathematics, p= a∙q+ b, for example. First of all, the four different letters are free of dimensions and scales, which virtually no macroeconomist pays attention to. As a consequence, their names are more mathematical than economic: respectively, price as a disciplined variable, the slope, quantity as an equally-disciplined variable and the intercept. Second of all, the causality, a must in accounting, is not minded “rationally” enough (cf. Gregory Mankiw’s Principle #3 of Economics).

 

As Meant in Economics   

             q: The quantity to be traded in a particular week, for instance, and in a certain  communal venue of market     

             p: The opportunity cost in the sovereign currency unit to be paid in return for the per-unit (read: marginal) benefit of product, say, orange, in the market over the week

             a: The inverse sensitivity of the quantity unit (1) to the currency units

             b: The (marginal) benefit of the very first unit to the most desperate buyer of  all in town

 

Some Takeaways

1)     In name, the straight line, p= a∙q+ b, is the demand “curve.”

2)     In name, the marginal unit is “infinitesimal,” or the curve is “continuous.”

3)     In name, the intercept is the “penalty”’ for a failure to bid a demand for benefit.

4)     In name, the “curve” remains “in equilibrium” in the period (T^-1, or per period). .

5)     In name, the "market price" (jointly determined with the supply “curve”) is of    “equilibrium” all across “the market” (L^-2, or per market). 

   

Nominalism Extended.    

1)     The orange can nicely be differentiated to atoms or even to the infinitesimal  (M⁰).

If so, buying nothing (L⁰) equals to buying something with a penalty (b in U∙m).

2)     The orange (M) can beautifully be integrated into the (orange)² (M²≠ M∙M).

3)     Best of all, taking advantage of “going fiscal” the economy of all different final goods and services can be in “the general equilibrium” all across the different periods of accounting (from t₀ to t_n). 

4)     After all, GAAP is out of question in Cambridge (L²∙T¹) to Eternity (L^∞∙T⁰).