From Cambridge to Eternity: “Dimension Algebra 02”
Differently
from algebra in general, dimension algebra is mostly of multiplication and division;
the latter for the purpose of performance accounting. Additions when applicable
do not add up, which is not much meaningful anyway.
Dimension Denotation
In physical sciences: “T” for time
period, “L” for length in space and “M” for mass
Additionally in economy: “U” for value of utility①
Homogeneity
“T” and “L” homogeneous; “M” heterogeneous
“U” heterogeneous in private, yet homogenous in public
T+ T= T
Line: L+
L= L. area: L2+ L2= L2, volume: L3+
L3= L3
M: un-addible
but in legal tender; U∙m + U∙m = U∙m
Dimensions
of Key Terms
Utility,
benefit, cost, worth and price: M∙U
Good, service
or asset eligible for trade: M∙U
Medium of
exchange in general: M∙U
The
sovereign currency name/unit/metric: “U” (legally)
Legal
tender: U∙m (“m” as public numeraire of mass)
“M”
for money stock: U∙m
ΔM/ Δt for money provision: U∙m ∙T-1 (≠ “money
supply” or Ms)
Venue of
the market: L2∙T-1 (as illustrated in a diagram)
The market
price: U∙m
The price
gap: U∙m∙L-1 (interspatial, or cross-sectional)
The price
change: U∙m∙T-1 (intertemporal, or longitudinal)
The
moment: no dimension (T0)
The dot:
no dimension (L0)
The mirage:
no dimension (M0)
The “of-no-use”②:
no dimension (U0)
*Note ① Borrowed from W.S. Jevons, The Theory of Political Economy (1871), “value” as the 6th dimension (U) is
limited to material value as opposed to spiritual. In practice, “value” sometimes means “utility” (M∙U).
② Irving Fisher says “Money is of no use
to us until it is spent” (The Theory of Interest, 1930). Paul Samuelson
and William Nordhaus second (Economics,
2010).
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