Go to the first, previous, next, last section, table of contents.

The Code for Units of Measure

When measurements are communicated any expression that does specify only the value and not the unit of the measure is incomplete and therefore meaningless, even though this incomplete communication is quite common especially in the medical field. By stating that the blood glucose level of a patient measures "80", some experienced health care professional will probably know that we are talking of "80 mg/dl", but the statement is nevertheless incomplete. Experienced human mind is capable of filling in informational gaps, however, computers cannot do so and it is therefore essential to the correct report of measurements to take care of the units.

Since units are algebraic terms it is pretty useless for a unit code to only list "all" possible ("defined") such terms of a code of units. It is just as bad to allow any string of characters to count as a unit. A unit has a special semantic meaning that can be expressed in numerical terms quite easily, compared with the difficulties in building a semantic system of other medical terms. Each unit is expressed as a coefficient and a vector of basic units. Thus, it is possible to define algebraic operations on units, like multiplication, division and exponentiation with an integer number. Units can be easily compared for commensurability and measures can be converted to other commensurable units: if the vector of base units is the same, the units are commensurable (of same dimension) and the conversion is simply done by multiplying the value of the measurement with the quotient of the coefficient parts of the respective units.

The Vector of Basic Measures

The base unit vector tries to enclose any measured phenomena while seeking minimality. The elements of the base unit vector are integer numbers which denote the exponent under which the corresponding basic measure counts to the derived measure. Consider a simple base vector [L, T] that is made up only of length (L) and time (T), at least the following measures can be expressed:

Measure       Vector
------------- -------
1             [ 0, 0]
length        [ 1, 0]
area          [ 2, 0]
volume        [ 3, 0]
time          [ 0, 1]
velocity      [ 1,-1]
acceleration  [ 1,-2]
fluid current [ 3,-1]
...           ...

The operations on these classes of vectors are: Addition and subtraction, which means multiplication resp. division of measures; and multiplication of a vector with a scalar (integer) n which means the n-th potence of the measure. The example below shows the calculation of the acceleration vector:

acceleration = length  / time    ^ 2
             = [ 1, 0] - [ 0, 1] * 2
             = [ 1, 0] - [ 0, 2]
             = [ 1,-2]

Minimality is the reason why the concept of SI base units had to be left almost completely. SI base units are the following:

Measure                       Unit
----------------------------- ------- -----------
length                        m       meter
mass                          kg      kilogram
time                          s       second
electric current              A       Amp`ere
thermodynamic temperature     K       Kelvin
amount of substance           mol     mole
luminous intensity            cd      candela

While there are no problems with length, time and temperature, it is certainly not useful to have a prefix `kilo' in a base unit as it is the case with mass. The reason for this is consistency with the rules of prefixing: If we would accept kg as a base unit, we had to allow

1kkg = 1Mg


1mkg = 1g

which is certainly not correct. Thus I decided to use the Gram (g) as the base unit for mass.

It might be just for my personal taste that I use the charge as the base unit of electrical phenomena instead of currency: it is the electron resp. the elementary charge that all electrical phenomena are based on.

Since the amount of substance represents just the number of particles, it is in fact a dimensionless measure (see The Feynman Lectures on Physics p.39-10). The mole will therefore be defined later as a pseudo-unit equal to Avogadro's number.

Finally, I am not yet finished with luminous intensity and I am thinking about dropping it as a base unit. Since the luminous phenomenon is either just another electromagnetic phenomenon or it belongs into the sensory physiology just like the intensity of sound. Since I'm not yet aware of the implications of the candela as a base unit, I'll leave it untouched for the time being.

The following table shows the basic measures as I will use them here:

Measure                       Unit
----------------------------- ------- -----------
length                        m       meter
time                          s       second
mass                          g       gram
electrical charge             C       Coulomb
thermodynamic temperature     K       Kelvin
luminous intensity            cd      candela   
angle                         circ    Circle

As can be seen, I admitted the angle to the list of basic measures. Otherwise I see no way how to be aware of the incommensurability of steradian and radian (1sr = 1rad^2). The angle is measured in whole circles, thus 360deg = 1circ is true.

Go to the first, previous, next, last section, table of contents.