Thursday, February 10, 2011

Evaluating units

I spend a lot of time thinking about units. As the framework in which we take the measure of all things, our choice of units is vital.

There are several desirable qualities one should strive for when considering the design of units. These qualities are often contradictory and we can evaluate a unit in terms of those it does satisfy. In my opinion, these are the most valuable properties a unit can have:

A unit that is natural arises directly from our understanding of nature. In order to be considered natural, a unit must reduce the complexity of the physical constants when they are considered with the unit as part of the basis. An example of a natural unit is the charge of a single electron, or the charge of a single quark. Examples of non-natural unit are pH mol and meter.

A unit that is anthropic corresponds directly to a low-variation fact of human life that is directly intuitive to the human imagination. An example of an anthropic unit is the day. An example of a non-anthropic unit is the meter, since Earth's radius is not a direct part of the human experience.

A primal unit is an anthropic unit that is in some sense the most directly related to human experience. A unit of this type is normally a reference point that cuts across all human cultures with little variation. Of all the distinctions I will draw here, this one is the least precise. Regardless, I feel it is an important goal to find the primal unit when designing anthropic units. A perfect example of a primal unit is human body temperature, for things are classified as "cold" and "hot" in reference to it. A non-example would be the boiling point of water (or in the case of centigrade, some fraction of it, but see 'simple' below).

A unit that is ratio produces a meaningful result when two values in that unit can be directly and meaningfully divided. An example of a ratio unit is the Kelvin. A non-example is Celsius.

A simple unit lacks arbitrary complexity such as named subdivisions, named supersets, extra ratios between subdivisions, and various caveats. By this I do not mean something like the SI prefixes, which do not belong directly to any one unit. Joules are a simple unit, whereas centigrade, which introduces a hundred gradations needlessly, is not.

Taking these metrics in hand, any unit can be directly scored and compared to those measuring the same dimension. While not perfect, this score provides a good qualitative comparison of the various units.

Lets look at a few units. Sometimes I propose a new unit. I have not presumed to name these and perhaps some already exist and I am merely ignorant of them. These I give shorthand names. For example, artime would be an instance of one possible anthropic ratio time. The others should follow in a similar and hopefully obvious vein.

natural anthropic primal ratio simple score notes
foot 0 0 0 1 0 1 non-simple subdivision inch
meter 0 0 0 1 1 2 non-simple usage cm
nrlength 1 0 0 1 1 3
arlength 0 1 1 1 1 4 average human height
fareheit 0 0 0 0 1 1
celcius 0 1 0 0 1 2
kelvin 0 1 0 1 1 3
nrtemp 1 0 0 1 1 3 absolute hot, absolute zero
artemp 0 1 1 1 1 4 body temp, absolute zero

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