Until the founding of The National Bureau of Standards , there prevailed what I call "The Right to Measure". This meant that any storekeeper could say what was a gallon of milk, a peck of potatoes, a yard of cloth, etc. The only kind of measures which were not open to the storekeeper's FIAT were digital measures deriving from counting -- say, a dozen eggs.

The National Bureau of Standards was established in 1970, on a plan adapted from that sketched by Charles Saunders Peirce (our greatest 19th century logician-mathematician, our greatest philosopher although incorrectly associated with "the pragmatic philosophy")> But Peirce was never given official credit. Today it is called The National Institute of Standards and Technology. But these metrologists (measurement-scientists), as with physics and engineering professors in the universities, ignore the integrity of "The Theory of Measurement Scales", as initiated in 1940 by the Harvard psychophysicist, S. S. Stevens.

A Stevens' measurement scale: (1) defining the scale in terms of that mathematical transformation leaving the scale invariant (thus, permutations for a type-scale); (2) clear listing of the "permissible statistics" of a given measurement scale (thus, the average for types is the mode, or most frequent -- not the arithmetic mean, since "you can't add apples and oranges".) I give an example of statistical abuse in "the bell curve" of IQ Test Scores.

In my listing of these scales in the Table below, I lead off with my own distinction of a nominal measure since I argue that critical things and events should be uniquely named -- postulating "The First Law of Measurement: LET ALL YOUR NAMES BE UNIVOCAL!"

If you read through The Report of the Presidential Commission On the Space-Shuttle Challenger Disaster (1986), the report to Congress about the Challenger Disaster of 1981 -- which killed 8 astronauts and a school teacher -- you'll see why. Between the lines, you discover that the good measurements of engineers were WASTED when the decision-making (as to take-off) was kicked upstairs to be discombobilated by the buzz-words of managers and beaucrat. For example, information at one point starts out, "All joints are leak checked to a 200 psig stabilization pressure, free of contamination in the seal area and meet O-ring squeeze requirements." But this apparently was translated as "The frenislaw is rigbik and the mome raths outgrabe." And note that investigating committee member and Nobel physicist, Richard Feyman, discovered that those O-rings, when dunked in ice-water, would not pass those "squeeze requirements", which had been conducted at higher temperatures -- and could allow gas to escape and explode! (The one engineer among the final decision-makers was ordered to "Take off your engineer's helmet and vote with us for take-off!")

MY POINT: STANDARDS SET UP FOR FEDERAL ENFORCEMENT REMAIN SUBJECT TO POLITICAL WRANGLING. But some one them TRANSLATE AS MEASUREMENTS! Transform FIAT into MEASUREMENT and nay-sayers can be put in the company of The Roman Catholic Church trying to make Galileo say that the earth does not move around the sun. Or John Calvin (x-y), Swiss Protestant leader, assenting to the burning-at-the-stake of Michael Servetus (x-y) for making the unBiblical claim that blood circulates through the body.

THE MORE THAT NORMS ARE SUPPORTED BY MEASUREMENT THE MORE SECURE THEY ARE!

(I've long had an interest this, having been a member of The American Association of Quality Control Engineers, and having taught quality control engineering many times.)

TABLE OF MEASUREMENT SCALES (after S. S. Stevens)

SCALE	TRANSFORMATION GROUP	ALLOWABLE STATISTICS	EXAMPLES
Nominal	Identity	Mode(s)	Proper names; technical terms
Typological	Permutation	Mode(s)	Taxonomy of plants and animals; etiology of diseases
Ordinal	Isotonic	Median; range	Moh mineral hardness scale; IQ; Richter-Kanamori earthquake scale
Interval	Linear	Arithmetic mean; variance	densities;Celsius & Fahrenheit temperature scales
Ratio	Similarity	all statistics	weight, length, etc.

We're growing partially deaf due to environmental noises, especially around airports, at rock concernts, and due to public boomboxes. The safety rules are based on the decibel scale, devised according to instrumental response to sound. Stevens create a sone measure (ONLINE), based upon human response to sound, which would be better for us, since small changes in the decibel scale may be equivalent to larger changes in the sone scale. It was because of challenges to his sone scale that Stevens created his "Theory of Measurement Scales".