In my previous post, with help from Alex Bellos, I explained that measuring is intrinsically fuzzy. A comment by Dave Chamberlain raised the point that there are times when a measurement is absolute on an individual datum by datum basis or, as I prefer to phrase it, accurate relative to the time that the measurement was taken.
“When you cannot measure, your knowledge is meager and unsatisfactory,” is a Lord Kelvin adage. In his book The Half-life of Facts: Why Everything We Know Has an Expiration Date Samuel Arbesman offered a corollary to Lord Kelvin’s adage: “If you can measure it, it can also be measured incorrectly.”
“When it comes to error,” Arbesman explained, “measurement revolves around two terms: precision and accuracy. Precision refers to how consistent one’s measurements are from time to time. Accuracy refers to how similar one’s measurements are to the real value.”
“If the true length of something is twenty inches, precision refers to how dispersed one’s measurements will be around the true value. If one’s measurement method always yields values of twenty-five inches, while another measurement method yields values within half an inch of twenty inches, but they are all variable, the former method is more precise, even if its results are wrong. If your measurements are always five inches too high, even if your measurements are very consistent (and therefore are highly precise), you lack accuracy.”
“Of course, all methods are neither perfectly precise nor perfectly accurate,” Arbesman concluded. “But we can keep on trying to improve our measurement methods. When we do, changes in precision and accuracy affect the facts we know, and sometimes cause a more drastic overhaul in what facts are and how they change. Through increases in measurement, what were once thought to be infinitely accurate constants are now far fuzzier facts.”
Not only is measuring intrinsically fuzzy, what is being measured is intrinsically fuzzy – it’s a variable, not a constant, constantly changing its value as we are in the process of trying to measure its value.
Measuring the quality of data is intrinsically fuzzy because measuring and quality, as well as the data, are far fuzzier than even the least fuzzy facts which we invariably pretend are constants.