In the last post, we looked at national and international measurement systems and another brief observation of randomness, ending again with the question how accurate and precise things need to be? If you examine a 12 ounce can of soda, it probably says 12 fluid ounces (fl. oz.) and 355 milliliters (ml). If you convert 12 fl. oz. to ml, it actually is 354.882744 ml. Probably good enough to wash down the hotdog at the barbeque. In a similar manner, one U.S. pint equals 472.176473 ml. Probably more than you wanted to know.
But suppose you want to buy some gold. Prices are stated (usually, generally, most of the time) for Troy ounces. One Troy ounce is equal to 1.097142857 ounces Avoirdupois, the ounce we use to measure the weight of apples at the grocery store. The difference is small, but the price is large and could make a large difference if you use the wrong scale.
In these examples, we used units defined by the CGPM (Conference Generale des Poids et Measures) and NIST (National Institute of Standards and Technology). Unfortunately, not everything is “regulated” by these standardized systems of measurement defined by these organizations. A good example is clothing size.
When I go to the store to buy an article of clothing, I have the option to try it on (maybe) or compare the garment with one of a different size designation. When I order online, I must rely on the size designation in the item description. While this generally is good enough, what if fit is important? In men’s shirts, for example, I look for neck size and sleeve length. Will small, medium, large and extra large work? Maybe, depending on the formality needed. But what about women’s sizes, children’s sizes, and infants’ sizes?
The International Organization for Standardization (ISO) has published 21,799 international standards. In the area of clothing, there are standards for body measurement procedures, men’s and boys’ outerwear, women’s and girls’ outerwear, infant garments, men’s and boys’ underwear, women’s and girls’ underwear, pantyhose, standard sizing systems and others. Reads well until you find China, Japan, South Korea, Russian Federation, Thailand, Australia, the European Standards Organization, Germany, France, United Kingdom, United States and others publish their own. As an example, the standard women’s dress size is calculated by bust circumference in centimeters (cm) divided by two; in France, it’s bust circumference divided by two minus four; and in Germany they subtract six. Is it important? It is growing in importance as we move closer and closer to ubiquitous online purchasing. It is a matter of accuracy and precision where randomness is not appreciated because it involves money.
Money, a perception of value, forms the basis for trading goods and services. It is a measurement system under continuous redefinition based on perception, which affects supply and demand. In our everyday existence, we view money to two decimal places: dollars and cents, marks and pfennigs, euros and cents, yuans and fens, and on and on. But often money is calculated to three decimal places. In 1786, the Continental Congress used the term mill, which represented on tenth of one cent. From 1789 through 2015, the average rate of inflation was 1.45 percent. If you use this value and calculate for 226 years of compound growth, a 1789 mill would be worth 2.55 cents today or half a nickel or a quarter of a dime. Should we use such small amounts? Who is we?
Next time you buy gasoline, note that the price is given in mills or, usually, to nine tenths of a cent. Many people view a price of 2.039, or 2039 mills per gallon as $2.03 per gallon. The nine extra mills get ignored. But on one million gallons of gasoline, the nine mills yield $9,000.00 in revenue. If you gas up and buy 15 gallons of gasoline, the mill cost is 13.5 cents of the bill. On a $30.00 plus purchase of fuel, one does not debate 13.5 cents; it is not that important. But to the gasoline company, it represents substantial revenues.
In the finance world, a broker charges five mills per share traded. That equals $5.00 per 1,000 shares traded. In property taxes, the local government wants to impose a five mill per year levy on all real estate properties. On a $100,000.00 property, the levy amounts to $500.00 per year. Is that too much? It is only five mills, less than the gasoline add on? Who cares? Go ahead, vote yes for the levy. But the real cost is $500.00 per year on every $100,000.00 of property
So how accurate and precise should one be in their everyday dealings? If you are the consumer, you have a greater tolerance because the difference you perceive is small. If you are the supplier, it might be important as the numbers grow. If it is the tax person…. We won’t go there.
We have big numbers, small numbers, accuracy, precision, and randomness. What does it mean for society and how we get along?