On Sending Mixed Measurements

As I’ve gone forward with my research on the metric system, I’ve come across more twists and turns than I could have ever expected. I’d always thought of numbers as a dispassionate construct used to describe the world and relativistic amounts. I’ve never been very good where math was concerned and so I’ve always tried to internalize what a friend (who was a mathematician) told me back when I was in college: “Numbers just show the relationships between things.”

On one level, say as in the fact that 26 is a larger number than 18, and it’s larger by 8 units, that makes sense to me, but when I think about the sorts of formulas scientists use to express unseen relationships in thing like quantum mechanics  \sigma_x \sigma_p \ge \frac{\hbar}{2} (the formula for the uncertainty principle), I’m glad someone else can do that in their heads, because I sure can’t.

One concept that’s starting to bubble down into my consciousness is the idea of mixed measures as in 5’7” tall and 1.5 hours long. I’m no expert, but on the surface (to me at least) such mixing presents problems. Let’s set aside that I just expressed my height in U.S. Customary Units and delve into the real issues I see: 1) I just used a fraction of the foot measurement and a foot measurement together, and 2) if I wanted to further manipulate these numbers I’d need to perform a conversion. (Why introduce a step if you don’t have to?)

Note: I’ll continue to use U.S. measures to help my fellow Americans more easily follow my thoughts though the overall concepts apply elsewhere as well. I’m also using numerals throughout rather than follow Associated-Press style and spelling out numbers smaller than 10—for consistency’s sake.

Why not just say I’m 91” tall?  Because that’s not our habit, but perhaps it should be.

It’s tough to express 7 inches in addition to the 5 feet because it doesn’t represent a nice decimal unit as in the metric system. The original height numbers mashes together units that somewhat relate to each other (after all, an inch is a subunit of a foot) but it doesn’t work readily since an inch represents 1/12 of the foot unit and not 1/10 of a unit as in the metric system (in that case you could use “.” followed by the remainder).

Now let me progress to the 1.5 hours. Why not just say 90 minutes? Some do.

So now let’s say (for some reason) that I knew of a movie that contained a swear word every 3 minutes and I wanted to figure out how many swear words there were in the 1.5 hour movie.

Of course, first I’d have to convert the 1.5 hour-long movie in only minutes to get my answer. (No, I won’t do the math. This is a hypothetical example.)

So, what I’m suggesting is that mixing units for the purpose of describing things might make them more complicated than necessary. Or, put another way, perhaps it would be best to use units that avoid fractions of any sort and rely solely on integers. (That was a word I hadn’t used since elementary school, but it just means whole numbers.)

As we move toward metric system adoption (my sincerest hope) it’s probably good to think about using grams as a measure and not fractions of kilograms or (God forbid) a mixed measure like 1 kg, 25g, as we currently use for things like height.

If we’re going to adopt new ways of doing things, let’s at least adopt them a way that makes the most sense and doesn’t introduce new problems.

But, even if one person decides on a measure in centimeters while avoiding fractions and another uses millimeters—and also avoids fractions—at least the conversions would be easier.

A case could be made (and has been) to avoid any measures that would result in fractions (as in measure everything in millimeters, milliliters and grams for us ordinary folks [while scientists work in different realms]) But if the above discussion has me swimming in deep philosophical water, I’m not well versed enough to argue that case and could possibly drown.

Discuss among yourselves……

Linda

5 thoughts on “On Sending Mixed Measurements

  1. Another great post! Thanks. I love reading your blog posts, Linda. I am 181 cm tall and I weigh a little too much (I try to stay under 100 kg but I am currently 2 or 3 kg over). Consider personally adopting SI (International System of Units; formerly known as Metric System) via MetricPioneer dot com where America can adopt SI one person at a time.

  2. A word that mathematicians like to use when something is simple, to the point and of great utility is elegant. The use of metric prefixes of mm, mL and grams for everyday life is elegant. The philosophical waters are quite warm when using them and a 350 mL drink with a small umbrella for your ice afterward would be appropriate.

    I have an old grade card from Junior High which lists my height in inches only—no feet. It is a good way to write the value of height. We view units as separate in the current muddle—because they were originally. 5280 feet in a mile was a reconciliation of English measurements and Roman (5000). Inches are different than feet and so on. In reality there is only one unit for length in metric, the meter. We only describe divisions or multiples of the same unit with km, mm, um and so on. So one should see 1500 mm as 1.5 meters seamlessly. When we use all the units of “our system” I would be 1 yard, 2 feet, 10 inches and 1 barleycorn (approximately). In metric 1791 mm or 1.791 meters are just different descriptions of the same base unit.

    Very nice post in my view.

  3. I read in a recent Yahoo News article headlined: Spiral Dust Clouds May Reveal Alien Planets that “The disk around SAO 206462 is an impressive 12.4 billion miles (20 billion kilometers) in radius, a distance about five times larger than Neptune’s distance from our sun.”

    The International System of Units – known as SI – has units that measure very small and very large distances. Would a person normally say that he drives 20 billion micrometers to work every day? No, but he might say that he drives 20 kilometers to work every day. Similarly, the article should conform to SI standards and state the radius as 20 terameters, not 20 billion kilometers. By the way, Neptune’s distance from our sun is about 4.5 Tm (terameters) and we here on Earth are one astronomical unit from our sun, which is about 150 Gm (gigameters) or 149,597,870,700 meters if you want to be precise. MetricPioneer.com

  4. Ask any kid around the world how many meters are in a kilometer. A thousand, of course, what a question! Now give me a harder question.

    Ask any kid in the United States how many feet or yards are in a mile and all you get is a blank stare.

    Ask any kid around the world at what temperature water freezes and boils. Water freezes at zero degrees Celsius and boils at one hundred, of course, what a question! Now give me a harder question.

    Ask any kid in the United States at what temperature water freezes and boils and all you get is a blank stare.

    Ask any kid around the world how many kilograms are in a ton. A thousand, of course, what a question! Now give me a harder question.

    Ask any kid in the United States how many pounds are in a ton and all you get is a blank stare.

    Our news article are dumbed-down for American consumption by adding parenthetical inch, mile, gallon, pound, mph and Fahrenheit equivalents, a unique practice only utilized for the mathematically illiterate. NASA is totally metric. US military is totally metric. Why are American civilians so afraid of SI? The International System of Units (SI) has been around since 1795. America adopted the Metric Act in 1866 then forgot all about it. American scientists use the International System of Units. The vast majority of people on Earth have decided to agree on one simple measurement system so that trade and commerce flows without a hitch. America adopting a National Metrication Policy is inevitable. The sooner we abandon our obsolete inches, gallons, pounds and Fahrenheit the better. Every great change in the way we do things starts somewhere, so become a Metric Pioneer and help bring the United States into rational measurement harmony with the rest of humanity. Think metric. Become an American Metric Pioneer. Visit MetricPioneer.com

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