The Metric System and Innumeracy

By The Metric Maven

Bulldog Edition

Many years ago, while attending a conference promoting science and scientific skepticism, I unexpectedly found myself interviewed by a reporter for a print newspaper. Her countenance revealed she did not either like the fact she had been given this assignment, or that she really didn’t care for the people there gathered. With a slight amount of impatience she asked me just why it was important to be skeptical. I replied with a question: “Suppose I told you that 350 million Americans purchased a car last year. Should you believe me?”  The woman looked at me with a slight amount of alarm and said “well, it depends on who said it.” I told her that was exactly the wrong answer for a scientific skeptic. She challenged me to explain what I meant. “Well,” I said “How many people are there in the United States?” She paused, and thought and thought. I finally said “About 315 million. [I changed both numbers to reflect today’s population estimate] “Did more than every person in the US including children all purchase a new car last year?” Her facial expression and statement appeared to indicate both “oh, that’s common sense, and you’re just being a smart-ass.” Obviously that exchange was never included in her newspaper article.

Not long before this conversation, I had read discussions about innumeracy  in an essay by Douglas Hofstater and in the book Innumeracy by John Allen Paulos. While I do not recall the particular information in either person’s works, I do recall some points they made which have remained with me. One of the most important was, know how many people are in the US, in your state, in your town. This will allow you to evaluate statements and assertions for numerical reasonableness. What these authors impressed upon me was that innumeracy starts with counting, and the ability to judge magnitudes of numbers, and to relate them with other important numbers. A person who does this can often find themselves on the wrong end of an emotional outburst. Innumeracy is something most people ignore and it is not seen as embarrassing—like illiteracy is—until innumeracy is revealed. People who cannot read are so ashamed they hide it. Often they cannot often admit they have a problem, and begin dealing with it. Innumeracy is assumed to not even exist in the minds of most people, so when it is revealed, the reaction can be visceral.

When I was taking Driver’s Education many moons ago, I heard the statement: “Most accidents occur within 25 miles of your house.” I immediately pointed out that most of us seldom drive further from our residences than that over the majority of our lives. I was told in no uncertain terms that most people thought accidents occurred on long car trips. “Why would they think that?” I thought. To this day I’m not certain why people would. But I do suspect it’s a form of innumeracy.

I often hear people who are interviewed about an accident or other common occurrence on television say with certainty: “it happened about 250 ft that way” or “the creek is about 200 yards over there.”  I have my deepest doubts that if one measured them, that the distances would be anywhere close to the distances quoted. One way to make a bad innumeracy problem worse, is to proliferate and use units that have no logical relationship. If I asked the person who had just given me the 250 ft estimate to guess that value in yards, I’ll bet it would take some cyphering.

While the metric system cannot by itself solve innumeracy, it can help to reduce it because of its continuous spectrum of overlapping prefix magnitudes. If a person said “it happened about 250 meters away” shifting to kilometers would be easy: 0.25 Kilometers, and it would be easy to realize this is also 250,000 millimeters away. It could all be done in one’s head. Metric has a logical overlapping continuum of values which are designated with standard prefixes. One does not have the strange numerical discontinuities of three barleycorns to an inch, twelve inches to a foot, three feet to a yard and five thousand two hundred and eighty feet in a mile. The Ye Olde English units used in the US only serve to preserve innumeracy in the same way that Roman Numerals preserved the inability to multiply and divide effectively until the advent of Arabic Numerals.

I have explained in an earlier blog how the use of Metric Ton or Tonne by members of the press obfuscates a person’s ability to relate the magnitudes of quantities reported by the media. The metric prefixes (without the prefix cluster about unity) allow for quick comparisons of magnitudes when they are used. Micro, milli, kilo, mega, giga, tera and peta, these should all be known and understood instantaneously to a numerate public. They are magnitude bins that one can immediately use to sort sizes and compare them. They form a measurement continuum with a simple relationship (i.e. 1000). How many people populate the US today? 315 MegaPersons. In 1900 it was 76 MegaPersons  In 1800 it was 5.6 MegaPersons. The first official census was in 1790 and totaled 3.9 MegaPersons. We can see that from 1790 to 1990 we went from 3.9 MegaPersons to 249 MegaPersons. How much bigger is a 250 MegaByte computer disk drive when compared to a 4 MegaByte? It’s quite a difference isn’t it.

So what about the top ten countries for population? How many people do they have?

China 1354 MegaPersons (or 1.35 GigaPersons)
India   1210 MegaPersons (or 1.21 GigaPersons)
US    315  MegaPersons
Indonesia 237 MegaPersons
Brazil 193 MegaPersons
Pakistan 183 MegaPersons
Nigeria  171 MegaPersons
Bangladesh 153 MegaPersons
Russia 143 MegaPersons
Japan 127 MegaPersons

The world’s total population is 6950 MegaPersons (or 6.95 GigaPersons)

If we include the Tiny Two:

Liberia 3.5 MegaPersons
Myanmar  39 MegaPersons

This gives us 358 MegaPersons who are not in metric countries and 6593 MegaPersons who are. Now remember, 6.593 GigaPersons is 6,593 MegaPersons and 6,593,000 KiloPersons or 6,593,000,000 Persons.

For people in the US we could make this world population clearer for them by starting with 6,950,000,000 inch-persons which is 579,400,000 foot-persons and 193,133,000 yard-persons or 1,316,000 mile-persons for comparison. I’m just making sure my fellow Americans can understand the values after the onslaught of the completely incomprehensible metric prefixes I used. I’m sorry I didn’t start with Barleycorns, but my understanding is we use the inch as our base now—well actually 25.4 mm since the Anglo-Saxon compromise of 1959.

One argument made by anti-metric people is that changing to metric would be “cost prohibitive.”  Well, let’s do some estimates which relate to the costs of not going metric. The Australian construction industry has saved about 10-15% on building costs since their switchover in the 1970s when compared to using Imperial. Suppose for a moment, we pretend that John Shafroth was able in 1905 to convert over just our US building industry to metric (with millimeters). Well that’s about 100 years ago. In recent years construction is about 5% of GDP. We can add up the GDP (in today’s dollars) over each year for the last 100 years and take 0.5 percent of it (10% savings of the 5% construction of the GDP [or 0.005]). That’s clearly a large waste of money we’ve tolerated over a century, in just one sector. The total GDP from 1905 to 2000 is about 25,000,000 Trillion dollars total so we are talking about 125,000 Trillion dollars of wasted construction value in the US. Do these numbers just seem too large to be correct?  Well how about just using last year’s estimates for GDP which is 13.67 Trillion dollars. Let’s just use 13.5 Trillion and take 0.5% (0.005) which is 0.0675 Trillion or 67.5 billion dollars wasted, just last year! And these losses are only for one sector of the economy which does not use metric. And, as we all know, 50 billion here, and 50 billion there, and pretty soon we’re talking real money. Knowing that we have around 300 million people in the US, it therefore costs every person about 225 dollars each year. Wouldn’t it be better to not have that expense and save the money instead.

Anti-metric people in Australia offered their own estimates to show the public that switching to metric was simply out of the question, because it cost too much. In Metrication In Australia  it is related that:

Opponents of metrication sometimes claimed that its cost in Australia was $2 500 000 000. This amount was first suggested in 1973 and had not been amended by 1982. It was clearly an estimate not based on facts, and in view of the difficulty the Board had in obtaining reliable figures, it seemed highly unlikely that a less well equipped organization could have been more successful in this regard.

Even assuming, for a moment, this cost to be accurate, it represented $179 per person or $18 per person per year for ten years which was a small enough cost compared with the benefits which resulted from metric conversion.

Dear Abby Column from 1977 (click to enlarge)

So even using the numbers offered by the anti-metric people in Australia, which I suspect were, considering their view, hysterically padded, the costs for one-year for a metric conversion would have been $180 per person. This is a one time cost. In the US, just for construction alone, this would be amortized in one year, and from that point on  it would all be savings. In ten years each person in the US would save $2,250 – $180 (using the value produced from the out-of-the-rear-end anti-metric Australian estimate) or $2070. I still see anti-metric people in the US just state with authority on threads that “metric conversion would cost too much money” and believe the discussion is over. It is—if you are innumerate and truth depends on who makes a claim. Every time metrication has occurred in a rational manner, it has saved money for the country which has implemented metric. You can count on it.

6 thoughts on “The Metric System and Innumeracy

  1. >I was told in no uncertain terms that most people thought accidents occurred on long car trips. “Why would they think that?” I thought. To this day I’m not certain why people would.

    I think people assume the longer you are on the road the greater your chances of meeting with an accident. Seems to make sense to me. Please do let me know if I am wrong, it will be a good learning experience for me.

    • “Time on the road” can mean more than one thing. On long car trips, fatigue is a danger. Drivers are far more likely to nod off after ten hours of highway-speed, than when fresh after a night’s sleep. It’s a particular problem on U.S. Interstate Highways, which often run laser-straight for hundreds of miles, horizon-to-horzon, through flat, undifferentiated country. There used to be a word for this in U.S. driver education: “highway hypnosis,” and U.S. highways can indeed make you feel like a chicken staring at a chalk line.

      (Irrelevant aside: How is it that an unexamined assertion that the U.S. is now “about fifty percent metric” seems to be becoming current in a nation where all roads, from village to continental, are signed in miles?)

      But for most of us, this sort of driving is rare — or should be — which is why you are right to think it’s largely the total time spent on the road over a lifetime that determines the likelihood of having accidents. This is the kind of duration being discussed here. And the “innumeracy” of thinking that if you can only get x miles from your home, then driving somehow becomes safer, may be worse than the Maven suggests. It’s really in the same class with the notion that if the last three spins of a roulette wheel have come up red, then you should bet on black. No, you should step back from the table, and ponder the spectacle of other members of your species, engaged in a fundamentally irrational act.

  2. In the Air Force, they told us that it was within 50 miles of home. That was back in ’82. I’ve yet to be in an accident on a long trip. The only crash I’ve had on my motorcycle was right in my front yard. I have some 80,000+ km riding experience on the bike. So, in my experience, accidents happen within 5 meters of home.

    Something that always sticks in my craw is when I’m listening to the financial report on the radio/TV. They say a stock went down by One and Seven tenths of One percent. why not say 17 permil? there is such a thing, and they use it in Europe and other places. % being percent and ‰ being permil. But, we keep ourselves oblivious.

  3. The Maven’s essay “The Metric System and Innumeracy” had me chuckling when he gave the estimate of the US population as 315 megapersons (315 Mp?) Such laughter was brought about not because of the the mega- prefix used like this (something I’ve been doing for years) but because of the innumeracy aspect.

    For many years at the start of the first class of an introductory stat class I teach I give the students a 10-question “diagnostic quiz”, with the last question as follows:

    10. Which of the following best estimates the population size of the United States today? (A) 100 million persons (B) 200 million persons
    (C) 300 million persons (D) 400 million persons

    Besides the fact that usually more than half the students answer the question incorrectly, for several of them it is the only one of the ten questions they get wrong!

    For the first class later this week, the question will read as follows:

    10. Which of the following best estimates the population size of the United States today? (A) 100 million persons (B) 300 million persons
    (C) 500 million persons (D) 700 million persons

    [I still expect too many students to answer the question incorrectly.]

    Maybe next time, I’ll make the choices something like this:
    (A) 100 megapersons (B) 200 megapersons
    (C) 300 megapersons (4) 400 megapersons

    • Of course the four choices should read:
      (A) 100 megapersons (B) 200 megapersons
      (C) 300 megapersons (D) 400 megapersons

      Also, in the spirit of the Maven’s posting are the following (rounded to nearest 0.1):

      1 megaseond (Ms) = 11.6 days

      1 gigasecond (Gs) = 31.7 years

      Add 1 Ts if desired…

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