People, Products, and Quantitities.
The U.S. “k through 12” educational system is presently burdened with many expectations — to get us more highly ranked internationally, make the sometimes less than brilliant children of wealthy and powerful people smarter, equip people to escape poverty and lead clean and rewarding lives, etc. etc. etc. This is a far cry from teaching the ABC’s with a little arithmetic thrown in. But to add my two cents, I wish our kids were being given a better feel for quantities than we were. I am not talking about more calculus tricks here, but rather the ability to make order of magnitude estimates, handle probabilities, and deal with quantities with which we have little experience.
Every time elections approach I become aware of the pleasure candidates get from throwing around large numbers (the national debt, the cost of Obama care, the number of immigrants in the country, and so on). They do this knowing that most of the electorate has little experience with or feeling for such numbers, and will agree that we are in bad shape and should vote for the candidate dropping words like billions and trillions. In a sense, their tactic is a good one, because we have not been trained to process such numbers.
We are first exposed to quantities by learning to count our fingers and toes (probably the reason we use ten-based numerical systems and why parents did not appreciate the “new math” introducing digital and octal systems). As we grew we picked up experience with thousands (car and house prices in the old days), and have now grown used to millions (the population of large cities, and the net worth of well-off people. But we are now being bombarded with quantities that we can’t handle with our intuition. We are cramming a billion transistors on a silicon chip, communicating with the Voyager spacecraft over 12 billion miles, and buying two terabytes (billion bytes) of computer memory for less than 100 dollars. Bill Gates is worth 70 billion dollars. On the other end of the scale, we are fascinated with nanotechnology (the manipulation of material on a molecular or atomic scale)—the nano refers to a billionth of a meter, or the order of 10-9 . meters, (If you are uncomfortable with this notation, you should be even more uncomfortable if I wrote 0.000000001 meters. The total number of particles in the universe has been estimated at 1085 You want to see 85 followed by 85 zeros? I doubt it.)
We also have difficulty thinking about long time periods. The government usually defines a generation as 25 years. The so-called Neolithic revolution, when we became hooked to agriculture and quit being nomad, was about 10,000 years ago, or about 400 generations. During that time, we have learned to do serious harm to our resources and environment. We are not going to repair the damage or even quit causing it in one generation. Yet we seem to have difficulty thinking and acting beyond our individual deaths.
Part of our problem is the U.S. refusal to completely adopt the metric system. We cling to our strange units such as inches, miles per hour, British Thermal Units, ounces, pounds, and so on. At present, Myanmar, Liberia, and the U.S. are the only countries in the world that have not adopted the metric system, and we are the only so-called developed one. In 1971 there was a major government study entitled “The Metric System, It’s Time Has Come”, led by Daniel DeSimone. The government accepted it, but it didn’t take. Can you imagine the price we pay in trade and travel for this, as well as needing to constantly figure out things like how many cups are in a gallon and how U.S. times in the 440 yard race compares with 400 meter times?
But the problem mostly stems from lack of experience with very large and small numbers, and being taught methods of gaining perspective on them. Orders of magnitude are important. My older son has some land on which he sometimes raises tomatoes. Modern machine-raised tomatoes can produce on the order of 50 tons per acre. Probably not too meaningful. Better we should think of 100,000 pounds. That’s a lot of trips to the store. If you have a spare one tenth acre on your lot, you should be able to raise 10,000 pounds of tomatoes. That get your attention? I used to have fun asking students to quickly tell me how many hairs were on their head, or how many blades of grass were on the football field. Over time they would get much better at order of magnitude guessing —not exact numbers, but a feeling for quantity. In 1977 Charles and Ray Eames produced a short film entitled “Powers of Ten”, which gives a feeling for what happens when one adds or subtracts a zero from a number. It’s still available, and worth watching if you have never seen it. It is here.
We all need to become more familiar with quantities. The probability of dying in a car accident in the U.S. is on the order of one in 10,000 per year. The probably of dying in an airplane accident is one in millions. Why do people sitting in airplanes seem more worried than those sitting in cars? There are approximately 12 million Mexican residents in the U.S. That is about one per each 30 non-Mexican residents. Is that too many? I sure don’t think so, since the ones I know are hard-working, non-complaining, fun loving people, and after all quite a bit of the U.S. was taken away from Mexico by armed force. Let’s not let ourselves be convinced that Mexico is taking us over. And let us face the fact that providing first class healthcare and education for everybody and keeping our highways in good order is very expensive, and someone will have to pay for it.