It’s amazing the things you realize, relatively late in the game, that you don’t really know, or that you sort of know but can’t readily explain to someone else in a comprehensible way. The lucky thing is, there’s usually a source that can help you.
Some years ago I came across a book called Innumeracy: Mathematical Illiteracy and Its Consequences by John Allen Paulos, a math professor who lamented that so many people fail to understand the basic concepts. He used some vivid images to illustrate those concepts. Here he is on the multiplication principle:
When the leaders of eight Western countries get together for the important business of a summit meeting—having their joint picture taken—there are 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320 different ways in which they can be lined up…. Out of these 40,320 ways, in how many would President Reagan and Prime Minister Thatcher be standing next to each other? To answer this, assume that Reagan and Thatcher are placed in a large burlap bag. The seven entities (the six remaining leaders and the bag) can be lined up in 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040 ways…. This number must then be multiplied by two since, once Reagan and Thatcher are removed from the bag, we have a choice as to which one of the two adjacently placed leaders should be placed first.
(Bear in mind that Paulos wrote his book in the 1980s; feel free to update his example by placing the world leaders of your choice into the bag.)
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Just this week I ran across another useful explanation aid, this time in a blog from the Arizona Municipal Water Users Association—a great source of information on many topics like water conservation, and one I refer to often. It defines, in readily understandable terms, different amounts of water and rates of flow, and gives some context for them: “No one would talk about the distance between Phoenix and Tucson in feet and water professionals do not generally talk about the amount of water stored behind Hoover Dam in gallons.” It covers acre-feet, ccf, cfs, and so on, comparing, for example, the amount of water the Mississippi River dumps into the Gulf of Mexico (600,000 cfs) vs. the amount the Central Arizona Project—a major source of water in the state—delivers to consumers (2,100 cfs). We know that an acre-foot is the amount of water needed to cover an acre of land to a depth of one foot—even I had a pretty good grasp of the concept—but do you know how many gallons that is, or how many Olympic-sized pools it would fill, or how many households use that much water in an average year? *
The post is mainly intended to help the AMWUA’s customers better understand their water bills and the like. I’m sure many of you are able to visualize these amounts easily and convert quickly in your mind from one to another, but even so, the post can serve as a useful reference to help explain them to others.
* The answers: 325,851 gallons, three Olympic-sized pools, and three households in the Phoenix metro area.