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I am loathe to start off a page with a dorky Star Trek reference, but trust me, there's a serious point to be made afterward. Just bear with me here:
My long-suffering kids have come to recognize this as "Kirk's question," which has everything to do with statistics and not much to do with Star Trek. In our language, the phrase "a lot" refers to a quantity that is large in proportion to its context. This is important to education, public policy, business, and journalism. As an example, take this headline - please! "Agency predicts fireworks will injure 400 on New Year's." A government agency says that as 2004 begins, 400 Americans will be hurt by the fireworks they set off to celebrate. Their conclusion is that such fireworks should be illegal, which is a public policy issue. 400 people! Is that a lot? If you line up 400 randomly-selected people and force them to hold onto lit fireworks, yes. As a self-selected group (of people who chose to be near the fireworks) from a population of 280 million people, no. That's one out of every seven hundred thousand - and most of them had the option of not being around the fireworks in the first place. Why should I care? The article continues: "Fireworks that contain more than 50 milligrams of flash powder are illegal... and should not be sold to consumers. M-1000's, for example, have about 27,000 milligrams of explosives - approximately 500 times the legal limit for consumers." Let's examine that in light of Kirk's question: One problem is that few people have the foggiest notion of what a "milligram" is. The article says that those scary fireworks have "27,000" of them. 27,000 milligrams! In other words, 27 grams - but 27 isn't as scary a number as 27,000. This is manipulative use of numbers. Notice the article also switches from "flash powder" to "explosives" in describing the legal and illegal fireworks. This is manipulative use of language - the explosive they are referring to is flash powder. The article also fails to explain what flash powder is, how it relates to other explosives, or the rarity of such a monstrous firecracker. The article does give some context at the end, saying the scary firecracker has "500 times the legal limit" for consumers. The 50mg standard is based on a firework that you could hold in your hand when it goes off - admittedly a dumb standard for dumb people. * Once you start looking, you find no shortage of manipulative numbers and language - and outright lies - in journalism and public policy. One of my favorite examples is the oft-repeated statistic that each year in the US, 60,000 children are abducted by non-family members. Is that a lot? Yes, it is so many that it can't be true. Think about it: just for comparison, the US lost about 50,000 people in the Vietnam war - and almost everyone knows a family that lost someone. How many families do you know that had a child abducted? The police would not have time to give out speeding tickets and donuts would grow stale on the shelf. But this erroneous number still influences public policy and the spending of tax dollars. The correct figure is around 600, according to the FBI - one one-hundredth of the popular figure. Is that a lot? It's certainly something for people who care for children to be aware of, and for the police to handle when it happens. But given the size of our country, it's not a reason for hysteria and ruining childhoods with visions of a bogyman behind every bush. What can be done to end the irresponsible practice of using context-less numbers to manipulate the taxpaying, insurance-rate paying public? For starters, schools could focus math education on understanding the actual world. This is controversial: the NCLB act makes math education principally a matter of passing high-stakes standardized tests. But the real world makes math a much higher-stakes game of assessing risk and reward. Suppose you're teaching a math/science course (they can be combined to good effect). If you're talking about milligrams, show the students a milligram of air (1 large soap bubble.) Show them a milligram of lead (they'll need a magnifying glass.) Have them measure out 1 milligram of table salt. Pour the salt into 1 oz (~30 ml) of water: how many parts per million (ppm) is that? Do a blind test against plain water: can you taste the difference? Actually, it's parts per thousand - that is, after reducing the figure to the smallest common denominator - another good practice for busting bad numbers. Teach the class about "sigs," or significant digits. Learn to distinguish between occasions when 3 sigs is enough (such as correlating grade point averages and prison recidivism,) and when more are needed (such as PCB's in drinking water.) Learn how measuring and sampling errors limit the number of possible sigs. Bring newspaper articles into the classroom, project them and dissect them to find manipulative or careless language. Parents - you can do this at home over the dinner table in a light-hearted spirit of making fun of idiots. For inspiration, read John Allen Paulos' Innumeracy or A Mathematician Reads The Newspaper. How about a high-school statistics course based on Larry Gonick & Woolcott Smith's Cartoon Guide To Statistics? (Undignified, yes - that's the beauty of it.) "Is that a lot?" is at the heart of every cost/benefit analysis. Just once I'd like to hear a politician say: "180 people were hurt by "x" last year, but there are 9 million people in our state so that means it doesn't really happen often enough to warrent spending tax dollars on it. I'm not going to do anything about this issue." Kirk's question has applications in business, too. Once upon a time, grocery stores made something like 20% clear profit on their sales. Along came bigger stores with a different business model, making around 1.5% profit - that's a penny and a half out of every dollar - and blew the 20% stores away by attracting all the business. 1.5% is a lot, in the context of 40 times the amount of total sales. Painful for the old style grocers, who should have asked the question of themselves. We all want a just society, and part of that justice is not expecting me to pay for someone else's overwrought concerns. It's forcing taxpayers, business owners, journalists and politicians to ask the important question when issues come up: "Is that a lot?" *I am not clear why our government sees fit to keep dumb people from injuring themselves. It leads to an annoyingly safety-padded, litigious society. The cost of the litigation - based on the assumption of idiot-proofness for all products - far exceeds the cost of the injuries themselves. This was not foreseen by the well-intentioned hand-wringers who prompted the original legislation. The money spent enforcing such laws would be better spent educating people about the dangers of big fireworks - and maybe how to handle them safely if the decision is made to use them. Ditto for ephedra, cigarettes, booze, and so on. |
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