Ethan suggested we discuss this visual display of information, available at http://xkcd.com/radiation/. We spent about 40 minutes in class going over the chart and understanding what it tells us. It’s an imperfect but very rich display of information. We did a few conversions (suggested by an article in The Guardian) showing that the average total by someone within a 10 mile radius of Three Mile Island after the accident there was 1/625th of the maximum yearly dosage allowed by the U.S. for a radiation worker. Our first attempt at the comparison used subtraction. In a way I was happy the students suggested this approach, as I’ve seen them do this on the homework and I hadn’t had an opportunity to really discuss it. We carried through the calculation and then put it in a sentence: “At Three Mile Island the average exposure was 49,920 microSv less than the maximum allowable exposure for a U.S. radiation worker.” All in all, fairly meaningless especially for someone who doesn’t know much about radiation units. So we tried again, this time with division, and got to the ratio of 1:625 which we used for the comparison.
After we worked through some other examples, a student asked, “is this going to be on the homework?” It may well be, if we can think of some questions in time. More importantly, I told them, it’s on the homework that is life. One of our main objectives is to get students to stop and look at the numbers (and the graphs). This is a great example of a graph that’s worth studying, especially as we try to understand and put in context the news from Japan. Should we panic? Should we buy iodine pills? How much of the frightening statements (on tv, in papers, on the web) should we believe? This is not just an issue for the Japan situation – it’s an issue in many contexts. Think of the swine flu scare from last year, or the SARS scare before that, or think of the current budget debate in the United States. Numbers impact us in so many ways and it’s awfully easy for words to distort how we approach the numbers. Being able to slow down, to think, to look at the numbers and the graphs – these are important life skills. Anyway, that was my lecture. I think showed them the Gapminder video of 200 countries in 200 years (http://www.gapminder.org/videos/200-years-that-changed-the-world-bbc/) as another example of how we can use data to understand the world.
From there we returned to the somewhat less exciting world of linear functions and used Excel to graph sales tax as a function of price. I’d like to talk about graduated income tax next time, which was why I took the time to do the sales tax example. We’ll see if we get there.
From Ethan
I suggested the xkcd radiation dose graphic above to Maura yesterday, not really expecting that either of us would take up my suggestion that it was worth a class. When I discovered she had, of course I did too. And it was (worth a class).
As usual, we spent lots of time on vocabulary – in this case exploring “radiation” – what it was, why it was bad. The most useful definition was that it’s an invisible something that streams from somewhere and may do damage when it hits you. You can get a sunburn. A radiator radiates heat. Then we started looking at the chart. The first issue that comes up is “what’s a Sievert?” – it’s a measure of the damage radiation can do (not a measure of radiation itself).
Why does eating a banana amount to a dose of 0.1 microSv? We didn’t know, just had to believe the author. Same for sleeping next to someone (0.05 microSv – is that once, or per year?). We did note that the radiation exposure from the banana was big when you ate it – presumably there’s no risk in sleeping next to a banana.
It took a while for people to remember, or look up, what “micro” meant. In order not to do all the talking, I stated and started a policy of not answering questions I asked, waiting instead for someone to answer. Long silences.
We compared the radiation damage cost of a dental x-ray to one of the arm; I stressed the fact that the relative change was more useful than the absolute change. It’s 5 times as much. That’s just what the picture shows (counting blue boxes).
Comparing the maximum to the average dose from the TMI accident was time consuming, because it required comparing milliSv and microSv. I was patient. Finally one student essentially gave up on the arithmetic and counted the green boxes: 50 for the max, 4 for the average, so the max is 12 and a half times the average. Hooray for common sense and data visualization, but I wonder if anyone other than that one student really learned the lesson.
The fact that everyone is exposed to at least 10 microSv every day just for living was very disturbing to some. One student said “if everyone is exposed then it’s not dangerous” which made no sense at all. He was really asking for the critical number that you had to stay below. He clearly had an all-or-nothing model of the danger. I puzzled for a while as to how to talk about the small but finite probability of a rare event. I used a lottery analogue. Imagine a lottery with many many tickets (zillions – I didn’t try to be quantitative). Suppose you are given, free, 10 tickets every day. Is that a good thing? Well, yes. You do have a small chance of winning (10 out of zillions, every day). Of course that doesn’t mean you will ever win. Winning the lottery is a good thing, getting cancer is a bad thing. Cancer is like a lottery, and the milliSv of radiation exposure are like tickets in that lottery. So even a few tickets are a bad thing, even though you’re not likely to get cancer from those few. (I didn’t go near the cancer lottery model – radiation damage to DNA.)
We did then scroll down to the red boxes and found the fatal dose: 8 Sv. With that many radiation lottery tickets you lose for sure (and not from cancer). But we knew enough by now to know that 8 Sv was millions of times any of the posted numbers of microSv, and thousand of times the numbers of milliSv.
Near the end someone noticed 390 microSv of exposure from the natural potassium in your body, and said “Aha! Bananas!” Bananas are a good source of potassium. Potassium leads to radiation exposure. That’s why bananas lead to radiation exposure (2 microSv for each one you eat).
Much more useful (dare I say more fun) than the planned lesson on income tax. Maura and I will both do that on Tuesday.
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