Occasionally, things go exactly as I’d hoped. We’re discussing scaling in my Physics of Life class, starting with things like the scaling of volume and area with size. I mentioned in passing that this issue comes up in advertising, and since students seemed interested, I brought the following to the next class — an interactive example adapted from Edward Tufte’s classic The Visual Display of Quantitative Information:
Inflation, the students hopefully know, refers to the change in purchasing power of a currency over time. Tufte shows a political ad in which the evils of Carter-era inflation are graphically depicted:
The original has five different dollars, from Eisenhower to Carter, and also shows a number for the relative value of each, which I’ve erased in the image above.
I asked the students, “Just looking at the images: A dollar in the bottom year is worth X times as much as a dollar in the top year. What’s X?”
The first three responses were 1/2, 1/3, and 1/4, so I made these the options for a clicker question for the whole class and then polled them. Here’s the outcome:
Two thirds of the class would assume, given the image, that the purchasing power of the Carter era dollar was ~1/4 that of the Eisenhower dollar — a very reasonable response. The true value:
0.44 (close to 1/2)!
So, I asked, were the makers of the ad being dishonest? The first few responding students guessed that the images were simply unrelated to the values, or that they were deliberately mis-scaled. I replied that there’s a way the makers of the ad could state that they were completely, perfectly honest. Then, a student cleverly suggested that the linear dimensions differ by 0.44. In other words, the length of the small dollar is 0.44 x the large one’s length, the width is 0.44 x the large one’s, and so the area is 0.44 x 0.44 = 0.19 x that of the large one! (You can measure the dollar images yourself and see that this is really the case.) So it’s a perfectly honest data visualization, but one that exploits scaling as well as the difficulty of accurately perceiving areas and lengths to manipulate the viewer. Watch out!
The Eighteenth Elephant 
This is largely irrelevant but this brought to mind the wide-spread practice of selling vending machine and supermarket sandwiches “front-loaded” so it looks like there is a solid 2 inches of ingredients. British folk seem particularly upset about it (I like reading phrases like “incensed by the lack of chicken in his butty”):
http://www.thenorthernecho.co.uk/news/local/southdurham/barnardcastle/11025235.Supermarket_sandwiches__front_loaded__to_make_them_appear_more_appetising__claims_customer/
or this one from Taiwan (I’m not sure that would even look like a solid 2 inches):
http://cdn2.thatsnerdalicious.com/wp-content/uploads/2011/11/crappy-sandwich-botom.jpg?313ab3
So… how about that lattice light sheet?
Weird (the sandwiches). This is what I miss by not keeping up with “The Northern Echo” and the news of Barnard Castle.
About the lattice light sheet — so far I’ve only read the abstract and skimmed the text, not thoroughly enough to figure out how the “lattice” differs from imposing structured illumination on a light sheet, which has been done, and which is neat. (I think it is different, but I need to stare at the paper more.) In any case, their system and their demonstrations as a whole are brilliant.