![]() ![]() This is particularly the case when we examine very small datasets. "The point is, even when we're using all our summary statistics, we might still be missing things," says Orlin. As for Defense Against the Dark Arts, that's the horizontal line with one crazy outlier-one annoying overachiever who studies for 19 hours and aces the test will artificially strengthen the average by a lot. Studying for more than 10 hours straight with the addition of fatigue will adversely affect your performance. Graphing the data for the Charms class produces a tidy parabola where studying may improve your score to a point but with diminishing marginal returns. Potions shows the data points scattered around a line, with some random noisy interference: more study helps, but it's not a sure thing. Transfigurations follows a neat straight line: every extra hour of study results in a 0.35 improvement in the test score. "But when you look at the actual data, they're totally different," says Orlin. But summary statistics can obscure these crucial differences. And finally, the fourth dataset makes a parabola. For yet another, there is a horizontal line with one crazy outlier. In another, the data is scattered around a straight line. In one, the data is a straight line with a single outlier. It tells the truth but never the whole truth." For example, when discussing the correlation coefficient, he cites "Anscombe's Quartet." Devised by the late English statistician Frank Anscombe, the Quartet consists of four datasets that look completely different when you graph them out. Statistics is another discipline ripe for Orlin's razor-sharp wit: "A statistic is an imperfect witness. ![]() But maybe Imperial steel is very, very dense and thus goes spherical much faster." Damn lies and statistics Orlin's conclusion: "The Death Star is not nearly big enough. That's why Orlin's hypothetical Imperial team physicist keeps insisting the Death Star should be more lumpy, shaped like an asteroid. "Bodies of ice, it's even larger, because ice is not as dense, so you don't get the same sort of gravitational critical point," he says. But when Orlin did the calculations, he found that the size at which objects take on the shape of a sphere is about 400 kilometers in diameter, which is significantly larger than the ~160km Death Star. The Death Star was constructed in space, a realm where massive things (moons, planets) tend to take on a spherical shape due to gravity. It has to remain in the vacuum of space, where there is no air resistance. So the Death Star cannot visit planets directly, meaning it could not enter an atmosphere and vaporize the occasional continent while blasting The Imperial March through loudspeakers. The air molecules are always hitting it at near-perfect right angles, so the vessel must bear the full brunt of the impact. This takes the form of imagined dialogues among the team responsible for constructing it.Īs Grand Moff Tarkin points out, unlike the sensibly designed Star Destroyers, where air molecules mostly glance off the sides as the spacecraft travel through the atmosphere, the Death Star is just one huge surface area. The Star Wars movies never really explain the specifics behind the construction of the Death Star, giving Orlin the perfect opportunity to indulge in speculation about what could have happened behind the scenes. Spheres in spaceĪrchitecture and design are filled with math, and "Geometry yields to no one, not even evil empires," Orlin writes. It's a great, entertaining read for neophytes and math fans alike, because Orlin excels at finding novel ways to connect the math to real-world problems-or in the case of the Death Star, to problems in fictional worlds. ![]() The book is a more polished, extensive discussion of the concepts that pepper Orlin's blog, featuring his trademark caustic wit, a refreshingly breezy conversational tone, and of course, lots and lots of very bad drawings. And thus, the "Math with Bad Drawings" blog was born. Since he had no particular artistic talent, he opted to just cop to it up front. When he started his blog, he knew that pictures would be crucial to helping readers visualize the mathematical abstractions. "To see the alleged expert reveal himself as the worst in the room at something-anything-can humanize him and, perhaps, by extension, the subject," he writes. He drew a figure of a dog one day on his chalkboard to illustrate a math problem, and it was so bad the class broke out in laughter. Orlin started using his crude drawings as a teaching tool. He investigates this burning question, and so much more, in his fabulous new book, Math with Bad Drawings, after Orlin's blog of the same name. Opting to build the Death Star in the shape of a sphere may not have been classic Star Wars villain Darth Vader's wisest move, according to math teacher Ben Orlin. ![]()
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