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Language Log: The physics and psychometrics of breakfast-cereal inequality

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Nicholas Watt, "Boris Johnson invokes Thatcher spirit with greed is good speech", The Guardian 11/27/2013: Boris Johnson has launched a bold bid to claim the mantle of Margaret Thatcher by declaring that inequality is essential to fostering "the spirit of envy" and hailed greed as a "valuable spur to economic activity". In an attempt to shore up his support on the Tory right, as he positions himself as the natural successor to David Cameron, the London mayor called for the "Gordon Gekkos of London" to display their greed to promote economic growth. This speech bolster's Mr. Johnson's already-strong claim to be the most Dickensian of modern politicians. I was especially impressed by the following passage: … and I'm afraid that violent economic centrifuge is operating on human beings who are already very far from equal in raw ability if not in spiritual worth. Whatever you may think of the value of IQ tests it is surely relevant to a conversation about equality that as many as sixteen percent of our species have an IQ below eighty five while about two percent - ((about- anyway sixteen percent of you want to put up your hands?)) sixteen percent have an IQ below- uh uh below eighty five uh two percent have an IQ above a hundred and thirty. And the harder you shake the pack the easier it will be for some cornflakes to get to the top. Mr. Johnson raises two scientifically-interesting issues. One is the Brazil Nut Effect — as explained in Matthias Möbius et al., "Brazil-nut effect: Size separation of granular particles", Nature 2001, Granular media differ from other materials in their response to stirring or jostling — unlike two-fluid systems, bi-disperse granular mixtures will separate according to particle size when shaken, with large particles rising [...] For particles of equal density, like corn flakes, the effect is generally due to smaller particles falling rather than to larger particles rising. But depending on other circumstances, larger particles can actually sink rather than rise — see e.g. Troy Shinbot, "Granular materials: The brazil nut effect — in reverse", Nature 2004. It seems that which breakfast-cereal fragments "get to the top" depends not only on relative size, but also on the distribution of densities, on air pressure, and on other parameters as well. The question of whether granular separation is a Good Thing also has different answers depending on circumstances. In general, granular separation of breakfast cereals and other bulk products is not what either producers or consumers want. The second issue is the quantification of corn-flake size intelligence. As Mr. Johnson explains, Whatever you may think of the value of IQ tests it is surely relevant to a conversation about equality that as many as sixteen percent of our species have an IQ below eighty five Some might question the relevance of IQ to the question of economic inequality by citing studies like Jeffrey Zax and Daniel Rees, "IQ, Academic Performance, Environment, and Earnings", The Review of Economics and Statistics 2002, which found that IQ explained only about 5-8% of the variance in earnings: But my point is a different one. Since IQ tests are carefully and elaborately calibrated to generate a normal distribution of scores, with mean = 100 and standard deviation = 15, it follows from the definition of "normal distribution" that about 15.87% of test-takers should score 85 or below. This would remain true if individual differences in the population being tested were ten times greater than they are now, or ten times less — the scores would simply be re-normed to conform to the definition. A few years ago, I commented on another attempt to derive socio-political theorems from statistical definitions: "There are serious problems in the legislation, and that was recognized when Congress passed the bill," said Education Prof. Fred Hess, director of NU's Center for Urban School Policy.  [...] Hess said some of the act's problems go beyond funding. The tests being used are formulated so that 50 percent of the test-takers will fall below the median score — in effect setting school districts up for failure no matter how much preparation students receive, he said. Mr. Johnson's rhetorical flourish about the distribution of IQ scores is similarly meaningless, though in a more complex way.      

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