Delta recently posted a surprising fact about the visible color spectrum:
Did you know that most color scientists no longer recognize "indigo" as a distinct color in the spectrum (as opposed to Newton's original 7-color scheme)?I also enjoyed his screed against the ever-popular PEMDAS acronym:
Wednesday night, I walk into a lecture room for my first-evening algebra class of the spring. And what do I see on the chalkboard? Some motherfucker has oh-so-carefully written out the PEMDAS acronym, with each associated word in a column sequence. . . . among its flaws are (1) leaving out radicals as the inverse of exponents, (2)overlooking that multiplication & division are tied, and (3) overlooking that addition & subtraction are tied.I ask you, if we can't rely on PEMDAS, what can we rely on? It makes one wonder how much of the information taught in schools and widely believed is (1) a gross over-simplification or (2) pure bunk. (In my own teaching, I've encountered a surprising number of incorrect beliefs relating to history and philosophy, many of which were picked up in schools.)
3 comments:
Though I take the point, I think that PEDMAS is simply one of many instructive falsehoods used as a starting point for a subject (e.g. solar system model of the atom). Once the caricature of the truth (or our best approximation) is presented, we proceed to dress it up with the gory details.
The problem lies in students never absorbing the full picture and simply parroting the simplified model, like the PEDMAS pedants that deface the order of operations entry in Wikipedia with their simplified view.
I really like his friend's summary of the big idea in the order of operations: "More powerful operations are done before less powerful operations". This is a better point to absorb than the simplified PEDMAS. A sense of the relative power of operations is very useful for understanding error propagation, the behavior of algebraic models, and much more besides.
John, I agree with your point about PEMDAS being a useful simplification. I remember learning it in junior high, and it seemed to work fine; I must have somehow internalized the correct rule without realizing it didn't match PEMDAS perfectly.
Regarding your second comment, I am too ignorant about mathematics to even understand what you mean by error propagation and the behavior of algebraic models. The idea of "more and less powerful operations" does seem intuitive and easy to grasp; I wonder how hard it would be to spell out exactly what this means, though!
Anyway, thanks for the comments. I hope you are doing well.
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