During the late 1980s I was good friends with an artistic couple in Detroit who were leaders in the local Neopagan community. They were the first ones in the area to organize large-scale public Sabbats and host high-profile lectures by people like Margo Adler (Drawing down the Moon) and Selena Fox (Circle Sanctuary). The husband, “Tree,” was writing a rock opera called Gaia. I’ll always remember him as a being of unbridled creativity: what was practical or possible was for other people to figure out, and he was charismatic enough to be surrounded by people eager to help him realize his ambitious visions. Ms. Tree—I won’t name her since I don’t know how public she is these days, but she was a talented artist—I recall saying that her alternative to “All things in moderation” is “Vary your excesses.”
|Tree signed my copy of this article featuring him in the Detroit Free Press (June 12, 1988, C1 & C6).|
And let us not forget Albus Weinstein’s Theory of Relativism.
As a statistician, I must agree that both “all things in moderation” and “vary your excesses” do in fact yield Aristotle’s Golden Mean. Consider three sets of numbers:
A: 100, 100, 100, 100, 100, 100The average, or mean, of each of them is 100. The difference is in what we in the business call variation and its closely related concept, the standard deviation…which basically tells you how far, on average, your numbers fall from the mean. Set A has no variation at all from the mean: it is “all things” in the cartoon at the head of this post, the line in the middle of the curve. Its standard deviation is 0. In Set B, the standard deviation is quite small because all of the numbers are very close to 100. In Set C, the standard deviation is much larger because the numbers are a lot further away from 100.
B: 99, 101, 98, 102, 99, 101
C: 199, 1, 198, 2, 199, 1
If you’re more of a visual thinker, picture it this way: Assume for the sake of argument that your data are in the shape of a normal distribution, or bell-shaped curve. This means that the higher the curve, the more observations you have in that area, and most observations are clustered around the middle and trail off smoothly from there to either side. The standard deviation defines how wide or narrow the bell is. The two figures below show two normal curves with the same mean/average, but differing in the amount of spread, or variation, around that mean.
|Both of the above two charts have the same mean (μ=4), but illustrate what happens with different amounts of spread, or standard deviation: σ=0.5 on top results in a narrow bell-shape, while σ=1.5 below gives us something much broader.|
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