The Edge Pushes to the Edge

A friend e-mailed a link to “What Is Your Dangerous Idea?” from Edge. She came by way of A&L and said it was worth browsing. I suspect Chicagoboyz & readers will find something of interest in these transgressive notions.

The series of “dangerous ideas” tend toward the scientific; I suspect about everyone else on this site will have more thoughtful positions than mine. Several are about global warming and some are about the nature of man. (Pinker apparently suggested the question last year.)

Joel Garreau’s dangerous idea is that perhaps Faulkner was right:

If Faulkner is right, however, there is a third possible future. That is the one that counts on the ragged human convoy of divergent perceptions, piqued honor, posturing, insecurity and humor once again wending its way to glory. It puts a shocking premium on Faulkner’s hope that man will prevail “because he has a soul, a spirit capable of compassion and sacrifice and endurance.” It assumes that even as change picks up speed, giving us less and less time to react, we will still be able to rely on the impulse that Churchill described when he said, “Americans can always be counted on to do the right thing—after they have exhausted all other possibilities.”

But more discuss hard science & stats. They led me to a topic for my more scientifically oriented brethren. Bart Kosko discusses bell curves; he observes

Thick-tailed bell curves further call into question what counts as a statistical “outlier” or bad data: Is a tail datum error or pattern? The line between extreme and non-extreme data is not just fuzzy but depends crucially on the underlying tail thickness.

Our understanding of such curves may misread ones with thick tails; of course, some have thick, some thin; some straggle out and others end quite abruptly after a sharp decline.

Ever since I first came back to teaching, I’ve found my rigorous & objective tests net a concave curve. After the first couple of semesters, I spoke to more seasoned teachers. They weren’t surprised, calling the inverse curve a junior college one. I have found it an accurate reflection of my students’ command of the material. But I wonder if it is a pattern often useful in understanding other data.

8 thoughts on “The Edge Pushes to the Edge”

  1. Whenever I see that fat tail skewed to one side, I immediately suspect that the data conflates two (or more) characteristics into one measurement.

  2. One area in which the standard bell curves breakdown is in the study of complex dynamic systems like the weather or biological systems. In these systems, you can’t really treat all the inputs as statistical equals. You often end up in a “for want of nail…” situations where seemingly extremely minor inputs drive the system in a radically new direction. A gaussien curve might be able to tell you how many thrown horseshoes one could expect in any particular engagement but it could not predict the effect that any one particular thrown shoe would have on the overall outcome.

    As a rule of thumb, I would say that the larger a role that feedback plays in a particular system, the worse bell curves will accurately model the system. Feedback can amplify the tails making them more important than they would appear.

  3. You may also want to check out the Cauchy distribution, which describes several natural phenomena. It superficially resembles the Gaussian distribution but has a smaller ‘lump’ in the middle and thicker tails.

  4. Furthermore, some measurements make no sense whatsoever as a bell curve — consider, for example, something like the length of fish caught by a particular fisherman. There’s no such thing as a zero-inch-long fish, so the distribution *must* have a minimum, but there’s not really a solid maximum. The curve will have a fat tail to one side and no tail to the other.

    Not all natural phenomena are best described with a gaussian.

    I think when you give a test and find a concave curve, what that shows is that there’s a very narrow gap between being able to master the material and not getting it at all. If there aren’t many people in the middle, it might very well be because there isn’t really much of a middle to be in.

  5. LotherBot,
    Point well taken. But I thought I’d explain.
    There is a middle, but it is relatively small. Those who read some of the assignments and attend class some of the time. Or those who are really not very capable. But either our students are ambitious, want to get into a school that has real requirements for admission, and are mature (attend class, do the readings thoroughly) or are here because they (or their parents) did not know what else they should be doing (and attend quite infrequently, seldom do the readings, and sometimes don’t buy the texts because they have other uses for the money). Those working have discovered “hard America” – where they have to work more than they did in high school if they intend to get into the college of their choice. And the others are in “soft America” – where either their parents or the government supports them while they sort out their lives, often with far too much help from friends like themselves and from the many bars around here. There are usually many, many more B’s than A’s, but there are few Cs.

    A B- to a strong A is probably what twenty or thirty years ago would have been from a D to an A. An A average here is very rare but a B one is not; we have a huge drop out rate and the state’s highest percentage who not only enter a 4-year school but also graduate within a reasonable period from that school.

  6. There are plenty of distributions that describe non-negative measurements. For example, if your dart-throwing accuracy is zero-mean Gaussian in both x and y, then your distance-from-the-bull’s-eye will fall as a Rayleigh distribution. Ricean and Poisson distributions are also non-negative, and related to the Gaussian distribution in a mathematically simple manner.

    I think the problem is that in real life, outliers are often caused by interacting rather than independent factors.

    Lots of interesting stuff in that article, lots of hilarious flakey stuff too.

  7. Thanks for the link Ginny. It’s interesting to read what great minds consider dangerous these days.

    I’ll “edge” up to the bar and suggest a “dangerous idea.”

    All of Earth’s terrestrial life, Man included, is simply an extension of our oceans, and represents just one more of the water cycle’s erosive agents.

    What fueled this dangerous idea was my observations managing roads in coastal California. Terrestrial life, from burrowing gophers to prying pine-trees, seem to facilitate the erosive actions of the water cycle. If one sees the continents as a giant salt-cube that the oceans are working deliberately to dissolve a molecule at a time, then terrestrial life can be seen to be hastening the process. Since we are 70-90% water, could it be we are simply osmotic agents for the oceans in their chemical drive to dissolve the Mineral?

    Another parrallel: the diverse social bonds formed among the gregarious homeotherms, like marsupials, mammals and birds, resemble the complex molecular bonds found in diverse, aqueous solutions. The energetics of our inter-personal bonds mimic the thermodynamics of molecular interaction: they require “heats of activation” and they have rates of reaction. And in human bonds of all sorts, from loose associations to dualistic “marriage,” the bond requires the correct “orientation,” sufficient “kinetic energy” and a stable environment to stick.

    This idea is dangerous because many will find it demystifies “the meaning of life.” Those who demand an anthro- or theo-centric explanation for the human condition (secular humanists or religionists) will consider threatening an idea that reduces life’s dramatic struggle to simple aqueous chemistry.

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