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Friday, February 18, 2011
File:Oort cloud Sedna orbit.svg - Wikipedia, the free encyclopedia
File:Oort cloud Sedna orbit.svg - Wikipedia, the free encyclopedia
Monday, January 10, 2011
Kent Slinker, Jared Lee Loughner's philosophy professor, on the shooting in Arizona. - By Christopher Beam - Slate Magazine
Truly sad that no one intervened and helped this kid out/got his stupid ass committed. Not for his sake, but ours. Hopefully If there is one brights spot out of this it will be I bet this policy changes.
How can it be that a prof can't initiate this kind of thing without a 'self identification'. That seems a horrible idea given the nature of mental illness
How can it be that a prof can't initiate this kind of thing without a 'self identification'. That seems a horrible idea given the nature of mental illness
Logic Puzzle
Jared Lee Loughner's philosophy professor reflects on the shooting in Arizona.
Posted Monday, Jan. 10, 2011, at 9:08 AM ET
The videos posted by Jared Lee Loughner on YouTube at first appear to be a jumble of disjointed thoughts. He claims to be a "conscience dreamer" concerned with "English grammar structure" and "mind control" who wants to see the United States return to the gold standard. Yet Loughner expressed these wild ideas in an organized form: the logicalsyllogism.A syllogism is a form of argument in which a conclusion is inferred from a set of premises. "All men are mortal. Socrates is a man. Socrates is mortal," goes the famous Greek inference. In one video, Loughner offers syllogisms of his own, including: "If A.D.E. is endless in year, then the years in A.D.E. don't cease. A.D.E. is endless in year. Therefore, the years in A.D.E. don't cease."
"Yeah, that's him," says Kent Slinker, when I read him some of Loughner's syllogisms over the phone. "That kind of nonsensical, disconnected thinking." Slinker, an adjunct philosophy professor at Pima Community College, taught Loughner in Introduction to Logic during the spring semester of 2010. Slinker's impression of Loughner was that of "someone whose brains were scrambled."
Loughner was a model student when it came to attendance—he always showed up on time to the twice-a-week class, at least before he dropped out toward the end of the semester. But in other respects, he was a mess. He didn't perform well on tests. He would ask questions that didn't make any sense. "His thoughts were unrelated to anything in our world," says Slinker. One time, he handed in an assignment with geometric doodles instead of answers. Slinker also remembers that Loughner would have "exaggerated 'Aha!' moments just completely not connected to anything in class." He was mentally checked-out. "He always was looking away, not out the window, but like someone watching a scene play out in his mind."
Starting about halfway through the semester, Slinker says, he tried repeatedly to talk to Loughner one-on-one. "I wrote [on his test] saying, Please talk to me after class so we can discuss your performance and explore alternative assignments," says Slinker. But at the end of class, Loughner would cast his eyes down and run out the door.
Eventually, Slinker and the chair of the philosophy department, David Bishop, who taught Loughner in a different philosophy class at the same time, discussed ways to get help for Loughner. But for the school to give a student special treatment, the student has to "self-identify" as having problems, says Slinker: "If we could get him to go to a testing center, then we could help him." But they were never able to engage him enough to raise the subject.
In retrospect, there were no conventional warning signs, says Slinker: "I never sensed violence from him." Asked whether Loughner ever brought up politics, Slinker says "never." The class didn't talk about current affairs. That said, Slinker did point students to political ads for examples of logical fallacies.
Slinker heard about the shooting of Rep. Gabrielle Giffords on Saturday while reading theArizona Daily Star online. The news was especially shocking, considering that Slinker had also taught Spencer Giffords, Gabrielle's father, in a philosophy class in the summer of 2009.
Slinker hit it off with the elder Giffords, who had handed the family tire company over to his daughter, so much so that Giffords invited Slinker to his 75th birthday party, where Slinker briefly met Gabrielle. "She was full of energy, full of life, always with a smile, very sincere," Slinker remembers. As for Giffords Sr., says Slinker, "It was like, this is my long-lost friend and we've been separated by so many years." Giffords gave Slinker a picture of his daughter with her husband and President Obama.
The odd thing about Loughner's syllogisms is that they're not far off from examples Slinker might use in class. "When you teach logic, you draw a distinction between truth and inference," says Slinker. To illustrate that, a teacher might say, "If chickens could fly upside down, then George W. Bush would be president in 2098." The statement isn't true. It just serves as a premise from which to draw conclusions. The purpose, says Slinker, is "to show it's the form of the argument rather than the content that's the expression of validity." But that only works when talking in the abstract. In real-world logic, premises matter. "If the premises aren't true," says Slinker, "all bets are off."
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The common statistical thread between psychiatric diagnosis and grad school rankings. - By Jordan Ellenberg - Slate Magazine
The common statistical thread between psychiatric diagnosis and grad school rankings. - By Jordan Ellenberg - Slate Magazine
The Mathematics of Narcissism
The common statistical thread between psychiatric diagnosis and grad school rankings.
Posted Wednesday, Jan. 5, 2011, at 6:32 AM ET
Another long-gestating project—the National Research Council's ranking of U.S. graduate programs in 59 subject areas—wrapped up in 2010 as well. The ranking came in five years overdue, and its results, like the new DSM, roused widespread dissatisfaction. Stephen Stigler, a professor of statistics at the University of Chicago, described the methodological problems as so severe that the project was "doomed from the start."
The particulars of the two scientific disputes are too gnarled to detail here. In a mathematical sense, though, the controversies are much alike. They both rest on the tension between two fundamentally different strategies of data analysis, clusteringand dimension reduction.
Suppose you've got a large collection of objects—say, graduate programs in mathematics, or psychiatric patients. For each object you have a large collection of measurements. For the graduate programs, you can assess the average time to degree or median publications per faculty member. For the patients, the measurements could be responses to diagnostic questionnaires or assessments by clinicians on various scales.
But when someone wants to know "what's wrong with my patient?" or "which graduate school should I go to?" a list of two dozen numbers isn't so helpful. You need a human-readable description of the object in question.
One way to do this is clustering—you look for divisions along which the objects of study cleave naturally into groups bearing common features. This is the DSM-IV approach to clinical diagnosis: Narcissists resemble other narcissists more than they resemble paranoids, or borderlines, or people without any personality disorder at all. Humans are born clusterers—we almost can't help doing it. Entities neither fish nor fowl discomfit us: Politicians are liberal or conservative, animals break up into phyla, pop songs are black metal or death metal or math rock or shoegaze or grime.
Then there's dimension reduction—here, we try to boil down the many measurements to a few numbers that really matter. This is what we do when we boil down all the aspects of a baseball player's performance to his batting average (or, nowadays, OPS and Wins Above Replacement). It's what the NRC was charged with doing—given all the data about graduate programs, put them in order from best to worst. And it's the way the DSM, in its latest edition, now proposes to reclassify personality disorders. Instead of partitioning patients into groups, they are now measured on six personality axes: negative emotionality, introversion, antagonism, disinhibition, compulsivity, and schizotypy. The patient previously known as "the narcissist" will now be a high scorer on four facets of "antagonism": callousness, manipulativeness, narcissism, and histrionism. In the new paradigm, there's no breakpoint where one personality disorder stops and another begins—there's such a thing as narcissism, but no such thing as a narcissist.
The tough part of dimension reduction is figuring out which few numbers to use. Getting to consensus on the six personality axes took years. And if that sounds hard, consider the charge given to the NRC, which had to capture the essential features of a graduate program with a single number. That's a tall order—imagine if the DSM group had to devise a linear scale to rank patients from sanest to most crazy!
In the end, the NRC group couldn't agree on a uniform ranking. Instead, they offered a range of possible metrics and an interactive tool where users can rank departments via various dimensions endorsed by the NRC or using their own homebrewed measures. This compromise, statistically principled though it may have been, satisfied nobody. After waiting 10 years for the rankings to come out, people wanted their department's standing to be more definitive than "between 6th and 16th, depending on which metric you choose." (And the complaints about the NRC rankings weren't purely methodological—many departments complained the dataset itself was hopelessly shot through with error.)
So, what's the right way to tame your data? It depends on the objects. The researchers driving the changes in DSM take the view, which has some empirical support, that peoplereally do vary continuously from normal to disordered. On that account, carving out various precincts of psychopathology is like divvying up people into "beanpoles," "fatties," and "pipsqueaks" instead of reporting their height and weight. Dimension reduction is the way to go.
The NRC, on the other hand, might have done better to toss the idea of rankings entirely, and just clustered the departments into natural groupings. The statistician Leland Wilkinson ran a quick and dirty clustering on the NRC data for math departments. He found that the departments broke up into five clusters: 10 elite departments, a big group of 59 upper-tier departments, 47 lower-tier departments, and two smaller clusters whose meaning, if any, isn't clear to me. This is much coarser information than a full ranking—but it has the advantage of not depending on politically contentious choices as to which criteria matter most.
In the end, dimension reduction and clustering are going to have to coexist. We rely on continuous metrics to describe baseball players, but at the same time we form mental clusters around prototypes like the plodding slugger and the crafty slap hitter. We cluster our music collections into genres and our politicians into parties, but it can be just as illustrative to map bands and senators in two dimensions using continuous coordinates. So narcissists, and the therapists who treat them, can breathe easy—the notion of the narcissist was alive before the diagnosis broke into the DSM in 1980, and it will persist after the diagnosis is gone.
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