Attention conservation notice: I have no taste. I also have no qualifications to opine on the history of Renaissance astrology.
Cardano's theories were not so obviously superior to rival ones as he would have liked. Accordingly, he buttressed them with replies to potential objections. To the argument that a given star should affect not a single city or state but everyone living anywhere on the parallel over which it passed perpendicularly, for example, Cardano replied with qualifications. The star would have such effects only if it had reach that position on the data when the city or state in question was founded, at noon, and in conjunction with the sun. What technical arguments could not achieve, the language of somber threat and mystification might. Cardano gave his readers not only clear, easily applied rules of prediction which anyone could easily grasp and use, but also rules of interpretation as rich in predictive force and slippery in practical application as any master of astrology could hope to provide:In every geniture there is a best position, which controls all good fortune, and a worst one, which controls all misfortune. The best place is the tenth house, or the first one, or a luminary, if there is joined with these fortune, or a propitious ray, or that of the other luminary, or a fortunate star, so that the good fortune is doubled. Thus the place of misfortune is misfortune multiplied twice.Anyone who could grasp the method laid out here --- and work out exactly which planetary and stellar positions must be taken into account in applying it --- obviously had access to a powerful tool for determining the effects of a given configuration of the planets unequivocally.Equally obviously --- or so it seems now --- no one could hope to use rules like these as rigorously as one could apply Cardano's instructions for determining the time at night or the position of Venus. The doctrine itself was complex: the multiple possible ways of applying it ensured that the results could turn out as seemed best, in a given situation, to the astrologer. [pp. 63--64]
As so often, Cardano's astrology lends itself to parody when seen in retrospect. Like good economists, the ancient author [Ptolemy] and his modern annotator [Cardano] explain in chorus why their discipline matters to humanity even though it cannot, and supposedly does not try to, predict specific outcomes with absolute certainty. Much of Cardano's practical advice --- like the suggestion that one travel in as large a group as possible, since if most of the passengers on any given ship are not foredestined to die in a wreck, the danger is lessened --- has all the precision and intelligence of a modern discount broker's newsletter. [p. 143]
The contrast between Cardano's practices [in mathematical and observational astronomy] and normal ones [of astrologers] was sharp. Most astrologers used their tables as social scientists sometimes apply software packages: they treated these paper devices as black boxes, understanding little or nothing of the principles on which they rested and having little or no ability to compensate for their defects. Their nasty remarks about their competitors rarely rested on a demonstrated mastery of astronomical materials and methods. [p. 61]
Cardano... never saw his own experiences of the autonomy of politics and the power of change [sic; read "chance"?] as reasons for rejecting astrology, either in the political or in the personal sphere. Though he sometimes explained particular events in terms that denied belief in occult influences, he consistently resorted to astrology, as a practice, a well-used set of tools, worn and polished by the use of decades. Even though some of his late comments sugges that he had less faith in astrology than in medicine, he still used it... to organize his last substantial work, his autobiography. Cardano's ability to wield other, radically different tools at the same time should occasion little surprise. Many scholars nowadays use computers to write and fax machines to submit the conference papers in which they unmask all of modern science as a social product, a game like any other. Though they hold that the laws of fluid dynamics are only one way, no more valid than many others, of describing the motion of air over wings, they take airplane trips to participate in the self-congratulatory discussions that ensue. Compared to the sterile credulity of the modern arts of analysis. Cardano's arts of prediction look bright, warm, and solid enough to explain their appeal to the wide range of intelligent readers they attracted and informed. [p. 176]
Nicole Oresme observed [in the 14th century] that it took millennia for celestial phenomena to recur even once; some never did. The astrologers, who had been working for only the few thousand years since Noah's Flood, could not possibly have derived their rules for interpreting the effects of conjunctions and oppositions from observation. They simply had not had enough time. [p. 51]I highlight this one because it applies, mutatis mutandis, to the macroeconomists. §
Books to Read While the Algae Grow in Your Fur; Pleasures of Detection, Portraits of Crime; Scientifiction and Fantastica; Writing for Antiquity
Posted at April 30, 2018 23:59 | permanent link
Attention conservation notice: Notice of an advanced statistics class at a university you probably don't attend, covering abstruse topics you probably don't care about. Also, it's the first time the class is being offered, so those who do take it will have the fun of helping me debug it.
This course is an introduction to the opportunities and challenges of analyzing data from processes unfolding over space and time. It will cover basic descriptive statistics for spatial and temporal patterns; linear methods for interpolating, extrapolating, and smoothing spatio-temporal data; basic nonlinear modeling; and statistical inference with dependent observations. Class work will combine practical exercises in R, some mathematics of the underlying theory, and case studies analyzing real problems from various fields (economics, history, meteorology, ecology, etc.). Depending on available time and class interest, additional topics may include: statistics of Markov and hidden-Markov (state-space) models; statistics of point processes; simulation and simulation-based inference; agent-based modeling; dynamical systems theory.
Co-requisite: For undergraduates taking the course as 36-467, 36-401. For graduate students taking the course as 36-667, consent of the professor.
Course materials will be posted publicly on the class website (once that's up).
Corrupting the Young; Enigmas of Chance; Data over Space and Time
Posted at April 27, 2018 09:15 | permanent link
Attention conservation notice: 1100+ words on a speculative scientific paper, proposing yet another reformation of psychopathology. The post contains equations and amateur philosophy of science. Reading it will not make you feel better. — Largely written in 2011 and then forgotten in my drafts folder, dusted off now because I chanced across one of the authors making related points.
As long-time readers may recall, I am a big fan of Denny Borsboom's work on psychometrics, and measurement problems more generally, so I am very pleased to be able to plug this paper:
In the initial construction of the graph here, two symptoms are linked if they are mentioned in the DSM as criteria for the same disorder. That is, Borsboom et al. think of the DSM as a bipartite graph of symptoms and disorders, and project down to just symptoms. (There is some data-tidying involved in distinguishing symptoms and disorder.)
The small-world stuff leaves me cold — by this point it might be more interesting to run across a large-world network — but the model is intriguing. Each node (i.e., symptom) is a binary variable. The probability that node $i$ gets activated at time $t$, $p_{it}$, is a function of the number of activated neighbors, $A_{i(t-1)}$: \[ p_{it} = a + (1-a) \frac{e^{b_i A_{i(t-1)}-c_i}}{(1-a)+e^{b_i A_{i(t-1)}-c_i}} \] In words, the more linked symptoms are present, the more likely it is for symptom $i$ to be present to, but symptoms can just appear out of nowhere.
Statistically, this is a logistic regression: $b_i$ is how much symptom $i$ is activated by its neighbors in the graph, $c_i$ is a threshold specific to that symptom, and $a$ controls the over-all rate of spontaneous symptom appearance and disappearance. Using a very interesting data set (the National Comorbidity Survey Replication of about 9200 US adults), Borsboom et al. in fact fixed the $b_i$ and $c_i$ parameters by running logistic regressions. The $a$ parameter, which was kept the same across symptoms, was tweaked to make the rate of spontaneous occurrence not too unreasonable.
What Borsboom et al. did with this model was to run it forward for 365 steps (i.e., a year), and then look at whether, in the course of the previous year, it would have met the DSM criteria for major depression, and for generalized anxiety disorder, and then repeat across multiple people. It did a pretty good job of matching the prevalence of both disorders, and got their co-morbidity a bit too high but not crazily so.
Now, as a realistic model, this is rubbish, for a host of reasons. Lots of the edges have to be wrong; the edges should be directed rather than undirected; the edges should be weighted; the logistic form owes more to what psychologists are used to than any scientific plausibility. (Why should psychopathology be a spin glass?) The homogeneity of parameters across people could easily fail. And yet even so it comes within spitting distance of reproducing the observed frequencies of different conditions, and their co-morbidities.
Notice that despite this, there are no underlying disease variables in this network, just symptoms. So why do we believe that there are unitary disease entities? I can see at least three routes to that:
Of course, it might be that to make any of these three defenses (or others which haven't occurred to me) work properly, we'd have to junk our current set of disorders and come up with others...
Posted at April 12, 2018 14:30 | permanent link
Attention conservation notice: Note the date.
A straight-forward argument from widely-accepted premises of evolutionary psychology shows that humans evolved in an environment featuring invisible beings with minds and the ability to affect the material world, especially through what we'd call natural forces.
Of course, none of this implies that those invisible beings aren't as extinct as mammoths.
To spoil the [not very funny] joke: even if the relevant modules exist, they are engaged not by intentional-agent-detectors, but by human mental representations of intentional agents. Once the idea starts that storms are the wrath of some invisible being, that can be self-propagating. For further details, I refer to the works of Dan Sperber, especially Explaining Culture (and to some extent Rethinking Symbolism). Credit for the phrase "ad hominid argument" goes, I believe, to Belle Waring, back in the Early Classic period of blogging.
Modest Proposals; Minds, Brains, and Neurons; The Natural Science of the Human Species; Philosophy
Posted at April 01, 2018 22:59 | permanent link