Three-Toed Sloth

Books to Read While the Algae Grow in Your Fur, March 2022

Attention conservation notice: I have no taste, and no credentials to opine on the sociology of education, political and moral philosophy, medieval Islamic science, or even, strictly speaking, pure mathematics.

Dana Stabenow, A Cold Day for Murder, A Fatal Thaw, Dead in the Water, A Cold-Blooded Business, Play with Fire

Mind candy mysteries, where the Alaskan environment is as much a character as any human being, or husky. Stabenow was, I believe, originally a science fiction and fantasy writer, and I think some of that comes through in the way the very strange world of Alaska is unfolded before the reader. It also comes through in the character of Kate Shugak, a hero of basically-royal birth who lives on the border between civilization and the wilderness, and who roams the countryside defeating monsters and malefactors, especially those who have offended against the laws of kinship and hospitality. (There are a lot of explicit references to Greek myths and I do not believe any of this is coincidence or even unconscious.) The fact that I read five of these in a month, and have more in the queue, tells you how easily they go down. §

Douglas B. Downey, How Schools Really Matter: Why Our Assumption about Schools and Inequality Is Mostly Wrong

I am not sure what to make about this one.

Downey studies some nationally-representative longitudinal data sets, which measure student achievement in reading and math at multiple points in the school year, over multiple years. "Longitudinal" here means that each student is being measured multiple times, allowing one to draw inference about how much was learned when. The basic finding Downey extracts from this is that during the school year, richer and poorer students, and black and white students, learn at basically the same rate. But they arrive at school at very different average levels of achievement, and their gaps grow while out of school each year. Thus, on this evidence, schools for the disadvantaged are in fact doing about as well at teaching reading and math as other schools. The inequality in educational outcomes, then, isn't due to inequality in schooling, but to (as Downey puts it) the other 87% of students' lives.

This is remarkably contrary to received opinion, what Downey calls "The Assumption", that schools for the poor are poor schools which do not teach effectively. I get the impression that Downey started by wanting to be talked out of this position, but came to embrace it for lack of intelligent opposition:

I don't think that the people questioning the evidence are bad people, but they are reluctant to let go of the dominant narrative about schools. It would be one thing if the reason was because they had issues with whether the ECLS-K item-response theory scales of reading can be considered truly interval, or if they questioned whether nonschool investments in children are constant across seasons, or if they thought that the approach scholars use to model the overlap days between test dates and the beginnings and ends of school years was insufficient. ... But while many have resisted the empirical patterns in chapters 1--4 and remain committed to The Assumption, the quality of evidence doesn't seem to be the obstacle. [p. 97]

I join Downey's audiences in astonishment. I also join him in thinking that "we really need to reform the distribution of rewards in the broader society", but I just have a hard time swallowing the findings. (Among other things, if he's right, why are parents so convinced otherwise?) But I also don't have any clever explanations to make this pattern in the data into a mere artifact. As a statistician, I do wonder about whether these surveys really cover a nationally representative sample of students and schools. (Though it's hard to imagine what sort of sampling bias would produce this pattern!) There is also the issue (which Downey highlights in the quote above) of whether these reading and math scores are really "interval". Concepts like "median" make sense with merely ordinal variables, but something like "the change in the median poor kid's reading score from September to May is equal to the change in median scores for rich kids", \( X_p(2) - X_p(1) = X_r(2) - X_r(1) \), needs us to be able to compare differences at arbitrary points along the scale. So this is resting a lot on the ways the survey researchers translate students' answers into numerical values, and I'd have liked to see a lot more about that. In particular I'd want to make really sure that this sort of parallel trajectories isn't an artifact of the scaling procedure.

It is unlikely, but not I guess impossible, that I will actually investigate this properly. In the meanwhile, I am informed, but puzzled and unsettled. §

(Text lightly edited 3 June 2022, to resolve some ambiguous pronouns etc.)

Update, 3 July 2022: a favorable review in the American Journal of Sociology.

Jürgen Jost, Postmodern Analysis

I should begin by admitting that I took real analysis as a sophomore, scraped out a C through the kindness of the teacher, and became a physicist. (I did eventually learn measure-theoretic probability.) So the idea of anyone taking advice from me on pure math textbooks is preposterous.

I should also say that I met Jürgen through Santa Fe more than twenty years ago, admire his work on information geometry and complex systems, have given talks at the Max Planck Institut he directs, etc. If I read one of his books and didn't like it, I'd just say nothing publicly.

With my throat now hopefully adequately cleared: When we all went home in March 2020, I got the idea that this would be when I finally learned some important areas of math properly. This fantasy led to downloading a large number of books from the library, and discovering that I would never read most of them for good reason. But this one I stuck with. It's a really good survey of crucial topics in analysis, starting with the basics of differentiation and Riemann integration, visiting things like ordinary differential equations as dynamical systems, Lebesgue integration, and function approximation, and ending up with the calculus of variations and partial differential equations and their interconnections. It's "postmodern" only in the sense that it comes after the classical works on modern analysis of the mid- / late- 20th century, and tries to give a survey of what a bright young mathematician should know now. The exposition is great, consistently just rigorous enough that I needed to inhibit my lizard-brain physicist impulses ("it'd be nice if that equation had a square-integrable solution, therefore it does"), but always with an eye on applications, i.e., on reality. It's really quite enjoyable, and makes me want to read Jost's other textbooks. §

(The obvious question is whether I would have done any better, as an undergrad, if this had been the text in my real analysis course. Honesty compels me to say: "not on your life"; our textbook was forgettable but decent, the problem was teenage me.)

Final disclaimer: I read the second (2003) edition; the third (2005) edition seems to mostly correct mis-prints, and add some results on coverings in the chapter on \( L^p \) function spaces. But I cannot swear to its content the way I can to the 2nd edition.

Stuart Hampshire, Justice Is Conflict

This is a strange (and short) little book of philosophy. The starting point is Plato's analogy, in the Republic, between conflict within the soul and conflict within the city (= polity). Hampshire says that, pace Plato, the way we really resolve conflict in the city is to make sure that all (he says "both") sides know that they have been able to make their case and be heard, even if they cannot get what they want. What ultimately matters is that there was a fair procedure, rather than a substantively just outcome. In the analogy of inner conflict, individual people just have more-or-less incompatible values, and we should not expect to find some way of reconciling them or subordinating one to the most correct values. Nor, he says, should we even want such a reconciliation or ordering.

I am sympathetic --- in some sense he's getting at the core of liberalism --- but I found the argument lacking. The analogy is obviously a bit weak: I don't think he ever really addresses what would correspond to a fair procedure in the soul. (Adversarial or critical thinking is all very well to endorse, but being your own critic has obvious limits.) Also, I think he equivocates about whether unifying values is impossible, or merely undesirable. That's fine by me, because I am strongly in the "impossible" camp --- I encountered "A heterarchy of values determined by the topology of nervous nets" at an impressionable age, and still regard it as irrefutable --- but philosophically a bit unsatisfying.

More frustrating was that Hampshire is fully aware that there are often disputes about which procedures are fair, and this doesn't seem to help us figure that out at all. To use a (banausic and depraved) analogy of my own: if I am writing new code to perform some task, i.e., devising a procedure, I check whether it works right by seeing if it gives the correct answer on test cases, i.e., is substantively correct in particular circumstances. But of course, just to make things circular, in other cases I work out what the answer is by using my procedure. At a much more elevated plane than numerical software, something like this would seem to be at work here, and could use some philosophical illumination. That is, I wish Hampshire would absorb something like Laudan's Science and Values. §

George Malagaris, Biruni [doi:10.1093/oso/9780190124021.001.0001]

Brief historical study of Abu Rayhan Muhammad ibn Ahmad al-Biruni (973 -- 1050?), emphasizing the historical context of Central Asia and the eastern Islamic world in general, giving the main facts of Biruni's biography (including puncturing some picturesque stories), and surveying his major works. Pride of place in Malagris's treatment goes to Biruni's India, fairly enough, but he's pretty comprehensive, and seems to understand the math. (I was astonished to learn that Biruni translated/adapted the Yoga sutras of Patanjali, which must have made some heads explode.) There's also some treatment of his correspondence with ibn Sina; it is simultaneously reassuring and depressing to see that a millennium ago, great scholars were just as capable of mutual incomprehension, dismissal, and pettiness as their modern counterparts, or online posters (cf.) (Actually, I suspect there's the possibility for a very interesting study of different conceptions of "science" in this exchange, and I wonder if someone has done it.) The book concludes with a treatment of Biruni's place in later historical memory, including the way he is claimed by multiple modern nation-states as part of their illustrious past. §

John Scalzi, The Kaiju Preservation Society

Mind candy comic science fiction. It's Scalzi, which means it's funny and mostly but not entirely lightheartedly, and reads extremely smoothly. §

Jane Langton, The Dante Game

Mind candy mystery: the umpteenth book in Langton's series, in which Homer Kelly stumbles his way into an artistic or literary enthusiasm and a homicide investigation. This time it's Dante, and the city of Florence, and the new pope's anti-drug crusade, which is far too successful for some people's liking. It's an old favorite which holds up very well. (Previously.) §

Books to Read While the Algae Grow in Your Fur; Pleasures of Detection, Portraits of Crime; Philosophy; Commit a Social Science; Scientifiction and Fantastica; Islam and Islamic Civilization; Afghanistan and Central Asia; Writing for Antiquity; Mathematics; Teaching: Statistics of Inequality and Discrimination