## December 31, 2018

### Books to Read While the Algae Grow in Your Fur, December 2018

Attention conservation notice: I have no taste. I also have no qualifications to discuss poetry or leftist political theory. I do know something about spatiotemporal data analysis, but you don't care about that.

Gidon Eshel, Spatiotemporal Data Analysis
I assigned this as a textbook in my fall class on data over space and time, because I need something which covered spatiotemporal data analysis, especially principal components analysis, for students who could be taking linear regression at the same time, and was cheap. This met all my requirements.
The book is divided into two parts. Part I is a review or crash course in linear algebra, building up to decomposing square matrices in terms of their eigenvalues and eigenvectors, and then the singular value decomposition of arbitrary matrices. (Some prior acquaintance with linear algebra will help, but not very much is needed.) Part II is about data analysis, covering some basic notions of time series and autocorrelation, linear regression models estimated by least squares, and "empirical orthogonal functions", i.e., principal components analysis, i.e., eigendecomposition of covariance or correlation matrices. As for "cheap", while the list price is (currently) an outrageous \$105, it's on JSTOR, so The Kids had free access to the PDF through the university library. In retrospect, there were strengths to the book, and some serious weaknesses --- some absolute, some just for my needs. The most important strength is that Eshel writes like a human being, and not a bloodless textbook. His authorial persona is not (thankfully) much like mine, but it's a likeable and enthusiastic one. This is related to his trying really, really hard to explain everything as simply as possible, and with multitudes of very detailed worked examples. I will probably be assigning Part I of the book, on linear algebra, as refresher material to my undergrads for years. He is also very good at constantly returning to physical insight to motivate data-analytic procedures. (The highlight of this, for me, was section 9.7 [pp. 185ff] on when and why an autonomous, linear, discrete-time AR(1) or VAR(1) model will arise from a forced, nonlinear, continuous-time dynamical system.) If this had existed when I was a physics undergrad, or starting grad school, I'd have loved it. Turning to the weaknesses, some of them are, as I said, merely ways in which he didn't write the book to meet my needs. His implied reader is very familiar with physics, and not just the formal, mathematical parts but also the culture (e.g., the delight in complicated compound units of measurement, saying "ensemble" when other disciplines say "distribution" or "population"). In fact, the implied reader is familiar with, or at least learning, climatology. But that reader has basically no experience with statistics, and only a little probability (so that, e.g., they're not familiar with rules for algebra with expectations and covariances*). Since my audience was undergraduate and masters-level statistics students, most of whom had only the haziest memories of high school physics, this was a mis-match. Others weaknesses are, to my mind, a bit more serious, because they reflect more on the intrinsic content. • A trivial but real one: the book is printed in black and white, but many figures are (judging by the text) intended to be in color, and are scarcely comprehensible without it. (The first place this really struck me was p. 141 and Figure 9.4, but there were lots of others.) The electronic version is no better. • The climax of the book (chapter 11) is principal components analysis. This is really, truly important, so it deserves a lot of treatment. But it's not a very satisfying stopping place: what do you do with the principal components once you have them? What about the difference between principal components / empirical orthogonal functions and factor models? (In the book's terms, the former does a low-rank approximation to the sample covariance matrix$\mathbf{v} \approx \mathbf{w}^T \mathbf{w}$, while the latter treats it as low-rank-plus-diagonal-noise$\mathbf{v} \approx \mathbf{w}^T\mathbf{w} + \mathbf{d}$, an importantly different thing.) What about nonlinear methods of dimensionality reduction? My issue isn't so much that the book didn't do everything, as that it didn't give readers even hints of where to look. • There are places where the book's exposition is not very internally coherent. Chapter 8, on autocorrelation, introduces the topic with an example where$x(t) = s(t) + \epsilon(t)$, for a deterministic signal function$s(t)$and white noise$\epsilon(t)$. Fair enough; this is a trend-plus-noise representation. But it then switches to modeling the autocorrelations as arising from processes where$x(t) = \int_{-\infty}^{t}{w(u) x(u) du} + \xi(t)$, where again$\xi(t)$is white noise. (Linear autoregressions are the discrete-time analogs.) These are distinct classes of processes. (Readers will find it character-building to try to craft a memory kernel$w(u)$which matches the book's running signal-plus-noise example, where$s(t) = e^{-t/120}\cos{\frac{2\pi t}{49}}$.) • I am all in favor of physicists' heuristic mathematical sloppiness, especially in introductory works, but there are times when it turns into mere confusion. The book persistently conflates time or sample averages with expectation values. The latter are ensemble-level quantities, deterministic functionals of the probability distribution. The former are random variables. Under various laws of large numbers or ergodic theorems, the former converge on the latter, but they are not the same. Eshel knows they are not the same, and sometimes talks about how they are not the same, but the book's notation persistently writes them both as$\langle x \rangle$, and the text sometimes flat-out identifies them. (For one especially painful example among many, p. 185.) Relatedly, the book conflates parameters (again, ensemble-level quantities, functions of the data-generating process) and estimators of those parameters (random variables) • The treatment of multiple regression is unfortunate.$R^2$does not measure goodness of fit. (It's not even a measure of how well the regression predicts or explains.) At some level, Eshel knows this, since his recommendation for how to pick regressors is not "maximize$R^2\$". On the other hand, his prescription for picking regressors (sec. 9.6.4, pp.180ff) is rather painful to read, and completely at odds with his stated rationale of using regression coefficients to compare alternative explanations (itself a bad, though common, idea). Very strikingly, the terms "cross-validation" and "bootstrap" do not appear in his index**. Now, to be clear, Eshel isn't worse in his treatment of regression that most non-statisticians, and he certainly understands the algebra backwards and forwards. But his advice on the craft of regression is, to be polite, weak and old-fashioned.
Summing up, the linear-algebra refresher/crash-course of Part I is great, and I even like the principal components chapters in Part II, as far as they go. But it's not ideal for my needs, and there are a bunch of ways I think it could be improved for anyone's needs. What to assign instead, I have no idea.
*: This is, I think, why he doesn't explain the calculation of the correlation time and effective sample size in sec. 8.2 (pp. 123--124), just giving a flat statement of the result, though it's really easy to prove with those tools. I do appreciate finally learning the origin of this beautiful and practical result --- G. I. Taylor, "Diffusion by Continuous Movements", Proceedings of the London Mathematical Society, series 2, volume 20 (1922), pp. 196--212 (though the book's citing it with the wrong year, confusing series number with an issue number, and no page numbers was annoying). ^
**: The absence of "ridge regression" and "Tikhonov regularization" from the index is all the more striking because they appear in section 9.3.3 as "a more general, weighted, dual minimization formalism", which, compared to ordinary least squares, is described as "sprinkling added power ... on the diagonal of an otherwise singular problem". This is, of course, a place where it would be really helpful to have a notion of cross-validation, to decide how much to sprinkle.^
Nick Srnicek and Alex Williams, Inventing the Future: Postcapitalism and a World Without Work
It's --- OK, I guess? They have some good points against what they call "folk politics", namely, that it has conspicuously failed to accomplish anything, so doubling down on more of it seems like a bad way to change the world. And they really want to change the world: the old twin goals of increasing human power over the world, and eliminating human power of other humans, are very much still there, though they might not quite adopt that formula. To get there, their basic idea is to push for a "post-work world", one where people don't have to work to survive, because they're entitled to a more-than-subsistence basic income as a matter of right. They realize that making that work will require lots of politics and pushes for certain kinds of technological progress rather than others. This is the future they want --- to finally enter (in Marx's words) "the kingdom of freedom", where we will be able to get on with all the other problems, and possibilities, confronting us.
As for getting there: like a long, long line of leftist intellectuals from the 1960s onwards, Srnicek and Williams are very taken with the idea, going back to Gramsci, that the key to achieving socialism is to first achieve ideological "hegemony". To put it crudely, this means trying to make your idea such broadly-diffused, widely-accepted, scarcely-noticed common notions that when madmen in authority channel voices from the air, they channel you. (In passing: Occupy may have done nothing to reduce economic inequality, but Gramsci's success as a strategist may be measured by the fact that he wrote in a Fascist prison.) Part of this drive for hegemony is pushing for new ideas in economics --- desirable in itself, but they are sure in advance of what inquiry should find *. Beyond this, and saying that many tactics will need to be tried out by a whole "ecology" of organizations and groups, they're pretty vague. There's some wisdom here --- who could propound a detailed plan to get to post-work post-capitalism? --- but also more ambiguity than they acknowledge. Even if a drive for a generous basic income (and all that would go with it) succeeds, the end result might not be anything like the sort of post-capitalism Srniceck and Williams envisage, if only because what we learn and experience along the way might change what seems feasible and desirable. (This is a Popperian point against Utopian plans, but it can be put in other language quite easily**.) I think Srnicek and Williams might be OK with the idea that their desired future won't be realized, so long as some better future is, and that the important point is to get people on the left not to prefigure better worlds in occasional carnivals of defiance, but to try to make them happen. Saying that doing this will require organization, concrete demands, and leadership is pretty sensible, though they do disclaim trying to revive the idea of a vanguard party.
Large portions of the book are, unfortunately, given over to insinuating, without ever quite saying, that post-work is not just desirable and possible, but a historical necessity to which we are impelled by the inexorable development of capitalism, as foreseen by the Prophet. (They also talk about how Marx's actual scenario for how capitalism would develop, and end, not only has not come to pass yet, but is pretty much certain to never come to pass.) Large portions of the book are given over to wide-ranging discussions of lots of important issues, all of which, apparently, they grasp through the medium of books and articles published by small, left-wing presses strongly influenced by post-structuralism --- as it were, the world viewed through the Verso Books catalog. (Perry Anderson had the important advantage, as a writer and thinker, of being formed outside the rather hermetic subculture/genre he helped create; these two are not so lucky.) Now, I recognize that good ideas usually emerge within a community that articulates its own distinctive tradition, so some insularity can be all to the good. In this case, I am not all that far from the authors' tradition, and sympathetic to it. But still, the effect of these two (overlapping) writerly defects is that once the book announced a topic, I often felt I could have written the subsequent passage myself; I was never surprised by what they had to say. Finishing this was a slog.
I came into the book a mere Left Popperian and market socialist, friendly to the idea of a basic income, and came out the same way. My mind was not blown, or even really changed, about anything. But it might encourage some leftist intellectuals to think constructively about the future, which would be good.