Three-Toed Sloth

Books to Read While the Algae Grow in Your Fur, December 2021

Attention conservation notice: I have no taste, and no qualifications to opine on the fountainheads of the western philosophical tradition, the history of 17th century science, political philosophy, cognitive psychology, the transmission of inequality, or even social-scientific measurement.

Plato, trans. and ed. Christopher Rowe, Theaetetus and Sophist

Theaeatetus is about knowledge, and more specifically how false belief is even possible --- say, falsely identifying someone else as Socrates, if we (supposedly) know Socrates. It's notable for Socrates propounding at least three distinct theories of knowledge, and undermining them all, ending in perplexity. There are some deeply interesting pieces here, including bits (like the analogies of the wax impressions, and of the aviary) where Plato is trying to think through how to make something knowledge-like work. Then there are the bits of metaphysics about being and not being which I frankly cannot comprehend, and have to hope sounded more plausible in Greek. (I do not think this is Rowe's fault.)

(The dialogue is also notable that early on Socrates makes a big song and dance about how he's just a "midwife" and is only going to help bring out the ideas already in young Theaetetus's mind. Then the whole rest of the dialogue is Socrates setting up and knocking down theories, with one piece of criticism from Theaetetus's teacher Theodorus [161]; the youth contributes exactly nothing, beyond the usual "just as you say, Socrates" or "I do not altogether follow, Socrates". [See also.])

Sophist is, supposedly, a sequel, where Theatetus converses with another distinguished visitor, an unnamed philosopher from Elea. (Socrates has vanished.) The goal here is to try to define the character of the sophist, by means of a series of binary distinctions. The visitor propounds a series of very distinct-looking definitions, all unflattering, which are held to be equivalent. To give something of the flavor, one definition (223) is

Then according to what we are saying now, Theaetetus, it seems that if we take expertise in appropriation, in hunting, in animal-hunting, in land-animal-hunting, in the hunting of humans, by persuasion, in private, involving selling for hard cash, offering a seeming education, the part of it that hunts rich and reputable young men is --- to go by what we are saying now --- what we should call the expertise of the sophist.

while another (268) is

The expert in imitation, then, belonging to the contradiction-producing half of the dissembling part of belief-based expertise, the word-conjuring part of the apparition-making kind from image-making, a human sort of production marked off from its divine counterpart --- if someone says that the one who is 'of this family kind, of this blood' is the real sophist, it seems his account will be the truest.

In between, there is a lot of discussion of, essentially, how multiple statements can all be true of the same object.

(Theaetetus opens with a frame-story about someone having witnessed, and taken notes on, the original conversation between Theaetetus, Socrates and Theodorus, and ordering his slave to read the dialogue that follows. This conceit is forgotten in Sophist.)

I am impressed with Theaetetus (though not with Theaetetus), but both books are strange, and left me feeling I'd missed the point. §

Mary Sisson, Tribulations

Mind candy science fiction, sequel to Trang and Trust. It's deeply enjoyable and I hope we don't have to wait another seven years for more. §

Lois McMaster Bujold, Penric and the Shaman, Penric's Mission, Mira's Last Dance, The Prisoner of Limnos, The Orphans of Raspay, The Physicians of Vilnoc, The Assassins of Thasalon, Knot of Shadows

Mind candy fantasy, following on from Penric's Demon but all, I think, self-contained. These are short, minor Bujolds (except for Assassins, which is a full-length novel), but even minor Bujold is a treat. (No purchase link since these only seem available electronically.) §

Domenico Bertoloni Meli, Mechanism: A Visual, Lexical, and Conceptual History

This is a brief but deeply erudite historical study of what "mechanism", "the mechanical philosophy" and mechanical explanations meant during the long 17th century that gave us the Scientific Revolution. Bertoloni Meli has read, seemingly, absolutely everything, in multiple languages, and can move skillfully and insightfully from historiographic debates about "the mechanization of the world picture" to contemporary ideas in the philosophy of science about explanation by mechanisms to the details of how ligature of arteries were drawn in anatomical texts, and what this tells us about how doctors' understanding of what ligatures did changed. All of this is done with very graceful writing and elegantly-chosen illustrations. It's incredibly impressive and makes me want to read a lot more of his work. §

(On a local and merely personal note, this book is based on lectures given at the University of Pittsburgh in 2016. I was told about those lectures and invited to attend them by a then-new acquaintance who worked in the history of science. Only in retrospect did I get why she seemed so disappointed when I had to cancel on short notice. I am not very swift on the uptake, but --- Reader, I married her.)

Joseph Heath, Enlightenment 2.0: Restoring Sanity to Our Politics, Our Economy, and Our Lives

2800 word review: Enlightenment Is Other People. §

Patrick Sharkey, Stuck in Place: Urban Neighborhoods and the End of Progress toward Racial Equality

Sharkey's primary emprical finding is that, among all black families, there is a substantial minority of very poor black families living from generation to generation in neighborhoods with many other poor black families, and who mostly move (if they move at all) from one such neighborhood to another. Moreover, these families are really much worse off than typical Americans, in every way which we can measure, and which drags down over-all averages for blacks as a group. What Sharkey wants to argue, on this basis, is that part of the reason for these persistently bad outcomes is that concentrating these poor, troubled families in neighborhoods with a lots of other poor, troubled families makes it harder for any of them to improve their situation.

The natural methodological worry goes like so: suppose that there are some poor, troubled families who will struggled to improve their situation, partly because of internal issues, partly because of larger social forces which would afflict them wherever they lived. But because they are poor and troubled, all sorts of processes, starting with housing costs, will concentrate them in neighborhoods with other families in similar situations. Even if the neighborhood has no effect on life prospects, it would still be a sign of those prospects. Under mild assumptions, it'd be a stronger sign the longer a family has been stuck in such a place. More plausibly: regressions of life outcomes on neighborhood of residence, neighborhood of origin, parents' or grant-parents' neighborhoods, etc., could all be explained through infinitely many combinations of genuine neighborhood effects, and neighborhoods acting as signs.

Now there are ways you can begin to pick apart this causal-inference tangle, and in various of the journal papers on which this book is based Sharkey does so. (Some, but not all, of this material is covered in the online appendix.) In particular, his joint paper with Felix Elwert on the inheritance of dis-advantage is actually just as good as I'd expect of Felix. But in this book I grew impatient, while reading, with the feeling that I was just being told about every possible linear regression which you could run on the Panel Study of Income Dynamics where both race and neighborhood poverty rate were regressors, as though that addressed the issue. I realize that this says more about my professional deformations than the merits of this book.

I read this for the inequality class, and while I didn't assign any of it this time, I might well do so if I re-teach it. I will definitely be recommending the backing papers as supplemental reading. §

Richard A. Zeller and Edward G. Carmines, Measurement in the Social Sciences: The Link between Theory and Data (1980)

I wish I liked this more, because it's heart is in the right place. In particular, trying to see what remains of psychometric's classical test theory after admitting that systematic error is possible is a worthwhile undertaking! But this book's faith in what can be achieved through factor analysis and comparing correlation coefficients is utterly misguided. (Cf., though Clark doesn't discuss this book specifically, Glymour.) I had hoped I could recommend this to The Kids, but an adequate exposition of necessary caveats would rival the text itself for length. §

ETA, 29 March 2022: this 2017 paper doesn't mention this book, but it does pretty thoroughly explode all its ideas. (It's a glorious, and scientifically valuable, piece of trolling.)

Scientifiction and Fantastica; Enigmas of Chance; Writing for Antiquity; Philosophy; Commit a Social Science; The Dismal Science; The Beloved Republic; Teaching: Statistics of Inequality and Discrimination; The Progressive Forces; Minds, Brains, and Neurons; The Collective Use and Evolution of Concepts; The Continuing Crises The Great Transformation

Books to Read While the Algae Grow in Your Fur, November 2021

Attention conservation notice: I have no taste, and no qualifications to opine about how to conduct either social science, or the German Social Democratic Party at the end of the 19th century.

Eduard Bernstein, The Preconditions of Socialism (1899; trans. and ed. Henry Tudor)

The original revisionist. Here are some of Bernstein's more important and representative heresies, from the viewpoint of orthodox, Second International Marxism: the dialectic is unhelpful and not actually essential to Marx and Engels's best work; the number of people who own capital is growing, not shrinking; class structure is not simplifying to a stark opposition of capitalists and proletarians; workers are not being increasingly immiserated; formal democracy is essential; it turns out that in even partially-democratic states, organized political action can do a lot to improve workers' lives, without waiting for the revolution; the state couldn't just take over running the economy successfully; etc., etc. As should be obvious from my tone, I find a lot of these ideas extremely congenial, though Bernstein was, it must be said, rather more sanguine about colonialism, and especially about European nationalism, than looks wise in retrospect. (Since, 15 years after this book, he was opposing World War I in the Reichstag, I wonder if he ever explicitly admitted errors on those points.) A dedicated proponent of orthodoxy could, naturally, argue that while the prophecies haven't been fulfilled yet, their hour will come round at last...

This edition is the first un-abridged English translation, with helpful footnotes explaining now-dated references, and giving full citations for his quotations etc. (The first, seriously abridged, English translation is online.) It says something about me that I found this an exciting read.

Scott Ashworth, Christopher R. Berry and Ethan Bueno de Mesquita, Theory and Credibility: Integrating Theoretical and Empirical Social Science

My remarks having passed the 900 word mark, they became a separate review.

C. J. Cherryh, The Paladin

Mind-candy fantasy, in a world of little magic, but a lot of superstition and a lot of desire for vengeance. Not Cherryh's identity-bending best, but I wanted a comfort re-read and this delivered.

Candice Fox, Hades

Mind candy thriller. What if (I refuse to regard this as a spoiler) Dexter, but the serial killer who hunts killers was a Sydney homicide detective? (I haven't bothered to go check the publication dates to see if that actually explains it, or it's just convergent evolution in the space of psycho-killer mysteries.) OK but left me without any desire to continue the series.

Lee Goldberg, Gated Prey

Extremely fluffy mind-candy mystery. (Previously.)

Books to Read While the Algae Grow in Your Fur; Pleasures of Detection, Portraits of Crime; Commit a Social Science; Constant Conjunction Necessary Connexion; The Progressive Forces

Call to Pittsburgh (2021 edition)

Attention conservation notice: An academic job ad.

We are looking to hire this year, both on the teaching track and the tenure track. It's a great department and you should apply if you're at all interested in professing statistics, even or indeed especially if your background isn't traditional stats. (I say this despite the fact that every application we get now means more work for me later.) If any reader has questions I might be able to answer, please don't hesitate to get in touch.

Kith and Kin

Import Substitution Is a Harsh Mistress

Attention conservation notice: 1400 words on the development economics of space colonization from someone who is neither an economist nor even a rocket scientist. Yet another semi-crank notion, quietly nursed for many years, drafted in this form in 2011, posted a decade later because I can't stand to do any more grading and want to procrastinate of Very Important Reasons I am not at liberty to reveal at this time.

So, what with the end of space shuttle flights and all, my feed-reader has been filled with people bemoaning the state of human space flight. While I share the sheer romantic longing for it (expressed with greater or lesser sophistication), if we want to consider other rationales for sending people into space, it's hard to come up with anything which can't be done better by robots. The only one I can think of is providing, as it were, a distributed back-up system for humanity --- places which could carry on the species should the Earth becomes uninhabitable. If this is the point, it imposes some constraints which are not, I think, sufficiently appreciated.

Colonies which could help in this way have to be at least potentially self-sufficient, without dependence on the Earth --- no spare parts, no processed intermediate inputs, nothing. Since there are no natural environments off Earth in which people can live, they will have to create artificial environments, which means that extra-terrestrial human societies must be industrial civilizations. Self-sufficiency means creating, in miniature, a whole industrial ecology.

Go read Brian Hayes's Infrastructure if you haven't already; I'll wait. We're talking about replicating all of those functions, and more. Now, remember that all the technologies whose complexities Hayes documents so lovingly have been developed to assume, and to make use of: gravity of 9.8 m s^-2, ambient temperatures between ~230 and ~320 K, an unlimited supply of atmosphere which is about 20% oxygen at a pressure of about 10⁵ N m^-2, abundant and cheap liquid water, etc. Moreover, our technologies assume that their environment is big, so they can dump waste products, starting with heat and mechanical vibrations, into the environment. Simply sticking terrestrial machinery inside a small, fragile, carefully-controlled artificial environment is not going to work well. (You want to try running a smelter inside your space habitat?) So duplicating these capacities for a space colony will mean re-designing everything to fit local conditions profoundly different from anything we've faced before.

This will take a lot of design work and trial-and-error, hence it will be expensive: the workers and designers could have been doing other things, the gear and machine parts and material resources could have been put to other uses. How are these development costs to be recovered? The extra-terrestrial market, we will have to assume, will begin and long remain very much smaller than Earth's, so sharing those fixed development costs over a small population implies high average costs. (Colonies in different parts of the solar system will face different local conditions, and need to develop largely different technologies, so we can treat this colony by colony.) What about expanding the market by exporting? Suppose momentarily a complete subsidy for the fixed costs, and so think about marginal cost pricing. For exportable items, their cost at Earth will equal marginal cost of production in space plus marginal cost of interplanetary transport. Unless making comparable items on Earth is (almost literally) astronomically more expensive, there will be no export market for the colonies. And this is assuming, again that investors were willing to write off all development costs.

(At this point, readers may be tempted to invoke comparative advantage, and say that even if Space is less efficient at producing everything than Earth is, both Space and Earth will be better off if Space makes what it is relatively better at. Carefully examined, however, what the classic Ricardian argument proves is that there is an opportunity cost to not using the less-efficient country's factors of production, viz., the stuff which it could have, inefficiently, produced. To minimize the opportunity cost of letting those factors go idle, they should be employed in their least-inefficient use. So even if making widgets costs 1000 times as much in Space as on Earth, if widgets are the least-inefficient of Space's factors of production, it should make widgets, and trade them for other things. But this presumes that Space and its factors would exist without the trade. Since, for us, the whole question is whether there should be any workers, capital, etc., in Space, this line of argument just doesn't apply.)

Unless people come up with something valuable which can be made in space but cannot, or almost cannot, be made on Earth, it's hard to think of any manufactured goods which it would be sensible to export from space. What might make sense would be for space colonies to find comparatively cheap natural resources, requiring minimal on-site processing, and export them to Earth, in exchange for, well, everything else. Ideally the exports from the colonies would also be very stable physically and chemically, so they could be sent by slow, low-energy, automated (and therefore cheap) orbits to Earth. When you figure out what those resources are, especially ones that Earth doesn't already have in abundance, let the worlds know; please don't say "helium 3". Alternatively, one thing which can be produced on (say) Titan vastly more cheaply than on Earth is the experience of being on Titan: encapsulated in the form of science or entertainment, that experience could be shipped very cheaply to Earth, which might be willing to pay for it. Of course, neither an economy based on resource-extraction nor one based on scientific papers and reality TV would be self-sufficient. The logic of endogenous comparative advantage would, in fact, lock in place the mother of all core-periphery divisions, with the space colonies as the eternally dependent periphery.

A colony could, I suppose, decide to impose on itself the costs of developing its own industrial infrastructure, so as to replace imports from Earth. Those costs, to repeat, would be very high. Moreover, there's really no substitute for experience and experiment in improving technologies, so the initial quality and reliability will be low. Since, again, the local market will be small, it will not be able to support many producers, perhaps just one in each sector. There will be little scope for a diversity of local approaches to the problems of the industry, slowing innovation. There will also be little or no competition, with all that entails.

The picture of space colonies which might actually become self-sufficient, then, looks something like this. The population is forced by its leaders to endure endless privations to build monopolistic industries which produce inferior goods to those already available on the universal market, grimly tending towards autarky while exporting primary goods for the time being, on the promise that one day all of these sacrifices will be redeemed when they become the future of humanity. Somehow, I doubt there are many who find the idea of building socialism in one habitat compelling; Ken MacLeod may know them all by name.

(I have assumed everything stays within the solar system, because, pace Krugman, interstellar trade makes no sense at all. A civilization which could command enough energy to accelerate a large object to a significant fraction of the speed of light, so that trips between nearby stars take only decades, has no economic problem. At perhaps-attainable velocities, with thousands or tens of thousands of years of travel time, exchange is economically irrelevant, though it might still be attempted for cultural reasons. The obstacles in the way of human interstellar travel are of course immense. I have long thought it vastly more plausible to send robots which could then build suitable environments in which to grow human beings [also recently proposed by Charlie Stross], and that involves bio-engineering hand-waving of epic proportions.)

Comment, Nov. 2021: On re-reading, my treatment of the Ricardian argument is a little cavalier, but I don't feel energetic enough to write out and solve a New Economic Geography model where population and comparative advantage are both endogenous. If anyone is inspired to do this properly, though, I'd be genuinely fascinated to read it, and promise to link here.

Update, 16 January 2022:: Tweaked the phrasing about opportunity costs in the 4th paragraph a little (and I hope removed more typos than I added).

The Eternal Science of These Infinite Spaces; The Dismal Science; Modest Proposals

Random-Feature Matching

\[ \newcommand{\ModelDim}{d} \]

Attention conservation notice: Academic self-promotion.

So I have a new preprint:

CRS, "A Note on Simulation-Based Inference by Matching Random Features", arxiv:2111.09220

We can, and should, do statistical inference on simulation models by adjusting the parameters in the simulation so that the values of randomly chosen functions of the simulation output match the values of those same functions calculated on the data. Results from the "state-space reconstruction" or "geometry from a time series" literature in nonlinear dynamics indicate that just \( 2\ModelDim+1 \) such functions will typically suffice to identify a model with a \( \ModelDim \)-dimensional parameter space. Results from the "random features" literature in machine learning suggest that using random functions of the data can be an efficient replacement for using optimal functions. In this preliminary, proof-of-concept note, I sketch some of the key results, and present numerical evidence about the new method's properties. A separate, forthcoming manuscript will elaborate on theoretical and numerical details.

I've been interested for a long time in methods for simulation-based inference. It's increasingly common to have generative models which are easy (or at least straightforward) to simulate, but where it's completely intractable to optimize the likelihood --- often it's intractable even to calculate it. Sometimes this is because there are lots of latent variables to be integrated over, sometimes due to nonlinearities in the dynamics. The fact that it's easy to simulate suggests that we should be able to estimate the model parameters somehow, but how?

An example: My first Ph.D. student, Linqiao Zhao, wrote her dissertation on a rather complicated model of one aspect of how financial markets work (limit-order book dynamics), and while the likelihood function existed, in some sense, the idea that it could actually be calculated was kind of absurd. What she used to fit the model instead was a very ingenious method which came out of econometrics called "indirect inference". (I learned about it by hearing Stephen Ellner present an ecological application.) I've expounded on this technique in detail elsewhere, but the basic idea is to find a second model, the "auxiliary model", which is mis-specified but easy to estimate. You then adjust the parameters in your simulation until estimates of the auxiliary from the simulation match estimates of the auxiliary from the data. Under some conditions, this actually gives us consistent estimates of the parameters in the simulation model. (Incidentally, the best version of those regularity conditions known to me are still those Linqiao found for her thesis.)

Now the drawback of indirect inference is that you need to pick the auxiliary model, and the quality of the model affects the quality of the estimates. The auxiliary needs to have at least as many parameters as the generative model, the parameters of the auxiliary need to shift with the generative parameters, and the more sensitive the auxiliary parameters are to the generative parameters, the better the estimates. There are lots of other techniques for simulation-based inference, but basically all of them turn on this same issue of needing to find some "features", some functions of the data, and tuning the generative model until those features agree between the simulations and the data. This is where people spend a lot of human time, ingenuity and frustration, as well as relying on a lot of tradition, trial-and-error, and insight into the generative model.

What occurred to me in the first week of March 2020 (i.e., just before things got really interesting) is that there might be a short-cut which avoided the need for human insight and understanding. That week I was teaching kernel methods and random features in data mining, and starting to think about how I wanted to revise the material on simulation-based inference for my "data over space and time" in the fall. The two ideas collided in my head, and I realized that there was a lot of potential for estimating parameters in simulation models by matching random features, i.e., random functions of the data. After all, if we think of an estimator as a function from the data to the parameter space, results in Rahimi and Recht (2008) imply that a linear combination of \( k \) random features will, with high probability, give an \( O(1/\sqrt{k}) \) approximation to the optimal function.

Having had that brainstorm, I then realized that there was a good reason to think a fairly small number of random features would be enough. As we vary the parameters in the generative model, we get different distributions over the observables. Actually working out that distribution is intractable, that's why we're doing simulation-based inference in the first place, but it'll usually be the case that the distribution changes smoothly with the generative parameters. That means that if there are \( \ModelDim \) parameters, the space of possible distributions is also just \( \ModelDim \)-dimensional --- the distributions form a \( \ModelDim \)-dimensional manifold.

And, as someone who was raised in the nonlinear dynamics sub-tribe of physicists, \( \ModelDim \)-dimensional manifolds remind me about state-space reconstruction and geometry from a time series and embedology. Specifically, back behind the Takens embedding theorem used for state-space reconstruction, there lies the Whitney embedding theorem. Suppose we have a \( \ModelDim \)-dimensional manifold \( \mathcal{M} \), and we consider a mapping \( \phi: \mathcal{M} \mapsto \mathbb{R}^k \). Suppose that each coordinate of \( \phi \) is \( C^1 \), i.e., continuously differentiable. Then once \( k=2\ModelDim \), there exists at least one \( \phi \) which is a diffeomorphism, a differentiable, 1-1 mapping of \( \mathcal{M} \) to \( \mathbb{R}^k \) with a differentiable inverse (on the image of \( \mathcal{M} \)). Once \( k \geq 2\ModelDim+1 \), diffeomorphisms are "generic" or "typical", meaning that they're the most common sort of mapping, in a certain topological sense, and dense in the set of all mappings. They're hard to avoid.

In time-series analysis, we use this to convince ourselves that taking \( 2\ModelDim+1 \) lags of some generic observable of a dynamical system will give us a "time-delay embedding", a manifold of vectors which is equivalent, up to a smooth change of coordinates, to the original, underlying state-space. What I realized here is that we should be able to do something else: if we've got \( \ModelDim \) parameters, and distributions change smoothly with parameters, then the map between the parameters and the expectations of \( 2\ModelDim+1 \) functions of observables should, typically or generically, be smooth, invertible, and have a smooth inverse. That is, the parameters should be identifiable from those expectations, and small errors in the expectations should track back to small errors in the parameters.

Put all this together: if you've got a \( \ModelDim \)-dimensional generative model, and I can pick \( 2\ModelDim+1 \) random functions of the observables which converge on their expectation values, I can get consistent estimates of the parameters by adjusting the \( \ModelDim \)-generative parameters until simulation averages of those features match the empirical values.

Such was the idea I had in March 2020. Since things got very busy after that (as you might recall), I didn't do much about this except for reading and re-reading papers until the fall, when I wrote it up as grant proposal. I won't say where I sent it, but I will say that I've had plenty of proposals rejected (those are the breaks), but never before have I had feedback from reviewers which made me go "Fools! I'll show them all!". Suitably motivated, I have been working on it furiously all summer and fall, i.e., wrestling with my own limits as a programmer.

But now I can say that it works. Take the simplest thing I could possibly want to do, estimating the location \( \theta \) of a univariate, IID Gaussian, \( \mathcal{N}(\theta,1) \). I make up three random Fourier features, i.e., I calculate \[ F_i = \frac{1}{n}\sum_{t=1}^{n}{\cos{(\Omega_i X_t + \alpha_i)}} \] where I draw \( \Omega_i \sim \mathcal{N}(0,1) \) independently of the data, and \( \alpha_i \sim \mathrm{Unif}(-\pi, \pi) \). I calculate \( F_1, F_2, F_3 \) on the data, and then use simulations to approximate their expectations as a function of \( \theta \) for different \( \theta \). I return as my estimate of \( \theta \) whatever value minimizes the squared distance from the data in these three features. And this is what I get for the MSE:

OK, it doesn't fail on the simplest possible problem --- in fact it's actually pretty close to the performance of the MLE. Let's try something a bit less well-behaved, say having \( X_t \sim \theta + T_5 \), where \( T_5 \) is a \( t \)-distributed random variable with 5 degrees of freedom. Again, it's a one-parameter location family, and the same 3 features I used for the Gaussian family work very nicely again:

OK, it can do location families. Since I was raised in nonlinear dynamics, let's try a deterministic dynamical system, specifically the logistic map: \[ S_{t+1} = 4 r S_t(1-S_t) \] Here the state variable \( S_t \in [0,1] \), and the parameter \( r \in [0,1] \) as well. Depending on the value of \( r \), we get different invariant distributions over the state-space. If I sampled \( S_1 \) from that invariant distribution, this'd be a stationary and ergodic stochastic process; if I just make it \( S_1 \sim \mathrm{Unif}(0,1) \), it's still ergodic but only asymptotically stationary. If I used the same 3 random Fourier features, well, this is the distribution of estimates from time series of length 100, when the true \( r=0.9 \), so the dynamics are chaotic:

I get very similar results if I use random Fourier features that involve two time points, i.e., time-averages of \( \cos{(\Omega_{i1} X_{t} + \Omega_{i2} X_{t-1} + \alpha+i)} \), but I'll let you look at those in the paper, and also at how the estimates improve when I increase the sample size.

Now I try estimating the logistic map, only instead of observing \( S_t \) I observed \( Y_t = S_t + \mathcal{N}(0, \sigma^2) \). The likelihood function is no longer totally pathological, but it's also completely intractable to calculate or optimize. But matching 5 (\( =2\times 2 + 1 \)) random Fourier features works just fine:

 

At this point I think I have enough results to have something worth sharing, though there are of course about a bazillion follow-up questions to deal with. (Other nonlinear features besides cosines! Non-stationarity! Spatio-temporal processes! Networks! Goodness-of-fit testing!) I will be honest that I partly make this public now because I'm anxious about being scooped. (I have had literal nightmares about this.) But I also think this is one of the better ideas I've had in years, and I've been bursting to share.

As \( r \) in the logistic map varies from 0 (dark blue) to 1 (light pink), time-averages of 3 random Fourier features trace out a smooth, one-dimensional manifold in three-dimensional space. Different choices of random features would give different embeddings of the parameter space, butthat three random features give an embedding is generic.

Update, 21 June 2022: a talk on this, in two days time.

Update, 12 September 2023: a funded grant.

Self-centered; Enigmas of Chance

Books to Read While the Algae Grow in Your Fur, October 2021

Attention conservation notice: I have no taste, and no qualifications to opine on the history of monsters in 18th century France, medieval political philosophy, the history and archaeology of images of monsters, trends in mortality and inequality in early 21st century America, or the comparative sociology of slavery. (Monsters, monsters everywhere.)

Jay M. Smith, Monsters of the Gévaudan: The Making of a Beast

A full-fledged historian of early modern France tackles the beast of the Gévaudan, with full attention to the cultural, political and journalistic (!) context. Smith disclaims wanting to tell the story of the beast, in favor of telling the story of the stories about the beast, but along the way he finds himself forced to make a good circumstantial case that "it" was, in fact, multiple hungry wolves. Strongly recommended for anyone with an interest in folklore, the intellectual history of early modern Europe, cryptozoology, or the dynamics of media-driven spasms of public and official attention.

Carol Goodman, Ghost Orchid

Mind candy: literary ghost story, involving a haunted writer's colony in upstate New York. About half of it might be a direct relation of the events a century before that set the haunting in motion, or might be the present-day heroine's novel in progress; they work either way.

Joan Aiken, The Green Flash, and Other Tales of Horror, Suspense, and Fantasy

Mind candy, displaying a remarkable range of flavors and tones. One uniformity: Aiken's men are all clueless about her female characters (it wouldn't be accurate to say "her women"), to comic and/or ominous effect.

F. G. Cottam, The Colony

Mind candy horror. There are some moments of real creepiness, but the whole plot for the last quarter or so is a bit rushed and sloppy.

Abu Nasr Muhammad ibn Muhammad al-Farabi (trans. and ed. Charles E. Butterworth), "Political Regime" and "Summary of Plato's Laws"

Political Regime opens with barely-comprehensible metaphysics (to put it kindly), before getting into an explanation of the different kinds of polities, and why the ones most favorable to philosophers are the best. (There are eventually connections between the metaphysics and the politics.) The Summary of Plato's Laws is, in fact, a summary of Plato's Laws, except for a few sections with no obvious antecedent in Plato's text as we now know it, and some very mysterious narratives (parables?) at the beginning. Reading between the lines, one has the clear impression that al-Farabi thought of Muhammad (pbuh) as a law-giver in Plato's sense... The translator is clearly a Straussian, which colors his commentary, and may contribute to this impression. (OTOH, I could believe that Strauss was right about al-Farabi, even if not right about the entirety of political philosophy before Machiavelli.) I found this fascinating in a "you are clearly very smart but also alien and just wrong, wrong, wrong" way, like many of the medievals, but mileage will vary. (Of course, as a denizen of one of the democratic cities or associations of freedom, I would think that.)

David Wengrow, The Origins of Monsters: Image and Cognition in the First Age of Mechanical Reproduction

This is an interesting historical/archaeological argument about the origin and spread of images of unreal, "composite" creatures combining distinct features of real animals (and/or distinct features of real animals and of human beings). Many at the borders of psychology and anthropology have claimed that such hybrid creatures are compelling and attractive objects of thought because they are "minimally counter-intuitive", they break just enough rules to focus the mind while still being amenable to various forms of intuitive cognition. (Obviously a griffin eats food, which it consumes through its mouth, it stabs with its beak, it rakes with its claws, it flies with its wings and walks with its legs --- but does it lay eggs?) If this is true, it suggests that composite animals are popular across time and space because they appeal to certain universal quirks of the human mind.

Wengrow, however, claims that hybrids are actually very rare in Paleolithic and Neolithic art, and only really take off with the appearance of cities, writing, modular thinking and technologies, and means of mechanical reproduction (like cylinder seals) in Egypt and, especially, Mesopotamia:

With the expansion of urban settlements throughout Mesopotamia during the fourth millennium BC, the trajectory toward standardization and modularity in material culture intensified markedly. Systems of modular construction, based on the assembly of standardized and interchangeable components, are evident not just in imagery at this time, but also across such diverse technological domains as mud-brick architecture and ceramic commodity packaging... These wider developments in material culture underpinned the invention, around 3300 BC, of the protocuneiform script. This new system of information storage was initially designed for bookkeeping purposes in large urban institutions, which acted as the religious and economic hubs of the earliest cities. It was based on a principle of differentiation whereby materials, animals, plants, and labor were divided into fixed subclasses and units of measurement, organized according to abstract criteria of number, order, and rank. Many of the earliest known administrative tablets thus functioned in a manner comparable to modern punch cards and balance sheets. In order for such a recording system to function, every named commodity---each beer or oil jar, each dairy vessel, and their contents, and each animal of the herd---had to be interchangeable with, and thus equivalent to, every other of the same administrative class. A smaller number of early inscriptions, known as lexical lists, appear to have had no direct administrative function, and may reflect the intellectual milieu of the earliest scribes, who engaged, as part of their training, in "fanciful paradigmatic name-generating exercises" for a wide range of subjects.
The invention of a novel repertory of composite figures can be seen to "fit" very logically into this urban and bureaucratic milieu. In pictorial art, new standards of anatomical precision and uniformity, evident in both miniature and monumental formats, echoed wider developments in material culture. Through the medium of sealing practices, miniature depiction remained closely tied to the practice of administration, which required the multiplication of standardized and clearly distinguishable signs for the official marking of commodities and documents. Variability among seal designs was generated through often-tiny adjustments in the appearance or arrangement of figures and motifs. These did not alter the overall visual statement, but allowed each design to fulfill its designated role as a discrete identifier within the larger administrative system to which it belonged.
In its search for new subject matter, it is hardly surprising that the "bureaucratic eye" was increasingly drawn to the possibilities of composite figuration... Not only did a composite approach to the rendering of organic forms greatly multiply the range of possible subjects for depiction. As Barbara Stafford points out, the counterfactual images that it produced also serve to emphasize details of anatomy that would normally "slip by our attention or be absorbed unthinkingly," becoming noticeable only when disaggregated from their ordinary contexts. Composites thus encapsulated, in striking visual forms, the bureaucratic imperative to confront the world, not as we ordinarily encounter it---made up of unique and sentient totalities---but as an imaginary realm made up of divisible subjects, each comprising a multitude of fissionable, commensurable, and recombinable parts. [pp. 69--73, omitting footnotes and references to figures]

(This doesn't quite say that composite animals were invented to increase the entropy of Sumerian passwords, but damn if it doesn't come close.)

From there he goes on to sketch their spread as Bronze Age civilization spread over the old world. He's quite aware that Mycenean Greece, to say nothing of Scythia, is very different from early dynastic Egypt or Sumer, and I don't think he ever quite reconciles the enthusiastic adoption of composite creature art by societies like those with his account of what motivated its creation. (Cf., in all seriousness, my reflections on Godzilla.) He does not consider new world civilizations at all.

It's interesting to me that Wengrow is explicitly "in dialogue" (as he might say) with Dan Sperber's "epidemiology of representations" school, but thinks he's uncovered something which forces a re-evaluation of key premises, on the grounds that composites were evidently not very compelling in pre-history, and something about how human minds are re-shaped by civilization is needed to make them compelling. In this I think he goes too far, for a number of reasons.

1. Sperber, at least, has always been clear that the "relevance" of an idea will depend on what other ideas are already being entertained.
2. Wengrow is making an argument from absence of evidence, when we're just missing lots of the visual media of pre-historic times (especially, perhaps, textiles), as he discusses himself. (Indeed, he suggests that pre-state societies might have had human-animal composites in the form of temporary rituals of transformation by shamans and the like, as opposed to enduring visual depictions.) But then the change might just have been who first figured out how to make compelling composites in sculpture and low relief. Even if we accept that there just weren't (e.g.) embroidered composite animals, a more cautious conjecture would be that the pioneering Bronze Age artists who gave us the griffin, the dragon, etc., were the ones who discovered how to create visual composite creatures in enduring media which were compelling enough to be successful (perhaps by activating mental modules for intuitive biology, etc.). This initial breakthrough may have been facilitated by the kind of society they were living in, but it might have spread and persisted for quite different reasons (cf., again, Godzilla).
3. Wengrow only considers visual depictions, and not stories (whether we call them folklore or mythology or something else). Obviously we don't have samples of pre-historic mythology, and using historic myths recorded from pre-literature cultures as a stand-in would be hazardous, but it'd at least be interesting to know if there are stories of composite animals from pre-literature societies which do not also make visual art of them of the kind Wengrow emphasizes. If we only found the stories where we also found the art, and we only found the art where it could (provably or plausibly) have been transmitted from the Bronze Age heartlands, well, that'd be pretty compelling support for Wengrow. But if the stories are more wide-spread than the art, that doesn't look great.
4. Wengrow rightly criticizes some earlier art-historical and archaeological writers for claiming that composite monsters are hard to remember or think about, without providing any kind of psychological evidence to back up this claim. But his own account of the origin of composite animals from the "bureaucratic imperative" is, in fact, an ambitious social-psychological hypothesis. It is supported by nothing more than his describing the purported cause and effect in ways which suggest an analogy. I realize this is a very common habit in the social sciences, but it has little to recommend it, and one goal the epidemiological approach is to demand a higher, and genuinely materialist, standard of explanation.

While I have gone on at some length about those critical points, I want to emphasize that I very much enjoyed the book, learned a lot of interesting things from it, and emerged with a lot to think on. It's also (fittingly) a very handsomely produced little tome.

ObLinkage, discovered after writing the above: A 2016 webinar on the book, with responses from Wengrow, at the International Cognition and Culture Institute, more or less the organizational home of the "epidemiology of representations" school. Many of these comments are interesting and sensible (I might particularly recommend the one by Karolina Prochownik). Wengrow's own replies to the comments are themselves constructive [*].

Edited to add in late November 2021: I had been meaning to read this for years, and finally did so this October for thematic reasons. I had no idea Wengrow had a new book coming out with the late David Graeber. In a very "Oh David Wengrow No" development, critics allege some really remarkable errors in that book [1, 2]. Those errors aren't relevant to this one, but also do not inspire confidence. On the other hand, they're far outside Wengrow's specialty of archaeology. On the third hand, this whole dispute is far outside my specialty, so who am I to judge?

[*]: Though he repeatedly (e.g., in response to Prochownik) shows he does not quite understand the idea of "attraction" as used by this school, since he contrasts "attraction" with "protection" and suggests that needs an immunological rather than an epidemiological metaphor. (This was also a theme he floated in the book, but it was less clear to me there that he didn't understand "attraction".) Sperber et al. are using "attraction" by analogy with "attractors" in dynamics --- an attractor is a configuration (or region in state space, etc.) which the system is drawn towards by its internal forces, even if it doesn't start there but more or less nearby. A cultural attractor, in Sperber's sense, need not be subjectively appealing, "attractive" in the everyday sense. Rather it needs to be mentally compelling, perhaps on an entirely automatic level, but perhaps also accompanied by such subjective emotions as dread, anxiety, or disgust. (On all this, see Chapter 5 of Sperber's Explaining Culture.) Using composite monsters apotropaically, Wengrow's "protective mode of transmission", might in fact be a cultural attractor in Sperber's sense, even though the point of such behavior is to drive dreaded or reviled things away.

Anne Case and Angus Deaton, Deaths of Despair and the Future of Capitalism

Read for the inequality class. It's depressing as hell. If you want a short version, you might try this from Case and Deaton, or this review by Atul Gawande. As always, the recommendations for action are the weakest part.

Susan Hill, The Various Haunts of Men

This is a skillfully-written mystery by the author of the exemplary The Woman in Black. While I (mostly) admired the artistry, and it's the first in a long series, some stuff happened towards the end which quite undid all my enjoyment, and it's extremely unlikely I'll read anything else in this series. However, after returning this to the library I immediately borrowed more of Hill's ghost stories.

ROT-13'd for spoilers: V jnf pbzcyrgryl ghearq bss ol gur jnl gur obbx xvyyrq bss Serln Tenssunz. V pbhyqa'g fnl fur jnf sevqtrq, rknpgyl, naq vg'f abg gung vg jnf haernyvfgvp, jvguva gur jbeyq bs gur fgbel, ohg vg frrzrq tenghvgbhfyl anfgl, naq n zrer cynlvat jvgu zl rzbgvbaf nf n ernqre. Lbhe zvyrntr znl inel, naq rivqragyl ybgf bs crbcyr rawbl gur frevrf n terng qrny.

Orlando Patterson, Slavery and Social Death: A Comparative Study

A deserved classic, which is why I read it downloaded from the ACLS Humanities E-Book website.

(There is an essay to be written --- it probably has been! --- on Patterson's flirtation with certain strands of Marxism here, and what it says about sociology, even or especially because Patterson is plainly not a Marxist.)

Elizabeth Hand, Black Light

Mind candy horror. Loosely, a sequel to Hand's magnificent Waking the Moon. It's set, mostly, in a town a little bit outside New York, full of eccentric actors who are, knowingly or not, engaged in a very dubious trade for their share of the limelight. I say "mostly" because important scenes take place in New York itself, and in places even stranger and creepier than Manhattan in the 1970s. It's not as good as Waking the Moon, but that's a very high bar, and this is very satisfying.

(I, for one, would be interested to know when and in what form Hand encountered the work of Mircea Eliade. The Sacred and the Profane plays a role in Generation Loss, while this book shows clear traces of Eliade's ideas about repetition of mythic patterns established in illo tempore (as we might say: "back in the day"), and at one point a character babbles out something which I am pretty sure is a paraphrase of the opening of ch. 14 of Shamanism. I am not sure whether Eliade-an themes could be detected in Waking the Moon, were I to re-read it.)

Books to Read While the Algae Grow in Your Fur; Commit a Social Science; Statistics of Inequality and Discrimination; The Dismal Science; Philosophy Islam and Islamic Civilization; Scientifiction and Fantastica; Writing for Antiquity; The Collective Use and Evolution of Concepts; Psychoceramics; Pleasures of Detection, Portraits of Crime

Books to Read While the Algae Grow in Your Fur, September 2021

Attention conservation notice: I have no taste, and no qualifications to opine on threats to modern democracies, the history of China and Europe c. 1600, or the sociology of the French Revolution of 1789.

William DeAndrea, Killed in the Ratings, Killed in the Act, Killed with a Passion, Killed on the Ice, Killed in Paradise, Killed in Fringe Time, Killed in the Fog

Mind candy. Obviously (?), a series of mystery novels, in which the protagonist, a fixer for a major TV network (back in the days when such mattered, and could be counted on one hand) solves a variety of business-related murders. These were re-reads for me, and obviously somewhat formulaic, but I enjoyed them even after I induced the formula.

Thomas M. Nichols, Our Own Worst Enemy: The Assault from within on Modern Democracy

This is, essentially, two-hundred-plus pages of moralizing scolding (as Nichols himself describes it), on the theme that life in rich democracies is so comfortable, but also so bland, that many people make up life-or-death political struggles into which they insert themselves, to their own detriment and that of the commonwealth. We are, in short, failing to exhibit proper (small-r) republican virtue. Now, I happen to find this a congenial length and topic for a moralizing sermon — after all, I don't feel existentially threatened, but I do feel like many of my fellow Americans are losing it, and I'm happy to devote a Sunday in a comfortable hammock to reading any scold as eloquent as Nichols — but I'm nonetheless a bit unsatisfied.

If I treated the matter seriously, I would want to see more of a case that current politics are not an existential threat to the republic as we have known it. (If nothing else, treating every election as though it might be the last could be a self-fulfilling prophecy! Nichols himself seems deeply concerned about this very prospect.) I would also want an account of how the same populace can simultaneously be in the grips of amoral familism and of political hobbyism [*]. (If one group of citizens is shrinking away from public life, while a different group obsesses over public affairs as a sort of sporting contest, that suggests very different diagnoses and remedies than if individuals spasmodically alternate between idiotic indifference and febrile excitement.) Nor am I re-assured by the way Nichols cites Jean Twenge as an authority on widespread narcissism, and more generally on what social media are doing to our minds.

No doubt, if I were to write a wide-ranging book about how the whole the world world is in a terrible state of chassis, I would do no better when it comes to confirmation bias and internal consistency. But I believe Nichols could have done better, and I wish he had.

[*]: Nichols never uses that phrase, which we owe to the political scientist Eitan Hersh, but it quite aptly sums up what Nichols sees as a common pathology. Even more oddly, he never cites Hersh's work on that topic, despite it being very much aligned with Nichols's themes, and Hersh himself popularized it in The Atlantic, for which Nichols often writes.

Rebecca Pawel, Death of a Nationalist, Law of Return, The Watcher in the Pine, The Summer Snow, What Happened After the War Was Over

Mind candy. The first four titles are mystery novels set in the aftermath of the Spanish Civil War. The main character is a (literal, no-exaggeration) fascist* policeman, and nonetheless extremely sympathetic, even though, or because, the author makes it very plain her sympathies lie with the losing, socialist-republican side in the civil war. (That Carlos and Elena are destined to end up together, despite their politics, is, I contend, obvious to anyone, except perhaps Carlos or Elena.) The last book is a collection of short stories which explore the fates of important characters after 1945; I think stopping at the fourth book is fine, but I'm glad I read the fifth. I had previously read the first book, back in 2004, but I enjoyed the re-read as much as I enjoyed plowing through the rest of the series, which is to say, a lot.

*: Technically a Falangist rather than a Fascist, but that's a distinction without a real difference, as Tejada would himself explain.

Jonathan D. Spence, The Memory Palace of Matteo Ricci

An engaging, and ultimately moving, portrait of both an individual and an age. Reading it makes me wonder at my own memory practices. You probably need some grounding in the history of both early modern Europe and early modern China to really get it, but if you have that background, it's a beautiful depiction of the work of cultural interchange.

(Thanks to AEO for lending me her copy, for discussing the book, and for allowing herself to be referred to.)

Paul McAuley, War of the Maps

Mind candy. This story of obsessive pursuit and alien invasion in a very, very old world --- one where we "Ur-Men" are a distant, reconstituted historical memory of a memory --- might not quite McAuley's best work, but it's still extremely good. Unusually for me, this was one where I alternated between the printed codex and the audiobook; I got so absorbed in the story that I didn't care.

Some of McAuley's self-expositions and excerpts: 1 2, 3, 4, 5, 6 7.

Alfred Cobban, The Social Interpretation of the French Revolution

If I take the facts presented here at face value, this is an absolutely devastating attack on the conventional interpretation of the French Revolution as the great bourgeois revolution. If I credit the much later introduction by Gwynne Lewis, I should do no such thing. I am clearly in no position to hold an opinion on these questions, so I will just recommend this as an extremely well-written historical polemic, albeit one whose implied reader knows a lot of the detailed events of the Revolution.

Books to Read While the Algae Grow in Your Fur; Pleasures of Detection, Portraits of Crime; Writing for Antiquity; Scientifiction and Fantastica; The Beloved Republic; The Continuing Crises; Tales of Our Ancestors

Books to Read While the Algae Grow in Your Fur, August 2021

Attention conservation notice: I have no taste, and no qualifications to opine on criticism of cultural criticism, the sociology and demography of race in America, the political philosophy of doing something about climate change, or Afrocentric historiography.

Jen Williams, A Dark and Secret Place, a.k.a. Dog Rose Dirt

Mind candy mystery: in which a young journalist dealing with her deceased mother's effects discovers just how messed up parts of the 1970s counter-culture could get. This is the same Williams who wrote some excellent fantasy novels [1, 2], and some of the same skills for the uncanny are deployed here, but in the end everything is definitely this-worldly (I think). I enjoyed this a lot and hope it does well, but not so well that Williams gives up fantasy for mystery entirely. §

Joseph Heath and Andrew Potter, Nation of Rebels: Why Counterculture Became Consumer Culture a.k.a. The Rebel Sell: Why the Culture Can't be Jammed

A scorched-earth attack on the theory and practice of the counter-culture, especially as we knew it in the period from, let us say, the end of the Cold War to Occupy Wall Street. There are places where I want to quibble with them [*], but over-all my reaction is "preach! preach!".

ObLinkage 1: A paper by Heath from 2001, summarizing the argument (and making explicit both, on the one hand, Heath's debts to both Habermas and game theory**, and on the other the affinity between Heath and Potter and the1990s Baffler crew.)

ObLinkage 2: the authors interviewed on the occasion of the 15th anniversary of the book. §

[*]: Simplifying, they attribute a lot of counter-cultural themes to a specific historical experience, viz., reacting against anything that seemed to lead to, or to resemble, Nazism. But (i) why should this remain persuasive for later generations? and (ii) lots of that reaction seems continuous with older patterns of disgust with mediocrity and conformity, which you can find in the 19th century easily enough. (I guess they might reply that the themes were old, but it took the 1940s to make them widely persuasive.) But their historical explanations are separate from their substantive criticisms.

[**]: More exactly, Habermas (partially) de-mystified through game theory. This fusion of actual (2nd wave) Frankfurt School critical theory and game theory is, I believe, unique to Heath, but I could wish it was more widespread among critical theorists.

Richard Alba, The Great Demographic Illusion: Majority, Minority, and the Expanding American Mainstream

This is a very detailed and thorough treatment of how the end of white America has been greatly, greatly exaggerated. One important contributor to this, in Alba's telling, was a decision on the part of the Census Bureau to produce summary statistics, and demographic projections, which count anyone with mixed white and non-white ancestry as non-white, i.e., to implement the old "one drop rule". (One of the ironies of Alba's account is that this was done to harmonize with decisions made by other parts of the federal government trying to enforce civil rights laws, and rather more defensibly on their part.) As Alba documents at some length, however, people of mixed white-Asian and white-Hispanic ancestry live and act very, very much like the children of unmixed non-Hispanic-white ancestry. In general, he shows, Asian and Hispanic groups are, in many ways, on a trajectory similar to those of immigrant groups from southern and eastern Europe in the 19th and early 20th century, being rapidly assimilated into a "mainstream" that is broadening its definition of what counts as, in some sense, fully American.

You will notice that this optimistic part of the story does not apply to black people or even to children of mixed black and white parentage.

I have only sketched a few of the highlights here. (If you want a few more details, the review in Dissent which lead me to the book is pretty good.) Alba is a careful if un-exciting writer who builds a detailed and persuasive case, and is good about admitting where the evidence is thin or ambiguous. If you're interested in these matters at all, I strongly recommend this. §

Horacio S. Wio, Path Integrals for Stochastic Processes: An Introduction

I have mixed feelings about this one. On the one hand, it's a perfectly decent introduction, for physicists, to calculating path integrals for continuous-time homogeneous Markov processes, especially when driven by Gaussian white noise. But it leaves out some of the things I'm most interested in learning about (Doi-Peliti formalism; the extent to which diagrammatic methods work for any stochastic process). Worse: Wio, sensibly enough for his audience, writes with physicists' customary level of mathematical hand-waving, and I have absorbed enough of the very different standards prevailing in theoretical statistics that I actually found myself, much to my surprise and even unease, craving more careful statements, more explicit theorem-proof organization, and more detailed regularity conditions. Since my middle-aged disciplinary-identity crisis is not Wio's problem, nor likely to be a concern for other readers, I think I can recommend this one generally to those who remember how Poisson brackets work. §

Joseph Heath, Philosophical Foundations of Climate Change Policy

I have rarely read any philosopher who so perfectly articulated my own prejudices and settled convictions on an important subject. Whether this is a recommendation for anyone else, I couldn't begin to say. §

Clarence E. Walker, We Can't Go Home Again: An Argument About Afrocentrism

Part of this is a very convincing argument that the Afrocentric historians don't know what they're talking about, and are indeed just providing an inverted Eurocentrism and a mythical Africa. Another part of this is tracing the origins of this historiographic tradition, to understandable efforts at highlighting black "contributions" and "achievements". A third is an argument about whether Afrocentric history was politically valuable in the conditions of America in the 1980s and 1990s. The first two aspects of this book remain solid; the third is inevitably less interesting now. §

Books to Read While the Algae Grow in Your Fur; Commit a Social Science The Beloved Republic; Philosophy; Pleasures of Detection, Portraits of Crime; Writing for Antiquity; Enigmas of Chance; Physics

Bayesianism in Math: No Dice

Attention conservation notice: Sniping at someone else's constructive attempt to get the philosophy of mathematics to pay more attention to how mathematicians actually discover stuff, because it uses an idea that pushes my buttons. Assumes you know measure-theoretic probability without trying to explain it. Written by someone with absolutely no qualifications in philosophy, and precious few in mathematics for that matter. Largely drafted back in 2013, then laid aside. Posted now in lieu of new content.

Wolfgang points to an interesting post [archived] at "A Mind for Madness" on using Bayesianism in the philosophy of mathematics, specifically to give a posterior probability for conjectures (e.g., the Riemann conjecture) given the "evidence" of known results. Wolfgang uses this as a jumping-off point for looking at whether a Bayesian might slide around the halting problem and Gödel's theorem, or more exactly whether a Bayesian with \( N \) internal states can usefully calculate any posterior probabilities of halting for another Turing machine with \( n < N \) states. (I suspect that would fail for the same reasons my idea of using learning theory to do so fails; it's also related to work by Aryeh "Absolutely Regular" Kontorovich on finite-state estimation, and even older ideas by the late great Thomas Cover and Martin Hellman.)

My own take is different. Knowing how I feel about the idea of using Bayesianism to give probabilities to theories about the world, you can imagine that I look on the idea of giving probabilities to theorems with complete disfavor. And indeed I think it would run into insuperable trouble for purely internal, mathematical reasons.

Start with what mathematical probability is. The basics of a probability space are a carrier space \( \Omega \), a \( \sigma \)-field \( \mathcal{F} \) on \( \Omega \), and a probability measure \( P \) on \( \mathcal{F} \). The mythology is that God, or Nature, picks a point \( \omega \in \Omega \), and then what we can resolve or perceive about it is whether \( \omega \in F \), for each set \( F \in \mathcal{F} \). The probability measure \( P \) tells us, for each observable event \( F \), what fraction of draws of \( \omega \) are in \( F \). Let me emphasize that there is nothing about the Bayes/frequentist dispute involved here; this is just the structure of measure-theoretic probability, as agreed to by (almost) all parties ever since Kolmogorov laid it down in 1933 ("Andrei Nikolaevitch said it, I believe it, and that's that").

To assign probabilities to propositions like the Riemann conjecture, the points in the base space \( \omega \) would seem to have to be something like "mathematical worlds", say mathematical models of some axiomatic theory. That is, selecting an \( \omega \in \Omega \) should determine the truth or falsity of any given proposition like the fundamental theorem of algebra, the Riemann conjecture, Fermat's last theorem, etc. There would then seem to be three cases:

0. The worlds in \( \Omega \) conform to different axioms, and so the global truth or falsity of a proposition like the Riemann conjecture is ambiguous and undetermined.
1. All the worlds \( \Omega \) conform to the same axioms, and the conjecture, or its negation, is a theorem of those axioms. That is, it is true ( or false) in all models, no matter how the axioms are interpreted, and hence it has an unambiguous truth value.
2. The worlds all conform to the same axioms, but the proposition of interest is true in some interpretations of the axioms and false in others. Hence the conjecture has no unambiguous truth value.

Case 0 is boring: we know that different axioms will lead to different results. Let's concentrate on cases 1 and 2. What do they say about the probability of a set like \( R = \left\{\omega: \text{Riemann conjecture is true in}\ \omega \right\} \)?

Case 1: The Conjecture Is a Theorem

Case 1 is that the conjecture (or its negation) is a theorem of the axioms. Then the conjecture must be true (or false) in every \( \omega \), so \( P(R) = 0 \) or \( P(R) = 1 \). Either way, there is nothing for a Bayesian to learn.

The only escape I can see from this has to do with the \( \sigma \)-field \( \mathcal{F} \). Presumably, in mathematics, this would be something like "everything easily deducible from the axioms and known propositions", where we would need to make "easy deduction" precise, perhaps in terms of the length of proofs. It then could happen that \( R \not\in \mathcal{F} \), i.e., the set is not a measurable event. In fact, we can deduce from Gödel that many such sets are not measurable if we take \( \mathcal{F} \) to be "is provable from the axioms", so even more must be non-measurable if we restrict ourselves to not seeing very far beyond the axioms. We could then bracket the probability of the Riemann conjecture from below, by the probability of any measurable sub-set (sub-conjecture?), and from above, by the probability of any measurable super-set. (The "inner" and "outer" measures of a set come, roughly speaking, from making those bounds as tight as possible. When they match, the set is measurable.) But even then, every measurable set has either probability 0 or probability 1, so this doesn't seem very useful.

(The poster, hilbertthm90, suggests bracketing the probability of the conjecture by getting "the most optimistic person about a conjecture to overestimate the probability and the most skeptical person to underestimate the probability", but this assumes that we can have a probability, rather than just inner and outer measures. This is also a separate question from the need to make up a number for the probability of known results if the conjecture is false. This is the problem of the catch-all or unconceived-alternative term, and it's crippling.)

Another way to get to the same place is to look carefully at what's meant by a \( \sigma \)-field. It is a collection of subsets of \( \Omega \) which is closed under repeating the Boolean operations of set theory, namely intersection, union and negation, a countable infinity of times. Anything which can be deduced from the axioms in a countable number of steps is included. This is a core part of the structure of probability theory; if you want to get rid of it, you are not talking about what we've understood by "probability" for a century, but about something else. It is true that some people would weaken this requirement from a \( \sigma \)-field to just a field which is closed under a finite number of Boolean operations, but that would still permit arbitrarily long chains of deduction from axioms. (One then goes from "countably-additive probability" to "finitely-additive probability".) That doesn't change the fact that anything which is deducible from the axioms in a finite number of steps (i.e., has a finite proof) would have measure 1.

Said yet a third way, a Bayesian agent immediately has access to all logical consequences of its observations and its prior, including in its prior any axioms it might hold. Hence to the extent that mathematics is about finding proofs, the Bayesian agent has no need to do math, it just knows mathematical truths. The Bayesian agent is thus a very, very bad formalization of a human mathematician indeed.

Case 2: The Conjecture Is Not a Theorem

In this case, the conjecture is true under some models of the axioms but false in others. We thus can get intermediate probabilities for the conjecture, \( 0 < P(R) < 1 \). Unfortunately, learning new theorems cannot change the probability that we assign to the conjecture. This is because theorems, as seen above, have probability 1, and conditioning on an event of probability 1 is the same as not conditioning at all.

There are a lot of interesting thoughts in the post about how mathematicians think, especially how they use analogies to get a sense of which conjectures are worth exploring, or feel like they are near to provable theorems. (There is also no mention of Polya: but sic transit gloria mundi.) It would be very nice to have some formalization of this, especially if the formalism was both tractable and could improve practice. But I completely fail to see how Bayesianism could do the job.

That post is based on Corfield's Towards a Philosophy of Real Mathematics, which I have not laid hands on, but which seems, judging from this review, to show more awareness of the difficulties than the post does.

Addendum, August 2021: I have since tracked down an electronic copy of Corfield's book. While he has sensible things to say about the role of conjecture, analogy and "feel" in mathematical discovery, drawing on Polya, he also straightforwardly disclaims the "logical omniscience" of the standard Bayesian agent. But he does not explain what formalism he thinks we should use to replace standard probability theory. (The terms "countably additive" and "finitely additive" do not appear in the text of the book, and I'm pretty sure "\( \sigma \)-field" doesn't either, though that's harder to search for. I might add that Corfield also does nothing to explicate the carrier space \( \Omega \).) I don't think this is because Corfield isn't sure about what the right formalism would be; I think he just doesn't appreciate how much of the usual Bayesian machinery he's proposing to discard.

Mathematics; Philosophy; Bayes, anti-Bayes

CLeaR 2022: Call for Papers

Attention conservation notice: An invitation to put a lot of effort into writing about a recondite academic topic, only to have it misunderstood by anonymous strangers.

Having agreed to be an area chair (area TBD), I ought to publicize the call for papers for the first Conference on Causal Learning and Reasoning (CLeaR 2022):

Causality is a fundamental notion in science and engineering. In the past few decades, some of the most influential developments in the study of causal discovery, causal inference, and the causal treatment of machine learning have resulted from cross-disciplinary efforts. In particular, a number of machine learning and statistical analysis techniques have been developed to tackle classical causal discovery and inference problems. On the other hand, the causal view has been shown to facilitate formulating, understanding, and tackling a broad range of problems, including domain generalization, robustness, trustworthiness, and fairness across machine learning, reinforcement learning, and statistics.

We invite papers that describe new theory, methodology and/or applications relevant to any aspect of causal learning and reasoning in the fields of artificial intelligence and statistics. Submitted papers will be evaluated based on their novelty, technical quality, and potential impact. Experimental methods and results are expected to be reproducible, and authors are strongly encouraged to make code and data available. We also encourage submissions of proof-of-concept research that puts forward novel ideas and demonstrates potential for addressing problems at the intersection of causality and machine learning.

The proceedings track is the standard CLeaR paper submission track. Papers will be selected via a rigorous double-blind peer-review process. All accepted papers will be presented at the Conference as contributed talks or as posters and will be published in the Proceedings.

Topics of submission may include, but are not limited to:

• Machine learning building on causal principles
• Causal discovery in complex environments
• Efficient causal discovery in large-scale datasets
• Causal effect identification and estimation
• Causal generative models for machine learning
• Unsupervised and semi-supervised deep learning connected to causality
• Machine learning with heterogeneous data sources
• Benchmark for causal discovery and causal reasoning
• Reinforcement learning
• Fairness, accountability, transparency, explainability, trustworthiness, and recourse
• Applications of any of the above to real-world problems

The deadline is 22 October 2021; further details are available at the conference website.

(I should write up my "Apology for Causal Discovery" as a proper paper or at least essay, rather than a pair of slide decks and a video which [like all recordings of me] I can't stand to watch, but that's so far back in the queue I could cry.)

Constant Conjunction Necessary Connexion; Kith and Kin

Books to Read While the Algae Grow in Your Fur, July 2021

Attention conservation notice: I have no taste, and no qualifications to opine on culture-bound syndromes and contagious hysterias, the history and economics of socialist planning, economic inequality, or Islamic theology.

Elaine Showalter, Hystories: Hysterical Epidemics and Modern Culture (Columbia University Press, 1997)

Showalter's theory is, roughly, as follows. Modern life produces lots of seriously unhappy, even traumatized, people. Some, at least, of those people are apt act out their unhappiness in various bodily symptoms and behaviors. This acting out is more or less unconscious, usually more rather than less. There is a certain amount of random flailing around (as it were) when it comes to these symptoms, but people tend to be attracted to patterns of behavior which have some sort of authoritative imprimatur among those around them as reflecting real distress. There is thus a symbiosis between clinicians who recognize syndromes-of-distress and patients who enact those syndromes. Showalter calls the syndromes forms of "hysteria", and the associated narratives "hystories". To really make the symbiosis work, however, one needs a mass medium to widely disseminate the scripts or schemata for the syndrome, perhaps as elements in popular fiction.

Showalter applies this theory to the original "classical hysteria" of Charcot et al. in the late 1800s, and, in the 1980s and 1990s when she was writing, to alien abduction, chronic fatigue syndrome, Satanic ritual abuse, recovered memory, Gulf War syndrome, and multiple personality disorder. The late-20th-century cases are distinguished from the late-19th-century ones by the fact that they all involve conspiracy theories; Showalter is very firm, and correct, about this development, but doesn't really try to explain it. (It's not as though the 19th century had any shortage of conspiracy theories, and it'd need little more than search-and-replace to turn The Awful Disclosures of Maria Monk into a tale of Satanic ritual abuse.) I want to single out the chapters on recovered memory, multiple personality disorder, Satanic ritual abuse and alien abduction for how carefully, and convincingly, Showalter shows they follow her model.

A quarter-century later, some of these syndromes have all but vanished, but there's no shortage of replacements. (Listing them is left as an exercise for the reader.) Why we should be so productive of "hystories" is not really something Showalter adequately explains, beyond gesturing at millennial anxiety and/or modern telecommunications.

At this point I'd like to make one complaint, two anthropological connections, and one mathematical aside.

• Showalter does not give enough weight to the possibility that something which looks like a hysteria with physical symptoms might in fact be a conventional illness. (That is, she doesn't consider how to distinguish social from biological contagion*.) I think in many ways this would have been a much stronger book if it had had a chapter on Lyme disease (which we now know is a bacterial illness transmitted by ticks) and the supposed chronic Lyme disease (which fits Showalter's ideas to a T). It wouldn't surprise me if some of the people who suffer from chronic fatigue syndrome are in fact dealing with currently-unrecognized organic conditions; it would surprise me very much if alien abductees were. (Cf. this contemporary review from Carol Tavris.)
• A lot of Showalter's ideas are close to those put forward by the anthropologist I. M. Lewis in Ecstatic Religion: A Study of Shamanism and Spirit Possession (first ed. 1971). What might be distinctly modern about Showalter's syndromes, as opposed to Lewis's, is the role of mass media in their spread and institutionalization.
• Dan Sperber would have a field day with this. In particular, Showalter's ideas seem extremely compatible with Sperber's about how the "epidemiology of representations" needs to combine transmission and "attraction".
• I'm tempted to model the growth of "hystories" using the classic Simon (1955) process: with some probability each unhappy person spawns a new form of hysteria, otherwise they attach themselves to an existing one with a probability proportional to its current size. (That is, preferential attachment to hysterias.) This will, of course, lead to a heavy-tailed distribution of hysterias. The flaw here is that this model wouldn't explain the disappearance of forms of hysteria; there might need to be some sort of recency effect.

I was alerted to this book, but put off from reading it, by a contemporary review in Nature; it now seems to me that the reviewer was unfair about the quality of Showalter's writing. (Perhaps my taste has been degraded by a quarter century of reading academic prose.) There are ways in which I'd re-write this book (it's still too Freudian, and in places too cutesy [e.g., the coinage "hystories" itself]), and, inevitably, parts are dated. I would really like to read Showalter giving the same treatment to the last quarter century, but, given her experiences after publishing this, I understand why she'd decline, to the public's loss. I urge the book on any reader with a serious interest in social contagion, or in the weirder reaches of modern culture.

*: My former student Dena Asta wrote did some nice research, back in 2012--2013, based on the idea that a social contagion will spread through "communities" or "modules" defined by the social network, while a biological contagion will need physical proximity. To the extent that network modularity and geographic propinquity cut across each other, we can get some handle on what form of contagion we're dealing with, assuming it's contagion at all. This, however, is taking us very far from Showalter's concerns.

Michael Ellman, Socialist Planning (3rd edition, 2014)

This is a very complete revision of a book whose first (1979) edition I reviewed earlier. The revision brings the story up to the early 2010s (in the case of China), and makes extensive use of sources and studies which have only become available since the collapse of the Soviet Union.

Geographically, coverage remains focused on the Soviet Union, but there are also extensive discussions of the Chinese experience, and a great deal more than I remember from the first edition about Yugoslavia, Poland, Hungary, and East Germany. Other eastern-European countries and Vietnam are mentioned sporadically, Cuba even less often, North Korea just a few times in passing. There is extensive information about how plans were drawn up, how the authorities attempted to implement them, what actually happened instead, etc. Coverage of the military sector, and the way preparation for another WWII-style conflict influenced every aspect of Soviet economic planning, is drastically expanded. (According to Ellman, much of the output of the aluminum and fertilizer industries was simply wasted year after year, because factories ran at levels suitable for producing vast numbers of warplanes and munitions, not actual needs.) The general tone is of trying to describe, and evaluate, a phenomenon which has passed and will never recur. To sum up Ellman's judgment: socialist planning was an attempt at modernization from above, driven by the imperative of being militarily competitive with industrialized European powers. In that goal, it succeeded, at least up through the 1950s. As a fulfillment of the ethical aims of socialism, it failed and was doomed to fail.

I find it hard to imagine that a better overview of socialist planning, as it actually existed, will be available any time soon.

Michele Alacevich and Anna Soci, Inequality: A Short History [JSTOR]

This isn't so much a history of inequality as of economists' ideas about inequality. Indeed, much of it takes the form of rehashing famous recent work. (E.g., chapter 4, "Inequality and Globalization", is largely about Branko Milanovic's Global Inequality. [It's a good book.]) They do make the interesting point that both classical and neo-classical economics focused on the distribution of income across factors of production, rather than the distribution of income (or wealth) across persons or households. But the point is somewhat undercut by the fact that the statistical study of income and wealth distributions owes so much to Pareto, who was also one of the founders of neo-classical economics! I found some of the history in ch. 3, "The Statistical Drift of Inequality Studies", to be interesting, though I think a bit unfair to Pareto (regular readers will understand what such a statement costs me). I also found Alacevich and Soci's repeated slagging on economists for merely doing empirical studies of income distribution a bit unfortunate --- surely before coming up with a theoretical explanation, it's important to know what the phenomena to be explained actually are!

Over-all, if you have read any two of Milanovic, Piketty and Bartels, you will not find much new here. I might assign some of the history-of-statistics portions in my class.

Karin Slaughter, The Last Widow and The Silent Wife

Mind candy, mystery/thriller division. Umpteenth volumes in Slaughter's long-running series, which I enjoy very much. The Last Widow is a 2019 publication which involves (not to spoil anything) biological terrorism, the CDC, and a right-wing attack on a seat of government. Looking back from mid-2021, therefore, I am very relieved that The Silent Wife is merely about personal betrayal and serial killing. Both are very well-written and enjoyable, if full of squicky parts.

(I think it is, however, a defect in construction that the dramatic, newsworthy, and emotionally-scarring events of Last Widow are basically not mentioned in Silent Wife, despite its taking place a mere six weeks later. It's also atypical of Slaughter, since one of the things I enjoy about her series is that there are consequences.)

John Renard (ed.), Islamic Theological Themes: A Primary Source Reader

Does what it says. I'm impressed by the range of texts --- ideologically, geographically, chronologically --- but utterly incompetent to evaluate it.

S. A. Chakraborty, The Kingdom of Copper

Mind candy fantasy: sequel to City of Brass. I found the continuing story enjoyable, but the language is, to borrow a phrase from Le Guin, very much that of Poughkeepsie rather than Elfland, despite being almost entirely set in Elfland (or, more precisely, Jinnistan). Still, I immediately got the sequel after finishing this.

Anna Lee Huber, A Wicked Conceit

Mind candy mystery. I think it's probably just as good as the earlier books, but that series fatigue has set in for me after nine volumes. They will, however, loose little from being read out of order.

Update, 28 August 2021: Fixed an editing fragment that turned a sentence about Alacevich and Soci into mush.

Books to Read While the Algae Grow in Your Fur; Islam and Islamic Civilization; Writing for Antiquity; Pleasures of Detection, Portraits of Crime; The Dismal Science; The Progressive Forces; Psychoceramica; Minds, Brains, and Neurons; Actually, "Dr. Internet" Is the Name of the Monster's Creator

Books to Read While the Algae Grow in Your Fur, June 2021

Attention conservation notice: I have no taste, and no qualifications to opine on cryptozoology, folklore, economics, or humanistic geography.

Anne Perry, The Cater Street Hangman

Mind candy historical mystery. Enjoyable, but I fail to see why this should have sparked a series of dozens of books over decades.

Benjamin Radford and Joe Nickell, Lake Monster Mysteries: Investigating the World's Most Elusive Creatures

Shorter: There are no lake monsters, just logs, otters, and stories about lake monsters.

Longer: Mostly this is an account of the authors' travels to various lakes which are claimed to have monsters, and the authors' (very tame) adventures debunking the stories, i.e., providing mundane accounts of what could have caused sightings or what's really in particular photographs. They are very fond of invoking logs, tree stumps, and otters. (I am persuaded about the timber and open-minded about the otters.) This is pretty standard fare, of the kind I have enjoyed since I was a boy and my mother would buy me issues of Skeptical Inquirer.

There is also a not-quite-fully-articulated theory of lake monsters hinted at here. If I try to draw this out explicitly, it'd be something like this: lake monsters are a modern myth, originating with Loch Ness in the 1930s, with the idea being that lakes are inhabited by surviving plesiosaurs, or something near enough. (One ancestor of the myth is thus the genre of "lost world" adventure stories.) Pre-modern stories about strange creatures in lakes get invoked by the myth as "evidence", regardless of their content or context; occasionally accounts of pre-modern stories are fabricated as needed. When people who know the myth see strange things on lakes, which is common enough, knowledge of the myth provides an interpretation for an ambiguous experience, and an opportunity for recounting the myth with an additional report attached. (It is enough for these purposes that the people be able to say "I don't know what I saw, but I saw something".) The myth spreads from lake to lake, partly through natural diffusion, and partly through the efforts of local chambers of commerce to drum up tourism.

As I said, the theory of lake monsters in the previous paragraph is me trying to articulate Radford and Nickell's hints by stringing their scattered remarks together with bits of Dan Sperber and Pascal Boyer. The authors themselves repeatedly refer to a work by an actual folklorist (Michel Meuger's 1988 Lake Monster Traditions: A Cross-Cultural Analysis) in ways which make me eager to track down a copy.

Jeff Lemire and Dean Ormston, Black Hammer: Secret Origins

Alex Robinson's Lower Regions

Rick Remender, Eric Nguyen et al., Strange Girl

Kel Symons and Mathew Reynolds, The Mercenary Sea

Comic book mind candy, assorted.

Pierro Sraffa, Production of Commodities by Means of Commodities: Preliude to a Critique of Economic Theory

This is a little book drafted in the 1920s and published in 1960, which became the subject of a huge literature. I have read a lot about it over the years, since it became a touchstone for some strands of heterodox economics, but never actually read it until this month. Having done so I find it very strange, not least because I feel like it could have be shortened still further, and yet clarified, if Sraffa had just used some basic theory for directed graphs and invoked the Frobenius-Perron theorem. (It's possible that the theory about directed graphs didn't exist when he first wrote, and even that the Frobenius-Perron theorem was then too obscure, but by 1960?) I am in fact tempted to re-write it doing just that, but I presume somebody out there in neo-Ricardian / post-Keynesian / post-Marxist land has done so, and I call upon the LazyWeb for a reference.

(Thanks to Z. M. Shalizi for lending me his copy.)

Yi-Fu Tuan, Dominance and Affection: The Making of Pets [JSTOR]

This is a beautifully-written and thought-provoking, perhaps even disturbing, book. It's an examination across history and time of the ways people make others --- plants, animals, and indeed other people --- into playthings, into objects which they can manipulate, and consequently bestow affection upon. I am sure there are people who can read it without coming to look at their own affections in a different light, but I'd prefer not to know them.

This book is part of a loose series that Tuan wrote, looking at what one might call the moral psychology of different aspects of humans' experience of their environments --- Segmented Worlds and Self, Landscapes of Fear, Escapism, Cosmos and Hearth, etc. These are all marked by the same virtues as this book: vast learning worn lightly, smooth-flowing writing, and an acute ethical sensitivity that is never preachy. I recommend them all very highly indeed.

(Thanks to Jan Johnson for the gift of this book.)

Norbert Wiener, The Fourier Integral and Certain of Its Applications

Recommended purely for historical interest. If you already are familiar with Fourier analysis and are curious to see it at any earlier stage in its development, this is interesting work from a pioneer. (And it's full of curious sidelights, such as the fact that Wiener in 1933 doesn't have the word "convolution" in its modern mathematical-English sense, but uses the German Faltung for lack of any translation.) But I don't think there are insights or techniques which aren't fully assimilated into the modern mainstream.

Glenn C. Loury, The Anatomy of Racial Inequality

Re-read for course prep. If it was in print I'd probably make it a required text; as it is I expect to assign passages from chapters 2 ("Racial Stereotypes") and 3 ("Racial Stigma") in the unit on mechanisms that create and perpetuate inequalities.

Books to Read While the Algae Grow in Your Fur; Scientifiction and Fantastica; Mathematics; Pleasures of Detection, Portraits of Crime; Tales of Our Ancestors; The Dismal Science; Commit a Social Science; Philosophy; Psychoceramics

Course Announcement: "Statistics of Inequality and Discrimination" (36-313)

Attention conservation notice: Advertisement for a course you won't take, at a university you don't attend. Even if the subject is of some tangential interest, why not check back in a few months to see if the teacher has managed to get himself canceled, and/or produced anything worthwhile?

In the fall I will, again, be teaching something new:

36-313, Statistics of Inequality and Discrimination
9 units
Time and place: Tuesdays and Thursdays, 1:25 -- 2:45 pm, location TBA
Description: Many social questions about inequality, injustice and unfairness are, in part, questions about evidence, data, and statistics. This class lays out the statistical methods which let us answer questions like Does this employer discriminate against members of that group?, Is this standardized test biased against that group?, Is this decision-making algorithm biased, and what does that even mean? and Did this policy which was supposed to reduce this inequality actually help? We will also look at inequality within groups, and at different ideas about how to explain inequalities between groups. The class will interweave discussion of concrete social issues with the relevant statistical concepts.
Prerequisites: 36-202 ("Methods for Statistics and Data Science") (and so also 36-200, "Reasoning with Data")

This is a class I've been wanting to teach for some years now, and I'm very happy to finally get the chance to feel my well-intentioned but laughably inadequate efforts crushed beneath massive and justified opprobrium evoked from all sides bore and perplex some undergrads who thought they were going to learn something interesting in stats. class for a change try it out.

Tentative topic schedule

About one week per.

1. "Recall": Reminders about probability and statistics: populations, distribution within a population, distribution functions, joint and conditional probability; samples and inference from samples. Reminders (?) about social concepts: ascriptive and attained social categories; status, class, race, caste, sex, gender, income, wealth.
2. Income and wealth inequality: What does the distribution of income and wealth look like within a population? How do we describe population distributions, especially when there is an extreme range of values (a big difference between the rich and poor)? Where does the idea of "the 1%" wealthy elite come from? How has income inequality changed over recent decades?
   Statistical tools: measures of central tendency (median, mode, mean), of dispersion, and of skew; the concept of "heavy tails" (the largest values being orders of magnitude larger than typical values); log-normal and power law distributions; fitting distributions to existing data; positive feedback, multiplicative growth and "cumulative advantage" processes.
3. Income disparities: How does income (and wealth) differ across groups? How do we compare average or typical values? How do we compare entire distributions? How have income inequalities by race and sex changed over recent decades?
   Statistical tools: permutation tests for differences in mean (and other measures of the average); two-sample tests for differences in distribution; inverting tests to find the range of differences compatible with the data; the "analysis of variance" method of comparing populations; the "relative distribution" method of comparing populations
4. Detecting discrimination in hiring: Do employers discriminate in hiring (or schools in admission, etc.)? How can we tell? When are differences in hiring rates evidence for discrimination? How do statistical perspectives on this question line up with legal criteria for "disparate treatment" and "disparate impact"?
   Statistical tools: tests for differences in proportions or probabilities; adjusting for applicant characteristics; deciding what to adjust for
5. Detecting discrimination in policing: Do the police discriminate against members of particular racial groups? When do differences in traffic stops, arrests, or police-caused deaths indicate discrimination? Does profiling or "statistical discrimination" make sense for the police? Can groups be simultaneously be over- and under- policed?
   Statistical tools: test for differences in proportions; signal detection theory; adjusting for systematically missing data; self-reinforcing equilibria
6. Algorithmic bias: Can predictive or decision-making algorithms be biased? What would that even mean? Do algorithms trained on existing data necessarily inherit the biases of the world? What notions of fairness or unbiased can we actually implement for algorithms? What trade-offs are involved in enforcing different notions of fairness? Are "risk-prediction instruments" fair?
   Statistical tools: Methods for evaluating the accuracy of predictions; differential error rates across groups; decision trees; optimization and multi-objective optimization.
7. Standardized tests: Are standardized tests for school admission biased against certain racial groups? What does it mean to measure qualifications, and how would we know whether tests really are measuring qualifications? What does it mean for a measurement to be biased? When do differences across groups indicate biases? (Disparate impact again.) Why correlating outcomes with test scores among admitted students may not make sense. The "compared to what?" question.
   Statistical tools: Predictive validity; differential prediction; "conditioning on a collider"
8. Intelligence tests: Are intelligence tests biased? How do we measure latent attributes? How do we know the latent attributes even exist? What would it mean for there to be such a thing as "general intelligence", that could be measured by tests? What, if anything, do intelligence tests measure? What rising intelligence test results (the Flynn Effect) tell us?
   Statistical tools: correlation between test scores; factor models as an explanation of correlations; estimating factor values from tests; measurement invariance; alternatives to factor models
9. Implicit bias: Do "implicit association tests" measure unconscious biases? Again on measurement, as well as what it would mean for a bias to be "implicit" or "unconscious". What, if anything, do implicit association tests measure?
   Statistical tools: Approaches to "construct validity".
10. Interventions on implicit bias: Can trainings or other interventions reduce implicit bias? How do we investigate the effectiveness of interventions? How do we design a good study an intervention? How do we pool information from multiple studies. Do implicit bias interventions change behavior? Does having a chief diversity officer increase faculty diversity?
    Statistical tools: Experimental design: selecting measurements of outcomes, and the importance of randomized studies; meta-analytic methods for combining information.
11. Explaining, or explaining away, inequality: To what extent can differences in outcomes between groups be explained by differences in their attributes (e.g., explaining differences in incomes by differences in marketable skills)? How should we go about making such adjustments? Is it appropriate to treat discrimination as the "residual" left unexplained? When does adjusting or controlling for a variable contribute to an explanation, and when is it "explaining away" discrimination? What would it mean to control for race, sex or gender?
    Statistical tools: Observational causal inference; using regression to "control for" multiple variables at once; using graphical models to represent causal relations between variables; how to use graphical models to decide what should and what should not be controlled for; the causal model implicit in decisions about controls.
12. Self-organizing inequalities and "structural" or "systematic" inequalities: Models of how inequalities can perpetuate themselves even when nobody is biased. Models of how inequalities can appear even when nobody is biased. The Schelling model of spatial segregation as a "paradigm". How relevant are Schelling-type models to actual, present-day inequalities?
    Statistical tools: Agent-based models; models of social learning and game theory.
13. Statistics and its history: The development of statistics in the 19th and early 20th century was intimately tied to the eugenics movement, which was deeply racist and even more deeply classist, but also often anti-sexist. The last part of the course will cover this history, and explain how many of the intellectual tools we have gone over to document, and perhaps to help combat, inequality and discrimination were invented by people who wanted to use them for quite different purposes. The twin learning objectives for this section are for students to grasp something of this history, and to grasp why the "genetic fallacy", of judging ideas by where they come from (their "genesis") is, indeed, foolish and wrong.
    Statistical tools: N/A.

Evaluation

There will be one problem set per week; each of these homeworks will involve some combination of (very basic) statistical theory, (possibly less basic) calculations using the theory we've gone over, and analysis of real data sets using the methods discussed in class. There will also be readings for each class session, and a short-answer quiz after each session will combine questions based on lecture content with questions based on the readings.

There will not be any exams.

My usual policy is to drop a certain number of homeworks, and a certain number of lecture/reading questions, no questions asked. The number of automatic drops isn't something I'll commit to here and now (similarly, I won't make any promises here about the relative weight of homework vs. lecture-related questions).

Textbook, Lecture Notes

There is, unfortunately, no one textbook which covers the material we'll go over at the required level. You will, instead, get very detailed lecture notes after each lecture. There will also be a lot of readings from various books and articles. (I will not agree with every reading I assign.)

Teaching: Statistics of Inequality and Discrimination; Corrupting the Young; Enigmas of Chance; Commit a Social Science

Books to Read While the Algae Grow in Your Fur, May 2021

Attention conservation notice: I have no taste.

Lauren Henderson, Dead White Female and Too Many Blondes

Mind candy mystery from the 1990s. I read all of the later books in this series with great delight as they came out, and while these first two are a bit rougher than her later work, they're still quite tasty, especially if you remember the fashions and mores of the time.

(I've included links to the old paper editions, but you'd be better off tracking down the electronic re-issues.)

Andre Norton, Gates to the Witch World (= Witch World, Web of the Witch World, Year of the Unicorn)

I don't remember what led me to pick this up, but damn could Norton write, and write compressedly. (For instance, a lot of the plot of the first two books here got recycled for the plot of Martha Wells's [very good] Fall of Ile-Rein series.) I had in fact read Year of the Unicorn as a boy, but remembered only a few fragments of the story.

ObLinkage: James Davis Nicoll on Witch World, Web of the Witch World, and Year of the Unicorn

Taylor Adams, No Exit

Mind-candy thriller, which I think conforms to every one of the classical dramatic unities.

L. G. Estrella, Two Necromancers, a Bureaucrat, and an Army of Golems and Two Necromancer, a Dragon, and a Vampire

Mind candy of the fluffiest sort. These have the pleasure, and the feel, of a Dungeons & Dragons campaign where vastly over-powered PCs engage in cheerfully cartoonish banter, violence and pillage. It's a bit of a guilty, regressive pleasure for me, but a real pleasure nonetheless. (No links because they're only available in electronic formats.)

On a different note, over the semester I re-read a lot of textbooks and monographs for the undergrad statistical learning class, so I provide some links here for the ones I mined for examples and problem sets found especially useful:

• Anthony and Bartlett, Neural Network Learning: Theoretical Foundations
• Boucheron, Lugosi and Massart, Concentration Inequalities: A Nonasymptotic Theory of Independence
• Cesa-Bianchi and Lugosi, Prediction, Learning, and Games
• Györfi, Kohler, Krzyzak and Walk, A Distribution-Free Theory of Nonparametric Regression
• Kearns and Vazirani, An Introduction to Computational Learning Theory
• Massart, Concentration Inequalities and Model Selection
• Mohri, Rostamizadeh and Talwalkar, Foundations of Machine Learning
• Pollard, Convergence of Stochastic Processes
• Shawe-Taylor and Cristianini, Kernel Methods for Pattern Analysis
• Vapnik, The Nature of Statistical Learning Theory

Books to Read While the Algae Grow in Your Fur; Scientifiction and Fantastica; Pleasures of Detection, Portraits of Crime; Enigmas of Chance;

Books to Read While the Algae Grow in Your Fur, April 2021

Attention conservation notice: I have no taste, and no qualifications to opine on ethics of any sort.

Michael J. Kearns and Aaron Roth, The Ethical Algorithm: The Science of Socially Aware Algorithm Design

There are, roughly speaking, three schools of thought when it comes to "fairness" and "ethics" in artificial intelligence machine learning predictive statistical modeling and data mining. I will caricature them as follows:

1. "Problem? I don't see any problem": maximize accuracy (or utility, etc.), and let the results take care of themselves.
2. "Everything is problematic": the data sets are biased, the objective functions to be maximized are biased (in some more obscure way), the very maximization algorithms are biased (in some yet more obscure way), and the only hope is to appoint duly-certified ethicists as censors trust that can all somehow be re-imagined after the arrival of the millennium / revolution.
3. "Problems? I'm good at solving problems! what penalty term should we add to the Lagrangian?"

This book is the best presentation I have encountered, and indeed about the best I can imagine, for this third, temporizing school of thought. (It is, in case that's not clear, the tendency with which I have the most sympathy.) That is, this book tends to regard ethical and political desiderata as constraints which should be imposed on algorithms that are otherwise seeking to optimize some well-defined objective function (such as travel-time for mapping software, or "probability that the user will watch the recommended movie" for recommender systems, etc.). There is a strong analogy here to a certain kind of technocratic, American-sense liberal approach to public policy, in which private firms maximize profit, subject (ideally) to constraints imposed by regulation ("don't dump too much dioxin into the water supply"). (I don't recall the book making this analogy explicit.)

I used this book quite successfully in my data mining class, but my students there found the most technical parts (like "possibility frontiers") the most congenial, and the more rhetorical-argumentative bits about fairness more preplexing. I strongly suspect this reflects having a very unusual audience. I would cheerfully teach from it again, and strongly recommend it to readers interested in these subjects, perhaps especially if they're new to this area. §

Disclaimers: I have been an admirer of Kearns's work since the 1990s, I know him a bit from conferences &c., and I requested an examination copy of this book before assigning it to my class.

Walter Jon Williams, Fleet Elements

Military space opera mind candy of the very highest grade. For one thing, it earns operatic levels of emotion. --- Previously. §

Ausma Zehanat Khan, The Black Khan

Continuing an epic fantasy saga where a lot of the details are the recent history of Afghanistan and environs with the serial numbers filed off. Only in this installment we spend a lot of time at the court of Isfahan Ashfall (via the ruins of Nishapur Nightshaper), complete with a scheming Nizam al-Mulk Nizam al-Mulk. Also, there is even more angsty romance than in the first volume. (Fortunately, AZK writes angsty romance well.) There are at least two more volumes to the saga, which I intend to devour as soon as I can arrange suitably long stretches of un-interrupted time. §

Dennis Culver and Justin Greenwood, Crone

Comic book swords-and-sorcery mind candy, in which the former Red Sonja Bloody Bliss, now the titular crone, is dragged out of retirement to re-confront a Dark Lord she knows she killed...

Tony Cliff, Delilah Dirk and the Pillars of Hercules

Comic book historical-fantasy mind candy. (Previously.)

K. C. Constantine, Joey's Case

Similar remarks to last month's entry.

Books to Read While the Algae Grow in Your Fur; Scientifiction and Fantastica; Pleasures of Detection, Portraits of Crime; Enigmas of Chance; Automata and Calculating Machines

Books to Read While the Algae Grow in Your Fur, March 2021

Attention conservation notice: I have no taste, and no qualifications to opine on the sociology of radio and the music industry, or on movies.

(I didn't finish a lot of books this month, since I'm not counting re-reading bits and pieces of arcane tomes on golem-making as needed for my own shambling creation.)

K. C. Constantine, Sunshine Enemies

Mind candy from 1990: the nth in a series of mystery novels set in the fictional western Pennsylvania town of Rockford, PA, somewhere in the environs of Pittsburgh — what I've heard called the yinzerlands. It's a good mystery novel, but what really sets it apart is the dialogue. Constantine has an incredible ear for the way locals of that generation spoke, and turns it into riveting dialogue. The depiction of the life-ways of these communities also feels authentic, but that's harder for me to judge. Strongly recommended if you like well-written detective novels, or are interested in fiction set around here.

Gabriel Rossman, Climbing the Charts: What Radio Airplay Tells Us about the Diffusion of Innovation

This is a short sociological treatise about, primarily, how songs become hits on commercial American radio, or fail to do so. It's well written (not just "well written for sociology"), and has a number of very interesting points to make about topics like the diffusion of innovation, corruption, the role of genres in popular culture, and more besides. The points which most interest me are the diffusion ones.

Rossman's starting point is to look at curves of cumulative adoption over time --- how many radio stations have, by a given date, ever played such-and-such a song? His main methodological tool is to distinguish between two types of adoption curves. One is the classic elongated-S curve, looking roughly like $\frac{e^{t\lambda}}{1+e^{t\lambda}}$, which one would expect to be produced by contagion, whether mediated by a network or by some more mean-field-ish process (like a best-seller list). The other ideal type of curve is "concave", indicating a constant probability of adoption per unit time, so looking like $1-e^{-t\lambda}$. The latter he interprets as indicating some shared external forcing. Most songs which become hits follow the latter pattern (though he has illuminating things to say about the exceptional endogenous hits). The obvious question is the identity of the external force. Rossman makes a compelling case that this is, in fact, the record companies, and not (e.g.) radio station chains; on this basis he goes in to an examination of the history and theory of payola. (Basically: radio "moves product" for the record companies, so you don't want to be the only record company which is not bribing radio stations to play your music.) He also has a less compelling but still fairly persuasive analysis showing that radio stations don't really decide what to play by imitating other radio stations (at least for one "format" of radio station, during one time period). I could go on --- Rossman packs a lot into only ~200 pages --- but forbear.

The central distinction here, between curves due to external forcing and curves due to endogenous contagion, is one that's persuasive in context, but isn't necessarily either airtight or generalizable. That promotional efforts by a record company would translate into a constant hazard for adoption seems plausible enough, but one could imagine a record company whose promotional efforts start small, ramp up rapidly when one song or another takes off, and which tapers when it becomes clear that the pool of new adoptees is almost exhausted, imitating a logistic, "endogenous" diffusion curve. (It doesn't seem like good business strategy, and I take Rossman's word for it that that's not, in fact, how record promotion works.) My efforts to come up with a "just so" story in which contagion produces a constant hazard are less convincing even to me, but I only gave five minutes to the effort. Returning to my perpetual hobbyhorse of the difficulty of establishing social contagion, I would say that this is an example of using subject-matter knowledge (i.e., actual science) to rule out alternatives, which couldn't be done on purely statistical grounds.

Recommended if you have any interest in the diffusion of innovations, or in social contagion. (Probably good if you're interested in the sociology of music, too.) Finally finished, 8 years (!) after I started it, because of reading a more recent paper by the author.

Chernobyl

Fukushima 50

Pandora's Promise

Quo Vadis, Aida?

Hotel Rwanda

Watchers of the Sky

Human Flow

The Rest

This is what happens when you live with a historian writing a chapter about 1980--2020... Chernobyl is very well done; some scenes which I thought were imitations of Soviet science fiction movies were in fact imitations of archival footage. Fukushima is a much lower level of art, but still decent. (There is a whole essay to be written about the role of America in that movie, which I am utterly incompetent to do.) Quo Vadis, Aida? is almost unbearably sad. Hotel Rwanda is somehow more purely horrifying than sad. Watchers of the Sky was comparatively optimistic, but having a sincere and committed campaigner against genocide as our UN ambassador did less to improve things than one might wish. Human Flow is the most beautiful movie of the lot. The Rest is fine on its own terms, but diminished by the comparison to the previous movie (not as visually striking, not as thematically wide-ranging, and with too little of Ai Weiwei in the role of the planet's eccentric cat-guy uncle).

Pandora's Power calls for special comment. I am, by temperament and training, receptive to nuclear power having more of a role than many on the left want it to. But this movie, if anything, pushed me away from that position, purely by reaction. The people it chose to showcase as advocates were, for the most part, completely unqualified, both in their earlier opposition and in their later advocacy. Shellenberger in fact seems like someone whose only real principle is attracting attention by outraging liberal piety, a well-trodden path. (Perhaps he's a lovely person and the movie showed him in an bad light.)

Turning from personalities to substance, the arguments here are just tissue thin. If the problem with solar and wind power is intermittency, the obvious solutions are (1) storage, (2) non-intermittent renewable power sources (like hydro power), and (3) a limited role for natural gas or other fossil fuels. (Humanity's carbon budget is not zero.) To listen to the movie, you'd think all of this was impossible, rather than well-studied. (Yes, there are technical challenges, but that'd lead to a serious comparison of alternatives, which the movie avoids at all costs.) Claims that Chernobyl was responsible for millions of deaths are absurd, and anti-nuclear campaigners who repeat them discredit themselves. But it's also absurd to claim that Chernobyl killed basically nobody. (Why oh why might Soviet successor states want to minimize the consequences, it is a mystery, and why might the UN and WHO fail to challenge even obviously falsified official figures, who can say? A village priest squatting in the exclusion zone insists none of his flock gets sick, obviously he's telling the truth.) Concerns about the safe disposal of waste for hundreds to tens of thousands of years, and about nuclear proliferation (particularly with the breeder reactors favored by the move-makers) are dismissed remarkably glibly. (ObRecOfAnInfinitelyBetterMovie: Containment.) That there's a correlation between a country's energy usage and its average lifespan is perfectly true, but that's because countries which use a lot of energy are also ones with sanitation, adequate food, etc., etc. (Obviously it takes energy to provide these goods.) In any case the argument isn't about whether to use lots of energy (*), but how to supply it. I can't tell whether the poverty-porn shots of children in third world slums arise from a clumsy-but-sincere concern for the kids' well-being, from a calculation that "why do you hate brown kids?" is an easy way to morally blackmail the intended audience, or from a feeling that this'd be an amusing way to own the libs.

The only thing which gives me any pause about saying the movie is unmitigated dreck is that Stewart Brand and Richard Rhodes, who I otherwise find to be thoughtful and serious authors from whom I've learned much, agreed to participate. But by the end this had the effect of lowering them a bit in my estimation, which is sad.

After watching, I found this review, which seems very fair, because the movie is, in fact, very bad.

*: Of course there are people who wish humanity would plunge back to pre-industrial levels of energy usage, motivated by some combination of nostalgia for the idiocy of rural life and mis-guided Malthusianism. They are few in number and, thankfully, completely without influence, which will continue to be the case. (Any country where they might, incredibly, manage to impose their views would quickly be stomped by rivals whose madmen in authority were not quite that crazy, assuming their own people didn't do it first.)

Books to Read While the Algae Grow in Your Fur; The Continuing Crises; Commit a Social Science; Networks; Pleasures of Detection, Portraits of Crime; Heard About Pittsburgh PA

Sub-Re-Intermediation

Attention conservation notice: 1000-word grudging concession that a bete noire might have a point, followed immediately and at much greater length by un-constructive hole-poking; about social media, by someone who's given up on using social media; also about the economics of recommendation engines, by someone who is neither an economist nor a recommendation engineer.

Because he hates me and wants to make sure that I never get back to any (other) friend or collaborator, Simon made me read Jack Dorsey endorsing an idea of Stephen Wolfram's. Much as it pains me to say, Wolfram has the germ of an interesting idea here, which is to start separating out different aspects of the business of running a social network, as that's currently understood. I am going to ignore the stuff about computational contracts (nonsense on stilts, IMHO), and focus just on the idea that users could have a choice about the ranking / content recommendation algorithms which determine what they see in their feeds. (For short I'll call them "recommendation engines" or "recommenders".) There are still difficulties, though.

"Editors. You've re-invented editors."

Or, more exactly, a choice of editorial lines, as we might have with different, competing newspapers and magazines. Well, fine; doing it automatically and at the volume and rate of the Web is something which you can't achieve just by hiring people to edit.

— Back in the dreamtime, before the present was widely distributed, Vannevar Bush imagined the emergence of people who'd make their livings by pointing out what, in the vast store of the Memex, would be worth others' time: "there is a new profession of trail blazers, those who find delight in the task of establishing useful trails through the enormous mass of the common record." Or, again, there's Paul Ginsparg's vision of new journals erecting themselves as front ends to arxiv. Appealing those such visions are, it's just not happened in any sustained, substantial way. (All respect to Maria Popova for Brain Pickings, but how many like her are there, who can do it as a job and keep doing it?) Maybe the obstacles here are ones of scale, and making content-recommendation a separate, algorithmic business could help fulfill the vision. Maybe.

Monsters Respond to Incentives

"Presumably", Wolfram says, "the content platform would give a commission to the final ranking provider". So the recommender is still in the selling-ads business, just as Facebook, Twitter, etc. are now. I don't see how this improves the incentives at all. Indeed, it'd presumably mean the recommender is a "publisher" in the digital-advertizing sense, and Facebook's and Twitter's core business situation is preserved. (Perhaps this is why Dorsey endorses it?) But the concerns about the bad and/or perverse effects of those incentives (e.g.) are not in the least alleviated by having many smaller entities channeled in the same direction.

On the other hand, I imagine it's possible that people would pay for recommendations, which would at least give the recommenders a direct financial incentive to please the users. This might still not be good for the users, but at least it would align them more with users' desires, and diversity of those desires could push towards a diversity of recommendations. Of course, there would be the usual difficulty of fee-based services competing against free-to-user-ad-supported services.

Imprimatur

To the extent there are concerns about certain content being banned by private companies, those are still there: the network operator, Facebook or Twitter or whatever, retains a veto over content. The recommenders are able to impose further vetoes, but not over-ride the operator.

Further: as Wolfram proposes it, the features used to represent content are already calculated by the operator. This can of course impose all sorts of biases and "editorial" decisions centrally, ones which the recommenders would have difficulty over-riding, if they could do so at all.

Increasing returns rule everything around me

Wolfram invokes "competition", but doesn't think about whether it will be effective. There are (at least) two grounds for thinking it wouldn't be, both based on increasing returns to scale.

1. Costs of providing the service: If I am going to provide a recommendation engine to a significant fraction of Facebook's audience, in a timely manner, I require a truly massive computational infrastructure, which will have huge fixed costs, though the marginal costs of each additional recommendation will be trivial. It's literally Econ 101 that this is a situation where competition doesn't work very well, and the market tends to either segment in to monopolistic competition or in to oligopoly (if not outright monopoly). As a counter-argument, I guess I could imagine someone saying "Cloud computing will take care of that", i.e., as long as we tolerate oligopoly among hardware operators, software companies will face constant scale costs for computing. (How could that possibly go wrong, technically or socially?)
2. Quality of the service: Machine learning methods work better with more data. This will mean more data about each user, and more data about more users. (In the very first paper on recommendation engines, back in 1995, Shardanand and Maes observed that the more users' data went in to each prediction, the smaller the error.) Result: the same algorithm used by company A, with \( n \) users, will be less effective than if used by company B, with data on \( 2n \) users. Even when the recommendation engine doesn't explicit use the social network, this will create a network externality for recommendation providers (*). And thus again we get increasing returns and throttled competition (cf.).

Normally I'd say there'd also be switching costs to lock users in to the first recommender they seriously use, but I could imagine the network operators imposing data formats and input-output requirements to make it easy to switch from one recommender to another without losing history.

— Not quite so long ago as "As We May Think", but still well before the present was widely distributed, Carl Shaprio and Hal Varian wrote a quietly brilliant book on the strategies firms in information businesses should follow to actually make money. The four keys were economies of scale, network externalities, lock-in of users, and control of standards. The point of all of these is to reduce competition. These principles work — it is no accident that Varian is now the chief economist of Google — and they will apply here.

Prior art

Someone else must have proposed this already. This conclusion is an example of induction by simple enumeration, which is always hazardous, but compelling with this subject. I would be interested to read about those earlier proposal, since I suspect they'll have thought about how it actually could work.

*: Back of the envelope, say the prediction error is $O(n^{-1/2})$, as it often is. The question is then how utility to the user scales with error. If it was simply inversely proportional, we'd get utility scaling like $O(n^{1/2})$, which is a lot less than the $O(n)$ claimed for classic network externalities by Metcalfe's law rule-of-thumb. On the other hand it feels more sensible to say that going from an error of $\pm 1$ on a 5 point scale to $\pm 0.1$ is a lot more valuable to users than going from $\pm 0.1$ to $\pm 0.01$, not much less valuable. Indeed we might expect that even perfect prediction would have only finite utility to users, so the utility would be something like $c-O(n^{-1/2})$. This suggests that we could have multiple very large services, especially if there is a cost to switch between recommenders. But it also suggests that there'd be a minimum viable size for a service, since if it's too small a customer would be paying the switching cost to get worse recommendations. ^

The Dismal Science; Actually, "Dr. Internet" Is the Name of the Monster's Creator

Actually, "Dr. Internet" Is the Name of the Monsters' Creator

I can't remember if Henry Farrell came up with this phrase, or I did, as the title for a possible joint project. I also forget whether we meant "Monster's", singular, or "Monsters'", plural; as time passes I lean towards the latter.

See also Linkage

Books to Read While the Algae Grow in Your Fur, April 2023

Cognitive Surplus: Creativity and Generosity in a Connected Age (Shirky)

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

The Misinformation Age: How False Beliefs Spread (O'Connor and Weatherall)

Don't @ Me

Books to Read While the Algae Grow in Your Fur, July 2021

Hystories: Hysterical Epidemics and Modern Culture (Showalter)

Sub-Re-Intermediation

An Appeal to the Hive Mind (Ironically Enough)

Books to Read While the Algae Grow in Your Fur, August 2020

The Internet Trap: How the Digital Economy Builds Monopolies and Undermines Democracy (Hindman)

Some Blogospheric Navel-Gazing, or, Strange Memories of the Recent Past

Books to Read While the Algae Grow in Your Fur, July 2017

Kill All Normies: Online Culture Wars from 4Chan and Tumblr to Trump and the Alt-Right (Nagle)

Books to Read While the Algae Grow in Your Fur, June 2017

Twitter and Tear Gas: The Power and Fragility of Networked Protest (Tufekci)

Experimental Considerations Touching on the Art of Winning Lotteries

Random Linkage, May 2015

Updates!

The Presentation of Self in Internet Life

Speaking Truth to Power About Weblogs, or, How Not to Draw a Straight Line

One Roll of the Dice Will Never Abolish Warblogging

Someone Has Found a Way to Make Money from the Internet!

An Appeal to the Hive Mind (Ironically Enough)

Attention conservation notice: Asking for help finding something that you don't know about, that you don't care about, and that a bad memory might have just confabulated.

I have a vivid memory of reading, in the 1990s, an online discussion (maybe just two people, maybe as many as four) about what online fora, search engines, the Web, "agents", etc., were doing to the way people acquire and use knowledge, and indeed to what we mean by "knowledge". My very strong impression is that one of the participants was linked somehow with the MIT Media Lab, and taking a very strong social-constructionist line (unsurprisingly, given that affiliation). At some point the discussion turned to her experiences with an online forum related to a hobby of hers (tropical fish? terraria?). The person I'm thinking of said something like, the consensus of that forum just were knowledge about \$HOBBY. One of her interlocutors made an objection on the order of, why do you trust those random people on the Internet to have any idea what they're talking about? To which the reply was, basically, come on, who'd just make stuff up about \$HOBBY?

I have (genuinely!) thought of this exchange often in the 20-plus years since I read it. But when I recently tried to find it again, to check my memory and to cite it in a work-in-glacial-progress, I've been unable to locate it. (The fact that I don't recall any names of the participants, or the venue, doesn't help.) I am prepared to learn that, because this is something I've thought of often, my mind has re-shaped it into a memorable anecdote, but I'd still like to see what this started from. Any leads readers could provide would be appreciated.

Update, the next day

The hive mind Lucy Keer (with an assist from Mike Traven) delivers:

Definitely me! :) I think you're referring to my story about a guy on USENET who was a legendary flamer/troll, EXCEPT when he talked about tropicalfish he was incredibly knowledgeable and helpful.

Incidentally, a lot of my book "Should You Believe Wikipedia? Online Community Design and the Social Construction of Knowledge" (coming out in a few months, Cambridge University Press) is about this general topic.

— Amy Bruckman (@asbruckman) March 26, 2021

Specifically, the seed around which this story nucleated in my memory may have been a January 1996 piece by Prof. Bruckman in Technology Review — it has the right content (sci.aquaria!), the right date, my father subscribed to TR and I'd even have been visiting my parents when that issue was current. Only it's not a conversation between multiple people but a solo-author essay, it's not primarily about the social aspects of knowledge but about how to find congenial on-line communities and make (or re-make) ones that don't suck (the lost wisdom of the Internet's early Bronze Age), and contains nothing like "who'd just make stuff up about \$HOBBY?" (In short: Bartlett (1932) meets Radio Yerevan.)

More positively, I very much look forward to reading Bruckman's book (there's an excerpt/precis available on her website).

Actually, "Dr. Internet" Is the Name of the Monster's Creator; The Collective Use and Evolution of Concepts

Regression, Thermostats, Causal Inference: Some Finger Exercises

\[ \newcommand{\Expect}[1]{\mathbb{E}\left[ #1 \right]} \newcommand{\Prob}[1]{\mathbb{P}\left( #1 \right)} \newcommand{\Cov}[1]{\mathrm{Cov}\left[ #1 \right]} \newcommand{\Var}[1]{\mathrm{Var}\left[ #1 \right]} \]

Attention conservation notice: An 800-word, literally academic exercise about an issue in causal inference. Its point is familiar to those in the field, and deservedly obscure to everyone else. Also, too cutesy and pleased with itself by at least half.

I wrote the first version of this for the class where we do causal inference long enough ago that I actually don't remember when --- 2011? 2013? (In retrospect I had probably read Milton Friedman's thermostat analogy but didn't consciously remember it at the time.) Posted now because I've gone over the point with two different people in the last month.

The temperature outside \( (X) \) is a direct cause of the temperature inside my house \( (Y) \). But every morning I measure the temperature, and adjust my heating/cooling system \( (C) \) to try to maintain a constant temperature \( y_0 \). For simplicity, we'll say that all the relations are linear, so \[ \begin{eqnarray} X & \sim & \mathrm{whatever}\\ C|X & \leftarrow & a+bX + \epsilon_1\\ Y|X,C & \leftarrow & X-C + \epsilon_2 \end{eqnarray} \] where \( \epsilon_1 \) and \( \epsilon_2 \) are exogenous, independent, mean-zero noise terms. We can think of \( \epsilon_1 \) as a combination of my sloppiness in measuring the temperature and in tuning the heating/cooling system; \( \epsilon_2 \) is sheer fluctuations.

Exercise: Draw the DAG.

To ensure that the expectation of \( Y \) remains at \( y_0 \), no matter the external temperature, we need \[ \begin{eqnarray} y_0 & = & \Expect{Y|X=x}\\ & = & \Expect{X - a + bX + \epsilon_1 + \epsilon_2|X=x}\\ & = & (1-b)x -a \end{eqnarray} \] Since this must hold for all \( x \), we need \( b=1, a=-y_0 \).

What follows from this?

• Internal temperature \( Y \) is uncorrelated with external temperature \( X \): \[ \begin{eqnarray} \Cov{X,Y} & = & \Expect{XY} - \Expect{X}\Expect{Y}\\ & = & \Expect{X\Expect{Y|X}} - \Expect{X}\Expect{Y}\\ & = & \Expect{X}y_0 - \Expect{X}y_0 = 0 \end{eqnarray} \] The internal temperature will fluctuate around the set-point \( y_0 \), but those fluctuations will not correlate with the external temperature.
• Internal temperature \( Y \) is correlated with the control signal \( C \) only through my sloppiness: \[ \begin{eqnarray} \Cov{C,Y} & = & \Expect{CY} - \Expect{C}\Expect{Y}\\ & = & \Expect{(-y_0 + X + \epsilon_1)(X+y_0-X-\epsilon_1+\epsilon_2)} - (\Expect{X}-y_0)y_0\\ & = & -y_0^2 - \Expect{\epsilon^2} + \Expect{X}y_0 -\Expect{X \epsilon_1} + \Expect{X\epsilon_2} + \Expect{\epsilon_1 \epsilon_2} - \Expect{X}y_0 + y_0^2\\ & = & -\Var{\epsilon_1} \end{eqnarray} \] since all the cross-expectations are zero, and \( \Expect{\epsilon_1}=0 \).
• The control signal \( C \) is correlated with the external temperature: \[ \begin{eqnarray} \Cov{C,X} & = & \Expect{CX} - \Expect{C}\Expect{X}\\ & = & \Expect{(-y_0 + X+\epsilon_1)X} + (-y_0 +\Expect{X})\Expect{X}\\ & = & \Expect{X^2} - \left(\Expect{X}\right)^2\\ & = & \Var{X} \end{eqnarray} \]
• A linear regression of \( Y \) on \( X \) and \( C \) will consistently recover the correct coefficients, namely \( +1 \) and \( -1 \). To see this, recall (e.g., from here) that the OLS estimates will tend towards the coefficients of the optimal linear predictor. Those coefficients, in turn, are the solution to \[ \beta = {\left[ \begin{array}{cc} \Var{X} & \Cov{C,X}\\ \Cov{X,C} & \Var{C} \end{array}\right]}^{-1} \left[ \begin{array}{c} \Cov{Y,X}\\ \Cov{Y,C} \end{array}\right] \] Plugging in our previous results, \[ \beta = {\left[ \begin{array}{cc} \Var{X} & \Var{X}\\ \Var{X} & \Var{X}+\Var{\epsilon_1} \end{array}\right]}^{-1} \left[ \begin{array}{c} 0\\ -\Var{\epsilon} \end{array}\right] \] After some character-building algebra, you can confirm that the covariance matrix is invertible as long as \( \Var{\epsilon_1} > 0 \), and then, as promised \( \beta = (1,-1) \).

Exercise: Build your character by doing the algebra.

So, as long as control isn't perfect, the naive statistician (or experienced econometrician...) who just does a kitchen-sink regression will actually get the relationship between \( Y \), \( X \) and \( C \) right, concluding that external temperature and the climate control have equal and opposite effects on internal temperature. Sure, there will be sampling noise, but with enough data they'll approach the truth.

Exercise: What do you get if you regress \( C \) on \( X \) and \( Y \)?

I have implicitly assumed that I know the exact linear relationship between \( X \) and \( Y \), since I used that in deriving how the control signal should respond to \( X \). If I mis-calibrate the control signal, say if \( C = -y_0 +0.999X + \epsilon_1 \), then there is not an exact cancellation and everything works as usual.

Exercise: Suppose that instead of measuring the external temperature \( X \) directly, I can only measure yesterday's temperature \( U \), again with noise. Supposing there is a linear relationship between \( U \) and \( X \), replicate this analysis. Does it matter if \( U \) is the parent of \( X \) or vice versa?

Exercise: "Feedback is a mechanism for persistently violating faithfulness"; discuss.

Exercise: "The greatest skill seems like clumsiness" (Laozi); discuss.

Engimas of Chance; Constant Conjunction Necessary Connexion

Books to Read While the Algae Grow in Your Fur, February 2021

Attention conservation notice: I have no taste, and no qualifications to opine about geology, policing, law, or the history of Islamic science.

Michael E. Wysession, How the Earth Works

This is basically a "rocks for jocks" geology course, but I learned stuff from it, so I'm not really in a position to review it.

Rosa Brooks, Tangled Up in Blue: Policing the American City

In which the author, almost on a whim, spends a sabbatical year from her career as a law professor becoming a reserve police officer in Washington, DC, including going through the (modified) police academy for those volunteers, working as a policewoman in Anacostia, etc. She stuck with it for over four years, basically until the book was about to come out. This was, as everyone told her and she freely acknowledges, crazy, but it produced a really good book, equal parts memoir, war stories, and intellectual reflection.

(There are also some quite personal passages about what was involved in doing this while having grown up as not just any red diaper baby, but specifically Barbara Ehrenreich's child. I thought those parts were interesting and even affecting, but I wonder if that shouldn't have been a separate essay.) §

Leigh Bardugo, Ninth House

Mind candy contemporary fantasy: what if the Yale secret societies were literally pursuing magic? And what if Yale were to admit an utterly un-well-rounded student with serious issues who happened to be really good at magic? (Bardugo graduated from Yale a surprisingly small number of years ago.) §

--- Sequel

Jim Al-Khalili, The House of Wisdom: How Arabic Science Saved Ancient Knowledge and Gave Us the Renaissance

This is mostly great. The subtitle is misleadingly Eurocentric; it's mostly about new science under the Abbasaid caliphate. As a practicising physicist, Al-Khalili is both very good at explaining the science done, and somewhat impatient of the meta-scientific subtleties. In particular he's very ready to claim that (a) there's such a thing as The Scientific Method, and (b) some at least of the scholars he's writing about grasped it and used it, along with, at a more implicit level, (c) those scholars were pursuing the same kind of endeavor that Al-Khalili is (and for that matter that I am). But I am frankly not familiar enough with the literature on al-Biruni or (especially) al-Haytham to be entitled to an opinion as to whether they thought they were following something that might be called "the scientific method". §

(Al-Khalili writes about "Arabic science" because that was the language used; he's quite clear that ethnically many if not most of these men weren't ethnically Arabs, any more than European scholars writing in Latin were Romans.)

Books to Read While the Algae Grow in Your Fur; Islam and Islamic Civilization; The Beloved Republic; Writing for Antiquity; Scientifiction and Fantastica

Teaching: Statistics of Inequality and Discrimination

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

Discrimination at Work: Comparing European, French, and American Law (Mercat-Bruns)

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

The Matthew Effect: How Advantage Begets Further Advantage (Rigney)

Elite Capture: How the Powerful Took Over Identity Politics (And Everything Else) (Táíwò)

Course Announcement: "Statistics of Inequality and Discrimination" (36-313)

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

Changing Inequality (Blank)

Race Experts: How Racial Etiquette, Sensitivity Training, and New Age Therapy Hijacked the Civil Rights Revolution (Lasch-Quinn)

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

How Schools Really Matter: Why Our Assumption about Schools and Inequality Is Mostly Wrong (Downey)

Books to Read While the Algae Grow in Your Fur, December 2021

Stuck in Place: Urban Neighborhoods and the End of Progress toward Racial Equality (Sharkey)

Books to Read While the Algae Grow in Your Fur, October 2021

Deaths of Despair and the Future of Capitalism (Case and Deaton)

Slavery and Social Death: A Comparative Study (Patterson)

Books to Read While the Algae Grow in Your Fur, July 2021

Inequality: A Short History (Alacevich and Soci)

Course Announcement: "Statistics of Inequality and Discrimination" (36-313)

Books to Read While the Algae Grow in Your Fur, September 2020

Understanding Class (Wright)

Books to Read While the Algae Grow in Your Fur, July 2020

W. E. B. Du Bois's Data Portraits: Visualizing Black America: The Color Line at the Turn of the Twentieth Century (Battle-Baptiste and Rusert, eds.)

Shadows of Doubt: Stereotypes, Crime, and the Pursuit of Justice (O'Flaherty and Sethi)

Books to Read While the Algae Grow in Your Fur, December 2015

The New Economics of Inequality and Redistribution (Bowles)

Books to Read While the Algae Grow in Your Fur, July 2014

Capital in the Twenty-First Century (Piketty)

Books to Read While the Algae Grow in Your Fur, March 2014

Caste and Class in a Southern Town (Dollard)

Books to Read While the Algae Grow in Your Fur, May 2013

Plutocrats: The Rise of the New Global Super-Rich and the Fall of Everyone Else (Freeland)

Durable Inequality (Tilly)

Books to Read While the Algae Grow in Your Fur, August 2007

Relative Distribution Methods in the Social Sciences (Handcock and Morris)

Books to Read While the Algae Grow in Your Fur, June 2007

The Anatomy of Racial Inequality (Loury)

Books to Read While the Algae Grow in Your Fur, January 2021

Attention conservation notice: I have no taste, and no qualifications to opine on the history of science.

Oystein Ore, Cardano, the Gambling Scholar: With a Translation from the Latin of Cardano's Book on Games of Chance, by Sydney Henry Gould [JSTOR]

Reading this a few years after Grafton's book on Cardano, I am struck by two things. The first is that while the two books are factually perfectly compatible, the impressions they give of Cardano are radically different. Grafton's Cardano is a touchy astrologer and medical man; Ore's Cardano is primarily a mathematician (but equally touchy). The second is that Cardano really did basically invent probability theory out of, seemingly, nothing. Reading the translation of his work was actually exciting. It really does seem like the first appreciation of a quantitative sense of probability, a century before Pascal and Fermat (and apparently independent of them). Interestingly Cardano, at least in translation, speaks of "odds" or "chances" but not "probability", or anything suggestive of degree-of-belief. §

Lee Goldberg, Bone Canyon

Mind candy mystery, sequel to Lost Hills, and enjoyable in a similar mostly-funny-except-when-really-not way. (Gangs inside the LA county sheriff's department turn out to be real.) --- Sequel. §

Books to Read While the Algae Grow in Your Fur; Writing for Antiquity; Enigmas of Chance; Mathematics; Pleasures of Detection, Portraits of Crime