Three-Toed Sloth

The Books I Am Not Going to Write

Attention conservation notice: Middle-aged dad contemplating "aut liberi, aut libri" on April 1st.

... and why I am not going to write them.

Re-Design for a Brain

W. Ross Ashby's Design for a Brain: The Origins of Adaptive Behavior is a deservedly-classic and influential book. It also contains a lot of sloppy mathematics, in some cases in important places. (For instance, there are several crucial points where he implicitly assumes that deterministic dynamical systems cannot be reversible or volume-preserving.) This project would simply be re-writing the book so as to give correct proofs, with assumptions clearly spelled out, and seeing how strong those assumptions need to be, and so how much more limited the final conclusions end up being.

Why I am not going to write it: It would be of interest to about five other people.

The Genealogy of Complexity

Why I am not going to write it: It no longer seems as important to me as it did in 2003.

The Formation of the Statistical Machine Learning Paradigm, 1985--2000

Why I am not going to write it: It'd involve a lot of work I don't know how to do --- content analysis of CS conference proceedings and interviews with the crucial figures while they're still around. I feel like I could fake my way through get up to speed on content analysis, but oral history?!?

Almost None of the Theory of Stochastic Processes

Why I am not going to write it: I haven't taught the class since 2007.

Statistical Analysis of Complex Systems

Why I am not going to write it: I haven't taught the class since 2008.

A Child's Garden of Statistical Learning Theory

Why I am not going to write it: Reading Ben Recht has made me doubt whether the stuff I understand and teach is actually worth anything at all.

The Statistics of Inequality and Discrimination

I'll just quote the course 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 and within groups.

The idea is to write a book which could be used for a course on inequality, especially in the American context where we're obsessed by between-group inequalities, for quantitatively-oriented students and teachers, without either pandering, or pretending that being STEM-os lets us clear everything up easily. (I have heard too many engineers and computer scientists badly re-inventing basic sociology and economics in this context...)

Why I am not going to write it: Nobody wants to hear that these are real social issues; that understanding these issues requires numeracy and not just moralizing; that social scientists have painfully acquired important knowledge about these issues (though not enough); that social phenomena are emergent so they do not just reflect the motives of the people involved (in particular: bad things happen just because the people you already loathe are so evil; bad things don't stop happening just because nobody wants them); or that no amount of knowledge about how society is and could be will tell us how it should be. So writing the book I want will basically get me grief from every direction, if anyone pays any attention at all.

Huns and Bolsheviks

To quote an old notebook: "the Leninists were like the Chinggisids and the Timurids, and similar Eurasian powers: explosive rise to dominance over a wide area of conquest, remarkable horrors, widespread emulation of them abroad, elaborate patronage of sciences and arts, profound cultural transformations and importations, collapse and fragmentation leaving many successor states struggling to sustain the same style. But Stalin wasn't Timur; he was worse. (Likewise, Gorbachev was better than Ulugh Beg.)"

Why I am not going to write it: To do it even half-right, relying entirely on secondary sources, I'd have to learn at least four languages. Done well or ill, I'd worry about someone taking it seriously.

The Heuristic Essentials of Asymptotic Statistics

What my students get sick of hearing me refer to as "the usual asymptotics". A first-and-last course in statistical theory, for people who need some understanding of it, but are not going to pursue it professionally, done with the same level of mathematical rigor (or, rather, floppiness) as a good physics textbook. --- Ideally of course it would also be useful for those who are going to pursue theoretical statistics professionally, perhaps through a set of appendices, or after-notes to each chapter, highlighting the lies-told-to-children in the main text. (How to give those parts the acronym "HFN", I don't know.)

Why I am not going to write it: We don't teach a course like that, and it'd need to be tried out on real students.

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

Why I am not going to write it: Henry will finally have had enough of my nonsense as a supposed collaborator and write it on his own.

Logic Is a Pretty Flower That Smells Bad

Seven-ish pairs of chapters. The first chapter in each pair highlights a compelling idea that is supported by a logically sound deduction from plausible-sounding premises. The second half of the pair then lays out the empirical evidence that the logic doesn't describe the actual world at all. Thus the book would pair Malthus on population with the demographic revolution and Boserup, Hardin's tragedy of the commons with Ostrom, the Schelling model with the facts of American segregation, etc. (That last is somewhat unfair to Schelling, who clearly said his model wasn't an explanation of how we got into this mess, but not at all unfair to many subsequent economists. Also, I think it'd be an important part of the exercise that at least one of the "logics" be one I find compelling.) A final chapter would reflect on the role of good arguments in keeping bad ideas alive, the importance of scope conditions, Boudon's "hyperbolic" account of ideology, etc.

Why I am not going to write it: I probably should write it.

Beyond the Orbit of Saturn

Historical cosmic horror mind candy: in 1018, Sultan Mahmud of Ghazni receives reports that the wall which (as the Sultan understands things) Alexander built high in the Hindu Kush to contain Gog and Magog is decaying. Naturally, he summons his patronized and captive scholars to figure out what to do about this. Naturally, the rivalry between al-Biruni and ibn Sina flares up. But there is something up there, trying to get out, something not even the best human minds of the age can really comprehend...

Why I am not going to write it: I am very shameless about writing badly, but I find my attempts at fiction more painful than embarrassing.

Self-Centered; Modest Proposals

Books to Read While the Algae Grow in Your Fur, March 2025

Attention conservation notice: I have no taste, and no qualification to opine on pure mathematics, sociology, or adaptations of Old English epic poetry. Also, most of my reading this month was done at odd hours and/or while chasing after a toddler, so I'm less reliable and more cranky than usual.

Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics [doi:10.1017/CBO9780511801655]

I should begin by admitting that I have never learned much combinatorics, and never really liked what I did learn. To say my knowledge topped out at Stirling's approximation to $n!$ is only a mild exaggeration. Nonetheless, after reading this book, I think I begin to get it. I'll risk making a fool of myself by explaining.

We start with some class $\mathcal{A}$ of discrete, combinatorial objects, like a type of tree or graph obeying some constraints and rules of construction. There's a notion of "size" for these objects (say, the number of nodes in the graph, or the number of leaves in the tree). We are interested in counting the number of objects of size $n$. This gives us a sequence $A_0, A_1, A_2, \ldots A_n, \ldots$.

Now whenever we have a sequence of numbers $A_n$, we can encode it in a "generating function" \[ A(z) = \sum_{n=0}^{\infty}{A_n z^n} \] and recover the sequence by taking derivatives at the origin: \[ A_n = \frac{1}{n!} \left. \frac{d^n A}{dz^n} \right|_{z=0} \] (I'll claim the non-mathematician's privilege of not worrying about whether the series converges, the derivatives exist, etc.) When I first encountered this idea as a student, it seemed rather pointless to me --- we define the generating function in terms of the sequence, so why do we need to differentiate the GF to get the sequence?!? The trick, of course, is to find indirect ways of getting the generating function.

Part A of the book is about what the authors call the "symbolic method" for building up the generating functions of combinatorial classes, by expressing them in terms of certain basic operations on simpler classes. The core operations, for structures with unlabeled parts, are disjoint union, Cartesian product, taking sequences, taking cycles, taking multisets, and taking power sets. Each of these corresponds to a definite transformation of the generating function: if $\mathcal{A}$s are ordered pairs of $\mathcal{B}$s and $\mathcal{C}$s (so the operation is Cartesian product), then $A(z) = B(z) C(z)$, while if $\mathcal{A}$s are sequences of $\mathcal{B}$s, then $A(z) = 1/(1-B(z))$, etc. (Chapter I.) For structures with labeled parts, slightly different, but parallel, rules apply. (Chapter II.) These rules can be related very elegantly to constructions with finite automata and regular languages, and to context-free languages. If one is interested not just in the number of objects of some size $n$, but the number of size $n$ with some other "parameter" taking a fixed value (e.g., the number of graphs on $n$ nodes with $k$ nodes of degree 1), multivariate generating functions allow us to count them, too (Chapter III). (Letting $k$ vary for fixed $n$ of course gives a probability distribution.) When the parameters of a complex combinatorial object are "inherited" from the parameters of the simpler objects out of which it is built, the rules for transforming generating functions also apply.

In favorable cases, we get nice expressions (e.g., ratios of polynomials) for generating functions. In less favorable cases, we might end up with functions which are only implicitly determined, say as the solution to some equation. Either way, if we now want to decode the generating function $A(z)$ to get actual numbers $A_1, A_2, \ldots A_n, \ldots$, we have to somehow extract the coefficients of the power series. This is the subject of Part B, and where the "analytical" part of the title comes in. We turn to considering the function $A(z)$ as a function on the complex plane. Specifically, it's a function which is analytic in some part of the plane, with a limited number of singularities. Those singularities turn out to be crucial: "the location of a function's singularities dictates the exponential growth of its coefficients; the nature of a functions singularities determine the subexponential factor" (p. 227, omitting symbols). Accordingly, part II is a crash course in complex analysis for combinatorists, the upshot of which is to relate the coefficients in power series to certain integrals around the origin. One can then begin to approximate those integrals, especially for large $n$. Chapter V carries this out for rational and "meromorphic" functions, ch. VI for some less well-behaved ones, with applications in ch. VII. Chapter VIII covers a somewhat different way of approximating the relevant integrals, namely the saddle-point method, a.k.a. Laplace approximation applied to contour integrals in the complex plane.

Part C, consisting of Chapter IX, goes back to multivariate generating functions. I said that counting the number of objects with size $n$ and parameter $k$ gives us, at each fixed $n$, a probability distribution over $k$. This chapter considers the convergence of these probability distributions as $n \rightarrow \infty$, perhaps after suitable massaging / normalization. (It accordingly includes a crash course in convergence-in-distribution for combinatorists.) A key technique here is to write the multivariate generating function as a small perturbation of a univariate generating function, so that the asymptotics from Part B apply.

There are about 100 pages of appendices, to fill gaps in the reader's mathematical background. As is usual with such things, it helps to have at least forgotten the material.

This is obviously only for mathematically mature readers. I have spent a year making my way through it, as time allowed, with pencil and paper at hand. But I found it worthwhile, even enjoyable, to carve out that time. §

(The thing which led me to this, initially, was trying to come up with an answer to "what on Earth is the cumulative generating function doing?" If we're dealing with labeled structures, then the appropriate generating function is what the authors call the "exponential generating function", $A(z) = \sum_{n=0}^{\infty}{A_n z^n / n!}$. If $A$'s are built as sets of $B$'s, then $A(z) = \exp(B(z))$. Turned around, then, $B(z) = \log{A(z)}$ when $A$'s are composed as sets of $B$'s. So if the moments of a random variable could be treated as counting objects of a certain size, so $A_n = \mathbb{E}\left[ X^n \right]$ is somehow the number of objects of size $n$, and we can interpret these objects as sets, the cumulant generating function would be counting the number of set-constituents of various sizes. I do not regard this as a very satisfying answer, so I am going to have to learn even more math.)

Arthur L. Stinchcombe, Information and Organizations [Open access]

A series of essays on organizations --- mostly for-profit corporations, but also universities --- as information-processing systems. The main thesis is that organizations "[grow] toward sources of news, news about the uncertainties that most affect their outcomes" (pp. 5--6), and then react to that news on an appropriate (generally, quick) time-scale. This is a functionalist idea, but Stinchcombe is careful to try to make it work, making arguments about how an organization's need to perform these functions comes to be felt by actual people in the organization, people who are in positions to do something about it. (Usually, his arguments on this score are persuasive.) This is by far the best thing I've seen in sociology about social structures as information-processing systems; I'm a bit disappointed in myself that I didn't read it a long time ago. §

Zach Weinersmith and Boulet, Bea Wolf

The first part of Beowulf, through the defeat of Grendel, adapted into a comic-book about joyously ill-behaved kids in an American suburb. Rather incredibly, it works.

(Thanks to Jan Johnson for the book.)

Books to Read While the Algae Grow in Your Fur; Mathematics; Automata and Calculating Machines; Enigmas of Chance; Commit a Social Science; The Dismal Science; The Collective Use and Evolution of Concepts; The Commonwealth of Letters

The Distortion Is Inherent in the Signal

Attention conservation notice: An overly-long blog comment, at the unhappy intersection of political theory and hand-wavy social network theory.

Henry Farrell has a recent post on how "We're getting the social media crisis wrong". I think it's pretty much on target --- it'd be surprising if I didn't! --- so I want to encourage my readers to become its readers. (Assuming I still have any readers.) But I also want to improve on it. What follows could have just been a comment on Henry's post, but I'll post it here because I feel like pretending it's 2010.

Let me begin by massively compressing Henry's argument. (Again, you should read him, he's clear and persuasive, but just in case...) The real bad thing about actually-existing social media is not that it circulates falsehoods and lies. Rather it's that it "creates publics with malformed collective understandings". Public opinion doesn't just float around like a glowing cloud (ALL HAIL) rising nimbus-like from the populace. Rather, "we rely on a variety of representative technologies to make the public visible, in more or less imperfect ways". Those technologies shape public opinion. One way in particular they can shape public opinion is by creating and/or maintaining "reflective beliefs", lying somewhere on the spectrum between cant/shibboleths and things-you're-sure-someone-understands-even-if-you-don't. (As an heir of the French Enlightenment, many of Dan Sperber's original examples of such "reflective beliefs" concerned Catholic dogmas like trans-substantiation; I will more neutrally say that I have a reflective belief that botanists can distinguish between alders and poplars, but don't ask me which tree is which.) Now, at this point, Henry references a 2019 article in Logic magazine rejoicing in the title "My Stepdad's Huge Data Set", and specifically the way it distinguishes between those who merely consume Internet porn, and the customers who actually fork over money, who "convert". To quote the article: "Porn companies, when trying to figure out what people want, focus on the customers who convert. It's their tastes that set the tone for professionally produced content and the industry as a whole." To quote Henry: "The result is that particular taboos ... feature heavily in the presentation of Internet porn, not because they are the most popular among consumers, but because they are more likely to convert into paying customers. This, in turn, gives porn consumers, including teenagers, a highly distorted understanding of what other people want and expect from sex, that some of them then act on...."

To continue quoting Henry:

Something like this explains the main consequences of social media for politics. The collective perspectives that emerge from social media --- our understanding of what the public is and wants --- are similarly shaped by algorithms that select on some aspects of the public, while sidelining others. And we tend to orient ourselves towards that understanding, through a mixture of reflective beliefs, conformity with shibboleths, and revised understandings of coalitional politics.

At this point, Henry goes on to contemplate some recent grotesqueries from Elon Musk and Mark Zuckerberg. Stipulating that those are, indeed, grotesque, I do not think they get at the essence of the problem Henry's identified, which I think is rather more structural than a couple of mentally-imploding plutocrats. Let me try to lay this out sequentially.

1. The distribution of output (number of posts) etc. over users is strongly right-skewed. Even if everyone's content is equally engaging, and equally likely to be encountered, this will lead to a small minority having a really disproportionate impact on what people perceive in their feeds.
2. Connectivity is also strongly right-skewed. This is somewhat endogenous to algorithmic choices on the part of social-media system operators, but not entirely.
   (One algorithmic choice is to make "follows" an asymmetric relationship. [Of course, the fact that the "pays attention to" relationship is asymmetric has been a source of jokes and drama since time out of mind, so maybe that's natural.] Another is to make acquiring followers cheap, or even free. If people had to type out the username of everyone they wanted to see a post, every time they posted, very few of us would maintain even a hundred followers, if that.)
3. Volume of output, and connectivity, are at the very least not negatively associated. (I'd be astonished if they're not positively associated but I can't immediately lay hands on relevant figures.) *
4. People who write a lot are weird. As a sub-population, we are, let us say, enriched for those who are obsessed with niche interests. (I very much include myself in this category.) This of course continues Henry's analogy to porn; "Proof is left as an exercise for the reader's killfile", as we used to say on Usenet. **
5. Consequence: even if the owners of the systems didn't put their thumbs on the scales, what people see in their feeds would tend to reflect the pre-occupations of a comparatively small number of weirdos. Henry's points about distorted collective understandings follow.

Conclusion: Social media is a machine for "creat[ing] publics with malformed collective understandings".

The only way I can see to avoid reaching this end-point is if what we prolific weirdos write about tends to be a matter of deep indifference to almost everyone else. I'd contend that in a world of hate-following, outrage-bait and lolcows, that's not very plausible. I have not done justice to Henry's discussion of the coalitional aspects of all this, but suffice it to say that reflective beliefs are often reactive, we're-not-like-them beliefs, and that people are very sensitive to cues as to which socio-political coalition's output they are seeing. (They may not always be accurate in those inferences, but they definitely draw them ***.) Hence I do not think much of this escape route.

--- I have sometimes fantasized about a world where social media are banned, but people are allowed to e-mail snapshots and short letters to their family and friends. (The world would, un-ironically, be better off if more people were showing off pictures of their lunch, as opposed to meme-ing each other into contagious hysterias.) Since, however, the technology of the mailing list with automated sign-on dates back to the 1980s, and the argument above says that it alone would be enough to create distorted publics, I fear this is another case where Actually, "Dr. Internet" Is the Name of the Monsters' Creator.

(Beyond all this, we know that the people who use social media are not representative of the population-at-large. [ObCitationOfKithAndKin: Malik, Bias and Beyond in Digital Trace Data.] For that matter, at least in the early stages of their spread, online social networks spread through pre-existing social communities, inducing further distortions. [ObCitationOfNeglectedOughtToBeClassicPaper: Schoenebeck, "Potential Networks, Contagious Communities, and Understanding Social Network Structure", arxiv:1304.1845.] As I write, you can see this happening with BlueSky. But I think the argument above would apply even if we signed up everyone to one social media site.)

*: Define "impressions" as the product of "number of posts per unit time" and "number of followers". If those both have power-law tails, with exponents \( \alpha \) and \( \beta \) respectively, and are independent, then impressions will have a power-law tail with exponent \( \alpha \wedge \beta \), i.e., slowest decay rate wins. )To see this, set \( Z = XY \) so \( \log{Z} = \log{X} + \log{Y} \), and the pdf of \( \log{Z} \) is, by independence, the convolution of the pdfs of \( \log{X} \) and \( \log{Y} \). But those both have exponential tails, and the slower-decaying exponential gives the tail decay rate for the convolution.) The argument is very similar if both are log-normal, etc., etc. --- This does not account for amplification by repetition, algorithmic recommendations, etc. ^

**: Someone sufficiently flame-proof could make a genuinely valuable study of this point by scraping the public various fora for written erotica and doing automated content analysis. I'd bet good money that the right tail of prolificness is dominated by authors with very niche interests. [Or, at least, interests which were niche at the time they started writing.] But I could not, in good conscience, advise anyone reliant on grants to actually do this study, since it'd be too cancellable from too many directions at once. ^

***: As a small example I recently overheard in a grocery store, "her hair didn't used to be such a Republican blonde" is a perfectly comprehensible statement. ^

Actually, "Dr. Internet" Is the Name of the Monsters' Creator; Kith and Kin