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

Attention conservation notice: I have no taste. I also have no qualifications to discuss folklore, structuralism, optics and painting in the early modern Netherlands, Aztec culture, or Cold War espionage.

Vladimir I. Propp, Morphology of the Folktale [as Morfologija skazki, Leningrad, 1928; translated by Svatava Pirkova-Jakobson, Indiana University Press, 1958; second edition, revised by Louis A. Wagner and with an introduction by Alan Dundes, Austin: University of Texas Press, 1968]

I'd known about this book for quite some time, and browsed in it long ago, but never actually read it until this year. It's a really incredible piece of work.

Propp set out to identify the basic elements of the plots of Russian fairy tales, working at a level of abstraction where "it does not matter whether a dragon kidnaps a princess or whether a devil makes off with either a priest's or a peasant's daughter". He came up with 31 such "functions". Just listing them (chapter 3) has a certain folkloric quality:

1. One of the members of a family absents himself from home ($\beta$)
2. An interdiction is addressed to the hero ($\gamma$)
3. The interdiction is violated ($\delta$)
4. The villain makes an attempt at reconnaissance ($\epsilon$)
5. The villain receives information about his victim ($\zeta$)
6. The villain attempts to deceive his victim in order to take possession of him or of his belongings ($\eta$)
7. The victim submits to deception and thereby unwittingly helps his enemy ($\theta$)
8. The villain causes harm or injury to a member of a family ($A$) or One member of a family either lacks something or desires to have something ($a$)
9. Misfortune or lack is made known; the hero is approached with a request or command; he is allowed to go or he is dispatched ($B$)
10. The seeker agrees to or decides upon counteraction ($C$)
11. The hero leaves home ($\uparrow$)
12. The hero is tested, interrogated, attacked, etc., which prepares the way for receiving either a magical agent or helper ($D$)
13. The hero reacts to the actions of the future donor ($E$)
14. The hero acquires the use of a magical agent ($F$)
15. The hero is transferred, delivered, or led to the whereabouts of an object of search ($G$)
16. The hero and the villain join in direct combat ($H$)
17. The hero is branded or marked ($J$)
18. The villain is defeated ($I$)
19. The initial misfortune or lack is liquidated ($K$)
20. The hero returns ($\downarrow$)
21. The hero is pursued ($Pr$)
22. Rescue of the hero from pursuit ($Rs$)

At this point, Propp observes, the tale can more or less begin over again, with the transition from the first "move" to the second being initiated by a new act of villainy, typically "Ivan's brothers steal his prize, and throw him into a chasm" ($\* A$). This leads to $C--G$ again.

23. The hero, unrecognized, arrives home or in another country ($o$)
24. A false hero presents unfounded claims ($L$)
25. A difficult task is proposed to the hero ($M$)
26. The task is resolved ($N$)
27. The hero is recognized ($Q$)
28. The false hero or villain is exposed ($Ex$)
29. The hero is given a new appearance ($T$)
30. The villain is punished ($U$)
31. The hero is married and ascends the throne ($W$)

Each abstract function has, naturally, a great many more concrete sub-types (e.g., seven distinct variants of pursuit, ranging from $Pr^1$, "the pursuer flies after the hero", to $Pr^7$, "He tries to gnaw through the tree in which the hero is taking refuge".

Based on extensive study of the corpus of Russian fairytales, Propp claims that the initial functions, designated by Greek letters, are less essential than the ones designated by Roman letters. In fact, in what I take to be the central finding of the book (ch. IX, sec. D, pp. 104--105), he claims that all the tales in the corpus belong to four, and only four, categories:

1. Tales with a struggle and victory, but no difficult tasks, following the scheme $ABC\uparrow DEFGHJIK\downarrow Pr Rs o LQ Ex TUW$.
2. Tales with difficult tasks, but no combat, following the scheme $ABC\uparrow DEFG o LMJNK\downarrow Pr Rs Q Ex TUW$.
3. Tales which include struggle-victory and difficult tasks, under the scheme $ABC\uparrow FH-IK\downarrow LM-NQ Ex U W$. (That is, the struggle always comes before the difficult tasks.)
4. Tales which include neither struggle nor difficult tasks, under the scheme $ABC\uparrow DEFGK\downarrow Pr Rs Q Ex T U W$.

As he remarks after making these claims,

To the variable scheme \[ ABC\uparrow DEFG \frac{HJIK\downarrow Pr-Rs o L}{LMJNK\downarrow Pr-Rs} Q Ex TUW \] are subject all the tales of our material: moves with $H-I$ develop according to the upper branch; moves with $M-N$ develop according to the lower branch; moves with both pairs first follow the upper part and then, without coming to an end, develop following the lower offshoot; moves without either $H-I$ or $M-N$ develop by bypassing the distinctive elements of each. [p. 105]

What I find so astonishing here is that this is a formal grammar, though propounded many years before that notion emerged in linguistics, logic and computer science. Specifically, it is a formal grammar which generates fairytale plots. Propp realized this, and used the schema to create new fairy tales [1] (unfortunately, not recorded). A basic principle of formal language theory is that a schema which generates all and only the valid strings of a language can also be used to recognize whether a string belongs to that language; Propp implicitly grasped this, and argued on this basis that some non-fairy-tales in his corpus were more properly classed with the fairy tales.

It's especially noteworthy to me that Propp's schema is a regular grammar, i.e., at the lowest level of the Chomsky hierarchy. These correspond to the regular expressions familiar to programmers, to finite-state machines, and to (functions of) Markov chains. The production rules would be something like \[ \begin{eqnarray*} Story & \rightarrow & ActI Act2 Act3\\ Act1 & \rightarrow & ABC\uparrow DEFG\\ Act2 &\rightarrow & (Struggle | 0) (Task | 0)\\ Act3 & \rightarrow & Q Ex TUW\\ Struggle & \rightarrow & HJIK\downarrow Pr-Rs o L\\ Task & \rightarrow & LMJNK\downarrow Pr-Rs\\ \end{eqnarray*} \] using $|$ as usual to represent alternatives, and $0$ to represent a null story element. There would, then, have to be further production rules where abstract villainy, pursuit, marking of the hero, etc., are differentiated into their more concrete types.

In a pure regular grammar, which choice gets made at each application of a production rule is totally independent of the choices made at every other application of a rule. (This is because regular languages are a sub-type of "context free" languages, and is what gives both kinds of language their madlibs flavor.) Propp is at some pains to argue (pp. 109--113) that this is very, very nearly true of fairytales. The exceptions are few enough that they could, I think, be handled within the finite-state, regular-grammar framework, by expanding the set of non-terminal symbols a little.

To sum up, Propp did grammatical induction on fairytales by hand, in 1928, and came up with a regular language.

Naturally, I have questions.

• How reliably can people identify his plot functions in the text of tales?
• Do all tales in his corpus in fact fit his grammar?
• How much interpretive violence is necessary to make an arbitrary story seem to fit his schema? If it's easy to warp anything so it seems to fit, this becomes much less interesting.
• Do other story corpora show the same set of functions? If so, do they follow the same story grammar? (My sense is that the overwhelming majority of fiction I read either conforms exactly, or is very close.)

I am sure that folklorists must have tackled questions like this, and I would very much appreciate pointers to the literature.

[1] Propp, pp. 111--112, on how his conclusions "may also be verified experimentally":

It is possible to artificially create new plots of an unlimited number. All of these plots will reflect the basic scheme, while they may not resemble one another. In order to create a tale artificially, one may take any $A$, then one of the possible $B$'s then a $C\uparrow$, followed by absolutely any $D$, than an $E$, then one of the possible $F$'s, then any $G$, and so on. In doing this, any element may be dropped (except possibly for $A$ or $a$), or repeated three times, or repeated in various forms. If one then distributes functions according to the dramatis personae of the tale's supply or by following one's own taste, these schemes come alive and become tales. Of course, one must also keep motivations, connections, and other auxiliary elements in mind.

Unfortunately, Propp provides no samples of tales generated in this manner. If they have survived, it would be very interesting to read them. (Dundes, in his introduction to the 2nd English edition, mentions "programm[ing] a computer" to do this, but I haven't tracked down that reference (Alan Dundes, "On Computers and Folklore", Western Folklore 24 (1965): 185--189).

He immediately goes on:

The application of these conclusions to folk creation naturally requires great caution. The psychology of the storyteller and the psychology of his creative work as a part of the over-all psychology of creation must be studied independently. But it is possible to assume that the basic, vivid moments of our essentially very simple scheme also play the psychological role of a kind of root.

Again, this cries out for follow-up study, which may well have been done. ^.

Indra Das, The Devourers

Mind candy, historical fantasy/horror division: European shapechangers (not werewolves, exactly) in Mughal India, and modern Calcutta. Angst ensues. (I was very disappointed that the narrator's deep dark secret, at the very end, proves to be something as mundane as cross-dressing.)

Laura J. Snyder, Eye of the Beholder: Johannes Vermeer, Antoni van Leeuwenhoek, and the Reinvention of Seeing

Parallel lives of two 17th century inhabitants of Delft --- not revelatory as either art history or history of science, but deftly done, even to the explanations of some fairly involved optics.

Garrett Birkhoff, Hydrodynamics: A Study in Logic, Fact, and Similitude

This is Birkhoff surveying the state of hydrodynamics in 1950, and in particular looking at why some theoretical results so conspicuously fail to match observations (the "logic" part), and when the uses of physical scale models can be justified (the "similtude" part). For the former, his diagnosis is not just mathematical sloppiness on the part of physicists, or making inappropriate approximations, but taking inconsistent assumptions. The latter part largely turns on the method of dimensional analysis, its limitations, and how it can be seen as a special case of more general group-theoretic approaches to finding similar solutions to partial differential equations.

These are, of course, more general morals about mathematical modeling, but nobody who isn't pretty familiar with hydrodynamics and group theory will get anything out of this book.

An incidental observation: It's striking to me that Birkhoff cites many much (relatively) older works than a contemporary writer would, and that he cites plenty of French- and German- language publications. (I can't remember if he cites any Italian or Russian works in the original, rather than translations.) There is a little lesson here about the transformation of post-war science...

Donald B. Rubin, Multiple Imputation for Nonresponse in Surveys

"Imputation" is the more dignified name statistics gives for "making stuff up to fill in missing observations". (To be fair, that's a mouthful.) Rubin was, back in the day, a very forceful and necessary advocate for multiple imputation, i.e., for making up a whole bunch of different things to fill in the missing observations, and trying them all out, to make sure that your results aren't just creatures of accidents in your imputation. While this is clearly almost always a better idea than single imputation, there are also, clearly, some details that will need to be pinned down. This short (258 pp.) book does a remarkably good job of pinning down those details in an easy-to-follow way. It also includes a summary of Rubin's equally-influential work on missing data, i.e., when exactly it's a problem for what kinds of inferences. Some of the computational advice is antiquated, and I could have wished it was less Bayesian, but it's still a very nice piece of work.

Ob. "Why Oh Why Can't We Have a Better Academic Publishing System": Wiley has kept the book in print, as a "classic", but the list price is \$ 158, or over sixty cents per page.

Inga Clendinnen, Aztecs: An Interpretation

This is a brilliant book, a learned, intelligent and sympathetic attempt to try understand something of how things must have felt to what must stirke most readers as a very strange and unsympathetic society. I also cannot help but feel that huge chunks of it are massive speculations, starting from the first substantive chapter on Aztec notions of "the sacred" and going on from there. The sources seem to me just too thin, and too peculiar*, to support the very elaborate interpretations Clendinnen erects upon them. (Which doesn't mean she was wrong.) But she was the expert who was immersed in the source material, not me.

[*]: Largely, they are accounts given many decades after the conquest, and it seems unclear how much of them was the sources recalling what happened, as opposed to giving their views about what ought to have happened, or what they wanted Spanish missionaries and their helpers to think happened. Even if they were doing their best to stick to their memories of the facts, they couldn't possible have experienced, say, the new fire ceremony which took place every 52 years more than once, and that, perhaps, when they were quite young. ^

David E. Hoffman, The Billion Dollar Spy: A True Story of Cold War Espionage and Betrayal

In which the poisonous legacy of the Stalinist purges inspires a Soviet engineer to volunteer to spy for the US, extremely successfully.

Books to Read While the Algae Grow in Your Fur; Writing for Antiquity; The Commonwealth of Letters; Physics; Scientifiction and Fantastica; Enigmas of Chance