Lee,
I sympathize with your lament about recursion. CF the use of the terms song, note, and phrase in the bird song literature. And these people were all working in the same narrow subfield of animal behavior. See at least the abstract of http://home.earthlink.net/~nickthompson/naturaldesigns/id60.html An incautious click on the abstract will down load the paper. By the way, my suggested clarification and simplification of the terminology has not only not been put into practice but, so far as I know, has been read only once. Nick Nicholas S. Thompson Emeritus Professor of Psychology and Biology Clark University http://home.earthlink.net/~nickthompson/naturaldesigns/ -----Original Message----- From: Friam [mailto:[email protected]] On Behalf Of Steve Smith Sent: Friday, October 11, 2013 11:01 PM To: The Friday Morning Applied Complexity Coffee Group Subject: Re: [FRIAM] Notions of entropy On the topic of language, this hyperpolyglot's description of his experience learning/speaking many languages is fascinating: <http://www.youtube.com/watch?v=Km9-DiFaxpU> http://www.youtube.com/watch?v=Km9-DiFaxpU His assertion that he "thinks differently" when he speaks different languages and that he begins learning a new language by listening to it a lot and emulating what he hears (television). > Nick writes, in relevant part: > >> I am, I think, a bit of what >> philosophers call an essentialist. In other words, I assume that >> when people use the same words for two things, it aint for nothing, >> that there is something underlying the surface that makes those two >> things the same. So, underlying all the uses of the word "entropy" is a common core, and .... > I'm not going to go anywhere near the mathematical question here. > What I want to do is challenge your "In other words" sentence (which, > by the way, I *hope* is not what philosophers would mean by calling > you "an essentialist"). > > One thing I have learned in the last three or four years, much of > which I have spent trawling through huge corpora of scholarly (and > less scholarly) writing, including Google Scholar (and just plain > Google Books), JStor, MUSE, PsycInfo, Mathematical Reviews, etc., is > that "when people use the same words for two things", it's > distressingly common that it IS "for nothing", or nearly > nothing--either two or more different groups of scholars have adopted > a word from Common English into their own jargons, with no > (ac)knowledge(ment) of the other groups' jargon, or two or more > different groups of scholars have independently *coined* a word (most > usually from New Latin or New Greek roots that are part of scholars' > common store). > > Actually, the first case of this that I really noticed was several > years before I got involved professionally. In a social newsgroup, a > linguist of my acquaintance happened to use the word "assonance". > And he used it WRONG. That is, he used it entirely inconsistently > with the meaning that it has had for eons in the theory of prosody, > and that every poet learns (essentially, assonance in prosody is vowel > harmony). When I challenged him on this, my friend said that the word > had been introduced to linguistics by the (very eminent, now very > dead) Yale linguist Dwight Bollinger. And he implied that the > linguists weren't about to change. Tant pis, said I. > > Then I got involved in the Kitchen Seminar (FRIAMers, you can ignore > that; it's a note to Nick), and began to hear psychologists (but not > Nick!) use the phrase "dynamic system" (or occasionally "dynamical > system"). As a mathematician I knew what that phrase meant, and they > were WRONG. > > After some years in the Kitchen, I began work on my book on > mathematical modeling for psychology; eventually I saw I needed to > write a chapter clarifying the uses of those phrases. > Three or four years of work on _The Varieties of Dynamic(al) > Experience_ later, I had accumulated *enormous* amounts of textual > evidence that there had been NO cross-pollination: > the two phrases arose entirely independently. (Then, unfortunately, > hapless psychologists and other "human scientists" started > appropriating [what they badly understood of] the mathematical results > that can be proved about mathematicians' "dynamical systems" to draw > ENTIRELY UNSUBSTANTIATED conclusions about psychologists' "dynamic > systems".) > > Most recently, I've been going through the same exercise (again for a > chapter, now not in a book of my own) for "recursion" and "recursive". > Again, I have accumulated (and documented) enormous amounts of textual > evidence (from all those corpora); here is a brief outline of the > situation (with examples and all, the whole thing is about 25 pages at > the moment, interlarded with another > 25 pages on "infinity" and topped off--I mean, bottomed off--with 15 > pages of references). Before the outline, however, I will quote four > practitioners of various human sciences who have had cause to complain > of the present mess. > > ==a sociologist of law:== > In the context of causal analysis, as carried on in empirical research > (e.g. path analysis) nonrecursive models are employed, to denote the > case of mutual influencing of variables. When the autopoesis > literature speaks of recursive processes, it is presumably those > nonrecursive models of causal analysis that are meant. What a tower of Babel! > (Rottleuthner, 1988, p. 119) > > ==a physicist turned cognitive scientist (via LOGO):== One is led to > wonder if all authors are talking about and experimenting with the > same notion and, if not, what this notion could be. As it happens, a > careful reading shows that it is not so and that, unless a very loose > and rather useless definition of the term ["recursive"] is assumed, it > could be worthwhile to separate this confusing braid into its > constituent strands [...]. (Vitale, 1989, p. 253) > > ==an evolutionary linguist:== > Definitions of recursion found in the linguistics and computer science > literatures suffer from inconsistency and opacity (Kinsella, 2010, p. > 179) > > ==a political scientist:== > The term `recursive´ [...] has multiple uses in the political science > literature. [... Political scientists should address] [t]he problem of > divergent meaning [...] through a survey of potential for > reconciliation or possible substitute terminology (Towne, 2010, p. > 259) === > > Now, the outline. > > o There are three distinct meanings of "recursive"/"recursion"--let > me abbreviate that to R/R from now on--in mathematics. The oldest one > describes so-called "recurrence relations" (like the one that defines > the Fibonnaci sequence: F1=1, F2=1, Fn = Fn-1 + Fn-2). The next > oldest, dating only from last century, is the one used in mathematical > logic; it's derived from the oldest but it's much more general > ("recursive functions"). There's an entirely UNrelated one used in a > minor branch of dynamical systems theory (which has had no influence > outside of a very small circle), apparently named because of a > connection to "recurrence" in colloquial English (think "Poincare > section" if that helps). > > o The oldest mathematical sense has spawned a meaning that started in > economics and then spread (it's the one that Rottleuthner was talking > about); mathematically, it corresponds to upper-triangular matrices > (coding causalities). > > o The next-oldest has spawned the present, barely coherent (cf. > Kinsella), use of R/R in linguistics and linguistics-inspired social > science. *Some* of Seymour Papert's--and, thence, the LOGO > community's--uses of R/R come from this tradition (one of his two > Ph.D.s is, after all, in mathematics). > > o Another sense of R/R comes from Piaget (with a nod towards > Poincare). *The rest* of Seymour Papert's--and, thence, the LOGO > community's--uses of R/R come from this tradition (his second Ph.D., > in Psychology, was supervised by Piaget). Piaget, I am afraid, is > responsible for a great deal of muddle on this subject. > > o Yet another sense of R/R, used in human ecology, anthropology, > political science, sociology, and educational theory > sprang--somehow--out of cybernetics and General Systems Theory (even > though none of the early cyberneticists like von Neumann, Shannon, and > Weiner, and none of the early GS people like Bertallanfy and Rapoport, > ever seem to have used the word AT ALL, except for a couple of times > in early papers of von Neumann where he was using it in the oldest > mathematical meaning). It really seems that Bateson pulled the word > out of the air (that is, out of his no doubt rigorous classical > education) at some point, and it spread from him, in a (typically) > incoherent fashion, and apparently mostly by word of mouth--he didn't > commit either word to print until the year before his death, though > his biographer Harries-Jones has seen a notebook in which Bateson > recorded using the word in a lecture in 1975. (Harries-Jones's title > for the biography, _A recursive vision: Ecological understanding and > Gregory Bateson_, is, in my opinion, irredeemably tendentious, and a > perfect example of muddle.) Insofar as Bateson ever tries to actually > *define* R/R, it's here: > > == > [T]here seem to be two species of recursiveness, of somewhat different > nature, of which the first goes back to Norbert Wiener and is > well-known: the "feedback" that is perhaps the best known feature of > the whole cybernetic syndrome. The point is that self-corrective and > quasi purposive systems necessarily and always have the characteristic > that causal trains within the system are themselves circular. [...] > The second type of recursiveness has been proposed by Varela and > Maturana. These theoreticians discuss the case in which some property of a whole is fed back into the system, producing a somewhat different type of recursiveness[...]. We live in a universe in which causal trains endure, survive through time, only if they are recursive. > (Bateson, 1977, p. 220) > === > > Needless to say, Wiener never called feedback (or anything > else) "recursive", and it's a real stretch to connect the mathematics > of feedback to mathematical notions of R/R. > Nor did Varela and Maturana EVER use R/R (in print at least) before > 1977; they instead coined "autopoeisis", which again, insofar as it > can be mathematicized, is not mathematical > R/R. (Later Maturana does use "recursive".) > > o An Australian economic geographer named Walmsley somehow came up > with a notion of R/R c. 1972; until and unless he answers my e-mail > (pending now for several months, so I'm not holding my breath), I can > only assume, from references he cites, that he somehow came up with > his idea by combining General Systems Theory (though the word doesn't > appear there) with Piaget. Given that he states in one place that > "Shopping is a form of recursive behavior", you won't be surprised > that his idea--whatever it may be--appears entirely unrelated to > mathematical (or linguistic) R/R. In any case, he doesn't seem to > have inspired any followers. > > o A sociologist named Scheff starts using the *words* "recursive" > and "recursion" c. 2005, for ideas (either his or others'; see > below) that were around starting in 1967. > > ==Scheff (2005):=== > In one of my own earlier articles (Scheff 1967), I proposed a model of > consensus that has a recursive quality like the one that runs through > Goffman's frame analysis. [...] As it happened, Goffman (1969) pursued > a similar idea in some parts of his book on strategic interaction. > [...] [A] similar treatment can be found in a book by the Russian > mathematician Lefebvre (1977), The Structure of Awareness. [...]I > wonder whether Lefebvre came up with the idea of reflexive mutual awareness independently of my model. He cites Laing, Phillipson, and Lee (1966), a brief work devoted to a recursive model of mutual awareness that preceded Lefebvre´s book (1977). > However, he also cites his own earliest work on recursive awareness, > an article (1965) that precedes the Laing, Phillipson, and Lee book. > It is possible that Lefebvre´s work was based on my (1967) model of > recursive awareness, even though the evidence is only circumstantial. > As Laing, Phillipson, and Lee (1966) indicate, their book developed > from my presentation of the model in Laing's seminar in 1964. Since > there were some 20 persons there, Lefebvre could have heard about the seminar from one of those, or indirectly by way of others in contact with a seminar member. > === > > However, despite all the heavy lifting involved in Scheff's > name-dropping, the words "recursive" and "recursion" appear nowhere in > the cited works by Laing, Phillipson & Lee (1966), Scheff (1967), or > Goffman (1969). Lefebvre (1977, but not 1965) does use "recursive" in > the two major mathematical senses, and even quotes Chomsky (although I > think it likely--I haven't been able to get the Russian originals of > Lefebvre--that all that was introduced by his translator, Rapaport of > GS fame). > Rather, Laing, Phillipson & Lee, Scheff, and Goffman consistently use > the words "reflexive", "reflection", and "reflexivity". These are > glossed by Scheff in a variety of ways: > "recursive awareness", "mutual awareness" (harkening back to Goffman´s > signature phrase, "mutual consideration"), "not only understanding the > other, but also understanding that one is understood, and vice versa", > "not only a first-level agreement, but, when necessary, second and > higher levels of understanding that there is an agreement", etc. > Sheesh. > > o Finally (thank you for the reference, Nick), Peter Lipton and Nick > Thompson published an article in 1988 titled "Comparative psychology > and the recursive structure of filter explanations." > It's a great article, but the sense in which it uses "recursive" > (Lipton's coinage) is unrelated to any of the other senses (nor has it > been taken up since, as far as I can tell). > > [Here endeth the outline.] > > The "common core", if there is one, is nothing more than the > collocation of the morphemes "re-" and "-cur-", of which the former is > still very productive in English, while the latter is (at most New) > Latin and no longer productive at all; semantically, this makes the > meaning of that common core approximately "RUN AGAIN", which I submit > is AT BEST a trivial commonality of the various different uses, and > (as far as I understand some of the woolier uses, which is not that > far) not a commonality AT ALL of the entire set. > If that be essence, make the least of it! > > Lee Rudolph > > > > ============================================================ > FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe > at St. John's College to unsubscribe > <http://redfish.com/mailman/listinfo/friam_redfish.com> http://redfish.com/mailman/listinfo/friam_redfish.com > ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe <http://redfish.com/mailman/listinfo/friam_redfish.com> http://redfish.com/mailman/listinfo/friam_redfish.com
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