HCC class lecture 8Vygotsky’s Genetic PlanesInternalizationExternalizationInternalization/ExternalizationPower LawsPower Law – alternate formExamples of Power LawsExamples of Power LawsExamples of Power LawsExamples of Power LawsExamples of Power LawsExamples of Power LawsExamples of Power LawsPreferential AttachmentYule’s law (1925)Literary Theory: StructuralismLiterary Theory: StructuralismBakhtin: “The Dialogic Imagination”Kristeva: IntertextualityBarthes: “S/Z”Simon’s model of textsSimon’s model of textsSimon’s model of textsGenetic LawsGenetic LawsLanguage as ActionGeorgia Tech HomeN-gramsN-gram statisticsN-gram statisticsConclusionsDiscussion questionsHCC classlecture 8John Canny2/23/09Vygotsky’s Genetic Planes Phylogenetic Social-historical Ontogenetic MicrogeneticWhat did he mean by genetic?InternalizationSocial functionsInternal (mental) functionsSocial PlaneInternal (mental) PlaneInternalizationScaffoldingShowing, explainingListening and readingExternalizationSocial/historical artifactsInternal (mental) functionsSocial/historical PlaneInternal (mental) PlaneExternalizationTalking, WritingInternalization/ExternalizationPower LawsPick a corpus such as: English (collection of many samples) Works of Shakespeare James Joyce’s “Ulysses”and count the occurrences of each word. Sort in decreasing order, let r be the rank in this order. Thenwhere is the frequency of the word of rankr. αrcrf ≈)()(rfPower Law – alternate formInstead of frequency vs. rank, we can plot frequency vs. number of sets with that frequency.The value β in this form is related to α via β=1/α+1.This was Zipf’s original form, and the one analyzed by Newell. βicig')( ≈Examples of Power LawsNote: size vs frequency of that size – Zipf’s original formExamples of Power LawsThese are in rank-frequency form.Examples of Power LawsExamples of Power LawsExamples of Power LawsExamples of Power LawsExamples of Power LawsAlso Number of users’ Facebook friends The popularity of Facebook apps Number of pages in web sites Number of links into a web site Number of links out of a web sitePreferential AttachmentYule’s law (1925)Number ofspecies ineach generaGeneraPure birth process:Only new species are addedLiterary Theory: StructuralismLooks for “structures” in the domain of study, e.g. literature or anthropology, and their relation to other Structure includes local (sentence) structure as on the next slide. Also includes deeper structures such as role and plot. E.g. “West Side Story” is the same plot structure as “Romeo and Juliet”  Structuralists often look for “universal” structures, e.g. Freud’s Oedipal complexLiterary Theory: StructuralismBakhtin: “The Dialogic Imagination”Multiple voices are evident in a text: heteroglossia or multivocality or polyphony.Kristeva: IntertextualityKristeva elaborated Bakhtin’s ideas into the theory of intertextuality: Texts borrowed and adapted from other texts.AllusionCharactersPlotFormSceneBarthes: “S/Z”“A text is... a multidimensional space in which a variety of writings, none of them original, blend and clash. The text is a tissue of quotations... The writer can only imitate a gesture that is always anterior, never original. His only power is to mix writings, to counter the ones with the others, in such a way as never to rest on any one of them”LexiaSimon’s model of textsText is built by sampling earlier texts: Association: sampling earlier passages in the same corpus. Imitation: “sampling segments of word sequences from other works he has written, from works of other authors, and, of course, from sequences he has heard.”Simon’s model of textsStatified sampling:Sampling and re-assembly of small segments of text. The choice of which segments to assemble does not have to be random.Simon’s model of textsSimon’s model explains the familiar Zipf curve.Limitations: Pure “birth” process* Should work for differentnotions of “strata”* But birth-death processesin equilibrium also produceZipf curvesGenetic LawsWe have given an explanation of Power Law behavior in texts via internalization/externalization:Genetic LawsOther similar phenomena may be explained in this way: Sales of books, or many other items Citations of scientific articles Number of pages in web sites Number of links into a web site Number of links out of a web site Number of users’ Facebook friends The popularity of Facebook appsLanguage as ActionWhat we have seen so far: Many choice phenomena show the fingerprint of internalization/externalization and genetic origin.  This includes language – both collective and individual. Is there a more general link between language and action, as Vygotsky and others have suggested?Georgia Tech Home26 occupancy sensorsData recorded over several weeksN-gramsN-gram are sequences of n tokens, in this case n sensorsThe following is a 6-gram sequence of locations:3-11-27-12-19-20N-gram statisticsNot only words in English, but n-grams of words in English follow power laws*. In the smart home data, n-grams are a more reasonable unit of analysis than individual sensor sites.We might expect to see power law behavior if movement about the house is governed by “familiar habit” rather than optimal movement or planning. * For small corpora, the n-gram stats for n>1 are often closer to an exact power law than for 1-grams (words).N-gram statisticsHere is the data from the smart home experiment in Zipf’soriginal form. All plots show a β close to 2, which corresponds to α close to 1. Slope β increases slightly as n increases (so α decreasing)ConclusionsThere appears to be a genetic mechanism at play, even in simple physical movement about the house. At least from one perspective (n-gram analysis), language and one type of action are remarkably similar. Many other human phenomena show power law behavior, either through internalization/externalization or purely internal mechanisms.Discussion questions1. Suggest another measure of human behavior that might show genetic dynamics, and research whether it shows power law behavior (do a web search). Be prepared to explain the genetic mechanism. 2. Discuss the freedom of the author given the statistical similarities of new texts to old