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How type frequency gives us S-curves

How type frequency gives us S-curves. Angus B. Grieve-Smith Saint John’s University angus@grieve-smith.com @ grvsmth. How type frequency gives us S-curves. S-curves Type frequency Productivity and language change Type frequency in French negation. A recurring pattern in language change.

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How type frequency gives us S-curves

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  1. How type frequencygives us S-curves Angus B. Grieve-Smith Saint John’s University angus@grieve-smith.com @grvsmth

  2. How type frequency gives us S-curves • S-curves • Type frequency • Productivity and language change • Type frequency in French negation

  3. A recurring pattern in language change • Slow, quick, slow • Periphrastic do in English (Ellegard 1953 in Kroch 1989) • Zero genitive with units of measurement in Russian (Altmann et al. 1983) Future tense markers in Brazilian Portuguese (Poplack & Malvar 2007:14, via Blythe and Croft 2012)

  4. Technology adoption curves (Consumption actually doesn’t spread faster today.) Graph: Felton (2008)

  5. S-curves are everywhere! Lab population of flour beetles4 International tourist visits per year3 Followers of @CraftBeerTime on Twitter1 New Facebook accounts2

  6. Other S-curves are relative too

  7. The mathematics behind S-curves Exponential growth: The more you have, the more you get. “Population growth finds its limit in the size and fertility of the land, and total population thus shows an increasing tendency to become stationary.” “The rate of population growth is slowed by the very increase in the number of inhabitants.” – Verhulst (1838) Based on data from Verhulst (1838)

  8. “incremental linguistic change seems often to reflect competition among alternative licensing principles for entire grammatical subsystems” Logistic model for language change (Kroch 1989)

  9. The ingredients of the logistic

  10. What are the forces producing S-curves in language?

  11. Type frequency French verb suffixes in children’s spontaneous speech, Guillaume 1927

  12. Guillaume 1927

  13. Morphological paradigms as categories • “Rather than seeing names as referring to classes of objects, in morphology we have modifications where classes of forms refer to classes of meanings or concepts. The difference is that, whereas the names are simple, formal realizations of modifications are themselves categories.” –Zager 1981 (45)

  14. Cue validity in categories “Categories form to maximize the information-rich clusters of attributes in the environment, and, thus, the cue-validity of the attributes of the categories. Prototypes of categories appear to form in such a manner as to maximize the clusters and cue validity within categories.“ – Rosch et al. 1976

  15. Cue validity and productivity • “Return to the speech act where the speaker has no rote form and no automatic modification, and so searches for the nearest semantic/pragmatic equivalent. If they find the intended product is a member of a locally prototypical category (i,e, if, -say, the preterite of a given verb is autonomous) then the nearest; form to select is -the autonomous form of the requisite intended form - say the 2s.” – Zager 1981 (46-47)

  16. Is this just paradigmatic? • “Not only paradigms, however, will fit into this model. Any morphological modification would do equally well — negation, denominals, adverb formation and so on. All cases where a word is not stored by itself, but is formed by altering the form and meaning of some other word obtain.” – Zager 1981 (48)

  17. Type frequency and productivity “The likelihood of the schema being extended to new items is directly dependent upon two factors: • the defining properties of the schema • its strength the latter property being derivable from the number of items that reinforce the schema” – Bybee 1995

  18. Type frequency isn’t a real frequency • Metonymic extension from token frequency • “Applicability” (MacWhinney 1978) • Measure of perceived generality Tutorvista.com

  19. Type frequency is inherently relative

  20. How type frequency helps us choose • “If the intended product is part of a category that is in direct competition with another category (especially one that is formed through automatic modification, since that implies that it is already a well-established prototype as a whole paradigm) then not only will the prototypical form be taken into consideration, but specifically those aspects of it that are maximally different from the competing category.” – Zager 1981

  21. How does productivity lead to change? • Child overregularization hypothesis (Andersen 1973) • Rejected by Bybee and Slobin (1982), “Why small children cannot change language on their own: Suggestions from the English past tense” • Adult (and older child) forgetting • Proportional to type frequency (not winner-take-all) gives us new irregulars like “snuck”

  22. The ingredients of the logistic

  23. Another S-curve

  24. Variation within plays, and within characters

  25. Test of the logistic model (Kroch 1989, Verhulst 1838). The R2 value of 0.867 indicates that the model explains 86.7% of the observed variation. Proportion of tokens of declarative sentence negation with any embracing negation construction, from 1200 through 1939

  26. The logistic doesn’t explain it all • Has no applicability to declining populations • How can we model competition? • What about entrenchment and token frequency? • Read my dissertation at grieve-smith.com! Photo: Erhardt / Wikipedia (2006)

  27. Conclusion • S-curves in language are driven by productivity • Productivity is primarily driven by type frequency/applicability • Productivity is resisted by high-token-frequency items • This is illustrated by the French shift from ne to ne…pas

  28. Future directions • How did ne and ne…pas come to be seen as “the same”? • More representative corpus • Bigger corpus • Other negation contexts • http://grieve-smith.com • http://stjohns.academia.edu/grvsmth • angus@grieve-smith.com • @grvsmth

  29. Modeling inter-species resource competition • Alfred J. Lotka (Johns Hopkins U., 1925) • Vito Volterra (U. of Rome La Sapienza, 1926) • Also modeled predator-prey relationships Photos: Unkown

  30. Lotka and Volterra’s insight • Competition coefficient • The effect that each member of species i has on each member of species j Original logistic formula (Verhulst, 1838): Inter-species competition (Lotka 1925, Volterra 1926): competition coefficient

  31. So what values of α did I use?

  32. How did these values work out?

  33. Type frequency, predicted change and measured change in type frequency of embracing ne ... pas for main verbs, excluding high-frequency verbs and hapaxes. r = 0.977 Modeling the evolution of embracing ne … pas (αij = 1.29)

  34. Image credits • http://www.craftbeertime.com/off-topic/crowdbooster-social-media-tool-review/attachment/crowdbooster2 • http://ogilvyentertainmentblog.com/2011/10/on-social-media-the-magic-is-in-the-outliers/growth-graph-4/ • http://www.bbc.co.uk/schools/gcsebitesize/geography/tourism/tourism_trends_rev1.shtml • http://www.bio.georgiasouthern.edu/bio-home/harvey/lect/lectures.html?flnm=grop&ttl=Population%20Growth&ccode=el&mda=scrn

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