ANGUS B. GRIEVE-SMITHSAINT JOHN’S UNIVERSITY

ANGUS@GRIEVE-SMITH.COM@GRVSMTH

How type frequencygives us S-curves

How type frequency gives us S-curves

S-curvesType frequencyProductivity and language changeType frequency in French negation

A recurring pattern in language change

Slow, quick, slowPeriphrastic 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)

Technology adoption curves

(Consumption actually doesn’t spread faster today.) Graph: Felton (2008)

S-curves are everywhere!

Followers of @CraftBeerTime on Twitter1

New Facebook accounts2

International tourist visits per year3Lab population of flour beetles4

Other S-curves are relative too

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)

1817

1818

1819

1820

1821

1822

1823

1824

1825

1826

1827

1828

1829

1830

1831

28.5

29.0

29.5

30.0

30.5

31.0

31.5

32.0

32.5

33.0

Population of France (millions)

Logistic model for language change (Kroch 1989)

“incremental linguistic change seems often to reflect competition among alternative licensing principles for entire grammatical subsystems”

k

xrx

dt

dx 1

The ingredients of the logistic

Population

Cell phones Language

Exponential growth

Birth Word of mouth ?

Limits Extent and fertility of the land

Language-using population

Checks Misery and vice

Conservatism and lack of interest

What are the forces producing S-curves in language?

Type frequency

French verb suffixes in children’s spontaneous speech, Guillaume 1927

Guillaume 1927

-er36%

-ir6%-re

23%

-oir35%

Tokens

-er76%

-ir6%

-re5%

-oir13%

Types (verbs)

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)

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

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)

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)

Type frequency and productivity

“The likelihood of the schema being extended to new items is directly dependent upon two factors:i. the defining

properties of the schema

ii. its strengththe latter property being derivable from the number of items that reinforce the schema” – Bybee 1995

Generali

ty

•Type frequency

Productivity

•New uses

Analogical

extensio

n

•Increased use

Type frequency isn’t a real frequency

Metonymic extension from token frequency

“Applicability” (MacWhinney 1978)

Measure of perceived generality

Tutorvista.com

Type frequency is inherently relative

Language

Alternation Favored Alternatives Source

French Verb paradigm

–er –ir, -re, -oir Guillaume 1927

German Plural –en –e, -er, -s, ∅ MacWhinney 1978; Bybee 1995

Portuguese

Possessives Definite article

Without definite article

Oliveira e Silva 1982; Kroch 1989

English Past tense –ed vowel changes, , ∅ -t, etc.

Moder 1992

German Past participle

weak strong Bybee 1995

Arabic Plural Iambic Sound McCarthy and Prince 1990; Bybee 1995

Hausa Plural High -óoCíi

-úCàa etc. Lobben 1991; Bybee 1995

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

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) forgettingProportional to type frequency (not winner-

take-all) gives us new irregulars like “snuck”

The ingredients of the logistic

Population

Cell phones Language

Exponential growth

Birth Word of mouth

Type frequency!

Limits Extent and fertility of the land

Language-using population

Envelope of variation

Checks Misery and vice

Conservatism and lack of interest

Entrenchment

Another S-curve

12th 13th 14th 15th 16th 17th 18th 19th 20th0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Declarative sentence negation in Parisian theater, 1160-1929

ne alonene…miene…pointne…pas

Century

Variation within plays, and within characters

REcos A1-Tabarin Clitd Eudox PsychM These1601 1622 1631 1641 1671 1675

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

alonepointpas

Proportion of tokens of declarative sentence negation with any embracing negation construction, from 1200 through 1939

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.

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)

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

Future directions

How did ne and ne…pas come to be seen as “the same”?

More representative corpus

Bigger corpusOther negation

contexts

http://grieve-smith.com

http://stjohns.academia.edu/grvsmth

angus@grieve-smith.com

@grvsmth

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

i

jijiii

i

K

xaKxr

dt

dx

Lotka and Volterra’s insight

Competition coefficient

The effect that each member of species i has on each member of species j

k

xrx

dt

dx 1

competition coefficient

Original logistic formula (Verhulst, 1838):

Inter-species competition (Lotka 1925, Volterra 1926):

So what values of α did I use?

effectof ne alone of ne … pas of ne … point of ne … mie

on ne alone 1.000 1.290 1.140 1.760

on ne … pas 0.274 1.000 0.000 1.530

on ne … point 0.000 1.670 1.000 0.302

on ne … mie 0.451 3.870 0.000 1.000

How did these values work out?

Function Competition Centuries

Correlation (r)

Presupposition denial

ne … pas vs. ne … point vs. ne … mie

12th-16th -0.418

Presupposition denial

ne … pas vs. ne … point

17th-19th 0.951

Predicate negation

ne alone vs. ne … pas

17th-20th 0.977

Modeling the evolution of embracing ne … pas (αij = 1.29)

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

Image credits

1. http://www.craftbeertime.com/off-topic/crowdbooster-social-media-tool-review/attachment/crowdbooster2

2. http://ogilvyentertainmentblog.com/2011/10/on-social-media-the-magic-is-in-the-outliers/growth-graph-4/

3. http://www.bbc.co.uk/schools/gcsebitesize/geography/tourism/tourism_trends_rev1.shtml

4. http://www.bio.georgiasouthern.edu/bio-home/harvey/lect/lectures.html?flnm=grop&ttl=Population%20Growth&ccode=el&mda=scrn