Transcript The evolution of negation in a corpus of French theatre

How type frequency
gives us S-curves
ANGUS B. GRIEVE-SMITH
SAINT JOHN’S UNIVERSITY
[email protected]
@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
 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)
Technology adoption curves
(Consumption actually doesn’t spread faster today.)
Graph: Felton (2008)
S-curves are everywhere!
International tourist visits per
year3
Followers of @CraftBeerTime
on Twitter1
Lab population of
flour beetles4
New Facebook
accounts2
Other S-curves are relative too
The mathematics behind S-curves
Population of France
(millions)
33.0
32.5
32.0
31.5
31.0
30.5
30.0
29.5
29.0
28.5
1817
1820
1823
1826
1829
Based on data from Verhulst (1838)
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)
“incremental
linguistic change
seems often to
reflect competition
among alternative
licensing principles
for entire
grammatical
subsystems”
dx
1 x 
 rx

dt
 k 
Logistic model for language change
(Kroch 1989)
The ingredients of the logistic
Population Cell phones
Exponential Birth
Word of mouth
growth
Limits
Extent and
Language-using
fertility of
population
the land
Checks
Misery and
Conservatism and
vice
lack of interest
Language
?
What are the forces producing S-curves in language?
Type frequency
French verb suffixes in children’s spontaneous
speech, Guillaume 1927
Guillaume 1927
Tokens
-oir
35%
-re
23%
-er
36%
-re
5%
-ir
6%
Types (verbs)
-oir
13%
-er
76%
-ir
6%
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
Generality
Productivity
Analogical
extension
• Type
frequency
• New uses
• Increased
use
“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 strength
the latter property being
derivable from the number
of items that reinforce the
schema” – Bybee 1995
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) forgetting
 Proportional to type frequency (not winner-take-all)
gives us new irregulars like “snuck”
The ingredients of the logistic
Population Cell phones
Exponential Birth
Word of mouth
growth
Limits
Extent and
Languagefertility of
using
the land
population
Checks
Misery and
Conservatism
vice
and lack of
interest
Language
Type
frequency!
Envelope of
variation
Entrenchment
Another S-curve
Declarative sentence negation in Parisian theater, 1160-1929
100%
90%
80%
70%
60%
ne alone
50%
ne…mie
40%
ne…point
30%
ne…pas
20%
10%
0%
12th
13th
14th
15th
16th
Century
17th
18th
19th
20th
Variation within plays, and within characters
100%
90%
80%
70%
60%
alone
50%
point
pas
40%
30%
20%
10%
0%
REcos
A1-Tabarin
Clitd
Eudox
PsychM
These
1601
1622
1631
1641
1671
1675
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
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
 http://grieve-smith.com
come to be seen as “the
same”?
 More representative
corpus
 Bigger corpus
 Other negation contexts
 http://stjohns.academia.
edu/grvsmth
 [email protected]
 @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
Lotka and Volterra’s insight
Original logistic formula (Verhulst, 1838):
dx
1 x 
 rx

dt
 k 
Inter-species competition
(Lotka 1925, Volterra 1926):
 K i   aij x j
dxi
 ri xi 
dt
Ki





competition coefficient
 Competition
coefficient
 The effect that each
member of species i
has on each member
of species j
So what values of α did I use?
effect
of 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
3.870
0.000
1.000
0.451
How did these values work out?
Function
Competition
Centuries Correlation (r)
Presupposition
denial
ne … pas vs. 12th-16th
ne … point vs.
ne … mie
-0.418
Presupposition
denial
ne … pas vs.
ne … point
17th-19th
0.951
Predicate negation
ne alone vs.
ne … pas
17th-20th
0.977
Type frequency,
predicted change
and measured
change in type
frequency of
embracing ne ... pas
for main verbs,
excluding highfrequency verbs
and hapaxes.
r = 0.977
Modeling the evolution of
embracing ne … pas (αij = 1.29)
Image credits
http://www.craftbeertime.com/offtopic/crowdbooster-social-media-toolreview/attachment/crowdbooster2
2. http://ogilvyentertainmentblog.com/2011/10/onsocial-media-the-magic-is-in-the-outliers/growthgraph-4/
3. http://www.bbc.co.uk/schools/gcsebitesize/geogra
phy/tourism/tourism_trends_rev1.shtml
4. http://www.bio.georgiasouthern.edu/biohome/harvey/lect/lectures.html?flnm=grop&ttl=P
opulation%20Growth&ccode=el&mda=scrn
1.