Models of phonetic variation and selection

1
Models of phonetic variation and selection

• Bjorn Lindblom
• Perilus XI, 1990, pp. 65-100

2
How Do Phonetic Systems Evolve?

• Three Accounts
• (with comments)
• I am grateful to Bjorn Lindblom who sent me a
  manuscript on this subject (Linblom, B. (2007)
  Draft of Evolution of Phonology. In P. Hogan
  (Ed.), The Cambridge Encyclopedia of the Language
  Sciences). The opinions, additions, and
  oversights are my own.

3
Account 1 (Just-So)The Big Brain Story(M.
Donald)

• Evolution of human cognition allowed
  vocal/auditory communication
• Supposedly adaptive
• Omnidirectional
• Can be done in the dark
• Does not impede movement
• Epistemological Issue Ex post facto stories
  cant be falsified

4
Account 2 (Just-So)The Vocal Tract Story(P.
Lieberman)

• Descent of larynx reduction in jaw size
• a. Adaptive advantages
• Full range of vowels (chimps make a single vowel)
• Non-nasal sounds
• b. Offset disadvantages
• Choking risk (newborns can breathe and eat
  simultaneously)
• Risk of impacted teeth and less efficient chewing
• Epistemological Issue Ex post facto stories
  cant be falsified

5
Account 3 (Existence Proof)Challenge of the
Phonetic Inventory and its Implications

• Models the mismatch between
• Sounds that vocal tract CAN produce
• Sounds that vocal tract DOES produce
• As a tug-of-war between perceptual ease and
  articulatory cost
• Epistemological Issue Suppose we ran this model
  on a computer. What is the truth-value of an
  existence proof?

6
What is this Challenge?

• UPSID database contains information on 317
  languages
• Average consonant inventory of 20-25/language
• 500-600 distinct segment types
• Sounds like a lot?
• UCLA Phonological Segment Inventory Database (as
  of 1990)

7
Suppose

• We are constructing languages
• Our language is to have 25 consonants
• We have an inventory of 500 consonants to choose
  from?
• How many distinct languages (not counting vowels)
  can we produce?

8
A Combination Problem

• Classic Formulation
• We have 7 people
• How many committees of 3 can we form
• Particular phrasing 7 Objects, 3 at a time
• General phrasing N Objects, R at a time
• General Formula N!/((N-R)! R!)
• Particular Formula 7!/((7-3)! 3!) 35

9
In the Case of Languages

• 500!/((500-25)! 25!) 1.043912884 1042

10
How Big is This Number?A First Pass

• Suppose
• We have a computer that generates descriptions of
  1,000,000 phonetic systems per second
• It runs round the clock for a year
• Then
• Our computer generates about 1014 phonetic
  systems in a year

11
How Big is This Number?A Second Pass

• Let P be the number of possible systems 1042
• Let R be the number of systems generated in year
  on our computer 1028
• Let U be the age of the universe 13.7 X 109
  years
• Let F be the time required to generate the full
  inventory of languages on our computer
• Let N be the number of universe ages required to
  generate the full inventory
• F P/R 1042/1014 1028 year using our
  computer
• 1028 years needed using our computer
• N F/U 1028/(13.7 X 109) 1017
• 100 quadrillion times the age our universe

12
How Big is This Number?A Third Pass

• Suppose our consonant inventories were placed in
  a great hat
• The probability of putting your hand in the hat
  and pulling out one of the 317 consonant
  inventories in the UPSID database is
• 317/( 1.043912884 1042) .303 X 10-39
• .000000000000000000000000000000000000000303
• By Comparison
• Winning Hot Lotto on 9/22/07 6 10 21 27 32 15
• Probability of picking this is 1/1012
• .000000000001

13
Implications

• The uniformity of the languages is striking
• Speech makes extremely fastidious use of the
  phonotory and articulatory dimensions in
  principle available (p. 67).
• There must be selection criteria involved in the
  evolution of phonetic systems

14
Plausible Assumptions

• Tug-of-war between
• Articulatory simplicity (speech production)
• Perceptual distinctiveness (speech perception)

15
Speech Production Articulatory Simplicity

• How to make i
• Jaw raised
• Tongue forms a palatal constriction
• Suppose we prevent the jaw from raising (by means
  of a 20 mm bite block)
• Tongue must compensate to produce i

16
Question and Answer

• If speakers can make i in two ways
• Why is i universally produced as a high vowel
  (p. 68)
• Why does the normal position involve a raised
  jaw (p. 68)
• Answer extreme articulations are avoided in
  speech (p. 68)

17
Vowel Reduction

• I said Will not Bill
• Robert will do it
• /i/ is part of a stressed syllable in Will
• /i/ is part of an unstressed syllable in will and
  is shorter
• /i/ in Will is pronounced I
• /i/ in will approaches U in color (p. 69)

18
The Undershoot Hypothesis

• As vowels in a CVC sequence get shorter, there is
  less time for articulators to move from the first
  to the second consonant.
• The articulators (for both consonants and the
  vowel) undershoot their targets.
• The reason is mechanical duration-dependent
  undershoot (p. 69)

19
And Can Be Made Precise

• Assumption articulators behave like damped
  springs with fixed time constants
• Consider /bab/
• Force applied to raise the jaw for /b/
• Force applied to lower the jaw for /a/
• Force applied to close the jaw for /b/
• If these forces dont change but are applied
  closer in time, the jaw gesture will exhibit
  more and more undershoot with respect to the
  opening for the vowel (p. 70).

20
How to Avoid Undershoot

• Let
• w work in joules
• f force in newtons
• d distance in mm
• p power in watts
• t time in seconds
• w f d and p w/t (f d)/t
• Where undershoot occurs, d is reduced
• To eliminate undershoot, requires an increase in
  force over the same time interval. This results
  in an increase in work over time.

21
Argument for Adaptive Benefit

• Undershoot is a type of coarticulation
• Ubiquitous in speech
• Why?
• The Motor Theory of Speech (Lieberman, again)
• without it, each phoneme becomes a syllable
• talkers could speak only as fast as they could
  spell (p. 70)
• Imagine spending your social life in a chat room.
  The adaptive benefits seem not great (to make up
  a just so story of my own)

22
Articulatory SimplicitySome Generalizations

• Articulatory configurations that
• Represent increased displacement from rest
  positions
• Require movements with greater velocities
• Become more rare
• (Example di requires less displacement and
  velocity than the retroflex ?i)

23
Articulatory SimplicityConclusion

• Articulators can be modeled as springs
• On-line speech production appears to operate as
  if physiological processes were governed by a
  power constraint limiting energy expenditure per
  unit time (p. 72)
• In a felicitous phrase
• Speech production prefers the physiological
  pianissimo (p. 72)

24
The Other Side of the CoinSpeech Perception

• Premise
• Speakers are extremely good at adapting their
  pronunciations to the varying demands of the
  speaking situation (p. 74)
• Implication
• Phonetic gestures are an adaptive and
  malleable means to more global communicative
  ends (p. 74)

25
Redundancy

• All languages exhibit structural redundancy
• Consequently words and phonemes of individual
  utterances show short-term variations in
  predictability. (p. 74)

26
Consider Minimal Pair Triads

• Sa mere sest fait beaucoup de soucis
• Sa mere sest fait beaucoup de soucis
• Sa mere se fait beaucoup de soucis
• French speakers have no problems
• Swedes without French perform poorly
• When sest/se is presented in isolation, Swedes
  improve dramatically relative to the French

27
Implication

• Speech perception is a product of
• Signal-driven information and
• Signal-independent information
• Knowledge of French is signal-independent
  information
• Speech signals are perceptually adequate
• when they match the listeners signal-independent
  info
• They need not be acoustically invariant, only
  perceptually sufficiently contrastive. (p.75).

28
Modeling the Evolution of Phonetic Systems Vowels

• Observations
• Languages favor high-low contrasts
• (over front-back, rounded-unrounded)
• A survey of 209 languages indicate a consistent
  preference for peripheral vowels

29
Vowel Hypothesis

• Drawn from typological data and three previous
  attempts at modeling
• A preference for front-back contrasts originates
  in the interaction
• Between a need for maximal perceptual contrast
  the dispersion principle (p.77)
• And the idiosyncratic shape of phonetic space for
  vowels

30
Idiosyncratic Space

• When both acoustic and motor dimensions are
  considered, the vowel space
• Offers more room for high-low than front-back or
  rounding gestures

31
Modeling the Evolution of Phonetic Systems
Consonants

• Inventory size is a predictor of how consonants
  pattern
• Lindblom divides consonants into three categories
• Basic (e.g., alveolar stop)
• Elaborated (e.g., click)
• Complex (e.g. breathy voiced palatal click)
• Where elaborated are departures from basic, and
  complex are combinations of elaborated.

32
Patterning

• If we graph the number of systems using each type
  of articulation as a function of consonant
  inventory size, we find that
• Basic Articulations used in small systems
• Basic Elaborated used in larger systems
• Basic Elaborated Complex used in largest
  systems

33
Size (of inventory) Principle

• The larger the system inventory, the more complex
  the articulatory elaborations needed to retain
  contrast

34
Vowels Pattern Similarly

• Lending support not to Maximal Contrast (as
  suggested earlier)
• But to Sufficient Contrast
• As the system grows in size, the use of vowels
  drawn from the corners of the chart increase in
  frequency.
• Slightly more central or neutral articulations
  appear to be permitted in the small systems. (p.
  86)

35
Conclusion

• Both vowel and consonant inventories show
  evidence of having been molded by similar
  processes. (p. 87)
• Articulatory simplification
• Perceptual distinctiveness

36
A Quantitative Model of the Observations

• A model consists of
• A state space (i.e., the domain of possible
  sounds)
• A set of constraints (i.e., why take this path
  rather than another through the space)
• Criteria for finding optimal solutions (i.e., how
  do we know one candidate solution is better than
  another)

37
Define a Vowel Articulation Space

• Begin with the variables
• Labial width and height
• Mandible position
• Tongue blade elevation and front-back position
• Tongue body front-back position
• Larynx position
• The set of all values for all variables defines a
  possible vowel articulation space
• Clearly, this is hypothetical. Were we to
  implement this, we would need some criteria to
  select particular sounds from the infinite number
  of sounds in the articulation space.
• Suppose we do this.
• From Lindblom, B. (1986) Phonetic universals in
  vowel systems. In J.J. Ohala J. Jaeger (eds.),
  Experimental Phonology. Orlando Academic Press.
  Pages 13-44.

38
Define a Vowel Perception Space 1

• Determine F1 and F2 for each value of the
  articulatory space. Call this the acoustic space.
• Map these frequencies onto the mel scale
• Mel Scale
• Scale of pitches judged to be equally distant
  from one another (e.g, the difference between 500
  mels and 1000 mels is the distance between 1500
  mels and 2000 mels).
• Now, for each possible vowel, N, for example, we
  have two mel parameters, M1 and M2, corresponding
  to F1 and F2.

39
Define a Vowel Perception Space 2

• Store these M1 and M2 values in an N X N matrix
• Define Lij, perceptual distance, between any two
  vowels, i and j, as follows
• Lij (M1i M2j)2 (M2i M2j)21/2
• (notice that this is just the Pythagorean Theorem)

40
Define A Vowel Perception Space 3

• We want to eliminate the diagonal and half of the
  cells.
• So, the
• Num of cells N(N-1)/2
• Apply distance formula to the remaining cells and
  fill them in.

41
Constructing a Vowel System

• We have N potential vowels in our system
• We want to construct all possible K vowel systems
  such that K lt N
• Technique
• Compute the intervowel distance across each
  possible K vowel system
• Choose each K vowel system that maximizes the
  distance

42
Reciprocals and Squares

• Recall the distance formula stored in each of our
  N (N 1)/2 cells
• Lij (M1i M2j)2 (M2i M2j)21/2
• Equivalent to
• Lij2 (M1i M2j)2 (M2i M2j)2
• Maximizing Lij2 has the same effect as minimizing
  1/Lij2

43
SupposeN 4K 3How many candidate systems do
we have?4!/((4-3)!3!) 4 a,e,i,a,e,o,e,i,
o,a,i,oThe best one is the one whose
perceptual distance among all members is maximized
44
Minimize the sum of the reciprocal of the
distances across the entire system, where i is
the row counter and j is the column counter
Lindbloms Listener Formula
45
Some Omitted Details

• Lindbloms formula will sum the perceptual
  distance among each of the uncolored cells, 6 in
  total.
• But is this what we want?
• For the a,e,i set we want to sum the distance
  from a-e, a-e, e-i and so on for the other 3
  sets.
• So, for each candidate vowel set we have to sum
  three values and choose the minimum.

46
An Alternative Minimization Procedure

• vowelSet computeOptimumVowelSet(k, n)
• minDistance ? 0
• minVowelSet ?
• NumVowelSets ? combination of n vowels taken k
  at a time
• Do NumVowlSets times
• vowelSet ? generate a set of vowels not yet
  generated
• sum ? perceptual distance between summed values
  of each
• pair in the set
• if (sum lt minDistance)
• minDistance ? sum
• minVowlSet vowelSet

47
Whats A Reader To Do

• If Im wrong (and I probably am)
• Continue with Lindbloms Formula
• If Im right, Lindbloms formulas can be easily
  adjusted. The adjustments dont change his
  argument

48
Articulatory Cost

• Recall the Listener Formula

Where Lij is the perceptual distance between
vowels i and j Experimentally determine another
variable, Tij, that represents the articulatory
cost of the pair vowels i and j
49
Minimize the Ratio

• Of articulatory cost
• To perceptual distinctivenes
• Over each vowel pair in the candidate k vowel
  system. Call this the Talker Formula

In English, this balances costs of production
against the benefits of perception
50
Social Factors

• A huge literature supports the idea that
  perceptual, articulatory and social factors
  interact in shaping phonetic structure (p. 89)
• Introduce a social factor, Sij
• Where, 0 lt Sij lt 1
• Giving

• Notice
• If sij 1, the formula is identical to the
  talker-oriented criteria
• If sij 0, all k vowel vowel sets will be
  equally attractive
• If sij is in the open interval (0 .. 1), it
  becomes an adjustable parameter

51
Major Problem

• We have developed a set of models that would be
  very hard to test (p. 89).
• Turns out that social factors are much less
  important than articulatory and perceptual factors

52
How Do We Know?

• Lindblom
• Divided all consonants in the UPSID database into
  obstruents and sonorants
• Divided the languages represented into 13
  language groups
• Almost all language groups had a roughly 70/30
  percent ratio of obstruents to sonorants.

53
Take Home Point

• This stability indicates that socio-cultural
  factors are not powerful enough to drastically
  overrule motoric and communicative constraints.
  (p. 93)

54
Conclusion

• Has been known since Fants work in the early
  sixties that the space of possible speech sounds
  has significant disjunctions
• Theory of Adaptive Dispersal
• Functional selective pressure resulted in the
  phonemic inventories of the worlds languages
• At the same time
• Maximize perceptual differences
• Minimize articulatory costs