P What's Story?

PoCS | @pocsvox

Language

Irregular verbs

Word lifespans

Meanings

References

NATUREJOBS Mentoring

awards

NUCLEAR WEAPONS

How to be an IAEA inspector

ATMOSPHERIC HUMIDITY

The human touch GENE SILENCING

Non-toxic RNA inhibition

The evolution of language

S WORDS ON THE BRINK

449, 637–754 11 October 20

07w

ww

.nature.com/nature

no.7163

11 October 2007 | www.nature.com/nature | $10 THE INTERNATIONAL WEEKLY JOURNAL OF SCIENCE

1 of 16

The structure and evolution of languagePrinciples of Complex Systems | @pocsvox

CSYS/MATH 300, Fall, 2013 | #FallPoCS2013

Prof. Peter Dodds | @peterdodds

Dept. of Mathematics & Statistics | Vermont Complex Systems CenterVermont Advanced Computing Core | University of Vermont

Story?CoP What’s

The

S

Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.

PoCS | @pocsvox

Language

Irregular verbs

Word lifespans

Meanings

References


awards

NUCLEAR WEAPONS







449, 637–754 11 October 20

07w

ww

.nature.com/nature

no.7163


2 of 16

These slides are brought to you by:

PoCS | @pocsvox

Language

Irregular verbs

Word lifespans

Meanings

References


awards

NUCLEAR WEAPONS







449, 637–754 11 October 20

07w

ww

.nature.com/nature

no.7163


3 of 16

Outline

Irregular verbs

Word lifespans

Meanings

References

PoCS | @pocsvox

Language

Irregular verbs

Word lifespans

Meanings

References


awards

NUCLEAR WEAPONS







449, 637–754 11 October 20

07w

ww

.nature.com/nature

no.7163


4 of 16

Irregular verbs

Cleaning up English:

“Quantifying the evolutionary dynamics of language” [1]

Lieberman et al., Nature, Vol 449, 713-716, 2007.


awards

NUCLEAR WEAPONS







449, 637–754 11 October 20

07w

ww

.nature.com/nature

no.7163


I Exploration of how verbs withirregular conjugationgradually become regularover time.

I Comparison of verb behaviorin Old, Middle, and ModernEnglish.

PoCS | @pocsvox

Language

Irregular verbs

Word lifespans

Meanings

References


awards

NUCLEAR WEAPONS







449, 637–754 11 October 20

07w

ww

.nature.com/nature

no.7163


5 of 16

Irregular verbs

Four of our six frequency bins, those between 1026 and 1022, allowus to estimate the relative regularization rates of irregular verbs.Calculating the relative regularization rates of verbs of different

frequencies is independent of time, which makes the dating of Oldand Middle English irrelevant for this calculation. We can plot regu-larization rate versus frequency and fit a straight line in a log–log plot(Fig. 1b). By comparing Old andModern English we obtain a slope ofabout 20.51. Therefore, an irregular verb that is 100 times less fre-quent is regularized 10 times as fast. In other words, the half-life ofirregular verbs is proportional to the square root of their frequency.By comparing Middle and Modern English we find a slope of about20.48, consistent with the previous result. Both comparisons showthat low-frequency irregular verbs are selectively forgotten.

Figure 2a shows the exponential decay of the irregular verbs in thefour frequency bins between 1026 and 1022 as a function of time.From these data, which depend on the dating of Old and MiddleEnglish, we can estimate actual half-lives of the irregular verbs indifferent frequency bins. Irregular verbs that occur with a frequencybetween 1026 and 1025 have a half-life of about 300 years, whereasthose with a frequency between 1024 and 1023 have a half-life of2,000 years. If we fit half-life versus frequency with a straight line ina log–log plot, we obtain a slope of 0.50, which again suggests that thehalf-life of irregular verbs is proportional to approximately thesquare root of their frequency (Fig. 2b). It is noteworthy that variousmethods of fitting the data give the same results.

We cannot directly determine the regularization rate for frequencybins above 1022, because regularization is so slow that no event wasobserved in the time span of our data; however, we can extrapolate.For instance, the half-life of verbs with frequencies between 1022 and1021 should be 14,400 years. For these bins, the population is so smalland the half-life so long that we may not see a regularization event inthe lifetime of the English language.

To test whether the dynamics within individual competing ruleswere captured by our global analysis, we studied the decay of indi-vidual classes of strong verbs (for example, hit/hit/hit, hurt/hurt/hurt; draw/drew/drawn, grow/grew/grown)26. Although our resolu-tion is limited by the small sample size, exponential decay is onceagain observed, with similar exponents (see Supplementary Fig. 1).Like a Cheshire cat, dying rules vanish one instance at a time, leavingbehind a unimodal frown.

Because adequate corpora of Old andMiddle English do not exist,we have estimated the frequency of an irregular verb of Old andMiddle English by the frequency of the corresponding (regular orirregular) verb of Modern English27. A large fraction of verbs wouldhave had to change frequency by several orders of magnitude to

a

b

70

10–5 10–4 10–3

Frequency

–0.51

–0.48

10–2 10–1

10–5 10–4 10–3

Frequency10–2 10–1

10–1

Old English

Old to Modern EnglishMiddle to Modern English

Middle EnglishModern English

Num

ber o

f irr

egul

ar v

erbs

Reg

ular

izat

ion

rate

60

50

40

30

20

10

1

0

Figure 1 | Irregular verbs regularize at a rate that is inversely proportionalto the square root of their usage frequency. a, The evolution of 177 verbsfrom Old English (green) over time, through Middle English (red) andModern English (blue). The fraction remaining irregular in each bindecreases as the frequency decreases. The frequency shown is that of themodern descendant, and was computed using the CELEX corpus. Error barsindicate standard deviation andwere calculated using the bootstrapmethod.b, The regularization rate of irregular verbs as a function of frequency. Therelative regularization rates obtained by comparing Old versus ModernEnglish (green) and Middle versus Modern English (red) scale linearly on alog–log plot with a downward slope of nearly one-half. The regularizationrate and the half-life scale with the square root of the frequency.

Table 1 | The 177 irregular verbs studied

Frequency

10−1−110−2−10−1

10−3−10−2

10−4−10−3

10−5−10−4

10−6−10−5

Verbs

be, havecome, do, find, get, give, go, know, say, see, take, think

begin, break, bring, buy, choose, draw, drink, drive, eat, fall, fight, forget, grow, hang, help, hold, leave, let, lie, lose,

reach, rise, run, seek, set, shake, sit, sleep, speak, stand, teach, throw, understand, walk, win, work, write

arise, bake, bear, beat, bind, bite, blow, bow, burn, burst, carve, chew, climb, cling, creep, dare, dig, drag, flee, float, flow, fly, fold, freeze, grind, leap, lend, lock, melt, reckon,

ride, rush, shape, shine, shoot, shrink, sigh, sing, sink, slide, slip, smoke, spin, spring, starve, steal, step, stretch, strike,

stroke, suck, swallow, swear, sweep, swim, swing, tear, wake, wash, weave, weep, weigh, wind, yell, yield

bark, bellow, bid, blend, braid, brew, cleave, cringe, crow, dive, drip, fare, fret, glide, gnaw, grip, heave, knead, low, milk, mourn, mow, prescribe, redden, reek, row, scrape, seethe, shear, shed, shove, slay, slit, smite, sow, span,

spurn, sting, stink, strew, stride, swell, tread, uproot, wade, warp, wax, wield, wring, writhe

bide, chide, delve, flay, hew, rue, shrive, slink, snip, spew, sup, wreak

Regularization (%)

00

10

43

72

91

Half-life (yr)

38,80014,4005,400

2,000

700

300

177 Old English irregular verbs were compiled for this study. These are arranged according to frequency bin, and in alphabetical order within each bin. Also shown is the percentage of verbs in eachbin that have regularized. The half-life is shown in years. Verbs that have regularized are indicated in red. As wemove down the list, an increasingly large fraction of the verbs are red; the frequency-dependent regularization of irregular verbs becomes immediately apparent.

LETTERS NATURE |Vol 449 | 11 October 2007

714Nature ©2007 Publishing Group

I Universal tendency towards regular conjugationI Rare verbs tend to be regular in the first place

PoCS | @pocsvox

Language

Irregular verbs

Word lifespans

Meanings

References


awards

NUCLEAR WEAPONS







449, 637–754 11 October 20

07w

ww

.nature.com/nature

no.7163


6 of 16

Irregular verbs

Four of our six frequency bins, those between 1026 and 1022, allowus to estimate the relative regularization rates of irregular verbs.Calculating the relative regularization rates of verbs of different






a

b

70

10–5 10–4 10–3

Frequency

–0.51

–0.48

10–2 10–1

10–5 10–4 10–3


10–1

Old English



Num

ber

of ir

regu

lar

verb

sR

egul

ariz

atio

n ra

te

60

50

40

30

20

10

1

0



Frequency

10−1−110−2−10−1

10−3−10−2

10−4−10−3

10−5−10−4

10−6−10−5

Verbs










Regularization (%)

00

10

43

72

91

Half-life (yr)

38,80014,4005,400

2,000

700

300




I Rates are relative.I The more common a verb is, the more resilient it is to

change.

http://www.uvm.edu/~pdodds/teaching/courses/2013-08UVM-300

http://www.twitter.com/@pocsvox

http://www.uvm.edu

http://www.uvm.edu/~pdodds




http://www.uvm.edu/~cems/mathstat/

http://www.uvm.edu/~cems/complexsystems/

http://www.uvm.edu/~vacc/

http://www.uvm.edu





http://www.uvm.edu




http://www.uvm.edu




http://www.uvm.edu




http://www.uvm.edu




http://www.uvm.edu


Irregular verbsFour of our six frequency bins, those between 1026 and 1022, allow

us to estimate the relative regularization rates of irregular verbs.Calculating the relative regularization rates of verbs of different






a

b

70

10–5 10–4 10–3

Frequency

–0.51

–0.48

10–2 10–1

10–5 10–4 10–3


10–1

Old English



Num

ber

of ir

regu

lar

verb

sR

egul

ariz

atio

n ra

te

60

50

40

30

20

10

1

0



Frequency

10−1−110−2−10−1

10−3−10−2

10−4−10−3

10−5−10−4

10−6−10−5

Verbs










Regularization (%)

00

10

43

72

91

Half-life (yr)

38,80014,4005,400

2,000

700

300




I Red = regularizedI Estimates of half-life for regularization (∝ f 1/2)

PoCS | @pocsvox

Language

Irregular verbs

Word lifespans

Meanings

References


awards

NUCLEAR WEAPONS







449, 637–754 11 October 20

07w

ww

.nature.com/nature

no.7163


8 of 16

Irregular verbs

interfere with the effects observed. To verify that large changes infrequency are rare, we compared frequency data from CELEX withfrequencies drawn from the largest available corpus of MiddleEnglish texts28. Of 50 verbs, only 5 had frequency changes greaterthan a factor of 10 (Supplementary Fig. 2).

Our analysis covers a vast period, spanning the Norman invasionand the invention of the printing press, but these events did not upsetthe dynamics of English regularization. Therefore, it is possible toretrospectively trace the evolution of the irregular verbs, movingbackwards in time from the observed Modern English distributionand up through Middle and Old English. Going still further back intime allows us to explore the effects of completely undoing the fre-quency-dependent selective process that the irregular verbs haveundergone. Eventually, the shape of the curve changes from unim-odal to a power law decline, with slope of nearly20.75 (Fig. 3). Thisfinding is consistent with the fact that random subsets of verbs (andof all types of words) exhibit such a zipfian distribution. The observedirregular verb distribution is the result of selective pressure on arandom collection of ancestral verbs.

We can alsomake predictions about the future of the past tense. Bythe time one verb from the set ‘begin, break, bring, buy, choose, draw,drink, drive, eat, fall’ will regularize, five verbs from the set ‘bid, dive,heave, shear, shed, slay, slit, sow, sting, stink’ will be regularized. If thecurrent trends continue, only 83 of the 177 verbs studied will beirregular in 2500.

What will be the next irregular verb to regularize? It is likely to bewed/wed/wed. The frequency of ‘wed’ is only 4.2 uses per millionverbs, ranking at the very bottom of the modern irregular verbs.Indeed, it is already being replaced in many contexts by wed/

wedded/wedded. Now is your last chance to be a ‘newly wed’. Themarried couples of the future can only hope for ‘wedded’ bliss.

In previous millennia, many rules vied for control of English lan-guage conjugation, and fossils of those rules remain to this day. Yet,from this primordial soup of conjugations, the dental suffix ‘-ed’emerged triumphant. The competing rules are long dead, and unfa-miliar even to well-educated native speakers. These rules disappearedbecause of the gradual erosion of their instances by a process that wecall regularization. But regularity is not the default state of a lan-guage—a rule is the tombstone of a thousand exceptions.

METHODS SUMMARYWe searched 11 reference works on Old and Middle English, compiling a list ofevery irregular verb that we found. We determined whether each verb is stillpresent in Modern English. For all Old English verbs whose descendantsremained in the English language, we checked whether they were still irregularusing a complete listing of themodern irregular verbs. If they had regularized, wedeterminedwhen regularization had occurred on the basis of the last time periodin which we found a positive annotation listing the verb as irregular. A list ofsources used and the entire resulting annotation are provided in theSupplementary Information.We determined usage frequencies for all the verbs using the CELEX database.

We then binned the Old English irregular verbs using a standard logarithmicbinning algorithm in Python. We used the resulting binning to determine regu-larization rates for verbs of differing frequencies. Regularization rates (Fig. 1b)for each bin were computed directly. The fits to exponential decay (Fig. 2) and tothe solution of the irregular equation (Fig. 3 and Supplementary Information)were produced using the method of least squares. The Python source code forproducing the figures and the table is available at http://www.languagedata.org.

Received 20 March; accepted 27 July 2007.

1. Chomsky, N. Aspects of the Theory of Syntax (MIT Press, Cambridge, 1965).2. Lightfoot, D. The Development of Language: Acquisition, Change and Evolution

(Blackwell, Oxford, 1999).3. Clark, R. & Roberts, I. A computational model of language learnability and

language change. Linguist. Inq. 24, 299–345 (1993).4. Abrams, D. & Strogatz, S. Modelling the dynamics of language death. Nature 424,

900 (2003).5. Nowak, M. A., Komarova, N. L. & Niyogi, P. Computational and evolutionary

aspects of language. Nature 417, 611–617 (2002).

60

10

10–6 10–5 10–4 10–3

Frequency10–2

8001200

200010–1 Ti

me

(yea

rs A

D)

1

Num

ber o

f irr

egul

ar v

erbs

Figure 3 | Extrapolating forward and backward in time using theobservation that regularization rate scales as the square root of frequency.The differential system is exactly solvable and the solution fits all threeobserved distributions. As we move backward in time, the distribution ofirregular verbs approaches the zipfian distribution characteristic of randomsets of words. The distribution for exceptions to the ‘-ed’ rule became non-random because of frequency-dependent regularization due to selectivepressure from the emerging rule.

a

b

60

Num

ber o

f irr

egul

ar v

erbs

8001200

2000

10–6

Time (years AD) 10–5 10–4 10–3

10–2

10–3

10–4

10–510–5 10–4

Frequency

Slope: –0.50

Reg

ular

izat

ion

rate

10–3 10–2

Frequency

10–2 10–1

10

1

Figure 2 | Irregular verbs decay exponentially over time. a, Specifyingapproximate dates of Old and Middle English allows computation ofabsolute regularization rates. Regularization rates increase as frequenciesdecrease, but are otherwise constant over time. b, Absolute rates ofregularization are shown as a function of frequency. Error bars indicatestandard deviation and were calculated using the bootstrap method. Thesquare-root scaling is obtained again.

NATURE |Vol 449 | 11 October 2007 LETTERS


I ‘Wed’ is next to go.I -ed is the winning rule...I But ‘snuck’ is sneaking up on sneaked. (�) [2]

PoCS | @pocsvox

Language

Irregular verbs

Word lifespans

Meanings

References


awards

NUCLEAR WEAPONS







449, 637–754 11 October 20

07w

ww

.nature.com/nature

no.7163


9 of 16

Irregular verbs

interfere with the effects observed. To verify that large changes infrequency are rare, we compared frequency data from CELEX withfrequencies drawn from the largest available corpus of MiddleEnglish texts28. Of 50 verbs, only 5 had frequency changes greaterthan a factor of 10 (Supplementary Fig. 2).

Our analysis covers a vast period, spanning the Norman invasionand the invention of the printing press, but these events did not upsetthe dynamics of English regularization. Therefore, it is possible toretrospectively trace the evolution of the irregular verbs, movingbackwards in time from the observed Modern English distributionand up through Middle and Old English. Going still further back intime allows us to explore the effects of completely undoing the fre-quency-dependent selective process that the irregular verbs haveundergone. Eventually, the shape of the curve changes from unim-odal to a power law decline, with slope of nearly20.75 (Fig. 3). Thisfinding is consistent with the fact that random subsets of verbs (andof all types of words) exhibit such a zipfian distribution. The observedirregular verb distribution is the result of selective pressure on arandom collection of ancestral verbs.

We can alsomake predictions about the future of the past tense. Bythe time one verb from the set ‘begin, break, bring, buy, choose, draw,drink, drive, eat, fall’ will regularize, five verbs from the set ‘bid, dive,heave, shear, shed, slay, slit, sow, sting, stink’ will be regularized. If thecurrent trends continue, only 83 of the 177 verbs studied will beirregular in 2500.

What will be the next irregular verb to regularize? It is likely to bewed/wed/wed. The frequency of ‘wed’ is only 4.2 uses per millionverbs, ranking at the very bottom of the modern irregular verbs.Indeed, it is already being replaced in many contexts by wed/

wedded/wedded. Now is your last chance to be a ‘newly wed’. Themarried couples of the future can only hope for ‘wedded’ bliss.

In previous millennia, many rules vied for control of English lan-guage conjugation, and fossils of those rules remain to this day. Yet,from this primordial soup of conjugations, the dental suffix ‘-ed’emerged triumphant. The competing rules are long dead, and unfa-miliar even to well-educated native speakers. These rules disappearedbecause of the gradual erosion of their instances by a process that wecall regularization. But regularity is not the default state of a lan-guage—a rule is the tombstone of a thousand exceptions.

METHODS SUMMARYWe searched 11 reference works on Old and Middle English, compiling a list ofevery irregular verb that we found. We determined whether each verb is stillpresent in Modern English. For all Old English verbs whose descendantsremained in the English language, we checked whether they were still irregularusing a complete listing of themodern irregular verbs. If they had regularized, wedeterminedwhen regularization had occurred on the basis of the last time periodin which we found a positive annotation listing the verb as irregular. A list ofsources used and the entire resulting annotation are provided in theSupplementary Information.We determined usage frequencies for all the verbs using the CELEX database.

We then binned the Old English irregular verbs using a standard logarithmicbinning algorithm in Python. We used the resulting binning to determine regu-larization rates for verbs of differing frequencies. Regularization rates (Fig. 1b)for each bin were computed directly. The fits to exponential decay (Fig. 2) and tothe solution of the irregular equation (Fig. 3 and Supplementary Information)were produced using the method of least squares. The Python source code forproducing the figures and the table is available at http://www.languagedata.org.

Received 20 March; accepted 27 July 2007.

1. Chomsky, N. Aspects of the Theory of Syntax (MIT Press, Cambridge, 1965).2. Lightfoot, D. The Development of Language: Acquisition, Change and Evolution

(Blackwell, Oxford, 1999).3. Clark, R. & Roberts, I. A computational model of language learnability and

language change. Linguist. Inq. 24, 299–345 (1993).4. Abrams, D. & Strogatz, S. Modelling the dynamics of language death. Nature 424,

900 (2003).5. Nowak, M. A., Komarova, N. L. & Niyogi, P. Computational and evolutionary

aspects of language. Nature 417, 611–617 (2002).

60

10

10–6 10–5 10–4 10–3

Frequency10–2

8001200

200010–1 Ti

me

(yea

rs A

D)

1

Num

ber o

f irr

egul

ar v

erbs

Figure 3 | Extrapolating forward and backward in time using theobservation that regularization rate scales as the square root of frequency.The differential system is exactly solvable and the solution fits all threeobserved distributions. As we move backward in time, the distribution ofirregular verbs approaches the zipfian distribution characteristic of randomsets of words. The distribution for exceptions to the ‘-ed’ rule became non-random because of frequency-dependent regularization due to selectivepressure from the emerging rule.

a

b

60

Num

ber o

f irr

egul

ar v

erbs

8001200

2000

10–6

Time (years AD) 10–5 10–4 10–3

10–2

10–3

10–4

10–510–5 10–4

Frequency

Slope: –0.50

Reg

ular

izat

ion

rate

10–3 10–2

Frequency

10–2 10–1

10

1

Figure 2 | Irregular verbs decay exponentially over time. a, Specifyingapproximate dates of Old and Middle English allows computation ofabsolute regularization rates. Regularization rates increase as frequenciesdecrease, but are otherwise constant over time. b, Absolute rates ofregularization are shown as a function of frequency. Error bars indicatestandard deviation and were calculated using the bootstrap method. Thesquare-root scaling is obtained again.

NATURE |Vol 449 | 11 October 2007 LETTERS


I Projecting back in time to proto-Zipf story of manytools.

PoCS | @pocsvox

Language

Irregular verbs

Word lifespans

Meanings

References


awards

NUCLEAR WEAPONS







449, 637–754 11 October 20

07w

ww

.nature.com/nature

no.7163


10 of 16

Word meanings

Preliminary findings on word frequency and numberof meaningsI Corpus: 10,000 most frequent words from Project

GutenbergI # meanings for each word estimated using

dictionary.com (�)I Friends: perl, regular expressions, wget.

PoCS | @pocsvox

Language

Irregular verbs

Word lifespans

Meanings

References


awards

NUCLEAR WEAPONS







449, 637–754 11 October 20

07w

ww

.nature.com/nature

no.7163


11 of 16

Word meanings

A. B.

0 1 2 3 43

4

5

6

7

8

log10

r

log 10

f

2 2.5 3 3.5 43.5

4

4.5

5

5.5

6

6.5

log10

r

log 10

f

slope = −1.21

A. Word frequency versus rank, slope α ∼ −1.2corresponds to to a frequency distribution with γ ∼ 1.8.B. Relationship between average number of meaningsand average frequency (bins are by rank, with each circlerepresenting 500 words). Slope of 1/3 lower than Zipf’s1/2 [4].

PoCS | @pocsvox

Language

Irregular verbs

Word lifespans

Meanings

References


awards

NUCLEAR WEAPONS







449, 637–754 11 October 20

07w

ww

.nature.com/nature

no.7163


12 of 16

Word meanings

A. B.

0 2000 4000 6000 8000 100005

10

15

20

25

30

35

r

n m

2 2.5 3 3.5 40.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

log10

r

log 10

nm

slope = −0.45

I Meaning number as a function of word rank.I The three exponents combine within error:

1.2× 1/3 = 0.4 ' 0.45.



http://www.uvm.edu


http://books.google.com/ngrams/graph?content=snuck%2Csneaked&year_start=1800&year_end=2000&corpus=0&smoothing=3



http://www.uvm.edu




http://www.uvm.edu


http://www.dictionary.com



http://www.uvm.edu




http://www.uvm.edu


PoCS | @pocsvox

Language

Irregular verbs

Word lifespans

Meanings

References


awards

NUCLEAR WEAPONS







449, 637–754 11 October 20

07w

ww

.nature.com/nature

no.7163


13 of 16

Word meaningsA. B.

100

101

102

103

10−3

10−2

10−1

nm

P(n

m )

10−1

100

101

10−3

10−2

10−1

favg −0.33 n

m

P(n

m )

I Scaling collapse for meaning number distributionI Each curve corresponds to approximately 500 words

group according to rank (1–500, 501–1000, ...).I With normalization

P(nm) = f−1/3G(

f−1/3nm

).

PoCS | @pocsvox

Language

Irregular verbs

Word lifespans

Meanings

References


awards

NUCLEAR WEAPONS







449, 637–754 11 October 20

07w

ww

.nature.com/nature

no.7163


14 of 16

Word meanings

Further work:I Check these scalings againI Explore alternate data sourcesI Think about why meaning number might scale with

frequency.I May be an information theoretic story.I If we add context, we may be able to use a modified

version of Simon’s approach [3]

I The city story here would be that there may be manycities and towns with the same name (e.g.,Springfield) with an uneven distribution inpopulations.

PoCS | @pocsvox

Language

Irregular verbs

Word lifespans

Meanings

References


awards

NUCLEAR WEAPONS







449, 637–754 11 October 20

07w

ww

.nature.com/nature

no.7163


15 of 16

References I

[1] E. Lieberman, J.-B. Michel, J. Jackson, T. Tang, andM. A. Nowak.Quantifying the evolutionary dynamics of language.Nature, 449:713–716, 2007. pdf (�)

[2] J.-B. Michel, Y. K. Shen, A. P. Aiden, A. Veres, M. K.Gray, T. G. B. Team, J. P. Pickett, D. Hoiberg,D. Clancy, P. Norvig, J. Orwant, S. Pinker, M. A.Nowak, and E. A. Lieberman.Quantitative analysis of culture using millions ofdigitized books.Science Magazine, 2010. pdf (�)

[3] H. A. Simon.On a class of skew distribution functions.Biometrika, 42:425–440, 1955. pdf (�)

PoCS | @pocsvox

Language

Irregular verbs

Word lifespans

Meanings

References


awards

NUCLEAR WEAPONS







449, 637–754 11 October 20

07w

ww

.nature.com/nature

no.7163


16 of 16

References II

[4] G. K. Zipf.Human Behaviour and the Principle of Least-Effort.Addison-Wesley, Cambridge, MA, 1949.



http://www.uvm.edu




http://www.uvm.edu




http://www.uvm.edu


http://www.uvm.edu/~pdodds/research/papers/others/2007/lieberman2007a.pdf

http://www.uvm.edu/~pdodds/research/papers/others/2010/michel2010a.pdf

http://www.uvm.edu/~pdodds/research/papers/others/1955/simon1955a.pdf



http://www.uvm.edu


P What's Story?

Documents

Transcript of P What's Story?