Laws in Quantitative Linguistics - User contributions [en]

File:Plot2neu.png

2007-07-03T12:34:56Z

Patzschke:

Morphological productivity

2007-07-03T12:34:46Z

Patzschke:

'''1. Problem and history'''

In the lexicon of a language there are two processes working:

(a) Birth of new lexemes by creating or borrowing

(b) Death by elimination of lexemes

Birth means either creation of new words or constructing them by morphological processes like derivation, reduplication, compounding etc. The construction is a case of (multidi-mensional) ''diversification'' (<math>\rightarrow</math>). At the same time it is a case of specification of meaning and word prolongation. Birth and death take place in rates called birth-rate <math>\lambda_x</math>and death-rate <math>\mu_x</math> respectively.
Since up to now only a case of derivation has been examined, the hypothesis must be restricted but we assume that it holds for other kinds of word building, too. It holds, of course, only under the condition that the given way of word buidling is actual in a language.
As far as known, the only model was proposed by Wimmer and Altmann (1995) in which the random variable x is the number of derivates built from a stem (x = 0,1,2,…) and <math>f_x</math> is the number of stems having x derivates.

'''2. Hypothesis'''

''Morphological productivity is the result of a birth-and-death process in which stems build new derivates and some derivates are eliminated. The probability of the number of stems having x derivates follows the Pólya distribution''.

'''3. Derivation'''

The creation of new morphological constructs is proportional to the class size x and can be generally symbolized as a + cx. Since creation cannot be infinite, there must be a limit n to it. The community controls the creation in the same linear way symbolized as b + (n-x-1)c. This results in the birth rate <math>\lambda = \frac{a+cx}{b+(n-x-1)c}\quad , x = 0, 1, ...n-1</math>. The death rate is similar, depending only on the class size and the morphological nature of language. It can be sym-bolized as <math>\mu = \frac{n}{n-x+1}\quad, x = 1, 2, ...,n</math>
Inserting the above birth-rate and death-rate in the balancing birth-and-death equations and reparametrizing

p = a/(a+b), q = b/(a+b), s = c/(a+b)

we obtain the Pólya distribution (Wimmer, Altmann 1995)

(1)<math> P_x = \frac{{-p/s \choose x}{-q/s \choose n-x}}{{-1/s \choose n}}\quad, x= 0, 1, ..., n, s>0, 0 =\le p\le1, q=1-p, n \epsilon N_0</math>
<math> \frac{p}{s}, \frac{q}{s}\ge 0</math> or <math> \frac{p}{s}, \frac{q}{s}\le 0</math>

'''Example''': Indonesian stem productivity

Wimmer and Altmann (1995) studied the productivity of stems in the Indonesian dictionary (Echols, Shadily 1963). There were 6970 stems having no derivates, 1961 stems having each 1 derivate etc. The data and the results of fitting are presented in Table 1 and Fig. 1.

<div align="center">[[Image:Tabelle11_MP.jpg]]</div>

<div align="center">[[Image:Plot2neu.png]]</div>
<div align="center">Fig. 1. Fitting the Pólya distribution to the data in Table 1</div>

'''4. Authors:''' U. Strauss, G. Altmann

'''5. References'''

'''Altmann, G., Bagheri, D., Goebl, H., Köhler, R., Prün, C'''. (2002). ''Einführung in die quantitative Lexikologie''. Götingen: Peust & Gutschmidt.

'''Echols, J.M., Shadily, H.''' (1963). ''An Indonesian-English dictionary''. Ithaca: Cornell University Press.

'''Wimmer, G., Altmann, G.''' (1995). A model of morphological productivity. ''J. of Quantitative Linguistics 2, 212-216.''

[[Category:Unfertig]]

File:Plot2.png

2007-07-03T12:31:04Z

Patzschke:

Morphological productivity

2007-06-29T09:19:04Z

Patzschke:

'''1. Problem and history'''

In the lexicon of a language there are two processes working:

(a) Birth of new lexemes by creating or borrowing

(b) Death by elimination of lexemes

Birth means either creation of new words or constructing them by morphological processes like derivation, reduplication, compounding etc. The construction is a case of (multidi-mensional) ''diversification'' (<math>\rightarrow</math>). At the same time it is a case of specification of meaning and word prolongation. Birth and death take place in rates called birth-rate <math>\lambda_x</math>and death-rate <math>\mu_x</math> respectively.
Since up to now only a case of derivation has been examined, the hypothesis must be restricted but we assume that it holds for other kinds of word building, too. It holds, of course, only under the condition that the given way of word buidling is actual in a language.
As far as known, the only model was proposed by Wimmer and Altmann (1995) in which the random variable x is the number of derivates built from a stem (x = 0,1,2,…) and <math>f_x</math> is the number of stems having x derivates.

'''2. Hypothesis'''

''Morphological productivity is the result of a birth-and-death process in which stems build new derivates and some derivates are eliminated. The probability of the number of stems having x derivates follows the Pólya distribution''.

'''3. Derivation'''

The creation of new morphological constructs is proportional to the class size x and can be generally symbolized as a + cx. Since creation cannot be infinite, there must be a limit n to it. The community controls the creation in the same linear way symbolized as b + (n-x-1)c. This results in the birth rate <math>\lambda = \frac{a+cx}{b+(n-x-1)c}\quad , x = 0, 1, ...n-1</math>. The death rate is similar, depending only on the class size and the morphological nature of language. It can be sym-bolized as <math>\mu = \frac{n}{n-x+1}\quad, x = 1, 2, ...,n</math>
Inserting the above birth-rate and death-rate in the balancing birth-and-death equations and reparametrizing

p = a/(a+b), q = b/(a+b), s = c/(a+b)

we obtain the Pólya distribution (Wimmer, Altmann 1995)

(1)<math> P_x = \frac{{-p/s \choose x}{-q/s \choose n-x}}{{-1/s \choose n}}\quad, x= 0, 1, ..., n, s>0, 0 =\le p\le1, q=1-p, n \epsilon N_0</math>
<math> \frac{p}{s}, \frac{q}{s}\ge 0</math> or <math> \frac{p}{s}, \frac{q}{s}\le 0</math>

'''Example''': Indonesian stem productivity

Wimmer and Altmann (1995) studied the productivity of stems in the Indonesian dictionary (Echols, Shadily 1963). There were 6970 stems having no derivates, 1961 stems having each 1 derivate etc. The data and the results of fitting are presented in Table 1 and Fig. 1.

<div align="center">[[Image:Tabelle11_MP.jpg]]</div>

(((Den Graph mit Excell machen, da 0 fehlt)
Fig. 1. Fitting the Pólya distribution to the data in Table 1

'''4. Authors:''' U. Strauss, G. Altmann

'''5. References'''

'''Altmann, G., Bagheri, D., Goebl, H., Köhler, R., Prün, C'''. (2002). ''Einführung in die quantitative Lexikologie''. Götingen: Peust & Gutschmidt.

'''Echols, J.M., Shadily, H.''' (1963). ''An Indonesian-English dictionary''. Ithaca: Cornell University Press.

'''Wimmer, G., Altmann, G.''' (1995). A model of morphological productivity. ''J. of Quantitative Linguistics 2, 212-216.''

[[Category:Unfertig]]

Morphological productivity

2007-06-29T09:05:17Z

Patzschke:

'''1. Problem and history'''

In the lexicon of a language there are two processes working:

(a) Birth of new lexemes by creating or borrowing

(b) Death by elimination of lexemes

Birth means either creation of new words or constructing them by morphological processes like derivation, reduplication, compounding etc. The construction is a case of (multidi-mensional) ''diversification'' (<math>rightarrow</math>). At the same time it is a case of specification of meaning and word prolongation. Birth and death take place in rates called birth-rate <math>\lambda_x</math>and death-rate <math>\mu_x</math> respectively.
Since up to now only a case of derivation has been examined, the hypothesis must be restricted but we assume that it holds for other kinds of word building, too. It holds, of course, only under the condition that the given way of word buidling is actual in a language.
As far as known, the only model was proposed by Wimmer and Altmann (1995) in which the random variable x is the number of derivates built from a stem (x = 0,1,2,…) and <math>f_x</math> is the number of stems having x derivates.

'''2. Hypothesis'''

''Morphological productivity is the result of a birth-and-death process in which stems build new derivates and some derivates are eliminated. The probability of the number of stems having x derivates follows the Pólya distribution''.

'''3. Derivation'''

The creation of new morphological constructs is proportional to the class size x and can be generally symbolized as a + cx. Since creation cannot be infinite, there must be a limit n to it. The community controls the creation in the same linear way symbolized as b + (n-x-1)c. This results in the birth rate <math>\lambda = \frac{a+cx}{b+(n-x-1)c}\quad , x = 0, 1, ...n-1</math>. The death rate is similar, depending only on the class size and the morphological nature of language. It can be sym-bolized as <math>\mu = \frac{n}{n-x+1}\quad, x = 1, 2, ...,n</math>
Inserting the above birth-rate and death-rate in the balancing birth-and-death equations and reparametrizing

p = a/(a+b), q = b/(a+b), s = c/(a+b)

we obtain the Pólya distribution (Wimmer, Altmann 1995)

(1)<math> P_x = \frac{{-p/s \choose x}{-q/s \choose n-x}}{{-1/s \choose n}}\quad, x= 0, 1, ..., n, s>0, 0 =\le p\le1, q=1-p, n \epsilon N_0</math>
<math> \frac{p}{s}, \frac{q}{s}\ge 0</math> or <math> \frac{p}{s}, \frac{q}{s}\le 0</math>

'''Example''': Indonesian stem productivity

Wimmer and Altmann (1995) studied the productivity of stems in the Indonesian dictionary (Echols, Shadily 1963). There were 6970 stems having no derivates, 1961 stems having each 1 derivate etc. The data and the results of fitting are presented in Table 1 and Fig. 1.

<div align="center">[[Image:Tabelle11_MP.jpg]]</div>

(((Den Graph mit Excell machen, da 0 fehlt)
Fig. 1. Fitting the Pólya distribution to the data in Table 1

'''4. Authors:''' U. Strauss, G. Altmann

'''5. References'''

'''Altmann, G., Bagheri, D., Goebl, H., Köhler, R., Prün, C'''. (2002). ''Einführung in die quantitative Lexikologie''. Götingen: Peust & Gutschmidt.

'''Echols, J.M., Shadily, H.''' (1963). ''An Indonesian-English dictionary''. Ithaca: Cornell University Press.

'''Wimmer, G., Altmann, G.''' (1995). A model of morphological productivity. ''J. of Quantitative Linguistics 2, 212-216.''

[[Category:Unfertig]]

Morphological productivity

2007-06-29T09:04:48Z

Patzschke:

'''1. Problem and history'''

In the lexicon of a language there are two processes working:

(a) Birth of new lexemes by creating or borrowing

(b) Death by elimination of lexemes

Birth means either creation of new words or constructing them by morphological processes like derivation, reduplication, compounding etc. The construction is a case of (multidi-mensional) ''diversification'' (<math>rightarrow</math>). At the same time it is a case of specification of meaning and word prolongation. Birth and death take place in rates called birth-rate <math>\lambda_x</math>and death-rate <math>\mu_x</math> respectively.
Since up to now only a case of derivation has been examined, the hypothesis must be restricted but we assume that it holds for other kinds of word building, too. It holds, of course, only under the condition that the given way of word buidling is actual in a language.
As far as known, the only model was proposed by Wimmer and Altmann (1995) in which the random variable x is the number of derivates built from a stem (x = 0,1,2,…) and <math>f_x</math> is the number of stems having x derivates.

'''2. Hypothesis'''

''Morphological productivity is the result of a birth-and-death process in which stems build new derivates and some derivates are eliminated. The probability of the number of stems having x derivates follows the Pólya distribution''.

'''3. Derivation'''

The creation of new morphological constructs is proportional to the class size x and can be generally symbolized as a + cx. Since creation cannot be infinite, there must be a limit n to it. The community controls the creation in the same linear way symbolized as b + (n-x-1)c. This results in the birth rate <math>\lambda = \frac{a+cx}{b+(n-x-1)c}\quad , x = 0, 1, ...n-1</math>. The death rate is similar, depending only on the class size and the morphological nature of language. It can be sym-bolized as <math>\mu = \frac{n}{n-x+1}\quad, x = 1, 2, ...,n</math>
Inserting the above birth-rate and death-rate in the balancing birth-and-death equations and reparametrizing

p = a/(a+b), q = b/(a+b), s = c/(a+b)

we obtain the Pólya distribution (Wimmer, Altmann 1995)

(1)<math> P_x = \frac{{-p/s \choose x}{-q/s \choose n-x}}{{-1/s \choose n}}\quad, x= 0, 1, ..., n, s>0, 0 =\le p\le1, q=1-p, n \epsilon N_0</math>
<math> \frac{p}{s}, \frac{q}{s}\ge = 0</math> or <math> \frac{p}{s}, \frac{q}{s}\le 0</math>

'''Example''': Indonesian stem productivity

Wimmer and Altmann (1995) studied the productivity of stems in the Indonesian dictionary (Echols, Shadily 1963). There were 6970 stems having no derivates, 1961 stems having each 1 derivate etc. The data and the results of fitting are presented in Table 1 and Fig. 1.

<div align="center">[[Image:Tabelle11_MP.jpg]]</div>

(((Den Graph mit Excell machen, da 0 fehlt)
Fig. 1. Fitting the Pólya distribution to the data in Table 1

'''4. Authors:''' U. Strauss, G. Altmann

'''5. References'''

'''Altmann, G., Bagheri, D., Goebl, H., Köhler, R., Prün, C'''. (2002). ''Einführung in die quantitative Lexikologie''. Götingen: Peust & Gutschmidt.

'''Echols, J.M., Shadily, H.''' (1963). ''An Indonesian-English dictionary''. Ithaca: Cornell University Press.

'''Wimmer, G., Altmann, G.''' (1995). A model of morphological productivity. ''J. of Quantitative Linguistics 2, 212-216.''

[[Category:Unfertig]]

Morph length

2007-06-26T13:22:30Z

Patzschke:

'''1. Problem and history'''

Morph length is a specal case of length or word length (<math>\rightarrow</math>) research. The segmentation of a text in morphs is a problem depending on language and grammar (cf. Best 2001 for German).
Morph lengths are focussed in Quantitative Linguistics in different ways:
Gerlach (1982) tested the interaction of word length with morph length in a German lexicon; the hypothesis was: the more morphs a word has, the shorter the morphs are. The test results were very good. Without any data Saporta (1963: 70) proposes the hypothesis: “The mean length of morphs will be inversely related to the number of phonemes in the inventory.” This idea is said to go back to R. Jakobson (Saporta 1963: 72, footnote 15).
Here we are confronted with another hypothesis: morph lengths in texts abide by a law in the same way as word lengths and other entities do.
Since up to now only a small number of data has been collected (Best 2000a, 2001a) the only distribution found rather inductively but belonging to the family of length-distributions (cf. Wimmer, Altmann 1996) was the 1-displaced Hyperpoisson distribution.
In a paper concerning morph segmentation Creutz (2003: 282) proposes the gamma distribution to be a model for morph lengths in the lexicon; but there is no proof of it. As soon as 1963 Saporta (²1966: 69) presents a little overview over morph lengths (in phonemes) in Spanish; testing the data (1679 morphs) the binomial distribution can be shown to be an acceptable model (C = 0.0166). He “cannot help wondering whether or not such a distribution is universal and, if not, what other factors correlate with different distributions.”
However, in Lakota the morphs have a specific form and their frequency distribution must be modelled by means of a difference equation of second order.

'''2. Hypothesis'''

''2.1. Morph length in texts abides by a regular probability distribution derived form the unified theory, namely the 1-displaced Hyperpoisson distribution.''

''2.2. If morphs have specific forms, the distribution is multimodal and must be modeled by an appropriate approach''.

'''3. Derivation'''

3.1. Substituting <math>a_0 = -1, a_1 = a, b_1 = b, a_2 = 0</math> in formula (10) of unified theory (→) and solving with displacement one obtains the Hyperpoisson distribution

(1)<math> P_x = \frac{a^{x-1}}{b^{x-1} _1 F_1 (1; b; a)}, \quad x = 1, 2, 3, ...; a, b > 0</math>

'''Example''': Morph length distribution in German

Best (2001a) used a text from Eichsfelder Tageblatt (6.3.1997, p.8): „Sieben Deutsche in Jemen entführt)“ and counting the length of morphemes he obtained the results in Table 1.

<div align="center">[[Image:Tabelle111_ML.jpg]]</div>

<div align="center">[[Image:Grafik1_ML.jpg]]</div>
<div align="center">Fig. 1. Fitting the 1-displaced Hyperpoisson distribution to morph length data</div>

3.2. In Lakota, morphemes usually consist of even number of syllables. In that case the usual approach must be extended and the distribution must be modeled by a difference equation of second order i.e.

(2)<math> P_x = g(x)P_{x-1}+h(x)P_{x-2}\quad</math>.

Pustet and Altmann (2005) set g(x) = a(k + x – 1)/x and h(x) = b(2k + x – 2)/x and obtained as solution the Gegenbauer distribution given as

(3)<math> P_x = (n)=\begin{cases} (1-a-b)^k,\quad x=0 \\ p_0 \sum_{j=0}^{[x/2]}\frac{b^j k^{(x-j)}a^{x-2j}}{j!(x-2j)!}, \quad x = 1, 2, 3,...\end{cases} </math>

where [.] is the integer part and k<sup>(x - j)</sup> is the ascending factorial function.

'''Example'''. Morpheme length in Lakota

Pustet and Altmann (2005) modeled the morpheme length distribution in Lakota and obtained the results in Table 2 and Fig. 2.

<div align="center">[[Image:Tabelle222_ML.jpg]]</div>

<div align="center">[[Image:Grafik2_ML.jpg]]</div>
<div align="center">Fig. 2. Fitting the Gegenbauer distribution to the Lakota data</div>

'''4. Authors: U. Strauss, G. Altmann, K.-H. Best'''

'''5. References'''

'''Best, K.-H.''' (2000a). Morphlängen in Fabeln von Pestalozzi. ''Göttinger Beiträge zur Sprachwissenschaft 3, 19-30.''

'''Best, K.-H'''. (2001a). Zur Länge von Morphen in deutschen Texten. In: Best, K.-H. (ed.), ''Häufigkeitsverteilungen in Texten: 1-14''. Göttingen: Peust & Gutschmidt.

'''Best, K.-H.''' (2001b). Probability distributions of language entities. ''J. of Quantitative Linguistics 8, 1-11.''

'''Best, K.-H'''. (2005). Morphlänge. In: Köhler, R., Altmann, G., Piotrowski, R. (eds.), ''Quantitative Linguistik - Quantitative Linguistics. Ein internationales Handbuch: 255-260''. Berlin/ N.Y.: de Gruyter

'''Creutz, M'''. (2003). Unsupervised segmentation of words using prior distributions of morph length and frequency. ''Proceedings of ACL-03, The 41st Annual Meeting of th Association of Computational Linguistics: 280-287''. Sapporo, Japan, 7-12 July.

'''Gerlach, R.''' (1982). Zur Überprüfung des Menzerathschen Gesetzes im Bereich der Morphologie. ''Glottometrika 4, 95-102''.

'''Gorot´, E.I.''' (1990). Izomorfnye i otličitel´nye čerty morfemy i sloga v raspredelenii dliny. In: ''Kvantitativnaja lingvistika i avtomatičeskij analiz tekstov: 32-36''. Tartu.

'''Krott, A'''. (1996). Some remarks on the relation between word length and morpheme length. ''J. of Quantitative Linguistics 3, 29-37''.

'''Nikonov, V.A'''. (1978). Dlina slova. ''Voprosy jazykoznanija 6, 104-111''.

'''Pustet, R., Altmann, G'''. (2005). Morpheme length distribution in Lakota. ''J. of Quantitative Linguistics 12(1), 53-63''.

'''Saporta, S'''. (1963, ²1966). Phoneme distribution and language universals. In: Greenberg, J.H. (ed.), ''Universals of language. Second edition. Report of a conference held at Dobbs Ferry, New York, April 13-115, 1961: 61-72''. Cambridge, Mass. & London: The M.I.T. Press.

'''Wimmer, G., Altmann, G'''. (1996). The theory of word length: some results and generalizations. ''Glottometrika 15, 112-133''.

[[Category:Unfertig]]

Frequency and polytextuality

2007-06-26T13:13:02Z

Patzschke:

'''1. Problem and history'''

Polytextuality measures the degree of independence of the usability of a word (in general of a linguistic unit) of its co-text or context. Linguistic units such as phonemes, syllables, morae, morphemes, words etc. differ in their usability with respect to different environments. The environment of a syllable, mora or morphem consists of the words in which they occur, the environment of a word consists of phrases, sentences, or texts. The number of different environments is often called the number of types. The frequency of a given entity in all its environments in, say, a corpus, is considered as the number of tokens. It can be shown that there exists a lawful relationship between the number of types (environments) and the number of tokens (frequency) of units on the given level.
The degree of independence of the unsability of a unit from its context (or, the variability of contextes with respect to a given unit), can be measured in several ways. Word polytextuality is often measured in terms of the number of different texts in a text corpus which contain at least one token of the given word. Polytextuality of morphemes or syllables are usually measured with reference to an inventory such as a dictionary.

The relationship between frequency and polytextuality has been postulated and investigated by R. Köhler (1986) as a complement to other quantitative properties, in order to integrate it into his synergetic control cycle. As a consequence of an erroneous identification with another “type-token” problem (<math>\rightarrow</math>), one can find this relationship also under the name “(morphological) productivity” (cf. Baayen 2001), which in turn represents a slightly different aspect (cf. Wimmer, Altmann 1995). The relationship was studied in different works on language synergetics (cf. e.g. Gieseking 2002), Köhler (2005) reformulated the pertinent part of his control cycle and Tamaoka, Altmann (2005) showed by means of Japanese morae that the unified theory (<math>\rightarrow</math>) leads to an identical result.

Usually one considers frequency as the spiritus movens, the independent variable of many relationships, but Köhler (1986) assumed here an inverse relationship.

'''2. Hypothesis'''

''The frequency of linguistic units depends on their polytextuality.''

'''3. Derivation'''

Since in most cases linguistic properties are related by their relative rates of change, Tamaoka (2007), taking into account some ceteris paribus factors, and leaning against the unified theory (<math>\rightarrow</math>) set up the equation

(1) <math> \frac{dy}{y}= \left( c+\frac{b}{x}\right)dx</math>

where x is polytexty, y is frequency and c represents some additional factors. The resulting solution,

(2) <math>y = ax^b e^{cx}\quad</math>,

was used to model polytexty and frequency of Japanese morae in a Japanese corpus.

Using Köhlers model (Fig. 1) one can write the relationships as follows:

(3) ln(F) = R ln(Appl) + B ln(PT) – C exp(ln(PT))

i.e.

ln(F) = R ln(Appl) + B ln(PT) – C (PT)

from which it follows that

<math>F = Appl^R PT^B e^{-c({PT})}\quad</math>.

Since in the framework of a synchronic study <math>Appl^R</math> can be considered as a constant, say A, and since we can set PT = x and F = y, we obtain

<math>y = A x^b e^{-cx}\quad</math>,

whih is identical with the above solution of the differential equation.

<div align="center">[[Image:Figur1_Freq.jpg]]</div>
<div align="center">Fig. 1. The relationship between polytextuality and frequency in general</div>

Thus Köhler´s model explains also the additional factors.

'''Example 1'''. Types and tokens of Japanese morae

Tamaoka and Makioka (2004) computed the frequencies of 103 Japanese morae in a corpus containing 341,771 different words with total frequency 287,792,797. For each mora its frequency and the contexts (different words) were ascertained. Tamaoka and Altmann (2005) showed that the best fit to these data (in logarithmic transformation) can be obtained by the curve

<math>y = 26.57366832x^{1.31502554}exp(-0.0000125937521x)</math>.

yielding a determination coeffciient D = 0.92. The result of fitting is displayd in Table 1 and graphically presented in Fig. 2.

<div align="center">[[Image:Tabelle11_Freq.jpg]]</div>

<div align="center">[[Image:Grafi1_Freq.jpg]]</div>
<div align="center">Fig. 2. Relation between types and tokens of Japanese morae</div>

'''Example 2'''. Polytextuality of German words as a function of their frequencies

Köhler (1986) published his result on data of a German text corpus (LIMAS), respresented here by the following graph:

[[image:Graph1.JPG]]

'''4. Authors: G. Altmann, R. Köhler'''

'''5. References'''

'''Baayen, R.H.''' (2001). ''Word frequency distributions''. Dordrecht: Kluwer.

'''Gieseking, K.''' (2002). Untersuchungen zur Synergetik der englischen Lexik. In: Köhler, R. (ed.), ''Korpuslinguistische Untersuchungen in die quantitative und systemtheoretische Linguistik: 387-433''. http://ubt.opus.hbz-nrw.de/volltexte/2004/279/

'''Köhler, R.''' (2006). Frequenz, Kontextualität und Länge von Wörtern. Eine Erweiterung des synergetisch-linguistischen Modells. In: Rapp, R., Sedlmeier, P., Zunker-Rapp, G. (eds.), ''Perspectives on Cognition''. Lengerich, Berlin, Bremen, Miami et al: Pabst Science Publishers, 327-338.

'''Tamaoka, K.''' (2007). On the relation between types and tokens of Japanese morae. In: ''Script problems (in print)''.

'''Tamaoka, K., Makioka, Sh.''' (2004). Frequency of occurrence for units of phonemes, morae, and syllables appearing in a lexical corpus of a Japanese newspaper. ''Behavior Research Methods, Instruments & Computers 36(3), 531-547''.

'''Wimmer, G., Altmann, G.''' (1995). A model of morphological productivity. ''J. of Quantitative Linguistics 2, 212-216.''

[[Category:Quantitative properties]]

File:Graph1.JPG

2007-06-26T13:12:03Z

Patzschke:

Char Complexity

2007-06-25T11:52:36Z

Patzschke:

'''1. Problem and history'''

The complexity of Chinese characters can be measured in terms of the number of strokes. The stroke is a segment written with one uninterrupted movement. The question arises whether complexity follows a regular distribution. Evidently, this is a special case of (→) length distributions. The pertinent statements can be qualified as laws only if they hold for any types of ideograms but up to now no other writing systems have been examined.
Sanada (1999) shows empirical data on the distribution of strokes in Japanese but does not present a model. Proceeding rather inductively Yu (2001) found that the distribution of character lengths in texts follows the 1-displaced binomial distribution. Previous studies (Herdan 1966, Bohn 1998) did not achieve this result.
The distribution in texts and in the dictionary may be quite different because in texts repetition is taken into account. The measurement in terms of the number of strokes is –as a matter of fact – the measurement of length, not that of complexity.
Another kind of complexity of script, in which not only the number of the composing entities but also the kind of their joining is relevant, can be measured according to Altmann (2004) but until now no testing has been performed.

'''2. Hypothesis'''

''The distribution of the complexity of Chinese characters follows a usual length distribution.''

Complexity = here the number of strokes in a Chinese sign.

'''3. Derivation'''

Solving a (reparametrized) recurrence relation which is a special case of length distributions, namely

(1)<math>P_{x+1} = \frac{n-x+1}{x}\frac{p}{q}, \quad x = 1, 2, ..., n+1</math>

one obtains

(2)<math>P_x = {n \choose x-1}p^{x-1}q^{n-x+1}, \quad x= 1,2,...,n+1, \quad 0<p<1, n\epsilon N</math>

'''Example''': Chinese characters in texts

Yu (2001) tested the above hypothesis on 20 Chinese texts, one of which can be found in Table 1 and Fig. 1.
<div align="center">[[Image:Figur11_CC.jpg]]</div>

<div align="center">[[Image:Figur2_CC.jpg]]</div>

<div align="center">Fig. 1. The distribution of character complexity in a Chinese text</div>

The result corroborates the hypothesis.

'''4. Authors''': U. Strauss, G. Altmann

'''5. References'''

'''Altmann, G. (2004). Script complexity'''. ''Glottometrics 8'', 68-74.

'''Bohn, H.''' (1998). ''Quantitative Untersuchungen der modernen chinesischen Sprache und Schrift.'' Hamburg: Kováč.

'''Bohn, H.'''(2002). Untersuchungen zur chinesischen Sprache und Schrift. In: Köhler, R. (ed.), ''Korpuslinguistische Untersuchungen in die quantitative und systemtheoretische Linguistik: 127-177.'' http://ubt.opus.hbz-nrw.de/volltexte/2004/279/

'''Herdan, G.''' (1966). ''The advanced theory of language as choice and chance.'' Berlin: Springer.

'''Menzel, C.''' (2002). Das synergetische Basismodell der Lexik und die chinesische Schrift. In: Köhler, R. (ed.), ''Korpuslinguistische Untersuchungen in die quantitative und systemtheoretische Linguistik: 179-207''. http://ubt.opus.hbz-nrw.de/volltexte/2004/279/

'''Sanada, H.''' (1999). Analysis of Japanese vocabulary by the theory of synergetic linguistics. ''J. of Quantitative Linguistics 6, 239-251.''

'''Yu, X.''' (2001). Zur Komplexität chinesischer Schriftzeichen. ''Göttinger Beiträge zur Sprachwissenschaft.5, 121-129.''

[[Category:Unfertig]]

Hierarchic relations

2007-06-25T11:44:21Z

Patzschke:

'''1. Problem and history'''

In different domains of language one observed the fact that the length of a construct influences the length of its consitutents. Usually the constituents get smaller with increasing length of the construct but not in all cases. The problem is to find a theoretical model encompassing all dependencies of this kind. The constructs whose length is the independent variable are: hreb, sentence, rhythmic unit, word, syllable; the constituents whose length or duration is the dependent variable are: sentence, clause, word, syllable, morph, sound. There is also the possibility to consider two independent variables, e.g. word (measured in number of syllables) and syllable (measured in number of sounds) , while the dependent variable is the syllable duration.
Up to now the following particular cases have been examined (see Table 1)

<div align="center">[[Image:Tabelle11_HR.jpg]]</div>

The origin of the problem can be found in 19th century, in phonetics, probably for the first time with Sievers (1876, 1901) who measured the syllable duration in rhythmic units (Sprechakte). A number of phoneticians tested different hypotheses, a part of which corroborated, another part falsified it. The isochrony hypothesis in English is a special case of this problem. The problem was generalized by Menzerath who stated that ''the greater the whole the smaller its parts'' (1954: 101). Different researchers proposed some empirical formulas (Fónagy, Magdics 1960; Nooteboom 1972, 1973; Landblom, Rapp 1972), Altmann (1980) set up the pertinent differential equation and called the result Menzerath´s law. Hřebíček (1992, 1995, 1997) showed that the whole hierarchy of textual levels is based on this dependence and called it ''Menzerath-Altmann´s law''.

There is a great number of individual examinations in different domains of languge. In phonetics the most exhaustive is Weber (1998), in textology the works by Hřebíček (see above) and a mixture of problems including biology and sociology can be found in Altmann, Schwibbe (1989). Bohn (1998) analyzed the relationship between Chinese characters and the complexity of composing graphemes, length of words and simplicity of characters, clause length and word length, sentence length and clause length (cf. also Menzel 2005).
The law has a strong corroboration not only within linguistics but displays analogies to other sciences. Thus the simple form of Menzerath´s law is identical with the allometric law in biology and with the power laws current in different sciences. Its correspondences can be found in (i) molecular biology, (ii) sociology of baboons, (iii) in the domain of self-organized criticality, (iv) in chaos research, (v) in the theory of fractals, (vi) in information theory.
It has been observed that construct length is not always the only cause of shortening of the constituents. Also accent, vowel quality, syllable structure, frequency etc. can intervene (cf. Weber 1998). In that case more complex formulas must be used.
The law has several consequences, all of which must still be tested (cf. Altmann, Schwibbe 1989: 8-14):
1. In longer words more phonetic changes occur than in shorter ones.

2. In languages with greater average word length more phonetic/phonemic changes occur than within the same time interval in languages with smaller average word length

3. The adding of an affix to a word evokes the tendency to reduce the inventory of consonants of the word.

4. The shortening of average syllable length in Hypothesis 3 can also be achieved by inserting epenthetic vowels between the stem and affix (or compounding stem).

5. Partial reduplication is more frequent in natural languages than full reduplication.

6. Short roots/morphemes/stems build more compounds or derived words than long ones.

7. The more elements there are in a compound the shorter they are (see the hypotheses on compounds <math>\leftarrow</math>)

8. Fenk-Fenk (to be inserted)

There are different interpretations of the law:

1. In general, long constructs contain more redundancy than short ones. In order to prevent excessive growth of redundancy one can reduce the size of the constituents. The size, the place and the time of this reduction is not known and cannot be predicted. The analogy to self-organized criticality of sand-piles is evident (cf. Bak 1996).

2. Köhler (1989) shows that mechanism of shortening is a consequence of restrictions of the memory: the longer the construct, the more place must be reserved for the structural information between the constituents, thus the size of the constituents must be reduced.

'''2. Hypothesis'''

''The size of the components is a function of the construct size''.

'''3. Derivation'''

The average size of constituents changes with the increase of the size of the construct. It is assumed that the relative rate of change of the size of components is proportional to the rate of change of the size of constructs, the proportionality function being

<math> g(x) = a_0 + \frac{a_1}{x} + \frac{a_2}{x^2}</math>.

Thus in case that all other variables other than construct size are subsumed under the ceteris paribus condition one obtains

(1)<math> \frac{dy}{y-d}= \left(a_0 +\frac{a_1}{x}+ \frac{a_2}{x^2}\right)</math>.

where d is the minimal value y can attain.
In case that there is another independent variable, z, one starts from

(2)<math>\frac{dy}{dx}\frac{1}{y-d}=a_0 + \frac{a_1}{x}+\frac{a_2}{x^2}\quad</math> and <math>\frac{dy}{dz}\frac{1}{y-d}=b_0 + \frac{b_1}{z}+\frac{b_2}{z^2}</math>

which can be extended to any number of variables.
The solution of (1) yields

(3)<math> y= Cx^{a_1}e^{a_0 x-a_2/x} + d</math>

the combining (2) the solution is

(4)<math> y= Cx^{a_1}z^{b_1}e^{a_0 x + b_0 z-a_2 /x-b_2 /z} + d</math>

In different applications the following special cases of (3) have been used (d > 0)

(1a) <math> y=ax^{-b}(+d), \quad x= 1, 2, 3, ...; \quad a, b > 0</math>

(1b)<math> y=ax^b e^{cx}(+d), \quad x= 1, 2, 3, ...; \quad a > 0</math>

(1c)<math> y=ae^{-cx}(+d), \quad x= 1, 2, 3, ...; \quad a, c > 0</math>

(1d) <math> y=ae^{c/x}(+d), \quad x= 1, 2, 3, ...; \quad a, c > 0</math>

Solution (4) is still very seldom. Both approaches are special cases of the unified theory (<math>\leftarrow</math>).

'''Examples''':

<div align="center">Mean clause length in dependence on sentence length</div>
<div align="center">(in H. Hesse, Der Steppenwolf)</div>

[[Image:Tabelle3-neu.JPG]]
yielding y = 11.5711x<sup>(-0.2285)</sup> and R<sup>2</sup> = 0.97.

'''4. Authors: U. Strauss, G. Altmann'''

'''5. References'''

'''Abercrombie, D'''. (1967). ''Elements of general phonetics''. Edinburgh: University Press.

'''Äima, F.''' (1918). Phonetik und Lautlehre des Inarilappischen. ''Mémoires de la Societé Finno-Ougrienne 43, 1-249.''

'''Altmann, G.''' (1980). Prolegomena to Menzerath´s law. ''Glottometrika 2, 1-10''.

'''Altmann, G'''. (1983). H. Arens´ „verborgene Ordnung“ und das Menzerathsche Gesetz. In: Faust, M., Harweg, R., Lehfeldt, W. (Hrsg.), ''Allgemeine Sprachwissenschaft, Sprachtypologie und Textlinguistik: 31-39''. Tübingen: Narr.

'''Altmann, G., Bagheri, D., Goebl, H., Köhler, R., Prün, C.''' (2002). ''Einführung in die quantitative Lexikologie.'' Götingen: Peust & Gutschmidt.

'''Altmann, G., Beöthy, E., Best, K.-H.''' (1982). Die Bedeutungskomplexität der Wörter und das Menzerathsche Gesetz. ''Zeitschrift für Phonetik, Sprachwissenschaft und Kommunikationsforschung 35, 537-543''.

'''Altmann, G., Schwibbe, M'''. (1989). ''Das Menzerathsche Gesetz in informationsverarbeitenden Systemen''. Hildesheim, Olms.

'''Arens, H'''. (1965). ''Verborgene Ordnung''. Düsseldorf: Schwann.

'''Asleh, L., & Best, K.-H.''' (2004/05). Zur Überprüfung des Menzerath-Altmann-Gesetzes am Beispiel deutscher (und italienischer) Wörter. ''Göttinger Beiträge zur Sprachwissenschaft'' 10/11, 9-19.

'''Auer, P., Uhmann, S'''. (1988). Silben- und akzentzählende Sprachen. ''Zeitschrift für Sprachwissenschaft 7, 214-259.''

'''Bak, P.''' (1996) ''How nature works. The science of self-organized criticality''. New York: Copernicus-Springer.

'''Bennett, S.G'''. (1935). Vergleichende experimentalphonetische Untersuchung der ungespannten Plosive im Englischen, Deutschen und Französischen. Diss.

'''Bohn, H.''' (1998). ''Quantitative Untersuchungen der modernen chinesischen Sprache und Schrift''. Hamburg: Kovač.

'''Bohn, H.''' (2002). Untersuchungen zur chinesischen Sprache und Schrift. In: Köhler, R. (ed.), ''Korpuslinguistische Untersuchungen in die quantitative und systemtheoretische Linguistik: 127-177''. http://ubt.opus.hbz-nrw.de/volltexte/2004/279/

'''Boroda, M.G., Altmann, G'''. (1991). Menzerath's law in musical texts. ''Musikometrika 3, 1-13.''

'''Changizi, M.A'''. (2001). Universal scaling laws for hierarchical complexity in languages, organisms, bahaviors and other combinatorial systems. ''J. of Theoretical Biology 211, 277-295.''

'''Collinder, B'''. (1964). Das Wort als phonetische Einheit. In: Collinder, B. (ed.), ''Sprachwissenschaft und Wahrscheinlichkeit: 203-217''. Uppsala: Almquist, Wiksells.

'''Cramer, I.M'''. (2005). The parameters of the Altmann-Menzerath law. ''J. of Quantitative Linguistics 12(1), 41-52.''

'''Cramer, I.M'''. (2005a). Das Menzerathsche Gesetz. In: Köhler, R., Altmann, G., Piotrowski, R.G. (eds.), ''Quantitative Linguistics - An International Handbook: 659-688''. Berlin: de Gruyter.

'''Debowski, L.''' (2007). Menzerath´s law for the smallest grammar. In: Grzybek, P., Köhler, R. (eds.), ''Exact methods in the Study of Language and Tests: 77-85.'' Berlin: de Gruyter.

'''Donner, K.''' (1912). Salmin murteen kvantiteettisuehtista. ''Suomi IV, 9, II''.

'''Elert, C.C.''' (1965). ''Phonological studies of quantity in Swedish''. Uppsala.

'''Evertz,''' (1929). ''Beiträge zur Phonetik der südfranzösischen Plosive''. Diss.

'''Faure, G., Hirst, D.J., Chafcouloff, M.''' (1980). Rhythm in English: Isochronism, pitch, and perceived stress. In: Linda, R., Schooneveld, C.H.v. (eds.), ''The melody of language: 71-79''. Baltimore: University Park Press.

'''Fenk, A., Fenk-Oczlon, G'''. (1993). Menzerath´s law and the constant flow of linguistic information. In: Köhler, R., Rieger, B.B. (eds.), ''Contributions to quantitative linguistics: 11-31''. Dordrecht: Kluwer.

'''Fenk-Oczlon, G., Fenk, A'''. (1995). Selbstorganisation und natürliche Typologie. ''Sprachtypologie und Universalienforschung 48, 223-238''.

'''Fenk-Oczlon, G., Fenk, A'''. (1999). Cognition, quantitative linguistics, and systemic typology. ''Linguistic Typology 3, 151-177.''

'''Fickermann, I., Markner-Jäger, B, Rothe, U'''. (1984). Wortlänge und Bedeutungskomplexität. ''Glottometrika 6, 115-126.''

'''Fischer-Jörgensen, E'''. (1964). Sound duration and place of articulation. ''Zeitschrift für Phonetik 17, 175-207''.

'''Fónagy, I'''. (1959).'' A költöi nyelv hangtanából.'' Budapest.

'''Fónagy, I, Magdics, K'''. (1960). Speed of utterance in phrases of different length. ''Language and Speech 3, 179-182''.

'''Gaitenby, I.H'''. (1965). ''The elastic word''. Haskins, Status Report on speech research 1965/SR-2,3.1-3.12.

'''Gerlach, R'''. (1982). Zur Überprüfung des Menzerathschen Gesetzes im Bereich der Morphologie. ''Glottometrika 4, 95-102''.

'''Geršić, S., Altmann, G'''. (1980). Laut – Silbe – Wort und das Menzerathsche Gesetz. ''Frankfurter Phonetische Beiträge 3, 115-123''.

'''Grégoire, A'''. (1899). Variation de la durée de la syllable français. ''La Parole 1''.

'''Grzybek, P'''. (1999). Randbemerkungen zur Wortlänge im Kroatischen. In: B.Tošović (ed.), ''Die grammatischen Korrelationen: 56-67.'' Graz: Gralis.

'''Grzybek, P., Stadlober, E.''' (2007). Do we have probelsm with Arnes´ law? A new look at the sentence-word relation. In: Grzybek, P., Köhler, R. (eds.), ''Exact Method in th Study of Language and Text: 203-215.'' Berlin: de Gruyter.

'''Hammerl, R., Sambor, J'''. (1993a). ''O statystycznych prawach jezykowych''. Warszawa: Polskie Towarzystwo Semiotyczne.

'''Hegedüs, L'''. (1956). Sprechtempoanalysen im Ungarischen. ''Zeitschrift für Phonetik 10.''

'''Heups, G'''. (1983). Untersuchungen zum Verhältnis von Satzlänge und Clauselänge am Beispiel deutscher Texte verschiedener Textklassen. ''Glottometrika 5, 113-133''.

'''Hřebíček, L'''. (1990). Menzerath-Altmann's law on the semantic level. ''Glottometrika 11, 47-56.''

'''Hřebíček, L''' (1990a). The constants of the Menzerath-Altmann law. ''Glottometrika 12, 61-71''.

'''Hřebíček, L'''. (1992). ''Text in communication: Supra-sentence structure''. Bochum, Brockmeyer.

'''Hřebíček, L'''. (1993b). Text as a construct of aggregations. In: Köhler, R., Rieger, B. (eds.), ''Contributions to quantitative lingusitics: 33-39''. Dordrecht: Kluwer.

'''Hřebíček, L'''. (1993c). Text as a strategic process. In: Hřebíček, L., Altmann, G. (Eds.), ''Quantitative text analysis: 136-150''. Trier: WVT.

'''Hřebíček, L'''. (1994). Fractals in language. ''J. of Quantitative Linguistics 1, 82-86''.

'''Hřebíček, L'''. (1994a). The stairway of subsystems. In: ''2nd International Conference on Quantitative Linguistics, September 1994, 210-222 Moscow''. Moscow: Lomonosov Moscow State University.

'''Hřebíček, L.''' (1995). ''Text levels. Language constructs, constituents and Menzerath-Altmann law''. Trier: WVT.

'''Hřebíček, L'''. (1995a). Phase transition in texts. ''ZeT – Zeitschrift für empirische Textwissenschaft 2, 52-58.''

'''Hřebíček, L.''' (1997). ''Lectures on text theory''. Prague: Oriental Institute.

'''Hřebíček, L.''' (2000). ''Variation in sequences''. Prague: Oriental Institute.

'''Hřebíček, L.''' (2004). The semantic space and Turkish ghazels. ''Archiv orientální 72, 175-191''.

'''Hřebíček, L.''' (2005). Text laws. In: Köhler, R., Altmann, G., Piotrowski, R.G. (eds.) (2005), ''Quantitative Linguistics - An International Handbook: 348-361''. Berlin: de Gruyter.

'''Hřebíček, L., Altmann, G'''. (1993). Prospects of text linguistics. In: Hřebíček, L., Altmann, G. (Eds.), ''Quantitative text analysis: 1-28''. Trier: WVT.

'''Hug, M.''' (2007). Das Menzerath-Gesetz in der Vulgata. In: Grzybek, P., Köhler, R. (eds.), ''Exact Method in th Study of Language and Text: 243-255.'' Berlin: de Gruyter.

'''Huxley, A'''. (1963). ''Evolution: the modern synthesis''. London 1942.

'''Jespersen, O'''. (1897-1899). ''Phonetik''. Copenhagen.

'''Jespersen, O'''. (1932). ''Lehrbuch der Phonetik''. Lepzig-Berlin.

'''Kaumanns, W., Schwibbe, M.H.''' (1983). Strukturmerkmale von Primatensozietäten unter dem Gesichtspunkt der Menzerathschen Regel. In: Altmann, G., Schwibbe, M. (1983): 99-107.

'''Köhler, R'''. (1982). Das Menzerathsche Gesetz auf der Satzebene. ''Glottometrika 4, 103-113''.

'''Köhler, R.''' (1984). Zur Interpretation des Menzerathschen Gesetzes. ''Glottometrika 6, 177-183''.

'''Köhler, R'''. (1986). ''Zur linguistischen Synergetik: Struktur und Dynamik der Lexik''. Bochum: Brockmeyer.

'''Köhler, R'''. (1989). Das Menzerathschen Gesetz als Resultat des Sprachverarbeitungsmechanismus. In: Altmann, Schwibbe (1989): 108-112.

'''Köhler, R.''' (1990). Linguistische Analyseebenen, Hierarchisierung und Erklärung im Modell der sprachlichen Selbstregulation. ''Glottometrika 11, 1-18''.

'''Krott, A.''' (1996). Some remarks on the relation between word length and morpheme length. ''J. of Quantitative Linguistics 3, 29-37''.

'''Krott, A.''' (2002). Ein funktionalanalytisches Modell der Wortbildung. In: Köhler, R. (ed.), ''Korpuslinguistische Untersuchungen in die quantitative und systemtheoretische Linguistik: 75-126''. http://ubt.opus.hbz-nrw.de/volltexte/2004/279/

'''Kułacka, A., Mačutek, J.''' (2007). ''A discrete formula for the Menzerath-Altmann law. J. of Quantitative Linguistics 14(1)'', 23-32.

'''Laurosela, J'''. (1922). ''Foneettinen tutkimus Etelä-Pohjanmaan murteesta''. Helsinki.

'''Lehiste, I'''. (1970). ''Suprasegmentals''. Cambridge, Mass.:M.I.T. Press.

'''Lehfeldt, W'''. (2006). The fall of jers in the light of Menzerath´s law. In: Grzybek, P. (ed.), ''Contributions to the Science of text and Language. Word Length and Related Issues: 211-213''. Dordrecht: Springer.

'''Lehfeldt, W., Altmann, G.''' (2000). Padenie reducirovannykh v svete zakona P. Mencerata. ''Russian Linguistics 26, 327-344''.

'''Lehfeldt, W., Altmann, G.''' (2000). Der altrussische Jerwandel. ''Glottometrics 2, 34-44''.

'''Lehtonen, J.''' (1970). Aspects of quantity in a standard Finnish. ''Studia Philologica Jyväskyläensia 6''.

'''Leopold, E.''' (2001). Fractal structures in language. The question of the imbedding space. In Uhlířová, L., Wimmer, G., Altmann, G., Köhler, R. (Eds.), ''Text as a linguistic paradigm: levels, constituents, constructs. Festschrift in honour of Ludek Hřebíček: 163-1176''. Trier: WVT.

'''Leopold, E. ''' (2007). Bemerkungen zum Menzerath-Altmannschen Gesetz. In: Grzybek, P., Köhler, R. (eds.), ''Exact Methods in the Study of Language and Text: 389-396.'' Berlin: de Gruyter.

'''Lindblom, B.E.F'''. (1968). Temporal organization of syllable production. ''Royal Institute of Technology, Stockholm, Speech Transmission Laboratory, Quarterly Progress and Status Report 2-3, 1-5''.

'''Lindblom, B, Rapp, K.''' (1972). Reexamination of the compensatory adjustment of vowel duration in Swedish words. ''Symposium on experimental and theoretical approaches to the role of time speech''. University of Essex.

'''Maack, A.''' (1949). Die spezifische Lautdauer deutscher Sonanten. ''Zeitschrift für Phonetik 3, 190-232''.

'''Malécot, A., Johnston, R., Kizziar, P.-A'''. (1972). Syllabic Rate and Utterance Length in French. ''Phonetica 26, 235-251''.

'''Malmberg, B'''. (1944). Die Quantität als phonetisch-phonologischer Begriff. ''Lunds Universitets Årskrift 41, 1-104''.

'''Menzerath, P'''. (1928). Über einige phonetische Probleme. ''Actes du premier congrès international de linguistique. Leiden, Nendeln/Liechtenstein, Kraus reprint: 104-105''.

'''Menzerath P.''' (1954). ''Die Architektonik des deutschen Wortschatzes''. Bonn, Dümmler.

'''Meyer, E.A.''' (1904). Zur Vokaldauer im Deutschen. ''Nordiska Studier Tillegnade A: 347-356''. Norken, Uppsala 1904.

'''Meyer, E.A., Gombocz, Z'''. (1908). Zur Phonetik der ungarischen Sprache. ''Le Monde Oriental 2, 122-187''.

'''Meyer, P.''' (2007). Two semi-mathematical asides on Menzerath-Altmann´s law. In: Grzybek, P., Köhler, R. (eds.), ''Exact Methods in the Study of Language and Text: 447-458.'' Berlin: de Gruyter.

'''Nemcová, E.''' (1994). On two realizations of Menzerath´s law. ''J. of Quantitative Linguistics 1, 107-112''.

'''Nooteboom, S.G'''. (1972a). The interaction of some intra-syllable and extra-syllable factors acting on syllable nucleus duration. ''IPO Annual Progress report 7, 30-39.''

'''Nooteboom, S.G'''. (1972b). ''Production and perception of vowel duration''. Eindhoven: Philips Research Laboratories.

'''Nooteboom, S.G.''' (1973). The perceptual reality of some prosodic durations. ''J. of Phonetiocs 1, 25-45''.

'''Palomaa, J.K'''. (1946). ''Suomen kielen äännekestoista puhumaan oppinen kuuromykän ja kuulevan henkilön ääntämisessä''. Publicationes Instituti Phonetici Universiatis Helsingforsiensis. Turku.

'''Polikarpov, A.''' (2000). Menzerath’s Law for Morphemic Structures of Words: A Hypothesis for the Evolutionary Mechanism of its Arising and its Testing. In: Baayen, R.H. (ed.), ''Proceedings of the fourth conference of the International Quantitative Linguistics Association: 26-27'', Prague, August 24-26, 2000.

'''Polikarpov, A.A.''' (2006). Towards the foundations of Menzerath´s law. On the functional dependence of the affix lengths on their positional number within words. In: Grzybek, P. (ed.) ''Contributions to the Science of Text and Language. Word Length Studies and Related Issues: 215-240.'' Dordrecht: Springer.

'''Prün, C.''' (1994). Validity of Menzerath-Altmann’s law: Graphic representation of language, information processing systems and synergetic linguistics. ''J. of Quantitative Linguistics 1, 148-155''.

'''Rothe, U.''' (1983). Wortlänge und Bedeutungsmenge. Eine Untersuchung zum Menzerathschen Gesetz an drei romanischen Sprachen. ''Glottometrika 5, 101-112''.

'''Roudet, L.''' (1910). ''Eléments de phonétique générale''. Paris: Welter.

'''Ruszkowski, M.''' (1991). ''Prawo Menzeratha w badaniach syntaktycznych. Jezyk
Polski LXXI'', 187-192.

'''Rykov, V.''' (1994). Menzerath law for printed speech. In: ''2nd International Conference on Quantitative Linguistics, September 20-24, 1994, Moscow: 199-200''. Moscow: Lomonosov Moscow State University.

'''Sambor, J.''' (1984). Menzerath’s law and the polysemy of words. ''Glottometrika 6, 94-114''.

'''Schindelin, C'''. (2005). Die quantitative Erforschung der chinesischen Sprache und Schrift. In: Köhler, R., Altmann, G., Piotrowski, R.G. (eds.), ''Quantitative Linguistics - An International Handbook: 947-970''. Berlin: de Gruyter.

'''Schwibbe, M.H'''. (1984). Text- und wortstatistische Untersuchungen zur Validität der Menzerathschen Regel. ''Glottometrika 6, 152-176''.

'''Schwibbe, M.H.''' (1989). Die Menzerathsche Regel als Modell psychischer Informationsverarbeitung. In: Altmann, G., Schwibbe, M.H. (1989): 84-91.

'''Sievers, E.''' (1876/1901). ''Grundzüge der Phonetik''. Leipzig: Breitkopf, Härtel.

'''Sovijärvi, A.''' (1944). ''Foneettis-äännehistoriallinen tutkimus Soikkolan inkeroismurteesta''. Suomi 103.

'''Tarnóczy, T'''. (1965). Can the problem of automatic speech recognition be solved by analysis alone? ''Reports of the Fifth International Congress of Acoustics II, Liège''.

'''Teupenhayn, R., Altmann, G'''. (1984). Clause length and Menzerath´s law. ''Glottometrika 6, 127-138''.

'''Weber, S.''' (1998). ''Das Menzerathsche Gesetz in gesprochener Sprache''. Magisterarbeit Universität Trier.

'''Wiik, K.''' (1965). Finnish and English vowels. ''Turku, Annales Universitatis Turkuensis, Series B, 94''.

'''Wilde, J., Schwibbe, M.H'''. (1989). Einige methodologische Überlegungen zur Menzerathschen Regel. In: Altmann, Schwibbe 1989: 113-116.

'''Wilde, J., Schwibbe, M.H'''. (1989a). Organisationsformen von Erbinformation im Hinblick auf die Menzerathsche Regel. In: Altmann, Schwibbe 1989: 92-99.

'''Wimmer, G., Altmann, G'''. (2005). Unified derivation of some linguistic laws. In: P. Grzybek (ed.), ''Contributions the the Science of Language. Word Length Studies and Related Issues: 329-337.'' Dordrecht: Kluwer.

'''Ziegler, A., Altmann, G.''' (2002). ''Denotative Textanalyse.'' Wien: Edition Praesens.

'''The allometric law in other sciences'''

'''Adolph, E.F'''. (1949). Quantitative relations in physiological constitution of mammals. ''Science 109, 579''-

'''Bertalanffy, L.v'''. (1949). Problems of organic growth. ''Nature 163, 1''56-

'''Bertalanffy, L.v'''. (1951). Theoretische Biologie. Vol. II, Stoffwechsel, Wachstum. 2nd ed. Bern:

'''Bertalanffy, L.v'''. (1951a). Growth types and metabolic types. American Naturalist 85, 111-

'''Bertalanffy, L.v., Pirozynski, W.J.''' (1952). Ontogenetic and evolutionary allometry. Evolution 6, 3287-.

'''Bertalanffy, L.v., Pirozynski, W.J'''. (1953). Tissue respiration, growth and basal metabolism. Biological Bulletin 105, 240-.

'''Bonin, G.v'''. (1937). Brain weight and body weight of mammals. J. of General Psychology 16,

'''Brody, S'''. (1945). Bioenergetics and growth. New York:

'''Hersh, A.H'''. (1941). Allometric growth: The ontogenetic and phylogenetic significance of differential rates of growth. 3rd Growth Symposium 113.

'''Huxley, J.''' (1932). Problems of relative growth. London.

'''Jerison, H.J.''' (1955). Brain to body ratios and the evolution of intelligence. Science 121, 477-

'''Kaumanns, W., Schwibbe, M.H'''. (1989). Strukturmerkmale von Primatensozietäten unter dem Gesichtspunkt der Menzerathschen Regel. In: Altmann, G., Schwibbe, M.H., ''Das Menzerathsche Gesetz in informationsverarbeitenden Systemen: 99-107''. Hildesheim: Olms.

'''Klatt, B'''. (1919). Zur Methodik vergleichender metrischer Untersuchungen, besonders des Herzgewichts. ''Biologisches Zentralblatt 39, 406-''

'''Naroll, R.S., Bertalanffy, L.v'''. (1956). The principle of allometry in biology and the social science. ''General Systems 1, 76-89''.

'''Needham, J.''' (1934). Chemical heterogony and the groundplan of animal growth. ''Biological Revue 9, 79-''.

'''Reed, W.J., Hughes, B.D.''' (2002). From gene families and genera to incomes and internet file sizes: why power laws are so common in nature. Physical Review E 66, 067103.

''' Reeve, E.C.R., Huxley, J.S.''' (1945). Some problems in the study of allometric growth. In: Clark, W.E.C., Medawar, P.B. (1945), ''Essays on growth and form, presented to D´Arcy Wentworth Thmpson: 121-''. Oxford:

'''Rensch, B'''. (1954). ''Neuere Probleme der Abstammungslehre''. 2nd ed. Stuttgart:

'''Robb, R.C.''' (1935-1937). A study of mutation in evolution. I-IV. J. of Genetics 31, 39-; 33, 269-; 34, 477-.

'''Sholl, D.A'''. (1954). Regularities in growth curves, including rhythms and allometry. In: Boell, E.J. (ed.), Dynamics of growth processes: 224-. Princeton:

'''Vining, R'''. (1955). A description of certain spatial aspects of an economic system. ''Economic Development and Culture Change 3, 147-''.

[[Category:Unfertig]]

Hierarchic relations

2007-06-25T11:42:05Z

Patzschke:

'''1. Problem and history'''

In different domains of language one observed the fact that the length of a construct influences the length of its consitutents. Usually the constituents get smaller with increasing length of the construct but not in all cases. The problem is to find a theoretical model encompassing all dependencies of this kind. The constructs whose length is the independent variable are: hreb, sentence, rhythmic unit, word, syllable; the constituents whose length or duration is the dependent variable are: sentence, clause, word, syllable, morph, sound. There is also the possibility to consider two independent variables, e.g. word (measured in number of syllables) and syllable (measured in number of sounds) , while the dependent variable is the syllable duration.
Up to now the following particular cases have been examined (see Table 1)

<div align="center">[[Image:Tabelle11_HR.jpg]]</div>

The origin of the problem can be found in 19th century, in phonetics, probably for the first time with Sievers (1876, 1901) who measured the syllable duration in rhythmic units (Sprechakte). A number of phoneticians tested different hypotheses, a part of which corroborated, another part falsified it. The isochrony hypothesis in English is a special case of this problem. The problem was generalized by Menzerath who stated that ''the greater the whole the smaller its parts'' (1954: 101). Different researchers proposed some empirical formulas (Fónagy, Magdics 1960; Nooteboom 1972, 1973; Landblom, Rapp 1972), Altmann (1980) set up the pertinent differential equation and called the result Menzerath´s law. Hřebíček (1992, 1995, 1997) showed that the whole hierarchy of textual levels is based on this dependence and called it ''Menzerath-Altmann´s law''.

There is a great number of individual examinations in different domains of languge. In phonetics the most exhaustive is Weber (1998), in textology the works by Hřebíček (see above) and a mixture of problems including biology and sociology can be found in Altmann, Schwibbe (1989). Bohn (1998) analyzed the relationship between Chinese characters and the complexity of composing graphemes, length of words and simplicity of characters, clause length and word length, sentence length and clause length (cf. also Menzel 2005).
The law has a strong corroboration not only within linguistics but displays analogies to other sciences. Thus the simple form of Menzerath´s law is identical with the allometric law in biology and with the power laws current in different sciences. Its correspondences can be found in (i) molecular biology, (ii) sociology of baboons, (iii) in the domain of self-organized criticality, (iv) in chaos research, (v) in the theory of fractals, (vi) in information theory.
It has been observed that construct length is not always the only cause of shortening of the constituents. Also accent, vowel quality, syllable structure, frequency etc. can intervene (cf. Weber 1998). In that case more complex formulas must be used.
The law has several consequences, all of which must still be tested (cf. Altmann, Schwibbe 1989: 8-14):
1. In longer words more phonetic changes occur than in shorter ones.

2. In languages with greater average word length more phonetic/phonemic changes occur than within the same time interval in languages with smaller average word length

3. The adding of an affix to a word evokes the tendency to reduce the inventory of consonants of the word.

4. The shortening of average syllable length in Hypothesis 3 can also be achieved by inserting epenthetic vowels between the stem and affix (or compounding stem).

5. Partial reduplication is more frequent in natural languages than full reduplication.

6. Short roots/morphemes/stems build more compounds or derived words than long ones.

7. The more elements there are in a compound the shorter they are (see the hypotheses on compounds <math>\leftarrow</math>)

8. Fenk-Fenk (to be inserted)

There are different interpretations of the law:

1. In general, long constructs contain more redundancy than short ones. In order to prevent excessive growth of redundancy one can reduce the size of the constituents. The size, the place and the time of this reduction is not known and cannot be predicted. The analogy to self-organized criticality of sand-piles is evident (cf. Bak 1996).

2. Köhler (1989) shows that mechanism of shortening is a consequence of restrictions of the memory: the longer the construct, the more place must be reserved for the structural information between the constituents, thus the size of the constituents must be reduced.

'''2. Hypothesis'''

''The size of the components is a function of the construct size''.

'''3. Derivation'''

The average size of constituents changes with the increase of the size of the construct. It is assumed that the relative rate of change of the size of components is proportional to the rate of change of the size of constructs, the proportionality function being

<math> g(x) = a_0 + \frac{a_1}{x} + \frac{a_2}{x^2}</math>.

Thus in case that all other variables other than construct size are subsumed under the ceteris paribus condition one obtains

(1)<math> \frac{dy}{y-d}= \left(a_0 +\frac{a_1}{x}+ \frac{a_2}{x^2}\right)</math>.

where d is the minimal value y can attain.
In case that there is another independent variable, z, one starts from

(2)<math>\frac{dy}{dx}\frac{1}{y-d}=a_0 + \frac{a_1}{x}+\frac{a_2}{x^2}\quad</math> and <math>\frac{dy}{dz}\frac{1}{y-d}=b_0 + \frac{b_1}{z}+\frac{b_2}{z^2}</math>

which can be extended to any number of variables.
The solution of (1) yields

(3)<math> y= Cx^{a_1}e^{a_0 x-a_2/x} + d</math>

the combining (2) the solution is

(4)<math> y= Cx^{a_1}z^{b_1}e^{a_0 x + b_0 z-a_2 /x-b_2 /z} + d</math>

In different applications the following special cases of (3) have been used (d > 0)

(1a) <math> y=ax^{-b}(+d), \quad x= 1, 2, 3, ...; \quad a, b > 0</math>

(1b)<math> y=ax^b e^{cx}(+d), \quad x= 1, 2, 3, ...; \quad a > 0</math>

(1c)<math> y=ae^{-cx}(+d), \quad x= 1, 2, 3, ...; \quad a, c > 0</math>

(1d) <math> y=ae^{c/x}(+d), \quad x= 1, 2, 3, ...; \quad a, c > 0</math>

Solution (4) is still very seldom. Both approaches are special cases of the unified theory (<math>\leftarrow</math>).

'''Examples''':

<div align="center">Mean clause length in dependence on sentence length</div>
<div align="center">(in H. Hesse, Der Steppenwolf)</div>

[[Image:Tabelle3-neu.JPG]]

'''4. Authors: U. Strauss, G. Altmann'''

'''5. References'''

'''Abercrombie, D'''. (1967). ''Elements of general phonetics''. Edinburgh: University Press.

'''Äima, F.''' (1918). Phonetik und Lautlehre des Inarilappischen. ''Mémoires de la Societé Finno-Ougrienne 43, 1-249.''

'''Altmann, G.''' (1980). Prolegomena to Menzerath´s law. ''Glottometrika 2, 1-10''.

'''Altmann, G'''. (1983). H. Arens´ „verborgene Ordnung“ und das Menzerathsche Gesetz. In: Faust, M., Harweg, R., Lehfeldt, W. (Hrsg.), ''Allgemeine Sprachwissenschaft, Sprachtypologie und Textlinguistik: 31-39''. Tübingen: Narr.

'''Altmann, G., Bagheri, D., Goebl, H., Köhler, R., Prün, C.''' (2002). ''Einführung in die quantitative Lexikologie.'' Götingen: Peust & Gutschmidt.

'''Altmann, G., Beöthy, E., Best, K.-H.''' (1982). Die Bedeutungskomplexität der Wörter und das Menzerathsche Gesetz. ''Zeitschrift für Phonetik, Sprachwissenschaft und Kommunikationsforschung 35, 537-543''.

'''Altmann, G., Schwibbe, M'''. (1989). ''Das Menzerathsche Gesetz in informationsverarbeitenden Systemen''. Hildesheim, Olms.

'''Arens, H'''. (1965). ''Verborgene Ordnung''. Düsseldorf: Schwann.

'''Asleh, L., & Best, K.-H.''' (2004/05). Zur Überprüfung des Menzerath-Altmann-Gesetzes am Beispiel deutscher (und italienischer) Wörter. ''Göttinger Beiträge zur Sprachwissenschaft'' 10/11, 9-19.

'''Auer, P., Uhmann, S'''. (1988). Silben- und akzentzählende Sprachen. ''Zeitschrift für Sprachwissenschaft 7, 214-259.''

'''Bak, P.''' (1996) ''How nature works. The science of self-organized criticality''. New York: Copernicus-Springer.

'''Bennett, S.G'''. (1935). Vergleichende experimentalphonetische Untersuchung der ungespannten Plosive im Englischen, Deutschen und Französischen. Diss.

'''Bohn, H.''' (1998). ''Quantitative Untersuchungen der modernen chinesischen Sprache und Schrift''. Hamburg: Kovač.

'''Bohn, H.''' (2002). Untersuchungen zur chinesischen Sprache und Schrift. In: Köhler, R. (ed.), ''Korpuslinguistische Untersuchungen in die quantitative und systemtheoretische Linguistik: 127-177''. http://ubt.opus.hbz-nrw.de/volltexte/2004/279/

'''Boroda, M.G., Altmann, G'''. (1991). Menzerath's law in musical texts. ''Musikometrika 3, 1-13.''

'''Changizi, M.A'''. (2001). Universal scaling laws for hierarchical complexity in languages, organisms, bahaviors and other combinatorial systems. ''J. of Theoretical Biology 211, 277-295.''

'''Collinder, B'''. (1964). Das Wort als phonetische Einheit. In: Collinder, B. (ed.), ''Sprachwissenschaft und Wahrscheinlichkeit: 203-217''. Uppsala: Almquist, Wiksells.

'''Cramer, I.M'''. (2005). The parameters of the Altmann-Menzerath law. ''J. of Quantitative Linguistics 12(1), 41-52.''

'''Cramer, I.M'''. (2005a). Das Menzerathsche Gesetz. In: Köhler, R., Altmann, G., Piotrowski, R.G. (eds.), ''Quantitative Linguistics - An International Handbook: 659-688''. Berlin: de Gruyter.

'''Debowski, L.''' (2007). Menzerath´s law for the smallest grammar. In: Grzybek, P., Köhler, R. (eds.), ''Exact methods in the Study of Language and Tests: 77-85.'' Berlin: de Gruyter.

'''Donner, K.''' (1912). Salmin murteen kvantiteettisuehtista. ''Suomi IV, 9, II''.

'''Elert, C.C.''' (1965). ''Phonological studies of quantity in Swedish''. Uppsala.

'''Evertz,''' (1929). ''Beiträge zur Phonetik der südfranzösischen Plosive''. Diss.

'''Faure, G., Hirst, D.J., Chafcouloff, M.''' (1980). Rhythm in English: Isochronism, pitch, and perceived stress. In: Linda, R., Schooneveld, C.H.v. (eds.), ''The melody of language: 71-79''. Baltimore: University Park Press.

'''Fenk, A., Fenk-Oczlon, G'''. (1993). Menzerath´s law and the constant flow of linguistic information. In: Köhler, R., Rieger, B.B. (eds.), ''Contributions to quantitative linguistics: 11-31''. Dordrecht: Kluwer.

'''Fenk-Oczlon, G., Fenk, A'''. (1995). Selbstorganisation und natürliche Typologie. ''Sprachtypologie und Universalienforschung 48, 223-238''.

'''Fenk-Oczlon, G., Fenk, A'''. (1999). Cognition, quantitative linguistics, and systemic typology. ''Linguistic Typology 3, 151-177.''

'''Fickermann, I., Markner-Jäger, B, Rothe, U'''. (1984). Wortlänge und Bedeutungskomplexität. ''Glottometrika 6, 115-126.''

'''Fischer-Jörgensen, E'''. (1964). Sound duration and place of articulation. ''Zeitschrift für Phonetik 17, 175-207''.

'''Fónagy, I'''. (1959).'' A költöi nyelv hangtanából.'' Budapest.

'''Fónagy, I, Magdics, K'''. (1960). Speed of utterance in phrases of different length. ''Language and Speech 3, 179-182''.

'''Gaitenby, I.H'''. (1965). ''The elastic word''. Haskins, Status Report on speech research 1965/SR-2,3.1-3.12.

'''Gerlach, R'''. (1982). Zur Überprüfung des Menzerathschen Gesetzes im Bereich der Morphologie. ''Glottometrika 4, 95-102''.

'''Geršić, S., Altmann, G'''. (1980). Laut – Silbe – Wort und das Menzerathsche Gesetz. ''Frankfurter Phonetische Beiträge 3, 115-123''.

'''Grégoire, A'''. (1899). Variation de la durée de la syllable français. ''La Parole 1''.

'''Grzybek, P'''. (1999). Randbemerkungen zur Wortlänge im Kroatischen. In: B.Tošović (ed.), ''Die grammatischen Korrelationen: 56-67.'' Graz: Gralis.

'''Grzybek, P., Stadlober, E.''' (2007). Do we have probelsm with Arnes´ law? A new look at the sentence-word relation. In: Grzybek, P., Köhler, R. (eds.), ''Exact Method in th Study of Language and Text: 203-215.'' Berlin: de Gruyter.

'''Hammerl, R., Sambor, J'''. (1993a). ''O statystycznych prawach jezykowych''. Warszawa: Polskie Towarzystwo Semiotyczne.

'''Hegedüs, L'''. (1956). Sprechtempoanalysen im Ungarischen. ''Zeitschrift für Phonetik 10.''

'''Heups, G'''. (1983). Untersuchungen zum Verhältnis von Satzlänge und Clauselänge am Beispiel deutscher Texte verschiedener Textklassen. ''Glottometrika 5, 113-133''.

'''Hřebíček, L'''. (1990). Menzerath-Altmann's law on the semantic level. ''Glottometrika 11, 47-56.''

'''Hřebíček, L''' (1990a). The constants of the Menzerath-Altmann law. ''Glottometrika 12, 61-71''.

'''Hřebíček, L'''. (1992). ''Text in communication: Supra-sentence structure''. Bochum, Brockmeyer.

'''Hřebíček, L'''. (1993b). Text as a construct of aggregations. In: Köhler, R., Rieger, B. (eds.), ''Contributions to quantitative lingusitics: 33-39''. Dordrecht: Kluwer.

'''Hřebíček, L'''. (1993c). Text as a strategic process. In: Hřebíček, L., Altmann, G. (Eds.), ''Quantitative text analysis: 136-150''. Trier: WVT.

'''Hřebíček, L'''. (1994). Fractals in language. ''J. of Quantitative Linguistics 1, 82-86''.

'''Hřebíček, L'''. (1994a). The stairway of subsystems. In: ''2nd International Conference on Quantitative Linguistics, September 1994, 210-222 Moscow''. Moscow: Lomonosov Moscow State University.

'''Hřebíček, L.''' (1995). ''Text levels. Language constructs, constituents and Menzerath-Altmann law''. Trier: WVT.

'''Hřebíček, L'''. (1995a). Phase transition in texts. ''ZeT – Zeitschrift für empirische Textwissenschaft 2, 52-58.''

'''Hřebíček, L.''' (1997). ''Lectures on text theory''. Prague: Oriental Institute.

'''Hřebíček, L.''' (2000). ''Variation in sequences''. Prague: Oriental Institute.

'''Hřebíček, L.''' (2004). The semantic space and Turkish ghazels. ''Archiv orientální 72, 175-191''.

'''Hřebíček, L.''' (2005). Text laws. In: Köhler, R., Altmann, G., Piotrowski, R.G. (eds.) (2005), ''Quantitative Linguistics - An International Handbook: 348-361''. Berlin: de Gruyter.

'''Hřebíček, L., Altmann, G'''. (1993). Prospects of text linguistics. In: Hřebíček, L., Altmann, G. (Eds.), ''Quantitative text analysis: 1-28''. Trier: WVT.

'''Hug, M.''' (2007). Das Menzerath-Gesetz in der Vulgata. In: Grzybek, P., Köhler, R. (eds.), ''Exact Method in th Study of Language and Text: 243-255.'' Berlin: de Gruyter.

'''Huxley, A'''. (1963). ''Evolution: the modern synthesis''. London 1942.

'''Jespersen, O'''. (1897-1899). ''Phonetik''. Copenhagen.

'''Jespersen, O'''. (1932). ''Lehrbuch der Phonetik''. Lepzig-Berlin.

'''Kaumanns, W., Schwibbe, M.H.''' (1983). Strukturmerkmale von Primatensozietäten unter dem Gesichtspunkt der Menzerathschen Regel. In: Altmann, G., Schwibbe, M. (1983): 99-107.

'''Köhler, R'''. (1982). Das Menzerathsche Gesetz auf der Satzebene. ''Glottometrika 4, 103-113''.

'''Köhler, R.''' (1984). Zur Interpretation des Menzerathschen Gesetzes. ''Glottometrika 6, 177-183''.

'''Köhler, R'''. (1986). ''Zur linguistischen Synergetik: Struktur und Dynamik der Lexik''. Bochum: Brockmeyer.

'''Köhler, R'''. (1989). Das Menzerathschen Gesetz als Resultat des Sprachverarbeitungsmechanismus. In: Altmann, Schwibbe (1989): 108-112.

'''Köhler, R.''' (1990). Linguistische Analyseebenen, Hierarchisierung und Erklärung im Modell der sprachlichen Selbstregulation. ''Glottometrika 11, 1-18''.

'''Krott, A.''' (1996). Some remarks on the relation between word length and morpheme length. ''J. of Quantitative Linguistics 3, 29-37''.

'''Krott, A.''' (2002). Ein funktionalanalytisches Modell der Wortbildung. In: Köhler, R. (ed.), ''Korpuslinguistische Untersuchungen in die quantitative und systemtheoretische Linguistik: 75-126''. http://ubt.opus.hbz-nrw.de/volltexte/2004/279/

'''Kułacka, A., Mačutek, J.''' (2007). ''A discrete formula for the Menzerath-Altmann law. J. of Quantitative Linguistics 14(1)'', 23-32.

'''Laurosela, J'''. (1922). ''Foneettinen tutkimus Etelä-Pohjanmaan murteesta''. Helsinki.

'''Lehiste, I'''. (1970). ''Suprasegmentals''. Cambridge, Mass.:M.I.T. Press.

'''Lehfeldt, W'''. (2006). The fall of jers in the light of Menzerath´s law. In: Grzybek, P. (ed.), ''Contributions to the Science of text and Language. Word Length and Related Issues: 211-213''. Dordrecht: Springer.

'''Lehfeldt, W., Altmann, G.''' (2000). Padenie reducirovannykh v svete zakona P. Mencerata. ''Russian Linguistics 26, 327-344''.

'''Lehfeldt, W., Altmann, G.''' (2000). Der altrussische Jerwandel. ''Glottometrics 2, 34-44''.

'''Lehtonen, J.''' (1970). Aspects of quantity in a standard Finnish. ''Studia Philologica Jyväskyläensia 6''.

'''Leopold, E.''' (2001). Fractal structures in language. The question of the imbedding space. In Uhlířová, L., Wimmer, G., Altmann, G., Köhler, R. (Eds.), ''Text as a linguistic paradigm: levels, constituents, constructs. Festschrift in honour of Ludek Hřebíček: 163-1176''. Trier: WVT.

'''Leopold, E. ''' (2007). Bemerkungen zum Menzerath-Altmannschen Gesetz. In: Grzybek, P., Köhler, R. (eds.), ''Exact Methods in the Study of Language and Text: 389-396.'' Berlin: de Gruyter.

'''Lindblom, B.E.F'''. (1968). Temporal organization of syllable production. ''Royal Institute of Technology, Stockholm, Speech Transmission Laboratory, Quarterly Progress and Status Report 2-3, 1-5''.

'''Lindblom, B, Rapp, K.''' (1972). Reexamination of the compensatory adjustment of vowel duration in Swedish words. ''Symposium on experimental and theoretical approaches to the role of time speech''. University of Essex.

'''Maack, A.''' (1949). Die spezifische Lautdauer deutscher Sonanten. ''Zeitschrift für Phonetik 3, 190-232''.

'''Malécot, A., Johnston, R., Kizziar, P.-A'''. (1972). Syllabic Rate and Utterance Length in French. ''Phonetica 26, 235-251''.

'''Malmberg, B'''. (1944). Die Quantität als phonetisch-phonologischer Begriff. ''Lunds Universitets Årskrift 41, 1-104''.

'''Menzerath, P'''. (1928). Über einige phonetische Probleme. ''Actes du premier congrès international de linguistique. Leiden, Nendeln/Liechtenstein, Kraus reprint: 104-105''.

'''Menzerath P.''' (1954). ''Die Architektonik des deutschen Wortschatzes''. Bonn, Dümmler.

'''Meyer, E.A.''' (1904). Zur Vokaldauer im Deutschen. ''Nordiska Studier Tillegnade A: 347-356''. Norken, Uppsala 1904.

'''Meyer, E.A., Gombocz, Z'''. (1908). Zur Phonetik der ungarischen Sprache. ''Le Monde Oriental 2, 122-187''.

'''Meyer, P.''' (2007). Two semi-mathematical asides on Menzerath-Altmann´s law. In: Grzybek, P., Köhler, R. (eds.), ''Exact Methods in the Study of Language and Text: 447-458.'' Berlin: de Gruyter.

'''Nemcová, E.''' (1994). On two realizations of Menzerath´s law. ''J. of Quantitative Linguistics 1, 107-112''.

'''Nooteboom, S.G'''. (1972a). The interaction of some intra-syllable and extra-syllable factors acting on syllable nucleus duration. ''IPO Annual Progress report 7, 30-39.''

'''Nooteboom, S.G'''. (1972b). ''Production and perception of vowel duration''. Eindhoven: Philips Research Laboratories.

'''Nooteboom, S.G.''' (1973). The perceptual reality of some prosodic durations. ''J. of Phonetiocs 1, 25-45''.

'''Palomaa, J.K'''. (1946). ''Suomen kielen äännekestoista puhumaan oppinen kuuromykän ja kuulevan henkilön ääntämisessä''. Publicationes Instituti Phonetici Universiatis Helsingforsiensis. Turku.

'''Polikarpov, A.''' (2000). Menzerath’s Law for Morphemic Structures of Words: A Hypothesis for the Evolutionary Mechanism of its Arising and its Testing. In: Baayen, R.H. (ed.), ''Proceedings of the fourth conference of the International Quantitative Linguistics Association: 26-27'', Prague, August 24-26, 2000.

'''Polikarpov, A.A.''' (2006). Towards the foundations of Menzerath´s law. On the functional dependence of the affix lengths on their positional number within words. In: Grzybek, P. (ed.) ''Contributions to the Science of Text and Language. Word Length Studies and Related Issues: 215-240.'' Dordrecht: Springer.

'''Prün, C.''' (1994). Validity of Menzerath-Altmann’s law: Graphic representation of language, information processing systems and synergetic linguistics. ''J. of Quantitative Linguistics 1, 148-155''.

'''Rothe, U.''' (1983). Wortlänge und Bedeutungsmenge. Eine Untersuchung zum Menzerathschen Gesetz an drei romanischen Sprachen. ''Glottometrika 5, 101-112''.

'''Roudet, L.''' (1910). ''Eléments de phonétique générale''. Paris: Welter.

'''Ruszkowski, M.''' (1991). ''Prawo Menzeratha w badaniach syntaktycznych. Jezyk
Polski LXXI'', 187-192.

'''Rykov, V.''' (1994). Menzerath law for printed speech. In: ''2nd International Conference on Quantitative Linguistics, September 20-24, 1994, Moscow: 199-200''. Moscow: Lomonosov Moscow State University.

'''Sambor, J.''' (1984). Menzerath’s law and the polysemy of words. ''Glottometrika 6, 94-114''.

'''Schindelin, C'''. (2005). Die quantitative Erforschung der chinesischen Sprache und Schrift. In: Köhler, R., Altmann, G., Piotrowski, R.G. (eds.), ''Quantitative Linguistics - An International Handbook: 947-970''. Berlin: de Gruyter.

'''Schwibbe, M.H'''. (1984). Text- und wortstatistische Untersuchungen zur Validität der Menzerathschen Regel. ''Glottometrika 6, 152-176''.

'''Schwibbe, M.H.''' (1989). Die Menzerathsche Regel als Modell psychischer Informationsverarbeitung. In: Altmann, G., Schwibbe, M.H. (1989): 84-91.

'''Sievers, E.''' (1876/1901). ''Grundzüge der Phonetik''. Leipzig: Breitkopf, Härtel.

'''Sovijärvi, A.''' (1944). ''Foneettis-äännehistoriallinen tutkimus Soikkolan inkeroismurteesta''. Suomi 103.

'''Tarnóczy, T'''. (1965). Can the problem of automatic speech recognition be solved by analysis alone? ''Reports of the Fifth International Congress of Acoustics II, Liège''.

'''Teupenhayn, R., Altmann, G'''. (1984). Clause length and Menzerath´s law. ''Glottometrika 6, 127-138''.

'''Weber, S.''' (1998). ''Das Menzerathsche Gesetz in gesprochener Sprache''. Magisterarbeit Universität Trier.

'''Wiik, K.''' (1965). Finnish and English vowels. ''Turku, Annales Universitatis Turkuensis, Series B, 94''.

'''Wilde, J., Schwibbe, M.H'''. (1989). Einige methodologische Überlegungen zur Menzerathschen Regel. In: Altmann, Schwibbe 1989: 113-116.

'''Wilde, J., Schwibbe, M.H'''. (1989a). Organisationsformen von Erbinformation im Hinblick auf die Menzerathsche Regel. In: Altmann, Schwibbe 1989: 92-99.

'''Wimmer, G., Altmann, G'''. (2005). Unified derivation of some linguistic laws. In: P. Grzybek (ed.), ''Contributions the the Science of Language. Word Length Studies and Related Issues: 329-337.'' Dordrecht: Kluwer.

'''Ziegler, A., Altmann, G.''' (2002). ''Denotative Textanalyse.'' Wien: Edition Praesens.

'''The allometric law in other sciences'''

'''Adolph, E.F'''. (1949). Quantitative relations in physiological constitution of mammals. ''Science 109, 579''-

'''Bertalanffy, L.v'''. (1949). Problems of organic growth. ''Nature 163, 1''56-

'''Bertalanffy, L.v'''. (1951). Theoretische Biologie. Vol. II, Stoffwechsel, Wachstum. 2nd ed. Bern:

'''Bertalanffy, L.v'''. (1951a). Growth types and metabolic types. American Naturalist 85, 111-

'''Bertalanffy, L.v., Pirozynski, W.J.''' (1952). Ontogenetic and evolutionary allometry. Evolution 6, 3287-.

'''Bertalanffy, L.v., Pirozynski, W.J'''. (1953). Tissue respiration, growth and basal metabolism. Biological Bulletin 105, 240-.

'''Bonin, G.v'''. (1937). Brain weight and body weight of mammals. J. of General Psychology 16,

'''Brody, S'''. (1945). Bioenergetics and growth. New York:

'''Hersh, A.H'''. (1941). Allometric growth: The ontogenetic and phylogenetic significance of differential rates of growth. 3rd Growth Symposium 113.

'''Huxley, J.''' (1932). Problems of relative growth. London.

'''Jerison, H.J.''' (1955). Brain to body ratios and the evolution of intelligence. Science 121, 477-

'''Kaumanns, W., Schwibbe, M.H'''. (1989). Strukturmerkmale von Primatensozietäten unter dem Gesichtspunkt der Menzerathschen Regel. In: Altmann, G., Schwibbe, M.H., ''Das Menzerathsche Gesetz in informationsverarbeitenden Systemen: 99-107''. Hildesheim: Olms.

'''Klatt, B'''. (1919). Zur Methodik vergleichender metrischer Untersuchungen, besonders des Herzgewichts. ''Biologisches Zentralblatt 39, 406-''

'''Naroll, R.S., Bertalanffy, L.v'''. (1956). The principle of allometry in biology and the social science. ''General Systems 1, 76-89''.

'''Needham, J.''' (1934). Chemical heterogony and the groundplan of animal growth. ''Biological Revue 9, 79-''.

'''Reed, W.J., Hughes, B.D.''' (2002). From gene families and genera to incomes and internet file sizes: why power laws are so common in nature. Physical Review E 66, 067103.

''' Reeve, E.C.R., Huxley, J.S.''' (1945). Some problems in the study of allometric growth. In: Clark, W.E.C., Medawar, P.B. (1945), ''Essays on growth and form, presented to D´Arcy Wentworth Thmpson: 121-''. Oxford:

'''Rensch, B'''. (1954). ''Neuere Probleme der Abstammungslehre''. 2nd ed. Stuttgart:

'''Robb, R.C.''' (1935-1937). A study of mutation in evolution. I-IV. J. of Genetics 31, 39-; 33, 269-; 34, 477-.

'''Sholl, D.A'''. (1954). Regularities in growth curves, including rhythms and allometry. In: Boell, E.J. (ed.), Dynamics of growth processes: 224-. Princeton:

'''Vining, R'''. (1955). A description of certain spatial aspects of an economic system. ''Economic Development and Culture Change 3, 147-''.

[[Category:Unfertig]]

File:Tabelle3-neu.JPG

2007-06-25T11:40:30Z

Patzschke:

Hierarchic relations

2007-06-25T11:24:31Z

Patzschke:

'''1. Problem and history'''

In different domains of language one observed the fact that the length of a construct influences the length of its consitutents. Usually the constituents get smaller with increasing length of the construct but not in all cases. The problem is to find a theoretical model encompassing all dependencies of this kind. The constructs whose length is the independent variable are: hreb, sentence, rhythmic unit, word, syllable; the constituents whose length or duration is the dependent variable are: sentence, clause, word, syllable, morph, sound. There is also the possibility to consider two independent variables, e.g. word (measured in number of syllables) and syllable (measured in number of sounds) , while the dependent variable is the syllable duration.
Up to now the following particular cases have been examined (see Table 1)

<div align="center">[[Image:Tabelle11_HR.jpg]]</div>

The origin of the problem can be found in 19th century, in phonetics, probably for the first time with Sievers (1876, 1901) who measured the syllable duration in rhythmic units (Sprechakte). A number of phoneticians tested different hypotheses, a part of which corroborated, another part falsified it. The isochrony hypothesis in English is a special case of this problem. The problem was generalized by Menzerath who stated that ''the greater the whole the smaller its parts'' (1954: 101). Different researchers proposed some empirical formulas (Fónagy, Magdics 1960; Nooteboom 1972, 1973; Landblom, Rapp 1972), Altmann (1980) set up the pertinent differential equation and called the result Menzerath´s law. Hřebíček (1992, 1995, 1997) showed that the whole hierarchy of textual levels is based on this dependence and called it ''Menzerath-Altmann´s law''.

There is a great number of individual examinations in different domains of languge. In phonetics the most exhaustive is Weber (1998), in textology the works by Hřebíček (see above) and a mixture of problems including biology and sociology can be found in Altmann, Schwibbe (1989). Bohn (1998) analyzed the relationship between Chinese characters and the complexity of composing graphemes, length of words and simplicity of characters, clause length and word length, sentence length and clause length (cf. also Menzel 2005).
The law has a strong corroboration not only within linguistics but displays analogies to other sciences. Thus the simple form of Menzerath´s law is identical with the allometric law in biology and with the power laws current in different sciences. Its correspondences can be found in (i) molecular biology, (ii) sociology of baboons, (iii) in the domain of self-organized criticality, (iv) in chaos research, (v) in the theory of fractals, (vi) in information theory.
It has been observed that construct length is not always the only cause of shortening of the constituents. Also accent, vowel quality, syllable structure, frequency etc. can intervene (cf. Weber 1998). In that case more complex formulas must be used.
The law has several consequences, all of which must still be tested (cf. Altmann, Schwibbe 1989: 8-14):
1. In longer words more phonetic changes occur than in shorter ones.

2. In languages with greater average word length more phonetic/phonemic changes occur than within the same time interval in languages with smaller average word length

3. The adding of an affix to a word evokes the tendency to reduce the inventory of consonants of the word.

4. The shortening of average syllable length in Hypothesis 3 can also be achieved by inserting epenthetic vowels between the stem and affix (or compounding stem).

5. Partial reduplication is more frequent in natural languages than full reduplication.

6. Short roots/morphemes/stems build more compounds or derived words than long ones.

7. The more elements there are in a compound the shorter they are (see the hypotheses on compounds <math>\leftarrow</math>)

8. Fenk-Fenk (to be inserted)

There are different interpretations of the law:

1. In general, long constructs contain more redundancy than short ones. In order to prevent excessive growth of redundancy one can reduce the size of the constituents. The size, the place and the time of this reduction is not known and cannot be predicted. The analogy to self-organized criticality of sand-piles is evident (cf. Bak 1996).

2. Köhler (1989) shows that mechanism of shortening is a consequence of restrictions of the memory: the longer the construct, the more place must be reserved for the structural information between the constituents, thus the size of the constituents must be reduced.

'''2. Hypothesis'''

''The size of the components is a function of the construct size''.

'''3. Derivation'''

The average size of constituents changes with the increase of the size of the construct. It is assumed that the relative rate of change of the size of components is proportional to the rate of change of the size of constructs, the proportionality function being

<math> g(x) = a_0 + \frac{a_1}{x} + \frac{a_2}{x^2}</math>.

Thus in case that all other variables other than construct size are subsumed under the ceteris paribus condition one obtains

(1)<math> \frac{dy}{y-d}= \left(a_0 +\frac{a_1}{x}+ \frac{a_2}{x^2}\right)</math>.

where d is the minimal value y can attain.
In case that there is another independent variable, z, one starts from

(2)<math>\frac{dy}{dx}\frac{1}{y-d}=a_0 + \frac{a_1}{x}+\frac{a_2}{x^2}\quad</math> and <math>\frac{dy}{dz}\frac{1}{y-d}=b_0 + \frac{b_1}{z}+\frac{b_2}{z^2}</math>

which can be extended to any number of variables.
The solution of (1) yields

(3)<math> y= Cx^{a_1}e^{a_0 x-a_2/x} + d</math>

the combining (2) the solution is

(4)<math> y= Cx^{a_1}z^{b_1}e^{a_0 x + b_0 z-a_2 /x-b_2 /z} + d</math>

In different applications the following special cases of (3) have been used (d > 0)

(1a) <math> y=ax^{-b}(+d), \quad x= 1, 2, 3, ...; \quad a, b > 0</math>

(1b)<math> y=ax^b e^{cx}(+d), \quad x= 1, 2, 3, ...; \quad a > 0</math>

(1c)<math> y=ae^{-cx}(+d), \quad x= 1, 2, 3, ...; \quad a, c > 0</math>

(1d) <math> y=ae^{c/x}(+d), \quad x= 1, 2, 3, ...; \quad a, c > 0</math>

Solution (4) is still very seldom. Both approaches are special cases of the unified theory (<math>\leftarrow</math>).

'''Examples''':

'''4. Authors: U. Strauss, G. Altmann'''

'''5. References'''

'''Abercrombie, D'''. (1967). ''Elements of general phonetics''. Edinburgh: University Press.

'''Äima, F.''' (1918). Phonetik und Lautlehre des Inarilappischen. ''Mémoires de la Societé Finno-Ougrienne 43, 1-249.''

'''Altmann, G.''' (1980). Prolegomena to Menzerath´s law. ''Glottometrika 2, 1-10''.

'''Altmann, G'''. (1983). H. Arens´ „verborgene Ordnung“ und das Menzerathsche Gesetz. In: Faust, M., Harweg, R., Lehfeldt, W. (Hrsg.), ''Allgemeine Sprachwissenschaft, Sprachtypologie und Textlinguistik: 31-39''. Tübingen: Narr.

'''Altmann, G., Bagheri, D., Goebl, H., Köhler, R., Prün, C.''' (2002). ''Einführung in die quantitative Lexikologie.'' Götingen: Peust & Gutschmidt.

'''Altmann, G., Beöthy, E., Best, K.-H.''' (1982). Die Bedeutungskomplexität der Wörter und das Menzerathsche Gesetz. ''Zeitschrift für Phonetik, Sprachwissenschaft und Kommunikationsforschung 35, 537-543''.

'''Altmann, G., Schwibbe, M'''. (1989). ''Das Menzerathsche Gesetz in informationsverarbeitenden Systemen''. Hildesheim, Olms.

'''Arens, H'''. (1965). ''Verborgene Ordnung''. Düsseldorf: Schwann.

'''Asleh, L., & Best, K.-H.''' (2004/05). Zur Überprüfung des Menzerath-Altmann-Gesetzes am Beispiel deutscher (und italienischer) Wörter. ''Göttinger Beiträge zur Sprachwissenschaft'' 10/11, 9-19.

'''Auer, P., Uhmann, S'''. (1988). Silben- und akzentzählende Sprachen. ''Zeitschrift für Sprachwissenschaft 7, 214-259.''

'''Bak, P.''' (1996) ''How nature works. The science of self-organized criticality''. New York: Copernicus-Springer.

'''Bennett, S.G'''. (1935). Vergleichende experimentalphonetische Untersuchung der ungespannten Plosive im Englischen, Deutschen und Französischen. Diss.

'''Bohn, H.''' (1998). ''Quantitative Untersuchungen der modernen chinesischen Sprache und Schrift''. Hamburg: Kovač.

'''Bohn, H.''' (2002). Untersuchungen zur chinesischen Sprache und Schrift. In: Köhler, R. (ed.), ''Korpuslinguistische Untersuchungen in die quantitative und systemtheoretische Linguistik: 127-177''. http://ubt.opus.hbz-nrw.de/volltexte/2004/279/

'''Boroda, M.G., Altmann, G'''. (1991). Menzerath's law in musical texts. ''Musikometrika 3, 1-13.''

'''Changizi, M.A'''. (2001). Universal scaling laws for hierarchical complexity in languages, organisms, bahaviors and other combinatorial systems. ''J. of Theoretical Biology 211, 277-295.''

'''Collinder, B'''. (1964). Das Wort als phonetische Einheit. In: Collinder, B. (ed.), ''Sprachwissenschaft und Wahrscheinlichkeit: 203-217''. Uppsala: Almquist, Wiksells.

'''Cramer, I.M'''. (2005). The parameters of the Altmann-Menzerath law. ''J. of Quantitative Linguistics 12(1), 41-52.''

'''Cramer, I.M'''. (2005a). Das Menzerathsche Gesetz. In: Köhler, R., Altmann, G., Piotrowski, R.G. (eds.), ''Quantitative Linguistics - An International Handbook: 659-688''. Berlin: de Gruyter.

'''Debowski, L.''' (2007). Menzerath´s law for the smallest grammar. In: Grzybek, P., Köhler, R. (eds.), ''Exact methods in the Study of Language and Tests: 77-85.'' Berlin: de Gruyter.

'''Donner, K.''' (1912). Salmin murteen kvantiteettisuehtista. ''Suomi IV, 9, II''.

'''Elert, C.C.''' (1965). ''Phonological studies of quantity in Swedish''. Uppsala.

'''Evertz,''' (1929). ''Beiträge zur Phonetik der südfranzösischen Plosive''. Diss.

'''Faure, G., Hirst, D.J., Chafcouloff, M.''' (1980). Rhythm in English: Isochronism, pitch, and perceived stress. In: Linda, R., Schooneveld, C.H.v. (eds.), ''The melody of language: 71-79''. Baltimore: University Park Press.

'''Fenk, A., Fenk-Oczlon, G'''. (1993). Menzerath´s law and the constant flow of linguistic information. In: Köhler, R., Rieger, B.B. (eds.), ''Contributions to quantitative linguistics: 11-31''. Dordrecht: Kluwer.

'''Fenk-Oczlon, G., Fenk, A'''. (1995). Selbstorganisation und natürliche Typologie. ''Sprachtypologie und Universalienforschung 48, 223-238''.

'''Fenk-Oczlon, G., Fenk, A'''. (1999). Cognition, quantitative linguistics, and systemic typology. ''Linguistic Typology 3, 151-177.''

'''Fickermann, I., Markner-Jäger, B, Rothe, U'''. (1984). Wortlänge und Bedeutungskomplexität. ''Glottometrika 6, 115-126.''

'''Fischer-Jörgensen, E'''. (1964). Sound duration and place of articulation. ''Zeitschrift für Phonetik 17, 175-207''.

'''Fónagy, I'''. (1959).'' A költöi nyelv hangtanából.'' Budapest.

'''Fónagy, I, Magdics, K'''. (1960). Speed of utterance in phrases of different length. ''Language and Speech 3, 179-182''.

'''Gaitenby, I.H'''. (1965). ''The elastic word''. Haskins, Status Report on speech research 1965/SR-2,3.1-3.12.

'''Gerlach, R'''. (1982). Zur Überprüfung des Menzerathschen Gesetzes im Bereich der Morphologie. ''Glottometrika 4, 95-102''.

'''Geršić, S., Altmann, G'''. (1980). Laut – Silbe – Wort und das Menzerathsche Gesetz. ''Frankfurter Phonetische Beiträge 3, 115-123''.

'''Grégoire, A'''. (1899). Variation de la durée de la syllable français. ''La Parole 1''.

'''Grzybek, P'''. (1999). Randbemerkungen zur Wortlänge im Kroatischen. In: B.Tošović (ed.), ''Die grammatischen Korrelationen: 56-67.'' Graz: Gralis.

'''Grzybek, P., Stadlober, E.''' (2007). Do we have probelsm with Arnes´ law? A new look at the sentence-word relation. In: Grzybek, P., Köhler, R. (eds.), ''Exact Method in th Study of Language and Text: 203-215.'' Berlin: de Gruyter.

'''Hammerl, R., Sambor, J'''. (1993a). ''O statystycznych prawach jezykowych''. Warszawa: Polskie Towarzystwo Semiotyczne.

'''Hegedüs, L'''. (1956). Sprechtempoanalysen im Ungarischen. ''Zeitschrift für Phonetik 10.''

'''Heups, G'''. (1983). Untersuchungen zum Verhältnis von Satzlänge und Clauselänge am Beispiel deutscher Texte verschiedener Textklassen. ''Glottometrika 5, 113-133''.

'''Hřebíček, L'''. (1990). Menzerath-Altmann's law on the semantic level. ''Glottometrika 11, 47-56.''

'''Hřebíček, L''' (1990a). The constants of the Menzerath-Altmann law. ''Glottometrika 12, 61-71''.

'''Hřebíček, L'''. (1992). ''Text in communication: Supra-sentence structure''. Bochum, Brockmeyer.

'''Hřebíček, L'''. (1993b). Text as a construct of aggregations. In: Köhler, R., Rieger, B. (eds.), ''Contributions to quantitative lingusitics: 33-39''. Dordrecht: Kluwer.

'''Hřebíček, L'''. (1993c). Text as a strategic process. In: Hřebíček, L., Altmann, G. (Eds.), ''Quantitative text analysis: 136-150''. Trier: WVT.

'''Hřebíček, L'''. (1994). Fractals in language. ''J. of Quantitative Linguistics 1, 82-86''.

'''Hřebíček, L'''. (1994a). The stairway of subsystems. In: ''2nd International Conference on Quantitative Linguistics, September 1994, 210-222 Moscow''. Moscow: Lomonosov Moscow State University.

'''Hřebíček, L.''' (1995). ''Text levels. Language constructs, constituents and Menzerath-Altmann law''. Trier: WVT.

'''Hřebíček, L'''. (1995a). Phase transition in texts. ''ZeT – Zeitschrift für empirische Textwissenschaft 2, 52-58.''

'''Hřebíček, L.''' (1997). ''Lectures on text theory''. Prague: Oriental Institute.

'''Hřebíček, L.''' (2000). ''Variation in sequences''. Prague: Oriental Institute.

'''Hřebíček, L.''' (2004). The semantic space and Turkish ghazels. ''Archiv orientální 72, 175-191''.

'''Hřebíček, L.''' (2005). Text laws. In: Köhler, R., Altmann, G., Piotrowski, R.G. (eds.) (2005), ''Quantitative Linguistics - An International Handbook: 348-361''. Berlin: de Gruyter.

'''Hřebíček, L., Altmann, G'''. (1993). Prospects of text linguistics. In: Hřebíček, L., Altmann, G. (Eds.), ''Quantitative text analysis: 1-28''. Trier: WVT.

'''Hug, M.''' (2007). Das Menzerath-Gesetz in der Vulgata. In: Grzybek, P., Köhler, R. (eds.), ''Exact Method in th Study of Language and Text: 243-255.'' Berlin: de Gruyter.

'''Huxley, A'''. (1963). ''Evolution: the modern synthesis''. London 1942.

'''Jespersen, O'''. (1897-1899). ''Phonetik''. Copenhagen.

'''Jespersen, O'''. (1932). ''Lehrbuch der Phonetik''. Lepzig-Berlin.

'''Kaumanns, W., Schwibbe, M.H.''' (1983). Strukturmerkmale von Primatensozietäten unter dem Gesichtspunkt der Menzerathschen Regel. In: Altmann, G., Schwibbe, M. (1983): 99-107.

'''Köhler, R'''. (1982). Das Menzerathsche Gesetz auf der Satzebene. ''Glottometrika 4, 103-113''.

'''Köhler, R.''' (1984). Zur Interpretation des Menzerathschen Gesetzes. ''Glottometrika 6, 177-183''.

'''Köhler, R'''. (1986). ''Zur linguistischen Synergetik: Struktur und Dynamik der Lexik''. Bochum: Brockmeyer.

'''Köhler, R'''. (1989). Das Menzerathschen Gesetz als Resultat des Sprachverarbeitungsmechanismus. In: Altmann, Schwibbe (1989): 108-112.

'''Köhler, R.''' (1990). Linguistische Analyseebenen, Hierarchisierung und Erklärung im Modell der sprachlichen Selbstregulation. ''Glottometrika 11, 1-18''.

'''Krott, A.''' (1996). Some remarks on the relation between word length and morpheme length. ''J. of Quantitative Linguistics 3, 29-37''.

'''Krott, A.''' (2002). Ein funktionalanalytisches Modell der Wortbildung. In: Köhler, R. (ed.), ''Korpuslinguistische Untersuchungen in die quantitative und systemtheoretische Linguistik: 75-126''. http://ubt.opus.hbz-nrw.de/volltexte/2004/279/

'''Kułacka, A., Mačutek, J.''' (2007). ''A discrete formula for the Menzerath-Altmann law. J. of Quantitative Linguistics 14(1)'', 23-32.

'''Laurosela, J'''. (1922). ''Foneettinen tutkimus Etelä-Pohjanmaan murteesta''. Helsinki.

'''Lehiste, I'''. (1970). ''Suprasegmentals''. Cambridge, Mass.:M.I.T. Press.

'''Lehfeldt, W'''. (2006). The fall of jers in the light of Menzerath´s law. In: Grzybek, P. (ed.), ''Contributions to the Science of text and Language. Word Length and Related Issues: 211-213''. Dordrecht: Springer.

'''Lehfeldt, W., Altmann, G.''' (2000). Padenie reducirovannykh v svete zakona P. Mencerata. ''Russian Linguistics 26, 327-344''.

'''Lehfeldt, W., Altmann, G.''' (2000). Der altrussische Jerwandel. ''Glottometrics 2, 34-44''.

'''Lehtonen, J.''' (1970). Aspects of quantity in a standard Finnish. ''Studia Philologica Jyväskyläensia 6''.

'''Leopold, E.''' (2001). Fractal structures in language. The question of the imbedding space. In Uhlířová, L., Wimmer, G., Altmann, G., Köhler, R. (Eds.), ''Text as a linguistic paradigm: levels, constituents, constructs. Festschrift in honour of Ludek Hřebíček: 163-1176''. Trier: WVT.

'''Leopold, E. ''' (2007). Bemerkungen zum Menzerath-Altmannschen Gesetz. In: Grzybek, P., Köhler, R. (eds.), ''Exact Methods in the Study of Language and Text: 389-396.'' Berlin: de Gruyter.

'''Lindblom, B.E.F'''. (1968). Temporal organization of syllable production. ''Royal Institute of Technology, Stockholm, Speech Transmission Laboratory, Quarterly Progress and Status Report 2-3, 1-5''.

'''Lindblom, B, Rapp, K.''' (1972). Reexamination of the compensatory adjustment of vowel duration in Swedish words. ''Symposium on experimental and theoretical approaches to the role of time speech''. University of Essex.

'''Maack, A.''' (1949). Die spezifische Lautdauer deutscher Sonanten. ''Zeitschrift für Phonetik 3, 190-232''.

'''Malécot, A., Johnston, R., Kizziar, P.-A'''. (1972). Syllabic Rate and Utterance Length in French. ''Phonetica 26, 235-251''.

'''Malmberg, B'''. (1944). Die Quantität als phonetisch-phonologischer Begriff. ''Lunds Universitets Årskrift 41, 1-104''.

'''Menzerath, P'''. (1928). Über einige phonetische Probleme. ''Actes du premier congrès international de linguistique. Leiden, Nendeln/Liechtenstein, Kraus reprint: 104-105''.

'''Menzerath P.''' (1954). ''Die Architektonik des deutschen Wortschatzes''. Bonn, Dümmler.

'''Meyer, E.A.''' (1904). Zur Vokaldauer im Deutschen. ''Nordiska Studier Tillegnade A: 347-356''. Norken, Uppsala 1904.

'''Meyer, E.A., Gombocz, Z'''. (1908). Zur Phonetik der ungarischen Sprache. ''Le Monde Oriental 2, 122-187''.

'''Meyer, P.''' (2007). Two semi-mathematical asides on Menzerath-Altmann´s law. In: Grzybek, P., Köhler, R. (eds.), ''Exact Methods in the Study of Language and Text: 447-458.'' Berlin: de Gruyter.

'''Nemcová, E.''' (1994). On two realizations of Menzerath´s law. ''J. of Quantitative Linguistics 1, 107-112''.

'''Nooteboom, S.G'''. (1972a). The interaction of some intra-syllable and extra-syllable factors acting on syllable nucleus duration. ''IPO Annual Progress report 7, 30-39.''

'''Nooteboom, S.G'''. (1972b). ''Production and perception of vowel duration''. Eindhoven: Philips Research Laboratories.

'''Nooteboom, S.G.''' (1973). The perceptual reality of some prosodic durations. ''J. of Phonetiocs 1, 25-45''.

'''Palomaa, J.K'''. (1946). ''Suomen kielen äännekestoista puhumaan oppinen kuuromykän ja kuulevan henkilön ääntämisessä''. Publicationes Instituti Phonetici Universiatis Helsingforsiensis. Turku.

'''Polikarpov, A.''' (2000). Menzerath’s Law for Morphemic Structures of Words: A Hypothesis for the Evolutionary Mechanism of its Arising and its Testing. In: Baayen, R.H. (ed.), ''Proceedings of the fourth conference of the International Quantitative Linguistics Association: 26-27'', Prague, August 24-26, 2000.

'''Polikarpov, A.A.''' (2006). Towards the foundations of Menzerath´s law. On the functional dependence of the affix lengths on their positional number within words. In: Grzybek, P. (ed.) ''Contributions to the Science of Text and Language. Word Length Studies and Related Issues: 215-240.'' Dordrecht: Springer.

'''Prün, C.''' (1994). Validity of Menzerath-Altmann’s law: Graphic representation of language, information processing systems and synergetic linguistics. ''J. of Quantitative Linguistics 1, 148-155''.

'''Rothe, U.''' (1983). Wortlänge und Bedeutungsmenge. Eine Untersuchung zum Menzerathschen Gesetz an drei romanischen Sprachen. ''Glottometrika 5, 101-112''.

'''Roudet, L.''' (1910). ''Eléments de phonétique générale''. Paris: Welter.

'''Ruszkowski, M.''' (1991). ''Prawo Menzeratha w badaniach syntaktycznych. Jezyk
Polski LXXI'', 187-192.

'''Rykov, V.''' (1994). Menzerath law for printed speech. In: ''2nd International Conference on Quantitative Linguistics, September 20-24, 1994, Moscow: 199-200''. Moscow: Lomonosov Moscow State University.

'''Sambor, J.''' (1984). Menzerath’s law and the polysemy of words. ''Glottometrika 6, 94-114''.

'''Schindelin, C'''. (2005). Die quantitative Erforschung der chinesischen Sprache und Schrift. In: Köhler, R., Altmann, G., Piotrowski, R.G. (eds.), ''Quantitative Linguistics - An International Handbook: 947-970''. Berlin: de Gruyter.

'''Schwibbe, M.H'''. (1984). Text- und wortstatistische Untersuchungen zur Validität der Menzerathschen Regel. ''Glottometrika 6, 152-176''.

'''Schwibbe, M.H.''' (1989). Die Menzerathsche Regel als Modell psychischer Informationsverarbeitung. In: Altmann, G., Schwibbe, M.H. (1989): 84-91.

'''Sievers, E.''' (1876/1901). ''Grundzüge der Phonetik''. Leipzig: Breitkopf, Härtel.

'''Sovijärvi, A.''' (1944). ''Foneettis-äännehistoriallinen tutkimus Soikkolan inkeroismurteesta''. Suomi 103.

'''Tarnóczy, T'''. (1965). Can the problem of automatic speech recognition be solved by analysis alone? ''Reports of the Fifth International Congress of Acoustics II, Liège''.

'''Teupenhayn, R., Altmann, G'''. (1984). Clause length and Menzerath´s law. ''Glottometrika 6, 127-138''.

'''Weber, S.''' (1998). ''Das Menzerathsche Gesetz in gesprochener Sprache''. Magisterarbeit Universität Trier.

'''Wiik, K.''' (1965). Finnish and English vowels. ''Turku, Annales Universitatis Turkuensis, Series B, 94''.

'''Wilde, J., Schwibbe, M.H'''. (1989). Einige methodologische Überlegungen zur Menzerathschen Regel. In: Altmann, Schwibbe 1989: 113-116.

'''Wilde, J., Schwibbe, M.H'''. (1989a). Organisationsformen von Erbinformation im Hinblick auf die Menzerathsche Regel. In: Altmann, Schwibbe 1989: 92-99.

'''Wimmer, G., Altmann, G'''. (2005). Unified derivation of some linguistic laws. In: P. Grzybek (ed.), ''Contributions the the Science of Language. Word Length Studies and Related Issues: 329-337.'' Dordrecht: Kluwer.

'''Ziegler, A., Altmann, G.''' (2002). ''Denotative Textanalyse.'' Wien: Edition Praesens.

'''The allometric law in other sciences'''

'''Adolph, E.F'''. (1949). Quantitative relations in physiological constitution of mammals. ''Science 109, 579''-

'''Bertalanffy, L.v'''. (1949). Problems of organic growth. ''Nature 163, 1''56-

'''Bertalanffy, L.v'''. (1951). Theoretische Biologie. Vol. II, Stoffwechsel, Wachstum. 2nd ed. Bern:

'''Bertalanffy, L.v'''. (1951a). Growth types and metabolic types. American Naturalist 85, 111-

'''Bertalanffy, L.v., Pirozynski, W.J.''' (1952). Ontogenetic and evolutionary allometry. Evolution 6, 3287-.

'''Bertalanffy, L.v., Pirozynski, W.J'''. (1953). Tissue respiration, growth and basal metabolism. Biological Bulletin 105, 240-.

'''Bonin, G.v'''. (1937). Brain weight and body weight of mammals. J. of General Psychology 16,

'''Brody, S'''. (1945). Bioenergetics and growth. New York:

'''Hersh, A.H'''. (1941). Allometric growth: The ontogenetic and phylogenetic significance of differential rates of growth. 3rd Growth Symposium 113.

'''Huxley, J.''' (1932). Problems of relative growth. London.

'''Jerison, H.J.''' (1955). Brain to body ratios and the evolution of intelligence. Science 121, 477-

'''Kaumanns, W., Schwibbe, M.H'''. (1989). Strukturmerkmale von Primatensozietäten unter dem Gesichtspunkt der Menzerathschen Regel. In: Altmann, G., Schwibbe, M.H., ''Das Menzerathsche Gesetz in informationsverarbeitenden Systemen: 99-107''. Hildesheim: Olms.

'''Klatt, B'''. (1919). Zur Methodik vergleichender metrischer Untersuchungen, besonders des Herzgewichts. ''Biologisches Zentralblatt 39, 406-''

'''Naroll, R.S., Bertalanffy, L.v'''. (1956). The principle of allometry in biology and the social science. ''General Systems 1, 76-89''.

'''Needham, J.''' (1934). Chemical heterogony and the groundplan of animal growth. ''Biological Revue 9, 79-''.

'''Reed, W.J., Hughes, B.D.''' (2002). From gene families and genera to incomes and internet file sizes: why power laws are so common in nature. Physical Review E 66, 067103.

''' Reeve, E.C.R., Huxley, J.S.''' (1945). Some problems in the study of allometric growth. In: Clark, W.E.C., Medawar, P.B. (1945), ''Essays on growth and form, presented to D´Arcy Wentworth Thmpson: 121-''. Oxford:

'''Rensch, B'''. (1954). ''Neuere Probleme der Abstammungslehre''. 2nd ed. Stuttgart:

'''Robb, R.C.''' (1935-1937). A study of mutation in evolution. I-IV. J. of Genetics 31, 39-; 33, 269-; 34, 477-.

'''Sholl, D.A'''. (1954). Regularities in growth curves, including rhythms and allometry. In: Boell, E.J. (ed.), Dynamics of growth processes: 224-. Princeton:

'''Vining, R'''. (1955). A description of certain spatial aspects of an economic system. ''Economic Development and Culture Change 3, 147-''.

[[Category:Unfertig]]

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