Diversification - Revision history

Vulanovic at 13:23, 15 June 2009

2009-06-15T13:23:33Z

Vulanovic at 13:20, 15 June 2009

2009-06-15T13:20:28Z

Vulanovic at 13:06, 15 June 2009

2009-06-15T13:06:28Z

Vulanovic at 12:36, 15 June 2009

2009-06-15T12:36:23Z

KHBest: lit erg

2009-03-05T17:33:56Z

lit erg

Ahans at 15:47, 18 July 2006

2006-07-18T15:47:31Z

Altmann at 07:10, 16 July 2006

2006-07-16T07:10:28Z

Ahans at 12:15, 11 July 2006

2006-07-11T12:15:00Z

Ahans at 12:14, 11 July 2006

2006-07-11T12:14:15Z

Ahans at 12:12, 11 July 2006

2006-07-11T12:12:21Z

@@ Line 108: / Line 108: @@
 (c)	The death of a variant is proportional to the number of variants and the length of the interval, i.e. <math>cx</math>Δ<math>t</math>.
-(d)	No change (birth, death or assertion) in Δ<math>t</math> is given as the complement to the above changes:  <math>1–[a+(b+c)x]</math>Δ<math>t</math>, ignoring intervals smaller then Δ<math>t</math>.
+(d)	No change (birth, death or assertion) in Δ<math>t</math> is given as the complement to the above changes: 1 – [<math>a+(b+c)x</math>]Δ<math>t</math>, ignoring intervals smaller then Δ<math>t</math>.
 (e)	The events are independent and the probability of more then one event in the interval is zero.

@@ Line 5: / Line 5: @@
 For the sake of illustration let us show some concrete examples:
-(1)	The word can enlarge its class membership without any change, e.g. through conversion: “the hand”, “to hand”.
+)	The word can enlarge its class membership without any change, e.g. through conversion: “the hand”, “to hand”.
-(2)	The stem enlarges its class membership through derivation, e.g. German "Bild", "bilden", "bildhaft", or vocalization in Semitic languages, etc.
+)	The stem enlarges its class membership through derivation, e.g. German "Bild", "bilden", "bildhaft", or vocalization in Semitic languages, etc.
-(3)	The stem can enlarge its applicability within one class through derivation e.g. German "Blut", "Blutung", "Bluter", or through vocalization, etc.
+)	The stem can enlarge its applicability within one class through derivation e.g. German "Blut", "Blutung", "Bluter", or through vocalization, etc.
-(4)	The stem can enlarge its applicability within one class through compounding e.g. "Blut", "Blutdruck", "Blutdurst", etc.
+)	The stem can enlarge its applicability within one class through compounding e.g. "Blut", "Blutdruck", "Blutdurst", etc.
-(5)	If a language abandons isolating morphology, then morphemes diversify into several morphs because of agglutination or inflection (sequential or syntactic dependence).
+)	If a language abandons isolating morphology, then morphemes diversify into several morphs because of agglutination or inflection (sequential or syntactic dependence).
-(6)	The word can enlarge its applicability in the sentence by acquiring several functions, i.e. it enlarges its dispositional properties, which are different from the constant grammatical properties, e.g. practically every word can become the subject of a sentence.
+)	The word can enlarge its applicability in the sentence by acquiring several functions, i.e. it enlarges its dispositional properties, which are different from the constant grammatical properties, e.g. practically every word can become the subject of a sentence.
-(7)	Verbs can enlarge their valence, i.e. their combinability with different cases.
+)	Verbs can enlarge their valence, i.e. their combinability with different cases.
-(8)	The word can enlarge its cotextuality (cf. Köhler 1986), i.e. its ability to occur in several contexts (where "context" can be defined in several ways). The reverse of this kind of diversification process is part of style formation, where a "position" diversifies, i.e., a position in a given context can be filled with different units (words, sentences, etc.).
+)	The word can enlarge its cotextuality (cf. Köhler 1986), i.e. its ability to occur in several contexts (where "context" can be defined in several ways). The reverse of this kind of diversification process is part of style formation, where a "position" diversifies, i.e., a position in a given context can be filled with different units (words, sentences, etc.).
-(9)	A concept can be expressed by different forms, giving rise to dialects, sociolects, idiolects, or to synonymy.
+)	A concept can be expressed by different forms, giving rise to dialects, sociolects, idiolects, or to synonymy.
-(10)	A word can acquire different meaning (polysemy).
+)	A word can acquire different meaning (polysemy).
-(11)	Every word can acquire different associations (connotations).
+)	Every word can acquire different associations (connotations).
 Diversified entities abide by a ranking law, i.e. if the members of the diversified entity are ordered according to their frequency, then the frequencies are “lawfully” connected.
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 The factors of diversification can be as follows (Altmann 2005):
-(a)	''Random fluctuation'' which is omnipresent in any language phenomena.
+a)	''Random fluctuation'' which is omnipresent in any language phenomena.
-(b)	''Environmentally conditioned variation'' forcing an element to acquire different forms or meaning nuances in different environments.
+b)	''Environmentally conditioned variation'' forcing an element to acquire different forms or meaning nuances in different environments.
-(c)	''Conscious change'' through conscious creation, borrowing, emotionality etc.
+c)	''Conscious change'' through conscious creation, borrowing, emotionality etc.
-(d)	''Self-organisatory triggering'' of a process to a limit, causing changes on other levels, too.
+d)	''Self-organisatory triggering'' of a process to a limit, causing changes on other levels, too.
-(e)	''System modification'' joined with local or global modifications in a subsystem,
+e)	''System modification'' joined with local or global modifications in a subsystem,
-(f)	''Köhlerian requirements'' (Köhler 1986, 1987, 1989, 1990, 1991) forcing to take into account collateral pressures form different sides. They are as follows: (i) ''The trend for minimal coding and deciding effort'', (ii) ''sufficient redundancy'', (iii) ''the coding requirement in general'', (iv) ''context economy vs. context specificity'', and (v) ''invariance vs. flexibility of relation between expression and meaning.''
+f)	''Köhlerian requirements'' (Köhler 1986, 1987, 1989, 1990, 1991) forcing to take into account collateral pressures form different sides. They are as follows: (i) ''The trend for minimal coding and deciding effort'', (ii) ''sufficient redundancy'', (iii) ''the coding requirement in general'', (iv) ''context economy vs. context specificity'', and (v) ''invariance vs. flexibility of relation between expression and meaning.''
 The concepts of diversification and unification go back to G.K. Zipf (1935, 1949). Together they are called “Zipfian processes”. The scope of the phenomena is enormous. Semantic phenomena have been examined by Beöthy and Altmann (1984a,b, 1991), Altmann (1985a), Altmann, Best, Kind (1987); grammatical phenomena  were analyzed in the omnibus volume edited by Rothe (1991), where also a study on spelling errors in English can be found, and dialectal diversification was studied by Altmann (1985b).
@@ Line 108: / Line 108: @@
 (c)	The death of a variant is proportional to the number of variants and the length of the interval, i.e. <math>cx</math>Δ<math>t</math>.
-(d)	No change (birth, death or assertion) in Δ<math>t</math> is given as the complement to the above changes:  <math>1 – [a+(b+c)x]</math>Δ<math>t</math>, ignoring intervals smaller then Δ<math>t</math>.
+(d)	No change (birth, death or assertion) in Δ<math>t</math> is given as the complement to the above changes:  <math>1–[a+(b+c)x]</math>Δ<math>t</math>, ignoring intervals smaller then Δ<math>t</math>.
 (e)	The events are independent and the probability of more then one event in the interval is zero.
@@ Line 195: / Line 195: @@
 yielding the solution
-(5)<math>P_x=P_1x^{-(a+b\ln x)}, \quad x=1,2,3,...</math>.
+(5) <math>P_x=P_1x^{-(a+b\ln x)}, \quad x=1,2,3,...</math>.
-If (5) is considered a probability distribution, then P1 is the norming constant, otherwise it is estimated as the size of the first class, x = 1. Since the frequency of the first class x = 1 is decisive for the form of the distribution, one usually ascribes it a special value α, modifying (5) as
+If (5) is considered a probability distribution, then <math>P_1</math> is the norming constant, otherwise it is estimated as the size of the first class (<math>x</math> = 1). Since the frequency of the first class <math>x</math> = 1 is decisive for the form of the distribution, one usually ascribes it a special value α, modifying (5) as
-(6)<math>P_x=\begin{cases}a, & x=1\\\frac{(1-a)x^{(a+b\ln x)}}{T}, & x=2,3,...,(n)\end{cases}</math>
+(6) <math>P_x=\begin{cases}\alpha, & x=1\\\frac{(1-a)x^{(a+b\ln x)}}{T}, & x=2,3,...,(n)\end{cases}</math>
-where  <math>T=\sum_{j=2}^nj^{-(a+b\ln j)}</math>, 0 < α < 1,  <math>a,b\in\mathfrak{R}</math>  so that <math>P_x</math> converges for <math>n\rightarrow\infty</math>. This version corroborates again the relevance of Menzerath´s law (<math>\rightarrow</math>). Distributions (5) or (6) are called ''Zipf-Alekseev distributions''. If ''n'' is finite, (6) is called ''modified right truncated Zipf-Alekseev distribution'' (see Wimmer, Altmann 1999).
+where  <math>T=\sum_{j=2}^nj^{-(a+b\ln j)}</math>, 0 < α < 1,  <math>a,b\in\mathfrak{R}</math>  so that <math>P_x</math> converges for <math>n\rightarrow\infty</math>. This version corroborates again the relevance of Menzerath´s law (<math>\rightarrow</math>). Distributions (5) or (6) are called ''Zipf-Alekseev distributions''. If <math>n</math> is finite, (6) is called ''modified right truncated Zipf-Alekseev distribution'' (see Wimmer, Altmann 1999).
 Even though (3) and (5) are quite different, it can be shown that they are special cases of the Siromoney-Dirichlet distribution
-(7)<math>P_x=\frac{a_xe^{-\theta b_x}}{f(\theta)}, \quad x=1,2,3,...</math> <math>f(\theta)=\sum_{j=1}^\infty a_je^{-\theta b_j}<\infty</math>
+(7) <math>P_x=\frac{a_xe^{-\theta b_x}}{f(\theta)}, \quad x=1,2,3,...</math> <math>f(\theta)=\sum_{j=1}^\infty a_je^{-\theta b_j}<\infty</math>
-(i) If <math>a_x = k^{(x)}/x!, b_x = x, e^{-\theta} = q\quad</math>, we obtain the positive negative binomial distribution with parameters (k, p) (q = 1-p);
+(i) If <math>a_x = k^{(x)}/x!, b_x = x, e^{-\theta} = q\quad</math>, we obtain the positive negative binomial distribution with parameters (<math>k</math>,<math>p</math>) (<math>q = 1-p</math>);
-(ii) if <math>\theta = 1, a_x = 1, b_x = (a+b \quad\ln \quad x)\ln x</math>, we obtain the Zipf-Alekseev distribution (a,b);
+(ii) if <math>\theta = 1, a_x = 1, b_x = (a+b \quad\ln \quad x)\ln x</math>, we obtain the Zipf-Alekseev distribution (<math>a,b</math>);
 (iii) the 1-displaced negative binomial distribution, which would be obtained with the conventional displacement of (4), would result if <math>a_x = k^{(x-1)}/(x-1)!, b_x = x-1, e^{-\theta} = q\quad</math>.
@@ Line 219: / Line 219: @@
 The connotations of a word diversify because everybody can have different associations. Nevertheless, within a community of speakers, they are distributed in a very regular way suggesting a background mechanism which can be captured as a law.
-In the dictionaries of word associations (see e.g. Palermo, Jenkins 1964), the responses to a stimulus word are ordered according to the number of test persons that gave the same response, i.e. they are ranked according to their frequency of occurrence. The test persons are usually classified according to age, sex, education, occupation, social status etc. Quantitative modelling began most probably in Horvath (1963) and continued in  Haight (1966), Haight, Jones (1974), Lánský, Radil-Weiss (1980) who used the logarithmic, the Yule, the Borel and the Haight-zeta distributions, none of which gave satisfactory results. Dolinskij (1988, 1994) proposed the Zipf-Alekseev distribution, Altmann (1992) added the 1-displaced negative binomial and modified the Zipf-Alekseev distributions.
+In the dictionaries of word associations (see e.g. Palermo, Jenkins 1964), the responses to a stimulus word are ordered according to the number of test persons that gave the same response, i.e. they are ranked according to their frequency of occurrence. The persons tested are usually classified according to age, sex, education, occupation, social status etc. Quantitative modelling began most probably in Horvath (1963) and continued in  Haight (1966), Haight, Jones (1974), Lánský, Radil-Weiss (1980) who used the logarithmic, the Yule, the Borel and the Haight-zeta distributions, none of which gave satisfactory results. Dolinskij (1988, 1994) proposed the Zipf-Alekseev distribution, Altmann (1992) added the 1-displaced negative binomial and modified the Zipf-Alekseev distributions.
 In Table 3 (Figure 3) one finds the fitting of the Zipf-Alekseev distribution to the rank-frequency of associations of the word “high” (4th grade, male) as given by Palermo, Jenkins (1964).

@@ Line 43: / Line 43: @@
 (f)	''Köhlerian requirements'' (Köhler 1986, 1987, 1989, 1990, 1991) forcing to take into account collateral pressures form different sides. They are as follows: (i) ''The trend for minimal coding and deciding effort'', (ii) ''sufficient redundancy'', (iii) ''the coding requirement in general'', (iv) ''context economy vs. context specificity'', and (v) ''invariance vs. flexibility of relation between expression and meaning.''
-The concepts of diversification and unification go back to G.K. Zipf (1935, 1949). Together they are called “Zipfian processes”. The scope of the phenomena is enormous. Semantic phenomena have been examined by Beöthy and Altmann (1984a,b, 1991), Altmann (1985a), Altmann, Best, Kind (1987); grammatical phenomena  were analyzed in the omnibus volume edited by Rothe (1991), where also a study on spelling errors in Japanese can be found, and dialectal diversification was studied by Altmann (1985b).
+The concepts of diversification and unification go back to G.K. Zipf (1935, 1949). Together they are called “Zipfian processes”. The scope of the phenomena is enormous. Semantic phenomena have been examined by Beöthy and Altmann (1984a,b, 1991), Altmann (1985a), Altmann, Best, Kind (1987); grammatical phenomena  were analyzed in the omnibus volume edited by Rothe (1991), where also a study on spelling errors in English can be found, and dialectal diversification was studied by Altmann (1985b).
 The laws hold usually for ranked nominal classes of limited size.
@@ Line 78: / Line 78: @@
 (1) <math>P_x=g(x)P_{x-1}\quad</math>, where <math>g(x)\le 1\quad</math>.
-Furthermore, g(x) can be written as
+Furthermore, <math>g(x)</math> can be written as
 <math>g(x)=\frac{f(x)}{h(x)}</math>,
-where f(x) is a function composed of a language constant a and the diversifying effect of the speaker bx, i.e. f(x) = a+bx, while h(x) contains the controlling, regulating effect of the hearer (community) cx, i.e.
+where <math>f(x)</math> is a function composed of a language constant <math>a</math> and the diversifying effect of the speaker <math>bx</math>, i.e. <math>f(x) = a+bx</math>, while <math>h(x)</math> contains the controlling, regulating effect of the hearer (community) <math>cx</math>, i.e.
-<math>g(x)=\frac{a+bx}{cx}</math>, <math>\quad a+bx\le cx</math> (a, b, and c are assumed positive),
+<math>g(x)=\frac{a+bx}{cx} \le 1</math>, (a, b, and c are assumed positive),
 so that
-(2)<math>P_x=\frac{a+bx}{cx}p_{x-1}</math>.
+(2) <math>P_x=\frac{a+bx}{cx}P_{x-1}</math>.
-In order to obtain a known distribution, one can reparametrize (2) by writing a/b = k-1 and b/c = q, and solving (2) for Px. One obtains
+In order to obtain a known distribution, one can reparametrize (2) by writing <math>a/b = k-1</math> and <math>b/c = q</math>, and solving (2) for <math>P_x</math>. One obtains
-(3)<math>P_x=\begin{pmatrix}k&+&x&-&1\\&&x\end{pmatrix}\frac{p^kq^x}{1-p^k}, \quad x=1,2,3,...</math>
+(3) <math>P_x=\begin{pmatrix}k&+&x&-&1\\&&x\end{pmatrix}\frac{p^kq^x}{1-p^k}, \quad x=1,2,3,...</math>
 yielding the zero-truncated (positive) negative binomial distribution. The condition <math>g(x)\le 1</math> is fulfilled if <math>kq\le 1</math>.
@@ Line 102: / Line 102: @@
 For the purposes of dialectal variation captured in terms of numbers of lexeme variants on maps of a dialect atlas, Altmann (1985) used the birth-and-death process based on the following assumptions:
-(a)	In a time interval Δt the birth of a new variant is proportional to the length of the interval, i.e. aΔt.
+(a)	In a time interval Δ<math>t</math> the birth of a new variant is proportional to the length of the interval, i.e. <math>a</math>Δ<math>t</math>.
-(b)	The assertion of a variant against x rivals is propotional to the number of rivals and the length of the interval, i.e. bxΔt.
+(b)	The assertion of a variant against <math>x</math> rivals is propotional to the number of rivals and the length of the interval, i.e. <math>bx</math>Δ<math>t</math>.
-(c)	The death of a variant is proportional to the number of variants and the length of the interval, i.e. cxΔt.
+(c)	The death of a variant is proportional to the number of variants and the length of the interval, i.e. <math>cx</math>Δ<math>t</math>.
-(d)	No change (birth, death or assertion) in Δt is given as the complement to the above changes:  1 – [a+(b+c)x]Δt ignoring intervals smaller then Δt.
+(d)	No change (birth, death or assertion) in Δ<math>t</math> is given as the complement to the above changes:  <math>1 – [a+(b+c)x]</math>Δ<math>t</math>, ignoring intervals smaller then Δ<math>t</math>.
 (e)	The events are independent and the probability of more then one event in the interval is zero.
-Thus the probability that there are x-1 variants and a new variant arises or asserts itself against x-1 rivals is
+Thus the probability that there are <math>x-1</math> variants and a new variant arises or asserts itself against <math>x-1</math> rivals is
 	<math>a\triangle tP_{x-1}(t) + b(x-1)\triangle tP_{x-1}(t)</math>;
-the probability that there are x+1 variants and one dies is
+the probability that there are <math>x+1</math> variants and one dies is
 	<math>c(x+1)\triangle tP_{x+1}(t)</math>;
-the probability that nothing happens in Δt is
+the probability that nothing happens in Δ<math>t</math> is
 	<math>{{1-[a+(b+c)x]\triangle t}}P_x(t)</math>.
-Putting these probabilities together we obtain the probability that in the interval (t, t+Δt) there will be exactly x variants as
+Putting these probabilities together we obtain the probability that in the interval (<math>t</math>, <math>t</math>+Δ<math>t</math>) there will be exactly <math>x</math> variants as
 	<math>P_x(t+\triangle t) = [a+b(x-1)]\triangle tP_{x-1}(t) + c(x+1)\triangle tP_{x+1}(t) + {1-[a+(b+c)x]\triangle t}P_x(t)</math>.
-Substracting Px from both sides and dividing them by Δt, we obtain
+Substracting <math>P_x</math> from both sides and dividing them by Δ<math>t</math>, we obtain
 <math>\frac{P_x(t+\triangle t)-P_x(t)}{\triangle t}= [a+b(x-1)P_{x-1}(t)+c(x+1)P_{x+1}(t)-[a+(b+c)x]P_x(t)]</math>.
-Letting <math>\triangle t\rightarrow  0</math> we finally obtain
+Letting <math>\triangle t\rightarrow  0</math> we finally get
 <math>\frac{dP_x(t)}{dt}=[a+b(x-1)P_{x-1}(t)+c(x+1)P_{x+1}(t)-[a+(b+c)x]P_x(t)]</math>
@@ Line 148: / Line 148: @@
 and setting b/c = q and a/b = k results again in the negative binomial distribution
-(4)<math>P_x=\begin{pmatrix}k&+&x&-&1\\&&x\end{pmatrix}p^kq^x, \quad x=0,1,2,...</math>
+(4) <math>P_x=\begin{pmatrix}k&+&x&-&1\\&&x\end{pmatrix}p^kq^x, \quad x=0,1,2,...</math>
-For dialect maps, (4) is to be understood as the probability that the basic lexeme has x variants, i.e. if on a map there is only one unique form, then x = 0.
+For dialect maps, (4) is to be understood as the probability that the basic lexeme has <math>x</math> variants, i.e. if on a map there is only one unique form, then <math>x</math> = 0.
 '''Example:  Goebl´s law (dialectal diversification)'''
-Goebl (1984) studied the dialect maps of North West France and Italy and brought the distribution of the numbers of variants in the atlases. Since dialectal variants of a concept arise by a birth-and-death process, the number of maps containing x variants must follow the negative binomial distribution. One of these distributions is shown in Table 1 (Fig. 1).
+Goebl (1984) studied the dialect maps of North West France and Italy and brought the distribution of the numbers of variants in the atlases. Since dialectal variants of a concept arise by a birth-and-death process, the number of maps containing <math>x</math> variants must follow the negative binomial distribution. One of these distributions is shown in Table 1 (Fig. 1).
@@ Line 168: / Line 168: @@
 '''Example: Beöthy´s law (semantic diversification)'''
-According to this law ''the ranked frequencies of the elements of a semantic class are distributed according'' to (3) or (5) (see below). Rothe (1991c) brings a survey of semantic classes abiding by these laws. Testing has been perfomed for meanings of different Hungarian verbal prefixes (Beöthy, Altmann 1984a,b, 1991), Slovak verbal prefixes (Nemcová 1991), the Japanese postposition ni (Roos 1991), German compounds (Raether, Rothe 1991), the German particle ''von'' (Best 1991), the German preposition ''auf'' (Fuchs 1991), the English preposition ''in'' (Hennern 1991), the Polish preposition ''w'' (Hammerl, Sambor 1991), Russian conjunctions ''a'' and ''no'' (Kuße 1991), the French conjunction ''et'' (Rothe 1986), the German genitive (Rothe 1991b), word class distribution in Latin, German and Chinese (Schweers, Zhu 1991), in German (Best 1994, 1997b, 2000b, 2001e; Hammerl 1989; Judt 1995), in Arabic (Altmann 1991a), in Portuguese (Ziegler 1998, 2001), in French (Judt 1995), spelling errors by Japanese English-users (Rothe 1991), word building patterns in Early High German (Best 1990).
+According to this law ''the ranked frequencies of the elements of a semantic class are distributed according'' to (3) or (5) (see below). Rothe (1991c) brings a survey of semantic classes abiding by these laws. Testing has been perfomed for meanings of different Hungarian verbal prefixes (Beöthy, Altmann 1984a,b, 1991), Slovak verbal prefixes (Nemcová 1991), the Japanese postposition ni (Roos 1991), German compounds (Raether, Rothe 1991), the German particle ''von'' (Best 1991), the German preposition ''auf'' (Fuchs 1991), the English preposition ''in'' (Hennern 1991), the Polish preposition ''w'' (Hammerl, Sambor 1991), Russian conjunctions ''a'' and ''no'' (Kuße 1991), the French conjunction ''et'' (Rothe 1986), the German genitive (Rothe 1991b), word class distribution in Latin, German and Chinese (Schweers, Zhu 1991), in German (Best 1994, 1997b, 2000b, 2001e; Hammerl 1989; Judt 1995), in Arabic (Altmann 1991a), in Portuguese (Ziegler 1998, 2001), in French (Judt 1995), spelling errors by Japanese English-users (Rothe 1991c), word building patterns in Early High German (Best 1990).
 In the example (Table 2, Fig. 2) one finds the ranked distribution of German neologisms of the type “Noun + Noun” categorized in 13 groups from Raether, Rothe (1991).
@@ Line 184: / Line 184: @@
 Hřebíček used two assumptions:
 (i) The logarithm of the ratio of the probabilities <math>P_1</math> and <math>P_x</math> is proportional to the logarithm of the classe size, i.e

@@ Line 1: / Line 1: @@
 '''1. Problem and history'''
-Diversification is a process of enlarging the number of forms or meanings of any linguistic entity. It can be ''paradigmatic'', e.g. the rise of cases, numbers, tenses, etc., ''syntactic'', e.g. the rise of allophones, allomorphs etc., ''geographical'', e.g. the increase of different expressions of a concept, ''social'', e.g. the rise different words or meanings of a word or different pronunciations, ''idiolectal'' within a community, ''semantic'', e.g. the increase of synonymy and polysemy, ''contextual'', e.g. the increase of using a unit in different contexts. It comprises a number of phenomena dispersed in this volume.
+Diversification is a process of enlarging the number of forms or meanings of any linguistic entity. It can be ''paradigmatic'', e.g. the rise of cases, numbers, tenses, etc., ''phono-morphemic'', e.g. the rise of allophones, allomorphs etc., ''geographical'', e.g. the increase in the number of different expressions of a concept, ''social'', e.g. the rise of different words or meanings of a word or different pronunciations, ''idiolectal'' within a community, ''semantic'', e.g. the increase in synonymy and polysemy, ''contextual'', e.g. the increase in the usage of a unit in different contexts. Diversification comprises a number of phenomena dispersed in this volume.
 For the sake of illustration let us show some concrete examples:
@@ Line 7: / Line 7: @@
 (1)	The word can enlarge its class membership without any change, e.g. through conversion: “the hand”, “to hand”.
-(2)	The stem enlarges its class membership through derivation, e.g. German "Bild",       "bilden", "bildhaft", or vocalization in Semitic languages, etc.
+(2)	The stem enlarges its class membership through derivation, e.g. German "Bild", "bilden", "bildhaft", or vocalization in Semitic languages, etc.
 (3)	The stem can enlarge its applicability within one class through derivation e.g. German "Blut", "Blutung", "Bluter", or through vocalization, etc.
@@ Line 13: / Line 13: @@
 (4)	The stem can enlarge its applicability within one class through compounding e.g. "Blut", "Blutdruck", "Blutdurst", etc.
-(5)	If a language abandons the isolating morphology, then morphemes diversify into several morphs because of agglutination or inflection (sequential or syntactic dependence).
+(5)	If a language abandons isolating morphology, then morphemes diversify into several morphs because of agglutination or inflection (sequential or syntactic dependence).
 (6)	The word can enlarge its applicability in the sentence by acquiring several functions, i.e. it enlarges its dispositional properties, which are different from the constant grammatical properties, e.g. practically every word can become the subject of a sentence.
@@ Line 19: / Line 19: @@
 (7)	Verbs can enlarge their valence, i.e. their combinability with different cases.
-(8)	The word can enlarge its cotextuality (cf. Köhler 1986), i.e. its ability to occur in several contexts (where "context" can be defined in several ways). The reverse of this kind of diversification process is a part of style formation, where a "position" diversifies, i.e., a position in a given context can be filled with different units (words, sentences, etc.).
+(8)	The word can enlarge its cotextuality (cf. Köhler 1986), i.e. its ability to occur in several contexts (where "context" can be defined in several ways). The reverse of this kind of diversification process is part of style formation, where a "position" diversifies, i.e., a position in a given context can be filled with different units (words, sentences, etc.).
 (9)	A concept can be expressed by different forms, giving rise to dialects, sociolects, idiolects, or to synonymy.
@@ Line 28: / Line 28: @@
 Diversified entities abide by a ranking law, i.e. if the members of the diversified entity are ordered according to their frequency, then the frequencies are “lawfully” connected.
 The factors of diversification can be as follows (Altmann 2005):
@@ Line 36: / Line 37: @@
 (c)	''Conscious change'' through conscious creation, borrowing, emotionality etc.
-(d)	''Self-organisatory triggering'' of a process to a limit, causing changes in other levels, too.
+(d)	''Self-organisatory triggering'' of a process to a limit, causing changes on other levels, too.
 (e)	''System modification'' joined with local or global modifications in a subsystem,
 (f)	''Köhlerian requirements'' (Köhler 1986, 1987, 1989, 1990, 1991) forcing to take into account collateral pressures form different sides. They are as follows: (i) ''The trend for minimal coding and deciding effort'', (ii) ''sufficient redundancy'', (iii) ''the coding requirement in general'', (iv) ''context economy vs. context specificity'', and (v) ''invariance vs. flexibility of relation between expression and meaning.''
 The concepts of diversification and unification go back to G.K. Zipf (1935, 1949). Together they are called “Zipfian processes”. The scope of the phenomena is enormous. Semantic phenomena have been examined by Beöthy and Altmann (1984a,b, 1991), Altmann (1985a), Altmann, Best, Kind (1987); grammatical phenomena  were analyzed in the omnibus volume edited by Rothe (1991), where also a study on spelling errors in Japanese can be found, and dialectal diversification was studied by Altmann (1985b)
 The laws hold usually for ranked nominal classes of limited size.
@@ Line 65: / Line 68: @@
 '''3. Derivation'''
-'''3.1.   Altmann´s approach  A (1991).'''
+'''3.1.   Altmann´s approach A (1991).'''
-Since the entities are ranked and the corollary holds, it is true that for the probabilities of classes it holds that
+Because the entities are ranked and because of the corollary, it is true that for the probabilities of classes it holds that
 <math>P_x\le P_{x-1}</math>
-Since <math>P_x</math> and  <math>P_{x-1}</math> (x = 2,3,…) are joined in a law-like manner, we can write
+Since <math>P_x</math> and  <math>P_{x-1}</math> (<math>x</math> = 2,3,…) are joined in a law-like manner, we can write
 (1) <math>P_x=g(x)P_{x-1}\quad</math>, where <math>g(x)\le 1\quad</math>.

@@ Line 284: / Line 284: @@
 '''Best, K.-H.''' (2007). Diversifikation bei Eigennamen. In: Grzybek, P., Köhler, R. (eds.), ''Exact Methods in the Study of language and Text: 21-31''. Berlin: de Gruyter
 '''Brüers, N., Heeren, A.''' (2004). Plural-Allomorphe in Briefen Heinrich von Kleists. ''Glottometrics 7: 85-90.''
@@ Line 338: / Line 342: @@
 '''Kuße, H.''' (1991). A und no in N.M. Karamzins Pis´ma Russkogo Putesetvennika. In: Rothe, U. (ed.), ''Diversification processes in language: grammar: 173-182''. Hagen: Rottmann.
 '''Lánský, P., Radil-Weiss, T.''' (1980). A generalization of the Yule-Simon model, with special reference to word association tests and neural cell assembly formation. ''J. of Mathematical Psychology 21, 53-65''.
 '''Leopold, E.''' (1998). ''Stochastische Modellierung lexikalischer Evolutionsprozesse''. Hamburg: Kovač.
 '''Nemcová, E.''' (1991). Semantic diversification of Slovak verbal prefixes. In: Rothe, U. (ed.), ''Diversification processes in language: grammar: 67-74''. Hagen: Rottmann.
@@ Line 348: / Line 356: @@
 '''Pawlowski, A.''' (1999). The quantitative approach in cultural anthropology: Application of linguistic corpora in the analysis of basic colour terms. ''J. of Quantitative Linguistics 6, 222 234''.
 '''Raether, A., Rothe, U.''' (1991). Diversifikation der deutschen Komposita. In: Rothe, U. (ed.) ''1991: 85-91''.

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	'''Best, K.-H.''' (2001). Zur Gesetzmäßigkeit der Wortartenverteilungen in deutschen Pressetexten. ''Glottometrics 1, 1-26''.		'''Best, K.-H.''' (2001). Zur Gesetzmäßigkeit der Wortartenverteilungen in deutschen Pressetexten. ''Glottometrics 1, 1-26''.
		+
		+	'''Best, K.-H.''' (2003). ''Quantitative Linguistik: eine Annäherung.'' 2nd ed. Göttingen: Peust & Gutschmidt.
		+
		+	'''Best, K.-H.''' (2007). Diversifikation bei Eigennamen. In: Grzybek, P., Köhler, R. (eds.), ''Exact Methods in the Study of language and Text: 21-31''. Berlin: de Gruyter

	'''Brüers, N., Heeren, A.''' (2004). Plural-Allomorphe in Briefen Heinrich von Kleists. ''Glottometrics 7: 85-90.''		'''Brüers, N., Heeren, A.''' (2004). Plural-Allomorphe in Briefen Heinrich von Kleists. ''Glottometrics 7: 85-90.''

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	According to this law ''the ranked frequencies of the elements of a semantic class are distributed according'' to (3) or (5) (see below). Rothe (1991c) brings a survey of semantic classes abiding by these laws. Testing has been perfomed for meanings of different Hungarian verbal prefixes (Beöthy, Altmann 1984a,b, 1991), Slovak verbal prefixes (Nemcová 1991), the Japanese postposition ni (Roos 1991), German compounds (Raether, Rothe 1991), the German particle ''von'' (Best 1991), the German preposition ''auf'' (Fuchs 1991), the English preposition ''in'' (Hennern 1991), the Polish preposition ''w'' (Hammerl, Sambor 1991), Russian conjunctions ''a'' and ''no'' (Kuße 1991), the French conjunction ''et'' (Rothe 1986), the German genitive (Rothe 1991b), word class distribution in Latin, German and Chinese (Schweers, Zhu 1991), in German (Best 1994, 1997b, 2000b, 2001e; Hammerl 1989; Judt 1995), in Arabic (Altmann 1991a), in Portuguese (Ziegler 1998, 2001), in French (Judt 1995), spelling errors by Japanese English-users (Rothe 1991), word building patterns in Early High German (Best 1990).		According to this law ''the ranked frequencies of the elements of a semantic class are distributed according'' to (3) or (5) (see below). Rothe (1991c) brings a survey of semantic classes abiding by these laws. Testing has been perfomed for meanings of different Hungarian verbal prefixes (Beöthy, Altmann 1984a,b, 1991), Slovak verbal prefixes (Nemcová 1991), the Japanese postposition ni (Roos 1991), German compounds (Raether, Rothe 1991), the German particle ''von'' (Best 1991), the German preposition ''auf'' (Fuchs 1991), the English preposition ''in'' (Hennern 1991), the Polish preposition ''w'' (Hammerl, Sambor 1991), Russian conjunctions ''a'' and ''no'' (Kuße 1991), the French conjunction ''et'' (Rothe 1986), the German genitive (Rothe 1991b), word class distribution in Latin, German and Chinese (Schweers, Zhu 1991), in German (Best 1994, 1997b, 2000b, 2001e; Hammerl 1989; Judt 1995), in Arabic (Altmann 1991a), in Portuguese (Ziegler 1998, 2001), in French (Judt 1995), spelling errors by Japanese English-users (Rothe 1991), word building patterns in Early High German (Best 1990).
	In the example (Table 2, Fig. 2) one finds the ranked distribution of German neologisms of the type “Noun + Noun” categorized in 13 groups from Raether, Rothe (1991).		In the example (Table 2, Fig. 2) one finds the ranked distribution of German neologisms of the type “Noun + Noun” categorized in 13 groups from Raether, Rothe (1991).
−
−
−	~~<div align="center">Table 2</div>~~
−
−	~~<div align="center">Rank-frequency distribution of German neologisms “Noun+Noun” of different grammatical-semantical categories according to Raether, Rothe (1991)</div>~~

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		+
		+	<div align="center">[[Image:DivFig1.JPG]]</div>
		+	<div align="center">Fig. 1.Fitting the negative binomial distribution to Goebl´s data</div>

−	~~[[Image:DivFig1.JPG]]~~

−	~~Fig. 1.Fitting the negative binomial distribution to Goebl´s data~~

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+[[Image:Tabelle11_Div.jpg]]
 [[Image:DivFig1.JPG]]
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+<div align="center">[[Image:Tabelle2_Div.jpg ]]</div>
 The result shows that nominal classifications of language entities abide by this type of diversification law.
 <div align="center">[[Image:Grafik_2_Div.jpg]]</div>