# Reconstruction of Uncertain Historical Evolution of the Polysyllablization of Chinese Lexis

Authors: Bing Qiu; Jie Li
Journal: Journal of Applied Mathematics
 (2014)

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## Abstract

Polysyllablization, closely related to phonetics, semantics, and syntactics, is one of the fundamental trends
in the development of Chinese lexis. However, with lots of uncertainties in the historical evolution of Chinese language, the quantitative modeling and reconstruction of polysyllablization remain open questions. Based on theComprehensive Dictionary of Chinese Words, a mapping from the words to their time of occurrence is built. With the inverse mapping on random samples, the newly produced words with different numbers of syllables in different time periods are obtained. Finally the total quadratic variation minimization model is adopted to estimate the trend of polysyllablization. As a novel exploration in the computational linguistics, the results agree with the stage division of historical Chinese and answer some difficult questions related to polysyllablization in a quantitative manner.


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## Body

## 1. Introduction

Language is always changing [1]. The change of language is variation over time in a language’s lexical, phonetic, syntactic, and other features. Old English (from the mid-5th century to the mid-11th century), for instance, would be greatly different from Modern English (from the late 15th century to the present) [2]. Language changes in many and varied ways. It is interesting to note that lexical change is one of the most obvious and important types of language change. One may observe that new words are formed and old words are tagged as “obsolete.” Slang terms, in particular, come and go every few years. Consequently, as far as a long historical period is concerned, the variation of lexis is a complicated issue, which is not only fundamental to historical lexicology but also related to many research fields ranging from historical linguistics [3], onomasiology, etymology, to sociolinguistics [4].Polysyllablization is one of the fundamental trends in the development of Chinese lexis. It is a prevailing view nowadays in the academic circle that there are three stages in the evolution of Chinese [5–8], that is, Old Chinese, Middle Chinese, and Modern Chinese. Old Chinese was the commonly used language during the early and middle Zhou Dynasty [9] (around 1046–256 BC). Middle Chinese was the historical Chinese dialect which was phonologically recorded inQieyun [10, 11], a rime dictionary first published in 601. Modern Chinese is mainly referred to as the form of Chinese varieties to the present. However, the boundaries of these stages are ambiguous. The periods between them are transitional phases. The vocabulary system of Old Chinese mainly consists of monosyllabic (i.e., single syllable) words, whereas that of Modern Chinese is mainly made up of polysyllabic (i.e., two or more syllables) words. The aforementioned evolution of Chinese lexis is called polysyllablization. Since each Chinese character represents a monosyllabic Chinese word or a morpheme, polysyllablization in the historical evolution of Chinese not only introduces the form expansion of words but also represents the combination of morphemes and meanings and depicts the coordination of grammatical relations, which reflect the inherent laws of Chinese phonetics, semantics, and syntactics. In addition, the importance of syllables in Chinese lies in their link to word recognition [12, 13]. Therefore, polysyllablization is one of the most principal research topics of Chinese language, which has attracted lots of attention from the academia.Most of the traditional studies on the polysyllablization of Chinese lexis are qualitative, of which the conclusions are mainly based on personal experiences. In fact, the difference in the number of syllables between Old Chinese words and Modern Chinese words is obvious and easy to be noticed. However, the following questions are not easy to answer based on the qualitative conclusions.(i)
What was the quantitative degree of polysyllablization during a certain period, for example, Qin or Han Dynasty? When did the polysyllabic words begin to occupy a major position in the vocabulary system?(ii)
What was the speed of polysyllablization at a certain time point? When was the lexis polysyllablized most rapidly?(iii)
How were the evolving trends for different kinds of polysyllabic words (i.e., disyllabic words, three-syllable words and so forth)?As a result, the related studies in recent years have put a particular emphasis on the adoption of quantitative methods. They usually focus on a specific range of language materials, for example, a specific chapter, a specific book, or all the books of a specific author. For these limited language materials, the numbers of monosyllabic words, polysyllabic words, and total words have been counted. The ratio of the number of polysyllabic words to that of total words, namely, polysyllabic word ratio, is then adopted to evaluate the degree of polysyllablization. In a sense, polysyllablization is studied in a quantitative manner. Although the statistics on the polysyllabic words in a specific range of language materials are closely related to polysyllablization, it is not the polysyllablization itself. The polysyllabic word ratio of a specific range of language materials seriously depends on the selected topic, the author’s habit, and the length of the corresponding text materials, so it is only a local weight of polysyllabic words and cannot represent the global degrees of polysyllablization. However, it is indeed very difficult to count all words of various numbers of syllables through different time periods for the purpose of depicting the trend of polysyllablization.The lexis, that is, the vocabulary system, of a language is related to many complex and dynamic features with lots of uncertainties. It is often very difficult to construct a mathematical model. To the best of our knowledge, the quantitative evaluation and modeling of the polysyllablization of Chinese are still open questions.Hanyu Da Cidian [14] (literallyComprehensive Dictionary of Chinese Words, abbreviated asCDCW in the following text) is the most inclusive Chinese dictionary available. It has a diachronic coverage of the Chinese language, tracing its usage over three thousand years from Chinese classic texts to modern slangs. Researchers useCDCW as a reference book to search and examine specific words and develop related lexicological studies. At the macrolevel, however, the enormous amounts of information inCDCW have not yet been effectively mined. To draw an analogy, if we compareCDCW to a building, the existing studies are focusing on the bricks; however, the structure of the building as a whole has been neglected. The data mining ofCDCW provides us with a novel approach to tackle the polysyllablization of Chinese language.This paper aims to answer the aforementioned open questions related to polysyllablization. In particular, our contribution lies mainly in the following aspects.(i)
We propose a novel approach based onCDCW to study polysyllablization of the Chinese lexis in a quantitative and impersonal manner. The words inCDCW, as a whole, are regarded as the maximum vocabulary so far. We can obtain the time of occurrence for each word inCDCW. Once a mapping from the words to their time of occurrence is built, the inverse mapping leads us to the newly produced words with different numbers of syllables in different time periods.(ii)
We introduce several techniques in the practical workflow to handle various uncertainties, including the repetitions and exceptions in the entries ofCDCW and inaccuracy of mapping from words to their time of occurrence. The statistical sampling method is adopted to avoid the huge workload to process hundreds of thousands of words. The total quadratic variation minimization model is adopted to estimate the trend of polysyllablization.(iii)
We obtain the statistical data and finally present the trend of polysyllablization of the Chinese lexis. We also discuss the results through comparison with the existing conclusions. As a novel exploration in the computational linguistics, especially for the Chinese language with such a long history and such a complex evolution, our approach is valuable to similar issues.The rest of this paper is organized as follows: Section2 briefly reviews related works. Section 3 introduces the formulation and the mathematical model. Section 4 presents the results and discusses the trends of polysyllablization. Finally, Section 5 concludes this paper.


## 2. Related Works

Since polysyllablization is among the most important rules in the development of Chinese vocabulary, in recent years, studies on Chinese polysyllabic words and polysyllablization have achieved rich results. For example, the syllabic structure of Mandarin Chinese is discussed in [15] based on the X-bar approach. From the viewpoint of the Buddhist and Taoist scriptures of Eastern Han Dynasty, the polysyllablization of Chinese vocabulary based on the new lexical items is discussed in [16]. Since most of polysyllabic words are disyllabic words, the development of disyllabic words in Chinese is discussed in [17]. Also, many quantitative surveys and analyses have been conducted on polysyllabic words in different monographs across different time periods. According to the statistics in [18], published papers on the vocabulary in Middle Chinese and Early Modern Chinese monographs have amounted to over 6,000. Generally, without uniform standards, scholars differ from each other on their subjective definitions of polysyllabic words; as a result, they have obtained different statistical results about the number of the polysyllabic words in the same monograph. TakeShi Shuo Xin Yu (literallyA New Account of the Tales of the World) for example, the number of polysyllabic words in it was said to be around 1,500 to 2,100 in different conclusions. Besides, due to the limitations of the subject, content, length of the book, and the authors mastery over the language, the vocabulary in one monograph alone cannot fully represent the complete picture of the its contemporary vocabulary system; as a matter of fact, sometimes there could be a great deviation. In other words, monographs are theme-based and scope-limited, so they can only reflect the vocabulary system from a restricted view rather than represent the whole. So far, many questions still remain unanswered, such as how polysyllablization evolved in the history of the Chinese vocabulary system.CDCW is among the most important dictionaries in Chinese lexicological studies. Since the publication of its first volume in 1986, it has been put into wide academic application and achieved plentiful research results.CDCW has 50 million characters, containing 22.7 thousand Chinese characters and 375 thousand polysyllabic words. Wenkan Xu, one of the editorial board members ofCDCW, said “Before the publishing ofCDCW, there was no such a dictionary which contains both modern and ancient words, as well as words that were developed intermediately, and proves itself to be a confluence of the entire Chinese vocabulary, for the purpose of search and reference” (translated from Chinese according to [19]). Thus it is feasible for researchers either to observe the change of a single word from a diachronic perspective or to observe the semantic structure of a group of words from a synchronic perspective. Additionally, such a large-scale historical Chinese dictionary, which collects, organizes, and explains hundreds of thousands of ancient and modern words, is a very valuable corpus itself. Corpus linguistics is one of the most important fields nowadays [20].CDCW is undoubtedly a huge corpus, and the reasonable utilization ofCDCW will probably lead us to a novel approach, excluding the subjective prejudice of the researchers, to tackle the polysyllablization of Chinese.


## 3. Formulation and Mathematical Model

The vocabulary system has two characteristics, namely, integrity and dynamics. Integrity means that the vocabulary system is a macrolevel concept and refers to the sum of all the words in the language. Dynamics means that the vocabulary changes over time. Equivalently, new words appear and old words fade. Thus, in order to illustrate the polysyllablization of Chinese lexis, two key issues must be solved in accordance with these two characteristics of the vocabulary system. The first issue is to obtain the complete set of the words from Old Chinese to Modern Chinese. The second one is to determine the first-appearing and last-appearing time points of each word.Unlike the English text in which sentences are sequences of words delimited by spaces, the word boundary in Chinese is fuzzy. A Chinese word may consist of one, two, or more Chinese characters (also referred to asHanzi). There is no immediate way of deciding which characters in the text should be grouped into words. The studies on word segmentation have attracted lots of attention from the academia [21–23]. Once the words are obtained, the numbers of syllables are easy to be counted.To assert the first-appearing and last-appearing time points of each word is complicated. A group of Chinese characters is possibly treated as a word at some time, but not considered as a word at another time. There are also various criteria to decide whether a group of characters is a word, most of which are personally prejudiced with lots of uncertainties.We introduce a novel method to solve the aforementioned issues and analyze the polysyllablization of Chinese lexis in an impersonal and quantitative manner based on the data mining ofCDCW. Briefly, we build a mapping from the words to their time of occurrence. The inverse mapping is used to count the newly formed words over different time periods. However, there are still lots of uncertainties to deal with. Thus we introduce a total quadratic variation minimization model and some related techniques to estimate the polysyllablization of Chinese lexis. The aforementioned issues finally lead to a constrained quadratic programming problem. The details are as follows.


### 3.1. Basic Idea

CDCW is the archive of Chinese vocabulary over time, containing 22.7 thousand Chinese characters (most of them are monosyllabic words) and 375 thousand polysyllabic words. Based on the entries ofCDCW, the whole set of Chinese words over time can be obtained.The structure of hundreds of thousands of entries inCDCW contains rich information and reflects many lexicological rules when examined at the macrolevel. Each entry has multiple properties, such as its pronunciation and explanation, which are directly listed inCDCW. In fact, more properties can be obtained indirectly with additional procedures. Among the indirect properties, the time of occurrence, which indicates when the word emerged, is of great significance to the studies of historical lexicology.InCDCW, the definition of an entry usually contains several terms of meanings, most of which can be traced back to their earliest reference through the documentary evidences provided byCDCW. As long as the approximate time when the documentaries were published or the years when their authors lived are possible to be acquired, we will be able to date all the documentaries available for each term of meanings for the word entry, the earliest one of them reveals the time of occurrence of the word, that is, the time when the word emerged. Note thatCDCW is a result of collective wisdom of more than 1000 scholars. Thus it offers us an authoritative and impersonal manner to deduce the time of occurrence for each word.Here is an example to illustrate the procedure from the entry to its time of occurrence. For the word entrySenlin (Chinese word, literally, forest; here Chinese charactersSen andLin both mean trees or woods), there is only one term of meaning. The earliest documentary evidence is a poem in Tang Dynasty. Thus, it is deduced that the wordSenlin was composited during Tang Dynasty. We also know the author, Xiji Cai, served as a junior officer in Luoyang City in 748. However, we know neither the exact year when he wrote the poem nor the birth year of him.The inaccuracy in defining the publishing time of the ancient documentaries is not occasional. In fact, limited by the records of ancient history literatures, the exact years of the publication of ancient documentaries or even the exact living years of the related authors are difficult to resolve. For most of ancient documentaries, we only know the dynasties of their publication.Figure1 is a diagram showing how to investigate the time of occurrence entry by entry inCDCW. Suppose that the earliest documentary evidence for Entry 1 is found in Wei Dynasty, then its time of occurrence can be determined to be Wei Dynasty and it will be put under the corresponding chronological category. The same procedure applies to the rest of the entries. In theory, following this method, the time of occurrence for all entries can be determined exhaustively.Figure 1
Determining the time of occurrence per word entry by the earliest textual evidence withCDCW.The above process is to determine the time of occurrence per word entry by exploring its earliest documentary evidence. However, in order to observe the dynamic evolution of the vocabulary system at the macrolevel, it is necessary to conduct another survey from the opposite direction, that is, to investigate words which occurred in the same time period. By gathering all words which share the same time span of occurrence inCDCW, we can obtain all the new words that emerged in the corresponding time period.The evolution of the vocabulary system is a metabolic process. On one hand, new words have been emerging constantly and entering the vocabulary system; on the other hand, some old words have been withering away and falling out of the vocabulary system. The emergence of new words usually reflects the reform of the society, the occurrence of new things, the transformation of concepts, the evolution of the language itself, and so forth. The emergence of new words is an active and positive factor in the development of the vocabulary system and constitutes the subject of most lexicological studies. In fact, even when we talk about the fading of the old words, they do not completely exit but still exist as a historical preservation in the vocabulary system. Considering that the emergence of new words takes a much more important position than the extinction of old words, we can obtain the general trend of the diachronic evolution of Chinese vocabulary system at the macrolevel by investigating the new words categorized in different time periods according to their time of occurrence inCDCW.Admittedly, omissions of entries and presence of errors can be found inCDCW, and it is also true thatCDCW cannot include all the new words in a given time period. However, the definitions and explanations of words inCDCW are the concerted efforts of a great number of researchers and scholars, and the defects and mistakes in it only account for a trivial proportion in the total number of its entries. As the “archives of ancient and modern Chinese vocabulary,”CDCW remains one of the most authoritative dictionaries. Therefore, it is not only feasible, but also conducive to excluding the subjective prejudice of the researchers and to use the time of occurrence per entry inCDCW for reference when studying the diachronic evolution of the Chinese vocabulary system.Theoretically speaking, it is possible to exhaustively obtain the time of occurrence of all word entries inCDCW. However, considering the fact thatCDCW contains as many as over 300 thousand entries, it would be too much work to analyze all the entries. Therefore, in the present study, under the guidance of statistical sampling theory, we only draw a moderate number of sample entries and then deduce the overall quantitative characteristics of the population.


### 3.2.  Formulation under Ideal Condition

LetW denote the word set for the Chinese lexis, from Old Chinese to Modern Chinese. An element w∈W is a Chinese word. The subsets of monosyllabic words, disyllabic words, and three-or-more-syllable (i.e., ≥3 syllables) words are written as W(1), W(2), and W(3+), respectively. The subset of polysyllabic words is written as W(2+) and satisfies W(2+)=W(2)∪W(3+). Notice that disyllabic words are processed independently because disyllabic words are extremely important in Chinese. Let the cardinality of a set be denoted as |·|. Thus the total number of the words is represented as N=|W|. Likewise, the number of words in W(1) is denoted as N(1)=|W(1)| and so forth.LetT represent the time (using year as the unit of time) for the evolution of Chinese language, which is in fact a range of integer number from tb to te. The time length in years of T is given by ∥T∥=te-tb+1.As illustrated in Figure1, there exists a function f which relates each word w∈W to its time of occurrence t=f(w)∈T. With the denotation, f-1(t) represents all the words which first occurred in the year t. The symbol nt=|f-1(t)| represents the total number of the words which first occurred in the year t. Considering that nt is the number of the newly formed words in the year t, we define it as the speed of new word production.The sequence{nt} constitutes a time series. Its partial sum sequence {ct} is the cumulative number of all the words which first occurred in or before the year t, satisfying
(1)ct=ctb-+∑τ=tbt‍nτ.
Here, ctb- means the initial cumulative number of all the words before time tb.In addition, letf|U:U→T denote the restriction of f to the subset U of its domain W, which is defined by the same rule as f but with a smaller domain set U. Thus, nt(1)=|f|W(1)-1(t)| represents the total number of the monosyllabic words which first occurred in the year t. Likewise, we have nt(2), nt(3+) and also their partial sum ct(2), ct(3+), and so forth.We introduce two indexes to evaluate the trend of polysyllablization. The first is the speed of new word production for polysyllabic words, which is, namely,nt(2+). It is in fact the number of the newly formed polysyllabic words per year and indicates how fast the new polysyllabic words are generated into the vocabulary system. The second index is named the polysyllablization degree index (PDI). It is the ratio of the cumulative number of the polysyllabic words to that of all the words at the time t, and indicates the weight of the polysyllabic words in the then vocabulary system, which is defined as
(2)PDI(t)≜ct(2+)ct.


### 3.3. Modeling with Uncertainties

However, there are still lots of uncertainties in the aforementioned formulation.Firstly, there are a small amount of repetitions and exceptions in the entries inCDCW. The repetitions mean that two entries have different forms but the same meanings, which is similar to the case “color” and “colour” in English. Basically, they are just different forms of one word and should be counted as one word only. The exceptions mean that some entries are not valid Chinese words, such as the Japanese characters included inCDCW. Thus, the set of the whole entries ofCDCW, E, is a superset of W; that is, W⊂E. The total number of entries in E is greater than that in W. The invalid entries, including repetitions and exceptions, should be preprocessed.Secondly, there are above 300 thousand of entries inCDCW. They are too many to be handled one by one. The feasible way is to handle part of them with the statistical sampling method, which subsequently introduces probabilistic uncertainty. Assuming that we take a certain number of samples which are uniformly randomly chosen from the entries ofCDCW, the set of the sampled entries is denoted as Es, in which the set of valid entries (i.e., words) is denoted as Ws.Based on the samples, the total number of word inCDCW can be estimated by
(3)N^=|W|^=|Ws||Es|·|E|=|E||Es|·|Ws|=K·|Ws|.
Here K is a constant factor and equals |E|/|Es|.Furthermore, the sequence{nt} can be estimated by the restriction of f to the subset Ws, which is similarly given by
(4)n^t=K·|f|Ws-1(t)|.
The cases to estimate n^t(1), c^t, and so on are similar and not listed here.Thirdly, the precise value of the functionf is usually difficult to decide. For most of the words, we can only know the dynasty of its occurrence rather than the time (accurate to year) of its occurrence. Thus the inaccuracy of time of occurrence will introduce lots of uncertainties.Now consider that the setT can be divided into several segments, mathematically speaking, T can be expressed as the union of a number of disjoint sets Di (1≤i≤nd) as follows:
(5)T=⋃1≤i≤nd‍Di,
where Di is a set of consecutive integers beginning with tb(i) and ending with te(i), that is, an integer interval with notation [tb(i)⋯te(i)]. The symbol nd represents the number of the segments. Let D denote the set {D1,D2,…,Dnd}.In fact,Di represents a dynasty or a similar time period in Chinese history. Such partitions are caused by the uncertainty of the mapping from the words to their times of occurrence. The exact time of occurrence of many words is difficult or even impossible to resolve due to the obscureness in the ancient documentaries. Since dates are usually written in dynasties or reign titles in the ancient Chinese literatures, the exact dynasties (or time segments) can be determined for the first occurrence of many words. Thus the dynasties are the ordinary and natural implementation of the time segments.Without loss of generality, we assume that the segmentsDi are sorted by the lower endpoint, which satisfies
(6)tb1=tb,tei+1=tbi+1,where1≤i≤nd-1,tend=te.The rough version of the functionf, which only maps from the word set W to the set of time segments (usually, dynasties) D, is written by
(7)g:W⟶D
and satisfies
(8)g(w)=d⟺f(w)∈d.Since the precise mapping from the words to their time of occurrence is usually unknown in the actual operation, we must estimate the parameters related to polysyllablization with the rough functiong. It can be noted that g-1(Di) represents all the words which firstly occurred in the time segment Di. In fact, there exits the following relation:
(9)g-1(Di)=⋃τ∈Di‍f-1(τ),where1≤i≤nd.Now thatf-1(τ) and f-1(ν) are disjoint sets if τ≠ν, we have
(10)di=|g-1(Di)|=∑τ∈Di‍|f-1(τ)|=∑τ∈Di‍nτ,00000000000000000where1≤i≤nd.
Here, di represents the number of all the words which first occurred in the time segment Di.Based on the statistical sampling, the sequence{di} can be estimated by the restriction of g to the subset Ws, which is similarly given by
(11)d^i=K·|g|Ws-1(t)|.
Let di(1) be the number of all the monosyllabic words which first occurred in the time segment Di and so on. The cases to estimate di(1), dt(2), and so forth are similar and not listed here.Language changes over time. As a complex social phenomenon, language may change smoothly or unstably. We know little about the actual trends of the evolution of language. Without any prior knowledge or assumption, we will build a total variation minimization model [24, 25] for the evolution of the language. Other methods, such as maximum entropy [26, 27] method for the time series, should also be feasible and constructive. However, only the total variation minimization model is discussed in this paper, since it is simply based on the assumption that the language of today is not far from that of yesterday. Thus it is probably one of the safest estimation methods to start our exploration in such an open research field.The total quadratic variation for a sequencex={xi}(1≤i≤n) is defined as
(12)V(x)≜∑i=1n-1‍(xi+1-xi)2.Our technique to estimate the sequencesnt(1), nt(2), and nt(3+) are similar. Generally, the case for the sequence nt(*) is illustrated as follows, in which the symbol “*” can be replaced by any one of the symbols including “1,” “2,” or “3+.” Basically, the issue to estimate the sequence nt(*) is equivalent to a constrained optimization problem as follows:
(13)minimizeV(n(*))=∑τ=tbte‍(ni+1(*)-ni(*))2subjecttont(*)≥0,wheretb≤t≤te,∑τ=tb(i)te(i)‍nτ(*)=di*,where1≤i≤nd.Here, the latter constraints can be similarly deduced as (10). Such a constrained optimization problem is a quadratic programming problem, which belongs to a relatively mature area and there are kinds of feasible techniques [28–30] to handle it. The problem can be solved in polynomial time with the ellipsoid method [31].


### 3.4. Work Flow

There are a series of steps to evaluate polysyllablization of the Chinese lexis based onCDCW in practice.(1)
Decide the endpoints of the timeT and split the whole time into segments Di.(2)
Obtain the setE of the whole entries ofCDCW and classify the set E into E(1), E(2), and E(3+) by the number of syllables of each entry.(3)
Draw appropriate samples of entries, that is,Es(1), Es(2), and Es(3+) from the sets E(1), E(2), and E(3+), respectively.(4)
Check each elemente in the sets Ew(1), Es(2), and Es(3+) to obtain the sets of word samples, Ws(1), Ws(2), and Ws(3+).(5)
Estimate the total number of monosyllabic wordsN^(1). Estimate N^(2), N^(3+) in the same way. Calculate the total number of words N^=N^(1)+N^(2)+N^(3+).(6)
Map each word inWs(1), Ws(2), and Ws(3+) to its time of occurrence.(7)
Count the number of words in the same time segment and estimated^i(1), d^i(2), and d^i(3+) according to (11).(8)
Solve the quadratic programming problem to obtain the estimationn^t(1), n^t(2), and n^t(3+).(9)
Calculaten^t(2+)=n^t(2)+n^t(3+) and n^t=n^t(1)+n^t(2+). Also, calculate their partial sum sequences.(10)
Calculate the indexes to evaluate the trend of polysyllablization.


## 3.1. Basic Idea

CDCW is the archive of Chinese vocabulary over time, containing 22.7 thousand Chinese characters (most of them are monosyllabic words) and 375 thousand polysyllabic words. Based on the entries ofCDCW, the whole set of Chinese words over time can be obtained.The structure of hundreds of thousands of entries inCDCW contains rich information and reflects many lexicological rules when examined at the macrolevel. Each entry has multiple properties, such as its pronunciation and explanation, which are directly listed inCDCW. In fact, more properties can be obtained indirectly with additional procedures. Among the indirect properties, the time of occurrence, which indicates when the word emerged, is of great significance to the studies of historical lexicology.InCDCW, the definition of an entry usually contains several terms of meanings, most of which can be traced back to their earliest reference through the documentary evidences provided byCDCW. As long as the approximate time when the documentaries were published or the years when their authors lived are possible to be acquired, we will be able to date all the documentaries available for each term of meanings for the word entry, the earliest one of them reveals the time of occurrence of the word, that is, the time when the word emerged. Note thatCDCW is a result of collective wisdom of more than 1000 scholars. Thus it offers us an authoritative and impersonal manner to deduce the time of occurrence for each word.Here is an example to illustrate the procedure from the entry to its time of occurrence. For the word entrySenlin (Chinese word, literally, forest; here Chinese charactersSen andLin both mean trees or woods), there is only one term of meaning. The earliest documentary evidence is a poem in Tang Dynasty. Thus, it is deduced that the wordSenlin was composited during Tang Dynasty. We also know the author, Xiji Cai, served as a junior officer in Luoyang City in 748. However, we know neither the exact year when he wrote the poem nor the birth year of him.The inaccuracy in defining the publishing time of the ancient documentaries is not occasional. In fact, limited by the records of ancient history literatures, the exact years of the publication of ancient documentaries or even the exact living years of the related authors are difficult to resolve. For most of ancient documentaries, we only know the dynasties of their publication.Figure1 is a diagram showing how to investigate the time of occurrence entry by entry inCDCW. Suppose that the earliest documentary evidence for Entry 1 is found in Wei Dynasty, then its time of occurrence can be determined to be Wei Dynasty and it will be put under the corresponding chronological category. The same procedure applies to the rest of the entries. In theory, following this method, the time of occurrence for all entries can be determined exhaustively.Figure 1
Determining the time of occurrence per word entry by the earliest textual evidence withCDCW.The above process is to determine the time of occurrence per word entry by exploring its earliest documentary evidence. However, in order to observe the dynamic evolution of the vocabulary system at the macrolevel, it is necessary to conduct another survey from the opposite direction, that is, to investigate words which occurred in the same time period. By gathering all words which share the same time span of occurrence inCDCW, we can obtain all the new words that emerged in the corresponding time period.The evolution of the vocabulary system is a metabolic process. On one hand, new words have been emerging constantly and entering the vocabulary system; on the other hand, some old words have been withering away and falling out of the vocabulary system. The emergence of new words usually reflects the reform of the society, the occurrence of new things, the transformation of concepts, the evolution of the language itself, and so forth. The emergence of new words is an active and positive factor in the development of the vocabulary system and constitutes the subject of most lexicological studies. In fact, even when we talk about the fading of the old words, they do not completely exit but still exist as a historical preservation in the vocabulary system. Considering that the emergence of new words takes a much more important position than the extinction of old words, we can obtain the general trend of the diachronic evolution of Chinese vocabulary system at the macrolevel by investigating the new words categorized in different time periods according to their time of occurrence inCDCW.Admittedly, omissions of entries and presence of errors can be found inCDCW, and it is also true thatCDCW cannot include all the new words in a given time period. However, the definitions and explanations of words inCDCW are the concerted efforts of a great number of researchers and scholars, and the defects and mistakes in it only account for a trivial proportion in the total number of its entries. As the “archives of ancient and modern Chinese vocabulary,”CDCW remains one of the most authoritative dictionaries. Therefore, it is not only feasible, but also conducive to excluding the subjective prejudice of the researchers and to use the time of occurrence per entry inCDCW for reference when studying the diachronic evolution of the Chinese vocabulary system.Theoretically speaking, it is possible to exhaustively obtain the time of occurrence of all word entries inCDCW. However, considering the fact thatCDCW contains as many as over 300 thousand entries, it would be too much work to analyze all the entries. Therefore, in the present study, under the guidance of statistical sampling theory, we only draw a moderate number of sample entries and then deduce the overall quantitative characteristics of the population.


## 3.2.  Formulation under Ideal Condition

LetW denote the word set for the Chinese lexis, from Old Chinese to Modern Chinese. An element w∈W is a Chinese word. The subsets of monosyllabic words, disyllabic words, and three-or-more-syllable (i.e., ≥3 syllables) words are written as W(1), W(2), and W(3+), respectively. The subset of polysyllabic words is written as W(2+) and satisfies W(2+)=W(2)∪W(3+). Notice that disyllabic words are processed independently because disyllabic words are extremely important in Chinese. Let the cardinality of a set be denoted as |·|. Thus the total number of the words is represented as N=|W|. Likewise, the number of words in W(1) is denoted as N(1)=|W(1)| and so forth.LetT represent the time (using year as the unit of time) for the evolution of Chinese language, which is in fact a range of integer number from tb to te. The time length in years of T is given by ∥T∥=te-tb+1.As illustrated in Figure1, there exists a function f which relates each word w∈W to its time of occurrence t=f(w)∈T. With the denotation, f-1(t) represents all the words which first occurred in the year t. The symbol nt=|f-1(t)| represents the total number of the words which first occurred in the year t. Considering that nt is the number of the newly formed words in the year t, we define it as the speed of new word production.The sequence{nt} constitutes a time series. Its partial sum sequence {ct} is the cumulative number of all the words which first occurred in or before the year t, satisfying
(1)ct=ctb-+∑τ=tbt‍nτ.
Here, ctb- means the initial cumulative number of all the words before time tb.In addition, letf|U:U→T denote the restriction of f to the subset U of its domain W, which is defined by the same rule as f but with a smaller domain set U. Thus, nt(1)=|f|W(1)-1(t)| represents the total number of the monosyllabic words which first occurred in the year t. Likewise, we have nt(2), nt(3+) and also their partial sum ct(2), ct(3+), and so forth.We introduce two indexes to evaluate the trend of polysyllablization. The first is the speed of new word production for polysyllabic words, which is, namely,nt(2+). It is in fact the number of the newly formed polysyllabic words per year and indicates how fast the new polysyllabic words are generated into the vocabulary system. The second index is named the polysyllablization degree index (PDI). It is the ratio of the cumulative number of the polysyllabic words to that of all the words at the time t, and indicates the weight of the polysyllabic words in the then vocabulary system, which is defined as
(2)PDI(t)≜ct(2+)ct.


## 3.3. Modeling with Uncertainties

However, there are still lots of uncertainties in the aforementioned formulation.Firstly, there are a small amount of repetitions and exceptions in the entries inCDCW. The repetitions mean that two entries have different forms but the same meanings, which is similar to the case “color” and “colour” in English. Basically, they are just different forms of one word and should be counted as one word only. The exceptions mean that some entries are not valid Chinese words, such as the Japanese characters included inCDCW. Thus, the set of the whole entries ofCDCW, E, is a superset of W; that is, W⊂E. The total number of entries in E is greater than that in W. The invalid entries, including repetitions and exceptions, should be preprocessed.Secondly, there are above 300 thousand of entries inCDCW. They are too many to be handled one by one. The feasible way is to handle part of them with the statistical sampling method, which subsequently introduces probabilistic uncertainty. Assuming that we take a certain number of samples which are uniformly randomly chosen from the entries ofCDCW, the set of the sampled entries is denoted as Es, in which the set of valid entries (i.e., words) is denoted as Ws.Based on the samples, the total number of word inCDCW can be estimated by
(3)N^=|W|^=|Ws||Es|·|E|=|E||Es|·|Ws|=K·|Ws|.
Here K is a constant factor and equals |E|/|Es|.Furthermore, the sequence{nt} can be estimated by the restriction of f to the subset Ws, which is similarly given by
(4)n^t=K·|f|Ws-1(t)|.
The cases to estimate n^t(1), c^t, and so on are similar and not listed here.Thirdly, the precise value of the functionf is usually difficult to decide. For most of the words, we can only know the dynasty of its occurrence rather than the time (accurate to year) of its occurrence. Thus the inaccuracy of time of occurrence will introduce lots of uncertainties.Now consider that the setT can be divided into several segments, mathematically speaking, T can be expressed as the union of a number of disjoint sets Di (1≤i≤nd) as follows:
(5)T=⋃1≤i≤nd‍Di,
where Di is a set of consecutive integers beginning with tb(i) and ending with te(i), that is, an integer interval with notation [tb(i)⋯te(i)]. The symbol nd represents the number of the segments. Let D denote the set {D1,D2,…,Dnd}.In fact,Di represents a dynasty or a similar time period in Chinese history. Such partitions are caused by the uncertainty of the mapping from the words to their times of occurrence. The exact time of occurrence of many words is difficult or even impossible to resolve due to the obscureness in the ancient documentaries. Since dates are usually written in dynasties or reign titles in the ancient Chinese literatures, the exact dynasties (or time segments) can be determined for the first occurrence of many words. Thus the dynasties are the ordinary and natural implementation of the time segments.Without loss of generality, we assume that the segmentsDi are sorted by the lower endpoint, which satisfies
(6)tb1=tb,tei+1=tbi+1,where1≤i≤nd-1,tend=te.The rough version of the functionf, which only maps from the word set W to the set of time segments (usually, dynasties) D, is written by
(7)g:W⟶D
and satisfies
(8)g(w)=d⟺f(w)∈d.Since the precise mapping from the words to their time of occurrence is usually unknown in the actual operation, we must estimate the parameters related to polysyllablization with the rough functiong. It can be noted that g-1(Di) represents all the words which firstly occurred in the time segment Di. In fact, there exits the following relation:
(9)g-1(Di)=⋃τ∈Di‍f-1(τ),where1≤i≤nd.Now thatf-1(τ) and f-1(ν) are disjoint sets if τ≠ν, we have
(10)di=|g-1(Di)|=∑τ∈Di‍|f-1(τ)|=∑τ∈Di‍nτ,00000000000000000where1≤i≤nd.
Here, di represents the number of all the words which first occurred in the time segment Di.Based on the statistical sampling, the sequence{di} can be estimated by the restriction of g to the subset Ws, which is similarly given by
(11)d^i=K·|g|Ws-1(t)|.
Let di(1) be the number of all the monosyllabic words which first occurred in the time segment Di and so on. The cases to estimate di(1), dt(2), and so forth are similar and not listed here.Language changes over time. As a complex social phenomenon, language may change smoothly or unstably. We know little about the actual trends of the evolution of language. Without any prior knowledge or assumption, we will build a total variation minimization model [24, 25] for the evolution of the language. Other methods, such as maximum entropy [26, 27] method for the time series, should also be feasible and constructive. However, only the total variation minimization model is discussed in this paper, since it is simply based on the assumption that the language of today is not far from that of yesterday. Thus it is probably one of the safest estimation methods to start our exploration in such an open research field.The total quadratic variation for a sequencex={xi}(1≤i≤n) is defined as
(12)V(x)≜∑i=1n-1‍(xi+1-xi)2.Our technique to estimate the sequencesnt(1), nt(2), and nt(3+) are similar. Generally, the case for the sequence nt(*) is illustrated as follows, in which the symbol “*” can be replaced by any one of the symbols including “1,” “2,” or “3+.” Basically, the issue to estimate the sequence nt(*) is equivalent to a constrained optimization problem as follows:
(13)minimizeV(n(*))=∑τ=tbte‍(ni+1(*)-ni(*))2subjecttont(*)≥0,wheretb≤t≤te,∑τ=tb(i)te(i)‍nτ(*)=di*,where1≤i≤nd.Here, the latter constraints can be similarly deduced as (10). Such a constrained optimization problem is a quadratic programming problem, which belongs to a relatively mature area and there are kinds of feasible techniques [28–30] to handle it. The problem can be solved in polynomial time with the ellipsoid method [31].


## 3.4. Work Flow

There are a series of steps to evaluate polysyllablization of the Chinese lexis based onCDCW in practice.(1)
Decide the endpoints of the timeT and split the whole time into segments Di.(2)
Obtain the setE of the whole entries ofCDCW and classify the set E into E(1), E(2), and E(3+) by the number of syllables of each entry.(3)
Draw appropriate samples of entries, that is,Es(1), Es(2), and Es(3+) from the sets E(1), E(2), and E(3+), respectively.(4)
Check each elemente in the sets Ew(1), Es(2), and Es(3+) to obtain the sets of word samples, Ws(1), Ws(2), and Ws(3+).(5)
Estimate the total number of monosyllabic wordsN^(1). Estimate N^(2), N^(3+) in the same way. Calculate the total number of words N^=N^(1)+N^(2)+N^(3+).(6)
Map each word inWs(1), Ws(2), and Ws(3+) to its time of occurrence.(7)
Count the number of words in the same time segment and estimated^i(1), d^i(2), and d^i(3+) according to (11).(8)
Solve the quadratic programming problem to obtain the estimationn^t(1), n^t(2), and n^t(3+).(9)
Calculaten^t(2+)=n^t(2)+n^t(3+) and n^t=n^t(1)+n^t(2+). Also, calculate their partial sum sequences.(10)
Calculate the indexes to evaluate the trend of polysyllablization.


## 4. Analysis of the Polysyllablization

We use the CD-ROM version ofCDCW published in 1998. This edition contains 27,989 character entries, 279,720 disyllabic word entries, and 63,587 three-or-more-syllable word entries, from which we draw 1000 character entries, 2,000 disyllabic word entries, and 1,000 three-or-more-syllable word entries. Here we perform uniformly random sampling on all the entries without replacement. We use python, a computer script language, to perform the data sampling and processing.The number of effective samples of monosyllabic words is 669 (66.9% of the drawn sample entries). According to the statistical sampling theory, the total number of effective monosyllabic words inCDCW is estimated to be about 27,898·66.9%≃18,724. The number of effective samples of the disyllabic words is 1,904 (95.2% of the drawn sample entries) and that of the words with three or more syllables is 876 (87.6% of the drawn sample entries). Likewise, the total number of disyllabic words inCDCW is estimated to be about 279,720·95.2%≃266,293 and that of three-or-more-syllable words is about 63,587·87.6%≃55,702. The total number of polysyllabic words in the Chinese lexis is about 266,293+55,702=321,995. Thus, the number of polysyllabic words is greatly more than that of monosyllabic words up to now. Disyllabic words constitute the major part of the whole vocabulary.We set the endpoints of the time axis to 1045 BC and 1949 AD. The former is approximately the beginning of Zhou Dynasty. The latter is the founding of the People’s Republic of China. The time axis is split into 8 segments. We map all these effective word samples to their time of occurrence and count the number of samples belonging to each time segment.The statistical data are listed in Table1. The words which were newly formed after 1949 are ignored to avoid boundary problems. Therefore the sum in the table is a little less than the total number of words.Table 1
Statistical data of words of various numbers of syllables.
i
Dynasties
Endpoints
Single syllable
Double syllables
Three or more syllables
d
i
t
b
(
i
)
–
t
e
(
i
)
g
^
i
(
1
)
d
^
i
(
1
)
g
^
i
(
2
)
d
^
i
(
2
)
g
^
i
(
3
+
)
d
^
i
(
3
+
)
1
pre-Qin
1045 BC–222 BC
274
7669
246
34406
55
3497
2
Qin, Western Han
221 BC–24 AD
44
1231
135
18881
33
2098
3
Eastern Han
25–219
56
1567
128
17902
22
1399
4
Three kingdoms, Jin
220–419
12
336
115
16084
23
1462
5
Southern and Northern
420–580
44
1231
238
33287
48
3052
6
Sui, Tang
581–907
23
644
275
38461
97
6168
7
5 dynasties, Song
908–1279
138
3862
243
33986
110
6995
8
Yuan, Ming, Qing
1280–1949
37
1036
391
54685
306
19458
Total
17576
247692
44129The data in Table1 show the total number of the newly emergent words in each time period. For example, there were about 33,287 disyllabic words produced in Southern and Northern Dynasties and 38,461 in Tang Dynasty, the latter exceeding the former. However, the span of the former time segment was only 160 years and that of the latter was as long as 327 years. If we distribute the newly emergent words evenly among the years, the annual average for the Southern and Northern Dynasties is 33287/161≃206.8 (word per year) and that for Tang Dynasty is 38461/327=117.6 (word per year), only about half of the number in Southern and Northern Dynasties.Notice that there were about 7,669 monosyllabic words produced in the pre-Qin period (1045 BC–222 BC). Part of them are generated during or before Shang Dynasty and known as Oracle Bone Script [32]. Several thousand bones and plastrons have been reconstructed and many thousands of texts have been studied. The texts contain over 30,000 distinct characters, which are thought to be variant forms of around 4,000 individual characters. Thus, the number of characters before Zhou Dynasty should be regarded as the initial cumulative number of the monosyllabic words. Now ctb(1) is set to be 4000, that is, the number of monosyllabic words at the beginning of pre-Qin period. We also subtract ctb(1) from the estimated number of the monosyllabic words in the pre-Qin period thereafter so as to make a revised estimation. The estimation on polysyllabic word is not revised because it is still argumentative whether there existed polysyllabic words in the Oracle Bone Script.Figure2 shows the final estimation on the speed of new word production. It illustrates that the speed is changeable. The speed of the new polysyllabic word production nt(2+) is above that of monosyllabic words nt(1) from the beginning of the time axis. It can be seen that the speed of new polysyllabic word production increased and reached two peaks at about 75 AD and 550 AD, that is, the Eastern Han Dynasty and Southern and Northern Dynasties. In the following years, new polysyllabic words still emerged, yet at a slower pace through Song, Yuan, Ming and Qing Dynasties. In fact, Southern and Northern Dynasties are treated as the center of Middle Chinese. Figure 2 shows that the Middle Ages are the critical transition period of polysyllablization. During Eastern Han and the following dynasties, the cultures from the western neighbors of China had a tremendous influence upon not only the Chinese traditional culture but also the Chinese language [33]. Linguistic evidences are available to reveal the early cultural exchange between China and India [34]. For example, the language contact [35] caused by the Buddhist texts translated from foreign languages (mainly Sanskrit) into Chinese was an important exterior influential factor to the evolution of the Chinese language. From this perspective, it can be concluded that the rising and falling in the above curves do reflect the evolution inside the Chinese language, agree with its historical stage division, and support the findings in other studies on the historical linguistics.Figure 2
The speed of the word production.Figure3 shows the final estimation on the cumulative number of new word production. It illustrates the increasing trend of the volume of Chinese vocabulary system. It is interesting to note that the amount of polysyllabic words ct(2+) exceeds that of monosyllabic words ct(1) before the ending of the first time segment. Thus polysyllabic words already were the major component of the lexis even in Old Chinese. However, back then, their frequency of use was very low, which has misled researchers to reach wrong judgments about the actual degree of the polysyllablization.Figure 3
The cumulative number of the word production.The trend that polysyllabic words became the major component of the Chinese lexis is also shown in Figure4. It indicates that the weight of polysyllabic words in the Chinese lexis increased all along. At the ending of the time axis (1949 AD), about 94% of the Chinese words were polysyllabic.Figure 4
The quantitative trend of the polysyllablization degree index (PDI).


## 5. Conclusion

Polysyllablization is among the most important rules in the development of the Chinese lexis. Furthermore, due to the peculiarity of Chinese language, polysyllablization is not only a key issue in lexis, but also closely related to phonetics, semantics, and syntactics. However, the existing studies on polysyllablization are either in a qualitative manner or limited to a quantitative survey of specific language materials. The quantitative trend of polysyllablization is yet to be explored.The lexis itself is an integral, dynamic, and complex system. With lots of uncertainties, its historical evolution is difficult to trace. As a novel exploration in the computational linguistics, we try to reconstruct the quantitative trend of polysyllablization of the Chinese lexis. A mapping from the words to their time of occurrence is built based onComprehensive Dictionary of Chinese Words, a large-scale historical Chinese dictionary, which collects, organizes, and explains hundreds of thousands of ancient and modern words. Related formulation, mathematical model, and corresponding algorithms are introduced. We finally deduce the reconstruction to a constrained optimization problem based on the statistical sampling data. Such solution is really a data-mining procedure on the dictionary. It is not only feasible, but also conducive to excluding the subjective prejudice of the researchers. The results agree with the stage division of historical Chinese and answer some difficult questions related to polysyllablization in a quantitative manner.Our research is only an initiatory exploration in this open research field. Our future research will focus on the revised mathematical models and algorithms, including statistical inference, maximum entropy estimation, and fuzzy mathematical theory based on more samples of word entries.



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*Source: 123983-2014-07-13.xml*