Lexical bloom, syntactic retreat: examining complexity trade-offs within Classical Chinese evolution across two millennia
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Jiamiao Song
und
Lei Lei
Abstract
The Complexity Trade-off Hypothesis suggests that when one language domain becomes more complex, another tends to simplify to maintain an overall balance of complexity in languages. Previous studies sought to test such trade-offs across languages, implying the equal complexity across languages. However, this assumption has been increasingly questioned. Furthermore, little attention has been given to diachronic changes and interactions in lexical and syntactic complexities, especially within ancient and non-European languages. Against this backdrop, this study explored the evolution of lexical and syntactic complexities and their possible trade-off in Classical Chinese over two millennia. Based on entropy and dependency distance metrics, we found a marked increase in lexical complexity alongside a decrease in syntactic complexity. Our findings provided support to the existence of trade-offs in an individual language and broadened the scope of the complexity trade-off analysis in historical language contexts.
1 Introduction
Historical linguistics, or diachronic linguistics, investigates the evolution of languages over time (Campbell 2013). This field has examined a variety of languages and has provided insights into their development and transformation. For example, Wang (1957) conducted a diachronic analysis of Chinese language development, which focused on phonetic, syntactic, and lexical changes. Similarly, Bauer (1994) systematically analyzed the language change in English, focusing on phonological, morphological, syntactic, lexical, and semantic developments. The analysis highlighted the shifts in these areas throughout the 20th century. Studies on the language change of other languages such as French (Holmes and Schutz 1938) and Hebrew (Sáenz-Badillos 1996) have also advanced our understanding of language evolution across different linguistic systems. Despite these significant contributions, historical linguistics has undergone a methodological shift from exemplar-based observation to quantitative approaches. The application of corpus data and quantitative methods represents a major innovation, which enables researchers to analyze linguistic changes in detail across various linguistic dimensions and with large dataset (Bentz et al. 2014; Jenset and McGillivray 2017).
Over the past two decades, interest in measuring the complexity of languages from a historical linguistics perspective has been growing. Research in language complexity has largely centered on the debate over whether all languages exhibit equal complexity. The Complexity Trade-off Hypothesis suggests that when one language domain (e.g., phonology, syntax) in a language becomes more complex, another is likely to simplify (Coloma 2017a; Fenk-Oczlon and Fenk 2014; Shosted 2006; Sinnemäki 2014). This kind of complexity trade-off is often as a proof for equal complexity of languages (Shosted 2006; Sinnemäki 2008; Kusters 2008). Numerous studies aim to test the balance through cross-linguistic investigations, specifically exploring how trade-offs can manifest in two primary ways: within a single language domain or across multiple domains (Shcherbakova et al. 2023). For example, the trade-offs of the subsystems within a specific language domain have been documented in specific areas such as phonemes and syllables (Fenk and Fenk-Oczlon 1993), the copular and verbal marking of stative predicates (Miestamo 2009), parts of speech and word order flexibility (Gulordava and Merlo 2015; Tily 2010), head words and subordinate markers in possessive noun phrases (Sinnemäki and Haakana 2023), indefinite pronouns (Denić et al. 2020), and gender (Di Garbo and Miestamo 2019; Sinnemäki 2019; Wälchli and Di Garbo 2019). However, the complexity of several parameters within a single domain may also increase (e.g., Maddieson 1984). In this case, trade-offs are more commonly seen across different language domains (Fenk-Oczlon and Fenk 2008). Cross-domain trade-offs have been proposed between phonology and morphology (Fenk-Oczlon and Fenk 2008; Shosted 2006; Yinon and Shaul 2025) as well as morphology and syntax (Bentz et al. 2023; Shcherbakova et al. 2023; Sinnemäki 2008). Although long recognized in modern linguistics, the point that complexity trade-offs between subsystems reveal an equal overall complexity across languages has recently been challenged. For example, Fenk-Oczlon and Fenk (2014) argued that while complexity trade-offs do exist within or across language domains, the overall complexity of a language cannot be captured by focusing on such balancing mechanisms. In other words, complexity trade-offs do not imply equal complexity of all languages (Bentz et al. 2023; Coloma 2017b; Fenk-Oczlon and Fenk 2014; Sinnemäki 2014).
Many studies also investigated the trends in the evolution of complexity within specific language domains, with a particular focus on syntax. Research has shown that human languages at the syntactic level are being optimized toward lower complexity to enhance greater efficiency in communication (Sampson et al. 2009; Trudgill 2011). Syntax and lexicon are widely recognized as the two fundamental components of language structure, together forming the expressive capacity and functional framework of language (Jackendoff 2002). However, examining diachronic changes in lexical complexity of a language is limited, with only a few studies exploring changes in lexical complexity across specific genres, such as speech (Zhu and Lei 2018a) and academic writing (Zhou et al. 2023). Even fewer studies have explored the interactions between lexical and syntactic complexities in the context of language evolution. For example, some studies have revealed trade-offs in other contexts, such as sociolinguistics (Reali et al. 2018) and psycholinguistics (Rezaii et al. 2022).
Numerous metrics have been developed to assess the language complexity at linguistic level. Two commonly used measures are entropy metrics (Shannon 1948, 1951) and dependency distance metrics (Ferrer-i-Cancho et al. 2004; Gibson 1998; Liu 2008). On one hand, entropy, introduced by Shannon (1948) in information theory to measure randomness and information content, has recently gained prominence in linguistic research. It is used to analyze the nonuniform distribution and complexity of linguistic features (Ehret and Szmrecsanyi 2019; Jiang and Liu 2015) and measure complexity at different levels of language structure (Bane 2008; Bentz et al. 2016; Hale 2016). The underlying assumption is that more complex texts contain greater amounts of information and thus require more cognitive effort and processing time (Hale 2001; Levy 2008). In this context, low-probability events are associated with higher entropy and increased complexity (Lin and Tegmark 2017; Shannon 1948). As a reliable metric for capturing both frequency and distributional information, entropy has been widely applied in various studies of linguistic complexity, including morphological complexity (Bane 2008; Bentz and Winter 2013), lexical complexity (Liu et al. 2022a; Xiao et al. 2023), syntactic complexity (Juola 1998, 2008; Lei et al. 2024; Liu et al. 2022b), and cultural complexity (Juola 2013; Liu 2016; Zhu and Lei 2018b). On the other hand, dependency distance (Liu 2008) or dependency length (Futrell et al. 2015) refers to the linear distance between a governor and its dependent within a syntactic dependency relation (Hudson 2010; Tesnière 1959). This measure is commonly viewed as an index of working memory load (Lei and Wen 2020; Liu et al. 2022a). In sentence processing, words remain active in working memory until they establish a dependency relation with their governor or dependent (Liu 2008). Therefore, the greater the dependency distance, the higher the cognitive load imposed on working memory. The increased cognitive load, in turn, increases the complexity of sentence comprehension (Gibson 1998; Jiang and Liu 2015). Building on the concept of dependency distance, Liu (2008) introduced the Mean Dependency Distance (MDD) to calculate the average dependency distance within a sentence. This metric reflects the overall sentence structure by averaging the positional distances between all pairs of syntactically related words. However, dependency distance is influenced by sentence length, with MDD increasing as sentence length increases (Futrell et al. 2015; Lei and Jockers 2018; Lei and Wen 2020; Liu 2008; Liu et al. 2022b). To address this limitation, Lei and Jockers (2018) proposed the Normalized Dependency Distance (NDD), which adjusts the traditional dependency distance by normalizing it based on sentence length. This normalization allows for more standardized comparisons of syntactic complexity across sentences of varying lengths and enhances its applicability in linguistic complexity studies. MDD and NDD are widely recognized as valuable metrics for measuring syntactic complexity (Agmon et al. 2024; Ferrer-i-Cancho et al. 2022; Lei and Wen 2020; Liu et al. 2022a). In recent decades, studies have identified a trend toward decreasing dependency distance in human languages. This phenomenon, known as Dependency Distance Minimization (DDM), is hypothesized to be a universal principle of language. It suggests that the syntactic complexity of languages tends to simplify over time (Lei and Wen 2020; Temperley 2007, 2008).
To summarize, existing studies of language complexity have primarily focused on complexity trade-offs within or across language domains, as well as on trends in the complexity of specific linguistic areas, particularly syntax. The following limitations are to be addressed. First, many studies have attempted to test the assumption that all languages share equivalent levels of complexity by examining complexity trade-offs across languages from a synchronic perspective (e.g., Shcherbakova et al. 2023). However, this assumption has recently been challenged (Fenk-Oczlon and Fenk 2014). There leaves a gap in exploring whether complexity trade-offs might exist within the evolution of an individual language. Second, research on diachronic changes in the overall lexical complexity of a language is scarce, let alone on interactions between lexical and syntactic complexities from a diachronic perspective. Furthermore, such studies have primarily focused on European languages (e.g., Chen and Kubát 2024; Lei and Wen 2020). In contrast, Chinese, one of the world’s most populous languages with over 1.2 billion native speakers (Rao 2019), has received relatively little attention. Third, most research has concentrated on modern languages (e.g., Fenk-Oczlon and Fenk 2014; Liu 2008) with few ancient languages investigated, such as Dutch and Greek (e.g., Futrell et al. 2015; Shcherbakova et al. 2023). Further exploration of ancient languages is needed.
The present study aims to address these concerns and examine changes in both syntactic and lexical complexity of Classical Chinese over a period of more than 2,000 years. The research questions of this study are as follows:
RQ1:
Do the lexical and syntactic complexities in Classical Chinese show diachronic changes across different historical periods? If yes, how do these complexities evolve over time?
RQ2:
Is there a trade-off between lexical and syntactic complexities in Classical Chinese, as suggested by the Complexity Trade-off Hypothesis? If yes, how is the trade-off manifested?
2 Methods
2.1 Corpus data
The corpus dataset for the study comprised historical texts, which serve as a reliable and rich resource of Classical Chinese. The dataset included the Twenty-Five Histories and a selection of Pre-Qin classical texts, such as the Book of Documents, Discourses of the States, Zuo’s Commentary on the Spring and Autumn Annals, Gongyang’s Commentary on the Spring and Autumn Annals, and Guliang’s Commentary on the Spring and Autumn Annals. While only the Twenty-Four Histories are officially recognized, the Draft History of Qing is still a valuable source for linguistic research. First, the Draft History of Qing was completed between 1914 and 1928, after the May Fourth Movement, a period when Modern Chinese was being promoted. However, like other historical records, it was written in Classical Chinese and preserved the linguistic conventions characteristic of the style in Qing Dynasty. Among all the historical records, the Twenty-Four Histories were developed by Zinin and Xu (2020). The remaining texts were sourced from the Chinese Wikisource[1] and underwent additional processing, including cleaning and reformatting of the downloaded texts.
We chose these texts as the data for this study for three reasons. First, these texts are all historical records of ancient China. China has a long-standing tradition of historiography. In the early periods, historical records were compiled by individuals, and from Tang Dynasty, the state officially commissioned historiographies. The tradition of historiography has been continued by successive dynasties without interruption across two millennia (Guo 2017). The consistency in genre across historical records allows us to control for the influence of genre differences on linguistic features, which enhances the validity of our observations of changes in lexical and syntactic complexities. Second, the lexical and syntactic structures of Classical Chinese have remained consistent over two millennia (Norman 1988; Pulleyblank 1995), which facilitates the observation of diachronic changes in lexical and syntactic complexities. Finally, the long temporal span of these texts, covering over 2,000 years, provides a sufficient timeline for observing linguistic changes, particularly the interactions between lexical and syntactic features.
Given the time span of over 2,000 years, the present study categorized the collected Classical Chinese historical records into eleven historical periods. This classification followed the compilation dynasties of the texts. The eleven historical periods are the Pre-Qin period (Period 1), Han Dynasty (Period 2), Wei and Jin Dynasties (Period 3), Northern and Southern Dynasties (Period 4), Tang Dynasty (Period 5), Five Dynasties and Ten Kingdoms (Period 6), Song Dynasty (Period 7), Yuan Dynasty (Period 8), Ming Dynasty (Period 9), Qing Dynasty (Period 10), and the Republic of China (Period 11), as shown in Table 1.
Diachronic corpus details.
| Period | Texts | Tokensa | Time span |
|---|---|---|---|
| Period 1 | The Book of Documents, Discourses of the States, Zuo’s Commentary on the Spring and Autumn Annals, Gongyang’s Commentary on the Spring and Autumn Annals, Guliang’s Commentary on the Spring and Autumn Annals | 362,908 | 21st century BCE – 221 BCE |
| Period 2 | Records of the Grand Historian, Book of Han | 1,156,882 | 202 BCE – 220 CE |
| Period 3 | Records of the Three Kingdoms | 351,695 | 220 CE – 420 CE |
| Period 4 | Book of the Later Han, Book of Song, Book of Southern Qi, Book of Wei | 2,641,847 | 420 CE – 589 CE |
| Period 5 | Book of Jin, Book of Liang, Book of Chen, Book of Northern Qi, Book of Zhou, Book of Sui, History of the Southern Dynasties, History of the Northern Dynasties | 4,256,233 | 618 CE – 907 CE |
| Period 6 | Old Book of Tang | 1,839,517 | 907 CE – 979 CE |
| Period 7 | New Book of Tang, Old History of the Five Dynasties, New History of the Five Dynasties, History of Yuan | 2,052,325 | 960 CE – 1276 CE |
| Period 8 | History of Song, History of Liao, History of Jin | 4,791,279 | 1271 CE – 1368 CE |
| Period 9 | History of Yuan | 1,385,809 | 1368 CE – 1644 CE |
| Period 10 | History of Ming | 2,504,178 | 1644 CE – 1911 CE |
| Period 11 | Draft History of Qing | 3,733,903 | 1912 CE – 1949 CE |
| Total | 25,076,576 |
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aThe reported token counts exclude punctuation marks.
2.2 Data processing
We performed word segmentation, part-of-speech tagging, and dependency parsing with the roberta-classical-chinese-large-upos model (Yasuoka 2019, 2023), a pretrained model derived from GuwenBERT. To further assess the model’s applicability across different historical periods and minimize possible biases, we conducted random sampling and manual validation. Specifically, 50 sentences were randomly selected from each period for manual annotation by the researchers. The results showed that the model achieved an overall accuracy of 95.82 % for tokenization, 89.17 % for Part-Of-Speech (POS) tagging, and 91.09 % for dependency parsing. Given the high overall accuracies, we believe that annotation of the model does not introduce systematic bias into the complexity measures across time. Table 2 presents a randomly selected sentence from each period in our dataset, including the results of word segmentation, POS tagging, dependency parsing, and English translation.
Example sentences illustrating segmentation, POS tagging, and dependency parsing across 11 historical periods.
| Category | Period 1 | Period 3 | Period 5 |
|---|---|---|---|
| Example sentence | 师从齐师于莘 | 释其缚而用之 | 帝乃潜军进讨 |
| Tokenized sentence | 师/从/齐/师/于/莘 | 释/其/缚/而/用/之 | 帝/乃/潜/军/进/讨 |
| POS Tag | NOUN/VERB/PROPN/NOUN/ADP/PROPN | VERB/PROPN/NOUN/ CCONJ/VERB/ PROPN | NOUN/ADV/VERB/NOUN/VERB/VERB |
| Dependency relation | nsubj/root/nmod/obj/case/obl:lmod | root/det/obj/cc/conj/obj | nsubj/advmod/root/obj/parataxis/ flat:vv |
| Translation | The army followed the Qi army to Xin | (Someone) untied the ropes that bind him and appointed him to service | The emperor then secretly mobilized his troops to launch an attack |
| Category | Period 7 | Period 9 | Period 11 |
|---|---|---|---|
| Example sentence | 遂杀之以起兵 | 竟帅众驰去 | 纳五龙河仍入之 |
| Tokenized sentence | 遂/杀/之/以/起/兵 | 竟/帅/众/驰/去 | 纳/五龙河/仍/入/之 |
| POS Tag | ADV/VERB/PRON/ ADV/VERB/NOUN | ADV/VERB/NOUN/VERB/VERB | VERB/PROPN/ADV/VERB/PRON |
| Dependency relation | advmod/root/obj/advmod/parataxis/obj | advmod/root/obj/parataxis/ flat:vv | root/obj/advmod/ parataxis/obj |
| Translation | (Someone) then killed him in order to raise an army | (Someone) eventually led the troops and galloped away | The Wulong River was channeled and still flowed into it |
The following is an example from period 1, which showcases how the model annotates a Classical Chinese sentence (taken from Zuo’s Commentary on the Spring and Autumn Annals, see Figure 1). The dependency relations between word pairs of the sentence are listed in Table 3.
Dependency relations of the example from period 1. Every word in the sentence is represented by a rectangular node, labeled with its corresponding part of speech. Arrows between nodes indicate dependency relations, with labels specifying the syntactic role of each relationship.
Dependency relations of the example from period 1.
| Dependency relation | Governor | Position of the governor | Dependent | Position of the dependent |
|---|---|---|---|---|
| Root | ROOT | 0 | 从 | 2 |
| nsubj | 从 | 2 | 师 | 1 |
| nmod | 师 | 4 | 齐 | 3 |
| Obj | 从 | 2 | 师 | 4 |
| Case | 莘 | 6 | 于 | 5 |
| obl:lmod | 从 | 2 | 莘 | 6 |
Then, the results of the segmentations and annotations were manually checked. Although this model worked effectively in our texts, we noticed that the model systematically annotated modifiers in amod (adjectival modifier) relations as verbs (VERB) with an additional feature label: Degree=Pos|VerbForm=Part. For example, in the word 大事dàshì “important things,” the character大 dà “important” was annotated as VERB rather than ADJ. This labeling aligns with the viewpoints of researchers such as Sackmann (1996) and Vogelsang (2021) that Chinese does not have a distinct category of adjectives. Hence, such modifiers are annotated as verb-derived forms similar to participles (e.g., “running water” in English). However, other researchers (e.g., Zadrapa 2011) suggest that adjectives should be regarded as an independent lexical category. To maintain consistency with the Universal Dependencies framework used across languages (De Marneffe and Nivre 2019; Nivre et al. 2020) and facilitate cross-linguistic comparisons for future research, we converted the POS tags in such cases to ADJ where appropriate.
As previously discussed, MDD and NDD are metrics that are used to measure syntactic complexity in a text. In this study, we also adopted the metrics to measure the syntactic complexity of Classical Chinese texts. The formulas for the calculation of MDD and NDD are as follows (Formulas 1 and 2. Also see Lei and Jockers (2018) for a detailed discussion of the formulas).
In Formula 1, n is the total number of dependency relations in a sentence. i indexes each dependency relation. d i is the linear position index of the dependent in dependency relation i, and d j is the linear position index of its governor. The term |d i − d j | represents their linear position difference. It should be noted that the calculation excludes two dependency relations, punct (punctuation marks) and root (the main verb or predicate in a sentence and has no governor) (Lei and Wen 2020; Liu 2008; Liu et al. 2022b).
In Formula 2, rootDistance is the position of the main verb in the sentence, while sentenceLength is the total number of words without punctuations. The formula first calculates the natural logarithm of the quotient. Next, the natural logarithm of the quotient is computed, and its absolute value is calculated. Taking the sentence in Example 1 as an example, we calculated its NDD and MDD based on the dependency relations listed in Table 1. To illustrate the calculation process, we constructed a symmetrical distance matrix, where each off-diagonal element represents the absolute linear distance between a dependent word and its head word. The resulting matrix is as follows:
Based on this matrix, we extracted the nonzero off-diagonal elements: {1, 2, 1, 4, 1}. The MDD and NDD were then computed as:
MDD (Example 1) =
NDD (Example 1) =
Last, three types of Shannon’s entropies, i.e., word type entropy, POS entropy, and dependency relation entropy, were calculated. Word type entropy, as a measure in token-based typology (Levshina 2016, 2019), is derived from word forms and measures the lexical complexity (Liu et al. 2022a). In contrast, POS entropy, which is based on part-of-speech tags, and dependency relation entropy, which is based on dependency relations, can capture syntactic complexity (Chen et al. 2017; Liu et al. 2022b; Lei et al. 2024; Shimorina et al. 2021). The formula for these entropy measures is presented in Formula 3.
In Formula 3, H(X) represents the entropy of X, where m is the total number of types in X, and P i is the probability of occurrence of a certain element, calculated as its relative frequency. This formula calculates entropy by summing the product of each element’s probability P i and the base-2 logarithm of P i to capture the distributional diversity within the data. In these three metrics, P i represents the probability of each word type, POS tag, and dependency relation, respectively. However, entropy measures are sensitive to text length and stabilize only when calculated over approximately 1000-token windows (Shi and Lei 2022). Considering that MDD and NDD must be calculated at the sentence level, we applied a sentence-based sampling method to construct windows of approximately 1,000 tokens within each historical period. We first calculated the average MDD and NDD within each window. Meanwhile, we calculated the entropy of word types, POS tags, and dependency relations within the same window. Once a window was processed, the selected sentences were not replaced, and the sampling continued until all sentences in the period were exhausted. After processing all windows in a given period, we calculated the average values of word type entropy, POS entropy, dependency relation entropy, MDD, and NDD to ensure comparability across historical periods.
All the above calculations were achieved with developed in-house Python scripts.
3 Results
3.1 Descriptive statistics and trend analysis
The descriptive statistics for word type entropy (a measure of lexical complexity), along with POS entropy, dependency relation entropy, MDD, and NDD (measures of syntactic complexity) across the eleven historical periods are presented in Table 4. A quartic polynomial fitting method was used to analyze and visualize the trends in both lexical and syntactic complexities over the examined two millennia (see Figures 2 and 3).
Descriptive statistics of the five metrics across the eleven examined periods.
| Metrics | Period 1 | Period 2 | Period 3 | Period 4 | Period 5 | Period 6 |
|---|---|---|---|---|---|---|
| Word type entropy | 8.051 | 8.515 | 8.677 | 8.780 | 8.766 | 8.746 |
| POS entropy | 2.846 | 2.682 | 2.628 | 2.561 | 2.579 | 2.545 |
| Dependency relation entropy | 4.215 | 4.215 | 4.197 | 4.169 | 4.167 | 4.150 |
| MDD | 2.235 | 2.793 | 2.980 | 2.708 | 2.758 | 2.860 |
| NDD | 1.105 | 1.199 | 1.241 | 1.217 | 1.209 | 1.259 |
| Metrics | Period 7 | Period 8 | Period 9 | Period 10 | Period 11 | Mean |
|---|---|---|---|---|---|---|
| Word type entropy | 8.740 | 8.769 | 8.717 | 8.832 | 8.920 | 8.683 |
| POS entropy | 2.543 | 2.499 | 2.473 | 2.492 | 2.436 | 2.571 |
| Dependency relation entropy | 4.141 | 4.121 | 4.102 | 4.115 | 4.081 | 4.152 |
| MDD | 2.863 | 2.877 | 2.978 | 2.564 | 2.702 | 2.756 |
| NDD | 1.195 | 1.173 | 1.169 | 1.189 | 1.190 | 1.195 |
Trend of lexical complexity. Each data point, represented by a blue circle, marks the entropy value for a specific period, with numerical annotations for clarity. A red dashed line represents the quartic trend.
Trend of syntactic complexity. The figure contains four subplots, arranged from top to bottom, each depicting changes in POS entropy, dependency relation entropy, MDD, and NDD across eleven periods, respectively. In each plot, blue circles represent data points with numerical annotations, and red dashed quartic trend lines illustrate the overall patterns.
As shown in Table 4, both the lexical and syntactic complexities in Classical Chinese exhibit variation over time. From a lexical perspective, the word type entropy increases from 8.051 in the Pre-Qin period to 8.920 in the Republic of China, indicating a trend of increasing lexical diversity. The most pronounced increase in word type entropy occurred from the Pre-Qin period to Han Dynasty. This increase continued through subsequent periods, stabilized from Northern and Southern Dynasties to Ming Dynasty, and then accelerated again from Ming Dynasty to the Republic of China. Compared to other research (e.g., Bentz et al. 2017; Wong and Ponn 1976), the average values obtained for each historical period in this study suggest a lower level of lexical complexity than other Modern languages. For example, Bentz et al. (2017) reported an average word type entropy of approximately 9.14 across 1,259 modern languages. Wong and Ponn (1976), on the other hand, revealed that Modern Chinese had an entropy of 9.63. Nevertheless, as the word type entropy increases, it gradually approaches the average value of modern languages.
The syntactic complexity, when analyzed from the POS entropy and the dependency relation entropy, shows a gradual simplification over time. On the one hand, POS entropy reveals a gradual decrease from 2.846 in the Pre-Qin period to 2.436 in the Republic of China. Notably, the most significant decrease in the POS entropy occurred from the Pre-Qin period to Han Dynasty, which aligns with the period of the most pronounced increase in word type entropy. This pattern supports a complexity trade-off in Classical Chinese, as an increase in syntactic complexity was found accompanied by a decrease in lexical complexity. Compared to modern texts such as news, essays, and official documents, where POS entropy averages around 4 (Chen et al. 2017), the POS entropy observed in this study is lower. On the other hand, the dependency relation entropy shows a decline from 4.215 in the Pre-Qin period to 4.081 in the Republic of China, which suggests a reduction in the diversity of syntactic relations. In terms of dependency distance, MDD ranges from 2.235 to 2.980 and NDD fluctuates between 1.105 and 1.259. Both MDD and NDD show no significant monotonic trend across periods. It should be highlighted that the mean, maximum, and minimum values of MDD in Classical Chinese remain consistently higher than those of NDD across all periods. The results are consistent with the findings by Lei and Wen (2020), which proposed that NDD values are calculated from MDD and then normalized by sentence length. Moreover, both MDD and NDD in Classical Chinese are lower compared to Modern Chinese, which has a higher average MDD of 3.662 (Liu 2008).
In Figures 2 and 3, the fitted curves for lexical and syntactic complexities trends align with the data in Table 4. The word type entropy displays an upward trend, which indicates the increasing lexical complexity over time. In contrast, the POS entropy and the dependency relation entropy show a declining trend, which suggests a reduction in the syntactic complexity. Similarly, the curves of MDD and NDD show that both MDD and NDD lack clear monotonic trend over time.
To determine whether the observed complexity trends are significant over time, we considered three commonly used methods for trend detection in time series data (i.e., Pearson’s correlation, Spearman’s Rank Correlation, and the Mann–Kendall trend test) (e.g., Hauke and Kossowski 2011; Novotny and Stefan 2007; Yue and Wang 2004). Among these, Pearson’s method assumes that the data follow a normal distribution (Armstrong 2019). To assess the suitability of these methods, we conducted Shapiro–Wilk tests for normality, given our relatively small sample size (n = 11). The results showed that word type entropy significantly deviates from normality (p < 0.001), whereas the other measures (e.g., POS entropy, dependency relation entropy, MDD, and NDD) did not show strong evidence against normality (p > 0.05). Hence, we adopted the Spearman’s Rank Correlation and Mann–Kendall trend tests in our analysis. The results were reported in Table 5.
Results of Spearman’s Rank Correlation Test and Mann–Kendall trend test for complexity measures over time.
| Metric | ρ | p-Value | S | p-Value | Trend |
|---|---|---|---|---|---|
| Word type entropy | 0.736 | 0.010 | 31 | 0.020 | Increasing |
| POS entropy | −0.982 | <0.001 | −51 | <0.001 | Decreasing |
| Dependency relation entropy | −0.982 | <0.001 | −51 | <0.001 | Decreasing |
| MDD | 0.036 | 0.916 | 7 | 0.640 | No significant monotonic trend |
| NDD | −0.273 | 0.417 | −11 | 0.436 | No significant monotonic trend |
In Spearman correlation analysis, the Spearman correlation coefficient (ρ) is categorized as strong (|ρ| = 0.7–1), moderate (|ρ| = 0.5–0.7), or low (|ρ| = 0.3–0.5), when only significant correlation (p < 0.01 or p < 0.05) values are taken into consideration (Schober et al. 2018). The results indicate a significant positive correlation between word type entropy and time (ρ = 0.736, p = 0.010). In contrast, both POS entropy (ρ = –0.982, p < 0.001) and dependency relation entropy (ρ = –0.982, p < 0.001) exhibit strong negative correlations, indicating a decline in syntactic complexity. Meanwhile, MDD (ρ = 0.036, p = 0.916) and NDD (ρ = –0.273, p = 0.417) show no significant correlation with time. The Mann–Kendall trend test yielded consistent findings. Word type entropy demonstrates a significant upward trend (S = 31.0, p = 0.020), while POS entropy (S = –51.0, p < 0.001) and dependency relation entropy (S = –51.0, p < 0.001) show significant downward trends. MDD (S = 7.0, p = 0.640) and NDD (S = –11.0, p = 0.436) exhibit no statistically significant change over time.
To summarize, the statistical and trend analyses reveal that the lexical complexity of Classical Chinese shows an upward trend, while the syntactic complexity demonstrates a downward trend.
3.2 Trade-off analysis
We calculated partial correlation coefficients to control for historical period as a covariate. Partial correlation coefficients are typically computed using Pearson’s, Spearman’s, or Kendall’s methods (Gripenberg 1992). Among them, Pearson’s method assumes that the variables are normally distributed (Armstrong 2019). To assess the suitability of these methods, we first conducted Shapiro–Wilk tests for normality on all complexity measures. The results showed that word type entropy significantly deviate from normality (p < 0.001), while others do not show strong evidence against normality (p > 0.05). Hence, we used Spearman’s and Kendall’s methods to calculate partial correlation coefficients. We then constructed two matrices to visualize the interdependencies and potential trade-offs between complexity measures (see Figure 4).
Partial correlation matrix based on Spearman’s and Kendall’s method. The figure presents two partial correlation matrices displaying the relationships between different linguistic complexity measures, with historical period controlled as a covariate. The left panel shows Spearman’s ρ coefficients, and the right panel shows Kendall’s τ coefficients. Partial coefficients marked with “×” indicate correlations that are not statistically significant (p > 0.05) and self-correlations are marked with “/”. Correlations meeting the criteria are left unmarked to emphasize potential trade-off relationships.
As shown in Figure 4, lexical complexity (measured by word type entropy) is negatively correlated with syntactic complexity (measured by POS entropy and dependency relation entropy) in Classical Chinese. Under both Spearman’s and Kendall’s methods, word type entropy is negatively associated with POS entropy (ρ = –0.700; τ = –0.581) and dependency relation entropy (ρ = –0.669; τ = –0.507), with all p values < 0.05. These results suggest a consistent trade-off between lexical and syntactic complexity across time. In contrast, MDD and NDD, though also syntactic measures, show no significant correlations with lexical complexity or with the other syntactic entropy measures (all p > 0.05).
4 Discussion
Based on the large-scale dataset of historical records spanning over 2,000 years, the present study investigated the diachronic changes in lexical and syntactic complexities and their interactions in Classical Chinese. To the best of our knowledge, this is probably the first study that explored lexical and syntactic complexities and their interactions in a classical language and across more than two millennia. The results of our study indicated that the lexical complexity has shown an upward trend, while the syntactic complexity has displayed a downward trend in Classical Chinese over two millennia. Furthermore, the results supported the complexity trade-off in an individual language, showing a compensatory relationship between lexical and syntactic complexities. The following discussion explores the possible explanations and implications of our findings.
First, our study demonstrates changes in both the lexical and syntactic complexities of Classical Chinese since the Pre-Qin period. The results reveal an increasing trend in the lexical complexity and a decreasing trend of syntactic complexity across the eleven historical periods. These shifts in complexity can be attributed to the factors as follows. One factor is the growth of lexicon, which is mainly driven by language contact. Language contact occurs when speakers of one language frequently interact with those of another language or dialect (Steiner 2008). In Han Dynasty, the Silk Road ushered in a new era of exchange between China and the other countries. The introduction of new philosophical, religious, and literary concepts during various historical periods expanded the lexicon by incorporating terms reflecting these innovations, which aligns with the findings in our study that the most rapid increase is from the Pre-Qin period to Han Dynasty. To further support this observation, we conducted a comparative analysis of the Pre-Qin period and Han Dynasty corpora. The Han Dynasty corpus contains 11,437 unique word types (excluding punctuation), among which 49.04 % are proper nouns, 22.18 % nouns, and 14.91 % verbs. Many of these newly word types reflect conceptual innovations and cultural borrowings. For example, 苜蓿mùxu “alfalfa” and蒲陶 pútáo “grape” are loanwords from Old Iranian or Ferghana/Yuan origin, introduced via the Silk Road (Jeong 2016). Hence, the growth in lexicon led to higher lexical complexity (Dahl 2004). Another factor is the increasing information brought about by lexical growth (Shannon 1948). As the lexicon expands, the human beings need to handle more information to encode and process it (Baddeley 2003). However, the capacity of the human brain is limited (Marois and Ivanoff 2005). As a complex adaptive system (Freeman and Cameron 2008), language adjusts to the constraints by simplifying syntactic structures. To further explore this pattern in our study, we examined the relative frequency distributions of POS tags and dependency relations in the Pre-Qin and the Republic of China. The results revealed a more skewed distribution toward a few high-frequency categories (e.g., NOUN and VERB; nsubj and conj), accompanied by a decline in lower-frequency ones (e.g., CCONJ and PRON; case and det). It suggested that as people acquire a larger size of vocabulary, they tend to rely more on familiar, frequently used syntactic constructions, which are easier to process and produce. This phenomenon reflects the concept of complexity trade-offs, which will be discussed in greater detail in the following point.
Second, our findings reveal a complexity trade-off between the lexicon and syntax in the evolution of Classical Chinese. As previously discussed, the limited processing and storage capacity of the human brain imposes cognitive constraints on information processing (Miller 1956). As a complex and dynamic system with hierarchical organization and regular patterns, a language must adapt to these cognitive constraints (Fenk-Oczlon and Pilz 2021). To enhance communicative efficiency, reduce cognitive load, and streamline information processing, the language system balances complexity across various linguistic domains (e.g., Levshina 2021; Rezaii et al. 2022). In our study, syntactic simplification functions as a compensatory mechanism to counteract the increasing lexical complexity. Furthermore, while we observed a complexity trade-off between the lexicon and syntax of Classical Chinese, our study does not provide conclusive evidence on whether the overall complexity of languages remains constant. As shown in the results section, Classical Chinese exhibits relatively lower levels of lexical complexity and syntactic complexity compared to other modern languages. However, the complexity of languages is not determined solely by lexicon and syntax. To explore whether the total complexity is preserved across languages, additional variables and metrics from various linguistic domains need to be included. This will be revisited below.
Another important point worth discussing is the differing ability of various metrics to reflect changes in the syntactic complexity. In our study, neither MDD nor NDD displays a significant trend across the eleven historical periods. This finding contrasts with the DDM hypothesis, which posits that human languages tend to shorten dependency distances over time (Futrell et al. 2015; Lei and Wen 2020; Liu 2008). Several factors may be responsible for it. On the one hand, Classical Chinese is a concise and efficient language (Vogelsang 2021). Its syntactic structure frequently omits subjects, objects, connectives, and pronouns (Wang 1957), which may result that the sentences in Classical Chinese tend to be short. This feature may make indices such as MDD and NDD that calculate sentence complexity based on length unable to effectively capture the changes in the syntactic complexity of Classical Chinese. On the other hand, dependency distance is also known to vary by genre (Oya 2013; Wang and Liu 2017). Zhu et al. (2022) found no significant trend in dependency distance for nonfiction texts. In the case of Classical Chinese, our study reveals a similar pattern, with no significant trend in dependency distance over 2,000 years. In contrast, as mentioned earlier, entropy metrics assess the diversity and uncertainty of language structures, which focus on informational variety rather than sentence length (Shannon 1948). They appear to be more sensitive to subtle shifts in syntactic complexity and offer a more accurate representation of diachronic syntactic complexity changes in formal written languages such as Classical Chinese. Additionally, MDD and NDD exhibit no correlation with other metrics. A possible explanation is that MDD and NDD measure a different dimension of syntactic complexity compared to entropy-based metrics. Specifically, MDD and NDD quantify the linear distance between words at the sentence level, whereas entropy-based measures capture the distributional diversity of lexical items and syntactic structures. This finding suggests that MDD and NDD may not be the most suitable indicators for studying lexical-syntactic trade-off.
The present study has theoretical contributions. First, the study provided new empirical evidence for complexity trade-offs in language evolution. By focusing on the lexicon and syntax of Classical Chinese, the study showed that as lexical complexity increases, syntactic structures tend to simplify over time. Second, the research extended the purview of the Complexity Trade-off Hypothesis, which was initially proposed to explore whether all languages exhibit equal complexity (Shcherbakova et al. 2023). Our study is probably the first to investigate the lexical and syntactic complexities and their interactions in a classical language over two millennia. We extended the hypothesis from cross-linguistic synchronic research to the diachronic dimension of a single language. In addition, the present research focused on Classical Chinese, an ancient language that has received little attention in language complexity research. The results suggested that complexity trade-offs also apply to the historical development of the ancient language.
The research also has methodological contributions. First, the present study enhanced the potential for quantitative exploration within subdomains of ancient languages. Entropy and dependency distance metrics were applied to measure the lexical and syntactic complexities in Classical Chinese. Second, our research demonstrated the differences in the applicability of entropy and dependency distance metrics. While dependency distance metrics have proven effective in capturing syntactic complexity in most modern languages, our findings suggested that entropy measures may better capture subtle syntactic shifts, particularly in a concise ancient language such as Classical Chinese.
Nevertheless, the present research has several limitations and offers directions for future research. First, the data used in this study include only historical records. Future research could expand on these findings by testing the complexity trade-offs in other genres, such as poetry and folk literature, in order to paint a fuller picture of evolution of linguistic complexities. Second, the availability of Classical Chinese historical records is uneven across historical periods. Some periods are represented by only a text composed at the time, which constrains the reliability of within-period analyses.[2] Future research could benefit from more balanced and representative corpora, allowing finer-grained diachronic comparisons and testing for complexity trade-offs within each period. Third, this study relied merely on entropy and dependency distance metrics to measure the lexical and syntactic complexities in Classical Chinese. Future studies can employ a more diverse set of metrics to assess these complexities, such as type-token ratios (Wälchli 2012), G algorithm (Wälchli 2014), and maximum incomplete dependencies (Rezaii et al. 2022). Fourth, the study focused solely on two language domains, i.e., lexicon and syntax. Future studies are suggested to investigate the complexity trade-offs either within these two domains or across other language domains such as semantics. Last, although we qualitatively discussed the possible influence of the Silk Road on lexical expansion, particularly during Han Dynasty, due to the absence of a full historical loanword database, we could not directly quantify the contribution of every foreign lexical item to the rise in lexical complexity. If historical loanword lists or relevant resources become available in the future, researchers can also conduct a systematic analysis to assess their impact across different periods.
Funding source: The Major Research Grant of Shanghai International Studies University
Award Identifier / Grant number: 23ZD011
Funding source: The 2024 Supervisor-Guided Academic Research Program of Shanghai International Studies University
Award Identifier / Grant number: 2024DSYL038
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