Chinese characters and graphs: language as image

Introduction

Imagine you are learning Chinese and want to say "three fish." Easy, right? But in Chinese, you cannot simply put a number and a noun together. You need a classifier. Why? Do fish require their own linguistic category? The answer not only tells us a lot about the structure of the language but also leads us to an unexpected connection with graph theory and how we organize reality.

Classifiers in Chinese: Function and Use

In Mandarin Chinese, classifiers (量词, liàngcí) are words used alongside numerals to count nouns, functioning as units of measurement or indicators of specific characteristics. Unlike in Spanish, where we simply say "three books" or "two tables," in Chinese, it is mandatory to use an appropriate classifier between the number and the noun. For example, 一本书 (yī běn shū, "one book"), which allows for greater precision in expressing quantity and type of object.

The Reason for Classifiers

Chinese does not distinguish between singular and plural in most nouns and lacks definite articles, so classifiers serve to specify quantity and nature, providing information about the shape, size, or function of the objects referred to. Their use follows a logic that does not necessarily obey universal rules but rather linguistic and cultural conventions unique to Chinese.

Examples of Classifiers and Their Use

Each classifier is associated with certain nouns based on their characteristics. Some examples include:

1. 条 (tiáo) – The Invisible Thread Connecting Long, Thin Objects. Tiáo is like an invisible string connecting thin and long objects: snakes slithering on the ground, rivers winding through the landscape, or even a pair of folded pants in a wardrobe.
2. 本 (běn) – The Classifier for the Written and Bound. Imagine holding a book in your hands. You flip through it, feel the weight of its pages, and sense its bound structure. In Chinese, simply saying "one" or "two" is not enough; you need the classifier běn, reserved for everything with pages organized in a volume. Interestingly, the character 本 also means root or origin, as it is a variation of the sinogram 木 (mù) with an extra stroke at the base, symbolizing the starting point or foundation of something.
3. 张 (zhāng) – The Classifier for Flat and Expanded Objects. Imagine spreading a sheet of paper on the table, buying a ticket for a trip, or looking at a framed photograph on the wall. In Chinese, all these objects share something in common: they are flat, thin, or extended. To count them, you need the classifier zhāng, which groups elements that can be unfolded or spread over a surface.

Classifiers and Their Relationship with Culture

The existence of classifiers can be linked to the concept of the Celestial Emporium of Benevolent Knowledge, mentioned by Jorge Luis Borges in his essay The Analytical Language of John Wilkins, which shows how any attempt to classify reality is conditioned by cultural factors rather than a universal logic. Thus, classifiers in Chinese are not based solely on physical characteristics but on how the language organizes and perceives objects.

The Relationship Between Classifiers, Sinograms, and Graph Theory

Sinograms (汉字, hànzì) form a visual writing system that conveys meanings through graphic shapes. Unlike phonetic alphabets, where letters represent sounds, Chinese characters have a strong connection to the image and idea they represent. Many of them have a pictographic origin, such as 日 (rì), which in its earliest forms resembled a circle with a dot in the center, or 木 (mù), which evokes the shape of a trunk with branches.

Just as in the Celestial Emporium of Benevolent Knowledge, we can imagine other ways of organizing reality. The classifiers that group nouns can be mathematically modeled through graph theory, which studies relationships between elements within a system. A graph consists of nodes and edges. In this case, the nodes represent classifiers and nouns, while the edges symbolize the linguistic relationships between them.

Types of Graphs Applied to Classifiers and Sinograms

For visual representation, I will use the wheel graph (Wheel Graph, Wₙ), which has a central node connected to several peripheral nodes. In this case, the central node represents the classifier, while the peripheral nodes correspond to the associated nouns. Additionally, the peripheral nodes are interconnected, forming a cycle. On the other hand, the bipartite graph (Bipartite Graph, Kₘ,ₙ) consists of two sets of nodes where connections only occur between different sets. Here, one set represents classifiers and the other represents nouns, establishing a specific membership relationship. In the image, a wheel graph is shown where the central node groups nouns under a single linguistic category.

Classifiers and Nouns

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