Kanjis, Clusters, and Gelb's Hypothesis

Paper

I'm still working on this page, but our paper is here. I (Daan van den Berg) welcome all feedback you might have. Look me up in the UvA-directory, on LinkedIn or FaceBook.

Japanese Kanji Characters

The whole idea was quite simple actually, and born from the language enthousiasm of three programmers. Japanese is not an easy language of choice, Japanese sports a 60,000-piece character set named Kanji. Although you 'only' need to learn about 2,000 though to read the language, this is still a formidable exercise. There is some systemacity though; many Kanji are comprised of one or more of 252 components. Individual Kanji are said to carry meaning in a word-like manner, and akin to how compound words are built up ("swordfish", "snowball", "fireplace"), kanji often derive meaning from their combined constituent components, and are thus explained as such in textbooks for Japanese children and foreign students of the language. But the process of learning Japanese as a Dutch grown up is quite different from Japanese children. As programmers we tried to 'understand the system', playfully drawing out networks, connecting two characters if they shared one or more components. As we got access to electronic dictionary files containing all Kanji and their constituent components we could eventually analyze the language network as a whole. The results were quite surprising, and actually turned out to fit in quite nicely with the exisiting scientific literature of language networks.

Some Japanese Kanji characters. The bottom-left character and its right hand neighbour can be seen sharing the tree-component.

Kanjis & Small-Worlds

The network of connected Kanji turned out to be a small-world network, which means it has a high clustering coefficient, a low average path length and a low connection density (explained in detail below). As we found out soon enough, computational linguists had already found a large number of small-worlds in different languages on various levels, but this network of Kanji sharing components was not yet one of them. As such, it neatly lined up with existing research in quantitative linguistics and was accepted for publication at IARIA's Data Analytics '17 conference. Remarkably enough, small-worlds are also found in brains, social networks, software architecture and power grids. This is somewhat counterintuitive, because randomly wiring up a network almost never leads to small-worlds. So why do all these these networks share these characteristics if their likelihood is so small? Maybe because they are subject to the same forces of formation. Some experimental models for artificial brains tend to build clusters and shortcuts while synchronizing activity between artificial neurons - by themselves. This kind of behaviour is called self-organization, and the resulting properties are sometimes referred to as emergent. But why would brains and languages self-organize to similar structures? Could it be that communication between two humans is in some very basic way similar to communication between two brain cells?

The functional connectivity graph of the brain is one of many well known small-worlds See Sporns & Honey (2006) and others. Image adapted from Sporns' book "Discovering the Human Connectome"

Kanji characters, when connected by shared components (labels on edges) form a small-world network.

Clustering Coefficient & Average Path Length (optional)

First let's have a brief look at what makes a small-world network a small-world network. First of all: it's about sparse networks, that is, networks with relatively low edge densities. Small-World networks have a high clustering coefficient. The clustering coefficient on a vertex is the fraction of connections between its neighbours. Vertex C has four neighbours. Between these four we have three edges, out of a possible six, so the clustering coefficient on C is 0.5. Similarly, the clustering coefficient on B is 1, and on F it is 0.33 if we disregard the two neighbours it must have outside the picture. If we don't disregard those, it has five neighbours with either one or two connections between them, so the clustering coefficient on F would be either 0.1 or 0.2. The cluster coefficient of the network is simply the average of all its vertices. The term "small-world" was originally associated with global connectivity of a graph, often cojoined by the metaphor of "six degrees of separation". For scientific quantification however, we need a more precise definition which is the average path length (shortest distance) between two vertices in a graph. In this graph, the path length from B to E is three, the path length from C to G is 2 and the path length from C to D is 1. The average path length is the average of all path lengths between vertice pairs. A small-world network has a low average path length. It's now easy to see why the term 'small-world network' is usually associated with sparse graphs, because the denser the graph, the higher the Clustering Coefficient and the lower the Average Path Length. In fact, for very dense graphs, it's impossible 'not' to have a small-world.

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Gelb's Hypothesis: from pictures to sounds

So many language networks have small-world properties. But for Japanese, there's a little more to it. Because as it turns out, there's an old conjecture by Ignacy Jay Gelb (1907-1985) and it appears to coincide with our findings. An American linguist from Polish descent, Gelb conjectured that all written languages go through a phase transition from being picture-based to being sound-based. Studied in more detail, the idea is quite coarse and the exact trajectory might differ from language to language, but the core concept remains alluring, especially where it concerns Japanese Kanji. Although many textbooks claim 'compound meanings' for Kanji characters, a few studies have been conducted to components corresponding to sounds rather than to meaning. In fact, a few convincing examples exist of Kanji that share a component, and a pronunciation, but not a meaning - at least not in our convincion. But what's more, an ancient character dictionary named Shuowen Jiezı, containing 9353 Kanji, adopts a 540-piece component index. This shows that the number of components has dropped through time. Possibly by deletion, possibly by merger, possibly by replacement but these reduction operations could account for the correspondence in components and pronunciation on the one hand, and discorrespondence in meaning on the other.

Ignace Jay Gelb (1907-1985), and his hypothesis as visualized by Tadao Miyamoto in his 2007-paper. Note how these initially quite pictorial characters in this Cuneiform script evolve to a set of characters built up from relatively repetitive components.

Kanjis correspond to sounds too

So it seems that succesive disappearance of visual features accounts for the clustering found in the network of Kanji. In other words: Kanji have become simpler through time. They are nowhere near the elaborate pictures they were around 2,000 years ago, but in many ways symbolic abstractions of their ancient precursors. In the mean time, there is some evidence that certain components imply pronounciation. For instance: many of the characters containing the 'middle'-component have a pronunciation "chuu", and many Kanji with the 'orders'-component have a pronunciation 'rei'. Yet, many of these Kanji seem a world apart when it comes to their meaning. Why do the Kanji for mushroom, wise, bell and actor all have an order-component? Is there really a shared meaning in these characters? Or is it imaginable that through

Kanji evolution through time. Notice how visual similarity has increased, especially between 'horse' and 'fish'. Adapted from www.tofugu.com

These seven characters all share a visual component, and a pronunciation ("rei"). Although Kanji meaning are often explained through combined components, this explanation looks unconvincing in some cases. Do components really add an element of meaning to a Kanji? Or is it actualy an element of sound?

Whoswho&where

Sil Westerveld (top left) is currently a programmer voor SuperSAAS but did a lot ground work for the analysis together with Mark. He programmed the algorithms and gathered the data. He was also resposinble for visualizing the networks. Sil sepaks, reads and writes Japanese. Sandjai Bhulai (top right) is full professor Data Analytics and Business Intelligence at VU University in Amsterdam. He helped write, correct and finalize the paper for publication at the 2017 IARIA Data Analytics Conference in Barcelona. Mark Jeronimus (naka) built up the first algorithms and analysis of Cluster Coefficient and Average Path Length calculations in the character network. He currently works as a programmer for AirSupplies BV and is a Japanese language enthousiast. Cees van Leeuwen (bottom left) is full professor at University of Leuven. He is an expert on self-organizing systems and small-world networks, especially when it comes to perceptual models of cognitive processing. Daan van den Berg (bottom right) currently works at University of Amsterdam as a researcher & lecturer in heuristics. He is a language enthousiast and did most of the writing of the paper.

Team Kanji.

More

Maybe later.