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. Not an easy language of choice though, as a set of characters named Kanji has approximately 60,000 characters. You only need to learn about 2,000 though to read Japanese, and a serious study also involves writing, but the process of learning Japanese as a Dutch grown up is quite different from Japanese children. As programmers, we started looking for patterns in the characters and quickly found that many characters shared components. As language enthousiasts we playfully drew out some networks, connecting two characters if they shared one or more components. But as we found access to electronic dictionary files containing all Kanji and their constituent components we could 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

{ |align="justify" | class="wikitable" | style= "align="justify"; valign="top"; text-align:center; margin-left: 10em; margin-bottom: 1em; font-size: 100%;" |- |valign="top"| 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. As we found out soon enough, computational linguists had already found a large number of small-worlds on phrase level on various levels in different languages, but this network had not been reported. As such, it neatly lined up with existing research in quantitative linguistics.

But small-worlds are also found in brains, social networks, software architecture and power grids. This is remarkable, because wiring up a network randomly almost never leads to small-worlds. So why do all these these networks share these characteristics? Because they are subject to the same forces of formation, we think. Some experimental models show that synchronizing activity between artificial neurons tends to build clusters and shortcuts in networks. Could it be that communication in humans share the same synchronizing properties as communication in brain cells?

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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"

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

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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. As we found out soon enough, computational linguists had already found a large number of small-worlds on phrase level on various levels in different languages, but this network had not been reported. As such, it neatly lined up with existing research in quantitative linguistics. But small-worlds are also found in brains, social networks, software architecture and power grids. This is remarkable, because wiring up a network randomly almost never leads to small-worlds. So why do all these these networks share these characteristics? Because they are subject to the same forces of formation, we think. Some experimental models show that synchronizing activity between artificial neurons tends to build clusters and shortcuts in networks. Could it be that communication in humans share the same synchronizing properties as communication in 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

First let's have a brief look at what makes a small-world network a small-world network, it's not all that difficult. First of all: it's about sparse networks, that is, networks with relatively low connection 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. The "six degrees of separation" is a graph is a metaphor for this phenomenon. 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 easy to see now 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

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Circumstantial Evidence

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Whoswho&where

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Small-World Networks

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More

Maybe later.