How is knowledge transmitted in a small world network through communicative interaction?

How is knowledge transmitted in a small world network through communicative interaction? Hidehito Honda (hito@muscat.L.chiba-u.ac.jp) Toshihiko Matsuka (matsukat@muscat.L.chiba-u.ac.jp) Department of Cognitive & Information Science, Chiba University 1-33, Yayoi-cho, Inage-ku, Chiba-shi, Chiba, 263-8522, Japan Abstract Social science studies have shown that people are connected in a “small world. ” In this network, people are connected with short path lengths and are highly clustered. To clarify how people in a small world acquire knowledge through communicative interactions, we constructed a multi-agent model and subsequently conducted a computer simulation. Results of the computer simulation showed that in a small world network, agents acquire correct and diverse knowledge. We discuss the adaptive nature of a small world network for knowledge acquisition. Keywords: knowledge acquisition; small world network; communicative interaction; multi-agent model Introduction Category learning is one of the most researched aspects of knowledge acquisition in cognitive science. In their studies, researchers often create experimental settings where participants learn (artificial) categories by receiving feedback. As a result, most research on category learning has clarified people’s knowledge acquisition through individual learning (e.g., Cohen & Lefebvre, 2005; Kruschke, 2008). However, in the real world people acquire knowledge not only through individual learning, but also through communication with others. Pentland (2007) argued that a research perspective involving social networks containing individuals is necessary to clarify human behaviors. Goldstone and Janssen (2005) emphasized the importance of research on collective behavior. For example, they point out that “interacting ants create colony architectures that no single ant intends,” and “populations of neurons create structured thought, permanent memories and adaptive responses that no neuron can comprehend by itself” (p.424). By implication, interactions among individuals produce unique processes of knowledge acquisition that are not clarified by research on micro processes of an individual’s knowledge acquisition. In this paper, we discuss knowledge transmission which occurs through interactions of individuals. This topic is very important in the consideration of knowledge acquisition, because people often communicate with each other in ways that result in learning (e.g., Mason, Conrey, & Smith, 2007). Research about knowledge transmission reveals not only the roles of collective behavior for knowledge transmission, but also individual cognitive aspects (e.g., Brighton, 2002; Kalish, Griffiths, & Lewandowsky, 2007; Griffiths & Kalish, 2007; Smith, Kirby, & Brighton, 2003). In the present study, we focus on one of the most intriguing network structures of people’s connectivity, called the small world, and examined the role of this connectivity in knowledge transmission. Connections in a small world Social science researchers have shown that connectivity among individuals is not random, but has some regularity (although not complete). Milgram (1967) and Travers and Milgram (1969) empirically showed that people were connected with short path lengths (around six degrees of separation), which is known as the “small world phenomenon. ” This is even more evident in recent research using email and online relationships (Dodds, Muhamad, & Watts, 2003). Another feature of individual connectivity is highly clustered relationships, where one’s acquaintances also have a high probability of knowing each other (we call this probability clustering coefficient). Watts and Strogatz (1998) called a network having these two features a small world network. They proposed a very simple mathematical model representing the small world network: Imagine the network starting from a ring lattice with 1000 vertices, each connected to its 10 nearest neighbors by edges. Then, each edge is randomly rewired with probability p by disconnecting one of its vertices and connecting it to a randomly chosen vertex. Watts and Strogatz (1998) showed that this model replicates the small world network with Figure 1. Relationship between rewiring probability and path length and clustering coefficient. These plots are based on mean values over a sample of 100 different graphs.