Emergence in learning: Understanding the evolution of knowledge via complex networks

Albert C T Cheung and Leung Chun Ming
The Open University of Hong Kong
Hong Kong SAR, China

Guanrong Chen
City University of Hong Kong
Hong Kong SAR, China

The major outcome of discovery learning is the emergence of concepts at higher taxonomy levels. The process mimics the pursuit of knowledge in research. By studying the evolution of key concepts at research frontiers, one may discover formation patterns of new ideas and gain insights into emergence in learning and how it may be measured.

Many natural and manufactured systems and activities can be described as complex networks (i.e. large networks of components characterized as being open, self-organizing, scalable and emergent) and modelled as scale-free networks with power-law degree distribution, e.g. the Internet, cities, insect colonies, immune systems, and scientific collaborations. Complexity sciences can be applied to studies of the emergence of new concepts in learning and research. Here we explore the networking and creation of knowledge, using tools which have proved to be effective in network science and social learning.

We use keywords in research papers (archived in http://iopscience.iop.org/) in 76 journals in the period 1997 to 2013 as proxies for knowledge in a specific corpus of knowledge, viz. astronomy and astrophysics, diverse disciplines rich in discoveries and rapidly evolving. We use papers as one set of nodes and single keywords as another. Together, they form a bipartite network which is well-studied in mathematical graph theory. The fact that keywords represent a suitable component of knowledge and would lead to emergence is reasonable because the author would have selected them to incorporate his/her knowledge in a paper. As the frequency of such keywords being re-selected and re-cited increases, at some threshold new knowledge will emerge as a deeper understanding of an unknown subject and/or as a better presentation of a vague concept in the initial thinking. In this respect, the selected keywords indeed create a new advancement of knowledge in the form of a peer-reviewed research paper.

Our results indicate that the frequency of occurrence of keywords in this corpus follows a power-law degree distribution, suggesting that the identified bipartite network structure provides a scale-free network paradigm. We then connect keywords pair-wise with an additional edge (or link) if they appear in the same paper. The strengths of these edges are the number of papers that share the same two keywords. We can follow the evolution of such pairings over time to explore the growth or mutation of keywords, which reflect the authors’ ideas, theories, methodologies and instrumentation, as well as their interactions, which will produce emergences. By further exploring the associated network of authors, we can analyse the interaction of the knowledge-emerging network with the authorship network and gain insights into the ecology and dynamics of a research discipline.