Human exploration of complex knowledge spaces

Driven by need or curiosity, as humans we constantly act as information seekers. Whenever we work, study, play, we naturally look for information in spaces where pieces of our knowledge and culture are linked through semantic and logic relations. Nowadays, far from being just an abstraction, these information spaces are complex structures widespread and easily accessible via techno-systems: from the whole World Wide Web to the paramount example of Wikipedia. They are all information networks. How we move on these networks and how our learning experience could be made more efficient while exploring them are the key questions investigated in the present thesis. To this end concepts, tools and models from graph theory and complex systems analysis are borrowed to combine empirical observations of real behaviours of users in knowledge spaces with some theoretical findings of cognitive science research. It is investigated how the knowledge space structure can affect its own exploration in learning-type tasks, and how users do typically explore the information networks, when looking for information or following some learning paths. The research approach followed is exploratory and moves along three main lines of research. Enlarging a previous work in algorithmic education, the first contribution focuses on the topological properties of the information network and how they affect the \emph{efficiency} of a simulated learning exploration. To this end a general class of algorithms is introduced that, standing on well-established findings on educational scheduling, captures some of the behaviours of an individual moving in a knowledge space while learning. In exploring this space, learners move along connections, periodically revisiting some concepts, and sometimes jumping on very distant ones. To investigate the effect of networked information structures on the dynamics, both synthetic and real-world graphs are considered, such as subsections of Wikipedia and word-association graphs. The existence is revealed of optimal topological structures for the defined learning dynamics. They feature small-world and scale-free properties with a balance between the number of hubs and of the least connected items. Surprisingly the real-world networks analysed turn out to be close to optimality. To uncover the role of semantic content of the bit of information to be learned in a information-seeking tasks, empirical data on user traffic logs in the Wikipedia system are then considered. From these, and by means of first-order Markov chain models, some users paths over the encyclopaedia can be simulated and treated as proxies for the real paths. They are then analysed in an abstract semantic level, by mapping the individual pages into points of a semantic reduced space. Recurrent patterns along the walks emerge, even more evident when contrasted with paths originated in information-seeking goal oriented games, thus providing some hints about the unconstrained navigation of users while seeking for information. Still, different systems need to be considered to evaluate longer and more constrained and structured learning dynamics. This is the focus of the third line of investigation, in which learning paths are extracted from advances scientific textbooks and treated as they were walks suggested by their authors throughout an underlying knowledge space. Strategies to extract the paths from the textbooks are proposed, and some preliminary results are discussed on their statistical properties. Moreover, by taking advantages of the Wikipedia information network, the Kauffman theory of adjacent possible is formalized in a learning context, thus introducing the adjacent learnable to refer to the part of the knowledge space explorable by the reader as she learns new concepts by following the suggested learning path. Along this perspective, the paths are analysed as particular realizations of the knowledge space explorations, thus allowing to quantitatively contrast different approaches to education.