Interactive Learning and Innovation: Conceptual and Mathematical Models. A District Study

Abstract

Aims: Explaining how social, cognitive and personal proximities influence interactive learning and innovation in an industrial district. Study Design: Drawing on a conceptual development, six proposals are presented and explored in a study based in the Venetian district. On the basis of these proposals, a mathematical model for knowledge transfer and innovation is developed. Results: A qualitative study of the Venetian glassmaking district shows how interactive learning in an industrial district occurs on both horizontal and vertical dimensions, along which proximities play different roles. Both horizontal and vertical learning takes place through social, cognitive and personal proximities. More precisely, it is demonstrated that knowledge of mathematical law, on both horizontal and vertical dimensions, are extensions of existing knowledge which can be found in the nevertheless scarce managerial literature on this subject. Conclusion: This study contributes to the literature on proximity within industrial districts by highlighting the role of personal proximity, which has hitherto been largely unexplored. This paper also considers the coevolution between dimensions of proximity and provides evidence of two mechanisms of coevolution: a compensation mechanism between social and cognitive proximity, and a substitution mechanism between personal proximity, and cognitive and social proximities. The elaboration of a mathematical model drawn from a qualitative conceptual model is rarely found in the existing literature. A theoretical expression of the equation of knowledge dynamics is also presented.