Dear Ewa,

I wonder if you might consider measures of Transfer Entropy and of Mutual Information, as per the note drawn from my paper to UKAIS last April:

Mutual Information (MI) is considered as ‘a measure of the amount of information one random variable contains about another’ (Cover & Thomas, 1991). MI does not have a time base and so cannot measure flows. Transfer Entropy (TE) is ‘a model-free measure of information flows between different time series’ which,

‘under weak assumptions, allows [for the quantifying of] information transfer without being restricted to linear dynamics’ (Dimpfl & Franziska, 2012; Kullback & Leibler, 1951). Unlike MI, Transfer Entropy is ‘based on rates of entropy change’ (Schreiber, 2000) and so ‘captures some of the dynamics of a system’ (Tenkanen, 2008). TE may therefore be seen also as a measure of the stability or instability of the system and so, potentially, of chaotic behaviour and cascades, in which ‘a failure of a very small fraction of nodes in one network may lead to the complete fragmentation of a system of several interdependent networks’ (Buldyrev et al, 2010).

Other work I / we have done examines Instability and Uncertainty and we can obtain measurements about the degree of uncertainty in a system or process. Uncertainty can lead to instability and vice versa. Where we see a rapid decrease in uncertainty, I might suggest is a moment when such a diffusion or understanding takes place. Equally, when we see a rapid increase in uncertainty then that may be a precursor to chaos and instability and / or the making of a step change - when the old rules and stabilities go out of the window?

Ewa, great question - let me know what you think. But, I think measurements of uncertainty in the system may be a key indicator of critical mass and technology diffusion.

Yours Ever

Simon

Dear Simon, Thanks for your feedback. My research work mainly concentrates on ICT diffusion. Bearing in mind the dynamics of the process I was trying to 'find' the minimal amount/number of users which make the process of diffusion self-sustaining (following the logitics growth models). Recently I have worked on the authored book (now submitted to Springer, and accepted for publication) where I present a novel approach to measuring the 'critical mass' regarding the ICT diffusion dynamics. I attach the file where I present the general logic of the methodology. It was elaborated basing on detailed calculation of country-specific ICT diffusion processes. However, I am still working on its futher improvments. Thanks for your guidlines - maybe I will try adopt this approach. 

Once again thaks for your feedback.

Best, Ewa Lechman ([email protected])

Critical mass would be defined as the threshold after which increasing returns take over. But critical mass itself is subjected to path dependence. Links on a paper that would perhaps be helpful? And Philip Ball's book on critical mass may provide leads to luminaries in the field.

http://www.druid.dk/uploads/tx_picturedb/dw2005-1650.pdf

http://jasss.soc.surrey.ac.uk/9/3/reviews/edmonds.html

Actually I think that the critical mass generally differs according to the type of innovation. Considering a network-based innovation would probably lead to a totally different result than a pure product innovation. Therefore I tackle this question mainly with simulation models.