The tale of two clocks

The main question that this paper addresses is how to identify critical events in the evolution of a social network. The paper uses ideas from psychology about time perception. It is well known that time flows differently in different emotional situations. Equipped with this idea, this paper studies the relationship between two clocks. As opposed to standard synchronization, where everything is done in order to force clocks to agree on the time, the paper embraces the discrepancy between the clocks. This paper presents a standard model where two natural clocks exists simultaneously: the event clock C_e and the weighted clock C_w. As the paper shows, using the drift between those two clocks is useful to understand the dynamics in social networks. The main claim is that the drift between different clocks points to a critical event in the evolution of the social network, similar to time perception in psychology. In order to demonstrate this claim, plays by William Shakespeare were used, and from them two clocks were created: the 'word time', which is the weighted clock, and the 'response time', which is the event clock. The paper will introduce the concept of a single clock drift. A play can have many, or a single clock drift events. It is shown that in the single clock drift plays, the beginning of the drift points to a critical event in the play. The results are compared with the 'standard common' opinion.