A two-phase model of collective memory decay with a dynamical switching point

TL;DR

This paper introduces a two-phase mathematical model for collective memory decay, combining exponential and power-law phases, validated with Wikipedia data across various event categories, revealing a common phase shift around 10-11 days post-peak.

Contribution

The paper presents a novel two-phase decay model that captures both fast and slow dynamics of collective memory, with a method to detect phase shifts in decay behavior.

Findings

The model outperforms existing models in most event categories.

Decay phase shifts occur approximately 10-11 days after peak across categories.

Model parameters are consistent across different types of events.

Abstract

Public memories of significant events shared within societies and groups have been conceptualized and studied as collective memory since the 1920s. Thanks to the recent advancement in digitization of public-domain knowledge and online user behaviors, collective memory has now become a subject of rigorous quantitative investigation using large-scale empirical data. Earlier studies, however, typically considered only one dynamical process applied to data obtained in just one specific event category. Here we propose a two-phase mathematical model of collective memory decay that combines exponential and power-law phases, which represent fast (linear) and slow (nonlinear) decay dynamics, respectively. We applied the proposed model to the Wikipedia page view data for articles on significant events in five categories: earthquakes, deaths of notable persons, aviation accidents, mass murder incidents, and terrorist attacks. Results showed that the proposed two-phase model compared favorably with other existing models of collective memory decay in most of the event categories. The estimated model parameters were found to be similar across all the event categories. The proposed model also allowed for detection of a dynamical switching point when the dominant decay dynamics exhibit a phase shift from exponential to power-law. Such decay phase shifts typically occurred about 10 to 11 days after the peak in all of the five event categories.