biexponential function decline

Maths shows how we lose interest 

The study applies maths and a big-data approach to questions that have been studied at length in the social sciences. Using attention as a proxy for memory, the authors analysed online views of the Wikipedia profiles of around 1,700 sports stars, citations of almost 500,000 physics papers and 1.7 million patents, and online play counts of some 33,000 songs and 15,000 film trailers.

Researchers had previously thought that the decline in the popularity of such cultural objects followed a smooth, steep curve. But analysis of the new study data revealed that a better fit was a shape called a biexponential function, which has two phases. It shows that collective memory dropped quickly, but that the subsequent decline in attention slowed considerably, and went down a much gentler slope. Although the shape was the same for each feature studied, the actual length of each phase was different. Music showed the shortest and sharpest initial decline in attention (taking 6 years) and the online biographies of the sports stars the longest (20–30 years).

How come? The researchers propose an explanation. The first, steep decline phase is dominated by the process of communicative memory, which is the direct word-of-mouth transfer of information. And the second, more enduring phase relies more on cultural memory, which is sustained by the physical recording of that same information.