Accelerating dynamics of collective attention

With news pushed to smart phones in real time and social media reactions spreading across the globe in seconds, the public discussion can appear accelerated and temporally fragmented. In longitudinal datasets across various domains, covering multiple decades, we find increasing gradients and shortened periods in the trajectories of how cultural items receive collective attention. Is this the inevitable conclusion of the way information is disseminated and consumed? Our findings support this hypothesis. Using a simple mathematical model of topics competing for finite collective attention, we are able to explain the empirical data remarkably well. Our modeling suggests that the accelerating ups and downs of popular content are driven by increasing production and consumption of content, resulting in a more rapid exhaustion of limited attention resources. In the interplay with competition for novelty, this causes growing turnover rates and individual topics receiving shorter intervals of collective attention.

i /L i ](t) = (L i (t) − L i (t + 1))/L i (t + 1) > 0 for the other datasets. a Losses distribution of n-gram counts in Google Books. b Losses in box-office sales of movies. c Losses in relative search queries on Google Trends. d Losses in comment count on Reddit. e Losses in citation count in the APS corpus. f Losses of traffic on English Wikipedia articles.
Supplementary Figure 5: Distributions of maxima P (L i (t peak )): a Peak height distribution of n-gram counts in Google Books. b Peak height distribution of box-office sales. c Peak height distribution relative search queries on Google Trends (here the value 100 stands out, because these are the maxima of each category used as a normalization). d Peak heights from the Reddit dataset e Distribution of maxima from the publication dataset (here the development towards more citations in general can be observed). f Distribution for the maximum of visitors wihtin each hour on English Wikipedia articles.

Books
Movies Google Supplementary Figure The same data as well as the results from the simulation as the logarithmic change log(L(t)/L(t − 1)). c The data shown in Figure 3 of the main text in a semi-log and d in a no-log representation.  , sorted by relative yearly volume 11120 (1930-1950), 11700 (1950-1970), 13100 (1970-1990), 12000 (1990-2004) Movies Popular movies of each week, 145 (1980-1985), 301 (1985-1990), 387 (1990-1995), sorted by box-office sales 466 (1995-2000), 714 (2000-2005)    . They are used as fitting parameters to minimize the KS-distance to the empirical distribution. The corresponding KS-statistics and p-values to each fit are listed below. 1870-1890 1900-1920 1930-1950 1950-1970 1970-1990 1990- 1990-1995 1995-2000 2005-2010 2010-2015    Supplementary note 1. The described developments of increasing relative gains and losses is not clearly pronounced for the datasets about scientific publications and Wikipedia (Figures 2 and Supplementary Figures 2-7). Only in the tails of the distributions is a small development towards higher values detectable ( Supplementary Figures 3 and 4). In Supplementary Figures 6 and 7 an increase of extreme events is shown, but this corresponds only to the outer most events in the distributions, while the largest part stays very stable. There are two possible explanations for this: The systems change on even longer time scales than we investigated here and if we increased the window of data collection, we could see a more pronounced change. On the contrary, the more likely reason is that these systems follow mechanisms that are different from the other datasets in this work. We intentionally focus on areas which are pop-culture driven, where the increasing communication rates and especially the concept of boringness play a specifically big role. In these two systems knowledge is communicated, rather than news or entertainment being consumed. The bottleneck in these systems might not be the pure rate of information transfer and other mechanisms, than our simple model incorporates, govern their dynamics. In these systems other parameters could have changed such as the competition among scientist or their dynamics is mostly governed by external factors (22,36). For the same reason the log-normal fit as well as our simulations do not match very well. Generally most systems are additionally exogenously driven and for a more realistic simulation one might have to combine endogenous and exogenous mechanisms, e.g. by adding an random external drive to the proposed model. Nevertheless there are small hints to the same direction of acceleration as in the other datasets, but we are not capturing them fully, either by missing other important systemic mechanisms or by too narrow observation windows.
In the Wikipedia dataset we observe another difference to the other observations, the decreasing heights of maximal traffic on the articles in the inset of Figure 2g. Our interpretation of this is that the effects of proportional growth due to imitation is not the strongest driving force on Wikipedia, which makes the traffic less concentrated in the top group and a growing N causes a broadening of its allocation and the lowering of the maxima (as in Supplementary Figure 12c).

Supplementary note 2.
To better understand the behavior of the model, we can show numerically how the boringness added to the existing Lotka-Volterra equations drives the system towards criticality. The competitive Lotka-Volterra equations can lead to chaotic behavior, if the following parameter set is used (31): (2) and K = 1.0. Supplementary Figures 9a-c show the three distinct dynamical regimes. The global coupling parameter c in Eq. (11) is increased from 0.3 to 3.0. Besides coexistence and dominance for small and large values of c respectively, for c = 1.0 the system is at the critical point and shows chaotic dynamics (31). Adding the boringness term yields with K = r c = 1.0. Then, the critical behavior can be observed in all three parameter regimes ( Figures S9d-f). The two states, coexistence and dominance of a single topic are constantly driven towards each other, where imitation prevents coexistence and boringness does not allow the dominance of a single topic. This can possibly explain the broad distributions resulting in systems that undergo self-organized criticality and is subject of future research.
Supplementary note 3. The simplistic nature of the model makes the eigenvalue of the Jacobian matrix of Eqs.
Near the fixed point its imaginary part gives an estimate for the relation of the rate r to the frequency of oscillating topics by Im(λ) ∼ √ αr 1 + αc .
This relationship shows the positive proportionality of the frequency to the rate r, which we can also observe in the simulation of the full system.