Waves of novelties in the expansion into the adjacent possible.

The emergence of novelties and their rise and fall in popularity is an ubiquitous phenomenon in human activities. The coexistence of popular evergreens with novel and sometimes ephemeral trends pervades technological, scientific and artistic production. Though this phenomenon is very intuitively captured by our common sense, a comprehensive explanation of how waves of novelties are not hampered by well established old-comers is still lacking. Here we first quantify this phenomenology by empirically looking at different systems that display innovation at very different levels: the creation of hashtags in Twitter, the evolution of online code repositories, the creation of texts and the listening of songs on online platforms. In all these systems surprisingly similar patterns emerge as the non-trivial outcome of two contrasting forces: the tendency of retracing already explored avenues (exploit) and the inclination to explore new possibilities. These findings are naturally explained in the framework of the expansion of the adjacent possible, a recently introduced theoretical framework that postulates the restructuring of the space of possibilities conditional to the occurrence of innovations. The predictions of our theoretical framework are borne out in all the phenomenologies investigated, paving the way to a better understanding and control of innovation processes

Comparison of the UMT and GUMT models.

<p>(Left-Panels) Frequency of occurrence <i>n</i>_<i>i</i> (suitably normalised with the maximum value <i>n</i>_<i>max</i>) of each element <i>i</i> ∈ <i>S</i> as a function of its first appearance time <i>t</i>_<i>i</i>. (Right-Panels) For each interval of length Δ<i>τ</i> we plot of the first appearance time of the most popular element within the interval, <i>t</i>_<i>max</i>(<i>I</i>). The length of each interval is Δ<i>τ</i> = 10000. Top Panels are results coming from a simulation of the UMT model with parameters <i>ρ</i> = 2, <i>ν</i> = 2 and <i>η</i> = 0.4 for the model. Bottom Panels correspond to simulations of the GUMT model with <i>ρ</i> = 2, <i>ν</i> = 15, <i>η</i> = 0.001, <i>γ</i> = 0.004 and the choice II of the function <i>f</i> and <i>g</i>.</p

Pictorial representation of the model.

<p>Supposing that at time <i>t</i>−1 the last extracted ball has label <i>κ</i>, we can divide the urn into two large classes of balls: the class including colours already appeared in <i>S</i> and the class including colours that never appeared, and thus belonging to the adjacent possible, at time <i>t</i>. These two classes are further subdivided in two classes of balls sharing (<i>κ</i>) and not sharing () the label <i>κ</i>. The probability of extracting a ball at time <i>t</i> is proportional to a weight depending on the sub-class it belongs to. In particular the weights are 1 and for sub-classes and , respectively and and for sub-classes and , respectively. (See the <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0179303#sec006" target="_blank">Methods</a> section for details). If at time <i>t</i> an already appeared colour is extracted, then <i>ρ</i> balls with the same colour are added to the urn; if instead a ball is extracted from the adjacent possible, <i>ρ</i> balls with the same colour are added to the urn (now within the class of the ball already appeared) and <i>ν</i> + 1 balls of different colours sharing the same brand new label are added to the adjacent possible class.</p

Beyond rich-get-richer.

<p>(Left-Panels) Normalised frequency of occurrence <i>n</i>_<i>i</i> of each element in <i>i</i> ∈ <i>S</i> as a function of its first appearance time <i>t</i>_<i>i</i>. (Right-Panels) For each interval of length Δ<i>τ</i> we plot of the first appearance time of the most popular element within the interval. Data are shown for the Last.fm (a-b), Twitter (c-d), Github (e-f) and Gutenberg (g-h) datasets. Colour is coding for the fraction of time the successful element has appeared within the corresponding interval. The length of the interval is Δ<i>τ</i> = 10000 for non-text datasets and Δ<i>τ</i> = 1000 for the Gutenberg one.</p

Youth coefficient and Gini-like coefficient.

<p>(A-B-C) Curves for the computation of the <i>Gini-like</i> coefficient: on the axes, <i>x</i>_<i>i</i> is the relative rank of an element according to its appearance time (older elements on lower ranks), and <i>y</i>_<i>i</i> is the cumulative frequency of occurrence of elements up to <i>i</i> in <i>S</i>. Results are shown for the Last.fm (A), Twitter (B) and GitHub (C) datasets. (D-E-F) Graphs for computing the <i>Youth</i> coefficient: Average introduction time of the elements within an interval of <i>S</i> as a function of the interval index, for the Last.fm (D), Twitter (E) and GitHub (F) datasets. In each panel, red curves represents the real datasets while blue curves represent the reshuffling of the data in which <i>S</i> has been randomly re-ordered.</p

Variability of popularity metrics.

<p>Variability of popularity metrics.</p

Waves of novelties in the expansion into the adjacent possible

The emergence of novelties and their rise and fall in popularity is an ubiquitous phenomenon in human activities. The coexistence of popular evergreens with novel and sometimes ephemeral trends pervades technological, scientific and artistic production. Though this phenomenon is very intuitively captured by our common sense, a comprehensive explanation of how waves of novelties are not hampered by well established old-comers is still lacking. Here we first quantify this phenomenology by empirically looking at different systems that display innovation at very different levels: the creation of hashtags in Twitter, the evolution of online code repositories, the creation of texts and the listening of songs on online platforms. In all these systems surprisingly similar patterns emerge as the non-trivial outcome of two contrasting forces: the tendency of retracing already explored avenues (exploit) and the inclination to explore new possibilities. These findings are naturally explained in the framework of the expansion of the adjacent possible, a recently introduced theoretical framework that postulates the restructuring of the space of possibilities conditional to the occurrence of innovations. The predictions of our theoretical framework are borne out in all the phenomenologies investigated, paving the way to a better understanding and control of innovation processes