Mathematics of Novelty and Innovation

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We experience new things every day—like meeting new people to learning new words. Typically, one novelty can pave the way for others in a process called “expanding the adjacent possible.” For instance, you’ve likely received a text or email with a new abbreviation you didn’t know. If you’re like me, you Googled the term and linked to a page that listed several other new terms and abbreviations. Voilà: novelty leads to novelty.

We experience new things every day—like meeting new people to learning new words.  Typically, one novelty can pave the way for others in a process called “expanding the adjacent possible.” For instance, you’ve likely received a text or email with a new abbreviation you didn’t know. If you’re like me, you Googled the term and linked to a page that listed several other new terms and abbreviations. Voilà: novelty leads to novelty.

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While all this seems random, new research examines the mathematical regularities behind how people encounter such novelties. A team of applied researchers share their findings in the new scientific paper, “The Dynamics of Correlated Novelties,” on Nature.com.

While all this seems random, new research examines the mathematical regularities behind how people encounter such novelties. A team of applied researchers share their findings in the new scientific paper, “The Dynamics of Correlated Novelties,” on Nature.com.

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The researchers include S. H. Strogatz of the Department of Mathematics for Cornell University, V. D. P. Servedio of the Physics Department for Sapienza University of Rome, and V. Loreto and F. Tria from the Institute for Scientific Interchange. They propose a simple mathematical model that mimics the process of exploring how a physical, biological, or conceptual space enlarges whenever a novelty occurs.

The researchers include S. H. Strogatz of the Department of Mathematics for Cornell University, V. D. P. Servedio of the Physics Department for Sapienza University of Rome, and V. Loreto and F. Tria from the Institute for Scientific Interchange. They propose a simple mathematical model that mimics the process of exploring how a physical, biological, or conceptual space enlarges whenever a novelty occurs.

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The model, a generalization of Polya's urn , predicts statistical laws for the rate at which novelties happen ( Heaps' law ) and for the probability distribution on the space explored ( Zipf's law ), as well as signatures of the process by which one novelty sets the stage for another. They tested these predictions on four data sets of human activity:

The model, a generalization of Polya's urn, predicts statistical laws for the rate at which novelties happen (Heaps' law) and for the probability distribution on the space explored (Zipf's law), as well as signatures of the process by which one novelty sets the stage for another. They tested these predictions on four data sets of human activity:

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  the edit events of Wikipedia pages

  the edit events of Wikipedia pages

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  the emergence of tags in annotation systems

  the emergence of tags in annotation systems

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  the sequence of words in texts

  the sequence of words in texts

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  listening to new songs online.

  listening to new songs online.

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“With the availability of extensive longitudinal records of human activity online, it has become possible to test whether everyday novelties crop up by chance alone, or whether one truly does pave the way for another,” the authors report.

“With the availability of extensive longitudinal records of human activity online, it has become possible to test whether everyday novelties crop up by chance alone, or whether one truly does pave the way for another,” the authors report.

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By quantifying the dynamics of correlated novelties, the results provide a starting point for a deeper understanding of the adjacent possible and its role in innovation and evolution. Specifically, the researchers plan on conducting future studies to explore “the subtle link between the early adoption of an innovation and its large-scale spreading, and the interplay between individual and collective phenomena where innovation takes place.”

By quantifying the dynamics of correlated novelties, the results provide a starting point for a deeper understanding of the adjacent possible and its role in innovation and evolution. Specifically, the researchers plan on conducting future studies to explore “the subtle link between the early adoption of an innovation and its large-scale spreading, and the interplay between individual and collective phenomena where innovation takes place.”