Dynamics on Expanding Spaces: Modeling the Emergence of Novelties

  • Vittorio LoretoEmail author
  • Vito D. P. Servedio
  • Steven H. Strogatz
  • Francesca Tria
Part of the Lecture Notes in Morphogenesis book series (LECTMORPH)


Novelties are part of our daily lives. We constantly adopt new technologies, conceive new ideas, meet new people, and experiment with new situations. Occasionally, we as individual, in a complicated cognitive and sometimes fortuitous process, come up with something that is not only new to us, but to our entire society so that what is a personal novelty can turn into an innovation at a global level. Innovations occur throughout social, biological, and technological systems and, though we perceive them as a very natural ingredient of our human experience, little is known about the processes determining their emergence. Still the statistical occurrence of innovations shows striking regularities that represent a starting point to get a deeper insight in the whole phenomenology. This paper represents a small step in that direction, focusing on reviewing the scientific attempts to effectively model the emergence of the new and its regularities, with an emphasis on more recent contributions: from the plain Simon’s model tracing back to the 1950s, to the newest model of Polya’s urn with triggering of one novelty by another. What seems to be key in the successful modeling schemes proposed so far is the idea of looking at evolution as a path in a complex space, physical, conceptual, biological, and technological, whose structure and topology get continuously reshaped and expanded by the occurrence of the new. Mathematically, it is very interesting to look at the consequences of the interplay between the “actual” and the “possible” and this is the aim of this short review.


Preferential Attachment Network Growth Polya Model Albert Model Preferential Attachment Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Vittorio Loreto
    • 1
    • 2
    • 3
    Email author
  • Vito D. P. Servedio
    • 1
    • 4
  • Steven H. Strogatz
    • 5
  • Francesca Tria
    • 2
  1. 1.Physics DepartmentSapienza University of RomeRomeItaly
  2. 2.ISI FoundationTorinoItaly
  3. 3.SONY-CSLParisFrance
  4. 4.Institute for Complex Systems (CNR-ISC)RomeItaly
  5. 5.Cornell UniversityIthacaUSA

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