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.
