Mathematical Models of Innovations

Interesting article spotted in The MIT Technology Review:

And yet the process of innovation is something of a mystery. A wide range of researchers have studied it, ranging from economists and anthropologists to evolutionary biologists and engineers. Their goal is to understand how innovation happens and the factors that drive it so that they can optimize conditions for future innovation.

This approach has had limited success, however. The rate at which innovations appear and disappear has been carefully measured. It follows a set of well-characterized patterns that scientists observe in many different circumstances. And yet, nobody has been able to explain how this pattern arises or why it governs innovation….

The adjacent possible is all those things—ideas, words, songs, molecules, genomes, technologies and so on—that are one step away from what actually exists. It connects the actual realization of a particular phenomenon and the space of unexplored possibilities.

But this idea is hard to model for an important reason. The space of unexplored possibilities includes all kinds of things that are easily imagined and expected but it also includes things that are entirely unexpected and hard to imagine. And while the former is tricky to model, the latter has appeared close to impossible.

What’s more, each innovation changes the landscape of future possibilities. So at every instant, the space of unexplored possibilities—the adjacent possible—is changing…

The team has also shown that its model predicts how innovations appear in the real world. The model accurately predicts how edit events occur on Wikipedia pages, the emergence of tags in social annotation systems, the sequence of words in texts, and how humans discover new songs in online music catalogues…

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