August 8, 2017

How Innovations Arise



Could it be true that innovations are not random but actually predictable?

That’s what a new mathematical study earlier this year by Vittorio Loreto and co. at the University of Rome concluded. Their research demonstrated that innovations can be modeled between the actual and the possible.

Actual - Possible

+ Mathematical Model Reveals the Patterns of How Innovations Arise

Complexity theorist Stuart Kauffman introduced the idea of the ‘adjacent possible‘ as a way of thinking about biological evolution in 2002.


When we take what we currently know – the actual – and push ourselves into a world of unexplored possibilities – the possible – innovations take form. This, in turn, creates a self-sustaining cycle, as the faster the rate of change for the landscape of future possibilities, the more innovations that arise, which in turn creates more of the possible.


Naturally, it would seem impossible to model such a phenomena, but that’s exactly what Loreto and his team of scientists were able to do. They started with a ‘mathematical sand box’ called Polya’s Urn. Polya’s Urn starts with an urn filled with balls of different colors; each ball is randomly picked from the urn and placed back in the urn with a number of other balls of the same color. This increases the odds that this color will be selected in the future.


This model enables scientists to model the expected consequences of an innovation but cannot account for the unexpected consequences of how innovation influences the adjacent possible; therefore the team adapted the Polya Urn model to account for all the unexpected consequences of how an innovation influences the adjacent possible.



Their model starts off in the same way as Polya’s Urn. If the color has been seen before, a number of other balls of the same color are also placed in the urn. But if the color is new and has never been seen before, then a number of balls of entirely new colors are added to the urn. The scientists then calculate how the number of new colors picked from the urn, their corresponding frequency distribution, changes over time. The result is that the model reproduces Heaps’ and Zipf’s Law (power laws and frequency distribution) in the real world for the first time in mathematical history. This model can be summed up as Polya’s Urn + innovation triggering. 


Their model has been used to predict innovations in the real world, such as:

  • how edit events occur on Wikipedia pages
  • the emergence of tags in social annotation systems
  • the sequence of words in texts
  • how humans discover songs in online music catalogues

What’s interesting is that these systems evolve into two different forms of discovery:

  1. there are things that already exist but are new to the individual who finds them, such as online songs
  2. there are things that never existed before and are entirely new to the world, such as Wikipedia edits

The interplay between old and new, actual and possible, past and future, opens the door to an entirely new context for looking at how we bring innovations into the world.


The triggering events that lead to new innovations stem from collisions, or connections, in our daily lives. These collisions are impossible to map out, but they need to be made in order for innovations to arise. Such triggering events in a business context could be a fortuitous meeting on an airplane, launching a website in a new language, learning a new skill in an unrelated discipline, having lunch with a scientist who studies something you know nothing about.

This model demonstrates that a lot of the ideas that governments have around innovation, where they effectively try and control and mandate it, are wrong. Rather than creating barriers (ie. taxes regulations, etc) and defining the participants (ie. researchers, venture capitalists, etc), they need to create open ecosystems that enable such collisions between people across disciplines, countries, and languages. They need to dismantle complex compliance procedures for taxation, create investment incentives for the retail public, and fast-track young people through universities into places where they can innovate rather than mundane jobs.

In a world where so many industries, technologies, and social systems are changing so quickly, we need to learn to look at innovation as a science, rather than a random occurrence, and open ourselves to opportunities between the actual and the possible.