Innovation can be defined as a “new idea, device or method.” It is still a mystery how one creates an idea, what makes it the person want to create change. A complexity theorist Stuart Kauffmann defined innovation as the idea that arises from the interplay between the actual and the possible. The pattern of innovation is hard to formulate because innovation consists of the expected and the unexpected possibilities. The unexpected possibility is vast as all kinds of things can be easily imagined and somehow be a connection to the idea I am thinking.

Vittorio Loreto at Sapienza University of Rome, and a few of his friends created the first mathematical model that accurately reproduces the pattern that innovation follows.

Their work took inspiration from the following laws-

Heaps’ Law- It states that the number of new things increases at a rate that is sublinear. It is governed by a power law of the form V(n) = knB where B is between 0 and 1. This law proves that innovation follows a predictable and easily measured pattern.

Zipf’s Law- This law describes how the frequency of an innovation is related to its popularity.

Both these laws are measurable, but it does not explain why the patterns arise. Loreto and his friends create “Polya’s Urn with innovation triggering.”

The exercise starts with an urn filled with colored balls. A ball is withdrawn at random, examined and replaced in the urn. If this color has been seen before, the number of other balls of the same color are also placed in the urn. But if the color is new- it has never been seen before in this exercise- then a number of balls of entirely new colors are added to this urn. Loreto then calculated how the number of new colors picked from the urn, and their frequency distribution, changes over time. Thus, this model presents a satisfactory first-principle based way of reproducing empirical observations. The team has also shown that its model predicts how innovations appear in the real world. One the one hand there are things that already existed but are new to the person who finds them, called novelties, and on the other hand are things that never existed before and are entirely new to the world, called innovations. Thus, this model surprisingly can be used to account for both phenomenon, that is, the pattern behind the way we discover novelties and the pattern behind the way we discover innovations.

References –

Emerging. Technology, ‘ Mathematical Model Reveals the Pattern of How Innovations Arise’, ‘Business Impact’, January 13, 2017.