New Math Reveals the Roots of Innovation – Digitalmunition

News New Math Reveals the Roots of Innovation

Published on June 26th, 2019 📆 | 6680 Views ⚑


New Math Reveals the Roots of Innovation

How do new things occur? New ideas? New words? New choices?

Scientists have been studying this question for years. And now, through the work of a team of mathematicians in Rome, they may have found equations for innovation that describe the emergence of the new in the real world for the first time.

For a long time, scientists have had equations that reflected what they observed about new concepts in human experience. In 2002, noted complexity theorist and MacArthur Fellow, Stewart Kauffmann, proposed the idea of the “adjacent possible” to explain biological innovation. The “adjacent possible” is the universe of everything that doesn’t exist lying one step away from everything that does exist. Change comes from incremental creep from the real to the adjacent possible. If you think about it, this process of small change can produce huge alteration quickly, because each adjacent shift opens up many possible new adjacencies.

This is a cool concept, but only that. Up until now, there has been no proof of it. What has been clear to scientists is that change does follow a clear pattern. This has spawned broadly accepted “laws” of observed emergence of the new.

One is Heap’s Law, which predicts the emergence of new words in written communication. What is says, simply, is that new words emerge in large bodies of text at a predictable but slow pace. Another such law is Zipf’s law, which describes the frequency of words based on their popularity. The most popular word (which is “the” in English) appears about twice as often as the next most popular, three times more than the third and so on. This rigorous distribution lies behind some aspects of Neuro-Linguistic Programming and cryptography systems.

These models certainly are interesting, but they don’t actually explain why these patterns emerge.

The new model from Vittorio Loreto at Sapienza University of Rome does. It comes from manipulation of a math model called Polya’s Urn. This is a kind of math sandbox of equations around power curves—how the rich get richer, or how a venture fund portfolio works. Loreto’s team modified Polya’s Urn to accept uncertainty. This meant it more closely reflected the increasing and uncertain complexity of the “adjacent possible.”

Think of a ball pit, full of balls that change color constantly. Now add to this the factor that whenever a brand new color appears in the balls, a whole fresh set of additional new colors also appear. Each innovation spurs additional unexpected potential innovations. The scientists call this Polya’s Urn with innovation triggering.

With that new factor, the Polya’s model confirms both Heap’s Law and Zipf’s law. In other words: “The model of Polya’s urn with innovation triggering, presents for the first time a satisfactory first-principle based way of reproducing empirical observations.” Loreto told MIT Technology Review. That is science speak for, “It works!”

This new math model does seem to be able to predict how innovations emerge in the real world. It can predict how edit events occur in Wikipedia, the emergence of new tags in social annotation systems, the sequence of words in texts, and even how humans discover new songs online.

This model appears able to reflect both how individuals find things that already exist but are new to them and how ideas that never existed before emerge.

This is heady stuff. As Loreto said: “These results provide a starting point for a deeper understanding of the adjacent possible and the different nature of triggering events that are likely to be important in the investigation of biological, linguistic, cultural, and technological evolution.”

Reprinted by permission.

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