Innovatio Mathematica

Mathematics, we love it or we hate it; for some it means clarity, but for others it is a complete gibberish. The language of the Universe, it has been called, but can it also be the language of Innovation? We are currently living a explosion of mathematical models and algorithm-based business which is basically modelling reality using lots of data (Big Data) and making predictions based on those models. But, can we model innovative behaviour and predict what conditions would yield more innovative results?

It has been too long since my last post, but I am centred in adjusting to my new job (Innovation Manager at Alstom Digital Mobility). So why am I writing this article about Mathematics in Innovation? Well, as usual, the idea comes from reading other people’s contributions.  I had the chance of reading an interesting MIT Technology Review article, shared by Professor Tim Minshall in LinkedIn, that got me thinking. The article is titled “Mathematical Model Reveals the Patterns of How Innovations Arise”. Intriguing, isn’t it? I am not going to go into the details of the explanation (you can read it at but I thought it would be an interesting thing to comment and get back posting again.

The main idea behind the article is that a team of mathematicians claim to have built a model which represents how innovations are developed. It is based upon the Pólya’s urn model, which is used to represent how initial imbalances are magnified over time (“the rich get richer”). The urn contains x white and y black balls; one ball is drawn randomly from the urn and its colour observed; it is then returned in the urn, and an additional ball of the same colour is added to the urn, and the selection process is repeated (quote from The team has modified this model (Pólya’s urn with innovation triggering) so that you start with balls of several different colours and when you draw one, if it has a colour you have already seen, you put it back adding an extra ball of the same colour (normal Polya’s urn behaviour), but if the colour is new, what you would put back is additional balls of totally new colours, representing the “adjacent possible”. Using some empirical observation laws, they have demonstrated the model works.

This is actually what makes this article most interesting for me. The way I interpret it, they include in the model how seeing a new thing opens the field for the adjacent possible things not considered yet, that is, being “exposed” to novelty implies new possibilities, greater creativity and the possibility of generation of new things. If you are not subject to different ideas and possibilities, your world remains very small. Even if you are a creative person with a problem to solve (you have the “drive” to innovate), the tools at your disposal, or the building blocks you have to work with, are very reduced. Intuitively or even empirically (based on actual observation), most of us can agree on the idea that being subject to new or different things favours creativity (one of the basic needs for innovation). But now we have mathematical “proof”! Maybe, if I had been aware of this proof many years ago, I could have shown it to a boss I had, who thought that reading news or opening discussions in employee forums was a waste of productive time.

Is this useful? Well, probably not much… for now!  Many models that were just mathematical artifacts when they were released, have become part of the backbone of this “data explosion” we are currently living. So we will see if this innovation model actually has some practical implications in the future. For me, I am just happy if I have been able to show you the “adjacent possible”, something that could open new interesting horizons for you and, who knows, maybe spark new innovations.


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