Predicting the future challenges our cognitive abilities since ever. And anticipating the future means guessing the most likely outcome of a given situation, out of a certain number of possibilities.

In the fifties, Claude Shannon, the father of information theory, proposed a game to measure the complexity of human Languages. The game consisted in reconstructing a whole text letter by letter. When we play this game we rely on our knowledge of language, its rules and its redundancies. In the case of Language we mostly know the set of outcomes. We would not expect a brand-new character appearing at some point. In this case the space of possibilities is given. Perhaps huge, but known. Well, almost known! Think about guessing the next word instead of the next letter. The number of combinations explodes and we can still expect the author stuffed unknown words in his/her text. In this case the space of possibilities is almost well-defined and we don’t have a clue to predict the occurrence of a crazy word just invented by the author. A real puzzle!

A puzzle that is spelled out very clearly in probability theory, in particular the branch of probability theory named “inference”. Inference is concerned with the estimation of probabilities of future events based on the observation of the past. But, what can we say when we observe an event whose existence we did not even previously suspect; this is the so-called problem of ‘unanticipated knowledge’. A special instance of this phenomenon is the so-called sampling of species problem. Imagine to be at a big gathering on an island and suppose you are interested in counting the number of guests (no one can get there or leave, at least while you count). So, you wander through the island and start meeting people and you count them. By the way, this operation would have been impossible for Funes, the main character of one of the most famous Borges’ tale. Funes, after falling off his horse and receiving a bad head injury, acquired the amazing talent –or curse- of remembering absolutely “everything”. So, he would not recognize the same person 10 minutes after because that person would not be identically the same! For instance, a different position of the hand. While you keep counting people, you may wonder about the probability to make a new encounter, i.e., being introduced to someone never met before. Well, that’s not easy at all. You’re about to estimate the probability of something that never occurred before. You don’t have a clue! This is very general problem, also affecting artificial intelligent agents. A big actor of self-driving cars recently admitted that its cars get confused by kangaroos, though they know how to avoid deer, elks and caribous! Novelties can baffle us!

All in all, we are left with the problem of charting what’s next, charting what it will be possible and, perhaps more importantly, which of the possible futures you like most or which one is heralding the best for you. These considerations have been beautifully summarized by the famous biologist and complex-systems scientist Stuart Kauffman. Kauffman coined the term “adjacent possible”, meaning all those things that are one step away from what actually exists, and hence can arise from incremental modifications and recombination of existing material. In Steven Johnson’s words: “The strange and beautiful truth about the adjacent possible is that its boundaries grow as one explores them.” This is the key point of the adjacent possible: the conditional expansion (or restructuring) of the space of possibilities, conditional to the exploration of the space itself and the experience of the new.

The very definition of adjacent possible encodes what Francois Jacob named the dichotomy between the “actual” and the “possible”, the actual realization of a given phenomenon and the space of possibilities still unexplored. In the example of counting people on an island, my “actual” at a given point in time, say 11pm, would be the set of people I already met till then. My “possible” would be the set of all people to whom I could be introduced by one of my acquaintances so far. Now, at 11:15pm, my friend Alice introduces me to Bob. Bob was already in my list of possible and after I meet him he starts enriching my “actual”. But this is not the only consequence. My encounter with Bob expands my adjacent possible because, immediately after my encounter with Bob, I could be possibly introduced to all Bob’s friends, not already my friend. From this perspective, it is like when you open a door and only after you opened that door you can see what is after and new possibilities are opening for you.

The notion of adjacent possible is a fascinating one. It tells a story about a space, the space of possibilities, very difficult to chart. Stuart Kauffman would say “unprestatable”. This means that we cannot prestate “all” the possibilities in front of us. Still this is the space we constantly explore and modify in our everyday life. It would be desirable to know more about that space, its structure, its restructuring, its dynamics, the way in which we explore it, individually or collectively.

Recently, in collaboration with Vito Servedio, Steven Strogatz and Francesca Tria, I have introduced a mathematical framework to investigate the dynamics of the new via the adjacent possible. The modeling scheme is based on older schemes, named Polya’s urns and it mathematically predicts the notion that “one thing leads to another”, i.e., the intuitive idea, I guess we all have, that innovation processes are non-linear and the conditions for the occurrence of a given event could realize only after something else happened. We had youtube only after we got broadband connectivity. Think about youtube with a 32k modem!

The expansion of the adjacent possible, conditioned on the occurrence of a novelty, is the crucial ingredient in this modeling scheme, to derive several testable and quantitative predictions. For instance, predictions about the rate of innovation, i.e., the rate at which we observe new things, along as the correlations between innovation events, the emergence of waves of novelties, trends, etc. For instance, we may wonder why, if a rich-get-richer mechanism is at play, we don’t keep listening classical music all the time instead of getting crazy for the ultimate boy band. The predictions we made based on our modeling scheme were shown to be borne out in several data sets drawn from social and technological systems: composing novels, editing Wikipedia pages, listening songs through Last.fm, writing open-source software, introducing hashtags in Twitter … and the list can be long, including examples in technology (patents) and biology.

Now, I think we are heading to the conclusions. I told you a story about surprise, complexity, space of possibilities. It is right the exploration of the space of possibilities, the adjacent possible, be it a physical (wandering on a space), conceptual (learning something), biological (evolving as a species), technological (innovating), that triggers our encounters with the new and drives what we call innovation. This is a fascinating journey and it is right through this journey that creativity emerges, in the way we create new dimensions and unprestatable solutions.

At Sony-CSL Paris we accepted the challenge and we just opened a new research line focused on Creativity, Innovation and Artificial Intelligence. A better understanding of the space of possibilities and how we explore is key to deploy human imagination, face the societal challenges of our era and conceive a better future. What is the structure of the space of possibilities? How do humans explore it? How do machines explore it? These are some of the questions we address. And those questions are relevant in many areas, for instance, how do we take decisions, how do we anticipate the impact of specific choices, how do we learn and create, how do we conceive new (sustainable) solutions. In addition, they touch upon key open problems in Artificial Intelligence, namely how machines cope with the unexpected (remember the history of the kangaroo) or could finally start dealing with the deep notion of meaning. Scientifically, I think we are just at the beginning of a fascinating path where many and new questions, “adjacent” and “possible”, are popping up just because we opened a dimension for them.