What comes to your mind when you hear the word “Complexity”?

I have my opinion on the topic of complexity, as it is sometimes used as a buzzword. Complexity is a property of a system and it can be measured. It can be shown whether a system is complex or not: for a complex system, the sum of its elements is higher than each one of them independently in superposition. Sometimes, people say “Yeah, I study complex system” but then no complexity is measured or tested. It is just a buzzword to say “We do something big or something complicated”, which is not the same thing as studying complexity. This is one take. As a theoretical computer scientist, another take is the computational complexity. It is a more subjective version of complexity. We know that a problem is complex, depending on the best algorithm that we know to solve it. Here, the definition of complexity depends on what we know. I guess, for biology, you consider more the first one. However, these complexities are some way related.

How are these two types of complexity related?

There is this idea of Kolmogorov complexity. The Kolmogorov complexity of a process is the shortest code that can reproduce it. In general, when you do physics or in natural sciences and you have to cope with complexity, you try to make a model, a minimal model that can reproduce the phenomena that you are studying. This approach would be very close to the notion of the Kolmogorov complexity. It becomes subjective again, because the shortest code that defines Kolmogorov complexity depends on our design efforts. You can indeed never be sure of the Kolmogorov complexity of something. There is a mathematical proof concerning the uncomputability of the Kolmogorov complexity. In your research, where do you encounter complexity? My research is focused on the analysis of humans. I put them all together. That makes quite a complex system. Society does not behave the same way as individuals. We are not separable from our interactions. There are many moments that we can really observe and analyze models of collective phenomena. These phenomena are complex by definition. Let’s illustrate it. You make an experiment with an individual: you measure certain things. Then, you take several individuals, put them together in a certain field: they are likely to behave completely differently. The question of how that has happened can be explained by the principles of complex systems.

What are the principles of complex systems?

In general, complexity is due to coupling between individuals, between humans. This coupling is a non-linear interaction. In a sufficiently large scale or in certain conditions,this nonlinear dynamics can make phenomena emerge. Emergent phenomena are high-order structures that you cannot infer from just analyzing one individual. Nowadays, with all the digital traces, social emergence is more measurable. For a long time, the best you could do is to observe riots or measure elections. It was very difficult to get microscopic data. Now, it has been much easier to get with microscopic data with higher resolution. That is why complexity in social systems became a question. It, indeed, became possible at least answer it to some extent.

What are the methods you apply in order to answer the question of complexity in social systems?

At first, there is not a question of complexity but a phenomenon . To explain it, you formulate a set of interactions between humans, because they are the basic elements of the system. In general, the phenomena like culture or collective opinions are not simple enough to be understood at the level of individuals. You need to see people interacting with each other to really get what they are going to do next. You approach the complexity question more or less motivated by the big phenomenon, while trying to explain bottom-up the collective phenomenon. Examples for bottom-up approaches are the creation of a model or the analysis of a large group of persons.

From observations of a collective behavior, you try to understand it and build a possible explanation of it, don’t you?

Exactly. That’s for example the case in my PhD thesis about collective emotions in online communities. When you interact in an online community, sometimes you can experience these collective phenomena. There are moments when something becomes viral, or there is a huge fight somewhere. In psychology, they have studied this for many years and they call it collective emotions. A collective emotion is an emotional state shared by a lot of people for some reason. That was the microscopic observation. There are many processes that psychology has identified. However, they cannot really make the explanation why the collective emerges from individuals and why this emerges more often online than offline. That was my question. I was motivated from the top. Even if I started at the top, the final model reproduces something collective from bottom to up. My model does not explain individual reactions well. You cannot predict with my model what a person is going to do next but you can understand much better what the collective is going to do next.

What was the process from collecting online data to the validation of a final model?

I collected online data and I saw that there were fluctuations of emotions that could not be explained by a group of persons talking and not listening to each other. It requires interactions in large waves. To reproduce this collective behavior, I proposed a simple agent-based model. An agent based model models an individual with some internal emotions and its interactions. But the question is what does it really mean? A model is just a simulation. It is not an empirical finding. But it helps to connect different fields. So there it helped me to connect the big data field with the experimental psychology field. The psychology that I set on the model was a set of a hypothesis. I worked with psychologists to make experiments to validate this individual dynamics and interactions in the model. We put people in front of a computer, with sensors and asking them what they feel. Most of the assumptions of the model were validated by the experiments. Surprisingly, there were other things that we did not hypothesize. Now, we are refining the model. We include the psychology observed experimentally as new assumptions and see if it produces something that we did not observe before.

What kind of assumptions, for example?

One assumption was that the text that we read has an emotional impact on how we feel. The precise shape of the impact over time has a saturation point. It makes an impact and then this impact relaxes with time. There are two dimensions of emotions in this model of short-lived emotions: valence (pleasure between positive and negative emotions) and arousal (corresponds to the activity). Arousal drives activity. In my model, the whole collective behavior was driven by this arousal fluctuations. One other assumption was that people write because they are in an arousal state. Experiments validated this. The model has a feedback: after you write, there is a relaxation of the arousal. The expression allows you to relax a little It creates a non-linearity in the collective emotions. The collective emotions do not last forever: the collective relaxes too. That happened indeed. Right after writing something, people had an instant of relaxation, which was faster that the normal emotions. In this experimental phase, there were also some surprises: after writing, there was also an increasing valence. The persons were not only more relaxed, but also feeling better. That was something that I never hypothesized. Another assumption was missing in my model: the feedback on emotions depends on the fact that they were starting a discussion or replying to one. In connecting both microscopy, here the experiments, and macroscopy, my model of online communities, there is the real complexity. From your point of view, humans are the building blocks of your model. Do you consider them as simple or as complicated? In this case, the individuals are quite complicated. They are described by two variables and are time-dependent. For people working in dialog systems (for example, artificial intelligence), it is a very simple model. But for a person working in opinion dynamics, it is a very complicated model. I wanted to be in the middle. I wanted it to be realistic so I could link to psychology but I also wanted it simple, so that I could analyze it. I can indeed solve my equations and have a mathematical understanding of why the collective emerges.

How do you define a system? Do you work with closed or open systems?

A system is a set of elements that interact with each other. They have a complexity depending on interactions and dynamics of the system. Complexity is a property of a system in that sense. In general, I include some noise term, some random factor for all the things that I don’t model: for example, something that happens much faster. This way, it appears in my dynamics. It is a source of uncertainty that can be seen as external. Sometimes, I analyze response functions of social systems. You model a set of people, something happens and they react. In this case, the stimulus of the shock is external. What I modeled is the dynamics after this external stimulus. Sometimes, there is something given like a network. You try to understand the evolution of the network given some assumptions and some dynamics. What is presupposed, here the network, is external to the model.

Would you link uncertainty and complexity?

No. When I said uncertainty, I meant more stochasticity. Uncertainty is that you don’t know what is going to happen, while stochasticity is that you know that it is going to be random. In the case of stochasticity, you don’t care and you try to understand the rest. I don’t think that complexity means unpredictability.

What is the link between complexity, order and disorder?

Complexity is a property of a model and by the means of a model, we can understand this complexity. For me, it is nothing different than other phenomena like order or disorder. To some extent, when we talk about complexity, we talk about that some level of order exists. Complexity is a qualitatively different phenomenon from the one that happens at a lower level. When something is only noise, you don’t say it is complex. You say it is complex when you see some patterns appearing.

In our project, we want to see a pattern appear on a grid of bacterial colonies. Even if it is more a biological project, we linked with complexity. That is one point our fields have in common. Do you think that transdisciplinarity could be a key to formalize complexity better?

So you chose complexity because it is a cool topic. People are starting to talk that there are many things in common across different fields in terms of this complexity idea. There is not enough effort made in order to put things together. And the one that tries to put it together is sometimes seen as pointless, crazy. But there are similarities between the fields handling complex systems, for example in the dynamics. If you go to a psychologist and say “What I observe here is the same for the stock market and for bacteria”, they don’t care. It is a matter of time. In a methodological sense, I am betting my career on interdisciplinarity. I think it is useful to transfer things from one community to another. It really amplifies the potential of new insights. If you are bringing the right expertise to a community, it can change this community completely. Whether the understanding of all the systems together can be made in a sort of additional field, I don’t really know if it is possible. I would like it of course but I am not completely convinced.

Thanks a lot for your time!

To learn more

[https://www.sg.ethz.ch/media/publication_files/dub1881p-Garcia.pdf Modeling Online Collective Emotions Garcia, David; Schweitzer, Frank Proceedings of the 2012 workshop on Data-driven user behavioral modeling and mining from social media-DUBMMSM '12, CIKM2012, Pages: 37, Publisher: ACM Press]