Combinatory Relational way of thinking: background of ideas

Though I previously wrote some articles about personal reflections on the process of Combinatory Relational thinking, it wasn’t explicitly emphasized how I came to it. Or at least not in the way explained in upcoming articles. The current series of articles is an extension and a work on topics that I presented in a chapter of the book “Uncertainty: Making Sense of the World for Better, Bolder Outcomes,” coauthored by the members of the Grey Swan Guild.

As sometimes happens in life, some ideas are just an outcome of answering the question ‘Why not?’. During the research on my doctoral thesis, the topic of some of my published research papers was opinion formation or opinion dynamics. The aim was to devise a computer simulation model of opinion exchange that would mimic real-life situations as much as possible. The outcome of computer simulation would be conditions resembling potential societal situations, like consensus, polarizations, etc.

Grounded on the paradigms of complex systems, the idea was to start with some group of agents (i.e., persons), associate opinions with them, and introduce rules of their exchange. Then, the dynamics of such a system, through computer simulation, will drive the society of agents toward some of the outcomes. The self-organization of this complex system of opinions imposes the unpredictability of the final social situation. So, starting from simple elements and rules, through complex dynamics, a state that appears is characterized by emergence, a well-known property of complex systems.

Though this roadmap seems simple, an adequate mathematical representation of opinions and rules of their exchange is rather challenging. The aim is to compromise between over-complicated and over-simplified models and remain meaningful and realistic. To overcome these challenges, I reached out to the conceptual background of mathematical formalism devised to analyze complex social systems, called the Q-analysis.

So, together with my collaborators, I hypothesized that opinions exhibit emergent property. Based on this presupposition, an opinion is a collection of bits (whatever they might be) that are in some relation. When formed, the opinion has a different meaning than each bit separately. If two opinions share bits, they are overlapping. Then, two agents having these two opinions are prone to exchange bits of opinions successfully — and further, many different opinions and their overlappings form a complex system of opinions.

Say, two persons are exchanging opinions about the epidemic of obesity, as sketched in the cartoon below. Each of them formed an opinion according to sets of arguments, and some of arguments are the same. This situation can be mapped on a mathematical objects called simplices (or simplexes).

Mathematically and for the purposes of simulation, the opinion is associated with an object called simplex, and their collection is called the simplicial complex of opinions. Then, some rules are needed under which opinions can be exchanged. Well, we reached the rules that are already considered in other opinion dynamics research, which, on the other hand, leaned on the findings from cognitive science and social psychology, such as information flows directed outwards (i.e., from the agent to its neighbors), social influence, homophyly, and bounded confidence.

Well, I thought, why shouldn’t I reverse the process from simulations in silica to in vivo? In other words, what if opinions, ideas, or whatever can be the product of the mind is still represented by a simplicial complex, but instead of agents, real persons are actors that run the dynamics of the system? Then, they will perform mental simulations instead of computer simulations. Well, it is necessary to impose the rules by which opinions, ideas, or whatever can be the product of the mind will be exchanged and recreated.

In the background of this setting are well-known properties of complex systems, but now applied to the complex system of opinions, ideas, or concepts. Say an idea is formed by the bits of knowledge in some relation, hence having the emergent property. When people exchange ideas, the complex system of ideas is evolving in a self-organized manner. Depending on the topic, this system is adaptable to the environment. I can go even further with these examples, though it is not the point of this article.

Now, one might ask: ‘Where is the Combinatory Relational thinking here?’ The relation between bits or elements is crucial in forming opinions or ideas. Having different chunks of knowledge is one thing, whereas making a relation between them and producing a new meaning is an entirely different thing. In a nutshell, the bottom line is integrating bits into the whole by introducing the relation.

Being combinatorial, this way of thinking can benefit only when there are general and broad guidelines, like underlying principles, rather than implementing some predisposed algorithm. This constraint by the rigid algorithmic steps can restrain the creativity process of making combinations of pieces and imposing the relation between them. By lacking the algorithmic steps, an open issue emerges of practicing and implementing the relational way of thinking.

Inspired by the process of training in sports, in which I am pretty much engaged, as can be noticed from some of my previous articles, my standpoint is that Combinatory Relational thinking can be exercised in a way the sports training sessions are organized. This way, after planned and structured exercises, the training participant spontaneously implements the underlying principles.

But from where can we borrow these underlying principles so that combinatory playing and relational thinking come spontaneously? I find that these principles can be harvested from cognitive science, like the Conceptual blending theory devised by G. Fauconnier and M. Turner. In this way, the externally imposed practice in the form of training sessions follows the internal thinking process of integrating concepts.

Now that we have rough outlines of the Combinatory Relational thinking, questions arise: Why do we need Combinatory Relational thinking anyway? Why is it important and valuable in the modern world? How can it contribute to practicing sensemaking, finding meaning in uncertainty, enhancing the innovation process, or tackling wicked problems? What are those mentioned underlying principles? How does the training session look like?…

Answering these questions are topics of articles on their own.

Applying the methodology, I aim to set the stage for making ‘hammers’ for a particular problem, avoiding the trap of Maslow’s Hammer.