My Part C (4th year) dissertation at Oxford was entitled 'Dynamics on Hypergraphs'. Prof. Renaud Lambiotte, my supervisor, was kind enough to give me the flexibility to choose a project that suited my interests. I wanted to do something related to the mind/brain, so I began working on a new network-based measure to quantify consciousness, building on the Perturbational Complexity Index. Sadly, this project didn't go very far, because the data wasn't what I'd hoped for. With just weeks to go until the dissertation deadline, and needing to come up with a new project quickly, I fell back to focusing on hypergraphs. Still wanting my dissertation to relate to the brain in some way, I chose to focus on abstract models of thinking. This didn't require any real-life data, just some (potentially over-)generalisations from cognitive science. Overall, my dissertation produced some novel contributions to hypergraph theory, all in the context of a visual model of thinking.

Non-mathematical intro.

(Get ready to read the word 'thinking' many, many times...)

  I've spent quite a lot of time thinking about thinking. In particular, I've spent a while thinking about how we can change our thinking. Suppose you have repetitive, unwanted thoughts. These could be as minor as 'I can't be bothered to go on a run today', or could be more serious thoughts that are part of a mental health disorder. An obvious question to ask is: what the best way to overcome that maladaptive pattern of thinking? That is, how can you harness your own thinking to turn maladaptive thoughts into adaptive ones?

  When contemplating the above question myself, I came up with a visual model that represented how I believed the process of turning maladaptive thoughts into adaptive ones worked in my mind. By this, I mean a way of visualising the process of changing bad thoughts into good ones, based on how I thought thinking worked. My model enabled me to successfully change my thinking for the better.

  This got me thinking: could visual models of thinking help others do the same? My gut feeling was 'yes', and after a bit of Googling, I found some research that supported this: it demonstrated that visual explanations can improve understanding of abstract concepts. However, the little model that I had conjured up myself was just based on my own perception of thinking; in order for the model to be useful to others, it would need to be backed up by cognitive science literature.

  So for my dissertation, I set out to create such a visual model (diagram below). The notion I used of what 'thoughts' are was based on cognitive science research, and similarly was the method in which to reappraise thoughts. Since my degree was in mathematics, the dynamics of turning maladaptive thoughts into adaptive ones was mathematically modelled. I ended up with a model of a network of thoughts that had simple diagrams, and demonstrated the success of changing from maladaptive to adaptive thoughts using simulations. Success!

  As I talk about in my conclusion, there are multiple ways that the model could be improved or extended. (And as I don't talk about, the success of the dynamics was ever-so-slightly fudged...) That aside, I feel like my dissertation could be the first steps towards having a visual model of thinking that could be used by anyone to help them change their thinking for the better, just like I did.

  If this has got you thinking, let me know! :)

The dissertation.