Why Ricci Flow?
How a concept in topology informs the way we think about health.
Ricci flow is a concept in differential geometry developed by Richard Hamilton in the 1980s to study surfaces and curvature. This mathematical approach was relatively niche, with few applications during the idea's infancy. Ricci flow is essentially a way in which shapes in multiple dimensions are moulded back to a singularity in a non-linear manner. It was used by Russian mathematician Grigori Perelman in the 1990s and 2000s to ultimately solve one of the millennium problems; the Poincaré Conjecture.1
When I learnt about this during my high school years, it always stuck with me how beautiful and elegant this topological idea was. It seemed to me that this idea of non-linearly shaping something abnormal to bring it back to pure symmetry was applicable to so many different ideas. I strongly felt it was relevant to music, where complexity and patterns combine to make memorable melodies, yet it also applied to cooking where adjusting the acid, sweetness and salinity of a Thai soup was like a nuanced dance.
Despite not understanding the deeper mathematics, the concept of Ricci Flow itself resonated with me deeply enough for me to hold onto it for many years. It was something I mostly related to through playing, writing and producing music, something I could see reflected in the models of topological transformation of Ricci Flow. When I became interested in health and nutrition, it became obvious to me quite early on that Ricci Flow was an apt analogy to capture the essence of individual uniqueness and gradual, non-linear journey towards vitality.
The more I read and learned about health and biology in general, the more I felt the concept was a great way of conceptualising health in the modern world. The idea represents a few key things:
Individual Uniqueness: The idea that no two people have the same starting point or require the same nourishment to thrive. Irregular topological features are a perfect metaphor for each person’s unique makeup.
Gradual Evolution: In these topological shifts under Ricci Flow, the changes to the shape are gradual, with each successive adaption informing the directionality of the next. The evolution towards a singularity also denotes that the journey is continual and there is no end.
Multidimensional Approach: In Ricci Flow and other similar flows, each and every point on the surface of the shape is adjusted relative to its position and characteristic on the surface itself. This type of self referencing at many point simultaneously is similarly vital when approaching health.
Simplicity: Simple is nature’s goal, simplistic is a lack of creativity and ingenuity. Ricci Flow as a concept is quite simple and lends itself as a metaphor for many pursuits.
Adaptive: To me, Ricci Flow is a representation of the idea of homeostasis. Whatever perturbations act on a shape, the new curvatures are immediately incorporated into the way flow behaves.
I have since used it as my moniker, a decision that is somewhat regretful as it is a bit of a mouthful and of course, no one knows what it means. Alas, I have stuck with it, so it only seems appropriate to offer some sort of explanation. Ultimately, I saw Ricci Flow as a beautiful metaphor for health and vitality. The ideas it represents have helped fortify me against simplistic and expedient approaches to learning and being a practitioner; things are are rife in the health space today.
Grigori turned down the million dollar prize and a Fields Medal (the mathematics equivalent of a Nobel Prize) after solving this problem.
Ahaaaaa… I thought maybe it was a play on a middle name or something đŸ˜‚ Thanks for sharing!