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Wednesday, December 16, 2020

The mathematics of consciousness: answering existential questions using graph theory | Mathematics - Medium

I have always been fascinated with the paradoxical nature of consciousness; everyone knows that they are experiencing it, yet we cannot seem to reconcile such a unique phenomenon with the rest of our universe by Ryan Vandersmith, Full-Stack Progressive Web App Developer.

The mathematics of consciousness: answering existential questions using graph theory

This topic is heavily saturated with philosophical and religious musings, with no definitive evidence pointing to any one explanation over another. I would like to share an interesting way of thinking about consciousness that is scientifically verifiable while providing a rather satisfying answer to long-standing existential questions such as “what really happens after I die?” 

A few weeks ago, I was discussing this topic with a mathematically precocious friend, specifically how we both had experienced the feeling of having some sort of “past life,” which vividly reminded me of a short story from a high school English class called The Egg, which had a very interesting and thought-provoking message about reincarnation and empathy. In short, the story describes a man who randomly dies, speaks with a “God” figure, and realizes that every other person is actually just himself in a different life. He is then sent off to his next life after realizing that each of his own actions is directly impacting “himself” at another point in his full lifetime...

In mathematical terms, given any graph G in which vertices represent life forms and edges represent interactivity between life forms, the line graph L(G) corresponds to interacting pairs of life forms which also fulfill the definition of life. More generally, every connected subgraph induced by G of order |V| corresponds to a “parent” life form composed of |V| smaller interacting life forms. An obvious example is how cells combine to form plants and animals; an individual cell and collective organism are independently alive at different scales. For some points of reference, the average human has a cell interactivity graph of order |V| ≈ 37.2 trillion, while the human race encompasses all of these in a graph where |V| ≈ 2.9 * 10²³. This logic also applies to ecosystems, continents, and any other set of interacting life forms, each with their own characteristic structure and complexity.

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Source: Medium