Equational

fractal based turbulent flow i put at github.com/equational/fractalturbulence2d3d Some quick remarks on OpenAI's Navier–Stokes Millennium Prize Problem work: ML does not do mathematics, it does computations that result in mathematical properties. This may seem a pedantic thing to write, but it is very different. One way to describe the difference is that OpenAI discovered a single mathematical fact. Yet now this fact needs to be connected into a broader mathematical space to become true mathematics. While some mathematicians deny it, innovation is much a search effort ( I wrote about it here ). So when Tristan Buckmaster writes : " I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer ", he is highlighting that OpenAI's search may have obtained a hint t...

The art of relativity as a distributed system I rarely do pure architecture. Yet today I wanted to push an old thought through an LLM to get a "current CS view". The theme is the entwining structure of combining monads , comonads , and traversals . The goal, one of my recurring themes, what are different ways to express approximate dualities of global and local continuities. LLMs need a goal. Here we are asking for an architecture . Interestingly, I did not actually ask the LLM (Gemini Pro) what I wanted to do with the architecture, the LLM thought it knew better, and came up with:  Robust large-scale system design is the process of defining an explicit adjunction at the local atomic level (to guarantee correct state transitions), embedding it into an overlapping topological comonad (to enable concurrent diffusion), and using a continuous distributive law to cross the bridge into the real world (to absorb the shock of metric uncertainty). It took me thirteen prompts to build ...