Complex functions need 4 dimensions to graph - o…（@0xEronn）

Complex functions need 4 dimensions to graph - one input, one complex output. This video solves that with five visualization methods: plane deformations, domain colouring, Riemann spheres, vector fields, and 3D plots. LLMs operate in that last mode - attention scores are dot products between query and key vectors, exactly the inner product that defines work along a curve in a complex vector field. The Riemann sphere is the wildest part. The reciprocal function 1/z is just a 180 degree rotation of the sphere. Branch cuts in the logarithm are not arbitrary - they are forced by the same topological constraint that makes transformer embeddings wrap around high-dimensional manifolds instead of collapsing to a point. The logarithm's 3D plot turns out to be a spiral staircase that is secretly identical to the exponential function viewed from a different 4D angle. 27 minutes. Bookmark & watch today. The most beautiful way to see what complex functions actually do.