🧪 Ultimate Technology Universal Knowledge Simulation

How much "universal knowledge" can a fixed-size vector space actually hold before it runs out of room? This simulator packs randomly-directed unit vectors — one per stored "concept" — into a tunable-dimension embedding space and computes the real pairwise cosine similarity between every pair, live. As you raise the concept count or lower the dimension, previously distinct concepts start to collide: their directions converge until the model can no longer separate them, exactly as the concentration-of-measure bound √(2·ln N / d) predicts. It is the same capacity limit that governs word2vec, sentence-transformer embeddings, and every retrieval-augmented-generation vector database — the concrete, measurable reason a "system that models all possible knowledge in the universe" needs either an enormous embedding dimension or an acceptance of collisions.