https://signal-and-syntax.com/tags/geometry/Recent content in Geometry on Signal & SyntaxHugoen-usTue, 07 Oct 2025 06:00:00 -0700https://signal-and-syntax.com/posts/how-large-language-models-think/Tue, 07 Oct 2025 06:00:00 -0700https://signal-and-syntax.com/posts/how-large-language-models-think/When you enter a sentence into a Large Language Model (LLM) such as ChatGPT or Claude , the model does not process words as language. It represents them as numbers. Each word, phrase, and code token becomes a vector — a list of real-valued coordinates within a high-dimensional space. Relationships between meanings are captured not by grammar or logic but by geometry. The closer two vectors lie, the more similar their semantic roles appear to the model.https://signal-and-syntax.com/posts/three-d-packing/Wed, 20 Aug 2025 09:00:00 -0700https://signal-and-syntax.com/posts/three-d-packing/My first full-time programming job was for Holiday on Ice, an international ice show. While I focused mainly on back office systems such as accounting, itinerary, and box office reporting, I knew that one of the biggest technical challenges faced by the show’s crew was efficiently loading trucks for the next city. One day, the controller asked me if I could code a system that took, as input, the trucks’ 3D dimensions and the 3D dimensions (and weight) of every object to be packed.