GoKawiilExplainer revisits von Neumann's Hilbert space framework for quantum mechanics
The piece explains how John von Neumann's 1927 mathematical formulation defines Hilbert space, the abstract structure underlying quantum mechanics, in which a system's possible states are represented as a vector. It describes how the number of dimensions in this space corresponds to the number of possible outcomes for a system, from a two-state qubit to an infinite-dimensional space for a freely moving particle, and how different choices of axes correspond to different measurable quantities like position or momentum.