LLMs face approximation error, not hallucinations

The term "hallucination" is a brilliant but dangerous marketing euphemism that anthropomorphizes statistical failure into a relatable human quirk. Shifting the vocabulary to "approximation error" reframes AI reliability from a mysterious psychological glitch to a manageable engineering constraint. LLMs never "malfunction" away from truth because they were never matched to the world, only to the probability distributions of their training text. Factual errors are inherent to lossy compression where model size, quantization, and training data quality dictate the "resolution" of the approximation. Anthropomorphizing LLMs hides the reality that the same math producing "correct" answers is exactly what produces the "errors." Framing errors as mathematical gaps makes the necessity of RAG, search tools, and context-injection obvious rather than optional "fixes" for a broken model.