Large-scale, single neuron resolution recordings are inherently high-dimensional, with as many dimensions as neurons. To make sense of them, for many the answer is: reduce the number of dimensions. In this talk I argue we can distinguish weak and strong principles of neural dimension reduction. The weak principle is that dimension reduction is a convenient tool for making sense of complex neural data. The strong principle is that dimension reduction moves us closer to how neural circuits actually operate and compute. Elucidating these principles is crucial, for which we subscribe to provides radically different interpretations of the same dimension reduction techniques applied to the same data. I outline experimental evidence for each principle, but illustrate how we could make either the weak or strong principles appear to be true based on innocuous looking analysis decisions. These insights suggest arguments over low and high-dimensional neural activity need better constraints from both experiment and theory.