A two-dimensional political map tells you which areas of the Earth's surface are under the jurisdiction of what government. In contrast, category "boundaries" tell you which regions of very high-dimensional configuration space correspond to a word/concept, which is useful _because_ that structure is useful for making probabilistic inferences: you can use your observastions of some aspects of an entity (some of the coordinates of a point in configuration space) to infer category-membership, and then use category membership to make predictions about aspects that you haven't yet observed.
But the trick only works to the extent that the category is a regular, non-squiggly region of configuration space: if you know that egg-shaped objects tend to be blue, and you see a black-and-white photo of an egg-shaped object, you can get _close_ to picking out its color on a color wheel. But if egg-shaped objects tend to blue _or_ green _or_ red _or_ gray, you wouldn't know where to point to on the color wheel.
A two-dimensional political map tells you which areas of the Earth's surface are under the jurisdiction of what government. In contrast, category "boundaries" tell you which regions of very high-dimensional configuration space correspond to a word/concept, which is useful _because_ that structure is useful for making probabilistic inferences: you can use your observastions of some aspects of an entity (some of the coordinates of a point in configuration space) to infer category-membership, and then use category membership to make predictions about aspects that you haven't yet observed.
But the trick only works to the extent that the category is a regular, non-squiggly region of configuration space: if you know that egg-shaped objects tend to be blue, and you see a black-and-white photo of an egg-shaped object, you can get _close_ to picking out its color on a color wheel. But if egg-shaped objects tend to blue _or_ green _or_ red _or_ gray, you wouldn't know where to point to on the color wheel.