The whole is more than the sum of its parts, but less than the product

High-dimensional space provides increased expressivity for points through complex relationships, more so than simply considering a list of linear axes. However, the manifold hypothesis claims that the high-dimensional space is rarely populated in its entirety, and only houses points across a manifold. This double constraint can be expressed as the fact that the whole is more than the sum of its parts, but less than the (Cartesian) product.

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