Selectively sampling dimensions facilitates manifold definition

When considering a space with an extremely high number of dimensions, it might suffice to selectively sample from a subset of dimensions for defining an expressive manifold. The resulting dimensionality of the manifold be lower than the one of selective sampling. An instance of this might render neural interfaces feasible, where reading from a subset of critical neurons might bring advanced imaging into our technological reach, as argued by Greg Egan in his short story titled “Learning To Be Me”.