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Just because your representation of choice for a problem space is high-dimensional doesn't mean that the problem is complex. There are impossibly many possible 400x400x3 uint8 tensors, but only a small subset of them are interpretable as natural images, and
only a tiny subset of these valid images would constitute a "dense sampling" of the space of natural images. The same is true of many other spaces, including the space of Go board positions.
Right! Wouldn't this point to investigate, whether it's possible to explicitly formulate the constraints effectively reducing the dimensionality? Even though it may still be preferable to use the high dimensions formulation for interpretability or calculations.
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