> If we thought in 100D, we might have a better sense for it, because we'd be able to see a hundred of them.

This is pretty clearly talking about getting a better sense of the asymptotic behavior in number of dimensions, and having a better intuition if you see a hundred steps than if you see three. The three steps of exponential growth mentioned are in transitioning from a single cube, to a line of 10 cubes, to a grid of 10x10 cubes, to a block of 10x10x10 cubes. But that's sort of where we tap out, because we're so heavily wired for 3D -- if we dealt with 100D, we'd have 100 such steps we could intuitively observe, and so have a better sense of asymptotics.

This is further seen in that the exercise is based on increasing the number of dimensions to explore the growth of the space as the dimensionality changes. It's literally adding more and more terms to a product space, and so clearly dealing with issues about dimensionality.

You're simply wrong, and incredibly uncharitable in your interpretation.

Further, geometric growth isn't a power law -- it's exponential growth. So the person asking the question was indeed confused, regardless of the fact you're wrong about what I was talking about. Geometric series are r^1, ^2, r^3, etc while a power law will look like 1^x, 2^x, 3^x, etc. Asking if an exponential growth is "just geometric growth" is being confused -- they're the same thing.