Comment by adolgert

I like that explanation, coming from the data side. I wonder if the article's author is working with data or a model for the data. There is a general rule that, especially for high-dimensional models, only a few parameters are important because eigenvalues of the sensitivity matrix fall off quickly (with logarithmic density). That means the data is well-separate, as you described, and only a few parameters control whether the model fits, while the rest are relatively unimportant. It's a different kind of pointy.