TFA does say this too, right after the Hamming lecture.
"So instead of considering n-balls to be spiky, it’s the space around them that outgrows them."
"So instead of considering n-balls to be spiky, it’s the space around them that outgrows them."
You should have seen how few replies read the last article I posted. https://news.ycombinator.com/item?id=40525629 The majority of the comments, including all the top ones, expressed insights as original, that were pretty thoroughly analyzed in the article. Just read my mildly frustrated replies.
I have thoughts about this, but I can find no way to contact you to open a conversation. You might want to think about adding something to your HN profile.
Meanwhile ... from this and other sources, I feel your pain.