By choosing to make rhetorical points though, he's merely perpetuating a generation of uninformed practitioners, rather than educating them. In the end, who is he kidding?

Does he really think that those readers who swallow his arguments uncritically won't do exactly the same when they read the gospel words from the next pop science writer? By eschewing solid ideas, it just makes it easy for others to discredit his claims. Nothing lasting can come of it, no solid core understanding of reality, if that's truly what he wants. It's argument from authority, and he's merely playing the trendy authority in people's reading list. Good for book sales, though....

The high-dimensional cube looks like a horrid, spikey thing, but the observations are indeed spread evaently in the hypercube, and there is no geometrically thin shell in this problem. The distribution of distance from the center, on the other hand, does start to peak away from the center, and more sharply as the number of dimensions increases.

No they're spread evenly in the shell, but the shell exists. Think of the unit cube [0,1]^n with the usual coordinates. The condition for a point to lie on a face is that one of the coordinates equals zero or one. When the number of dimensions goes up, the chance of getting at least a single coordinate close to zero or one becomes closer and closer to a certainty. Therefore, the points cluster near the faces of the hypercube, which is the (nonspherical) spikey shell I'm talking about.

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$E(X_t|F_s) = X_s,\quad t > s$