Um, so much of that first article just shows the author's own ignorance... i.e.:
"I know there are 17 wallpaper groups, and that many of patterns with these symmetry groups appear in the Alhambra. In fact last summer I went to the Alhambra and checked this myself! But I don’t know if there are “exactly 17 two and three Stein spaces’” with total sum of dimensions equal to 686 — I know what a Stein space is, but I don’t know what “two and three Stein spaces” are, or if that even makes sense."
"The Nash embedding theorem does give a bound of roughly this sort, but I don’t know if this particular formula is correct. Regardless of that, he then applies the formula to the case of a surface (n=2) and gets the number 17. I have no reason to believe that 17 is the optimal bound in this special case, or of any special significance"
Remember your Kuhn. Something can sound nutty and peculiar to the current paradigm without being valid or of value.
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