Um, so much of that first article just shows the author's own ignorance... i.e.:I don't think it's exposing Baez' ignorance so much as criticizing the use of non-standard terms. If you look at Springer's Math Encyclopedia's page on Stein Spaces, you'll see that there's no reference to what a [2|3]-Stein Space is. It's possible that it means a Stein Space with the condition that the [2nd|3rd] Cousin Problem is solvable. But who the hell knows?
"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.See, that's the thing about math and science. Nutty and peculiar is quite common. And it can be a virtue. But most of the time, nutty is just nutty. But the lovely thing about good math and science is there's empirical ways to verify whether a nutty idea has merit or not. You do experiments, you check proofs. Bullshit is much less ambiguous than in the humanities.
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posted by Wolfdog at 8:09 AM on November 12, 2008