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+1 Dan. I completely agree.
Just thought I'd mention, going by this webpage http://mathworld.wolfram.com/PowerTower.html, tetration is a less frequently used term for what is commonly known as a "power tower." If you look at the list of references, you can see it's definitely not an active area of research, but nor is it a fringe or hobbyist-only topic. The question of fractional towers is akin to the idea of extending factorials and derivatives to non-integers.
This amateur vs professional pissing match is silly. Most of the academic mathematicians I know would never publicly acknowledge posting on Mathoverflow as they see it only a small step up from Yahoo Answers. It's all relative.
Could we close this thread please, and possibly delete the previous post?
I second Scott's request to close the thread, but think the post preceding his - which, in my view, misses the point and is grinding a separate axe - should be left as is.
Readers can make up their own minds as to whether, say, Bill Johnson and Mark Sapir think of MO as a small step up from Yahoo Answers (I'm sure they don't find it ideal, but their activity suggests they find something worthwhile here).
I "third" the request for closure.
This thread had more than completed its purpose on Nov. 9th, 2010.
From the 9th on it seems to have become some weird pool of contention over... I'm not sure what.
So I also encourage this thread to be closed.
Before this is closed, let me repeat something:
Of course, you are free to have whatever opinion you want about MO, its participants and anything. If you intend to voice it here, and it ends up being as negautve as the one you have just voiced, it would be best, though, not to do so anonymously.
In any case, please tell those academic professionals you know to keep up their unavowed, anonymous participation on the main site!