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Is this question acceptable?: [Closed] Tetration

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    There's a tetration thread on MO: http://mathoverflow.net/questions/45277/how-close-are-we-to-extending-tetration-to-the-real-and-complex-numbers

    IMO the question is worded in a rather ambiguous way. If the author could turn it into a question that has a clear answer I'd be okay with it but as-is it's not clear to me what the question is asking for.

    Does anyone know a clear statement of this question, or what they think the question is?
    • CommentAuthorWill Jagy
    • CommentTimeNov 8th 2010
     
    Hi, Ryan. I looked at the comments. My impression is also that this is a subject pursued by enthusiastic amateurs, and the questions and answers all have an element of finding publicity for the subject. The two who give names are my age, so I understand their feelings. I started collecting key words, users, etc. For the circle of ideas there are actually quite a number of questions on MO. I don't believe I know what to do or whether to do anything.

    "tetration" or "fractional iteration" "Abel function" "superfunction"
    http://en.wikipedia.org/wiki/Tetration
    http://en.wikipedia.org/wiki/Abel_equations

    http://mathoverflow.net/users/7710/gottfried-helms
    http://mathoverflow.net/users/10059/anixx
    http://mathoverflow.net/users/10089/daniel-geisler
    http://mathoverflow.net/users/10629/bo198214
    http://mathoverflow.net/users/10662/sheldonison
  3.  
    This is a fair criticism. As the author of the question I will try and edit the question into something with a more focused answer.
    • CommentAuthorAndy Putman
    • CommentTimeNov 8th 2010 edited
     
    I'm usually pretty liberal about what kinds of topics we allow, but I think that one rule we need to stick with is that questions should concern the kinds of mathematics that professional mathematicians (interpreted broadly) study. Allowing questions about topics that no professionals study would seem to contradict aim of MO to be a tool for research mathematicians.

    I also worry about MO being used to "promote" non-mainstream topics. As other internet sites have discovered, this tends to strongly decrease the signal-to-noise ratio.

    By the way, this should not be interpreted as an attack on the many amateurs and semi-professionals on MO who make fantastic contributions to the site. I've learned lots of things from them!
  5.  
    After reading the comments here I agree to the question removed. There is much on this thread that I need to reply to in the near future.
    • CommentAuthorAnixx
    • CommentTimeNov 9th 2010
     
    @# Andy Putman, can you tell me how do you determine who is a professional mathematician? For example, I pointed to this paper http://www.ils.uec.ac.jp/~dima/PAPERS/2009sqrt2.pdf in my first comment to this question. Is it written by professional mathematicians or not enough professional or what?
  7.  
    @Will Jagy, I largely agree with your assessment. Let me fill you in a bit on your detective work. I am loosely connected with a group of researchers on the Tetration Forum http://math.eretrandre.org/tetrationforum/index.php . A couple of the members mentioned that have posted here have PhDs. so I would argue are not strictly amateurs. Tetration Forum members were not the ones who put up the original factional-iteration questions on MO, but they are trying to improve the answers. As far as whether to do anything or not, I think talking would be appropriate.

    @Andy Putnam, please check out the extensive list of articles that the tetration question provides before concluding that professionals do not research tetration. Note in particular Knobel's "Exponential Reiterated" about the constant rediscovery of tetration and related questions in fractional-iteration. It is disturbing to research a subject for forty years only to hear someone say, "hey that's not mathematics research!" There has been some concern expressed that scientist are being forced to research areas with quick payback. Doing long term research almost by definition has to be done outside normal channels. I didn't think I could get tenure studying tetration, but I never dreamed someone would try and argue that tetration wasn't research mathematics.
    • CommentAuthorjbl
    • CommentTimeNov 9th 2010 edited
     

    Edit: retracted

  9.  

    @Andy Putnam

    Fatal mistake..

  10.  
    @jbl: I wasn't aware the employment status of the poster was an issue. I hope we don't get distracted by this relatively unimportant side-thread.
  11.  
    I strongly agree with the second part of Andy Putman's post. Some of the recent questions on fractional iteration seen not to have been posed entirely in good faith. By this I mean that the questioner does not expect anyone here to be able to answer the question, rather, the purpose of the question is to draw attention to his/her favorite field of mathematics. The fact that this goes against the intended purpose of MO can be seen for instance in the rule against posting something that is known to the questioner to be a hard open problem.

    That this particular mathematical subfield is far outside of the mainstream seems irrelevant to me; that type of question would be bad even it was about higher derived oo-topoi or whatever.
  12.  

    +1 Dan. I completely agree.

  13.  
    @Dan Petersen - tetration is out but mind reading and pop psychology is in? Is tetration a hard problem? Once again, please look at what I wrote instead of judging that I am not acting in good faith. As I mentioned, Wikipedia appears to indicate that the problem is solved. I believe that the appearance of the subarticle in Wikipedia on tetration for real and complex heights is a bit early, but I'm open to being convinced. I am asking questions I believe can be answered, although I may be a fool for thinking someone has the answer, I am not asking questions to "advertise" anything.
  14.  
    Several comments.

    1. I never said that the employment status of a questioner was relevant. All I care about is the topic of the question.

    2. I also never said that tetration was not mathematical research. All I claimed was that it was pretty far outside the mainstream of mathematics research, which I think is uncontroversial.

    3. There is apparently a large community outside of the usual professional math community that is interested in tetration. They have developed their own language, notation, etc.

    I don't think we should allow questions expressed using the language, notation, etc of the "tetration community". The MO community is unlikely to have any clue what is being asked and is also unlikely to have the sort of specialized knowledge necessary to say anything. That's what I mean by "too localized".

    I do think that if someone is interested in tetration and can ask a specific technical question about it using the language of mainstream mathematics, then that would be fine. Indeed, how would we be able to tell the difference between that question and other odd technical questions that pop up on MO?
  15.  
    Possibly Dan Petersen wasn't referring to your own question, Daniel. Could have been someone else's question.
    • CommentAuthorAndy Putman
    • CommentTimeNov 9th 2010 edited
     
    By the way, I just realized that I forgot to respond to Anixx's question. Dmitrii Kouznetsov is a perfect example of the type of person I'm talking about. Looking at his CV, he has a PhD in some kind of physics related to lasers, is a professor at the Institute for Laser Science at the University of Electro-Communications, and has published extensively in physics journals (btw, this means "real physics" journals, not "mathematical physics" journals that sit on the border between math and physics). It looks like he has written a couple of papers about tetration, but on a brief glance those appear to be his only forays into mathematics. Summing up : he appears to be a professional physicist who dabbles in math on the side.
    • CommentAuthorAnixx
    • CommentTimeNov 9th 2010 edited
     
    @ # Andy Putman, so questions about works of professional physicists who occasionally publish on mathematical topics are unwelcome here? Does a mathematician have to publish on different filds of mathematics, not just one topic of interest to be qualified professional enough? And please tell me what so "special language and notation" did you spot in this paper? http://www.ils.uec.ac.jp/~dima/PAPERS/2009sqrt2.pdf
    • CommentAuthorAnixx
    • CommentTimeNov 9th 2010
     
    This seems to me like some people just want MO to be entirely dedicated to the topics they welcome themselves, first time I saw the topic of indefinite summation attacked and now - fractional iteration.

    The question by Daniel Geisler showed or pretended that he did not know the recent developments and I pointed him to a relevant paper. This type of question may be or may not be acceptable for MO, but I see no reason to attack the general topic.
  19.  
    @Anixx: please let's not steer this thread off course.
  20.  
    @Anixx : You are twisting my words. We welcome posts by anyone, but the ground rules are that they have to express those posts in the language of mainstream mathematics. Otherwise, everyone's time is wasted, and it is highly unlikely that a useful answer will be posted.

    Let me repeat what I said in my post above:

    "I don't think we should allow questions expressed using the language, notation, etc of the "tetration community". The MO community is unlikely to have any clue what is being asked and is also unlikely to have the sort of specialized knowledge necessary to say anything. That's what I mean by "too localized".

    I do think that if someone is interested in tetration and can ask a specific technical question about it using the language of mainstream mathematics, then that would be fine. Indeed, how would we be able to tell the difference between that question and other odd technical questions that pop up on MO?"

    The type of post that I'm objecting to is the kind that inspired this meta thread, namely
    http://mathoverflow.net/questions/45277/how-close-are-we-to-extending-tetration-to-the-real-and-complex-numbers
    • CommentAuthorAnixx
    • CommentTimeNov 9th 2010
     
    @# Andy Putman "I don't think we should allow questions expressed using the language, notation, etc of the "tetration community".

    Well can you please point me to a place in that question which uses the so-called "notation of the tetration community" whatever it means which is not the language of the "mainstream mathematics"?

    In my understanding the question is not even mathematical in its nature, it's like "hey, what's new with tetration, please point me to some recent publications". How such type of a question can be expressed in "non-mainstream" notation even if intended so?
    • CommentAuthorAnixx
    • CommentTimeNov 9th 2010
     
    @ # Ryan Budney

    This thread would be of little interest for me if not the name-calling started and me included in the "enemies list" for whatever reason in the second post here.
    • CommentAuthorAndy Putman
    • CommentTimeNov 9th 2010 edited
     
    @Anixx : Asking about tetration in general is off-topic. Specific technical questions are fine, but general "tell me about a subject" questions have a high bar no matter what the subject.

    I'm done with this thread. I have no desire to get into a protracted argument with you -- the last time such an argument occurred it ended up being a waste of everyone's time (yours included).
  24.  
    For my part I apologize. I took peoples issues under consideration, reread the FAX and now agree my question about the status of tetration is to vague.
    • CommentAuthorAnixx
    • CommentTimeNov 9th 2010 edited
     
    @ Andy Putman "Asking about tetration in general is off-topic. "

    In that case why do you attack notation which is not used in the question? Can you point to a question which annoys you with so-called "notation of the tetration community"? If you said the notation annoys you, you should answer for your words and point us to the qustion which sparked such annoyance.
  26.  

    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.

  27.  

    Could we close this thread please, and possibly delete the previous post?

  28.  

    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).

  29.  

    I "third" the request for closure.

  30.  

    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.

    • CommentAuthorMariano
    • CommentTimeOct 4th 2011
     

    Before this is closed, let me repeat something:

    Dear Dick,

    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!

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