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    Some years ago there was what certainly appeared to be an interesting pair of articles side by side in the Bulletin of the AMS (January, 1992), both about information-based complexity theory (about which I know nothing), initiated by Traub and Wozniakowski. The first, by Beresford Parlett, was an extended critique of work of IBCT, focusing on two representative papers and claiming that parts of IBCT are "true, but mistaken" (i.e., seriously misleading, in spite of the fact that the mathematical proofs were impeccable). The second was by Traub and Wozniakowski, defending their work and the IBCT program generally. Preceding this pair of articles were remarks by the Editors, Morris Hirsch and Richard Palais, recognizing not only the controversy witnessed by the two articles themselves, but the controversial nature of their decision to open the pages of the Bulletin to such a debate.

    At the time of reading it, I felt unable to reach a conclusion of which side had the stronger case, but I've always been curious about this and particularly what has transpired since. My general question would be: has the apparent disagreement been resolved by now, and if so, how?

    Such a question might be considered controversial for MO (just as the debate was controversial for the Bulletin). In addition, this is not a question arising from my own research; it's more like idle curiosity on my part, so I'm afraid the motivation for the question is not very strong, except that I like to see mathematical issues resolved to everyone's satisfaction.

    Is such a question acceptable for MO, or could it be made acceptable?

    • CommentAuthorgrp
    • CommentTimeMar 3rd 2013
    If I were to be rude, I would say "Did you not do your homework?"

    I don't want to be rude, especially to Todd who has been quite kind
    to me. Rephrasing thusly, "There is a subsantial Wikipedia article as
    well as other items that occur when I do an obvious web search
    on infomation based complexity theory. Is
    there something that remains unanswered for you after doing this?"

    I am unsure what the goal is for having a question near to this.
    I am guessing the coarse answer is that T and W have the future
    history on their side. (Just seeing an assertion that more than dozens
    of works cite W and T convince me that there was merit in their position,
    and I haven't seen their position yet.) It might be that the real question for Todd
    is if Parlett's criticisms have any merit after twenty years, but it
    is not clear to me if Todd wants that.

    I am sure a good related question could be asked, and perhaps
    even motivated. It may even be that my assessment above is
    faulty. My rephrased question should still be apropos, and I
    advise doing a little more web searching before posting a
    version of Todd's question.

    Gerhard "Intending Much Respect To Todd" Paseman, 2013.03.03

    Gerhard: thanks for your kind words.

    I did a quick web search. A sizable percentage of the first few hits I got were versions of the Parlett article. I can't tell the degree of scholarship that went into the WP article. A number of articles on IBCT are not by mathematicians (which of course is not to imply they were in any way deficient, of course, but I'm even less able to judge articles by electrical engineers than I am articles by mathematicians). Some are from before Parlett's 1992 article. And I'm not sure a "safety in numbers" argument, while it has at least some prima facie weight, convincingly trumps whatever Parlett, who is generally a well-regarded researcher, had to say on matters of interpretation he felt were subtle. In summary, a google search is a very superficial way to someone outside this area to do his "homework"; it would be much better to hear from someone acquainted with the issues that were brought up.

    A rephrasing along your lines might be good and appropriate, but I want to avoid appearances of prejudging (e.g., casting subtle doubt on Parlett's article).

    • CommentAuthorgrp
    • CommentTimeMar 4th 2013
    After reading your post and response, I have the sense that the question will best be something like the following. Pick a particular point Parlett proferred on which you wish a resolution, and ask about that specific issue. It should be easy to present it as an uncontroversial question. After that, you can give some background and state how much you want to avoid/stir up controversy, as well as your interest in having the other points resolved.

    I think it reasonable to express interest on a simple technical issue, e.g. "Is it valid to infer the value of the mean for a small group drawn from a large population and use it the way these guys do?", and ask if there were further research done to resolve the issue. At the very least, it can serve as a kind of reference request. Also, if your intention is academic (and mathematical) and not political, and you make that clear, MathOverflow can handle it.

    Gerhard "Likes Stirring Up Cookie Batter" Paseman, 2013.03.04

    Thanks again, Gerhard. I'll think it over, but my inclination at this point is not to ask after all, even though I find the situation curious and interesting.

    I think you should ask it. Talking about a controversy isn't necessarily controversial itself.