I was pleased to see that my recent Powerset experiments attracted the attention of Powerset Product Manager Mark Johnson, even if his comment appeared only on Net News Publisher, rather than on this site! Most important was that he called attention to a Powerset feature that I had not really explored and that had received only a passing reference in Eric Auchard's Reuters report:
Powerset offers richly annotated ways for searching inside Wikipedia entries to find related concepts. Called "Factz", these related ideas generate outlines, summaries and automated answers to users' questions.
I must confess that, when I first encountered this feature while running my experiments, I found it very appealing. I have long believed that, when faced with the challenge of coming up to speed in a new area, it is good to have a view of the topic that gives a general sense of the content and how that content relates to other areas. If you are familiar with any of those other areas, they may provide you with your best individual approach to getting familiar with the new material. When I was doing some research in this area, I spent some time examining those "dummies" and "idiots" guides and appreciated how well they provided this kind of perspective on the subject matter; and I conjectured that it was such a perspective that had made those publications so successful. Thus, my first impression of the Powerset Factz was that they were pursuing the same strategy but (at least in the material available for testing) on the smaller scale of Wikipedia articles. So, since Johnson's comment encouraged me to play around with Factz, I decided to do so in the setting of my original test set of questions.
I began, as Johnson had suggested in his comment, with the Factz display associated with the Wikipedia article for George Eliot. It was certainly easier to skim than the article itself, but I suspect that I would have found many of the entries confusing without some personal background knowledge about Eliot. (Actually, with the background knowledge I had, some of the Factz were still confusing; and I suspect that some of them would confuse my wife, who holds a Master's degree in English Literature from New York University, where she had to so some pretty strenuous work in the area of Victorian literature!) Faced with what we might call "the dummies/idiots challenge" (without making any assumptions about the sort of technology I might be able to use), I probably would have written a few introductory paragraphs (not like the two that begin the Wikipedia article, which are valuable in their own way) that would encompass a higher-level classification of all of those Factz and, like the Factz, would include hyperlinks into the body of the article.
Note that in this case I was reading the article on Eliot, rather than the one on The Mill on the Floss; so I was looking at material I had not read when I performed my experiments yesterday. Nevertheless, the questions of whether or not Eliot's geographical names were fictitious and, if so, whether they had "real" models (as Marcel Proust's locations did) remained unresolved. The Factz did help me home in on that portion of the Eliot article that discussed The Mill on the Floss; but, as I pointed out yesterday, this was a situation in which the answer to my question was beyond the scope of the content that Wikipedia provided.
My next exploration involved the Factz provided for the Johann Sebastian Bach entry. In this case I was pleased to find "theology informs structure" among the Factz under the "Style" heading. This was basically the concept I was getting at in the last of my test questions, "Who tried to analyze the music of Bach in terms of religious interpretation?" Unfortunately, the author of the Wikipedia entry did not explicitly credit Albert Schweitzer with identifying or promoting this structural insight. Indeed, by doing a text search I discovered that Schweitzer's name only appeared among the References and there under the heading of "Earlier scholarship," along with Philipp Spitta and Johann Nicolaus Forkel, both of whom are so much earlier that Schweitzer's text is almost an outlier (although he might also count as an outlier in the "Modern scholarship" section).
This brings me to the question that I had initially formulated incorrectly, the one test case in which AskWiki prevailed (probably accidentally) by figuring out that I was asking about the general algebraic solution for quintic, rather than cubic, equations. Since Johnson had suggested that I did not need to state my queries in natural language, I decided to type "algebraic solutions" into Powerset. This only gave me a list of Wikipedia articles without any Factz, but I continued my search by clicking on the "Timeline of algebra" link in the first ten hits. This entry also did not have any Factz; but that did not surprise me, since it was already in summary form. Down at the bottom of the timeline I found two entries relevant to my question. The entry for 1824 was:
Niels Henrik Abel proved that the general quintic equation is insoluble by radicals.
The one for 1832 was:
Galois theory is developed by Évariste Galois in his work on abstract algebra.
This led me to guess that Abel had achieved his result without using Galois theory, because Galois had not yet developed it; so I decided to consult the Abel entry. Here I did find facts, but none of them addressed any questions concerned with algebraic solutions of equations. It was only by skimming the entry that I found the following text in the "Career" section:
While learning languages, Abel published his first notable work in 1824, Mémoire sur les équations algébriques ou on démontre l'impossibilité de la résolution de l'équation générale du cinquième degré (Memoir on algebraic equations, in which the impossibility of solving the general equation of the fifth degree is proven). While others were questioning ‘what is the solution’, Abel asked ‘is there a solution’ and he proved the impossibility of solving quintic equation in radicals in 1823 (see Abel–Ruffini theorem). This work was in abstruse and difficult form, in part because the page count was severely restricted in order to save money on printing. A more detailed proof was published in 1826 in the first volume of Crelle's Journal.
This time I was able to visit the Abel-Ruffini theorem entry with a Powerset enhancement; and, sure enough, the "Galois connection" (pun intended for the specialists) was there among the Factz! Through those Factz I was able to dismiss an incorrect conjecture, which was that Ruffini had simplified Abel's "abstruse and difficult" proof with the benefit of Galois theory. Actually, Ruffini had attempt his proof in 1799; but it had a gap that Abel had filled! The applicability of Galois theory only surfaced in 1885, which I learned from the final paragraph of the Wikipedia text.
All this leads me to conclude that my "personal jury" is still out on just how much benefit the Factz feature provides. I think that, if I want to be fair, I need to give it more opportunities when I am trying to use Wikipedia more seriously, which is mostly when I am writing my music posts, since that is where I have found Wikipedia to be most reliable for my own needs. I could see that I might have drawn upon the Factz provided for the Francesco Cavalli entry, even if no Factz had been supplied for the specific article on Egisto. In other words it is time for me to start thinking about Powerset in terms of my day-to-day writing activities, rather than in terms of the results of contrived experiments!