Talk:William George Horner

Is Fuller's article a hoax?

A. Thomas Fuller published an article, Horner versus Holdred: An Episode in the History of Root Computation that appeared in Historia Mathematica early in 1999 a few months before he died (the exact reference is Hist. Math., 26 (1999), 29–51). Although the subject and periodical were novel for him, he enjoyed a distinguished record for scholarship. The article reads in accordance with this - until you begin checking the details. The flaws that turn up are then so numerous and so strange that it is difficult to to explain them, especially give the strong undercurrent of aspertion throughout the article, not only against Horner, but against J. R. Young, Thomas Stephens Davies, Augustus De Morgan and others. Hence the question: might the article be a hoax?

Fuller cites two contemporary reviews from The Monthly Review, in April and December, 1820, but in a partial or lopsided manner; you would never know, for example, that the reviewer is so welcoming of Horner's article. But then you would also not know from Fuller that there is a third review, in September, 1821, that specifically looks at the booklet of Theophilus Holdred and finds it wanting. The reviewer is exceptionally well-informed and, suggested in Horner's Method, would seem to be Peter Barlow. These reviews, taken together, upset, if they do not altogether scuttle, Fuller's advocacy of Holdred as the first published proponent of Horner's Method.

It is much the same with Fuller's quotation of the writings of J. R. Young, who, at first, drew on Holdred's booklet in his own exposition, possibly because Holdred first seems to have come to attention in The Gentleman's Mathematical Companion, where Young and Peter Nicholson, Holdred's associate-cum-rival, were both active. Reading Young more fully, we find that Fuller's presentation is biased: Young does say the things Fuller has him say, but he says a lot more. In the first place, Young acknowledges Horner's work as superior, but for his own purposes, specifically in the cubic case, he prefers to work with Holdred's formulation. But he is also at pains to assess Holdred's work, finding that Holdred's first method is that of Henry Atkinson in 1809 while his second method, inserted after Holdred's booklet had already appeared so that the booklet had to be reissued, followed that already proposed by Horner.

Young was not alone in fancying Holdred's handling of cubics. Fuller calls attention to an obscure footnote to the same effect which Fuller holds against Augustus De Morgan. It is true that it appears in a volume sandwiched between two pieces by De Morgan, but as many library index cards make clear, and as is made explicit in the second edition, this piece is the work of one, J. Parker. Is is difficult to see how anyone has the detective skills to track down such a footnote without following up on the authorship.

But it gets worse. Fuller tells us three times of the misprints in Horner's article in 1819, without ever saying what they are, but suggesting that the propensity of others to reprint the article without correction is indicative of their lack of understanding. T. S. Davies is one of these miscreants: he reprinted the article in The Ladies' Diary for 1838, appearing in late 1837, the year Horner died. What Fuller does not tell us is that a key points throughout this reprint, Davies supplies editorial notes. So much then for someone who might not have understood the article.

Fuller also tells us that Horner, in a contribution to Leybourn's Mathematical Repository does not acnkowledge Holdred's work whereas Horner devotes an entire section of his sequence of notes to Holdred's method as it had been presented by Nicholson. Fuller is also suspect on the dating of what appears in the Repository, failing to recognize that individual issues came out sporadically, to be bound up in volumes, with four to a volume - problems with Glendinning the printer meant that the fourth volume appeared in 1819 but the fifth only in 1830.

There is more, but I shall leave off here, in the hope that someone can answer the question.

The answer is that it is not a hoax For omissions and bias you could only make the accusation of careless non-objective work. You cannot make another wild accusation of a hoax without a shred of evidence. So I think you should withdraw the word 'hoax' which is defamatory and against the spirit of Wikipedia. If what you say is true, there are no doubt reasons for it which you might have used your detective skills to find. For example, Fuller was retired and, as can be seen from his address given in the paper, was living in the countryside. So he might not have had the same excellent library services as you obviously enjoy. And, as you observed, he wrote shortly before his death so other reasons may easily be imagined. It is not unusual for older people to be less mentally alert. And again assuming everything you say is true, you still have not proved your case because you limit yourself to the who-said-what-when about someone else’s work. You do not appear to have done, as Fuller did, the harder work of reading and understanding the ideas in the quoted works. Have you, for example, actually read and understood Horner 1819 and Holdred 1820 in the original? If so, which is closer to what is nowadays called 'Horner's method' ? — Preceding unsigned comment added by JFB80 (talk • contribs) 19:13, 16 July 2012 (UTC)

We must be grateful to JFB80 for coming forward to help with these enquiries. It is to be hoped that others will do so. For example, as JFB80 no doubt noticed, A. Thomas Fuller acknowledges at the end of his paper two anonymous referees and a J. F. Barrett. So, there may, indeed, be others, familiar with either Fuller or his paper, who can help.

I should like to take this opportunity of reassuring JFB80 and other concerned readers that we are only at the stage of questioning. With all due respect, a question is not a wild accusation, neither can it of itself be held to be defamatory. As for the word 'hoax' it would not not appear to be against the spirit of Wikipedia if the entry Sokal affair is anything to go by: for some, being the perpetrator of a hoax is a badge of honour - so it might be for A. Thomas Fuller, as much as it is for Alan Sokal. Of course, it might be that Fuller was incompetent or incapacitated, possibly lapsing into senescence or otherwise not in the best of health, but I should merely put it to JFB80 such possibilities might be far more detrimental to Fuller's reputation than, say, the suggestion that he was had been a prankster.

Does JFB80 know of anything in the record to indicate that Fuller was mentally less acute than he had been at the University of Cambridge or that, in his rural retreat in Hampshire - in communting distance for the University of Southampton, Brighton for the University of Sussex at Falmer, and London, for the British Library among many others - he was any less in contact with library services than he had been? At first blush, his paper does not read as if there were anything untoward in those regards; for that matter, it did get by the referees and editors into print, where it has been quoted.

JFB80 seems to want to have things both ways, going on to insist that Fuller did the harder work of reading and understanding the ideas in the quoted works, as though someone who points out flaws in Fuller's paper, showing that Fuller's reading and understanding was repeatedly unsound, might not be so diligent. We are not involved with some kiss-and-tell story, a matter of who-said-what-when about someone else’s work, and to suggest otherwise, as JFB80 seems to, is to impugn the scholarly judgement of the reviewer for The Monthly Review, J. R. Young and others gratuitously, although, of course, that is exactly what Fuller is inclined to do, as though the only person capable of reading and understanding is Fuller himself. Let us recall that Fuller was a distinguished scholar with a strong reputation of meticulous research, a denizen of libraries who would know, not to check just one volume of a periodical, but a run of volumes on either side; not to check just one edition, but successive editions, who prided himself on such attention to detail, and who would pounce on anyone not coming up to this standard. How does someone of this calibre miss the denouement in s sequence of reviews to which he has called attention by quoting the opening episodes?

Readers can now go to all three parts of the sequence via the above links and make their minds up for themselves. As for Horner's paper of 1819, there is also a link which I hope will make it more directly accessible. I regret not having Holdred's booklet in both editions in a form that can readily be made available. In the meantime, JFB80 might like to rest reassured that it was the discovery that A. Thomas Fuller gave evidence against himself of not having understood Horner's article that prompted further investigation of Fuller's other assertions. If I have written about these later findings first of all, that is only because they are so passing strange.

But, once again, let me leave off here, in the hope that others will be coming forward to assist with enquiries.— Preceding unsigned comment added by 129.96.121.71 (talk • contribs) 01:30, 23 July 2012‎

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