There is a style of argument which people trained in the classics often use. In this approach, one goes through the evidence piece by piece, artfully arranging it and discussing how to interpret the difficult points, then sums up by drawing it into a grand conclusion. This evidence is mostly widely available, great pains having been taken to publish Greek and Roman literature, the more important inscriptions and vases, and other remains of the ancient world in cheap editions and translations. Anyone with access to a library and the willingness to search should be able to find the main sources which lie behind a book on ancient history, and a growing number are available on the Internet. This style of argument can be great fun to read, with impressive learning and elegant transition from author to tombstone to vase. But eventually the lover of the ancient world discovers that learned and literate scholars can use this approach to write completely contradictory studies of the same topic. By selecting which passages to cite, by glossing the complicated ones, and by leaving out the inconvenient ones or sticking them in a dim corner of one’s scholarly edifice, its possible to present a case for whatever one wishes to argue. And the custom of going through the evidence piece by piece can make a lot of weak, hard to interpret pieces of evidence look solid (or many weak pieces of evidence which all lean in the same direction seem feeble). Just organizing a long list of pieces of evidence and commenting on them does not necessarily lead to the truth.
The promotion of Ada Lovelace Day and the publication of Sydney Padua’s steampunk graphic novel The Thrilling Adventures of Lovelace and Babbage has kindled the coals of the debate about whether Ada Lovelace was a capable mathematician or an enthusiast who needed her hand held. I do not care very much about 19th century mathematicians, but I do care about the truth, so I have been following this from a distance. And one thing which I notice is that people on both sides don’t really quote their sources at all.
In a podcast interview Padua confessed that she found it difficult to obtain Ada Lovelace’s mathematical works, and to understand the ones which she could find, so decided to trust Charles Babbage’s statements that Lovelace was an impressive mathematician. On the other hand, thonyc, an amateur historian of science living in Germany, passionately insists that:
The surviving letters of their [Ada’s and her tutor’s] mathematical correspondence clearly show that although Ada is obviously the possessor of a bright and inquisitive mind she never really grasped several important fundamental mathematical concepts and her acquisition of the secrets of mathematics never progressed beyond that of a failed first year undergraduate. To call Ada a mathematician is a perversion by any stretch of the imagination. As Dorothy Stein, who has analysed the De Morgan – Ada mathematical correspondence in detail, puts it in her excellent biography Ada: A Life and a Legacy (1985):
At twenty-eight, […] and after ten years of intermittent but sometimes intensive study, Ada was still a promising “young beginner”.
Her only ‘scientific’ contribution was to translate a memoire on Babbage’s Analytical Engine from French into English to which are appended a series of new notes. There is very substantial internal and external evidence that these notes in fact stem from Babbage and not Ada and that she only gave them linguistic form. What we have here is basically a journalistic interview and not a piece of original work.
Those are some firm statements by someone with an air of having studied the problem and with the training to study it well. The problem is that thonyc does not quote “the surviving letters” or explain this “very substantial internal and external evidence” or point readers to where either could be found. While of course one can’t compress the experience of learning 19th century ways of talking about mathematics then reading several volumes of correspondence between a student and her tutor into a short quote, one could give enough evidence that a reader could decide whether the argument was broadly reasonable. One has to chose whether to accept either the authority of Charles Babbage, whom Padua cites, or that of the unnamed historians and biographers whom thonyc cites, because neither gives any other kind of evidence. This is pretty common when people talk about history in journalistic contexts. An opinion piece by a historian of science in the Guardian which attempts to gently deflate Lovelace’s importance and promote other role models is equally evidence-free, although it does refer readers to an article in that distinguished academic venue Wikipedia. Wikipedians have a taboo against citing original sources, and today (2015-01-17) the page which she cites simply quotes what biographers have said about Lovelace’s contribution rather than referring readers to 19th century sources. An outsider who wants to know the truth seems advised to buy a biography of Lovelace and hope that it quotes or cites enough of the sources on her mathematical work to let a reader judge whether the author’s evaluation is well-supported.
This style of argument also has a name, and its an ugly one: appeal to authority. That name appears on lists of logical fallacies because simply invoking an authority does not explain why one should believe them over those who say differently. In case of Ada Lovelace’s mathematical works, the debate is clearly tied to powerful ideals and political factions in the broader culture, and it is very tempting to accuse those who say things one does not wish to hear of being biased. The only way to answer that charge is to test their arguments for coherence with the evidence rather than for political allegiance. But because neither side quotes or cites evidence and explains how they think it supports their opinion, this is hard to do. (For the record, Padua says that her graphic novel is full of footnotes and quotes from sources, and if so that puts her ahead of many promoters or critics of Ada Lovelace’s importance).
So there is something to be said for the classical style of argument. At the very least, it encourages everyone involved to consult the primary sources. And that has rewards even if the debate about the big questions in ancient history will never end. Moreover, as long as people can access the evidence, they have a chance to decide for themselves whether the experts’ arguments are plausible. Of course a casual knowledge of ancient literature is not the same as forty years studying the sources for a problem in the original- expertise does matter. But quite a bit of bad history can be rejected by anyone casually familiar with the sources, and that leaves more time to pay attention to the real experts. So I think that the classical style of argument is more scientific than those used by people trained in some other disciplines.
As for me, maybe I will see if any of the letters of Babbage, Lovelace, and their colleagues have been digitized, or if there are any biographies of Lovelace by historians of science in the local library. The truth matters, and sometimes you can’t find it in the newspaper or on a blog.
Further Reading: thonyc, “Christmas Trilogy 2012 Part II: Charles and Ada: A tale of genius or of exploitation?,” The Renaissance Mathematicus (link)
Edit 2016-02-15: A correspondent recommends the videos of the Oxford Lady Lovelace Symposium as better supported and balanced than many opinions about her work. I should also probably link to Sydney Padua’s website and her short comic Lovelace- The Origin which does have a charming set of links to further reading at the bottom.