An overview of the secondary literature on Flatland should correctly begin with the various notices and reviews of the period. A number of these are admirably collected and posted by Thomas Banchoff here, so rather than commenting, I’ll allow the reviewers of the period to speak for themselves. The breadth of the publications in which notices were published demonstrates the immediate reach of the book, and the second flurry of reviews follows the publication of the third edition with a foreword by William Garnett, in 1926.
Despite the fact that it remained in print pretty much throughout the 20th century, the only writing on Flatland to be found in the middle of the century was Banesh Hoffman’s 1952 intro to the Dover edition, which has been reproduced several times since. In laudatory mode, Hoffmann situates the text in scientific history as a pre-relativity work: ‘In these days space-time and the fourth dimension are household words. But Flatland, with its vivid picture of one and two and three and more dimensions, was not conceived in the era of relativity. It was written some seventy years ago, when Einstein was a mere child and the idea of space-time lay almost a quarter of a century in the future.’ He describes it as ‘no trifling tale of science fiction. Its aim is to instruct, and it is written with subtle artistry.’
David W. Davies took a more literary historical approach in 1978, penning a brief biography of Abbott and citing the reviewers of the day and Abbott’s own article from The Contemporary Review in 1890, ‘Illusion in Religion’, to contextualise Flatland. Noting also Abbott’s engagement with Bacon and Cardinal Newman, Davies’s short intro is surely the wellspring for more recent criticism. Significantly, Davies closed by comparing Abbott’s application of ‘a mathematical way of thinking to literature’ to that of the OULIPO writer Harry Matthews, concluding: ‘Mathew’s permutations are for fun, and as the Boston Advertiser reviewer noted, that is the purpose of Flatland.’
Interest really began to increase in the 1980s, and I’d suggest a couple of reasons for this: the impending centenary of publication in 1884 and the advent of computing that could facilitate the rendering of four-dimensional images. This surge of interest was led by SF writers, publishers and the critics who had begun to found a scholarly response to the genre. So in 1982 Isaac Asimov contributed as dry an introduction as one might expect from the hardest of hard SF writers, praising Flatland as an essentially educational text, while Ray Bradbury’s 1983 introduction responded in far softer terms to the satirical intent of the novel. Rudy Rucker, meanwhile, commented on and responded to dimensional work by both Abbott and Hinton extensively in his fiction and non-fiction writing of this period, and will receive closer attention in a future post. For now I want to look at Bradbury’s response, which is rare in Flatland criticism by paying particular attention to the literary qualities of the work and taking considerable joy in them. It’s worth quoting a sizeable chunk of this:
Why has the book remained so popular for almost a hundred years? Because, like Mark Twain, Professor Abbott must have thought: I refuse to be serious about a serious subject. Churches brim with seriousness and snoozers snooze. Scientific conferences of one denomination or another drone on through endless and ungoiden afternoons and one chooses the catnap as against suicide. The only medicine is high spirits and good humor. Professor Abbott has both in tonic proportions. I cannot help feeling that those who shared his home with him while he was flattening his concepts to fit his pen must have heard quick bursts of laughter from his den when it suddenly struck him to write, for instance, those sections on ’feeling’ as a means of identification amongst the Flatlanders. There are serene and marvelous sexual under-and-overtones here perhaps more for us in this neo-barbarian age, than for those who inhabited the three-plus-one dimensions of 1884. Abbott, in other words, is able to play himself and win. Given the measurements of Flatland he moves out intuitively and with huge delight to ’feel’ his own creations, sum them up in shapes, and report back to us. We go with him, because it is not often we have such a guest, in our living room, so full of mathematical logic leaning into fun that we are quite content to shut our mouths and score his game.
The same year witnessed the publication of the first scholarly genre pre-history of science fiction by Darko Suvin. The progressive strain in Flatland was central to Suvin’s elevation of the text to lofty status within his pantheon of Victorian Science Fiction. For Suvin, Flatland is categorised as a ‘sophisticated alternative history’. He’s highly approving of ‘the first concrete account of a plebeian rebellion in UK SF’ (372) (despite its failure, which he doesn’t mention) and describes Abbott’s abstraction as ‘not unworthy of the fertile analytical abstractions of Darwin and Bacon (of whom he knew) or indeed of Marx (of whom he did not know).’ (370)
Roger Luckhurst’s dismissal of Suvin’s definition of SF as a literature of ‘cognitive estrangement’ – on the grounds that this definition is so ideologically conditioned that it fails to account for important texts that don’t conform to a Marxist perspective, and here’s a list of such texts by the man himself – should be noted, but need not concern us unduly here, because Flatland gets the thumbs up from Suvin and is therefore given considerable attention. (In Luckhurst’s account, mechanisation defines the genre of SF, which clearly excludes Flatland, and here it’s hard to disagree. As any fule no, Flatland is in fact math-fi, so perhaps we shouldn’t get too hung up on generic definitions.)
Suvin makes one particularly useful observation which I would like to stet, writing: ‘Cleverly adapting Carroll’s and Verne’s strategy of subsuming but transcending the juvenile reader, Abbott’s is in truth “A Romance of Many Dimensions”; in its thoroughgoing democratism, it is addressed to the best minds in the new reading public, issuing from the newly introduced obligatory primary schooling.’ (373) As has been noted numerous times subsequently (Jameson, Stableford, Luckhurst, among others), the idea that a new generation of lower middle class readers had been produced by the primary system by the 1880s has been pretty much put to bed, but let’s not lose the first part of Suvin’s point, that Flatland works for both younger and older readers. Secondary criticism since Suvin has tended to ignore this younger readership.
Such criticism has been more concerned with contextualising Flatland in the broader cultural field. In 1986 Rosemary Jann argued that ‘as part of Abbott’s wider commentary in the role of imagination in cognition, Flatland alludes to contemporary debate over the role of hypothesis in scientific discovery and the relationship between material proof and religious faith’ (473). For Jann, Flatland is a paean for ‘the progressive force of the imagination’ (486), and negotiates a middle way through inductive science, responding to debates over the unseen in the natural world, and dogmatic faith, allowing for a less absolute faith in the literal truth of the written scriptures.
Jann’s work informed Jonathan Smith, writing a decade later, in his chapter ‘Euclid Honourably Shelved’, which offers a Baconian reading of Abbott. Suvin’s comment (above) on Abbott being aware of Bacon doesn’t really do justice to the relationship: Abbott published two books on Bacon, and Smith charts the trajectory of his modulating opinion. In so doing he positions Flatland among the contemporary arguments for and against non-Euclidean geometry, working deftly with the detail of the primary material. Smith’s overview of secondary writing on Flatland is worth quoting:
When not treated as a joke, Flatland has tended to be approached in ways that divorce it from its cultural position in the debate over non-Euclideanism and its implications. Historically, literary critics have treated it as an early example of science fiction and fantasy, while scientists and mathematicians have used it as a clever way to introduce their students to concepts of dimensionality and non-Euclideanism. It has only been recently that the book has been brought back to the center of the study of Victorian culture, and it will be to further that movement that I approach the novel here. (191)
The party most guilty of treating Flatland as a joke in Smith’s account was Bertrand Russell, who addressed ‘metageometry’ in his Essay on the Foundations of Geometry, published in 1897 and based on his PhD thesis. It’s not strictly accurate, however, to say that Russell treated Flatland as a joke: he actually wrote that Abbott used the dimensional analogy as a joke, and this seemingly subtle difference is quite significant, I think.
Shortly after the publication of his book on Bacon in 1996, Smith contributed to an essay co-written with Berkove and Baker that responded to Rosemary Jann’s reading of Flatland’s ending as ambivalent by highlighting what the authors argued was an implied criticism of the theology of Cardinal Newman. Most interestingly for me, Smith et al. draw out from Flatland not an analogical inspiration, but rather an extended critique of misapplied analogy, of which they argue that Abbott believed Newman was guilty. They draw attention to English for English Readers, a textbook Abbott compiled with his friend J.R. Seeley, and its sections on analogy. English was aimed at the improving native reader and writer of English – the schoolboy – and its lessons on analogy, and the parent category of induction, are clear.
Analogy meaning Likeness. – Analogy meant originally an Equality of Ratios, or Proportion. It is sometimes, however, loosely used to represent not so much proportion, as the similarity and regularity of natural phenomena. (265) So far as it is an argument at all, [it] comes under the head of Induction. Otherwise it is not an argument, but a metaphorical illustration of an argument. (273)
What’s more, induction itself is unsound:
The Induction that proceeds from enumeration of instances to a general statement about a class […] is evidently an insecure method of proof […] It is based upon the principle of uniformity in nature, “what has been is and will be” […] Induction is always incomplete […] Thus all statements that result from merely enumerative induction are temporary and liable to correction. They may therefore be called provisional. (262-263)
Smith et al therefore turn Jann’s conclusion on its head: ‘Flatland is a cautionary tale about the dangers of the imagination when wrongly applied.’ (129-130)
Most recently K.G. Valente has done some serious digging and found an essay published in the City of London School Magazine in 1877 dealing with higher dimensioned space. Please click through the scans below to read ‘A New Phbilosophy’ for yourself.
It’s a striking find for a number of reasons: like Flatland it presents a humorous response to very recent writing on n-dimensions; it was published anonymously in the magazine of the school at which Abbott was headmaster during his tenure; and it also essays the sketching of a parodic belief system based on the reductio ad absurdum of the dimensional analogy. Is it Flatland in utero? It’s certainly a fantastic piece of writing for a schoolboy audience, ably demonstrating the euphoric headlong rush into error through rigid application of a woolly logic, eerily similar to that upon which Zollner was just embarking in Leipzig.
Valente wisely refrains from pointing the finger directly at Abbott (and how frustrating it must be not to be able to stand it up!) Of course, it could have been Abbott who authored the piece, but it could just as easily have been William Garnett, the headboy at City of London in Abbott’s third year as headmaster, who had by 1877 begun work as Clerk Maxwell’s assistant and would go on to be his biographer (Garnett would have been just as well versed in the contemporary discussions of n-dimensioned space taking place in The Academy, Nature, Mind and at the BAAS: Clerk-Maxwell alluded to it in his verse on a number of occasions in this period). Or it could simply be the work of an unusually bright pupil at City of London. We’re unlikely ever to know.
While I would follow Valente in leaving the question of authorship tantalisingly open (the beauty of blogging – I can have my cake and eat it by adding my own wild speculations before retreating rapidly!), I wouldn’t necessarily subscribe to his reasoning. Valente writes that
even with such satirical potential there is one element of the piece that would not be subjected to [Abbott’s] ridicule. Recall that the author identified serious limitations that materialism represented regarding religious contemplation; this is a conviction Abbott would not wish to mock. Although Jann noted ambivalent elements in Flatland (488), testimonials by students and peers strongly suggest that Abbott’s intellectual integrity made it difficult for him to condone ambiguity. Consequently, attributing “A New Philosophy” to him would require the problematic approbation of contradictory ideological juxtapositions as well as an explanation for their amelioration by 1884. (66)
But ‘A New Philosophy’ is monomaniacal. I can’t help but feel that while Valente acknowledges that ‘A New Philosophy’ is a humourous piece, he reads it with too straight a face, and as I’ve suggested two pars back, I think it’s intended as a piece of absurdist reasoning and is parodic to its bones: it could certainly contain ‘ideological juxtapositions’ to Abbott’s stated beliefs without entertaining any ambiguity. I also believe it has a specific satirical target in its sights, and, once again, I plan to develop that idea in a later post.
The trajectory of current criticism on Flatland, then, follows Smith’s aim to bring the text back to the ‘center of the study of Victorian culture’. While this shift in emphasis has produced some inspiring work and has rescued Flatland from ghettoisation as a sci-fi precursor text, it also, by bedding it so thoroughly into the contexts of religious or scholarly discussion of significance in this period, risks obscuring the anomalous nature of the text and the very source of its popularity. Not only was Flatland the only fiction published by the prolific Abbott in a thirty-year writing career, but it is also, like ‘A New Philosophy’, less than serious.
I’m likewise suspicious when the secondary criticism positions Flatland as an element in some kind of smooth-surfaced theological project on the part of Abbott. I think it’s important, particularly when attempting to recreate the ‘cultural position’ of the text, to hold in mind William Garnett’s description, in his preface to the third edition, of the book as a ‘jeu d’esprit’, and the comments of earlier respondents like Bradbury and Davies: Abbott was having fun with this book, and writing for a broader audience than that he habitually addressed. Russell recognised this, as did contemporary reviewers. There are certainly consistencies with his theological writings, as one would expect, but we must remember that what we are reading is not a manifesto (in the case of Flatland, at least: a manifesto is exactly what ‘A New Philosophy’ is, and a very good a priori spoof of the form it is too.)
Of course, to argue for a reading of Flatland responsive to its humourous intent is to create a rod for my own back – is satire necessarily actually funny? can intent be assumed? – but what I’m really advocating is the recuperation of elements of earlier criticism rather than the dismissal of fresher discoveries. It goes without saying that I think Smith’s work in contextualising Flatland in discussion of non-Euclideanism was entirely necessary; it’s important, too, to hold in mind Abbott’s position on miracles and the imagination; I’m particularly persuaded by the argument that Flatland critiques rigid and literalised analogical reasoning; and I’m totally thrilled by ‘A New Philosophy’. None of this stops Flatland being an amusing book written with a schoolboy audience in mind: this is a crucial point when it comes to the spread of the concepts of higher space. It’s important that we don’t ‘divorce it from its cultural position’ as a funny and popular book. And I also think it’s overstating the case to think of Flatland as an integrated part of a theological project when it is enmeshed in a complex matrix of contemporary social and cultural concerns and responsive to such a broad range of ideas as Galton’s eugenics, ‘plebeian rebellion’, geometrical pedagogy and the education of women.
So that’s a fairly breezy overview, which has doubtless missed some significant contributions, but it’s a reasonable launch-pad for some consideration of thee text itself, which I always seem to be threatening without ever actually doing…