Charles Howard Hinton was a Victorian mathematician and theorist of the fourth dimension, the scandal of whose conviction for bigamy led him to lose his job as a schoolmaster and to exile himself with his family, travelling first to Japan and then to America. Mark Blacklock’s novel shrewdly and even slyly manages to reflect Hinton’s theories without staking the success of the book on them. The contents page offers mild reassurance, in the shape of a timeline and a family tree, but also mild intimidation, since the chapters are named after geometrical objects or concepts, adding a dimension each time, from ‘Point’ to ‘Line’ to ‘Square’ to ‘Cube’ to ‘Tesseract’, then back down through the dimensions again. The word ‘tesseract’ was coined by Hinton himself in a book published in 1888 to describe a four-dimensional object that has the same relationship to a cube as a cube does to a square. You can enumerate the edges and vertices of a tesseract – 32 and 16 respectively – without necessarily asserting its reality: conceptual existence is quite enough to make zero or the square root of minus one useful in calculation.
It’s not uncommon for historical figures to rematerialise suddenly after a long eclipse – Ada Lovelace, Claude Cahun, the Chevalier de Saint-Georges, Hildegarde of Bingen – as if to meet a new cultural need. Alan Turing, who now has a government educational scheme named after him, was not only obscure but disgraced for more than a quarter-century after his death. Hinton isn’t of Turing’s calibre, and Blacklock doesn’t oversell him as a pioneer, though he quotes encomia by Borges and Iain Sinclair. Hinton published an essay called ‘What Is the Fourth Dimension?’ a few years before the appearance in 1884 of Edwin Abbott’s novel Flatland, in which a two-dimensional narrator, a Square, resists being educated into acceptance of a higher realm by a visiting Sphere. Abbott’s novel made a powerful impression on Hinton, inspiring him to write a fictional sequel or addendum, An Episode of Flatland, which wasn’t published until 1907. He may have anticipated being considered ‘not so much a heretic as an afterthought’.
Hinton starts at a relatively late point in its protagonist’s life, with a number of his books already published and the disgrace of the court case in the past, as his family prepares to embark on the SS Tacoma from Yokohama to America. Large families are hard to get straight, and readers will rely on the timeline and family tree to help with navigation until they get independent bearings on the narrative. The Hintons had four sons: the oldest, George, was born in 1882, the youngest, Sebastian, in 1887. In between came Eric, born 1883 (according to the family tree) or 1884 (according to the timeline); and William, born 1884 (family tree) or 1886 (timeline). A pair of quantum children, impossible to pin down! The journey between continents took place in 1892 (timeline) or 1893 (according to the ship’s manifest quoted). Hinton himself died in 1904 (family tree) or 1907 (timeline), so at the time of the voyage had between eleven and fifteen years to live. Something postmodern must be going on, as might be expected from a novel with a fourth-dimensional theme – and there are postmodern touches elsewhere, as with the unnamed ‘compositor’ who explains what is ‘almost’ the method of the actual book. But the multiple date discrepancies seem just to be mistakes.
Misprints pullulate wherever there is text, and the errata slip for Hinton’s book The Fourth Dimension (1904) corrects six mistakes, three of them numerical, which must count as particularly damaging in a scientific volume. It seems unlikely that Blacklock would make deliberate errors of his own without a strategy, though his approach in Hinton is consciously uneven as far as historical fidelity goes. The illusion of the past is sometimes solid, sometimes not. At intervals he inserts letters (presumably authentic) from Howard’s father, James, who died in 1875, into the account of later events, in a way that efficiently characterises a respectable Victorian man’s expectations of his son. The novel’s dialogue mainly reflects period decorum but in his authorial descriptions Blacklock allows himself greater lexical freedom. While teaching at the College of New Jersey, which became Princeton, Hinton tests a baseball-throwing machine of his own design which Blacklock compares to a ‘bazooka upon a tripod’. Although the term ‘bazooka’ wasn’t coined until the Second World War this doesn’t burst the bubble of plausibility as would happen if the word was spoken aloud. The use of ‘upon’ rather than ‘on’ has a happily ageing effect, a semantic counterpart of the furniture-distressing dodge that allows new items to pass as antique.
When Hinton imagines the possibility that a human being might be turned inside out on his return from four-dimensional space, the passage seems to represent writerly intoxication (and access to a medical glossary, though it’s true that Hinton’s father was a surgeon) rather than abstract thought: ‘The abductor hallucis unfolds. The scaphoid opposes the piriformis. Infraspinatus describes an arc. The buccinator reverts, effloresces … The lateral pterygoid imbricates the latissimus and the risorius oscillates itself throughout. Orbicularis oculi deliquesce and the sacrum deviates from the norm. An obturator metastasises. The rhomboid is extrapolated. The trapezius blossoms.’ A similar exuberance, floating free of the scene described but still enriching it, drives the splendid large-font onomatopoeisms (‘FTDOOINGchump’, ‘HAKKTOMPF’, ‘tthhRHAKKTuuuk’) that represent successive detonations of the baseball cannon as its mechanism is refined.
The internal world of Hinton’s wife, Mary, is quieter. On the SS Tacoma she passes some of the time stitching:
One commences with the plotting of points in a grid and joins these points with the thread, each line both bisecting and augmenting its fellows, tangents on the cards combining to form curves and parabola. She works presently towards a cardioid design. The work is rhythmic and builds towards satisfaction, its angles perpetually softened and arced until a perfect form is achieved.
In another context this would seem a forced importation of geometry into domestic handicraft, except that Mary’s mother taught her this activity as a form of ‘direct contact with mathematics’ – and her father was George Boole, whose invention of algebraic logic underpins computer systems.
When they arrived in America, Hinton’s sons went their different ways; Eric drops out of the historical record, his date and place of death unknown. In Blacklock’s version Eric becomes a gambler and a speculator during the Gold Rush, which makes him a rebellious reflection of the eldest brother, George, a mining engineer. It is the third son, William, who has the furthest to fall. When Sebastian tracks him down to inform him of the death of their father, he is working in a carnival freak show, earning a pittance by biting the heads off animals. For the duration of this strand, Hinton seems less like literary fiction than a lost episode of the HBO series Deadwood, and the partial embargo on anachronism is lifted (‘yomped’, ‘shitshow’, ‘fuckups’), though Deadwood itself stylises period language without breaking the illusion.
Hinton’s death occurs at the halfway mark of the book, with crucial events such as the conviction for bigamy only obliquely acknowledged. (Blacklock reproduces the illicit marriage document at the point in the text where his readers might expect the death certificate.) It wasn’t something Hinton himself was eager to discuss, as one weirdly mishandled scene demonstrates. He is by now teaching at the University of Minnesota and the couple spend a holiday in California, visiting Ralph Radcliffe Whitehead and his wife, Jane, wealthy idealists seeking to set up a utopian community. The dialogue here strikes a number of false notes, with ‘trial’ used as a verb (a piece of organisational jargon not cited by the OED before 1981) and an experience described as something that ‘grew our solidarity’. A little later a conversation ‘is progressed’. The name of Ruskin comes up in the conversation – Hinton and Whitehead supposedly became friends when working on the road-digging scheme Ruskin organised at North Hinksey in the 1870s to introduce students to the virtues of labour and public service. Mary seems unaware that her husband had been a disciple of Ruskin’s. Hinton ‘suppresses his shame at this absence of knowledge and what it reveals. [He] has inherited so many acquaintances, so much of his father’s world.’ This is almost odder as an explanation than what it is called on to explain. The Hintons have been married for almost twenty years, and Ruskin was a major public figure. Never mind. Then another name comes up.
Oscar Wilde also claimed to have visited the Hinksey scheme and these sophisticated people refer to him as if his name was still mainly associated with epigrams and comedies. ‘His work is terrifically funny!’ Jane Whitehead says. But Hinton’s Minnesota employment, from 1897 to 1900, coincided with the last years of Wilde’s life, after his release from Newgate Prison. News of a downfall that makes Hinton’s own disgrace seem trivial seems not to have arrived. Why introduce Ruskin and Wilde into your characters’ conversation if the effect is to whittle away their plausibility rather than build it up?
Ralph Whitehead wants to hear about what he calls Hinton’s ‘difficulties in London’, and questions him while the women are busy with the children, but Hinton doesn’t react, preferring to discuss the wine they are drinking. Is it an Italian varietal? Yes, as a matter of fact – Primitivo, which grows well here. This distraction ploy falls flat on the page, since the word ‘varietal’ was introduced in the 1920s, and anyone who went to the trouble of planting imported Primitivo vines rather than the Zinfandel that was the California staple would be wasting his time, since the two strains are genetically identical.
Elsewhere Blacklock’s carpentry can be exquisite: marquetry might be a better description of a four-page ghost story called ‘The Four Brothers’, supposedly by Lafcadio Hearn, inlaid in the narrative. I can’t find a story of Hearn’s by that name and it is presumably a pastiche, but it’s hard to say which possibility is more satisfying: that a perfectly snug niche has been found for an existing text or that a fable has been fabricated to dovetail with Hinton’s preoccupations. In the story, four boys come across a river creature called a kappa reading from a scrap of paper. ‘This piece of paper,’ the kappa explains, ‘describes the way to another world, a world more spacious than this one. It is a place in which those things that are inside are brought outside and there are no secrets between beings.’ The boys try to steal the paper but the kappa is too quick for them and disappears into the water, taking one of them, Katsuro, with it. In the end the three other boys are able to find a priest who can reverse the vanishing process. He manipulates the paper and Katsuro returns thanks to a sort of human origami: ‘Before their eyes a limb appeared, unnaturally folded upon itself. It began to unfold, and as it did so, a torso followed, uncrumpling itself; a head, expanding from a dot; more limbs, in sickening swirls. Katsuro was reborn into their space.’ He is as he was, except that from this day on he can write only upside down and back to front.
This could be a version of Ian McEwan’s celebrated early story ‘Solid Geometry’ with a happy ending – though McEwan’s narrator doesn’t seem particularly unhappy when his yoga-limber girlfriend, compared to a paper flower, disappears for good under his manipulation (‘her head and legs were in place in the hoop of her arms … As I drew her arms and legs through Maisie appeared to turn in on herself like a sock’). Late in the book, Mary Hinton mentions in a diary entry about her time in Japan that her husband befriended Hearn and invited him to live with them, inviting the speculation that Hearn, an Irishman partly of Greek descent who ended up marrying a Japanese woman, made up or tailored a story to beguile four particular brothers, the Hinton children.
Much of the construction of Blacklock’s book is sweetly deceptive. Readers may be daunted in advance by the presumed difficulty of the ‘Tesseract’ chapter. What would constitute hypercubical writing, given that ‘higher beings’, thanks to their access to the fourth dimension, have complete knowledge of three-dimensional beings? The analogy is with the way that a two-dimensional object can’t hide from a three-dimensional observer. In the words of Blacklock’s Hinton (and perhaps the historical one, since he claims to be quoting a letter from 1885 printed in Nature):
There is a new three-dimensional space for each successive instant of time; and, by picturing to ourselves the aggregate formed by the successive positions in time-space of a given solid during a given time, we shall get the idea of a four-dimensional solid, which may be called a sur-solid … Let any man picture to himself the aggregate of his own bodily forms from birth to the present time, and he will have a clear idea of a sur-solid in time-space.
Other writers and thinkers have imagined such an interface differently. For Proust, the fourth dimension could be attained by the use of conscious effort to consolidate the flashes of involuntary memory – in his cosmology the fourth dimension was a private realm of retrieved experience (though art might generalise it), a treasury of moments. The aeronautical engineer turned philosopher J.W. Dunne, whose An Experiment with Time, published in 1927, helped shape J.B. Priestley’s time plays, saw the fourth dimension as constantly lapping at the other three. Every night the dreaming mind melts back into a medium in which the artificial barrier between the future and the past imposed by consciousness no longer exists.
But nothing resembling a sur-solid materialises in the ‘Tesseract’ section, where readers find merely a series of documents and letters from the period leading up to the scandal and the court case, none of them written by those immediately involved, though a number of the names are familiar (Havelock Ellis, Olive Schreiner). This couldn’t be less like hypercubical consciousness, amounting instead to a rather retro experience of reading. It requires the sort of filling in of gaps appropriate to epistolary novels. If this sounds like a criticism of the author’s formal choices it isn’t meant to be. The effect is of a sudden shift in emphasis, with Hinton no longer being regarded as a special case, whether visionary or crank, but as part of a wider turbulence of social attitudes on ‘the woman question’. Information that Blacklock has withheld is now released, though in modest quantities. Before it denoted Hinton’s ideas about dimensionality, if it ever did, ‘Hintonianism’ referred to his father’s sexual theories and practices, which set out to free women, particularly those of the lower classes, from the oppressiveness of conventional marriage, though it could look a lot like predatory slumming. Dotted lines on the family tree, denoting presumed relationships, connect him not only to his sister-in-law, Caroline, but to Mary Everest, mother of the Mary he married, but can’t indicate whether the presumed relationship predated her marriage to George Boole. Other dotted lines leave the diagram at its upper edge, like arrows fired into the air.
Howard’s bigamy, which only came to light because he confessed it, was an attempt to square the circle of respectability by giving the twins born to his mistress, Maud, at least ‘a colour of legitimacy’. It also involved any amount of hypocrisy, since he introduced Maud into his social circle without revealing the true situation, at least to Mary. Blacklock follows the twins, whose lives are not documented, into a possible future, and gives Maud a more reconciled assessment of what happened than Mary seems ever to have reached: ‘There was love in all of this, though what it became – what extrapolation led to – was no longer love.’
There seems to be no necessary link between dimensional speculation and a preoccupation with gender roles, but Abbott’s Flatland itself has a definite element of satire on the subject, with men being shapes with two dimensions while women are mere lines. A woman is required to give notice of her proximity and peaceful intention, for fear of puncturing a Circle (the highest rank of male), as if she was the prophetic personification of a suffragette’s hatpin. Hinton was a member of the Men and Women’s Club, founded in 1885 to discuss gender relations, and Blacklock’s ‘Tesseract’ section shows rather delicately the way his self-imposed disgrace created complex ripples among the membership. There was personal sympathy for Hinton and Mary, with a little left over for Maud, there was blame visited on the baleful influence and example of Hinton’s late father, but there was also concern for the impact of a criminal scandal on the reputation of a club whose discussions were never far away from potential controversy.
The substitution of partial knowledge and vested interest for the transcendent knowledge that seemed to be promised by this section is an internal contradiction with a beneficially bracing effect. Kurt Vonnegut pursues a similar strategy in Slaughterhouse-Five (1969), where a thought experiment about time clashes richly with one of the book’s core assumptions. Vonnegut’s experience of the firebombing of Dresden, which he gives to his hero Billy Pilgrim, was the event around which his life pivoted, a revelation of horror and meaninglessness after which nothing could be the same again. But for the purposes of the novel he invented the planet Tralfamadore and its inhabitants, who kidnap Billy. The Tralfamadorians could have been devised to dramatise Hinton’s notion of sur-solid perceptions, since they don’t perceive sequence at all. They see the sky as filled with ‘rarefied, luminous spaghetti’, because the lifetime of each star is played out in superimposition, and see human beings not as two-legged creatures but as super-millipedes ‘with babies’ legs at one end and old people’s legs at the other’. Vonnegut might have been working from Hinton’s blueprint of a sur-solid in time-space. The logic, strongly opposing the central thrust of the novel, is that no one day can be determinative of a life, any more than a single segment of a millipede can take precedence over any other. This cross-bracing, however perverse it seems, has played its part in the book’s durability.
In Hinton the non-appearance of a transcendent perspective does the book the great service of going against teleology, the sense of moving towards a predestined end that makes most historical novels so unsatisfying. Incoherence is not a flaw in the design but a truth deeper than design. At different points in the book Mary Hinton is resigned, despairing and raging, though against Maud rather than her husband: ‘There is a woman on the surface of the earth … who has caused such pain to me that I find all of humanity distorted by her image.’ She also considers Hinton’s ‘progeny’, a category which must include her four sons, ‘all but corrupted’. But the boys, with their clashing precocities, seem to be treasured by the book in its early sections. With his love of documentation both authentic and made up, Blacklock has gone to the trouble of commissioning drawings, by James Nunn, to illustrate their wonderfully divergent responses to an exercise their father sets them during their sea voyage, to chart the SS Tacoma’s course. Their magnetism seems to fade over the course of the novel in the author’s eyes, as perhaps it did in their parents’.
In a book about a scientist and his work the reader is always subconsciously dreading the arrival of equations and complex diagrams. Pages 276-77 of Hinton seem, to the riffling hand and skipping eye, to announce the arrival of that moment, with its lattice of grids and inscribed numbers. This is another example of Blacklock’s expert misdirection, since these pages in fact reproduce Sebastian Hinton’s 1923 patent application for the design of a climbing frame. Yet there is a connection with his father’s work: Hinton built his sons just such a piece of equipment, and would call out the co-ordinates of the places on the frame he wanted them to occupy. He could no more stop trying to visualise the tesseract than Thomas Browne could stop seeing quincunxes. If Blacklock can risk pulling back from Hinton’s theories, the reason must be not that they are hopelessly alien but that they are deeply embedded in the ordinary experience of reading. If the requirement for entering into a higher realm of thought is that we be ‘extended in dimensions beyond the three we physically occupy’, it happens every time we read a novel, and literature has always inhabited four-dimensional space.