[Review] Dangerous Dimensions: Mind-bending Tales of the Mathematical Weird

A superb new anthology of Weird Maths – from the Victorian era to the Space Age – takes Paul Gorman for a very strange and thrilling trip indeed…

   I’ve no head for mathematics, but the premise of this anthology – the latest in the British Library’s Tales of the Weird series – had me excited. I looked forward to having my brain twisted into new and strange configurations by tales of unearthly geometry and sinister equations, and I wasn’t disappointed. 

   Chronologically sequenced, the early stories date from the 1890s to 1920s, are mostly by British authors, and have the air of anecdotes told by the fireside in a gentlemen’s club. The later tales (from the 30s to the 60s) were mostly published in pulp magazines of the day, and their ebullient prose style tends to reflect this.

   Of the early tales, ‘The Plattner Story’ by HG Wells isn’t, it must be said, a particularly auspicious start. Not one of Wells’s finest, it feels like two half-stories stuck together, each one embodying a different idea. Although these ideas are worthy of exploration – Gottfried Plattner becomes anatomically reversed (his heart moves to the right-hand side, facial features swap places, and so on) and he slips into a dimension which overlaps our own – the execution feels clunky and a little aimless. 

   In Mary Eleanor Wilkins Freeman’s ‘The Hall Bedroom’, a landlady who has recently moved into a new house lets rooms to lodgers. The hall bedroom has an odd reputation preceding her arrival, and sure enough – or so she gleans from the unfinished narrative of its most recent occupant – it stretches in dimensions intimated by the faintly disturbing painting hanging on the room’s wall. This tale is one of two in the anthology by female authors, and is an interesting take on the ‘bigger on the inside’ story. 

   The collection really hits its stride with ‘Space’ by John Buchan, whose weird tales are increasingly attracting attention. It’s the story of Hollond, who becomes convinced that space – not outer space, but the gaps between material objects – is not empty, and that whatever fills it explains such things as our sense of direction, or the homing instinct of pigeons. His experiments take him to Chamonix, shorthand since Frankenstein (Mary Shelley, 1818) for the notion of the Romantic sublime: alpine vistas which inspire a sense of awe laced with terror. Hollond, of course, falls victim to his obsession and comes close to terror when he senses that there may be sentience among the ‘corridors and alleys’ of ostensibly empty space. ‘Space’ is a superb tale which benefits from its anecdotal framing, and like the others is absolutely literary: it’s hard to imagine many of these works being translated to film.

   Editor Henry Bartholomew has selected two stories from his favourite weird author, Algernon Blackwood. ‘A Victim of Higher Space’ features Blackwood’s occult detective John Silence, investigating here Racine Mudge, a man whose childhood education was atypical, and as a result has no knowledge of the ‘deceitful’ mathematics taught in schools. Instead, he plunges into his own experiments in maths and becomes able to fall into a fourth dimension. He becomes dimensionally incontinent, though, and the slightest excitement – the sound of Wagner, for instance – can tip him over. The story is played for gentle humour, and there’s little sense of drama or cosmic unease: certainly nothing to compare to such Blackwood classics as ‘The Willows’ or ‘The Wendigo’, but it’s a diverting little tale all the same. 

   The second Blackwood story is ‘The Pikestaffe Case’. Like ‘The Hall Bedroom’, this story refracts the action through the perspective of a female householder. And that’s not the only echo – or, to be more appropriate, mirror image – of another story in the collection. HP Lovecraft and Henry S Whitehead’s collaborative tale, ‘The Trap’, like ‘The Pikestaffe Case’, features a protagonist who, accompanied by a child prodigy, vanishes into the dimensions beyond a mirror: ‘a direction at right angles to all we know’. ‘The Pikestaffe Case’ drip-feeds its weirdness slowly, and like ‘Space’ is another story in which the narrative distance between action and viewpoint works to heighten the sense of unease.

   Moving into the pulp era, Frank Belknap Long’s ‘The Hounds of Tindalos’ is always a welcome addition to any Weird anthology. Occult writer Halpin Chalmers takes a fantastic drug in order to mentally travel back through time. What he finds there regarding the origins of life is as shocking as anything in Lovecraft. On the face of it, the talk of ‘outrageous angles’ and ‘curves’ may sound silly, but the narrator’s scepticism draws the sting of reader disbelief, and it’s a thrilling tale that works in spite of this.

   Donald Wandrei’s ‘Infinity Zero’ is another highlight. Set in a putative – though fairly accurately predicted – Second World War, newspaper photographer Conway is sent to investigate the bombing of an experimental factory. All that’s left of the site is a crater which is growing steadily, eating away at all matter as it does so. In the anthology’s one moment of explicit violence, Physicist Marlow is undone in a truly shocking manner. A superb tale of cosmic terror.

   The most mind-bending story (and lots of fun with it!) is Robert Heinlein’s ‘– And He Built A Crooked House –’. An architect designs a four-dimensional house in the shape of a tesseract. Despite the seeming impossibility, everything goes perfectly until a minor Californian earthquake sends it tumbling into itself, with Escher-like consequences for the protagonists.

   The appearance of Jorge Luis Borges may seem incongruous, but Bartholomew fully justifies the great Argentinian’s inclusion with ‘The Library of Babel’. A story with no narrative drive, instead it takes to the farthest logical conclusion the superficially whimsical notion: ‘what if’ the entire world were a library, and that library were infinite?

   Some of the stories in this volume belong to the noble tradition of ‘Doctor Faustus’ (Christopher Marlowe, c.1592) and ‘Frankenstein’, in which the pursuit of knowledge comes at a terrible cost. Others are more playful, where the story is simply the full exploration of a speculative hypothesis. Henry Bartholomew’s introduction provides a brief history of maths and science in fantastical literature, and the broad context of the period – from Relativity to Sputnik – in which the stories in Dangerous Dimensions were written. This excellent anthology, which deserves to be read and re-read, takes us to a place where, as the narrator of John Buchan’s ‘Space’ puts it, ‘mathematics fades into metaphysics’.