Ian Stewart's Flatterland
Edwin A. Abbott's 1884 classic Flatland tells of a two-dimensional world, a world in which lines and polygons inhabit a flat Euclidean plane, ruled by narrow-minded, Victorian attitudes. These two-dimensional attitudes are shattered for the book's protagonist, A. Square, when he encounters a visitor from an extra-dimensional world, The Sphere, who introduces him to the world of three-dimensionality.
Flatland was an immediate hit and has become somewhat of a cult classic amongst the realm of popular science and mathematics, inspiring numerous derivative works such as Dionys Burger's Sphereland, A. K. Dewdney's The Planiverse and now, Ian Stewart's Flatterland.
Flatterland tells the story of A. Square's great-great-granddaughter, Victoria Line, a modern young Flatlander living in a society which has progressed somewhat since great-great-granddad's time, but not enough for young Vikki, who yearns for liberation from the sexist views of her father and the other polygons. Vikki is rumaging through the cellar of her family's pentagonal home when she makes a discovery which will ultimately change her life - and possibly those of all of the females and males of Flatland as well.
Vikki's discovery is an old book, a diary of sorts, written by one A. Square. Vikki mentions the book to her father Grosvenor Square, who blanches at the revelation. Great-great-grandfather Albert, you see, is not spoken of within the Square clan. This is because the polygon was a lunatic who died in prison - locked up for his insistance on the existence of a three-dimensional world, which the folk of Flatland considered to be both insane and heretical.
Victoria's father orders her to hand over the book, which he promptly destroys, declaring that it is not fit material for a young lady - or for anyone for that matter - to be reading. Unbeknownst to her parents, however, Vikki has already made a copy of the book for herself, which she then proceeds to study in private. Even Vikki's modern sensibilities are shattered by the revelations in old Albert's text, but the real prize is not the text itself, but a secret code which Vikki finds faintly printed at the end of the book. By this point, Victoria Line is thoroughly obsessed with her great-great-grandfather's treatise, and it is not long before she has cracked his code and is on her own wild adventure in the Outlands - the worlds beyond Flatland.
As Albert Square had The Sphere to guide him through his journey to the "Land of Three Dimensions", Vikki has her own guide, but a simple sphere will not suffice for Vikki's journey. Abbott's Flatland of course, was not really a treatise on the existence of three dimensions. Abbott's readers were already well versed in the realm of 3D. He simply introduced a society of 2D characters so that, by illuminating A. Square's struggle to come to grips with a three dimensional universe, he could introduce to his three-dimensional readers their similar relationship to four-dimensionality. The "Mathiverse" (as Vikki's guide calls it) however, has progressed by leaps and bounds in the 117 years between Flatland and Flatterland, and a simple sphere is far too mundane for the journey through the bizarre realms to which Vikki travels in Flatterland. What then, does Ian Stewart come up with for Vikki's guide? None other than the Space Hopper!
I must admit, the Space Hopper alone was enough to sell me on this book. Our North American readers may not be familiar with the Space Hopper - I have not seen the creature over here, except for the one which I brought across the ocean myself - but fellow Brits (from my generation, at least) will surely remember ol' Hoppy. The Space Hopper was a large, orange, thick rubber balloon, painted with a face on one side, the mouth spread wide in a grin reminiscent of Alice in Wonderland's Cheshire Cat. From the top of the Space Hopper sprouted two spiral horns. Hoppy, you see, was an alien, but a small child could sit upon it, holding onto the horns, and thus hop around the yard, up and down the street, or into whatever imaginary realms the child could envision. Hoppy and I travelled to all kinds of fantastic places, but none quite so bizarre as some of the worlds to which the Space Hopper takes Victoria Line.
Once Victoria and the Space Hopper meet up, Flatterland reads like a math and physics textbook, although still couched within the context of a science fiction novel. Vikki travels not only to the "Planiturthians" three dimensional world, but also to the Fractal Forest, Quadratic City, Topologica, the Projective Plain, Platterland and the Domain of the Hawk King. Along the way, she travels through wormholes, meets her future and past selves, Schrödinger's cat "Superpaws", the Paradox Twins and the Space Girls: Minkowski (Minny) Space, Curvy Space, Bendy Space, Pushy Space and Squarey Space.
Sound like a whirlwind tour? It is. The concepts are thrown at the reader fast and furiously, but the antics of the Space Hopper, along with Vikki's engagement with the material, make such weird and abstract ideas as 10th, 11th and even fractional dimensions both relevant and interesting.
Flatterland is no pulp fiction easy read, and those unfamiliar with England may not register some of the plays on words with which the book is rife (such as Vikki's square father and brothers, Grosvenor, Berkeley and Lester being named for famous squares in London, and the linear Victoria and her mother Jubilee being named for major London Underground railway lines), but there is still plenty to entertain in this book, and many of the concepts which are more difficult to explain with words alone are also illustrated with diagrams and other pictures. I highly recommend Flatterland to anyone with even a passing interest in higher mathematics and the science behind such popular science fiction devices as wormholes and time travel.