{"id":12464,"date":"2022-07-07T03:14:43","date_gmt":"2022-07-07T03:14:43","guid":{"rendered":"https:\/\/www.booksofall.com\/ja\/?post_type=product&p=12464"},"modified":"2022-07-07T03:15:12","modified_gmt":"2022-07-07T03:15:12","slug":"aspiring-to-a-higher-plane","status":"publish","type":"product","link":"https:\/\/www.booksofall.com\/ja\/aspiring-to-a-higher-plane\/","title":{"rendered":"Aspiring to a Higher Plane"},"content":{"rendered":"

In 1884 Edwin Abbott Abbott published\u00a0Flatland: A Romance of Many Dimensions<\/em>, perhaps the first ever book that could be described as “mathematical fiction”. Ian Stewart, author of\u00a0Flatterland<\/em>\u00a0and\u00a0The Annotated Flatland<\/em>, introduces the strange tale of the geometric adventures of A. Square.<\/strong><\/p>\n

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Edwin Abbott Abbott<\/a>, who became Headmaster of the City of London School<\/a> at the early age of 26, was renowned as a teacher, writer, theologian, Shakespearean scholar, and classicist. He was a religious reformer, a tireless educator, and an advocate of social democracy and improved education for women. Yet his main claim to fame today is none of these: a strange little book, the first and almost the only one of its genre: mathematical fantasy. Abbott called it\u00a0Flatland<\/em>, and published it in 1884 under the pseudonym A. Square.<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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On the surface \u2014 and the setting, the imaginary world of Flatland, is a surface, an infinite Euclidean plane \u2014 the book is a straightforward narrative about geometrically shaped beings that live in a two-dimensional world. A. Square, an ordinary sort of chap, undergoes a mystical experience: a visitation by the mysterious Sphere from the Third Dimension, who carries him to new worlds and new geometries. Inspired by evangelical zeal, he strives to convince his fellow citizens that the world is not limited to the two dimensions accessible to their senses, falls foul of the religious authorities, and ends up in jail.<\/p>\n<\/div>\n<\/div>\n

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The story has a timeless appeal, and has never been out of print since its first publication. It has spawned several sequels and has been the subject of at least one radio programme and two animated films. Not only is the book about hidden dimensions: it has its own hidden dimensions. Its secret mathematical agenda is not the notion of two dimensions, but that of four. Its social agenda pokes fun at the rigid stratification of Victorian society, especially the low status of women, even the wives and daughters of the wealthy.<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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Flatland\u2019s inhabitants are triangles, squares, and other geometric figures. In the planar world\u2019s orderly hierarchy, one\u2019s status depends on one\u2019s degree of regularity and how many sides one has. An isosceles triangle is superior to a scalene triangle (all sides different) but inferior to an equilateral triangle. But all triangles must defer to squares, which in turn defer to pentagons, hexagons, right up to the pinnacle of Flatland society, the Priestshood. Referred to as \u2018circles\u2019, the priests are actually polygons with so many sides that no one can distinguish them. The sons of squares are usually pentagons, the grandsons hexagons, so there is a general progression along the greasy pole (there is no \u2018up\u2019 in Flatland).<\/p>\n

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But what of the wives and daughters? Flatland\u2019s women are mere line segments, actually very thin triangles, whose social standing is zero. Their intelligence is little greater. They are required by law to wiggle from side to side so that they can be seen, and to emit loud cries so that they can be heard, because a collision with a woman is as fatal as one with a stiletto. Abbott took a bit of stick from some of his female contemporaries, who failed to appreciate his irony. But we know from his own life, including his daughter\u2019s education, that he did a lot to improve the status of women and to ensure they received the same level of education as men.<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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Abbott wasn\u2019t particularly good at, or keen on, mathematics, but his book tackled an issue of great interest in Victorian times, the notion of four (or more) dimensions. This idea was becoming fundamental in science and mathematics, and it was also being invoked in areas like theology and spiritualism, because an invisible extra dimension was just the place to locate God, the spirit world, or ghosts. Charlatans like the American medium Henry Slade were exploiting conjuring tricks to claim access to the Fourth Dimension. Legitimate hyperspace philosophers were speculating about the role that additional dimensions might play in illuminating the human condition.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"