T H E F O U T H D I M E N S I O N
"You are traveling through another dimension, a dimension not only of sight and sound but of mind. A journey into a wondrous land of imagination. Next stop, the Twilight Zone!"
THE TWILIGHT ZONE - 1959
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Do you know, I've always felt a little cramped in three dimensions. Nice to be able to stretch out a bit in 4D isn't it. Anyway here's the science bit. In mathematics, four-dimensional space (4D) is an abstract concept derived by generalizing the rules of three-dimensional space. It has been studied by mathematicians and philosophers for almost three hundred years, both for its own interest and for the insights it offered into mathematics and related fields.
Algebraically it is generated by applying the rules of vectors and coordinate geometry to a space with four dimensions. In particular a vector with four elements (a 4-tuple) can be used to represent a position in four-dimensional space. The space is a Euclidean space, so has a metric and norm, and so all directions are treated as the same: the additional dimension is indistinguishable from the other three. In modern physics, space and time are unified in a four-dimensional Minkowski continuum called spacetime, whose metric treats the time dimension differently from the three spatial dimensions. Spacetime is thus not a Euclidean space. The possibility of spaces with dimensions higher than three was first studied by mathematicians in the 19th century. In 1827 Möbius realized that a fourth dimension would allow a three-dimensional form to be rotated onto its mirror-image,[1] and by 1853 Ludwig Schläfli had discovered many polytopes in higher dimensions, although his work was not published until after his death.[2] Higher dimensions were soon put on firm footing by Bernhard Riemann's 1854 Habilitationsschrift, Über die Hypothesen welche der Geometrie zu Grunde liegen, in which he considered a 'point' to be any sequence of coordinates (x1, ..., xn). The possibility of geometry in higher dimensions, including four dimensions in particular, was thus established. An arithmetic of four dimensions called quaternions was defined by William Rowan Hamilton in 1843. This associative algebra was the source of the science of vector analysis in three dimensions as recounted in A History of Vector Analysis. The fourth dimension was popularised by Charles Howard Hinton, starting in 1880 with his essay What is the Fourth Dimension? published in the Dublin University magazine. He coined the terms tesseract, ana and kata in his book A New Era of Thought, and introduced a method for visualising the fourth dimension using cubes in the book Fourth Dimension. Cognition Research using virtual reality finds that humans in spite of living in a three-dimensional world can without special practice make spatial judgments based on the length of, and angle between, line segments embedded in four-dimensional space. The researchers noted that "the participants in our study had minimal practice in these tasks, and it remains an open question whether it is possible to obtain more sustainable, definitive, and richer 4D representations with increased perceptual experience in 4D virtual environments."[10] In another study, the ability of humans to orient themselves in 2D, 3D and 4D mazes has been tested. Each maze consisted of four path segments of random length and connected with orthogonal random bends, but without branches or loops (i.e. actually labyrinths). The graphical interface was based on John McIntosh's free 4D Maze game. The participating persons had to navigate through the path and finally estimate the linear direction back to the starting point. The researchers found that some of the participants were able to mentally integrate their path after some practice in 4D (the lower dimensional cases were for comparison and for the participants to learn the method). |
Edwin Abbott Abbott was the eldest son of Edwin Abbott (1808–1882), headmaster of the Philological School, Marylebone, and his wife, Jane Abbott (1806–1882). His parents were first cousins.
He was educated at the City of London School and at St John's College, Cambridge, where he took the highest honors in classics, mathematics and theology, and became a fellow of his college. In particular, he was 1st Smith's prizeman in 1861.[2] In 1862 he took orders. After holding masterships at King Edward's School, Birmingham, he succeeded G. F. Mortimer as headmaster of the City of London School in 1865 at the early age of twenty-six. Here he oversaw the education of future Prime Minister H. H. Asquith. He was Hulsean lecturer in 1876.
He retired in 1889, and devoted himself to literary and theological pursuits. Dr. Abbott's liberal inclinations in theology were prominent both in his educational views and in his books. His Shakespearian Grammar(1870) is a permanent contribution to English philology. In 1885 he published a life of Francis Bacon. His theological writings include three anonymously published religious romances - Philochristus (1891), where he tried to raise interest in Gospels reading, Onesimus (1882), and Silanus the Christian (1908).
More weighty contributions are the anonymous theological discussion The Kernel and the Husk (1886), Philomythus (1891), his book The Anglican Career of Cardinal Newman (1892), and his article "The Gospels" in the ninth edition of the Encyclopædia Britannica, embodying a critical view which caused considerable stir in the English theological world. He also wrote St Thomas of Canterbury, his Death and Miracles (1898), Johannine Vocabulary (1905), Johannine Grammar (1906).
Abbott also wrote educational text books, one being "Via Latina: First Latin Book" which was published in 1898 and distributed around the world within the education system.
Abbott's best-known work is his 1884 novella Flatland: A Romance of Many Dimensions which describes a two-dimensional world and explores the nature of dimensions. It has often been categorized as science fiction although it could more precisely be called "mathematical fiction". With the advent of modern science fiction from the 1950s to the present day, Flatland has seen a revival in popularity, especially among science fiction and cyberpunk fans. Many works have been inspired by the novella, including novel sequels, short films, and a feature film called Flatland.
He was educated at the City of London School and at St John's College, Cambridge, where he took the highest honors in classics, mathematics and theology, and became a fellow of his college. In particular, he was 1st Smith's prizeman in 1861.[2] In 1862 he took orders. After holding masterships at King Edward's School, Birmingham, he succeeded G. F. Mortimer as headmaster of the City of London School in 1865 at the early age of twenty-six. Here he oversaw the education of future Prime Minister H. H. Asquith. He was Hulsean lecturer in 1876.
He retired in 1889, and devoted himself to literary and theological pursuits. Dr. Abbott's liberal inclinations in theology were prominent both in his educational views and in his books. His Shakespearian Grammar(1870) is a permanent contribution to English philology. In 1885 he published a life of Francis Bacon. His theological writings include three anonymously published religious romances - Philochristus (1891), where he tried to raise interest in Gospels reading, Onesimus (1882), and Silanus the Christian (1908).
More weighty contributions are the anonymous theological discussion The Kernel and the Husk (1886), Philomythus (1891), his book The Anglican Career of Cardinal Newman (1892), and his article "The Gospels" in the ninth edition of the Encyclopædia Britannica, embodying a critical view which caused considerable stir in the English theological world. He also wrote St Thomas of Canterbury, his Death and Miracles (1898), Johannine Vocabulary (1905), Johannine Grammar (1906).
Abbott also wrote educational text books, one being "Via Latina: First Latin Book" which was published in 1898 and distributed around the world within the education system.
Abbott's best-known work is his 1884 novella Flatland: A Romance of Many Dimensions which describes a two-dimensional world and explores the nature of dimensions. It has often been categorized as science fiction although it could more precisely be called "mathematical fiction". With the advent of modern science fiction from the 1950s to the present day, Flatland has seen a revival in popularity, especially among science fiction and cyberpunk fans. Many works have been inspired by the novella, including novel sequels, short films, and a feature film called Flatland.