Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-07-04T06:26:14.741Z Has data issue: false hasContentIssue false

Math for Math's Sake: Non-Euclidean Geometry, Aestheticism, and Flatland

Published online by Cambridge University Press:  23 October 2020

Abstract

This essay argues that Edwin Abbott's Flatland brings into focus the wide-ranging implications of the dethroning of what Victorians regarded as the preeminent representational system: Euclidean geometry. The contemporary debate surrounding the challenge to Euclid, conducted not just in mathematical but also in psychological, philosophical, and aesthetic terms, turned on an anxiety that signs might not have the capacity to bridge subjective and objective worlds, and Flatland seeks solace for this uncertainty by granting even empty signs unprecedented virtues.

Type
Victorian Cluster
Copyright
Copyright © Modern Language Association of America, 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Works Cited

Abbott, Edwin A. The Annotated Flatland: A Romance of Many Dimensions. Ed. Stewart, Ian. Cambridge: Perseus, 2002. Print.Google Scholar
Abbott, Edwin A. Apologia. London: Black, 1907. Print.Google Scholar
Abbott, Edwin A. The Kernel and the Husk: Letters on Spiritual Christianity. London: Macmillan, 1886. Print.Google Scholar
Isobel, Armstrong. Victorian Poetry: Poetry, Poetics, and Politics. New York: Routledge, 1993. Print.Google Scholar
Matthew, Arnold. “Dover Beach.” Victorian Verse. Ed. MacBeth, George. New York: Penguin, 1969. 166–67. Print.Google Scholar
Lewis, Carroll. Through the Looking Glass and What Alice Found There. The Annotated Alice: Alice's Adventures in Wonderland and Through the Looking Glass. Ed., introd., and notes Gardner, Martin. New York: Meridian, 1960. 167345. Print.Google Scholar
Clifford, William Kingdon. “The Exactness of Mathematical Laws.” The World of Mathematics. Ed. Newman, James R. Vol. 1. New York: Simon, 1956. 548–51. Print. 4 vols.Google Scholar
Clifford, William Kingdon. “The Postulates of the Science of Space.” The World of Mathematics. Ed. Newman, James R. Vol. 1. New York: Simon, 1956. 552–67. Print. 4 vols.Google Scholar
Coleridge, Samuel Taylor. Lay Sermons. Ed. White, R. J. The Collected Works of Samuel Taylor Coleridge. Vol. 6. Princeton: Princeton UP, 1972. Print. 14 vols.CrossRefGoogle Scholar
Coleridge, Samuel Taylor. “On Mathematical or Intuitive and Logical or Discursive Synthesis a Priori.” Logic. Ed. Jackson, J. R. de J. The Collected Works of Samuel Taylor Coleridge. Vol. 13. Princeton: Princeton UP, 1981. Print. 14 vols.CrossRefGoogle Scholar
De Morgan, Augustus. “On the Signs + and – in Geometry (Continued) and on the Interpretation of the Equations of a Curve.” Cambridge and Dublin Mathematical Journal 7 (1852): 242–49. Print.Google Scholar
De Morgan, Augustus. Rev. of A Treatise on Algebra, by George Peacock. Quarterly Journal of Education 9 (1835): 293311. Print.Google Scholar
George, Eliot. The Mill on the Floss. Ed. Haight, Gordon. Oxford: Oxford UP, 1981. Print.Google Scholar
Euclid. The Thirteen Books of Euclid's Elements. Introd. Thomas Heath. 3 vols. New York: Dover, 1956. Print.Google Scholar
Michael, Fried. Manet's Modernism. Chicago: U of Chicago P, 1996. Print.Google Scholar
Catherine, Gallagher. The Industrial Reformation of English Fiction. Chicago: U of Chicago P, 1985. Print.Google Scholar
Helmholtz, Hermann von. “The Origin and Meaning of Geometrical Axioms.” Mind 1 (1876): 301–21. Print.Google Scholar
Helmholtz, Hermann von. “The Origin and Meaning of Geometrical Axioms (II).” Mind 3 (1878): 212–25. Print.Google Scholar
Olaus, Henrici. “Modern Geometry and Graphical Statics.” Univ. Coll., London. College Calendar (1876–77): n. pag. Print.Google Scholar
Rosemary, Jann. “Abbott's Flatland: Scientific Imagination and ‘Natural Christianity.‘Victorian Studies 28.3 (1985): 473–90. Print.Google Scholar
John, Kelland. “On the Limits of Our Knowledge respecting the Theory of Parallels.” Transactions of the Royal Society of Edinburgh 23 (1861–64): 433–50. Print.Google Scholar
John, Locke. An Essay concerning Human Understanding. Ed. Woozley, A. D. New York: Meridian, 1964. Print.Google Scholar
Mansel, H. L. Metaphysics; or, The Philosophy of Consciousness Phenomenal and Real. Edinburgh: A. and C. Black, 1860. Print.Google Scholar
John, Mulcahy. Principles of Modern Geometry with Numerous Applications to Plane and Spherical Figures. Dublin: Hodges and Smith, 1852. Print.Google Scholar
Joan, Richards. Mathematical Visions: The Pursuit of Geometry in Victorian England. San Diego: Academic, 1988. Print.Google Scholar
Samuel, Roberts. “Remarks on Mathematical Terminology, and the Philosophic Bearing of Recent Mathematical Speculations concerning the Realities of Space.” Proceedings of the London Mathematical Society 14 (1882–83): 515. Print.Google Scholar
John, Ruskin. The Stones of Venice. Vol. 2. New York: John W. Lovell, 1851. Print.Google Scholar
George, Salmon. A Treatise on the Higher Plane Curves. Dublin: Hodges and Smith, 1852. Print.Google Scholar
Jonathan, Smith. “‘Euclid Honourably Shelved’: Edwin Abbott's Flatland and the Methods of Non-Euclidean Geometry.” Fact and Feeling: Baconian Science and the Nineteenth-Century Literary Imagination. Madison: U of Wisconsin P, 1994. 180210. Print.Google Scholar
William, Spottiswoode. “Presidential Address.” Report of the Forty-Eighth Meeting of the BAAS Held at Dublin in August, 1878. London: John Murray, 1879. 132. Print.Google Scholar
James, Sylvester. “Presidential Address: Mathematics and Physics Section.” Report of the Thirty-Ninth Meeting of the BAAS Held at Exeter in August, 1869. London: John Murray, 1870. 19. Rpt. of “A Plea for the Mathematician.” Nature 1.9 (1869): 237–39; 1.10 (1870): 261–63. Print.Google Scholar
Whistler, James McNeill. “Mr. Whistler's Ten O'Clock.Whistler on Art. Ed. Thorp, Nigel. Washington: Smithsonian Inst., 1994. 7095. Print.Google Scholar
William, Wordsworth. The Prelude: 1799, 1805, 1850. Ed. Wordsworth, Jonathan, Abrams, M. H., and Gill, Stephen. New York: Norton, 1979. Print.Google Scholar