The Emergence of the Fourth Dimension

I’ve just submitted my revised manuscript to the publisher so now seems the right time to announce here that The Emergence of the Fourth Dimension, the book that has itself emerged from the research blogged about here, is contracted to Oxford University Press. I hope we’ll see it in physical form sometime next year (2016). Avanti!

In Praise of the Tour de France (and the Fourth Dimension)

Jean Metzinger, At the Cycle-Race Track (Au Vélodrome), 1912. Oil and collage on canvas, 130.4 x 97.1 cm. Peggy Guggenheim Collection, Venice

Spiral

Next Wednesday, 7 May,I’m leading a session for Birkbeck students on the MAs in Modern & Contemporary Literature and Contemporary Literature & Culture

Time: 18:00 – 19:20 

Place: Room B04, 43 Gordon Square

Please come along if you’re around and interested. This work runs on from a piece I wrote earlier this year for the LRB website and is the first element of a new project-in-progress on geometric form.

‘Spiral: Ballard, Smithson and Archaeologies of the Future’, Dr. Mark Blacklock (Chair: Dennis Duncan)

Investigating the relationship between the work of J.G. Ballard and Robert Smithson, focusing on their mutual interest in spirals, this session will work outwards from consideration of this naturally occurring and geometric form. Having established a set of readings of spirals from divergent bodies of thought and practice – geometry, art history, cosmology, anthropology – and engagements in the work of contemporary practitioners – Tacita Dean and Tom McCarthy – it will move on to consider what work form does in Ballard and Smithson, the benefits and pitfalls of adopting an inter-disciplinary apparoach to reading the forms encountered therein, and what occurs in the passage between literary and visual cultures.

19: Space

 

The new issue of 19, in which my essay ‘The Higher Spaces of the Late Nineteenth-Century Novel’ appears in some highly esteemed company, has just gone live. Many thanks to all those at 19 who worked on the issue! Read it here.

Suicide while of unsound mind

Suicide while of unsound mind

Doctoration

I successfully defended my thesis at the end of June so I have ammended the title of this blog to reflect the fact that it no longer relates to a work-in-progress, although, in truth, when is a work like this ever really finished?

I’m working to propose a revised version of the project as a book to scholarly publishers and will continue to post related materials here. I also hope to put together a reader of cubic materials, for which I think there would be an audience.

In the meantime, the most useful thing I think I can post here is my completed bibliography, a resource for anyone else looking at higher space and dimensionality. Like many scholars, I should imagine, the bibliography is the section of any book I first read, so let’s cut to the chase! A great deal of these are available online, and if I ever find myself languishing in airport transit lounge, Snowden-like, with wi-fi and time to kill, I might make some of these hotlinks. (BTW, if you spot errors in this bibliography, TOO LATE! The deed is done. But I’d be most grateful if you’d bother me with your eagle-eyed pedantry so that the errors don’t creep forward into any print project).

 

Bibliography

Primary sources

A Collection of Prospectuses of the Educational Exhibition of 1854, 3 vols (London: Royal Society of Arts, 1854)

A Square, ‘The Metaphysics of Flatland’, Athenaeum, 2980 (1884), 733

Abbott, Edwin A., Flatland: A Romance of Many Dimensions, 2nd edn (London: Seeley and Co., 1884; repr. New York: Dover Publications, 1992)

–         The Annotated Flatland: a romance of many dimensions, ed. by Ian Stewart (Reading, MA; Oxford: Perseus, 2002)

–         Flatland: an edition with notes and commentary ed. by William F. Lindgren, Thomas F. Banchoff. (Cambridge: Cambridge University Press; Washington, D.C.: Mathematical Association of America, 2010)

–         The Kernel and the Husk: letters on spiritual Christianity (London: Macmillan, 1886)

–         A Shakespearean Grammar (London and New York: Macmillan and Company, 1870)

–         Hints on Home Teaching (London: Seeley, Jackson, and Halliday, 1883)

Anon [probably William H. Harrison], ‘On Space of Four Dimensions’, Daily Telegraph, 2 April 1878, p.2

Anon, ‘Modern Spiritualism’, Spectator, 2739 (1880), 1661-2

–         Astronomical Society Monthly Notices, Feb 1883, 185

–         ‘Literary Gossip’, Athenaeum, 2978 (1884), 660

–         ‘Flatland’, Literary World, 15 (1884), 389-390; reproduced on Flatweb [http://library.brown.edu/cds/flatweb/1884litworld.html] [17 January 2013] (para 1)

–         ‘Flatland’, Athenaeum, 2977 (15 November 1884), 622

–         ‘Flatland: a Romance of Many Dimensions’, Spectator, 2944 (1884), 1583-1584

–         ‘Flatland’, New York Times, 23 February 1885, 3

–         ‘Humor and Satire’, Literary News, 6 (1885), 85

–         ‘Flatland’, Literary World, 16 (1885), 93

–         ‘The Political Euclid’, Punch, 1 (1841), 149

–         ‘A New Philosophy’, City of London School Magazine, 1 (1877), 277 -281

–         ‘Summer Meeting of the London Branch. Flatland’, The Mathematical Gazette, 7 (1914), 228-231

–         ‘Proceedings of Societies’, Chemical News and Journal of Industrial Science, 37 (1878), 271-272

–         ‘Societies and Academies’, Nature, 31 (1885), 328-332

–         ‘Scientific Romances. No. II’, Mind, 10 (1885), 613

–         ‘Civilization: its Cause and Cure and Other Essays’, Lucifer, 6 (1890), 159-160

–         ‘What is the Nature of Intuition, and Which are the Best Means of Developing this Faculty?’, Vahan, 2 (1892), 5

–         ‘An Oxford undergraduate’s suicide’, Jackson’s Oxford Journal, 7676 (1900), 8

–         I Awoke! Conditions of Life on the Other Side Communicated by Automatic Writing (London: Simpkin and Marshall, 1893)

Aksakow, Aleksander, ‘A New Manifestation with Dr. Slade at Leipzig University’, Spiritualist, 12 (1878), 78

Aristotle, ‘Physics’, in The Complete Works of Aristotle: The Revised Oxford Translation ed. by Jonathan Barnes (Princeton: Princeton University Press, 1984), I, pp. 315-446

–         ‘Poetics’, in The Complete Works of Aristotle: The Revised Oxford Translation ed. by Jonathan Barnes (Princeton: Princeton University Press, 1984), II, pp. 2316-2340

–         ‘Rhetoric’, in The Complete Works of Aristotle: The Revised Oxford Translation ed. by Jonathan Barnes (Princeton: Princeton University Press, 1984), II, pp. 2152-2269

 

Barrett, William, ‘Invisible Beings’, Nonconformist and Independent, 4 (1881), 16-17

–         On the Threshold of the Unseen (London: Kegan Paul, 1918)

Bartlett, Rev. J. B., ‘A Glimpse of the “Fourth Dimension”’, Boy’s Own Paper, 12 (1890), 462

Besant, Annie, and C.W. Leadbeater, Thought Forms (London; New York: The Theosophical Publishing House, 1905)

Bierce, Ambrose, The Collected Works, 12 vols (New York: The Neale Publishing Company, 1909-1912)

Blackwood, Algernon, ‘A Victim of Higher Space’, in The Complete John Silence Stories, ed. by S. T. Joshi (New York: Dover Publications Inc., 1998), pp. 230-246

Blavatsky, H.P., The Secret Doctrine, 2 vols (London: The Theosophical Publishing Company, 1888)

–         Isis Unveiled, 2nd edn, 2 vols (Point Loma: Theosophical Publishing Co., 1910)

Busch, Wilhelm, Edward’s Dream, trans. and ed. by Dr. Paul Carus (Chicago: Open Court Publishing Company, 1909)

 

Canning, G., John Hookham Frere, G. Ellis., ‘The Loves of the Triangles’, in Poetry of The Anti-Jacobin, ed. by Charles Edmonds, 3rd ed (London: Sampson Low, Marston, Searle & Rivington, 1890), pp. 151-164

Carpenter, Edward, ‘Underneath and After All’, Lucifer, 6 (1890), 248

–         My Days and Dreams (London: G. Allen & Unwin, 1916)

–         From Adams Peak to Elephanta (London: Swan Sonnenschein, 1892)

Carroll, Lewis, Through the Looking Glass and What Alice Found There (London: Academy Editions, 1977)

Cayley, Arthur, ‘Chapters in the Analytical Geometry of (n) Dimensions’, Cambridge Mathematical Journal, 4 (1843), 119-127.

–         ‘Sur quelques théorêmes de la géometrie de position’, Crelle’s Journal, 31 (1846), 213-227

–         ‘A Memoir on Abstract Geometry’, Philosophical Transactions of the Royal Society of London, 160 (1870), 51

Child, Lydia Maria, Philothea: A Romance, 2^nd edn (Boston: Otis, Broaders and Company, 1839)

Clifford, W. K., ‘Problems and Solutions from The Educational Times’ in Mathematical Papers, ed. by Robert Tucker (London: Macmillan and co., 1882), pp. 565-627

–         ‘On the Space-Theory of Matter’, Transactions of the Cambridge Philosophical Society, 2 (1876) 157-158 (reprinted in Mathematical Papers, pp. 21-22)

–         ‘The Philosophy of the Pure Sciences III: The Postulates of the Science of Space’ in Lectures and Essays, ed. by Leslie Stephen and Sir Frederick Pollock, 2 vols (London: Macmillan and Co., 1879), I, pp. 295-323

Collins, Frank S., ‘The Fourth Dimension, A Paper read by Frank S Collins, Part 1’, The Path, 4 (1889), 17-19

Conan Doyle, Arthur, The History of Spiritualism, 2 vols (London: Cassell and Company Ltd., 1926)

Conrad, Joseph, and Ford Madox Hueffer, The Inheritors (London: Dent, 1923)

Coryn, Herbert, ‘The Fourth Dimension’, Lucifer, 12 (1893), 326-332

Crosland, Newton, E.T.B., ‘The Fourth Dimension’, Light, 1 (1881), 23

Crosland, Newton, C.C.M., G.W., M.D., ‘The Fourth Dimension’, Light, 1 (1881), 31

De Cyon, E., ‘The Anti-Vivisectionist Agitation’, The Contemporary Review, 43 (1883), 498-510

Dick, Frederick J., ‘The Meaning of Separated Life – A Mathematical Story of 2, 3 & 4 Dimensions’, Lucifer, 6 (1890), 243-245

Diogenes Laertius, ‘Xenophanes’ in The Lives of Eminent Philosophers, trans. by R. D. Hicks, 2 vols (London: William Heinemann ltd, 1950), II, 425-429

Dodgson, Charles Lutwidge, The Dynamics of a Parti-cle (Oxford: James Parker and Co., 1874)

 

Edge, H.T., ‘Popular Misconceptions About the Fourth Dimension’, The Path, 4 (1889) 252

Ellis, H. Havelock, ‘Hinton’s Later Thought’, Mind, 9 (1884), 384-405

Engels, Friedrich, ‘Natural Science and the Spirit World’, Marxists.org, <http://www.marxists.org/archive/marx/works/1883/don/ch10.htm> [accessed 9 February 2012] (repr.of Illustrierter Neue Welt-Kalender für das Jahr 1898).

Euclid, The Elements, trans. by Sir Thomas Heath (New York: Dover Publications, 1956)

–         Euclid’s Elements of Geometry: the First Six Books and the Portions of the Eleventh and Twelfth Books Read at Cambridge, ed. by Robert Potts (London; New York: Longmans, Green and Co., 1895)

 

Fechner, Gustav Theodor, ‘Zöllner’s Mediumistic Experiments: extracts from the diary of Gustav Theodor Fechner, late Professor in Vienna, died November 19th, 1887’, Light, 8 (1888), 256-257

–         ‘The Comparative Anatomy of Angels’, trans. by Hildegard Corbet and Marilyn E. Marshall, Journal of the History of the Behavioral Sciences, 5 (1869), 135-151

Freeman, Mary E. Wilkins, ‘The Hall Bedroom’, in Short Story Classics (American) ed. by William Patten,  (New York: P.F. Collier and Son., 1905), pp. 1275-1302

Fullerton, George S., ‘On Space of Four Dimensions’, Journal of Speculative Philosophy, 18 (1884), 113-121

–         ‘A Letter from Professor Fullerton to Mr. C. C. Massey’, Light, 7 (1887), 451

Fullerton, George S., and others, Preliminary Report of the commission appointed by the University of Pennsylvania to investigate modern spiritualism in accordance with the request of the late Henry Seybert (Philadelphia: J.B. Lippincott Co., 1887)

Funk, Isaac K., The Widow’s Mite and Other Psychic Phenomena (New York: Funk and Wagnall’s Company, 1904)

 

Gauss, Helen Worthington, Gauss, a Memorial (Colorado Springs, 1966) (trans. of Sartorius von Walterhausen, Gauss zum Gedächtniss (Leipzig: S. Hirzel, 1856))

Griffith, George, The Mummy and Miss Nitocris (Milton Keynes: Tutis Digital Publishing Private Limited, 2008; repr. of London: T. Werner Laurie, 1906)

–          ‘The Justice of Revenge’, The Newcastle Weekly Courant, 28 April 1900, p. 2

Grove, William Robert, Address to the British Association for the Advancement of Science (London: Longmans, Green and Co., 1867)

 

Halsted, George Bruce, ‘Bibliography of Hyper-Space and Non-Euclidean Geometry’, American Journal of Mathematics, 1, 3 (1878), 261-276

Hartmann, Franz, The Talking Image of Urur (New York: John W. Lovell and Company, 1890)

von Helmholtz, Hermann, ‘The Axioms of Geometry’, The Academy, 1, (1870), 128-131

– ‘The Axioms of Geometry’, The Academy, 3 (1872), 52-53

– ‘The Origin and Meaning of the Axioms of Geometry’, Mind, 1 (1876), 301-321

– ‘Integrals of the Hydrodynamical Equations, which express Vortex-motion’, trans. by P.G. Tait, Philosophical Magazine, 33 supplement (1867), 485-511

– ‘On the Use and Abuse of the Deductive Method in Physical Science’, Nature, 11 (1874) 149-151

Heun, Karl, ‘Science Note-Book’, Nature, 31 (1884), 51-52

Hinton, C. H., ‘What is the Fourth Dimension?’, The University Magazine, 96 (1880), 15-34

–          ‘What is the Fourth Dimension?’ in Scientific Romances (London: Swan Sonnenschein, 1886), pp. 3-30

–         ‘The Persian King’ in Scientific Romances (London: Swan Sonnenschein, 1886), pp. 33-128

–         ‘A Picture of Our Universe’ in Scientific Romances (London: Swan Sonnenschein, 1888), pp. 161-204

–         C. H. Hinton, ‘Many Dimensions’ in Scientific Romances: Second Series (London: Swan Sonnenschein, 1896), pp. 28-44

–          ‘What is the Fourth Dimension?’, The Cheltenham Ladies College Magazine, 8 (1883), 31-52

–         A New Era of Thought (London: Swan Sonnenschein, 1888)

–         ‘Fourth Dimension’ in Hazell’s Annual Cyclopaedia, 1886 (London: Hazell, Watson and Viney, 1886), pp. 183-185

–         Stella and an Unfinished Communication: Studies in the Unseen (London: Swan Sonnenschein, 1895)

–         An Episode of Flatland: or How a Plane Folk Discovered the Third Dimension (London: Swan Sonnenschein, 1907)

–         ‘On the Education of the Imagination’ in Scientific Romances: Second Series (London: Swan Sonnenschein, 1896) pp.

Hinton, James, Man and his Dwelling Place (London: John W. Parker and Son, 1859)

–         Life in Nature (London: Smith, Elder and Co., 1862)

–         The Mystery of Pain (London: Smith, Elder and Co., 1866)

Hodgson, Shadworth, ‘Introduction’ in Chapters on the Art of Thinking, ed. by C. H. Hinton (London: C. Kegan Paul and Co., 1879)

Hodgson, William Hope, The House on the Borderland and Other Novels (London: Gollancz, 2002)

Hopkins, Ellice, Life and Letters of James Hinton (London: C. Kegan Paul, 1878)

Huxley, T. H., ‘The Scientific Aspects of Positivism’, Fortnightly Review, (1869), 653-70

 

Ingleby, Dr. C. M., ‘Transcendent Space’, Nature, 1 (1870), 289

 

Jacob, Alexander, Henry Moore’s Manual of Metaphysics: A Translation of the Enchiridium Metaphysicum (1679) with an introduction and notes (Zürich: Georg Olms Verlag Hildesheim, 1995)

James, Henry, ‘The Art of Fiction’ in The Art of Criticism: Henry James on the Theory and Practice of Fiction, ed. by William Veeder and Susan M. Griffin (Chicago; London: University of Chicago Press, 1986), pp. 165-183

–         The Spoils of Poynton (Oxford: Oxford University Press, 1982)

–         The Art of the Novel: Critical Prefaces, ed. by Richard P. Blackmur (New York, London: Charles Scribner’s Sons, 1934)

–         Henry James, ‘The Great Good Place’ in The Complete Tales of Henry James, ed. by Leon Edel, 12 vols (London: Rupert Hart-Davis, 1962-1964) XI,  pp. 13-42

Jevons, William Stanley, ‘Helmholtz on the Axioms of Geometry’, Nature, 4 (1871), 482

Jinarajadasa, C., The Golden Book of the Theosophical Society: a brief history of the Society’s Growth from 1875-1925 (Adyar, Madras: Theosophical Publishing House, 1925)

–         C. Jinarajadasa, ‘Introduction’, in C. W. Leadbeater, The Astral Plane (Adyar: Theosophical Publishing House, 1970), pp.vi-xx

Johnston, Charles, ‘Psychism and the Fourth Dimension’, The Theosophist, 9 (1888), 423

Jung, C.G., The Zofingia Lectures, trans. by Jan van Huerck (London: Routledge and Kegan Paul, 1983)

 

Kandinsky, Wassily, On the Spiritual in Art, trans. by Hilla Rebay (New York: The Solomon R. Guggenheim Foundation, 1946)

Kant, Immanuel, ‘Thoughts on the True Estimation of Living Forces (selected passages)’ in Kant’s Inaugural Dissertation and Early Writings on Space, trans. and ed. by John Handyside (Westport, CT: Hyperion Press, Inc., 1979), pp. 3-18

–         ‘Concerning the Ultimate Ground of the Differentiation of the Directions in Space’ in Cambridge Edition of the Works of Immanuel Kant: Theoretical Philosophy 1755-1770, trans. and ed. by David Walford in collaboration with Ralf Meerbote (Cambridge: Cambridge University Press, 1992), pp. 361-372

–         ‘On the form and principles of the sensible and the intelligible world [Inaugural dissertation]’ in Cambridge Edition of the Works of Immanuel Kant: Theoretical Philosophy 1755-1770, trans. and ed. by David Walford in collaboration with Ralf Meerbote (Cambridge: Cambridge University Press, 1992), pp. 373-416

–         The Critique of Pure Reason, trans. and ed. by Paul Guyer and Allen W. Wood (Cambridge: Cambridge University Press, 1998)

–         ‘Prolegomena to any future metaphysics’ in Cambridge Edition of the Works of Immanuel Kant: Theoretical Philosophy After 1781, ed. by Henry Allison and Peter Heath, trans. by Gary Hatfield, Michale Friedman, Henry Allison and Peter Heath (Cambridge: Cambridge University Press, 2002), pp. 29-170

Kendall, May, Dreams to Sell (London: Longmans, Green and Co., 1887)

Kepler, Johannes, Mysterium Cosmographicum, trans. by A.M. Duncan (Norwalk, CT: Abaris books, 1981, 1999)

Klein, Felix, ‘Ueber der zusammenhang der flachen’, Mathematische Annalen, 9 (1876), 476-482.

–         Development of Mathematics in the 19th Century, trans. by M. Ackerman (Brookline: Math Sci Press, 1979)

 

Land, J.P.N., ‘Kant’s Space and Modern Mathematics’, Mind, 2 (1877), 38-46 (pp.38-39)

Leadbeater, C. W., The Astral Plane: its Inhabitants and Phenomena (London: The Theosophical Society Publishing Company, 1895)

–         How Theosophy Came to Me (Adyar: Theosophical Publishing House, 1930)

–         The Devachanic Plane (London: The Theosophical Publishing Society, 1896)

–         Clairvoyance (London: The Theosophical Publishing Society, 1899)

–         The Fourth Dimension (A lecture given by C. W. Leadbetter [sic] before the Amsterdam Lodge T.S. in April, 1900. Stenographic notes in Dutch by J.J. Hallo, Jr.; translated into English by Mrs. Marie Knothe) (San Francisco: Mercury Publishing Office, 1900)

–         The Other Side of Death (London: Theosophical Publishing Society, 1903)

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MacDonald, George, Lilith, (London: Chatto & Windus, 1895; repr. Grand Rapids, MI: Wm. B. Eerdmans Publishing Company, 2000)

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Massey, C. C., ‘The Fourth Dimension’ Light, 1 (1881), 15

–          ‘M. E. DE CYON AND THE LATE PROFESSOR ZÖLLNER’, Light, 3 (1883), 188

 

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du Maurier, George, The Martian (London & New York: Harper & Bros, 1897)

 

 

Möbius, August, ‘On Higher Space’ in Sourcebook in Mathematics ed. by D. E. Smith (New York: McGraw Hill Book Company, 1929) pp. 525-526

 

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–         The Revelations of A Square (London: Richard Spencer, 1855)

 

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“S”, ‘Four Dimensional Space’, Nature, 31 (1885), 481

Schofield, A.T., Another World (London: Swan Sonnenschein, 1888)

Schubert, Hermann, ‘The Fourth Dimension: Mathematical and Spiritualistic’, Monist, 3 (1893), 435-449

Shaw, Nellie, A Czech Philosopher on the Cotswolds; being an Account of the Life and Work of Francis Sedlak (London: C. W. Daniel Co., 1940)

Shelley, Percy, Prometheus Unbound, ed. by Lawrence John Zillman (Seattle: University of Washington Press, 1959)

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–         A.P. Sinnett, The Occult World, 3rd edn (London: Trübner and Co., 1883)

Skilin, ‘Zöllner’, Medium and Daybreak, (1882), 803-804

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–         ‘Throughth: Or, On the Eve of the Fourth Dimension: A Record of experiments in Telepathic Automatic Handwriting’, Review of Reviews, 7 (1893), 426-432 (p. 426)

–         ‘“On the Eve of the Fourth Dimension, Mathematical and Spiritualistic”’, Review of Reviews, 7 (1893), 542.

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–         The Letters of Robert Louis Stevenson, ed. by Sidney Colvin, 3 vols, 10th edn (London: Methuen and Co. Ltd, 1911)

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–         ‘Zöllner’s Scientific Papers’, Nature, 17 (1878), 420-422

–         ‘Johann Benedict Listing’, Nature, 27 (1883), 316-317

–         ‘On Knots’, Transactions of The Royal Society of Edinburgh, 28 (1877), 145-190

Tait, P.G., and Balfour Stewart, The Unseen Universe or, Physical Speculations on a Future State, 4th edn (London: Macmillan and Co., 1876)

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–         The Invisible Man: a Grotesque Romance (London: J. M. Dent, 1995)

–         ‘The Plattner Story’, in Selected Short Stories (London: Penguin, 1968), pp. 193-211

–         The Time Machine (London: Phoenix, 2004)

–         Experiment in Autobiography: discoveries and conclusions of a very ordinary brain (since 1866), 2 vols (London: Gollancz, 1934)

–         In the Days of the Comet (London: Macmillan, 1912)

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Wundt, Wilhelm, ‘Spiritualism as a Scientific Question: An Open Letter to Prof. Hermann Ulrici of Halle’, Popular Science Monthly 15 (1879), pp. 578-593 (repr. and trans. of Der Spiritismus: Eine Sogenannte Wissenschaftliche Frage (Leipzig: Engelmann, 1879))

 

Zöllner, Johann Carl Friedrich, ‘On Space of Four Dimensions’, Quarterly Journal of Science, 8 (1878) 227-237

–         Transcendental Physics, trans. by Charles Carleton Massey (Banner of Light, Boston: 1901)

 

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–         ‘X Rays and the Quest for Invisible Reality in the Art of Kupka, Duchamp, and the Cubists’, Art Journal, 47 (1988), 323-340

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Unpublished Manuscripts

London, London Metropolitan Archives, MS Monro correspondence, ACC/1063/2109a

–         MS Monro correspondence, Acc 1063/2457

London, Royal Institution, MS John Tyndall, RI MS JT/1/H/48

Reading, Reading University Library, MS Swan Sonnenschein and Co., 4058, Charles Howard Hinton to William Swan Sonnenschein, 22 February 1887

Hintonian Cubism (part 1)

Diagram of original catalogue cube from A New Era of Thought (1888)

Most visitors to this blog – and, indeed, to my academia.edu profile – come seeking Charles Howard Hinton and his system of cubes. No surprises there. Hinton’s biography is quite something and his work on visualising – or, perhaps more accurately, imagining – the fourth dimension of space was innovative, influential and almost completely out of its time.

The purpose of this post is to update a project I began almost four years ago and am only really now in a position to continue: the construction of a set of Hinton’s cubes, the material demonstration models that anchored his pedagogical enterprise.

Inside front fold-out plate of The Fourth Dimension (1904)

Hinton began working with cubes early in his career. The essay ‘On the Education of the Imagination’ (1888) may well have been written before ‘What is the Fourth Dimension?’ was first published in 1880. In this he describes working with a system of cubes with his school students, and he began teaching in 1876. The system is also based on what he termed ‘poiographs’ in a paper presented before the Physical Society in 1878, so it seems likely to have been a foundation stone for his project. Certainly, his proficiency with it was advanced by 1887, when he was able to claim that he’d memorised a cubic foot of his named cubes.

He refined the system of cubes over the course of his career. The system described in A New Era of Thought (1888), taking up the entire second-half of that remarkable, visionary text, described cubes with a different colour and name for each vertex, line and face. Relying on description and line drawings it is, unsurprisingly, fiendishly complicated. By 1904’s The Fourth Dimension he had developed a system of ‘catalogue’ cubes and plates to enable a more step-by-step working through of cubic training. There are also many more and far clearer illustrations in this text, so this is the version I’ve followed.

The first task is to paint the correct number of one inch cubes the correct colours, which are as follows:

Null	16
White	8
Yellow	8
Light yellow	4
Red	8
Pink	4
Orange	4
Ochre	2
Blue	8
Light blue	4
Green	4
Light green	2
Purple	4
Light purple	2
Brown	2
Light brown	1

I used model paints of the kind you use to paint Airfix aeroplanes. As a newbie to this game this process caused me more problems than you might imagine. For example, metallic paints sound exciting in the shop – wooh-hooh, electric pink! – but they are more liquid, don’t necessarily look all that great on wood, and can even look largely indistinguishable from lighter, non-metallic shades. Also, on which side do you rest a painted cube to dry? I never discovered the answer to this gnomic poser so my cubes are slightly messy. But hey! They’re my cubes – and they don’t need to be perfect.

Home-made wooden cubes

After the set of 81 coloured cubes there are the catalogue cubes. These are coloured to distinguish vertices, lines and faces and the fold-out colour-plate at the front of The Fourth Dimension shows how they should look.

As you can see, painting lines a fifth of an inch proved beyond me, either freehand or using tape to mask off. In the end I decided to print out coloured nets of the cubes onto card and cut these out and tape them together. Again, slightly imperfect, but I think they do the job nicely.

Printed onto nets and sellotaped together

There are also coloured slabs, to aid you in thinking like a plane being, as you will be asked to do in the first chapter of exercises, ‘Nomenclature and Analogies Preliminary to the Study of Fourdimensional Figures’ (pp.136-156). These I printed out on card aswell.

I’m going to break these posts up into a series in case anyone wants to join in so I’ll begin with the exercises in the next post sometime in the next week or so. In the meantime, an observation (owing entirely to Dr. Caroline Bassett who pointed it out to me at Weird Council, the China Mieville conference) that will be useful in understanding what’s to come. If, like me, you have about 50 pairs of 3d glasses sitting around the house because you have to buy a new pair every time you go to the cinema to watch Matt Damon Running Really Fast! 3D!, break a set out and take a squizz at the coloured plate above. Your colour-coded anaglyph glasses will be doing all kinds of funky things to the projection diagrams of cubes. Hinton intuitively recruited a colour-coding system to suggest the qualium of an extra dimension of space, which is kind of how we trick out puny brains into registering three dimensions when we drool at a FLAT screen for 90 minutes watching Matt Damon running really fast.

So, ponder that then get thee to a modelling shop (where the staff will be perfectly used to people using the archaic form of the vocative in that way and will possibly be dressed like hobbits).

Bon chance!

Charles Carleton Massey: corrections

Marc Demarest, who maintains the excellent Emma Hardinge Britten archive, a shining example of open-source web scholarship, has been in touch with a couple of corrections regarding the CCM post below. With apologies for sloppiness, here’s Marc’s message:

Thanks for the post. Too few people looking into CCM’s life.

Couple of things:

– William Stainton Moses was the co-editor of *LIght* (to which periodical CCM was perhaps the most regular contributor in the 1880s), not *The Medium and Daybreak* (as your post says). James Burns was the editor of the M&D, and the M&D stands, in relation to Light, like the New York Post to the New York Times 🙂

– WSM was not a founder of the TS. I’m not sure he was ever even a read-in member of the TS. He and Henry Steel Olcott were correspondents, and Blavatsky woo’d him for the TS, but (like Emma Hardinge Britten and CCM) he eventually turned against the TS in public.

– CCM didn’t just defend Slade; perhaps more importantly, in the broader sweep of things, he defended Penny, the astrologer, when he was brought up on the charge of violating English laws against fortune-telling. That case was the opening salvo in a battle that went on until Helen Duncan’s trial under the same act in the mid-1940s (if memory serves). CCM also acted for several other spiritualists and occultists in different matters.

I’m grateful for the pointers – they’re all spot-on. It’s never less than productive to make contact with other researchers in the field and a great advantage to have engaged readers. I can also heartily recommend Marc’s Chasing Down Emma blog, where he posts updates on his ongoing research. This recent post expands the picture of Massey’s legal activities defending spiritualists and occultists by reproducing a report on his defence of the astrologer Richard Henry Penny.

Keep an eye out for more updates on CCM.

An orphaned footnote on Thomas Reid and Flatland

Flatland’s critique of analogy is reminiscent of Thomas Reid, writing in 1767. Reid noted both the utility and frequency of analogical thinking, and the way in which it was particularly common in figuring thought itself as a material parallel to make clear the abstract: ‘The second, and the most common way in which men form their opinions concerning the mind and its operations we may call the way of analogy. There is nothing in the course of nature so singular, but we can find some resemblance, or at least some analogy, between it and other things with which we are acquainted. The mind naturally delights in hunting after such analogies, and attends to them with pleasure.’ Thomas Reid, An Inquiry into the Human Mind on the Principles of Common Sense, ed. by Derek R. Brookes (Edinburgh: Edinburgh University Press, 1997), p. 203.

Reid argued that philosophers were not immune from such a tendency and that until Descartes philosophy was liable to ‘materialize the mind and its faculties.’  (209) He doubted that many were capable of the rigorous reasoning required to reach concepts by other means: ‘If one attentively examines the systems of the ancient philosophers, either concerning the material world or concerning the mind, he will find them to be built solely upon the foundation of analogy.’ (204)

Intriguingly, in the same text from which these lines are taken Reid set out a thought experiment in which a race of two-dimensional beings he called Idomenians, confined to the surface of a sphere and having only the sense of sight, were unable to conceive of a three-dimensional geometry.

Hinton biographical erratum

Here’s one just for the Hinton spotters.

For some reason I was lying awake at 3 a.m. last night wondering if Charles Howard Hinton had met his bigamous bride Maude Florence while teaching at Cheltenham Ladies College. Perhaps she’d been a student: wouldn’t that be just scandalous! I thought to check it out this morning before dealing with REAL WORK and tried to find registers online. Searching for those came up null, but did reveal this: Charles Howard worked at Cheltenham College, not the Ladies College which of course makes total sense in retrospect. Seems worth correcting because every biographical account since Rudy Rucker (and possibly it was Marvin Ballard who was the source for this?) has him at Cheltenham Ladies. 

Another curiosity: he was on a list of examinees of the University of London in 1871, the year in which he matriculated as an non-collegiate student at Oxford. Any ideas on that would be interesting.

This heinous task-avoidance may be some use. I promise extensive higher-dimensional bibliographies imminently.