An X-Ray of Cubism? Jouffret and Visualizing the Fourth Dimension, 1903 and 1906.

JF Ptak Science Books   Post 1361

Is this an X-Ray of Cubism?

Emile Jouffret brought an amazing and lovely pair of books to the mathematical dining table, both coming at about the mid-point of a period of perhaps the most sweeping multidisciplinary revolutions in human history.  Published in 1903¹ and 1906² [and both originals available at our blog bookstore] they both may have had an impact as a visualization tool for the newest movement in art since the creation of Impressionism (1850's-1870's): Braque and Picasso's  Cubism. When you compare the illustrations in the Jouffret books you cannot help but to see a connection to the work of (the morally-lonely) Picasso (and especially in his 1910 portrait of the movement-molding art dealer Ambroise Vollard, below). Georges Braque and the that the two would make in 1906, the first year of the Cubist movement. 

Jouffret's 1903 book was hardly the first on the topic, though it may be the first of the major, book-length treatments of the topic, as well as the most  heavily illustrated.  Thinking on the fourth dimension goes back as far as Kant, at least, and the real work begins in the first half of the 19th century.

The first major³ work arrives with Hermann Grassmann's "Die Lineale Ausdehnungdlehre" (Theory of Linear Extensions) in 1844 (and the subsequent translations of the work as well as original work by Arthur Cayley); followed by Ludwig Shclafli (1814-1895) "Theorie der vier flachen...." (Theory of Continuous Manifolds, 1852 but not published until 1906), Riemann's 1854 speech (which was not published until 1867 and which appeared translated by William Kingdom Clifford in Nature in 1873, G.F. Rodwells "On Space of Four Dimensions" (Nature, May 1873),  Dodgson/Carroll's  Through the Looking Glass (1872) deep references, Zollner "On Space of Four Dimensions" 

(April 1878 and subsequent publications, and who is referenced in Kandinsky's [difficult -to-me On the Spiritual in Art of 1912), W.I. Stringham (1847-1909) "Regular Figures in n-Dimensional Space" (American Journal of Mathematics, 1880), and E.A. Hamilton Gordon, "Fourth Dimension", April 1887, to name some of the major figures.  And then of course comes Edwin Abbott's Flatland, a Romance of Many Dimensions, by a Square (1884) and Charles Howard Hinton, who published a number of different works beginning in 1880 ("What is the Fourth Dimension?", 1880 plus Scientific Romances 1884, and The Fourth Dimension, 1904) and lasting through the turn of the century.  There is also H.G. Wells, whose The Time Machine began to appear in parts as early as  1894, though it did appear in the same issue of the  Science Schools Journal as the Hamilton Gordon article, in April 1887, as the "Chronic Argonauts"). Wells' also approaches the fourth dimension in "The Plattner Story", in 1896 and The Invisible Man in 1897. Other literary contemporaries of Wells who used the fourth dimension in their work include Oscar Wilde ("The Canterville Ghost", 1891), George Macdonald (Lilith, 1895), and Joseph Conrad and Ford Maddox Hueffer The Inheritors, (1901)--the most convincing and scientific of all of these literary efforts though lies with Wells. From about this point on--from the time that Jouffret enters the scene in 1903--the fourth dimension has become part of the culture, and a popular culture at that...especially after the Cubists begin their assault on visual representation in about  1906.

The Jouffret books are beautiful, and very interesting--they would have been better served with a bibliography, which would have been very nice to have--that said, Jouffret does have a fair number of footnotes to earlier work, so it is not as though his work is without attribution.  But it is a very interesting adventure. (Just a note--the fourth dimension and non-Euclidean geometries would get their first bibliography in D.M.Y. Sommerville's classic  Bibliography of Non-Euclidean Geometry in 1911, which is a must-have for all of those interested in this topic...it is massively packed with all manner of major and minor works as well as obscuriana.  It is not, unfortunately, annotated.)

1. Jouffret, E.  Traite Elementaire de Geometrie a Quartre Dimensions et Introduction a la Geometrie a n-Dimensions. 

2.  Jouffret. Melanges de Geometrie a Quatre Dimensions.  Paris, Gauthier-Villars, 1906.  220pp.

3. Most of the data in this long and winding sentence has been culled from Linda Dalrymple Henderson's terrific The Fourth Dimension and Non-Euclidean Geometry in Modern Art, Princeton, 1983--most of my references come from the first 45 pages or so of her book, which is the Bible of all modern works on the fourth dimension/math/physics/art.