Photographing the Tesseract
The tesseract is a “four-dimensional analog of the cube,” and is typically represented as a cubic shape with extruded sides. It represents a theoretical space having more than three dimensions.
This project is about photographing a trail of clues left by Marcel Duchamp, arguably the most challenging and influential artist of the 20th century. Those clues stem from one particularly inscrutable note that leads back to an 18th century geometry text and that by association, “blossoms” to index Duchamp’s “definitively unfinished” masterwork, The Bride Stripped Bare by Her Bachelors, Even (also known as The Large Glass). Duchamp published the note (below) in À l'infinitif (also known as the White Box).
Niceron (the F. J-Fr).
In the first half of the 20th c. many artists were inspired by writings on the “fourth dimension.” Of these, Marcel Duchamp is probably the only one who approached this subject from the point of view of a skeptic. His ironic engagement with the tesseract in particular, arguably trumps the vision of other artists from the same period who were also inspired by higher dimensions. For his own creative amusement, Duchamp explored this content by constructing a complex web of associations, interpretations and meanings, where each unique fact is abstracted from its original function in order to become a sign of something else (unless of course, it’s a “red herring”).
One aspect of Duchamp’s involvement with higher dimensions originated in his discovery of an unusual drawing in an esoteric 17th c. perspective manual. The drawing shows a binary geometric structure sitting on a pedestal (a scaled-up segment) that Duchamp employs in a taxonometric, trans-historical, conceptual montage. Here Duchamp connects a specific 17th c. geometrical drawing with what in the 20th c. we recognize as the universal symbol of the tesseract. What is more interesting is that he utilized that observation within the larger framework of his “definitively unfinished” conceptual masterwork, The Large Glass.
Jean Francois Niceron was a 17th c. perspective master known for an esoteric volume with the dramatic Latin title, Thaumaturgis Opticus (Magic Optics). Back in the early days of the internet I decided to see if I could find out something about the book and by sheer serendipity came upon a California bookseller selling an original copy for $375.00, a bargain for an arcane perspective treatise dating back to 1646, that also offered the possibility of discovering new insights into Duchamp's oeuvre. Inquiring further, the individual on the phone said that if I wasn't completely satisfied I could return the book for the full purchase price, and so I became the proud owner of a monogrammed, leather bound, folio-sized edition of a recondite, 17th c. perspective manual, which by the way also places it mid-career Rembrandt and Vermeer. These other artists would have likely been read the book since too since at that time it was a primary source for information on the latest experimental drawing technologies, including anamorphosis. However, a central question remained, why did Duchamp decide to refer future researchers to this particular volume? The agreement entered upon by artist and spectator is that in some way, Duchamp’s reference had to relate to The Large Glass. Art historians have referred to the note before but without offering any substantive insights.
We do know that Duchamp invented numerous new strategies for art making, all designed to side-step traditional “hand-made” painting, drawing, and sculpture techniques. He also disdained all approaches where good taste was deployed in artistic production for the primary goal of achieving financial success. Such thinking lead Duchamp to create the Readymades. He selected these not from the perspective of good or even bad taste, but rather with dispassionate or neutral taste. In these works, similarly to The Large Glass, associations had to appear logical without being exclusive, and never a calculus of 1:1 correspondences where one plausible explanation trumped another, otherwise the gestalt would collapse.
Niceron was a Roman Catholic friar in the order of Minims. A possible reading of Niceron’s diagram is that it symbolizes the world connected to the divine by way of a geometrical cipher, that at the same time happens to be the tesseract, tangent to a star figure. Niceron’s actual intentions notwithstanding, we know the image was important to him because in an engraved self-portrait, he elected to depict himself holding an engraving of the tesseract image, mise en abyme. This “picture within a picture” (cf. Shakespeare’s play within a play) or replica of a picture within another picture, was featured as the frontispiece for the Thaumaturgis Opticus and in the French edition of the book, la Perspective Curieuse. In this remarkably reflexive self-portrait, Niceron’s visage functions as a demonstrator figure gesturing towards the tesseract engraving with drawing calibers. The same tesseract drawing also appears by itself as a separate plate bound into the back of both editions. One can easily imagine that Duchamp, working at the time as a librarian in the Bibliothèque Sainte-Geneviève, found his discovery of a reflexive fourth dimensional engraving, depicting a 17th c. perspective master hawking a 20th c. icon of the 4th dimension, totally amusing. With this sly association, Duchamp, ever the chess master, managed to checkmate the cubist competition with irony, essentially inventing a new conceptual approach to collage involving a taxonomy of symbols from different time periods in a conceptual art making strategy apparently intended to resonate more in our time than in his own.
The scenario I favor most is that Duchamp embraced the Niceron drawing as an antecedent or prototype for his bipartite Large Glass. The “picture within a picture” trope surely has the fingerprint of a device that would have attracted Duchamp’s attention. Also Duchamp’s own drawing of a star figure labeled “Space Continuum,” though somewhat different from Niceron’s, is still typologically similar enough that it may be associated with the star element in Niceron’s binary figure. Duchamp further states that we should “see differences defined by n-dimensional geometricians.” Of these of course, Duchamp is first on the list.
In these photographs, I am looking for details that may provide clues to Duchamp’s art-making process, how a single fact coupled with an association can expand or “blossom” into a sign of something else, suggesting new interpretations and meanings regarding The Large Glass. By extension Duchamp’s highly varied conceptual approaches to art also function as prototypes for Post-Modern art making strategies.
Note 1: The aforementioned Niceron self-portrait “picture within picture” (cf. play within a play) frontispiece was unfortunately removed from the edition of the Thaumaturgus Opticus that I worked from, and so far, I have not had the opportunity to examine it within the photographic series.
However, I also discovered that there were two different Niceron “picture within picture” portraits, and both were used as a frontispiece, each in a different edition of the work. In this second portrait, Niceron is seen on the scroll carried by the flying angel. Presumably, this symbolizes Niceron’s death prior to the publication date of the Latin edition, in the same year that he died.
Also interesting is that in this second portrait, the putto (bottom right) observes an additional geometrical image situated within the scene (it’s also presented in the form of a picture within picture trope) through a viewing tube, with the result that the anamorphic figure would appear in corrected perspective. The point of view from Niceron’s flying portrait however, is instead distorted as if seen from a different dimension. Also in the reference containing the two frontispieces arranged side-by-side, where the Niceron portrait figure at left appears to make eye contact with the flying portrait in the second frontispiece, the two images are revealed to have several formal points in common inviting further analysis.
Note 2: The timeworn imperfections of this copy of Thaumaturgus Opticus stand in stark contrast to the pure mathematical concepts described within. In fact, this book bears no slight resemblance to Duchamp’s Unhappy Readymade. Duchamp had asked his sister, Suzanne to expose a geometry textbook to the elements from the balcony of her Paris apartment until it had become weather-beaten and had therefore learned “the facts of life.”
Both this time ravaged copy of Niceron’s text along with the Unhappy Readymade, embrace more complex geometries than originally intended because of the distressed conditions of the drawings. There are suggestions of post-Euclidean surfaces, or even higher dimensions. In addition, even anamorphosis, Niceron’s central topic adds a second “curious” perspective to many of the representations within the book. For Duchamp, anamorphoses was likely seen as another analogy to the fourth dimension. Though Duchamp employed the agency of weather in the Unhappy Readymade, this force is analogous to time in its effects, though a faster way to achieve a similar result. Duchamp was surely working in the field of such associations.
Note 3: An additional image related to Duchamp’s artwork emerged in another taxonometric observation made by artist, Guy Berard. Berard noted a connection between Duchamp’s perspective note, Niceron’s tesseract figure, and a photograph appearing near the end of this series portraying jazz greats, Thelonius Sphere Monk and Sonny Rollins in performance at the Five Spot. A purely fictional description is that the energy generated by their performance has caused the materialization of an n-dimensional star figure appearing cropped-off at center top of the image. Berard describes the structure as “a lamp or leftover Christmas decoration.” This observation again models Duchamp’s associative strategy where layers of associations can suggest a new interpretation, and it underlines the “definitively unfinished” aspect of Duchamp’s artwork.
Note 4: Marcel Duchamp was apparently not the only artist from a time prior to our own who became interested in the Niceron drawing. The drawing referenced here is by Joseph Mallord William Turner (Tate Museum) and similarly is based on Niceron’s tesseract figure. Turner made the drawing to use in the lectures on perspective he presented at the Royal Academy. Looking at the image today it is apparent that Turner deliberately chose not to render the upper star element. We know beyond the shadow of a doubt that Turner was aware of Niceron because in another diagram from the same lecture series, entitled Perspective Method [for drawing] a Cube, he clearly inscribes the word, “Niceron” twice on the same sheet of drawing paper (see reference).
If one mentally combines Turner’s drawing with the Sphere Monk photo, in essence you reconstruct Niceron’s completed figure thus forming another trans-historical collage. In other words, these two images not only relate but also complete each other. Where in the Turner drawing the absent star figure would be expected to appear, instead we see not merely negative space, but a space that is diagrammatic, theoretical, and even possibly a schematic that evoking a multidimensional space (cf. Duchamp’s Large Glass) as suggested by the visible erasures of the various perspectival schemata. This then suggests a further connection to Rauschenberg’s Erased de Kooning Drawing though perhaps that ranges too far, despite the fact that Duchamp’s influence is clearly present. If for no other reason, such exercises model Duchamp’s associative workflow yielding new interpretations that suggest new meanings, a process that is logical yet never falls into the trap of being explicit.
Note 5: In his essay “Eadweard Muybridge: Fragments of a Tesseract,” Hollis Frampton discusses Muybridge’s magnificent long exposure waterfall photographs that he captured in Yosemite Valley, identifying them with the tesseract. Though as Frampton argues, the connection between Muybridge’s time duration landscapes and the later animal locomotion series certainly has merit, I think Frampton’s decision to incorporate tesseract terminology is misleading since the Muybridge images have little to do with the hypercube except in a most imprecise way.