A letter of inquiry / Franz Gnaedinger / www.seshat.ch




Poseidon from Cape Artemision, geometrical analysis from 1980, prepared for the Internet in 2005:  gia01.JPG  gia02.GIF  gia03.GIF  poseidon.htm


Kouros from Tenea, Getty Kouros, Kroisos from Anavyssos, geometrical drawings from 1992, prepared for the Internet in 2006: kouros1a.JPG  kouros1b.JPG  kouros1c.JPG  kouros1d.JPG  kouros2a.JPG  kouros2b.JPG  kouros2c.JPG  kouros2d.JPG  kouros2e.JPG  kouros3a.JPG  kouros3b.JPG  kouros3c.JPG  kouros3d.JPG  kouros3e.JPG  kouros3f.JPG


Mona Lisa, an Allegory of Seeing (interpretation from 1974/75, geometrical reconstruction from 1979)  seeing.htm

Leonardo da Vinci, The Last Supper (interpretation and geometrical analysis from 1979)  ls.htm

Villa Farnesina, in honor of Gertrud Batschelet  farnes.htm


Geometry in Art, John the Baptist, geometrical analyses from 1980-1995, prepared for the Internet between 2003 and 2006:  gia.htm





Zurich, April 11, 2003



Dear Mrs. Colkin,

thank you very much for your letter from April 3. Unfortunately you have been unable to play my compact disk, and so you ask me to submit a letter of inquiry. I checked the returned CD on my HP Omnibook XE-3 and had no problem opening the file "homepage" using Explorer 6. Did you try opening the CD using another program than Microsoft's Internet Explorer 5 or 6? Anyway, let me outline my letter of inquiry, and firstly excuse myself for my poor English. I hope the lack of style will be outweighed by what I have to say.



Taking the long way


Out of financial reasons I had to give up my studies at the university of Zurich. Since then I work outside of academe, almost 29 years by now, with all the difficulties and all the freedom of my position, which allows me to investigate new alleys of research. In that I am a follower of Richard Feynman's, the eminent American physicist, and, in my opinion, a worthwhile theorist of the sciences as well, who wrote that it ain't no use if thousand scientists are trying to tackle the same problem using the very same set of scientific tools; at least someone should try the other way round, using different methods. My scientific work began with an exhibition of Cy Twombly at Berne in Switzerland, back in 1974. The catalogue mentioned Leonardo da Vinci's drawings of water, and so I lent a Leonardo monograph from my library. I remember well spending half an hour looking at John the Baptist without understanding anything at all. Half a year later, absolving an art school, I began carrying out visual experiments, in the course of which I discovered the same effect Margaret Livingstone, neurologist of Harvard, has rediscovered and published recently: a certain flicker of the lips of the Mona Lisa when one moves ones look over her face. Look on her lips, and she is hardly smiling. Look into her eyes (into her left eye in the center of the circle of her head) and you can't see her lips clearly anymore, the corners of her mouth and shadows of her cheeks are joining, we can't really see the corners of her mouth any longer, but we sure know they are there, and so we project them somewhere into the shadowy region where they can be expected, however, misguided by clever Leonardo, who said that only the central rays of vision are true and strong, all others weak and deceptive (debole e bugiarde) we place the corners of her mouth a little beside the actual corners and above them, what results in a smile, and if we are surprised by her smile and smile in return, she will unfold her true and loving smile ... My discovery led me to a complete interpretation of the Mona Lisa as an Allegory of Seeing, and the Mona Lisa made me understand John the Baptist: this one must be Leonardo's alter ego as a painter, symbolizing his career from a pupil of Andrea del Verrocchio (left angel in this ones and Leonardo's Baptism of Christ) via his initiation as a master of the fine arts (young John entering the grotto of the Madonna of the Rocks) and his remembering of the early days (replica of the Madonna of the Rocks, where Leonardo is present in the way the angel is looking over to young John/Leonardo) to his final work, namely John the Baptist, where Leonardo is speaking in the Italian manner, using his hands: "God created the world [raised arm, brilliant right hand]; I, Leonardo, once born in his world, have seen it. Much of what I have seen [eyes] and studied [front of the head] found its way into my work [left hand]. However, my work is incomplete and only a weak reflex of the beauty of Nature, God's work. - My dear pupils, friends and followers, I will soon leave you. The black shadows behind me are already enveloping my half naked body. What are the dark veils hiding? You may see or merely guess a hint of a bush and eventually some hills or mountains, but as soon as this happens the space is closing in and you are again confronted with the black wall no one can see through. I am already half taken by the darkness, and sooner or later I shall be gone. But don't be sad, and if you loose a great artist, study the work of a far greater one - study Nature, God's work that surpasses all human works.


My interpretations of the Mona Lisa as an Allegory of Seeing and of the Baptist series as an illustration of Leonardo's career stem from 1974. In the same year my then professor of art history invited me to explain to him my views of Leonardo's Baptist pictures. Which I gladly did, however, my professor warned me to project my own limitations onto a painting. The Swiss Tagesanzeiger-Magazin told me in around 1984 that my work is very interesting, however, according to the opinion of the entire redaction, everything had already been said and told about the Mona Lisa. My work was not welcome. So I worked on in private, on my own. I found that I was not the first one to interpret the Mona Lisa. Long before me Marcel Duchamp must have come to the same conclusion: his seemingly iconoclastic L.H.O.O.Q actually is the first true interpretation of the Mona Lisa: pronounce the letters in English and you obtain LOOK. The very fine ends of her moustache are pointing precisely to the pupils of her eyes, and if you are patiently looking into her eyes (into her left eye) you see her loving smile appear. Pronounce the same letters in French, however in a spirited way, namely by adding "aire" (air, an age old symbol of mind and spirit, cf. Hebrew ru-ach, Greek pneuma, Latin spiritus), you obtain something like "elle a chaud occulaire". Now please understand that in Duchamp's elaborate symbolic language "warm" means lively, and so you will get about this message: Mona Lisa appears lively regarding her eyes - look into her eyes and you see her come to life ... 1979 followed my interpretation of Leonardo's Last Supper, which, in my opinion, ponders the question whether we humans have a free will or not. Leonardo's answer: we humans can't really understand the world as a whole from one single perspective; only God can see the world as one, we humans have to deal with broken perspectives, we have and  will always have to consider different and plain contradictory aspects (cf. the double perspective in the background of the Mona Lisa). Since 1979 I examine surface geometry in selected works of art, for example in Leonardo's and Raphael's paintings and preparatory drawings. Not all the painters made use of surface geometry, far from that, but some very good ones did, and I found that surface geometry almost always goes along with the meaning of a picture. Consider again the case of the Mona Lisa. The original format was 4x3 units, one unit given by the vertical measurement of the head on the level of the eyes, more precisely on the height of the small bending of the veil. Add one unit to the left and one to the right of the hair, and you obtain the original width of the painting, while the left line of the balustrade marks the 2/3 height (1.6 plus 2.4 units). Now draw the large middle circle (radius 1.5 units); it will seize the bow of the hair of the Mona Lisa. Then draw arcs of the radii 4 units around the corners of the original format 4:3. The arcs will touch the circle in the same points wherein the long diagonals (5 units) cross the circle. The arcs around the lower corners touch the woman's head. Now draw circles around the four points, wherein the large circle, the diagonals and the arcs meet and cross, and let the radii measure 0.1, 0.2, 0.3, 0.4 ... units or 1, 2, 3, 4 ... small units. The resulting waves explain both the figure of the woman and the shifting of the landscape. As if Leonardo anticipated the physical double nature of matter and wave ... Moreover, four circles meet in a mathematically very close double point on a height of 35 small units (half a unit below the frame), and this close double point is marked by a special iconographic point, namely by the begin of the parting of the woman's hair, hence a point on the front of her head, symbol for the mind, relating seeing (activity of the eyes) with reasoning (activity of the mind).


Meanwhile I examined the geometry of more than 200 (two hundred) paintings, drawings, statues and buildings, what allows me to answer several important questions: is a given work an original, perhaps painted over by a less gifted artist and thus long overseen? begun by the master but finished by a pupil? a copy? a free one or a true one? even a copy of a copy? perhaps a true copy of a true copy? has the canvas been cut? and if so, what was the original format? and what may the composition mean?


For example I can show that the Getty Kouros is a) an original, and b) related both with the Kouros from Tenea (kept at Munich) and the Kroisos from Anavyssos (National Museum Athens.) I even dare say that we may speak of Master A and B: Master A was the creator of the Kouros from Tenea and the teacher of Master B, who created the Getty Kouros as a juvenile masterwork, with an almost lyrical quality to the lines, and the Kroisos from Anavyssos on the summit of his career, making use of a fully developed and proudly unfolded geometry. The school of Master A and Master B may also have produced the unknown master of the wonderful Poseidon from Cape Artemision. In this bronze statue I found another geometry worth of the Greek mind, displaying the artistic principles of measure and rhythm (articulating a composition), of symmetry and a-symmetry (holding a composition together and bringing it to life), and self-reference (the equivalent to autopoiesis in biology). Furthermore, and most rewarding in my opinion, are geometrical reconstructions, for example the ones of the formerly shorter saloon of the Villa Farnesina at Rome and its picture program. One of my results: Leonardo's famous drawing of Neptune and his four sea-horses was originally planned as a wall-painting for the saloon of Agostino Chigi's villa, and so was Raphael's Galatea (the original format of which having been a square). Another reconstruction regards a pair of hypothetical Leonardo wall-paintings in the Belvedere of the Vatican (former audience room, today's parrot chamber in the Museum): John the Baptist on one bank of the River Lete, and the Nymph on the opposite bank. If you pass the hypothetical wall-paintings from the side (following the gangway) you will observe another amazing optical illusion: John, pointing beyond his shoulder, is now pointing toward the side of the Nymph, while she, pointing toward the right in her picture plane, is now seemingly pointing into the depth of her mysterious landscape ... Did Leonardo dare give us a glimpse into the beyond? and if so, could he have painted Elysium or paradise in bright daylight? No, certainly not. He would have rendered that landscape no one ever saw in a hazy manner, veiled by layers of deep air, so that one will more guess than actually see (have a look at Leonardo's Nymph drawing at Windsor: you have to guess about the landscape, more than you can really see). How could Leonardo possibly have obtained such an effect? By covering his hypothetical and probably never carried out Nymph painting with a special varnish. What we know for sure is that he got a commission from the Pope, but instead of drawing and painting he began experimenting with all kinds of varnishes, whereupon the Pope exclaimed in despair: This man will never complete anything, because he begins with the end.



In short


Having worked in vain but very productively for 10'000 days or nearly 29 years now, having published brief summaries of a part of my related work in the Art History section of my web site www.seshat.ch (work in progress, with 529 illustrations, designed for Explorer 5 and 6): Poseidon from Cape Artemision, the geometry of a Greek masterwork / Broken Perspective, Leonardo da Vinci's Last Supper / Mona Lisa, an Allegory of Seeing / Villa Farnesina, in honor of Gertrud Batschelet / John the Baptist, German summary / Die Symbolsprachen von Marcel Duchamp und Pablo Picasso, and having much more to publish that would be lost otherwise, I ask the Getty Center for a contribution to my work, knowing well that I will hardly match any given grant program, but kindly asking you to consider that progress in the sciences can never really be anticipated and regulated; one has always to be prepared for the unexpected and cope with new insights, which, after all, are the aim of scientific endeavors. Living modestly, needing hardly any money for myself I can do a lot with a small sum. As a first reward for an eventual contribution you will obtain a ring binder with drawings of mine, ready for 3-dimensional CAD reconstructions, and copies of all my further works, both as Bitmap graphics and word documents on CD, and if you wish as laser prints on paper. All new texts in English, corrected by Katherine (daughter to an American physicist). If someone at the Getty Center should be working on similar topics, he or she may always get my advice online via fgn(a)bluemail.ch.


Sincerely yours, Franz Gnaedinger, Zurich, Switzerland




Kouros from Tenea  kouros1a.JPG  kouros1b.JPG  kouros1c.JPG  kouros1d.JPG // Getty Kouros, in my opinion the work of a young pupil of the master of the kouros from Tenea (photograph courtesy J. Paul Getty Museum)  kouros2a.JPG  kouros2b.JPG  kouros2c.JPG  kouros2d.JPG  kouros2e.JPG // Kroisos from Anavyssos, in my opinion a work of the mature master of the Getty Kouros  kouros3a.JPG  kouros3b.JPG  kouros3c.JPG  kouros3d.JPG  kouros3e.JPG  kouros3f.JPG