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13. LEONARDO da VINCI (1452 - 1519) London. "The Virgin of the Rocks" London Version December 2003. AS PAINTED: London Version (1503 - 06). Paris Version (1483 - 86). It would be strange indeed if the great polymath Leonardo da Vinci, listed as one of the Grand Masters of the Priory of Sion (1510-1519), did not paint at least one masterpiece conforming to the Grail Geometry. My inclination was to focus on the London and Paris versions of "The Virgin of the Rocks". Although the Paris version was done earlier, in the London version there is an intriguing cross -- straight lines make the analysis easier -- so I'll tackle the London version first. The scene is presumably of an encounter among the Virgin Mary with Baby Jesus and an Angel with Baby John the Baptist. Such a scene is consistent with the "flight into Egypt" when Mary might have taken shelter in a cave. Several commentators have expressed confusion over which baby is which --but that need not occupy us -- or deter our search. STEP 1. London Version -- The Cross and The Hexagram. Step 1. The cross that leans on the baby provides two excellent reference lines. Inspection of the diagram below shows that these two reference lines may be developed into a large hexagram. The angle between the shaft and the crossbar is very nearly 60 degrees -- the sure sign of hexagonal geometry. While it is true that any number of hexagrams could be drawn using those lines of the cross, we want to assure ourselves that da Vinci actually intended the angle to be 60 degrees and in consequence used the hexagram we settle on. Therefore we wish to maximize the painted features that fall on the lines of the hexagram. A persistent puzzle for me has always been the nondescript assembly of bright golden fabric -- all wrinkled and suspended at Mary's midsection. One strange fold looked like an intentional point for a registration marker (to facilitate the continual transfer of the geometric pattern from a prepared "cartoon" -- cartone -- Italian for large piece of paper). I have circled it and labeled it "MARKER". A diagonal of the large hexagram goes precisely through this point (see below). Exploratory Lines Yield a Large Hexagram.
The two lines collinear with the cross account for two of the lines above. What of the other ones? I drew a line displaced angularly 30 degrees to the crossbar line and by moving it around, I found I could leave it on the Marker fold in the bright fabric at Mary's midsection. Assuming this to be a diagonal of a hexagram, I then had three (3) lines to work with. The next guess was to assume that a vertex would fall on the left edge of the image (always wary that the image could have been cropped . . . or worse . . .). In any case, that seemed to work at that juncture, which, in fact, defined a unique hexagram that I proceeded to complete -- hoping that some confirming features would fall on it. As may be seen above, a bisecting line at the cross (circled) goes through a peak above it (also circled). Most encouraging. One of the right-hand side lines runs nicely tangent to the angel's face -- also encouraging. But the clincher is that, fortuitously, I decided to run the crossbar line up to the circular border of the image -- where then I dropped a line parallel to a diagonal and -- Bingo! -- that dashed line not only hits exactly a red spot that Leonardo painted on the baby's knee (circled), but also it clips the baby's nose! Moreover this line forms one of the minor diagonals of the hexagram, showing that Leonardo carefully planned the "tablet" borders of this painting on wood panel -- 6 FEET by 4 FEET! The Master Spins a Fine, Tight Web!
There is hardly a feature in this masterpiece -- this geometric tour de force -- whose position is not governed by a line or a circle that fits in with the basic Grail Geometry! Small wonder that Vermeer -- who may very well have studied copies of Leonardo's paintings -- was inspired to paint a visual metaphor of a spider spinning a web in his "The Lacemaker". If so, then "The Sphinx of Delft" was a worthy disciple of the "The Grand Master of Sion" To establish this geometrical aspect of the composition is great -- BUT -- it's not the Grail Geometry -- at least not yet it isn't . . . STEP 2. The Tilted Regular Hexagram of the Grail Geometry. STEP 2. The objective is to see whether there is a confirmed tilted square whose diagonals intersect at an "X marks the Spot" that falls on a significant painted feature of the composition. According to the rules of the Grail Geometry, the square is dictated by a Tilted Equilateral Triangle (usually developed into a Tilted Regular Hexagram). The hexagram of Step 1 is obviously too big -- so we search for a likely smaller one. We try to enter the thinking of the artist in conducting our search -- assuming that he will not make things unduly complicated nor onerous for himself. Therefore it is reasonable to look for a smaller hexagram for STEP 2 that is constrained by the larger one of STEP 1. Following this hunch, I have retained the large hexagram of STEP 1 below as a collection of dashed lines. I've chosen the line labeled 1--2 of that collection to be part of the smaller hexagram -- one of the reference lines for it. I need more lines to define the smaller hexagram, so I look to the line that forms the diagonal of the large hexagram through point "1" and I displace it parallel wise to the right to go through the end of the thumb of the Virgin. This will be a diagonal of the new and smaller hexagram -- and I have labeled it LINE A--A. Now I have two lines of the new hexagram and they intersect on the rock formation to the upper left. Next I look to the long line of the cross and displace it to the right so as to go through the intersection of the two lines I just drew. This third line I have labeled B--B. Next I use the top of the cross as a reference point, drawing the next line through this point, parallel to the appropriate dashed line of the large hexagram (see below): The Tilted Regular Hexagram of the Grail Geom.
This procedure is repeated using the intersection point of the cross, and so forth, until the smaller hexagram and its diagonals are realized (solid lines, above). The confirmations are ample and remarkable for the craftsmanship in evidence. We have identified the Tilted Regular Hexagram of the Grail Geometry in a Leonardo da Vinci painting. STEP 3. The Tilted Square of the Grail Geometry. STEP 3. Having identified a tilted triangle, and having developed it into a tilted hexagram in STEP 2, we are in a good position to identify the associated tilted square. This has been done below in the straightforward method explained in this website. I doubt we are much surprised to see that the diagonals of the square intersect where they do -- exactly on that curious penile-shaped fold (circled and marked with a white dot) in what appears to be the rich golden lining of the Virgin Mary's cloak. The label is "PX" -- the point where "X marks the Spot" in treasure-map argot. (continued below). The Grand Master of Sion.
STEP 3 continued. I have shown a fan of lines radiating from the so-called "Northwest Point" of the Grail Geometry (GG), which incontestably has been used by Leonardo in this masterful geometric composition. The cross, supposedly emblematic of John the Baptist, plays a key role in the composition. Considerable planning must go into a big project such as this -- the dimensions are 6 feet by 4 feet -- oil on wood panel. One wonders about the construction of a suitably smooth and sturdy panel, not to mention very large pieces of paper for the layout "cartoons" -- and the technical problems in transferring the pattern to be followed during the course of applying the paint, waiting for it to dry, etc. Leonardo has been faulted for seldom finishing what he started, but here he demonstrates no evidence of a short attention span! The radiating lines are drawn to conform to the hexagonal geometry -- that is, they are separated by angles obtained from dividing the basic 60 degrees by successively larger whole number divisors. Thus we deal with 60, 30, 15, 7.5, and 3.75 degree separations among the lines -- each one of which has been responsible for the positioning of an important feature of this work. Furthermore, the "right" angle -- 90 degrees --is utilized, together with half of it, 45 degrees; both angular relationships being common when working with squares and their diagonals. Note the mastery with which Leonardo positioned, for example, the Virgin's fingertips and thumb. But a big surprise was building up as I studied this painting -- and there is no better discipline than looking for confirmations of geometric guide lines to facilitate the study of a painting. It was in the back of my mind that Leonardo had a grand overall design for this work -- and finally it occurred to me that he would not have planned the positions of the four heads to be at random, in an uncontrolled fashion. The obvious thing was to try a circle -- and indeed the four heads are positioned on a circle. But this is da Vinci at work -- and there's more than meets the eye -- at first (see below). A Tribute To The Tools Of The Trade.
As a boy I took a course in "Mechanical Drawing" in junior high school. It was a first introduction to draftsmanship, and we learned to use traditional (and quite ancient) drawing tools, including the humble T Square and the two "set triangles": the one, a "thirty - sixty - ninety" (30 - 60 - 90); the other, a "forty-five - forty-five - ninety" (45 - 45 - 90). With these and a compass for drawing circles, some of the most remarkable works of art have been realized.
(Completed 12/15/2003) An Afterthought: Color serves to camouflage some of Leonardo's subterfuge. Puzzled for a long time about why the master painted the Virgin's cloak as he did, I tried deleting the color to see whether something might be hidden in the black--grey--white values of this composition.
It doesn't seem there's anything to get excited about. Maybe just a little one-eyed dog wearing a jaunty, peaked, bemedaled beret -- and not so well defined, either. |
