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12. "LAS MENINAS" by DIEGO VELAZQUEZ (1599-1660)

Diego Rodriguez de Silva y Velazquez

(According to Michael Atlee, this is "The World's Best Painting"!)

Analysis in progress Nov. 30, 2003

AS PAINTED -- cropped detail:

STEP 1.  Exploratory lines.

STEP 1.  The uncropped image is shown below, together with my first foray into the depths of this masterpiece, wondering if yet another Old Master artist was a "cognoscenti" -- in on the secret of the Grail Geometry.  I will leave it to the viewer to decide. The geometry of this painting speaks answers across the centuries.

 Diego Velazquez (white arrow) presents his paint brush to us, and says: "See?"  And we have to wonder how many have seen, over more than three centuries, the basis for the geometric perfection of this composition.

STEP 1.  (continued):  Diego's brush is presented at a left-leaning, sixty (60) degree angle to the horizontal geometric reference lines of this composition.  Such horizontal reference lines are approximately ( but not always exactly, in some of these analyses) the same as the horizontal edges of the image. Now a 60 degree angled line portends a possible Grail Geometry composition -- so we hopefully draw a line collinear with the paintbrush. And there it is (displaced slightly to the right) -- the beginning of a huge hexagram.  HUGE? Oh yes!  This painting is approximately 10 1/2 ft.  by  9  1/2 ft. --  FEET not inches!  Consider the challenge of employing a little paint brush to cover about one hundred (100) Square Feet (!) of canvas with a masterly rendition of many regally attired ladies and gentlemen, including a noble dog (and a few other hidden examples of the devilish side of our Diego).

A smaller image of my STEP 1 exploration is given below.  Note how Velazquez has divided the canvas into equal quarters.  I have emphasized the exact center with a small square oriented as a diamond. Note how the horizontal line through this diamond runs tangent to the image of the artist's head (white arrow). Of more interest is the fact that the vertical line through this central diamond runs precisely down through the tip of the nose of the little princess!

This is no coincidence -- and by now, you don't need anyone to tell you.  I have circled a few confirmatory features -- the most important being that 60 degree paint brush that says there's hexagonal geometry here! But -- is the geometry the full-fledged Grail Geometry? Was Diego Velazquez a member of the secret Priory of Sion society -- a membership that once counted the great Leonardo da Vinci as Grand Master? In answer to this question, we may be able to use our new-found geometric skills at analyzing paintings to make some educated guesses.

STEP 2.  Devoted to Hexagrams.

Arthur C. Danto in "Disembodied Meanings" says that Velazquez sought to "dazzle and puzzle us at once"; Michael Atlee in "LAS MENINAS: The World's Best Painting" (in Mark Harden's 'The Artchive' website http://artchive.com) says -- paraphrasing -- 'Las Meninas beguiles the viewer, provoking the question: What's going on here?'  My answer to what's going on with the dazzling and the puzzling here is: GEOMETRY.  

Until the availability of good quality reproductions on the web (e.g. the one I'm using from 'The Artchive'), together with powerful geometric software (e.g. the one I'm using: Adobe Illustrator, together with Photoshop) there was little opportunity or incentive to explore paintings for an underlying skeleton -- a geometric basis for the composition. There's no denying that Velazquez employed the hexagram (three, so far) to guide his hand in placing the features of "Las Meninas".  I have been able to discover the double hexagram below -- every line of which is geometrically determined by that paintbrush thrust at the viewer as a challenge: "See?  I'm also a geometer -- I'm in the know."-

STEP 2.  Assuming the paint brush (white arrow pointing to the ellipse) designates a line of a different, smaller hexagram, that line was drawn exactly collinear with the paintbrush (it was necessary in STEP 1 to displace the paint-brush line of the "huge" hexagram). It turns out that there are TWO hexagrams that can be identified at this stage of the game in STEP 2. To those who have followed a few other analyses here, the procedure is self-explanatory now -- by inspection. The exhibit above says it all -- or at least most of it.  An astounding tour de force with the head of little Princess Margarita in a central position -- BUT -- sharing it with the dwarf somewhat "upstage right", and that wonderful, noble canine upstaging them all!  Arthur Danto makes much of Velazquez' "marvelous dogs", saying, "One has a sense that everything [in Velazquez] means something awesome, which intensifies the pleasure one takes in this tremendous painter we know we will never fully understand."  True -- and I note that in "Meninas" the dog's head is very definitely tied to a node in the geometry -- as is his tail end!

The representation of the two hexagrams and their diagonals, circumscribing circles, and various extensions to circled features (above) is suggestive to me of a spider web (and it brings back the recognition of Vermeer's "The Lacemaker" -- the first analysis in this SPIDER WEB series.)  Now just about any artist knows about hexagrams -- but not every artist in the seventeenth century knew the secrets of the Priory of Sion nor their secret Grail Geometry.  We haven't seen yet in Velazquez the signature combination of the Tilted Triangle and its associated Tilted Square whose diagonals intersect on an important feature that often (not always) conveys the suggestion of the legend of the burial of "The Holy Grail" (whatever that might be) on a mountain side in southern France (not so far from the Franco-Spanish border!).

STEP 3. Searching for the Square

STEP 3.  It would be remarkable enough to assert that Velazquez started with huge layout sheets carrying the outlines of the three hexagrams identified above.  But "Las Meninas" isn't merely a remarkable masterpiece of artistic-geometric draftsmanship.  It is an astounding tour de force that ALSO conformed to at least two more patterns -- two (2) Grail Geometry Tilted-Equilateral-Triangle/Tilted Square patterns merging seamlessly with the other three (3) hexagrams -- yielding a stunning, virtuoso example of Diego's theme: "Look what I can do with my paintbrush -- see?"  Yes, we start seeing below -- by taking very seriously the (dashed) line presented by the paint brush, and displacing it to the right (another dashed line) to go precisely through the tip of the nose of the little Princess Margarita!

The objective is to establish "The Northwest Point" from which will radiate a fan of lines displaced successively from one another by fifteen (15) degrees.  Why 15 degrees? -- because The Grail Geometry is a hexagonal geometry employing combinations of angles 7.5, 15, 30, 45, 60, 75, 90 degrees, and multiples thereof.  The image below exhibits just such an exploratory fan of lines (I've included 7.5 degree lines).  Now it's true that anyone can draw a fan of lines on any painting -- and it's likely that a few lines will hit this or that by coincidence.

 STEP 3 (continued).  There's no coincidence here, though!  How can I be so sure?  Well, a remarkable circumstance emerged -- it turns out that, like his successor countryman Goya, Velazquez left at least two (2) registration markers showing!  I have circled them and labeled them "MARKER" (see above). There are more than a few features that fall on these lines -- I have not labeled nor circled them yet; the sharp-eyed critic may inspect the exhibit above to note these confirmations.  Indeed, there is possibly a third marker (by that I mean a painted feature that contributes little or nothing to the composition other than to facilitate the repeated registration of layout sheets for retransferring the painted-over geometry to the canvas. A possible technique would be the well-known "pounce" method, where powdered chalk dust is applied to the canvas through pin holes located in the layout sheet).  This third marker is on the artist's left sleeve -- where one of the fan lines goes exactly through it -- and the painter's left eye!  We're not dealing with coincidental here, my friends.

Two of the exploratory fan of lines clip the bottom of each marker as shown above.  Encouraging -- but better yet -- an educated guess led me to attempt to complete a tilted equilateral triangle by drawing a line through the two lower tips of each marker.  BINGO!  That conjectural (bold) line completed a tilted equilateral triangle whose sides are made bold and labeled "T".  This triangle is tilted down 15 degrees from one of the fan lines labeled "H".  I have sketched in parts of the square associated with this fan -- a square which must be tilted down 15 degrees to obey the rule of The Grail Geometry, There will be no problem doing this -- and no problem drawing the diagonals of that exploratory square.  BUT -- will the intersection of those exploratory diagonals fall on a significant feature painted there purposely?  And will this exploratory "X marks the Spot" convey some arcane and esoteric message?  We can see about all that in the next step.

STEP 4. The Grail Geometry (GG) Revisited

STEP 4.  The diagram below is copied from "The Grail Geometry" section of this website in order that we may correlate the labeling of the geometric exploration of "Las Meninas" with this standard representation.  (Please note -- the basic 3 by 3 grid portion in the diagram below should have its corners labeled A--J--K--L.  The K and the L are missing from the diagram below, but they do appear in the STEP 4 analysis further below)

STEP 4 (continued). Full GG pattern in registration with two markers:

The fan of lines developed on STEP 3 has given rise to a full Grail Geometry (GG) pattern -- but with the guess that the Tilted Equilateral Triangle (labeled A-V1-V2) is completed with a line that clips both "MARKERS" as shown below. This was my best guess.  Once the decision has been made on how to complete the triangle, it is a straightforward procedure, following the rules of "GG", to draw the associated Hexagram, the associated Tilted Square, and the all-important diagonals of the square to yield the "PX" -- the "X marks the Spot" -- dear to the hearts of the treasure- seeking gold diggers.  Note -- I have marked the seminal paint brush line with a "P", and the line parallel to it (through the tip of the princess' nose) with a "P*". Both are dashed lines, labeled at the bottom.

I have done all that below -- and I find some substantial confirmation.  The discerning viewer will recognize that the hand of the master was guided by this pattern (among others!).  I have noted with exclamation points [!] two remarkably unexpected confirmations -- the left edge of the image seems to have been dictated by, in the case at the top, the intersection of the dashed line from the paint brush with the circumscribing circle of the hexagram. In the lower one marked [!], the lower corner (also labeled "L") of the basic untilted square also seems to have dictated the approximate terminus of the left edge of the image. Of course we are dealing with a huge canvas, about 350 years old, whose image has no doubt been cropped so that the painter's edge remains indeterminate. Yet this is a further confirmation to my mind.

However -- I am not yet satisfied -- because the "PX" -- the "X marks the Spot" (emphasized above with a little square) falls not on a feature of suggestive mystery, but simply on the forehead of one of the solicitous "meninas" (ladies-in-waiting) as shown above. Maybe this is all that Velazquez was aiming for -- but maybe not!

Hmmm . . . what's that object being proffered to the little princess? I have surrounded it with a square labeled "?" Since it falls on the diagonal A--N, it will be interesting to draw the square whose diagonals will fall exactly there. Will such a square convince us that Velazquez prepared it in advance for this painting? And what can be the significance of the object jointly held at "X marks the Spot"?  We must pursue this in STEP 5!

STEP 5.  Force the "PX" on that strange object to see what's what!

STEP 5.  I followed my hunch -- and look at what resulted!  Diego Velazquez has presented us with a textbook case of composing an Old Master masterpiece in perfect adherence to the Grail Geometry!  (Actually, I could have said that at STEP 4 -- but the STEP 5 exhibit, below, is even better).  For the "X marks the Spot" -- where the diagonals of the Tilted Square A-M-N-O intersect -- I circled that spot twice, in white and in dashed-line red, and I labeled it "PX".  I removed the lines within the red circle for clarity, because whatever it is in there, we'll have to discuss.  But for now, I'll say a bit on how I came up with the exhibit below.

The fan of lines emanating from "A" (PNW -- the Northwest Point) are identical with those of STEP 4.  But the basic tilted equilateral triangle is bigger.  It is labeled A--V1--V2, and I chose the position of the third side V1--V2 so that the tilted square resulting from this triangle (obeying the GG rules) has line M--O for one diagonal, perpendicular to the other diagonal, line A--N, the same fan line that goes through the diamond in STEP 4.  A--N and M--O are the diagonals made to intersect on the curious red object that the "menina" on the left seems to be handing to the princess.  Once the diagonals are chosen, it is a straight forward geometric exercise to complete the appropriate square that goes with them, obeying the GG rules,  so that the Tilted Square A--M--N--O is the correct one for the Tilted Equilateral Triangle A--V1--V2.

Well and good, you may say,  but how do we know Velazquez actually used that pattern in composing "Las Meninas"? We are completely confident of it, because of the many features of the painting that conform exactly to the "GG" superimposed. But let's start with that thundering hint -- the paintbrush.  That paintbrush line has governed every other line of the GG in this analysis.  It established the "Northwest Point" using the little princess's nose and the Marker on the right of the picture. (I must keep reminding the reader that it was the pattern that established the location of the painted features at the creation.  Working backwards, it is all to easy to talk as if  I'm using the features to create the geometry.)  I have circled a few features that were positioned right on some of the fan lines -- and there are many more for your inspection.  To facilitate our discussion, I will present an amplified cropped image below:

Is it not remarkable to contemplate the symmetric interplay between the paintbrush line(dashed) and the marker line (dashed) on the left portion of the image? Look at how Velazquez positioned his face -- one fan line goes through his right eye (lines through eyes is a favorite with the GG masters); and although it is hard to see on this image, there is a "red cross of the Order of Santiago (St. James)" painted on Velazquez' chest.  It runs parallel with the marker line! The story is that King Felipe of Spain painted that after the death of our Diego. If so, the king must have been one of the "cognoscenti".

I myself was amazed to see the fan lines, when drawn at the various angles referenced to the paintbrush line, hit certain features so precisely. Look at the dwarfs hand (circled) -- look at the other circles -- including the big one around the "apple" held by both the menina and the princess.  But look closely and ask yourself if it's an apple. We may be sure Diego could paint a convincing apple . . . if he wanted to.  So why does what's in the circle look like the red head of a goose with a mop cap on?  Like Vermeer, like Goya, like El Greco and who knows how many other artists of ancient days -- Diego Velazquez grew bored with just straight painting, and he amused himself with making everything dual. There is more in "Las Meninas" ("the world's best painting") than meets the careless, hasty eye.

Not for the hasty eye:  Look closely at the face of the "menina" on the right.  Good heavens!  Is that a MASK? And what about her "hair"? What's on her sleeve?  What about her whole light-colored over-dress -- is that an EYE on the front??  Look closely at the "menina" on the left -- what's that on her bosom?? Doll fin on porpoise? What's on the back of her head? It's only the artist's palette!  Oh . . .  What about the darling little girl, extreme stage right --with her little slipper on the dog's back (is it just a dog's rear end? Dead rabbit? -- no way, ho zay!).  What is she gingerly, tentatively doing with her right hand?  What does she see on the dwarf's sleeve?  Is she afraid that the lamb might bite her?!  What?   NOT a lamb??  Not another skull,  I hope . . . animal skull or not:   Et Cetera!

 GET THE PICTURE?

bobdic@comcast.net

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