Found this very interesting so wanted to share it with all of you
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?
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