8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

8. WOMAN WITH A WATER JUG

"YOUNG WOMAN WITH A WATER PITCHER"

The Metropolitan Museum of Art, New York City

"THE GIRL WITH THE MIRACULOUS PITCHER"

(In which I explain how I analyzed this one -- work completed, Oct. 26, 2003)

This is "raw data" below -- all the exploratory lines I drew to begin with.  I'll explain this analysis step-by-step, as I select promising features, points, and lines for further exploration.

STEP 1. In the exhibit below, I begin selecting promising features, points, and lines from the exploration above.  The corner of the window is an obvious choice for the main reference point ("The Northwest Point" -- point "A"):

Line A--1:  I guessed that this line would be the most likely top line of The Tilted Triangle -- assuming (hoping) that Vermeer employed the Grail Geometry here, too. Line A--1 was drawn from point A, tangent to the girl's forehead at "a". We see that the line also goes tangent to the knob of the map rod at "b" -- and exactly clips the corner of the map right there at  b' !  Encouraging!  (explanation continued below:)

LINE A--2:  Assuming LINE A--1 is one side of the equilateral triangle, I drew A--2 from A at an angle of 60 degrees (geometers will understand that this is the rule.)  Bingo -- LINE A--2 hits point "c", the corner just below the dark window frame!  Looks promising now . . .

LINE A--3:  POINT C, the sharp point on the girl's cowl (head dress),  presented an enticing possibility. I drew a line from A through C down to 3 (just an arbitrary length), and found LINE A--3 divides the angle at A in half!  Grail Geometry a distinct possibility!  (POINT C turns out to be the center point of a large hexagram -- to be developed in due course . . .)

LINE B--4:  From POINT B, where LINE A--3 crosses the bottom border of the tray, I drew LINE B--4 parallel with LINE A--2 and -- Bingo! Not only did LINE B--4 clip the tip of the spout of the jug (small arrow) -- but it went tangent to the head dress at "d"! No doubt now -- Grail Geometry is here -- but there's more to do to make sure that it's the standard Tilted Hexagram and associated Tilted Square used by Vermeer in the previous fifteen (15) analyzed paintings. It turns out that the tip of the spout of the "jug" (I much prefer "pitcher") is the center of a neat, small hexagram that guided Vermeer.  Again -- I'll develop and explain that in due course.)

LINE B--5: (See below as well as above) From B tangent to the curve of the tray at "e", LINE B--5 runs parallel to LINE A--1, making the angle 4-B-5 equal to the angle 1-A-2. A solid confirmation here that we have another painting composed in registration with a geometric pattern -- and it will be The Grail Geometry!  There's more work to do . . .

Next I duplicated the angle 4-B-5, reproducing it as angle 6-C-7 as another exploration. LINE C--7 is exactly co-linear with the bottom left side of the head dress collar. The black dashed line labeled 6' (drawn parallel with LINE C--6) runs tangent to the left side of the girl's face. Vermeer has obviously painted the girl's face within the small triangle (formed by two dashed lines and LINE A--1) exhibited both below and above. (The exploratory line 7' does not figure in any future development.)

* NOW NOTE -- the diamond shape formed by the LINES A--1, A--2, B--4, and B--5.  Note how the dashed-line diagonal of the diamond runs tangent to the girl's cheek.  Note how her face is framed by the little equilateral triangle formed by LINE A--1 and the two dashed black lines (see above). This is no coincidence!  We have located some of the geometric lines that Vermeer prepared BEFORE painting this picture -- some of the lines he transferred to the canvas FIRST from layout sheets to guide the features of this -- one of his most profoundly affecting masterpieces.

STEP 2. Based on the results of STEP 1. I drew another set of exploratory lines and a circle (below) to see if I could identify the major Tilted Triangle:

This illustration for STEP 2 (above) is based on STEP 1, and is comprised of a set of more exploratory lines consistent with equilateral triangular and regular hexagonal geometry.  I have removed some of the STEP 1 lines and alphanumeric labels for clarity. Careful inspection of the illustration above will convince the viewer that Vermeer shaped this composition with the guidance of a geometrical plan. Several confirming features in addition to the ones shown in STEP 1 are evident above.

Continuing the analysis below, I will endeavor to pick out the most promising lines from those above in STEP 2 to proceed with more clarity towards identifying the major Tilted Triangle, Tilted Hexagon, and Tilted Square of the Grail Geometry -- assuming that Vermeer provided these for himself in planning the composition.

STEP 3. Based on the exploratory lines of STEP 2, I chose to focus on the largest tilted triangle shown above -- the one that has its apex at POINT A, and its right-hand vertex on the right-hand border of the image above.

At this stage of the exploration, I believed I had identified below the equilateral triangle A-F-G as the one basic Tilted Equilateral Triangle of the Grail Geometry pattern that Vermeer used -- as consistent with most of my analyses thus far.  But in my book, I found that he sometimes used two hexagrams in the same composition.

In my opinion, the exhibit presented above is the most beautiful of all the images I have presented. It is testimony to the surpassing superiority of Vermeer as the most gifted genius in the history of painting. It is one thing to identify the guiding overlay drawing that Vermeer must have used; it is another thing indeed to achieve a masterpiece of painting in registration with this pattern.  How did he do it !? -- how did he transfer this pattern repeatedly to the canvas-in-progress -- leaving no hint of the process -- rendering so effortlessly such a free and graceful image -- yet so tightly controlled in composition?   Genius! -- the short and oversimplified answer to explain Vermeer's powerful talents!. . .

More prosaic explanatory detail seems superfluous at this point -- but skeptics abound -- so I will continue to explain:  Given the adoption of equilateral triangle A-F-G as confirmed by painted features, I then found that the center of the triangle fell at POINT C (the tip of the big, white, downward-pointing arrowhead formed by the fabric draped over her right shoulder . . . typical Vermeer! ),  so I used point C to draw the big circumscribing circle enabling me to position the second equilateral triangle D-E-H, to form a regular hexagram -- The Tilted Hexagram of The Grail Geometry.  (But it turns out that this one is not the only hexagram here . . . !)

Have Vermeer's painted features and the whole composition been governed by this hexagram? Yes, indeed.  Look, for example, at "I" and "F": -- the circumscribing circle of the hexagram runs tangent to the top and right side of the image. Vermeer sized his image and canvas accordingly. In addition, I have indicated a few more obvious confirmations -- the features labeled  a, b, c, d -- see also previous images explaining d -- h, i, j, and k. Confirmed again and again,  the concentration of Diagonals at POINT C, the Center of The Hexagram -- positioned exactly on the point of the white collar -- is positively stunning!

Beyond the ten (10) labeled confirmations, the sharp-eyed observer will identify others. This is no coincidence -- there has been no arbitrary forcing of this painting into a "Procrustean Bed" of "any old lines" and "any old figures"!    (But the skeptics ye shall always have with you . . .)

STEP 4. Building on the progress made in STEP 3 above, I explored the possibility that Vermeer had used a Tilted Square based on the Tilted Hexagram of STEP 3.

When I surveyed the situation, I became convinced that there must be another Tilted Triangle somewhere, because the one I had identified -- triangle A-F-G -- would have, according to the rules of the Grail Geometry, its associated tilted square; BUT -- that square's diagonals would cross at a location with no painted feature there at all!  Therefore, either Vermeer used no tilted square at all in this one -- OR -- there's another tilted triangle somewhere! It must have an associated tilted square pointing to a significant and symbolic feature positioned by Vermeer!

***  My guess -- a guess educated by a lot of trial-and-error exploration -- was that the most promising feature would be The Tip of the Spout of the "Miraculous Pitcher" -- labeled as POINT "h" above, and labeled as POINT "PX", and circled twice below.

Pursuing this hunch, I was able to draw -- prior to drawing anything else -- my best guess as to the crossed diagonal lines whose intersection would fall precisely on the Tip of the Spout of the Pitcher. They are DIAGONAL LINES I--K and J--L (see below).    I was aided in this guesswork by adding those diagonal lines to the developing pattern of STEP 3.  (Here the diagram becomes complicated with many lines -- but I'll simplify it in the next exhibit.)

 The previously determined POINT "I", at the top, provided me with the crucial key. Using that point as an additional "Northwest Point" (like POINT A), it was easy to draw The Tilted Square I-J-K-L that is associated with these diagonals.   (continued below)

(continued from above. . .)  Now that Tilted Square I-J-K-L is established, by using the Grail Geometry rules, I was consequently able to draw Tilted Triangle I-M-N. How very reassuring that side A--N of that triangle goes exactly through our old friend POINT C on the collar!       Looks like we've got it now!

It is a simple procedure now to draw the Tilted Hexagram associated with Tilted Triangle I-M-N and Tilted Square I-J-K-L -- by adding another equilateral triangle O-R-S to the previously identified Tilted Triangle I-M-N -- see the exhibit below.  (continued . . .):

I have twice circled where the diagonals cross on The Tip of the Spout -- designated as POINT PX (an "X marks the Spot") -- SYMBOLIC of a SOURCE!  Exactly what Vermeer or his commissioner for this masterpiece could have had in mind as being represented here (assuming it WAS a commission, probably by a fellow member of a secret society -- The Priory of Sion?) -- we can only speculate -- but it seems clear that The Spout of a Pitcher represents The Source of a flow of something desirable.

The new smaller hexagram ties in perfectly with the geometry of the previous large hexagram:

* Witness the LINES A--M and A--O drawn from the upper corner of the window frame -- the original reference POINT A of the larger hexagram -- to POINTS M and O of the smaller hexagram.

* Witness the LINES V--M and V--R drawn from POINT V -- the opposite corner of the window frame -- to POINTS M and R of the smaller hexagram.

Not only are LINES A--M and A--O symmetric to POINT A -- but they frame the girl's head (in yet another way!), clipping her chin and the peak of her head dress!

LINE V--R -- the mirror image of LINE A--O -- crosses right under the girl's chin!

Let the skeptics continue to scoff "implausible". This is not a fluke! (Fifteen --15 -- Vermeers with the same Grail Geometry, so far . . . You can't do this sort of thing if it's not really there to begin with!

What is the girl looking at?  In my opinion her eyes are focused on point "j", where her hand marks the exact center of the of the window frame.  "LOOK IN THE CENTER!" she says!  Not the center of the window frame -- but THE CENTER OF THE TILTED SQUARE!  LOOK AT POINT "PX" -- "X marks the SPOT"!  THAT'S WHAT THIS MESSAGE IS ABOUT -- THE SOURCE!

WHAT A BEAUTIFUL SERIES OF GEOMETRIC LAYOUTS THAT VERMEER PREPARED IN PLANNING THIS PAINTING! "THE GIRL WITH THE MIRACULOUS PITCHER" IS AN EXAMPLE, IN MY OPINION, OF THE EPITOME, ACME AND ZENITH OF HIS PROWESS AS A GEOMETER, DRAFTSMAN, AND FINE PAINTER! -- JOHANNES REYNIERSZOON VERMEER IS THE CONSUMMATE ARTIST!

And don't forget that he is not only "The Sphinx of Delft" -- he is "The Jester of Delft", too! DO YOU SEE THE BIRD that Vermeer has slyly painted in the shadows on the girl's head dress?

HAS VERMEER INVENTED THE WEATHER VANE? (That's a JOKE, son!) And is that the bird's wing?  Is it a "JANUS" bird?  I see more "supernumerary" faces and beasties in this painting -- just as I see them in almost every other analysis. But don't tell the skeptics ABOUT ANY OF THIS . . .

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