| <Home J. Vermeer "The Astronomer" |
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The Tilted Triangle: What is the Astronomer pointing at with both index fingers?
" As above -- So below " "The Astronomer" as painted. Figure 1. The Tilted Triangle.
Figure 1. The Tilted Triangle: What is the Astronomer pointing at ? The composition of this painting is constrained by the Grail Geometry, whose sine qua non is the equilateral triangle. Vermeer has arranged certain features of this painting to lie on the lines of the equilateral triangle as I have drawn them on the reproduction. He has placed five features in alignment: A) the corner of the window pane; 1) the corner of the second window pane; 2) the corner of the book; 3) the corner of the cupboard; 4) the bump on top of the picture frame.
In analyzing this painting, the writer drew a straight line through those five points. Assuming that this line is the top side of the triangle, another line making a 60 degree angle at A was drawn to see if a confirmation emerged. Indeed a confirmation may be seen at 5, where the second line is just tangent to the astronomical globe. (Note: a line tangent to a curve on a painting is a standard confirmation that the curved feature was painted to conform to the geometric guide line.) Having obtained six confirmations, we may confidently search for the third side of an equilateral triangle. Finding the proper third side is often difficult, but in this case it turns out that 7, the lower corner of the picture frame, is the sought after confirmation that completes the Tilted Triangle used by Vermeer to guide this composition. Note how remarkable it is to see the index finger of each hand of the Astronomer point to a vertex of the triangle! A situation such as this could not possibly arise by chance. If Vermeer had not arranged these features as he did, no amount of trial-and-error drawing could possible force such a pattern if it were not there. We may be confident in searching for the Tilted Square that usually accompanies the Tilted Triangle in the Grail Geometry: Figure 2. The Tilted Square.
Having established the Tilted Triangle in Figure 1, we may then apply the procedure for finding the associated Tilted Square and its associated ‘X marks the Spot’ in Figure 2 (see the GRAIL GEOMETRY section). The associated Tilted Square AMNO is drawn according to the Grail Geometry procedure, and the diagonals AN and MO are drawn. The intersection of these diagonals is marked with a cross designated PX, signifying the “X marks the Spot” for transferring this geometry to a map. Note
that the ‘X marks the Spot’ falls on the left hand
of the Astronomer. This is profoundly symbolic of something hidden
– and Vermeer uses the same symbolism in a companion painting
(see “The Geographer” section). What better or more convincing proof could be asked to show that Vermeer knew and used the then secret Grail Geometry to guide the positions of these painted features? He was evidently devoted to this method, since he composed at least fifteen paintings (at this writing, Oct. 28, 2003) out of his oeuvre of thirty-five paintings in this way.
But Vermeer was much more than a competent draftsman and a consummate artist -- he was a jester, too. The Jester of Delft and The Spinx of Delft. Consider the following exhibit and ask yourself if this was just another visual joke -- and he's made a lot of them: What's that on the sleeve!? Looks like a SKULL on a BOX . . . There's a wealth of symbolism here. It goes back to a burial site on a mountainside in France . . . Now please make a comparison of the analysis of "The Astronomer" with the analysis of "The Geographer" in the next section. Please click on the "Geographer" button on the upper left hand section of this page.
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