Vermeer

01.01.1011

Vermeer's view of the Little Street

Vermeer The Geographer
Vermeer The Geographer

Abstract

The goal of this article is to refute the generally accepted theory of camera obscura and its claimed usage by Johannes Vermeer. It will prove that behind Vermeer's perspectival space stands sophisticated geometrical system. Upon analyzing The Geographer it becomes clear that Vermeer used window as a picture plane for his external scene of The Little Street. The geometry also reveals that the viewing point of The Little Street is distant of about 11.5 meters from the building on the other side, implying that the paintings was created on Voldersgracht Street.

The Geographer

Vermeer's pictures has been examined and inspected closely from every possible angle to find out more about their construction. Infrared reflectography and other scientific techniques that has been used in recent years can peek under the surface to reveal some hidden secret. Yet Vermeer's canvases contain no underdrawings or any other hints. He made his preparatory and structural drawings, not on the canvas, but on a sheet of paper, the similar sheet of paper we can see in The Geographer. If there is not much below the surface, we should examine the surface once again more closely.

Many attempts have been made to confirm the theory of camera obscura, but all have been unconvincing. Vermeer's concept of space, his precise placement of the objects within the depth of picture in correlation to the real space, is a matter of a perspective system and its skillful implementation. There was no camera obscura behind his perspective mastery.

After visit to Vermeer's studio in June 1669 Pietr Teding van Berkhout wrote that the most "extraordinary and curious aspect" of Vermeer's art consists in "perspective." 1 There is nothing "extraordinary and curious" about retracing image projected by the camera obscura and van Berkhout was certainly referring to Vermeer ability construct the space geometrically.

Fortunately, Vermeer left many clues in his paintings which demonstrate his expertise and excellent knowledge of the Renaissance perspective system. To obtain the right proportions and scale in his painting The Geographer Vermeer used the same perspective system as in many of his earlier paintings. The system Vermeer employed to construct his perspectival space is described in more details in my earlier study Vermeer and art of the Renaissance perspective.2

Upon analyzing The Geographer some interesting and unexpected consequences emerge. This picture provides lucid testimony of his geometrical method. He was not tracing upside down images in a cramped space, he was using a secret knowledge and scientific and rational reasoning.

Utilizing a compass, Vermeer set the F point at the distance based on sacred geometry and on the Golden ratio. That is, if the side of the base square AB is 1, then the distance from the F point to the vanishing point V is 1.618.

Subsequently the tiers point or lateral points are derived and constructed from the focal point or F point.3

The space of The Geographer is not deep and in this particular case the cube's back wall (EFGH) aligns with the room's back wall. The side of the cube measures 198cm, which corresponds to 7 Amsterdam's voet at that time.4  7 x 28.3 = 198cm. If we know the measurement of the front wall, then we know all other walls too, because they are all equal, and can orientate ourselves in three-dimensional space of the picture.

In the picture we can see a compasses in man's hand and a tool that closely resembles a compass lying on wooden box. Neither is there by chance and both aims (green lines) to the important points in the perspective construction. One arm of the compass aims to the corner of the base square, point B. The other arm aims to the point J, where the large circle (determining the F point) and line j coming from the left corner of the bottom square meet. The line j determines the tiers point T2. One arm of a tool on the wooden box aims to where the horizon and smaller φ circle meet, point K. Its other arm aims to the tiers point, point T2.

When we look more closely on individual parts of the image we find sufficient evidence of the level of precise planning involved. The resulting consequences will transfer our attention unexpectedly outside of the picture frame.

If we know the dimensions of the cube (7 Dutch feet) we can find out dimension of any objects within the picture. The subject of this analysis is The Geographer' view, it is his view from the window and dimension of the window we will find out as follows.

The width of the window is foreshortened and therefore we have to apply the principles of projection. Drawing lines (red lined) from lateral point or tiers point through the marked points on 45° diagonal we arrive at the unforeshortened distance at the base line. Using proportionality constant of a1/a2 x 198cm we get 44cm.

Things will get interesting, when we focus our attention to the window "The Geographer" is looking out (marked red). Again using proportionality constant we find out that the length of the window comes to around 83cm. Nothing special about it, but if we measure the dimension of the window without its two upper segments, without those segments covered by the curtain, and then apply same proportionality constant formula of b1/b2 x 198cm, we arrive at the dimension of around 54cm. One of the few Vermeer's exterior scenes The Little Street measures exactly 54.3 x 44cm. It is no matter of chance that Vermeer conceived the window in The Geographer as a picture plane for The Little Street. It is he himself who is looking out of the window and across the street while constructing the perspectival layout for The Little Street. The presence of a globe does not necessarily mean we are looking at a geographer. Vermeer with a compass, painter's indispensable tool, in his hand is just telling us that he is constructing The Little Street. The Geographer or The Astronomer could be Vermeer's lost self-portrait, item 3 from Dissius auction,5 which is now presumed missing.

The Little Street and so called The Geographer are interconnected and bound together by a window, by the Vermeer's view, which starts inside of the room and ends outside on the street.

The testimony of meticulous planning is also brought to us by the wooden box. The dimensions wooden box, which Vermeer put it in the foreground and elevated the floor level, is 28.3 x 45.7 x 22.5cm. These dimensions are derived from already mentioned proportions of the Golden Ratio. 28.3 x 1.618 = 45.7 and 28.3/√1.618 = 22.5. Vermeer ingeniously placed the box so that its base sits outside of the picture plane and thus entering our space. He suggests that image space itself does not end with a frame, that things happen outside, and that the boundaries of the picture plan can be crossed. Elevated floor level gives different data thus tiers point of the box are closer to the vanishing point.

Also notice also slight tilt of the floor, this was caused by shift of a tracing paper, which contained a geometric construction. This thin paper was pinned to the canvas at the vanishing point and a slight rotation about the axis caused the tilt. It is very similar to a tilt we can see in The Music Lesson and very likely done intentionally as a slight hint of imperfection, as a human touch to an otherwise perfect perspective.

The Little Street

Using the Renaissance perspective tool, we not only managed to reveal the identity of the person in the picture, but we can also try to find out where Vermeer is looking. One of the consequences of Vermeer's view through the window is that we are able by reverse analysis to define the viewing distance of The Little Street. The first step is to convert the dimensions of the canvas or window (without two segments) to a square. Then, using the system of the Renaissance perspective perspective dividing space further into the depth, we can figure out the necessary dimensionscontained in the picture, including the distance of the viewer. The viewer is in this case Vermeer himself. A divider in his hand suggest he is constructing perspectival scheme and window's dimensions imply that the scheme is of The Little Street.

The space divided into squares (or cubes) can be easily calculated: 450 cm (396 x 1.136) - the distance from the viewing point to the first square + 396 cm - first foreshortened square + 300 cm - to the opposite wall. This all equals 1146 cm or 11.46 meters or in original measuring unit it would be 15.9 + 14 + 10.6 = 40.5 Dutch feet.

According to the google distance finder the width of the Voldersgracht Street plus the canal at this point is 10.6 meters.6 We know that Vermeer is 55 centimeters away from the picture plane, from the window. There is around 30 cm remaining, which have to be taken into account for the width of the wall. It comes out to 10.6 + 0.55 + 0,3 = 11.45 meters or 40.5 Dutch feet or 37.5 US feet from the opposite wall to the eye of the beholder, Vermeer's eye itself.

This assertion is in complete accordance with Philip Steadman and Pieter Swillens, who first suggested that the painting shows a building in the Voldersgracht Street, just across from the building where Vermeer lived before his marriage.7

To simplify the layout I only provided the square grid, which is enough to figure out other dimensions. For example, the woman in the passageway is around 17.5 meters away from Vermeer.

Or that the ground floor of the building on the right is 5.2 meters high.

As you could see Vermeer was not constrained to one viewing distance or one focal point. He based his F point positions on the proportional variations of Golden ratio and its square root.

For The Little Street he utilized the same scheme as for The Music Lesson, where F point has been derived from √φ. And for The Geographer he used same scheme as for The Art of Panting, where the F point has been derived from √5/2.

Conclusion

Today, most scholars disagree with the theory of camera obscura or lucida, but still hardly accept the fact that anyone would be able to find a universal geometric system that refutes this erroneous theory. In the meanwhile the general public is deluded by growth of studies and books about how old masters crammed in a small hot dark boxes were tracing upside down images.

The best Renaissance and Baroque minds have contributed to the method of spatial construction and thanks to their scientific knowledge, the paintings of superior and enduring authenticity have been created. It was my aim to disclose some of the secrets hidden in Vermeer's masterpieces, because the Renaissance Perspective system was recognizable as an intellectual and visual tool for several centuries and stands at the beginning of the artistic era unparalleled in the world.

Finally, I would like to hope, based upon these new facts, that the art of old masters will be perceived with an increased visual alertness and the criteria for their comprehension will become more objective and scientifically substantiated.8

Copyright©2020 Petr Bouc. All Right Reserved  

 

NOTES


1. Philip Steadman, (2002). Vermeer's Camera. Oxford University Press, p55. ISBN 0-19-280302-6

2. https://www.renaissanceperspective.eu

3. More about how to determine the tiers points, which leads to the construction of the base cube and consequent quadrature, at www.renaissanceperspective.eu

4. https://en.wikipedia.org/wiki/Dutch_units_of_measurement#Length

5. Elizebeth Neurdenburg, "Johannes Vermeer. Eenige opmerkingen naar aanleiding van de nieuwste studies over den Delftschen Vermeer,"Oud-Holland 59, 1942,

6. https://www.mapdevelopers.com/distance_finder.php

7. https://www.essentialvermeer.com/delft/little-street-steadman/little-street-steadman.html

8. https://www.renaissanceperspective.eu