The ladder of MELENCOLIA

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1 A new understanding in Art History Mathematics - History of Art - Esotericism - Visual Arts The ladder of MELENCOLIA Albrecht Dürer Yvo Jacquier COMPARATIVE GEOMETRY April on 16

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3 THE PERPSECTIVE SYSTEM There are so many ways to take elements of geometry, and to put them in art. The most known applied mathematics are called perspective system. VISUAL N 1 - The vanish point We are used to think that composition in art concerns only this precise practice. But this opinion has been built during the XXth century. Philosophers and historians thought that the main progress in history of art is in the mastering of reality with drawing. For sure, we can rebuild what we see in a precise way with the lines of perspective - meeting on vanish points, and dealing the measures of the work with the plans of architecture. VISUAL N 2 Perspective building 3 on 16

4 Albrecht Dürer, pioneer of the perspective system The theoretical skills, i.e. the final principles of this practice have been established during the Renaissance. Albrecht Dürer came in Italy, which was the melting-pot for art at this time, and he entered in this fabulous adventure. However this pioneer in the perspective system, who even invented a famous machine to catch the truth in drawing, was also a great master of an other practice : sacred geometry. VISUAL N 3 - Dürer's machine Albrecht Dürer explains the presence of the both systems in his famous engraving «MELENCOLIA I». The work respects mainly the rules of a simple perspective (with one vanish point, located on the horizon at the vertical of the sphere). Left - VISUAL N 4 The perspective of Melencolia 4 on 16

5 First approach of the ladder in «MELENCOLIA I» Left - VISUAL N 5 The ladder of Melencolia as it is Some subjects of MELENCOLIA seem to escape the rules of perspective. The ladder is the most impressive case. 1 The bars are parallel, and that seems to be impossible with the disposition of the uprights. 2 The bars are not equidistant! The size of the gaps have no sense. Right - VISUAL N 5 bis The ladder of Melencolia as it should be In the perspective system, as well as for our eyes in a usual conception, the bars are parallel when the ladder is in front of us. And the gaps may increase from the bottom to the top. Dürer was he practicing axonometric perspective? 5 on 16

6 3 The incredible size of the ladder Last provocation : if we apply the perspective's rules to the ladder, we realize that it is over-sized. This ladder is built for giants. Right - VISUAL N 6 The ladder and St Michael 6 on 16

7 WHY AND WHAT FOR? On at least three points, the ladder of MELENCOLIA challenge the rules of the perspective system, when the author is a great practicer, even a founder of this art. In this sense, this could not be an error from him, especially in the most famous work of Renaissance. Dürer is a master, and this ladder shows us something precise. What? Aesthetic arguments are all of them precarious to explain this provocation : Dürer insists three times to show that this ladder is apart. He could twist one of the rules, in the game of his drawing, but not three when the entire work is built with the perspective system. In clear terms, this object sounds wrong. The reason of why Like his colleagues of Renaissance (Verrocchio, Botticelli, Vinci, Raphael etc), Albrecht Dürer practices two systems of composition in the same works. The emerging perspective is completing the ancient geometry, also called sacred geometry. The preoccupations are not the same : perspective system cares about the concrete appearance, while sacred geometry bears the symbolic meaning of the work. And because we understand the new one, we have missed the other one, which is besides or behind perspective. Step by step The first step is to show this ladder as it is in the reality, by using the traditional rules of perspective system. It could become a sculpture for the festival of contemporary art Tina B, in June It is the best way to open the debate about the lost culture of sacred geometry. For the moment, we need specialists of perspective system, to achieve the demonstration. Then I will realize the ladder to show the original message of Albrecht Dürer. So here are the elements gathered for professional of 3D conception. 7 on 16

8 THE ELEMENTS OF MELENCOLIA The first idea is to rebuild the scene with its volumes. The only one objective element at the beginning is the vanishing point leading the panel behind the scales. This point noted V1 is on the horizon, at the vertical of the sphere (its center). It seams to be one step zigzagging behind the stone wheel. Left - VISUAL N 7 The sketch of volumes The front lines of the great panel (of the magic square) are parallel to the plan of the picture. It doesn't mean that it is an axonometric perspective. We can not conclude so fast. Right - VISUAL N 8 The extremities of the ladder We may take options to solve. Eg the ladder leans evidently on the top of the "house", at the top of the picture. But below? We have to take an option. It could be one gasp (the one between the first low bar and the second) under this first bar. But we have to be prudent. We are not sure that the ladder is right angle with the side panel. And so much other things... 8 on 16

9 Left - VISUAL N 9 The vanishing point The first certitude is the vanishing point which manage the side panel. We will use this panel as a reference to observe the sand-glass. The sand glass has an hexagonal section. Normally, if the side panel of the house was right angle with the front panel, the line coming from V1 to the top of the sand-glass would be below. Below - VISUAL N 10 The lines of the sand-glass On the contrary, the line is over the one of the hexagram. We have to focus on this. 9 on 16

10 Above - VISUAL N 11 The lines of the sand-glass The sand-glass has a closer vanishing point : it means that the side panel has a wider angle with the front panel! This vanishing point is at the vertical of the point of the cartouche (and of course, on the horizon). The distance between the two points is, on the scale of the composition of tarots that we reconstituted : π/ 7! The white sphere gives the unit with its diameter 2. If we consider that the house is a regular form in its floor plan, it could be an octogram or an heptagram. In the case of octogram, the ladder would show its profile. So, let us try the heptagram. A difference in the two sides of the sand-glass (length) shows that the focal point is on its left. Maybe on the vertical line between the panels, maybe on the middle of the scales. It is to be noticed that the position of the observer is a bird's-eye view, over the head of the angels. Left - VISUAL N 12 Sketch of the floor plan The proposal of the heptagon for the floor plan. In yellow, the option of the panel part appearing on Melencolia, if we consider that the bell is in the middle of the front panel. 10 on 16

11 A rough idea of the ladder Left - VISUAL N 13 The ladder We could get informations, just with the measures of the pixels on the picture... Left - VISUAL N 14 The ladder in pixels Below - VISUAL N 15 The translation in angles (Top view) 11 on 16

12 A rough idea of the floor plan Left - VISUAL N 16 The translation on the heptagonal plan Here are some sketches before the real assault of 3D construction... Right - VISUAL N 17 Other pixels Left - VISUAL N 18 7, the key number of Melencolia 7 bars with the ladder, 7 colors with the rainbow, π/7 everywhere in the composition - drawn by Dürer on the sleeve of St Michael. 12 on 16

13 CONTINUATION OF THE WORK This ladder has to be constructed from the drawing of architects. They will reconstitute its reality with the rules of the perspective. The patterns presented here are an intuitive approach to this result, and they will be the support of a work that is far to be complete Envisioned materials : PVC plumbing plastic + colored rope / wire, and plastic fabric. 13 on 16

14 The perspective Box The reconstitution of the ladder has been the subject of a presentation in a contemporary art festival : Tina b - Prague/Kutná Hora (Gask gallery) This is a part of a larger installation, called «MELENCOLIA de», a tribute to the work of Dürer and to his symbolism. A box, called «Perspective box», shows the picture of «MELENCOLIA I» from its focal point. A hole in the engraving allows to see the 3D reconstitution of the ladder behind the window of the picture, and represented by white strings. Here is the instructions of this perspective box. THE LADDER OF «MELENCOLIA I» This is not at all a ladder! This engraving by Albrecht Dürer, printed by his hand in 1514, shows several elements which have won a mythical statute in the history of art. The polyhedron and the magical square are the objects of many thesis, besides a usual inventory of tools and winged creatures. The ladder in the background is classically identified as the ladder of Jakob. Without anything particular, just the correspondence of its seven bars with the seven colors of the rainbow (theme of this collective exhibition). In fact, this piece of wood is a doorway to the culture of Renaissance on 16

15 This perspective box allows to compare two different points of view concerning the same ladder. On the front of the picture, the sign > points a precise place for the eye, called focal point. It is the position of the observer, according to the laws of the perspective system. When we put one eye at this place, the orientation of the uprights and the bars are the same like in the engraving of Dürer. It fits with the hole. The second point of view is behind the scenes : a 3D reconstitution. We discover that the ladder that we see in the conditions of the perspective is not normal! More : this proposal belongs to an infinity of possibilities! But this position is the less abnormal one, and it is the limit of a geometrical equation... It has to be noticed that the focal distance is abnormally short from the eye to the frame of the work. However this distance can be established due to the lines of the sand glass, which is hexagonal, and confirmed by other elements. The general study of the perspective of Melencolia has been viewed and approved by a specialist in the school of architecture of Paris. So this ladder uses the rules of perspective for showing a virtual image without respecting the rules of the reality. This first lesson from Albrecht Dürer, pioneer of the perspective system, is to warn us about the illusions that abuse our judgement. This consciousness appeared since Renaissance, and didn't wait for the great Escher! The second lesson needs more developments. In Melencolia, the perspective system is under the control of an other one, called sacred geometry. This engraving belongs to a huge project of Dürer, explaining the rules of this other practice through several images (including the four engravings called Meisterstiche, and the model of Tarots that 15 on 16

16 Nicolas Conver will continue to copy in 1760). The images definite a real language by mixing their drawings like the words of a text. The syntax is assumed by sacred geometry, which has been used at first by old civilizations to build their temples, and their pyramids, up to the apotheosis of Renaissance - last epoch before the decline of this culture. There is reason to believe that Albrecht Dürer had planned this box. Indeed, Brunelleschi built a device to introduce the perspective system, so new at the time, with great success. 16 on 16