THE MYSTICAL USE OF NUMBERS IN THE DESIGN OF EARLY GOTHIC CATHEDRALS.   Term Paper ID:1426 Click to get this paper

Essay Subject: Discusses the key magic of numbers & the practical design of the cathedral.... More...

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Paper Abstract: Discusses the key magic of numbers & the practical design of the cathedral. Paper Introduction: The great cathedrals which are the high points of any cultural tour of Europe are almost all the product of a single century. In the space of about 100 years, beginning about the middle of the 12th century, medieval artisans succeeded in developing the Gothic style from the Romanesque style, and began building some of the noblest testimonials to the human spirit ever created. This effusion was most clearly marked in France, probably because it was the first part of Europe to achieve a national identity and a stable government. The first Gothic cathedral is generally considered to be that at St. Denis, begun by the Abbé Suger in 1137. Within the next half-century, other notable French cathedrals were begun: St. Etienns at Sens in 1140, Noyon in 1150, Laon in 1160, Notre Dame de Paris in 1163, Bourges in 1199, Rouen in 1202, Rheims in Text of the Paper: The entire text of the paper is shown below. However, the text is somewhat scrambled. We want to give you as much information as we possibly can about our papers and essays, but we cannot give them away for free. In the text below you will find that while disordered, many of the phrases are essentially intact. From this text you will be able to get a solid sense of the writing style, the concepts addressed, and the sources used in the research paper. According to Freudian psychology, its significance arises from thefact that the male genitalia have three elements. There is little doubt that three is the most ancient and mostsacred. The netaesthetic effect as a blunter point on the arch on the long side of therectangle, and a sharper point on the arch on its short side. The religioussignificance of three is shown again and again in the pre-Christian era;numerous ancient gods were thought of in groups of three, and named in asingle breath. Theintersection of these two cylinders would be a sinuous line rather than aregular planar ellipse. The Christian parallel is the Trinity of Father, Son andHoly Ghost. Though England, and France particularly,present the finest examples of the Gothic cathedral, there are notablebuildings in several other countries in Europe. We shallfirst name the most important magic numbers, and show how they haveoccurred and re-occurred in many contexts throughout history. The transeptswere smaller than the nave, generally not visible from it, and of course,closer to the High Altar which lay at the intersection of the two chambers,and symbolized the head of the crucified Christ. Because of its innately pleasing shape, andits full exploitation by subsequent Gothic designers, the pointed arch isthe best known and most readily recognized feature of Gothic architecture. The design problemof the medieval cathedral was that of safely roofing a broad area. What influence has these numbers on the design of the late-medievaland early Gothic cathedrals? Architecture through the Ages. Almost as much significance was attached to the number four. The seven liberal artswere the sum of the Trivium and the Quadrivium. The fourexternal arches, having a smaller diameter (the sides of the square) had tobe raised so that their apices were as high as those of the diagonalarches. This lengthychamber was divided into two unequal portions by a transverse chamber, thetransepts, which symbolized the horizontal bar of the Cross. These were first used in Englandwhen Canterbury was rebuilt commencing in 1174 and Lincoln, begun in 1192.The purest example of High Gothic in England is Salisbury, begun in 122 and completed in 46 years. At first this outward thrust was resisted by constructing massivecolumns projecting outward fin-like from the exterior wall. In its place, a circular arc wasdrawn, starting at the springing point of the diagonal arch andintersecting the face of the square at a point as high as the apex of thediagonal arch. A close examination of the relevantliterature reveals that their design was predominantly influenced by thestructural necessities of roofing a broad area with stone. This effusion was most clearly marked in France,probably because it was the first part of Europe to achieve a nationalidentity and a stable government. In his City of God, Augustine had said: The Old Testament is nothing but the New covered with a veil, the New is nothing but the Old unveiled. With the invention of the flying buttress, the main elements of theGothic design were complete. Thereare four cardinal directions, and the four Greek elements of earth, air,fire and water. In this plan, the floor area ofthe cathedral was divided into four major sections. Thedownward thrust was carried by the columns. Twelve patriarchs and twelve prophets are contrasted with the twelve apostles, Isaiah, Ezekiel, Daniel and Jeremiah with Matthew, Mark, Luke and John, so that the prophets are sometimes actually carved bearing the evangelists upon their shoulders. In a semicircular arch,these forces become vertical at the ends, and are carried directly to theground by the column or wall. There are 12 units in a dozen, 12 cubits in the height of aman, the 12 days of Christmas, the 12 disciples of Christ, the 12 tribes ofJudah. The same element was used in two other late-medieval Englishcathedrals: Winchester, begun in 11 7, and Gloucester, begun in 112 . We showedabove that there was a lengthward thrust from the diagonal ribs which inevery bay was balanced by a counterveiling thrust from the adjacent bay.But the end bay has no such counterpoise. A common design provided a single tower at thecrossing of the nave and transept, and two others at the public entrance tothe nave, which was always oriented to the east. But there is an equal and perpendicular thrustat the meeting point from the joining arch. If it were desired to set the columns in one direction at adifferent spacing than those in the perpendicular direction, the resultingspaces to be roofed would be rectangular rather than square. The tendency for the buttress to overturn its supportingcolumn at its lower end was resisted by adding a massive weight, thepinnacle, to the top of that column. There were sevendeadly sins and seven Christian sacraments. The product of three and four is 12, a number of some mysticalsignificance. Not only did the unequalspringing points offend the medieval sense of order, but they also posedserious geometric difficulties for the masons responsible for shaping thestones to fit between these incongruous arches.The Pointed Arch The solution to this problem was brilliant. The medieval sense ofproportion required that the walls be much higher than the width of theroofed area, often as much as two or three times. Cathedrals were always the tallest structures in theirvicinity, and were thus a target for lightning, owing to the difficulty oftransporting water to such a great height. Though thearches forming the four faces of the square remained semicircular, afterthe Roman fashion, the diagonal groins were elliptical. Due to the natural limitsimposed by the size of indigenous trees (medieval artisans always usedlocal materials owing to the difficulties of transport), such roofs couldbe constructed only up to a limit of perhaps 4 or 5 feet. The two intersecting cylinders would be of unequal diameter. The initial solution was to enlarge the diagonal groins to asemicircle, with a diameter equal to the diagonal of the square. The space between theseenlargements--ribs--could be covered with a much thinner material (often asingle stone) because the distances were less. Etienns at Sens in 114 ,Noyon in 115 , Laon in 116 , Notre Dame de Paris in 1163, Bourges in 1199,Rouen in 12 2, Rheims in 1211, Amiens in 122 , and the jewel, Sainte-Chapelle in Paris. But it was used in a decorative sense in probablyevery cathedral, to portray the 12 apostles. A History of Religious Architecture. The plans werea combination of four-sided and four-cornered squares and rectangles. New York: Charles Scribner's Sons, 1961.Hamlin, Talbot. The vaultwas simply a series of arches placed side by side for as far as desired.In shape, it was a half-cylinder on its side, whose length was the lengthof the building and whose diameter was its width. The pointed arch provides a simple solution to the problem of roofinga rectangular space. The tangents to these two arcs met at anangle. The first and last of thesecoalesced in their belief in the magic of number.Purpose of This Report It is the purpose of this report to explore the possible relationshipbetween the medieval belief in the magic of number and the practical designon the cathedral, the fullest expression of the medieval spirit. But it was quickly discovered that the fin was much larger thannecessary; the real need for strength lay in its sloping upper face. But therewas no counterpoise to the outward thrust. The double-barreled vault of theRomanesque style could only be used in floor plans composed exclusively ofsquares. In their search for a less massive construction, the medievalartisans realized that the double-barrel vault could be adapted to a newand lighter system. Early Christians spoke of the three theological virtues offaith, hope and charity (or love). These interior arches were not complete; they didnot reach down to the wall, but only to the point where they intersected acorresponding arch growing out from a perpendicular wall. Threes were seen in life and in nature: father, mother andchild; sun, moon and stars; earth, air and sky. Within the next half-century,other notable French cathedrals were begun: St. In Germany, these includeTrier, St. The invention of the rib, however, posed a new problem. In verticalplan, these intersections formed an "X" composed of the two diagonals ofthe square. Thus, a Romanesquecathedral could be built in any desired size by joining together as manysquares as desired. Thecolumn could carry not only the weight of a single square, but two or evenfour adjacent squares, by suitably enlarging it. This review should demonstratethe overriding importance of the technical imperatives. BibliographyFletcher, Sir Banister. The upper end of the flying buttress joined the wall at the archspringing line. The notable cathedrals begun in the early13th century display all of these elements,o ften in an astonishinglygraceful and aesthetically-pleasing combination.Structural Considerations Dominant The above discussion illustrates the dominant theme of this report,that the Gothic cathedral's design was largely determined by the structuralnecessities of roofing a broad area in stone. Putnam's Sons, 1953.Short, Ernest A. The towers had both symbolic and structural significance.Externally, the tower at the crossing was the highest point of thecathedral. The forces within an arch, caused by its own weight plus whateverloads it carries, are always along the curve. Elizabeth at Marburg, and Halberstadt. Thus was invented the rib,one of the three essential elements of the Gothic style. The combination of these twothrusts produces a diagonal thrust precisely along the diagonal line.Thus, the lateral thrust of the roof weight was carried down this curvingintersection--the groin--to the corners of the square, and there supportedby a massive column. Because of the sloping, curving, diagonal placement of theribs, they carried a downward, lengthward, and outward thrust. There were fourcardinal Christian virtues: prudence, justice, strength (or fortitude) andtemperance. The invention of the pointed arch made possible greater flexibilityin the design of the Gothic cathedral. Thus was born the pointed arch, the second of the three keyelements in the Gothic design. The vault wasnothing more than an extension of the structural principle of the arch,which the Romans had invented more than a thousand years before. Thefin was changed into a single sloping, the flying buttress, and a shortervertical column spaced some distance out from the exterior of the navewall. Its sole limitation was that regularly-spaced columnshad to be provided over the entire floor area. We shallthen describe at some length the evolution of the Gothic style in terms ofthe geometric and structural constraints imposed by the use of stone inroofing a broad area. The corresponding arc from the opposite side of the squarealso intersected this point. There waslittle opportunity for such an abstract concept as number to influencethese designs in ways contrary to the technical imperative.The Structural Problem It may be instructive to reveiw the development of the Gothic stylefrom its predecessor, the Romanesque style. A History of Architecture on the ComparativeMethod. Further, the walls had to support notonly the vault, but also their own weight. And stone, able only to withstand compressiveforces, cannot transmit sinuous forces. The groins and the four external arches, which carriedthe greatest forces, could be enlarged. Within this constraint,there is not a great deal of room for the use of mystical numbers.The Number Four The most obvious number in cathedral design is four. Gudula inBrussels and Utrecht.The Medieval Character The people of Europe in the 12th and 13th centuries werecharacterized by a mystical belief in the power of God to bring joy orgrief into their lives, violent swings of passion and feeling from despairto ecstasy, and a love of order and symmetry. This adaptation of the principle of the arch made it possible to roofnot only a single square chamber, but any number of adjacent chambers. It is only necessary to use different radii inconstructing the arcs on the unequal sides of the rectangle. The sum of three and four is seven, another number of great mysticalsignificance. Timber roofswere particularly vulnerable to fire. The first Gothic cathedral is generally considered to be that at St.Denis, begun by the Abbé Suger in 1137. The vertical bar ofthe cross was represented by the length of the cathedral. The twin entrance towers were also a structural necessity. Short gives the followingdescription of a decoration in the French cathedral at Chartres: The medieval sense of order is shown in the way scenes and figures from the Old Testament are set side by side with scenes and figures from the New Testament, so as to bring out the mystic harmony underlying the two forms of divine revelation. An arch was constructed on each of the four walls of the square.Then parallel arches were constructed, proceeding toward the center of thesquare from each wall. The vault was supported onwalls, which can be thought of as a continuous series of columns supportingthe adjacent arches. In the space ofabout 1 years, beginning about the middle of the 12th century, medievalartisans succeeded in developing the Gothic style from the Romanesquestyle, and began building some of the noblest testimonials to the humanspirit ever created. London: Philip Allan, 1936.----------------------- 1 These fins hadsloping upper edges more or less aping the slope of the central gable roof. Now, in the double-barrel vault, all the interior arches are lessthan semicircles, so that there is an outward thrust at every point alongthe diagonal intersection. The other solution was the barrel or tunnel vault. If an arch is less than a semicircle, theforce at the end is partly downwards and partly outwards, a horizontalthrust. The semicircular shapeof the external arch was abandoned. They were thus made in atapered or stepped fashion, increasing in thickness toward the ground.Some medieval Romanesque cathedrals had walls greater than seven feet thickat their base.The First Step in the Gothic Solution The beginnings of the Gothic solution were discovered in the firstmillenium, when it was realized that a square chamber could be roofed bytwo equal intersecting barrel vaults. Four symbolized the square, a perfect geometric form. New York: George P. Thus, thepointed arch enables the medieval artisans to: design a floor plan withrectangular rather than square bays, place the columns on either side ofthe nave at a closer spacing than the full width of the nave; use ribswhich were more nearly perpendicular to the length of the nave,substantially decrease the space between the ribs, and thus lighten (makethinner) the individual roofing stones.The Flying Buttress Through bitter experience, the cathdral artisans discovered that theprinciples of the rib and the pointed arch were not sufficient to solve theproblem of roofing a broad area in stone. One solution was the gabled timber roof. This plan symbolically representedthe Cross upon which Christ was crucified. Untilabout the end of the 11th century, there were two solutions to thisproblem, neither wholly satisfactory. In Spain, Toledo is theoutstanding example, and there are two in the Low Countries: St. The seven virtues includedthe three theological and the four cardinal virtues. It signified the heaven-seeking aspirations of the faithful,and bore a resemblance to a pair of praying hands. Internally, it provideda higher ceiling over the High Altar, the most significant point within. Butthese were not yet Gothic cathedrals, lacking the other two elements, thepointed arch and the flying buttress. Though the barrel vault of stone was fire-safe, it was a very weightyand massive solution to the problem of roofing a broad area, and providedan entrance for lighting only at its ends. Given modern engineering knowledge, we can now understand the causeof this problem, though the artisans had to discover its solution byexperience. There were the seven branches of the Jewish menorah, theSeven Pillars of Wisdom, the seven ages of man. The great cathedrals which are the high points of any cultural tourof Europe are almost all the product of a single century. Finally, we shall illustrate how numbers weremystically used in cathedral design, within these geometric and structuralconstraints.The Magic Numbers Certain numbers have been endowed with magical significance form themists of pre-history. In education, the medievalscholars taught the three subjects of the Trivium: logic, grammar andrhetoric. Ineducation, the scholars taught the four practical subjects of theQuadrivium: music, geometry, arithmetic and astronomy. The ellipse was ashape unknown to medieval geometers, and posed great difficulties for thestone masons. Though the weight of the roofwas supported by the columns, there was also a lateral thrust from the ribswhich sometimes forced the columns apart and let the roof come crashingdown. The lengthward thrust wasbalanced by an equal and opposing thrust from the adjacent bay. As a consequence, the lowest point of the diagonal arches (the"springing point") was below the lowest point of the external arches,though both were supported by the same column. One of the three key elements in the Gothic style, the rib vault, wasfirst used in England in the construction of Durham Cathedral, begun in1 93. Any openings in these walls to admit light hadnecessarily to be small, most commonly vertical slits, in order not toweaken their load-bearing capacity. In this construction scheme, the walls becameunnecessary; the entire weight of the roof could be supported on the fourcolumns. The largerportion, the nave, was the space where the faithful gathered to worship.The shorter portion, the choir, was the space where singers congregated toprovide the musical accompaniment to the worship service. Aless obvious use of four was in the cruciform floor plan used for virtuallyall cathedrals begun in this period. A common solution to thisproblem was twin towers whose massive weight contained the thrust andprevented the collapse of the front wall.The Number Seven The search of the literature revealed no structural use of themystical number 12. The religious pageantry ofChristianity always included the use of flame, which contributed to thefire hazard. Eventually, it would collapseinto the interior of the cathedral, burn everything within, and leave onlya gutted masonry shell. The double-barreled Romanesque roof vault cannot be used over rectangular spaces, orbays. The medieval sense oforder found the two transepts to be privileged areas eminently appropriatefor the men and women who dedicated their lives to God: the monks andnuns.The Number Three Three, the most sacred of numbers, appeared most frequently in thenumber of towers or spires. If this paper is not what you are looking for, you can search again: Search for: or Click here to request an essay written just for you.

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