Posted by Dr Joachim Langhein on October 08, 2002 at 04:42:08:
In Reply to: PROPORTION is a very imp factor of architecture...... its easy to visualise but difficult to put in words..... can anyone explain what exactly is it ! posted by pracks on September 29, 2002 at 01:10:12:
First Part of my Berkeley Lecture of July 4, 2002; I send you the whole paper or an abstract on request. -
Dr Joachim Langhein
On the Path to a General Proportion Theory: Research Perspective for the 21st Century.
In my research paper, “On the Path to a General Theory of Proportion: Research Perspectives for the 21st Century,” I propose strategic guidelines that are required for the establishment of a general theory of proportion.
I am an economist and ecologist, and I hold a Ph.D. in geography. I identify environmental aesthetics as a basic resource that is required for the ecological survival of our global civilization. I started research on architectural aesthetics and proportion as a geographer approximately 20 years ago. Originally I wanted to become an architect, but after spending half a year as a trainee on building sites I became disgusted by the ugliness of modern German architecture.
Proportion research should be established as a decisive means for gaining objective and operational tools for preserving and re-establishing this "basis resource” that is the aesthetics of man's environment.
My theory focuses on the fact that the aesthetic qualities of beauty found in ancient architecture depend primarily on the balance between order and diversity and on a number of "figurative levels", including the patterns that mediate between them. This "mediation by patterns" creates a unified or balanced perceptual effect for the whole form and each of its figurative levels. Referring to proportion, the overall patterns are primarily those of geometry, (primarily Euclidean and non-Euclidean geometry). Today, there can also be no doubt that fractal geometry is a proportion generating pattern because fractal geometry can organize whole spaces according single mathematical formulas. Since proportion refers to extensional ratios, it is bound to systems of geometrical or mathematical ratios. Therefore, symmetric and topological regularities are in principle also patterns of visual math, but they differ from proportion because their patterns relate either to invariants in transformation and regularity (symmetry, e.g. the 247 symmetry groups) or invariants of positions and networks (topology, e.g. knots). Beauty unfolds if the whole, (the combined forms and objects, of architecture, and of environs), is governed by a balance of unity and order, i.e. by (a harmonious blend of) unifying principles that transcend the whole and its parts. An interesting quote which can be found in the first Encyclopaedia Britannica of 1773 states just this: “Architecture, being governed by proportion, requires to be guided by rule and compass.”
Visual math is comprised of at least three major visual or figurative levels (principles). Each of these figurative levels contain systems patterns that have a strong effect on man’s perception, and are mathematically, physically, or psychologically definable. Many more pattern ratios exist in art and architecture, including those defined by Gestalt Psychology. The overlapping of these patterns in the same building and in its parts creates the impression of beauty. “Beauty” can be defined in terms of Gestalt Psychology as “gestalt pragnanz” or “good form.”
I have defined four main functions and at least 15 sub-functions of proportion. Information reduction is the most important of these main functions. It initiates the aesthetic modes of perception. Although the function information reduction is not specifically related to aesthetics or beauty, it is a prerequisite because it ensures the comprehensibility and legibility of (architectural) objects. Proportion helps us to reduce sign diversity to sign order better than any other principle of visual pattern or figurative level. In art and ancient architecture, patterns are interconnected. Our perception system is able to reduce 2 mln bits to 200 bits within fractions of a second. This reduction brings this amount of information into the capacity of the short-term memory. If information reduction can proceed step-by-step, as this slide demonstrates, then multiple ordering patterns such as proportions, the harmony of colours, and patina can be experienced as a whole. Figure 1 illustrates the way that the human perception attempts to reduce complexity to super-signs. Since proportion is the all-comprehensive principle of extensional order – definable by math functions – a proportioned whole promotes information reduction as well as information enrichment. After the (order and structure) super signs have been identified, perception immediately reverses to regain variety and analyze the diversity of the parts. It can achieve this only if the effect of unity or order is stronger than diversity. Aesthetic pleasure unfolds if the perception can freely play between the pleasing figures of the whole and the parts, between texture and patina, rhythms and motion, light and shade.
Perception and its extraordinary capacity of performance depends upon proportion. In a famous statement LEIBNIZ of 1712 speaks of the acoustical perception of music; the same principles can be applied to the research of visual perception: "Music is a hidden arithmetic exercise of the mind unconscious that is calculating, because it does many things by way of unnoticed conceptions which with clear conception it could not do…” LEIBNIZ correctly states that the perception processes information in a systematic way, particularly by the unconscious identification of mathematical patterns, of ordered contrasts, tensions, motions etc.
Perfect visual beauty can be based on simple geometric figures, regular polygons or solids. They comply simultaneously with the mathematical visual patterns of geometry, symmetry, and topology: examples include the regular triangle, square, and pentagon, or their polytopes and duplications (hexagons, octagons, decagons etc.), and the regular polyhedra (Platonic and Archimedean solids).
The beauty of shapes with simultaneously perfect geometrical, symmetrical, and topological patterns (e.g. knot patterns) is present in Gothic rose windows and in the classic Islamic architectural ornamentation (Arabesques); many of these decorations embody all 17 plane symmetry groups (H. GÖTZE 1991, MONTESINOS AMIBILIA 1987). The overlapping of these three forms of visual patterns, geometrical, symmetrical, and topological, may explain why simple polygonal geometry has such strong aesthetic appeal.
In regard to the “architectural proportion systems,” the three regular core polygons are of the highest importance: these are the regular triangle, square, and pentagon. They were probably present in most ancient civilizations and used as powerful design tools in pre-industrial architecture. The equilateral triangle, square, and pentagon, can be used to develop approximately 300 proportion codes which are present in world architecture. Pre-industrial designers were able to derive these polygons using the basic geometric constructions of practical geometry.
Rules can assist, but cannot substitute the creativity of the designer. In order to create the diversity that is inherent in beauty, designers must create a mental environment that fosters the flow of intuition and creativity. A proportional theory would facilitate this freedom by creating a base of simple rules and limits. This blending of intuition and the rules derived from proportion was characteristic in the buildings of the past. Pre-industrial designers understood the "the old way of seeing" (J. HALE 1994), the principles underlying harmonious design, and that "intuition is not [merely] raw feeling.”
HALE (1994, 1) impressively describes the magic of architecture:
"The old buildings smiled, while our new buildings are faceless. The old buildings sang, while the buildings of our age have no music in them" … "the principles that underlie harmonious design are found everywhere and in every time before our own; they are the historic norm." (ibid.).
"There was a time in our past when one could walk down any street and be surrounded by harmonious buildings. Such a street wasn’t perfect..., but it was alive. The old buildings smiled, while our new buildings are faceless. The old buildings sang, while the buildings of our age have no music in them.
The designers of the past succeeded easily where most today fail because they saw something different when they looked at a building. They saw a pattern in light and shade. When they let pattern guide them, they opened their ability to make forms of rich complexity. The forms they made began to dance.
About a hundred and sixty years ago, early in the Victorian age, the old way of seeing began to go out of American design. With it went the magic, and with the magic went the old feeling of being in a real place.”
“The difference between our age and the past is in our way of seeing. Everywhere in the buildings of the past is relationship among parts: contrast, tension, balance. Compare the buildings of today and we see no such patterns. This disintegration tends to produce not ugliness so much as dullness, and an impression of unreality. The principles that underlie harmonious design are found everywhere and in every time before our own; they are the historic norm.” (ibid., 2)
I make my first conclusion:
Proportion is inherent in the majority of the architecture of pre-industrial civilizations. Since the days of Classical Greece, proportions were regarded as being imperative to the beauty of art and architecture. The Germany philosopher GADAMER (1900-2002) regarded the deliberate desecration of beauty as an essential task of the 20th century. This may have been achieved. However, now we on the edge of 21st century at a time when the global survival of man is at stake. The earth's basic resources must be used in a wiser way. Beauty of environment and of architecture is one of these basic resources. It is neither costly nor limited, and yet it is one of the higher needs of man.
Our knowledge of proportion as well as of beauty is still fragmentary despite it being a high-ranking basic resource. Prior research has not identified proportion’s status as an ecological resource. We can state with GOETHE that "beauty can only exist with proportion," (Max. & Refl. 1110). Beauty is one of the intangible environmental conditions that corresponds best to the true nature of ecological man. The German poet SCHILLER (1795) wrote in "Letters on the Aesthetical Education of Mankind" that beauty creates links between the two contrasting powers in man, between emotion and intellect, enabling their reciprocal reinforcement and self-organization. Beauty stimulates the totality of human ability. This complies with the idea of the American psychologist MASLOW, that aesthetic conditions promote the "fully functioning of human beings.” Truly, ecological man requires beauty in architecture.
GOETHE has written the often quoted passage:
"A noble philosopher described architecture as frozen music ... [In a beautiful town] remains the harmony. The citizens of a town of this kind walk and work surrounded by eternal melodies; the spirit cannot sink, action cannot fall asleep, the eye takes over the function, the due work, the duty of the ear, and on the most ordinary day the citizens feel they are in an ideal sate. ...
The citizens of a badly built town, on the other hand, where fate has swept the houses together with a slack broom, unknowingly live in a desert of dismal conditions; ..."
GOETHE and HALE agree that beauty in the built environment has enhancing and promoting effects on the ecological life conditions of man. Beauty is not a luxury, but an ecological prerequisite for a sound human existence. SCHILLER and MASLOW agree that beauty is a prerequisite for man to activate his full potential as rational and emotional being. These statements stress the importance of the integration of intellect and intuition for design as well for ecological behaviour of man.
The buildings of the past, in addition to their balanced figurative qualities, show unified schemes of micro-fractality in material texture, colour, and the play of light and shadow. Rhythm and substructures were harmoniously balanced by proportional order, and the sequences of Gestalt laws were masterfully respected.
2. High and Folk Architecture
When I speak of the architecture of the past, I think of both high and folk world architecture. I conducted comprehensive research on the vernacular architecture of more than 50 countries, including most European and South Asian countries and made approximately one thousand proportion analyses of folk houses from European countries. In the 1980s, I carried out an international enquiry on vernacular proportion by mailing approximately 6,000 inquiring letters in 18 languages; I received 800 answers in 25 languages. Since then, I have put particular stress on searching and documenting this literature in my database (see introduction http://home.t-online.de/home/DrLanghein). A large number of proportional analyses of folk houses have been shown which display for the period of 1400 to 1830 more regional than temporal changes.
Proportion analyses of high and vernacular architecture clearly show that in Europe the proportion codes of high architecture primarily varied with time (styles), while that of folk architecture primarily varied with space (regions). Religious architecture generally has the most sophisticated proportions. The geometry that contributed to the formal perfection of religious architecture was both visible and invisible.
3. Easy Learnability and Historic Aspects
The rules of ancient proportions are and were easy to learn. In many civilizations these rules were based on practical geometry. In Antiquity and the Renaissance practical geometry became more formalized. In regard to the practical geometry of Gothic church constructions, the influence of Euclid, rediscovered and translated in the early 11th century from Arab sources, may have had some influence, particularly through the broad-based Cistercian building activities of that time. In general we can be very sure that the vast majority of master builders, masons, and carpenters had a sophisticated knowledge of practical geometry. However, even the leading master builders of the famous cathedrals may not have carefully studied Euclid until the Renaissance. (Euclid’s “Elements,” is still an optimal textbook of geometry, now 2,300 years old, but seems not to have been translated into Latin during the centuries of Roman rule.)
Again, the majority of ancient builders, in Europe and the U.S. until the 19th century, used craft geometry. These rules could easily be used as a tool for assisting and sometimes controlling design procedures. To learn these rules, a formal study of math or geometry is not required.
I return to the super principles of order & diversity inherent in the majority of ancient architecture. This balance ensured the gestalt pragnanz of architecture and was the outcome of a high degree of professionalism and intuition. The balance between order and diversity was a kind of trading on and among the figurative levels. Modern architecture has lost this balance in general as well as the ancient design wisdom. As the balance between order and diversity decayed, order degenerated to stiffness and monotony, diversity to chaos and confusion. Extreme order leads to monotony and depression; whereas, extreme diversity without all-comprehensive unifying structures creates feelings of unreality, confusion, and chaos. The human mind rejects such unstructured diversity, and the result may be disgust and dereliction. Ancient music, architecture, and landscapes generally achieved this overall balance between order and diversity; yet, modern architecture and environs generally do not. Like Gothic, Baroque and classical music, old artefacts are rich in variety, but also possess a strong, logical order that makes them comprehensible and legible. The result of this balance is the elevating feeling that only beauty can impart.
So, the primary focus aesthetics based on proportion is on the way that this overall balance between order and diversity can be achieved. The predominance of order or diversity can be counterbalanced by four proportion-related functions and sub-functions, particularly in architecture. The gestalt pragnanz (beauty) of form in pre-industrial art, architecture, artefacts, and landscapes depended on this balance also. Research should be intensified in this area. As mentioned, proportion represents the extensional part of the unifying principles (in 2D, 3D, 4D objects and environs), and may inhere some danger of overstressing the part of order within the figurative balance of order and diversity. An efficient means to counterbalance order is rhythm, the micro-fractality of texture, colours, light and shadow, and the fractally structured environs (cultural landscapes, gardens).
There are four main functions of proportion in relation to perception:
1. information reduction,
2. unity between the whole and its parts in regard to the structural compatibility between the whole and the diversity of parts,
3. characteristics of grace and elegance (in high and traditional architecture), and
4. ensemble or complementary relationships between architectural objects and the natural environment, e.g. regularity and irregularity.
The sub-functions of proportion reinforce the order-diversity balance in very complex ways. Rhythm introduces directly stimulating counterbalances to proportional order. Further examples include the micro-fractal patterns of texture, colour and patina, light and shadow play, ornaments, symbolism, and the Gestalt laws, (which have much in common with symmetric and topological patterns).
GOETHE formulated that "there is much more learnable and traditionable in art, as we normally think, and there are many mechanical advantages suited to achieve the greatest effects. If you know such artifices, much is game that looks like a miracle."
Since the basic principles of proportion and composing were so simple in their basic methods, ancient builders and carpenters were almost unable to build ugly architecture (H. WINTER 1956).
4. Principles of Proportion. Polygonal Proportion Systems in Architecture
3.1 The Three Proportion Systems of Pre-industrial Architecture
The three most important ancient systems were: Triangulation, Quadrature, and Quinture (the proportions of Golden Mean). The Quadrature was probably the most used proportion system and the most flexible because it allowed various combinations of integers in the horizontal and vertical line; diagonal regulating lines could also be created. Thus, e.g., the Pythagorean Theorem could be ascribed to Quadrature proportions. It appears that Quadrature proportion systems were predominant in Roman Antiquity, the Middle Ages until the Gothic, in Hindu, Buddhist and Islamic civilizations, and in the vernacular architecture many regions through out history. However, examples of Triangulation and Quinture can be found since prehistory or early civilizations such as Egypt also.
3.2 Triangulation, Regulating Lines and Regulating Arcs
Please look at the figure of the geometrical construction of DÜRER 1525, entitled “Instruction in Measuring,” which he took from Matthew RORICZER's Geometria Deutsch (1486). By drawing two circles with a constant compass, where both circles cut the other's centre (A, B), both circles cut each other in C & B. By this simple operation the medieval builder had already three important results: (1) the right angle, (2) the equilateral triangle, and (3) the ratio 1:Ö3. If one continues to draw circles with a constant compass, starting at C or D, one needs only to repeat this five times to construct a hexagon, which can be - as the regular triangle and square, arranged to completely tile a plane. By this simple operation, master masons were able to construct their basic figures for ground plans and elevations
The ancient masons or carpenters used these tools to compose, by simple means, simultaneously the whole and of parts. They could do it with regulating lines or regulating arcs (circles) or both. HALE has written with inspiration on regulating lines and arcs:
"In every Gothic church, he writes, the shape [of the vesica piscis] is repeated like an incantation wherever one looks, where it becomes an enclosing geometry of regulating arcs. The geometry of a Gothic building is an efflorescence of overlapping circles. …." (HALE, 77)
In non-religious buildings, regulating lines, circles and curves were derived from hundreds of proportion codes deduced from these three proportion systems, to create harmonious architecture in high and folk architecture. HALE again:
"To explore the regulating lines in a building is to delve into the guiding thoughts, the connections, the happy coincidences, that make up its design, for these lines organize the geometry of forms. The lines are usually, but not always, hidden; they may come to the surface in gables … or elements" (ibid., 45).
"The regulating lines merely connect the parts; to read them is not to solve the mystery but to be presented with more and more mysteries. We are all well equipped with an unconscious … ability to recognize such relationships and to figure them out during the design process. …
The most common type of regulating lines is the diagonal connecting key points on a rectangle. The eye relates any element placed along that line to whole even if the line is invisible … Lines parallel to it might become the roof slope. The roofline, carried through space to the ground beyond the building, might determine the location of a gate or an outbuilding, or it might point to a natural object such as a boulder.
From any point on the diagonal, lines parallel to the sides of the rectangle create two new rectangles of the same shape. For shapes to relate to one another, at least three key points have to fall on the regulating lines. One of those points may be the invisible centre of the overall shape." (HALE, 45-48).
"Analysis of regulating lines can be useful to one's own work when some part of the design doesn't seem to fit." (ibid, 52)
In my opinion, regulating lines and circles can be extremely useful at any stage of the design procedure to produce beauty and magic in architecture. This doesn’t depend on mimicry or imitation but on a creative play with new forms.
The architectural proportion system of triangulation was used very often in vernacular architecture, e.g. of New England, different parts of Europe and, of course, in the Gothic period for religious architecture and town houses. Here one can see that whole areas of folk architecture follow similar proportion codes and the same proportion system.
The procedure with regulating lines can be done with all proportion systems and codes. Quadrature proportions often radiate the impression of calmness, prosperity, and overall satisfaction with life. Quadrature can be found in much of the vernacular architecture in the countryside and towns of the German speaking Switzerland. I will show you some of these houses, many of them are proportioned into the regulating lines of a standing square. The sophisticated beauty of these houses cannot be praised enough. The basic figure of a standing square could be found also in New England's salt-boxes. Here are some examples of Swiss farm and rural storage buildings. In the greater South-Alemannian territories, e.g. in western Austria and adjacent German territories, vernacular architecture with laying squares - like in Swiss towns - is still existent.
Other Quadrature folk architecture exists in many West-Slavic territories and in Frisia.
The Quinture, based on the pentagon and pentagram, is the proportion of the Golden Mean. It appears to be the proportion of mystery. I still cannot explain on the base of scientific argumentation why the Golden Mean seems to be more beautiful than other proportions. It would, however, be wrong to assume that the Golden Mean is the only proportion system that is capable of adding aesthetic value.
The pentagon and pentagram were the great secrets of the Pythagoreans. Luca PACIOLI called it "Divina Proportione" (Divine Proportion). If you know HAMBIDGE's "Dynamic Symmetry" (1920), e.g. his proportion analyses of Greek vases, you will be easily convinced of the beauty of Golden Section.
There are riddles of math, enigmas of nature, and mysteries of cultural traditions surrounding the quinture, pentagon, pentagram, and pentacle. I treat quinture proportions in the same way as the other two systems of proportion. I have many ideas why Golden Mean may be something that is peculiarly beautiful, but I have no proof at this time.
Quinture proportions can be found in most ancient Egyptian pyramids, in Greek architecture, Renaissance architecture and in many house types of European vernacular architecture. Interestingly, the direct contrast between the mentioned German-Swiss quadrature houses and the quinture houses of Suisse Romande has a very impressive effect on every sensitive beholder.