Beauty and Architecture A model on proportions by Dom Hans van der Laan
Architecture should fullfill three principles according to Vitruvius: firmitatis, utilitatis and venustatis.  These terms mean durability or strength, utility and beauty. While for the first two one can imagine the principles and models that can be used to solve an architectural design, the last one seems rather subjective. Though over time much theories about beauty where formed and some of them actually applied as a tool in architectural design. Perhaps the most famous one in modern architecture is the modulor, by Le Corbusier, describing a numberic model based on the golden ratio and proportions in the human body. This system was much criticized and does not form a complete solution to the problem of creating beauty in Architecture. A less known principle, which I will discuss here, is the plastic number, by Dom Hans van der Laan. We will see that this is like Corbusier’s modulor a model derived from proportions in nature that could be used to design beauty. Dom Hans van der Laan was a Dutch architect who lived from 1904 to 1991. As a kid he always had been obsessed by nature as a kid, but found that a study in biology had nothing in common with his interests. “I never knew the names of plants or birds. What I saw ... was great trees, shrubs, flowers, moss – the rhythm of things: that is what interested me.”  He started a study Architecture in Delft, but withdrew in 1927 to a monastery in Vaals. He kept studying nature and the order of the world there and also practiced architecture in his spare time. One of the most important buildings he made was the extension to the abbey St. Benedictus in Vaals.
Extension Benedictus abbey Source: http://rempei.web.infoseek.co.jp/photo/syasin/laan/laan2.jpg
Dom Hans van der Laan’s life ran parallel with but independent from the modern movement. In modernism there was a search for a source and an origin to begin anew. For Dom Hans van der Laan Architecture was the reconciliation of man and nature and it is not just a
shelter: “this first objective of house-building, purely bodily in nature, is not sufficient, either from the point of view of the person who must live in the house, or with respect to the natural environment in which it is placed. The natural order is disrupted ... when the form of the house we place in it is not governed by an artistic order that comes from the intellect.”  Dom Hans van der Laan wants his buildings to have a link with the nature that surrounds them. For this he is looking for an order in nature which he can resound with his designs. Architecture is for him the solution on the conflict between man and nature, like the shoe is between our feet and the ground. This idea of the artist that is making a reflection of nature can be traced back to St Thomas Aquinas, who wrote in De Veritate: “Our intellect receives knowledge from natural things, and is measured by them; but they are measured in turn by the define intellect, which contains all created things in the same way that artefacts are contained in the mind of the artist. Therefore the divine intellect measures, but is not measured; natural things both measure and are measured; and our intellect is measured, but does not measure natural things, only artificial ones.”  This is based on the assumption that the whole world is based on a define being, God, that gives everything on this planet its meaning and consistency. For Dom Hans van der Laan God also is the model for nature, which we have to adapt to in Architecture. This gives him the idea that there is a consistency in nature which could be discovered and understood. In fact there where many scientists and artists in history that studied nature and its beauty in order to be able to create beauty. One of the fields in which these studies play an important role in contemporary science is for instance plastic surgery, which studies beauty of the human body. Here the increase of procedures in healthcare for facial and body contour aesthetic procedures raises the question how the beauty of the final ‘product’ can be defined. “In contemporary society, the media are largely responsible for providing universal yardsticks against which individual faces and body shapes are measured.” The exposure of a selection of individuals seems to create a model that determines the image of beauty for the masses. It is suggested that this beauty can be expressed as ideal proportions that can be described in numberic relations. From the 1960’s the interest in the Golden Number phi (0.618033988), derived from the Fibonacci sequence, was revived. This resulted for the field of plastic surgery in the Marquardt mask, a model that is entirely based on the number phi and based on other studies to ideal proportions in the human face.  It seems that there is a primitive and inborn psychological effect that creates a positive response to people that have the phi based proportions in their face and body.
Maquardt mask applied om women of different races Source: http://library.thinkquest.org/trio/TTQ05063/phibeauty1.htm
The idea of expressing beauty in numeric relations is not new: “The very same idea was already suggested in antiquity by Pythagoras who maintained the idea that mathematics underlies all and serves as the basis of beauty.”  Pythagoras was obviously convinced that there was an order behind the beauty of the visible world that could be understood and expressed in numbers. Plato’s Timaeus even claimed that within the properties of numbers themselves, the essence of the universe could be found, and aesthetics is seen as a branch of this numeric cosmology.”  This goes even further and suggests a model behind all processes in the universe that also underlies beauty of the visible world. These ideas where actually practiced in the ancient world “The Egyptians and Greek were known to use body measurements of good looking individuals to create their sculptures and paintings.”  The Egyptians used a model that divided the body figure in 22 ¼ parts from top to bottom, but their system did not include marks as knees and nipples. The greek used a system that described the proportions of the human body and by which for instance the famous Doryphorous statue was sculpted. In the Renaissance these originally Greek canons of proportion were formulated and documented by scholars and artists such as Durer, Alberti, Francesca, Cennini, Savonarla, Pacioli, and da Vinci.  According to the modern definition of beauty in the human race is “excelling in grace or form, charm or colouring, qualities which delight the eye and call forth that admiration of the human face in figure or other objects.”  It is the observer who appreciates the person that is looked at. This observer recognizes beauty with his minds eye, bound by culture, knowledge and personal history. As suggested we get used to a certain form that we see a lot, in case of faces nowadays through mass media. However: “Recent research shows however that beauty in human faces can exist independent from these boundaries and regardless of age, sex, race and other variables.”  This means that there is something as objective beauty which is appreciated by every human. And: “Faces judged to be very attractive in one society are judged to be equally attractive in other societies”  “The general body of facial attractiveness research has shown that subjective attractiveness represents only a thin layer of personal preferences overlaid on a much larger and inevitable biologic objective assessment of attractiveness”  So for beauty and attraction between humans there seems to be an objective order that is recognized as beautiful to everyone. Only a small part of our feelings about persons seem to be based on personal preferences. This implies that there is a rule behind the beauty of these faces, a model that is equally appreciated by every human being. These studies to attraction to human faces and bodies thus can be described as a geometrical order, which can be understood and maybe even reconstructed. For Architecture Vitruvius once wrote "Symmetry is a proper agreement between the members of a work itself, and relation between the different parts and the whole general scheme, in accordance with a certain part selected as standard. Thus in the human body there is a kind of symmetrical harmony between the forearm, foot, palm, finger, and other small parts; and so it is with perfect buildings. [...] In case of temples symmetry may be calculated from the thickness of a column, from a triglyph, or even from a module [...]"  This means that the actual theory used in plastical surgery as described should be implied on the architecture of a temple, according to Vitruvius. Dom Hans van der Laan started studying proportions in old Dutch buildings like the Dom in Utrecht and a chapel in Baarle-Nassau. He was strengthened by his fascination for proportion and by the discovery of the golden section, through the Benedictine architect Dom Paul Bellot of Solesmes. In his studies he discovered that the golden section did not completely satisfied to analyse these buildings, expecially the tower of the chapel in BaarleNassau. “Dom Berrot’s golden section had the great disadvantage that a second division in that ratio produced a measure identical to the smaller part resulting from the first, and therefore gave no sufficient basis for a series of proportional relationships.” . Dom Hans
van der Laan saw this discovery not as something new, but as a rediscovery of fundamental human knowledge from ancient times. This is not unlikely as we saw the effort the ancient world made to catch the beauty of nature. Van der Laan did see this proportion system as the only theory that corresponds to the way we perceive space. Plastic Number ratios 1:1 7:8 3:4 2:3 4:7 1:2 3:7 3:8 1:3 2:7 1:4 3:14 3:16 1:6 1:7
Pythagorean ratios 1:1 unison 8:9 tone 3:4 fourth 2:3 fifth 9:16 two fourths 1:2 octave 4:9 two fifths 3:8 octave + fourth 1:3 octave + fifth 8:27 three fifths 1:4 two octaves 2:9 two octaves + tone 3:16 two octaves + fourth 1:6 three octaves 4:27 three octaves + tone
Source: Richard Padovan (1994) Dom Hans van der Laan – modern primitive, p90
In his book “The Plastic Number” Van der Laan quotes Vitruvius’ six fundamental principles on symmetry.  He is unique in using the second one: “There must be a direct relation between the whole or largest measure and an elementary part or module.” This is not used in the Modulor, nor in the Pythagorean system.  By using this principle he restricts the number of relations that can be made and in this way he deals with the problem of creating an endless and meaningless chain of measurements. In this way it creates more boundaries and can be less random. The system is about groupings of distinct sizes into types of size in order to solve the conflict between continuity and discretion in everyday life.  That is why this theory of Dom Hans van der Laan is not completely derived from nature -nature is not discrete-, but it is also not completely intellectual. It is an abstraction of the continuous values in nature in order to be able to create buildings with discrete measurements. This is based on the graduations that the eye is able to see: “For the eye that difference [in graduations] is about 1/50 of the size, but the formal difference, which enables us to recognize the distinct sizes and as it were name them, is much larger.”  This links our perception of beauty to the eye itself, which also works according to proportions found in nature. We end up with the notion that we are living as creatures formed by nature in the natural world that we are trying to analyze and we cannot objectively study these things. Though this does underline the importance of the values found in nature and abstracted by this system. The system of the plastic number is not yet a system to create beauty, but a system to create sizes that are related to each other in a natural way, a proportional system. It is an underlying principle that can be used in an attempt to create beauty. Beauty itself consists out of more than only proportion. Like the measurements of the Greek for the Doryphorous statue, the Plastic number creates limits the randomness for creating beauty, which does not guarantee that every man can now actually achieve this beauty in his creations. On the other hand
seems unlikely that an image of beauty can be achieved without the use of these proportions since there is something fundamental in man that influences our appreciation of object with these proportions. But in order to create beauty there are more systems that we will need to be understood than only the one of visible and grouped proportion. It is good to know that we reinvented some of the valuable knowledge of the ancients, but we will need to search further in our understanding of beauty in Architecture in order to be able to create the real architecture as Vitruvius defined it.
Literature: 1. D. Rowland - T.N. Howe: Vitruvius. Ten Books on Architecture. Cambridge University Press, Cambridge 1999 th 2. Van der Laan, transcription of a TV-interview, June 30 1988 3. Van der Laan, het plastische getal, p26 +118 + 136 4. Aquinas, Quaestones disputatae de veritate, p6 5. Marquardt’s Phi Mask, Aesthetic Plastic Surgery, Volume 32, Number 2 / March, 2008 6. Green CD (1995) All that glitters: A review of psychological research on the aesthetics of the golden section. Perception 8:937–968 7. McManus IC (1980) The aesthetics of simple figures. Br J Psycho l71:505–524 8. Vegter F, Hage J (2000) Clinical anthropometry and canons of the face in historical perspective. 1090–1096 9. Numeric Expression of Aesthetics and Beauty, Aesthetic Plastic Surgery, Volume 32, Number 2 / March, 2008 10. Eisenthal Y, Dror G, Ruppin E (2006) Facial attractiveness: Beauty and the machine. Neural Computat 18:119–142 11. Ishi H, Gyoba J, Kamachi M, Mukaida S, Akamatsu S (2004) Analyses of facial attractiveness on feminised and juvenilised faces. Perception 33:135–145 12. Bashour M (2006) History and current concepts in the analysis of facial attractiveness. Plast Reconstr Surg 118:741–756 13. Richard Padovan (1994) Dom Hans van der Laan – modern primitive, p87-104