The “Inverse Design problem”

In Medieval Wooden Churches of Norway

Jørgen H. Jensenius. At the 6^th^ Asian Design International Conference in Tsukuba, Japan, 14-17 October 2003.


  1. Approach

1.1 Background

There are archaeological remains of a 30-odd early wooden churches in Norway, and 28 stave churches, dating from c. 1130 CE and onwards, are left standing. As a building archaeologist I study the history of the standing buildings and building remains in the ground. The research methodology is based on direct observations, survey and description; the primary sources of evidence are selected measurements. This paper ** discusses the “inverse design problem” of reconstructing a first planning principle: Is it possible to verify alleged original intrinsic design ** systems in medieval churches? The paper develops the conclusions of my thesis from 2001 [1].     

1.2. Research

Applied mathematics may be regarded as design theory of size and shape. The modern researcher ** has his/her knowledge from the building remains of today; no literary descriptions are left. In the course of surveying the stave churches, we have come across incised lines, notches and other marks that may have been put on the timbers to guide the builders during the subsequent assembly work. Attention to measurements and ratios was obviously essential to ensuring a sound construction. The task of the building archaeologist is quite opposite; he/she has to compute the floor area and the volume of a church. With this interpreted documentation it is possible to put equal elements in groups, to adjust the measurements found within acceptable limits. The measurements thus found are then used in a search for ratios in elements connected to each other. At the end this procedure can lead to a possible overall geometrical figure, or set of figures. There may be made several “best-fit” figures on any plan and elevation, they may be “best-fit” but it is difficult to prove that one of them actually was the original ratio and figure thought by the builder. The options are contingent on different materials, static necessities, economy, Biblical symbolism, sub-Euclidean geometry and local building traditions. Often researchers did not discuss different options, just selected and developed one more or less arbitrary “best-fit” solution for the hypothetical original intrinsic design of medieval churches. One may also ask if churches in Norway were copied accurately from specific, topographically identified churches, or if they are paraphrases of types of churches. With all the uncertainties the discussion of the genesis of the wooden churches is far from concluded. In my doctoral thesis I identified and described some 30-odd Norwegian wooden churches which pre-date the year 1100 [2]. I did deconstruct the notion of form of the buildings into a series of constructional actions and ritual ceremonies to reconstruct the process and result of planning and design.

  1. Historical setting

2.1 Transference of Christianity

Christianity arose ** and developed in countries bordering the Mediterranean, where clay or stone were the principal building materials. In the New Testament there are no rules for how to make a Christian place of worship, and in the Middle East no normative type of church building seems to have been preferred in the early period of Christianity [3]. Description of various elements may be found normatively documented through records of patronage, the choreography of liturgies and the placement and programme of decoration [4]. In the East churches copied synagogues, in the West private homes or civic buildings may have been the prototype.  In the Southern Europe pagan temples may have been renovated and consecrated as churches, but in Northern Europe pagan temples may have been unfit, if there were temple buildings at all.

2.2. Prototypes

The early missionaries who worked to spread the Gospel in Northern Europe encountered a wide range of building styles, but common to them all was the use of wood, and the first churches in most of the newly converted territories were therefore built of this material. The missionaries brought with them the features, practices and traditions of their own background. They may also have tried to introduce architectural elements of an imaginary or real tradition, like descriptions of the Temple in Jerusalem or St. Peters’ in Rome. To what extent this was a formulated program of design is not known. There must have been many wooden churches in Northern Europe in the early Middle Ages but these buildings have left very few traces [5]. As a result not much is known about them, not even how long they lasted. In any event the Church had no normative policy in church building; the control of new churches was obviously left to the decision of the local bishops. Wood or stone, with or without aisles, large or small, opulent or simple, these were matters for the individual community to decide. It is to be assumed that the churches were built mainly as copies of older buildings. Symbolic explanations were added or deduced from the finished buildings for reasons of exegesis. When copying the next time, the building could be slightly changed due to the new symbolism. There was a migration of the iconic image of the Holy Sepulchre, pictorial representations showing this and other buildings are well known in the Middle Ages. Such pictures include both real and imaginary concepts of Jerusalem and of well-known churches. They are descriptions with varying degree of accuracy, but at their best, they may provide valuable information about structural systems. Among medieval models are the ones held by the donors, patrons or saints. The form and construction of these models may be very general [6].

2.3 The church building

The transferring of ideas of architecture may have been a minor part of the Christian mission to Norway, but it may have been a strong wish to enhance the idea of universality of the Church through the architectural tradition as well. Acceptance of Christianity by the Norwegians was not simply a matter of confessional change, of dogma, or of religious belief and observance. The diffusion of a Roman ethnocentricity brought Mediterranean customs and values, and habits of thought to Northern Europe. The means for this was literature, books and the Latin language in addition to Roman notions about liturgy, law, authority, property and government, even if it was brought via England or Germany. ** As far as we know, the Church generally wanted churches to be built anew. There were probably no norms for size, material or form of church buildings ever given by the ecclesial authorities. A wooden church was undoubtedly expected to have certain properties, characteristics or qualities different from vernacular buildings. Churches consist of elements adjusted to function and use, defined in a European ecclesial tradition. The Christian mystery is to the Eucharist, and not to the volume created around the place of worship. The function of a church is its use, and the main use of a church, is the liturgical practice. This practice requires room for movement and action. The Divine Service was not centred on a cult object and did not need a special altar.

  1. Transference of design/knowledge of form

3.1 Copying of prototypes

It seems that the responsibility of bishops and people in the local church was emphasized: to build in the vernacular tradition, with inspiration of prototypes from elsewhere. The ecclesial prescriptions seem to admonish that a designer work from principles, not just from paradigmatic forms. Following the same string of thought, the essence of this early, wooden architecture must be the detailed, technical knowledge of the way the building was planned, designed and put together. All buildings are the result of a planning and design process, however modest the construction may seem, and however unrecognized such a process was by the people it involved. In the ecclesial tradition the normative seems to have been laying in the copying of churches from abroad, certain prototypes were seen as norms. But even without written codes or norms, unspoken traditions may have been influential in planning and design of churches. The number of variations seems without end, not two churches seem to be replicas of one another [7].

Transference of knowledge of form from one country to another must have happened with the travelling of craftsmen. This travelling may have been of two kinds: Norwegian craftsmen visiting building sites in other countries, or craftsmen hired from abroad. In the first place, the Norwegian craftsmen would experience, learn and remember; they would bring back home new ideas. In the second place, one could also expect vernacular practices from another country transferred to Norwegian soil. In addition, the sort of order the craftsmen had received is important. On the one hand, he could have been told to copy a prototype; on the other hand, the specifications could have been rather general, just with the main characteristics of a church.

3.2. Travelling craftspeople

Norse traders, ** raiders and mercenaries must have become acquainted with Christianity in the 8^th^ and 9^th^ centuries, if not earlier. Nordic chieftains who settled temporarily in the Viking territories of Western Europe may have allowed themselves and their followers to be baptized as a part of their stay. The first wooden churches in Denmark were erected in the towns of Slesvig and Ribe, following the establishment of the archaepiscopal see of Hamburg in 831. So, even before the arrival of the first missionaries in Scandinavia, Norse craftsmen travelling abroad may have become acquainted with how to plan, design and construct churches. Many of these early churches were of wood and the principal load-bearing elements consisted of earth-bound posts. In the early 12^th^ century, the most common way of building wooden churches in Norway was with the posts/staves on low foundations of stone. The early wooden churches of Norway may have been built by the kings, the nobility, gentry and others encouraged by the kings and the missionaries. Broadly speaking, three parties were involved in planning, design and construction, namely the bishop, the patron and the craftsmen. The bishop represented the tradition of the international Church; the patron was responsible for ensuring that sufficient funds were available, while the craftsman with his knowledge discussed the possible solutions with the two others. They would then have an over all expression of church form, but would be recognizable Norwegian in its materials, construction, joining and treatments of details [8].

3.3. Planning

The craftsman had to start his construction at the bottom without being able to modify what was built in the light of what followed. So mistakes done at the very beginning, for example in setting out, might have been difficult to correct; one had to deal with these problems for the rest of the construction work. Buildings had to be dimensioned to be built. Therefore, the craftsman had to have a plan before starting up, techniques that would allow him to visualize on beforehand, to assure that all elements would be there, and that they could adapt to each other. The craft lore of the carpenter may have been obtained by long time of practical training, at the guidance of a master. This perceptual knowledge may hardly be describable and cannot be learned from theory alone. Form and material are largely interdependent; by experience is found that some solutions are better than others. Rules of ratios and proportion were formulated so that appropriate size for each element could be devised from a dimension already decided. These rules may have been important in formal as well as technical matters. Such rules may have been the main way of recording and systematise a design. They may have been remembered by being formulated systematically into rules (what, how, when). Some of these rules may have been the organising of lengths, areas and volumes, and may have helped to solve problems of setting out, dimensioning, proportioning and measuring each element and the whole, and help the carpenter answer the questions of how to articulate surfaces and formulate space. The rules may have been the easiest way of transmitting good and accepted norms over a large area of space and time [9].

3.4. Old methods

Craftsmen apprenticed into a building tradition in Norway could combine another building tradition with their own vernacular when returning from foreign lands. To design a new church they had to combine the memory of a church somewhere else to their vernacular way of building; they glued new knowledge of form into existing knowledge. The carpenter had to find a scheme, or schemes, that had a given floor area and height, as a combination of economy, requirement, topography, climate, construction, materials, traditions, prototypes and aesthetics. This had no particular answer; each craftsman would give an answer bearing his own distinctive signature of the local tradition. The tradition represented the sum of the knowledge acquired by generations of builders before him. He was therefore duty-bound to follow the old methods and to copy the old forms, and tradition ensured that practices of proven worth were handed down to succeeding generations of craftsmen. They all had to work different techniques out by trial-and-error, to adjust the necessary, the economic, the practical and the beautiful to easy remembered and easy executed rules of thumbs. If the builder wanted a church similar to another, the rules of ratios would also have to be similar to the prototype. Even one length taken from another church may have been accepted as a “copy” [10].

Planning praxis, design rules and construction techniques may have been sufficiently extensive and detailed as to require a conceptual framing, linking non-written praxis and written theories. Medieval craftsmen insisted that their whole craft was based on the “art and science of geometry”, but the prescriptions were not occupied with the mathematical side of geometry or arithmetic. The term geometry, as well as the content, varied through the centuries, from any practical rule of the craft, to the most theoretical at the universities [11]. Such a practical geometry is not simply an application of the theoretical work of Euclid; rather it is based on reflective thoughts on form, size, technique and constructions. Until proven otherwise, one may suppose that rules for planning and design of wooden architecture in Northern Europe were transmitted by word of mouth entirely, with simple means of memory; no design manuals are left. If the form, size or appearance was judged unsatisfactorily, one had to change the elements and construction and thereby the rules [12].

3.5. Norms in planning

However, in the praxis of planning, design and construction process one may presume there were both general and detailed norms regulating the design and construction of medieval wooden churches, concrete, contextualised descriptions communicating fundamental aspects of the construction. But for us there are no historical oral mnemonics available for study, except what can be interpreted from the building remains. For the craftsmen knowledge of form was the means; while utility and economy were the ends. In most cases, there were not many options for what form the design of a church should take, the plan and elevation was in its basis a pragmatic labour of craft. Churches were copied selectively by imitating sequences of actions and were adapted to vernacular materials and economies. In this interrelationship between thought and action the individual craftsman did the remembering, but all memories were attached to membership of the social group of builders. Systematic thinking on knowledge of form was transferred through the ages as a “living” narrative text, with intervention, developments and change by different craftsmen at different times.

3.6. Practical geometry

Some contemporary texts describe design procedures vaguely as “the right way” of proceeding [13]. If geometry can be regarded as design theory of size and shape, “the right way” may have included transference of numbers, ratios and geometry as scalable standards of accuracy. Churches were not designed by geometry; rather geometry was adapted to any successful construction. The geometry of the carpenters may therefore have been arbitrary in terms of mathematical or logical reasoning. It was not connected to a philosophical rationalisation of its procedures, but it must have been clear for those involved what the right and wrong ways of doing things were. Such knowledge of technique is more than can be expressed in writing, and what can be written down is not more than that which can be quantified. Much of this knowledge is undercurrent, the planning, design and building techniques were requisite codes of materials and scalable standards of accuracy. This was based on the builders’ experience memorised as steps of action and not put forward by an authority. To follow these steps carefully would guarantee that the final result would look like a prototype. One could say that the builders practiced their crafts scientifically, by empirical testing of different hypotheses for solutions in design and construction. Since this was not registered, written down and elaborated methodologically it could not be called a theory proper; but it may be called an architectural sub-theory. Obviously, such a narrative undercurrent of the builders had to be rejected by scholarly discourse. Planning, designing and constructing churches were not ideological or theological actions, but a series of methods of manipulating and systematize the materials.

  1. Searching for original principles of design

4.1 Design principles in Norwegian churches

Medieval church design remains elusive. Despite more than 160 years of descriptions of Norwegian wooden churches, no modern theory satisfactorily accounts for the reproducibility of design intentions. There is a potential knowledge in the reconstruction of the chain of decisions taken in the original process of planning and designing of the churches. In Norway round the year 1000, a small, rectangular plan with earthfast posts seems to have been common for a church, the buildings copying features of prototypes locally and elsewhere. The form of the simple church plan is highly predictable, from the beginning the morphology of the churches was governed by conventions. There are four basic stages to the study of wooden churches from a historiographic perspective: The first step is a consideration of historiography and history as they apply to medieval church architecture. The second step is description, this is important since architecture is contextually bound to particular political and power situations and to economics and technological stages. The third step is a discussion about the building remains or the buildings proper. Finally, the fourth step is the discussion of methodological problems involved in the reconstruction of any original design. The reconstruction of theories of church design can only be inferred from the evidence of the buildings themselves, by employing a direct, empirical and inductive approach.

4.2. Best-fit

One may ask if this type of research is discovering or creating a supposed design scheme. To answer this, it was argued in my dissertation that some of the investigated church plans share ratios of lengths and geometrical figures; clearly intrinsic design as variants of a common systematic way of thinking [14]. However, although many of the churches are superficially alike, they display a huge variety of measurements and ratios. Different “best-fit” possible solutions for the plans are shown, and it is concluded that it is not possible from these results to tell what the design intentions of the builder were. 

To search for a Vitruvian tradition in North European wooden architecture may be in vain, the proposals of Vitruvius were bound to a Mediterranean stone tradition [15]. The idea that the vitruvian aesthetics is part of a universal law may have been a late invention by scholars. It may be surmised that craftsmen working with their mnemonic sub-theories on wooden churches in Norway would look upon their own rules and canons as normative and timeless, maybe “timeless principles” were ideas beyond the practical craft. The notions centre and periphery must be defined in a relative way. Often the largest church in the city is assumed to be a prototype. Elements and forms are described as percolating out to rural communities from this building. For a local church in Norway, the bishop’s town comprised a centre; for Norway, Hamburg or Aachen constituted centres; and for Hamburg, Rome and Jerusalem were in turn centres. The paths of influence may have been more complicated. Obviously, there must have been a variety in terms of planning, design and building, both through the ages, from team to team and from place to place. The prototypes were different, the local conditions changed and craft practices developed. Small changes in numbers, ratios or geometrical forms would produce noticeable differences in the final design product. In this way one attained the variety that is the hallmark of medieval design.

4.3. Norwegian churches

What has emerged is that Norway’s medieval wooden churches have a number of features in common, even though they may differ in many respects. Most scholars have used an approach that involves describing and comparing the buildings’ stylistic and structural features. It has been shown that medieval scholars as mediators of ideas pointing beyond the form of existing buildings, provided analogies which were devoid of fundamental information for the craftsmen. The prescribed way of writing was not written at the level of execution, but at the level of generalisation. However, the craftsmen who acted as mediators of practical work used oral and tangibly transferred knowledge of form. Their sub-theory did not require written discourses to initiate, fund, plan, design, construct and develop the buildings that were required [16].

  1. Conclusion

The paper presents the inverse design problem in a research situation, exemplified by research in the medieval wooden churches of Norway. It has been discussed how it can be possible to come closer to the original design. The building researcher has to solve the problem by extrapolating from the existing solution to several possible options, searching for the original principles of planning and design. Even if this problem may not have a solution in a strict mathematical sense, my research has shown that it may be possible to find lengths and ratios which explain much of the original design. The probability of one selected option to another has to be discussed and evaluated before one elaborates a hypothetical design system.


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  8. as [1] 115.
  9. as [1] 117-118.
  10. as [6].
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  14. as [1] 89-194.
  15. Vitruvius. Ten Books on Architecture. Rowland ID. and Howe TN. Cambridge University Press, Cambridge (1999).
  16. as [1] 119.