SALINGAROS, N. A. (1995). The Laws of Architecture From a Physicist’s Perspective

Nikos A. Salingaros (1995) The Laws of Architecture From a Physicist's Perspective

(SALINGAROS, 1995)

Abstract

Three laws of architectural order are obtained by analogy from basic physical principles. They apply to both natural and man-made structures. These laws may be used to create buildings that match the emotional comfort and beauty of the world's great historical buildings. The laws are consistent with Classical, Byzantine, Gothic, Islamic, Eastern, and Art Nouveau architectures; but not with the modernist architectural forms of the past seventy years. It seems that modernist twentieth-century architecture intentionally contradicts all other architectures in actually preventing structural order.

1. INTRODUCTION

Architecture is an expression and application of geometrical order. One would expect the subject to be described by mathematics and physics, but it is not. There is no accepted formulation of how order is achieved in architecture. Considering that architecture affects mankind through the built environment more directly than any other discipline, our ignorance of the actual mechanism is surprising. We have concentrated on understanding natural inanimate and biological structures, but not the systematic patterns reflected in our own constructions.

(…) This set of empirical rules has been analysed and collected in the Pattern Language of Alexander.

The laws can be applied to classify architectural styles in a way that has not been done before (Section 4). Whereas most traditional architectures follow the three laws, modernist buildings do the opposite of what the three laws say. This result categorizes traditional and modernist architectures into two separate groups. It appears that all buildings are created by a systematic application of the same three laws, whether in following them or in opposing them.

(…)

Rules that are genuinely independent of any specific culture and time can be derived by approaching architecture as a physics problem.

(…) very different buildings and objects are seen as beautiful by most people today, who live outside the time and culture that produced them. This implies the existence of universal laws governing structural order.

(…)

Modernist buildings are perceived as unpleasant by many people (…) Public reaction against modernism has been noted before (…)

3. THE THREE LAWS OF ARCHITECTURE

1.       Order on the smallest scale is established by paired contrasting elements, existing in a balanced visual tension.

2.       Large-scale order occurs when every element relates to every other element at a distance in a way that reduces the entropy.

3.       The small scale is connected to the large scale through a linked hierarchy of intermediate scales with scaling factor approximately equal to e = 2.718.

3.1   Order on the Small Scale

(…)
The smallest scale consists of paired elements with the opposite characteristics bound together. Coupling keeps opposites close to each other but does not allow them to overlap, because they would mutually annihilate; this creates a dynamic tension.

(…)
We now apply this concept to architecture. "Order on the smallest scale is established by paired contrasting elements, existing in a balanced visual tension". There are several ways to achieve contrast with materials: shape (convex-concave); direction (zig-zags); color hue; and color value (black-white). Local contrast identifies the smallest scale in a building, thus establishing the fundamental level of geometrical order. The scale is relevant to the observer - in regions where a person walks or sits or works, contrast and tension are needed at the smallest perceivable detail; in areas far from human activity, the scale is necessarily much larger.

Structural order is a phenomenon that obeys its own laws. Its fundamental building blocks are the smallest perceivable differentiations of color and geometry. Whereas visible differentiation on the small scale is not necessary to define structure, it is necessary for structural order. This is demonstrated in architecture and in most objects made before the twentieth century. Classical Greek temples have marvellous contrasting details. This was also true of color, but the original coloration has been lost with time.

(…)

There are several important consequences of the first law.

Basic elements, like elementary physical components, have to be simple. That means that the fundamental units are simple in shape, for example, triangles, squares, and their combinations.

Basic units are held together by a short-range force. The only way to do this using geometry is to have interlocking units with opposite characteristics.

The smallest units occur in contrasting pairs, like fermions. When these pairs of units repeat, the repetition is not of a single unit, but of a pair, leading to alternation rather than simple repetition.

The contrast concept recurs on different scales, thus actually preventing detail from filling all the space. A region of detail will need to contrast with a plainer region, and the two regions combine to form a contrasting pair. In the same way, roughly built areas are necessary to complement those areas built with a very fine finish.

3.2 Order on the Large Scale

In physics, when noninteracting objects are juxtaposed, nothing happens. An interaction induces a rearrangement that leads to higher order for the large-scale structure, and therefore to a reduction of the entropy. The process could be as complex as the growth in a crystal lattice, or as simple as the alignement of compass needles.

One consequence of organization is that similarities appear between different subregions. This has to be mimicked in architecture and used to tie the small-scale structures together into a harmonious whole. "Large-scale order occurs when every element relates to every other element at a distance in a way that reduces the entropy". This basic prescription suffices to generate large-scale order in both color and geometry. Mimicking a long-range interaction determines the orientation and similarity of spatially separated units.

Thermodynamic entropy relates different arrangements of the same number of particles according to their probability of occurring. Entropy applies to structural order in a slightly different way, because it relates different states with the same number of basic contrasting units. Architectural order is inversely proportional to the entropy of a fixed number of interacting structural components. The entropy of a design could be lowered by reducing the local contrasts, but this also reduces the structural order - that would be analogous to eliminating the molecules in a gas.

The consequences of the second law are the distinct ways in which global order is achieved.

Large-scale ordering arranges the basic units into highly symmetric combinations. As in crystallization, the global entropy is lowered by raising the local symmetries. The smaller scales are therefore characterized by a high degree of symmetry, which is not required of the large scales, however.

Order is also achieved by having units on a common grid, taking the cue from crystal lattices. Continuity of patterns across structural transitions raises the degree of connectivity.

In the absence of a physical force between areas, visual similarity connects two design elements through common colors, shapes, and sizes. Global harmony represents the opposite effect from local contrast.

Insisting on "purity" can destroy the connection process, because connections may be misinterpreted as impurities and eliminated. Therefore, imperfections are both useful and necessary; just as in a doped crystal, where impurities enhance the structure.

The second law makes it easier to understand the visual interaction of two objects placed near each other, well known from optical illusions. The brain creates connecting lines that appear to tie two units together. Now, if we take two objects, draw the virtual connections that we see on paper, then construct them from some material, the resulting structure will hold together against stresses. This establishes a physical relevance for a strictly visual phenomenon. It appears that the brain "sees" the proper physical connections for a stable structure.

The entropy of a design is perceived by our innate ability to visualize connections. The main spaces of any building, and their relation to each other, are governed by the mutual interaction of all the walls and any other structural elements. Certain dimensions, certain combinations, will appear to "resonate" when all components interact harmoniously. These correspond to the states of least entropy. Making adjustments to a complex structure so as to lower its entropy conforms precisely to the process that gives rise to natural forms.

3.3 The Natural Hierarchy of Scales

The third law of architecture is based on the idea of similarity and scaling. "The small scale is connected to the large scale through a linked hierarchy of intermediate scales with scaling factor approximately equal to e = 2.718". Surfaces interact; they define subdivisions; all that one has to do is to create structures at the appropriate scales, and link them together. The different scales have to be close enough so that they can relate, and the linking is accomplished through structural similarities.

The physical reasoning is that material forces are manifested differently on different scales. The shape of natural structures is influenced by stresses, strains, and fractures in solids, and by turbulence in moving fluids. Matter is not uniform: it looks totally different if magnified by a factor of 10 or more. We want the scaling factor for which two distinct scales are still related empirically, this factor is around 3. In fractal geometry, the Koch, Peano, and Cantor self-similar fractal patterns that most closely resemble natural objects have similarity ratio r = 1/3 or r = 1/7^1/2 = 1/2.65 , supporting the scaling factor 1/r = 2.7.

These arguments may appear totally heuristic, and yet they reveal a basic phenomenon best seen in biological structures. The secret of biological growth is scaling, either via a Fibonacci series, or an exponential series. Ordered growth is possible only if there is a simple scaling so that the basic replication process can be repeated to create structure on different levels. Thus, different structural scales must exist, and they must be related, preferably by only one parameter. The exponential scaling factor e fits both natural and man-made structures.

Take one view of a building as a two-dimensional design. Then decide whether to measure areas, or linear dimensions, depending on the situation. Different substructures of roughly the same size will group themselves into distinct sets of measurements. The number of different scales will be denoted by N. Call the maximum scale x_max and the minimum perceivable scale x_min . An ideal structure will have n sets of subunits with sizes corresponding to every element of the following sequence:

{x_min, ex_min, e2x_min, ..., e^n-1x_min = x_max }.

(1)

Solving the last term of the sequence (1) for n relates the ideal number of scales n to the smallest and largest measurements (in the same units). We have,

n = 1 + lnx_max - lnx_min

(2)

where n is the nearest integer value. One measure of structural order is how close the theoretical index n (2) comes to the number N of distinct scales in a structure. This rule measures only if the hierarchical scaling exists; it does not determine whether similarities actually link the different scales together.

For example, a three-storey building with 1-in. (2.5-cm) detail requires n to be about 7. In many modernist buildings, however, N is nearer 2, regardless of size, because there are intentionally no structures in the intermediate scales. Modernist buildings are "pure", meaning that they have large empty surfaces. On the other hand, some postmodernist buildings with unorganized structures of many different sizes might have N higher than n. A building with a natural hierarchy of scales, regardless of what it looks like, should have N very close to the theoretical index n.

There are several consequences of the third law.

Every unit will be embedded into a larger unit of the next scale in size. This naturally leads to a very wide boundary for each object in a design. The whole design is a hierarchy of wide boundaries within other boundaries.

As already mentioned, similarity of shape should link the different scales together; for example, the same curve or pattern repeated at different sizes.

The different scales can collaborate to define a gradient through similar shapes of decreasing size. Each building requires an entrance gradient as well as other functional gradients, and these succeed only when they correspond to structural gradients.

A building must be placed into the environment in a way that fits the existing hierarchy of scales. The surrounding nature and other buildings will then define the largest scales of the ensemble.

The wide-boundary principle (1) states that an interacting object has a boundary of similar size as the object itself. For example, a square embedded symmetrically in another square has a ratio of areas A₂/ A₁ = e . This gives a ratio of the width of the border to the width of the smaller square as w/x₁ = (e^1/2-1)/2 = 0.32. One illustration comes from physics. The magnetic field around a spherical dipole magnet of radius R goes out to infinity, yet the effective region of field is comparable to the size of the magnet. The field strength along the axis falls to 1/10 of its surface value at 2.15R , giving the thickness of field as 0.58 times the magnet's diameter.

4.       A CLASSIFICATION OF ARCHITECTURAL STYLES

We can classify all architectural styles into two groups: natural and modernist. This classification is based on whether they follow or oppose the three laws of structural order and has nothing to do with the age of the buildings. Many people have always instinctively separated modernist from traditional buildings, but, without a set of written rules, there was never a systematic way of doing this.

5. THE UNNATURALNESS OF CONTEMPORARY BUILDINGS

This section discusses two criteria for choosing between natural and modernist architectures: (1) the emotional response to a building; and (2) the deeper connection between architectural order and nature.

5.1 The Emotional Basis of Architecture

Successful buildings have one overriding quality: they feel natural and comfortable. Man connects with his surroundings on the small scale and needs to feel reassured about any large-scale structure. There is a built-in human reaction to threats from the environment, and structures threaten our primeval sense of security when they appear unnatural. A building, regardless of shape or use, is perceived as beautiful when an emotional link is established with the structural order. This is independent of opinion and fashion.

(…) Man relates to the detail in a design or structure immediately, because the connection to the small scale is emotional. By contrast, perceiving the overall form often requires some thought, which is a more intellectual process. According to the three laws of structural order, our connection to architecture occurs via the smallest scale, through the intermediate scales, and finally to the large scale - and is successful only if all the scales are connected.

5.2 Uniqueness of Structural Order

(…) man can visualize connections intuitively. This innate ability has enabled humans to develop architecture early in the evolution of mankind. The mind establishes patterns and connections not only between objects, but also between ideas and concepts.

SALINGAROS, N. A. (1995). The Laws of Architecture From a Physicist’s Perspective. Recuperado el 3 de junio de 2018, a partir de http://web.archive.org/web/19970428105136/http://www.math.utsa.edu:80/sphere/salingar/Laws.html#CONCLUSION