建筑几何学︱由统一到变化

观察者收到的视觉信息中的链接越少，他付出的努力就越大。然后，建筑师引入一些结构，这些结构通过加强元素之间的关系来将元素分组。大多数城镇和建筑作品的特点是在特定于结构的层次结构中叠加了几个层次的组织。工作的兴趣程度并不在于使用这些方法或组织中的一个或另一个，而是这些方法的知识增加了我们对可用设计资源的意识和处理它们的技能。

The fewer links there are in the visual information the observer receives, the greater the effort he has to make. The architect, then, introduces structures which make it possible to group the elements by strengthening their relationships. Most towns and architectural works are characterized by several superimposed levels of organization in a hierarchy specific to the composition. The level of interest of a work does not lie so much in the use of one or other of these methods or organization, but the knowledge of these methods increases our consciousness of the design resources available and our skill in handling them.

肌理

当一个表面的各个部分足够接近、相似且数量众多时，眼睛就会感知到纹理，而不再将它们单独视为图形。通过类比，当同样的原理应用于空间中的物体或建筑物(例如森林，北非的麦地那，等等)时，我们可以谈论同质结构。因此，最基本的结构是简单地通过接近、重复、相似，有时通过元素的方向来创建的。

某些纹理有解体的危险，因为它们包含了太多的断裂和不规则(图46)。在以前的农业分区中随机排列的道路和建筑的引入常常是我们现代郊区混乱的根源。规则一旦确立就会被打破。织物没有机会被编织。我们是根据鸟瞰图来论证的，因为它们是可比较的文件。我们也可以观察到立面的纹理或立面的碎片。

The eye perceives texture when the parts of a surface are sufficiently close, similar and numerous that they are no longer seen individually as figures. By analogy we can talk about a homogeneous structure when the same principle is applied to objects or buildings in space (for example a forest, a medina in North Africa, etc.). The most elementary structure is thus created simply by proximity, repetition, similarity and, sometimes, by the orientation of the elements.

Certain textures are in danger of disintegrating because they contain too many breaks and irregularities (Figure 46). The introduction of roads and buildings on the random alignment of previous agricultural subdivisions is often the root cause of the confusion of our modern suburbs. No sooner is a rule established than it is broken. The fabric does not get its chance to be woven. We have based our argument on aerial views because they are comparable documents. We could just as well have observed the texture of façades or of fragments of façades.

渐变的韵律

在一个重复的结构中，如纹理或序列，间隔或元素可能会逐渐改变其形式、大小或方向。因此，层次结合了两个相互矛盾的特征:没有明显层次的关系和差异。在我们的环境中，渐变随处可见。很多大自然的元素都以这种方式结构。没有太多重视类比和人体之间的拉土雷特修道院。在自然中经常发现的渐变，然而，在建筑中很少使用。更有规律的节奏通常是首选的，因为显而易见的经济建设的方法。

In a repetitive structure like texture or series, the intervals or elements may gradually change their form, size or orientation. Gradation thus combines two contradictory characteristics: relationship and difference without a pronounced hierarchy . Gradation is found everywhere in our environment. Many of the elements of nature are structured in this way . Without attaching too much importance to an analogy between the human body and the façade of the Convent of La Tourette. Frequently found in nature, gradation is, however, little used in architecture. More regular rhythms are generally preferred, for obvious reasons of economy of building methods.

存在一种特殊的渐变形式，它在平面和剖面中比在立面中更常用：级数。它是一个没有周期性变化的渐强的连续递变。因此，在奥古斯特·索伊斯(Auguste Choisy)绘制的底比斯南部寺庙的图画中可以清楚地看到等级制度的建立，朝向圣殿中心的发展不仅可以从平面图上看出来，还可以从剖面图上看出来。最重要的不是最高和最大，而是相反。层次不是大小的问题，而是元素在其上下文中的相对位置的问题。

There exists one particular form of gradation which is used more often in plan and section than in façades: progression. It is a continuous gradation of crescendo without cyclical variation. Thus a hierarchy is established as can clearly be seen in the drawings of the southern temple at Thebes by Auguste Choisy where the progression towards the heart of the sanctury can be read not only in the plan but also in section. It is not the highest and the largest which is the most important, but the opposite. Hierarchy is not a question of size but of the relative position of an element in its context.

层次结构

层次结构意味着主元素和次元素。这些要素之间存在依存关系;他们中的一个或几个支配着其他的。在这些元素中，同样的现象也会发生:通过把注意力集中在一个元素上，这个元素就会成为主要的元素，然后我们就会发现次要的元素。在多样性中，等级制度是一个强大的统一因素。它使得在更大、更简单和更容易识别的实体中组合元素成为可能。

A hierarchy implies primary and secondary elements. There is a dependent relationship between these elements; one or several of them dominate the others. Within these elements the same phenomenon can take place: by concentrating attention on one element, this one can become primary and we then discover secondary elements. In diversity, hierarchy is a powerful unifying factor. It makes it possible to combine elements in bigger, simpler and more recognizable entities.

谈到建筑环境中的“等级”，人们很容易想到“轴”、“对称”、“中心性”等。列举所有可能导致某一因素在其范围内占优势的手段是毫无意义的。无论如何，对称并不是实现这一目标的唯一手段。即使是简单地改变建筑的朝向与其他建筑的关系，作为一个例外，也足以建立一个完整的层次结构（柯布西耶卡朋特艺术中心）。

Whoever talks about ‘hierarchy’ in the built environment thinks only too readily of ‘axis’, ‘symmetry’, ‘centrality’, etc. It would be pointless to enumerate all the means which can contribute to the dominance of an element in its context. In any case, symmetry is not the only means of achieving it. Even the simple changing of the orientation of a building in relation to others is sufficient, by being an exception, to establish an unabiguous hierarchy.

因此，等级意味着空间或对象的支配地位。我们每天都在思想的组织中使用层次结构。我们需要这些参考来帮助我们在复杂空间中的定位。当有太多等价的层次结构时，层次结构的清晰度就会下降。

Hierarchy thus implies a dominance of spaces or objects. We use hierarchies every day in the organization of our thoughts. We need these references to facilitate our orientation in complex space. When there are too many hierarchies of equal value, the clarity of the hierarchy breaks down.

对比

对比给两个正式的体系一个直接而明确的同一性。它导致了相互强化，而不必诉诸于明确的等级制度。各要素之间的相互依存是通过它们对立的特性所产生的张力来实现的。

• 积极的和消极的
• 实/空
• 凸出/凹入
• 曲 /直（柯布西耶）。
• 光明与黑暗
• 光和影，反射/吸收
• 大/小、宽/窄、高/低
• -水平及垂直
• 天然与人造
• 粗糙/光滑

Contrast serves to give an immediate and unambiguous identity to two formal systems. It leads to mutual reinforcement without necessarily resorting to explicit hierarchy. The interdependence of the elements is achieved by tension resulting from their opposing characteristics.

对比使我们能够建立差异:我们已经看到它与图底现象。此外，两个对立的人处于一个对立的环境中，他们之间就建立了一种“对话”。有了三个，四个或更多，这就变得困难，甚至不可能。对比是我们调整环境的一个原则。一种形式的意义由它的反面来强调。

Contrast enables us to establish differences: we have seen it with the figure/ground phenomenon. Moreover, two opposites placed in a contrasting situation establish a ‘dialogue’ between them. With three, four or more, that becomes difficult, or even impossible. Contrast is a principle for ordering our environment. The meaning of a form is accentuated by its opposite.

复杂性与透明性

体系结构中的复杂性概念可以通过其对简单性的对立面来定义，实际上是对清晰而基本的东西的对立。从一个倾斜的角度看帕台农神庙，我们可以猜出它隐藏的侧面。它的所有元素，基础，柱子，柱顶，架构等等，混合在一起，创造了一个统一的整体，避免了所有的歧义。虽然是无限的完善，但同时，这座寺庙仍然是最简单的。眼睛被邀请去接受它，而不是去探索它。这与米开朗基罗的圣洛伦索立面完全是两码事。尽管对称性是一个强大的统一因素，我们发现自己在几个协调和叠加相似的形式结构的存在。这些元素以一种向观察者呈现多种解释的方式组合在一起——这就是我们所说的复杂性。假设立面已经建成，我们逐渐接近它——尽管从一个固定的观点来看是一样的——立面在几个依次主导的正式组织中交替出现。它成为一个有待探索的外观。柯林罗和Robert Slutzky引入了透明的概念，他们从中开发了一个有趣的、关键的工具来分析和组合这些叠加现象。

The concept of complexity in architecture can be defined by its opposition to simplicity, indeed to what is clear and elementary. Looking at the Parthenon from an oblique angle, we can guess at the sides hidden from view. All its elements, base, columns, capitals, architraves, etc., blend to create a unity, preventing all ambiguity of interpretation. Whilst being infinitely refined, this temple remains, at the same time, of utmost simplicity. The eye is invited to accept it more than to explore it. It is quite a different matter with Michelangelo’s façade of San Lorenzo. In spite of the symmetry, which is a powerful unifying factor, we find ourselves in the presence of several co-ordinated and superimposed similar formal structures. The elements are grouped in such a way as to present more than one interpretation to the observer – that is what we call complexity. Supposing the façade were built and we gradually approached it – although the same holds true from a fixed viewpoint – the façade alternates among several formal organizations which dominate in turn. It becomes a façade to explore . Colin Rowe and Robert Slutzky have introduced the concept of transparency from which they develop an interesting, critical tool for analysing and composing with these phenomena of superimposition.

然而，我们在建筑中遇到了许多无意识的、笨拙的复杂性(和简单性)。圣洛伦索的非凡品质在于控制元素和几何图形之间的依赖关系。它们之间的平衡使立面复杂而不复杂，就像帕特农神庙简单而不平庸一样。对建筑复杂性的掌握，如同对简单性的掌握一样，只能是勤奋劳动的结果。这不仅仅是天赋的问题，就像Bernhard Hoesli在画米开朗基罗的草图时所表现的那样。第一个设计仍然“笨拙”:几何子系统尚未相交形成一个整体;它们并置。还有其他处理复杂性的方法，例如，偏离规范。它可以是由于对已建立的对称性的偏离，或者甚至是由于对规则图案的异常，或者仅仅是由于对熟悉图形的扭曲。

We meet, however, many involuntary and clumsy complexities (and simplicities) in architecture. The exceptional quality of San Lorenzo lies in the control of the dependency between the elements and the geometries. The balance between them makes the façade complex without being complicated, in the same way that the Parthenon is simple without being banal. The mastery of complexity in architecture, as with simplicity, can only be the fruit of assiduous labour. It is not simply a question of talent, as Bernhard Hoesli51 shows very clearly when he lines up the preliminary sketches of Michelangelo. The first design is still ‘clumsy’: the geometric subsystems do not yet intersect to form a whole; they are juxtaposed. Other methods also exist for working with complexity, as for example, deviation from a norm. It can result from the introduction of divergences from an established symmetry, or even from an anomaly in a regular pattern, or simply from the distortion of a familiar figure.

让我们以理查德·迈耶的亚特兰大高等博物馆为例。在这种几何复杂性、大量的体量和空间环境中，凝聚力来自哪里?在这里，“受控的复杂性”不再局限于立面。在外观上，材料的大一统来自方形的包层，金属面板形成了独立于几何形状和个体功能的均匀纹理。这种纹理的连续性对于将不规则的纹理组合成一个外行人可以识别的单元非常重要。在内部空间的组织中，变形特别多。从一个角度到另一个角度的改变打破了最初的正交性，如此坚持地存在完全无序的风险。布局的三个特点防止这样的碎片:

• 最后角度的变化至少部分地在它们之间创造了一种新的正交关系
• 它们几乎总是通过截线与外部联系起来
• 大的中心空间以象限的形式，作为整个建筑长廊主要阶段的参考。

Let us examine, as an example, Richard Meier’s High Museum in Atlanta. Where does the cohesion come from in this geometric complexity and multitude of volumes and spatial situations? Here the ‘controlled complexity’ is no longer restricted just to the façades. On the exterior, a great unity of materials comes from the cladding of square, metallic panels which form a homogeneous texture independent of the geometry and function of the individual volumes. This continuity of texture is essential to combine the irregularities into one unit identifiable by the layman. In the organization of the internal space, the de-formations are particularly numerous. The initial orthogonality is broken from one change of angle to another, so insistently that there is a risk of total disorder. Three features of the layout prevent such fragmentation:

• the changes of angle in the end create, at least partially, a new orthogonality between them;
• they almost always relate back to the exterior by transversals;
• the large central space, in the form of a quadrant, acts as a reference throughout the main stages of the architectural promenade.

这种凝聚力是不稳定的、耐人寻味的和挑衅的。不确定这是否是展示艺术作品的最佳场所，但Meier坚持认为建筑本身就是“艺术”。这种明显的秩序、隐藏的秩序和无序之间的平衡是脆弱的。这就是让人着迷的地方，当这样的作品不仅反映了诗意的灵感，还反映了技巧与知识相结合的实现它的方法，就像这两个例子，几个世纪过去了，证明了。

The cohesion is precarious, intriguing and provocative. It is not certain that this is the best place for displaying works of art, but Meier insists on the ability of the architecture itself to be ‘art’. This balancing act between obvious order, hidden order and disorder is fragile. This is what fascinates the minds, when such a work reflects not only poetic inspiration, but also skill combined with knowledge of the means for achieving it, as these two examples, several centuries removed, demonstrate.

矛盾

文艺复兴的纯洁性后来被摒弃，取而代之的是表达和讽刺的自由，允许通过修改编纂的元素来实现功能上的反复无常的不和谐。我们也在19世纪和20世纪早期的建筑中发现了矫揉造作的痕迹，旨在将建筑从学术的理性主义中解放出来。也许我们可以同意塞里奥的观点，他在16世纪就说过，新奇是令人愉悦的，因为它不会消除所有的规则。在当代建筑中， 罗伯特·文丘里已经着手重建矛盾和模糊的概念，以期将自己从现代建筑中有时教条的简单性中解放出来。他通过他的计划和他的作品来表达自己:“我追求意义的丰富性，而不是意义的明确性。”他把混合的东西与“纯的”对立起来，把妥协的东西与“纯的”对立起来，把模棱两可的东西与“铰接的”对立起来。建筑是否同时具有大与小、连续与铰接、开放与封闭、结构与装饰，关系到局部与整体的联系。这些双重选择通过对历史先例的刻意选择，表达了对质疑现代建筑简单性的承诺。

The purity of the Renaissance was then rejected in favour of an expressive and sarcastic freedom, allowing the caprice of functional discord by the modification of codified elements. We also find traces of Mannerism in the architecture of the nineteenth and early twentieth centuries, aimed at freeing architecture from academic rationalism. We can perhaps agree with Serlio who said, already in the sixteenth century, that novelty is pleasing in so far as it does not erase all the rules. In contemporary architecture it is Robert Venturi who has set his hand to a re-establishment of the notions of contradiction and ambiguity with a view to freeing himself from the sometimes dogmatic simplicity of modern architecture. He expresses himself through his schemes and his writings: ‘I am for richness of meaning rather than clarity of meaning’.53 He sets the hybrid against the ‘pure’, the compromising against the ‘clean’, the ambiguous against the ‘articulated’. Whether architecture is at the same time large and small, continuous and articulated, open and closed, structure and decoration, relates to the links between the parts and the whole. These double choices express a commitment to questioning the simplicity of modern architecture by using a deliberate selection of historical precedents.

混沌

在混乱中，根本没有连贯性的因素在起作用。如果有任何一个维护者存在，它们就会彼此抵消，因为没有任何结构、形式或语义主题更占优势，既不在个别部分中，也不在整体中。存在冲突或缺乏规则。冲突元素的数量很多。正如阿恩海姆所指出的，无序不是同质性，即使后者是一个非常简单的层次，而是部分秩序之间的无序。“有秩序的安排是由总体原则支配的;而不守规矩的人则不然。”

In chaos, no factor of coherence at all is at work. If any subsist they cancel each other out, because no structure, no formal or semantic theme is any more dominant, neither in the individual parts, nor in the whole. There is a conflict or absence of rules. The number of conflicting elements is high. As Arnheim points out, disorder is not homogeneity, even if the latter is at a very simple level, but a disorder between partial orders. ‘An orderly arrangement is governed by an overall principle; a disorderly one is not.’

在本世纪的进程中，我们城市的某些居民区逐渐呈现出一种混乱的形态。这种混乱反映了他们最近转变成一种只考虑自身效用的交通系统、物体和建筑的积累，而没有任何创造城市的共同目标。弗里德里希·辛克尔早在1840年就提出警告:“没有一种需要能产生美，没有混乱就没有环境效用能决定形式。”

Certain neighbourhoods of our cities have gradually taken on a chaotic form in the course of this century. This disorder reflects their recent transformation into an accumulation of transportation systems, objects and buildings which take only their own utility into consideration, without any common objective of creating a city. Friedrich Schinkel was already warning in 1840: ‘No single need produces beauty, circumstantial utility cannot determine form without engendering chaos.

混沌本身能成为创造和生命的源泉吗?尼采说混沌是恒星诞生的必要条件。如果真是这样的话，我们可以期待看到一颗非常美丽的星星。除非社会完全崩溃，忘记它的过去，被连根拔起，失去所有希望的能力，否则它的建筑师和规划者没有权利成为混乱的帮凶。城市混乱是一种不稳定的状态。一方面，它倾向于由职业的标志来组织。另一方面，习惯一个城市有助于我们了解它的更多的秘密秩序。同质的kasbah的居民有一个有组织的中心——他的房子——从那里他构建了一个复杂的关系网络，使明显的混乱变得容易理解。

Could chaos itself become a source of creation and life? Nietzche said that chaos was needed for a star to be born. If that is really the case, we can expect to see a very beautiful star. Unless society has completely crumbled away, forgotten its past, been uprooted and lost all capacity for hope, its architects and its planners do not have the right to be the accomplices of chaos. Urban chaos is a state of instability. On one hand, it tends to become organized by signs of occupation. On the other, being accustomed to a city helps us to learn about its more secret order. The inhabitant of the homogeneous kasbah has an organized centre – his house – from were he constructs a complex network of relationships which make the apparent confusion intelligible.

Elements of Architecture：From Form to Place