Spring对《In The Footsteps of le Corbusier》的笔记(1)

第11页 Le Corbusier's Modulor

本文的作者，Rodolf Wittkower (22 June 1901 – 11 October 1971, German art historian)，又一个德国学者，写的英文让我觉得不太好翻译......有些内容做不到逐句翻译，便草译之，或者总结了中心思想。

Wittkower站在史学家的立场上，分析了Modulor的历史背景，从古希腊的“音乐比例”，到中世纪的“积分法”，再到文艺复兴，到启蒙运动，到19、20世纪的学者们对黄金分割的研究，在宏大的背景下娓娓道来Proportion这个在建筑和艺术中几乎永恒被讨论的话题。在文章后半段，讲解了柯布的Modulor，并批判性的评价了Modulor，感觉分析的很中肯。然而，我亦怀有许多人在关注Modulor时候同样的疑惑，Modulor是如何在实践中被应用的呢？Wittkower只是说，要在诸如马赛公寓这样的作品中去找答案了。（当然，不排除文中有个别的段落让我感觉论述的比较牵强，也是Rodolf Wittkower的一家之言，做个参考罢了。）
At a recent meeting at the Royal Institute of British Architects in London to which I was a party (June 18, 1957), the motion was before the house “that Systems of Proportion make good design easier and bad design more difficult.” The motion was defeated. But in the debate Le Corbusier’s Modulor was constantly referred to, and the distinguished architect, Misha Black, even said apologetically that “it must inevitably be in our minds as we discuss the motion.” Indeed, after the Modulor we must be for it or against it; it would mean deluding ourselves if we tried to be escapist or neutral.
以作者近期参加的于伦敦的英国建筑师皇家研究院召开的一次会议（1957年8月）为引子，表达出这样的观点：在Modulor出现之后，我们必须追随它，或者反对它；如果我们想要逃避或者保持中立的话，无疑是自我欺骗。
In 1948 Le Corbusier surprised the architectural world with his Modulor. The book was quickly sold out. Le Corbusier himself, whom I may (perhaps not to charitably) describe as a cross between a prophet and a salesman of rare ability, brought the story up to date in 1954, with the publication of his Modulor 2.

What was the reason for the world-wide response to the Modulor? Was it due to Le Corbusier’s prophesy or his salesmanship? Each may have played a part, but many a prophet has cried in the wilderness, unheard. In all fairness, we must admit that the time was ripe for the Modulor.
1948年，勒·柯布西耶发表了他震惊建筑界的Modulor；在1954年他发表了Modulor 2。勒·柯布西耶可以说是拥有杰出能力的先知和推销员的交集。

为什么Modulor会引起世界范围内的反响？是因为柯布的预言，或者是他的推销术？公平的说，我们必须承认，Modulor的时机成熟了。
The Beaux Arts tradition, according to which proportion is something vague, indefinable, irrational – a “something” that must be left to the individual architect’s sensibility – that tradition is as dead as a doornail. If it is not, it should be.

Be that as it may, I find it difficult or even impossible to give paternal advice to practitioners regarding the suitability of the Modulor for the design of, say, skyscrapers. As an historian I am concerned with the past rather than with the future, and I can only discuss the Modulor in its historical context. Such an investigation may at least help to assess the validity of Le Corbusier’s basic assumptions.
根据布扎艺术的传统认知，比例是暧昧的、不可定义的、无理性的——是某种属于建筑师个人的敏感的东西——传统已经彻底死掉了。如果不是这样的话，那么它应当如此。

要给出在诸如摩天楼的设计中如何应用Modulor的建议，我觉得是很难甚至是不可能的。作为一个历史学者，我更关心的是过去，而非未来，并且我只能在Modulor的历史文脉中来讨论它。这样的调查至少可以帮助评价勒·柯布西耶最基本的想法。
So far as I can see, the belief in an order, divine and human, derived from numbers and relations of numbers was always tied to higher civilizations. All systems of proportion are implicitly intellectual, for they are based on mathematical logic. Without a grasp of geometry and the theory of numbers, no system of proportion is imaginable.
就目前所知，发源于数字和数字关系的对于秩序的信仰，不管是神性的和人性的，都依赖于更高度化的文明。所有的比例系统都是含蓄的文明，因为他们都基于数学逻辑。没有对几何学的领悟和数字的理论知识，是不可能建立任何比例系统的。
It must be regarded as one of the most extraordinary events in the early history of mankind when a bridge was created between abstract mathematical thought and the phenomenal world that surrounds us; when geometry and numbers were found to govern the skies as well as all creation on earth. The Bible reflecs this remarkable alliance between life and mathematics, between endless variety and numerical limitation. In the Wisdom of Solomon (XI, 20), we read, “By measure and number and weight thou didst order all things.”
把抽象的数学与我们的生活相联系的，这是人类早期历史中一个非同寻常的事件。在圣经中，也反映出，在无止境的变化和数字限制之间的、显著的生活和数学的关系。在“Wisdom of Solomon”中我们读到，“通过测量、数字和重量，你制定了所有一切。”
（注释：询问了rossiegent 同学后得知，Wisdom of Solomon属于次经，不是圣经的内容，基督教普遍是不认可次经的。那么，这个论据好像非常不充分啊～）
The intellectualism of this daring hypothesis must not lead us astray, for in reality we are here faced with a biologically conditioned sublimation. The quest for symmetry, balance, and proportional relationship is deeply embedded in human nature. Modern antagonists always claim that systems of proportion interfere with, and even impede, the release of creative energies. In actual fact, however, such systems are no more, and no less, than intellectual directives given to an instinctive urge which regulates not only human behavior but even the behavior of higher species of animals. 
这个大胆的设想并没有引导我们误入歧途，因为在现实中，我们面对着生物学上的有条件的升华。对于对称、均衡和比例关系的寻求已经深深根植于人的本性之中。现代的反对者们总是声称，比例系统妨碍了、甚至是阻止了创造力的释放。然而，实际上，这样的系统与其它调控人类甚至其它高等动物的原始行为的智力指导原则并无二样。
Man’s predisposition for ordering complex sensory stimuli can easily be tested. For instance, we interpret automatically irregular configurations as regular figures (see Arnheim, Art and Visual Perception, fig. 44). Such incontestable observations permit us to conclude that we seek ordered patterns; systems of proportion are the principal vehicles to satisfy this urge.
人类有把复杂感官规整化的倾向。例如，我们自动的把不规则的构造翻译为规则的形体。这个毋容置疑的事实允许我们得出这样的结论：我们寻找秩序的图案；而比例系统是满足这种需求的首要工具。
（这样的结论仿佛是有道理的，但是，作者没有科学合理的论据和论证啊～）
All systems of proportion in Western art and architecture, the only civilization we are concerned with, are ultimately derived from Greek thought. Pythagoras, living in the sixth century B.C., is credited with the discovery that the Greek Musical scale depends on the division of a string of the lyre in the ratios 1:2 (octave), 2:3 (fifth), 3:4 (fourth), and 1:4 (double octave). In other words, the ratios of the first four integers 1:2:3:4 express all the consonances of the Greek musical scale. This discovery of the close interrelationship of sound, space, and numbers has immense consequences, for it seemed to hold the key to the unexplored regions of universal harmony. Moreover, if the invariable of all octaves is the ratio 1:2, it must be this ratio, the Greeks argued, that is the cause of the musical consonance. Perfection and beauty were therefore ascribed to the ratio itself.
西方艺术和建筑的所有比例系统，这个我们唯一关心的文明，最终要追溯到希腊思想。生活在公元六世纪的毕达哥拉斯（Pythagoras）发现，希腊音乐的和弦取决于里尔琴琴弦的长度而受到赞誉。当琴弦比例为1：2的时候奏出的是八度，2：3的时候奏出的是五度，3：4的时候奏出的是四度，1：4的时候奏出的是两个八度。 这个关于声音、空间和数字的密切关系的发现有着极为重要的地位，因为它仿佛是宇宙和谐中未被研究的领域的关键。另外，如果所有八度音阶的比率永远是1:2，希腊人认为，一定是这个音阶，是音乐和谐的原因。因此，完美和美丽归于比率本身。
（在这里，感谢Charles Rosen对Lyre琴的解释：“琴弦比的问题，其实无论拿弦，还是绳子一根，按住某一处再进行拨动，它都会发出不同的音高的。至于八度、五度、四度，举个例子：do-高音do是八度，do-sol是五度，do-fa是四度，是讲两音之间的关系的。这里的意思指的应该就是原来的弦的音高（空弦）的声音和在不同的地方拨奏的关系......至于音乐是不是“跟建筑一样，可以追溯到西方世界proportion的起源”，我个人并不觉得这一点很被强调。但要说有，可能是能讲到一些的，尤其是弦乐、弹拨乐的比例。因为它们的乐音和弦长、乐器形态有直接关联。 ）
Plato, in his Timaeus, expounded a geometrical theory which was no less influential. He postulated that certain simple figures of plane geometry were the basic stuff of which the universe was composed. I have no doubt that it was mainly owing to Plato’s never forgotten cosmological theory that such figures as the equilateral triangle, the right-angled isosceles triangle, and the square were charged with a deep significance and played such an important part in the Western approach to proportion. 
柏拉图在他的Timaeus中解释了一个几何学理论，现在依旧很有影响力。他认为，平面几何的一些基本形体是宇宙构成的基础。我毫不怀疑，这是由于柏拉图的宇宙哲学理论而得出的，即正三角形、等边直角三角形和正方形有着深刻的重要性，并且在西方比例方法中扮演了一个重要角色。
We have overwhelming evidence that many medieval churches were built ad quadratum or ad triangulum, reflecting a platonic pedigree. Milan Cathedral is a well-known example: discussions on whether the church should be erected according to triangulation or quadrature dragged on for years.
我们有足够的证据显示，许多中世纪教堂按照“积分法”或者“三角测量法”（ad quadratum or ad triangulum）来建造，反映出一种柏拉图式的血统。米兰大教堂是一个著名案例：关于教堂应该按照 “三角测量法”还是“积分法”来建造的争论持续了数年。
（ad quadratum or ad triangulum，或者triangulation or quadrature，应该如何翻译比较精准呢？）
From the fifteenth century on, attention was focused on musical proportion. Although never entirely excluded from consideration, the Renaissance and post-Renaissance periods preferred an arithmetical theory of proportion derived from the harmonic intervals of the Greek musical scale, in contrast to the Middle Ages, which favored platonic geometry. The Renaissance, in addition, fully embraced ancient anthropometry. Following Vitruvius (whose treatise reflects Greek ideas), Renaissance theory and practice pronounced axiomatically that the proportions of architecture must echo those of the human body. This ancient theory lent itself to being incorporated into a Christian conception of the world. The Bible tells us that Man was created in the image of God. It logically follows that Man’s proportion are perfect. The next axiom appears unavoidable: man-made objects, such as architectural structures, can only be attuned to universal harmony if they follow man’s proportions. You may approve or disapprove of these deductions; you may find Renaissance architect’s demonstrations of the connection between man and architecture naïve and even funny, but some of you may detect that we are moving close to the Modulor. Moreover, because of – or in spite of – such convictions, the world was enriched by most beautiful buildings.
从十五世纪开始，音乐的“比例”受到关注。与推崇柏拉图体的中世纪恰恰相反，文艺复兴和后文艺复兴时期，偏爱一种源于希腊音乐尺度的和谐停顿的算术比例理论。另外，文艺复兴完全推崇了古代人体测量学。文艺复兴的理论和实践追随维特鲁威（他的论述也反映出古希腊的理念），公理地宣扬建筑的比例必须回应人体的比例。这个古代理论有助于将其与世界基督教观念融为一体。圣经告诉我们，人是按照上帝的样貌创造的。从理论上来说，人的比例是完美的。接下来便有了一个不可避免的公理：人造物，例如建筑物，只有当它们追随人体比例的时候，才能融入宇宙的和谐之中。你可以赞同或者不赞同这些推论；你可能认为，文艺复兴的建筑师的证实的建筑与人之间的联系是很天真甚至可笑的，但是你们中的某些人可能会发现我们正在接近Modulor。更进一步说，因为——或者说尽管——有这些信念，世界充满了最美丽的建筑。
To postulate such a relationship between human and architectural proportion is, perhaps, not so farfetched. The human body lends itself to an investigation of metrical relationships between parts and between the parts and the whole. You can express the parts in terms of submultiples of the whole; or you can operate with a small unit of measurement such as the face or the hand as a module, the multiples and submultiples of which guarantee metrical coordination.
提出这样一个人和建筑比例之间的关系，也许并不是特别牵强的。人体有助于探索部分和部分以及部分和整体之间的度量关系。你可以把部分解释为是整体的因数；或者你可以操作一个小的测量单位，例如把脸或者手作为模数，以模数的倍数与因数来保证度量上的调和。
Precisely the same principle may be applied to architectural structures: all the parts may be metrically interrelated by making them submultiples of a grand unit or multiples of a small unit. For the Renaissance, the tertium comparationis between man and buildings consisted in this: just as the beauty of the human body appears to be regulated by and derived from the correct metrical relation between all its members, so the beauty of a building deeps on the correct metrical interrelation of all its parts.
同样的原则可以精准的应用于建筑学的结构：所有的部分可以通过度量而相互关联，它们共为一个大单元的因数，或者是一个小单元的倍数。对于文艺复兴来说，人和建筑共有的品质存在于此：人体的美受控于并且源于身体各部分正确的比例关系，所以建筑的美取决于它的各部分相互之间的正确度量关系。
In the eighteenth century the old approach to proportion broke down. Enlightenment and empiricism militated against the notion that mathematical ratios as such can be beautiful. Romantic artists had no use for intellectual number theories which would seem to endager their individuality and freedom. In the nineteenth century it was mainly scholars who kept the interest in problems of proportion alive.
在十八世纪，旧的比例方法被废除了。启蒙运动和实证论妨碍了这样的观念，即这样的数学的比率是美丽的。浪漫主义的艺术家根本不需要那些可能会危机他们的个性和自由的理论。在十九世纪，主要是学者们对比例问题仍旧持有兴趣。
（启蒙运动，以及可以被视为对启蒙运动反扑的浪漫主义，都对“比例”的问题是不感冒的。）
The mid-nineteenth century, however, saw two events which had a direct bearing on the modern approach to proportion – and on Le Corbusier’s Modulor. First, Joseph Paxton built the Crystal Palace in London, the first structure of colossal size erected of standardized units over a gird. The logic inherent in the industrial revolution enforced a dimensional order. Secondly, the German, Adolf Zeising, published a book, Neue Lehre von dem Proportionem des menschlichen Körpers, 1854, in which he persuasively argued that Golden Section was the proportion pervading macrocosm and microcosm alike.
然而在十九世纪中期，可以看到两个事件，与现代比例方法和勒·柯布西耶的Modulor都有直接关系。首先，Joseph Paxton在伦敦设计了水晶宫，第一个用基于网格的标准单元来建造的巨大建筑。工业革命固有的理性形成了空间的秩序。其次，德国人Adolf Zeising在1854年出版了名为《从人体比例学到的新知》的一本书，在此书中，他极具说服力地在阐述，遍及宏观世界和微观世界的比例，均与黄金比例是相同的。
The wonderful properties of the Golden Section, of course, had been known to the Greeks. The Golden Section is the only true proportion consisting of two magnitudes (instead of 3 or 4), and in it as you know, the ratio of the whole to the larger part always equals that of the larger to the smaller part: a/b=b/a+b=0.618/1=1/1.618
当然，神奇的黄金分割来源自希腊人。黄金分割是唯一真正的由两个数字（而不是三个或者四个）构成的比例，并且如你所知，整体与较大部分之比等于较大部分与较小部分之比：a/b=b/a+b=0.618/1=1/1.618。
In the early thirteenth century Leonardo da Pisa, called Fibonacci, discovered that on a ladder of numbers with each number on the right being the sum of the pair on the preceding rung, the arithmetical ratio between the two numbers on the same rung rapidly approaches the Golden Section. Thus, for practical purpose, the Golden Section may be approximated to such ratios as 5:8, 8:13, 13:21. (Expressed algebraically, the Fibonacci series runs: a, b, a+b, a+2b, 2a+3b, 5a+8b…)
在十三世纪早期，Leonardo da Pisa，也叫做Fibonacci，发现了一个梯状数列，即每个后面的数字，是前面两个起始数字之和，这两个相邻的数字之比，接近于黄金分割。因此，黄金分割可以近似于以下比率，如5:8, 8:13, 13:21. （根据代数法，Fibonacci数列推演为：a, b, a+b, a+2b, 2a+3b, 5a+8b等等。）
Although the Golden Section remained a treasured heirloom of Western thought, it played no significant part in art and architecture. But after Zeising, the Golden Section found enthusiastic partisans, and a straight line leads from him to Hambidge’s Dynamic Symmetry (1917) and to Matila Ghyka’s books in the nineteen-twenties and thirties – from Ghyka to Le Corbusier.
尽管黄金分割依旧是西方思维中的传家宝，然而它在艺术和建筑中并没有什么重要作用。但是继Zeising之后，黄金分割拥有了热情的队伍，建立了一条直接的联系和影响，从Zeising到Hambidge的“动态对称” (1917年)，再到Matila Ghyka在十九世纪二十至三十年代著作，再从Ghyka 到勒·柯布西耶。
Here briefly are the constituent elements of the Modulor one after another:

First, the Modulor is a measuring tool based on the human body. Anthropometry is its essence. Le Corbusier is thus in line of descent from Vitruvius and the Renaissance. When you look at his design of the “Stele of the Measure,” built at the Unité d’Habitation at Marseille, you are right back at the anthropometric Renaissance exercises which seemed so strange before.
这里简要的依次罗列了Modulor的几个要素：

首先，Modulor是一个基于人体的测量工具。人体测量学是它的本质。勒·柯布西耶与维特鲁威和文艺复兴一脉相承。当你看到马赛公寓上柯布设计的“Stele of the Measure”的时候，正是看到了在以前看来很奇怪的文艺复兴的人体测量训练。
Secondly, basic geometrical units, the square and the double square, form Le Corbusier’s point of departure. Quadrature, we saw, played an overwhelming part in the Middle Ages, and the square and the double square with their ration of 1:2 has Pythagorean connotations. Le Cobusier saw these units in their relations to man: the solar plexus lies at the centre of a man with arm raised. Needless to say, this was well known to Renaissance artists.
其次，基本几何单元，方形和双重方形，形成了勒·柯布西耶的初始观点。我们可以看到，积分法在中世纪有主导地位，而这个方形和双重方形以及它们1：2的比例，蕴含着毕达哥拉斯式的内涵。勒·柯布西耶看到这些单元与人体的关系：solar plexus（腹部神经丛？）位于一个举起手的人体的中央。不用说，这是被文艺复兴艺术家所熟知的。
Thirdly, two Golden Section means are introduced, one added to the square, the other subtracted from the double square. The Golden Section subtracted from the double square determines the relationship from the foot to the fork and from the fork to the tips of the figures of the upraised arm.
第三，黄金分割的含义得到了两种阐述，一是对方形做加法，另一个是对双重方形做减法。对双重方形做减法的黄金分割决定了从脚部到腰部和从腰部到举起的手指顶部打高度。
The proportions of the human body defined in terms of the Golden Section were derived by Le Corbusier from his erroneous belief that “it has been proved, particularly during the Renaissance, that the human body follows the Golden Rule.” In actual fact, Renaissance artists found in the human body only commensurate musical proportions. Le Corbusier’s implicit acceptance of the Golden Section stems from the mystique of Matila Ghyka.
“这已经得到了证实，特别是在文艺复兴时期，人体是遵循黄金法则的。”——柯布这个错误的观念，导致了他将人体比例用黄金分割来定义。实际上，文艺复兴的艺术家们只是发现了人体与音乐的比例是相称的。柯布对黄金分割的接受源自于Matila Ghyka的神秘理论。
Fourthly, the Modulor is no module in the ordinary sense. It consists of a scale of dimensions derived from the six-foot man. As we have seen, the irrational divisions of the Golden Section can be approximated by numbers of the Fibonacci series (Le Corbusier used centimeters, but he may as well have used inches). In his Modulor, the figures 43, 70, 113 belong to a Fibonacci series which originated from the square (the red series, in Le Corbusier’s terminology), and 86, 140, 226 belong to another Fibonacci series, which originated from the double square (the blue series). In other words, the ratio of 1:2 is always present.
幸运的是，Modulor不是通常意义上的模数。它由一系列源自于6英尺高的男子的尺度数字而构成。正如我们所看到的，不严谨的黄金分割可以近似于斐波纳契数列（柯布西耶使用了厘米为单位，他也使用过英寸）。在他的Modulor中，从方形发展出来的数字43，70，113属于斐波纳契数列（用柯布的术语来说，即“红数列”），以及从双重方形发展而来的数字86，140，226（蓝数列）也属于斐波纳契数列。换言之，1：2的比率总是存在的。
（注：斐波纳契数列，一种整数数列, 其中每数等于前面两数之和。）
By combining the two series, one arrives at a series the terms of which have a special bearing on man in space, as Le Corbusier attempts to demonstrate. These Fibonacci series, single or in combination, may be prolonged in both directions. An illustration published by Le Corbusier shows that each series can be drawn as a grid which engenders a great variety of spatial shapes.

Another figure gives the points of intersection of superimposed red and blue series, and here the interweaving of the original unit, the double unit and the Golden Section may be noticed.
结合这两个数列，我们可以得到一系列关于人体空间关系的数据，正如柯布西耶想要证明的那样。这些斐波纳契数列，不管是单独的还是结合起来看，都可以在各自的方向上再进行延伸。由勒·柯布西耶出版的图像展示出每个数列都可以被画作为格状的，并创造出丰富的空间形态。

另外一幅图像给出了红蓝数列的交叉点，在这里，初始单元、双重单元和黄金分割应当被注意。
For the Modulor, Le Corbusier makes some special claims: First, the spatial combinations obtained by the Modulor are infinite. Secondly, the Modulor is a perfect means of unification in the mass production of manufacture articles. In contrast to an arbitrary module, it offers the possibility of harmonious integration of standardized products. Such considerations show Le Corbusier in line of descent from Paxton and competing with the propagators of standardizations through modular coordination. Thirdly, in contrast to the technologists among architects, who consider a module esthetically neutral, for Le Corbusier esthetic satisfaction overrides all other considerations. Harmony, regulating everything around us, is his ultimate quest. His aesthetic judgment is buttressed, thus, by a metaphysical belief in a divine order of things. Fourthly, the Modulor is a precision instrument, comparable to the keyboard of a piano; like the keyboard, the Modulor does not interfere with the individual freedom of the performer. Nor does it help to make bad designs good.
对于Modulor，勒·柯布西耶做出了一些特别声明：首先，Modulor的空间结合是无穷尽的。第二，Modulor是统一大量人造产品的完美工具。与那些任意的模数相比，Modulor为标准化生产提供了达到和谐统一的可能。这样的考虑显示出柯布西耶与Paxton的思想一脉相承，并且通过模数协调与标准化的传播者相竞争。第三，与建筑师中的把模数审美看作不确定的技术人员相比，因为柯布西耶的审美要求压过其它一切考虑。和谐，调节我们身边的一切事物，是他的终极要求。因此，他的审美标准基于事物的神圣秩序这样一个的形而上的信仰。幸运的是，Modulor是一个精准的工具，类似于钢琴的琴键；像琴键那样，Modulor不会妨碍表演者个人的自由。并且它也并不能有助于把坏的设计变好。
Meanwhile, modular coordination is on the march. An almost unbelievable amount of research has been devoted to it in recent years. The main purpose of these enterprises is to economize on all levels: in the architect’s and the contractor’s office as well as in the factory. Designs consist of multiples of the basic module, and since F. Bemis’s Evolving House published in 1936, the four-inch grid has been given preference in this country. The difference between the static – sterile, one is tempted to say – quality of the normal modular gird and the dynamic quality of Le Corbusier’s gird is most striking.
同时，模数的调和正在进行中。近年来，多到几乎不可置信的研究都已经在为此做贡献。这些活动的主要目的是在各个层面做到节约：无论是在建筑师和承包商的办公室，还是在工厂里。设计由多个基本模数组成，自从F. Bemis在1936年发表了《进化的房子》，四英寸的网格在这个国家便得到了偏爱。在普通模数网格的静态特性——人们可能会说是贫乏的特性——和勒·柯布西耶的动态网格特性之间的差异是最为显著的。
What is the balance sheet? As I see it, Le Corbusier’s Modulor, the creation of one man, has to assert itself against the combined efforts of hundreds or even thousands working on modular coordination. The odds favour the advocates of modular coordination: their work is scientific, sober, and objective. It is to the point, easily intelligible, and eminently practical. Le Corbusier’s is the opposite in every respect: it is amateurish, dynamic, personal, paradoxical, and often obscure. When you think you have it all sorted out, you wonder how practical the Modulor really is. Le Corbusier’s own buildings at Marseille, Saint-Dié, Algiers, Chandigarh, supply the answer.
“收支平衡”如何？如我所见，勒·柯布西耶的Modulor，这个一个人的创造物，必须与来自成千上百的相结合的模数协调工作相抗争。胜利的机会偏爱模数协调的拥护者：他们的工作是科学的、冷静的、客观的。是可理解的，并且非常容易实践的。而勒·柯布西耶的Modulor在各个方面都是相反的：它是不专业的、动态的、个人的、荒谬的，并且往往是晦涩的。当你以为你都理解了Modulor的时候，你会好奇它在实践中是如何被应用的。勒·柯布西耶再马赛，Saint-Dié，阿尔及尔，昌迪加尔的项目回答了这个问题。
Nevertheless, all his claims have been challenged. Against his faith in the immense variability of design offered by the Modulor, it is said that its range enforces unsatisfactory limitation. Against his canon derived from the six-foot man, it is claimed that in order to be universal, other human heights should be taken into account. His assertion of freedom of design guaranteed by the Modulor is dismissed as “just another rigid academic system.” His play with the Golden Section and the Fibonacci series is criticized as schoolboy mathematics wrapped in a cloak of mystification.
然而，他的所有宣言都被挑战了。相对于他所坚信的Modulor能够提供的极大的可变性，有评论说它的范围强制出不令人满意的局限性。相对于他源自6英尺高的男子的规范，有评论说为了实现其通用性，其他身高也应当考虑在内。他对由Modulor提供的自由设计的宣言被嘲弄为“只是另一个严格的学术系统”。他对黄金分割和斐波纳契数列的演绎被批判为是笼罩在神秘主义面纱下的小学生数学水准。
I do not want to continue this list of censure, for when all is said and done, it is only Le Corbusier whose instinct guided him to the sources of our cultural heritage; who transformed it imaginatively to suit modern requirements; who attempted a new synthesis, and once again, intellectualized man’s intuitive urge with which I began. It is only Le Corbusier who brings to bear on the old problem of proportion a prophetic, unceasingly searching, and, above all, poetic mind… the poetic and illogical mind of a great artist.

Since the breakdown of the old systems of proportions, no architect has been deeply engaged and none has believed so fervently that “architecture is proportion.”
我不想再继续责难，因为说到底，有且只有勒·柯布西耶能用以自己的本能引导他到达我们文化传统的根源；并将其转化为适用于现代要求；他实验着新的综合体，并再一次的，将人们本能的渴望理智化。有且只有勒·柯布西耶能够瞄准比例这个旧话题，带来一个预言性的、不断的研究，并且最重要的是，带来了诗意的思维，来自于一个伟大艺术家的诗意和无逻辑的思维。

随着旧的比例系统的瓦解，没有建筑师再如此深深的投入于此，并没没有人再热诚的认为“建筑就是比例”。

（全文完，尚未配图）

日记中配有图片：http://www.douban.com/note/216040576/

Spring
May 23, 2012, Berlin