ARC 4301A
Issues in architectural theory and design
Fall 2004–05

1, Defining languages of designs

Enumerative and generative descriptions of sets

Given the subset R = {1, 2, 3} of some larger set T = {1, 2, 3, …} of numbers, what does it mean to understand T? Stiny and Mitchell (1978, 17) propose three requirements:

1. You can name another number in T.
2. You can evaluate whether a newly “discovered” number is in T.
3. You can explain what the numbers in R have in common.

Suppose you have a larger subset S of T, demonstrate your understanding of T.

Two types of descriptions of a set: enumerative and generative.

An enumerative description is just a list of elements. It cannot satisfy the third requirement of understanding.

A generative description is a recipe or a set of instructions for determining those elements. It can satisfy the third requirement.

The Yingzao fashi 營造法式 (Building standards)

A building manual for both officials and builders. To reduce corruption and introduce standards.

Covers a range of subjects: from fortifications and foundations to finish carpentry and painted decoration. We are interested in structural carpentry (da muzuo 大木作).

Written by Li Jie 李誡 (d. 1110), court architect to the Huizong 徽宗 emperor (reigned 1101–1126) of the Song 宋 (960–1127). Published in 1103.

For our work, Liang’s (1983) and Chen’s (1993) studies are indispensable. For an English translation of the sections on structural carpentry, see Guo (1999). For background information, see Glahn (1984).

A generative description in the Yingzao fashi:
roof sections (juzhe 舉折)

Two rules: ju 舉, ‘raise,’ and zhe 折, ‘lower.’

Raise the ridge purlin (ji tuan 脊槫) above the eaves purlin (liaoyan fang 撩檐方). Draw a line between these two purlins; this is the working roofline.

Lower the succeeding purlin below the working roofline. Draw a line between this purlin and the eaves purlin; this is the new working roofline. Repeat for the remaining purlins. The segmented curve is the roof section.

This is a generative description. We can satisfy all three requirements.

Instead of elements and sets, we now refer to designs and languages of designs.

Enumerative description in the Yingzao fashi:
ting tang sections

Three building types: dian tang 殿堂, ting tang 廳堂, yu wu 餘屋 (other). These differ in their structure and the rank of the occupant.

There are 18 sections of ting tang, each with a written description. A typical description:

Bajia chuan wu, qian hou ru fu, yong si zhu
八架椽屋前後乳伏用四柱
Eight-rafter building, 2-rafter beam in front and in back, with 4 columns

Each description has three parts:

1. The depth of the building, measured in (horizontally projected) rafters. Each section has a depth of 4, 6, 8, or 10 rafters.
2. The disposition of the lowermost beams. The lengths of such beams are also given in rafters. Each such beam is supported by a column; thus to specify the lengths of beams is to imply the locations of columns.
3. The total number of columns.

This set of 18 sections and descriptions is an enumerative description. We cannot satisfy all three requirements.

Terms

Formal language

“[A]ny language designed for use in situations in which natural language is unsuitable for the required precision, as in formal logic or in computer programs. the symbols and formulae of such a language stand in precisely defined syntactic and semantic relationships” (The HarperCollins dictionary of mathematics). In other words, there are clear rules for understanding the meanings of symbols and of combinations of symbols. Distinguish language of designs, below.

Design

“An n-ary relation among drawings, other kinds of descriptions, and correlative devices as needed” (Stiny 1990). In other words, the representation of a thing, not the thing itself.

Set

“[A] collection, possibly infinite, of distinct numbers, objects, etc., that is treated as an entity in its own right, and with identity dependent only upon its members” (The HarperCollins dictionary of mathematics). In other words, as far as the identity of the set is concerned, it is irrelevant whether the set is described enumeratively or generatively.

Enumerate

To list individually.

Generate

“To provide a precise criterion for membership in a set, in the form of an algorithm whose application recursively yields all and only the members of the set.” (The HarperCollins dictionary of mathematics).

Algorithm

“A step-by-step procedure by which an operation can be carried out without any exercise of intelligence, and so, for example, by a machine” (The HarperCollins dictionary of mathematics).

Language of designs

A set of designs. Distinguish formal language, above.

Legal design

A design that belongs to a language under discussion.

Corpus

A body of designs on which an analysis is based (adapted from The new shorter Oxford English dictionary: “A body of spoken or written material on which a linguistic analysis is based.”)

Style

“When several buildings each create a similar impression, they are said to exemplify a particular architectural style” (Stiny and Mitchell 1978, 17, original emphasis). In other words, a language of designs that are perceived to be similar.

A computational approach to Chinese traditional architecture

Computational: formal and generative

Chinese traditional architecture: beginning with the Yingzao fashi

Assignment 1 out

Create three new ting tang sections, including descriptions. Explain why they are legal. If you need to make any assumptions, state them clearly.

Exchange the three sections with a classmate. State which are legal, according to you (not according to your classmate). Explain why or why not.

Submit hard copy and PDF file. Due next class, 16 September.

Writing: some basic tips

Make it easy for your readers to receive your message. Communication relies on shared conventions, from the spelling to the meaning of words. You must know and follow the conventions that your readers expect. Otherwise you make it unnecessarily difficult for them; they may decide to spend their effort on something else. To be specific:

• Spell correctly. This is easy, so not doing it damages your credibility. Use a spell checker, but because spell checkers have their limitations, you should use your eye too. If you’re not sure, use a dictionary. For Chinese romanization, use Hanyu pinyin 漢語拼音; check in a dictionary such as Xinhua zidian 新華字典 . Do not invent your own system.

• Learn and follow one bibliographical format. The author-date system is recommended; it is used in these handouts. Turabian (1996) is a standard source.

• Use correct grammar. For instance, make sure subjects and verbs agree in number (he is, not he are).

• Use words correctly. Use a dictionary. Say what you mean; mean what you say.

• Beyond conventions, which are essentially arbitrary, lie human perception and information processing, which are more innate. Effective graphic presentation (layout, choice of typefaces, etc.) works within known constraints to enhance communication. Make sure your presentation works for you. Leave margins for comments. It goes without saying that you should produce your papers on a computer.

List of references

Chen Mingda 陳明達. 1993. Yingzao fashi da muzuo zhidu yanjiu [A study of structural carpentry in the Yingzao fashi] 營造法式大木作制度研究. 2nd ed. Beijing: Wenwu.

Glahn, Else. 1984. Unfolding the Chinese building standards: research on the Yingzao fashi. In Chinese traditional architecture, edited by Nancy Shatzman Steinhardt, 47–57. New York: China Institute in America.

Guo, Qinghua. 1999. The structure of Chinese timber architecture. London: Minerva.

Liang Sicheng 梁思成. 1983. Yingzao fashi zhushi [The annotated Yingzao fashi] 營造法式註釋. Beijing: Zhongguo jianzhu gongye.

Stiny, George. 1990. What is a design? Environment and planning B: planning & design 17: 97–103.

Stiny, George, and William J. Mitchell. 1978. The Palladian grammar. Environment and planning B: planning & design 5: 5–18.

Turabian, Kate L. 1996. A manual for writers of term papers, theses, and dissertations. 6th ed. Chicago: University of Chicago Press.