ARC 4303A
Aspects of Asian architecture
Fall 2003–04

4, Grammatical versus stylistic correctness

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Student papers

week 1, 2 Sept.
Defining languages of designs

week 2, 9 Sept.
The Yingzao fashi

week 3, 16 Sept.
Defining style formally: shape grammar

week 4, 23 Sept.
Grammatical versus stylistic correctness

week 5, 30 Sept.
The Yingzao fashi, shape grammar, and extant buildings

week 6, 7 Oct.
AL away

week 7, 14 Oct.
Paper topics

week 8, 21 Oct.
Special topic, consultations

week 9, 28 Oct.
Special topic, consultations

week 10, 4 Nov.
Presentations

week 11, 11 Nov.
Presentations

week 12, 18 Nov.
Presentations

week 13, 25 Nov.
Review week

Assignment 3 in


The meanings of legal

  • We have been using the word legal a bit sloppily, which has led to some confusion. We have been using one word for two meanings:

    • Producible by the grammar in question. Test: can you create it by applying the rules?

    • Exemplifying the same style as (similar to) the designs in the corpus. Test: interpretation based on knowledge from outside the corpus.

  • Let us use the terms grammatical for the first and in the same style or stylistic for the second.

  • The difference and the way we reconcile this difference underlie our approach to history.


How to apply shape rules, precisely

  • Last time we learned how to apply shape rules, but in an informal way. Some questions came up then, and to answer them properly we need to be more precise. This is how to apply shape rules:

    if t(A) ≤ C, then C′ := [C – t(A)] + t(B), where

  • t(x), read t of x, is a shape x under transformation t.

  • t is a Euclidean transformation (reflection, rotation, scaling, translation) or a finite composition thereof.

  • A is the left shape.

  • B is the right shape. A shape rule has the form A → B.

  • C is the current shape.

  • C′ is the next shape.

  • ≤ is read is a part of. Roughly, if you take a shape S on tracing paper and align it (using the registration marks) on another shape T, and every piece of S lies on a piece of T, then S ≤ T. There are formal definitions of ≤, +, and –, but we will try to avoid them.

  • := is read is replaced by.

  • + is read plus. Roughly, it means draw.

  • – is read minus. Roughly, it means erase.


Parametric grammars

  • You may notice that the expression above does not actually describe the way you use the section grammar. This is because the left shape can match the current shape in more ways than just the Euclidean transformations. Strictly speaking, the left shape is parameterized; the shape itself is just a placeholder. For instance, it could be a 30°–60° triangle that can be matched, not just with other 30°–60° triangles, but with all right triangles (like 10°–80°, 20°–70°). You may not realize it, but when you studied geometry you used parameterized shapes all the time (and unparameterized shapes almost never).

  • The section grammar is a parametric grammar. Parametric grammars are extensions of regular grammars, and work like this:

    • if t(g(A)) ≤ C, then C′ := [C – t(g(A))] + t(g(B)),

    where g is a parametric assignment subject to some constraint. This looks complicated, but it’s just a formal way of writing down something that you do almost without thinking. By writing it down, we can examine it, make sure we understand it, and, perhaps most important, make sure we all understand the same thing.

  • In the section grammar, the parametric constraints are not explicitly stated. The author assumes that the reader will know what the constraints are; the author is living dangerously.


A grammar of the Yingzao fashi

  • The grammar creates diagrammatic designs of ting tang. By diagrammatic is meant that only global features (e.g., numbers and dimensions of bays) are represented; component-level features (e.g., column diameters) are not represented.

  • Each design consists of 7 diagrams and 9 descriptions.

  • A next stage of development would be to represent component-level features, like the dimensions of each component (see Li forthcoming). Think of it as a three-dimensional, scale version of the section grammar. Rather than go into the complexities of the larger grammar, we examine the subtleties of the section grammar.


Assignment 4 out

  • Investigate the language of 6-rafter ting tang sections by reconciling a grammatical definition of that language and your understanding of stylistic correctness. We now make use of what we noticed in assignment 3. Follow these steps:

    1. Using the section grammar, generate all the (final) designs in the language of 6-rafter sections.

    2. You may feel that some of the designs are not in the style. Show them and explain why each is unstylistic. Eliminate them by articulating unambiguous (indisputably clear) constraints to eliminate them, such as:

      • 1-rafter beams may occur only at the frontmost and backmost columns.

      • The center column is instantiated only by the fen xin rule.

    3. You may feel that there are stylistic designs that are not created by the grammar (these may or may not be in the corpus). If so, show them, and modify the grammar so that it creates them.

    4. Repeat steps 1, 2, and 3 until the grammar generates all and only the stylistic designs.

    5. Explain how this step-by-step process affected the way you evaluated the stylistic correctness of the designs and the way you thought about the language. For instance,

      • What criteria did you use? Why? What criteria would you have liked to use but did not? Why not?

      • Which parts of this process are formal? Informal? Objective? Subjective? Explain.

  • Some hints:

    • Show all parts of each iteration:

      1. Grammar, grammatical designs (both stylistic and unstylistic), stylistic but ungrammatical designs.

      2. Modified grammar, constraints, grammatical designs (both stylistic and unstylistic), stylistic but ungrammatical designs.

      3. Modified grammar, constraints, grammatical designs (both stylistic and unstylistic), stylistic but ungrammatical designs.

      4. Etc.

    • If you show a derivation, you can leave out the completion stage between the distinctive design and the final design.

    • When you show a design, show the final design (not the distinctive design).


List of references

Li, Andrew I-kang. Forthcoming. The Yingzao fashi in the information age. Paper read at The Beaux-Arts, Paul-Philippe Cret, and 20th-century architecture in China, at University of Pennsylvania.