ORGANIZATIONAL FIGURES SIMPLE ORGANIZATION CONTINUED On the right,two illustrations render the previous formal organizational figures as walled figures.In con- trast to simple extrusions,the presence of a distinct envelope hints at rudimentary construction. The upper image shows the figures in overhead per- spective(3).The lower image shows the same group in parallel projection (4).Notice that,even in perspec- tive,a figure-ground reading dominates the plan view as compared with the preponderant volumetric aspect conveyed by the angled projection. The top row of figures shows the ideal shapes as solid projections that illustrate their figure-ground dynamic.All three of the forms project their centers outward.However,there are differences.The square's orthogonal axes are parallel to its bounding perimeters and its diagonal axes pass through its corners.For the Figure 3:Overhead view of the fifteen organizational figures rendered with walled perimeter. circle there exist infinite axes and tangents-the orien- tation of its conditional boundary will likely take cues from its context.The visual dynamic of the triangle reflects one of its principal features-each of its three axes pass through a corner,the center and a face. The second row of figures exhibit related figure- ground relationships.Thus the octagon projects an axis every 22.5"and is similar to the square in its axis- boundary relationships.The pentagon's axes,like those of the triangle,pass through corner,center and face.Three of the hexagon's face axes share their geom- etry with the triangle,however,each corner axis has a companion face axis at go'.The resulting ambiguity is not dissimilar to that of the circle. These forms allow us to understand the organiza- tion of the more complex figures in the next three rows.The relevant formal difference,as we see in later chapters,is the active negative space both along the perimeter and/or within a center courtyard. Figure:Thesame walledfigures shown in parallepomkngacbinetobiqerwing. 14
On the right, two illustrations render the previous formal organizational figures as walled figures. In contrast to simple extrusions, the presence of a distinct envelope hints at rudimentary construction. e upper image shows the figures in overhead perspective (). e lower image shows the same group in parallel projection (). Notice that, even in perspective, a figure-ground reading dominates the plan view as compared with the preponderant volumetric aspect conveyed by the angled projection. e top row of figures shows the ideal shapes as solid projections that illustrate their figure-ground dynamic. All three of the forms project their centers outward. However, there are differences. e square’s orthogonal axes are parallel to its bounding perimeters and its diagonal axes pass through its corners. For the circle there exist infinite axes and tangents – the orientation of its conditional boundary will likely take cues from its context. e visual dynamic of the triangle reflects one of its principal features – each of its three axes pass through a corner, the center and a face. e second row of figures exhibit related figureground relationships. us the octagon projects an axis every .° and is similar to the square in its axisboundary relationships. e pentagon’s axes, like those of the triangle, pass through corner, center and face. ree of the hexagon’s face axes share their geometry with the triangle, however, each corner axis has a companion face axis at °. e resulting ambiguity is not dissimilar to that of the circle. ese forms allow us to understand the organization of the more complex figures in the next three rows. e relevant formal difference, as we see in later chapters, is the active negative space both along the perimeter and/or within a center courtyard. Figure 3: Overhead view of the fteen organizational gures rendered with walled perimeter. Figure 4: The same walled gures shown in parallel projection, mimicking a cabinet oblique drawing
1-INTRODUCTION DEMONSTRATION 1-2 The courtyard schema* ENCLOSURE AXIS *SCHEMA The courtyard SCHEMA follows an ARCHETYPE for The schema is a representation of a plan or concept organization.With origins in the campfire,ceremony in the form of an outline or model.The plural form is and fortification,examples appear in the architec- schemata. ture of nearly all cultures throughout time and across locale.They may be either open or roofed,geometric or organic,but all share formal themes of center and edge. Diagram:Perimeter Diagramming courtyards as Big Ideas begins with schema. distinguishing the relationships between perimeter and path,enclosure and axis.The images to the left use the square form as their starting place. In the first diagram,the perimeter schema shows a continuous form surrounding a central space(11). Rectangles and other straight-sided figures,circles and ellipses all follow from this basic idea. The second row demonstrates single-axis schemata Diagram 12:Single-axis Diagram1-3:Single-axis Diagram 14:Single-axis Each diagrams a path or parallel paths through or schema. schema. schema. across the central space (12-4).In the examples, the axes cross through the space at or near edges. Incomplete transit and central locations are also possible. The third row illustrates dual-axis schemata.Dia- grams15&6 both show incomplete transit,leading in and out of but not through the courtyard,the first located centrally,the second at the extreme Diagram 15:Dual-axis schema. Diagram 1-6:Dual-axis schema. Diagram17:Dual-axis schema. corner.Example 17 contains both central and edge paths,complete and incomplete transits. In the fourth row,three cross-axis schemata demon- strate complete axial symmetry (18)and two variet- ies of partial or hybrid symmetry (10). :show perimeter schemata aug- mented to include satellite forms. Diagram18 Cross-axis schema Diagram 1-9:Cross-axis :Cross-axis schema. schema. Figure 5:Thirteen courtyard schemes beginning with a simple perimeter and showing nine path variations and three symmetrical satellite configura- tions(left). Diagram:Perimeter with Diagram 1-12:Perimeter with Diagram1-13:Perimeter with comner satellites. center satellites. comer and center satellites 15
– DEMONSTRATION The courtyard schema* Diagram 1·1: Perimeter schema. Diagram 1·2: Single-axis schema. Diagram 1·5: Dual-axis schema. Diagram 1·8 Cross-axis schema. Diagram 1·11: Perimeter with corner satellites. Diagram 1·3: Single-axis schema. Diagram 1·6: Dual-axis schema. Diagram 1·9: Cross-axis schema. Diagram 1·12: Perimeter with center satellites. Diagram 1·4: Single-axis schema. Diagram 1·7: Dual-axis schema. Diagram 1·10: Cross-axis schema. Diagram 1·13: Perimeter with corner and center satellites. * e schema is a representation of a plan or concept in the form of an outline or model. e plural form is schemata. e courtyard follows an for organization. With origins in the campfire, ceremony and fortification, examples appear in the architecture of nearly all cultures throughout time and across locale. ey may be either open or roofed, geometric or organic, but all share formal themes of center and edge. Diagramming courtyards as Big Ideas begins with distinguishing the relationships between perimeter and path, enclosure and axis. e images to the left use the square form as their starting place. · In the first diagram, the perimeter schema shows a continuous form surrounding a central space (·). Rectangles and other straight-sided figures, circles and ellipses all follow from this basic idea. · e second row demonstrates single-axis schemata. Each diagrams a path or parallel paths through or across the central space (·–). In the examples, the axes cross through the space at or near edges. Incomplete transit and central locations are also possible. · e third row illustrates dual-axis schemata. Diagrams · both show incomplete transit, leading in and out of but not through the courtyard, the first located centrally, the second at the extreme corner. Example · contains both central and edge paths, complete and incomplete transits. · In the fourth row, three cross-axis schemata demonstrate complete axial symmetry (·) and two varieties of partial or hybrid symmetry (·). · Diagrams ·–: show perimeter schemata augmented to include satellite forms. Figure 5: Thirteen courtyard schemes beginning with a simple perimeter and showing nine path variations and three symmetrical satellite con gurations (left)
COURTYARDS AS OBJECTS DEMONSTRATION I-3 Courtyards as objects 1 Figure Overhead view of the twelve courtyard figures rendered as pure Figure2:The twelve courtyard figures rendered with walls in parallel projection. extrusions. Figure 3:The character of satellite perimeters can change dramatically when ordered around a dominant cross-axis scheme. 1 雪 Diagram3-1:Satellite perim Diagram3-2:Satellite perim- Diagram33:Satellite Figure 4:The organizational diagram of a Roman camp contains complex eter with cross axis schema. eter interrupted by cross axis perimeter modified by cross intemal paths ordered around a dominant cross-axis scheme. schema. axis schema. 16
DEMONSTRATION I Courtyards as objects Diagram 3·1: Satellite perimeter with cross axis schema. Diagram 3·2: Satellite perimeter interrupted by cross axis schema. Diagram 3·3: Satellite perimeter modi ed by cross axis schema. Figure 1: Overhead view of the twelve courtyard gures rendered as pure extrusions. Figure 2: The twelve courtyard gures rendered with walls in parallel projection. Figure 3: The character of satellite perimeters can change dramatically when ordered around a dominant cross-axis scheme. Figure 4: The organizational diagram of a Roman camp contains complex internal paths ordered around a dominant cross-axis scheme
1-INTRODUCTION DEMONSTRATION 1-4 Additional courtyard schemata PARTIAL ENCLOSURE Along with the fully enclosed courtyard,partially enclosed organizations also define interior space using perimeter forms.Their geometries vary broadly,but they result in defined and implied allied spaces. One category,the alphabetic schemata,derives its name from letter-form figures.They relate easily Diagram11:℃'schema. Diagram 1-2:T'schema. Diagram13:'H'schema. to ideal geometries by virtue of their regular form (1-1-3,586,889).In this context,there is little dif- ference between the square and most rectangles -they both have four sides,parallel and perpen- dicular.Similarly,the circle and ellipse correspond closely to one another and the all triangles share a common identity. Parallel (1-1-4)and perpendicular (17-8)forms can also suggest archetypal configurations while par- Diagram 1:Parallel schema. Diagram 1-5:''schema. Diagram 1-6:E'schema. tially enclosing space. Linear elements and smaller figures-dots-take the architectural structure of walls and columns and, by changing scale,define quite nuanced courtyard enclosures (110-12). Diagram 17:Pinwheel schema. Diagram 1-8:Cruciform Diagram 19:Hybrid 'U'schema schema. Diagram 1-11:Hybrid elements :Hybrid elements schema. schema. schema. Figure 1:Twelve partial courtyard figures shown as figure-ground diagrams (above). Figure 2:The twelve partial courtyard figures rendered with walls in paral- lel projection. 17
– Diagram 1·1: ‘C’ schema. Diagram 1·2: ‘T’ schema. Diagram 1·3: ‘H’ schema. Diagram 1·4: Parallel schema. Diagram 1·7: Pinwheel schema. Diagram 1·10: Hybrid elements schema. Diagram 1·5: ‘L’ schema. Diagram 1·8: Cruciform schema. Diagram 1·11: Hybrid elements schema. Diagram 1·6: ‘E’ schema. Diagram 1·9: Hybrid ‘U’ schema. Diagram 1·12: Hybrid elements schema. DEMONSTRATION I Additional courtyard schemata Along with the fully enclosed courtyard, partially enclosed organizations also define interior space using perimeter forms. eir geometries vary broadly, but they result in defined and implied allied spaces. · One category, the alphabetic schemata, derives its name from letter-form figures. ey relate easily to ideal geometries by virtue of their regular form (·–, , ). In this context, there is little difference between the square and most rectangles – they both have four sides, parallel and perpendicular. Similarly, the circle and ellipse correspond closely to one another and the all triangles share a common identity. · Parallel (·–) and perpendicular (·–) forms can also suggest archetypal configurations while partially enclosing space. · Linear elements and smaller figures – dots – take the architectural structure of walls and columns and, by changing scale, define quite nuanced courtyard enclosures (·–). Figure 1: Twelve partial courtyard gures shown as gure-ground diagrams (above). Figure 2: The twelve partial courtyard gures rendered with walls in parallel projection
CHAPTER Sorting through ideas Diagrams as method We have defined the diagram as an agent of analysis.The diagram reveals or proposes an underlying conceptual organization of some aspect of the physi- cal environment.Further,we have proposed that diagrams,in addition to representing architecture,actually constitute a kind of architecture,in and Circuit Symbol of themselves in the sense that they demonstrate or embody intellectual structure. 0 Push Switch ”,sh--mue In architectural study,diagrams are ubiquitous.They are also frequently sh-0-8kSwt中 idiosyncratic.At first glance,there appear to be few generalized conventions 00 On-fSwitch with which to read and to generate diagrams.The reasons for this intertwine with the historical narrative wherein architecture became a formal discipline Figure1:Electrical diagrams of both study and practice.It is a complex tale.However,our focus here is for switches.Even for these 0 most elemental functions,the practical,not historical.The underlying visual principles and intellectual atti- diagrams show a highly devel- tudes interest us.History aside,the lack of agreement upon a common prac- oped symbol system at work. tice results from the diagram's strengths-its inherent adaptability to purpose and context. The definitions in two dictionaries point to a first issue:do diagrams rep- ing Switch resent?"We believe they do,but that they are selective representations.They demonstrate,through abstraction,a particular subset of the fullness of real- ity.In the same way that we recognize x-rays as a selective picture of the body, diagrams tell us more by showing us less.More precisely,this suggests the diagram as a form of modeling.A MODEL,after all,chooses particular char- acteristics and places them in relation for common study and comparison. It translates select properties of a system or object into an alternate frame- *TWO DEFINITIONS work.In mathematics and the sciences,models make the very large and very Webster's defines the diagram as a 'graphic design that small manageable and graspable.Similarly,in mythology,models explain the explains rather than represents;especially a drawing unfamiliar with elements of the familiar."In both cases,they act through that shows arrangement and relations(as of parts).'In representation. contrast,the Oxford English Dictionary describes the Categorizing the diagram as a subset of the model clarifies its principal role: diagram as'a simplified drawing showing the appear- analysis,during or after the design process.A diagram attempts to under- ance,structure,or workings of something;a schematic stand something by selectively defining and isolating specific components. representation.' To analyze,after all,means to unbundle or pull apart,thereby enabling us to abstract the relevant from the whole.By utilizing only a fraction of the data available of its subject,the diagram operates with a high signal-to-noise ratio. **ON MYTH It makes things obvious (1). 'A myth is not a fairy story,it is the presentation of A good diagram engages simple elements to separate and convey complex facts belonging to one category in the idioms appropri- interactions for study and verification.The elements depend on the recogni- ate to another.'Gilbert Ryle,The Concept of Mind,p.8. tion of fundamental representational tactics and strategies to function.Thus
Circuit Symbol Component • function Push Switch • push-to-make Push-to-Break Switch On-O Switch • SPST 2-way Switch • SPDT Dual On-O Switch • DPST Reversing Switch • DPDT Figure 1: Electrical diagrams for switches. Even for these most elemental functions, the diagrams show a highly developed symbol system at work. * Webster’s defines the diagram as a ‘graphic design that explains rather than represents; especially a drawing that shows arrangement and relations (as of parts).’ In contrast, the Oxford English Dictionary describes the diagram as ‘a simplified drawing showing the appearance, structure, or workings of something; a schematic representation.’ ** ‘A myth is not a fairy story, it is the presentation of facts belonging to one category in the idioms appropriate to another.’ Gilbert Ryle, e Concept of Mind, p. . Sorting through ideas CHAPTER Diagrams as method We have defined the diagram as an agent of analysis. e diagram reveals or proposes an underlying conceptual organization of some aspect of the physical environment. Further, we have proposed that diagrams, in addition to representing architecture, actually constitute a kind of architecture, in and of themselves in the sense that they demonstrate or embody intellectual structure. In architectural study, diagrams are ubiquitous. ey are also frequently idiosyncratic. At first glance, there appear to be few generalized conventions with which to read and to generate diagrams. e reasons for this intertwine with the historical narrative wherein architecture became a formal discipline of both study and practice. It is a complex tale. However, our focus here is practical, not historical. e underlying visual principles and intellectual attitudes interest us. History aside, the lack of agreement upon a common practice results from the diagram’s strengths – its inherent adaptability to purpose and context. e definitions in two dictionaries point to a first issue: do diagrams represent?* We believe they do, but that they are selective representations. ey demonstrate, through abstraction, a particular subset of the fullness of reality. In the same way that we recognize x-rays as a selective picture of the body, diagrams tell us more by showing us less. More precisely, this suggests the diagram as a form of modeling. A , after all, chooses particular characteristics and places them in relation for common study and comparison. It translates select properties of a system or object into an alternate framework. In mathematics and the sciences, models make the very large and very small manageable and graspable. Similarly, in mythology, models explain the unfamiliar with elements of the familiar.** In both cases, they act through representation. Categorizing the diagram as a subset of the model clarifies its principal role: analysis, during or after the design process. A diagram attempts to understand something by selectively defining and isolating specific components. To analyze, after all, means to unbundle or pull apart, thereby enabling us to abstract the relevant from the whole. By utilizing only a fraction of the data available of its subject, the diagram operates with a high signal-to-noise ratio. It makes things obvious (). A good diagram engages simple elements to separate and convey complex interactions for study and verification. e elements depend on the recognition of fundamental representational tactics and strategies to function. us