Patterns of physical space – data collection and analysis

The methods used to establish meso level patterns of space are those developed by the Space Syntax community in the field of architecture. Two key concepts are used, that of configuration, defined on page 31, and correspondence, defined on page 32.

3.6.1.1 Spatial configuration

Configuration of space is the relationship of all spaces in a spatial system to all others. The methods developed by the Space Syntax community are used to quantify patterns in the configuration of the spatial systems studied. Space Syntax is a network theory of space and hence the methods used avoid the problem of methodological individualism in the analysis of space.

Space Syntax researchers use software called ‘depthmapX’ to analyse spatial relationships in complex buildings. The software calculates lines of sight, movement paths and distances from all positions to all other positions across spatial systems of any size and complexity. These basic measures are then manipulated using graph theory to calculate the range of measures developed by Space Syntax to describe spatial configuration in a wide variety of ways. The analysis starts with a detailed scale plan of the office layout used by the organisation with each of the rooms used labelled according to the descriptions used in practice. In

‘depthmapX’, the spatial system is divided into a grid of 60cm squares, roughly the width of a person’s shoulders, placing the analysis on an intuitively understandable human scale. Patterns of configuration are established by calculating lines of sight for every square on the grid. This is done by connecting the centre of each square, known as the node, to every other node in the spatial system with which it has a direct line of sight. A visibility relationship between every node in the grid with every other node in the grid can then be calculated using graph theory. The spatial system in ‘Law’ contains 6,300 nodes. At its core, Space Syntax uses the idea of depth, usually referred to as ‘visual step depth’, in its analysis of spatial configuration. A node is a visual step depth of 1 from every other node to which it has a direct line of sight. A node in the spatial system that cannot be seen directly from the first node but can be seen from a node that is a step depth of 1 away, is a step depth of 2 from the first. In other words, if a person needs to turn once, from a direct visible path, to a second visible path in order to reach a second point, the starting point is a step depth of 2 from the finishing point. Visual step depth, therefore, describes the relationship between any two points in a spatial system. In this way, the depth of any point from all other points in the system can be calculated and shown graphically. Figure 3.9 shows visual step depth to all points in a spatial system from the main entrance of the building marked as A.

Figure 3.9: ‘Heatmap’ showing step depth from entrance point A in ‘Law’

Source: Output from depthmapX software Figure 3.10: ‘Heatmap’ showing visual mean depth on ground floor of ‘Law’

Source: Output from depthmapX software

The main entrance to the building is marked ‘A’. The map is colour coded to represent step depth from 'A’. Orange represent all the points in the office that are a step depth of 1 from the main entrance. Yellow, a step depth of 2 and dark blue a step depth of 8. All three floors of the building are shown and these are connected via a staircase and lift.

‘A’

Breakout

Boardroom Open plan office

Atrium

Client meeting rooms

The numerical value for visual mean depth of every point are shown, each colour represents a band of values. More integrated points, those with a lower step depth to every other point, are shown in the warmest colours. In this case, the red areas are the most integrated in the building with a visual step depth on average to all other points of approximately 3.8. The blue areas are the most segregated, they have a visual step depth of approximately 7.2.

The measure of visual step depth forms the basis of the Space Syntax measure which highlights how integrated or segregated any space is in the wider system. The integration of any space in a spatial system is calculated as the average step depth to all other points and is known as visual mean depth (VMD). A point that has a low VMD is well integrated within the spatial system, so is a low average step depth to all other points. Whereas a point with a high VMD is considered segregated (see figure 3.10) because the average step depth to all other points is high. The average of the visual mean depths for all points in the system, that is the average visual step depth of all points to all other points, provides a system level value labelled the average visual mean depth (AVMD). This system level value provides a measure for how well connected are all spaces and is commonly referred to as the level of integration

of a spatial system.

In the system shown in figure 3.10, the AVMD is 4.6, but this varies for each point in the spatial system and ranges from the most integrated space with an VMD of 3.8 to the most segregated space of 7.2. The AVMD gives a sense of the degree of integration of the entire system and can be compared with other spatial systems. This measure has been related to the notion of a ‘generative’ building. Buildings with more integrated spatial systems overall (lower than AVMD’s) were considered ‘generative’ because they have been shown to generate more unplanned interaction than more segregated spatial systems (all other things being equal) (Sailer et al., 2012).

The areas allocated to each type of space were also measured. Spaces were divided into four categories in the spatial system studied: 1) Workspaces: typically, the areas where desks for use of inhabitants or employees are placed; 2) Areas of transit: any space whose primary use is to move people from one area of the office to another; 3) Flexible facilities: any space that was not allocated to either desks or transit, and does not require booking for its use (such as breakout areas); 4) Bookable facilities: any facility that does require booking for its use (such as meeting rooms). These four categories of space are mutually exclusive and in combination account for the entire spatial system.

3.6.1.2 A quantitative measure for correspondence/non-correspondence

Correspondence is a socio-spatial concept central to Space Syntax theory. However, a quantitative measure for correspondence has not been developed by the Space Syntax community and is therefore not possible in depthmapX.

This is an important omission because quantifying the spatial structure alone is insufficient to meet the objectives of this research. The literature chapter identified the potential problem of placing too great an emphasis on spatial analysis and relegating the importance of social analysis. Therefore, this research also needs a measure for the relationship between the social structure and spatial structure, known as correspondence. This section develops a measure for correspondence specifically for this research.

On page 34 of the literature chapter, the examples of Tallensi and Hopi societies were described as examples of correspondent and non-correspondent socio-spatial systems respectively. A quote by Tom Peters was used to illustrate non-correspondence in an organisational context; “jamming people from disparate functions together in the same room” (Peters, 1990, p. 23), takes people who are socially distant and places them close spatially. Non-correspondence socio-spatial systems are of particular interest to this thesis because they describe systems with weak boundaries between groups and thereby encourage broader social interaction that leads to generative or emergent social relationships (Sailer et al., 2012; Hillier and Hanson, 1984; Hillier, 1996; Kornberger and Clegg, 2004).

Conceptually, correspondence is the degree of overlap between transpatial (social) affiliations between people and their position within a spatial structure. Correspondence represents a high degree of overlap between transpatial and spatial relationships and non- correspondence a low overlap. A measure of association between transpatial affiliations and positions within spatial structure that shows the strength of the relationship between the two will give an indication of the level of correspondence in a socio-spatial system. For this, a measure of association between two dichotomous variables was required.

Yule’s Q is a measure of association used in social sciences (Bryman, Liao and Lewis-Beck, 2004) which highlights the strength of relationship between two dichotomous variables. Yule’s Q is expressed as a single ratio of association that falls between -1 and 1. 1 represents

a perfect positive association between the two variables, -1 a perfect negative association and 0 (zero) no association.

The two variables required for a measure of correspondence in an organisation’s socio-spatial system are spatial closeness/separation and transpatial (or social) closeness/separation. For example, people who work at the same desk cluster might be considered spatially close and people working at different desk clusters to be spatially separated and people who work for the same department might be considered transpatially close. However, this thesis uses a dynamic definition of spatial closeness developed by Kabo et. al. (2015) that includes movement to capture the possibilities of encounter, thereby avoiding the limitations of simple distance between desks. This means that spatial closeness is defined as the total number of people each individual is spatially close to at some point during a typical day, not just those that are close by virtue of the position of a desk.

One of the transpatial bonds between individuals in an organisation tends to reflect reporting structures in the organisation chart, for example the department they work for. In that case members of the same department would be considered to be transpatially close and members from different departments transpatially separated.

The figures for spatial closeness/separation and transpatial closeness/separation are calculated for each individual. To calculate correspondence for groups the scores for the individuals within that group are averaged.

The formula for calculating Yule’s Q using the variables for correspondence is as follows; Q = (ad-bc)/(ad+bc).

The variables a,b,c and d are described in table 3.3 below. In table 3.3, each variable represents the average of all individual scores: a represents the number of individuals who are both spatially close and transpatially close; b represents the number of individuals who are spatially separated but transpatially close; c represents the number of individuals that are spatially close but transpatially separated; and d represents the number of individuals that

are both spatially and transpatially separated. Table 3.4 defines each of these variables from the perspective of the individual.

Table 3.3: Variables used in Yule’s Q for the measure of correspondence

Spatially Close Spatially Separated

Transpatially Close a b

Transpatially Separated c d

Defined this way the correspondence being measured is an intra/inter departmental correspondence between people within the same social network – in this case the organisation. It is also possible to calculate correspondence for multiple social networks by including data for visitors to the organisation. In this case, rather than define the main transpatial relation as the department, in this broader definition, the main transpatial relationship is classified as working for the organisation. People would be considered transpatially close if they worked for the organisation being studied (an inhabitant in Space Syntax terms) and transpatially separated if not working for that organisation (a visitor in Space Syntax terms). Defined this way, the correspondence being measured is between inhabitants and visitors. In this thesis these two types of correspondence are labelled Q(intra/inter) and Q(inhabitant/visitor) respectively.

Table 3.4: Calculation of correspondence: Q(intra/inter)

Q(intra/inter) Spatial Closeness Spatial Separation Totals

Transpatial

Closeness Number of people in my department that I am spatially close to at some point in a typical day Number of people in my department that I am not spatially close in a typical day

Total number of people in my department (minus one because excludes the individual responding) Transpatial

Separation Number of people not in my department that I am spatially close to at some point during the day Number of people not in my department that I am not spatially close to in a typical day Total number of people not in my department

Totals Total number of

people I am spatially close to at some point during a typical day

Total number of people that I am not spatially close to at some point in a typical day Total number of people in the organisation (minus one)

Table 3.5 defines each of the variables for correspondence in Q(inhabitant/visitor) from the individual’s perspective.

Table 3.5: Calculation of correspondence: Q(inhabitant/visitor)

Q(inhabitant/visitor) Spatial Closeness Spatial Separation Totals

Transpatial

Closeness Number of people in my organisation that I am spatially close to at some point in a typical day Number of people in my organisation that I am not spatially close to in a typical day Total number of people in my organisation (minus one because excludes person responding) Transpatial

Separation Number of visitors that I am spatially close to at some point during the day

Number of visitors that I am not spatially close to in a typical day Total number of visitors

Totals Total number of

people I am spatially close to at some point during a typical day

Total number of people that I am not spatially close to at some point in a typical day Total number of people in the organisation (minus one) plus the

number of visitors in a typical day

The two measures for correspondence, Q(intra/inter) and Q(inhabitant/visitor) represent a measure internal to the organisation and external respectively. An internal Yule’s Q(intra/inter) of 1 represents perfect correspondence between the spatial structure of the organisation and the transpatial structure and means that the only people that interact are in the same department. In an organisation with a Yule’s Q(intra/inter) of close to 1 we would expect to find a profile of interaction weighted towards intra-departmental and away from inter- departmental. A Yule’s Q(intra/inter) of -1 represents a perfect negative correspondence. In other words, the only people that interact are from different departments. In an organisation with a Yule’s Q(intra/inter) tending towards -1, we would expect to find a profile of interaction weighted towards inter-departmental and away from intra-departmental. A Yule’s Q(intra/inter) of 0 (zero) represents non-correspondence which means the odds of interacting with people from your own department are the same as the odds of interacting with people from other departments. In an organisation with a Yule’s Q that tends towards 0 (zero) we

would expect to find an interaction profile that is well balanced between intra and inter- departmental.

The external measure of correspondence has been labelled Q(inhabitant/visitor). An external Yule’s Q(inhabitant/visitor) of 1 means that inhabitants only ever interact with each other and never with visitors. An external Q(inhabitant/visitor) of -1 means that inhabitants only ever interact with visitors and never with each other. Both 1 and -1 are forms of socio-spatial correspondence. An external Q(inhabitant/visitor) of 0 means that the odds of interacting with a visitor are the same as the odds of interacting with someone from your own organisation. Relating these calculations for correspondence back to the theory, scores for Yule’s Q tending towards -1 and 1 represent high levels of correspondence that suggest a conservative socio- spatial system. Scores for Yule’s Q tending towards 0 (zero) represent non-correspondence that suggest a generative socio-spatial system, one where new and unexpected social interactions are likely to be generated and the characteristics of strategy emergence are evident. The profile of interaction for socio-spatial systems with Yule’s Q closer to 0 (zero) reflects a greater diversity and more even spread of unplanned interaction across the population.

3.6.1.3 Gathering data required to calculate correspondence

To gather the data required to calculate spatial closeness in the case of ‘Law’, typical movement paths of people using the spatial system were observed. These were plotted in real time onto representations of the office space and transposed into the depthmapX software. An example is shown in figure 3.11 of the most common movement paths of an individual in ‘Law’ where the thickness of each line represents the frequency of movement along that path. For example, the most common movement path for the individual represented in figure 3.11 was from the rear staff entrance of the building, up the rear stairwell and across the open plan office to their desk.

The definition of spatial proximity used in this thesis is that proposed by Kabo et. al. (Kabo et al., 2015) where two people are considered to be spatially proximal if their paths overlap. To calculate the number of people this individual was in spatial proximity to this path was with

those of the others using of the building. The chance of overlap was reduced as the frequency of movement along a path reduced.

In total fifty-four observation sessions of four to five hours each were conducted, totaling two-hundred and thirty hours of observation over the nine-month period. These observation sessions were used to gather interaction data as well as data on movement paths.

Figure 3.11: Typical movement path for an individual in ‘Law’

Source: Output from depthmapX software The calculations of spatial proximity using the method described above were verified by observing the actual spatial proximity of fifteen individuals for a total of eight hours each (a typical day), a total of 120 hours of observation. Field notes were made of the number of people with whom each individual was spatially proximate at some point and these actual results were compared with those obtained by the path overlap calculation described above. This allowed for refinements to be made to the path overlap calculation such that it reflected the spatial proximity observed in practice.

In the calculations for correspondence, two measures were used for transpatial closeness. For internal correspondence someone was considered transpatially close if a member of the

same department and any member of a different department (or a visitor to ‘Law’) was considered transpatially separated. For inhabitant/visitor correspondence, someone was considered transpatially close if employed by ‘Law’ and transpatially separated if a visitor to ‘Law’. In combination, this data was used to calculate internal and inhabitant/visitor correspondence and is reported in the findings chapter 4.

In phase two of the research, calculations of correspondence were made in comparative