Space Syntax A Tool For Understanding Spatial Organization and its Change Over Time. Dr Abir Bandyopadhyay National Institute of Technology, Raipur

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1 Space Syntax A Tool For Understanding Spatial Organization and its Change Over Time Dr Abir Bandyopadhyay National Institute of Technology, Raipur In the 15 th Century, many European communities came to India in order to establish trade that resulted in colonization of whom, the British were most successful. In India, the initial colonial buildings (of the Europeans) were designed to meet the specific demands of colonial style of life and they were consciously designed to differ from original native styles. Over time, British builders in the Empire also had to take into account the demands of the climate of the region. (Metcalfe, 37-65). This resulted in development of bungalows and other forms of houses for the Europeans in India. The Indians, on the other hand, were also influenced by the colonizers and, hence, they frequently used classical motifs and European styles in their own houses. The influences resulted in buildings, various functional spaces are organized as per the behavioral patterns of users. These behavioral patterns are, in turn, governed by the cultural and social norms, which get ingrained in the spatial organizations of the buildings. 1 Discursive statements about these cultural and social factors have enough scope of personal biasing, individual understanding, and interpretation of meanings. To avoid these shortcomings, the present paper uses Space Syntax Analysis as a tool to analyze and understand the pattern of spatial organization and how this has changed over time. Space Syntax is a tool by which buildings are transformed into dimensionless forms or into the form of adjacency graphs to represent, quantify and interpret spatial configuration in buildings in such a way that their underlying social logic can be understood. These syntactic statements are the abstract (inequality) genotypes. Recent studies have defined the inequality genotypes with a slight modification of this definition. It has also been defined as the ranking of programmatic labeled spaces according to their mean depth (most often represented in terms of their integration values) of nodes of the graph of spatial configuration to which they correspond or as a statistically stable pattern of variation of a given rank order of space labels (Bafna, ). For the present study, 104 independent houses, made of permanent materials, in and around Kolkata during the Colonial Period, and also in modern era, were selected. The houses made during the colonial period were basically of two types with courtyards (31 in number in the sample) and without them (23 in number in the sample). The houses with courtyards are typical examples of hybrid styles made for the traditional Bengali elites. The houses without courtyards were made for the European colonizers (and for the anglicized Indians) during the late 19 th and early 20 th century. In the sample there are 50 modern houses. THE METHODOLOGY For the present study, the plans of the buildings are reduced to abstract maps known as access graphs that depicts the topographical properties. Here, the spaces are designated as circles and lines radiating from it signify access points to and from the space. The access graphs are converted into justified (or j-graphs), where, any one circle of the access graph as the root and the spaces in the graph are then aligned above it in levels according to how many spaces one must pass through to arrive at each space from the root. The concept of depth of a space from the root is the height of that space in the justified graph. From the depth of a node in a j-graph the integration values, or RRA (Real Relative Assymetry values) are found. The RRA values are the normalized version of the average depth of any given node from all other nodes in a graph. Higher RRA values indicate greater 1 See Hillier and Hanson (1984), especially chapters one, two and for a detailed description of the concept and process. 426

2 segregation and lower values indicate higher integration of the node with respect to the entire graph. The spaces are arranged as per the order of RRA values. This reduction reveals a set of patterns that partially manifest a culture s social presuppositions in a way plans themselves do not immediately reveal. If a consistent pattern of spatial organization is observed across a sample, then such spatial patterning is known as inequality genotype. The genotype describes the integration (and segregation of spaces) as per their access relations. The mathematical formulae to describe these are described as : The mean depth of a space i (MD i ) can be shown as: MD i = n " j = 1 d ij ( n! 1).(1) where n is the number of spaces, d ij is the shortest distance between two points i and j in a graph G, and! n d ij j = 1 is the total depth of the i th space. The MD is generalized by comparing how deep the system is from a particular point with how deep or shallow it theoretically could be the least depth existing when all spaces are directly linked to the original space and the most depth when all spaces are in a unilinear sequence away from the original space. This generalization is represented through relative asymmetry (RA) value, which is the mean depth expressed as a fraction of the maximum possible range of depth values for any node in a graph with the same number of nodes as the system. This is calculated by: 2( MDi! 1) RAi = (2) ( n! 2) This will give a value between 0 and 1, with low values indicating a space from which the system is shallow (i.e. more integrating) and high values indicating a space from which the system tends to be segregated. However, if comparisons are to be made across systems that differ significantly is size, one has to make some transformations in the RA values to eliminate the effect of size on the levels of RA values in the real system. These transformed RA values are known as Real relative asymmetry (RRA) values. The transformation of RA to RRA values is shown as: RAi RRA i =..(3) Dn where RRA i is the Real relative asymmetry value of space i, and D n is the transforming factor. The D n values may be calculated by a formula which is: 2( n( log2( n + 2) / 3)! 1) + 1) D n =.(4) ( n! 1)( n! 2) The spaces are then arranged as per the order of integration (or RRA) values. This arrangement reveals a set of patterns that partially manifest a culture s social presuppositions in a way plans themselves do not immediately reveal. If a consistent pattern of spatial organization is observed across a sample, then such spatial patterning is known as inequality genotype. To show how strong or weak the inequality genotypes are, Hillier et al. has developed an entropy based measure called difference factor to quantify the degree of difference between integration values of three (or more, with modified formula) spaces of functions. This is shown as: = &, )# &, )# &, )# -. a a b b c c H $ ln * '! + $ ln* '! + $ ln* '! % t + t (" % t + t (" % t + t..(5) (" where H is the unrelativised difference factor for three spaces a, b and c, and t is their sum. This H is relativised between ln2 and ln3 to give a relative difference factor (RDF), H*, whose value ranges between 0 (the maximum difference, or minimum entropy) and 1 (the minimum difference, or maximum entropy) (Hillier et al., ). 427

3 ln2 H * = H!..(6) ln3! ln2 The second configurational property of choice is measured by the number of alternative routes from one node to another in a j-graph.. Hillier et al. has used the space-link ratio (SLR) as measure of relative ringiness. It is expressed as: e +1 SLR =.(7) n where, SLR is the space link ratio, e is the number of links (edges) in the complex and n is the number of nodes. SLR has been systematically used in space syntax studies to get the indication of the degree of ringiness in the complex. A perfect tree has a value of 1, and a value above 1 denotes the degree of ringiness in a complex. Amorim argues that SLR does not allow the comparison between systems of different sizes as the value that expresses maximum ringiness of a system depends on its size (Amorim, 19.3). He has suggested the use of relative connectivity to account for number of connectivity in a graph. The relative connectivity is measured as: e! ( n! 1) RC =..(8) 2n! 5 where, RC is relative connectivity, e is the number of links in a complex, and n is the number of nodes in the graph. RC would have a value of 0 for a perfect tree and 1 for the maximum possible number of links a graph can have. The other tools that are frequently used for the description of the structure of a gamma map are the connectivity and the control values. Connectivity of a single space (or room) is simply the number of doors into it; or the degree of a particular node i.e. the number of edges incident on a node in a graph. n c i =! a ij..(9) j = 1 where c i is the connectivity of a space i and a ij is the entry of i th row and j th column of the adjacency matrix A. The number of connections that are two doors (or two edges) away in a j-graph is also sometimes useful for description of the spatial organization. These are called second-order connectivity and are defined as: n n c2 i =! aijcij "! aij (10) j = 1 j = 1 where c2 i is the second order connectivity of a space i; a ij is the adjacency vector the row of 0 s and 1 s in the adjacency matrix A, and c ij is the connectivity vector for all the spaces. The products for the spaces (a ij and c ij ) that are directly connected will equal their number of edges, while they will equal 0 for those rooms that have no direct connection. The sum of the products is therefore the sum of the edges for all the connected spaces. However, these edges include those leading from the space in question to the connected spaces. Therefore, to convert the total spaces to unique routes, the number of edges that lead from the space in question to the connected spaces has to be subtracted (Neiman, 4 ). Control is a measure of the extent to which a given space controls the access to the spaces that are adjacent (immediately connected by an edge) to it. If each space has a certain number of n immediate neighbours, then each space gives to its immediate neighbours 1/n, and these are then summed for each receiving space to give the control value of that space (Hiller and Hanson, 109). The control of space is inversely proportional to the connectivity of the adjacent spaces. The formula is: 428

4 n 1 ctrli =! aij (11) j = 1 cij In other words, the control for the i th space can be computed by multiplying its adjacency vector the row of 0 s and 1 s in the adjacency matrix A by the reciprocal of connectivity values of all the spaces and summing the products. The products for the spaces that are directly connected will equal the connectivity reciprocals, while they will be 0 for the those spaces that are not connected. The sum of the products is therefore, the sum of the connectivity reciprocals of the connected spaces (Neiman, 5). THE ANALYSES The syntactic data compiled thus, are compared to find any difference in the spatial organisation between the houses of colonial and modern periods. Overall comparison of colonial and modern houses The inequality genotypes of the three types of houses (i.e. houses having courtyards (CY), houses without courtyards (WCY) and modern houses (MOD) at a broad abstract level, as analysed form the collected samples, comes as: CY: Circulation area < Bedrooms< Other family spaces = Service spaces < less frequent spaces. WCY: Circulation spaces < Dining spaces < Other family spaces = Service spaces. MOD: Dining spaces < Circulation spaces < Bedrooms < Other habitable spaces= Service spaces (and other circulation spaces). From these abstract genotypes, it is observed that in colonial houses, circulation spaces are most integrating. The next integrating position in the houses without courtyard (WCY) is the dining room; and in the houses with courtyard (CY), the next most integrating space is the bedroom. In modern houses (MOD), the dining is the most integrating space and after it, the genotype shows a similar pattern as seen in colonial houses with courtyard (CY). Thus, the integrating dining of WCY and the general pattern of CY are both amalgamated in modern houses (MOD). The mean RRA values of the houses in CY, WCY and MOD are statistically tested to find out any syntactical differences in them. For this, side-by side box plots are drawn. The side-by-side box plots (Figure 1) show overlapping distributions but slightly different midspreads and ranges in CY and WCY. MOD shows that the data is little skewed and have a deeper range. Statistical difference of the mean integration values was found out. The mean RRA values of the three types of houses were transformed to natural logarithmic values and then were put to Levene s test of homogeneity of variance. It was found to be homogenous (p=0.101) after transformation. The normalities of the transformed data sets are tested by Lilliefors and Anderson-Darling tests, and are found as normally distributed. The results of ANOVA show that the data sets are significantly different (p<0.001). Bonferroni s multiple comparison test showed the difference among the groups. CY was not significantly different from WCY (p=1.000), but different from MOD (p=0.004). WCY was found to be significantly different from MOD (p=0.001). 429

5 Figure 1. A Box plots of mean RRA values in three types of houses. A significant difference between old houses and modern houses suggests that spaces within modern houses are deeper and more segregated. The observed differences in the distribution of RRA values over CY, WCY, and MOD require closer examination of patterning of spatial placement and functions. To do this, the syntactic data are compared along with the ordering of spaces and other information of all the house types. The comparisons are done to understand the differences among the house types in two broad areas. These areas are: differences in the general features of the houses, and in the syntactical values of the houses The following sections discuss these differences. Comparison of the general features of the house-types To understand the differences in the general features of the house-types, the number of spaces, the number of links, the SLR and RC values of the three types of houses are compared. These are shown in Table 1. The mean number of spaces and the mean number of links reduces from CY to WCY to MOD. However, when the mean space-link ratio and RC values are compared, it is observed that the houses without courtyards (WCY) have more numbers of rings in them, providing multiple accesses to various spaces. Table 1 Comparison between numbers of spaces, numbers of links, SLR and RC values Types CY Change CY-WCY WCY MOD CY-MOD WCY-MOD Amount Percent Percent Percent Amount Amount change change change number of spaces number of links space-link ratio (SLR) RC value Note: CY-WCY represent the difference between CY and WCY; similarly, CY-MOD and WCY- MOD represent the differences between the first type and the second type of houses respectively. 430

6 Comparison of syntactical values The comparisons of the syntactical values highlight differences in the intrinsic characters of the spatial organisation in the three types of houses under consideration, which are not apparent from the layout of the spaces in them. The average MD, mean RRA, mean RDF, access levels, mean connectivity, mean second-order connectivity and the mean standard deviation of the control values are compared to emphasize the differences. Figure 2 and Table 2 compares these syntactic measures. This shows that the functional differentiation among spaces in the modern houses is stronger than the other types of houses. The table also shows that the houses without courtyard had more inter-connections among the spaces than the other two types. In CY, the second order connectivity (c2) is 3.39% higher than the houses without courtyard; and it is 44.64% higher than the modern houses. Because of large number of spaces in the houses with courtyard, the circulation and transitory spaces have played an important role in providing the connections to various spaces and at the same time segregating the spaces from one another. Whereas in modern houses, due to lesser number of spaces and more functional differentiation among them (as they have strong RDF values), specific functional accesses to various spaces are found. There is 36.23% reduction in the mean standard deviation of control values from houses with courtyard to modern houses. The comparison between the control values between the houses without courtyard and modern houses show that there is a slight difference in their standard deviations (a reduction of 9.66%). This shows that in modern houses it is less likely that one or two spaces dominate the access to others spaces, and in houses with courtyard, it is observed that one of two spaces (mostly the circulation spaces) control the access to other spaces. Figure 2 Comparison between syntactic data 431

7 Table 2 Comparison between syntactic data. Spaces CY Change WCY MOD CY-WCY CY-MOD WCY-MOD Amount Percent Amount Percent Amount Percent Average MD Average RRA Average RDF Access levels connectivity (c) (c2) SD of control values Note: 1.CY-WCY represent the difference between CY and WCY; similarly, CY-MOD and WCY- MOD represent the differences between the first type and the second type of houses respectively. 2. The RDF is calculated between the mean, maximum, and minimum RRA values. Table 3 shows two most controlling and two least controlling spaces in the three types of houses. The figures in brackets show the percentage of houses in the sample having these spaces as most controlling and least controlling. Table 3 Comparison of the most and the least controlling spaces Types Most controlling of houses CY WCY MOD Least controlling Veranda (64.52%) Bed (29.7%) Passage, garden, courtyard (9.68% each) Store (28.22%) Garden (30.43%) Store and bathroom (13.43% each) Veranda (26.09%)) Exterior (8.96%) Dining room (25.49%) Bathroom (28.99%) Garden (19.61%) Bedroom (19.57%) The control values are more evenly distributed amongst the spaces in modern houses, whereas in houses with courtyard, about 93.5% of the accesses are controlled by circulation spaces like veranda, passage, garden, and courtyard. In 78.26% of the houses without courtyards, most controlling spaces are the circulation spaces like garden, veranda and passage; whereas in modern houses, the maximum control is through the dining space (in 25.49% cases) and the garden (in 19.61% cases). Changes in colonial and modern houses over time To understand how the colonial and modern houses have changed over time, the houses in the sample are re-grouped based on their year of construction (from 1900 A.D. to 2000 A.D.) and the period is divided into 5 equal groups of 20 years each. The houses made before 1900 is taken under one group and the houses constructed between 1900 and 2000 are grouped in four parts as per their year of construction. Table 4 shows these groups with the house numbers in each group, total number of houses and the mean number of spaces. Houses constructed between 1940 and 1959 were not collected in the sample to show the changes in modern houses more prominently. The basic syntactic data of the houses belonging to each group are compared to find out any trend in them. These trends are only indicative and to get any assertive trend of changes that has taken place over time, more number of houses are required to be incorporated in the groups; which is beyond the scope of the present study. 432

8 Table 4 Grouping of houses by year of construction House type CY WCY MOD Year Total Number of number houses spaces Total of Number of houses number of spaces Total Number houses of number spaces < of Table 5, Figures 3 and 4 give the changes that have taken place on the access levels, space-link ratio (SLR), and relative connectivity (RC) of the houses. Table 5 Changes in access levels, SLR, and RC over time House type CY WCY MOD Year Access Level SLR RC Access Level SLR RC Access Level SLR RC < Values of Access Levels Access level WCY Access level CY Access level MOD < Years Figure 3 Changes in mean Access Levels over time 433

9 Between year-groups and , the mean access levels in CY have reduced and during the same periods, the access levels of WCY has increased. The access levels of CY and WCY in the period are similar (in WCY it is slightly higher by 0.084). The modern houses show an increase in the access levels (by 0.617) in between and This is due to more functional asymmetry in the spatial organisation in these houses. The decrease in access levels in CY shows that in time, these houses have become less deep due to lesser number of spaces (Table 5). The change in presence of rings in these houses is reflected in the changes in the SLR and RC values. It is observed that all the RC and SLR values have decreased in time, signifying that the interconnections among the spaces are getting less and thus the spaces are gaining more functional identity SLR of WCY SLR of MOD 1.2 Values SLR of CY RC of WCY RC of CY RC of MOD 0 < Years Figure 4 Changes in mean SLR and mean RC values over time. The mean number of connectivity, the mean second order connectivity and the mean standard deviation of the control values are also compared. The results are given in Table 6 and Figures 5 and 6. In CY, the mean connectivity of the spaces in the years has remained almost the same (showing only a slight reduction in time), but the mean connectivity of spaces in WCY is much higher between 1900 and This shows that the average number of connections of spaces has greatly reduced from 1900 to 1939 in the houses without courtyard. It may be said that the number of connections in a room in MOD (during ) was similar to the houses with courtyard (having a value around 2), where as WCY always had more numbers of connectivity. 434

10 Table 6. Changes in connectivity, second-order connectivity (c2) and standard deviation of control values over time. House type CY WCY MOD Year Connectivity c2 SD of Ctrl Connectivity c2 SD of Ctrl Connectivity c2 SD of Ctrl < Values C2 of WCY C2 of MOD C2 of CY C of WCY C of CY C of MOD < Years Figure 5. Changes in connectivity and second order connectivity values over time. The second-order of connectivity of both CY and WCY has sharply reduced. In modern houses, the second order connectivity remains much lower than the old houses (Figure 5). SD of Ctrl CY Values SD of Ctrl WCY < SD of Ctrl MOD Years Figure 6. Changes in standard deviations of control values over time 435

11 The standard deviations of control of CY are higher than that of WCY of the same period. The multiple numbers of spaces, their interconnections through verandas and other circulation spaces lead to higher control values of these spaces. In MOD the standard deviation of control values are much lower. Comparison is also made on the average mean depth, average RRA and mean RDF values in the three types of houses over time. The findings are tabulated as Table 7 and are shown in Figures 7 and 8. Table 7. Changes in average MD, mean RRA and mean RDF values over time House type CY WCY MOD Year MD RRA RDF MD RRA RDF MD RRA RDF < Note: The RDF values are computed between maximum, minimum and mean RRA values. The average mean depth of the houses with courtyard shows a decrease in values over time but in WCY it has increased from 1900 to In MOD the average mean depth also shows some increment. The mean RRA value of modern houses remains mostly constant from 1960 to The overall mean RRA value of modern houses is higher than that of the old houses, showing a much asymmetric (segregated) structure of spatial organisation. The mean RDF in CY has decreased from 436

12 MD of CY MD of MOD Values RRA of CY MD of WCY RRA of WCY RRA of MOD < Years Figure 7. Changes in average MD and mean RRA values over time RDF WCY Value RDF CY RDF MOD < Years Figure 8. Changes in mean RDF values over time to in the years showing that in the houses with courtyard there was an increased trend of differentiation of the minimum, mean and maximum RRA values (or in other words, the spaces were getting more functionally differentiated). The RDF of WCY has also decreased from 1900 to In the modern houses, the RDF remains mostly same, suggesting that the functional differentiation among the spaces have become more or less stabilised in these houses. Conclusion From the comparative analyses it is observed that the houses with courtyard (most of the examples were constructed during 1880 and1938) were made in response to the then social need of the orthodox Hindu families. Segregation of groups of spaces by verandas and circulation corridors diminished the functional differences among the spaces. Houses without courtyard were made for the Europeans or for the anglicised Indian families. Most of the houses in the sample were made during 1900 and 1940 (some of them are bungalows made for European officers; where others were made for the Indians, mostly in high government posts). These houses, in their own contexts, also met the social demands. Lesser requirement of in-house functional 437

13 segregation in these houses led to the development more number of rings (and less RDF values) among the spaces. Though the spaces were having more interconnections, the movement restrictions within these houses were achieved through control. In modern houses, the functional segregation is much more than that in the old houses. Comparing the houses over the time, it is observed that the differences in the syntactical data that existed in the courtyard and without courtyard type houses in the early 1900s, were gradually narrowing down. The number of spaces were reducing, the RRA values were also getting closer and so also the connectivity and second-order connectivity of the spaces. The social, economical and political changes that were done in the early colonial and early imperial times were gradually changing the life of the Indians in this region and all the changes lead to the development of a new culture, that was to change the life-style of the Indians. These changes were reflected in the late colonial houses, where the differences between the Indian and the anglicised, between native and European was narrowing down. The development of modern houses is a step forward, and even when the samples were collected 20 years after independence, it is observed that they still have similar syntactical character of the late colonial houses, of course with certain modifications (like more functional identity of spaces), transformations (like, changing nature of dining spaces and bathrooms) and adaptations (like incorporating drawing and dining together to create a hall for occasional family use). 438

14 Works Cited Amorim, Luix. Houses of Recife: From diachrony to synchrony. Third International Space Syntax Proceedings 7-11 May 2001: Bafna, Sonit. Geometrical Intuitions of Genotypes. Third International Space Syntax Proceedings 7-11 May 2001: Hillier, B. and Hanson, J. The social logic of space. Cambridge: Cambridge University Press, Hillier, B. et al. Ideas are in things: the application of the space syntax method to discovering house genotypes. Environment and Planning B: Planning and Design.Vol : Metcalfe, T. R. Architecture and the representation of empire: India, Representations 6 : Neiman, Fraser D. A Very Brief Introduction to Space Syntax Analysis. Issues in Historical Archaeology, Anthropology 589a. Spring 2003: