Introduction

The temporal experience of the physical environment is a relatively ignored research issue in urban design. Unlike other temporal art such as music, movies and dance, which are strictly controlled by a time period of performance, the temporal form of urban space, or the sequential experiences of walk-through in urban spaces, is more indeterminate, loose and uncontrollable. Although urban space is not frozen music, the temporal continuity of music and movies is comparable to the sequential experience of urban space, even if an audience or viewer's attention is deliberately more focused on music and film than walking in urban space (Lynch, 1972). In the context of urban space, the quality of the personal image of time is crucial for individual well-being and also for our success in managing environmental change, while the external physical environment plays a role in building and supporting the sense of time. The relationship between the design of urban space and our sense of passing time is therefore reciprocal (Lynch, 1976).

The sequential experience of urban space is the foundation for individual perception of time duration, which can be associated with a perception of change. Fraisse (1984) has proposed that there is no perception of duration without succession, because 'events are perceivable but time is not' (Fraisse, 1984). How then can the 'sense of time' be defined in the sequential movement of pedestrians in urban space? Fraisse made a distinction between two kinds of temporal sense: firstly immediate awareness and secondly a retrospective sense of time. He also noted that a tract of time containing few experiences appears longer in passing than a time filled with varied experiences, while a variety of experiences may actually make the pedestrians feel that more time has passed (Fraisse, 1984; Issacs, 2001).

What constitutes the sense of time in urban space, particularly for the retrospective reflection of how much time has passed? We assume that the perception of urban form, such as perceived distances and a sense of openness, will contribute to the creation of temporal experiences of either motion or movement within the urban physical environment. The physical configuration of urban elements will influence the environmental perception in general and the temporal perception in particular. Furthermore, the 'sense of time' in urban space can be exaggerated or diluted through intentional urban form design practices. For urban designers, it is especially interesting to understand how the different temporal experiences can be manipulated through the arrangement of physical urban elements and their spatial configuration.

The spatial–temporal perception in the urban environment

Discussions on the perception of distance and duration

Some precedent research works have defined spatial–temporal perception as a function of the perception of distance and the perception of passing time. Humans perceive their environment by orienting their changing positions with other elements within the environment over time, as a process of formulating a mental model of space through visual and temporal perception. The temporal perception of directional passage of time is formed by successive changes within a visual experience (Block, 1998). Furthermore, the visual perception of distance correlates with the complexity of a route through which a person moves (Canter and Tagg, 1975). Distortion of either perceived passing time or distance in a subjective space happens when the visual experience and attributes become more complex, such as when walking along the route which contains angularity, turns, impediments and intersections (Block, 1998). The distortion is typically reflected in the overestimation of a short distance or duration and the underestimation of a long distance or duration, which conforms to Vierordt's law (Block, 1998). The effect of distortion on the perception of duration is caused by the stimuli, in which more stimuli cause a lengthened duration of remembering (Mitchell and Davis, 1987). With a stimulated condition, a person should perceive both a longer distance and a shorter duration of time passed than that which was actually experienced.

These precedent studies were conducted in isolated laboratory environments and mostly cover analyses of short duration, which is very different from the experience of walking in the exterior environment of urban space (Isaacs, 2001). In an urban context, a legible urban space means an arrangement of identifiable urban elements that an observer can mentally relate one to another, while also understanding their pattern in space and time (Lynch, 1968). It has been defined as a balance of complexity and coherency through scale, context and continuity of space, encompassing interior, exterior and habitation (Isaacs, 2001). In the light of Lynch's legibility theory, urban characteristics are understood through perceptual stimulation. Urban space and its enclosures are essentially fields of information that interact with the observer (Salingaros, 1999). But what are the variables that cause the distortion of temporal perception in an urban environment, and what are the stimuli shaping the perception of urban forms?

There are very few empirical studies in the recent literature relating to the issue of sense of time from the experiential perspective of urban spatial analysis. Some urban researchers have made the proposition that the scale (DeLong, 1981; Mitchell and Davis, 1987), spatial complexity (Ornstein, 1969; Hogan, 1978) and available choices resulting from the number of intersections and blocks (Isaacs, 2001) will contribute to a different quality of street space and hence will influence the perception of time. Interestingly, successful and stimulating urban spaces tend to be irregular, often with fractal boundaries and formed by the enclosure of surrounding buildings, while urban spaces with formal plan geometry have not created urban spaces that are well used (Salingaros, 1999).

Reviews of precedent experiments and formulation of research questions

Bosselmann (1998) showed how the walking experience in some cities may appear much longer or shorter than others, and this notion surprises many urban professionals. Bosselmann used 39 eye-level images to suggest the experience of 'awareness of passing time' on a 300 m, 4 min walk through Venice. He then compared the length of this walk through Venice to walks of identical length in 14 cities. The walks are depicted on 14 figure-ground maps of the same scale and dimension to represent various types of urban fabric and grain, including Venice; San Francisco; Washington, DC; Kyoto and Barcelona (Bosselmann, 1998). The discussion focused on the differences between the perceived sense of passing time. It was suggested that the sense of passing time appears longer when walking the path with a finer urban fabric.

Bosselmann actually compared both his 'awareness of passing time' from the actual walking experience with his 'retrospective reflection of how much time would pass' and correlated the comparison with the figure-ground maps. However, Bosselmann's conclusion appears to be inferred by correlating his durational experiences with the two-dimensional (2D) figure-ground maps based on his empirical quasi-experiment, rather than a quantifiable statistical inference of perceptual distortion. Additionally, the physical factors in the walking sequence that affected the distortion were not clearly defined. How much a walk feels shorter or longer in fine-grained urban fabric was unclear. The conclusion that the dimensions and placement of urban elements influence the perception of time appears intuitively derived. They are subjective claims without verification through empirical evidence. Bosselmann's experiment was also inconsistent in describing the differences resulting from the various walks he took, making it impossible to assess quantitatively.

Issacs later conducted an experiment on perceived sense of time within the urban environment of Dresden, Germany, based on the assumption that a person would perceive a longer duration if more stimulation is given. Specifically, the research focuses on the second category of 'sense of time', which is the retrospective perception of how much time has passed. A simple field survey was conducted, where the hypothesis was suggested that smaller spatial dimensions, shorter block sizes, more intersections and more variations along the path may cause a longer estimated 'sense of time' (Isaacs, 2001). Issacs's experiment emphasized that stimulation in the physical environment plays a major role in determining the sense of time. He attempted to verify Bosselman's observation by conducting the analysis of variations based on the pedestrian experiences of the estimated time along designated urban paths with different spatial configurations. The result suggests that spatial features of the urban environment do influence an individual's perception of time. However, the characteristics of the Euclidean spatial features of the streets are shown as diagrams in a descriptive manner. Although Isaacs has related his findings to some psychophysical studies of temporal perception, such as Ornstein's complexity (Ornstein, 1969), the relationship between the temporal perception and urban form is still unclear and the measurement is preliminary. The correlations between the attributes of urban spatial configurations and the pedestrians' sense of time remain unexplored. We argue that it is because of the Euclidean nature of Isaacs's experiments that it is not possible to determine any particular feature of the spatial environment that is responsible for the variation in the time estimates (Isaacs, 2001).

So, what attributes of an urban form and spatial configuration are most relevant to shaping our perceived sense of time? Based on the previous literature and experiments, it is clear that the question has not yet been fully explored. Previous work has been either too intuitive and observation-oriented (Jacobs, 1993; Bosselmann, 1998) or too descriptive (Isaacs, 2001). In this paper, two major propositions are suggested for further developing the research questions further.

Firstly, although the relationship between urban form and the environmental perception of time could be intuitively understood, the analysis of the form–perception relationship should go beyond simple spatial descriptions by improving its measurability, which can make the visual effects of urban form more predictable. In this study, we propose quantifiable indices for constructing the relationship between urban form and the perception of time.

Secondly, the Gibsonian approach (Gibson, 1986) has been chosen to replace the Euclidean method that focuses on geometric measures such as street width, building height, building frontage, number of intersections and number of directional changes. The fundamental distinction between Gibsonian 'ecological perception' and the Euclidean approach is that the Gibsonian approach focuses on the various cues concerning the distance between the subject and his or her environment that the subject's visual system directly picks up. Therefore, we agree with Batty's argument that the actual physical morphology of complex urban buildings and streetscapes is not best measured by the geometry itself, but is more likely to be represented by the visual objects or spaces that emerge as a result of visibility analysis of this geometry (Batty, 2001). Based on the 3D analysis of the ecological perception simulated in a geographic information system (GIS), we propose quantifiable indices that are closer to the direct human perception or sequential experience from the pedestrian level. The relationship between the 'retrospective reflection of how much time has passed' and Gibsonian urban form indices is therefore constructed in this paper.

The Singapore experiment

In this paper, the relationship between urban form and temporal perception of pedestrians is to be elaborated through empirical studies based on Singapore's urban environments. The research design comprises two major components: the measure of urban spatial visibility by GIS computation and the measure of pedestrian temporal perception by field survey. A correlation analysis of the results from both components was conducted for supporting the arguments and discussions. Through the computation of the attributes of four distinctively different spatial configurations of Singapore's streets and districts, the analysis responds to the question of how different urban spatial attributes contribute to the sense of time and which particular aspect of urban form is responsible for the formulation of the sense of time in urban space.

Research design and hypotheses

What constitutes the sense of time in urban space? Which attributes of urban form are the most recognizable, memorable, remarkable or dominant in the formulation of environmental perception? We hypothesize that there are possible correlations between urban spatial attributes and pedestrians' 'sense of time', or the temporal perception of 'passed' retrospective duration. A field survey of temporal perception was designed for testing the hypothesis. There are two issues in the field survey to be considered in the research design.

Firstly, how could we elicit the mental images of pedestrians' sense of time, and what kind of survey techniques and tools would be appropriate? The potential techniques of urban field surveys such as street interviews and map recognitions were considered and tested for probing the environmental perception of time of the respondents. It was decided that when a variety of probes are employed a composite picture would not be too far from the deep reality of people's minds.

Secondly, the estimation of time is a very subjective matter. The retrospective reflection of time duration may vary due to individual differences in walking speeds, the social status of interviewees, the purpose of walking or the familiarity of the area, and all these factors might need to be taken into consideration. However, this study did not intend to explore the issue of social distinction or the individual mental process of perceiving time. Instead, the strategy of field survey has been to get as many samples as possible in the street interviews in order to provide substantial statistical results.

Concurrently, a laboratory simulation of urban spatial visibility has also been conducted along the same paths as the field survey using 3D GIS visibility analysis. To measure the visibility according to urban form attributes, we introduce the Gibsonian approach of the 'ambient optic array' of urban visibility based on the direct perception of viewers. The ambient optic array is measured spatially based on the collective amount of geometric Cartesian space occupied by the ambient optic array, which is reflected from physical surfaces that are visually perceivable from a particular vantage point (Gibson, 1986).

The simulation is conducted by a 3D urban form and visibility analysis tool called Viewsphere, which is generated by the customized GIS-based Viewsphere Analyst, an extension to the GIS software ArcGIS^TM, developed by the first and second authors (Yang et al., 2007). Several indices are obtained from the analysis: firstly, the Volume of Sight index (VoS) is defined as the visible 'volume' of ambient optic arrays, which are constructed by 'scanning' surrounding environmental obstruction points using the lines of sight. The 3D representation in GIS appears like a collection of triangular array fans originating from an observer's point in the centre (Figure 1). Secondly, the Viewsphere index (VSI) is defined as the 3D visible volume based on the operation of the VoS, divided by the hypothetical volume of hemisphere HS (Yang et al., 2007). The Viewsphere 3D analysis is operated by directional visibility analysis, which is based on human eyesight capability. In this experiment, human eyesight capability is modelled as the ambient optic array formed by arrays coming from the urban geometry within human viewing angles (approximately 150° horizontal and 120° vertical viewing angles). In the directional Viewsphere analysis, we assume that the viewing direction goes in parallel with the movement direction; the factor of head movement is ignored. Through setting multiple vantage points of equidistance along a sequential path, we can compute the degree of visibility and simulate the sequential experience of pedestrians using a series of directional Viewsphere indices. For each district and street, we set 22 sequential points along a 300 m path. We do not include animate objects such as pedestrians, vehicles and trees in the GIS model as attributes of urban form, although these factors may generate significant impact on the viewer's sequential experience. Furthermore, we tested other planar indices of 2D urban form and visibility indices, including visible area (A), visible perimeter (P), mean radius (r) and mean vertical view angle ().

Figure 1.

Viewsphere analysis in operation; the radiating 'rays' are the viewsphere array.

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Urban visibility, visible distance, openness and scale are represented by 3D volumetric indices (VoS and VSI) and 2D planar indices (A, P, r, ). There are two states applicable for these indices: static and dynamic. The static state can be derived from the mean of the indices, while the dynamic state, which represents 'perceived change', is obtained from the coefficient of variances of the indices.

Subsequently, the results from both GIS simulation and field survey have then been correlated. The main hypothesis is to be validated by a significant correlation between the urban visibility indices of the GIS simulation and the mean perceived duration of the field survey. We hypothesize that radical changes in visible distance and volume, scale, openness and perceived density may significantly affect the retrospective reflection of duration.

Selected urban districts

For the purpose of eliciting the perception of time of pedestrians in urban space, a field survey was conducted at four Singapore downtown urban districts with distinctively different urban fabrics: Orchard Road (the main shopping street), Rochor (a pedestrian market street), Chinatown (a historical district), Robinson Road and Tanjong Pagar (the central business district (CBD)). Six pedestrian paths of equal length of 300 m were assigned to the four urban districts. In the laboratory, a 3D GIS spatial model of the four districts was built, and the same paths as the field survey were assigned for computing purposes.

Orchard Road is the major urban shopping street of Singapore. The urban forms in the area consist of four-storey podiums with mixed-use building towers (shopping malls, hotels, condominiums and offices) with wide pedestrian walkways along the two sides of the six-lane road, canopied by large mature trees. The paths were set between two mass rapid transit (MRT) stations in Orchard Road: the Orchard MRT Station and the Somerset MRT Station. The designated pedestrian path is a 300 m straight and linear space without any intersections. Orchard Road Path 1 starts at the Orchard MRT Station, passes several podium tower buildings and ends at the Ngee Ann City shopping centre. Orchard Road Path 2 starts at the street level of the underground Somerset MRT Station, which is an open space shaded with trees, and continues to reverse the direction of Path 1, passes several low-rise shophouses and podium tower buildings before finally ending at the Mandarin Hotel (Figure 2 and 3).

Figure 2.

Plan view of Orchard paths 1 and 2.

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Figure 3.

Photos of Orchard road paths 1 (a) and 2 (b).

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The Rochor area is a shopping area and traditional market street dedicated for pedestrians. The urban forms in this area consist of a combination of four-storey shopping centre podiums and towers, low-rise shophouses and a traditional market street. The market street is characterized by a large and crowded pedestrian mall, and is surrounded by semi-permanent street shops and outdoor market stalls with a variety of building edges and a less formal ambience compared with the Orchard area. For simulation purposes, this type of complex urban environment was simplified and represented by a 2.5D raster-based GIS urban model. Path 3 in Rochor area starts at an entrance of Bugis MRT Station from the east and ends at the intersection of Sim Lim Square at the western side of the path. It is an approximately 300 m long straight and narrow path with three intersections (Figure 4 and 5).

Figure 4.

Plan view of Rochor path 3.

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Figure 5.

Photos along Rochor path 3: (a) along the path at Bugis village and (b) in front of Burlington square.

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The Chinatown district is characterized by a network of crowded and narrow pedestrian streets. It is flanked by low-rise colonial shophouses and scattered with outdoor stalls. As a famous tourist attraction in Singapore, this district is bustling with activities and is characterized by its fine-grained development and has a variety of uses such as antique shops, cafes, restaurants, hotels and religious buildings. Path 4 is a straight path with three turns, starting from Chinatown MRT Station entrance at Pagoda Street and ending in front of Sri Mariamman Temple entrance (Figure 6 and 7).

Figure 6.

Plan view of CBD path 4 and Tanjong Pagar path 6.

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Figure 7.

Photos of raffles CBD path 5 (a) and Tanjong Pagar CBD path 6 (b).

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The CBD area is surrounded by high-rise office buildings. Its urban form is characterized by tall skyscrapers along busy four-lane roads with narrow pedestrian walkways along its two sides with a minimum separation from the vehicular road. The ground floor consists of both entrances to the office buildings and cafes. Compared with the other areas in the field survey, the area is not as vibrant with human activity, due to the small amount of street-level commercial activity in the area. Two pedestrian paths along the walkways were assigned to this district, path 5 (Raffles Place CBD) and path 6 (Tanjong Pagar CBD). Path 5 starts from the southern entrance of Raffles Place MRT Station and ends at the intersection of Lau Pa Sat Hawker Center, which is a low-rise building. Path 6 starts from the eastern entrance of Tanjong Pagar MRT Station and ends at the point of 300 m away from the starting point along Robinson Road (Figure 8 and 9).

Figure 8.

Plan view of Chinatown path 5.

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Figure 9.

Photos of Chinatown: (a) path 4 starting point and (6) aerial view of Chinatown district.

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Field survey

The field survey samples consist of two series. The first series was obtained by distributing questionnaires randomly to people incidentally walking on the survey area. After pointing towards a landmark at the end point viewed from the starting point, people were asked to approximate the time taken to walk to the end point in terms of minutes. The second series was obtained by distributing questionnaires to pre-selected people who are less familiar with the area.¹ People were asked to approximate the time taken to walk from the starting point to the end point by looking at the map of the area indicating the two points. Both series were combined, yielding more representative samples to help achieve a more general conclusion. Combining both series is justifiable on the basis that the differentiating factor, for example familiarity, only affects people's personal cognitive level and does not distort the general perception of environmental attributes per se. A significant number of 379 samples were collected from the six different locations or paths (Table 1).

Table 1 - Descriptive statistics of time duration.

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To understand whether differences in duration judgements are influenced by the urban forms at different locations, we performed the test of homogeneity of variances on all six paths sets, and discovered that the location is a significant differentiating factor for people's perceived duration. Levene's test shows that among the six paths' responses, the variances are not equal (Table 2). This means that there are significant differences of variances among the location groups. It implies that the location and its urban form attributes along the paths are strong determining factors affecting peoples' perception of duration judgements. Furthermore, an analysis of variance (ANOVA) was conducted. Since the value of ANOVA's significant value is lower than 0.05 (Table 3), we can conclude that the locations or paths that contain different urban form attributes result in significant differences in perceived duration (Table 3), and these differences cannot be attributed to sampling variation alone.

Table 2 - Test of homogeneity of variances.

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Table 3 - ANOVA.

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Significant differences of the sense of time were exhibited among all locations and paths. Through post hoc Scheffe analysis, they can be classified into two groups: one with shorter duration and another with longer duration. Orchard Road 2 (path 2) is the location statistically grouped as the shortest duration, while the durations at Chinatown (path 4), Orchard Road 1 (path 1), and Tanjong Pagar CBD (path 6) appear longer (Table 4). Path 2 with the shortest duration contains the urban configuration of podium towers, open spaces, shophouses and parking lots along the path. The locations with longer durations have a more homogeneous built form, for example path 4 with predominantly shophouses, and both path 1 and path 6 with podium towers.

Table 4 - Homogeneous subset – Scheffe.

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What constitutes the relationship between the attributes of urban form and the sense of time of pedestrians? The variance level among the six locations is clearly depicted by ANOVA results. However, it is still unclear which particular urban spatial attributes will influence the different values of perceived duration. The attributes of urban form were measured and their relation to the sense of time was constructed. We assumed that the quantitative measure of urban visibility by the GIS simulation can contribute to further correlation analysis and help clarify the issue. The detailed correlation analysis such as Pearson's correlation was conducted with the results of the GIS-based urban visibility simulation to determine the extent to which each urban form attribute influences the retrospective sense of time.

GIS simulation

Viewsphere analysis was conducted on 3D GIS models of the six paths in the four urban districts. The sequential experience of pedestrians was simulated using the directional visibility approach by setting 22 sequential vantage points along the six 300 m long designated pedestrian paths of Figure 10. The results of the volumetric and planar indices of urban visibility are shown as the static state by the mean value (Table 5) as well as the dynamic state derived from the coefficient of variance (Table 6).

Figure 10.

3D GIS geometric models of the four urban districts and the sequential vantage points along the designated paths: (a) Orchard Road, (b) Rochor, (c) CBD and (d) Chinatown.

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Table 5 - Descriptive statistics (mean) of urban form attributes from six pedestrian paths.

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Table 6 - Descriptive statistics (coefficient of variance) of urban form attributes from six pedestrian paths.

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One-way ANOVA was performed to determine the significance of Viewsphere indices among the six different pedestrian paths. The results of ANOVA's test of homogeneity of variances show how urban spatial attributes vary differently among the six pedestrian paths. The results in Table 7 imply that different urban locations are significantly distinctive based on their VoS and VSI. The results are less significant in the measure of 2D indices such as the visible area A, which implies that pedestrians will generate a closer amount of visible area A in the six urban locations. These results lead to a preliminary conclusion that the 3D urban visibility index VSI can easily differentiate the attributes of urban visibility of the six urban locations. In this case, the 3D volumetric parameters perform better than the 2D planar indices. Furthermore, the hypothesis is elaborated and discussed in the next section by Pearson's correlation analysis.

Table 7 - Test of homogeneity of variances of the urban visibility indices.

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Correlation analyses of results from field survey and GIS simulation

How do different urban form attributes and urban visibility contribute to the temporal perception of urban space? The results of the mean perceived time duration of field survey are correlated to the indices of urban visibility computed by the interplay of different urban geometries and pedestrian movement generated by the GIS simulation. Pearson's correlation analyses were applied to the field survey and GIS simulation of the six different locations for understanding the relationships between urban form and temporal perceptions. The logarithmic regression curve's estimation will determine the degree of any relationship (Table 8, 9 and 10).

Table 8 - Pearson correlations results by investigating urban visibility (static state by the mean of the indices).

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Table 9 - Regression results by investigating static indices and the sense of time.

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Table 10 - Sense of time and their Pearson's correlation to urban visibility (dynamic state by the coefficient of variances of indices).

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To calculate the coefficient of variance, the 379 responses indicating the mean perceived time duration from the field survey were aggregated into the six urban locations, each with 22 sequential observation points. As suggested in the previous discussion, urban spatial perception is represented by both the static indices (the mean value) and the dynamic perception or sequential change (the variation of the indices). For each path, values of these indices were collected from the GIS simulation of the 22 sequential points. Using Pearson's correlation and regression, the perceived time duration and urban visibility indices of all 132 points were analysed comparatively.

Correlational and regressional studies: static perception of urban space

The results of the correlation analysis revealed in Table 8 show significant Pearson correlations between mean perceived time duration with static indices, particularly clear in the indices VSI (0.489) and r (-0.506) (Table 8). These correlations imply a significant impact of the perceived density (VSI) and visible distance (r) on the perception of passed time duration, in which higher perceived density and nearer perceived distance increase the perceived duration. These spatial indices are significantly correlated (with sig value <0.05). However, Pearson's correlation values below 0.5 are not sufficient to indicate strong relationships between the indices and the mean perceived duration.

Quadratic regression analysis of the 2D and 3D indices reveal a similar pattern (Table 9). The coefficients of correlation and the regression of mean VSI reveal that the relationships are significant but inadequate. From regression analysis, the indices that are highly correlated with the mean perceived time duration are mean VSI and r, which may be hypothetically explained as indices of perceived density and visible distance. We argue that the perceived density (VSI) and the visible distance (r) of urban space may be the most influential factors affecting temporal perception of urban space.

Correlational and regressional studies: the dynamic perception of urban space

The degree of change in the coefficient of variance of the indices and their Pearson correlations are exhibited in Table 10. The results from the regression analysis show that the volumetric (3D) indices are generally more correlated with the mean perceived time duration than the planar (2D) indices. This finding validates the hypothesis that the 3D Gibsonian understanding of urban space characteristics is an imperative in predicting the impact of urban form on a pedestrian's temporal perception. We argue that the traditional 2D and Euclidean approach of geometrical measurement of the urban environment is less effective in predicting temporal perceptions.

Additionally, the regression analysis shows stronger correlation between the coefficient of variance of the indices and the mean perceived time duration. This implies that the static perception of urban space may be less significant to the perceiver's sense of time compared to the dynamic aspects. In line with the findings of the field survey, urban locations with a more homogeneous urban fabric as reflected in the low coefficient of variance of the indices (such as path 6 of Tanjong Pagar CBD) tend to result in a longer perceived duration, which implies overestimation of the retrospective duration. Conversely, an environment with diverse types of urban fabrics (such as path 2 of Orchard Road) tends to result in shorter perceived duration, which implies underestimation. We conclude that sense of time is greatly influenced by the perceived changes of urban visibility, which are generated by the interplay of dynamic movement and variation of the urban environment.

Logarithmic regressions were also conducted (Table 10). The logarithmic model shows the great influence of changes in VSI or . It means that the logarithmic relationship between the perceived time duration and perceived density VSI of the urban environment is more coherent and acceptable. The high regression value of reveals that changes in urban space's vertical dimension is another determining factor affecting pedestrians' perception of time duration. We conclude that pedestrians perceive the retrospective duration, or the sense of time, while they are moving in a dynamic state and perceiving the density and the z dimension of the urban form attributes.

Summary and discussion

The results show that there is a relationship between urban form attributes and their retrospective perceived duration. We found that pedestrians overestimate or perceive longer passed time duration after passing the urban space with less perceived change or a lower degree of variation as represented by its lower coefficient of variance of VSI. Conversely, an intensively perceived change and a higher variation in urban space or the higher coefficient of variance of VSI causes a decrease in the perceived retrospective duration.

The findings of this study imply that there is a logarithmic correlation between perceptual space and perceptual time, and supports Hogan's (1978) curved relationship theory. The findings also confirm the conclusion from Angrilli et al. (1997) that the variety of experiences may make pedestrians underestimate or feel less time has passed, while the absence of sensations resulting in 'boredom' may make one overestimate or feel more time has passed. However, both Angrilli et al. (1997) and the findings of this study are contrary to Issacs's conclusion that increasing complexity leads to the perception that more time has passed and the illusion of a longer subjective duration (Issacs, 2001). The strong correlation between coefficient of variance and mean perceived time duration implies that movements and changes in the sequential experiences of walking through a dynamic urban environment are important factors in determining its complexity and legibility (Lynch, 1976). As reflected in the coefficient of variance of the VSI, the 3D Gibsonian approach is more effective than the 2D Euclidean approach for measuring the temporal perception of the urban environment.

The finding emphasizes the importance of two factors in constructing and facilitating pedestrians' perception of time in the urban environment, namely the dynamic sequential movement and an adequate provision of diverse and dynamic vertical urban landmarks. The finding validates the propositions for the management of sequential experiences by Lynch (1972), Freundschuh (1998) and Block (1998). Specifically, this finding confirms Issacs's (2001) conclusion that 'more variation in the spatial dimensions along the path' influences the subjective duration of time. However, a more measurable way and quantitative approach was conducted in this paper. As Lynch (1972) remarks that the stimuli shape the perception of time in sequential urban space, the research also shows how the dynamic spatial variations as stimuli influence the perception of time. The research reminds us that the temporal perception of the urban environment is constructed by the interplay of pedestrian movement and urban form, in which the spatial and sequential variation of urban visibility contributes to the temporal orientation and the sense of time. A good urban design should incorporate the issue of temporal perception by designing a dynamic urban form for enriching the spatial and temporal experiences of the pedestrian.

Notes

¹ By comparing the two series side by side, we found that the lack of familiarity of the area contributed to the increase of mean perceived duration.

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