Enhancing Sustainable Public Library: Spatial Relationship Implementation to Foster Optimal Social Interaction

The public library holds great potential as a community space for people to gather, learn, and socialize outside of their homes and workplaces. However, it’s unfortunate that many libraries have not been able to fully embrace their communities, leading to a decline in involvement and interest. This lack of engagement can lead to decreased interest in reading, less involvement from middle-class individuals, and other challenges. To address this issue, spatial organization and social interaction can be used to create a more inclusive and welcoming environment. Through a quantitative study using contingency analysis to find the relationship between social interaction and spatial relationship, eight relationships are found to be applied in libraries.


Introduction
Public library is one of the public spaces that known as a reading collections place and an educational facility support, and it has the potential to become a "third place" as a community space that attracts people from all ages, social statuses, physical conditions, and various backgrounds [1] to engage in similar activities or share common goals [2].Moreover, it can also serve as a sustainable public sphere by providing knowledge and cultural disclosure, fostering educated and informed citizens, as well as offering spaces for public discussions [3], consequently play a pivotal role in actively achieving the objectives outlined in the 17 Sustainable Development Goals [4].
According to Aabø, Audunson, and Varheim, there are several activities that can be outdone in a library, with result show that 25% of people visit the library to read, >20% go with friends or colleagues to work on tasks together, 17% use the internet or surfing online, 16% to study politics and social issues, 14% participate in community gatherings, and 10% see the library as a meeting point [5].
However, most public libraries are still perceived as rigid, too serious, boring, and quite challenging to be a visited place for community engagement [6].Hence, this perception raises several issues including a lack of involvement and cooperation among the people in the library, a decrease in middleclass users as the largest user group, a reduction of library studies interest [7], as well as a decrease in reading interest at the library [8].Besides, due to relentless advancements in both technology and social structures, more and more people are gaining easy and rapid access to information through various forms of media, which results in more challenges concerning public library's roles in society, potentially impacting the relationship between the public library and the community it serves [3].Considering the phenomenon mentioned before, it's important for public libraries to have a welcoming environment that encourages user participation and involvement, and social interaction approach has been found to be effective in creating successful public spaces [9].Social interaction is defined as dynamic relationships between individuals that involve conveying meaning, interpreting, and giving mutual responses.In addition, people with more active social lives also tend to feel that they have a better quality of life [10].
Spatial relationship in the public library is an important aspect of creating a functional building that enhances users' activities.By clarifying the organization of spaces, well-arranged buildings can provide clear circulation and create better proportions of space.This helps to support social interaction among library users and ensures that the library is a welcoming and comfortable place for everyone [11].There are initially five different types of social interaction may occur, which are Exchange, Cooperation, Conformity, Coercion, and Conflict [12].However, in this study, there are only four types that show more visible indications in the library as shown in Table 1.As for the spatial relationship, there are four types [11] that can potentially support social interaction activities, which are Space Within Space, Interlocking Space, Adjacent Space, and Space Linked by A Common Space, as shown in Table 2.In which an individual or a group act in a certain way towards the other one/ones to receive a reward or response, and the reply is not necessarily in the form of physical material, but becomes an element of the exchange itself, such as verbal communication.

Cooperation
In which individuals or a group act together to foster common interest or achieve common goals, as they share the same interest.Cooperation could occur in four ways: Spontaneous, Directed, Contractual, and Traditional.

Conformity
In which behavior occurs to adapt to a group, with a tendency to change their behavior to join another party that has bigger influence after observing them.The behavior to suit others itself is adaptive and functional, but not always realized by the first person.

Conflict
In which individuals or a group are with each other to achieve one or more objects or values that are equally valuable.Conflict can occur in extreme ways or as simple as disagreements between individuals.

Type Definition/ Characteristic Space Within Space
The main feature is the existence of a space in another space with a clear difference in size between them.In this type of SR, the larger space envelops the smaller volume space, and an adjustment is required between the two spaces' sizes to have a good relationship.
Interlocking Space The main feature is there are spaces that interlock each other, but still have their respective functions.This type can be implemented in three ways: Equally Sharing, Emerging, and Connecting.

Adjacent Space
The main feature is a boundary that is being used by two spaces/areas and allows two spaces that are close to each other to have their own function.This type becomes the most common type of spatial relationship to be recognized and applied in space organization.

Space Linked by A Common Space
The main feature is there are spaces that can be accessed from one to another through an intermediate space/ area.

Methodology
The methodology used quantitative method.However, there is a mapping stage that should be conducted.Beforehand, it begins with the collection of data from 26 precedents of the library building, which results in an elaboration of social interaction activities.It continues by mapping social interaction (SI) types, resulting in 93 data obtained, followed by mapping the spatial relationship (SR) types based on each social interaction activity in the precedents.Then, proceed with mapping the relationship between two of them by coding the type of SR; Space Within Space as SS, Interlocking Space as IS, Adjacent Space as AS, and Space Linked by A Common Space as CS to the activities of SI that has been listed.The final data is analyzed through four contingency analyses in JMP software to produce a correlation on the mosaic plot and validation test on the chi-square table, that at the end find which spatial relationship's type that can support each of social interaction type in the library.

Mapping SI -SR
This stage is the final mapping of the types of spatial relationship that occur into each activity according to the type of social interaction by inserting spatial relationship codes: SS, IS, AS, or CS, as shown in Table 3.

Contingency Analysis of Social Interaction Type: Exchange (E)
One of the results of contingency analysis, mosaic plot, will show two visible axes: the X axis and Y axis.The X axis represents the type of spatial relationship that supports each type of social interaction, while the Y axis represents the social interaction activities that are commonly done in libraries.In the mosaic plot shown in Figure 1, the X axis represents the type of spatial relationship that supports Exchange -social interaction activities, while the Y axis represents Exchange social interaction activities that are commonly done in libraries.Based on the graph below, the essential points that can be reviewed are described in subsection 3.2.1 and 3.2.2:

X Axis (Type of Spatial Relationship)
• The most relevant/ correlated type of spatial relationship: On the X axis, it shows that Space Linked by a Common Space (CS) is the most relevant type in a library as it involves activities such as greeting, asking, and talking, which commonly happens in almost every activity and are usually located at open spaces area in the building.Then followed by Adjacent Space (AS), where the activities that occur are in a room or area that shares the same boundary and is commonly used for discussion activities in the library.
• The less relevant/ correlated type of spatial relationship: On the X axis, it shows that Space Within Space (SS) and Interlocking Space (IS) are not very relevant to support Exchange activities.Even so, discussion activities seem to mostly occur in those types compared to the Space Linked by A Common Space (CS) type.

Y Axis (Social Interaction Activities -Exchange)
• The most common Exchange activities: On the Y axis, it shows that the most common Exchange activities occur in library are greeting, asking questions, chatting, discussing, buying, and selling, and studying and discussing together.• The least Exchange activities: On the Y axis, it shows that Exchange activity that are less frequent is creative activity.Based on the validation test result shown in Table 4, the Likelihood Ratio and Pearson yielded a relatively small P-Value of <.0001 (less than 1%) or showed only 1 incorrect or error sample in the data from 1000 samples, which showed a significant value that was convincing and mean that the data obtained was quite valid.

Analysis Result
Based on the analysis above, there will be formed a group of relationships between the exchange activities that occur and the spatial relationships that can support them.Thus, each relationship (R) will be coded as SI x SR.The relationship can be made as follows: • R: Exchange -Space Linked by A Common Space (E x CS) • R: Exchange -Adjacent Space (E x AS) In the mosaic plot shown in Figure 2, the X axis represents the type of spatial relationship that supports Cooperation -social interaction activities, while the Y axis represents Cooperation social interaction activities that are commonly done in libraries.Based on the graph below, the essential points that can be reviewed are described in subsection 3.3.1.and 3.3.2.:

X Axis (Type of Spatial Relationship)
• The most relevant/ correlated type of spatial relationship: On the X axis, it shows that Adjacent Space (AS) is the most relevant type in a library which involves activities carried out in an insulated or closed space to participate in joint activities, such as music, making art, etc., then studying and discussing together which in public libraries take place in a closed place to not cause too much noise.Then followed by Space Within Space (SS) with activities like the previous one, and Space Linked by a Common Space (CS) for joint activities.• The less relevant/ correlated type of spatial relationship: On the X axis, it shows that Interlocking Space (IS) is the type that is not very relevant to Cooperation activities.

Y Axis (Social Interaction Activities -Cooperation)
• The most common Cooperation activities: On the Y axis, it shows that the most common Cooperation activities are participating in joint activities, as well as studying and discussing together.• The least Cooperation activities: On the Y axis, it shows that the less frequent Cooperation, are discussions and other supporting activities.Based on the validation test result shown in Table 5, the Pearson yielded a small P-Value of <.0001 (less than 1%) or showed only 1 incorrect or error sample in the data from 1000 samples, meanwhile the Likelihood Ratio yielded a P-Value around 0,0184 or 18.4%.However, the Likelihood Ratio's result is still considered significant because it is below 0.05 or 50% of α (Alpha) rate as the JMP software standard.Therefore, the data obtained was quite valid.

Analysis Result
Based on the analysis above, there will be formed a group of relationships between the cooperation activities that occur and the spatial relationships that can support them.Thus, each relationship (R) will be coded as SI x SR.The relationship can be made as follows: • R: Cooperation -Adjacent Space (C1 x CS) • R: Cooperation -Space Within Space (C1 x SS) • R: Cooperation -Space Linked by A Common Space (C1 x CS)

. Mosaic Plot of Conformity
In the mosaic plot shown in Figure 3, the X axis represents the type of spatial relationship that supports Conformity -social interaction activities, while the Y axis represents Conformity social interaction activities that are commonly done in libraries.Based on the graph below, the essential points that can be reviewed are described in subsection 3.4.1.and 3.4.2.:  Based on the validation test result shown in Table 6, the Likelihood Ratio and Pearson yielded a relatively small P-Value of <.0001 (less than 1%) or showed only 1 incorrect or error sample in the data from 1000 samples, which showed a significant value that was convincing and mean that the data obtained was quite valid.

Analysis Result
Based on the analysis above, there will be formed a group of relationships between the conformity activities that occur and the spatial relationships that can support them.Thus, each relationship (R) will be coded as SI x SR.The relationship can be made as follows: • R: Conformity -Adjacent Space (C2 x AS) • R: Conformity -Space Within Space (C2 x SS) 8 In the mosaic plot shown in Figure 4, the X axis represents the type of spatial relationship that supports Conflict -social interaction activities, while the Y axis represents Conflict social interaction activities that are commonly done in libraries.Based on the graph below, the essential points that can be reviewed are described in subsection 3.5.1.and 3.5.2.:

X Axis (Type of Spatial Relationship)
• The most relevant/ correlated type of spatial relationship: On the X axis, it shows that Adjacent Space (AS) is the most relevant type to support Conflict activities, which are defined as argumentation when carrying out activities such as discussing.• The less relevant/ correlated type of spatial relationship: On the X axis, it shows that Space Linked by A Common Space (CS) and Space Within Space (SS) are not very relevant to Conflict activities.Interlocking Space (IS) is not reviewed for Conflict activities because it is not included in a sufficiently supportive spatial relationship.

Y Axis (Social Interaction Activities -Conflict)
The most common Conflict activities: On the Y axis, it shows that Conflict activities can occur when there are learning activities and joint discussions at the library.Based on the validation test result shown in Table 7, the Likehood Ratio yielded a P-Value around 0,0012 or 1.2% and the Pearson yielded a P-Value around 0,0089 or 8.9%.However, both results are still showed a significant value that was convincing and mean that the data obtained was quite valid.

Analysis Result
Based on the analysis above, there will be formed a group of relationships between the conflict activities that occur and the spatial relationships that can support them.Thus, each relationship (R) will be coded as SI x SR.The relationship can be made as follows: • R: Conflict -Adjacent Space (C4 x AS)

Result
From all the study' research stages; mapping and analysis, eight groups SI x SR relationships are made, which then will be further detailed as follows: 4.1.R1: Exchange -Space Linked by A Common Space (E x CS) This relationship supports activities that involve exchanging material and language, such as asking questions, greeting, talking, buying, selling, etc.These activities are typically done in relatively open space locations, which makes it difficult for users in buildings to do high-urgency task activities.The open space can be divided into outdoor and indoor areas.Outdoor areas include parks, plazas, amphitheatres, or other easily visible and accessible locations, meanwhile, indoor areas include lobbies, lounges, reception areas, waiting areas, etc.For example, some activities based on this type are exchanging cards at the lobby area, chatting with friends at a coffee shop, or asking for directions in the reception area.

R2: Exchange -Adjacent Space (E x AS)
This relationship supports the same activities as R1: E x CS as described in in subsubsection 4.1.1.but all of them are done in a space where there is a boundary between the two areas.For instance, classroom activities, art studios, or activities that need directions commonly employ brick walls to prevent any loss of focus during the activities.This relationship is highly probable and applicable to a diverse range of building types.

R3: Cooperation -Adjacent Space (C1 x CS)
This relationship supports activities that involve cooperation between at least two individuals in achieving a common goal, so it's important to have a designated space that allows for easy communication and collaboration.This can include work discussions, brainstorming sessions, group study sessions, and more.The ideal environment for these activities is one where the participants are in spaces that are adjacent to each other but separated by a boundary of some kind.This boundary can be created using materials like brick, wood, or glass, or by applying different textures and levels to the different areas.This type of setup is common in schools, where classrooms are arranged in a similar way to facilitate group learning and collaboration.

R4: Cooperation -Space Within Space (C1 x SS)
This relationship involves activities that are quite similar to R3: C1 x CS as those described in subsubsection 4.1.3.However, they require a lot more privacy from the outside area due to the high urgency involved.That's why the activities in this relationship take place in a separate area, inside another bigger area.The room where these activities take place tends to be small, with limited human capacity, depending on the function.For instance, it could be an office pod and be applied to building typologies that require low sound intensity but with higher sound intensity activities like libraries and offices.

R5: Cooperation -Space Linked by A Common Space (C1 x CS)
This relationship involves more joint activities with a larger number of individuals and better take place in areas without any furniture or dead partition inside.The activities can be in the form of group competition activities, game events, etc.This relationship involves activities that are like R6: C2 x AS as those described in subsubsection 4.1.6,but only involve a few individuals as they happen in a smaller area.One of the examples is when a student decides to go along with their classmates' choices, even if they don't express their own thoughts while discussing school subjects.

R8: Conflict -Adjacent Space (C4 x AS)
This relationship involves conflict activity that occurs, with the conflict context as opinion differences to arguments between individuals, that can possibly create more intense argumentation.One approach to mitigate the impact of these arguments is to utilize enclosed environments that provide sound insulation, such as meeting rooms with fully separated adjoining walls, like solid brick partitions.This helps to any sound from leaking out and causing disruptions to others outside of space.

Conclusion
Based on the analysis conducted, it was revealed that to promote and enable social interaction or engagement within a calm and quiet library setting, three out of four types of spatial relationships play a more significant role.These types are Space Within Space (SS), Adjacent Space (AS), and Space Linked by A Common Space (CS).This result paves the way for the identification to a total of eight distinct relationships (SI x SR) between social interaction and spatial relationship.These relationships can be strategically implemented across various sections of the library to accommodate a wide range of activities based on the nature of social interaction.Ultimately, this study aims to optimize social interaction, with the aspiration of enhancing the sustainability of our local public library and contributing to the enrichment of community members' lives over an extended period.

Figure 1 .
Figure 1.Mosaic Plot of Exchange

Figure 2 .
Figure 2. Mosaic Plot of Cooperation

Figure 4 .
Figure 4. Mosaic Plot of Conflict

Table 1 .
Social Interaction Type

Table 4 .
Validation Test of Exchange

Table 5 .
Validation Test of Cooperation 1. X Axis (Type of Spatial Relationship) • The most relevant/ correlated type of spatial relationship: On the X axis, it shows that Adjacent Space (AS) and Space Within Space (SS) are the most relevant types to support Conformity activities, where a person adjusts their to a group, which means the activities are carried out in groups.The Adjacent Space supports activities in the form of participating in joint activities and discussing, while the Space Within Space type is dominated by participating in joint activities, studying, and discussing together.Both have similarity which is carried out in a closed room.• The less relevant/ correlated type of spatial relationship: On the X axis, it shows that Space Linked by A Common Space (CS) and Interlocking Space (IS) are not relevant to Conformity activities.
3.4.2.Y Axis (Social Interaction Activities -Conformity)• The most common Conformity activities: On the Y axis, it shows that the most common Conformity activities are participating in joint activities, discussing, and studying and discussing together.• The least Conformity activities: On the Y axis, it shows that the less frequent Conformity activities are communicating, children's activities, being creative, and other activities.

Table 6 .
Validation Test of Conformity

Table 7 .
Validation Test of Conflict This relationship supports activity that involve an individual consciously or unconsciously adjusting and changing themselves to fit in a group.This action usually happens when the group made greater decision and influence.This can include seminars, talk shows, group discussions, collaborative task, educational sessions (classes), and various other activities.The design implementation of this relationship is similar to R3: C1 x CS as described in subsubsection 4.1.3.