Society has a space

Physical distance

We know well about physical space as we live every day in it. You travel to pick up grocery at the riverside market, it would take 30 minutes walking. When you ride bike though, the time for the trip reduces to 10 minutes. You still traverse across the same distance in the physical space. As you go down under into the ocean, you travel vertically a few feet deep, you bounce back with paddles to the sea surface and it took another few feet.

You learned about this long time ago. Regarding the distance we traverse in the physical space, even elementary pupils know how to calculate the distance using Euclidean rule. Suppose a moving item is traveling on a two-dimensional space with only x and y coordinates. The distance covered by moving from one point on this two-dimensional space to another is D=Sqrt[(x1-x2)²+(y1-y2)²]. When there are more than two dimensions, just repeat the process by getting a D1 first and then apply the same rule to D1 and D2, which is in the third dimension.

When there are multiple mobile items traversing a space, to the distance between all possible pairs of these items, we use something called distance matrix. In a distance matrix, the rows are these items, objects, or people, and columns are coordinates — the categorical dimensions in a physical space.

Like here, the raw table shows moving items from A to F. Their respective locations in the X and Y coordinates are also listed. Applying Euclidean rule to raw data results in Distance Matrix, “a square matrix (two-dimensional array) containing the distances”. In the distance matrix, larger number denotes farer distance between the row and column item. It takes 16 unit to go from A to B, 47 units from A to C, etc.

These are all simple geometry learned in middle school by every educated pupil around the world.

Social distance

This is not your covid moral panic measure for disease prevention. What people refer to, the transmissible disease prevention technique, is actually quite oxymoronic. When you ask people to stand 100 feet apart from you, the distance created is purely physical. There is nothing social in social distancing as people deploy in the covid pandemic.

Social distance has been discussed sporadically in the segregation and network analysis works of sociology, but people don’t use this concept very often, perhaps out of a distaste of the abuse of adding the word “social” to every commonplace term and making the combination a new fancy chimera that is of little use in rigorous study. The abuse of forcing social onto every word is eminently repulsive in “social distancing”. Dan Olson @Purdue told me there was a term called “social fabrique” during the time he was a junior scholar. The term did not age well.

But I realize social distance is a rigorous concept. Most people have not realized this. Its coincidental resemblance to physical distance is a valuable juncture that links the two concepts and puts them in a new light: social distance may interact with physical distance and formulate a number of ideal types of significant implication for how people of one type may interact with those of another category.

First, some technical stuffs. The raw data used to get distance matrix, if you are familiar with data frames, are just a data set with rows as individual records and columns as variables. In network analysis, the raw data here look exactly in conformity with how data are presented for two-mode network, aka bipartitie networks. Suppose A to F are individual peopel, X is an organization, event, or group, Y is another organization or group. How individual A to F belong in X and Y determines the distance between every pairs of people.

2-mode networks are important representation of how individuals are connected/separated to each other through their belonging in some organized foci or collective categories. Omar Lizardo has a better and rudimentary introduction here. The affiliation matrix of 2-mode network is just the raw data for distance matrix, and it can be converted into a square distance matrix at ease. The conversion process is just technical, it’s called unipartitie projection of bipartitie network.

Again look at the raw data for distance matrix. If X means Han ethnicity, Y is male gender. a checks 1 and 1 for both, b checks 1 and 0, and c checks 0 and 0. The distance between a and b, using the Euclidean rule, is Sqrt(1²+0)=1. The distance between a and c is Sqrt(1²+1²)=1.41. A is a Han male, b is a Han female, c is a minority female. It makes sense that the social distance between a and b is shorter than that between a and c, just by applying the same rule for physical space. There is a social space just like physical space, and the principle to measure them is fundamentally the same. This principle is also the root of hierarchical clustering technique.

Techniques apart, social space and physical space may have different combinations. You may run into a person with very close social distance from you: you listen to the same genre of music, enjoy the same cuisine, belong to the same class, from the same religion. Or you may find people nearby are from a very distant social space: different cultural taste and different class background, etc. Most of the type, social space overlaps with physical space, particularly in the past times when mobility was limited. But, they do not have to be. Many times social space and physical space form interesting patterns.

                  Physical distance
Social distance   Far      Near
                 |---------------  
Far              |Alien    Guest
Near             |Expat    Fam

For example in the table above, four ideal types for distance show how people define and may interact with each other. Guest is a Simmelian stranger, is someone who is physically nearby but socially and emotionally very agile at getting away from you and your community. The guest, who in Simmel’s word “is not radically committed to the unique ingredients and peculiar tendencies of the group, and therefore approaches them with the specific attitude of “objectivity”, will not conform to your expectation reserved for your own kins, but nor is he a total alien to your collective interest — at least he lives in your community. Guest type of populace show up as the Hakka of southern China, Jews of the Europe, Dungan in the Central Asia. Throughout Canton, native people are very distant and apathetic to politics and patriotism. Hakka is an exception. The endonym of Hakka literally means “guests”. They live in Canton for centuries since, but retained a loyalty to the imagined central government and China nation. They are enthusiastic about education and government posts, unlike the commercial oriented Cantonese and Hokkien people.

For another example, someone with proximate social distance but remote physical distance from you may be called an “expat”, although I haven’t come up with a better and more accurate name for it. An expat is gone but retained social characteristics of your own. He is not around anymore, you don’t see or touch him, but something kept him in the guard of your community. An expat cannot aid you physically due to the remote physical distance, but s/he feels you just as he feels the lifeworld of his own community. In practice, expats will send remittance, donate a lot of money for disaster relief, etc.

Overall, social space is just as real as physical space. Those near you physically may not understand or feel close to you because your social distance is quite enormous. On the other hand, those far from you may have very tight social ties to you. Physical space and social space are fundamentally two types of distance matrices by definition, but their overlap makes the multiplexity of social networks.