Mathematical sociology in the context of "Arc (geometry)"

In social psychology, an interpersonal relation (or interpersonal relationship) describes a social association, connection, or affiliation between two or more people. It overlaps significantly with the concept of social relations, which are the fundamental unit of analysis within the social sciences. Relations vary in degrees of intimacy, self-disclosure, duration, reciprocity, and power distribution. The main themes or trends of the interpersonal relations are: family, kinship, friendship, love, marriage, business, employment, clubs, neighborhoods, ethical values, support, and solidarity. Interpersonal relations may be regulated by law, custom, or mutual agreement, and form the basis of social groups and societies. They appear when people communicate or act with each other within specific social contexts, and they thrive on equitable and reciprocal compromises.

Interdisciplinary analysis of relationships draws heavily upon the other social sciences, including, but not limited to: anthropology, communication, cultural studies, economics, linguistics, mathematics, political science, social work, and sociology. This scientific analysis had evolved during the 1990s and has become "relationship science", through the research done by Ellen Berscheid and Elaine Hatfield. This interdisciplinary science attempts to provide evidence-based conclusions through the use of data analysis.

In social network analysis and mathematical sociology, interpersonal ties are defined as information-carrying connections between people. Interpersonal ties, generally, come in three varieties: strong, weak or absent. Weak social ties, it is argued, are responsible for the majority of the embeddedness and structure of social networks in society as well as the transmission of information through these networks. Specifically, more novel information flows to individuals through weak rather than strong ties. Because our close friends tend to move in the same circles that we do, the information they receive overlaps considerably with what we already know. Acquaintances, by contrast, know people that we do not, and thus receive more novel information.

Included in the definition of absent ties, according to the American sociologist Mark Granovetter, are those relationships (or ties) without substantial significance, such as "nodding" relationships between people living on the same street, or the "tie", for example, to a frequent vendor one would buy from. Such relations with familiar strangers have also been called invisible ties since they are hardly observable, and are often overlooked as a relevant type of ties. They nevertheless support people's sense of familiarity and belonging. Furthermore, the fact that two people may know each other by name does not necessarily qualify the existence of a weak tie. If their interaction is negligible the tie may be absent or invisible. The "strength" of an interpersonal tie is a linear combination of the amount of time, the emotional intensity, the intimacy (or mutual confiding), and the reciprocal services which characterize each tie.

Hard science fiction is a category of science fiction characterized by concern for scientific accuracy and logic. The term was first used in print in 1957 by P. Schuyler Miller in a review of John W. Campbell's Islands of Space in the November issue of Astounding Science Fiction. The complementary term soft science fiction, formed by analogy to the popular distinction between the "hard" (natural) and "soft" (social) sciences, first appeared in the late 1970s. Though there are examples generally considered as "hard" science fiction such as Isaac Asimov's Foundation series, built on mathematical sociology, science fiction critic Gary Westfahl argues that while neither term is part of a rigorous taxonomy, they are approximate ways of characterizing stories that reviewers and commentators have found useful.