For a relation to exist amongst two things, there must be a common property, or shared properties. In value. In degree. In proximity. In character. In direction. In force.
Relations are associations. They are links amongst objects. These relationships are intangible, simply observations of patterns.
They exist arbitrarily, except that they provide utility by allowing the subject stating them the ability to understand them by perceiving their existence, by creating distinctions, by separating them from general sensory experience, by labeling or naming or denominating them. In this way they form concepts of the mind that can be manipulated, that can be controlled via reason to formulate activity.
Metaphor is a distillation of a preconceived relation applied to another set of objects to illustrate the nature of a relationship. It transposes the nature of a relationship from one set of familiar objects, to another set of objects, in order to establish an understanding without having to fully experience the second set of objects.
Relationships cannot exist without mutual interest, without similarity, without a common denominator. The word denominate means “to give a name to”, such as a group, in order to classify.
When we communicate to another person, we “make common”.
Communicate (v.) 1520s, “to impart” (information, etc.), from Latin, past participle of communicare “to share, communicate, impart, inform”. The word impart means to give a part of ones things or possessions to another, to share out, be it tangible or intangible.
The secret to relationships is to appeal, to make yourself as familiar as possible to another. To make your “self” appear as their “self”, or congruent to whatever ideas or values they are more comfortable with. Exchanging information, so that they understand you. Pointing out commonalities.
Of course, the analysis of relationships apply to everything, from physical objects to nature and organisms. Taxonomy is the task of identifying commonalities and creating structure around the common features of organisms, and grouping or classifying them together.
There are relationships in mathematics. Relationships in physics. Relationships in chemistry.
Understanding the relationships among things, or whatever object or subject of study you’re reflecting on, is crucial to understanding the properties, the very nature of these things, not as static entities, but as fluid entities, existing in a context, supported by relationships amongst other objects and subjects.
An ecosystem is simply the life supporting relationships amongst organisms.
There are static properties of relations and fluid properties of relations. For instance, physical characteristics, and behavioral characteristics.
Given a context:
Function: Intended purpose or activity