|Image from makingsociologymatter.com|
When it comes to Christian community, our model is the Trinity. Speaking about three persons who are one grates a bit on the logical mind, but the idea of a communal God needs to be understood relationally, not logically. Part of the problem in understanding the idea of Trinity is that we in the Western world believe that the "one-ness" of God holds sway over the "three-ness" of God. This emphasis on one-ness can lead us down some sketchy paths both theologically and practically, because it directs our attention to uniformity instead of complexity, to authority rather than equanimity, to unifying doctrines and creeds instead of the movement of love.
Brazilian theologian Leonardo Boff writes: "We believe that God is communion rather than solitude. It is not a 'one' that is primary but the 'three.' The Three come first. Then, because of the intimate relationship between the 'three' comes the 'one' as expressing the unity of the three. Believing in the Trinity means that at the root of everything that exists and subsists there is movement; there is an eternal process of life, of outward movement, of love. Believing in the Trinity means that truth is on the side of communion rather than exclusion; consensus translates truth better than imposition; the participation of many is better than the dictate of a single one. Believing in the Trinity means accepting that everything is related to everything and so makes up one great whole, and that unity comes from a thousand convergences rather than from one factor alone." 
What Boff points out here is that beginning with one-ness (insisting on uniformity) perpetuates inadequate models of community and church. It also leaves us with problematic hierarchical forms of leadership and authority. Even more basically, our understanding of Trinity impacts how we interact with those we deem "the other." If we begin with one-ness, we are prone to trying to assimilate those who are not like us.
The mysterious specificity of a community of three is not immediately obvious, especially to those of us who live in a society which champions individuality. Boff explains, "If there were only one Unique One, only one God, solitude would ultimately be all there was. Underlying the whole universe, so diverse and so harmonious, would not be communion but only solitude."  If God is One and only ever One, there is no foundation or reason for community, and it makes sense that we are forever doomed to live as fractured humanity futilely trying to impose some sense of uniformity on each other. Boff continues, "If there were two Unique Ones, the Father and the Son, separation would be uppermost. One would be different from the other; and so there would be exclusion; one would not be the other."  Separation and exclusion are rife in our society; it is our lived experience. We are constantly comparing ourselves to others, noting the differences between us and them, and as a result of these differences, excluding people from our circle of friends. The reason for three-ness becomes clear. "Through the Trinity, the solitude of the One is avoided, the separation of the Two (Father and Son) is also overcome, and the exclusion of one from the other (Father from Son, Son from Father) is overcome. The Trinity allows for communion and inclusion. ... The Trinity shows that underlying everything existing and moving there dwells an impulse of unification, communion, and eternal synthesis of those who are distinct in an infinite, living personal, loving, and absolutely fulfilling whole." 
The source of all community is the Trinity: three persons who give themselves to each other with such abandon that one cannot see one without seeing the other. Not one of them comes before the other, they are all first and all last. Their embrace and communication are eternal, having no beginning and no end. Their differences are not erased but celebrated through mutual surrender. "The fundamental characteristic of each divine Person is to be for the others, through the others, with the others, and in the others. Each living Person is eternally vivified by vivifying the others and sharing the life of the others."  This is a great and wonderful mystery. And perhaps an even greater mystery is the generous invitation of the Trinity to share in their loving communion, to be one as they are one.
Father, Son, and Holy Spirit. Teach us what it means to live together in community, joined together by your bond of love.
 Leonardo Boff, Holy Trinity: Blessed Community (Maryknoll, NY: Orbis Books, 2000), xvi.
 Boff, 6.
 Boff, 48.