Howard Snyder writes on the Trinitarian nature of the church in Decoding the Church..

1. The church as a trinitarian worshipping community.

The church in its worship, and often most explicitly in its hymns, worships the trinity. Further, the trinity forms the basis of the church’s mission as the community responds to the call of the trinity to participate in the missio Dei. In worship the community draws near to God and comes to understand the Father’s creative love and care for all God has made, the Son’s self-giving in becoming a servant for our salvation, and the Spirit’s call and push to go into the world “as the Father” has sent the Son. Genuine worship impels into mission.

The church has a mission to God as well as a mission to the world. There is a reciprocal action here that is grounded in the perichoresis of the trinity. We give ourselves to God (our mission to God) and he gives himself back to us with an overflow of love that impels us into mission. This seems, in part, to be what is in view in John 17: “As you sent me into the world, I have sent them into the world…. I in them and you in me. May they be brought to complete unity to let the world know that you sent me and have loved them even as you have loved me” (Jn. 17:18, 23).
In other words, mission in trinitarian perspective is not one-way: we go out in mission because the trinity sends us in mission. Rather, it is reciprocal and even “perichoretic” as, in response to God’s grace, we carry out our mission to God and thus are “carried” into mission in the world by the Holy Spirit.

2. The trinitarian community is especially sent to the poor.

Though “being in the very nature God,” Christ “made himself nothing, taking the very nature of a servant” (Phil. 2:6-7) and carried out his mission. This is in fact a demonstration of the “wisdom of God” as expounded by Paul in 1 Corinthians 1:27-30.

It can be argued that God’s special concern for the poor, and Jesus’ explicit mission to the poor, is grounded in the trinity. Since the trinity is unbounded self-giving love each to the other, always seeking the best for the other and receiving back love in return, and since the church’s mission grows out of the overflow of this love, the church’s mission is to all people. But in the incarnation Jesus Christ becomes the suffering trinity, and thus the Father and the Spirit have particular compassion for him in his sufferings.

This is mirrored in God’s particular concern for “the widow, the orphan, and the alien” that we see throughout Scripture. God loves all, but particularly those who suffer. It is the very mutual love of the trinity that impels God, and thus the church, to incarnate the gospel among the poor. And thus Jesus can say, in words that echo the reality of the trinity, “The Spirit of the Lord is on me, because he has anointed me to preach good news to the poor” (Lk. 4:18). The so-called “preferential option for the poor” is grounded in the trinity.

3. The church’s ministry is also grounded in the trinity.

The trinity is the opposite of hierarchy. The book makes the point that the church’s ministry, including its leadership, is non-hierarchical. But the deepest theological grounding of this is in the trinity itself.

The trinity, and the very nature of the material creation God has made, show us that we should conceive of the church and its ministry in organic, relational (rather than mechanical-hierarchical) terms. The church is not so much a rational organization (a social machine) as it is a complex organism.

Here some of the emerging insights of complexity theory may be of some use to the church. Complexity theory has been described as “the emerging science at the edge of order and chaos.” This new science studies the way order seems suddenly to emerge from seemingly chaotic systems. It looks at the highly complex interaction of multiple factors in such systems as weather patterns, economics, or living cells. A complex system is one in which “a great many independent agents are interacting with each other in a great many ways.” M. Mitchell Waldrop, Complexity: The Emerging Science at the Edge of Order and Chaos. New York: Simon and Schuster, 1992, p. 11)It seems to me that viewing the church as a complex organism at least suggests to us 1) that the church is a totality of complex factors, not a linear cause-and-effect system; 2) that small actions have complex, long-range, not fully predictable significance; 3) that size is always a function of other factors, not an end in itself; and 4) that “emergent structures” arise from the church’s complex vitality as they are needed. That is, the growth of the church in vitality, ministry, and numbers will often itself give rise to the necessary structures if the church pays priority attention to what it fundamentally is in Christ.

The complexity perspective suggests that missional churches will focus on the multiple small actions that collectively give visible expression to the life of Jesus Christ in the world. Missional churches will pay attention to the many small things that constitute the church’s vitality, as well as watching for the small things that destroy life, whether a lying tongue, an unkind word, unresolved conflict, or a seemingly innocent but outdated tradition. More basically, the complexity model means we should understand the vital importance of Christian character and community in the life of the church. Too often in the church we focus on trying to get people to do things rather than on helping them to become the disciples God intends. Of course, our actions do build or destroy character; this is not an either/or dynamic.