One of the central tenets of orthodox Christianity is the doctrine of the Trinity. Formally established in 325 at the Council of Nicea, this doctrine gives us the language of "persons" and "substance" while helping us understand this God that we worship. All too often unfortunately, Christianity has reduced our notion of the Triune God to a mere requirement so that Christianity can continue to claim a seat at the table of monotheism. Modern Christians get hung up on the three-in-one examples, offering those up for proof. But the ice-water-steam examples are not at all proof, nor are they authoritative. In the end, these examples most likely do more than good, by building up a false sense of what is really important with Christians, and seeming like complete idiocy to non-Christians.
The doctrine of the Trinity cannot remain as just a set of logical deductions that exist independent of the early Church's experience of Jesus. All of the three in one language becomes absurd without understanding that Jesus made this discussion necessary. When the early followers of Jesus see this human being claim the authority to forgive sins, as well as the mastery over the powers of nature and chaos, they begin to contemplate who exactly this is. When Jesus is crucified and resurrected, these followers must enter into the mystery of the divine relationship. Jesus addresses God as "Father" and in addition claims a unity with him that is blasphemous for many.
Some Christians reject the doctrine of the Trinity because they do not find it laid out anywhere in Scripture. If we were to take Scripture at face value... no, it's not. However, there are plenty of implicit openings for our considerations of the Trinity. Along with Jesus claiming unity with the Father, there is also the passages where God speaks as a plural subject--"Let us make humankind in our image..." There is the baptism of Jesus where the voice from heaven speaks, the spirit descends, all centered on Jesus.
Ultimately to speak of the Trinity, we too must center our gaze on Jesus. In our continued experience of Jesus coming to us, we are left to wonder about what this Incarnate deity says about the nature and character of God. Of course, this position is unhelpful if all we want is rational argumentation to prove that God exists. Plus, we are left with a real human being who comes and claims us. An abstract deity that exists as some sort of Godhead might actually make us feel better, but Jesus changes our focus.
In her book The Triune God of Christian Faith, Mary Ann Fatula writes:
We need to recognize first of all that our Christian faith in a triune God did not come to us as a result of logical deduction about an esoteric, abstract truth. On the contrary, our faith in a triune God is rooted in our concrete human history; first of all, in the paschal event--the human experience of Jesus in his life, death, resurrection, ascension, and pentecost; second, upon the Christian community's actual experience of the triune God in the past; and, finally, upon our own experience in the present. Our faith today, therefore, is not a matter of mere intellectual assent to the Trinity as if we were accepting the answer to a complicated math problem without understanding how the problem really works: "Yes, I believe that two plus two equals four, but in God's case, one equals three."