While I certainly don't claim to have a great grasp of the trinity, I have found that there is some wonderful wisdom I gleaned when stepping outside of my personal experience of Western Protestant thought. Not only has this been helpful for my understanding of the trinity, but as we work with those from an Eastern background, it helps to connect with them as well. So let me share with you three big insights which have helped me embrace the teaching of the trinity.
I want to start with apophaticism because I think it helps us to move forward with an appropriate awe of God and humility of our limited understanding. Apophatic theology is also known as "negative theology" (the opposite of cataphatic theology) because it describes God in negative terms rather than positive ones. Gregory of Nyssa gives us a good explanation of this sort of theology.
Imagine a sheer, steep crag, of reddish appearance below, extending into eternity; on top there is this ridge which looks down over a projecting rim into a bottomless chasm. Now imagine what a person would probably experience if he put his foot on the edge of this ridge which overlooks the chasm and found no solid footing nor anything to hold on to. This is what I think the soul experiences when it goes beyond its footing in material things, in its quest for that which has no dimension and which exists from all eternity. For here there is nothing it can take hold of, neither place nor time, neither measure nor anything else; it does not allow our minds to approach. And thus the soul, slipping at every point from what cannot be grasped, becomes dizzy and perplexed and returns once again to what is connatural to it, content now to know merely this about the Transcendent: that it is completely different from the nature of the things that the soul knows.
While I think the Orthodox tend to take apophatic theology too far, their tendency towards embracing mystery and their willingness to stop short of trying to box God up in formulas and rigid understanding is invaluable, especially for someone like me who likes his boxes. As our men's group tries to work through the trinity, it's great to be able to begin in humility by acknowledging that we stand on Nyssa's precipice, recognizing how big God is and how limited we are. I don't think there is anything more important in this discussion than starting from a position of humility and awe.
Energies and Essences:
One of the most difficult aspects of the trinity is trying to comprehend how God can be one thing (essence), yet three different things (persons) at the same time. That just doesn't compute for us and seems to defy the law of noncontradiction. This is where I find the analogy of the Orthodox concept of "energies" and "essences" helpful.
I was first introduced to energies and essences in Staniloae's work, a Romanian Orthodox I read prior to moving to Romania. At first I thought it was extremely strange because one of the topics he discussed was what the Orthodox call "theosis" or "divinization." Literally, it's a concept of humans becoming divine. That sounded extremely heretical to me. We're going to become gods!?! But really this is something we Protestants believe. We just call it something more bening sounding. We call it "glorification." We believe that we are being conformed to the image of Christ. God views us as he views Christ, through Jesus's work on the cross, the imputation of Christ's righteousness to us, and his intercession on our behalf. We will be made like Christ. If you think about that, we're saying we will become gods in a sense. If Jesus is divine and we are going to be glorified to be like Christ, then we will be divine.
This is where the energies and essences distinction is helpful in Orthodox thought. The Orthodox distinguish between an essence or substance, and an energy or ... I don't really know how to describe that one. Perhaps an action or outpouring of self? So the Orthodox explain glorification/theosis/divinization as our energies becoming divine, but distinguishing the fact that our essences will never be divine. We will never have the essence of our being share in the eternality of God's being. We will never share in the essence of omnipotence. However, our energies (perhaps spirit, character, actions, etc) will be like the divine.
It doesn't matter whether you agree with the Orthodox conception of energies and essences. The point is that it is a helpful analogy, especially in an Eastern culture. It is much easier to grasp this notion that we will one day be like Christ in one sense, though not like him in another sense. We are essentially differentiating between two aspects of individuals, and you can call those aspects what you'd like. This understanding can then carry over to analogize the trinity. We can see that in one sense God is one, yet in another, he is differentiated as father, son, and spirit. While our experience of persons is only the experience of individual essences, our understanding of energies in terms of glorification can help us see that there isn't necessary a violation of the law of noncontradiction. We can be one thing, yet another thing at the same time.
Theology as Experience:
"The Spontaneous Expansion of the Church" is one of the best books I've read on missions (you can read my summary of it here) and was written by an Anglican named Roland Allen. There is one particular section which blew my mind in regard to the trinity. Allen writes,
THE REASON WHY THE SPONTANEOUS ZEAL OF NEW CONVERTS DOES NOT BREED THAT SPIRIT [of heresy] IS NOT HARD TO FIND. SUCH CONVERTS ARE ALMOST INVARIABLY MEN WHO HAVE HAD SOME REAL RELIGIOUS EXPERIENCE. THEY HAVE HEARD SOMETHING OF CHRIST; THEY HAVE RECEIVED SOME TEACHING ABOUT HIM; THEY HAVE GENERALLY LEARNED TO REPEAT THE CREED AND TO READ THE BIBLE; THEY HAVE CALLED UPON CHRIST AND BEEN HEARD; AND THIS HAS WROUGHT A CHANGE IN THEIR WHOLE OUTLOOK UPON LIFE, SUCH A CHANGE THAT THEY ARE EAGER THAT OTHERS SHOULD SHARE THEIR EXPERIENCE. HENCE THEY BEGIN TO TEACH OTHERS, AND TO SHARE THEIR EXPERIENCE WITH OTHERS. NOW ALL RELIGIOUS EXPERIENCE DEMANDS DOCTRINE FOR ITS PROPER STATEMENT AND EXPLANATION. IF THEN THESE MEN ARE NOT WELL INSTRUCTED IN THE CHRISTIAN DOCTRINE, WHEN THEY ATTEMPT TO SHARE THEIR EXPERIENCE WITH OTHERS THEY FEEL THAT THERE IS MUCH IN IT WHICH THEY CANNOT UNDERSTAND. CONSEQUENTLY INSTRUCTION IN CHRISTIAN DOCTRINE COMES TO THEM WITH AN ENLIGHTENMENT AND A POWER WHICH IS A JOY, AND THEREFORE THEY GLADLY RECEIVE IT, BECAUSE IT SUPPLIES A FELT NEED OF THEIR SPIRITUAL EXPERIENCE. IN SUCH AN ATMOSPHERE CHRISTIAN DOCTRINE IS IN LITTLE DANGER, FOR THOUGH FALSE OR INADEQUATE TEACHING, IF THEY RECEIVED SUCH, MIGHT PREVAIL FOR A TIME, YET THE TRUE TEACHING WHEN IT COMES MUST INEVITABLY DRIVE OUT THE FALSE. FOR THE EXPERIENCE IS A TRUE EXPERIENCE, AND A TRUE EXPERIENCE DEMANDS A TRUE DOCTRINE.
IT IS AS THE COMPLEMENT OF EXPERIENCE THAT CHRISTIAN DOCTRINE FIRST TOOK SHAPE. IT IS NOTORIOUS THAT THE CHRISTIAN DOCTRINE OF THE TRINITY, FOR INSTANCE, WAS FORMULATED THROUGH THE ATTEMPTS OF THE DISCIPLES OF CHRIST TO EXPLAIN THEIR EXPERIENCE. CHRIST APPEARED, AND THE APOSTLES EXPERIENCED HIS POWER: THE HOLY GHOST DESCENDED, AND THE APOSTLES AND THEIR IMMEDIATE FOLLOWERS KNEW HIS INDWELLING; THE CHRISTIAN DOCTRINE OF THE TRINITY AROSE OUT OF ATTEMPTS TO EXPRESS THAT EXPERIENCE. AS THE COMPLEMENT OF EXPERIENCE, DOCTRINE RENEWS ITS YOUTH FROM AGE TO AGE; BUT DIVORCED FROM EXPERIENCE IT IS NOTHING MORE THAN THE STATEMENT OF AN INTELLECTUAL THEORY, AND TO REST IN SOMETHING WHICH AN INTELLECTUAL PROCESS HAS CREATED IS TO REST IN THAT WHICH AN INTELLECTUAL PROCESS CAN DESTROY
Let's look at how this plays out with the trinity. When Peter walked with Jesus, experienced his love and forgiveness, touched his hands, felt his feet washed, etc - Peter experienced Jesus as a man. When Peter walked on water, when he experienced the storm calmed by Jesus's voice, when he saw loaves and fishes multiply before his eyes, and when he saw a raised to life Lazarus and Jesus - Peter experienced Jesus as God. And when Peter observed Jesus's baptism, when Peter was able to heal others and cast out demons, and when Peter experienced the Spirit at Pentecost - the Spirit to which Jesus attested he would send - Peter experienced Jesus as Spirit.
The theology of the trinity, then, was not some formulaic thing which people in ivory towers came up with and attempted to construct over centuries. The Apostles knew their experiences and they knew the truths of the trinity, though they didn't have a word or system to explain it yet. But they had experienced God as triune. The three centuries it took to define the trinity was not an attempt to explain an abstract God or fix a broken theological system, but rather an attempt to explain real life, tangible experiences which were hard to explain logically.
Why is this important to the trinity discussion? Because rather than grounding theology in thought which can make sense to our minds, it grounds theology in experience, which grounds truth in something tangible and provides a frame of reference from which to work. While my experiences of God haven't been as tangible as Peter's, I know my own experiences of God. But I also know that Peter must have experienced something for real because he was willing to die for what he experienced to be true. A lot of people die for causes, but they don't die for causes they know to be false. Peter must have experienced Jesus post-resurrection, and Peter must have experienced Jesus as God because Peter would not have sacrificed his life had Jesus died a false prophet. So not only do I have my experiences I can rely on, but those of Peter and the other Apostles as well. I've experienced many relationships, and this experience tells me that nobody would willingly die for a charlatan. If Jesus was not God himself raised form the dead, Peter and the Apostles would never have died for him. Knowing all this, it is important for our discussions of the trinity that we don't keep things only in the intellectual realm, but that we recognize the importance of our own experiences, along with the well attested experiences of others (particularly the New Testament authors who directly experienced Christ).
The three helps I've identified here don't perfectly explain the trinity. In fact, one of them actually amplifies the sense of mystery while another undercuts the need for perfect logical understanding. However, as we work through the trinity, it is important to recognize that logic and understanding extend well beyond the Western formulaic, pragmatic, boxy thought. We are not only physical creatures. We have real emotions and experiences. But at the same time, we are physical creations, meaning we have severe limitations in regard to our understanding of the universe. Keeping all these things in mind helps us to approach the trinity with humility and gives us more angles to understanding.