There is an old Spiritual that says, My God is so high, you cant over him, hes so low, you cant under him, hes so wide you cant round him, you must come in, by and through the Lamb.
Not a bad way of saying that God is other, He is beyond what human words can tell or describe, He is beyond what human thoughts can conjure. And on the Feast of the Most Holy Trinity we do well to remember that we are pondering a mystery that cannot fit in our minds.
A mystery though, is not something wholly unknown. In the Christian tradition the word mystery refers to something partially revealed, much more of which lies hid. Thus, as we ponder the teaching on the Trinity, there are some things we can know by revelation, but much more is beyond our reach or understanding.
Lets ponder the Trinity by exploring it, seeing how it is exhibited in Scripture, and how we, who are made in Gods image experience it.
I. The Teaching on the Trinity Explored Perhaps we do best to begin by quoting the Catechism which says, The Trinity is One. We do not confess three Gods, but one God in three persons: [Father, Son and Holy Spirit]
The divine persons do not share the one divinity among themselves but each of them is God whole and entire. (Catechism, 253).
So there is one God, and the three persons of the Trinity each possess the one Divine nature fully. The Father IS God, He is not 1/3 of God. Likewise the Son, Jesus, IS God. He is not 1/3 of God. And so too, the Holy Spirit IS God, not a mere third of God. So each of the three persons possesses the one Divine nature fully.
It is our experience that if there is only one of something, and I possess that something fully, there is nothing left for you. Yet, mysteriously each of the Three Persons fully possess the one and only Divine Nature fully while remaining distinct persons.
One of the great masterpieces of the Latin Liturgy is the preface for Trinity Sunday. The Preface, compactly, yet clearly sets for the Christian teaching on the Trinity. The following translation of the Latin is my own:
It is truly fitting and just, right and helpful unto salvation that we should always and everywhere give thanks to you O Holy Lord, Father almighty and eternal God: who, with your only begotten Son and the Holy Spirit are one God, one Lord: not in the oneness of a single person, but in a Trinity of one substance. For that which we believe from your revelation concerning your glory, we acknowledge of your Son and the Holy Spirit without difference or distinction. Thus, in the confession of the true and eternal Godhead there is adored a distinctness of persons, a oneness in essence, and an equality in majesty, whom the angels and archangels, the Cherubim also and the Seraphim, do not cease to daily cry out with one voice saying: Holy Holy, Holy
Wowza! A careful and clear masterpiece, but one which baffles the mind as its words and phrases come forth. So deep is this mystery that we had to invent a paradoxical word to summarize it: Triune (or Trinity). Triune literally means, Three-one (tri+unus) and Trinity is a conflation of Tri-unity meaning the three-oneness of God.
If all this baffles you, good. If you were to say, you fully understood all this, I would have to call you a heretic. For the teaching on the Trinity, while not contrary to reason per se, does transcend it.
A final picture or image, before we leave our exploration stage. The picture at the upper right is an experiment I remember doing back in High School. We took three projectors, each of which projected a circle: One was red, another green, another blue. As we made the three circles intersect, at that intersection, was the color white (see above). Mysteriously, three colors are present there, but only one shows forth. There are three but there is one. The analogy is not perfect (no analogy is, it wouldnt be an analogy) for Father, Son and Spirit do not blend to make God. But the analogy does manifest a mysterious three-oneness of the color white. Somehow in the one, three are present. (By the way, this experiment only works with light, dont try it with paint )
II. The Teaching on the Trinity Exhibited : Scripture too presents images and pictures of the Trinity. Interestingly enough most of the pictures I want to present are from the Old Testament.
Now I want to say, as a disclaimer, that Scripture Scholars debate the meaning of the texts I am about to present, thats what they get paid the big bucks to do. Let me be clear to say that I am reading these texts as a New Testament Christian and seeing in them a Doctrine that later became clear. I am not getting in a time machine and trying to understand them as a Jew from the 8th Century BC might have understood them. Why should I? Thats not what I am. I am reading these texts as a Christian in the light of the New Testament, as I have a perfect right to do. You of course, the reader are free to decide if these texts really ARE images or hints of the Trinity from your perspective. Take them or leave them. Here they are:
1. Then God said, Let us make man in our image, after our likeness
(Gen 1:26) So God speaks to himself in the plural: let us
.our. Some claim this is just an instance of the Royal We being used. Perhaps but I see an image of the Trinity. There is one (God said) but there is also a plural (us, our). Right at the very beginning in Genesis there is already a hint that God is not all by himself, but is in a communion of love.
2. Elohim?? In the quote above, the word used for God is אֱלֹהִ֔ים (Elohim). Now it is interesting that this word is in a plural form. From the view point of pure grammatical form Elohim means Gods. However, the Jewish people understood the sense of the word to be singular. Now this is a much debated point and you can read something more of it from a Jewish perspective here: Elohim as Plural yet Singular. My point here is not to try and understand it as a Jew from the 8th Century BC or a Jew today might understand it. Rather, what I observing is that it is interesting that one of the main words for God in the Old Testament is plural, yet singular, singular yet plural. It is one, it is also plural. God is one, yet he is three. I say this as a Christian observing this about one of the main titles of God. I see an image of the Trinity.
3. And the LORD appeared to [Abram] by the oaks of Mamre, as he sat at the door of his tent in the heat of the day. He lifted up his eyes and looked, and behold, three men stood in front of him. When he saw them, he ran from the tent door to meet them, and bowed himself to the earth, and said, My Lord, if I have found favor in your sight, do not pass by your servant. Let a little water be brought, and wash your feet, and rest yourselves under the tree, while I fetch a morsel of bread, that you may refresh yourselves, and after that you may pass on since you have come to your servant. So they said, Do as you have said. (Gen 18:1-5). Now this passage from a purely grammatical point of view is very difficult since we switch back and forth from singular references to plural. Note first that the Lord (singular) appeared to Abram. (In this case יְהוָ֔ה Yahweh (YHWH) is the name used for God). And yet what Abram sees is three men. Some have wanted to say, this is just God and two angels. But I see the Trinity being imaged or alluded to here. And yet when Abram address them he says, My Lord (singular). The tortured grammar continues as Abram asks that water be fetched so that he can wash your feet (singular) and that the LORD (singular) can rest yourselves (plural). The same thing happens in the next sentence where Abram wants to fetch bread that you (singular) may refresh yourselves (plural) In the end the LORD (singular) gives answer but it is rendered: So they said Plural, singular
.. what is it? Both. God is one, God is three. For me, as a Christian, this is a picture of the Trinity. Since the reality of God cannot be reduced to words we have here a grammatically difficult passage. But I see what is going on. God is one and God is three, he is singular and yet is plural.
4. Having come down in a cloud, the Lord stood with Moses there and proclaimed his Name, Lord. Thus the Lord passed before him and cried out, The Lord, the Lord, a merciful and gracious God, slow to anger and rich in kindness and fidelity (Exodus 34:5). Here we see that when God announces his name He does so in a threefold way: Lord!
The Lord, the Lord. There is implicit a threefold introduction or announcement of God. Coincidence or of significance? You decide.
5. In the year that King Uzziah died I saw the Lord sitting upon a throne, high and lifted up; and his train filled the temple. Above him stood the Seraphim; each had six wings: with two he covered his face, and with two he covered his feet, and with two he flew. And one called to another and said: Holy, holy, holy is the LORD of hosts; the whole earth is full of his glory. (Is 6:1-3) God is Holy, Holy, and yet again, Holy. Some say this is just a Jewish way of saying very Holy but as Christian I see more. I see a reference to each of the Three Persons. Perfect praise here requires three holys, why? Omni Trinum Perfectum (all things are perfect in threes), but why? So, as a Christian I see the angels not just using the superlative but also praising each of the Three persons. God is three (Holy, Holy, Holy) and God is one, and so the text says, Holy IS the Lord. Three declarations Holy: Coincidence or of significance? You decide.
6. In the New Testament there are obviously many references but let me just refer to three quickly. Jesus says, The Father and I are one (Jn 10:30). He says again, To have seen me is to have seen the Father (Jn. 14:9). And, have you ever noticed that in the baptismal formula Jesus uses is bad grammar? He says, Baptize them in the Name (not names as it grammatically should be) of the Father and of the Son and of the Holy Spirit (Matt 28:19). God is One (name) and God is three (Father, Son and Holy Spirit).
Thus Scripture exhibits the teaching of the Trinity, going back even to the beginning
III. The Teaching of the Trinity Experienced We who are made in the image and likeness of God ought to experience something of the mystery of the Trinity within us. And sure enough we do.
For, it is clear that we are all distinct individuals. I am not you, you are not me. Yet it is also true that we are made for communion. Humanly we cannot exist apart from one another. Obviously we depend on our parents through whom God made us. But even beyond physical descent, we need one another for completion.
Despite what old songs say, no man is a rock or an island. There is no self-made man. Even the private business owner needs customers, suppliers and shippers, and other middle men. He uses roads he did not build, has electricity supplied to him over lines he did not string, and speaks a language to his customers and others he did not create. Further, whatever the product he makes, he is likely the heir of technologies and processes he did not invent, others before him did. And the list could go on.
We are individual, but we are social. We are one, but linked to many. Clearly we do not possess the kind of unity God does, but the three oneness of God echoes in us. We are one, yet we are many.
We have entered into perilous times where our interdependence and communal influence are under appreciated. That attitude that prevails today is a rather extreme individualism wherein I can do as I please. There is a reduced sense at how our individual choices affect the whole of the community, Church or nation. That I am an individual is true, but it is also true that I live in communion with others and must respect that dimension of who I am. I exist not only for me, but for others. And what I do affects others, for good or ill.
The Its none of my business, what others do attitude also needs some attention. Privacy and discretion have important places in our life, but so does having concern for what others do and think, the choices they are making and the effects that such things have on others. A common moral and religious vision is an important thing to cultivate. It is ultimately important what others think and do, and we should care about fundamental things like respect for life, love, care for the poor, education, marriage and family. Indeed, marriage an family are fundamental to community, nation and the Church. I am one, but I am also in communion with others and they with me.
Finally there is a rather remarkable conclusion that some have drawn, that the best image of God in us is not a man alone, or a woman alone, but, rather, a man and a woman together in lasting a fruitful relationship we call marriage. For, when God said, Let us make man in our image (Genesis 1:26) the text goes on to say, Male and female he created them (Genesis 1:27). And God says to them, Be fruitful and multiply (Gen 1:28). So the image of God (as God sets it forth most perfectly) is the married and fruitful couple.
Here of course we must be careful to understand that what we manifest sexually, God manifests spiritually. For God is not male or female in His essence. Thus, we may say, The First Person loves the Second Person, and the Second Person loves the First Person. And so real is that love that it bears fruit in the Third Person. In this way the married couple images God, for the husband loves his wife and the wife loves her husband, and their love bears fruit in their children. 
So, today as we extol the great mystery of the Trinity, we look not merely outward and upward to understand but also inward to discover that mystery at work in us who are made in the image and likeness of God.