It is the practice of many theologians to attempt to find analogies for explaining the doctrine of the Trinity. We believe that God is triune: three hypostaseis in one ousia, three personae in one substantia, three persons in one nature. But this is impenetrable to the intellect, because it is difficult to distinguish between this polytheism. Does the doctrine of the trinity mean that there are three gods?
In order to explain to questioners how the doctrine of the trinity can be true, some theologians and philosophers give analogies from the created order. Consider the way the three leaves of a clover are one thing; or the way that the sun, its heat, and its light are all in some way united though distinct; or -- which is an even worse example, to my mind -- how Cerberus is a single dog but with three centers of consciousness. All of these examples, however, fall short in important ways. God is not composed of Father, Son, and Holy Spirit in the way that a clover is composed of its three leaves. Indeed, God is entirely immaterial, and so the analogies which play on the material composition of certain sorts of objects will all inevitably fall short.
Lately I have been reading from John of Damascus, and have found in him a kindred spirit in what concerns philosophy and theology. I quite like him. Consider what he says about the nature of God in a treatise On Heresies:
And so, let the faithful adore God with a mind that is not overcurious. And believe that He is God in three hypostases, although the manner in which He is so is beyond manner, for God is incomprehensible. Do not ask how the Trinity is Trinity, for the Trinity is inscrutable (§103).
And in his De Fide Orthodoxa, he makes a distinction between what has been revealed to us and what hasn't. It has been revealed to us that God is three in one, but the precise manner in which this can be has not been revealed. Because of God's own nature as utterly transcendent and unlike the things which he has created,
it is impossible either to say or fully to understand anything about God beyond what has been divinely proclaimed to us, whether told or revealed, by the sacred declarations of the Old and New Testaments (I:2).
Indeed, it is clear that God exists, but what He is in essence and nature is unknown and beyond all understanding (I:4). Because of this, all of our terms and descriptions of God do not show what He is, but, rather, what he is not, since it is impossible to say what He is in His essence. This is because [God] does not belong to the number of beings, not because He does not exist, but because transcends all beings and being itself.
And later on, he emphasizes the radical distance between God and the created order in order to limit our confidence in any particular analogies for the trinitarian relations:
For it is impossible to find in creation any image which exactly portrays the manner of the Holy Trinity in Itself. For that which is created is also compounded, variable, changeable, circumscribed, having shape, and corruptible; so, how shall it show with any clarity the supersubstantial divine essence which is far removed from all such? (I:8).
Following the Damscene, then, I hold that it is better to limit ourselves to the language of the creeds regarding the doctrine of the Trinity, rather than trying to find an analogue in the created order for interpreting the theological statement itself. God in his divine nature is utterly unlike any of us. We bear some resemblance to him, of course, but it would be a mistake to work the other way around, from us to him, in order to come at a definitive understanding of his essence. So the doctrine of the trinity remains mysterious, even while it is necessary for maintaining the orthodox faith.