The history of discussions about the Holy Trinity is littered with dead analogies and metaphors which fail to do justice to the God they are trying to represent. The hallowed Ice-Water-Steam analogy ends in the heresy of Modalism. Patrick's Three Leaf Clover inevitably leads to Unitarianism. The "mother who is a daughter who is a wife" analogy leads to Modalism yet again, while the analogy of "three men who share a common human nature" leads to Polytheism. The Triangle is too impersonal, whereas Augustine's analogy of Lover-Beloved-Love seems too personal, and makes the Trinity seem to be three separate consciousnesses. We could also heap up "1x1x1=1", or "Thinker-Thinking-Thought", or "Giver-Giving-Gift", or one Person as "Mind-Heart-Will", or one Family as "Father-Mother-Child", on the pile of analogies that are too inaccurate or mundane to be definitive examples of the Trinity.
All fail. All fall apart. None fully conveys, or captures, the Mystery of the Trinity. Like I saw online the other day: The Trinity is a Mystery, not a Puzzle.
And yet. And yet!
The opposite end of over-explaining is under-explaining: The Trinity is a Mystery we cannot understand, so don't even try. Just affirm it and go about your life. Keep calm and don't think too much.
This attitude may keep one generation content and humble, but it leads to the next generation being filled with Deists and Unitarians. Study after study shows that younger generations trend toward a tepid "Moralistic Therapeutic Deism" rather than a robust and passionate commitment to any particular God. And that is because we have the bland leading the bland into what they market as "profound mystery" but in reality is merely pretend agnosticism. Because if an idea about God has no definable meaning, it is literally meaningless. And meaningless things get abandoned by those who have no emotional connection to them.
So, if we are going to help future generations experience the Trinity as a vital Reality, we need to say SOMETHING about the Trinity, even if that something is insufficient and even potentially problematic. In fact, if the Holy Trinity is the pulsing Heart of all worlds, creating and upholding the cosmos in a Divine Love which has always been the essence of God and always will be, we need to have some way of saying and showing this. And all of the analogies above, despite their defects, are ways into that conversation of saying something about the Trinity, even if that something is not sufficient.
So, with this in mind, let me throw out one of my favorite visual metaphors. Like all analogies and metaphors, it falls apart at key places. And if this analogy does not work for you, feel free to abandon it. But the reason for this metaphor is to get the conversation started, not provide all the answers. And I think this analogy moves that conversation in the right direction.
Thus, I think the Möbius strip can be a helpful yet limited visual metaphor for the Trinity. When you compress the strip to be perceived in two dimensions (as above) it must necessarily be seen as THREE distinct sides, while in reality it is all ONE surface. And just as the Möbius strip hints at a continual dance and movement, as the ONE surface expresses itself continually in THREE sides, so also the Trinity is an interconnected dance of self-giving Love which is called "perichoresis" or "circumincession" in the Great Tradition.
Thus, just as the Möbius strip is necessarily three-fold in relation to a two-dimensional world, so also, God in relation to ANY finite universe must necessarily, because of God’s Nature, be experienced in a threefold way, although in Godself, God is one. In Godself, outside of any possible finite universe, God is whole, integral, fully actual, singular (in Thomas Aquinas’ terms “God is simple”).
But in relation to any finite universe, no matter how big, nor how many dimensions, God will necessarily be threefold: God is transcendent, beyond any of the limits of that finite universe (as Father); God is immanent, as the very Being that upholds all beings (as Spirit); God is personal, intentional, sensed in the Pattern which gives the universe rationality, intelligibility, and meaning (as Logos, who becomes incarnate in Jesus Christ).
If God did not transcend the world (or all possible worlds) God would not be God. If God did not fill all worlds as the immanent Spirit, God would not be God. If God was not a Person discerned through the Pattern we find in creation, God would not be God. But if this "Transcendent-Immanent-Personality" was not somehow one, single, unified Divine Reality, God would not be God. For God to be the Ultimate Reality which grounds all other realities, and in which all worlds inhere, all of these dimensions of the Divine must be Real.
Various religions and philosophies place certain emphases on God (or the gods) as transcendent, and/or immanent, and/or personal, and/or one, and/or many. But only through Christ, by the Spirit, do we finally get the heuristic we need to put all the pieces together in a coherent whole. And it took a good 3-4 centuries after Christ for the Church to begin to develop sufficient conceptual clarity to proclaim this Triune Reality incarnate in Christ.
In the Holy Trinity we find God to be the solution to the Biblical paradox of how the singular God of the ancient Jews was experienced by Jesus' followers in the parental providence of the Father, and the saving atonement of the Son, and the creative empowering of the Spirit. But the Trinity is also the solution to the perennial paradoxes of the One and the Many, of Diversity and Particularity, of Transcendence and Immanence, or Personality and Pattern, unified in the singular Divine Source.
Much more could be said (and should be said) about God. God may be an infinite number of things in addition to the Triune Reality fully embodied in the Incarnation, but God can never be LESS than that, or OTHER than that.
So, let me throw the Möbius strip on the heap of failed Trinitarian analogies, in the hopes that it will push the conversation in the right direction, so we may learn to more fully know the Triune God we love, and more deeply love the Triune God we confess. Because for me there is something about the Möbius strip pressed flat that visually captures the absolute oneness of God in relation to Godself, and the essential threeness of God in relation to any finite world.
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