The Trinity is one of the more vexing doctrines in all of the Catholic tradition. God is one, and yet God is three: the father, the son Christ who walked on earth, and the Holy Spirit. To make matters worse, God even has a mother, to whom one prays quite like one prays to God. My understanding of this vexing system is that it encodes the concept of “auto-production” or “bootstrapping,” the paradoxical capacity of systems to generate themselves ex nihilo.
The Trinity provides an impressively intelligent counterpoint to the naïve creationist tendency, in which the Gospels sometimes sound as if some magical kind of person created the universe by himself. There's nothing evil about such a linguistic device, but it is obviously naïve and inadequate technically. Any half-educated atheist can tell you, correctly, that such a model cannot plausibly account for who or what created the conditions for the creator; that such a naive model merely halts an infinite regress by brute force. More realistically, as cybernetics and the study of complex systems have shown, systems can very well bootstrap themselves from random perturbations among a few initial elements or particles. Which particular element or particle moved first is often impossible to determine, for it is their interaction that kicks off the systems’ dynamics. Auto-production is at work in the cosmological model known as the Big Bang, for instance.
The Catholic Trinity, plus the strangely important figure of Mary, is an intuitive approximation of a complex-systems model. God is one, the one name for that which created everything, but the nature of this one is to be a set. It is the circulation and mutual-stimulation of the elements in this one set that is the essential miracle of life.