One of the strange things about the Trinity is that
the Father, Son and Holy Spirit are all equally God, yet there seems an
inevitable order in which we pray “In the name of the Father, and of the Son,
and of the Holy Spirit.” It doesn’t seem quite right to pray “In the name of
the Holy Spirit, Father and Son” or any other variant - yet if they are all
equally God, it might be strange that the order matters.
I suspect the revealed order “In the name of the Father, and of the Son, and of the Holy Spirit” is primarily to do with the fact that the Father is active in the world before the Son, and then the Son is active in the world by becoming Incarnate, and then the Holy Spirit is sent to deepen the intimacy of the relationship.
No analogy can fully capture the essence of God, but perhaps we can think of it a bit like our interaction with the sun. The sun’s energy gives us the trinity of light, heat, and warmth – but its light reaches us first, not because it travels faster (it doesn't), but because we perceive visible radiation immediately; then heat follows as matter absorbs the radiation, and warmth is the personal experience that results. Similarly, the Father’s creative act is like light, the Son’s incarnate presence is like heat, and the Holy Spirit’s indwelling is like the warmth.
