I've been looking over a couple of posts by VJ Torley, here and here, about what happens to people who have had surgery to permanently divide their left brain from their right brain. Apparently they often experience something like split personalities, where each side of their brain tries to control their actions, or where they even have contradictory beliefs. From what I understand the left brain is the linguistic, analytic part of us, and controls the right side of our bodies. The right brain is the intuitive, emotional side of us, and controls our left side.
What I find interesting is the similarity in characteristics and function to two of the personalities of the Trinity. God the Son is also know as the Word of God, and would be comparable to the linguistic, analytic side of God. God the Spirit, or the Holy Spirit, would be comparable to the intuitive or emotional side of God. The Spirit is also the part of God that is associated with God's activity.
In the first chapter of Genesis, the Spirit of God hovers over the waters, waiting for God to speak. Once God's Word is given, the Spirit acts on it and creates. So there is order in the Persons of the Trinity: God the Father speaks the Word of God and the Spirit of God acts. Both the Word and the Spirit are in submission to the Father.
I imagine something like that is supposed to happen with us. I don't know what part of us, if any, is comparable to the Father. But we are to be in submission to God the Father also, both our left and right brains, both our analytic and emotional sides. And there should be the same order that we see in the Trinity.
But what's even more interesting is that all this time everyone has been complaining that we do not understand the Trinity - how three persons can be one thing. Yet all this time we have been two persons in one thing.