In chapter 2 of his book Think, John Piper gives an explanation of why we think and feel. We think and feel because God thinks and feels, and we, of course, are made in God’s image (Genesis 1:27).
In fact – and this is the point at which I may have dropped my sandwich – the reason God exists in three persons is precisely because He both thinks and feels:
“Prepare to be boggled. Here is [Jonathan] Edwards’s remarkable description of how the persons of the Trinity relate to each other. Notice that God the Son stands forth eternally as a work of God’s thought. And God the Spirit proceeds from the Father and the Son as the act of their joy.
This I suppose to be the blessed Trinity that we read of in the Holy Scriptures. The Father is the deity subsisting in the prime, unoriginated and most absolute manner, or the deity in its direct existence. The Son is the deity generated by God’s understanding, or having an idea of Himself and subsisting in that idea. The Holy Ghost is the deity subsisting in act, or the divine essence flowing out and breathed forth in God’s infinite love to and delight in Himself. And I believe the whole Divine essence does truly and distinctly subsist both in the Divine idea and Divine love, and that each of them are properly distinct persons.
In other words, God the Father has had an eternal image and idea of himself that is so full it is another Person standing forth – distinct as the Father’s idea, yet one in divine essence. And God the Father and the Son have had an eternal joy in each other’s excellence that carries so fully what they are that another Person stands forth, the Holy Spirit – distinct as the Father and Son’s delight in each other, yet one in divine essence. There never was a time when God did not experience himself this way.”