http://upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Shield-Trinity-Scutum-Fidei-English.svg/2000px-Shield-Trinity-Scutum-Fidei-English.svg.png
So basically trinity is:
Jesus is God, the Holy Spirit is God, the Father is God, each of them is a full and perfect God, and Jesus is not the Father, and the Holy Spirit is not Jesus, despite that the three Gods are one God.
That is either internal incoherence or that isn't English.
Lets go through the sun analogy, so the Father is the source of the sun, and the son is the light, and the holy spirit is the heat. Well, the analogy just refuted trinity.
First of all, the sun is what is being described, and heat and light are inseparable properties of the sun. You can't have a man somewhere, and his kindness somewhere else.
Furthermore, heat and light are contingent, meaning that they are created and not eternal. (God is not eternal?)
If we assume that they are part of God's nature (ie. God is wisdom, knowledge and reason is the Son, life is the Holy Spirit). So... can we have a God that doesn't have wisdom, knowledge, or life? So there is no objection in dividing God into more persons then?
If one of them is an actual perfect God, then what is the need for other persons?
X+Y+Z=1, and the three variables are equal then each of them is equal 1/3. If one of them equals one, then the other two are equal zero.
I've heard that it is actually 1x1x1=1, but it is more like 3x1=1, DollarXPennyXEuro=?, or PeachXTomatoXApple=...something else.
Bottom line is: Either the three persons are equal, but they are partially divine (1/3 each), in which no God actually exists.
Or the three persons are equal in essence, and all represents one God, leading to three different Gods.
It is non-sense that the three persons are equal in essence, all represents one God, but their addition equals one God.