This is one of three "canned" responses to questions on the Trinity
and Incarnation.  The others focus on the Biblical motivation for the
doctrines, and a critique of the way in which the doctrines
traditionally have been explained.  (Although my explanation is
intended to be equivalent to the orthodox one, and meets the
requirements of the standards, I do not use the traditional
terminology.)  The response tries to summarize what the doctrine is
(and is not).  It is an attempt to respond to a number of postings
that simply misunderstand what the Trinity is saying.

This posting is in three sections: the Trinity, the Incarnation,
and a discussion of some misunderstandings:

1. The Trinity

At least in the West, the Trinity shouldn't be thought of as having
much to do with the number three.  There is only one God.  There
aren't separate "things" you can count three of.  In what I regard as
the authoritative explanation of the Trinity for the West (Augustine's
"De Trinitate"), the distinction among the persons is defined strictly
in relational terms.  The West always started with God as One.  The
three persons aren't separate entities exactly, but are separate ways
in which the one God exists.  The Trinity is really a consequence of
the fact that God is personal.  He has within himself a relationship
-- love.  This implies that God is both lover and loved, Father and
Son.  (The Holy Spirit is generally associated with the relationship
between the two.)  

The Trinity is important to us, because it means that the role of
obedient child that we are called on to play is something that God can
help us with.  He's not asking us to do something that is outside his
own experience.

But we're talking about three modes of existence, i.e.  three ways in
which God relates to himself, not three Gods.  (The term "mode" is a
dangerous one because it was associated with a heresy called modalism.
However I'm using it in a different way.)  They are not physically
separated, because we're not talking about parts.  It's not like the
north half of God is the Father and the south half is the Son.
Everything God is and does involves Father, Son, and Holy Spirit.
Father, Son, and Holy Spirit are distinguished only by the
relationship among them, because they aren't separate *things* so much
as separate ways in which God relates to himself.

2. The Incarnation

Questions about Jesus' death, etc., involve a bit more than the
Trinity.  The relationship between God and Jesus is really the subject
of the Incarnation, not the Trinity, though the Trinity is involved.

The Incarnation says that Jesus is God present with us in the flesh.
("The Word became flesh.")  In him two things are going on: a real
human life, and God's presence.  God is present in at least the
following senses: (1) Jesus makes God visible to us, in his teachings,
actions, death, and resurrection, and (2) God identifies himself with
Jesus in such a way that God himself experienced death through Jesus.

Jesus has a real human existence.  He is not simply God animating a
human body.  Jesus has a human will distinct from God's, though of
course Jesus' human will and God's operate together.  (This is not
modern "liberal" revisionism.  The idea that Christ had only one will
was rejected as the "monothelite heresy".)  

Note that this theology has no problem with the fact that Jesus prayed
to God and otherwise distinguished himself from God on some occasions.
(Of course he also identified himself with God on others.)  It's clear
that there is a distinction between a human being and the immortal,
invisible God.  To say otherwise would be insane.  The claim is that
despite this distinction, this human being is the way God chose to be
present with us.  

In classical theology, this is described by the "two nature" model.
This is another way of saying that in Christ, there are two things
going on: a human being, and God's presence, and God is present in
such a way that the integrity of Jesus' human existence is not
threatened, but that we still encounter God himself, and not something
less.

I'd like to suggest that for people who have experience with
computers, this sort of thing should actually be easier to believe
than for people in the 4th and 5th Cent.  We've experienced systems
where a single physical processor supports multiple virtual systems,
and where multiple physical processors are combined into a single
virtual system.  When reading science fiction, most of us have no
trouble dealing with the idea of colonial intelligences, where
multiple bodies are part of a single entity.  All of these are
examples of things that are in some ways like a single entity and in
other ways like multiple entities.  I don't believe any of these
examples is exactly like God.  But that's not the point.  I'm not
currently trying to formulate a computer-based theology.  Rather, I'm
saying that we've seen enough examples to believe that there are ways
to exist other than the human one.  I think they make it plausible
that there could be an entity that is in some ways like one person and
in other ways like several separate people.  I think that's all the
Trinity really says.  It says that in some ways God is best thought of
as one entity, and in other ways he best thought of as three entities.
There is also some understanding of in what areas it's most accurate
to think of him as one and what areas it's most accurate to think of
him as three.