The Trinity is something that we all believe in as Christians, right? Great! Now, go explain it to your children so they can understand their faith. Difficult, isn't it? It's no wonder that so few people attempt to teach about the trinity or try to find an analogy to explain it. The problem with the first approach is that the trinity is far too important of a doctrine to avoid, but the second one isn't much better. Despite the best efforts of many talented teachers (many, no doubt, more gifted than I), I haven't seen an analogy for the trinity that I think works. However, I do think that they accidentally show us how NOT to think about the trinity and can help us avoid some critical errors.
God is not like the sun
This analogy says that God is like the sun. You have the sun itself and light and heat produced by the sun. This is incorrect because it makes the Son and the Spirit creations of God rather than God Himself. After all, light and heat are not the sun; they are products of the sun. This is what the early church called "Arianism," named for a man called Arius who taught that there was a time where the Son did not exist. This is wrong, because the Son as a divine person is eternal, meaning He has no beginning, just as the Father and Spirit have no beginning (John 1:1).
God is NOT like water
This analogy says that God is like water. Water can exist as a liquid or as ice or steam, but it's always water. A similar analogy says that God is like one man who is simultaneously a father, brother, and uncle. This analogy doesn't work because it blends together the persons of the trinity. The technical term for this is "modalism." Modalism sees God as taking on different roles or modes at different times, sort of like an actor in different masks. In each analogy, you have the same thing (H2O, the same man, the same actor), just in a different form. Applied to God, you could say that in the Old Testament, he was the Father, but on earth, he was the Son and is now with us as the Spirit. It is important that while we uphold the unity of God (that there is one God, and that He is one substance), we maintain distinctions between the persons of God. The baptism of Jesus illustrates why (Mark 1:9-11). All at once, we see the Son being baptized, the Spirit descending like a dove, and the Father's voice coming from heaven. Father, Son, and Spirit were all present at once interacting with each other. It wasn't as though they were all one thing taking on three different roles at once. Instead, the Father, Son, and Spirit each revealed themselves as unique persons.
God is NOT like a shamrock
According to legend, this analogy goes all the way back to St. Patrick, who used it to try to explain the trinity to the Irish while he was a missionary. The analogy states that God is like a shamrock (clover). Just as the shamrock has three leaves and is yet one plant, so God is three and yet one. Another similar analogy uses an egg to make the same point, noting that an egg has a shell, yolk, and white. This analogy fails because it breaks up the unity of God. While the persons of God are distinct (Father, Son, and Spirit), they are united. They are persons, not parts. I could easily separate the leaves of a clover or the parts of an egg. This is what we call "partialism," which (you guessed it) sees God as three parts. The problem with seeing God as parts means that parts could be taken away or separated, which leads to a bigger problem that we call "tritheism." Tritheism is the belief in three gods, which would make Father, Son, and Spirit each a distinct god. Jesus clearly didn't see himself this way when he said, "I and the Father are one" (John 10:30).
What is God like?
The problem with our analogies is that they seek to describe the creator with things that are created. The analogies don't work because there is nothing like God. Our minds and our language are already not capable of describing God completely, and the task is only further complicated with these analogies. All we can say, then, is that God is like God. He is totally unique. We have to come up with new language and categories to describe Him because He is so different from our everyday experiences. The Athanasian creed does well to tell us to "neither blend the persons nor divide the substance." Of course, you might then ask, "what's the difference between persons and substance?" But that's a question for another post. For now, it is enough to say that God is three persons (Father, Son, and Spirit), but only one substance. The Father, Son, and Spirit are all God, but the Father is not the Son nor the Spirit, the Son is not the Father nor the Spirit, and the Spirit is not the Father nor the Son (say that five times fast). That's only the tip of the iceberg, but it's a good start that will keep our thoughts about God on track.