I have to admit, I've used these crude analogies in my Bible lessons to third graders before, but I usually qualify them, explaining that regardless of how hard we try, we can't wrap our minds around the trinity. Then I try to emphasize how marvelous it is that the depths of our God are so vast the human mind cannot search them, and although we cannot comprehend all of God's nature, we can know him and be assured of his great love for us. That's what makes Christianity different from any other religion.
Muslims believe in the one-dimensional god, Allah. They praise his self-sufficiency, and worship him for his love, compassion and mercy. They exalt Allah's oneness over the three-dimensional nature of the God of the Bible, claiming that Christians are guilty of shirk, the sin of worshipping more than one god.
Allah's one-dimensional nature is certainly easy to comprehend, but it's got one major problem: it makes it impossible for us to trust in his love.
Love, by its nature, must have an object. I love my sister, my mom loves my dad, my students love recess, my best friend loves to sing--love always has an object. Without something to love, there is no love. So, imagine Allah (or any one-dimensional god for that matter) before the creation of anything. He is alone in a great black void with no one and nothing to love. Can he have love?
Allah has two options at this point: he can love himself or he can create something to love. If he loves himself, his love is self-serving and counterfeit--imagine a world where everyone's love is self-serving like that! If he creates something to love, then his ability to love is contingent on his creation, diminishing his character and making his love no more enduring or trustworthy than a fickle human's love.
The trinity, on the other hand, perfectly explains God's love: love originates from and is fully expressed within the Father, the Son, and the Holy Spirit--everlasting love flows from God's character.
This perfect love compelled God to put on skin and live among us in order to show us how to love: "This is how we know what love is: Jesus Christ laid down his life for us. And we ought to lay down our lives for our brothers" (1 John 3:16).
This perfect love drove God to give us a helper and life-guide through the Holy Spirit who indwells all Christians. "But the Counselor, the Holy Spirit, whom the Father will send in my name, will teach you all things and will remind you of everything I have said to you" (John 14:26).
The trinity is a daily reminder to me that God will continue to pursue humanity relentlessly because he loves us fiercely. His infinite grandeur didn't stop him from taking on bodily form so that he could live with us, and then die for us; his perfectly selfless love compels him to dwell within and equip all Christians with the riches of his glorious power through the Holy Spirit!