God's infinity mirror

1. As a young boy, I remember sitting in a barbershop. I was sitting in the barber chair, having my hair cut. It was one of those neat swivel pump chairs. Behind me was a mirror all along that side of the shop. In front of me was another mirror. The combination of the two mirrors generated an infinity mirror. Sitting in the chair, I could see my reflection multiplied, receding into the never-ending distance, in ever smaller images. Boxes within boxes. 

In theory, the entire system–the boy, the mirrors, and the barbershop–could be boxes within boxes of an even larger image, like a picture on a wall. The observer could be standing outside the picture, looking at the picture of the boy in the barbershop. 

2. By the same token, I can say the Trinity is "God" as well as each person of the Deity. To take a comparison, consider an infinity mirror: An infinity mirror is a pair of parallel mirrors that generate a series of smaller scale reflections that seem to recede into an infinite distance. The same image (or information) is contained in the whole series as well as each individual reflection. In this case, unlike (1), the Persons are the mirrors.  

They're not the same Person, just as mirror-images have right-handed and left-handed orientations. There's exact one-to-one correspondence, yet a distinction remains due to chirality. The Trinity is a kind of symmetry (or the exemplar of symmetry).