Hahaha Ginny!!
Steve - the ants and peonies benefit from the activity of one another. Peony flowers provide nectar for ants and in turn the ants protect the blossoms from other floral-feeding insects. In my area the buds would be eaten if not for the ant "guards."
Casey - I will get back to you on the name. I keep losing the tag on this one. It is a pretty peony.