ƒ_u, and ƒ_u^2

Today’s photo is of some diagrams of lattices for Laurie’s math paper that involve bumping, ƒu and ƒb (ƒ unbounded and ƒ bounded) along with functions ƒ, g and h. P’s & M’s get bumped along the lattice, and when bounded, may be a kind of mathematical S&M. The M’s & m’s don’t come in plain or peanut, but they do bump along the lattices, can be bound, and, either way, melt in your mind not in your hand. All this has to do with monoids, which can be thought of as multiplication challenged, because only addition is involved. Who said pure math was boring?