In Animate Form Lynn co-opts math terms to define new terms for discussing animation and digital process. He is generally right, but not in precise ways, and sometimes wrong. For instance, he defines a type of animate form as “topologically entities” and discusses the implications of “topological form.” There is no topological form. Topology is field of geometry that is concerned with determining when things are the same. Determining when two things are exactly the same is nearly impossible and not practical to study. In topology two things are considered the same when there exists a homeomorphic map between them. Simply (and not rigorously), this means that two things are the same when you can deform one into the other with out adding or taking away any holes. Lynn takes the term topology from this idea, using it to describe surface manipulation. Not quite right.
Lynn further describes the temporal component of topology as, “the immanent curvatures that result from the combinatorial logic of differential equations.” This makes absolutely no sense. Simply, combinatorics is a type of pure math concerned with counting. A differential equation is an equation or an unknown function of one or several variables that relates the values of the function itself and of its derivatives of various orders. (wikipedia) One is a type of equation in calculus and one is a branch of pure math. While there are relationships between the two, I’m not convinced Lynn knows what he is actually saying. He is taking combinatorial to be synonymous with combination. I think he really means the immanent curvatures that result from the combination of differential equations.
Lynn needs to either describe (correctly) why and how he is using math terms or not use them at all.