Each object in the world (as Thom sees it) is associated with a dynamical system. The shape, or form, of this object for an observer is nothing but the catastrophe set associated with this dynamical system. The object itself lies in the parameter space, usually three-dimensional Euclidean space, but it is not clear at all where the dynamical system lies, or even if it has a physical reality. For instance, the shape of a breaking crest wave does call to mind a hyperbolic umbilic, but no one has ever been able to build a dissipative potential for the wave from hydrodynamic considerations. Thom himself is not very concerned with this problem. He seems to be content, either with a Platonic attitude of having the dynamical system happen in some supernatural world or with locating it in the neurological phenomena which carry perception to our brain.
“Mathematics And The Unexpected”