Abstract: In elementary terms and by using the toy noncommutative geometry models,
we shall explore the three mechanisms for differential one-forms to be
anti-permutable (that is, to acquire the minus sign factor whenever swapped
- so that the predictions of theories involving the calculus of
differential forms match the experimental data. But why should they?). The
models to-consider are borrowed from Kontsevich's formal noncommutative
symplectic geometry and its variational extensions serving the
Batalin-Vilkovisky or Poisson formalisms.