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.