It is proved that if E, F are infinite dimensional strictly convex Banach spaces totally incomparable in a restricted sense, then the Cartesian product E × F with the sum or sup norm does not admit a forward shift. As a corollary it is deduced that there are no backward or forward shifts on the Cartesian product `p1 × `p2 , 1 < p1 6= p2 < ∞, with the supremum norm thus settling a problem left o...