Imagery of symmetry in current physics

We consider a remarkable symmetry duality that is broken under a phase transition permitting the appearance of superconductivity and superfluidity. This is a wine-bottle rotation symmetry in a semi-phenomenological description in the spirit of Ginzburg and Landau, while it is a phase symmetry responsible for the conservation of the number of particles (helium atoms, Cooper electron pairs) in Bogoliubov's quantum theory. This duality is interesting in the context of the contraposition of logic and intuition or Science and Art. We also briefly discuss another aspect of distorted symmetry connected with varying the geometry of space–time and with dimensional reduction in particular.