Symmetry breaks and asymmetries –yet another bridge between science and art?

In a recent article, the concept of “symmetry” has been suggested to serve as a rare discursive bridge between physics and the arts. While most of the ancient and modern art conceptions regard symmetry as an essential criterion of beauty, theoretical physics of the twentieth century discovered in it a grounding principle in mathematical disguise. The article could have given rise to the impression that symmetry is the only structural principle in both physics and art. Such a statement, however, would not be appropriate for either.

Even if symmetrical forms are omnipresent in nature, art, and architecture, art historians are largely united in stating that a perfect symmetry comes with a certain sterility, which often even runs counter to our aesthetic perception. Regular geometric bodies in images and sculptures are considered rather uninteresting. Thus writes Kant in his “Critique of Judgment”:

Everything with stiff-regular structures (which come close to mathematical regularity) runs counter to taste because it does not allow us to be entertained for long by our contemplation of it. On the other hand, what our imagination can play with searchingly and purposefully is always new to us, and we are not weary of its sight. (I. Kant, Critique of Judgment, General Note on the First Section of Analytics, § 22, p.242, translated by L.J.)

For example, completely symmetrical faces are hardly considered attractive, some appear even bizarre (which one can try out by simply reflecting the right part of a face on a portrait on the left half). The interesting and essential thing about symmetry is rather that we perceive itsviolation so particularly strongly.A small symmetry break, be it a birthmark on the cheek or a slightly oblique smile, thusmakes a facemuch more attractive.

Symmetry is thereforehardly ever used as the determining criterion for beauty or even as a chosen ideal, neitherin art nor in our aesthetic perception. On the contrary, artists regardand value their work in its uniqueness most often only through the breaking of symmetry. In the history of art and architecture we can thus often observe an evolution from simple symmetrical forms to more complex asymmetry, as for example in the development from the symmetrical Byzantine and Gothic architecture tothat of the Late Renaissance and the Baroque period.

This can also be said for many social and biological systems. The world seems to be asymmetric on many different levels –which gives things and humans their respective uniqueness in the first place. While many basic patterns are of symmetrical structure, the particular and the individual is often associated with asymmetrical features which make it interesting (while too much asymmetry drifts towards the chaotic and becomes uninteresting). After all, symmetry means reducibility: it is much easier for us to hold on to something symmetrical than something asymmetrical. This also applies atlast in information theory: It takes far fewer bits and bytes to specify (and store) symmetric structures then what it take for asymmetric ones.

Thus symmetry and asymmetry manifest themselves in numerous contrasts: rest and movement, monotony and unpredictability, lifeless stiffness and lively diversity, boredom and fascination, law and chaos, simplicity and complexity. One can say that the new and interesting unfolds itself dynamically only out of breaking away from the symmetrical and the statically known. Only the breaking of symmetry leads to new developments, to the formation of structures.

Here we discover an interesting parallel in physics, and this directly in the center of its fundamental theory, the standard model of elementary particle physics. Were the gauge symmetries of modern quantum field theories (Yang-mills fields) completely intact (i.e. weretheir equationsentirely invariant under corresponding gauge transformations), there would be no mass in the world. In fact, the masses of the elementary particles do not arise from the symmetries of the fundamental equations in quantum field theories – strict gauge symmetries in those equations would lead to anentirely massless world – but from their violation, i.e. from the breaking of these symmetries. It was the theoretical physicist Peter Higgs and some of his colleagues who introduced the mechanism of “spontaneous symmetry breaking”(what is called the “Higgs mechanism” today) as a necessary element and foundation of the mathematical-theoretical description of the elementary particle world for the manifestation of matter’s massiveness of. This results in the existence of the well-known “Higgs particle” (the field quantum of the “Higgs field”). The rest of the storyis well known: On 4 July 2012, CERN announced that the Higgs particle had finally been discovered (60 years after Higg’s work).

This does not mean, of course, that symmetries have lost their importance in physics. On the contrary, it is the mathematical symmetries in the field equations of physics which makethe symmetry breaking possible in the first place. Whilemass in our universe manifest itself from the symmetry breaking of the Higgs mechanism,the world as a whole is not yet asymmetric. Symmetries are still essential determinants of any physical theory today. In fact, in the antagonistic pair “symmetry – anti-symmetry”we can observe the unfolding of an interesting dialectical process: In both, the arts as well as the natural sciences, asymmetry can only manifest itself in its relation to (basic)symmetricalforms. It is only from a known and easily ascertainable symmetrical basis that the individual and complex can unfold in its uniqueness as a deviation from the symmetrical norm.

Thus symmetry is a grounding principle both in theoretical physics and in art, but at the same time the multiplicity of phenomena in the world and their interesting and unique properties constitute themselves only through asymmetries, i.e. the breaking of symmetries. A statement by the physicist Nils Bohr puts this to the point: There are certain deep truths, the opposite of which contain yet other deep truths.