21/08/2019

In Folha, Viana shows that the Universe is made of symmetries.

Pilares do monumento criado por Appie Drielsma. Os quatro pilares do monumento simbolizam os quatro grupos religiosos (Neutro, Católico Romano, Protestante e Judeu) que viviam na Holanda durante a Segunda Guerra Mundial – Flickr/Frans Persoon

Reproduction of Marcelo Viana's column in Folha de S.Paulo.

Our first experience with symmetry occurs in front of a mirror, in early childhood. The fascination of discovering the world "on the other side," strangely similar to our own, is unforgettable. But symmetry is much more: we now know that it is a fundamental aspect of the fabric of the Universe.

“It is only a slight exaggeration to say that physics is the study of symmetry,” stated Phillip Anderson, Nobel Prize winner in physics in 1977. The mathematician Emmy Noether proved that “to each mathematical symmetry of a system corresponds a physical quantity preserved by the evolution of that system.” This theorem plays a fundamental role in physics, especially in quantum mechanics, where it explains properties of subatomic particles (charge, spin, etc.) as a result of certain mathematical symmetries of the Universe.

The influenza virus membrane is made up of only four types of proteins, which fit together in a repetitive geometric pattern: the genetic code to build such a structure is more economical than would be necessary for a less symmetrical pattern. Living organisms take advantage of symmetries in many other ways to economize on resource use. And minerals structure themselves in crystalline forms full of symmetries because these require less energy.

Symmetry also plays a prominent role in art, of course. Leonardo da Vinci based his "Last Supper" on a symmetrical composition: the isolated position of Christ in the center dramatically accentuates his solitude on the eve of his passion. Perfect symmetry of features is part of what makes Nefertiti, queen of ancient Egypt, "the most beautiful woman of all time." The aesthetic charm of the Taj Mahal also emanates from the symmetry of its architectural elements. Even Johann Sebastian Bach made use of symmetrical patterns in some of his musical compositions.

Dictionaries contain many definitions of symmetry, most referring to "beauty," "balance," and "harmony." I prefer this one, which says more about the concept: "invariance (of the object or system) under the action of one or more transformations." In the case of a mirror, the transformation is reflection on the mirrored surface. There are more complex versions: for example, kaleidoscopes use combinations of mirrors, usually three, to create fascinating images.

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