Book Review: “A Beautiful Question” by Frank Wilczek

A Beautiful Question: Finding Nature's Deep Design
By Frank Wilczek
Penguin Press (July 14, 2015)

My four year old daughter recently discovered that equilateral triangles combine to larger equilateral triangles. When I caught a distracted glimpse of her artwork, I thought she had drawn the baryon decuplet, an often used diagram to depict relations between particles composed of three quarks.

The baryon decuplet doesn’t come easy to us, but the beauty of symmetry does, and how amazing that physicists have found it tightly woven into the fabric of nature itself: Both the standard model of particle physics and General Relativity, our currently most fundamental theories, are in essence mathematically precise implementations of symmetry requirements. But next to being instrumental for the accurate description of nature, the appeal of symmetries is a human universal that resonates in art and design throughout cultures. For the physicist, it is impossible not to note the link, not to see the equations behind the art. It may be a curse or it may be a blessing.

For Frank Wilczek it clearly is a blessing. In his most recent book “A Beautiful Question,” he tells the success of symmetries in physics, and goes on to answer his question whether “the world embodies beautiful ideas” with a clear “Yes.”

Lara’s decuplet

Wilczek starts from the discovery of basic mathematical relationships like Pythagoras’ theorem (not shying away from explaining how to prove it!) and proceeds through the history of physics along selected milestones such as musical harmonies, the nature of light and the basics of optics, Newtonian gravity and its extension to General Relativity, quantum mechanics, and ultimately the standard model of particle physics. He briefly touches on condensed matter physics, graphene in particular, and has an interesting digression about the human eye’s limited ability to decode visual information (yes, the shrimp again).

In the last chapters of the book, Wilczek goes into quite some detail about the particle content of the standard model, and in just which way it seems to be not as beautiful as one may have hoped. He introduces the reader to extended theories, grand unification and supersymmetry, invented to remedy the supposed shortcomings of the standard model. The reader who is not familiar with the quantum numbers used to classify elementary particles will likely find this chapter somewhat demanding. But whether or not one makes the effort to follow the details, Wilczek’s gets his message across clearly: Striving for beauty in natural law has been a useful guide, and he expects it to remain one, even though he is careful to note that relying on beauty has on various occasions lead to plainly wrong theories, such as the attempt to explain planetary orbits with the Platonic solids, or to the idea to develop a theory of atoms based on the mathematics of knots.

“A Beautiful Question” is a skillfully written reflection, or “meditation” as Wilczek puts it. It is well structured and accompanied by many figures, including two inserts with color prints. The book also contains an extensive glossary, recommendations for further reading, and a timeline of the discoveries mentioned in the text.

My husband’s decuplet.

The content of the book is unique in the genre. David Goldberg’s book “The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality,” for example, also discusses the role of symmetries in fundamental physics, but Wilzcek gives more space to the connection between aesthetics in art and science. “A Beautiful Question” picks up and expands on the theme of Steven Weinberg’s 1992 book “Dreams of a Final Theory” that also expounded the relevance of beauty in the development of physical theories. More than 20 years have passed, but the dream is still as elusive today as it was back then.

For all his elaboration on the beauty of symmetry though, Wilczek’s book falls short of spelling out the main conundrum physicists face today: We have no reason to be confident that the laws of nature which we have yet to discover will conform to the human sense of beauty. Neither does he spend many words on aspects of beauty beyond symmetry; Wilczek only briefly touches on fractals, and never goes into the rich appeal of chaos and complexity.

My mother used to say that “symmetry is the art of the dumb,” which is maybe a somewhat too harsh criticism on the standard model, but seeing that reliance on beauty has not helped us within the last 20 years, maybe it is time to consider that the beauty of the answers might not reveal itself as effortlessly as does the tiling of the plane to a 4 year old. Maybe the inevitable subjectivity in our sense of aesthetic appeal that has served us well so far is about to turn from a blessing to a curse, misleading us as to where the answers lie.

Wilczek’s book contains something for every reader, whether that is the physicist interested to learn how a Nobel Prize winner thinks of the connection between ideas and reality, or the layman wanting to know more about the structure of fundamental law. “A Beautiful Question” reminds us of the many ways that science connects to the arts, and invites us to marvel at the success our species has had in unraveling the mysteries of nature.

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[An edited version of this review appeared in the October issue of Physics Today.]