Friday, October 02, 2015

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.

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


  1. We've got the beautiful question. May I be the one to ask the stupid question. Two times stupid really: stupid for having nothing to do with this book; and stupid for just being stupid and making not a lot of sense on its own terms.

    In quantum theory, or if not there then one or more of the interpretations of quantum theory, does entanglement perform a critical function? Is it part of a process that without which something wouldn't work or even, reality wouldn't happen.

    We know it happens, but my (stupid, stupid) perception is that it doesn't get 'placed' in terms of utility. Even in the interpretations. But I could just have a dose of layperson-head-stuck-where-no-sun-no-shine syndrome

    You can help me! Help extract my head.

  2. "our currently most fundamental theories, are in essence mathematically precise implementations of symmetry requirements" Empirical physics demands unending symmetry breakings. A filled 2-sphere in 3-space is maximally symmetric. Four cuts obtain either two left or two right shoes. Is beauty a styrofoam ball or
    a non-plectonemically coiled 4(2)-symmetric double helix whose two parallel strands and interstrand grooves are homotopically related by a C(2)axis coincidental with the helical axes for 2N cuts? (2N + 1) cuts give odd-fold symmetries.

    "'the world embodies beautiful ideas'" Reality is quantized, GR is continuous. The difference is emergence. The ball's hidden chirality is quantum gravitations' malfunction. Observation is also beautiful. Look.
    First 20 pages

  3. Chris,

    That's a good question, I'll have to think about whether entanglement does perform any critical function in the evolution of the universe (other than being used for quantum cryptography now). Off the hand I'd say no because it's too fragile. As to the foundations, I'm not sure what you mean. Entanglement is a consequence of quantum mechanics, you can't get rid of it. I don't know what sense it makes to ask for its utility in the theory - without it the theory would just be wrong. Best,


  4. It is a good question. I think of entanglement as an inevitability when you have quantum indeterminism plus conservation laws. So you don't know what value one thing has, but you do know what value two things must have, due to, say, conservation of angular momentum.
    So it kind of arises as a result of more fundamental things, Possibly.

  5. Does entanglement occur naturally absent spontaneous parametric down-conversion crystals? Natural fiberoptics (ulexite, satin spar gypsum) require a planet and reside in darkness. The universe is rich with lasers (Phase 1/3), lasers entangle (Phase 3/3), arXiv:0302023,1302.6444,1306.2074,1407.0944.
    Phase 2/3 - not natural.

    An entangled universe lacks efficient mechanisms for reduction to practice, then clean propagation.

  6. Chris and Bee:
    If I can throw in my two cents worth;whether you can measure entanglement or not,is based on your experimental accuracy. In principle, everything is entangled with everything else if you have infinite accuracy!! So I am reasonably sure that it has something to do with quantum origin of universe!

  7. kashyap,

    Not everything is connected with everything. Entanglement is the exception rather than the rule.

  8. Bee,
    If you believe Penrose and perhaps some philosophers(!!), everything in the universe is interconnected! Observed entanglement is an exception because of the limited accuracy.Our approximate local theories agree with experiments because of limited accuracy! Am I overstating the case?

  9. Well, I don't believe "Penrose and some philosophers"... Why would I?


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