Monthly Archives: October 2016

Fearful Symmetry – Zee

Fearful Symmetry – Author Blurb

The concept of symmetry has widespread manifestations and many diverse applications–from architecture to mathematics to science. Yet, as twentieth-century physics has revealed, symmetry has a special, central role in nature, one that is occasionally and enigmatically violated. Fearful Symmetry brings the incredible discoveries of the juxtaposition of symmetry and asymmetry in contemporary physics within everyone’s grasp. A. Zee, a distinguished physicist and skillful expositor, tells the exciting story of how contemporary theoretical physicists are following Einstein in their search for the beauty and simplicity of Nature. Animated by a sense of reverence and whimsy, Fearful Symmetry describes the majestic sweep and accomplishments of twentieth-century physics–one of the greatest chapters in the intellectual history of humankind.

Fearful Symmetry Cover

Fearful Symmetry: The Search for Beauty in Modern Physics

This is a review of the 1986 Macmillan pressing. Believe it or not, it has been sitting on my bookshelf for 30 years! In fact, while putting together this review, it seems that Princeton University Press released the 2nd edition last month (September 2016). Time flies.

The premise of the book is that simplicity is built into nature’s design. Beautiful equations have a running chance at being true. Ugly equations have no chance. That was Einstein’s acid test when reviewing equations. Zee follows Einstein’s school of though on beauty and reality. One form of beauty is symmetry:

On one side stand Einstein and his intellectual descendants. To them, symmetry is beauty incarnate, wedded to the geometry of spacetime. The symmetries known to Einstein–parity, rotation, Lorentz invariance, and general covariance–are exact and absolute, frozen in their perfection. On the other side stands Heisenberg with his isospin, shattering the aesthetic imperative of exact symmetry. Heisenberg’s child is approximate and plays apart from spacetime. Unlike spacetime symmetries, isospin is respected only by the strong interaction.

Lorentz Invariance, Parity, General Covariance: It’s Greek to Me!

Perhaps one reason the book sat on the bookshelf for 30 years is because it is hard to understand. Although Zee writes for the layperson, it is a tough go: cutting edge physics in multiple dimensions is hard to understand. But I’m glad I read it. It solved a long standing mystery in my mind concerning philosophy.

A long time ago, I got some pretty good advice from Professor Keith Bradley. Actually, it wasn’t directly from him, but through one of his students, Professor Leslie Shumka, who had heard it from him. This was at the University of Victoria. Incidentally, I always found it ironic that the University of Notre Dame poached Professor Bradley (who is the world authority on Roman slavery) away from us. The irony is that he is anything but Catholic and far from being religious. The University of Notre Dame, of course, is a Catholic university. Oh yes, the advice: the advice was to read widely in subjects that are not in your field of specialty. This way, you pick up novel insights: it encourages you to think outside of the box. And this is what happened when I read Fearful Symmetry.


Have you heard of the ancient quarrel between the rationalists and the empiricists? The Stanford Encyclopedia of Philosophy sums it up as follows:

The dispute between rationalism and empiricism concerns the extent to which we are dependent upon sense experience in our effort to gain knowledge. Rationalists claim that there are significant ways in which our concepts and knowledge are gained independently of sense experience. Empiricists claim that sense experience is the ultimate source of all our concepts and knowledge.

Rationalists like to point out that the mind can grasp things independently from sense experience. The most quoted example is that of the interior angles of a triangle. That the angles equal 180 degrees can be comprehended by pure thought. Empiricism argues the opposite, that knowledge comes from sense perception. The scientific method of coming up with a hypothesis and testing the hypothesis by observation is an empirical method.

Zee points out that the 19th century, ‘a large collection of experimental facts were summarized into equations which in turn revealed a symmetry in Nature’s design’. In other words, 19th century physicists were empiricists: they made many observations. Their knowledge came from observing the world. They modelled their equations after what they saw. But this all changed in the 20th century.

In the 20th century, equations were driven by the idea of symmetry. Einstein’s theory of gravity is not the result of carefully measuring planetary orbits (i.e. making the equation fit empirical observations), but rather, his theory of gravity is the result of applying an understanding of Lorentz invariant symmetry on space-time. Regardless of whether or not I understand what Lorentz invariant symmetry is (I don’t), I do understand that his theory of gravity is a rationalist theory.

Yang-Mills Theory and Rationalism

Zee describes how, in 1954, two physicists, Chen-ning Yang and Robert Mills, invented a theory based on a symmetry of dazzling mathematical beauty. Their theory was based on aesthetics rather than any experimental observation. Although physicists recognized its beauty, they had no idea what to do with it, or, for that matter, what could be done with it. That changed in the 1970s when physicists started to believe that the electromagnetic and weak interactions could be unified into a Yang-Mills theory.

If you want to find out how the Yang-Mills theory rolled together the electromagnetic and the weak interaction, you’ll have to read the book. What is important to me was that know I can see the ancient quarrel between the empiricists and the rationalists breaking out in my own lifetime. What I had thought was an academic debate (the priority or thought or sense/experience) was a real debate in the physics community. If nature is ugly, then empiricism is the way to go: make many observations and sum them together in an equation. But if nature is beautiful (and symmetry is a form of beauty), then nature can be comprehended by thought alone.

When the Yang-Mills theory came out, it was a mathematical model that predicted the existence of particles that had not been discovered yet. Furthermore, the measured masses of known particles did not square with what the Yang-Mills theory predicted (it required gauge bosons, which are massive, to be massless). But it turned out that Yang-Mills was right. Particle accelerators eventually found the particles predicted by Yang-Mills theory. And it turned out that at higher energy levels (i.e. moments after the Big Bang), gauge bosons become massless.

The implication of all this is that there is something to rationalism. The mind is the most complicated machine in the universe and it can make some crazy predictions about what the world is like prior to observation. The only caveat is that it must be guided by beauty, in this case, the beauty of symmetry.

The moral of the story: read lots and read widely. Until next time, I’m Edwin Wong and I’m Doing Melpomene’s Work by reading books on physics.