God, Beauty, and Symmetry in Science

| 11-24-AD2013 | [6]

Bob Kurland - Science Beauty

“Now, may our God be our hope. He Who made all things is better than all things. He Who made all beautiful things is more beautiful than all of them. …Learn to love the Creator in His creature and the Maker in what He has made.(St.Augustine of Hippo, Commentary on Psalm 39)

..and there is no doubt of the supreme mathematical beauty of Einstein’s general relativity.” (Roger Penrose, The Road to Reality)

The Einstein field equation, shown above in abbreviated form, is considered by most physicists to exemplify the most beautiful of all physical theories; general relativity.  What are the requirements for a beautiful theory and how do these manifest, as St. Augustine has it, the Creator’s handiwork? The beauty is displayed in the mathematics of the theory, in the equations that relate it to the world.  A first requirement is generality/profundity.  The equation has to be the basis for understanding a very broad and deep range of phenomena as Einstein said:

“I want to know how God created this world. I am not interested in this or that phenomenon. I want to know His thoughts; the rest are details.” (as quoted by A.Zee in “Fearful Symmetry”

A second requirement is conciseness, what theoretical physicists would call elegance: Hemingway versus Faulkner or Henry James. An equation that covers a page or so of symbols may be important and general, but it would not be beautiful. Much is summarized in the tensor notation of the general relativity field equations, but this beautiful form did not come easily.   It was not the result of sudden inspiration, unlike the lay view of how great science is done, but the result of eight years of dedicated effort; as Professor John Norton said in his discussion of Einstein’s notebooks “General relativity was an achievement of creative imagination.”

There are other beautiful equations: Dirac’s equation combining quantum mechanics and special relativity, which led to the discovery of anti-matter and the theoretical basis for particle spin. And it was Dirac who said “It is more important to have beauty in one’s equations than to have them  fit experiments;” a sentiment with which I do not entirely agree.

Dirac’s Relativistic Equation for the Free Electron

In this connection both the theory of general relativity, and the Dirac equation have been confirmed experimentally. General relativity was confirmed initially by the bending of light during a solar eclipse, and by its quantitative explanation of the advance in the perihelion of the orbit of Mercury (as well as many other confirmatory experiments since then).
 The Dirac equation explained the existence of electron spin and predicted the existence of the positron (a positively charged electron), found experimentally some four years later.

There is one other beautiful equation I want to mention, which in my opinion is as important as the two above: Boltzmann’s equation for entropy (S) in terms of thermodynamic probability (W).

S= k logarithm(W)

(k is the Boltzmann constant). This equation (engraved on his tombstone and tattooed on my younger son’s arm) justifies the Second Law of Thermodynamics (the scientific version of Murphy’s Law: the universe is running down, no matter what (or, you can’t unscramble eggs without doing work), a physical law that, according to Einstein, will still be true many hundreds of years from now, even if all other theories are invalidated.


Given that mathematics and mathematical physics have elements of beauty, what does this have to do with God? The notion that mathematical truths are Divine is ancient history, going back to Pythagoras and Plato in ancient Greece. Augustine, and more recently Cantor (19th Century), argued that infinity is a manifestation of God’s ineffability (see Mathematics, the Handmaiden of Theology).

Why is science explained mathematically? Or, as the renowned mathematical physicist, Eugene Wigner, puts it in his article, whence “The Unreasonable Effectiveness of Mathematics in the Natural Sciences?” The question was, of course, answered some 500 years ago by Galileo, “The laws of nature are written by the hand of God in the language of mathematics.”

We want to understand the world and to recognize, as Scripture declares, that God looked on His Creation and saw that it was good. When you see children playing with toy cars or other objects and arranging them neatly in a line, you see the first beginnings of a desire for order and sequence.

Mathematics has an intrinsic beauty that is not constructed by our minds, but is discovered by us.

Nautilus shell pattern illustrating the Fibonacci Sequence(from “Heritage Math”, by Savannah Morrow)

In nature, the pattern of sunflower florets, the nautilus shell, the growth of tree limbs is governed by the Fibonacci sequence: 0,1,1,2,3,5,8,13 . . . The rectangles combined from all the squares of the Fibonacci sequence have sides that have the “Golden Ratio” (“Golden Mean”), which the Greeks appreciated as beautiful proportion.

I want to emphasize that the beauty of pleasing proportion comes from more than symmetry. Symmetry can be an element of beauty, but it neither a necessary element nor always a sufficient element. It is the apprehension of order, an order that appeals to our intellect, that is the core of beauty. This appeal to intellect distinguishes beauty from that which is simply good, according to St. Thomas Aquinas:

The beautiful and the good are the same in the concrete existent (in subjecto), for they are based on the same thing, namely on the form. For this reason the good is approvingly called the beautiful. Yet, they differ in their intelligibility (ratione). For the good appeals to the appetite; indeed, the good is what all desire. So, it has the intelligible nature of an end, for appetite is sort of a motion toward a thing. On the other hand, the beautiful appeals to the cognitive power: for things that give pleasure when they are perceived (quae visa placent) are called beautiful. St. Thomas Aquinas, Summa Theologiæ

Aquinas also requires that which is beautiful be profound (he uses the term “large” or “big” but I think that can be construed as profound, as applied to beauty in science): “Beauty is found in a large body.” I think Aquinas also shows the connection between Beauty and God in his Fourth Way (the fourth of five ways of demonstrating the existence of God) which can be stated using the conclusion of the syllogism given in the link, “Thus, there is something that causes the being and goodness of every perfection in all things, and this is God.”

My own appreciation of the beauty of nature (I was too young and ignorant to realize the beauty of science) came as a teen-ager, going to the Griffith Park Planetarium in Los Angeles, and later, working one summer in the Forest Service at Yosemite and seeing the Big Trees in their then unspoiled setting.

And all this became reinforced, later on when I became a Catholic and saw that all of science was realized in Psalm 19a, “The Heavens declare the glory of God.”


About the Author:

Retired, cranky, old physicist. Convert to Catholicism in 1995. Trying to show that there is no contradiction between what science tells us about the world and our Catholic faith. Intermittent blogs at Rational Catholic and adult education classes here to achieve this end. Extraordinary Minister of Communion volunteer to federal prison and hospital; lector, EOMC. Sometime player of bass clarinet, alto clarinet, clarinet, bass, tenor bowed psaltery for parish instrumental group and local folk group. And, finally, my motivation: “It is also necessary—may God grant it!—that in providing others with books to read I myself should make progress, and that in trying to answer their questions I myself should find what I am seeking. Therefore at the command of God our Lord and with his help, I have undertaken not so much to discourse with authority on matters known to me as to know them better by discoursing devoutly of them.” St. Augustine of Hippo, The Trinity I,8.
Filed in: Faith, Science
  • http://www.dianemckelva.com/ Diane McKelva

    Bob, you may define yourself as a “cranky, old physicist,” but in my book you are inspired. Confession: I was the worse math student. I believe I have dyscalculia, but was never diagnosed. I still to this day dread Algebra like the plague of death. Thank you for allowing me to view math through a different lens. God bless you.

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  • K.A. Elkins

    “Therefore at the command of God our Lord and with his help, I have undertaken not so much to discourse with authority on matters known to me as to know them better by discoursing devoutly of them.” St. Augustine of Hippo, The Trinity I,8″ (Kurland).

    To write in praise of such qualities requires the willingness to be regarded as
    just another grumpy old man. But wisdom often wears the face of a grumpy old
    man. I am delighted to find your message today. I was compelled to complement your message with the following edited excerpt:

    Pope John Paul II’s 1999 Letter to Artists provides my introduction to the brilliance of
    beauty beyond mere symmetry.

    “The link between good and beautiful stirs fruitful reflection. In a certain sense, beauty is the visible form of the good, just as the good is the metaphysical condition of beauty. This was well understood by the Greeks who, by fusing the two concepts, coined a term which embraces both: kalokagathía, or beauty-goodness. On this point Plato writes: ‘The power of the Good has taken refuge in the nature of the Beautiful’” (Letter to Artists, 1999, ¶ 3).

    The ancients viewed beauty as The Splendor of Truth. Beauty sprang from goodness and goodness sprang from truth. Beauty could draw the self out of the self toward the ultimate, transcendent mystery—the God of Possible Things. Modern art, however, has abandoned beauty and devolved into an ideology opposed to or closed off from the universal—no matter how brilliant the style or production. C. S. Lewis characterized this type of radical shift as a dungeon of the self, within the self, leading to loss. From an article written in 2003, Dr. Peter Chojnowski draws our attention to the limitations imposed on goodness and beauty by the rampant relativism of the modern age.

    “It is the task . . . to free the reality of ‘beauty’ from the artsy-craftsy constraints placed upon it by those who thought they could master it. How far are we away from the Greeks who regularly spoke of the kaloskagathos, that is, the ‘beautiful and good man,’ the man of moral excellence, the ‘beauty’ of whose virtues shone through in the
    decorum, nobility, and fetching vitality of his actions. It is such a beauty, form, and clarity in the individual man or woman that lays to rest all the confusions of this earth, which can bring tears to our eyes and yearning to our hearts” (¶ 2).

    At the heart of it all, the way of beauty focuses the inner sight of vision and yearning. Testing the teachers and spirits of any generation requires more than casual observation. The signs of the times call for discernment and discrimination. If modern secular art is viewed as more earthbound, then modern, sacred art neglects to reach greater heights as well. At the start of the twenty-first century, genuine and dedicated expressions of the Faith are needed in Western cultures—expressions that reflect the heart, mind, body, and soul of everyday men and women. Culture is always supporting the arts, but the arts are not always supporting the culture.

    In 2001, art sculptor and educator Hamilton Reed Armstrong recognized—“most
    ‘traditionalist’ art is mass produced and peculiarly sentimental. It reflects less a visual manifestation of the mystery of faith than a longing for the comfort of the lost childhood of both the individual and the Church” (quoting Jaffe, 395). Volumes of sacred artwork from past cultures provide inspiration for contemplating truth, goodness, and beauty. Secular samples of the modern age seduce the arts and humanities with a false spirit and artificial light. Armstrong located one possible source of light that guides the modern perspective–

    “The spirit in whose mystery art was submerged was an earthly spirit . . . alien to the ‘heavenly’ spirit. Indeed, it was Christianity’s dark adversary that was forging its way in art . . . . In the religious language of /Christianity it is called the devil . . . Lucifer—literally the light bringer” (393/394).

    Through much of recorded history, humanity has been distracted with an attractive, splintered light in the long odyssey to discover what is true, good, and beautiful. The best that was thought and said in the world has always contended against the worst elements of human nature.

    Excerpts from: Mr. E. 2003: Manifest Lessons from Ohio’s Bicentennial Celebration (Elkins, K. A., 2011. iUniverse, Bloomington)

  • Teilhard

    Thank you for sharing. I have a similar story in that I rediscovered by Catholic faith through science and the beauty of nature. Thank you for sharing.

    W. Ockham

  • duhem

    Thank you all for your kind comments.
    Bob Kurland

  • John_QPublic

    The beauty of the heavens are a testament to the Creator, for sure. The beautiful sign he imprinted on the CMB, pointing right back to us is hard to miss!

    Congrats on your conversion! I am also a convert.