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Is Science Simply Beautiful?

August 26, 2019

My elementary school education was fueled by the public domain. School boards don't want to spend money on expensive textbooks, so textbook publishers will use as much free content as possible to keep prices low. Music class contained such classics as the U.S. Field Artillery March and Stephen Foster's Camptown Races, while our English Literature curriculum included George Eliot's Silas Marner, Nathaniel Hawthorne's The Scarlet Letter, and Mark Twain's The Adventures of Tom Sawyer.

Samuel Langhorne Clemens, a.k.a., Mark Twain, c. 1865

Samuel Langhorne Clemens (1835-1910), a.k.a., Mark Twain, as a young man in a photograph possibly taken around 1865.

Twain had a great interest in science and technology. He was friends with Nikola Tesla, and he was granted U.S. Patent No. 140,245 (June 24, 1873), for a scrapbook in which adhesive on the pages was moistened to affix items.[1]

Twain lost $300,000 (about $9 million in today's money) in his funding of the development of the Paige Compositor. This typesetting machine had many problems, and it was surpassed by the Linotype.

(Wikimedia Commons image.)

Likewise, the 1794 poem, The Tyger, by English poet, William Blake (1757-1827), would always be a part of every poetry section; so much so that saying the first line, "Tyger Tyger, burning bright," to a group of my generation will still evoke as a chorus the second line, "In the forests of the night." The poem continues, "What immortal hand or eye, Could frame thy fearful symmetry?" Blake saw symmetry in the tiger, since symmetry is ubiquitous in nature.

Since atoms will align themselves into regular arrays in crystals, we see symmetry in natural gemstones. With the advent of the microscope, the symmetry of snowflakes, caused by the regular arrangement of hydrogen-bonded water molecules as ice grows from a central seed, became apparent. The symmetrical body plan of animals is also apparent, and this is seen also in microscopic organisms.

Figure caption

Left images, snowflakes photographed at Jericho, Vermont, by Wilson Alwyn Bentley in 1902. Right image, portion of Plate 58 (Tripocyrtida, Sethocyrtida, Phormocyrtida et Theocyrtida), an engraving by Adolf Giltsch (1852-1911), from the Report on the Radiolaria collected by H.M.S. Challenger during the years 1873-1876, Part III, by Ernst Haeckel (1834-1919). (Images via Wikimedia Commons.)

Not only does nature exhibit many examples of symmetry, it seems that humans are designed to admire symmetry. In particular, we find facial symmetry to be attractive, possibly as a marker of genetic quality, the possessor having good genes. A 1999 study by psychologists at the University of St. Andrews (Scotland, UK) demonstrated that the more symmetric a face, the more attractive the person, with the possibility that facial symmetry might be a factor in mate selection.[2]

Our preference for symmetry extends to our art and artifacts. While the symmetry of pottery can be explained by its traditional method of manufacture on a potter's wheel, buildings are symmetric for no reason other than aesthetics. Textile items, such as quilts, carpets and rugs, usually contain a symmetric pattern. Humans appear to have a definite affinity for symmetry.

Figure caption

Symmetry in lacework.

My maternal grandmother would crochet similar items hour after hour in her rocking chair.

(Wikimedia Commons image by Rodrigo Argenton)

Symmetry was so important to early cosmologists that they supposed that the universe was built from nested celestial spheres. When that notion became suspect, Kepler decided in his 1596 book, Mysterium Cosmographicum (1596), that the Solar System was modeled on nested regular polyhedra. Eventually, the search for physical laws became a search for symmetry, and this is no more apparent than the evolving models of the elementary particles that led to the Standard Model.

Galileo, the father of modern physics, applied mathematics to his experimental data, and he was one of the first to believe that nature obeys mathematical laws. As he wrote in The Assayer:

Why the universe can be explained this way is a mystery. Eugene Wigner expressed this idea in a 1960 paper entitled, The Unreasonable Effectiveness of Mathematics in the Natural Sciences.[4] As he writes in this paper,
"It is difficult to avoid the impression that a miracle confronts us here... The observation which comes closest to an explanation for the mathematical concepts' cropping up in physics which I know is Einstein’s statement that the only physical theories which we are willing to accept are the beautiful ones. It stands to argue that the concepts of mathematics, which invite the exercise of so much wit, have the quality of beauty."

Perhaps Isaac Newton thought that his 1687 equation for gravitation, discovered more than a centuryy and a half after Galileo's 1604 falling body equation, was beautiful. Newton's beautiful equation needed a application of makeup in the 20th century when its deficiencies led to Einstein's 1915 general theory of relativity. Similarly, the early models of the Solar System and the Universe, while simple and thereby beautiful, needed extensive reworking into uglier depictions with circles being replaced by ellipses and a steady state cosmology being replaced by universal expansion.

A woodcut from Camille Flammarion, L'Atmosphère: Météorologie Populaire (Paris, 1888), pp. 163

A wood engraving from page 163 of Camille Flammarion's, L'Atmosphère: Météorologie Populaire (Paris, 1888).

In this image, a pilgrim breaks through a barrier to view the inner workings of the universe that includes a wheel-in-a-wheel mechanism.

Flammarion was an astronomer and a science fiction author who believed that intelligent life existed on Mars.

(Wikimedia Commons image. Click for larger image.)

In a recent article on Aeon, Massimo Pigliucci, a professor of philosophy at the City University of New York, writes that the idea that truth is recognizable by its beauty and simplicity is indefensible.[5] Indeed, the idea that "beauty is in the eye of the beholder," a variant of the Latin adage, "de gustibus non disputandum est," ("there's no accounting for taste") should have been sufficient warning of the problem with this approach. In the Aeon article, Pigliucci further states that this idea of beauty has generated today's unfortunate focus on mathematics in physics theory. Similar sentiments have been registered on Aeon by Sabine Hossenfelder, a research fellow at the Frankfurt Institute for Advanced Studies, who has written a book on this topic.[6-7]

Pigliucci cites Lee Smolin's book, The Trouble with Physics,[8] a diatribe against String Theory, for evidence against today's idea that we should follow the math to the exclusion of all else. I wrote about Smolin's book in an earlier article (Falsifiability, September 15, 2016). Such sentiments are also contained in Peter Woit's book, Not Even Wrong.[9-10] The title of Woit's book derives from Wolfgang Pauli's famous assessment of a proposed physics theory. Pigliucci wrote about String Theory in an earlier article in Aeon in which he states that physicists don't seem to hold philosophy in high regard.[11]

Pigliucci writes that the connection between beauty and truth was first proposed by Plato in his Symposium.[12] The idea that physical theories should be both simple and beautiful was held by the Nobel Physics Laureate, Paul Dirac; and his fellow Laureate, Richard Feynman, said that "You can recognize truth by its beauty and simplicity."[5] As Pigliucci explains, the simplicity of which Dirac and Feynman spoke is not the simplicity manifest in Ockham's razor. Ockham’s razor is an epistemological principle about how things are known, while Dirac and Feynman's simplicity is a metaphysical principle about the fundamental nature of reality.[5] I wrote about how metaphysical ideas have influenced science in an earlier article (Metaphysics, November 12, 2018).

Pigliucci concludes that "there is absolutely no reason to think that we evolved an aesthetic sense that somehow happens to be tailored for the discovery of the ultimate theory of everything."[5] He suggests that physicists should engage with philosophers in an interdisciplinary dialogue.


  1. Samuel L. Clemens, "Improvement in scrap-books," US Patent No. 140,245 (June 24, 1873).
  2. David I. Perrett, D. Michael Burt, Ian S. Penton-Voak, Kieran J. Lee, Duncan A. Rowland, and Rachel Edwards, "Symmetry and Human Facial Attractiveness," Evolution and Human Behavior, vol. 20, no. 5 (September, 1999), pp. 295-307, https://doi.org/10.1016/S1090-5138(99)00014-8.
  3. Galileo quotations on Wikiquotes; Selections of a translation of The Assayer; Stillman Drake, "Discoveries and Opinions of Galileo," Doubleday & Co.(New York, 1957), pp. 231-280.
  4. E.P. Wigner, "The unreasonable effectiveness of mathematics in the natural sciences," Communications on Pure and Applied Mathematics, vol. 13, no. 1 (February, 1960). pp. 1-14. A PDF file is available, here.
  5. Massimo Pigliucci, "Richard Feynman was wrong about beauty and truth in science," Aeon, June 28, 2019.
  6. Sabine Hossenfelder, "Beauty is truth, truth is beauty, and other lies of physics," Aeon, July 11, 2018.
  7. Sabine Hossenfelder, "Lost in Math: How Beauty Leads Physics Astray," Basic Books (June 12, 2018), 304 pp., ISBN-13: 978-0465094257 (via Amazon).
  8. Lee Smolin, "The Trouble With Physics: The Rise of String Theory, The Fall of a Science, and What Comes Next," Mariner Books (Reprint edition, September 4, 2007), 416 pp., ISBN-13: 978-0618918683. Also at Amazon.
  9. Peter Woit, "Not Even Wrong: The Failure of String Theory & the Continuing Challenge to Unify the Laws of Physics,"Basic Books (Reprint edition, September 4, 2007), 320 pp, ISBN-13: 978-0465092765 (via Amazon).
  10. Not Even Wrong, This Blog, July 29, 2008.
  11. Massimo Pigliucci, "Must science be testable?" Aeon, August 10, 2016.
  12. Plato, Symposium (360 BC), Benjamin Jowett, Trans., MIT Classics Website.

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