A Thing of Beauty is Joy for Ever

In Physics, beauty does not automatically ensure truth, but it helps.
In mathematics, beauty must be true – because anything false is ugly.
-- Ian Stewart in “Why Beauty is Truth? p.280


I am writing here not about physical beauty per se but about the beauty of mathematical and scientific formulations. Many mathematicians and scientists have marveled on the beauty of mathematics and laws of physics and scientific theories. For instance, who will not exult in appreciating the beauty of Einstein’s equation
E = mc^2
in which E = energy, m = mass, and c = the speed of light)? The same is more or less true of the Pythagorean relationship between the sides of a right-angled triangle, namely,
a^2 + b^2 = d^2
in which a = altitude (height), b = base, and d = diagonal of the right-angled triangle.

Paul Dirac, among many others, was simply possessed by the idea of beauty of the mathematical and scientific formulations. According to Ian Stewart, “Paul Dirac believed that in addition to being mathematical, nature’s laws had to be beautiful. In his mind, beauty and truth were two sides of the same coin, and mathematical beauty gave a strong clue to physical truth,” (Ian Stewart in “Why Beauty is Truth?” p.277). His faith in beauty of science was so deep and immense that he went on “to say he would prefer a beautiful theory to a correct one, and that he valued beauty above simplicity.”

Dirac’s equation predicted the existence of a particle which had a mass equal to that of an electron but had a positive charge. No body had ever encountered such a particle before. Dirac was initially nonplussed by such a ‘queer’ prediction of his equation and he hesitated to publish it. But in the end, he had faith in his equation and he went ahead and published it. In a few years, Carl Anderson detected this particle in his cloud chamber experiments. Both Dirac and Anderson received Nobel Prize for their respective discoveries. Dirac called this particle a positron, i.e., an electron with a positive charge. It was later discovered that all the particles of matter have their counter-particles. The counter-particles in general are called antimatter.

First evidence of the correctness of Einstein's theory of general relativity was provided by Eddington who measured the bending of light in the vicinity of Sun during the solar eclipse of 1918. His measurement was in close agreement with the theoretical prediction. “When asked what he would have thought if Eddington’s expedition had not found the bending of light by the Sun, he said, ‘Then I would have been sorry for the dear Lord; the theory is correct,’” (David Lindley in “The End of Physics,” pp. 11-12). His theory was simply too beautiful to be wrong.

Quantum Mechanics was born as a result of Planck’s formulation of a model of radiation spectrum. “In 1900, he found such a model, but its meaning was hard to fathom. As a mathematical trick, Planck decided to add a restriction to classical theory: he specified that the energy carried by radiation could be only a whole number of energy units,” The End of Physics, p. 64). Later, these whole numbers of energy units were called quanta. Planck’s theory predicted that energy was discrete like matter. His prediction from his theory held sway against the common belief (that energy was continuous) of his time.

The beauty of mathematical formulation is such that it provides a solution to some existing problem yet at the same time it is capable of making prediction about some unknown phenomena as well. On the one hand, it answers a question which had baffled the scientists and on the other hand it gives birth to several new questions. For example, Dirac’s equation that had predicted the existence of antimatter also predicts the existence of monopole which has not been discovered yet. The new questions provide stimulus to find their solution and the scientific activity keeps marching ahead.

Beauty in any form is appealing. Iqbal’s poetry is so beautiful that even those who do not necessarily agree with the ideas expressed in his poetry are nonetheless touched by the beautiful expression. However, beauty of mathematics and science is very compelling. It is absolutely impressive both in content and form. For example, complete books have been written to explain what Einstein’s simple equation E = m c^2 means and implies. Omar Khayyam was both a poet and a mathematician. His Rubiyat are as beautiful as his mathematics but in their own respective ways. English translation of Rubiyat by Edward Fitzgerald has immortalized Khayyam’s poetry all over the world. His distinguished contribution to mathematics was his geometrical solution of a cubic equation.

Let me finish this essay by describing a consequence of Einstein’s theory of general relativity. His theory predicted a universe that was expanding with time. Scientists including Einstein believed that the universe was static and unchanging. Einstein was perturbed at this “unreasonable” prediction from his theory. In order to bring his theory in line with the common wisdom which asserted that the universe was static, Einstein introduced a (fudge) constant in his theory, which he called the cosmological constant. Later, in the late 1920’s, Hubbell’s astronomical observations indicated that the universe is indeed expanding. Einstein was so embarrassed that he called his cosmological constant as the biggest mistake of his life. His theory was true and beautiful.

The above kind of fudging often takes place in science in order to explain the known facts which a theory fails to predict. But this underlines, more than any thing else, a need to search for a more general and natural (unconstrained and un-fudged) theory.