Thought Experiments


Beautiful Losers

Are beauty and truth two sides of the same coin? It is charming to believe so. As Nobel Prize laureate Paul Dirac, who helped lay the mathematical groundwork for quantum mechanics, put it:

It seems that if one is working from the point of view of getting beauty in one’s equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one’s work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further developments of the theory.

The poet John Keats expressed it more concisely:

Beauty is truth, truth beauty – that is all
Ye know on earth, and all ye need to know.

But, in science, does a beautiful hypothesis necessarily lead to deep truth about nature?

Several famous success stories suggest that it does, at least in physics:

James Clerk Maxwell arrived at his celebrated system of equations for electromagnetism by codifying what was thought to be known experimentally about electricity and magnetism, noting a mathematical inconsistency, and fixing it. In doing so, he moved from truth to beauty. The Maxwell equations of 1861, which survive intact as a foundation of today’s physics, are renowned for their beauty. The normally sober Heinrich Hertz, whose experimental work to test Maxwell’s theory gave birth to radio and kickstarted modern telecommunications, was moved to rhapsodize:

One cannot escape the feeling that these mathematical formulae have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them.

Albert Einstein, on the contrary, arrived at his equations for gravity—the general theory of relativity—with minimal guidance from experiment. Instead he looked for beautiful equations. After years of struggle, in 1915 he found them. At first, and for decades afterwards, few testable predictions distinguished Einstein’s new theory of gravity from Newton’s venerable one. Now there are many such tests, and it is amply clear that Einstein moved from beauty to truth.

Yet even in physics, the record is more mixed than is commonly known. Despite Keats and Dirac, beauty’s seductions don’t always give birth to truth. There have been fascinating theories that are both gorgeous and wrong: Beautiful Losers.

Like surgeons, physicists bury their failures. But the most beautiful of the Beautiful Losers deserve a better fate than oblivion, and here they’ll receive it. I’ve written brief accounts of three Beautiful Losers: Plato’s Geometry of Elements, Kepler’s Harmonic Spheres, and Kelvin’s Vortex Atoms.

Plato’s Geometry of Elements: Plato believed that he could describe the Universe using five simple shapes. These shapes, called the Platonic solids, did not originate with Plato. In fact, they go back thousands of years before Plato; you can find stone models (perhaps dice?) of each of the Platonic solids in the Ashmolean Museum at Oxford dating to around 2000 BC. But Plato made these solids central to a vision of the physical world that links ideal to real, and microcosm to macrocosm in an original, and truly remarkable, style. Read more

Kepler’s Harmonic Spheres: Like Plato, the German astronomer Johannes Kepler believed that five Platonic solids provided an essential blueprint for our universe. Six planets were known to Kepler, and he believed that they were carried around on nested globes that he called the celestial spheres. Kepler reasoned that five solids could correspond to six planets, if the solids—or more precisely, their bounding surfaces—marked the spaces between planetary spheres. He described this elegant construction in his Mysterium Cosmographium in 1596. Read more

Kelvin’s Vortex Atoms: A tornado is just air in motion, but its ominous funnel gives an impression of autonomous existence. A tornado seems to be an object; its pattern of flux possesses an impressive degree of permanence. The Great Red Spot of Jupiter is a tornado writ large, and it has retained its size and shape for at least three hundred years. The powerful notion of vortices in fluids abstracts the mathematical essence of such objects, and led William Thomson, the 19th century physicist whose work earned him the title Lord Kelvin, to ask: Could atoms themselves be vortices in a ether that pervades space? Read more

It’s wonderful, and comforting, that each of my Beautiful Losers, though wrong, was in its own way fruitful. Today more than ever physicists working at the frontiers of knowledge are inspired by beauty. In the alien realms of the very large, the very small, and the extremely complex, experiments can be difficult to perform and everyday experience offers little guidance. Beauty is almost all we’ve got!

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Frank Wilczek

    Frank Wilczek has received many prizes for his work in physics, including the Nobel Prize of 2004 for work he did as a graduate student at Princeton University, when he was only 21 years old. He is known, among other things, for the discovery of asymptotic freedom, the development of quantum chromodynamics, the invention of axions, and the exploration of new kinds of quantum statistics. Frank is currently the Herman Feshbach professor of physics at MIT. His latest book is A BEAUTIFUL QUESTION: Finding Nature’s Deep Design.

    • Wayneewald

      Beautiful essay

    • The cool thing is, even though the universe cannot be explained via Plato’s Geometry of the Elements. It is true that the elements themselves when join to each other do form geometric shapes. For instance, all H2O molecues form the same geometric shape, etc. The forces within the particles (e.g. positive and negative forces, etc.) govern how molecues fall into their shape. It is because of the forces within the elements that all hemoglobin proteins are the same shape. (as long as there in no mutation in it’s DNA sequence.)

      Also, when stars and planets are formed they for nice beautiful spheres. I would go as far as to say that as long as the spin of a star and it’s gravity are nearly perfect with in their perameters then that star will be realatively smooth and would almost be a perfect looking sphere.

    • Adel

      This is the real beauty of nature , how could it have been otherwise

    • Katypentakota

      As long as we wonder at the beauty of microcosm and the macrocosm of the Universe….the pursuit of Truth is beautiful

    • Jcbolow

      This Program is one of the best i have ever seen, with my Eye’s or without!

      something is running the whole Universe or Multiverse and Nova is on top of it!

    • Mary

      “How can that be a real thing which is never in the same state? … for at the moment that the observer approaches, then they become other … so that you cannot get any further in knowing their nature or state …. but if that which knows and that which is known exist ever … then I do not think they can resemble a process or flux ….”

      He was really close.
      Thank you for this essay.

    • Jcbolow

      What you see, or seem, is but a dream within a dream!

      Edgar Allen Poe

    • Anonymous

      Precisely! as Edgar Allan Poe wrote “What You see, or Seem, is but a Dream within a Dream!

    • Khalidcustoms

      Beauty is time, time beauty – that is all
      Ye know on earth, and all ye need to know.
      Khalid Masood

    • Khalidcustoms

      Time is truth, truth time – that is all
      Ye know on earth, and all ye need to know.

      Khalid Masood

    • Khalidcustoms

      Time is God, God time – that is all
      Ye know on earth, and all ye need to know.

      Khalid Masood