by Ashutosh Jogalekar
I shamelessly borrow the title of this essay from my mentor and friend Freeman Dyson’s marvelous talk on birds and frogs in mathematics. Birds are thinkers who look at the big picture and survey the landscape from a great height. Frogs are thinkers who love playing around in the mud of specific problems, delighting in finding gems and then polishing them so that they become part of the superstructure that birds survey. Einstein was a bird, Hubble was a frog. Science needs both birds and frogs for its progress, but there are cases in which one kind of creature is more important than another.
Most of the great thinkers in physics of ancient times were birds. They went by the name of natural philosophers. The fact that they were birds speaks both to the raw state of scientific knowledge at that time and the attitude that these thinkers had toward what we call science, an attitude that we should resurrect. Aristotle, Plato, Newton and Kepler saw science as a seamless part of a worldview that included religion. Many of them were alchemists and astrologers. Unlike many scientists today, they saw no conflict between science and mysticism and believed both to be created by God for man to study. Newton was a supreme bird, seeing Nature as a book written by God, a puzzle whose solutions had room for both calculus and alchemy, both gravitation and an Arian rejection of the Holy Trinity. Newton kept his Arian convictions secret for fear of persecution, but there is no doubt in his own mind that they were as legitimate as his scientific inquiries. At the beginning of the third volume of his famous Principia, Newton said, “It remains that, from the same principles, I now demonstrate the system of the world”, leaving no doubt either about his ambition or his grand birdlike worldview.
Even before Newton, Francis Bacon who can rightly be called the father of the modern scientific method of fact-finding and theorizing was a superb frog. Bacon rejected the Aristotelian theorizing that had characterized much of the history of science before him and said, “All depends on keeping the eye fixed upon the facts of Nature, for God forbid that we may give out a dream of our own imagination for a pattern of the world.”
Bacon firmly believed that the way to know more about Nature is to go out there and seek facts. We can build theories only after we have enough facts, which is still the way science generally works. The contrast to Bacon was Descartes, a prominent bird who famously said, “I think, therefore I am”. Descartes put a premium on thought, Bacon on fact-finding. As the somewhat apocryphal story goes, Bacon met his end while investigating the effects of cold on a chicken, thus revealing the flip side of fact-finding. Experimenters have it hard.
It is interesting to ask if birds and frogs in physics can be broadly classified. The boundaries can be fluid, but generally speaking, Cartesian thinkers tend to be birds while Baconian doers tend to be frogs. This is partly because thinking about a broad landscape of ideas is easier than getting your hands dirty even on a single, well-crafted scientific experiment. Similarly, physicists who are unifiers tend to be birds, while physicists who are diversifiers tend to be frogs. One of the great and continuing themes in the history of physics is that of unifying different theories and different forces of nature. For instance it took a bevy of birds like Rudolf Clausius, Gustav Kirchhoff, Sadi Carnot, Lord Kelvin and Willard Gibbs to unify the phenomena of mechanics and heat, inaugurating the science of thermodynamics. Around the same time, the great James Clerk Maxwell was inaugurating the science of electromagnetism by unifying electricity and magnetism. Maxwell was building on the foundational work done by Michael Faraday who had proved that electric fields can generate magnetic fields and vice versa.
But the example of Faraday, Carnot and Gibbs raise the interesting possibility of a new creature – the frogbird. Frogbirds are an exotic and rare species who start out as frogs, but who through their persistent and creative frog-like explorations inevitably turn into birds. In one of the very few examples of an engineer making fundamental contributions to science, Carnot was trying to find out the maximum efficiency of heat engines when these investigations led him to a fundamental law of nature – the Second Law of Thermodynamics. Faraday was a modest experimenter who loved getting his hands dirty with string and sealing wax. His main goal was to do simple experiments which would help him understand phenomena like the electric decomposition of salts. This research philosophy had been inspired by his mentor Humphrey Davy who had investigated the effects of laughing gas and discovered many new elements in bursts of frog-hopping. But Faraday discovered much more through his experiments than what he might have hoped for, glimpsing a hidden symmetry in the laws of nature, a symmetry that Maxwell was to fully exploit. Willard Gibbs also started out as a highly skilled theoretical frog, manipulating vector calculus to study specific thermodynamic phenomena. In the process, he became the father of statistical mechanics, and his contributions were so deep that Einstein called him the greatest mind in American science. But Gibbs was an exceedingly shy frogbird, publishing his great theory in an obscure Connecticut journal and quietly working until the end of his life at Yale University. His reputation as a bird was resurrected by others after his death.
As the 20th century dawned, physics started becoming more specialized and it started becoming harder for physicists to be birds. But a classic frogbird at the beginning of the century set in motion a series of events that paved the way for the greatest bird of the century. Working at the turn of the century, Max Planck embarked on a desperate mathematical fix to rescue the thermodynamics of black body radiation. Part of Planck’s efforts came from helping out the German lightbulb industry which was trying to maximize the efficiency of their filaments. Trying to explain the emission of energy by a blackbody, Planck made the inspired suggestion that the only way to explain the data was to assume that the energy was emitted in small chunks called quanta. The chunks were exceedingly small and could be quantified by a tiny parameter which came to be called Planck’s constant. Planck was a conservative physicist, and by his own account he wasn’t trying to create a new theory but simply trying to explain some odd results. In fact, contrary to what the public thinks sparks great scientific discoveries, breakthroughs in science often happen when someone tries to explain a mundane but persistently odd phenomenon, say the beak of a specific bird, the anomaly of a specific planet’s orbit or the behavior of a specific atom like radium. But when Planck explained blackbody radiation using his quanta, all hell broke loose and a new force was unleashed upon the world.
This force partly came in the form of the great bird, Albert Einstein, who in his annus mirabilis of 1905 wrote five groundbreaking papers, one of which was about the special theory of relativity. Perhaps the more important paper, and one that won him the Nobel Prize later, was an explanation of the photoelectric effect which could only be explained using Planck’s constant. What Planck had thought merely to be a mathematical trick, Einstein found was a crowning edifice in the structure of nature. Einstein was the quintessential bird, thinking of disparate phenomena – the absence of the so-called ether, the speed of light, the specific heat of solids, the unification of Newton’s laws of motion with Maxwell’s theories of electromagnetism. Curiously, one of the foundations of relativity came from a famous experiment by Albert Michaelson and Edward Morley who were frogs extraordinaire. Their careful experiments which failed to find the luminiferous ether through which Maxwell’s electromagnetic waves traveled were masterpieces of frog-like exploration. And yet these experiments enabled the work of the bird Einstein. Later Einstein the bird rose even higher and started to survey the landscape at cosmic scales, trying to make sense of relativity in the context of accelerated frames of motion. This gave rise in 1915 to general relativity, one of the greatest achievements of human thought. To create general relativity, the bird had to soar not just over realms of physics but those of mathematics as well, taking the help of Riemannian geometry to describe curved spacetime. In these efforts Einstein was helped by two very competent frogs, his friends Marcel Grossmann and Michele Besso. Einstein’s collaboration especially with Grossmann shows that often the best results come when birds collaborate with frogs instead of pecking at them.
Later Einstein’s birdlike abilities unfortunately suffered because he failed to take into account all the discoveries frogs were making. He thought that quantum theory was incomplete, and at the end of his life embarked on a quest to come up with a grand unified theory that would unify all the forces of physics. But Einstein was no longer paying attention to the new particles and forces frogs were discovering. Without incorporating these findings in his theories, Einstein’s quest was doomed. Einstein also failed to realize the intense frog-like interest in creations that were logically derived from his own general relativity – black holes. He showed no inclination toward studying them. On the other hand, he was very much interested in the implications of his theory for another supremely important discovery, that of the expansion of the universe. This discovery was made by Edwin Hubble, a formidable frog who liked to sit at his telescope on Mount Wilson on cold nights and plot the speeds and luminosities of nebulae. Hubble was a former boxer-turned-astronomer; one suspects that boxing provides a good foundation for frog-like focus in reducing specific problems to their quivering logical conclusions. But Hubble owed his own work to a set of remarkable frogs working successively at the Harvard Observatory – women like Henrietta Leavitt, Annie Cannon and Cecilia Payne who were paving the way to a grand theory of the universe by painstakingly cataloging periods and luminosities of thousands of stars. The progression from Leavitt to Einstein to Hubble again shows how the work of frogs and birds inevitably builds on top of each other.
If Einstein can be called a supreme frog, so can Paul Dirac. But Dirac was a frog whose visions were so grand that they were more similar to the 17th century mysticism of Newton. Dirac was one of the fathers of quantum mechanics who invented an equation of the electron that deduced the existence of a particle with the same mass as the electron but opposite charge. In proposing the existence of these antiparticles, Dirac was going beyond what any frog’s work would imply, deriving rarefied conclusions that could only be supported by mathematics. But Dirac’s birdlike visions were quickly given the twang of reality when Carl Anderson discovered the positron in a cloud chamber. Birds can soar all they want, but even when they see things that others don’t, frogs have to be recruited on the ground to verify what is only a dream. Many of the other fathers of quantum mechanics during the same period were also birds, although it is interesting to note that both Schrödinger and Heisenberg started out as frogs intent on verifying some of the conundrums raised by their illustrious bird-father, Niels Bohr. What Einstein had done for the photoelectric effect Bohr did for atomic structure, catapulting him into the first rank of birds. But Bohr’s theory raised as many questions as it answered because it was exceedingly hard to apply it to atoms more complex than hydrogen and get answers that agreed with experiment. One of the thorniest problems was to explain the thicket of emission and absorption spectra that had served as the basis of Bohr’s work. It was while trying to explain this spectral transition that Heisenberg, while recovering from a bad attack of hay fever on an island in the North Sea, turned into a bird, took flight and invented matrix mechanics which was the first version of quantum mechanics. Similarly, Schrödinger was trying to solve a specific problem, that of finding a wave equation for the matter waves that Louis de Broglie had postulated. In the process he too became a bird.
If Einstein and Bohr were the grand birds of 20th century physics, then Enrico Fermi was the ultimate frog king. There was not a branch of physics Fermi did not touch, but he would have almost certainly thought of himself as first and foremost a frog, trying to solve specific problems with the simplest possible approach. With this philosophy Fermi built the world’s first nuclear reactor and co-invented Fermi-Dirac statistics that explain the behavior of particles with integer spin. But on the way he made a grand birdlike discovery when he came up with a consistent theory of beta decay that would give rise to a new force of nature – the weak force. Fermi’s strength was to look at a specific problem, visualize it physically and then plough straight ahead to solve it using all the mathematical tools at his disposal. Fermi of course was also unique in the annals of 20th century physics in being supremely accomplished in both experimental and theoretical physics.
Another great frog, and one who Fermi deeply influenced, was Hans Bethe. Just like Fermi, there was not a branch of modern physics Bethe did not touch. Unlike Fermi who died tragically early, Bethe lived into his nineties and his last paper was published after his death in 2005. The term “force of nature” seems to have been coined specifically for Bethe. He was famous for sitting at his desk hour after hour and turning out hundreds of pages of calculations with almost no mistake. No problem would faze him, and his colleagues called him “The Battleship”; a later newspaper profile would describe him as a man “who reduces problems to their essential solutions by the sheer force of his mental artillery.” Just like Fermi he became one of the world’s top nuclear physicists in the 1930s, writing a set of three exhaustive reviews on the state of the art in nuclear physics that were considered so authoritative that they were called Bethe’s Bible. Moving effortlessly from pure to applied physics problems, in 1938 Bethe made his Nobel Prize winning discovery of the nuclear reactions that make the sun shine. It was Bethe’s unsurpassed facility with frog-like problem solving that prompted Robert Oppenheimer to pick him as head of the theoretical division of the Manhattan Project.
During his work on the Manhattan Project, frog Bethe met his match in a young and hyperactive bird whose name was Richard Feynman. Fresh out of Princeton, Feynman would become one of those chosen birds who soared over all of physics and sought to see everything in a new light. When he met Bethe Feynman was already working on a spacetime view of quantum theory which saw antiparticles as particles traveling backward in time. He was working out this theory with John Wheeler, a physicist whose birdlike abilities were so unique that he would become known for thinking in pictures and poetic visions. Bird Feynman and frog Bethe got along exceedingly well, and Bethe’s invitation to Feynman to become his colleague at Cornell University allowed Feynman to make his famous discovery of Feynman diagrams. Feynman also inspired my own mentor, Freeman Dyson, who considered himself the quintessential frog. Throughout his long and stunningly diverse career, Dyson looked for problems in branches of physics and mathematics where elegant mathematics might make a difference. Dyson made his mark by explaining the disparate theories of Feynman, Julian Schwinger and Sin-Itiro Tomonaga to the public. He became a particularly joyous frog, jumping around in particle physics, solid-state physics, evolutionary biology, nuclear spaceship and reactor design and pure mathematics, finding gems and often leaving them for others to polish.
How do the distributions of frogs and birds look like in late 20th century physics? The three most important branches of physics during this time have been particle physics, cosmology and condensed matter physics. Of these condensed matter physics is especially notable in having a huge practical impact on our daily life in the form of semiconductors and computers. Most condensed matter physicists like John Bardeen, William Shockley and David Thouless were highly accomplished frogs. But one big bird among them stands out – Philip Anderson who passed away last year. Anderson soared over the world of not just condensed matter physics but also made fundamental contributions to particle physics and complexity studies. His proposal of a particle that later became known as the Higgs boson by drawing parallels of symmetry breaking between particle physics and solid-state physics has to be one of the greatest birdlike feats in physics of the recent past.
In particle physics, the theoreticians have mostly been birds while their experimental counterparts have been frogs. Steven Weinberg, Murray Gell-Mann, Gerard ‘t Hooft and Abdus Salam have continued the grand tradition of seeking unification of particles and forces through powerful avian tools. Meanwhile, experimentalists like Leon Lederman and C. S. Wu set up decisive experiments as frogs to prove or disprove the grand theories that birds like Chen Ning Yang and Tsung Dao Lee came up with. Meanwhile cosmology benefited from its own mix of frogs and birds. Alan Guth who came up with the theory of inflation is a bird, trying to solve several problems from the early history of the university in one fell swoop. But in the late 1990s, Saul Perlmutter and other frogs discovered the startling phenomenon of the universe accelerating by studying the characteristics of supernovae, continuing the illustrious tradition of their frog forebears Leavitt, Hubble and Payne.
Perhaps the ultimate bird of the recent past is Edward Witten. Along with a select few other birds, Witten is trying to bring about what is perhaps the last big bird unification, that of general relativity with quantum theory. So far Witten has flown over a vast landscape of physics and mathematics, making unexpected connections between both fields that made him the only physicist to win the Fields Medal in mathematics. But the bigger connection that he and his colleagues have made, one that sees reality in multiple dimensions and pointlike strings, has yet to be verified by frogs. Perhaps it’s fitting that Witten might be the last great mystic in the tradition of Paul Dirac, throwing a gauntlet down. We can only hope that there will be enough brave and competent frogs playing down in the mud who catch the gauntlet and run with it. If the history of physics with its creative interplay between frogs and birds is any guide, there is much cause for optimism that this will be true.