Tag: history of science

Complementarity and the world: Niels Bohr’s message in a bottle

Posted on by Ashutosh Jogalekar

by Ashutosh Jogalekar

Niels Bohr (Getty Images)

Werner Heisenberg was on a boat with Niels Bohr and a few friends, shortly after he discovered his famous uncertainty principle in 1927. A bedrock of quantum theory, the principle states that one cannot determine both the velocity and the position of particles like electrons with arbitrary accuracy. Heisenberg’s discovery foretold of an intrinsic opposition between these quantities; better knowledge of one necessarily meant worse knowledge of the other. Talk turned to physics, and after Bohr had described Heisenberg’s seminal insight, one of his friends quipped, “But Niels, this is not really new, you said exactly the same thing ten years ago.”

In fact, Bohr had already convinced Heisenberg that his uncertainty principle was a special case of a more general idea that Bohr had been expounding for some time – a thread of Ariadne that would guide travelers lost through the quantum world; a principle of great and general import named the principle of complementarity.

Complementarity arose naturally for Bohr after the strange discoveries of subatomic particles revealed a world that was fundamentally probabilistic. The positions of subatomic particles could not be assigned with definite certainty but only with statistical odds. This was a complete break with Newtonian classical physics where particles had a definite trajectory, a place in the world order that could be predicted with complete certainty if one had the right measurements and mathematics at hand. In 1925, working at Bohr’s theoretical physics institute in Copenhagen, Heisenberg was Bohr’s most important protégé had invented quantum theory when he was only twenty-four. Two years later came uncertainty; Heisenberg grasped that foundational truth about the physical world when Bohr was away on a skiing trip in Norway and Heisenberg was taking a walk at night in the park behind the institute. Read more »

Monday, October 4, 2021

How to think like Albert Einstein

Posted on by Ashutosh Jogalekar

by Ashutosh Jogalekar

Considered the epitome of genius, Albert Einstein appears like a wellspring of intellect gushing forth fully formed from the ground, without precedents or process. There was little in his lineage to suggest genius; his parents Hermann and Pauline, while having a pronounced aptitude for mathematics and music, gave no inkling of the off-scale progeny they would bring forth. His career itself is now the stuff of legend. In 1905, while working on physics almost as a side-project while sustaining a day job as technical patent clerk, third class, at the patent office in Bern, he published five papers that revolutionized physics and can only be compared to Isaac Newton’s burst of high creativity as he sought refuge from the plague. Among these were papers heralding his famous equation, E=mc^2, along with ones describing special relativity, Brownian motion and the basis of the photoelectric effect that cemented the particle nature of light. In one of history’s ironic episodes, it was the photoelectric effect paper rather than the one on special relativity that Einstein himself called revolutionary and that won him the 1922 Nobel Prize in physics.

But in judging Einstein’s superlative achievements, both in terms of his birth and his evolution as a physicist, it is easy to think him of him as an entirely self-made genius. Nothing could be further from the truth. Einstein stood on the proverbial shoulders of giants – Newton, Mach, Faraday, Maxwell, Lorentz, among others – men who had laid the foundations of physics for two centuries before him and who he always had effusive praise for. But quite apart from learning from his intellectual ancestry, Einstein also honed useful habits and personal qualities that enabled him to triumph in his work. Too often when we read about brilliant men and women, there’s a tendency to enshrine and emphasize pure intellect and discard the personal qualities, as if the two were cleanly separable. But the fact of the matter is that raw brilliance and qualities are like genes and culture, each feeding off of each other and nurturing each other’s growth and success.

As psychologist Angela Duckworth described in her book “Grit”, genius without effort and determination can fail, or fail to live up to its great promise at the very least. And so it was for Einstein. Which makes it a matter of curiosity at the minimum ,and more promisingly a tool for measurably enhancing the efficiency of our own more modest work, to survey the personal qualities that Einstein embodied that made him successful. So what were these? Read more »

Monday, July 12, 2021

Kurt Gödel’s Open World

Posted on by Ashutosh Jogalekar

by Ashutosh Jogalekar

Gödel and Einstein in Princeton (Source: Emilio Segre Visual Archives)

Two men walking in Princeton, New Jersey on a stuffy day. One shaggy-looking with unkempt hair, avuncular, wearing a hat and suspenders, looking like an old farmer. The other an elfin man, trim, owl-like, also wearing a fedora and a slim white suit, looking like a banker. The elfin man and the shaggy man used to make their way home from work every day. Passersby and motorists would strain their heads to look. Everyone knew who the shaggy man was; almost nobody knew who his elfin companion was. And yet when asked, the shaggy man would say that his own work no longer meant much to him, and the only reason he came to work was to have the privilege of walking home with the elfin man. The shaggy man was Albert Einstein. His walking companion was Kurt Gödel.

What made Gödel, a figure unknown to the public, so revered among his colleagues? The superlatives kept coming. Einstein called him the greatest logician since Aristotle. The legendary mathematician John von Neumann who was his colleague argued for his extraction from fascism-riddled Europe, writing a letter to the director of his institute saying that “Gödel is absolutely irreplaceable; he is the only mathematician about whom I dare make this assertion.” And when I made a pilgrimage to Gödel’s house during a trip to his native Vienna a few years ago, the plaque in front of the house made his claim to posterity clear: “In this house lived from 1930-1937, the great mathematician and logician Kurt Gödel. Here he discovered his famous incompleteness theorem, the most significant mathematical discovery of the twentieth century.”

The author in front of the house in Vienna where Gödel was living with his mother and brother when he proved his Incompleteness Theorems

The reason Gödel drew gasps of awe from colleagues as brilliant as Einstein and von Neumann was because he revealed a seismic fissure in the foundations of that most perfect, rational and crystal-clear of all creations – mathematics. Of all the fields of human inquiry, mathematics is considered the most exact. Unlike politics or economics, or even the more quantifiable disciplines of chemistry and physics, every question in mathematics has a definite yes or no answer. The answer to a question such as whether there is an infinitude of prime numbers leaves absolutely no room for ambiguity or error – it’s a simple yes or no (yes in this case). Not surprisingly, mathematicians around the beginning of the 20th century started thinking that every mathematical question that can be posed should have a definite yes or no answer. In addition, no mathematical question should have both answers. The first requirement was called completeness, the second one was called consistency. Read more »

Monday, June 14, 2021

The ethics of regulating AI: When too much may be bad

Posted on by Ashutosh Jogalekar

by Ashutosh Jogalekar

‘Areopagitica‘ was a famous speech delivered by the poet John Milton in the English Parliament in 1644, arguing for the unlicensed printing of books. It is one of the most famous speeches in favor of freedom of expression. Milton was arguing against a parliamentary ordinance requiring authors to get a license for their works before they could be published. Delivered during the height of the English Civil War, Milton was well aware of the power of words to inspire as well as incite. He said,

For books are not absolutely dead things, but do preserve as in a vial the purest efficacy and extraction of that living intellect that bred them. I know they are as lively, and as vigorously productive, as those fabulous Dragon’s teeth; and being sown up and down, may chance to spring up armed men…

What Milton was saying is not that books and words can never incite, but that it would be folly to restrict or ban them before they have been published. This appeal toward withholding restraint before publication found its way into the United States Constitution and has been a pillar of freedom of expression and the press since.

Why was Milton opposed to pre-publication restrictions on books? Not just because he realized that it was a matter of personal liberty, but because he realized that restricting a book’s contents means restricting the very power of the human mind to come up with new ideas. He powerfully reminded Parliament,

Who kills a man kills a reasonable creature, God’s image; but he who destroys a good book, kills reason itself, kills the image of God, as it were, in the eye. Many a man lives a burden to the earth; but a good book is the precious lifeblood of a master spirit, embalmed and treasured up on purpose to a life beyond life.

Milton saw quite clearly that the problem with limiting publication is in significant part a problem with trying to figure out all the places a book can go. The same problem arises with science. Read more »

Monday, October 26, 2020

What John von Neumann really did at Los Alamos

Posted on by Ashutosh Jogalekar

by Ashutosh Jogalekar

John von Neumann (Image: Life Magazine)

During a wartime visit to England in early 1943, John von Neumann wrote a letter to his fellow mathematician Oswald Veblen at the Institute for Advanced Study in Princeton, saying:

“I think I have learned a great deal of experimental physics here, particularly of the gas dynamical variety, and that I shall return a better and impurer man. I have also developed an obscene interest in computational techniques…”

This seemingly mundane communication was to foreshadow a decisive effect on the development of two overwhelmingly important aspects of 20th and 21st century technology – the development of computing and the development of nuclear weapons.

Johnny von Neumann was the multifaceted intellectual diamond of the 20th century. He contributed so many seminal ideas to so many fields so quickly that it would be impossible for any one person to summarize, let alone understand them. He may have been the last universalist in mathematics, having almost complete command of both pure and applied mathematics. But he didn’t stop there. After making fundamental contributions to operator algebra, set theory and the foundations of mathematics, he revolutionized at least two different and disparate fields – economics and computer science – and made contributions to a dozen others, each of which would have been important enough to enshrine his name in scientific history.

But at the end of his relatively short life which was cut down cruelly by cancer, von Neumann had acquired another identity – that of an American patriot who had done more than almost anyone else to make sure that his country was well-defended and ahead of the Soviet Union in the rapidly heating Cold War. Like most other contributions of this sort, this one had a distinctly Faustian gleam to it, bringing both glory and woe to humanity’s experiments in self-elevation and self-destruction. Read more »

Monday, July 6, 2020

Brains, computation and thermodynamics: A view from the future?

Posted on by Ashutosh Jogalekar

by Ashutosh Jogalekar

Rolf Landauer who discovered a fundamental limit to the efficiency of computation. What can it tell us about human brains?

Progress in science often happens when two or more fields productively meet. Astrophysics got a huge boost when the tools of radio and radar met the age-old science of astronomy. From this fruitful marriage came things like the discovery of the radiation from the big bang. Another example was the union of biology with chemistry and quantum mechanics that gave rise to molecular biology. There is little doubt that some of the most important future discoveries in science in the future will similarly arise from the accidental fusion of multiple disciplines.

One such fusion sits on the horizon, largely underappreciated and unseen by the public. It is the fusion between physics, computer science and biology. More specifically, this fusion will likely see its greatest manifestation in the interplay between information theory, thermodynamics and neuroscience. My prediction is that this fusion will be every bit as important as any potential fusion of general relativity with quantum theory, and at least as important as the development of molecular biology in the mid 20th century. I also believe that this development will likely happen during my own lifetime.

The roots of this predicted marriage go back to 1867. In that year the great Scottish physicist James Clerk Maxwell proposed a thought experiment that was later called ‘Maxwell’s Demon’. Maxwell’s Demon was purportedly a way to defy the second law of thermodynamics that had been proposed a few years earlier. The second law of thermodynamics is one of the fundamental laws governing everything in the universe, from the birth of stars to the birth of babies. It basically states that left to itself, an isolated system will tend to go from a state of order to one of disorder. A good example is how a bottle of perfume wafts throughout a room with time. This order and disorder was quantified by a quantity called entropy. Read more »

Monday, June 8, 2020

Von Neumann in 1955 and 2020: Musings of a cheerful pessimist on technological survival

Posted on by Ashutosh Jogalekar

by Ashutosh Jogalekar

Johnny von Neumann enjoying some of the lighter aspects of technology. The cap lights up when its wearer blows into the tube.

“All experience shows that even smaller technological changes than those now in the cards profoundly transform political and social relationships. Experience also shows that these transformations are not a priori predictable and that most contemporary “first guesses” concerning them are wrong.” – John von Neumann

Is the coronavirus crisis political or technological? All present analysis would seem to say that this pandemic was a result of gross political incompetence, lack of preparedness and impulsive responses by world leaders and government. But this view would be narrow because it would privilege the proximate cause over the ultimate one. The true, deep cause underlying the pandemic is technological. The coronavirus arose as a result of a hyperconnected world that made human reaction times much slower than global communication and the transport of physical goods and people across international borders. For all our skill in creating these technologies, we did not equip ourselves to manage the network effects and sudden failures in social, economic and political systems created by them. An even older technology, the transfer of genetic information between disparate species, was what enabled the whole crisis in the first place.

This privileging of political forces over technological ones is typical of the mistakes that we often make in seeking the root cause of problems. Political causes, greatly amplified by the twenty-four hour news cycle and social media, are illusory and may even be important in the short-term, but there is little doubt that the slow but sure grind of technological change that penetrates deeper and deeper into social and individual choices will be responsible for most of the important transformations we face during our lifetimes and beyond. On scales of a hundred to five hundred years, there is little doubt that science and technology rather than any political or social event cause the biggest changes in the fortunes of nations and individuals: as Richard Feynman once put it, a hundred years from now, the American Civil War would pale into provincial insignificance compared to that other development from the 1860s – the crafting of the basic equations of electromagnetism by James Clerk Maxwell. The former led to a new social contract for the United States; the latter underpins all of modern civilization – including politics, war and peace.

The question, therefore, is not whether we can survive this or that political party or president. The question is, can we survive technology? Read more »

Monday, April 13, 2020

The greatest artist

Posted on by Ashutosh Jogalekar

by Ashutosh Jogalekar

A dinosaur fossil found in China with a clearly visible feathered exterior (Cosmos Magazine)

Neil Shubin’s “Some Assembly Required” is a delightful book whose thesis can be summarized in one word – “repurposing”. As Steve Jobs once put it, “Good artists create. Great artists steal”. By that reckoning Nature is undoubtedly the most magnificent thief and the greatest artist of all time. Repurposing in the history of life will undoubtedly become one of the great paradigms of science, and its discovery has not only provided immense insights into evolutionary biology but also promises to make key contributions to our understanding and treatment of human disease.

Among many other achievements of Darwin’s great theory was the explanation and prediction that similar parts of organisms had similar functions even if they might have looked different. One of the truly remarkable features of “On the Origin of Species” is how Darwin gets almost everything right, how even throwaway lines attest to a level of understanding of life that was solidified only decades after this death. The idea of repurposing came about in the “Origin” partly as a reply to objections raised by  a man named St. George Jackson Mivart. Mivart was in the curious position of being a man of the cloth who had first wholeheartedly embraced Darwin’s theory and studied with Thomas Henry Huxley, Darwin’s most ardent champion, before then rejecting it and mounting an attack on it, timidly at first and then vociferously. Mivart’s own tract on the subject, “On the Genesis of Species” made his not-so-subtle dig at Darwin’s book clear.

Darwin’s response to Mivart’s objections in the “Origin of Species” (from the author’s collection; 1882 edition)

Mivart’s basic objection was similar to that raised then and later by creationists. Darwin’s theory crucially relied on transitional forms that enabled major leaps in life’s history; from fish to amphibian for instance or from arboreal life to terrestrial life. But in Mivart’s view, any such major transition would involve not just a sudden change in one crucial body part, say from gills to lungs, but a change in multiple body parts. Clearly the transition from water to land for instance involved hundreds if not thousands of changes in organs and structures for locomotion, feeding and breathing. But how could all these changes arise out of thin air? How could gills for instance suddenly turn into lungs in the first lucky fish that crawled out of water and learnt how to survive on land? This problem according to Mivart was insurmountable and a fatal flaw in Darwin’s theory. Darwin took Mivart’s objections seriously enough to include a substantial section addressing them in the sixth and definitive edition of his book, first published in 1872. In it he acknowledged Mivart’s problems with his theory, and then did away with them succinctly: There is no problem imagining organs being used in different species, Darwin said, as long as they are “accompanied by a change in function.” In writing this Darwin was even further ahead of his time than he imagined. Read more »

Monday, January 20, 2020

The Fermi-Pasta-Ulam-Tsingou problem: A foray into the beautifully simple and the simply beautiful

Posted on by Ashutosh Jogalekar

by Ashutosh Jogalekar

In November 1918, a 17-year-student from Rome sat for the entrance examination of the Scuola Normale Superiore in Pisa, Italy’s most prestigious science institution. Students applying to the institute had to write an essay on a topic that the examiners picked. The topics were usually quite general, so the students had considerable leeway. Most students wrote about well-known subjects that they had already learnt about in high school. But this student was different. The title of the topic he had been given was “Characteristics of Sound”, and instead of stating basic facts about sound, he “set forth the partial differential equation of a vibrating rod and solved it using Fourier analysis, finding the eigenvalues and eigenfrequencies. The entire essay continued on this level which would have been creditable for a doctoral examination.” The man writing these words was the 17-year-old’s future student, friend and Nobel laureate, Emilio Segre. The student was Enrico Fermi. The examiner was so startled by the originality and sophistication of Fermi’s analysis that he broke precedent and invited the boy to meet him in his office, partly to make sure that the essay had not been plagiarized. After convincing himself that Enrico had done the work himself, the examiner congratulated him and predicted that he would become an important scientist.

Twenty five years later Fermi was indeed an important scientist, so important in fact that J. Robert Oppenheimer had created an entire division called F-Division under his name at Los Alamos, New Mexico to harness his unique talents for the Manhattan Project. By that time the Italian emigre was the world’s foremost nuclear physicist as well as perhaps the only universalist in physics – in the words of a recent admiring biographer, “the last man who knew everything”. He had led the creation of the world’s first nuclear reactor in a squash court at the University of Chicago in 1942 and had won a Nobel Prize in 1938 for his work on using neutrons to breed new elements, laying the foundations of the atomic age. Read more »

Monday, October 28, 2019

Making far out the norm: Or how to nurture loonshots

Posted on by Ashutosh Jogalekar

by Ashutosh Jogalekar

Vannevar Bush – loonshot pioneer (Picture credit- TIME magazine)

What makes a revolutionary scientific or technological breakthrough by an individual, an organization or even a country possible? In his thought provoking book “Loonshots: How to Nurture the Crazy Ideas that Win Wars, Cure Diseases and Transform Industries”, physicist and biotechnology entrepreneur Safi Bahcall dwells on the ideas, dynamics and human factors that have enabled a select few organizations and nations in history to rise above the fray and make contributions of lasting impact to modern society. Bahcall calls such seminal, unintuitive, sometimes vehemently opposed ideas “Loonshots”. Loonshots is a play on “moonshots” because the people who come up with these ideas are often regarded as crazy or anti-establishment, troublemakers who want to rattle the status quo.

Bahcall focuses on a handful of individuals and companies to illustrate the kind of unconventional, out of the box thinking that makes breakthrough discoveries possible. Among his favorite individuals are Vannevar Bush, Akira Endo and Edwin Land, and among his favorite organizations are Bell Labs and American Airlines. Each of these individuals or organizations possessed the kind of hardy spirit that’s necessary to till their own field, often against the advice of their peers and superiors. Each possessed the imagination to figure out how to think unconventionally or orthogonal to the conventional wisdom. And each courageously pushed ahead with their ideas, even in the face of contradictory or discouraging data. Read more »

Monday, September 2, 2019

Spooky factions at a distance

Posted on by Ashutosh Jogalekar

by Ashutosh Jogalekar

For me, a highlight of an otherwise ill-spent youth was reading mathematician John Casti’s fantastic book “Paradigms Lost“. The book came out in the late 1980s and was gifted to my father who was a professor of economics by an adoring student. Its sheer range and humor had me gripped from the first page. Its format is very unique – Casti presents six “big questions” of science in the form of a courtroom trial, advocating arguments for the prosecution and the defense. He then steps in as jury to come down on one side or another. The big questions Casti examines are multidisciplinary and range from the origin of life to the nature/nurture controversy to extraterrestrial intelligence to, finally, the meaning of reality as seen through the lens of the foundations of quantum theory. Surprisingly, Casti himself comes down on the side of the so-called many worlds interpretation (MWI) of quantum theory, and ever since I read “Paradigms Lost” I have been fascinated by this analysis.

So it was with pleasure and interest that I came across Sean Carroll’s book that also comes down on the side of the many worlds interpretation. The MWI goes back to the very invention of quantum theory by pioneering physicists like Niels Bohr, Werner Heisenberg and Erwin Schrödinger. As exemplified by Heisenberg’s famous uncertainty principle, quantum theory signaled a striking break with reality by demonstrating that one can only talk about the world only probabilistically. Contrary to common belief, this does not mean that there is no precision in the predictions of quantum mechanics – it’s in fact the most accurate scientific framework known to science, with theory and experiment agreeing to several decimal places – but rather that there is a natural limit and fuzziness in how accurately we can describe reality. As Bohr put it, “physics does not describe reality; it describes reality as subjected to our measuring instruments and observations.” This is actually a reasonable view – what we see through a microscope and telescope obviously depends on the features of that particular microscope or telescope – but quantum theory went further, showing that the uncertainty in the behavior of the subatomic world is an inherent feature of the natural world, one that doesn’t simply come about because of uncertainty in experimental observations or instrument error. Read more »

Monday, May 13, 2019

Life and Death in New Jersey

Posted on by Ashutosh Jogalekar

by Ashutosh Jogalekar

On a whim I decided to visit the gently sloping hill where the universe announced itself in 1964, not with a bang but with ambient, annoying noise. It’s the static you saw when you turned on your TV, or at least used to back when analog TVs were a thing. But today there was no noise except for the occasional chirping of birds, the lone car driving off in the distance and a gentle breeze flowing through the trees. A recent trace of rain had brought verdant green colors to the grass. A deer darted into the undergrowth in the distance.

The town of Holmdel, New Jersey is about thirty miles east of Princeton. In 1964, the venerable Bell Telephone Laboratories had an installation there, on top of this gently sloping hill called Crawford Hill. It was a horn antenna, about as big as a small house, designed to bounce off signals from a communications satellite called Echo which the lab had built a few years ago. Tending to the care and feeding of this piece of electronics and machinery were Arno Penzias – a working-class refuge from Nazism who had grown up in the Garment District of New York – and Robert Wilson; one was a big picture thinker who enjoyed grand puzzles and the other an electronics whiz who could get into the weeds of circuits, mirrors and cables. The duo had been hired to work on ultra-sensitive microwave receivers for radio astronomy.

In a now famous comedy of errors, instead of simply contributing to incremental advances in radio astronomy, Penzias and Wilson ended up observing ripples from the universe’s birth – the cosmic microwave background radiation – by accident. It was a comedy of errors because others had either theorized that such a signal would exist without having the experimental know-how or, like Penzias and Wilson, were unknowingly building equipment to detect it without knowing the theoretical background. Penzias and Wilson puzzled over the ambient noise they were observing in the antenna that seemed to come from all directions, and it was only after clearing away every possible earthly source of noise including pigeon droppings, and after a conversation with a fellow Bell Labs scientist who in turn had had a chance conversation with a Princeton theoretical physicist named Robert Dicke, that Penzias and Wilson realized that they might have hit on something bigger. Dicke himself had already theorized the existence of such whispers from the past and had started building his own antenna with his student Jim Peebles; after Penzias and Wilson contacted him, he realized he and Peebles had been scooped by a few weeks or months. In 1978 Penzias and Wilson won the Nobel Prize; Dicke was among a string of theorists and experimentalists who got left out. As it turned out, Penzias and Wilson’s Nobel Prize marked the high point of what was one of the greatest, quintessentially American research institutions in history. Read more »

Monday, July 9, 2018

The wisdom of John Wheeler and Oliver Sacks

Posted on by Ashutosh Jogalekar

by Ashutosh Jogalekar

A rare and happy coincidence today: The birthdays of both John Archibald Wheeler and Oliver Sacks. Wheeler was one of the most prominent physicists of the twentieth century. Sacks was one of the most prominent medical writers of his time. Both of them were great explorers, the first of the universe beyond and the second of the universe within.

What made both men special, however, was that they transcended mere accomplishment in the traditional genres that they worked in, and in that process they stand as role models for an age that seems so fractured. Wheeler the physicist was also Wheeler the poet and Wheeler the philosopher. Throughout his life he transmitted startling new ideas through eloquent prose that was too radical for academic journals. Most of his important writings made their way to us through talks and books. Sacks the neurologist was far more than a neurologist, and Sacks the writer was much more than a writer. Both Wheeler and Sacks had a transcendent view of humanity and the universe, a view that is well worth taking to heart in our own self-centered times.

Their backgrounds shaped their views and their destiny. John Wheeler grew up in an age when physics was transforming our view of the universe. While he was too young to participate in the genesis of the twin revolutions of relativity and quantum mechanics, he came on stage at the right time to fully implement the revolution in the burgeoning fields of particle and nuclear physics. Read more »

Monday, September 4, 2017

Heisenberg on Helgoland

Posted on by Ashutosh Jogalekar

by Ashutosh Jogalekar

Helgoland_Vogelperspektive_BW_2The sun was setting on a cloudless sky, the gulls screeching in the distance. The air was bracing and clear. Land rose from the blue ocean, a vague apparition on the horizon.

He breathed the elixir of pure evening air in and heaved a sigh of relief. This would help the godforsaken hay fever which had plagued him like a demon for the last four days. It had necessitated a trip away from the mainland to this tiny outcrop of flaming red rock out in the North Sea. Here he could be free not just of the hay fever but of his mentor, Niels Bohr. Perched on the rock, he looked out into the blue expanse.

For the last several months, Bohr had followed him like a shadow, an affliction that seemed almost as bad as the hay fever. It had all started about a year earlier, but really, it started when he was a child. His father, an erudite scholar but unsparing disciplinarian, made his brother and him compete mercilessly with each other. Even now he was not on the best terms with his brother, but the cutthroat competition produced at least one happy outcome: a passion for mathematics and physics that continued to provide him with intense pleasure.

He remembered those war torn years when Germany seemed to be on the brink of collapse, when one revolution after another threatened to tear apart the fabric of society. Physics was the one refuge. It sustained him then, and it promised to sustain him now.

If only he could understand what Bohr wanted. Bohr was not his first mentor. That place of pride belonged to Arnold Sommerfeld in Munich. Sommerfeld, the man with the impeccably waxed mustache who his friend Pauli called a Hussar officer. Sommerfeld, who would immerse his students not only in the latest physics but in his own home, where discussions went on late into the night. Discussions in which physics, politics and philosophy co-existed. His own father was often distant; Sommerfeld was the father figure in his life. It was also in Sommerfeld’s classes that he met his first real friend – Wolfgang Pauli. Pauli was still having trouble attending classes in the morning when there were all those clubs and parties to frequent at night. He always enjoyed long discussions with Pauli, the ones during which his friend often complimented him by telling him he was not completely stupid. It was Pauli who had steered him away from relativity and toward the most exciting new field in physics – quantum theory.

Read more »