Only wholeness leads to clarity,
And truth lies in the abyss.
But it was not in Møller that Bohr found solid footing. He needed more than a novel, however apposite, for that. He needed what we all need for sanity: he needed love and work.
“I took a great interest in philosophy in the years after my [high school] examination,” Bohr said in his last interview. “I came especially in close connection with Høffding.”232 Harald Høffding was Bohr’s father’s old friend, the other charter member of the Friday-night discussion group.233 Bohr had known him from childhood. Born in 1843, he was twelve years older than Christian Bohr, a profound, sensitive and kindly man. He was a skillful interpreter of the work of Søren Kierkegaard and of William James and a respected philosopher in his own right: an anti-Hegelian, a pragmatist interested in questions of perceptive discontinuity. Bohr became a Høffding student. It seems certain he also turned personally to Høffding for help. He made a good choice. Høffding had struggled through a crisis of his own as a young man, a crisis that brought him, he wrote later, near “despair.”234
Høffding was twelve years old when Søren Kierkegaard died of a lung infection in chill November 1855, old enough to have heard of the near-riot at the grave a somber walk outside the city walls, old enough for the strange, awkward, fiercely eloquent poet of multiple pseudonyms to have been a living figure. With that familiarity as a point of origin Høffding later turned to Kierkegaard’s writings for solace from despair. He found it especially in Stages on Life’s Way, a black-humorous dramatization of a dialectic of spiritual stages, each independent, disconnected, bridgeable only by an irrational leap of faith. Høffding championed the prolific and difficult Dane in gratitude; his second major book, published in 1892, would help establish Kierkegaard as an important philosopher rather than merely a literary stylist given to outbursts of raving, as Danish critics had first chosen to regard him.
Kierkegaard had much to offer Bohr, especially as Høffding interpreted him. Kierkegaard examined the same states of mind as had Poul Martin Møller. Møller taught Kierkegaard moral philosophy at the university and seems to have been a guide.235 After Møller’s death Kierkegaard dedicated The Concept of Dread to him and referred to him in a draft of the dedication as “my youth’s enthusiasm, my beginning’s confidant, mighty trumpet of my awakening, my departed friend.”236 From Møller to Kierkegaard to Høffding to Bohr: the line of descent was direct.
Kierkegaard notoriously suffered from a proliferation of identities and doubts. The doubling of consciousness is a central theme in Kierkegaard’s work, as it was in Møller’s before him. It would even seem to be a hazard of long standing among the Danes. The Danish word for despair, Fortvivlelse, carries lodged at its heart the morpheme tvi, which means “two” and signifies the doubling of consciousness.237 Tvivl in Danish means “doubt”; Tvivlesyg means “skepticism”; Tvetydighed, “ambiguity.” The self watching itself is indeed a commonplace of puritanism, closely akin to the Christian conscience.
But unlike Møller, who jollies the licentiate’s Tvivl away, Kierkegaard struggled to find a track through the maze of mirrors. Høffding, in his History of Modern Philosophy, which Bohr would have read as an undergraduate, summarizes the track he understood Kierkegaard to have found: “His leading idea was that the different possible conceptions of life are so sharply opposed to one another that we must make a choice between them, hence his catchword either-or; moreover, it must be a choice which each particular person must make for himself, hence his second catchword, the individual.” And, following: “Only in the world of possibilities is there continuity; in the world of reality decision always comes through a breach of continuity.”238, 239 Continuity in the sense that it afflicted Bohr was the proliferating stream of doubts and “I’s” that plagued him; a breach of that continuity—decisiveness, function—was the termination he hoped to find.
He turned first to mathematics. He learned in a university lecture about Riemannian geometry, a type of non-Euclidean geometry developed by the German mathematician Georg Riemann to represent the functions of complex variables. Riemann showed how such multivalued functions (a number, its square root, its logarithm and so on) could be represented and related on a stack of coincident geometric planes that came to be called Riemann surfaces. “At that time,” Bohr said in his last interview, “I really thought to write something about philosophy, and that was about this analogy with multivalued functions.240 I felt that the various problems in psychology—which were called the big philosophical problems, of the free will and such things—that one could really reduce them when one considered how one really went about them, and that was done on the analogy to multivalued functions.” By then he thought the problem might be one of language, of the ambiguity—the multiple values, as it were—between different meanings of the word “I.” Separate each different meaning on a different plane and you could keep track of what you were talking about. The confusion of identities would resolve itself graphically before one’s eyes.
The scheme was too schematic for Bohr. Mathematics was probably too much like ratiocination, leaving him isolated within his anxiety. He thought of writing a book about his mathematical analogies but leapt instead to work that was far more concrete. But notice that the mathematical analogy begins to embed the problem of doubt within the framework of language, identifying doubt as a specialized form of verbal ambiguity, and notice that it seeks to clarify ambiguities by isolating their several variant meanings on separate, disconnected planes.
The solid work Bohr took up, in February 1905, when he was nineteen years old, was a problem in experimental physics.241 Each year the Royal Danish Academy of Sciences and Letters announced problems for study against a two-year deadline, after which the academy awarded gold and silver medals for successful papers. In 1905 the physics problem was to determine the surface tension of a number of liquids by measuring the waves produced in those liquids when they were allowed to run out through a hole (the braided cascade of a garden hose demonstrates such waves). The method had been proposed by the British Nobelist John William Strutt, Lord Rayleigh, but no one had yet tried it out. Bohr and one other contestant accepted the challenge.
Bohr went to work in the physiology laboratory where he had watched and then assisted his father for years, learning the craft of experiment. To produce stable jets he decided to use drawn-out glass tubes. Because the method required large quantities of liquid he limited his experiment to water. The tubes had to be flattened on the sides to make an oval cross section; that gave the jet of water the shape it needed to evolve braidlike waves. All the work of heating, softening and drawing out the tubes Bohr did himself; he found it hypnotic. Rosenfeld says Bohr “took such delight in this operation that, completely forgetting its original purpose, he spent hours passing tube after tube through the flame.”242
Each separate experimental determination of the surface-tension value took hours. It had to be done at night, when the lab was unoccupied, because the jets were easily disturbed by vibration. Slow work, but Bohr also dawdled. The academy had allowed two years. Toward the end of that time Christian Bohr realized his son was procrastinating to the point where he might not finish his paper before the deadline. “The experiments had no end,” Bohr told Rosenfeld some years later on a bicycle ride in the country; “I always noticed new details that I thought I had first to understand. At last my father sent me out here, away from the laboratory, and I had to write up the paper.”243
“Out here” was Naerumgaard, the Adler country estate north of Copenhagen. There, away from the temptations of the laboratory, Niels wrote and Harald transcribed an essay of 114 pages. Niels submitted it to the academy on the day of deadline, but even then it was incomplete; three days later he turned in an eleven-page addendum that had been accidentally left off.
The essay, Bohr’s first scientific paper, determined the surface tension only of water but also uniquely extended Rayleigh’s theory. It won a gold medal fro
m the academy. It was an outstanding achievement for someone so young and it set Bohr’s course for physics. Unlike mathematicized philosophy, physics was anchored solidly in the real world.
In 1909 the Royal Society of London accepted the surface-tension paper in modified form for its Philosophical Transactions. Bohr, who was still only a student working toward his master’s degree when the essay appeared, had to explain to the secretary of the society, who had addressed him by his presumed academic title, that he was “not a professor.”244
Retreating to the country had helped him once. It might help again. Naerumgaard ceased to be available when the Adler family donated it for use as a school. When the time came to study for his master’s degree examinations, between March and May 1909, Bohr traveled to Vissenbjerg, on the island of Funen, the next island west from Copenhagen’s Zealand, to stay at the parsonage of the parents of Christian Bohr’s laboratory assistant. Niels procrastinated on Funen by reading Stages on Life’s Way. The day he finished it he enthusiastically mailed the book to Harald. “This is the only thing I have to send,” he wrote his younger brother; “nevertheless, I don’t think I could easily find anything better. . . . It is something of the finest I have ever read.”245 At the end of June, back in Copenhagen, again on deadline day, Bohr turned in his master’s thesis, copied out in his mother’s hand.
Harald had sprinted ahead of him by then, having won his M.Sc. in April and gone off to the Georgia-Augusta University in Gottingen, Germany, the center of European mathematics, to study for his Ph.D. He received that degree in Göttingen in June 1910. Niels wrote his younger brother tongue-in-cheek that his “envy would soon be growing over the rooftops,” but in fact he was happy with his progress on his own doctoral dissertation despite having spent “four months speculating about a silly question about some silly electrons and [succeeding] only in writing circa fourteen more or less divergent rough drafts.”246, 247 Christensen had posed Bohr a problem in the electron theory of metals for his master’s thesis; the subject interested Bohr enough to continue pursuing it as his doctoral work. He was specializing in theoretical studies now; to try to do experimental work too, he explained, was “unpractical.”248
He returned to the parsonage at Vissenbjerg in the autumn of 1910. His work slowed. He may have recalled the licentiate’s dissertation problems, for he again turned to Kierkegaard. “He made a powerful impression on me when I wrote my dissertation in a parsonage in Funen, and I read his works night and day,” Bohr told his friend and former student J. Rud Nielsen in 1933. “His honesty and his willingness to think the problems through to their very limit is what is great. And his language is wonderful, often sublime. There is of course much in Kierkegaard that I cannot accept. I ascribe that to the times in which he lived. But I admire his intensity and perseverance, his analysis to the utmost limit, and the fact that through these qualities he turned misfortune and suffering into something good.”249
He finished his Ph.D. thesis, “Studies in the electron theory of metals,” by the end of January 1911. On February 3, suddenly, at fifty-six, his father died. He dedicated his thesis “in deepest gratitude to the memory of my father.”250 He loved his father; if there had been a burden of expectation he was free of that burden now.
As was customary, he publicly defended his thesis in Copenhagen on May 13. “Dr. Bohr, a pale and modest young man,” the Copenhagen newspaper Dagbladet reported under a crude drawing of the candidate standing in white tie and tails at a heavy lectern, “did not take much part in the proceedings, whose short duration is a record.”251 The small hall was crowded to overflowing. Christiansen, one of the two examiners, said simply that hardly anyone in Denmark was well enough informed on the subject to judge the candidate’s work.
Before he died Christian Bohr had helped arrange a fellowship from the Carlsberg Foundation for his son for study abroad. Niels spent the summer sailing and hiking with Margrethe Nørland, the sister of a friend, a beautiful young student whom he had met in 1910 and to whom, shortly before his departure, he became engaged. Then he went off in late September to Cambridge. He had arranged to study at the Cavendish under J. J. Thomson.
29 Sept. 1911
Eltisley Avenue 10,
Newnham, Cambridge
Oh Harald!252
Things are going so well for me. I have just been talking to J. J. Thomson and have explained to him, as well as I could, my ideas about radiation, magnetism, etc. If you only knew what it meant to me to talk to such a man. He was extremely nice to me, and we talked about so much; and I do believe that he thought there was some sense in what I said. He is now going to read [my dissertation] and he invited me to have dinner with him Sunday at Trinity College; then he will talk with me about it. You can imagine that I am happy. . . . I now have my own little flat. It is at the edge of town and is very nice in all respects. I have two rooms and eat all alone in my own room. It is very nice here; now, as I am sitting and writing to you, it blazes and rumbles in my own little fireplace.
Niels Bohr was delighted with Cambridge. His father’s Anglophilia had prepared him to like English settings; the university offered the tradition of Newton and Clerk Maxwell and the great Cavendish Laboratory with its awesome record of physical discovery. Bohr found that his schoolboy English needed work and set out reading David Copperfield with an authoritative new dictionary at hand, looking up every uncertain word. He discovered that the laboratory was crowded and undersupplied. On the other hand, it was amusing to have to go about in cap and gown (once he was admitted to Trinity as a research student) “under threat of high fines,” to see the Trinity high table “where they eat so much and so first-rate that it is quite unbelievable and incomprehensible that they can stand it,” to walk “for an hour before dinner across the most beautiful meadows along the river, with the hedges flecked with red berries and with isolated windblown willow trees—imagine all this under the most magnificent autumn sky with scurrying clouds and blustering wind.”253, 254 He joined a soccer club; called on physiologists who had been students of his father; attended physics lectures; worked on an experiment Thomson had assigned him; allowed the English ladies, “absolute geniuses at drawing you out,” to do their duty by him at dinner parties.255
But Thomson never got around to reading his dissertation. The first meeting had not, in fact, gone so well. The new student from Denmark had done more than explain his ideas; he had shown Thomson the errors he found in Thomson’s electron-theory work. “I wonder,” Bohr wrote Margrethe soon after, “what he will say to my disagreement with his ideas.”256 And a little later: “I’m longing to hear what Thomson will say. He’s a great man. I hope he will not get angry with my silly talk.”257
Thomson may or may not have been angry. He was not much interested in electrons anymore. He had turned his attention to positive rays—the experiment he assigned Bohr concerned such rays and Bohr found it distinctly unpromising—and in any case had very little patience with theoretical discussions. “It takes half a year to get to know an Englishman,” Bohr said in his last interview. “ . . . It was the custom in England that they would be polite and so on, but they wouldn’t be interested to see anybody. . . .258 I went Sundays to the dinner in Trinity College. . . . I was sitting there, and nobody spoke to me ever in many Sundays. But then they understood that I was not more eager to speak to them than they were to speak to me. And then we were friends, you see, and then the whole thing was different.” The insight is generalized; Thomson’s indifference was perhaps its first specific instance.
Then Rutherford turned up at Cambridge.
He “came down from Manchester to speak at the annual Cavendish Dinner,” says Bohr. “Although on this occasion I did not come into personal contact with [him], I received a deep impression of the charm and power of his personality by which he had been able to achieve almost the incredible wherever he worked. The dinner”—in December—“took place in a most humorous atmosphere and gave the opportunity for several of Rutherford’s collea
gues to recall some of the many anecdotes which already then were attached to his name.”259 Rutherford spoke warmly of the recent work of the physicist C. T. R. Wilson, the inventor of the cloud chamber (which made the paths of charged particles visible as lines of water droplets hovering in supersaturated fog) and a friend from Cambridge student days. Wilson had “just then,” says Bohr, photographed alpha particles in his cloud chamber scattering from interactions with nuclei, “the phenomenon which only a few months before had led [Rutherford] to his epoch-making discovery of the atomic nucleus.”260
Bohr had matters on his mind that he would soon relate to the problem of the nucleus and its theoretically unstable electrons, but it was Rutherford’s enthusiastic informality that most impressed him at the annual dinner.261 Remembering this period of his life long afterward, he would single out for special praise among Rutherford’s qualities “the patience to listen to every young man when he felt he had any idea, however modest, on his mind.”262 In contrast, presumably, to J. J. Thomson, whatever Thomson’s other virtues.
Soon after the dinner Bohr went up to Manchester to visit “one of my recently deceased father’s colleagues who was also a close friend of Rutherford,” whom Bohr wanted to meet.263 The close friend brought them together. Rutherford looked over the young Dane and liked what he saw despite his prejudice against theoreticians. Someone asked him later about the discrepancy. “Bohr’s different,” Rutherford roared, disguising affection with bluster. “He’s a football player!” Bohr was different in another regard as well; he was easily the most talented of all Rutherford’s many students—and Rutherford trained no fewer than eleven Nobel Prize winners during his life, an unsurpassed record.264, 265
Bohr held up his decision between Cambridge and Manchester until he could go over everything with Harald, who visited him in Cambridge in January 1912 for the purpose. Then Bohr eagerly wrote Rutherford for permission to study at Manchester, as they had discussed in December. Rutherford had advised him then not to give up on Cambridge too quickly—Manchester is always here, he told him, it won’t run away—and so Bohr proposed to arrive for spring term, which began in late March.266 Rutherford gladly agreed. Bohr felt he was being wasted at Cambridge. He wanted substantial work.