Certainly I have seen thoughts put on paper before; but since I have come distinctly to perceive the contradiction implied in such an action, I feel completely incapable of forming a single written sentence… I torture myself to solve the unaccountable puzzle, how one can think, talk, or write. You see, my friend, a movement presupposes a direction. The mind cannot proceed without moving along a certain line; but before following this line, it must already have thought it. Therefore one has already thought every thought before one thinks it. Thus every thought, which seems the work of a minute, presupposes an eternity. This could almost drive me to madness.

Or this complaint, on the fragmentation of the self and its multiplying duplicity, which Bohr in later years was wont to quote:

Thus on many occasions man divides himself into two persons, one of whom tries to fool the other, while a third one, who is in fact the same as the other two, is filled with wonder at this confusion. In short, thinking becomes dramatic and quietly acts the most complicated plots with itself and for itself; and the spectator again and again becomes actor.

“Bohr would point to those scenes,” Rosenfeld notes, “in which the licentiate describes how he loses the count of his many egos, or [discourses] on the impossibility of formulating a thought, and from these fanciful antinomies he would lead his interlocutor… to the heart of the problem of unambiguous communication of experience, whose earnestness he thus dramatically emphasized.” Rosenfeld worshiped Bohr; he failed to see, or chose not to report, that for Bohr the struggles of the licentiate were more than “fanciful antinomies.”

Ratiocination — that is the technical term for what the licentiate does, the term for what the young Bohr did as well — is a defense mechanism against anxiety. Thought spirals, panicky and compulsive. Doubt doubles and redoubles, paralyzing action, emptying out the world. The mechanism is infinitely regressive because once the victim knows the trick, he can doubt anything, even doubt itself. Philosophically the phenomenon could be interesting, but as a practical matter ratiocination is a way of stalling. If work is never finished, its quality cannot be judged. The trouble is that stalling postpones the confrontation and adds that guilt to the burden. Anxiety increases; the mechanism accelerates its spiraling flights; the self feels as if it will fragment; the multiplying “I” dramatizes the feeling of impending breakup. At that point madness reveals its horrors; the image that recurred in Bohr's conversation and writing throughout his life was the licentiate's “bottomless abyss.” We are “suspended in language,” Bohr liked to say, evoking that abyss; and one of his favorite quotations was two lines from Schiller:

Nur die Fiillefuhrt zur Klarheit, Und im Abgrund wohnt die Wahrheit. Only wholeness leads to clarity, And truth lies in the abyss.

But it was not in Moller 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 Hoffding.” Harald Hoffding was Bohr's father's old friend, the other charter member of the Friday-night discussion group. 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 Soren 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 Hoffding student. It seems certain he also turned personally to Hoffding for help. He made a good choice. Hoffding had struggled through a crisis of his own as a young man, a crisis that brought him, he wrote later, near “despair.”

Hoffding was twelve years old when Spren 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 Hoffding 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. Hoffding 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 Hoffding interpreted him. Kierkegaard examined the same states of mind as had Poul Martin Moller. Moller taught Kierkegaard moral philosophy at the university and seems to have been a guide. After Moller'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.” From Miller to Kierkegaard to Hoffding 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 Moller'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. Tvivl in Danish means “doubt”; Tvivle-syg means “skepticism”; Tvetydighed, “ambiguity.” The self watching itself is indeed a commonplace of puritanism, closely akin to the Christian conscience.

But unlike Moller, who jollies the licentiate's Tvivl away, Kierkegaard struggled to find a track through the maze of mirrors. Hoffding, 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 reahty decision always comes through a breach of continuity.” 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. 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

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