Sunday, 23 May 2010
John F Nash’s B Theory (from Bach to The Beatles)
At Princeton as an undergraduate, ‘Nash soon acquired a reputation for being both brilliant and odd. In the quadrangle, he rode a bicycle in figure-eights, over and over, and paced the hallways obsessively whistling Bach’s Little Fugue’ (Samels, 2002).
Bach’s Little Fugue was John F. Nash’s signature refrain, his calling-card; it is the thing that most people remember about him, according to his biography and most other accounts of his life, providing the point either of sympathy or more often annoyance in his relations with others. At Princeton, ‘the ten or so first year students were a cocky bunch, but Nash was even cockier. He loved sparring in the common room. He avoided classes. He was rarely seen cracking a book. Pacing endlessly, whistling Bach, he worked inside his own head’. Associated indelibly with his thought, his arrogance and his annoying presence, Nash’s whistling produced a number of complaints. Nasar reports that the mathematics secretaries at Princeton complained about him to his tutors and superiors (Nasar 2001). The whistling was annoying no doubt because of its monotony, but perhaps also because it established a relation of (dis)connectedness with people. It heralded his presence but also his absence, his indifference to those around him, being lost in thought. But there is evidence that Nash was also very aware of this effect, that the refrain had a representative function. It seems to have been in some ways analogous to speech, a statement not to anyone in particular, but concerning his existence: ‘I am thinking’ or ‘genius at work’.
John Nash’s paranoid schizophrenia became apparent at the age of 30 when he suffered a psychotic break triggered, among other things, by the prospect of fatherhood, a common trigger since it exposes the subject to the gap or void where the paternal signifier should be. Devoid of a paternal metaphor, there is no anchoring point for the psychotic, no ‘permanent monologue’, just ‘some kind of music for several voices’ (Lacan). With Nash music became the model both for repetition, the refrain that provides a point of stability, and the dissonant voices that constituted the major hallucinatory part of delusional activity. With Nash it could also be said to take on metaphorical significance to the degree that Bach’s Little Fugue functioned as his ‘signifier’. On one occasion, ‘knowing that his whistling irritated one particular music-loving mathematician, who frequently asked him to stop ... [Nash] once left behind a recording of his whistling on the man’s Dictaphone’ (Nasar, 2001). It is not just, here, that Bach’s Little Fugue comes to signify Nash or his thought, but that it can do so in his absence and in the absence of his interlocutor, and moreover through the vehicle of a dictaphone. It is a joke in which Nash’s own whistling substitutes for the other’s voice through the mechanism of the machine whose functioning betrays the presence and symbolic mediation of the Other in so far as the latter can be regarded as designated by music as an ambivalent form of social bond.
On a later occasion when Nash was teaching at Princeton and managed to solve a particularly intractable and coveted problem posed to him by colleague and rival Warren Ambrose, ‘Is it possible to embed any Riemannian manifold in a Euclidian space?’, Ambrose was generous and ‘took to telling his musical friends that Nash’s whistling was the purest, most beautiful tone he had ever heard’. Nash’s whistling, therefore, as both irritating noise and beautiful tone, is the point of amusia by which Nash is established in an extimate relation with the Other, qua bearer of the symbolic pattern, something that, as a psychotic, he would be unable to achieve in language.
Bach's Little Fugue in G Minor is more than just a simple refrain, as recognizable as it is to lovers of Classical music. It has a characteristically precise and mathematical structure in which initially two and then four ‘voices’ or tunes are counterpointed. No doubt the mathematical precision appealed to Nash, Bach along with Mozart was his favorite composer. Bach's Little Fugue has a precipitous momentum, starting relatively simply and sedately and then increasing its tempo, voices imitating and cutting across and undercutting each other. It could be easily imagined that these voices offer a model, even a metaphor, for schizophrenic subjectivity, described by Lacan as ‘some kind of music for several voices’; except, of course, that the four voices are held in exquisite aesthetic tension by Bach’s ‘math-musical’ structure.
In 1968, deep in the heart of his lost years of mental illness, Nash came up with his own metaphor for his subjectivity, ‘a metaphor that he couched in his first language, the language of mathematics’ (Nasar). On a postcard, Nash wrote of himself: B squared + RTF = 0. This ‘very personal’ equation represents, according to his biographer, ‘a three-dimensional hyperspace, which has a singularity at the origin, in four-dimensional space. Nash is the singularity, the special point, and the other variables are people who affected him – in this instance, men with whom he had relationships’ (Naser). They were the high-point of a narcissism that was noted by one of Alicia Larde’s confidantes who recalled that he was far from being infatuated with his wife, ‘he was infatuated with himself’. This self-infatuation became the basis for increasingly intense but brief relationships with young men like himself that culminated in his arrest – he was the victim of entrapment by a police officer at Muscle Beach, a location notorious for homosexual liaisons – and no doubt in reaction, marriage, fatherhood and breakdown in 1959.
The libidinal intensity of his narcissism is revealed in a letter he wrote to his sister. As Sylvia Nasar writes
After John Nash lost everything – family, car, the ability to think about mathematics – he confided in a letter to his sister Martha that only three individuals in his life had ever brought him any real happiness: three ‘special sorts of individuals’ with whom he had formed ‘special friendships’. Had Martha seen the Beatles’ film A Hard Day’s Night? ‘They seem very colorful and amusing’, he wrote. ‘Of course, they are much younger like the sort of person I've mentioned ... I feel often as if I were similar to the girls that love the Beatles so wildly since they seem so attractive and amusing to me’.
The four young men that he loved at MIT, the ‘RTF’ that culminates in the ‘B’ (for Jack Bricker, his greatest love of all the young men) are squared by The Beatles, four voices singing in counterpoint and in harmony, like Bach’s Little Fugue. At the other side of the equation is Nash at the 0 point of a singularity, screaming like the thousands of Beatles’ fans featured in A Hard Day’s Night, at Kennedy airport, at Shea Stadium, Nash’s Beatlemania opening up a fourth dimension. This structure can easily be mapped onto Lacan’s Schema L which features in Seminar III.
In this figure eight: 0 = Nash as singularity / void; o-o1 = Nash’s objects RTF, the sum of which is B for Bricker; B2 = the audio unconscious from Bach to The Beatles.
The 0 of the subject devoid of a signifier nevertheless locates the egoic image of its self-love in its objects, the young men designated by RTF that find their ideal image in the ‘B’ for Bricker. This is squared by The Beatles and Bach’s Little Fugue that provides the ‘speech’ of the subject in Nash’s whistling. However, the Other is a locus not here of signification but of music, the canon of music from Bach to The Beatles that runs from the fugue to the screams of Beatlemania that issue from the infinity of the singular point ‘0’ that opens up the fourth dimension.
As Nash’s delusions of persecution grew to cosmic scale, informed by theories that were ‘astronomical, game theoretical, geopolitical, and religious’. The dominant theory remained B theory, the math-musical theory that reached ‘sinthomic’ proportions: ‘I’ve discovered a B theory of Saturn’ he wrote in one of his many ‘Joycean monologues [that were] written in a private language of his own invention ... All the while he was working through his theories, B theory provided the organizing pattern, the theory of theories, as he would for days pace ‘round and round the apartment, his long fingers curled around one of [his mother's] delicate Japanese teacups ... sipping Formosa oolong, whistling Bach’.