VolXII #4 September 9, 1998

Editor, Roy Lisker 8 Liberty Street # 306 Middletown, CT. 06457 aberensh@lynx.neu.edu rlisker@yahoo.com

Note: A tribute was presented to me on my 60th birthday (September 24th, 1998) in the form of a webpage. It contains photographs and news clippings about me going back to the activism of the 60's; also writings, and commentary from Kenn Thomas, editor of Steamshovel Press, (free wheeling political conspiracy magazine published in St. Louis.) It's better than any resume I've ever put together on my own. Internet access is at http://www.umsl.edu/~skthoma/royalien.htm.

"A Beautiful Behind" Book Review: Sylvia Nasar: A Beautiful Mind, a biography of John Forbes Nash, Jr.; Simon & Schuster, 1998; $25; ISBN: 0-684-81906-6 I. This is a bad book: bad in its social philosophy, bad in its conception, bad in its scholarship, of bad mentality. It is intellectual biography reduced to the level of pulp fiction. However, it's a bad book about an important subject. As this subject is rarely written about, this may make the book important. Furthermore, the badness of the book is closely tied to the importance of its subject, and the importance of its subject has something to do with the importance of the word "important" in the meta-vocabulary of science , that is to say, the language scientists employ when talking to one another about science . I hope later to devote a section of this review to my insights on this important matter. The concerns of this biography ought to concern us for many other reasons as well, reasons which for the most part, probably never occurred to its author : A Beautiful Mind is the story of how the unstable psyche of an intelligent man, the mathematician John Nash descended, under the encouragement of the irresponsibility and corruption of an appallingly sick professional community, within the decadent institutional frameworks of a s ick civilization, into a psychotic breakdown lasting 30 years. I herein break with the self-reinforcement of tradition, in calling John Nash an intelligent man, not a genius; though many people would argue that there has been considerable evidence for the latter, but not much for the former. My own opinion is that Nash is not, and never was, a genius: the arguments will be grouped in the final section of this review. It makes some sort of sense to say that Archimedes, Gauss, Newton, Poincare and Einstein were geniuses - though I do not willingly undignify such accomplished beings with this trashy label. John Nash has never walked with them on their august promontory. Before the onset of his misfortune, between 1948 and 1958, Nash produced a steady stream of mathematical research papers of a high quality, nothing that anyone need feel ashamed of. Among the general public, raised on a diet of journalistic drivel, there are plenty of people who think that anyone who does research worth publishing in mathematics is a genius. And Nash was better than most. We need only retain the word, 'genius' in the vocabulary to describe an historical phenomenon dating back to the Enlightenment that has inflicted immense damage on our civilization. It is not going too far to say that the mystique of genius as it was applied to John Nash - by colleagues, university administrations, Cold War think tanks, journalists, friends, male and female sexual intimates, and inevitably, by Nash himself - was a major contributing factor in the destruction of Nash's life and mind. Indeed, a more woeful saga of make-believe, spoilage, vanity, ignorance, insensitivity and exploitation is scarcely to be imagined. Although Sylvia Nasar, via this book, places herself at the head of the groupie pack , her narrative gift and the thoroughness of her research go far to undermine her monument to 'genius infatuation' . Those of us able to read between the lines will value it for its documentation of the pitiable moral character of the American mathematics community in the latter half of the twentieth century. This review is divided into 3 parts. The first is a precise of the life and career of John Forbes Nash, Jr. The second discusses the merits and demerits of Nasar's biography. The third will be a general meandering on mathematics, mathematicians, and the value of Nash's mathematical opus. II. John Forbes Nash, Jr. was born in 1928 in Bluefield, West Virginia. His father, J.F. Nash, Sr., was an electrical engineer, his mother Virginia an elementary school teacher. In 1945 he won a Westinghouse scholarship to Carnegie Tech, majoring in chemical engineering. The chairman of the mathematics department at this time was John Lighton Synge, the noted relativist from the Institute for Advanced Study in Dublin, Ireland. Under Synge's guidance, Nash's outstanding talent for mathematics quickly manifested itself, and in 1948, Nash was offered scholarships from both Harvard and Princeton. He chose Princeton. although he has ever afterwards felt diminished by not being able to call himself a Harvard man. In the 1930's and 40's Princeton University set out, in typical American fashion, to create a world class research center through infusions of huge amounts of money. The predictable result was a nightmare. Princeton's reputation at the time was that of a finishing school for jocks from the deep South. They were being sent there for the business contacts and social veneer that might later prove useful in professional life. More specifically, "During the 19th and early 20th century Princeton University was a seed-bed for the education of southern white leadership. As a member of the class of 1928 once put it, 'Princeton is popular through the south because it is the one eastern school which does not enroll negroes.' Throughout much of its history the university has been described as a northern town that has its spiritual heart in the south. The social attitudes that prospered in the south were given free reign and support at the university and the town that sustained it." ( Web page of The Historical Society of Princeton ) By the end of WWII , Princeton's mathematics department was, if little more commendable, very different from the rest of the university. Exceptional mathematical talents, prodigies and whiz-kids recruited from all over the country were immersed in a mathematics pressure cooker, whipped into shape by the bully tactics of Solomon Lefschetz and others. This was to be a factory, unique in scientific history, for churning out mathematics theorems like automobiles from a Detroit assembly line. " On Nash's second afternoon in Princeton, Solomon Lefschetz rounded up the first-year graduate students in the West Common Room. He was there to tell them the facts of life, he said, in his heavy French accent, fixing them with his fierce gaze. And for an hour Lefschetz glared, shouted, and pounded the table with his gloved, wooden hands, delivering something between a biblical sermon and a drill sergeant's diatribe." ( A Beautiful Mind, pg. 58 ) The social life of Princeton University thus precessed erratically between the barracks life of the genius incubator and the drunken brawls of the 'true sons of the Confederacy'. The enormous differences between the groups at the polar extremes are obvious, but one should also note their similarities; callowness, rudeness, arrogance, inadequate or failed socialization, and a conviction of superiority over the rest of the human race, the jocks because of their breeding, the whiz-kids because they knew they were smarter than everybody else. It is clear that Princeton University of the late 40's served to catalyze Nash's life of mental illness. Its' unwholesome artificiality was compounded by an additional factor: the enforcement by the Cold War of tendencies to conformity, personified by the Princeton faculty and administrators, including math department inhabitants like right- wing hawk, John von Neumann. In 1944 von Neumann and Oskar Morgenstern published their Theory of Games and Economic Behavior . This treatise, and its subsequent editions of 1947 and 1953 , lit-up the halls of academic economics like a big light-bulb. This was due in large part to the promulgation of the paradigm of the "zero-sum, two person game" , which enables anyone to talk at great length about economic behavior, but has never had any application to situations encountered in the real world. Since Game Theory could thereby reduce much of economics to a Theoretical Game, it was highly fungible, which means that it could be readily adapted to such purposes as writing PhD theses, awards , honors, promotions and tenure, all in the name of the fatuous elaboration of the what-might-be-if-only. This being the oldest 'game' in academic life, Game Theory won its place in the living tradition that goes back to the scholastics of the Middle Ages, next to psycho-analysis, structuralism, the New Criticism, linguistic analysis and deconstructionism. In 1948 the twenty-year old Nash noticed that, by a slight modification of von Neumann's initial assumptions to include the notion of the 'non-cooperative game', one could treat each pure strategy as an independent coordinate in a multi-dimensional Euclidean space. This opened the way to the application of classical 'fixed point' theorems ( Brouwer, Kakutani), to prove the existence of equilibrium solutions ( situations in which no player can change his strategy without reducing his pay-off). Not every game has a Nash equilibrium point; not every equilibrium point constitutes an optimal strategy for anyone; and since Nash uses existence rather than constructive proofs, the only way to find these points in most cases is by trial and error. Uselessness thereby being pushed to a higher level, the result was hailed far and wide as the undeniable manifestation of "genius". The Nash legend was born. His insight was clever, but the actual mathematics involved is a triviality. Almost half a century later it was this footnote to an otherwise exciting mathematical career that would, in 1994, earn him the Nobel prize in economics. Any evidence that would lead me to concede that the Nobel prize has any real meaning would have upset me. As a general rule, the Nobel prize in physics is a fairly accurate indicator of the priorities of the science, the Nobel prize in literature is totally capricious, while the Nobel prize in economics is consistent in its emulation of mediocrity. Nash's prize does not provide a counter- example. On the other hand, he has deserved most of the prizes awarded to mathematicians , The Fields medal, Bocher prize, Crafoord prize, although he's never received them. Justice and politics come together at best by accident. Nash joined the faculty of MIT in 1951 , where he remained until quitting in 1959. From Nasar's account we learn that Nash carved out a special niche for himself in the pantheon of the world's worst mathematics instructors. Students in his classes were regularly derided and ridiculed. He called them "stupid" and "idiots" - to be fair, he didn't treat his colleagues any better. He ignored both questions and requests. He was fond of springing mid-term exams without prior notification. On a moment's notice he would turn his classes over to unprepared graduate students and hop off to the West Coast to cruise with his network of boy-friends. He was fond of placing classical unsolved conjectures, ( including Fermat's Last Theorem), on final exams, and questions like 'What is your name?' If the student simply wrote down his name rather than ' My name is ________' , Nash deducted 25% points from the grade. Although Nash was tottering on the brink of insanity by the winter of 1958, MIT's math department voted in January of 1959 to grant him tenure. This indicates the utter contempt in which it held its' students. There is a mythology which would have us believe that the granting of tenure at American universities is based on 4 factors: teaching ability, research, getting along with colleagues, and community service. Nash provides a paradigmatic example of the elementary truth, that research alone counts: this being the only factor for which his record was not abysmal. Perhaps, even as the mental hospital kept Ezra Pound out of the penitentiary, so MIT kept John Nash ( temporarily) out of the mental hospital. What is more mysterious than the way of the genius? In the early 50's, Nash also did some thinking of the unthinkable for the RAND corporation, the Cold War think tank in Santa Monica. The military's addiction to game theory has a lot to do with why the US persisted in and ultimately lost the Vietnamese war. John Nash, John von Neumann, John Milnor, Donald Spencer, Lloyd Shapley and other gamers from Princeton were not adverse to taking money from the government for 'research' that they well knew amounted to little more than esoteric fooling around. In 1955 Nash fell into a clumsy entrapment 'strategy' designed by the Santa Monica police department for catching homosexuals, and was summarily dismissed from RAND. Sylvia Nasar, with her admirable thoroughness, devotes an unbelievable amount of space to tracking down every one of Nash's homosexual liaisons. At the same time , A Beautiful Mind says almost nothing about his tastes in art, music, poetry, literature, philosophy, religion, cooking, flowers, wall paper, sports, etc. When his politics is discussed, it is only with reference to his insane delusions of the 60's and beyond. The words 'Civil Rights' and 'Vietnam' do not appear in the index. All does indeed look jaundiced to the jaundiced eye. It was in the period of his employment by MIT that Nash produced the 3 remarkable results that make him famous among mathematicians: the differentiable manifold-real algebraic varieties papers (1952); the solution to the isometric embedding problem (1954-56); and his work on bounding estimates for multi-dimensional parabolic partial differential equations (1957) . These will be discussed in a separate section which can be skipped by the amathematical or anti-mathematical reader. In 1953, John David Stier was born to Eleanor Stier and John Nash. Further commentary on this event is limited by my dependence on the account Sylvia Nasar's biography, the number of factual errors of which is of the same order as magnitude as its number of footnotes. Given her extensive documentation , we can assume that when she does make a mistake it is not a deliberate lie. Although the intellectual level of her discourse rarely rises above a television talk show ( Geraldo or, at best, Oprah Winfrey), one ought not forget that most of the social life of mankind, including that of great geniuses, is conducted at this level. By observing the world from a low perspective she is able to connect with the low behavior that people actually exhibit, which has the effect of making many of her observations reliable . Sticking with Nasar's story, John Nash's interest in Eleanor Stier seems to have been restricted to going to bed with her. He refused to marry her. It appears that he was too ashamed of her poor education and too vain of his ' superior social class' ( a fiction that Nasar relentlessly invokes) , to introduce her to any of the MIT illuminati. That his son, John Stier, migrated through two dozen foster homes before the age of 12, ( including refuges with delightful names like the " New England Home for Little Wanderers"), seems never to have ruffled him: why concern yourself with a mewling brat when you're busting your balls to give the world an isometric embedding theorem? Recall that for the first three years of John Stier's life, Nash was raking in a king's ransom from his work as a RAND consultant. Eleanor Stier found the nerve to sue him for child support in 1956, after she surprised him in his apartment together with his fiancée, Alicia Larde. Up until that moment she had continued to live and sleep with him: he did, after all, have a beautiful behind. His mental collapse ended a decade of astonishing productivity in mathematics. Between 1964 to 1966 he rallied somewhat to produce a handful of lesser results, after which, as far as we know, ( and the history of science is full of surprises, though not so many as nature itself ) , he has done nothing notable in his fields . His teaching career was over by 1959, which is something of a shame, as it should have ended in 1951. His manner of going insane was utterly admirable. Whatever nobility there is in the man surfaced in this period. One might even argue that his "genius" never deserted him, but merely changed fields from non-linear partial differential equations to guerrilla theatre. That most of his colleagues were too spaced out to recognize the Hamlet in their midst is entirely their fault, not his. The first hard evidence of insanity proclaimed itself on the afternoon of January 20th , 1959 ( Nasar, op, cit., pg. 241 ) in the lounge of the mathematics department of MIT. Setting the scene requires that we now devote a few paragraphs to the description of a typical afternoon in the common room of a typical mathematics department at a major university, something that can only be understood from direct experience. Further , it must be savored, studied, mediated in tranquillity, pondered in fascination. As a class, research mathematicians are competitive, rude, introverted, irritable and poorly endowed by disposition or training with the conventional social graces. It is a noisy silence, rather than voluble discourse, that fills the corridors and common rooms of research departments. People in divergent disciplines, logic and differential equations for example , use such incompatible vocabularies that they, literally, have nothing to talk about. Persons in somewhat similar fields, with overlapping vocabularies but perhaps a slightly different focus, may experience severe culture shock , similar in many respects to that of the average American tourist wandering about London, when they try to communicate with one another. Persons in exactly the same area of research also don't tend to talk to each other. On one level they may be concerned that others will steal their ideas. They also have a very understandable fear of presenting a new direction of inquiry before it has matured, lest the listening party trample the frail buds of thought beneath a sarcastic put-down. When an idea has developed to the point where they realize that they may really be onto something , they still don't want to talk about it . Eventually they want to be in a position to retain full credit for it . Since they do need feedback from other minds to advance their research, they frequently evolve a 'strategy' of hit-and-run tactics, whereby one researcher guards his own ideas very close to the chest, while trying to extract from the other person, usually by deceit, as much of what he knows as possible. Above everyone's head at a gathering of mathematicians hangs the scimitar of exposure of ignorance. Say you get into conversation with someone who brings up the concept of a "Riemann surface". You decide to risk all by confessing that you don't know what a Riemann surface is. The words are barely spoken when already the eyes of almost everyone else in the lounge is fixing you with a look of long-suffering, malevolent and self-righteous disgust . Never mind that your field is mathematical logic, or discrete semi-groups, or computability, or combinatorics, in which the concept of a Riemann surface rarely, if ever, enters. You are now forever type-cast as ignorant . Excessively insecure individuals, notably graduate students, may even start wondering aloud, ( behind your back naturally), what somebody like you is doing in their great department in the first place. Because just about everyone fears lest his ignorance be disclosed, people rarely open their mouths for any purpose other than that of speaking innocuous banalities. Or sometimes they may venture to talk about other subjects altogether, music, or politics, or Elizabethan drama. Yet one must be careful not to do too much of this, since there are some sorts who may begin suggesting that he's covering up his ignorance of 'real mathematics' by vaunting his knowledge of something else. Furthermore since many mathematicians do not cultivate interests outside of mathematics, such conversations on complementary subject matter soon peter out. Departmental teas tend to be held around 3:30 or 4:00, just before the afternoon seminars and colloquia. People sit apart, or in little groups, their minds consumed by calculation: (1) The obsessive-compulsive calculation of solutions to problems and equations. This goes on relentlessly , even in dreams. (2) The calculation of how much of what one thinks or knows may be safely revealed in a room of many potential enemies and few allies. At those times the climate of a mathematics lounge will be crippled by an oppressive and surly silence. Conversations will be punctuated with long, vacant silences, abstract gazing at the empty walls or out the windows, and excessive caution in speaking out. Hostility in all of its forms, subtle or crude, is omnipresent. Indeed the atmosphere may be so thick with tension that only a saber could cut it. On the afternoon of January 20th, 1959, John Forbes Nash Jr. , brandishing that day's copy of the New York Times, walked into something resembling the above in the mathematics lounge at MIT. In a strong voice he announced that he'd discovered that the little box in the upper left-hand corner of the front page ( the off-lede) carried a message from outer space aliens to the governments of Earth, which he alone was able to decipher. Pandemonium reigned long after he'd left. It's probably the only correct way to deal with such people. Most of us haven't got the guts to pull it off ; Nash did only because he was going crazy. Subsequent events would reveal that there was considerable method in his madness, though few people in the community got the message. Its' basic response appears to have been to try to help him get back to normalcy; no-one seems to have seen anything wrong with the way of life that produced his condition . Even so do Polonius,Gertrude, Claudius go to their deaths. Nash then ventured into the domain of Mail Art, a genre much cultivated by the Dadaists and Surrealists. A letter sent to the French mathematician, Claude Berge written in 4 different colors of ink complained that his career was being ruined by aliens from outer space. It was; I happen to be acquainted with several of those aliens personally. His next bold act of emancipation was the rejection of an attractive job offer from the University of Chicago. He wrote back thanking them for the offer, explaining that he could not accept it because he was about to be crowned Emperor of Antarctica. Most of us never get the chance to write such a letter. We can be grateful to Nash for rising to the occasion. Around the same period, one of his personal friends, the gentle Eugenio Calabi visited MIT and gave a lecture. Nash walked into the seminar room in the middle of his talk and started ranting at a student named Al Vasquez because he'd discovered a photograph of himself on the cover of Life Magazine, thinly disguised as Pope John XXIII. Nash had just discovered numerology: my experience as a "mathematics consultant for the arts" has revealed to me that numerologists ascribe horrendous "significance" to the number 23. Calabi ignored the disturbance, the audience ignored it. Only Vasquez, apparently, realized that something was amiss. This doesn't surprise me, since I've often witnessed similar things at mathematics lectures . One example: in the early 90's a famous Russian geometer was invited to UC Berkeley to give a series of lectures. His audience was so large that we had to be moved to the auditorium of the Bechtel Engineering Building. The stage on which he was standing was pitch-black. He assiduously covered 4 blackboards with equations, of which no-one in the audience could see so much as a decimal point. Yet such was the veneration in which the man was held, that nobody had the audacity to suggest that the stage lights be turned on. It was, in every sense, the 'Emperor's New Math' . In fact there was one exception - after 15 minutes of this bizarre performance, I was the one who stood up, left the auditorium, and roamed the building looking for a janitor. Of course, for the five minutes that I was gone, I was missing perhaps the most precious distillations of his wisdom. She came back with me, walked onto the stage, and turned on the lights. Seating myself once again , I'd the impression that I'd upset numerous members of the audience with the crime of distracting them from their distraction. On the afternoon of February 28th, 1959, at Columbia University in New York City , like Samson chained in the temple of the Philistines, John Nash finally brought the walls crumbling about everyone's head, not the least his own. He did this by presenting his stream-of-consciousness proof of the Riemann Hypothesis, the most intractably difficult conjecture in all mathematics. It was guerrilla theater at the acme. By that evening, most of the mathematics community between Boston and Princeton knew that Nash was mad. So what? The only victims of his madness would be undergraduate students, disposable cannot fodder in the best of times. However , by the end of April, Nash had been committed to McLean Hospital in Belmont, Greater Boston. Something had to be done; I don't fault people for turning to mental asylums in serious emergencies. They may at times be the only thing that the primitive psychiatric medicine of our society has to offer. If you're dying of malaria in the Amazon jungle, and the only remedy the local Native Americans have to offer is rattlesnake dung, you take it. The commitment was done by his wife, Alicia, the MIT administration, and the MIT psychiatric staff. He shared a room with Robert Lowell, who wrote poetry that hardly anyone reads, but who is famous nevertheless. Their co-habitation provides one of the narrative's moments of high comedy. As a regular feature of their daily routine, Lowell and Nash's room filled up with staff, students and other worshippers of genius. As the twin gurus expanded fulsomely on their delusions, ( most of the fulsomeness being Lowell's ) , the reverent crowds wrote down every word dropping, like sea-gulls darting for herrings, from their lips. Upon his release from McLean, Nash resigned his tenured post at MIT. This was to his credit , as he could probably have hung on there for the rest of his life and gotten away with doing nothing. There is a 'genius alcove' on the 4th floor of the MIT mathematics department where few dare to tread. His second son, John Charles Martin , having been born in the interim , his wife left him in the care of his mother-in-law and took Nash to Paris. There he embarked on what appears to have been the one truly noble gesture of his entire career: the renunciation of his American citizenship and self-declaration as a "citizen of the world", in the manner of Gary Davis. That it didn't work was only because the governments he had to deal with were as crazy as he was. It is characteristic of certain forms of insane behavior that they would be considered sane in a sane world; but since it isn't, they aren't. John Nash's realization that nationalism is an outmoded, ignorant and destructive delusion, aroused degrees of paranoia in many respects comparable to his own, in the officialdom of France, Luxemburg, Switzerland, Liechtenstein and East Germany. On April 21,1960, he was rounded up by the French police in his apartment on the rue de la Republique, escorted to Orly airport and put on a plane bound for the United States. In less than a year he would be undergoing insulin shock treatments at Trenton State Hospital. In some respects he was lucky . In this and subsequent incarcerations, doctors who raised the spectre of electroshock therapy were successfully thwarted by Nash's friends, family and colleagues, who managed to convince them of the obligation of protecting Nash's grey matter for the good of humanity. I myself have reason to be grateful for such type- casting. There is no doubt that the quasi-prodigy status that I acquired at the age of 15, when I was skipped out of 10th grade into a graduate program in mathematics at the University of Pennsylvania, was a principal influence on the decisions of my various doctors not to put me through electroshock therapy during my own brief bouts with psychosis in 1957 and again in 1973. Being labeled a "genius" has definite advantages: don't knock it. There was a temporary remission of his symptoms in 1965 . In 1967 he returned to his family , now living in Roanoke , Virginia. In the 3 years he stayed with them his mind was totally inflamed, engulfed by delusions of an intensity beyond anything he'd known up to that point. It was the worst period of his ordeal. In 1970 he returned to Princeton. His mother had died and his sister could no longer take care of him. On the threshold of homelessness, his ex-wife Alicia Larde, though no longer married to him, invited him into her house in Princeton Junction. He had good reason to be grateful to her: Nash never had to move into the New England Home for Little Wanderers. Nash's return to Princeton initiated his transformation from the local genius of the 50's to the genius loci of the next 2 decades. As the "Phantom of Fine Hall" , he wandered through the rooms and corridors of the Princeton mathematics department, wild, unkempt and harmless, obsessed with numerology, chalking cryptic messages on the blackboards. Some of them were prophetic . On a blackboard in the basement corridor linking Jadwin and Fine Halls, this message was uncovered in 1970 : " N5 + I 5+ X5 + O5 + N5 = 0 " His condition was indeed pitiful, his reason, ( according to any reasonable definition thereof), unhinged, and to some he served as an ambulatory object lesson to those who would offend the gods through forcing their intellects to dizzying heights at the cost of their immortal souls. This role actually turned him into a far more interesting human being than the one who, in those bygone days, divided his time between crapping on his students, working for 12-hour stretches on the isometric embedding theorem, then walking across the Harvard Bridge late at night to fuck Eleanor . All through the 60's and beyond, even in times when he was most extravagantly deranged, friends and colleagues kept trying to line up teaching positions for him, at the University of Michigan, Northeastern University, MIT, Princeton. The salvation of a genius seemed to them well worth the price of killing all joy in mathematics for generations of undergraduates. The general attitude of the mathematics community is best summed up by this quote from a member of Nash's legion of hero- worshippers, the mathematician Donald Spencer: "When I look at the human race all over the world, I think there's zero reason for humanity to survive. We're destructive, uncaring, thoughtless, greedy, power hungry. But when I look at a few individuals, there seems to be every reason for humanity to survive. [Nash] was worth doing the very best for." (op. cit., pg. 304 ) Spencer fails to tell us in what particulars Nash differed from his description of the rest of the human race; but I know what he means: All hail the eubermensch . The following example suggests that in some ways John Nash's outlook on the world was wiser in his mad period than in his previous sane state. After his return from Paris in 1960, Oskar Morgenstern offered him a high-paying consultant's job as a game theorist. The deal fell through when Nash refused to fill out the W2 forms: he could not because he was a citizen of Liechtenstein. Apparently John Nash differed from most of the world around him in at least 3 respects: he was a genius; he was mad; and he had a sense of humor. John Nash's remission from 'schizophrenia' began around 1983. By 1992 he was once again, in a manner of speaking, sane. He has remained so ever since , and we can only hope that his condition has stabilized. In 1994 he was awarded the Nobel prize in Economics for the clever take he'd done on Game Theory in his thesis of 1948, (a document of such awesome importance for the fate of mankind that no-one has ever thought it worth the effort to publish it ) . John Charles, after demonstrating real promise in college, has also been crippled by severe mental illness for most of his life. His story is perhaps more tragic than his father's, in that he has never had a chance to develop his potential. Given that society as a whole has absolutely no conception of what is genuinely productive, it may be that only the supreme deities know the definitions of usefulness , meaning and fulfillment in life. John Stier and his father have established strained relations. If we can believe Nasar, Nash still treats his son badly, but no longer irresponsibly. Guilt casts a long shadow. This concludes our obviously unbiased summary of the life of John Forbes Nash, Jr. We now turn our attention to the literary merits of " A Beautiful Mind". The fatuousness of Nasar's mentality complements that of the community she describes, but she is on her own when she plummets to levels of ignorance where it does not normally tread. III. The most benign of all the charges that one might level against A Beautiful Mind is that Nasar, almost without exception, garbles every mathematical example or explanation she presents . By itself that would not be a serious failing: she is not a mathematician and the book is not about mathematics. What is rather strange , given the hundreds of mathematicians she's interviewed , is that none of them took the time to correct her mistakes. Mathematicians tend to be an insolent and condescending clan. They may have glanced at the manuscript and, with a silent sneer, concluded that her intellectual powers were insufficient to the task. Still, it is odd that Simon & Schuster did not assign or hire an editor with a good mathematics background to weed out the more obvious errors. Starting on page 52 she elaborates her history of the origins of modern mathematics. In the 1920's, she says, David Hilbert made Göttingen in Germany the center of a "drive" to axiomatize mathematics. His disciples, arriving at our shores during WW2, continued his crusade to its eventual triumph in Princeton in the 40's. It is a charming fantasy but has nothing to do with the history of mathematics. Quote: " The axiomatic approach ... was in its heyday at Princeton in the late 1940s. Nash's paper [ The Bargaining Problem,] is one of the first to apply the axiomatic method to a problem in the social sciences. " Commentary : there never has and never will be an "axiomatic method ", in mathematics or any other science. An axiomatic exposition of human nature was the magnificent achievement of Spinoza in the 17th century. She herself, starting on page 12, raves about the way Nash's intuitive artistic mind operates by flashes of insight and is impatient with proofs that must be laboriously derived, often by others. On page 68 she quotes a conjecture posed by Nash that was worked on by John Milnor. The book's version goes like this: " Let V be a singular variety of dimension k, embedded in some variety M, and let m equal G(m ) the Grassmann variety of tangent k- planes to M. Then V lifts naturally to a k-dimensional variety V included in M. Continuing inductively, we obtain a sequence of k-dimensional varieties. Do we eventually reach a variety V which is non-singular?" Here is the correct version: " Let V0 be a singular variety of dimension k, embedded in some smooth variety M0 , and let M1 = Gk (M0 ) be the Grassmann variety of tangent k-planes to M0 . Then V0 lifts naturally to a k-dimensional variety V1 contained in M1 . Continuing inductively, we obtain a sequence of k-dimensional varieties V0<-- V1 <--V2 <--.... Do we eventually reach a variety Vq which is non-singular?" ( John Milnor, Mathematics Intelligencer,, Vol. 17, #3, 1995) Nasar's version is gibberish. Even someone who doesn't understand what the statement is saying can see that she drops all of the indices from Milnor's version, so that V0 , V1, V2 ,.... , and Vq all become "V". M0 and M1 become "M" , ( sometimes "m" ). The fact that these indices distinguish between different entities is vital to making sense out of the statement. On page 85 she refers to von Neumann's basic game theory result as the "stunning min-max theorem " . No more stunning than 6,000 other theorems. Can I give you my new proof of the stunning Pythagorean Theorem? On page 128 she reveals to us that "manifolds were a new way of looking at the world. " No more so than rap poetry, multi-culturalism or color television! She herself states in another place ( pg. 157) that the concept of a manifold has been around for a century, that the important conjecture proved by Nash's isometric embedding theorem was stated by Schläfli in 1870. On page 140 she presents an example of Nash's habit of putting unsolved conjectures on examinations. She claims that it isn't known if a certain sequence ( the successive iterates of the decimal expansion of _) has more than one limit point. In fact because _ is an irrational number, it has an infinite number of limit points. The real question must have been whether the limit point set was countable or uncountable. On page 157, she announces that "Riemann discovered examples of manifolds inside Euclidean spaces. " Yes; they're called doughnuts. All references to the life of George Bernhard Riemann are preceded by the catch-phrase "the sickly German genius" ; which could , of course, also be used to characterize Adolf Hitler. Further along on the same page she utterly garbles a description of a "Klein Bottle". In her hands it becomes an ordinary cylinder. On page 157 she confuses an embedding with an isometric embedding. This is not serious: many details are ignored or incorrectly stated with are apparent to a mathematician, but her discussion does convey the flavor of the idea to an informal audience. On page 201 however she produces the most thorough garbling of de Moivre's Theorem I've ever seen: " e equals i to the _ minus -1 ". That is to say, either e = i _____ or e = i _ - 1 . The correct equation is e i_ = - 1 . On page 217 she garbles something as elementary as the definition of a differential equation. On page 230 she informs all of us that mankind has yet to prove the Prime Number Theorem, a result known to all mathematicians that was proven over a century ago. On page 231 she asserts that 4-dimensional geometry and non- Euclidean geometry are the same thing. On page 336 she reveals that she is on shaky ground even in high school algebra. A formula such as "A to the fourth plus B to the fourth " is quoted as an example of "deep abstraction of the sort that real mathematicians perform. " As has already been stated, I don't fault her very much for these mistakes, although it is rather sad that she never gets anything right, doesn't know what she's talking about, and could have easily corrected all these mistakes by consulting a mathematician. One wonders why, since she expresses such unbounded veneration for mathematics, she didn't bother to check at least one of her mathematical examples carefully . The answer of course, is that deification is rarely appreciation, and hasn't got much to do with respect. ____________ We now shift our attention to a domain where her sins are more numerous and more consistently egregious: her embarrassing infatuation with 'genius'. This obsession permeates every paragraph, often every sentence. One can begin almost anywhere and arrive at the same place, but we have chosen to focus on three aspects of the phenomenon : (1) The density of the application of words such as "genius" and its many synonyms; (2) Shrewd observations about the traits geniuses allegedly possess (3) Adulation of the sexual characteristics of geniuses. (1) Synonyms for Genius The very first sentence of "A Beautiful Mind", opens with "John Forbes Nash, Jr. - mathematical genius " . The first sentence of the second paragraph begins " The young genius from Bluefield, West Virginia ". The first sentence of the third paragraph begins with "Genius, the mathematician Paul Halmos wrote... " Within the first 3 pages, genius or synonyms for the same idea, are used 15 times. In this same space she invokes this welter of attributions: ".... the eminent geometer Mikhail Gromov..." " ... great mathematical intuitionists.. ( Riemann, Poincare, Ramanujan)..." " ..the high priests of twentieth century science ( Einstein, von Neumann, Wiener) ..." "...supermen like Newton and Nietzsche..." "... the great Hungarian-born polymath, John von Neumann..." This emulatory verbiage grows in quantity and density until page 52, at which point her style virtually collapses under the weight of flatulent hype: ".... Kurt Godel, the Viennese wunderkind of logic..." "... Hermann Weyl, the reigning star of German mathematics..." ".. Einstein, the biggest star of them all..." "... Einstein ,..the pope of physics..." ".. Einstein, a world cult figure ..." " ... a bright light from the new generation, von Neumann..." " ... Princeton stars .. Hermann Weyl and John von Neumann.." "...Princeton...the new Göttingen..." " ... two young geniuses of Hungarian origin, John von Neumann ... and Eugene Wigner..." "... William James, the preeminent American philosopher..." "...Norbert Wiener, the most brilliant American-born mathematician of his generation ..." "..[Harvard's] legendary chairman, G.D. Birkhoff ..." "... [Harvard's] brightest young stars... Marshall Stone, Marston Morse and Hassler Whitney ..." " ...Harvard, once the jewel of American mathematics ..." "... the .,... critical mass of geniuses" " the .. German mathematical genius, David Hilbert ..." Like the media bombardment of advertising clichés for detergents and automobiles, the words quickly lose all meaning and fade into the background. Staples of her vocabulary include: .... Geniuses; giants; stars; superstars; supermen; bright young stars; crops of young geniuses; Olympian auras; Olympian perspectives; Olympian speech; intellectual Olympus ; Olympian detachment ; high priests; popes; intellectual elite ; mathematical elite; social elite; Catholic elite ; hotshots; fair-haired boys; bad boys; golden boys; ; boy wonders ; wunderkinder ; royalty; brilliant academics; brilliant young geniuses; undeniable brilliance ; royalty ; authorities ; idols ; leading lights; the most worthy; aka Great Man (capitals) ; Nobel Laureate (capitals) ; King ( capitalized ); visionaries; powerhouse departments; behemoth state universities; hothouse atmospheres ..... The writing style drips with this fatuous slop . One might be tempted to conclude from a perusal of this catalog that the book was targeted only for super-market shopping carts. However, when she is not writing about mathematics, mathematicians or universities, when she covers life in the mental hospitals, or Eleanor and John Stier's struggles for survival, or Nash's wanderings about Europe, the writing improves remarkably, becoming informative and even enjoyable. The unfortunate fact of the matter is that, as a writer per se , she is really quite good. It can only be the ideological universe that she inhabits that is deplorable. ____________ (2) Theories of Genius Paul Halmos' theory of two kinds of geniuses appears on page 12: " We can all run, and some of us can run the mile in less than 4 minutes; but there is nothing that most of us can do that compares with the creation of the G-minor fugue." The comparison is redolent with paradigm-worship; as much as I admire J.S. Bach, I think he might rather resent being type-cast as some kind of academic evidence of the existence of genius. Few musicologists would make such a statement: they would see Bach in the context of an extraordinary age of musical culture lacking which this fugue could not have been written. Halmos claims for himself the special ability to dissect a 'genius' out of the body of the vitality of an age in which was conducive to the production of great music. The quotation from Halmos establishes a tone of eugenic fascism that underlies the book like the deep structure of a Schenkerian analysis of Bach's G-minor fugue! To wit: (i) There is a special class of persons called 'geniuses'. (ii) Experts like Nasar and Halmos can tell us who they are (iii) They are born, not made (iv) Their names circle the roofs of high schools and teaching colleges; 90% of them are Europeans; 99.99% of them are men. (v) They are worth more than the rest of us (vi) One must apply different standards of morality to them (vii) Since there is no hope for the rest of mankind, we must enslave ourselves , heart and soul, to this saving remnant. Yet when one carefully examines the list of traits Nasar believes typical of geniuses, they turn out to be tired reruns of cliches traceable to the cult of the romantic hero of the early 19th century: geniuses are Napoleanic; they are 'men of sorrows' like Christ; or hedged about with eccentricity like Beethoven; they are lonely as Frankenstein's monster, indeed, they suffer torments of loneliness; sometimes, like Nietzsche it drives them mad; they are above petty morality, like Raskolnikov. Quote, page 24: , "...rejection is the price that genius must pay. " Nasar also has the tendency of taking very ordinary traits, found in millions of people, and treating them as traditional signs of the presence of genius: On page 15 she notes that " Many great scientists and philosophers ... have had similarly strange and solitary personalities. " Among them she includes Rene Descartes, Ludwig Wittgenstein, Immanuel Kant, Thorstein Veblen, Isaac Newton and Albert Einstein. From the witty Veblen to the ponderous Kant, from the humanitarian Einstein to the misanthropic Newton, a more diverse gang of rowdies is hard to imagine. If they had anything is common it was a tendency to introversion: ( translation, they thought a lot) . She does not display for us the sampling methods whereby she derives a statistical correlation of genius with introversion. On page 69 she writes: " a strong compulsion to learn by doing is one of the most reliable signs of genius. " And , I would hazard to guess, 94% of the human race. In the spring of 1949, while still a graduate student at Princeton, Nash " astounded everyone by inventing an extremely clever game. " The game was called, surprisingly , "Nash", sometimes "John". This, to Nasar is, " ...the first hard evidence of genius. " In fact, ( as she admits), the game was invented independently two years earlier by a clever Dane named Piet Hein. It was called Hex and marketed by Parker Brothers. She does not however assert that the invention of Hex was the first hard evidence of Piet Hein's genius! Hein is better known to the public for his collection of charming child-like cartoons, "Grooks". In the same way, in talking about Nash's work on parabolic non- linear differential equations, she uses the work "genius" three times in five sentences. Then she concedes that the same ideas had been published independently a few months earlier by an obscure Italian mathematician named Emilio DeGiorgi ; but she doesn't call him a genius even once. On page 128 she is impressed by the fact that Nash "works backwards in his head. " Elementary, dear Watson. On page 174 there is this revealing sentence which shows that she has made an exhaustive study of the history of the genius personality: " Matches between egocentric and childish men and self-abnegating and maternal women abound in the history of genius. " Well, you don't have to be a genius to be egocentric and childish, but it helps. Going even further on page 199 she attributes even his choice of a marriage partner as evidence of genius: " It was part of Nash's genius to choose a woman who would prove so essential to his survival. " What about Eleanor Stier? Sylvia Nasar is not alone. Without much difficulty she has uncovered Nash fan-club , more knowledgeable of mathematics than she , who trumpet the same tedious cant: "Nash} is the most remarkable mathematician of the second half of the twentieth century', Mikhail Gromov: page 12. What ever happened to Thom, Gelfand, Grothendieck, Weil, Wiles, Conway, Witten, .....and all my mathematician friends, whom modesty dares not allow me to list? " No one has a right to rob a genius of his freedom! " Adriano Garsia, hearing that Nash had been incarcerated in McLean, pg 257 "It blew my mind that someone who gave the appearance of being so simple could be a genius. " Jean-Pierre Cauvin, pg. 284 " I drove down to Trenton State...The attendant kept calling him Johnny. I told the people there, "This is the legendary John Nash." I kept thinking, my God, those shrinks! Who's going to figure out what's wrong with a genius? " John Danskin, on his first visit with Nash at Trenton State mental hospital, page 291. "Everybody wanted to help him. He was a mind too good to waste." Fagi Levinson. pg. 318 . Why not just help him because he's a friend in trouble? And the statement by Donald Spencer, quoted above, which renders explicit the eugenic fascism which is clearly at the core of these observations. Nash seems to always have had the ability to assemble followings of idol worshippers, less interested in what he has actually accomplished than in reveling in the intangible mystique of the man, his talents , his domineering personality, his mental instability or his sexual prowess: David Gale, Lloyd Shapley, John Danskin, Donald Spencer, Donald Newman, Mikhail Gromov, Jacob Bricker, Paul Cohen, Frank Wilczek , Ariel Rubinstein, Jorgen Weibull, etc.... ( To be continued over one or two more articles. As the material is already assembled, this review will be sent out to Ferment's subscribers in two -week intervals.) ************************************************************************ FERMENT IS A MONTHLY PUBLICATION. MANY OF ITS ARTICLES ARE ABOUT MATHEMATICS AND MATHEMATICIANS. IN THE PAST IT HAS INCLUDED ARTICLES DEALING WITH RENE THOM. ALEXANDRE GROTHENDIECK, ANDREW WILES, ALEXANDRE YESENIN-VOLPIN AND BENOIT MANDELBROT. SUBSCRIPTIONS ARE $25 PER YEAR. CONTACT ROY LISKER 8 LIBERTY STREET#306 MIDDLETOWN, CT 06457. THANK YOU.


Vol. XII #5 September 24, 1998 Editor, Roy Lisker 8 Liberty Street #306 Middletown, CT. 06457 aberensh@lynx.neu.edu rlisker@yahoo.com

Book Review:(Part II)

Sylvia Nasar: A Beautiful Mind, a biography of John Forbes Nash, Jr.; Simon & Schuster, 1998; $25; ISBN: 0-684-81906-6 The first article of this series concluded with some remarks on the pervasive "genius infatuation" of A Beautiful Mind. We continue with a visit to Sylvia Nasar's meditations on the erotic charms of a genius. Her views on psychiatry and schizophrenia lay the foundation for her theories of the causes of John Nash's insanity, and for its remission. A final essay on the many uses of the word importance in mathematical discourse includes a short assessment of the importance of Nash's work for mathematics, science, history, and all civilization. <<<>>> It may have been from an intention of enlivening public interest in her subject, that Sylvia Nasar never passes up an opportunity to remind us of the uniqueness of John Nash's sex appeal. Her frequent references to his cute legs seems to suggest that these continue even today to dominate all other attractions. On page 196 Joyce Davis, classmate of Nash's ex- wife , recollects 50 years after the fact that it was indeed his legs which attracted Alicia to Nash, to which she adds: "He looked like Rock Hudson." I encourage readers of A Beautiful Mind to browse through the photographs grouped after page 224 , to see if, in any of them, John Nash bears the least resemblance to Rock. On the same page Nasar startles us with the revelation that even the name "John Nash" has the power to arouse sexual desire. Its twin monosyllables, explains , “John” followed by “Nash”, signify some kind of high-born Anglo-Saxon ancestry: anyone who thinks I’m making this up is invited to consult the passage in question. In context, it seems to indicate that Alicia would have turned down her nose at some fellow ethnic suitor with a name like “ Jose Domingo Loyola Gonzalez Rivera de San Miguel y Salamanca ” ! Warding off the implication that she herself considers Alicia to be a member of some sort of sub-standard ethnicity, Nasar assures us that although Alicia was born in El Salvador, her roots sink deep into the humus of royalty. Page 191 is certainly the most depressing - shall we rather say appalling- performance in the entire book. After setting the tone of high pulp with the sentence "Alicia glowed like a hothouse orchid. " Nasar reveals that noble blood runs in Alicia's veins, Romanov or Hapsburg, she’s not sure which, and, for good measure, Bourbon as well. Side- stepping possible ties to Prince Norodom Sihanouk or the dynasty of Ibn Saud, this pretty much covers the terrain. From the footnotes we learn that this entire fabric of legend reflects the beliefs of uncle Enrique L. Larde. In his son's self-published book , the assertion is made that Enrique is the post-Mayerling bastard son of Archduke Rudolf. I did some work for vanity presses in the 60's, and I immediately recognized the kind of testimonial that provides the bread-and-butter of those shysters. Sylvia Nasar also suspects that these cobwebs of Enrique's brain may not be credible - all to the good, given that Alicia didn't inherit the Hapsburg nose/chin connection - so she digs up additional support for her thesis , that the Harrison-Lopez- Arthes -Larde family fits snugly into El Salvador's "social elite" . She knows this because, back in the 30’s, it “mingled with [El Salvador's] presidents and generals. Which, if true, can only mean that : (1) they were among the 300 families owning 98% of the nation's wealth, and, (2) they were welcome to come and go at the homes of card-carrying Nazis. And Nazis they were in those days! From 1932 until 1944, the year in which the Larde family fled to the United States, El Salvador was ruled by a real loony-bunny of a fascist dictator, General Maximiliano ( "El Brujo") Hernandez Martinez . After a coup-d’etat in which he ousted the elected government of Arturo Araújo, Martinez consolidated his power with La Matanza , a massacre in which 30,000 people were murdered in 2 months. Martinez soon established close diplomatic relations with Germany, Italy, Spain, Japan and of course the United States. El Salvador's army was trained by German colonels, its air force stocked with planes from Italy: “ In January 1932 Martinez permitted local elections to be held with the participation of the Communists ... After the Communists had won the vote [in certain districts ] the generals refused to allow them to take office. The Communists called for an uprising ... the uprising came to grief due to the division between the pure wage owners and the colonos and worker- peasants. The generals butchered between twenty and thirty thousand workers. Martinez found a modus vivendi with the Salvadoran bourgeoisie. The military kept the office of President and the politically important ministries, while the key positions in economic policy were filled by representatives of the bourgeoisie.. ( El Salvador, Central America in the New Cold War; Grove Press, 1981 ;Harold Jung, "Class Struggle and Civil War in El Salvador ", pg. 73 ) It is significant that the Larde family waited until 1944 to escape, the year in which Martinez was forced out of office by a coalition uniting left- and right-wing elements. The rise to prominence of which Nasar speaks , had to be bound up with this modus vivendi . This is not to imply that the Lardes were, or are, fascists, ( except for uncle Enrique, who seems to fit the part ) ; yet such connections hardly qualify them as aristocrats, or upper class, or distinguished, or elite, or whatever. Nasar continues through several pages to imply that they do . On page 193 she relates , in hushed tones of awe, that "Admission [ to Marymount High School for Girls in New York] was based strictly on families' social standing; the El Salvador ambassador wrote Alicia's letter of reference, attesting to the Lardes family social position. While establishing the claims of Prince John and Princess Alicia to the thrones of the Romanovs, Hapsburgs, Bourbons and, presumably, Plantagenets, Nasar takes time out to ogle Nash's physique. At age 20, she writes, (page 67) : "He had the build, if not the bearing of an athlete, 'a very strong, very masculine body', one fellow graduate student recalled. He was, moreover, 'handsome as a god', according to another student." Lest we think that Nasar is merely quoting citing 50-year old recollections of former class-mates, she adds: " His high forehead, somewhat protruding ears, distinctive nose, fleshy lips and small chin gave him the look of an English aristocrat." Imagine what Daumier would have done with that recipe ! In between she casts a few side glances at other mathematicians, telling us that (page 71) " John Milnor ..was..tall, lithe, with a baby face and the body of a gymnast. Milnor was only a freshman but he was already the department's golden boy." And that (page 73) Emil Artin, refugee mathematician from Germany, looked like a 1920's German matinee idol. " Back to Nash. On page 149, she reminds us that "Nash was built like a Greek God. " The legs surface again in a few places, even, on page 385, at the age of 70. Nasar's personal opinions, free from the protective coloration of quotation marks, emerge, resplendent in shameless nakedness when , on page 196, she calls him "A genius with a penis." Here is the exact quote: "It was his good looks, however, that made Alicia's heart beat faster, 'A genius with a penis. Isn't that what we all want?' an actress once quipped, and the quip captures the combination of brains, status and sex appeal that made Nash so irresistible." I guess I'm bemused, and more than a little flattered, to learn that mathematicians have any sex appeal at all, It makes me want to consider going back to doing mathematics full time. I doubt that I'd be able to reconcile the effort involved in fighting off all the women eager to get at me, with the long hours required for my research. <<<>>> Psychiatry The topic of "schizophrenia" is treated at some length in "A Beautiful Mind" . In the first article I stated that "schizophrenia" is known abroad as "the American diagnosis." My source for this refers to the 50's, (the period of Nash's first hospitalization) , and I'm sure it's still true today. Here is the reference: "...a given patient might be diagnosed quite differently from one country to another...The English call almost any kind of emotional trouble 'neurosis', said Henri Ellenberger, the great historian of psychiatry, in the mid-1950s. 'The French apply the diagnosis of feeblemindedness very liberally.' As for the Swiss, 'The French say that the Swiss diagnose schizophrenia is 90 percent of the psychotics and 50 percent of the normal.'" But nobody used the diagnosis of schizophrenia more often than the Americans. Schizophrenia was the great foible of American psychiatry. ..In one study, 46 American psychiatrists and 205 British psychiatrists watched a videotape of "patient F", a young man from Brooklyn who had a hysterical paralysis of one arm and a mood fluctuation associated with alcohol abuse. Afterward, 69 percent of the Americans diagnosed "schizophrenia", 2 percent of the British ( pg. 296, Edward Shorter, "A History of Psychiatry", John Wiley and Co, 1997) Sylvia Nasar's theories of schizophrenia are no worse than the fantasies current in modern psychiatry. Since she is a painstaking referencer, one need only consult her footnotes to learn the sources of her ideas. For the most part they come from the books cited in her bibliography. These writers emphasis the genetic theories of schizophrenia and the neuroleptic drug regimes in use today. Although Nasar does not regard psychiatry with my acerbic skepticism, she should not be charged with accepting all of its dogmas at face value. Here is her description of psychiatry as practiced at McLean's hospital at the time of John Nash's first incarceration: Fagi [Levinson] recalled that Alicia's pregnancy was thought to be the culprit. It was the height of the Freudian period-all things were explained by fetus envy. [Paul] Cohen said : "His psychoanalysts theorized that his illness was brought on by latent homosexuality." .....Freud's now discredited theory linking schizophrenia to repressed homosexuality had such currency at McLean that for many years any male with a diagnosis of schizophrenia who arrived at the hospital in an agitated state was said to be suffering from ‘homosexual panic.'" ( pg. 259) This, together with the above citation from Edward Shorter, implies that American doctors considered the density of repressed homosexuality in American society to be greater than that of England by a factor of 35 ! Which, combined with the oft-quoted figure of 1% for the percentage of schizophrenics in the human race, plus the ratio of 6 to one for the population of the United States over that of the United Kingdom , implies that........ Mazel Tov! If Nasar's picture of the symptoms and causes of schizophrenia lacks coherence, this is only because the contemporary psychiatric identifier , "schizophrenia", is not coherent. Drawing from the books of such psychiatric authorities, Nasar spreads the following list of "schizoid" symptoms across the pages of "A Beautiful Mind": ...The "schizoid state" is characterized by a sense of meaningless and futility.' ...John Nash was exceptional because "Men of scientific genius, however eccentric, rarely become truly insane", ... schizophrenia has a genetic basis and 'tends to run in families' ( Most of the literature in defense of this assertion can be traced to a single research finding, the Copenhagen twins study done in 1995 , a remarkable example of shoddy science. See Peter Breggin, "Toxic Psychiatry", St. Martin's Press, 1991, pg. 97 ) ... Schizophrenia 'leads to a lifelong pattern of social isolation and indifference to the attitudes of others' . ... consistent with her reactionary , even monarchist tone, she explains on page 271 , more or less, that radical political activity 'has long been a hallmark of a developing schizophrenic consciousness.' This assertion, if true, stands in stark contradiction to the one just above it. ... 'voices... are the most characteristic delusion of schizophrenia.' . What this statement says is that when a patient tells his psychiatrist that he's hearing voices, the psychiatrist is likely to write down a diagnosis of 'schizophrenia'. ....schizophrenics are 'insensitive to physical pain' . Finally, on page 258, we are provided with a bargain - basementful of symptoms: ...simultaneously grandiose and persecutory beliefs - tense, suspicious behavior - relative coherence of speech - ( relative to what? To other mental diseases? To what one ought to expect? To normal people?) - blankness of facial expression - extreme detachment of voice - reserve to the point of muteness ...... By now we begin to realize that the word 'schizophrenia' is a grab- bag into which one is welcome to throw anything that may be considered abnormal. This conclusion is evaded by Nasar's psychiatric experts through the use of traditional political loopholes of the form: Symptoms vary so much between individuals and over time for the same individual that the notion of a 'typical case' is virtually non-existent ...self-contradiction is also characteristic of schizophrenia, every symptom being matched by a 'counter-symptom...' , and so forth. Finally, as if to exculpate psychiatry from its vagaries , a former psychiatrist of Nash at McLean Hospital suggests , (page 318, footnote 36) , that Nash may not have been suffering from ‘paranoid schizophrenia at all, but ‘bipolar disorder’: “ The quality of ...two papers [written between 1965 and 1967] - the first of which geometer Mikhail Gromov called 'amazing' - constitutes the single strongest reason for questioning Nash’s diagnosis of paranoid schizophrenia. Being both everything and nothing, 'schizophrenia' can be conveniently employed to say everything and nothing. Nasar's account of modern psychiatric dogma is competently done, though I feel that she takes too much of it at face value. Unfortunately, she then abandons her doctrinal moorings to wander far out to sea with numerous theories, all of a sentimental, ad hoc or silly character, about the causes for Nash's insanity and its long-postponed remission in the late 80s. Most of these theories are her own, some were proposed by Nash's colleagues. Nash's own theories shed an interesting light on his character. Among them we find: .... teasing in elementary school ( page 188) .... the stress of teaching ( page 125. Proposed by Nash himself) .... fear of being drafted into the Korean war ( page 126) .... the horrible stories his father made of about what would happen if the Japanese invaded West Virginia. ( page 36) .... McCarthyism at MIT ( page 154) .... dismissal from RAND after his arrest ( page 188) .... because Emilio di Giorgi published his research on parabolic partial differential equations a few months earlier than his own (page 220. This theory was proposed by mathematician Gian Carlo-Rota ) .... agonizing too much over the contradictions of quantum theory ( page 221. Another Nash theory ) .... the rejection of his amorous advances by young logician Paul Cohen ( page 243) .... his failure to win the Bocher Prize ( page 243) .... the humiliation he was exposed to after the presentation of his proof of the Riemann Hypothesis ( Quote:, page 232: Nash's compulsion to scale this most difficult, most dangerous peak proved central to his undoing.) Apparently unaware of what she was doing, Sylvia Nasar systematically followed each account of every misfortune or setback suffered by Nash, with a statement to the effect that this was probably the cause of his mental collapse. It must be admitted that, given that "amateur" and "professional" psychiatry overlap so completely in our own day, her list of theories stands up fairly well against "fetus envy", 'homosexual panic' and the like. Nasar's views on the causes of his remission are grouped together in the 20 pages starting at page 335. Here she claims that Princeton functioned as a therapeutic community. The assertion is not unreasonable , although 20 years does seem like a long time for therapy to reveal its benefits . There exist mathematics departments that are dangerous for certain kinds of people, functioning as negative potential wells, in which they risk getting stuck in stable regimes for decades, sometimes their entire lives. The department at Stanford University apparently had that effect on Ivan Streletsky. His 20 years sojourn in its doldrums led to a major tragedy in the early 80s with the brutal murder of his thesis adviser . This Twilight Zone phenomenon is known to everyone who has spent a fair amount of time wandering about the mathematics community, yet I've never seen it described in published accounts . My own encounters with it have been at U. Pennsylvania, M.I.T. and U.C. Berkeley. It's very easy, by the way, to get typed as one of these individuals . They acquire a reputation as fixtures hanging around in the lounges and libraries. They may show up at lectures and colloquia where they tend to ask questions that have no connection with the subject matter. The public reaction to their remarks on these occasions hovers between a suppressed laugh and an embarrassed silence. Beyond making fun of them, few persons take much interest in their situation. Nobody does anything for them. They may live with their families, like Nash did, or have some other form of guaranteed income. Basically, provided they don't run interference with the grinding of the wheels of the great theoremizing engine, they're allowed to rot. Sitting alone in the departmental reading rooms, they appear to be off in a world of their own, perhaps with a math book or article on their lap or the table before them, perhaps with nothing at all. An unhappy young man whom I got to know, fitting this description, installed himself as the “phantom of the MSRI ( Math Sciences Research Institute) during the years 1983 to 87 when I lived in Berkeley. At that time he was in his 20’s. When I came back for a visit in 1996 he was still there, essentially unchanged. The staff and administration of the MSRI are very aware of his presence. I doubt that anyone has ever suggested constructive ways to help him. It's not their style. High-principled decisions to respect others' privacy are sometimes the easiest way out for those who just don't give a damn. Gangrene no doubt sets in elsewhere as well, ( I recall a few 'phantoms' around the NE Conservatory in the 80's. Of course there will always be administrators who think that anyone who isn't paying money to the institution is a phantom.) , but I suspect that it's only in mathematics where such situations are allowed to continue indefinitely, without anything being done about them. John Nash fit this category, with the very important difference that he had something to recover back into. Sylvia Nasar is certain that the "gentle manner" of his ex-wife Alicia Larde, "played a substantial role in his recovery." Alicia adds her own comments: (page 342) "Did the way he was treated help him get better? Oh, I think so. He had his room and board, his basic needs taken care of, and not too much pressure. That's what you need: being taken care of and not too much pressure." The issue is controversial, isn't it? Since Nash's marriage, the birth of their son, and Nash's first mental breakdown all occurred in the late 50s, one could argue, ( with as little scientific foundation), that it was the marriage itself that caused his illness, and that it took him thirty years to recover from it! Strongly motivated persons often thrive in situations in which basic needs are guaranteed. Many however go to seed , turning to alcoholism and self-justifying abusiveness or violence for lack of meaningful work. Still others may coast along for 20 years or more under such a regimen, getting neither better nor worse. All 3 elements seem to have been at work in Nash's case. These speculations of Nasar's are at least reasonable. On page 336, however, she makes the bizarre assertion that Nash's dabblings in Cabbalistic numerology kept his grey matter intact : "The immense effort [ of calculating and writing down numerological messages] may have played a role in preventing Nash's mental capacities from deteriorating." Her remaining suggestions are brought together in a single paragraph on page 353. All reveal a peculiar shallowness of perspective: " ..... high social class .... " ( A constant refrain, although no evidence is provided anywhere in the biography to show that Nash’s social class is higher than anyone else's . ) " ... high IQ ... "( Has anyone established a meaningful correlation between IQ and recovery from mental illness? ) "... high achievement ... " ( ditto. Our unlucky friends, Robert Schumann, Vaslav Nijinsky, Jonathan Swift, Vincent van Gogh, Friedrich Nietzsche , Antonio Salieri , John Ruskin ,Georg Cantor, Kurt Gödel ?..... ) " ... no schizophrenic relatives ... " ( what about grandfather Alexander Nash? ( page 26) : " a strange and unstable individual, a ne’er- do-well, a drinker and philanderer who either abandoned his wife and three children ... or, more likely, was thrown out." ) "... disease acquired in 3rd decade .. " (Although Nasar's own documentation of Nash's borderline pathology in his 20s. is excellent.) This somewhat arbitrary list is followed by ruminations on the role of hospitalization, psychogenic drugs, and even Nash's rejection of them. Everything and its opposite somehow contributed to his spontaneous remission. Nash's own theory appears to be the most sensible: I emerged from irrational thinking , he said in 1996, "ultimately, without medicine other than the natural hormonal changes of aging." ____________ On the Importance of "Importance" in Mathematics Take a hecatonicosihedrigon and multiply by four A sexicosihedrigon plus half as many more: Put in some polyhedrigons whose gaps suggest a minus And you'll have a polyhedral- perpendodicahedrinus! - ( Luran W. Sheldon, NY Times, 1910, in honor of William Sidis’s lecture on 4-dimensional geometry at Harvard at the age of 11) What is mathematics? Although mathematics is largely about values, that is to say numbers and their many generalizations, mathematicians tend to believe that mathematics is value-free. That this is far from the truth is seen by the fact that the science lay dormant for a thousand years between the time of Diophantus in the 3rd century G.R. and the revival of learning in the 13th. Still, most of us agree that numerical value, moral worth, and pragmatic usefulness ought not be confused. At the same time, "importance" is the word most abused in mathematical discourse . As part of their professional equipment, mathematicians are required to have a sense of what is "important" in the history of mathematics, in contemporary mathematics, and certainly in their own field. Sensible people do not work for very long on a difficult problem that they did not consider "important". Why the properties of prime numbers should be considered more "important" than the mathematical prodigy William Sidis's encyclopedic knowledge of the properties of trolley car transfers is not easy to put into words. The uses and interpretations of the word "important" vary so much from one person to the next that, were mathematicians as perspicacious as they should be, they would recognize how arbitrary it has become, and discard it as meaningless. Here, for example, is a short list of statements made by his colleagues about the value of Nash's research: "The embedding theorem .... is one of the most important pieces of mathematical analysis in this century. " John Conway. ( Although not an analyst, Conway is a great mathematician. I suspect him of making this comment because it sounded at the time like the right thing to say.) "[Nash's work on parabolic differential equations] .. which many mathematicians regard as Nash's most important work ." ( Sylvia Nasar. She doesn't tell us who they are, but they presumably work in the field of partial differential equations.) "The concept of a Nash equilibrium n-tuple is perhaps the most important idea in non-cooperative game theory." Economist P. Ordeshook. ( Notice the "universal qualifier" perhaps! Lots of people feel that Game Theory is "not important". ) "Let me describe an important application [ of the manifold-real varieties paper of 1951] " John Milnor. ( The application, the Artin-Mazur Theorem , is important to the theory of dynamical systems. One can find mathematicians who think that the field of dynamical systems is "not of much importance". ) "During these three years [ 1945-48, when he was still a teen-ager] , Nash completed an important piece of work on bargaining. " ( Harold Kuhn, mathematical economist at Princeton. ) "It gives me great pleasure to chair this seminar on the importance of John Nash's work on the occasion of the first Nobel award that recognizes the central importance of game theory in current economic theory." ( ditto. How "important" is current economic theory?) "In the short period of 1950-53 John Nash published four brilliant papers in which he made at least three fundamentally important contributions to game theory." John Harsanyi, co-recipient of the Nobel prize in economics, 1994. Without going into the details, everyone of these statements attributes a different meaning to the word "important". One is reminded of the story about the student employed by Thomas Kuhn's to proof-read the original manuscript of his "Structure of Scientific Revolutions". He told Kuhn that the word "paradigm" was being used in 64 different ways! The valuator, or validator "important" cannot be dropped from the meta-vocabulary because it is the very pillar, the spine of the entire enterprise: what sane person would spend weeks, months, even years, on a mathematics problem unless he ( and, increasingly, she ) thought it was important? The word determines careers, causes quarrels, ruins friendships, alienates the profession from the public, and vice-versa . One example: after Louis DeBranges of Purdue proved the "Bieberbach Conjecture" around 1986, he barn-stormed the nation, ranting and bullying conference audiences for not giving him the credit he deserved. No one , he fumed , thought that anything coming out of Purdue could be "important"! He finally descended into that black Slough of Despond, his own "proof' of the Riemann Hypothesis. When a lecture presented in a research department is poorly attended, there are usually two reasons for it: the first is that it's on a topic the department deems "unimportant". In 1997 I attended a lecture given by a woman whose very name is revered in applied mathematics, Olga Ladyshenksaya . Only a devoted handful were present at her talk. Applied mathematics is considered of "no importance" at Berkeley. The second reason is that it's too specialized topic, with so esoteric a vocabulary that only a few can understand it. Some people may be sitting in anyway, though uncomprehending : the subject is "important"! A life in mathematics conditions people to apply the powerful law of contradiction to many situations, even where inappropriate. It is easy to over-generalize but many mathematicians strong in computational ability and the gift of pattern recognition will be lacking in the kind of judgment that weighs alternatives, decision-making of the sort that is done by doctors, judges, politicians, etc. in their professional activity. The same criticism applies of course to their perceptions of the value, meaning, worth, or "importance" of their own fields . Such notions can be inflexible, biased, often unreliable. It is easier to say what is important in applied mathematics, because one can speak of its effect on the field of application. A new way of computing solutions to the Navier-Stokes equation will be deemed an "important" advance if these solutions lead to a deeper understanding of hydrodynamics, oceans, clouds, tornadoes, jet streams, etc. Thus the concept of the fractal is very important from the viewpoint of applied mathematics, though pure mathematicians see it as just slightly above the obvious. If one now defines pure mathematics as applied mathematics in which the field of application is mathematics itself, it becomes easier to decide matters of relative importance. Observe that discoveries of applied mathematics are not directly evaluated . It is in the effect of these results on the field of application that importance resides. Ingenuity of reasoning, prolonged labor of computation, high levels of abstraction, extensive command of knowledge count for little . "By their fruits shall you know them" is the only reliable criterion for judging the "importance" of advances in any scientific field. Take the two well-known theorems of Fermat. His last theorem is a conjecture. It might have been made by anyone, but because it was made by Fermat, mathematicians took a look at it. Formulating it required no particular insight; it's the kind of conjecture anyone might make after reading a book on number theory. Its importance is incontestable: it lay the ground for 4 centuries of incredible effort. Fermat's little theorem is also "important". This states that , where p is a prime and a is any positive integer. It can be proven by any talented high school student who's learned something about congruences in his course on the "new math". It is also among the most frequently employed tools in Number Theory. "Nash equilibrium" is even easier to "prove" than Fermat's Little Theorem. It gave economists the feeling that they were doing something useful. They therefore considered it very important; and to many people, Sylvia Nasar among them, a Nobel Prize proves that a result is important. Freudian psycho-analysis, the paradigm of a pseudo-science, is likewise important because it shaped world civilization for a century, The movie Jurassic Park was extremely important for Paleontology because it led to increased funding for dinosaur research. The flap of that butterfly's wing in the Amazon was also very important because it caused all the dreadful floods in China we've been reading about. The adjective "important" when applied to mathematics ought to be given essentially the same meaning that it has in other sciences. There are five of these: I. Tool-making: methodologies for problems solving II. Discoveries III. Solutions of outstanding unsolved problems IV. Introduction of new concepts V. Practical applications (I. ) In terms of problem-solving methods , Nash's and diGiorgio's papers on higher dimensional parabolic partial differential equations are indeed important. ( II. ) Discoveries in mathematics are like Vaughn Jones' discovery of the "Jones polynomial" in Knot Theory, or Euler's discovery of the properties of the number e = 2.718281828….., or Feigenbaum's discovery of the universality of the "Feigenbaum constant",__ . Nash has, to date, not made any discoveries of this nature . (III.) John Nash is unquestionably one of the great problem-solvers of history. The isometric embedding theorem is an "achievement" comparable, in mathematical terms, to batting 65 home runs. Surprisingly, it does not require that much of a command of mathematics to read his papers . Nash did not cultivate an encyclopedic knowledge of mathematics, or even of his area. He was rather like a mountain climber who, rising to a certain height, decides that he needs oxygen or an ice-ax, goes back to base camp to get them, then returns to the assault. Nash only learned what he needed to attain his objectives. It's amazing how much he did with so little, particularly when he is compared to those who know enormous amounts of mathematics but never do any notable research. (IV.) Nor did Nash introduce any new concepts: things like "transfinite number", "category derivatives", "fractal", "topos", "group", "manifold" , etc. These are ideas that illuminate the whole domain of mathematics . Another example is the idea of "probability" developed by Pascal and Fermat. The closest that Nash ever came to inventing a concept is the "non-cooperative game", a variant on the "cooperative game". In arguing that Nash was (is) or was (is) not a genius, one needs to look at all five of the above categories and judge him separately relative to the requirements of each. This already shows how unprofitable the label of "genius" is, mathematics being a field so rich in its diverse aspects that it is very difficult to judge the worth of discoveries without relating them to the purpose for which they were intended. Although it may be possible, in thought, to separate brilliance from the results of brilliance, it remains a futile exercise that is best carried out by journalists and their public, who will always be in need of miracle-workers and wizards to inspire them in their journey through this trackless wilderness of earthly existence. Mathematics is a monumental ediface. Some are the architects, others work on its construction. Still others design the wallpaper, decor, furniture, etc. If the word "genius" be applied to all of them, what term can we reserve for the Master Builders: Pythagorus, Brahmagupta, Archimedes, Descartes, Newton, Laplace. Gauss, Riemann, Galois, Jacobi, Kowalewski, Hilbert , Grothendieck ...? John Nash's remarkable gifts have been attested to by everyone qualified to understand them. Nor ought one discount his heroic accomplishment in rising above a prolonged ordeal of terrible suffering to return to the world of rationality, however fragile that world itself may seem. Unrelieved flattery is not complimentary, and its real , often hidden intent may yield destructive consequences. ____________ ____________ The Crown Prince Rudolf. His Mysterious Life After Mayerling; Dorrance, 1994 I. Gottesman, “ Schizophrenic Genesis: The Origins of Madness”, W.H. Freeman, 1991 ; G. Winokur and M. Tsuang, “The Natural History of Mania, Depression and Schizophrenia” American Psychiatric Press, 1996 ; L. Sass, “Madness and Modernism”, Basic Books, 1992; E. Fuller-Torrey, “Surviving Schizophrenia, A Family Manual”, Harper & Row,1988 Favorable as it might appear in comparison with the length of time for a classical psycho-analysis. Gregorian Reckoning The Prodigy, Amy Wallace; E.P. Dutton, 1986 ‘ blind luck’, some mathematicians claim , anxious to discredit its ‘importance’. #0...