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 :
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 a generation 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 Uebermensch .
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 do so in good faith, he explained because he was a citizen of Liechtenstein. Evidently John Nash differed from most of the world around him in at least 3 respects: (1) He was a genius; (2) He was mad; and (3) He had a sense of humor.
John Nash's remission from 'schizophrenia' ('Schizophrenia' is invoked so frequently in this country, that the international psychiatric community refers to it as ' the American diagnosis' ) 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 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 world outlook complements that of the community she describes; however she is on her own when she plummets to depths of ignorance where it does not normally swim .
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 I don't consider this 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 and Schuster did not assign or hire an editor with a good mathematics background( Lisker Enterprises Ltd. , perhaps? ) 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 tells us , David Hilbert made Goettingen University 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 the sense of a methodology for solving problems, in mathematics or any other science. Axiomatic expositions of human psychology and human communities have their beginning in the works of Spinoza in the 17th century.Somewhat illogically Nasar 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. Her 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 ;... etc. Question: 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 Schlaefli 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 pi ) has more than one limit point. In fact because pi is an irrational number, its iterates converge to 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 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 encountered : " e equals i to the pi minus -1 ". That is to say, either e = i to the( pi - 1) or e = (i to the pi) - 1 . The correct equation is e to the i times pi = -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 of them by consulting any 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 :
The very first sentence of A Beautiful Mind is
"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:
This emulatory verbiage grows in quantity and density until page 52, at which point her style virtually collapses under the weight of flatulent hype:
.... 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; (page 141: " They considered [Nash] a bad boy, but a great one, a great golden boy" ) ; 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 rhetoric 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 actually quite competent . It must therefore be the ideological universe that she inhabits which is so deplorable.
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. No competent musicologist would make such a statement: he would see Bach in the context of an extraordinary age of musical culture which made the composition of this fugue possible.Saxony's composers,Bach,Handel,Hasse,Telemann,Zelenka, etc., dominated European art music in the first part of the 18th century. Is one to conclude that Saxony's soil had a unique "something" which, at that time and at that time only, germinated some kind of "musical genius" gene? Halmos arrogates to 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.
This quotation from Halmos does however establish a tone of eugenic fascism that underlies Nasar's biography 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 a tendency to take 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 explain for us the sampling methods used to derive 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, 94.73372 % 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 Sylvia 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 a relatively obscure Italian mathematician named Emilio DeGiorgi . She doesn't call DiGiorgio 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, .....as well as 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, upon 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 ( Quote : "He remembered feeling ... in the presence of a great mind", page 333. This was when Nash had become 'legendary' as the Phantom of Fine Hall. ) , Ariel Rubinstein, Joergen Weibull, etc....
We now turn to the examination, first, of Sylvia Nasar's meditations on the erotic charms of a genius. Afterwards we will look at her views on psychiatry and schizophrenia and relate them to her theories of the causes of John Nash's insanity, and its remission. A final essay on the many uses of the word 'importance' in mathematical discourse will include a brief assessment of the importance of Nash's work for mathematics, science, history, and the future of 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, adding : "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, John followed by Nash , together signify some kind of high-born Anglo-Saxon ancestry. Anyone who thinks I'm making this stuff 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, say, Jose Domingo Rodriguez Gonzalez Rivera de San Miguel y Salamanca ! As if to ward 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 (1The Crown Prince Rudolf. His Mysterious Life After Mayerling; Dorrance, 1994 ) 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 supplies the bread-and-butter for 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 Ara£jo, 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