a man who changed all our lives, although nine-tenths of humankind has never heard of him. The cheapest way to make the world richer would be to get lots of his like.
In each century there are a handful of people who, grappling with problems in their lonely brains, write a few equations on a few blackboards, and the world changes.
He marked up nearly all his achievements while he was mainly engaged in something else.
“Quantum mechanics,” said one physicist at Johnny’s death, “was very fortunate indeed to attract, in the first years after its discovery in 1925, the interest of a mathematical genius of von Neumann’s stature. As a result, the mathematical framework of the theory was developed and the formal aspects of its entirely novel rules of interpretation were analyzed by one single man in two years
that judgment was far too optimistic
Weimar Berlin’s horrid nightclubs and worse, was — once
Johnny in his German youth wanted to return math to the role of leading all intellectual progress, instead of so much of it being ad hoc. He wanted, by axiomatization, to rescue the then most modern part of math (set theory) from its alleged contradictions.
After reading Gödel’s paper in 1931, he instantly accepted his argument, called him the greatest logician since Aristotle, and (storing his own early experience as a German logician to architect the modern computer) turned to doing something else.
Because the reader will live with Johnny von Neumann for the next few hundred pages, it is time to introduce him physically and temperamentally.
Johnny’s fellow professors felt he looked like a banker instead. He nearly always wore a business suit, even when riding up a Colorado mountain on a mule. One of his colleagues urged him to “buy an old jacket, sprinkle chalk on it, and look more like us.”
Deep down, this apparently confident man was self-critical and rather shy. He hated arguments with anybody less intelligent than himself (i.e., almost all mankind), especially when he could crush that person with indisputable facts. He felt that crushing people was hurtful and rude and (most important) always resented. He was puzzled that most other thoughtful people had not noticed that resentment by anybody — from a Nobel Prize-winning colleague, to the president of the United States, or to a waiter — would usually hamper whatever thoughtful people wanted next to influence or do.
he had accumulated an inexhaustible stock of dirty rhymes and stories with which he would turn aside boring conversations that could degenerate into wrath.
he had concentrated hard when first reading them — in these two cases when he was trying to get a feel for proper English syntax before emigrating to the United States.
Johnny’s “talents as a host were based on his drinks, which were strong, his repertoire of off-color stories, which was massive, and his social ease, which was consummate. Although he could rarely remember a name, von Neumann would escort each new guest around the room, bowing punctiliously to cover up the fact that he was not using names when introducing people.”
When scientific groups at Los Alamos and elsewhere heard von Neumann was coming, “they would set up all of their advanced mathematical problems like ducks in a shooting gallery. Then he would arrive and systematically topple them over.”
A graduate student sometimes felt he was “riding a bicycle after an express train in which Dr. von Neumann was carrying away... more and more wonderful expansions of [other people’s] original ideas.”
when the Rand Corporation asked whether his computers could be modified to tackle a particular problem, which — as Rand staff explained to him for two hours on blackboards and with graphs — would understandably be beyond computers in their present state. For two or three minutes (see that obituary in Life again), Johnny stared so blankly that a Rand scientist later said he looked as if his mind had slipped his face out of gear. Then he said “Gentlemen, you do not need the computer, I have the answer.” While the scientists sat in stunned silence, von Neumann reeled off the various steps which would provide the solution... Having risen to this routine challenge, von Neumann followed up with a routine suggestion: Let’s go to lunch.
The slow way of answering is to calculate the distance that the fly travels on its first trip to the southbound front wheel, then the distance it travels on its next trip to the northbound wheel, and finally to sum the infinite series so obtained. It is extraordinary how many mathematicians can be fooled into doing that long sum. The short way is to note that the bicycles will meet exactly an hour after starting, by which time the 15-miles-per-hour fly must have covered 15 miles. When the question was put to Johnny, he danced and answered immediately, “15 miles.” “Oh, you’ve heard the trick before,” said the disappointed questioner. “What trick?” asked the puzzled Johnny. “I simply summed the infinite series.”
matters that, in one of his favorite phrases, could “potentially jiggle the planet.”
He felt the whole concept of numbers had to be reoriented for the computer age, and feared it had not been.
To these four challenges — the atom (pressing on to secure virtually free energy via nuclear fusion), the brain, the gene, and the physical environment — he sometimes added his hopes for the introduction of mathematical rigor (i.e., proper science) into the worthy but twittering faculties of economics and their even weaker sisters in today’s social half-sciences.
My own guess is that, once he had completed the modernization of America’s deterrent under Eisenhower, he would have wanted to go back to help mathematize lots of other people’s subjects. Mathematics has proved a marvelous tool for guiding developments in physics, but it is aggravating that nobody has yet managed to make such activities as psychiatry and stimulation of the human learning process into mathematically respectable professions. Johnny was worried that too few of his fellow professors could, in their own subjects, like economics, show that one thing will always follow from another.
The languages we use, he said, are clearly a historical accident, as is shown by the multiplicity of them. “Just as languages like Greek or Sanskrit are historical facts and not absolute necessities, it is only reasonable to assume that logics and mathematics are similarly historical, accidental forms of expression.” He thought that “when we talk mathematics we may be discussing a secondary language, built on the primary language truly used by the central nervous system.”
he waxed rather rude (unusual for him) about the “ignorance” of modern economics. He snorted that “economic problems are often stated in such vague terms as to make mathematical treatment appear a priori hopeless because it is quite unclear what the problems really are.” He found economics and much other social science to be incomparably cruder than physics was in the seventeenth century — before “God said: let Newton be,” and so mechanics and the scientific and industrial revolutions began.
Newton’s breakthrough to the mathematization of physics, said Johnny, “brought about, and can hardly be separated from, the discovery of the infinitesimal calculus... It is therefore to be expected — or feared — that mathematical discoveries of a stature comparable to that of calculus will be needed in order to produce decisive success in this field [economic and other social science]... It is unlikely that the mere repetition of the tricks which served us so well in physics will do for social phenomena too.”
“a considerable segment of chemistry could be moved from the laboratory field into the mathematical field if one could integrate the applicable equations of quantum theory.”
Remember that when Johnny plotted how to control the world’s weather, and to do so many other things, he was operating with the equivalent of a pocket calculator like that. ~
Remember that when Johnny plotted how to control the world’s weather, and to do so many other things, he was operating with the equivalent of a pocket calculator like that.
Johnny believed that sometime after the 1950s scientists should have made sufficient advances in meteorology to start to control the weather, not merely to forecast it.
he thought we would discover a manageable sort of nuclear fusion. “In a few decades” the release of energy from storage in matter (“the transmutation of elements, alchemy rather than chemistry”) would bring mankind a new sort of energy that would be as free as “the unmetered air.”
It was typical of Johnny that he reacted in the early 1950s to these interesting thoughts, about the greenhouse effect and potential Krakataus, not with despair but with a determination to turn them to man’s advantage.
His antennae bristled with his usual suggestions for seize-the-opportunity projects, such as painting the ice caps a different color. “The persistence of large icefields,” he said, “is due to the fact that ice both reflects sunlight energy and radiates away terrestrial energy at an even higher rate than ordinary soil. Microscopic layers of colored matter spread on an icy surface, or in the atmosphere above one, could inhibit the reflection-radiation process, melt the ice and change the local climate.”
He foresaw horrid problems such as possible nasty forms of climatic war (perhaps the Soviet Union might threaten to fasten an ice age on North America), but he did not expect computational difficulties.
he would be delighted that his computers had increased so much in number and power. He would be astonished that they were used so widely, but depressed that they were not used with greater scientific success.
the notion of adults fulminating against computers as corrupters of youth in the form of video games would have amused and perhaps secretly pleased the playful, childlike aspect of his personality.”
imprecise sciences (including economics and club-of-Rome-type ecology) use too many models that stench ludicrously of garbage in and therefore garbage out.
the fashion in very clever mathematics has swung back to saying that matters are infinitely more complicated than some precomputer mathematicians thought, that the movement of a butterfly’s wings over Beijing today can affect next month’s storm patterns over New York, that a beautiful chaos rules where old-fashioned calculators assumed there should be order. Johnny’s whole bent, from about age nine, was to try to restore order where other people saw chaos.
This division — between those who find the unfathomable inevitable and beautiful, and those who find it irrational and thus needing to be changed — has been a usual split, or perhaps cycle, among mathematicians for twenty-five hundred years.
“we meet these two distinct and antagonistic types of mind: the justifiably cautious who hang back because the ground quakes under their feet, and the bolder pioneers who leap the chasm to find treasure and comparative safety on the other side.”
Johnny exuded a genuine bewilderment that minds like Zeno’s cannot see that infinitely many quantities such as one, one-half, and one-fourth can add up to a finite quantity, including the position where the tortoise is.
Archimedes (287-212 B.C.). By calculating the value of 𝜋, discovering the science of hydrostatics, and nearly discovering calculus, Archimedes did even more for his generation of mathematicians than Johnny did for ours. Archimedes ended his life by hurling stone shots, each weighing over a quarter of a ton, from his supercatapult to destroy a Roman fleet. Like Johnny, he thus ended as his country’s most mathematical armorer.
Both the cautious and the chasm leapers are needed, but the leapers matter more.
the cautious ones generally “committed but few mistakes and were comparatively sterile of truth no less than of error”; whereas darers, like Archimedes and Johnny, have “discovered much of the highest interest to mathematics and rational thought in general, some of which may be open to destructive criticism,
This book is a study of an exceptionally well-balanced man who — without pushfulness or expenditure on public relations — became the most quietly effective mathematical mind of this century.
the early twentieth-century Hungarian education system that (this book will argue) was the most brilliant the world has seen until its close imitator in post-1945 Japan.
If he stayed in his native country, Johnny had no great hope of success. He therefore had to do his profound thinking (the ordinary mind boggles at this) in three different workaday languages in succession.
brilliant intellectual atmosphere — with academic colleagues making scientific breakthroughs almost every month
even the materialism of the United States, which was greater than that of Europe, appealed to him.” A liking for material wealth possibly is a usual characteristic of men with effective minds (which Johnny was), although not of saints (which Johnny was not).
Two problems of this book are, first, a danger of being rude to various scholars who were slightly less clever than Johnny but much cleverer than you or me; and, second, a danger of praising Johnny too glutinously.
His mind was not as original as Leibniz’s or Newton’s or Einstein’s, but he seized other people’s original (though fluffy) ideas and quickly changed them in expanded detail into a form where they could be useful for scholarship and for mankind.
He rightly deemed that this was clever people’s duty and their great fun, so he was not worried that he was not credited with all his due by the general public and the newspapers
One of the professional ways in which he wrung more than twenty-four hours’ work out of a twenty-four-hour day was to get the boring research on some projects done by collaborators whom he enthused by gasping that they were famously expanding their own original ideas.
we were all surprised at the first question from a professor of philosophy at the University of Amsterdam (John Dorling). He asked whether Johnny thought of himself as a philosopher, because it was arguable that he was the most versatile philosopher of the century. “In about six areas of philosophy, von Neumann made very substantial contributions... turning vague problems into ones that could be precisely formulated mathematically.
The daunting problem about these geniuses is that at first perhaps only about three hundred people understand what on earth they are saying.
Johnny’s especial skill was to pick out work that seemed surprising and therefore interesting. He was bored with mathematical discoveries that he assumed should have (and perhaps had) been made long ago.
in 1945-53, when he thought that an eventual war between the United States and Stalin’s Russia was very probable. He deemed it his duty to think out ways in which, despite such a catastrophe, his United States and some other parts of the planet could be saved from destruction.
Johnny was not as neurotic about spies as were most of those who understood Stalin. He thought Russia would find that the secret of the A-bomb was an easy one for educated men to work out.
He also worked out, again coldly and mathematically, how deployment of this would be most effective. He was clear about what needed to keep on being said.
This pacifism within his profession grieved Johnny because most of the near-pacifists were nicer men than his allies the hawks. He did not argue with many appeasers of Russia. Here again he showed the characteristic that he did not like to argue with anybody. He much preferred to give advice to those who asked for it, not to quarrel with those who did not.
At first this made him a bad chairman of committees, which may sound strange to those who regarded him as the Eisenhower administration’s master committee chairman in his last three years. The difference came when he could pick his committees’ membership himself.
“He had the invaluable faculty of being able to take the most difficult problem, separate it into its components, whereupon everything looked brilliantly simple, and all of us wondered why we had not been able to see through to the answer as clearly.”
among all the scientists then arguing about how not to destroy the world, “Dr. von Neumann is one of the very few men about whom I have not heard a single critical remark. It is astonishing that so much equanimity and so much intelligence could be concentrated in a man of not extraordinary appearance.” This equanimity was one of the ways in which Johnny quietly got things done.
The booming Budapest of 1903, into which Johnny was born, was about to produce one of the most glittering single generations of scientists, writers, artists, musicians, and useful expatriate millionaires to come from one small community since the city-states of the Italian Renaissance.
New York and Chicago had gained in confidence in 1865 as the biggest cities on the winning side in a civil war, in a food-producing prairie country that knew it could emulate and then surpass antique Europe. Hungary felt the same surge by winning home rule within Austria-Hungary in 1867, in a food-surplus prairie country that felt it could emulate and then surpass antique Austria.
Within a booming city, where the biggest taxpayers were a progressively changing group, Budapest acquired rather nationalist and sometimes nouveaux riches city fathers who wanted to spend what was largely their families’ own money on making Budapest a more cultured and more beautiful city than Vienna.
Krudy claimed that even Budapest’s prostitutes “were pretty and young enough to be princesses in Berlin.”
These qualities (both for 1890 Jews and 1990 East Asians) included family traditions of togetherness and hard brain work and hunger for education, a willingness not to annoy host communities by turning very political, general classlessness in not aiming for the most prestigious life-styles but going instead for the main chance.
The younger daughter Vilma, always known as Lily, conceived in her teens a passion for Alcsuti. She pouted and went into sulks until he married her.
The next great Budapest surge in 1910-30 was a burst of creativity in science and mathematics, to which Jews appear to be drawn wherever they are found,
Johnny often made Jewish jokes to his fellow mathematicians. “Die Goim haben den folgenden Satz bewiesen” (The Goys have proved the following theorem), he once said to Stan Ulam in Princeton about some non-Jewish mathematicians’ results — implying that, as Jews, Ulam and he should have got to it first.
Max turned the family lunch table and supper table into formidable seminars on every conceivable intellectual and topical subject, enlivened by his wit and by his singing of his Edward Learish ditties, in which the children and Margaret delightedly joined.
There was an especial early emphasis on learning foreign languages. Max thought that youngsters who spoke only Hungarian would not merely fail to prosper in the central Europe then darkening around them. They might not even survive.
There was also a music teacher to teach piano, but she, too, failed somewhat with Johnny. An attempt to teach him the cello proved bizarre. The family was disappointed that he never appeared to move beyond practicing scales. It turned out that he had learned to prop a math or history book on the music stand. He was devoting his full attention to his reading while his fingers moved routinely through the exercises. He was dangerously apt to do the same thing later while driving an automobile.
Children and even some adults still sometimes ask, “What is the use of learning Latin?” Henceforth the answer should be: it could give you a sufficiently tidy mind to grow up and invent something logical like the modern computer.
Max did not push his oldest son, but he quietly saw to it that the path ahead was clear.
When his mother once stared rather aimlessly in front of her, six-year-old Johnny asked: “What are you calculating?”
In political conversations from the 1920s to the 1950s he would sometimes avoid controversies by reminding people how unexpectedly some political events had turned out in 500 B.C.
Nicholas was particularly impressed by the minilectures that Johnny gave at the supper table after reading Oncken and other books, sometimes only recording what he had read but often throwing up new thoughts that had occurred to him while reading.
The mealtime habit that Max encouraged was that the members of the family, including himself, should each present for family analysis and discussion particular subjects that during the day had interested them.
the star of these seminars (as the sometimes present Alcsuti insisted) was the governing Max. He would bring his workaday banking decisions back to the family. He asked the children how they would have reacted to particular investment possibilities or balance-sheet risks, weighing social responsibility in helping worthwhile sponsorable projects against the obligation to make money for all connected with the firm, including the shareholders but the workers too. He discussed which activities he had delegated to which of his staff. He asked whether the children thought he should have reserved more or fewer of the difficult decisions for himself.
Johnny was also introduced to banking as a romantic occupation.
one part of his brain from school days was taught always to assess anything he did in terms of potential yield to the community, as measured against what could otherwise be too escalating a cost.
Max did not use these meals to show off Johnny to such men, but did draw out their minds for Johnny to observe.
the gymnasium system gives dignity to those who provide instruction in top secondary schools. A scholar or scientist who knows that his talents lie in pedagogy rather than in research does not feel he is falling back if he spends his whole life teaching in such a school.
The average Japanese eighteen-year-old is today more advanced in math than all except the top 1% of American eighteen-year-olds.
The answer to “the huge mystery of 1890-1930 Hungary’s educational achievement” lies largely in those figures. Hungary’s post-1870 willingness to import middle-class Jews — because of its Magyar aristocracy’s contempt for its majority of non-Magyar peasants — attracted the brightest and most educationally ambitious of Europe’s Jews to Budapest.
Many arrived in the 1890s when Hungary’s counts and barons and monks and pastors had a new ambition: to produce more brilliant scholars and generally cultured young men than Vienna did. A discriminately excellent supply streamed into a competitively excellent schools system.
Theodore von Karman (born 1883) was senior to all the famous Hungarian scientists who made their way to the United States, where he pioneered the science of aerodynamics, enjoyed a long and productive career at California Institute of Technology (CalTech), and was accused of inventing consultancy.
Thirdly, there were the Real gymnasia, the word “Real” being pronounced in two syllables and signifying urban or practical rather than genuine. There were several such schools in Budapest, which provided comparatively little Latin and less Greek. They concentrated more on modern languages and such mundane courses as engineering drawing.
It was designed to produce candidates for technical institutions rather than classical universities — in American terms, for MIT and CalTech, rather than for Harvard and Stanford.
For Johnny, Max von Neumann chose the Lutheran. It could be relied on to deliver a serious education in Latin and Greek, which was no small matter to Max. To his father, Johnny was not so inevitably a mathematician as he might appear to others, and avenues should not be closed when a child is nine or ten.
It is the myth of four extraordinary young Hungarian Jews, born at much the same time in more or less the same district of Budapest, who attended the same school together, became brilliant scientists there, and emigrated en bloc to the United States where they created, with only modest assistance, the A-bomb.
Szilard hurried to patent the idea of a chain reaction and assigned the patents to the British admiralty for safekeeping. It is not clear whether in wartime he intended to tell Hitler or Los Alamos that blowing up the world was a breach of his private patent.
Johnny’s most usual motivation was to try to make the next minute the most productive one for whatever intellectual business he had in mind.
William Fellner, one of his schoolmates, recalled with admiration that Johnny not only clearly enjoyed those classes but also was in his own fashion working to learn from them, although what he was learning was not what the courses were designed to teach. He had understood that already, before the age of ten.
Wigner, it turned out, knew quite a few of those useful theorems but was ignorant of others. Johnny paused for a few moments of deep thought. Using only the subsidiary theorems with which Wigner was acquainted, he then provided a proof of the theorem with which the discussion had begun. It made the proof a good deal clumsier than it had to be, but Johnny’s view appeared to be that if Wigner wanted a proof, he was entitled to have one.
Wigner selected the two numbers and set himself to totting up their product in the conventional way while Johnny marched into his corner. Several minutes of muttering ensued; it was not proving to be easy. But Johnny eventually turned and delivered his answer. Wigner congratulated his friend warmly; he was impressed. Was his answer correct? Johnny asked. Wigner was obliged to reply that it was not. “Then why on earth,” Johnny asked, “are you congratulating me?” Wigner was not to be shaken. Johnny, he said, had come remarkably near.
Because complications usually disappeared before him, he would sometimes go the more complicated way around. In one lecture he once got lost while scribbling on the blackboard. “Um,” he said, “I know three ways of proving this point but I have unfortunately chosen a fourth one.”
In many mathematical conversations on topics belonging to set theory and allied fields, von Neumann even seemed to think formally. Most mathematicians, when discussing problems in these fields, seemingly have an intuitive framework based on geometrical or almost tactile pictures of abstract sense, transformations, etc. Von Neumann gave the impression of operating sequentially by purely formal deductions.
The reader will have most fun tracing Johnny’s achievements through the rest of this book if he or she grasps that they sprang from a brain that operated in this way. In almost everything he did, from inventing new sorts of pure mathematics to calculating how best America could deter Stalin, he was moving shorthand algebraic notations in rigorously permitted directions across the moving chessboard of his mind.
Johnny was always brilliant on any topic but did not always know what the topic of yesterday’s homework was. Johnny did the homework very quickly and then dived into something else. There was much else to dive into.
she recalls an occasion when Johnny went to the lavatory and took two books with him — for fear he would finish the book he was currently reading before he was ready to emerge.
the Horthy government in 1920 brought in Hungary’s first specifically anti-Semitic measures in over fifty years. Entry admissions into university, it ruled, should “correspond as nearly as possible to the relative population of the various races and nationalities.”
This meant that only about 5% of university entrants should be Jews, which was absurd in a country where Jews made up 50%-80% of the lawyers, doctors, and other learned professions.
This was a letter from Lenin on how to run revolutions. Lenin’s broad lines were, “Make these promises to the peasants... Make these pledges to the proletariat... Give these assurances to the bourgeoisie... Do not feel in any way bound by these promises, pledges or assurances.”
the 1920 Treaty of Trianon stripped Hungary of much of its territory. This was not of enormous emotional moment to the von Neumanns, who were internationalists rather than nationalists.
Committee, convened in 1954 in Washington in order to harry
The academic progression in Europe has never been as formalized as that in the United States, but what seventeen-year-old Johnny proposed was not an ordinary program. He planned to carry on his undergraduate and graduate education simultaneously, in two distinct disciplines and in three cities several hundreds of miles apart.
The seventeen-year-old seemed to suggest that he would try to jog up Everest in gym shoes, although only as a part-time gig.
It was partly because of his disappointing early ETH results that young Einstein was initially deemed too dumb to get a research grant. He had to go off first to be an ill-paid clerk in the Swiss patent office. From there he thought through the shattering truth of the special theory of relativity while in furnished lodgings, cut off from communion with academic minds.
On that September 1921 train to Berlin he was accompanied by his father. A future Wall Street banker met him on it and said, “I suppose you are coming to Berlin to learn mathematics.” “No,” replied the seventeen-year-old, “I already know mathematics. I am coming to learn chemistry.”
This was an achievement because chemistry was not a subject that Johnny had done much at school, and most of his school-learning in it will have been in Hungarian. He therefore had to do some reading in German of chemistry and chemical engineering
“It is not enough for a European to be rich,” said Johnny later. “He also needs a bank account in Switzerland.”
Ex ungue leonem — spotting a lion from the claw — was the phrase Daniel Bernoulli had used about Newton two and a half centuries before. Bernoulli had been sent a mathematical paper that was at that stage anonymous,
Ex ungue leonem — spotting a lion from the claw — was the phrase Daniel Bernoulli had used about Newton two and a half centuries before.
Hilbert had said that the axiomatization of set theory was needed to put mathematics back in the driver’s seat of new technological advances. Now the axiomatization appeared to have been carried forward by a young man who had not yet sat even for his first degree. If these were Johnny’s two lost years of 1921-23, they appeared to his early contemporaries to be about as lost as the two years of the Great Plague in the 1660s when Newton had dragged himself away to rural Lincolnshire, where he more or less invented modern science.
In the taverns another talent bloomed: for ribald stories and dirty limericks, at which, according to Fellner, Johnny was better than he was at engineering but not nearly as good as he was at mathematics.
Johnny’s debt to Max and his family was that he was brought up to think relaxedly, instead of being turned taut in childhood as so many other infant mathematical prodigies are. If a family finds it has bred a precocious little genius, the most important qualities to encourage are — as Max saw — (a) a sense of calmness and humor, (b) an inquiring mind that finds inquiring to be fun.
It is right to be brutal in analyzing this, even at the risk of annoying their many admirers and pupils and friends, because similar great minds are being ruined in upbringing now. The handicap does not always lie in financial underprivilege in youth.
The time was one of intellectual intoxication... For years I had been endeavouring to analyze the fundamental notions of mathematics, such as ordinal and cardinal numbers. Suddenly, in the space of a few weeks, I discovered what appeared to be definitive answers to the problems that had baffled me for years. And in the course of discovering these answers I was introducing a new mathematical technique, by which regions formerly abandoned to the vagueness of philosophers were conquered for the precision of exact formulae. Intellectually, the month of September 1900 was the highest point of my life.
A contradiction essentially similar to that of Epimenides can be created by giving a person a piece of paper on which is written: “The statement on the other side of this paper is false.” The person turns the paper over and finds on the other side: “The statement on the other side of this paper is true.” It seemed unworthy of a grown man to spend time on such trivialities, but what was I to do?
While Bertie Russell’s grandparents had rather discouraged book learning, Norbert Wiener’s father gave a press conference at his birth in 1894 to announce that the child was to be turned through forced book reading into a genius. So Wiener was put at age nine into a high school class where the average age was sixteen; he graduated from university at age fourteen; and then went to Harvard graduate school. He was driven from the age of one by lessons at home that,
While Bertie Russell’s grandparents had rather discouraged book learning, Norbert Wiener’s father gave a press conference at his birth in 1894 to announce that the child was to be turned through forced book reading into a genius. So Wiener was put at age nine into a high school class where the average age was sixteen; he graduated from university at age fourteen; and then went to Harvard graduate school.
With that sort of upbringing the brilliant Wiener immatured with age, right from his terror in the nursery to his death at sixty-nine
When the twenty-two-year-old Johnny reached Göttingen in 1926, the thirty-one-year-old Wiener had just flounced out of it, after having accused his professors (especially the great Richard Courant) of plagiarizing from his work. Young Johnny would have regarded any plagiarism by such a professor as flattery.
it is more restful to have thoughtful scholars who are driven by calm observation of current facts rather than by passions like great winds, blowing hither and thither, on a wayward course, over a deep ocean of anguish, reaching the very verge of despair.
Johnny saw mathematics as a road into logic.
He believed, with others, that mathematics really began when our primitive ancestors turned from merely counting how many beans made five to realizing that “two of anything plus two of anything else equalled four, not just usually but all the time.” This was the crucial advance in human reasoning power. Dogs, gorillas, dolphins, and the sorts of politician you and I vote against have not noticed it even yet.
Once people saw that two plus two always equals four, the notation existed for very clever people to find what other things always happen: in other words, for advances to other abstract proofs. Unfortunately, those clever people too often hasten to escape from us grosser folk, and to make their subject as nearly as possible a free construct of the human mind.
He preached that there were three stages in the history of a mathematical idea. They might be called the practical, the aesthetic, and healthy recognition of the absurd.
Mathematically one is in a continuous state of uncertainty, because the usual theorems of existence and uniqueness of a solution, which one would like to have, have never been demonstrated and are probably not true in their obvious forms...
“There probably exists a set of conditions under which one and only one solution exists in every reasonably stated problem. However we have only surmises as to what it is and we have to be guided almost entirely by physical intuition in searching for it. It is therefore impossible to be very specific about any point. And it is difficult to say about any solution which has been derived, with any degree of assurance, that it is the one which must exist in nature.”
A British chancellor of the exchequer once said that an economist is a man who “can tell you 394 ways to make love, but has never actually met a woman.”
One expects a mathematical theorem or a mathematical theory not only to describe and classify in a simple and elegant way numerous and a priori disparate special cases. One also expects elegance in its architectural, structural make-up. The ease in stating the problem, great difficulty in getting hold of it and in all attempts at approaching it, then again some very surprising twists by which the approach, or some part of the approach, becomes easy... If the deductions are lengthy or complicated there should be some simple general principle involved, which explains the complications and details, reduces the apparent arbitrariness to a few simple guiding motivations... These criteria are clearly known to any creative art, and the existence of some underlying empirical worldly motif in the background — often in a very remote background overgrown by subsequent developments and followed into a multitude of labyrinthine variants — all this is much more akin to the atmosphere of art pure and simple than to that of the empirical sciences.
Johnny recommended that pure mathematicians feel patient rather than guilty.
As a mathematical discipline travels far from its empirical source... it is beset with very grave dangers. It becomes more and more purely aestheticising, more and more purely l’art pour l’art. This need not be bad if the field is surrounded by correlated subjects which still have close empirical connections, or if the discipline is under the influence of men who have an exceptionally well-developed taste. But there is a grave danger that the subject will develop along the line of least resistance, that the stream so far from its source will separate into a multitude of insignificant branches, and that a discipline will become a disorganised mass of details and complexities. In other words, a great distance from its empirical source, or after much abstract inbreeding, a mathematical subject is in danger of degeneration. At the inception the style is usually classical. When it shows signs of becoming baroque, then the danger signal is up. It would be very easy to give examples, to take specific evolutions into a baroque and very high baroque... Whenever this stage is reached the only remedy seems to me to be the rejuvenating return to the source: the re-injection of more or less directly empirical ideas.
comparisons between Johnny and men as towering as Aristotle, Galileo, and Newton.
he interestingly did make study of their processes of thought, the reasons for their effectiveness, and their public-relations mistakes. Pioneering mathematicians at the frontiers of their science, such as Johnny, do feel some glee that they are daily adding ideas that were not quite thought of by the most remarkable minds of the past two and a half millennia. As a classical scholar, Johnny felt this to high degree, but he was also intrigued at the pitfalls into which his greater predecessors sometimes fell.
For the Egyptians 3,456,789 would not be a nice round and divisible number, but would be shown by three amazed men, four tadpoles, five pointed fingers, six lotus blossoms, seven coiled ropes, eight circles, and nine vertical lines. An economist analyzing the current (1992) U.S. budget deficit would have to start by drawing around four hundred thousand pictures of amazed men.
The American historian Carl Boyer says that after the Pythagoreans “mathematics was more closely related to a love of wisdom than to the exigencies of practical life; and it has had this tendency ever since.”
To some extent Aristotle invented pure mathematics by seeing that mathematicians’ primary question needs to be: not What do we know? but How do we know it?
The four Greeks mentioned so far (plus Archimedes) had
Euclid, who came to the University of Alexandria just before 300 B.C. not as a researcher, not as an administrator, but as a good teacher — which too few universities still have.
The great virtues were that mathematics remained rigorously free from emotional content, free from ethical content, and free from political content.
It allowed people to try to rise to the top by being reasoning scientists and scholars, instead of being bullying politicians or priests.
There are big advantages in having a tradition passed down from revered ancients that clever men should think axiomatically, in terms of “if we do this, the logical result should be this, and then this.”
Most other early societies missed this. Even the ancient (well, pre-European) Chinese inventors of gunpowder, printing, and compasses never tried to attain philosophical understanding of why their inventions worked; that is one reason why their progress faltered.
Leaders of such societies then rely on that fear and superstition to get rid of more inquiring minds who might otherwise take these tribal dictators’ places.
through measuring time against his pulse, it is said that Galileo noticed that an erratically swaying lamp above the altar completed both its wider and narrower swings in the same time. He thereby saw that the time taken by a pendulum’s swing varies not with the distance it covers but with the pendulum’s length. This discovery made it possible to invent accurate clocks.
Would Johnny have similarly recanted if some dictator had shown him instruments of torture, and asked him to deny his latest tenets in von Neumann algebra? My impression is that he would have recanted like a shot, while some of the mathematicians to whom this chapter has been ruder (like Russell and Wiener) would not have. But I also think this would have been entirely logical of Johnny. He would have argued that Galileo’s truths were already written down, and that bright minds would soon carry them further.
Newton was conservative in politics and enjoyed holding dignified government posts. Indeed Newton — whose illiterate father could not have become a “von” — pretended to have aristocratic ancestors, whom he had simply invented.
Heisenberg lectured on the difference between his and Schrödinger’s theories. The aging Hilbert, professor of mathematics, asked his physics assistant, Lothar Nordheim, what on earth this young man Heisenberg was talking about.
Although Bohr was a kind and obliging person, he was able in matters which he considered important “to insist fanatically and with almost terrifying relentlessness on complete clarity in all arguments.” He was so relentless with Schrödinger that the latter sensibly retired ill to bed, but Bohr followed him. Sitting on the edge of the bed he would say, “But you must surely admit that...?”
Bluntly, although Hilbert had had the space named after him, the old boy in 1926 knew rather little of the mysteries that existed there.
Hilbert’s rules about infinite matrices had been stimulating for a beginner in the subject (Johnny in 1926) but were cramping for the world’s greatest expert in it (Johnny by 1927).
Johnny had spent his undergraduate years explaining what Hilbert had got magnificently right but was now into his postgraduate years where he had to explain what Hilbert had got wrong.
Hilbert was by then very old, said the eighty-nine-year-old Wigner to your sixty-five-year-old author in 1989. “Actually,” said your author, “Hilbert by 1926 will have been aged 64.” “Well, people must have aged earlier in those years,” said Wigner.
Wigner said sixty years later that some of their work was then unpopular, because it obliged physicists to learn new mathematics. The greatest joy of any physicist is to discover something new, but there is resentment at being told to go back to school.
He hardly ever lectured from a prepared text. He wrote equations on the blackboard at what seemed the speed of light. Sometimes he reached the end of the blackboard and erased to get more space at the top, before some of his audience had imbibed what he was now rubbing out. Among those who doubted him, Johnny’s system of “proof by erasure” became an irritated joke.
A lot of other people’s talks at colloquia were boring. Johnny did not mind because he could shut them off and mutter to himself while thinking up other mathematics, or even fall asleep. He had a hand-over-mouth sitting position that enabled him to wander away mentally while looking politely engrossed. Sometimes his colleagues had to nudge him as he sat in an emptying lecture room, still looking politely engrossed.
Bethe told me that he rated seminars in ten grades. “Grade one was something my mother could understand. Grade two my wife could understand. Grade seven,” said this Nobel Prize winner, “was something I could understand. Grade eight was something only the speaker and Johnny von Neumann could understand. Grade nine was something Johnny could understand, but the speaker didn’t. Grade ten was something even Johnny could not yet understand, but there was little of that.”
one German professor praised the habit of asking Ph.D. students “unsolvable questions” at their oral exams. If the student instantly said, “That’s unsolvable,” he was deemed to have the right sharp set of mind. The professor put his favorite unsolvable equations on the blackboard as an illustration. Johnny muttered at the ceiling for a few minutes, and then solved some of them.
another Hungarian’s euphemism for a near lie: a topological version of the truth.
Johnny was the only man he had known who could tell jokes (including doubles entendres) in three languages simultaneously.
In many university towns across Europe in the 1920s mathematical teachers and their brightest students would gather in cafés at tables with marble tops. You can write equations on marble tops and then wash them off.
a later Polish test when Banach deliberately spiked his drinks with vodka, to the point where Johnny had to dash to the lavatory to vomit. He returned from vomiting to pick up the equations he had been expounding at the exact point where he had left off.
He never argued with people who said anything emotional or politically convinced. He did not believe that public argument changed such people’s views, and he thought preaching back at them simply brought boredom and bad blood. But he asked probing questions of anybody who said anything interesting, and “interest” was a word to which he gave a wide range. Johnny preferred people who laughed at the world rather than whined at it.
France and Britain had imposed a settlement on central Europe that those two war-weary countries would not risk new horrors to maintain.
He had devised a cunning way of getting the syntax in foreign languages, such as English, right. He read selected books in the language he wanted to get the feel of, very quickly but with enormous concentration, so that every word in the passages he chose was implanted in his mind.
It is difficult for anybody with a photographic mind to think in terms of more than three dimensions. Johnny had no difficulty in thinking in terms of a quarter of a dimension or of some minuscule fraction of a dimension or several hundred thousand dimensions or infinite dimensions. He just moved the algebraic symbols for these across the chessboard of his mind.
It may be that he also did not bother to record faces the first time he saw them. Committing faces to memory would be a waste of effort if they proved to be faces of people who would never have anything interesting to say.
Because his nightly four hours of sleep might interrupt his thinking, he devised a way to do some thinking during sleep. He thought of some problems before dropping off and would dart to a notebook with new notations at 4 a.m. because his subconscious had been working while his body was at rest.
He joked that in one dream he was working through a proof that set theory really is consistent, if based on his axioms; he woke up before the proof was completed. The next night he dreamed again and got very near to completion. It is a mercy, he said, that he did not dream on the third night; otherwise he would have confidently proved what Gödel later showed to be untrue.
his main worry was that he did not want Mariette to see that Mrs. Einstein regarded the henpecking of a genius as good, cruel, feminine sport.
The familiar old man bore on his arm this slight but enormously pregnant figure with reddish brown hair. There were press photographs and comments the next day, along the lines of Who would have thought the old man had it in him?
There was one worse driver in Princeton — namely Wigner — but in a different mode. Johnny drove fast down the middle of any road. Wigner drove very slowly, keeping well to the right side — unfortunately, so far to the right side that his wheels generally moved down the sidewalk like a very slow steamroller, sweeping terrified pedestrians from the path.
the 1930s to hire full-time domestic servants, the domestic
The first reaction of professors across the world was to say that this little IAS research institute, without traditions and infrastructure, was an Institute for Advanced Salaries that was going to lure a tiny number of greedy scholars into a dead end. The second reaction of many of them was to apply for such appointments themselves.
~~~ While triumphant storm troopers
You cannot easily disguise through your prejudices when one physicist or mathematician is better than another, but you can disguise whether an art historian is.
The physicists and other scientists driven to emigration from Germany in and after 1933 included eleven existing or eventual Nobel laureates, and more than a dozen scientists who helped America invent the A-bomb in 1945.
“Marina does not talk yet,” he wrote when the child was six months old, but “this is for fear that Mariette’s family would instantly make her play bridge.”
Johnny’s second wife, Klari, once asked him to get a glass of water quickly in some minor medical emergency. He came back worriedly and asked her where they kept the glasses.
Johnny’s second wife, Klari, once asked him to get a glass of water quickly in some minor medical emergency. He came back worriedly and asked her where they kept the glasses. “We had only been in the house seventeen years,” said Klari.
John Maynard Keynes, who had called Karl Marx the author of an “obsolete economic textbook which I know to be not only scientifically erroneous but without interest or application for the modern world.” An especial sadness was that James Alexander (a jolly, mountain-climbing mathematician) turned near-Marxist during the depression. He felt guilty because he had been born rich. Johnny was puzzled that even the brightest minds did not understand what was happening under Stalin, although it paraded before their eyes.
Princeton has instead developed as one of the liveliest intellectual communities anywhere, partly because bright minds congregated to be in the same town as the glittering early stars.
“Why do mild mathematicians turn into ogres, anxious to devour directors?” One good answer to him was that the IAS’s powerful mathematicians did all the mathematics that anybody can bear “in a few hours of the morning, and then they’ve got the rest of the day to bug other people.”
Johnny, by contrast, believed that America’s greater materialism saved it from being as childish as Europe. He could not see such emotional doctrines as Nazism or Marxism ever really gaining ground among the sensible, money-seeking masses of the United States.
Because Johnny was a cherubic twenty-six-year-old when he arrived in America as a professor, he took the trouble of always wearing a business suit. If he did wear casual clothes, he was apt to be mistaken for a student — which he thought was more embarrassing for the perpetrator of the mistake than for himself.
Gödel was a loner, who worked well in isolation anyway. Indeed, Mariette says Gödel used to wander into their house to borrow one of Johnny’s books, sit down to read it on the spot, and then wander out without saying a word.
He saw that nonlinear equations would have to be solved if he was ever to advance to his pet project of eventually controlling the weather.
In the distant precomputer 1914, the firing tables for guns on the western front proved to be based on equations that had been wrenched into a form that would be easy to solve rather than one that described what would actually happen. That sort of nonsense is still sometimes found in military and economic and some other “practical” mathematics to this day.
He got the same 100% in his exam in May 1938 on Military Discipline, Courtesies, Customs. Sample Johnny answer: “He should stand to attention, and salute.” His 100% mark tickled him. He told Veblen that he was due to become the army’s master of ceremonies.
the “only sensible move now in Europe is out.”
A third lecturer was to be England’s Sir Arthur Eddington, who still did not really believe in what he called “the theory of quanta.” Johnny thought he would rather enjoy joining with future enemies such as Heisenberg to tell future allies such as the English that Eddington was daft.
“I can only say that Mr. Chamberlain obviously wanted to do me a great personal favour,” he wrote to Veblen from Budapest in early October. “I needed a postponement of the next world war very badly.”
He thought that those who believed in communism or socialism deserved the same sympathy as other simpletons who could not understand even linear equations. But he also did not believe that being a communist meant that anybody became a bad mathematician or bad scientist, and he was anxious to recruit into mathematics and science all the able brains he could.
In Johnny style, he said that America would have to accept the unpopular advice given “by a court physician to a septuagenarian German prince and princess, on announcing the birth of a daughter: ‘I regret that your majesties will need to move yourselves about energetically once again.’“
A scientist with a contribution to make could see from the different offers before him where he could contribute most at any time, and in practice all these bodies worked together to win the war. Any planned top-down research program, allocating this scientist to that job for that number of years, would have failed to take advantage of changing knowledge and opportunities. The American research system provided the nearest equivalent that wartime secrecy could have allowed to a free market.
“Oh no, no, you are not seeing it. Your kind of visualising mind is not right for seeing this. Think of it abstractly. What is happening [on this photograph of an explosion] is that the first differential coefficient vanishes identically, and that is why what becomes visible is the trace of the second differential coefficient.” As he said, that is not the way I think. However, I let him go to London. I went off to my laboratory in the country. I worked late into the night. Round about midnight I had his answer. Well, John von Neumann always slept very late, so I was kind and I did not wake him until well after ten in the morning. When I called his hotel in London, he answered the phone in bed, and I said “Johnny, you’re quite right.” And he said to me, “You wake me up early in the morning to tell me that I’m right? Please wait until I’m wrong.” If that sounds very vain, it was not. It was a real statement on how he lived his life.
In both Hitler’s and Stalin’s day, Johnny was more concerned to save the world from dictators who were trying by brute force to impose a single system of values on us.
“I think that I have learned here a good deal of theoretical physics,” he wrote to Veblen, “particularly of the gas dynamical variety, and that I shall return a better and impurer man.
Because Szilard was no motorist, he was driven on one visit to Einstein by Wigner (who had been taught driving by Desmond Kuper) and on the other by Teller (“I entered history as Szilard’s chauffeur”).
What did “Maud Ray Kent” mean? The British decided they were an anagram for “radyum taken,” and thus gave warning that the Germans were moving fast to develop an A-bomb. Perhaps that was the reason the Nazis had occupied Bohr’s Copenhagen, and were capturing Norway and its heavy water too? Down in her home in Kent, Miss Maud Ray, the former English governess to Bohr’s children, remained uncontacted because nobody had heard of her. She now entered history because the team of British boffins to examine nuclear prospects was named the Maud Committee, as a tribute to Meitner’s supposedly brilliant anagram.
Churchill had that week been in some danger under German bombing in the blitz on Britain. He minuted with his usual chutzpah: “Although I personally am quite content with existing explosives, I feel we must not stand in the path of improvement, and I therefore think action should be taken in the sense proposed by Lord Cherwell.”
The best comment on Groves came from Louis Alvarez: “Almost everyone disliked him heartily except the men who worked closely with him.
A later great historian called Oppie “the most captivating, commanding and worshipped teacher of theoretical physics of his generation,” whose students “devotedly imitated his mannerisms, even his walk.”
Johnny thought that Oppenheimer’s political and economic beliefs were unscientific and therefore regrettable
“Robert at Los Alamos was so very great,” Johnny insisted, “in Britain they would have made him an Earl. Then, if he walked down the street with his fly buttons undone, people would have said — look, there goes the Earl. In postwar America we say — look, his fly buttons are undone.”
It was not, said Bethe (and Johnny agreed), the primary function of the director of Los Alamos in 1943-45 “to make technical contributions. What was called for from the director was to get a lot of prima donnas to work together, to understand all the technical work that was going on, to make it fit together, and to make decisions between various possible lines of development. I have never met anyone who performed these functions as brilliantly as Oppenheimer.”
He saw that deterrence would not be achieved through endless committees of the United Nations, as some of his optimistic colleagues pretended.
Ulam usually spent his free Sundays calling unannounced on other colleagues to discuss (in Johnny’s phrase)
Ulam usually spent his free Sundays calling unannounced on other colleagues to discuss (in Johnny’s phrase)
Ulam usually spent his free Sundays calling unannounced on other colleagues to discuss (in Johnny’s phrase)
Ulam usually spent his free Sundays calling unannounced on other colleagues to discuss (in Johnny’s phrase) “this and that, and especially everything else.”
On the day Johnny went walking Ulam had nobody to talk to, so he joined the first part of the hike. Two hundred yards up the trail is the spot where Ulam stopped. It is known at Los Alamos to this day as “Ulam’s landing.”
Most of the physicists were used to doing experiments, but it was not easy to do experiments on how to blow up the world.
Johnny’s forte was to pick up the daring ideas of brilliant men and advance them.
A graduate student explained to me Johnny’s usefulness at the bottom. “When Dr. von Neumann came out of a room, he would be besieged by groups of people who were stuck by some calculation. He would walk down the corridor, with these people around him. By the time he walked into a door for the next meeting he would likely have suggested either the answer or the best shortcut to getting it.”
Johnny became a principal Los Alamos calculator of the height from which to drop them and the other mathematics of delivery. He was therefore on the target committee in Washington to decide which four Japanese cities should be put on the list to die. Unusually his notes on the target committee’s deliberations on May 10 (held in Los Alamos) are still available in the Library of Congress.
Von Neumann got very excited when J. M. put production functions on the board and jumped up, wagging his finger at the blackboard, saying (approx): “But surely you want inequalities, not equations there?” Jascha said that it became difficult to carry the seminar to conclusion because von Neumann was on his feet, wandering around the table, etc., while making rapid and audible progress on the linear programming theory of production.
Probably the loudest protests against the EEM came from the Left, some of whom assumed that Johnny was advocating a slave economy in which wages were kept near the lowest possible subsistence level. He was not. He was pointing out that growth is fastest when, as happened in countries such as Japan just after his death, labor can be absorbed from low-productivity work on the land into more productive jobs in new technology industries without too big a rise in the real wage.
Consider two examples from Johnny himself: When he played poker he quite often lost because he felt it was boring during a relaxation to visualize too many matrices when there were better things to think about. He just stuck to the general rules that emerge from his mathematics in another paper specifically on poker playing (with many equations including the letter n). Those general rules are if you have a strong hand, always bid high; if you have a weak hand, sometimes bid high to bluff or sometimes bid low and pass; but never bid low and then see. Many thinking poker players do that anyway.
the earlier pages of the Theory of Games. In these Johnny annoyed some economists by saying that much mathematics “had been used in economics, perhaps even in an exaggerated manner,” but “had not been highly successful.”
Those social scientists, said Johnny, are “utterly mistaken.” The main reason for the failure of mathematics in economics is that economic problems are “often stated in such vague terms as to make mathematical treatment a priori hopeless because it is quite uncertain what the problems really are. There is no point in using exact methods when there is not clarity in the concepts and issues to which they are to be applied.”
Johnny said economists should ponder how the mathematization of physics was achieved in the seventeenth century.
After physics was mathematized by Newton (1642-1727), there arose a need for reams of tables. Some were tables for mass consumption (such as logarithms, cosines, navigation tables). More had to be worked out by inquiring scientists themselves, as they noted down their observations and drew up tables to test hypotheses. The compiling of each table was dead boring.
Wailed Leibniz, (1646-1716), “It is unworthy of excellent men to lose hours like slaves in the labor of calculation which could safely be relegated to anyone else if machines were used.”
“I should like a little previous consideration,” explained the ablest of these chancellors, Sir Robert Peel, “before I move in a thin house of country gentlemen a large vote for the creation of a wooden man to calculate tables for the formula x2 + x + 41.”
Mr. Babbage’s analytical engine, enthused the poet Lord Byron’s daughter by the 1830s, “weaves algebraical patterns just as the Jacquard loom weaves flowers and leaves.”
one of Johnny’s virtues in 1944-54 was that he did the opposite. He saw that the arrival of the computer and other automata would make new methods of numerical analysis important. He started striving to develop (instead of wait for) them.
Hollerith saw it was nonsense that hundreds of clerks were tabulating the details of all the fifty million Americans by scratches of their quill pens. This meant that the census’s interesting figures became available only after several more years of surging immigration had made them completely out of date. There must, thought Hollerith, be a better Jacquard-loom-like system of using a punched card for every respondent to the census: with different holes showing whether male or female, immigrant or native born, black or white, ability to speak English, parent of how many children.
By running twenty-four hours continuously, it was said that new versions of these machines might soon do in a day what could take a human with a desk calculator six months. Indeed, enthusiasts for them feared they would run too fast for their commercial good. One of the Harvard’s inventors allegedly warned that America could not have use for more than about five of his machines.
How did this small pre-Johnny team on the ENIAC go as fast as it did?
The other advantage for infant ENIAC was that Goldstine knew of Babbage’s history of never finishing anything on time. Goldstine was determined to push the project through to operational prototype even though everybody kept finding ways to make it far better — if only he would permit some extra delays. These proposals for making ENIAC better were stored for implementation only in ENIAC’s successor, which was to be called the Electronic Discrete Variable Computer (EDVAC).
When it became clear to von Neumann that I was concerned with the development of an electronic computer capable of 333 multiplications per second, the whole atmosphere of our conversation changed from one of relaxed good humour to one more like the oral examination for the doctor’s degree in mathematics.
Eckert and Mauchly hoped they could become rich by taking out patents on the ENIAC first and the EDVAC after. They hired patent attorneys who encouraged them, instead of instilling caution. When anything as innovatory as the computer appears, the first models nowadays usually will not make money. Customers know that the next models a few years down the road will be much better.
Goldstine’s book, The Computer from Pascal to von Neumann
This fact explains his attitude to Eckert and Mauchly and their commercialism. He wished them and others luck with trying to meet the demands of the market, although he thought the technology would be improving so fast that their models would be out of date before they were completed.
Johnny had a wider conception of where computers could lead than anybody before him — or, much more surprisingly, than anybody since.