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Ehrenfest sought relentlessly what he called der springende Punkt, the leaping point, the heart of the matter, as for him deriving a result by logical means was never enough: “That is like dancing on one leg,” he would say, “when the essence lies in recognizing connections, meanings and associations in every direction.”
Speak the truth, write with clarity, and defend it to your very end was Boltzmann’s personal motto, and Paul, his disciple, took it to heart.
In nature, Nelly said, there are such things that surpass proportion and cannot be likened to any other. They obey no measure and refuse categorization, because they exist outside the order that encompasses all phenomena. These outliers, these singularities, these monstrosities, will not be governed or compared by means of a number, because they lie at the root of what is disharmonious, chaotic, and unruly about the world.
We lie on our knees, praying to the wrong god, a childish deity who hides at the center of a corrupted world that he can neither govern nor understand. Or is it that we have made him ourselves, in our own fetid image, but then forgotten we have done so, as young boys birth the monsters and demons who haunt their dreams, without ever realizing that they have only themselves to blame?”
According to Father, it took roughly four thousand punched cards to manufacture a single textile; he told us that he had seen a portrait of the gadget’s inventor, a Frenchman by the name of Joseph-Marie Jacquard, which had taken over twenty-four thousand cards to weave. The magic of it all, he said, is that once it had been set up with the proper instructions, a single Jacquard loom could produce unlimited copies of a pattern, without the intervention of human workers, so its impact on the weaving industry had been enormous.
Janos squealed with delight when Father said that Jacquard had been nearly lynched by an angry mob, as hundreds of thousands of laborers had been suddenly put out of work. He told us that many of the original looms had been hacked to pieces, burned, and destroyed, and this only served to incite my older brother’s desire all the more.
I stayed with him even though I could hardly keep my eyes open, because Janos was always there for me when I needed him—during my entire life, he was there when I needed him the most.
Yes, it was terrible, but no major battles were fought inside our country. Hungary was the breadbasket for Austria-Hungary, and wartime shortages boosted wheat prices so much that the rich actually became richer. So many of us acted as if nothing was happening. This might seem shocking, I know, but it taught me a simple human truth that I learned very early on, which is that you can dance even with the devil knocking at your door. Because that is what I did, what a lot of us did. And could you really blame us? The Hungary that I was born in was a plutocracy going through a belle epoque.
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Not him. He just closed his eyes and then he raised his hand. When I called on him, he walked to the blackboard and wrote down a completely stunning proof. In a second. With no effort. No thinking even, only doing. I could not believe it. Years, all my years of work, passed by in a second. And this thing he did . . . it was so beautiful, so elegant, I remember asking myself, What is this? This boy . . . What kind of a boy is this? I still don’t know, but after that, I was afraid of von Neumann.
This otherworldly capacity to see into the heart of things, or—if viewed from its opposing angle—this characteristic shortsightedness, which allowed him to think in nothing but fundamentals, was not merely the key to his particular genius but also the explanation for his almost childlike moral blindness.
That meeting included titans like Werner Heisenberg—already lauded as a genius for his discovery of matrix mechanics and the uncertainty principle—but Jancsi was the golden boy, preceded by such a sterling reputation that it had given rise to a saying: Most mathematicians prove what they can. Von Neumann proves what he wants.
The philosophical implications of Gödel’s logic were astonishing, and his incompleteness theorems, as they later came to be known, are now considered a fundamental discovery, one that hints at the limits of human understanding.
From Gödel onward, I was always afraid for him, because once he abandoned his juvenile faith in mathematics he became more practical and effective than before, but also dangerous. He was, in a very real sense, set free.
In the United States, von Neumann became a renegade mathematician, a mind for hire, increasingly seduced by power and by those who could wield it. He would charge exorbitant fees to sit with people from IBM, RCA, the CIA, or the RAND Corporation, sometimes for no longer than a couple of minutes, and worked on so many private and government projects that he seemed to possess the ability to be in many places at the same time.
We were all little children with respect to the situation which had developed, namely, that we suddenly were dealing with something with which one could blow up the world. John von Neumann
We knew the world would not be the same. A few people laughed, a few people cried, most people were silent. I remembered the line from the Hindu scripture, the Bhagavad Gita: Vishnu is trying to persuade the prince that he should do his duty, and to impress him takes on his multiarmed form and says, “Now I am become Death, the Destroyer of Worlds.” I suppose we all thought that, one way or another. J. Robert Oppenheimer
We had created a sort of mass-production system, a mathematical assembly line where each “computer”—that’s what we called people hired to do mathematical calculations—had to do a single type of operation, over and over and over again, this one was the multiplier, and she was the adder, and this one cubed, so all she did was cube this number and send it to the next one down the line, and with that we achieved amazing speeds to try and get these massive, multilayered computations ready on time for the big test at Trinity. It was uncanny watching these women (most of them were women) behaving
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When we finally finished and set the bomb computation going, we went for a walk in the desert, and he gave me a piece of advice that still haunts me: “You don’t have to be responsible for the world that you’re in, you know?” he told me.
There is no middle point with these great men, at least that is my experience, they are either morbidly lustful or completely cut off from their genitals, and my husband, who really had to excel at everything, was perhaps the most disgusting in his relationship with women. It’s no surprise that most of them found him unsettling, he had some sort of fetish, because he would fixate on any pair of legs that walked by him, and even had the appalling habit of peeking underneath the desks of the secretaries at the institute. Some of those poor women had to stick pieces of cardboard there, just so
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He must have felt some small measure of resentment, however, because one time, when Albert was supposed to go to New York, Johnny offered to drive him to the Princeton train station in a brand-new Cadillac he had just bought for me, and then purposely put him on a train going in the wrong direction.
He once told me that, just as wild animals play when they are young in preparation for lethal circumstances arising later in their lives, mathematics may be, to a large extent, nothing but a strange and wonderful collection of games, an enterprise whose real purpose, beyond any one stated outright, is to slowly work changes in the individual and collective human psyche, as a way to prepare us for a future that nobody can imagine.
Life is so much more than a game. Its full wealth and complexity cannot be captured by equations, no matter how beautiful or perfectly balanced. And human beings are not the perfect poker players that we envisioned. They can be highly irrational, driven and swayed by their emotions, subject to all kinds of contradictions. And while this sparks off the ungovernable chaos that we see all around us, it is also a mercy, a strange angel that protects us from the mad dreams of reason.
Once, when he and I were discussing his theories of nuclear deterrence, he asked me if I knew what had remained inside Pandora’s box after she had opened it and let out all the evils and ills into the world. “Right there,” he said, “at the bottom of the jar—because it was a large urn or a jar, you know, not a box at all—right there, waiting quietly and obediently was Elpis, which most people like to regard as the daimona of hope and counterpart to Moros, the spirit of doom, but to me, a better and more precise translation of her name and of her nature would be our concept of expectation.
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In 1946, von Neumann promised the United States military that he would build them a computer powerful enough to handle the intricate calculations needed for the hydrogen bomb. All he asked for in return was to freely dispose of any computing time left over from the bomb calculations, and to dedicate it to whatever he desired.
The thing about the ENIAC was that you could actually see the calculations taking place. You could walk inside it and watch the bits flipping. Nobody was quick enough to keep up with the numbers. Not in real time anyway. But Johnny was.
Turned out nobody wanted us there. The mathematicians were disgusted. Dirty men with dirty fingers would pollute their hallowed environment. “Engineers in my wing? Over my dead body!” Senior paleontologist said that. No kidding.
It’s hard to overestimate the importance of what we did. Our computer wasn’t the first. Wasn’t even the third. But it was a stored-program computer. And the one that everyone copied. We published and made public every step of the process. So it was cloned in 1,500 places around the world. It became the blueprint. The DNA of the entire digital universe.
The ENIAC? Glorified calculator compared to ours. It was a music box that could only play one tune. If you wanted something new you had to physically rewire it. Thousands of cables connected by hand. So hours, days, for a single programming change. We built an instrument. A grand piano. With our machine you simply introduced new instructions. Change the software without touching the hardware. It was also twenty times faster. With a fully random-access memory.
This was 1951. So we had to use war surplus parts and vacuum tubes that would fail without warning. In summer the room got so hot, tar would splatter on the machine. Months of work ruined in an instant. And the memory was incredibly fragile. Someone wearing a woolen sweater could wipe it clean. Passing cars and planes did that too. And this mouse crawled inside it once. Chewed on some wires and was burned to a crisp. We rescued the machine but never managed to get rid of the stench. It always smelled of charred meat, singed hair, and burned whiskers.
“This species of device is so radically new that many of its uses will become clear only after it’s been put into operation.” It’s what he said to me. ’Cause he understood. He knew the real challenge was not building the thing but asking it the right questions in a language intelligible to the machine. And he was the only one who spoke that language.
We christened our machine the Mathematical Analyzer, Numerical Integrator and Computer. MANIAC, for short.
The first goal that von Neumann set for the MANIAC was to destroy life as we know it: in the summer of 1951, a team of scientists from Los Alamos traveled to the Institute for Advanced Study in Princeton and introduced a large thermonuclear calculation into the computer. It ran twenty-four hours a day for two months, processed more than a million punched cards, and yielded a single YES/NO answer.
You insist that there is something a machine cannot do. If you tell me precisely what it is a machine cannot do, then I can always make a machine which will do just that. John von Neumann
In his paper, he divided his theoretical construct—which he called the “automaton”—into three components: the functional part, a decoder that reads the instructions and builds the next copy, and a device that takes that information and inserts it into the new machine. The astounding thing is that right there, in that paper written in the late 1940s, he depicts the way in which DNA and RNA work, long before anyone had ever glimpsed the strange beauty of the double helix.
“Cavemen created the gods,” he said. “I see no reason why we shouldn’t do the same.”
After all, when the divine reaches down to touch the Earth, it is not a happy meeting of opposites, a joyous union between matter and spirit. It is rape. A violent begetting. A sudden invasion, a violence that must be later purified by sacrifice.