Who was John von Neumann?

to science and technology. This is the first part of a two part episode. His achievements were remarkable, perhaps made even more astonishing by the fact that he only lived to his mid fifties, and yet he was an incredibly prolific thinker. But he also had his flaws, and I'll talk about those as well, because I think it would be a disservice to just gloss over them. So while he was a genuine whenly intelligent, brilliant man, he had

some some flaws to his character as well. So John von Neumann was born Neuman Ya nash Law Josh margin Tie in Budapest, Hungary, in December. And I know, I know, I butchered the pronunciation of that, but I'm doing the best I can. He was born into a nonpracticing Jewish family, so uh, ethnic Jewish family, but not a practicing Jewish family. Now, according to the biography, as I read, the household liberally mixed in Jewish and Christian traditions together. His father was

a successful banker. His mother came from a prosperous family, so in those biographies they also mentioned that he came from a wealthy background. He was the oldest of three boys. His younger brothers grew up to be a doctor and a lawyer, respectively, and the family would employ governesses to look after the children and from them, Vaughn Neuman began to learn French and German and English and other languages as well. Even as a kid, he was obviously gifted.

He could talk with his father in Greek and tell jokes in Greek. He could memorize an entire page out of a phone book in just a few minutes and answer questions about who had which number or what a person's street address was. They would do this as like party tricks. When he was six years old, John von Neumann was an apt student in school, and he attended the Lutheran High School starting in nineteen thirteen. This was

one of the best schools in Hungary. He earned the award of being the best Mathematician of the fifth class in nineteen eighteen and he won Best Hungarian Student in Mathematics in nineteen twenty. Now, in between that time there were some bumps in the road, but it wasn't due to his academics, was due to world politics. In nineteen nineteen you had the end of World War One. Hungary

fell under the governance of a commune. This leader named bellah Kun, and he and his Hungarian Soviet Republic moved to nationalize a lot of private property in other words, sees the property of wealthy individuals in order to redistribute that to the rest of the population. Now, the Noumans didn't really like the sound of that, and so they fled temporarily to Austria. After about a month, they came back to Budapest and the Soviet Republic didn't last very long. It,

I mean it ultimately it fell. But in the wake of its failure, that added more problems for this family. So namely, the failing government had many Jewish representatives in it. It was a largely Jewish government, and so public opinion towards Jewish people in general turned very, very negative. So it didn't matter that John's family had been in opposition to that government. The fact that they were Jewish meant that they would receive a lot of the ill will

of the people. He would go on to study mathematics in one university and chemistry at another at the same time. Sort of all right, so here's the story behind that. His dad didn't want him to pursue a career that wasn't going to accumulate wealth, and he felt that an advanced degree in pure mathematics wasn't going anywhere. It wasn't a real money maker. So he and John sat down

and together they agreed upon the subject of chemistry. There were a lot of rising stars in the world of chemistry out of this part of Europe, and so John von Neumann agreed he would study chemistry. So he enrolled in the University of Berlin. However, at the same time he also enrolled in the University of Budapest for mathematics. Now, Hungary's universities had really strict limitations on the number of

Jewish students would be allowed to attend at any one time. However, von Neuman's academic record was beyond impressive, so he was able to get in. And then he did something pretty darn baller. He would attend classes at the University of Berlin learning about chemistry, and he would skip nearly all of the lectures and classes at the University of Budapest

in mathematics. He would just come back to the University of Budapest to take exams or whenever he was absolutely required to be there, and he aced those exams even though he wasn't going to the lectures. He graduated with a pH d in mathematics from the University of Budapest in ninety without really going to lectures there. He was

twenty three years old. He transferred out of the University of Berlin as he was studying chemistry, and he would ultimately receive a diploma in chemical engineering in ninety six from a school in Zurich, Switzerland. I wish I could tell you the name of that school, but I'm looking at it and it would do such a terrible job with this one. I don't even dare attempt to pronounce it. So I'm just gonna leave it be now. When he

was twenty. When he was still in school, John von Neuman published a definition for ordinal numbers, and an ordinal number is a way to describe the position of an object within a sequence of objects that are inside a set. So, for example, if you consider a set to be people who are in line for pizza, and there are four people ahead of me, I am the fifth person in that line or set. So the ordinal number that is my designation is five because I'm the fifth person in line.

Von Neuman's definition of ordinal numbers is the same one that we use to this day now. Von Neuman's dissertation for his PhD had the title The Axiomatic System of set theory. Set theory concerns collections of objects, typically mathematical objects, as opposed to you know, like hammers and Set theory was established in the late nineteenth century by George Cantor in an article titled on a property of the Collection of all real algebraic numbers. Basically, this is the theory

that can be described like this. Sets are collections of objects or elements. So in a real world example, the classification of mammals includes all animals that are vertebrates, that have for that typically give birth to live young, and they produce milk for offspring. So a cat fits that definition. A cat fits the set of mammals. All cats are mammals. However, sets themselves can be objects that belong to larger sets. So in this example, mammals is a set, but it's

also an object. It belongs to the larger set of all animals. So a cat belongs to the set mammal as well as to the set animals, and mammals are a subset of animals. If you've seen a Venn diagram in which you have two circles that overlap in some way, you've seen a representation of one aspect of set theory. So let's give an example of a Venn diagram. Let's

say we have two circles. One circle represents people who love they might be giants, and the second circle represents people who love Andrew w K. These circles each represent different sets. The overlap, or the intersection of those two sets is where you have people who fit both categories. They love they might be giants and they love Andrew w K. We could even give this group a new name.

We could call it something else. Like weirdos like Jonathan Strickland because I love both, they might be giants and Andrew w K. But we could also talk about the set difference of this Venn diagram. The set difference for the people who love they might be giants would include all the people who only love Andrew w K. And the opposite would be true for the set difference for the people who love Andrew w K. You also have

symmetric differences. The symmetric difference of these two sets would include all the people who only loved one of the two bands, but not both. There are many other ways you can describe sets, but you get the general idea. As for axioms, those are statements that are self evidently true, things that are true because of common sense. We can declare them to be true. It's about as fundamental as you can get. In fact, it is as fundamental as you can get with truth. So one of those might

be parallel lines will never intersect. By definition, parallel lines will never intersect. That is an axiom. It is a fundamental truth. It's a common sense statement. It's not based on earlier or or even more granular statements. So these axioms can be used to deduce further conclusions. But doing that hand be tricky. If you build deductions on axioms and you find that two different deductions you have based off the same axiom end up contradicting each other, then

you've got a problem on your hands. So let's say you've got your axiom A. This is your fundamental statement, the one that you've declared to be true. Then from A, you deduce that because A is true, statement B, which is based on A, must also be true. And then from statement B you deduce that statement P is also true. Now let's get back to A. Let's say that we start from A again, and now we're making a different deduction and we deduce a new statement. We're calling this

statement D, and that one must be true. But now from statement D we make a deduction, and from statement D we deduce that statement P has to be false. So this is a problem. You have one line of reasoning that states P has to be true because A is true, B is true, P is true. Then you have another one that says P has to be false because A is true, D is true. That means P must be false. This is a paradox or a contradictory statement, and it means we have to look over the entire system.

We have to look at the axioms to make sure that they are actually sound, and we have to look at the process we've used to deduce the truth or falsehood of the statements that followed from this axiom. This falls into an area of logic that I absolutely loved studying in college. Now, I'm no von Neumann, not by a long shot, but I got a brag for just a second. So when I was in college, I took a course in symbolic logic, and I found that my

professor was teaching directly from the textbook. So I made a tough decision. I decided to stop going to classes. I only took the exams and I aced the course. Now, granted, the version of logic I was studying was the most basic version of symbolic logic. It was child's play for someone like von Neuman. He would have breathed through the class back when he was six years old. So I can't brag too much, but it did give me a little bit of insight into his mind, at least in

that aspect. I've got a lot more to say about John von Neuman. But first, let's take a quick break to thank our sponsor. Set theory would become one of many areas that von Neuman would continue to study and develop over the course of his life. There's a concept

in mathematics called the von Neuman universe. In fact, although some scholars like Gregory H. Moore have gone on to say that this attribution is somewhat misleading, but we'll leave that for now, because would otherwise be diving into an area of mathematics so far outside of my expertise and understanding that I would just be reading from textbooks or history books, and I don't think that makes very good podcasting.

In addition to mathematics and chemistry, the young von Neumann was also fascinated by technology and aviation, and it began to work in an area that would have a really big effect on many different different industries, different careers moving forward. That would be game theory. Now, personally, I find the term game theory to be a little misleading because it undersells what it's all about. You could use game theory to describe how people play a game like poker, but

it's actually way more than that. In psychology, you might refer to it as the theory of social situations, and it really comes down to how human beings interact with one another in specific types of situations. And generally you can break it down into two large branches, cooperative game theory and non cooperative game theory, and the names kind of are self explanatory. Cooperative game theory describes how people

will work together to achieve a common goal. How will they leverage their strengths, how will they compensate for their weaknesses, how do they manage to go after this goal together. Non Cooperative game theory, you could call it competitive game theory, describes how intelligent people will interact with each other as they each are working toward achieving their individual goals. Now, those individual goals might be the same, so it may be that everyone's trying to go after the same prize

and only one person can get it. Or it might be that each person has a different individual goal, and it may be that some of those individual goals are at conflict with one another. For example, maybe my goal is to get a certain trophy and someone else's goal is to get a certain medal. But the problem is that the when one person achieves one of those goals, the path to achieving the other one is cut off,

so that would be another example. Now, John von Neumann was not the first mathematician to suggest using mathematics to describe game theory, or to study game theory, or to come up with various strategies in game theory. Numerous thinkers had worked on various applications, some for specific games like chess, before von Neuman had ever come onto the scene. But von Neuman's work was some of the first general purpose

game theory work not dedicated to a specific implementation. His scholarship effectively established game theory as its own distinct field of study. John von Neumann published his first paper on game theory in nineteen twenty eight. It had the title Theory of Parlor Games. He recognized that a game like poker had a lot more going on than just probabilities.

So if poker just was reliant upon chance, then you could memorize all the possible outcomes of a round of cards, and you would have a good chance of being able to play your hand to the best of its effectiveness. Right, you would know that the odds of someone having a better hand would be higher or lower than um any given hand that you have and that would help you make a decision. However, that does not take into account

the human element of bluffing. So with bluffing, a person can act as if his or her hand is stronger than it really is, or maybe they are giving off the implication that they aren't working with a very strong hand and they're hoping that you will get out of the game. There's a lot of psychology in their doubt

enters into the equation. So von Neyman started to work on this idea and he saw how it could be applicable to all sorts of stuff, not just games, but stuff like economics, and he partnered with an Austrian economist who was at print Sston University named Oscar Morgan Stern, and together they would publish a book titled Theory of Games and Economic Behavior. In the introduction of that book, they lay out the fact that economics is a really

complicated science. There are a lot of contributing factors to economic outcomes, and not all of them are identified, let alone understood. So out of the factors that we can say yes, this definitely impacts economics, we don't necessarily understand how, but we know it happens, and then there are others

that we may not have identified yet. So the authors maintained that because of that, because of this uncertainty, this lack of knowledge, this gap in our knowledge, it's pretty much the case that anyone who claims to have a universal theory of economics has got to be wrong because we don't have that full understanding of all the factors and how they interact with one another in any given situation,

how they're weighted in any given situation. So in a way, this would mirror another big challenge von Neuman would encounter later, which would involve predicting the weather. I'll talk a bit about that in our next episode. Now, one of the central concepts of von Neumann's game theory was called mini max. Emil Borel had previously theorized about mini max, and this is all about minimizing the possible loss in the event

of a worst case scenario. So, considering considering a scenario where the absolute worst happens, the maximum bad happens, how do you minimize the impact to you in that event? And this could be applied to all sorts of situations. How do you limit the setbacks you're going to suffer should the worst happen. There's also a concept called maximn This is sort of the opposite. How can you make the absolute most gains with the minimum success you might

have in any given scenario. So these two on steps together would become part of game theory, and game theory wasn't the only scholarly work von Neumann was pursuing in the nineteen twenties. At the same time, he was also studying quantum mechanics, which would ultimately form the foundation of his book, The Mathematical Foundations of Quantum Mechanics. So I've talked about quantum mechanics before, but what the heck doesn't

actually mean. Well, the simple answer is that it's a branch of physics that's concerned with the very very very small. We're talking atomic and subatomic levels generally. So at that scale, the physics that we observe in our day to day lives. The behavior of larger stuff, you know, stuff like tractors and puppy dogs and skyscrapers and people. The physics that we encounter day to day that breaks down when you

get down to this atomic and subatomic level. So in our day to day world, I cannot walk up to a wall and then in an instant appear on the other side of the wall. I would have to have a door to walk through or a window decline through, or I'd have to burst kool aid or hulk like through the barrier. There would have to be an opening,

or I would have to make one. Those are the only two options if I want to get onto the other side of a wall, or I guess I could walk around it if if that's an option, but you get what I mean. On the quantum level, however, this is not the case. You can actually have a quantum particle come up to a barrier and sometimes appear on the other side of the barrier as if it had just passed through, without even having to pass through. This tendency can have consequences in our macro world. So take

electrons for example. So for convenience sake, we talk about electrons inhabiting an orbit around a nucleus of an atom, and we usually depict this in some way that makes sense to us on a macro scale. And you might have a very simple drawing where you've got the the very uh icon drawing of an atom where you've got the nucleus as a big dot in the center, and they have a circle around the nucleus, and around in that circle you have a dot that represents an electron.

So that's sort of saying, in this moment of time, the electron is right here. But that's misleading. That's not really what we can definitively say. Electrons have wave like properties. They don't act just as particles. They also connect as a wave, and waves don't just abruptly end when they hit a barrier. They actually taper off. If the barrier is thin enough, some of the wave will continue through the barrier to the other side. Now, the wave represents

a probability function. Now essentially that tells us the chance of the electron inhabiting any part along that wave at any given time. So that means there is a probability, albeit a small one, that the electron could exist on the other side the barrier. Because it's it still exists on the other side, it represents a probability, and as long as there's a probability, it means that sooner or

later it'll happen. So that means that if you have enough electrons near a barrier like this one, some of those electrons will just from probability, appear on the other side of the barrier as if it had passed through, and we call it electron tunneling. Now there's no actual tunnel created, there's no hole made in the barrier. It just was a fact of probability. There was a small probability that the electron could be on the other side,

and so sometimes that happens. This is one of the big challenges that microprocessor manufacturers make when they miniaturize elements on the chips because if the gates, the actual gates that are controlling the pathway of electrons are thin enough, then it's possible for the electron probability function to overlap the barrier, and then you have electrons passing through these gates as if they were open even when they're closed,

and that creates errors. So that's why this has real world uh impact, even though we don't see this kind of behavior in the macro world. Like I said, I can't walk up to a wall and then magically appear on the other side of it just because of probability. There's zero probability that that will happen. Concepts like these are hard to wrap our minds around because we occupy

a world in which quantum mechanics do not apply. This is also or if they do apply, they apply, it's such a tiny, tiny amount that it's imperceptible to us. So this is why I get grouchy when I see people try to use these concepts from quantum mechanics to describe or predict stuff in our real world macro environments, because it really doesn't apply there, at least not on a level that is at all, you know, noticeable. At this point, you're either dangerously close to using pseudoscience or

you've fully jumped into the pseudo science science boat. So be where people who try to describe real world scenarios in quantum mechanics um you know, methods or approaches. I've got more to say about John von Neuman in just a second, but first let's take another quick break to thank our sponsor. Now, John von Neumann was working on quantum mechanics at a really exciting time. Heisenberg had just

proposed his uncertainty principle. Now that's largely based off the fact that matter can act as both a wave and a particle, and that would mean there's a limit to how precisely. We might know a particle's properties, like an electron's position and speed, for example. So the more precisely we know one of those two things, the less we know about the other. So the more precisely we can talk about the electron's position, the less we know about

its speed, and vice versa. John von Neumann's contributions were unsurprisingly related to the application of mathematics when it comes to quantum mechanics. Von Neumann's emphasis was on mathematical rigor. That is, his approach emphasized the degree to which a mathematical representation of a concept and quantum physics is logically sound. He wanted the math to be as strong and a method of proof as possible to logically support these various

principles and quantum mechanics. Now, that put his approach in contrast with a another physicist named Paul de rac who argued for a more pragmatic approach that was less mathematically rigorous, but it was also more efficient. It was easier to apply, and it would lead to conclusions that were easier to understand than these very complicated mathematical formulas. So you had these two very different styles coming at quantum mechanics at

the same time. So John VA Neuman. By the late nineteen twenties was already something of an intellectual celebrity, at least in academic circles, and he was doing groundbreaking work in game theory and quantum mechanics. In ninety nine, he was invited to lecture at Princeton University on the subject of quantum theory, and he said he would be happy to do so, but first he had to attend to a small personal matter. That small personal matter was a wedding.

His wedding, he got married to a woman named Marietta Covechi. Now Covechi and von Neumann had known each other since childhood. Covechi was a talented economics student at the University of Budapest. She was also something of a socialite in Hungary. She was known for appearing at parties and being very glamorous. Von Neumann was also a fan of the nightlife. Apparently, he was quite well known as a patron of the

cabaret circuit in Berlin. He would teach in the daytime and go out for a night on the town in the evening, and his love of parties and alcohol would follow him as he relocated to the United States. In addition to marrying Covechi, von Neumann converted from being a nonpracticing Jew to a Catholic. Now this was not an indication that he had found religion. He was agnostic through most of his life. I'll talk a little bit about

that in the next episode as well. It was more of a practical decision so that he could actually marry Covechi. So he converts to Catholicism and then he and his newlywed wife move over to the United States. Now, von Neuman would become a professor at Princeton, but reportedly it was one of the few things in academia that he was not great at, or at least people didn't really

like his style. So the trouble mostly appeared to be that von Neuman was super duper wicked smart, and he had a phenomenal memory as well, so he could work out complex equations in his head, and he would leap around the topic quickly, which left a lot of students struggling in his wake. They couldn't keep up, they didn't weren't able to connect the dots like he was. He got a reputation for scribbling out important equations hurriedly on a chalkboard and then erasing them before anyone knew what

they meant or could even copy them down. However, he also had a reputation for being able to communicate complicated ideas in a very straightforward way in a one on one setting that would allegedly make sense even to dullards

like myself if I had been given the opportunity. Now, since von Neuman died decades before I was born, I can't actually put this claim to the test, but by many accounts, he was talented at explaining complicated ideas to people who didn't have the expertise in mathematics to understand all of the bells and whistles. In nineteen thirty three, he was named a mathematics professor for the Institute for Advanced Study in Princeton. That was a brand new department.

He was one of the six experts in the original group of professors. He was also the youngest of those six. Uh. Those professors included some really smart people, including one that I'm sure you've all heard about. That would be Albert Einstein, so he was in really good company. Three was also the last year that von Neumann would lecture for a term in Germany. He was going back and forth. He would do a term in Germany, he would come back and do a term in the United States, and so

on and so forth. The Nazi Party, however, was starting to consolidate power in Europe around this time, so Neuman withdrew to work solely in the United States. Now, some of his peers would leave continental Europe in an effort to escape the Nazi regime as it got more powerful, but von Neuman had already relocated in an effort to find steady employment as an academic. Now I say this only because as I was researching von Neumann, I came across differing accounts, some of which said, you know, he

was fleeing the Nazi regime. But from the information I could find, it sounded more like he was looking for a steady gig and he got one at Princeton, and that was the guiding force in his decision. It just happened to pre date the rise of Nazis in Europe, so he had already left by the time the Nazi Party was starting to pick up steam in Germany in the mid nineteen thirties. Von Neumann would become interested in the problem of hydro dynamic turbulence and the theory of shocks.

This would become really important the next decade. This area of interest was also really complicated. Is so complicated even von Neuman's mind couldn't tackle some of these equations because hydro dynamics is very counterintuitive, especially when it comes into shock waves. So he would need a device to help him suss out the more complicated nuances, and that began von Neuman's interest in computer science. I'll talk a lot

more about that in the next episode as well. Now, in his personal life, John and his wife Marriott had a daughter named Marina, but von Neuman's private life was not one of matrimonial bliss. According to biographies I researched, he was affectionate towards his daughter, but he wasn't really involved in her upbringing at all, or in the care

of the household in general. He considered that to be the work for his wife, and that he was going to just dedicate himself to his scholarly work and then tying one on occasionally getting rip roaring drunk at parties. That was his Those were his two interests. So his relationship was strained. Now, Eventually Marriott would leave him and the two would divorce. Interestingly, Marriette would go on to Mary again. She married a physicist named James Brown Horner Cruper,

sometimes known as Desmond for some reason. This guy Cooper. He was part of the radiation laboratory at m I T. And you might remember I talked a lot about that particular lab on my episodes about Alfred Loomis. So if you want to learn more about that, look into the Tech Stuff archives for the Alfred Loomis stories. Now, von Neuman would be married a second time. His second wife was Clara Dan. Clara was, like von Neuman, from Budapest. She was also from a wealthy Jewish family. She was

born in nineteen eleven. As a teenager, she had become a championship figure skater. She also had been married twice already. She got married in nineteen thirty one to a man named Farrank Ingle, but they were divorced a few years later. Her second marriage was in ninety six to a man

named and Or Rapos. He was still married to her when von Neuman struck up a relationship with her, so they were technically they were both having affairs because von Neuman's marriage had not come to an indiet the divorce was still in process, so they end up getting into a relationship with each other. Clara ends up divorcing her husband, then Mary's von Neumann, and together they immigrate to the United States. Clara was a remarkable woman in her own right.

Absolutely she made significant contributions. She would become the head of statistical computing over at Princeton. She would become one of the early computer programmers of the Mathematical Analyzer, Numerical Integrator, and computer a k A. Maniac. More on that in the next episode two. And she was also a tragic figure. So John von Neumann died in nineteen fifty seven not a spoiler alert, happened decades ago, but we'll talk about

that more in the next episode two. So after his death, she would go on to Mary for a fourth time. This time it was to a physicist named Carl Eckhart, and in nineteen sixty three, she drove out to a secluded beach in California. She walked out into the surf and she drowned. The San Diego Coroner's office would rule her death a suicide, so a very tragic ending for her back to von Neuman to To wrap up this episode, I've covered a lot of his work, his early work

in mathematics. In our next episode, we're going to learn more about his involvement in the Manhattan Project. That's the of course, the super secret project that was dedicated to designing the atomic bomb. We'll also learned about how he helped design computer systems, and we'll learn more about some of his contributions to tech and science, as well as some of what people have generously described as his personality quirks. I would call them severe character flaws. We'll talk more

about those in the next episode. If you want to learn more about the show, including how to get in touch with me, go over to our website the addresses tech Stuff Podcast dot com, and don't forget we have a cool merchandise store. How cool while you're gonna have to go check it out and see it's a t public dot com slash tech Stuff, And remember every purchase you make goes to hell the show and we greatly

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