John von Neumann and the Bomb

this time to a woman named Clara Dan. Clara, who hadn't had any real formal advanced training in mathematics, would prove herself to be an incredibly adept mathematician and computer programmer in her own right, a remarkable woman. But back to von Neuman and the world as it was when this was all going around. So at this point, Europe was on the verge of war. This was ninety seven, so still two years before Germany would invade Poland, but

tensions in Europe were mounting. I guess it was safe to say so it seemed like a foregone conclusion that there was going to be some sort of war, and that if war were to break out on a large scale, the United States would probably get involved eventually. And so von Neumann made another decision. This time, he decided to become a naturalized citizen of the United States. He had been living in the US since nineteen thirty, but he

had not yet applied for citizenship. However, it was clear that if the United States were to go to war, he would need to be a citizen to guarantee his employment. He was worried that if he did not become a citizen, he might be barred from working in his field if he were seen as a European just living in the United States. So, according to one story about his application process, von Neumann was coached by his collaborator Oscar Morgenstern, who in the future would write that book on game theory.

I mentioned in the last episode that that book wouldn't come out till but the two of them were already working closely together. He and another mathematician and logician named Kurt Girdle were both on their way to their immigration interviews.

That is, von Neuman and Girdle together were on their way to these immigration interviews when Morgenstern asked if they had any questions about the Constitution, and reportedly Kurt Girl said that he had no questions, but he had seen several inconsistencies in the wording in the constitution, and he wondered if perhaps he should point those out to the immigration officers to make them aware of those inconsistencies, and Morgenstern reportedly discouraged that it sounds a little bit too

cute and like a punchline to me. But I like the story, so I decided I want to share it. Lighten things up a little bit anyway. Also around this time, John von Neumann received a request from a British mathematician from Cambridge uh The request was for a proctor visitor fellowship at Princeton University. That mathematician's name was Alan Turing. This would be the same Alan Touring who would later

propose what we now call the Turing test. This is the same Alan Turing who would go on to work on an early computer and help the British military crack Germany's secret codes during World War Two. Von Neumann had supported Turing's request. He had observed Touring a work on

several occasions. He had seen Touring when he visited Cambridge, and he said that he had also observed Touring at Princeton when Touring had visited for a while and Touring von Neumann would both be instrumental in the early days of computer science, two of the really important pioneers in that world. Now, speaking of early computer science, in the early nineteen forties, von Neumann was said to have a funny conversation with Claude Shannon, and I've done an episode

about Claude Shannon in the past. He was a mathematician who would go on to found information theory, so another very important person in this world. Anyway, in Shannon was preparing to present the result of his postdoctoral research work

and he wasn't sure what he should call it. He was torn between referring to his logarithmic statistical formulation of data as either information or uncertainty, and he didn't know which way he should go, So he asked von Neuman's opinion on the matter, and John von Neumann reportedly said something to the effect that what Claude Shannon should call it is entropy, because the mathematical mechanics in his logarithmic statistical formulation were the same as those used in entropy equations.

And more importantly, no one really knew what the heck entropy was in the first place, so there'd be very little chance of anyone challenging his thesis, which I thought was a pretty clever way of getting around it. So if you have to defend your ideas, just go with something so obscure that no one has enough expertise to contradict you. At least that seems to be the the

the key of the matter. John von Neumann never wanted to sit around without something to think about, began to look into the UH, the question of logical design, and eventually what would become computer science. He was also studying the mathematics of explosives. He became an expert on shaped charges, which is an explosive that is shaped in a way to focus and direct the explosive energy in a very specific way. So you've probably heard about this. These are

different ways of designing explosive devices for different purposes. It was likely this work that would lead to him being tapped to join a top secret research project for the United States military, the development of the atomic bomb, also known as the Manhattan pro object. Work had already been going strong on the Manhattan Project by the time John

von Neumann was tapped to join it. UH J. Robert Oppenheimer managed the laboratory with lots of top notch scientists working alongside him like Ernest Lawrence, Stanislav Oulam, Neils bore Seth Neddermeyer. Tons of very intelligent, very influential scientists and engineers were working on this project, all of them trying to develop working atomic bombs. There were three main areas

of research in the Manhattan project. There was using uranium as the nuclear material that would be at the heart of the atomic bomb, using plutonium, and then the hydrogen bomb or the fusion bomb, that would be the most powerful of the three, and it was also the most complex and the one that was on the longest timeline for development. For the uranium atomic bomb, the team had decided to go with a firing mechanism inside the bomb

to detonate the actual nuclear UH payload. So this was referred to in general as a gadget, the gadget that would make the bomb go off. And what it would do is it would shoot one mass of subcritical uranium, essentially a hollow uranium bullet, into another mass of subcritical uranium. In this sense, subcritical means that individually the two masses would not have enough uranium two thirty five atoms to

sustain a nuclear reaction. I've talked about this in the Nuclear Power episodes, but essentially what's happening is uranium when it decays, gives off some high speed neutrons, and if those neutrons were to collide with another unstable uranium atom, they could induce another split, another fission, and the reaction would continue. And in a nuclear power plant, you do this in in the hopes of creating a contained and sustainable nuclear reaction. When the nuclear bomb, you want something

that's going to escalate two explosive force. So the challenge was you've got to find a way of doing this in a predictable and controllable matter, in the in the sense that you don't want a bomb to go off prematurely. So this that's why you're using subcritical masses of uranium. That way, if atom were to decay, it would not set off a chain reaction that would cause the bomb

to go off prematurely. So when you fired this hollow uranium bullet at this massive uranium, those two subcritical masses would combine into a supercritical mass and that would start off the reaction that would perpetuate, releasing lots of energy, and in the grand scheme of things, that particular method would be easier to achieve than would be required for a plutonium bomb. So the gun method was not going

to cut it with a plutonium based bomb. For one thing, they had determined that they would need more purified plutonium than they would be capable of producing. It would require too much uranium to go through the purification process to

get the purified plutonium. It just wasn't feasible. But the team did determine that if they could sit around a subcritical mass of plutonium with a chemical explosive so it's got a chemical explosive coding around it essentially, and then ignite that chemical explosives so that it would direct the explosion inward. Instead of it being an explosion, it's an implosion. It all goes inward and creates a shock wave that compresses the subcritical plutonium mass so that it becomes super

critical and then boom, there's your atomic bomb. But Seth Neddermeyer, who was working on the implosion approach, was having a heck of a time getting a symmetrical emplode, which would be necessary to make this work. His implosions were coming off asymmetrical, and he wasn't sure how to fix that,

So enter John von Neumann. He took a look at the problem and suggested changes that would make the implosion method viable, and his ideas encouraged Oppenheimer, who dedicated more resources to testing out von Neumann's calculations, and it would become the operating principle that made the fat Man atomic bomb work. The atomic bomb Little Boy would use the uranium gun approach. There was another one called the thin Man, but that one never saw real operation because of problems

with its design. Work continued for a while to try

and make the plutonium work with this gun method. But they also discovered that if you had enough plutonium to set off the explosion, it would by itself release enough high speed neutrons to make a pre detonation reaction a near certain d. So, in other words, if you went with the gun approach and you were holding onto that nuclear bomb for any length of time, there was almost a percent chance that it was going to go off prematurely, just because the plutonium would be giving off enough neutrons

to set everything off. And if there's one thing you don't want with your atomic bombs, it's the tendency for them to go off prematurely. Now. I've talked about the Manhattan Project before and how complicated it was, not just from a technological standpoint, but also an ethical standpoint. When the Army took over the atomic bomb project in the early forties, experts determined that it would take about three years.

There's two, so I take about three years to produce enough uranium and plutonium to serve as the material in an atomic bomb. The projection ended up being correct, and it put the possibility of launching in attack with an atomic bomb in nineteen forty five. So even when people were working on these projects in forty two and forty three or d four, they knew that ninety five would be the earliest that they would be able to detonate

an atomic bomb. And uh, this puts you in a really weird position, I would imagined, because if you're working on something and you're hoping to prove that it's a a viable weapon, then part of you might be hoping for award to stretch on long enough for you to be able to use it, which seems pretty dark to me. It doesn't seem it is super dark. But anyway, the production of the nuclear material was just one of the

challenges that the group faced. Everything else would have to be designed and produced to make the atomic bomb of possibility in that tight time frame. So getting enough nuclear material was one challenge. Putting together the actual physical bombs, the the structures that would make this weapon viable, that was a separate challenge that also had to be completed in that same time frame. On July six, the researchers were able to conduct the first full scale test in

New Mexico. A little more than a decade later, in nineteen seven, John von Neumann's cause of death would be determined to be bone cancer, and there have been more than a few researchers who suggested his presence at atomic tests at Bikinia to all actually and his proximity to radioactive material likely contributed to the development of that cancer.

So while he played an instrumental role in the development of atomic bombs, at least the fat Man variety of atomic bombs, it would ultimately at least apparently contribute to his eventual demise. I have a lot more to say, but first let's take a quick break to thank our sponsor John von Neumann would work on the mathematics side of the Manhattan Project, so he wasn't actually building bombs.

He was working out calculations using out through math how an explosion would happen, essentially creating simulations in this way. This was incredibly important because it was not practical to do lots of real world tests with these designs, so he was using mathematics to test these ideas and say, well, based upon the various components, will this work. The project had access to IBM tabulating machines, which von Neumann would

work with. These would use punch cards to read and perform operations on data and then produce output that's on

yet more punch cards. Von Neumann felt that a general purpose machine similar to the ones he worked with at Los Alamos would be useful for all sorts of scientific applications, so he immediately saw the potential for computers, but he wanted something that would be much more flexible, capable of running lots of different types of calculations, not something that's set up to run a specific type of calculation and

that's all it can do. So he was also during the Manhattan Project selected to serve on the Target Selection Committee in nineteen he would be one of the people to recommend the future target site of the atomic bombs being built in the Manhattan Project, and the selection process for where the bombs would be dropped gets super duper

squiacky for me. The committee decided that for the atomic bomb to be seen as effective and to act as a deterrent, it should be dropped on an area that it would have the largest impact as far as devastation was concerned, and so that started to create the parameters that they were using to make their choices. It had

to be someplace within bombing range. They wanted someplace that would have closely built frame buildings because that would really show off the destructive power of the bomb, so it would have to be a city, and they also wanted to try and find a place that had not been bombed previously, so that way it would be evident how

destructive this atomic bomb would be. The atomic bomb would create most of its damage from the primary blast of the weapon, and then the fires that would follow would create a lot more damage in a wider area beyond the blast range. So the committee selected Hiroshima and Nagasaki. Nagasaki would become the target of fat Man as the bomb with the implosion detonation gadget that von Neumann had

worked on. According to Stanford, von Neuman also contributed directly in this effort by calculating the optimal flight path for the bombers to take to minimize the risk of being

shot down en route to the target sites. There was another example of the men maxing theory von Neuman had worked on nearly two decades earlier, and when he was talking about game theory, John von Neumann would go on to consult for the Rand Corporation, which at the time was operating as a think tank dedicated to running nuclear war scenarios. Neuman would argue for a concept called preventive war.

You could refer to this as a preemptive strike, or maybe more appropriately a nuclear sucker punch, because the preemptive strike is typically a strategy we associate with two nuclear powers. It's the concept of a nuclear power launching an initial attack in an effort to knock out the second nuclear powers nuclear capabilities as much as possible so that no retaliation is is is available. Uh Nouman was going further

than that. He was actually suggesting that the United States used nuclear weapons against the Soviet Union before the USSR could become a nuclear power at all. So essentially, he's saying, launch a full scale attack on Moscow because sooner or later they're going to build nuclear weapons. It's likely going to be sooner, so let's do it. Let's wipe them

out before they can build these nuclear weapons. So his argument was, assuming that nuclear war is inevitable once the Soviet Union developed the ability to make nuclear weapons, the best thing would be to launch that nuclear attack against Moscow. But it was based on that assumption that nuclear war is in fact inevitable once enough superpowers have nuclear capabilities. Uh, so far that hasn't proven to be the case. So ya for that. But Neuman wasn't convinced that that was

necessarily gonna hold true. He was actually quoted as having said, if you say why not bomb them tomorrow, I say why not today? If you say today at five o'clock, I say, why not one o'clock. So he was gung ho on this at the time. The United States, suffice it to say, did not follow up on von Neuman's suggestion, and at least so far, nuclear war has not happened, though I'm personally not a fan of the mutually assured destruction strategy that various countries have taken either, but that's

for a different podcast. Back at Princeton, von Neuman would become the manager of the Electronic Computer project. The goal was to design and build an electronic computer capable of using a stored program. Von Neuman had served as a consultant on an earlier project out of the University of Pennsylvania. He had by chance met the leaders of that project. That was called the Electronic Numerical Integrator and Computer, better known as NIAC. ENIAC was built as a general purpose

programmable electronic computer. It was funded by the Army Ordinance Department, which wanted a computer capable of calculating complicated ballistics tables. Earlier computers were mostly electro mechanical devices, which meant they had real moving parts that operated as switches. But that also meant those computers were subject to wear and tear, and worse, for the terms of running lots of cut relations. Their speed was limited because they had to rely on

this mechanical action of these various components. And electronic computer would eliminate all those moving parts and speed things up considerably. While ENIAC was still being constructed. Von Neumann would end up working with the ENIAC creators J. Pressper Eckert and John V. Mochley to design the successor to the ENIAC, and this would be EDVAC. That stood for Electronic Discrete variable Automatic Computer. So what was different about EDVAC. What

made it different from ENIAC. That would be the computer's internal memory. EDVAC had it ENIAC didn't. EDVAC would have enough and memory to store a program in it as well as the data that the program would work on. So you could take a program, feed it to the computer and the associated data, and the computer would hold it in what we would now call RAM or random access memory, and the computer's processor would follow the instructions

on the program and perform operations on the associated data. Now, essentially that's how all computers or most computers anyway, work today, But at the time it was revolutionary and the name people used to describe it was Von Neumann architecture. Now, before EDVAC, the program a computer would run was essentially part of the machine itself. So, like I said, with the tabulating machines in some cases, and then you had specific purpose computers, they could run one program because that's

physically what they were capable of doing. They were the actual design of the computer itself was the program in part. But other computers you could technically change the program, but it would require physically rewiring the computer, like removing plugs from a plug board and plugging them into different outlets, and that was a laborious process and it was really easy to mess up. If you plug a plug in the wrong place, suddenly you've got errors in all of

your programs. Where in all your your operations, I should say, because the plugging was the program. Now, while we call this approach to design the von Neuman architecture, it's important to remember this was actually a group effort. It wasn't just coming from John von Neuman. He's the guy who wrote about it and who popularized it, and he already had a celebrity status, so his name was associated with it,

but he was not the sole contributor. He actually had lengthy discussions with lots of other computer pioneers like Eckered Emotally, also Arthur Burke's Herman Goldstein, and together they all published the formal explanation for what people would later call von Neuman architecture back in in a paper titled Preliminary Discussion of the Logical Design of an Electronic Computing Instrument. In just a note here, I'm not saying this to diminish

John von Neuman's role in this. He was absolutely pivotal in the development of how computers work today. But it's also irresponsible to ignore the other contributors, so we have to make sure we we take time to acknowledge their work as well. While the internal memory element of ADVECS design tends to get the most attention, technically the von

Neuman architecture includes more than just that. So in addition to internal memory, the von Neuman architecture would describe a computer that would also have an arithmetic UH logic unit which would kind of evolve into a cential processing unit, a control unit which was in charge of sending information to different parts of a computer. UH. There was an interface for input and an interface for output, and a

bus the pathway that would allow data to transfer. So you had the control unit that was telling data where to go essentially, and you had the buses that would allow the data to go from one part of the computer to another. Then you had the arithmetic logic unit that would actually execute the operations. This computer would follow

specific steps. So a typical program would be fetch an instruction from internal memory according to the address designated by the program counter, add the length of the instruction to the program counter, use the control unit to decode the instruction, and then direct the computer to execute whatever that instruction might be, and then go back to step one and do the next step in the instructions. So that was

your basic computer program, which again sounds super primitive. There would never be a pure von Neumann architecture computer necessarily. There were a lot of variations on that, essentially improvements really to do stuff like error checking, which the original architecture did not account for. But it was the foundation for modern computing as we know it. I'm not done yet. I've got some more things to talk about with John von Neuman, but first let's take another quick break to

thank our sponsor. The AdVac team worked hard and had a working computer in nineteen fifty one in limited operation. They expanded that to normal operations in nineteen fifty two. But the ad back wasn't the first computer to make use of the von Neuman architecture. That honor would go to the Manchester Mark one in England, which performed its first operations in nineteen EDVAC was part of the Ballistics Research Laboratory and it would run operations for several hours

a day, every day until nineteen sixty two. Meanwhile, over at the Institute for Advanced Study in Princeton, which von Neumann was heading up, he was he was a part of that for all of his life. The I A S Machine was under construction. This was another von Neumann architecture computer and it also was ready to go in nineteen fifty one. Like d VAC, it was a binary computer, It had internal memory, and it weighed half a ton.

It was a big, big machine. This is well before the age of manaturization, when you're using stuff like vacuum tubes for your instead of transistors. Another area of computer science that von Neuman would pioneer was cellular automata. So what the heck is that? Well, cellular in this case means cells within a grid. So imagine you have a sheet of grid paper and now imagine that every square on that sheet of grid paper is a cell. So

what does the concept of automata come in? Well, now, Imagine that each of those cells in that grid paper has certain rules associated with that cell, and those rules relate to the states of the neighboring cells. So let's imagine you've got a sheet of grid paper in front of you. You pick a grid somewhere in the middle of the page. Now, in this case, it would mean that the rules for that cell that you're looking at depend in part on the state of the four cells

that border it. In the cell above, below, and to either side of it. This is what we would call a von Neumann neighborhood. By the way, Now, let's say that all the rules have to do with the color of the cell. So maybe the central cell that you've picked, you you create a rule for that set that says, if the cell above me is red, then I should turn blue. Now, imagine all the cells in this grid have their own rules that relate to their neighboring cells,

and all of these rules relate to color. Now imagine all those rules will carry out a according to time steps, almost like turns in a board game. And so you designate one cell to have a certain color. You're you're starting everything off. You say, all right, I'm going to change the color of this cell to blue, you advance the time step by one. Every rule that is in

place for those neighboring cells then takes effect. So some cells might and that our neighboring and might say, all right, well that means I have to turn red, or another one might say I have to turn yellow. Another one might say, I do nothing at all, because the the fact that that cell is blue doesn't change anything for me. And then you advance the time step again. And now the neighboring cells of the cells that changed are reacting to those changes, and you advance the time step again,

and so on and so forth. Now that approach has been used in a number of really interesting applications. I gave a very abstract, simple version, but there are real world applications for this, and it would also become one of the components in something von Neuman theorized about that I mentioned any podcasts about Maker Bought, and that would be the universal constructor. Von Neuman's universal constructor was an abstract notion of a self replicating machine that he was

able to prove through this cellular automata approach. So when you would run this machine that was a universal constructor, it would be able to make a copy of itself. It would have blueprints for its own design, a method of following those blueprints and creating a copy of them, producing a copy of itself, including a copy of the blueprints, so that the copy of itself could then go on

to make a copy of itself. So he could program each cell in one of these grids, so that would follow a sequence within a certain number of time steps in order to create a specific pattern to initiate a hoppy of the original and in the next cycle of time steps, it could do a copy of itself, and so on and so on, over and over and over again. Each cell in von Neuman's original proposal could have one of twenty nine different states at any given time step,

based on the rules he had created. So, you know, I was saying red or blue, you know, or maybe it's clear or red or whatever. That's very you know, that's obviously binary. It's that's two states. You're either clear or your red or your red, or you're blue, or whatever it may be. He had twenty nine different states that each cell could be in. Now, this did not create an actual physical machine capable of doing work, but it acted kind of like a simulator for such a device,

and he could make this work. He could make a set of rules that a grid that applied to a grid, and that if you were to initiate the action, it would actually create copies of a design over and over and over again, and within a certain number of time

steps per copy. So it it acted as kind of a starting point for a lot of other work in this field, ranging from stuff like the rep rap project, where I was talking about a three D printer capable of printing its own copy, to the proposal of nanotechnology devices like molecular assemblers. This is a kind of a science fiction e sort of concept. These would be microscopic a similars that could construct material molecule by molecule or maybe even atom by atom um and that would allow

us to make all sorts of stuff. If we could get down to construction on the molecular level and scale it so that you could produce something in a reasonable amount of time, you can make all sorts of things. This is kind of the basis of the Star Trek concept of of having the replicator. Von Neumann wrote a book on the subject, but it was not published until after he died, so his health was beginning to fail

in the mid nineteen fifties. He received the Enrico Fermia Award from the Atomic Energy Commission in nineteen fifty six, and at that time he already knew he had cancer and that his time was short. Towards the end of his life, von Neumann, who up to that point had been agnostic, he didn't have any real belief in the existence or non existence of God. He actually converted to Christianity.

The prevailing thought is he did so because he was terrified of death, and according to one biographer, he was said to have entertained the notion that Blaze Pascal was onto something in the form of Pascal's wager. This is a philosophical argument that states human beings should really believe in God because they're betting their existence of God with

their lives. So the argument goes that a rational person should behave as if God definitely exists, and they should seek to believe in God, because if God does not exist, you don't really lose much when you die, You encounter the exact same fate as everybody else. However, if God does exist, and believing in God and behaving in a certain way is a prerequisite to going to Heaven versus going to Hell. Then you stand everything to gain if

you go by that philosophy. So this falls in line with von Neuman's game theory that whole minimize your losses in the event of a worst case scenario. John von Neuman died on February eighth, nineteen fifty seven. He truly was a genius, and he made numerous contributions to our understanding of mathematics, not to mention the foundations of modern computing.

And I did say at the beginning of these episodes that I would also address a few traits that some people have finally described as quirks, but I feel are actually much deeper flaws. One was his love of fast cars. Now that in itself isn't a flaw. There are a lot of people who love fast cars. Scott Benjamin is a good friend, and he loves cars. But von Neumann would drive so fast and so carelessly that he earned

a reputation for wrecking cars for totaling them. It happened so regularly that one intersection at Princeton was called von Neumann Corner because he had wrecked more than one car in that location. He was said too often drive while

he was distracted, including while he was reading. So that's not ideal as it shows a level of irresponsibility that could into the injury or death of someone, whether it's von Neumann or or someone completely not connected to the event at all other than you know, being in a colle vision. Von Neuman was also something of a hedonist.

He was known to eat and drink to excess. His love of parties would continue throughout his life, and again, that's not necessarily a flaw unless it is taken to extremes, and from what I've read, it sounds like there might have been a few extreme cases in von Neuman's life. And he was also known to be kind of creepy. He liked being around young women, and he liked looking

at their legs a lot. Apparently he would go so far as to lean down to look underneath desks in order to get a look at legs and maybe even pick up the skirt of a woman, which is absolutely despicable.

It got to a point where he had such a reputation for doing this that some of the secretaries at Los Alamos during the Manhattan Project actually would have cardboard sheets that they could slide in front of their legs under their desks to blow his view, which is pretty darn creepy not cool anyway, There's no question that he

was brilliant and a genius. But I'm also glad that, even though he was a genius, that not all of his ideas were adopted readily, because his argument that the United States should launch a preventive strike against the Soviet Union to wipe out that country before it could develop its own nuclear weapons seems particularly horrific to me. Millions of innocent people who had no say in the nuclear aspirations of the country they lived in and no contribution

toward the development of nuclear weapons would have died. If that were the case, it would have been a massive slaughter of people who had no say in the eventual development of nuclear weapons. I find this notion impossible to justify.

And while von Neuman argued that a nuclear war would be inevitable should the Soviets develop the capability to manufacture such weapons, and that a nuclear war would re devastation much much larger than launching a preventative strike against the Soviet Union, it turns out that that didn't happen at least it hasn't happened yet, So maybe one day there will be a nuclear war, which would in fact be absolutely terrible. But it may be that it's not a

foregone conclusion the way von Neumann believed. So we can look back and say, at least so far, it seems like not bombing a country out of existence h for fear of them developing nuclear weapons was the right choice, because they did not launch a nuclear attack against us. They developed nuclear weapons, but we haven't had a war, so we would have killed millions of people and not

prevented a war because the war hasn't happened anyway. But still, all of that being said, we have to remember von Neumann made incalculable contributions towards multiple disciplines, and the world would be a very different place if he had not done that. So for that I am thankful, and I think it is important that we take it to consideration all of a person's traits, their strengths, their weaknesses, their virtues, and their flaws. We should not just idolize people without

critical thought. That is not a responsible thing to do, nor should we dismiss all the contributions. We have to weigh everything in kind and try and take a human perspective. All of us have contributions, all of us have flaws. Ah, but yeah, that that sums up my thoughts on von Neuman. He has written a ton of very information, informational, very educational, very interesting papers on numerous subjects. I urge you to go out and find some of those if you are

really interested in the various topics I've talked about. They are very academic, so if you don't have the schooling or the expertise in those areas, you may rapidly find yourself, uh finding it really challenging to understand what is going on. I know I did, I've It's been a long time since I've taken calculus, for example. Uh. But they are incredibly important papers, so if you want to learn more, you can seek that out. I'm still looking for a

really good biography about von Neuman. I've read a couple, and I don't think either are the ones I've read have been exactly what I'm looking for. So if you happen to know of a really good biography about von Neumann, I'm interested to learn more about that too, So hit me up. You can go to our website that is tech Stuff podcast dot com. There you're gonna find all the different ways to contact me, you'll learn more about the show. You can visit our merchandise store that's at

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