Mathematical Games [Episode 7: History and Science of the Manhattan Project and Oppenheimer Movie]

Hello everyone, I'm Ed Peg Jr. And I'm waiting at the moment for others to join. So we'll give this a few minutes. And somewhere here I've got another link. And I think we're ready to start. So I met Peg Jr. And I'm going to be talking about things related to the Manhattan Project. You might have heard that there's a, a movie coming out called Oppenheimer Today. In fact, here's, here's part of the trailer for it. I'm not sure what that structure is there, but I think that's the, the soccer ball configuration of, of hexagons and pentagons for a 32 part series, but not totally sure. So I guess we can get into it. Let me see here and let me just sign in here, Make sure chat's working. So anybody who wants to feel free to, to post something on chat and I'll be glad to pause at that point. So Mathematical Games was run by Martin Gardner for Scientific American. And that was a big influence on my life. Martin Gardner ran the column for, for 25 years. And since then there's frequently things that relate to work that Martin Gardner has done. So I've started this series to try to go in depth for things related to recreational mathematics. And many times we end up going back to material that Martin Gardner talked about. So one person mentioned several times was Feynman by Barton in Martin Gardner's columns. And there's many things in recreational math and interesting physics and cellular automata and other things that relate to Richard Feynman, who was one of the people who worked on the Manhattan Project. Richard Feynman was also the advisor to our company's founder, Steven Wolfram, and they worked together for several years on things like cellular automaton. So I'll get to Feynman's objects at the end. We, I think we have more of his demonstrations relating really into Feynman on demonstrations than anyone else of people who were on at the Manhattan Project. But there might be more items related to Einstein. So here's a bit more on Richard Feynman worked in quantum computing, particle physics, and he was one of the people who talked about the Challenger disaster. One of the people he talked to was the person who installed the O rings on the Challenger, who happened to be my office mate for two years back when I was in Lockheed Martin. I found that out when the Challenger came up in the news and he nearly passed out at his desk because it was difficult for him. So I'll be using a couple of Functions. Here's a new function that just got posted to the function repository Credit Demonstration. So if you know the name of a demonstration, you can just use this and it automatically inserts it into a notebook. So I use that to help build this talk. And without further ado, Chadwick, Rutherford and Thompson is an interesting trio. Thompson taught Rutherford and he taught Chadwick. And Chadwick discovered the neutron. Rutherford found the proton. Thompson developed the electron. They all knew each other. James Chadwick was the person in charge of the British wing of the Manhattan Project. And he was the only person other than Oppenheimer and the lead military people that had access to everything except for the plutonium. He wasn't given access to that area. So he, Chadwick was one of the people who worked on the Manhattan Project. With all these new things being found about atoms, Einstein wrote a letter with help from Enrico Fermi and Al Sparg. I'm probably mispronouncing various of these names. Albert Einstein wrote this letter to Roosevelt saying that it was important to look at what nuclear forces could do because the Nazis were were investigating it. One of the people that helped write that letter was Eugene Wigner, who is one of the people who figured out how the atomic nucleus and symmetries and everything else work. And the Wigner distribution is one of the things we have a demonstration for. So as we change the quantum number of something, the Wigner distribution changes. And this is one of the functions in our demonstration area. There's also the Wigner quasi probability distribution, also known as the Wigner 3J symbols. And here's a demonstration done by Stephen Wolfram. And as you change the parameters of the 3J items, you get these different fields. The Wigner 3J symbols give amplitudes for pairs of quantum spins in different states. So one of the people that wrote, helped write the letter did many things in math and physics and we just happened to have quite a few demonstrations relating to him. Leo was another who was involved with the creation of the letter. He was the one who patented the idea of a chain reaction. He helped with the Einstein letter and worked with Enrico Fermi to get a patent for the first nuclear reactor. He also worked on the electron microscope, linear accelerator and cyclotron. And here's. And also the refrigerator Refrigeration was something that he and Einstein worked together on and relating to the refrigerator. You have excited states of atoms and how you can perhaps cool with them. And Maxwell had this thought experiment called the Maxwell's Demon. And it was Leo Slizzard who managed to solve the Problem with help from Leon Brion. Let's see here. So they wrote the letter that uranium would possibly build a bomb with a destructiveness vastly greater than anything now known. One person who was brought in for that, for the actual report to Roosevelt was Edward Teller. And he did a lot of work with Oppenheimer. And he was one of the people that stayed on the project when Oppenheimer left. It was mostly Edward Keller that was, was the one who stuck around to try to develop more such as the hydrogen bomb. Most physicists tried to get away from the project. He was a little bit of a difficult personality. And the person who was sort of his foil in all this, who I'll mention more at the end, is Stan Ulam. Whenever Edward Teller had an idea for something, it was Stan Ulam's job to try to show that what he wanted to do was impossible. And with the, with those calculations by Stan Ulam, the United States ended up saving billions of dollars on projects that wouldn't work. So one of the things Teller worked on was the mechanism for the plutonium bomb. And so as the ignition starts, it basically forces everything towards the center and then chain reaction starts. And that is the same device that's shown here in the trailer where you've got a 32 object structure all aimed at a center point. And those 32 objects, this, the soccer ball configuration, gives the 32 charges. See anything else I want to mention here? John von Neumann is one of the people who also worked on this, helped develop the first computers. And here in the University of Illinois it was von Neumann and Oppenheimer that got the first computer built here at the University of Illinois back in the. Well, I'm not sure the year at this point, but iliac2, Let's see. And here's another that Teller worked on is posh Teller potentials. Here's a demonstration by, by Klaus where you can adjust the fields and get the different results of non relativistic wave equations that come out from post Teller potentials. So these are different items that relate to people that worked on the Manhattan Project. Let's see here. Another is another with posttellar potentials. And this is by Psy. Blender is the one who put together this demonstration and he describes them here. Schrodinger equations for classic potentials of this form are known as Klaus partial Teller potentials. And they're exactly solvable. And at the end, as Psy mentions, a remarkable property of these as they change these. These functions have various special properties. And they will eventually be available on the community site. This whole talk will go on to the community site and all of these are demonstrations that are available in the demonstration project. So another person who brought in in 1941, plutonium was discovered by Glenn Seaborg and his understudy. And the day before Pearl Harbor, Ernest Lawrence was brought in to figure out how to separate uranium 235 from uranium 238 electromagnetically. Here's a picture of him. But we were in the midst of a war as soon as it started. So in order to build the cyclotron they couldn't use copper because it was, it was important for the war effort. So what they did is they went to the repository and got 14,000 tons of silver instead, shipped it to a place in New Jersey and there was refined into billets which were then sent to Oak Hill, Tennessee and they built what's called the racetrack, the, I think the Y12 racetrack. And it's basically the largest object ever made with silver in human history. And with that they separated isotopes for building this big bomb project. And here's a demonstration that shows a bit of how about how the cyclotron works developed by Ernest Lawrence. So this was built in concept and then they built it in giant scale 10 years later using silver. I'm not sure if that will be in the movie, but it'll be cool if they did show the racetrack. So we have Robert Oppenheimer here and Ernest Lawrence. Well, my friend Si here, he drove this car and he mentions it here. On a personal note, I spent the summer of 1956 in the T dimension in Los Alamos where Oppenheimer once reigned. For a month I lived in a house with my supervisor Rolf. While he was away, he was in possession of a beat up 1937 Plymouth that had once belonged to Eipenheimer. And as I drove that car, I drove that car to work for a month. The one Oppie drove to San Francisco to see Gene Tatlock. So possibly in our audience right now is Cy Blender who drove Oppenheimer's car and it features prominently in the movie. Here's more on Oppenheimer, the father of the atomic bomb. He also wanted to get control of nuclear power afterwards. Let's see. And one of the things he worked on was limits of gravitation. The Tolman Oppenheimer Volkov limit of two solar masses is an important limit for whether a star will collapse or turn into a black hole or a neutron star. The, I guess the Tendrisikar limits. I'm probably watching that name later added more bounds to to how these work. So but here's a demonstration by Sai who once drove Oppenheimer's car. That's in our demonstration project. And Oppenheimer was one of the people who worked on this. Another Oppenheimer is the Born Oppenheimer approximation. And another demonstration by Psi as these are changed the. Let's see how he describes this diabetic. When a diatomic molecule undergoes a transition it changes its vibrational and rotational quantum numbers. And he this is all explained in gory details. And the Born Oppenheimer approximation is, is one of the things used in these calculations. Let's see. So. Another person who worked there is Hans Beth and he worked on on astronomy things, astrophysics, quantum electronics. But one thing he's known for is righty tighty lefty Lucy which he based on relating the right hand rule of vector products. That's how he remembered it, how tightening bolts work. Hans Beth also applied double groups to physics. The Mollen series uses double groups. And he was the one who, who wrote the original articles in 1929 for how to describe these. Klein was the, was the one who first applied them to Mathematic. Another item is the BETH ansatz of quantum integrable models. And in 1980, in 2006 this model was expanded to make this periodic box ball system. Let's see if I can expand this more. That seems pretty simple. I'm not exactly sure how these work, but these develop periodic boundary conditions leading to quotient states, spaces and rigged configurations. And these came out of study of the BETH Ansats. BETH lattices which are useful for calculating the effects of a chain reaction are also known as Kary trees. So, so here's a sample K ary tree in Mathematica, but they're also called BETH lotuses. Another person who's in the movie Isadore Robbie, played by David Krumholtz is this person. He won the Nobel Prize right when the project was getting started off for nuclear magnetic resonance, which is now used in CAT scans, magnetrons, microwave ovens, microwave radars. In fact, when he got older he needed to go to the hospital to have something study and he was put into a CAT scan. And he was quite amazed that this thing he developed was actually being used to save his life. Another thing he worked on was rabbi frequencies. So here's a demonstration. Polarized polytron fields on the point car sphere. And we can change the rabbi frequency and see how that changes the model. Let's see. And there's various things you can change in the demonstration, such as the rabbi frequency and the polaritron lifetime. Werner Heisenberg of the famous uncertainty principle also developed the Heisenberg real matrix group. And that has what's called a null space that can be defined. And this demonstration shows how you can modify the null space torus based on the Heisenberg real matrix group. Let's see. Paul Dirac, another person who worked there, Worked with Schrodinger and he came up with various tricks to show how these seemingly impossible items might work. One of them is called the belt trick, where you've got a middle object which can't change, but things need to twist in strange ways. So here we have a twist going on. The middle part is, is basically staying unmoving. But as, as things move around the way Dirac described, we get a desired result in terms of spins. And basically he's shown that all these weird items can happen on an atom in such a way that the spins can change a state without affecting the central part of the object. So this belt trick was, was developed by, by Dirac to show how it was possible for, for with the concept of double twist for everything to work out nicely. So you start with a belt, you want to get it into a different set of spin states. And this belt trick shows how that is possible to do and it does various homotopy work on the lie group. Much of this stuff I, I do not well understand, But I'm, I'm trying to familiarize myself with all the people that were going to be in the movie so I can perhaps enjoy it more. I haven't seen the movie myself by the way. It, it only comes out today. So Enrico Fermi was another who worked in the project with Oppenheimer. And here's a whole bunch of names mentioned in one demonstration. The quantum mechanical effects of a gas can be predicted in various ways. And there's a Fermi Dirac formulation of Bose Einstein formulation and a Maxwell Boltzmann formulation. And at high temperatures they, they all tend to agree and things get stranger at some point, at this point here, I suppose. But there's good agreement between these three items in terms of quantum mechanical effects. Albert Einstein is another who started the project off. I don't think he actually worked went to the Manhattan Project directly. Probably a good thing because Albert Einstein was very well known and if he traveled anywhere the press would have, would have gotten wind of it. So the fact that he kind of stayed at one place and was kind of stayed boring help keep the project secret. And of course, we've got many things related to Einstein and demonstrations, including gravitational lensing, where if you, you can change the mass of the lens to show how it, how it works on different field. These are all predicted effects on different lattices. For gravitational lensing purposes. We can also look at Einstein solids and there's a description of how these work here. A simplified model of a solid where each cell is represented by an oscillator. And as you change these, you get different results of energy and occupancy. Working on Boltzmann distributions. And we get back to Feynman, who was kind of the. The popular guy at the Manhattan Project. And one, one thing he worked on later was called the wobbling plot plate. So as he describes it, I was in the cafeteria and some guy fooling around throws a plate in the air. As the plate went up, I saw it wobble. And it was obvious that when the medallion went around faster than the wobble. So he started figuring out the motion of the rotating plate. And as he did his research, the difference of angle and the velocity and the time changed, the number of turns and wobbles. So he figured out that when the angle was slight, the medallion rotates twice as fast as the wobble, 2 to 1. And it came out to a complicated equation. He worked out the equations of the wobbles, and then he recalled electron orbits and revativity and the Dirac equation for electrodynamics, and then brought in quantum electrodynamics. And then from this equation he got from the wobbling plate, he came up with a discovery that won the Nobel Prize. And now the replica of this Cornell plate is at the exhibit for the centennial of the Nobel Prize. So basically, he just started to work on a somewhat silly problem. How does this plate wobble? And he wound up making a major discovery and won the Nobel Prize. That's sort of the. One of the natures of recreational mathematics is sometimes you'll get results that you don't expect. Here's another Feynman object. You've got a circle here, and you've got basically two points. You've got the green point and the blue point. And you basically start drawing the circle, and you do the perpendicular bisector of the line segment of the blue point, and you use that to make a. A point on the, on the radius as it's rotating around. So here on the blue, we've got a perpendicular bisector. And we're just basically figuring out the intersection point with the line. That's Drawing the circle. And Newton showed that if you do this set of steps, you get an ellipse with the center of the circle and the other point that you picked as the foci of an ellipse that generated. And Feynman used this particular construction in his, in his famous lecture here. And Bob Bremer came up with a demonstration that basically shows exactly what Feynman showed in his talk. Another is a stellar automaton, what's called the Mazoyer Firing Squad. In Lectures of Computation he talks about message passing. You can only influence neighbors to either side. And basically from some starting configuration, you want all the characters on the entire line to reach the same color. And based on the number of soldiers, this is one method that, that works. It's. And the seller automaton solution is known as the Firing squad. And this, this demonstration by Brad Klee is a demonstration of how the seller automaton works. It's a seven color rule. And for the original problem it would be, it would take a long time this many steps in order to. Reach a particular value. And Stan Ulam also worked on the Manhattan Project and he did more later. He also did a lot of initial work with seller automaton and a lot of work on computers. So here's one of his solar automatons. And the way this works is down here. Here are the rules. And basically if the growth touches itself, there's an elimination step and it grows somewhat oddly. So there's a little bit further back. Another item he worked on was the primality bit spiral. So as he describes it, he was at the most boring lecture ever given. So he started doodling and he basically put the numbers in a spiral. 1, 2, 3, 4, 5, 6, 7, 8, 9, so on. And he just basically wrote it in a spiral. And the lecture didn't stop. So he circled the prime numbers and he noticed that they made this pattern and he thought that was generally interesting. So we had a computer make a much larger grid for what this looked at, looked like. And then he sent the result to Martin Gardner. And Martin Gardner liked it enough that he wrote a column about Ulam spiral. And so it got nicely popularized. And it turns out when you do enough structure on the primes, you'll get these different patterns that fall out. One thing that was noticed by Euler with the polynomial, if I remember off the top of my head, x squared plus x plus 41 will give a prime number up to x equals 40. Another item Olam worked on was the early experiments with chess on a computer. But it was difficult so they tried simplifying it. And it was Sy Blinder who happened to be the one who worked with ULAM on this project. And this computer chess, which is things that Martin Gardner wrote up in mathematical games under the name Los Alamos Chess. So it basically has a smaller board, simpler pieces, Castlene is still possible, but there's no in passant. And with this smaller board they were able to get the 1950s era computers to actually work on chess problems on the Maniac 1 computer. And it's possible that SAI is in the audience with us if he wants to say something in chat. Foreign. Let's see. So we have all these people that worked on the Manhattan Project and I wanted to get familiar with, with these people before I saw the movie. And it turns out that we had many demonstrations and there, there's, there's about a hundred more on the demonstration site relating to these people. So I thought I'd go over them. And that I believe is what I had prepared. Yes, I'll be glad to go over any of this if anybody would like to see more. And I'll be glad to talk to anyone. And go ahead and post in chat if you have anything. I'll be glad to try to answer any questions. And I believe this is going to start playing tonight. Thank you, Dugan. And you can basically look up any of these people at the demonstration site and you'll see them and I'll have this posted to community probably within a few hours. Yes, many thanks. I think we do have a few things related to go, but they don't actually play go. Well, you can play a two player game, but I don't think we have any computer GO demonstrations at this point. I, I believe some of the early computers did try to solve go, but they didn't get very far. But they've gotten much further with plain GO recently though I think that is a good place to call it for now. And I thank everyone for att.