Folks, I'd like to invite you to settle into this space, to settle into the space. This is the workshop entitled Stories from the Movement, and very important, Implications for the Future. Meet Hollis Watkins. He is someone from whom I continue to learn so much in the telling of his very personal story, and in the story of the larger movement, and its focus on righting wrongs and making justice. You will also have the opportunity to share in the music of the movement. Yes? All right, without further ado, Hollis Watkins. Thank you very much.  I say a little bit because when you have a story that spans over 50 years, the amount of time we have forces you to reduce it to a little bit. I am the youngest of 12 children. My parents were sharecroppers when I came on the scene. At the time that I was born and growing up, racism was very much alive and well in Mississippi.  Because if I didn't do that, I could reap negative consequences, such as them initially considering that I was disrespectful to them, and if they considered me to be disrespectful, they might slap me, they might kick me, they might beat me, or they might even have me put in jail.  And if you were charged with eyeball-rape, then that meant an all probability death for you. Now, I don't know whether most of us are familiar with what I mean when I say eyeball-rape does not take much to eyeball-rape someone. I say that because from the time that I first mentioned the word of eyeball-rape, I have for the most part eyeball-rape every female that is in this small audience. That's just how easy it was. We look at that, but that was a reality for blacks. The public educational system was very, very poor for blacks. There were no public libraries that I could go to, none. I was an athlete of some sort, played baseball and basketball. When the five of us black guys got out on the court playing basketball, there were times when you could see at least three different uniforms that we wore. Why was that? That was because they would not buy uniforms for black students to play basketball in. They bought those uniforms for the whites. And when the whites felt that they could no longer play in those uniforms and needed some new, the white was given the new, and we were given those that the white students were discarded. We look at a lot of Eden facilities. We could not do that. We didn't have facilities by which black could go and eat, and especially if they were owned or if white people attended were the owners of those facilities. We had to go somewhere else. As time began to change, they allowed us to come to the back of the building where they had a wooden window and you knocked on the wood window. And that's where you place your order.  And once they completed their waiting on the whites, then they would bring your order. Many times we didn't have the time to wait for the 30 or 45 minutes of an hour to get a hot dog, to get a comb of ice cream, to get a hamburger. But this is what we had to live with. I remember when I first started going to school, we had to walk. The black children had to walk. Can you imagine me at the age of five and six walking to school and it was nearly three miles from my house to the school. The white students were riding the bus and when it would rain, the bus would splash mud upon us if we didn't jump out of the road and get in the edge of the woods. These are some of the treatments that I was a part of. My first time having first hand knowledge and information and seeing discrimination prejudice taking place right before my eyes, I think I was about four and a half years old. I went in the town with my father. My mother gave him the list that he needed to bring back. One of the items on that list, I never will forget it, was sugar. My daddy came out of the store and he didn't have sugar and sugar was one of my main items because my mama could throw down making some things, you know, using a little sugar. So I wanted to make sure. So we came out of the store and I assumed that they didn't have sugar in the store. He was standing on the sidewalk in the streets there talking with some other black man. And I saw white people coming out of the store with sugar. So I said to my father, look, they got sugar.  So he told me, be quiet, be quiet. And I said, no, you know, mama told you to be sure to get some sugar.  And what I found out a little bit later was that there was a shortage of sugar that particular year. And because of there being a shortage of sugar, they were not selling sugar to black people. These are some of the things in my early years that I had to go through. But I must say, my father laid a foundation for me in a few words that I'm still standing on today. What was that foundation? What was those few words? My father said to me, he said, son, he said, I want you to always stand up for what is right, even if you are the only one standing. I thought about that, I looked at that, and then it came to me that if I'm standing up for that which is right, then that means I'm going to have to stand up against all of that what is wrong. And I said, wow, that's a huge task.  All of this stuff that folks is doing to us, and he's not bringing forth a little punishment, I don't understand that. And when I would attempt to approach some of the older people with that question where I could get a better understanding, they tell me, we can't talk about that now, you understand by and by. So I was in such of what was wrong and how and what I could do and when I could do things and what would be the best manner for me to stand up against all of the evil and the wrong doing that I saw taking place. And finally, it said that I needed to hook up with some other organizations, some other groups of people that was doing something about some of these different things that I was seeing. And that's when I got my first start, I walked out to be involved in the movement. See at that particular time, you were risking your life to let the public know that you were a member of the NAACP. For a number of years, I didn't know my father was a member. Too scared to ask because, you know, children didn't meld around in old folks' business. So I never asked him. But lo and behold, one day we were working in the field. He had on his overalls and we were working on a plow, trying to get it fixed. And all of his wallet and everything fell out of that top pocket on the ground. And it looked like it was just perfectly placed where his NAACP membership card ended up being on top of everything that came out of his pocket and his wallet. So I looked at that and then I looked at him. He looked at me. He never said anything and I never said anything. We kept on working. But in my mind, I'm saying, uh-huh, he's doing some things. And I got involved with the NAACP when I was 17, I became a part of the youth's chapter of the NAACP. And then that was in 59. And then in 1961, I got involved with the Student Unviolent Coordinating Committee. And that's where I was blessed to have all kind of experiences that I had not thought of or didn't believe, you know, because I had the opportunity to go to the Woolworth lunch counter and attempt to get a cup of coffee. And that granted me 34 days in jail for attempting to do that. You know, another friend of mine, well, three other friends of mine decided that they were going to go to the Greyhound bus station and attempt to buy a ticket. That granted them 30 days in the county jail. And after getting out of jail, one of the students, the young lady, attempted to go back and enroll in school where she was attending. And they said, not here. But the students had been organizing why we were in jail. And they had said that if their fellow students were not allowed to come back to school, they were going to have a school walkout. They did that and they walked out. Over a hundred and something were arrested. All of those that was over the age of 18 had to spend time in jail. But those that was under 18 was relieved to their parents. So these are some of the things that we've had to go that's a part of my story. There are many times when I was chased by white men in vehicles where had I been caught, I would have been killed. And that's why today, it's not because I'm originally an old country boy that I'm thankful for dirt roads. It's because the dirt roads saved my life and saved the life of a number of other civil rights workers, both black and white. Why? Because when those men in those vehicles started to chase us, we were out there in the rural, with them dirt roads, the tires from our vehicle kicked up dust that created a buffer where they could only get close enough. They couldn't get close enough to shoot us. So it saved our lives by the dust creating the buffer. So I say that to say it's too often that a lot of times we overlook and ignore the little bitty things that happens, but in many cases the little bitty things has huge, large significance, large meanings. Some people have asked us, well, how could you keep the attitude? How could you keep the spirit? One of the ways we kept up the spirit of ourselves and one another was through singing. And I'm going to invite and ask all of you to join in with me in just a little bit in singing some of the songs. And we didn't just sing the songs for the heck of singing it, the songs had meaning. All of them had meaning and we sang them for specific purposes. And we'll talk a little bit about that. But another road for trying to get our people registered to vote, coming out of some of you may have heard of Greenwood, Mississippi. This is where the man named Byron D. Lebeckwood came from that killed Mecca Evers. He came from Greenwood. But that's where we were trying to get large numbers of blacks registered to vote and was arrested, sent to the county farm and then after being sent to the county farm was transitioned and transferred over to Parchman, the Mississippi State Penitentiary where I spent 55 days in maximum security unit on death row. When you're on death row, on one end of the row they have a place that's called Maximum Security Unit. And they also call it the whole. They call it solitary confinement. That's what was at the end, one end. And at the other end of death row was the electric chair where they threatened to take me to every day. They handcuffed me to the bars where I'm handcuffed to the bars like this so I had to stand up the way I'm standing now or I could bend my knees slightly in this position. But that's what I had to deal with for trying to get black people registered to vote. And we know and learned from what happened with the three civil rights workers in Mississippi during 1964. They would set up traps and tricks for you. At one particular time, I don't know whether it was a trap or a trick or whatever. But when the police finished questioning me, they put me in a little room all by myself. That was approximately 10 feet by 10 feet. And I'm sitting there and next thing I know the door is opening. Three white men walked in the room. They had a rope in their hand. The rope had a hanging noose in it. And they will forget just beneath that noose that was a red ribbon. And they looked at me and they said, okay, they used the N word. Yes, they said, okay, nigga, get up and let's go. So we're going to have a hanging here tonight and you're black. I won't say what those words were. It's going to be first. So me having been brought up in a very religious family and having faith in myself and especially in my God, I just leaned back in my chair. And looked him in the eye and slightly smiled because deep within, I felt God had previously talked to me about my activities and said to me that I would never be killed in the civil rights movement. He talked to me about another thing and said to me that if you ever go into the military, you'll never make it out alive. So there were two things I always had. I ain't got to worry about going to the military because I intend to stay alive. So I am not going and I never did go. And when those three white men had the rope coming after me and me looking them in the eye, I'm saying to myself, I know what you know not. My God has promised me that I would not be killed in the civil rights movement.  And that's why I could kind of smile and they walked away. Now, there was a time when I was truly set up, attempted to be set up. The jailer came and told me, Sir Hollis, since you've been such a good nigga, haven't caused us any trouble, we're gonna let you go. I was supposed to be excited about getting out of jail and all of that. So I asked him, I says, who put up my bond money? He said, nobody, since you've just been good, haven't caused us any trouble, we're gonna let you go. So I let him know that I knew that the system don't work like that. I knew I had not served my time. If nobody had put up my bond money, it was something wrong with that picture. So I told him, that's all right, I'm going back into the cell. And when I turned to go back, he told me, Sir, hold it right there. Don't you move.   Because if you had, I was gonna whistle. And when I whistle, them boys was gonna come from around the side of that building with them dogs and the dogs was gonna have their dinner in your backside. And then he actually whistled. And when he whistled, two black men that were trusted came from around the side of the building with bloodhound dogs. And I'm saying, just look here. The jailer had two choices. He had a choice of putting the dogs on me. And he had a choice of shooting me in the back and saying I was attempting to escape. And since I would not adhere to him telling me to stop, he had to shoot me to stop. That was a trick that they tried to set up for me. Very briefly, one other trick that they tried to set up was with a white woman. They put her on a sale for about three minutes across from my sale. And then they came and they opened the door where she had full access to the entire hall in front of my sale and in the other sales. And she was acting as if she was drunk. Because when she came in, she was starting like this as if she was drunk. And she telling me all about how the police had beat her all under her clothes. And she wanted to show me the bruise on her body. So when she said that, I backed up to the back of my sale and said no, I don't want to see, show it to somebody else. And since I decided that I didn't want to see and didn't fall for the trap, they came and they called her by her name and told us to come on out of there. And when they called her, she turned and she walked out. Now, what could have been the consequences? Had I been inquisitive, wanting to see the bruises?  And if I had come to inspect, to see the bruises, all she had to do was reach through the bars and grab me and scream.  So these are some of the pitfalls that even while in jail, you had to be mindful and cautious of. I mentioned the songs and I want us to sing a couple of songs. Then some of you may have some questions, if you do, allow opportunities to ask a few questions. And then we'll talk and sing a little bit more. There was an invitation of song that we sang, which is called Get On Board, Little Children, Let's Fight for Human Rights. How many of you know that song? Good enough, this is enough of us to teach you to the rest of us that don't know it. Are we ready? All right. Get on board, children, children, get on board, children, children, get on board, children, children, let's fight for human rights. Once more, now this time I want us to sing it like we said. Let's fight for human rights. I hear those mobs howling. They're coming round the square and catch those freedom fighters. But we're going to beat them there. Oh, get on board, children, children, get on board, children, children, get on board, children, children, let's fight for human rights. As fighters, we go hungry. Sometimes we go to jail. But when you fight for freedom, a friend will go your bed. Get on board, children, children, get on board, children, children, get on board, children, children, let's fight for human rights. As fighters, we go hungry. Sometimes don't sleep or eat. But when you fight for freedom, in the end you'll be free. Oh, get on board, children, children, get on board, children, children, get on board, children, children, let's fight for human rights. Every time when we would meet each other initially for the first time during the day, in the morning, whenever we would generally ask one another, how did you wake up this morning? Because we knew based on how you woke up would partially determine how the rest of the day would go. And generally when you ask one another that question, you would get a response in song that says, I woke up this morning with my mind. My mind, it was, stay on freedom. Oh, well, I woke up this morning with my mind. My mind, it was, stay on freedom. I woke up this morning with my mind. My mind, it was, stay on freedom. Hallelujah, hallelujah, hallelujah, hallelujah, hallelujah. Now on this next verse, I want us to put a little more of ourselves into it. You know, put a little tap in the hands and all of that. All right? I'm walking and talking with my mind. My mind, it was, stay on freedom. Oh, well, I'm walking and talking with my mind. My mind, it was, stay on freedom. I'm walking and talking with my mind. My mind, it was, stay on freedom. Hallelujah, hallelujah, hallelujah, hallelujah, hallelujah. Preaching and teaching. I'm preaching and teaching with my mind. My mind, it was, stay on freedom. Oh, well, I'm preaching and teaching with my mind. My mind, it was, stay on freedom. I'm preaching and teaching with my mind. My mind, it was, stay on freedom. Hallelujah, hallelujah, hallelujah, hallelujah, hallelujah. Singing and shouting. I'm singing and shouting with my mind. My mind, it was, stay on freedom. Oh, well, I'm singing and shouting. My mind, my mind, it was, stay on freedom. I'm singing and shouting with my mind. My mind, it was, stay on freedom. Hallelujah, hallelujah, hallelujah, hallelujah. All right. You know, at that time, as I talked about, there were places that we couldn't go, but places that we had expected to go to at some point. And one of the songs that we sang to indicate that was a song that we called The Back of the Bus. We had to sit back there. Didn't intend to stay back there forever. You know, we had to swim in the rivers. Couldn't swim in the pools. We didn't intend to be in that position always. We could not go to schools in Mississippi, like Mississippi State Ole Miss. We could only go to schools like Jackson State, Toulou, All Corn, Mississippi Valley. So we put a lot of that into this song that's called Back of the Bus. How many of you know that? All right. We want the rest to just come on with us. You can make it if you try.  I'll be riding up there in the front. I'll be riding up there, not the back. I'll be riding up there. Come on up to the front of the bus. I'll be riding up there. If you miss me from the Mississippi River and you can't find me nowhere, come on over to swimming pool. I'll be swimming in there in the pool. I'll be swimming in there, not the river. I'll be swimming in there. Come on up to the swimming pool. I'll be swimming in there.  I'll be driving up there in the front. I'll be driving up there. I'll be driving up there. Come on up to the front of the bus. I'll be driving up there. If you miss me from Jackson State and you can't find me nowhere, come on up to Ole Miss. I'll be standing up there. And if miss, I'll be standing up there. I'll be standing up there. Come on up to Ole Miss. I'll be standing up there. Because of change in politics and everything, it forced me to add this next verse, which we're going to sing, because we wanted to deal with reality as much as possible. Verse goes like this. If you miss me from the picket line and you can't find me nowhere, come on down to City Hall. I'll be serving as mayor, as a mayor. I'll be serving as mayor. I'll be serving as mayor. Come on up to City Hall. I'll be serving as mayor. And sometimes when those of us seem to be getting afraid a little bit, we sing the song that helped to overcome fear, which was called Ain't Scared of Nobody, because I want my freedom. See the hands that know that one? Not as many. I can teach you in less than 30 seconds. All right? Got you watching set? Ready? Let's go. Ain't scared of nobody, because I want my freedom. I want my freedom. I want my freedom. Ain't scared of nobody, because I want my freedom. I want my freedom now. 24 seconds. What did you watch? OK. All right, let's sing it. Ain't scared of nobody, because I want my freedom. I want my freedom. I want my freedom. Ain't scared of nobody, because I I want my freedom, I want my freedom now. I march downtown cause I want my freedom, I want my freedom, I want my, I march downtown cause I want my freedom, I want my freedom. When they brought the dogs out and said, if you don't turn around, we're going to put the dogs on you. But we added a verse for the dogs and said, ain't scared or no dog, cause I want my freedom. I want my freedom, I want my freedom. Ain't scared or no dog, cause I want my freedom. I want my freedom. And then they said, if you don't turn around and go back, we're going to put all of you in jail. So what's the big deal about jail? At that time, for black people, especially black men, most of them that made it into jail never made it out alive. So saying you're going to be put in jail was, in a way, giving you a death sentence. But instead, we kept on marching. And we added a verse for the jail and said, ain't scared to go to jail, cause I want my freedom. I want my freedom, I want my freedom. Ain't scared to go to jail, cause I want my freedom. I want my freedom. So we're going to take a pause now on the singing and see if any of you got questions that you'd like to ask me. My name's Pat Richter. I'm from Brooklyn, New York. Thank you so much for a wonderful presentation. I have read in numerous sources that the song I Love Everybody was such an important song. And I have not found any recordings or YouTube footage or any, would you be able to sing that for us and lead us in that? You did. But just that verse. OK. Yeah. I was trying to remember the other verse, cause see, if you look at that one, it says, I love everybody. I love everybody. I love everybody in my soul. I love everybody. I love everybody. I love everybody in my soul. Thank you. Hero worship is a dangerous thing, but you. So first I want to say thank you. Thank you for your courage. Thank you for your commitment. What I'd like to know is, was there a specific event that happened in your life that called you to this work? Or what was it within you that put you on this path? This specific event, as I mentioned a little earlier, that put me on the path was when my father said to me, son, that you must stand up for what is right, even if you are the only one standing. You have to do that. And when I begin to look at that statement and analyze that statement, then I look, turn that diamond, so to speak. And it also says to me, you can't stand up for what is right, unless you're standing up against that which is wrong. So you've got to figure out how to begin to stand up against all of that which is wrong that will enable and help you to be able to stand up for what is right. Those were the few words that put me on the path that led me into this work. I'm saying to myself, I don't know how I'm going to do this, but I know I've got to do it. And what has kept me so long is that I made a commitment that my daddy has always said as well, you be a man of your word. I made a commitment that I was going to do whatever I could to make things better for underprivileged people in this world, you know, as long as I could, I didn't expect it to take all this time. But still, you know, I guess that's why in real estate, they say, let the buyer be well. Thank you. So that's what has called me. The other thing that I must say is that I'm thankful that Almighty God has given me inspiration to keep on going and given me that motivation and inspiration for the most part through young people. So when I look at the work that young people are doing and all of that, I mean, it motivates me.  So that's a little bit of the answer to your question. Sure. Hello, I'm Carolyn Owen Toll from San Diego, and I'm very moved by what you've shared. I know what your father told you. I know what you've held to. But what helped you with the bitterness you must have felt at the mistreatment when there was so much of it and it was so relentless? Growth and development is what enabled me to deal with that. And I'm thankful that God blessed me to be able to see that and understand that because he calls me to realize and understand that if I am bitter, if I am angry, it's all get out towards you. That's a burden that I'm carrying on my shoulder.  So I was blessed to be able to see that and know that and says, hey, look, if you're going to be yourself and do what you were put here to do and get the maximum benefit from all of that, you got to rise above emotion and deal with those realities.  I deeply admire your respect.  And I thank you very much. Sure. Thank you. Janice Marie Johnson, Living Legacy Project. We of the Living Legacy Project are blessed to have you work with us year in, year out whenever we take another group of pilgrims on the journey. Last year, I was truly inspired when we stood in a circle outside of the home of the Evers, Medgar Evers, a home without a front door, the only home on the street without a front door, and that didn't protect him. But you shared a song with us that will forever live in my heart. And I would ask you if you would share that song with us today. Yes. I will definitely attempt to do that. Oh, you're going to do it. I want to do it. I want to get it off my plate. This is a song that one of the SNCC workers, who was a part of the SNCC freedom singers, wrote this. The brother is no longer with us. He's deceased. His name was Matthew Jones. He wrote this song. Jackson, Mississippi in 1963. There lived a man who was brave. He fought for freedom all of his life.  They laid Medgar Evers. He spoke words of truth for men to know. Both black and white, it was the same. Till a hate-filled white man named Bob Labeg with lay Medgar. Now Medgar has some company in his heavenly home.  For they died. For they died. For some of this already, but you said when you were young, you wondered how God could let so many terrible things happen. And yet, you have a relationship with God that carries you through and or carries you still to be so certain when you're in the jail. And you talked about how you don't let that bitterness get in the way, but could you talk about how did that happen? How did you get from wondering where many people have been to where you are now, if you could talk about that? Well, see, that's hard to say because we don't really know exactly where other people are. And in many instances, the actions that's exhibited does not truly reflect to indicate where they really are. So I say that to say that based on what all I had heard and what was said to me and what I gathered from my reading of scriptures, et cetera, that in order for God to help me us, we had to be about doing something. So that says, I can't sit here and think about it and only think about this and think about that. But I've got to get up and do something. And I've got to motivate, inspire, and get others to get up and do something. And when we get up and begin to do something, if we listen to his voice as he speaks to us, then he will bless us not through our thoughts, not through what we say, but he will bless us through our actions and that's how I got to where I am little by little growing on that. And if you come out of the state of denial and admit what it is you see, where you are, then it'll show it to you. I begin to look and says, yeah, this is this way. This is where I am. This is where I need to be. So having that understanding, now I know I got to move out on it. And so many of us are taught that what is it? Faith without work is dead. So looking at that, then I'm saying I'm being blessed for him to reveal certain things for me. He's given me his commitment that I'm going to make it. Didn't say I wouldn't be beaten. Didn't say all of these kinds of things. But my life would be there. As long as my life is there, then there's something that I can do. So I can't pinpoint the specific pieces and periods and time or events or things that I move from here to here. But it was a gradual process that I developed mentally and looking at that and realizing the reality of that that caused me to continuously go down the path of growing. And that's how I see it. That's how it has happened. Yes, sir? I'm Charlie Collier from the Zep Center for Non-Violence and Peace Education. And I think many of us associate you with the city and the community of Jackson, Mississippi. And I wonder if you could bring us up to date about Jackson and what are the issues there currently? And what are some of your activities at the present time? In Jackson, not just Jackson, but we are still delinquent in terms of voter registration. We are still delinquent in terms of voter participation. We are still delinquent across the board in having what I consider to be good accountable elected officials. We bragged that we got more black elected officials than any other state in the United States. Fine, we do. How many of those are accountable? How many of those will overcome fear and say what need to be said, when it need to be said, to whomever it need to be said? We're very, very delinquent as a part of that. So I'm in the process. And there are a number of others when we look at the educational system and the state legislature in trying to really destroy the public education system in Mississippi just like it is in so many other places across the country. So I'm trying, one of the ways I'm trying to counteract some of that, I'm putting more of my emphasis on youth leadership development. Because for the most part, young people today don't have the same degree of fear that we as the older ones have. But while doing that, express and try to give people an understanding, it's important for us, both the older and the young, though, to work together to come up with a collective vision, a meaningful program of work. I mean, meaningful strategy that's going to help bring this vision into fruition. So these are some of the things that I'm working on trying to do. And I'm trying to do that through having relationships with all kinds of organizations throughout Mississippi, trying to do that through the organization that I started a little over 20-something years ago, which is Southern Echo, trying to do that through the organization that we started what, 10 years or so ago, that's called Veterans of the Mississippi Civil Rights Movement. So I'm working through, but I'm really focusing on trying to get our young people and see one of the things that I say to young people, there are so many of our young people who emphatically know that they don't intend to and will not be going to college. We know that. We're still in the state of denial that we don't know that, but we know that. So my thing is that come out of the state of denial and admit that. And even though you're not going to college, that does not mean that you would not make a good state legislator. Does not mean that you would not make a good man. It does not mean that you would not make a good board or supervisor, a good chairperson of the school board. So there, we want to look at the things that directly affects us positively or negatively. And we move in and begin to put young people into these positions that's going to be accountable. See, I define accountable as some individual that puts community interest over self-interest. That's how I define it. So these are the kinds of people that we're looking for, that we're working with, trying to develop, so that we can break this cycle that takes us nowhere. So that's just a little bit of some of the things that I'm doing, some of the situations that's in Jackson and Mississippi. My name is Pat Lamana, and I'm from Poughkeepsie, New York, which is about a half an hour north of Beacon, New York, where Pete Seeger lived. And about a year and a half ago, Pete had this idea that he wanted Beacon to have a Martin Luther King Day Parade. And there were certain songs that he really wanted sung at that parade. So I actually have two song questions for you. One of the songs that he really wanted sung, but he was too ill to come to rehearsals and teach it to us. And again, we couldn't find any extant recordings of it. And it goes something like, oh, Wallace, you never can jail us all. And I was wondering if you know that song, and if you can tell us some of the story, because he really wanted us to sing it, because he said it was sung at Selma. Well, while I read in the paper, ta-da-da-da-da-da, just the other day, ta-da-da-da-da-da, that the freedom fighters, ta-da-da-da-da, they were on their way, ta-da-da-da-da, they were coming by bus, ta-da-da-da-da-da, and the airplane, too, ta-da-da-da-da-da, they were even, whoa, ta-da-da-da-da-da, if you ask them to, ta-da-da-da-da, Governor Wallace, oh, no, you know you can't jail us all. Governor Wallace, discrimination bound to fall, ta-da-da-da-da-da. Ta-da-da-da. So that was sung here, and OK, the other song I have a question about is, It Isn't Nice by Melvina Reynolds, that apparently, we're told the legend is she wrote it with a certain tune, and that's the tune that's in the songbook, but that it was rewritten by Snake or the Freedom Writers or somebody, to make it a little more rock and roll-y. Is that one that, you know? It isn't nice to block the doorways. It isn't nice to go to check in. I can't move out on that one, unfortunately. But since you mentioned that, I'll see what I can find, and maybe next time when we meet, I might be able to, hey, lay it out there for you. Thank you. My name is Joe Janks from Chicago, and thank you so much for being here with us today. I have read many times different accounts of how when Reverend Dr. King was hired by the first church that hired him out of seminary, part of why they hired him is they were hoping that they could form a younger minister into a less political vehicle, that their previous minister had been too political for them, and they hoped that if they drew a minister right out of seminary that they would get someone a little less political and a little more focused on the work of the church. And this brings up a question that has always been at this juncture of faith and social justice, which is there are people in one camp that say we are doing the work of saving people's souls. Politics is not our job. And there's other people that say, what good does it do to save somebody's soul if you're letting their body rot, if you're letting them suffer under the weight of injustice? And I'm curious if you can speak to how you, at different times in your life and your work as an activist, as a civil rights worker, as a song leader, as a cultural worker, have found yourself trying to bridge this gap between politics and faith and the people that see them as being at odds, where you clearly see them as being one and the same. To me, people that have problem with that, for the most part, are people that are not looking at the whole picture or the whole body. We are not just one, but we are all of that. So my thing is that we have to make an honest assessment of where we all are, where the people are that we're working with, and see which one of those is being stopped, which one is being fed, because both or all of them need to be fed. So understanding that they all both need to be fed, then it's a matter of how you begin to balance the feeding of those. And you get them to the point where that you got them pretty much equalized in terms of balance. Then you got all of the different fronts. It's the same thing where you say, well, I'm going to eat food, but I'm not going to drink water.   So we need all of these different things. So that's how when it gets into the deep, ditches and dealing with those kinds of things, I ask people to look at the whole person. Where does the greatest need lie? It's the kind of thing where that if you run up on a man that's out in the desert, and he tells you, some man said, I've been out here for two days. I have not had any water to drink for almost two days. I am really thirsty. But you want to give him a good dose of religion. Chances are, you are not going to be very successful. But you do know that he has a serious need, and you can bear witness to that. So you have to be able to say, hey, look, in order for me to get this man to even listen at what I got to say, let alone accept it and become a part of it, I've got to see about him getting some water. And that's the creating of the balance. And it's not easy, because we have not been taught to look at things and that we have been taught to look at either this or that. And it comes out in a lot of the times when we hear people ask questions. You know, and I hate them kind of questions because it takes a long time to deal with them when they say, well, what was the most in your 50-something years the most of this, most of that? You know, and all of the different entities have played a part, you know. Because if you look at it in terms of the most, it takes me to the question of you got three groups for people. You got one group of people that provide food and shelter for young people to work in the community. And you got those young people that worked in the community and arranged different meetings for the superstars to come in and talk to. So who played the greatest part? Was the people that provided the food and the shelter? Or was it the young people that actually organized the meeting? Or was it the person that came and delivered a message? All of them had a role to play. And that's part of the kind of mentality that we have to get our people to come out of, is that I'm the best. I did the biggest, and all of that. Because all of that creates the vision of which we don't really need. We have to get beyond that. Just a. Are you bending my rules? Are you bending my rules? One more yes. I just want to check in with folks. It's after 4.15. I want to respect everyone in here. Respect your time. If you need to go, please do. If you can stay, then please do. Last question. Here we go. Last question. Thanks. Manuel Brown from East Shore, Unitarian, and Seattle, Washington. I just want to know from your perspective, what is next?  And in their lifetime, they have a lot more work to do. And that, you know, I just want to know, how do we teach them what's next? What's next? What's next is dependent upon how we deal with and how, what's now. It's like the little boys that was going to fool the wise man. You know, the story about the wise man, the wise man, they got a thing in their hand and say, if they ask them if it's alive or is it dead, they say, if he said it's dead, they're going to let it fly away.  We see all of the things that is happening in the world and around us today. And based on how we deal with this today, we'll determine what's next for us, or whether we'll even be around to look at and talk about what's next. You know, and most of us hate to look at, for example, the whole environmental thing that covers all of the poisoning and stuff that's being put into food that we eat. And see here again, the thing about children, I've learned that if you got enough nerve to come straight and clear with them, they'll understand most of that which you think that they don't have no idea of what it is that's going on. So we've got to free our children out of the box that we are locked into and let them be creative. You know, what's your idea on this? You know, and they're hard to deal with sometimes. I remember one of my sons once when he was a little bit of fellow, the toughest question I think I've ever had in my life was he asked me something and I gave him what I thought was this brilliant answer. And he just looked at me and says, why? And when I laid all of that out, he says, why? Lay it off, why? You know, it just took me down this road of why. But that's where we have to go and that's what we have to do. We have to become as knowledgeable as possible ourselves so we can share that with our children while at the same time giving them the opportunity to participate in that and help us find solutions. That's why I like the whole intergenerational model of doing things so well. See, when we first started in Southern Echo working with youth and talking about the intergenerational model, and I think I'm going to be talking some more about Southern Echo tomorrow, but we initially said, we're going to start working with the college students. We find out that they were lost, too many of them.  And we brought it on down and we finally reached the level where we said, we need to make sure that we start working with young children when they are in about the fifth and sixth grade. But we realized that was a good start, but in reality today we got to go beyond that, go on down. So that's it. I would like for us to do two verses of one other song. Can we do that? OK. All right. And this is one, go like this. Freedom, give us freedom. Hey, freedom, come and it won't be long. Again, freedom, give us freedom. Hey, freedom, come and it won't be long. I took a little trip on the Greyhound bus, yeah. Freedom, come and it won't be. Justified discrimination and a dissweet bus, yeah. Freedom, come and it won't be long. Freedom, freedom, hey. Freedom, come and it won't be long. If you don't believe that I've been to hell. Freedom, come and it won't be long. Just so follow me down to the Parchment Jail. Freedom, come and it won't be long. Freedom, freedom, hey. Freedom, come and it won't be long. Thank you, thank you. Thank you, thank you, thank you, thank you. And just as an announcement, I think my wife had some CDs of mine that has about 18 different freedom songs on it. So for those that didn't get your recording, some of those that we sang today is on there and there are others. And we'll work it out. So just wanted to share that with you. But thanks, thanks, thanks, thanks. Love you.


Hi everyone, Joe for jaspyscasebrakes.com, coming at you with 2019-2020 Panini Chronicles Soccer, three box, random team break number two from jaspyscasebrakes.com. Some teams aren't represented on this list, so we'll randomize those cards as one lot to one person at the end of the break. Also, there'll be a total of 40 spots on the randomizer, but there's only 39 clubs. There's a 50th spot that's gonna be $50 of break credit, the cost of the spot right here. So one person on this list, let's W up really quick. One person will get a team and 50 bucks of break credit. Everybody else will get two. All right, let's roll it, let's randomize it. Two and a four, six times for each list. One, two, three, four, and six. After six times, we got Jonathan down to Jonathan. After six times, we've got two's on top here, one, two, and six, six in final time. We've got Manchester United all the way down to Udinese. So Jonathan with men, United, Jeff with Arsenal, Craig with Milan, AC Milan, Rory, $50 of break credit, and Westham United. Josh with Fiorentina, Peter with Uve, Steven with Barma, David with Atletico Madrid, baseball for Greg, Valencia for James, Chris with Burnley, Leicester City for Greg, Josh with Villarreal, Greg with Bournemouth, Steven with Sheffield United, James with Barcelona, Rory with Cagliari, Josh with Genoa, Roma, and Bologna, three Serie A teams right there. Greg with Southampton and Inter, Jeff with Man City, Greg with Newcastle United, Celta de Vigo for Josh, David with Tottenham Hotspur, Douglas with Chelsea, Josh with Real Betis, Douglas with Liverpool, that's my club right there, Steven with Dorino, Greg with Napoli, Chris with Lazio, Rory with my rivals Everton, they're in the same city as Liverpool. Peter with Watford, Greg with Real Madrid, Josh with Wolverhampton, Steven with Sevilla, Craig with Crystal Palace, and Jonathan Udinese right there. All right, so I can't really get all 40 teams on one list, but let me alphabetize by team, let me know if you need to see your team again, and I think I have a checklist for you. Did I save that checklist? No, I cannot. I do not have that ability, so I'll just send you a separate one. Let me find you a checklist, everybody, if you're watching live, if you're watching a replay of this, you gotta go to groupratechecklist.com. I should probably save this on my spreadsheet here. All right, so there's the checklist right there, there it is on your screen right there, on groupratechecklist.com, any trades? Everybody's asking, is Everton, Everton's got Jordan Pickford, and Tim Howard, remember Tim Howard? Great American keeper there. Theo Walcott's on that team too. Didn't quite work out at Arsenal, but they're doing okay in Everton, mid-table team. All right, looks like no trades, so let's roll, TWC, trade window closed, let's print, let's rip. All right, so let's flip here. All right, now what's cool about this is that each mini box is a different league. One's the English Premier League, the other is La Liga, and the other is Serie A, the Italian League, which I thought was a pretty neat way of doing it. All right, and we've got three autos or memorabilia boxes on that, usually it's one. Sometimes they're two. I guess if you're lucky, you can get three. All right, so we're gonna do the logos, we're gonna do Serie A first, then we'll do La Liga, then we'll do the EPL. I think we're shipping everything in this, Chronicles we usually do. There's extra points, Dmitri Bisole, there's Gabriel, one of one for a second, and we've got double coverage. I think are these both, yeah, these are both international players. That is Samir Handanovic and Tonio Candreva. Double coverage for Inter, and that is for Greg, Greg Brewer with that one. That King's design I think is really nice. And there's Rookie Bastoni, also for Inter. Now we're gonna go to Spain.  Someday we can do that again. All right, there's the biter, he bites. Luis Suarez, and there's Jose Luis Morales, Oyer, and Jose Imanes. And the relic is for Atlético Madrid, throwback threads, Nico Gaetan for David, and Atlético Madrid. Lucas Perez, Ferran Torres, and I like the Rookie Ticket Cards right here. Cunde. All right, now to the EPL. I don't think there are any today, where they're saturday and sunday. They've been kind of running them all week though, but really pleased that Liverpool finally knocked out a title. And we've got Javier Monquil for Newcastle to 50. We've got Will Hughes to 75 for Watford, and Andros Townsend for Crystal Palace to 99. There's Alan Sontemaxiaming for Newcastle 99, and we've got an autographed Dean Henderson, 58 out of 400 keeper for Sheffield United. They've been having a great season, and a part of it is because of this goalkeeper, Dean Henderson. I think they just got promoted this season, and they're not too far off a Champions League spot, which is wild. So they've been having an absolute peach of a season. All right, Sheffield United, that goes to Stephen Hines with Sheffield United. That's not a bad idea. Mike Tower, yeah, the Kings looking cards, they pitch Kings, right? Court Kings, Gridiron Kings, pitch Kings, nice. Mike Tower, you should, I don't know what you do for work, but we'll get you on the Panini creative team. All right, back to Italy. I guess maybe next time, next time I'll do all three Italy's, and then all three, I'll figure it out. It's the lead I'm least familiar with, so I'm getting out of the way first. Out of 199. Stefano Ocaca, for Odinesi. Out of 55, that is for Salsullo, and we've got more double coverage. Irving Lozano and Davido Spina. That is for Napoli. And that's gonna go to, where are you on my list here? Not where, yes, Napoli, no. SSC Napoli, yeah, Greg Brewer with Napoli. Francesco Caputo, I feel like we haven't seen these, right? That looks special. We've got some rookie cards here. I think that's Odinesi, the green. All right, so there you go. All right, now we're going to Spain. Oh, you're saying that's what they are called? Mike Tower? I don't remember a pitch Kings. Oh, maybe on the checklist they call it pitch Kings. I see. Back off the creative team now. On the research team. Well, we've transferred you to the research team. We've got Sergio Reguillon. It's kind of hard to see the dark purple against the dark background. And I've heard of this guy, Leo Messi. Over 700 career goals, that's ridiculous. Barca, with that one. That'll be for James. And we go to their rivals. It's a Luca Modric, two-color, dual relic, and autographed 1650 for Real Madrid. That's for Greg. Part of that Croatian team that just seemed to have boundless energy. There's Samuel Etto. I like these level three pitch Kings cards. Back to Jolly Old England. Roberto Firmino and Wilfred Zaha to 99, Crystal Palace. Robbie Brady for Burnley. And David Tilt from Manchester City, 48 out of 50. There's Guilfee Sugurtson. And Ryzenstein Robin van Persie. His man United gear. And that'll be for Jonathan. Jonathan H with that. What's the best soccer nickname? Not sure. Are there good soccer nicknames?   That Kubo base card where, I don't know, everything ships. And we'll get it back to Italy. Well, I don't know if they, do they call him that, though? That's a 99, that's, why is the number of stamps? The stamps are like the other way. It's not weird. But yeah, that, yeah, Maradona's that action in the World Cup is known as the hand of God. I don't know if they call him the hand of God, though. Maybe they do. I don't know. At a 445 extra points autograph, Gary Medell for Bologna, that goes to Josh, Christian Romero and Mira de Meral. And La Liga. Rory, $50 break credit. And La Liga. Rory, $50 break credit is in the Jaspis Premier League. The Everton is in the English Premier League. Do you have another one? And Westham United also in the Premier League. There's Mark Andre Terstigen for Barca to 35. And that is Takashi Inue, Pau Torres. And we've got Alvaro Morata for Atlético Madrid. Fabric of the Game. Is he back on there now? That'll be for David. It was Eden Hazard and Mesut Ozil. I think Mesut Ozil and Ines Cantor are at odds. All right, and the last mini box. English Premier League. We'll close things out. I feel like as soon as I turn this around, it'll all be upside down. Maybe not Trent Alexander Arnold. Great player for Liverpool. There's Ryan Fredericks to 99. Kyungmin Sun, I think not numbered, but there's Neil Moupe to 75. And Aaron Wan Besaka for Manchester United. 363 out of 400 on that one for Man U. Jonathan, another Liverpool rival here. And then we've got Mateo Genduosi and Javier Hernandez, Ciccerito, who's on the LA Galaxy now for L3. Or no, this is for Man United edition there.  Three box random team two. Chronicles, soccer in the books. Check out the website for more. And we'll see you next time. jaspyscasebreak.com, I'm Joe, I'm out.


Thank you very much for the introduction. Also thanks for organizing this conference. I'm really having the time of my life here. It's really good. And thank you for giving me the opportunity to speak here. So I want to start with a question of Stephen Gubkin, who posted on my overflow. He said in the middle, it is convenient to reason about toposes and their own internal logic. Has there been much done about the internal logic of the gross or risky topos, or what the logic of the topos required too much communicative algebra to feel like logic? I think that Stephen has a very good point here.  And schemes are locally ringed spaces, which are locally isomorphic to the spectrum of a communicative ring. So it shouldn't come as any surprise that many notions in algebraic geometry are like sheafy notions or globalized notions of ordinary notions in communicative algebra. And also, you know the business with the proofs in algebraic geometry. Often they go like blah, blah, blah. Therefore, without loss of generality, we may assume that the scheme is affine. And then it's a simple consequence of the following theme of a communicative algebra. Other proofs go like blah, blah, blah. Therefore, it suffices to check the condition of stocks. They are trivial because of communicative algebra. Okay, and I think topper's logic has a contribution to make there. The starting point is to realize that any scheme has its structure sheaf OX, and this is of course a sheaf, a sheaf of rings. But if you switch to the internal logic of the Piotr Zeliski toppers, the toppers of sheafs on X, this complicated sheaf of rings will look just like an ordinary plain old ring, non-sheafy, okay? So and if you have a sheaf of X modules on your scheme, then from the internal point of view, this will simply look like an ordinary module on that ordinary ring, okay? This is the starting point. This was already noticed in the 70s when the internal language was developed by several people. And so I quite want to see how far we can bridge, how far we can push the theory. So what we want to do is like build a dictionary between external notions and internal notions. Build this dictionary once and then we can use it as often as we want. So I just want to give you a few of those items. For instance, a sheaf of finite type, okay? So externally, a sheaf given on your space X, a sheaf of modules is a finite type if and only if from the internal point of view, it simply looks like an ordinary, finitely generated module, okay? Okay, we can push it forward. For instance, a sheaf which is externally finite locally free. This is precisely the same thing as from the internal point of view, an ordinary module, which really is finitely free, not locally but really globally from the internal point of view, okay? So the internal language is a device which allows you to pretend that the base scheme you're working over is in fact the point, yeah? To reduce to the situational point on a single point. Okay, let's just do a few more examples. So for instance, maybe when you're a beginner and then you're learning algebraic geometry, then maybe you are scared of the definition of a tensor product of sheafs, tensor product of sheafs of modules. I mean, there's nothing scary about them in fact but when you're just learning it, then you might be scared. The problem is like the naive definition only gives you a pre-sheaf and then you have to sheafify.  Okay, anyway, from the internal point of view, the tensor product of sheafs of modules is simply the ordinary tensor product which you have learned in your first semester in linear algebra or something, yeah? Okay. A particular nice example is the sheaf of rational functions, Kx. So this is a sheaf of rational functions and so if you know its definition, then you also know that it's a little bit delicate. In fact, there's a short paper by Stephen Kleinman titled Misconceptions About Kx where he lists like three definitions about Kx which are very commonly found in the literature and which are wrong. Which do not even define a pre-sheaf, for instance, yeah? Okay, so the definition is a little bit delicate but not from the internal point of view. From the internal point of view, you obtain the sheaf of rational functions very simply, namely, take Ox. Ox is just an ordinary ring from the internal point of view, yeah? Okay, and then take its total quotient ring. But if you don't have elements, how do you take the quotient quotient ring? Yeah, I mean you have to use the topos magic, yeah? So you use the internal topos language and there Ox is simply an ordinary ring and it has its sets of regular elements and then you localize it then. This is exactly the beauty that it becomes so easy in the internal language. Actually, there are other kinds of quotient ring considered by algebraics which are less often used but I saw in some references that they have some other ways to define it. It's not interesting the regular elements. Yeah, I mean you can localize at many sets, yeah? In fact, at any subset if you want to, yeah? I mean, there will always be a quotient ring but if you localize at the set of regular elements, then you will obtain the thing commonly called Kx. And with this, for instance, you can give a beautiful internal account, purely internal account of the basics of the theory of Cartier divisors, okay? Let me make one more remark. So we had in a Booth lecture the situation that we had a theorem which hold it if and only if the topos was Boolean. We have a similar situation here, namely, from the internal point of view, you can ask yourself, what is the Krull dimension of the ring Ox? Any ring has a Krull dimension, yeah?  And then you can use this definition and ask yourself, what's the Krull dimension of Ox? The answer is the Krull dimension of Ox is precisely the dimension of the scheme, the base scheme, okay? And then you have the following observation. The dimension of Ox, the Krull dimension of Ox is zero if and only if the scheme is zero dimensional if and only if the internal language is Boolean, okay? So in some sense, the ring Ox, the structure sheath controls the logic of the topos. I want to take a minute to explain why in some sense this talk is like a praise for Mike Schulman, you see? So there have been several lectures on the internal languages of topos this year and most of the time geometric logic was stressed which is very fine, yeah? But in fact, the topos can interpret more higher fragments of logic. They can interpret full first order logic, they can interpret higher order logic, they can also interpret dependent types which some of you might not know about but I promise to you, you're using dependent types all the time, yeah? And if you really want to import all of constructive mathematics into the topos setting you also need dependent types. Okay, but the thing why I want to praise Mike Schulman is because he made it possible to use unbounded quantification in the internal language. So unbounded quantification is when you say for all rings it should hold that, for all modules it should hold that, yeah? This is unbounded quantification and of course you need it all the time because you want to formulate universal properties, okay? And Mike Schulman wrote this little paper which you can totally understand even if you don't know what a stack is. We just give a small addition to the usual cryptocryptial semantics of the topos to be able to speak about unbounded quantification and locally internal categories in contrast to only internal categories, okay? Okay, so with this small extension we can really import all of constructive mathematics into a topos setting. Okay, and I want to give examples for this. Are there any questions up to this point? Okay, then let's have a basic example. So in your first semester in university you'll learn that if you have a short exact sequence of ordinary non-sheafy modules and you know that the two outer ones are finally degenerated then solve the middle one. This is a basic theorem and this basic theorem has an obvious proof and this obvious proof is constructive. Therefore, you can interpret this statement in the internal language of any topos and then it will automatically give rise to a more advanced statement, the statement which you see on the board about sheaves. Okay, okay, so this is a first example where the topos magic allows you to like prove a theorem once and then interpret it in many, many contexts at once without further work. One remark, so you might object that the ordinary proof of this statement is not difficult at all. You might remark that it's simply routine and that it's very easy to do. Okay, then you're right. In fact, you can, if you're familiar with the notation then you will probably be able to proof the statement at the bottom in like a minute, okay? But I argue that this is not a minute where I spent. It's a minute spent with like saying, okay, we have this generator on these open subsets. Well, the open subset is too big. I have to shrink it if necessary. I have to shrink it again and mm-hmm, mm-hmm, mm-hmm. It's routine, but it's like 60 seconds where you could have done something different, okay? And with a topos language you can, you have this 60 seconds for free, they're given to you, yeah? Because you simply look at the statement, realize because of the dictionary that it's the interpretation of the well-known statement of linear algebra and then you are done, okay? You're going from 60 seconds to one second. This is, I think, a great idea. Also, you gain conceptual understanding because you now really know where this sheaf theory comes from. Before that, you only had like a feeling but now you have like a formalized rigorous proof. A more advanced example is the following. So, take a scheme X, assume that it's reduced. Take a sheaf of all the modules of finite type over it. Then the statement is that this sheaf will always automatically be locally free on a dense open subset, okay? This is statement in the sheaf theory. So, for instance, Ravi Vakil in his excellent lecture notes in algebraic geometry says that this is an important hard exercise. It's an exercise with like a hint which goes over like half a page, yeah? Okay, but in fact, this is not a hard exercise at all. It's a trivial consequence of the constructor theorem of linear algebra at the top. In constructor of algebra, you know that any finitely generated vector space is not not free, does not not possess a basis. Okay, so constructor, you cannot prove that any finitely generated vector space really is free. You can only prove the slightly weaker statement and the not not translates to on a dense open subset. Okay? I really like this example because otherwise you would have to like follow through this hint which just goes over half a page and then do Nakayama once and do Yakanama twice and so on and so on. And in fact, it's a trivial consequence. And you can also prove, for example, the level of generic flatness in this, in this, in this, I mean, it's true in this form. Yeah. And there you have to work a little bit more in the usual way. So if you're an algebraic geometry, then anyway you have to do the usual for me because. Yeah, well, at some point in time, you will have to work. But the point is that you can shift lots of this work into work which has already been done in constructively linear algebra. Yeah? And you can automatically import these kinds of things. Any more questions at this point? Okay. Then let's continue the tour of the putesia-risky-topos of the scheme. I want to show you a curious property which the internal universe of the putesia-risky-topos of any scheme always has. Namely, so from the internal point of view, or X is a ring, yeah? And this ring has the following curious property. Any element which is not invertible is nile potent. Any element which is not invertible is nile potent. So or X is almost a field, yeah? If you were to quotient by the nile potent elements, you would have a field in this sense. So this is a statement which holds in full generality on a scheme, even if your base scheme is a base ring, for instance, is really a ring and not a field, yeah? It always holds. So this was already noticed in a special case by Mulvey in the 70s. And here you see Tierney commenting on it. He says, this is surely important for its precise significance is still somewhat obscure, as at the case with many such non-geometric formulas, non-geometric in the sense as explained in Olivia's lectures, okay? So in the one purpose of this talk is to convince you that there is actually a real meaning behind this statement, that it's not at all obscure. This will come in a moment. First, let's have a purely Topos theoretical interlude. It's a thing which I stumbled upon. I presume that it's well known, but I have never seen a written reference to it. Okay, say you have a Topos E and you have a Sub-Topos given by a local operator, a modal operator, topology on it. There are several synonyms, yeah? Okay. So I have the Sub-Topos and you have the Super-Topos and now take a formula. And you might be questioning yourself, what's the relation between the formula holding on the Sub-Topos and the formula holding on the Super-Topos? Is there any relationship? Okay. And the answer is yes, there is. Namely, the relationship is exactly given by this observation. So a formula phi holds in the Sub-Topos if and only if its diamond translation holds in the Super-Topos. The diamond translation is given recursively by these rules. They are just the rules for the in logic, well-known double negation translation just with a diamond instead of the not-not, okay? Good, and this is the answer. This is a very useful observation because it allows you to use the internal language of the Super-Topos to speak about the Sub-Topos, okay? And we'll see why this is very useful in algebraic geometry on the next slide. The diamond translation, is it a geometric morphism? No, I mean the diamond translation is a purely syntactical operation on formulas. Given a formula, your pain is diamond translation by like putting diamonds everywhere in front of everything.  So the top left, this is a geometric morphism on the top axis. And the diamond is an internal reflection on the universe, on the Sub-Topos. Maybe I should say that I'm a little bit envious of the philosophers. Re-Mathematicians, we only study what's true. But the philosophers are to study things what should be true, what do I know, what does he know, what can be true, what is necessarily true and so on. So the philosophers, they study model logic. And so with stopper theory, model logic is actually useful in like real world applications in algebraic geometry as well. We'll see it just in a second. The thing is, depending on which model operator you choose, you can incorporate like a whole host of statements in one. I just want to concentrate on, for instance, the first one. So if you choose for diamond, the double negation topology, then diamond phi will mean that phi holds on a dense open subset. Okay, you can check that with a Krippke-Jouill mathematics. Okay, and then you can also wonder what phi to the omega means, the diamond translation of phi. And if you do the calculation, you will see that, I'm assuming the scheme to be irreducible for the moment, that phi to the diamond means that this formula phi holds at the generic point. So in algebraic geometry, it's an important question when properties spread from the generic point to some dense open subset. This does not always occur, it's a good thing when it occurs. Okay, and you can analyze this question politically because you can put it in this form. When does phi to the diamond imply diamond phi? When does phi holding at the generic point imply, implies that it holds on a dense open subset? Okay, and the good thing about it is that you then can import well-known theorems of logic to tackle this. For instance, the theorem that for any geometric formula, phi, this always holds, okay? And in that way, you have like one meter theorem which gives you a whole host of individual statements about spreading from points to open neighborhoods. And in fact, if you vary the modal operator, you gain even more statements. Yeah? Should phi in this case have intuitively like one free variable which is a point of the scheme X or should it be have no free variables and when you say it holds on a dense open subset, you mean like? Yeah, it may have three variables. For instance, it may refer to a given sheeps or something, yeah? So... But not to points of the space X. Yeah, yeah, not the points of the space X. The confusion is some of these feel like quantifiers, but quantifiers eliminate variables. Yeah. Or bind variables, and this doesn't. Maybe I have time for one very short example for this. So you might know that the following does not hold. If you have a sheaf of modules and you know that it's stock vanishes, then it does not hold in general that it will vanish on a nape of the point. This is because the, so you know again a conceptual understanding for this non-theorem. This is because the formulation for a module to be zero is non-geometric. It's for all X in M, X should be zero. Because of the universal quantifier, this is not a geometric formula. Okay, but now presume that the sheaf is known to be a finite type, yeah? So internally, this means that the module is finally generated. So you have generators, X1, X2, Xn. And now you know that you can rewrite the condition that M is zero, simply as X1 is zero, X2 is zero, and so on, Xn is zero. And this is manifestly a geometric formula, okay? So now you have a conceptual understanding of why in general, spreading does not occur for being zero and why it does occur when the sheaf is a finite type. Let's talk about quasi-coherence. The condition for a sheaf of modules to be quasi-coherent is very important in algebraic geometry. In fact, there are arguments that sheaf of modules, which are not quasi-coherent, should never be studied because they're like not geometric, yeah? Okay, so of course you're wondering whether it's possible to characterize quasi-coherence in the internal language. And it turns out that yes, you can. The condition is on the board. And I quite like this condition because, so normally you're always reduced to well-known constructive algebra. But in this case, you create new constructive algebra because this is a condition which is not normally seen in constructive algebra. Okay, so the condition is that, finally F of OX, if you localize this module E away from F, then this new module should be a sheaf with respect to a certain internally defined model operator which we can see on the board, okay? So it's possible to give the whole of sheaf theory, separateness condition and so on and so on in the internal language. In fact, I'll do it for you. This is the separateness condition, just the separateness condition. And I quite like it because it's of our curious logical form. It says that if you are able to deduce that S is zero, given the assumption that F is invertible, then you can unconditionally deduce that some power of F times N really is zero, okay? So, and we can return to Mulvay. If you take for E, in a special case, simply O or X, the structure sheaf, and if you take for S one, then you exactly reduce to Mulvay's curious formula. And then now you know the deeper meaning of this formula. This was just like a little shadow of a greater picture than the picture of quasi-coherenceness, okay? The last few slides are for all fans of Munik Hakim and Peter Arndt, especially his really great answer on overflow on how to motivate schemes. Okay, so an abstract motivation of how to motivate schemes is the following. Take a ring A. You want to construct the free local ring of it. Okay. So this is the universal property. It should hold that, like you have a morphism from A to A prime, then to be constructed ring. And it should hold that for any map into a local ring R, this map should uniquely factor over a local map of rings from A prime to R, okay? And then you do the calculation and are disappointed because this optimization problem has a solution in set if and only if the ring A has exactly one prime idea. Okay, this is about the situation. Okay, and now we read this answer by Peter Arndt and I'm delighted to know that this optimization problem does have always a solution.  The solution is the structure sheet O-spec A in the scheme spec A, yeah? Of course you have to define what it means for what a morphism of rings living in different toposes is, but you can do it. It's very easy. And the side is the spectrum with the Zaris ketopology. Yeah, right, yeah.  Now you want to construct the free local ring over any ring, not necessarily a ring in set. Okay, so what you do, you do. It's by the general theory of this topos magic, it suffices to give a constructive account of the theory of the usual spectrum inside the topos. So our first attempt might be to define the spectrum as the topological space of the prime ideals of A, but you know that prime ideals are elusive in constructive mathematics. This will not have the right universal property. Okay, so a better attempt might be to consider this topological space of all the prime filters of A. A prime filter is classically the same as a complement of the prime ideal, only that it's directly axiomaticized. It fulfills exactly the dual notions. Okay, this is much better, but also prime filters are elusive in constructive mathematics. There's a count example by Jo-Yal where he constructs a ring, which is not trivial, but doesn't have any prime filters, okay? What you instead have to do is build the locale of the prime filters of A. And in fact, this definition was already on the board. Remember Olivia's last lecture? She had this long chain of equivalences. Here was the shift topos of a spec A. This had a non-constructive definition, it doesn't work. And then there were three more topos, all of which you can constructively use. And I just kind of randomly decided for the final one, which is a locale, okay? Okay, and in this way, you obtain an internal characterization of Monique Harkim's very general spectrum functor, which gives an adjoint to the forgetful functor from local ring toposes to ring toposes. If you check her feeders, she does this like explicit site construction. So she has to build a site. And we know by Olivia's lectures that sites are good. But even better, it's to not have to construct them by hand, but use a general meta theorem about toposes over X and toposes internal to X, which does this kind of construction for you, okay? Okay, and if you're familiar with algebraic geometry, then you also know the relative spectrum. Given quasi-Korean chief of algebras, or X algebras on a scheme X, there's the relative spectrum, which has a scheme of this into X, yeah? Okay, and you might wonder how this can be described internally. So the obvious choice, the obvious guess, would be to just take Monique Harkim's spectrum functor, right? It's very general. It applies to the situation. But then you make the calculations and realize that Monique Harkim's spectrum functor gives a different result than the relative spectrum considered in algebraic geometry. In fact, you can check that Monique Harkim's spectrum gives the correct result if and only if the scheme, your base scheme you started with is zero-dimensional, which of course is not the general case, yeah? So it's interesting to see how you have to change, fix the definitions. And here's how you do it. You again define the relative spectrum as a local, so you give it frames. But you don't take as a frame the frame of all radical ideals, but only the quasi-Korean ones, okay? And you can do a few correlations to arrive at this short characterization of when radical ideal of a quasi-Korean algebra is itself quasi-coherent. Again, notice this curious-looking behavior. So this ideal E, i has to satisfy the condition that if an element s is an element of i under the assumption that f is invertible, then f times s really should be an element of i without any assumptions. Okay, and just want to end with a remark on the points. So this local is not spatial from the internal point of view, but you might still be interested in the points, just to have a better feeling for it, yeah? To know the theory which this spectrum classifies. And it turns out it's not the theory of all prime filters, but only of those which fulfill this additional condition. Okay, and then you can, of course, generalize it. X doesn't have to be a scheme. It can be an arbitrary topos, ring topos. And then you can understand the limits in the category of locally-ringed toposes much more conceptually. Namely, they are simply given by the naive limits in the category of ringed toposes, and then given by relocalizing using this construction. Okay. So, and in my last zero minutes, let me turn to Peter Ahn's answer. You can also, like, give a very nice account of the relative spectrum, of the universal property of the relative spectrum, of the relative spectrum as used in algebraic geometry. And then you very clearly see the difference to the spectrum of monikarkeum. Namely, the question in algebraic geometry is to construct the free local ring over A, which is also free over the base over B, over all X in applications. This is a small but important difference. Okay. I hope I've convinced you that using topos magic, topos internal language in algebraic geometry is a very fruitful thing. It allows you to simplify proofs and allows you to gain a better conceptual understanding of the notions and of the statements in algebraic geometry. Thank you very much for your attention. Do you have any questions? Yeah. Yes. Can you go back to the reconstruction of the universal property of the relative spectrum? Yes, this one. How does the relative spectrum compare to the other one? The monikarkeum spectrum. Yeah. Is this a subspace? Yeah, yeah. This is always a subspace, a sublocale of monikarkeum spectrum. Okay, it's precisely the subspace where the morphism from B to A prime is local. Yeah, yeah. And in fact, you know this from Olivia's talk because the theory which the relative spectrum classifies is a quotient theory of the theory which the monikarkeum spectrum classifies because you have one extra axiom. Yeah? It's a subspace and if and only if the base scheme is zero dimensional, then these two notions coincide. So maybe I have a general mark. Yeah. The commutative algebra is very much non-constructive. Yeah, several people here in the audience would disagree. Would disagree vehemently, yeah? So there's a notion that commutative algebra is non-constructive, but in fact it's not. So for instance, these two guys here have a great program where you can just take a non-constructive proof of commutative algebra. For instance, you have an element in order to show that it's null potent and you show it by showing that it's an element of every prime idea. Okay, you take this non-constructive proof, you put it in the machine developed by those guys and several others and out comes a perfectly fine, constructively acceptable proof which explicitly gives you bounds on the nile potent index. It's a rumor that classical commutative algebra is non-constructive. What's the name of that proof? Kokor, Lombardi, and... Oh, program doesn't mean program. No, no, the research program of dynamical methods in algebra. Yeah, yeah. If I Google that, do I find your... Yeah, yeah. Thank you very much.


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