When I decided to go wedding dress shopping, it was kind of out of the blue. I was like, hmm, I kind of need to go do this. And so I just scheduled an appointment at David's Bridal, which is one of a known wedding dress shop place.  And we just all kind of went and pretty much everybody was able to make it that I invited. And yeah, so when we arrived, they were basically like, okay, here's all the dress options. Pick the ones that you like and then we'll choose them in your sides. So I go ahead and I look through and all of my friends kind of are looking through and my mom and everything and so what you do is like you turn them out so that they can see them and then they pick some options for you. Hi everybody, we're here at David's Bridal. I have some of my bridesmaids and my maid of honor who's behind the camera and and we're looking at dresses. I picked out a couple to try on and we'll see which one looks good. So she's like, oh, I like it, but I didn't love it. And then I didn't like the shoulders coming kind of over to the side like this. That wasn't my favorite look. So I kind of just went on to the next one. And then number two was very Cinderella-y, which was cute, but it's not quite the vibe I was going for. And I really liked the top and it was like kind of poofy. But I don't know, it just wasn't quite my cup of tea there. And then the next one, yeah, sleeves just, they just weren't my thing. I really think they're pretty and on some styles they are, but I don't know. This one just, the sleeves just didn't work for me and I just didn't like that. The fourth one, so this one was in the running for a very long time. I really loved it. It was just gorgeous and a downside to it. It was very expensive for the budget that I was trying to keep. So it was like, I think maybe a thousand, three hundred or two hundred or something like that. And so to me, I was like, this is very beautiful, but I also tried to like move in it and it was very difficult. So that's why I didn't end up choosing it was for the price and the ability to move around and everything like that. And then number five was the kind of mermaid, I think they call it A-line or something like that. I just felt like it was too form fitting and then kind of flared out and I just didn't love that look. I think it's really pretty to show off my curves and stuff, but I'm a little more modest and so I just didn't want something that was so like showy in that way. So we went without that one. And then number six, my mom wanted me to try on something short. And while I did kind of like it, I just felt like it didn't represent a wedding. So I just didn't go with that one. And then number seven, oh my gosh, everybody said when I came out in this dress, I just had like the biggest, happiest smile on and it was so beautiful and the minute she told me that it was $400 from the clearance rack, I was like, I'm taking it like this is the one. I just loved that it was like flowy, it had the cute top. I even said in that moment it was like this reminds me of a dress that I used to have that I absolutely loved. And then I kind of grew up and I'm too big for it now, so I'm not able to wear it. And I really love my dress because this is the dress that I chose. But it's very summery and flowy and it's not quite what I pictured myself in, but it's what I ended up really loving. And I feel like that's part of doing this experience is that you think or you have something in mind and then you get there and it's all changed and different once you have things on yourself and you see how that looks. But yeah, this was the one. I loved the price. I loved the flowy and I loved that I could move. I didn't feel restricted. I felt great. I could do squats. I could move around and it just feels really, really good and I love it so much. So that's the one I ended up going with and I'm super happy. So I hope you guys enjoyed seeing my wedding dress shopping experience and I'll see you next time. So whoever is going to bust with me, so know how to. There are going to be buttons in the dress that help them but they're you have to they're going to have to learn how to bust. Because I have my friend who's got married and I had to bust with it and it was really hard and I had to practice. So not working. Have a good friend. Carrie. That's really pretty. That's what I like to hear. I like that. I can see it. You can just watch. Hug your family. You can wobble. Look natural, do we? We like to put a natural face. Cute. Blingy. Oh now your feet hurt? Oh yeah, they've been hurting for a while. Well it's only been what? Like I've looked at all of them. Oh no, I didn't wear my watch today. Oh yeah, I was pulling from the show. That's pretty. That's very bridal looking. Where did you come up with that? I like the feet. And if you wanted to see, you can always have it. I feel like this reminds me of an old dress I used to have that I loved and then I got Ann. We're good. I'm good. There's tricks over a chair. Breaks my leg.


103.9 FM, WOZO Radio, Knoxville. Ladies and gentlemen, Digital Freethought Radio Hour. Hello, and welcome to the Digital Freethought Radio Hour on WOZO Radio, 103.9 LP FM, right here in Knoxville, Tennessee. Today is Sunday morning, July 11th, 2021. I'm Larry Rhodes, or Douter 5. And as usual, we have our co-host, Wombat, on the line with us. Hello, Wombat. Vinnie, I'll come help you. I'll be right there. Just give Daddy an hour. Who was that? That's my cat. He's going crazy. Yeah, that's the only other cat. Excuse me. With us today, also, our guests are Doubtfire. Hello, Doubtfire. Hello, hello, hello. And George Buffalo. Welcome from New York. Boudreau from the UK. Hello, everyone. George Brown, Brooklyn, but he's in Tennessee with us and down there in Athens. Yes, good morning, everybody. And Dred Pirate Higgs, also from, well, out of the States. He's up in Canada. Welcome. Oh, you're there. And a special guest this morning, Isaiah Diesel. Diesel. Where are you located? You're in an out-of-the-country location, too, aren't you? I'm located in South Korea. So good evening, Annyeonghaseyo. South Korea, cool. Very cool. International show right here. Annyeongseyo. Digital Freethought Radio Hour is a talk radio show about atheism, free thought, rational thought, humanism, and the sciences. And conversely, we'll also talk about religion, religious faiths, gods, holy books, and superstition. And what's our topic today there in Wombat? Today we're going to be introducing friends, Isaiah Diesel, and talking about should we be judged by our actions. But before we get into it, we have a full house of people. International show, I'm digging it. Let's all gather together for a moment of respect to appreciate this wonderful moment by leading it up to our own Dred Pirate Higgs for our weekly vacation. I'm going to dawn my holy colander. Give me a second. Go for it.  Oh, a red one this time. Finally, brethren, whatsoever things are true, whatsoever things are honest, whatsoever things are just, whatsoever things are pure, whatsoever things are lovely, whatsoever things are of good report, if there be any virtue, and if there be any praise, think on these things. And that is from Saul of Tarsus. Lead us into a raw man, Dred Pirate. Dred Pirate, where's our raw man? I can't hear where that is. Where's our raw man, Dred Pirate? Raw man. Thank you, thank you, thank you. Can't believe that, can't believe it. Gotta get that bit. Okay, so guys, we have a really cool opportunity to introduce a new guest coming all the way from South Korea. That's a surprise for me. Hello, Isaiah. Nice to meet you. Okay, cool. I only know that and Kogi, and that and then a bunch of K-pop. And what else are you going to do, right? But I want to crack into, like, everything that you're doing on there, but I just want to check in with everybody else on the show. And then we'll get to you. So, Boudreau, haven't seen you in a while. How you been? What's going on with you? Also, I like your shirt. What's your shirt all about? Run for ice cream. It's a 3K. It's not a very long run, but in the hot, hot summer, you got ice cream. Oh, cool. Did it with the kids. Nice. Yeah. Good time? What were we doing? Yeah, yeah. Actually, the race was canceled last year, but it's going to happen in about a week. Again, this year. So I'm looking forward to it. Fantastic. Trying to run again. But, yeah. Does the dog ever go out with you on these runs? Because I think that would be a wonderful opportunity. We have, we have a new puppy. She's about eight months old. So we try not to run her too much because that's not great for, but she goes for miles and she'll be a runner. I think she's not 50 pounds too. So nice. Nice. Nice. Scott, what's going on with you? And are you still on tour? How have you been? Oh, man, I'm having a blast. I've been working again with the new materials that Mike Greenlee and Debra McGone, the Grammy songwriters, and just really thrilled about like these upcoming projects. You know, they're just, I don't know what to say. It's kind of like, enough of a man. But yeah, it's having a great time with the music, all that good stuff. And also my, my exploring epistemology channel, that's going really strong. And yeah, it's been really real, man. I dig it. I dig it. Keep up the love, man. Keep up the effort. You're doing the good, you're doing the real hustle. And we appreciate it. The good stuff. Putting out music, putting out good thought. Love it. George, the second one half coming all the way. You said you were from Athens. Did I hear that right? Or was this a different part of Tennessee that you're in? We're, we're exactly. I am exactly halfway between half, between Knoxville and Chattanooga. Does your, does your, your grass patch have a name? Oh yeah. I'll send you all letters. Okay. Okay. Okay. Okay. Athens, Tennessee. Yes. How's life been down there? So I'm, well I'm, I have been exploring alternatives and computing. I've always been interested into that. So I have been given a new, a new laptop machine to explore. And I, I work in Linux. I want to be really off of the commercial computing grid.  Why don't you just get an advocate at this point? I didn't know what an advocate is. What is it? I will happily show you after this, this conversation. Okay. Okay. But in general, I'm very opposed to surveillance capitalism and surveillance on the net. So I take special efforts to avoid being surveilled. Yes. If they can't use it to get rid of climate change, why do we have it in the first place? Right. Okay. Dred Pirate. I love that red colander. Was that a brand new one? Or is it only one that used for special occasions? No, that's actually used for firefighting purposes. The red, the red fire colander in case something burns on the stove. Okay. I don't imagine it can hold water very well, right? So how does that thing work? Is it, is it powered? Yeah, that's it. It's just so people recognize the factors in emergency. So for videos of the show, you have a t-shirt that has some text on it. I want to know what that's all about. Demand evidence and think critically. That's what he says on the shirt. Love it. Dred Pirate, how you been? What's going on with you? Good. Good. A couple of really good things. Recently, I think I mentioned it last week that Australia had been died. Forming a religious organization or nonprofit. So we've started a campaign through our international pastafarian captain's conclave, which is our international captains group to do a letter writing campaign to the Australian ambassadors to our country. Okay, in support, in support of them being able to do as they wish, just like anyone else. And also we got together yesterday to talk about, I mentioned this before, the World Cruise 2021, which is this initiative that pastafarians around the world are looking to lead in order to form a delegation to the U.N. Nice. And request a special day in November or two days, November 20th and 21st to be a day of truce. Just like the Christmas truce in the First World War, very same sort of idea, but having it secular and led by pastafarians. So do we have other days of truce that are recognized right now or is it a grab bag or outdated? What's going on? Yeah, I'm not aware of one. You know, I looked around and tried to see if there was anything official, but I haven't seen anything. So it'll be something new. Just a call for peace in November. No, not peace. Peace. Temporary peace. Yeah, peace is a goal of a longer journey. Right? So truce is the time that you get to sit down and have conversations. Peace is when you've done all that negotiating and understanding one another and coming to terms with each other's differences. So truce is just the time to contemplate those things. Okay. That's actually really, really thoughtful. And I appreciate you telling me that particularly at a time like this, because there were a lot of things I was thinking about where it's like, peace seems almost improbable, but a truce as you're defining it now does seem good. And there's always time for good conversation, I think, right? Well, and the thing is if it does work out, you know, then we can expand it because of course next year will be 2022 and 2023. So you expand on the idea that the truce becomes longer and longer, giving more time for that reflection. I dig it. George Buffalo with the tan.  What's going on with you? How you been more from my gardening? That went very well. And Eric and his family shared in that. Well, I guess one of what I've done, knew very briefly is I took a very interesting trip to Cherokee, North Carolina below Gatlinburg to the middle of the Cherokee Indian Reservation. And I learned a lot about their culture and the wonderful peace-loving people you see over here, some artifacts that I brought back. Yeah. Why don't you talk to me about some of that stuff? Yeah. A blow gun down on the bottom. Okay. So back up. Back up. You just said peace-loving people. And then you point at two weapons of like, and there's this peace-loving rifle. And here's this peace-loving blow dart. You're overthinking it. You're overthinking it. About 15% of their diet was meat. And they use both weapons, not as weapons, but as ways of sort of stunning their prey, which mostly birds, pheasants and the like. And that's what they were used for. Actually, the blow gun works, and it's got a very mild impact, but it's enough to stun a potential meal and then go and grab it. But really wonderful history of those people. And of course, they suffered like so many of the American Indian tribes did, and they were forced off their land. But enough of them stayed in the mountains so that when it was time to establish the reservation where folks came around to giving reservations, they were there. And now they have a casino, so they're doing very well. Okay. Okay. Let's hope for a long-lasting wellness for a lot of the Indian tribes. Let's hope they keep control of the casino. It's the most important thing. I'll tell you this. I went into a TED Sporting Good this weekend, and I was expecting there to be sports equipment. But it turns out, TED Sporting Good is for sporting equipment, which is not sports, but hunting. And that made me upset because I was like, where's your disc golf disc? They're like, we don't have them here. You have sports on the signs. Like, no, we do sporting. Completely different thing. I'm like, that ING. That was my weekend. How was yours? Oh, it was fine. Uneventful. It rained, so I didn't get to work out on the deck as much as I wanted to. Just watch TV, play it on the computer. It just wasn't that much to it. Not that much to it? Nice and keeping it simple. Okay. Just trolling on the internet, making people angry, making some memes. I do that, as well, through... Okay, cool. I don't troll though. I take exception to the word troll. I don't troll. It's troll light or wheat trolling, if anything, right? It's just little pokes and stuff like that. Get people thinking. Well, I answer questions and make points. I don't go on there just to rage among people. Is that what you kids call it these days? Yeah, I know. I know. I know. I understand. We're going to have to ask Larry to explain the internet to us. Hi, Bruce. Isaiah Diesel. So happy to see you. Would you mind taking some time to explain your entire life story in the next couple of minutes? Go for it. Well, thank you for having me on, Larry. Thank you. Larry was on my show. So I have a podcast I do with an aegis man. But sometimes I do people one-on-one. So Larry came on. But I'm a former aegist. And I had a religious conversion about seven years ago. And I live in South Korea. I'm a missionary here. And thank you all for having me. We'll just stop there. Yeah. Where are you in South Korea?  What have you been up to since you've been down there? How's the Kogi? Talk to me. So currently I'm right now in Seoul, but that's because I'm doing some, I'm helping out a church here. But I live at the bottom of South Korea, which is called Mokpo. And it's kind of like out in the countryside. So I moved from Seoul to go out there. And I've been here for about 10 years. My wife's Korean. I have a daughter who's Korean. So I love living here. Cool. I spent a lot of summers in Korea, myself. A lot of time in Busan area. My whole family's military's in this big base, as you know, in Seoul. And so a lot of the times we would spend it in the military base is very open. So like, I wouldn't even be surprised if you notice it. You notice it because they're all the military there. But like Busan is nearby. Well, not nearby, but it's southern. And it has a ferry that takes you up to Japan, Fukuoka. And we'd spend time bouncing back and forth. Right. It's really, really nice up there. Food is too small. The proportions are too small. Would you agree? Like when you get a food, you're like, it's only like the size of a calculator.  It's like, no, that's your three-day meal. It's like, no, I can't eat this much. I need more food. Anything like that. What do you like about Korea? What do you hate about Korea? Right. You can be from your perspective. What's your favorite things? What's the things you're like, man, America, come on, I missed July 4th. What's going on?  That's a bit of a trouble. But I think by and large, I prefer living here to America because people here tend to be more communal minded. So they generally think about as good as society rather than the good of the individual. In America, there's like a fixation on individual freedom. And so that just doesn't really jive well in my mind. But I love the food. I love the people. Okay. Okay. Okay. Are you near Kwan-Ju? Yeah, actually very, very near. Okay. I spent a year and a half in Kwan-Ju in the military. Thank you for your service. Really appreciate it. Thank you for your service. Thanks. My mom was a Vietnam veteran, but as an American here, I'm very grateful to the military people who serve. So thank you. So part of your mission, sort of part of your missionary work, what's your daily schedule like? Can you take me through a typical day of a Korean patriot missionary? Yeah, well, it's been the first year down here. So it's been mostly just making connections, but I do teach English and I also do talk to people online and just generally being out and meeting people. So I'm still establishing things. It's been extremely difficult, obviously, because of corona. So almost all the activities I would normally be able to do I can't do right now. So just trying to wait it out right now. That's a good question. How is corona over in Korea? Hey, and Larry, we're going at, Larry, what's your input? I'd just like to get back to something you said earlier that he used to be an atheist. What convinced you that going to Christianity or believing in God? I mean, we're all atheists here and we are open minded. So I was wondering what your evidence or your experience was that brought you back into the fold of religion? Well, so about eight years ago, I was living with my friend and I took a trip from Greece over to Israel. And while I was in Israel, I got this tattoo right here, which is a North Korean atheistic body, which means Juche, it means self-reliance. So I got that tattoo on me in Israel. So I was pretty far off of being a Christian as you come. And amazingly, just four months after I left there, I was in my room and Jesus Christ spoke to me at the age of 32. And I gave my life to him for the first time in my life. So did you actually hear a voice or were you just moved? No, I heard him when he said that. Okay, did he appear to you? Did he appear to you? No, I just heard it. I know it sounds crazy, but... Dred? As I said, I was in Israel four months before getting tattoos and smoking weed and drinking. Religion was as far, you know, Jesus Christ was the last thing on my mind. So, yeah. What would you say, Dred? Yeah, I was going to say, so how did you know it was Jesus Christ? So he told me. He said, I'm Jesus Christ. Yeah, so it's been a very interesting last seven years. You're on mute, Ty. Weird comment. If there was, if he told you as any other person, would you have the same standard to believe whatever the voice was if they said, like, hey, I'm George Collarlin. Or, hey, I'm Muhammad. I'm Muhammad. Would you believe it then? Or, like, hey, I'm Zeus, actually. Would you believe in Zeus? Why not? I mean... Why not? Some people want to ask me, like, what do I think about other people's experiences if they've heard from Muhammad or met Muhammad? And I'm like, I don't... I'm not going to get involved with anyone else's experiences. I can just talk about my experience. And that's what I experienced. So I'm not saying Muhammad doesn't exist. I'm not saying Buddha isn't whatever out there. Like, that's not what I do. I had this experience and it changed my life. And, yeah, I'm a better person as a result of it. Yeah, I don't even know if you had the experience or that it was changing your life.  Does that make any sense? Like, is there any possibility that I could have a voice in my head tell me that it's something that it's not that thing? Like, is that even possible? Yeah, certainly. George, I would say...  Look at this guy. Sorry, what's up? Oh, you're on Meet My Friend. You're on Meet My Friend. Still on Meet My Friend, George Buffalo? There you go. There you go. For a radio audience, he put himself on unmute in the left room. I guess he had to say... Maybe I could ask a question? Yeah, Scott, go for it. Yeah, just this is an epistemic question. So what method would one use to distinguish between imagination and God speaking to them? Or auto-relationation. Or a way to know the difference. Okay, so you speaking in general? In general. In general. What's a good way to know about a voice in your head is actually what that voice is and compare it to an imagination? Okay, so in general, I would say if he's able to confirm something externally, which I can only speak for my case, which he did multiple times. So for example, one of the times he used someone else to tell me one of the things that he told me, which was part of multiple different things to confirm what I experienced. But I would say, yeah, some other kind of external confirmations. That would be good. External confirmation, would you be open to doing one right now? Or does the voice only talk to... Like, could you externally ask this voice to confirm something for you right now or does it only work when it's convenient to the voice? So just let me tell you how that works in my own personal life. I don't know, maybe there are other people who can, but in the first six months afterwards, maybe about the first five months, I believe he spoke to me about six times, and then I literally did not hear one peep for five and a half years until I got onto the mission field. And then when I got onto the mission field, he spoke to me again, and now it's been an entire year where I've not heard from him. So difficult to test. I never know what he's going to speak to me, so I have no idea. Jared Pirate? Jared, you're on mute. Yeah, so I was wondering if there was anything that you can think of that would disconfirm your belief that what you heard was what you heard? Probably not. Honestly, it's been seven years. And mind you, prior to this, like my parents and ministers, I went to Bible college. I became an atheist while I was at Bible college. I got all the world religions tattooed on me later on. And I was even served as a missionary for some time. So I did all the things on the outside, but I didn't have an experience with Jesus Christ. So at the age of 32, after that, it just was a life-changing experience. It just... True.  For example... Is that it? It's a short show. I don't want to make sure we get to Scott's question, but it sounds like, at least so far, it's unfalsifiable. You want to believe it. Your parents were missionaries. And what was it? It's sporadically testable. It's utilitarian and it's sporadically testable. Scott, what's your question before we head out to the break? I was just going to throw this out for some of our Christian listeners and others that I know listen in, at least go back to the show. There's a lot of Christians that will say, well, Jesus doesn't speak to people like that anymore. That's not scriptural. And then they'll say, if you heard a voice and the voice confirms things externally, that's the double, man. How do you respond to that? Well, first of all, my family, when I told them what happened, they did make me seek counseling after. And so I did go to counseling for a year.  Even a lot of Christians, I have told a lot of Christians and I have heard a response that says basically what you said. So if it was a devil, then I don't have any way to confirm it was or it wasn't a devil or it wasn't some kind of alien who was shooting audible sounds at me, some kind of sound waves. But I don't have any way to confirm that. I know what happened. Yeah, so. No way to confirm. That's totally fine. One way or the other. It was a devil or another.  Well, I don't know that Islam is the right way. And the Jesus voice was just trying to keep me away from the one true religion, which is Islam. So I don't know that one way or the other. Isaiah, I'll ask you this one last thing. Why were you an atheist? Do you mind like describing that?  And so that made me have some kind of natural resentment towards, I don't know, some kind of being out there, but whatever creator. So I was already that. But then when I went to Bible college, it was during the Clinton impeachment and they were making fun of Bill Clinton. And they were saying things like, you can't be a Democrat and Christian. And my mom was a Democrat and Christian. So just those experiences. And then I was in love with the girls. She went on a missions trip to Indonesia and she got bit by a snake and died. And just like the last month I was there, I just became an atheist. So just a combination of lots of different things.  I mean, nobody should go through that. I'd be interested if you want to ask us any of the questions that we ask you, particularly like why are we atheists? Or what it takes for us to believe claims if even if we did have a voice in our head speaking, but unfortunately we're at the bottom of the half hour. Larry, you're going to have to take us out and then bring us back in again. Talking with Isaiah Diesel. All right. This is the digital free thought radio hour on WOZO radio. 103.9 LP FM right here in Knoxville, Tennessee. We'll be right back after this short break. 103.9 FM WOZO radio. Knoxville. Hello and welcome back to the second half of the digital free thought radio hour on WOZO radio. 103.9 LP FM right here in Knoxville, Tennessee. Today is Sunday morning, July 11th, 2021. Let's talk about the atheist society of Knoxville or ASK for just a moment. Counted in 2002, we're in our 19th year. ASK has over a thousand members and we have weekly Zoom meetings during COVID and we're still doing those, but we now have our in-person meetings starting at Barley's Tapton and Pizzeria in Knoxville's Old City out on the patio. We're there every Tuesday evening after work, say from 5.30 to 8. You can also find ASK online on Facebook, on meetup.com or just go to KnoxvilleAtheist.org. By the way, if you don't live in Knoxville and you can still go to Meetup and search for an atheist group in your town. One, start one. Start one. Where do we want to pick up there? I'll bet. All right, so we were talking to Isaiah Beasel about some things involving his path from his identification as an atheist to his identification as a Christian. Was that fair? Isaiah? Okay. Cool. He's currently a missionary in Korea doing some good work there and helping out, I imagine, during COVID. We appreciate the work that you're doing. What we'd like to be able to do is have a chance to have the questions that we had asked you sent back to us. And so we made a really short list about, you know, what made you an atheist? Is it important to have beliefs that are falsifiable? Is personal experience reliable? How would you confirm a voice in your head? Why is it important to have high standards of evidence? We don't want to just put you on the plate. We'd hopefully like to share our answers as well. And I'll actually start with a round table question on why are you an atheist? And we can start even with Boudreaux. Boudreaux, why are you an atheist? Or why did you become an atheist, if anything? Yeah, mostly I just wasn't convinced of what was being told. And of course I was brought up Catholic as we've talked about in the past, but it just didn't sound believable.  So I just not convinced. Okay. And, you know, and it gave me comfort. I felt better about it because I always had these doubts anyway. So, you know, much like Isaiah, I felt, I don't know, like a better person. Yeah. Nice. Judd Pirate, why did you become an atheist? Pretty much the same thing. I've always had a scientific bent and sort of an investigative proclivity. So, and I was actually working towards being a Catholic priest. But as I, the more I investigated, the more I learned outside of what is generally taught the common person with respect to the religion, generally it's cherry picked so that the most favorable aspects of the policies and for instance, are the ones that are out there mostly for the flock. And as I investigated more in more studious fashion, the more I realized that the contradictions were just overwhelming. And then of course my investigation spread to other consideration of other religions and the conflicts or the fact that they're all mutually exclusive. And the additional fact that over the, you know, 100,000 year history of humankind, 99% of all religions are no longer in existence. So it just seems like to me it was, it just became glaringly apparent to me that there was something wrong with that. And I do want to just make a distinction here and perhaps this is something that I should have done way earlier, but when I say atheists, I don't mean person who believes that there is no God. I just mean someone who doesn't believe in a God. Or doesn't have sufficient evidence. To be convinced that a God actually exists, which is a nuanced statement, but it's a very, very important one because we're not making the claim that no God exists. We're making the claim that we don't believe in any God claim. So it's not an issue of we know that there's no God. It's that we don't believe people who say that there is a God. And so that we are asking for evidence to be convinced that that's true. And until then we don't believe it's a lack of belief. It's not a statement that we know that there is no God. Just making that point. Scott, why are you an atheist? So I guess the reason I'm an atheist is I decided one day to be very honest with myself and others and also be genuine in my beliefs. So I couldn't, I never had like a personal revelation from God and reading the Bible, reading the Quran, exploring Hinduism. It seems like the method that people use to get at those beliefs are all the same. It's faith. It's taking what is written as gospel or as the truth. But they all come to different beliefs even within the religions themselves. So it all kind of created a lot of doubt in me. And so I left Christianity as a result of it. I just got to the point where I couldn't be honest about it or I couldn't be dishonest in light of myself and others anymore. And so I just decided to be more honest with myself and live my life accordingly. So for me, it just seems like I cannot tell the difference between a hidden God and one that doesn't exist. Until I can, I'm just going to withhold beliefs either way. I like that. Obviously, I like that. You're talking to the choir right now. I want to actually throw it up to Brooklyn George. You're going to be an interesting case, Isaiah. I think this will be an interesting story. George Brown, why are you an atheist and why are you still an atheist? Well, first of all, I was simply brought up without God and I was brought up without religion. These two things were simply not present in my household. My parents were atheists and I think each one of them had their own reasons and I'm not privy to know exactly what they were. But they were both, I would say free thinkers and at times we attended the Brooklyn Society for Ethical Culture, which was a humanist organization. And I was dragged off to humanist lectures, I think from the age of four when I didn't understand a bit of it and in a way I still don't. So my cultural background is Jewish and so it's like I'm a double outsider in this culture in the United States. This is a very Christian-oriented country and so the belief system simply has never made sense to me. George Buffalo, listen, I know you're going to say something scientific. I want to pressure you not to mention anyone whose name begins with the letter S or mention any curves of Gaussian nature in this explanation. But why are you an atheist, my friend? Also, take yourself off mute. You've had the whole thing backwards since the last half of the show. There you go. So just hit the mute button again. There you go. Okay, so I've always been a scientist, but even before that I've not been an adherent. I'm an independent. I'm not an adherent. I like that distinction very much. And so that's where I come from. I always have and I'd like to see the evidence just like Dredd's shirt says. And if there's something that I don't understand and I have a path toward understanding it, or I'm not going to buy in. I'm not an adherent. Nice, very cool. Larry, I'm buckled up.  Yeah, I'll try to get you. It's a special time for me. All right, I'm buckled up. Larry, why are you an atheist? Well, I was born into a Baptist family, so I was raised Christian. But from an early age, it was mainly the outrage that made me skeptical. You know, talking snakes and donkeys, parting of the waters, the arc and the global flood, Tower of Babel, virgin births, angels, et cetera. But later on, I mean, I went through high school and the Navy and then got into college before I ever started really questioning it. I met a atheist and during conversations with her and studying anthropology, physics and geology in college. Which gave me the scent of man, the age of the earth and how the universe is working basically. I lost all belief in anything supernatural at all. Souls, sin, heaven, hell, all of that. And I've been an atheist for now for almost 50 years. Oh, very, very cool. Very cool, very cool. And look, Larry didn't even mention souls. Eric didn't mention Sam Harris. George Buffalo didn't mention Gaussian curves.  Keeping my blood pressure low. I really appreciate that. Isaiah is looking a little confused. Sorry. There's just these buttons that everybody keeps hitting all the time. I'll do mine real quick and then we'll get some feedback from Isaiah. Simply put, the reason why I'm an atheist is because I've raised my standard of evidence for the things that I deeply care about. And really for everything, really honestly. And for the things that I deeply am concerned with and the things that I desperately want to know more about. I've raised my standard of evidence such that when I think about things that are generally mundane, like did I go to the gym today? Am I a black guy? Does my mom love me? I can find enough evidence to support that and be reasonable with it. But for greater claims that are a bit more complicated, like does a supreme being exist over everything? Or is it possible for someone to break the laws of physics to feed a bunch of people fish or offer dietary advice through a talking snake? I need a little bit more evidence to support those claims. And not to be cheeky, but it's essentially just, I haven't been convinced that those claims are even feasible for me to begin belief in them. Not to say that they haven't existed. It's just that they're not an option for me to begin believing in until I have better evidence to support it. In fact, I found that there are much more mundane explanations for a lot of the things that Christianity or other religions may claim to be the answer for that I found explain much more better in secular fashion. And in a simple sense, in the most simple sense, I had a lot of religious answers, but I was desperately looking for explanations and I didn't get any of them from religion. And so I was looking for a way to figure out, okay, well, what's the best way for me to be able to take away things that are true? I mean, take away things that are not true and keep the things that are true. And I found the best way to separate the two is to have a high standard of evidence. And if what I believe in is true, it'll withhold, it'll stay in there. It'll stay in that standard. I'll still believe it. But if it turns out to be not true or if I just don't have enough evidence to support it, I can put it in the separate category, which doesn't mean that it's not true. It just means I don't know yet. And I'm comfortable with there, with God being in that box, because it feels like a much more intellectually honest position for me to just say, I don't have enough evidence to believe in a God, but I can have a high standard of evidence. And if God ever wants to meet that, I'll be ready to believe it. But until then, it's up to the people who do believe in God to present that burden of evidence to me. It's not my job to reach my standard and reach out for other people. A lot of reasons going in. Isaiah, what are your thoughts on everybody? Well, you know, I have three different Atheist co-hosts. So, I mean, you guys really haven't said anything that I haven't heard before. So, I mean, I'm familiar with those arguments. And for many years, I was an Atheist slash agnostic. I could just tell you on a personal level, kind of like a really big, a really big crack in the ceiling was going to North Korea and seeing the oppression of the North Korean people firsthand and trying to balance that out in my atheism. And I really couldn't find the proper reasoning to condemn that inside of what I was believing. Could you? I'm going back to you. Because it sounded like, at least in this example, you're saying atheism comes with a codification of some sort of morals that will allow you to look at subjugation of people and come through a realization that it's wrong or right. Whereas in very much in the context of this conversation, atheism is just a lack of belief in a higher or in a God claim. It does not come with a set of morals to come up with a judgment on how people should be treated.  But because I believed in evolution and I believed that in the survival of the fittest, I also saw that Kim Jong-un in his mind, actually his father, Kim Jong-il, believed that he was more highly evolved than the Korean people there and he was using them as, I would use a sheep or goat or whatever. And I was just trying to reconcile that inside of my atheism and beliefs in evolution. And I just, I couldn't do it. Yeah, I wouldn't be able to do it either. I don't find a faculty in, there are atheists who believe in religion or evolution and the ones who don't. And I would say it's not a vehicle to determine how to treat people. It's just a lack of belief in God. Hey, Doubter 5, what do you got to say? I was just going to say, his proximity to North Korea may have influenced his thoughts there. But I mean, if he had lived near Scandinavia or Holland or any of those countries there or predominantly anywhere in Europe, which becoming more and more atheistic, China, any of those other ones who don't have overarching oppression of their people, who are also atheists, countries that actually support the people, socialistic countries that take the welfare of their people very much to heart. Yeah. It may have been, well, how would you have felt about that if you did have lived in that proximity instead of one that, I mean, they're not using atheism per se to oppress their people. They may be using evolution as an excuse to, or that particular person did, but any excuse and an argument like that cannot weather. Just want to throw it a silly thing. I think over half the people on this call are over 52. Is that accurate? If that is the case. So most of the people who are on this call right now were born in a time when black people couldn't even marry white people legally in the country that I'm in right now. And my mom, it was illegal for her to attend the school that I eventually got my PhD in just because of the color of her skin. So like there's been subjugation. We don't have to look across seas to find subjugation. I know we're an international show, but I can look at my window and still see attitudes of people who, living through generational changes that are stymying and inhibiting progressive change that are necessary to just allow black lives to matter as much as everybody else's. In this state that I'm in right now. But I don't need an atheist perspective to see that as a bad thing. Like I have a set of morals on just humanism or just how people should be treated with egalitarian values that complement, if anything, my impression of what it means to be a well, a good person in society and treat people with well-being. But it has nothing to do with my atheist perspective. It is, my atheism is just an answer to just one question, and that's whether or not do I believe that a God exists or not? And it's not that. It's no for me. It's yes for some other people, and that's it. And then everything else is up to me to decide. I saw a lot of hands raised. We're going to go Dred Pirate first. What's up? I just wanted to mention that you were bringing up segregation in America. I think it's worth noting that most of the improvements, societal improvements are as the result of secular values, changes in secular values and humanistic values. Because certainly my experience and my understanding of history is that it's always been the religious contingent that represses change in favor of their conservative values, and that's through humanism and secularism these things change, and we have a better society. It's really hard to get rid of slavery when it's promoted in the Bible. Doubt or five, and then Scott, doubt or five? Well, I mean, if he's going to look at a country and say, well, that's an atheistic country, and they oppress their people, you need to look back through history and see how religion has been used to oppress people. I mean, I've got a whole blog page I think I sent it to you one time that you could look at what religion and superstition is responsible for, but I mean, just looking at the inquisition, like 400 years of human oppression in the name of Jesus, you've got to take that into account as well, I would think. Scott, what do you got? Yeah, I just wanted to make sure we weren't talking past Isaiah here because I think it, you know, I may be wrong, but I think basically what Isaiah is saying is not that Christians can't do bad things or Christians can't, you know, impose bad policies in countries. I think what he's saying is that if your grounds for morality is evolution, then it should be no surprise that you have a North Korea. I agree. So that's, I think that's mainly what he was trying to figure out in his atheism that it provided no answer for with regards to evolution and naturalism, but I would just to maybe push back on that idea to maybe help you understand is that empathy and being humanistic is also a product of evolution if evolution is true because we see animals being empathetic towards their common you know, tribe or animals like apes and dolphins and... Crossby, she's too... Correct. So it seems that while evolution does you know, kind of promote in many cases tribalism like this is kind of seen in countries like North Korea, in America and other Christian countries as well it also promotes empathy and a pathway to morality and then we get into a whole other conversation about subjective morality versus objective morality and blah blah blah but I just wanted to put that out there to let you know that I think I understand what you're saying Isaiah. So I do want to clarify something like... Isaiah, if you would mind, I'd just like to clarify what Scott says then we'll leave it to you and then we'll close out the show. Is that okay? Sure. So you'll have the final words for sure. So yes, I agree with Scott's point. Evolution makes for a really bad moral barometer because it doesn't really offer any I would say guidance in terms of how to treat people or how to assess behavior, right? It's simply what it is and it's trial and error and it's a fairly murky system. Atheism likewise is not a moral system or moral codification of any code. It is simply an answer to one question, do you believe or not in a God are you convinced or not? And so what I do find appealing behind Christianity is not only is it an answer on whether or not a God exists but it also comes with a set of morals and a set of dogma to follow which can make things a lot more clear and the thing would be not so much for us to assess whether or not that's a good moral code. It's just an issue for us. Are we convinced that that is one that's given to us by a God or not? And if we're not convinced, then it's just another set of morals that are provided to us by most likely people by society and then if that's the case, is that even the best one? Or has society come up with even better codification rules for us to follow and then what would be the better set for the best consequences of behavior and I feel like I have found a higher standard of principles to follow than one that's been codified in a book multiple thousands of years ago that I know for a fact has actually been used to propagate a lot of harm and distrust among people today and ones that we're still going to fight by today. I know we're getting close to the show. Kira, final words. What do you got? We'll give it to you. Yeah, your criticisms about religion, like I share the same exact concerns and I have a degree in history so I definitely understand that. My experience in North Korea, I'm not saying God exists because of that. That was a crack in the ceiling that just made me stop and scratch my head and say can I really rectify these two conflicting beliefs that I have and I just, I couldn't internally. I'm not saying you guys can't, I'm not saying aegis are immoral or bad people because the secular humanists I've met by and large almost consistently every time been more moral than the Christian that I've personally encountered especially now when I saw in the last four years the Trumpsters who were going along with some very vile stuff and it seemed like it was the secular people who were standing up for themselves more on the stuff that they were doing that was blatantly anti-religious and anti-Christian. That was not intended to bash you guys so you guys lack morals. It was just a matter of I was presenting my own experience. Thank you guys for hearing me out. Sure, thanks for hearing us out. Yes. Getting down toward the end of the moment. Dred, go ahead. You're on mute. I just had a comment here from my data's trading room when you talk about North Korea of course many of you ought to know I've heard in the news that what happened here at residential schools in Canada so he makes the comment how about what's going on in Canada now with the Catholic Church who oversaw essentially the deaths of over 1,500 indigenous children that we know of so far that we know of so far so it's certainly not limited to fascist countries religion sometimes has foul effects in more liberal liberal societies. I also was fortunate enough to spend a lot of time in Sweden too and I can tell you that's a very atheistic society. That's where I actually came out as an atheist. I wanted to do that and for every North Korea that's presented as one's extreme I can just as easily point to Sweden and be like this is the exact same thing and everybody here is happier and if not at least the metal music is fantastic right off the vine so good, so good. Boudre, what would you recommend? What's up? Just last thought because I recently was preparing for a debate with an atheist and I went to all those Norwegian countries they're totally Norwegian Scandinavian, Swedish almost all of them with exception to the Netherlands which I went to had at least a 75% rate of belief in God so this idea that they're like all or most atheists is a total it's just not sure. I live there. That would be interesting I can show you my World Factbook every one of those countries where at least 75% either Lithuanian or Catholic so yeah there's a myth that they're mostly atheists, it's 25% of them Interesting Even Sweden I'd like to see this one Yeah, go to ciai.gov World Factbook I would love for you to have the same standard for these numbers that you're saying then for the God voice that's in your head I'm very eager to come up with these citations and quotes for the statistical ambiguity that we have but for the idea that a God could talk to you and say oh yeah I am Jesus by the way and you will believe it face value there's a discordant lack of similar standards there but maybe we can talk about that more in the future Boudreaux, what do you have is there anything for you? Are you talking about anything to check out? Yeah, yeah, check out, what's up? I did want to point out this is maybe a bit silly but everyone's looking for things to occupy their time there's a Netflix show called Manifest that I just got sucked into in Isaiah, I think you'd like the premise of it because it's actually all about callings like hearing voices and having them fulfill these things to almost pass a test or something so it's actually Manifest, yeah a bunch of people were on a plane and the plane disappeared for five and a half years back but anyway just my point I think with it it's a fun entertaining show but I think the interesting part about it is there's a lot of conversations about you hear these voices, how can I trust that you heard that voice and then the trick of the show is they actually come true so they hear a voice and it says there's a kid buried here they dig it up, there's a kid and I'm like well did you put the kid there? No, no, I heard the voice and it gets into a really interesting I don't know, there's some evidence that all of a sudden he's under arrest for murder Right, and I'm sorry we ran out of time on the show so Larry why don't you just take us out Okay, let me get to my point This has been the Digital Freethought Radio Hour, be sure to check out thedigitalfreethought.com slash blog, be sure to click on that blog button for our radio show archives Atheist songs and many articles on the subject if you're interested I have a book out there called Atheism, what's it all about it's available on Amazon if you have any questions for the show send them to askanatheistat noxfilatheist.org and if you're a member of a clergy you're a preacher, pastor, priest but no longer believe in the claims of religion there's a group for you it's called the clergy project go to clergyproject.org for more information if you're watching this on YouTube be sure to like and subscribe remember everybody is going to somebody else's hell, the time to worry about it is when they prove that heavens and hells and souls are real until then, don't sweat it enjoy your life and we'll see you next Wednesday say bye everybody bye everybody bye everybody bye bye who's hell am I going to I heard a voice in my head that told me that only atheism is true


Hello and welcome to the session. In this session we discussed the following question that says, would that the points minus three zero, one minus three and four one are the vertices of an isosceles right angle triangle. So we have given three points. We need to show that these three points are the vertices of isosceles right angle triangle. For that we will need distance formula according to which we have that if we have a point say p with coordinates x1, y1 and q with coordinates x2, y2 then the distance between the two points is given by pq and this is equal to square root of x2 minus x1 whole square plus y2 minus y1 whole square. This is the key idea to be used in this question. Now we move on to the solution. We take let point A has coordinates minus three zero, B has coordinates one minus three and C has coordinates four one then we need to show that ABC are the vertices of an isosceles right angle triangle. Let's find out AB that is the distance between the points A and B. This is equal to square root x2 that is the x-coordinate of point B that is one minus of minus three that is x-coordinate of point A whole square plus minus three that is y-coordinate of point B minus y-coordinate of point A that is zero whole square. So from here we have AB is equal to square root of one plus three whole square plus minus three whole square. This gives us AB is equal to square root of 16 plus 9 that is AB is equal to square root 25 and this is equal to 5. So thus we get the distance between the points A and B that is AB is equal to five units. Now let's find out BC that is the distance between the points B and C. This is equal to square root x2 that is x-coordinate of point C four minus one that is x-coordinate of point B whole square plus y2 that is the y-coordinate of point C that is one minus y-coordinate of point B that is minus three whole square. So from here we get BC is equal to square root of three square plus four square. Now BC is equal to square root of 9 plus 16 and this is equal to square root of 25 and that is equal to 5. Thus we have BC is equal to 5 units. Next we find out AC that is the distance between the points A and C. This is equal to square root of x2 that is the x-coordinate of point C four minus x1 that is x-coordinate of point A that is minus three whole square plus y2 that is the y-coordinate of point C which is one minus y-coordinate of point A that is zero whole square. So from here we get AC is equal to square root of four plus three whole square plus one square that is AC is equal to square root of 49 plus 1 that is equal to square root 50 which means we get AC is equal to 5 root 2 units. Thus we have AB is equal to 5 units, BC is equal to 5 units and AC is equal to 5 root 2 units. Now as AB is equal to BC they both are of measure 5 units therefore triangle ABC is an isosceles triangle. Now we need to show that it is an isosceles right angle triangle. So for that we will first find out AB square which is equal to 5 square that is we have AB square is equal to 20 5 units then BC square is equal to again 5 square therefore BC square is equal to 25 units then AC square is equal to 5 root 2 square therefore AC square is equal to 50 units. So as you can see we get that AB square plus BC square is equal to AC square so AB is of measure 5 units BC is also of measure 5 units and AC is of measure 5 root 2 units. Now as you can see we are getting AC square is equal to AB square plus BC square so this means triangle ABC is right angled B thus triangle ABC is a right angled isosceles triangle. So the points minus 3 0 1 minus 3 and 4 1 are the vertices of an isosceles right angled triangle. So this completes the session hope you have understood the solution for this question.


I don't know what to say. I feel very lucky to be here. I feel very lucky to know Alain, to have known him for a while. He's been a good friend. Once I lost a CD and he bought a new copy for me. What kind of a friend does that? That's a good friend. Exactly, Francis Cabral. Yeah. Right, so I want to talk about something which I Well, you may see in a little while why I chose this subject besides the fact that I actually have been thinking about it. So this is my title on the co-homological dimension of automorphism groups of right-angled art and groups. Can you actually see that? I mean the highlighting. Okay, so I started this project some time ago with Ruth Charney and we have some very recent results with Ben Millard, who's a student at University College in London. So I'm going to talk about right-angled art and groups. Most people here probably know what they are already, but let me just go through the definition. So they're finitely generated groups. What makes it a finitely generated group, a right-angled art and group, is that some of the generators make mute and there are no other relations. Meaning you don't have to say any other relations in order to define the group. That gives you the defining relations of the group. So the way you usually describe a right-angled art and group, a general right-angled art and group, is by drawing a graph. So if you have a simplicial graph, then the art and group you get, this is the rag, the generators are the vertices of gamma, and the relations, well, you say that two generators commute, if and only if there's an edge between those two vertices of the graph. Well, there's v and there's w and they're joined by an edge in the graph. Okay, so that way, by just drawing a simple graph, you can describe exactly what your group is. So I thought I would draw some examples on five generators. There's an example of a graph. It doesn't have very many edges. In fact, it doesn't have any edges. So it's got five generators and none of them commute, so that's the free group. I could, on the other hand, I could go to the other extreme, take the same five generators and draw an edge between every pair of vertices. Did I miss any? No, I missed one. Okay, so every two generators commute, so that's a free abelian group. I'm used to having a lectern that's a little taller, but I don't, yeah, but anyway. And then, but in general, you can have pretty much anything. You could have, for instance, these three generators commute giving you a little free group of rank, a free abelian group of rank three, and here's a free abelian group of rank two, and those aren't connected, so the top three don't commute with the bottom three, so you get a z cubed free product with a z squared, etc. Basically, you can do anything you want and you get a group, a gamma. Okay, so if I draw you a picture of a graph like that, then that gives me some, some groups, right angle art and groups. So these are amazingly simple to define, and if you've been paying any attention at all to geometric group theory or pre-manifold theory, you've learned that they have lots, in spite of the fact that they're so simple, they have an extremely rich class of subgroups, which include, for instance, virtually, they include all hyperbolic three-manifold groups, for instance. Sorry? No, finite graphs. These are finitely generated groups. Right, so what I wanted to talk about today is automorphism groups of right-angled art and groups. So if you start on the left-hand side, if you look, you get the group of automorphisms of a free group, on the right-hand side over here, you get the automorphism group of z to the fifth, z to the n, which, of course, is the same as the general linear group, and since I'm basically a topologist, instead of thinking about, I don't, well, I'm the sort of a topologist that doesn't like to keep track of base points, which means I'm not a really good algebraic topologist, but I'm a low-dimensional topologist, so instead of thinking about automorphisms of free groups, I want to think of outer automorphisms of free groups, and of course that doesn't change anything about GLNZ. So these are two classes of groups that have been, we've been studying for quite some time now, and we know a lot of things about them. What I want to do now is try to take the things that we know about these, things that we understand, about them, and try to see what I can learn about, in particular, the outer automorphism group of a general right-angled art and group. So here's a list of properties. There's actually quite a long list of properties by now that are both everything on the left and everything on the right share. There are, for instance, lots and lots of finiteness properties. They're finitely presented, and so that implies in particular that their two-dimensional homology is finitely generated and their one-dimensional homology, and it's also true that in every dimension the homology is finitely generated. Both of them have torsion-free subgroups of finite index. So that means the co-homological dimension of those, you can compute the co-homological dimension of those subgroups, and it turns out to be finite. And this is big news. This is basically Kaluba, Kilek, and also you have to put Ozawa in there. Okay, so if you read Alain's book about property T, there's a section at the end where he has a list of open problems. Number one on the list is does, out of FN and out of FN, do they have property T? Okay, so I'm actually not going to talk. I wish I could talk about property T. Actually Alain invited me to Neuchâtel in 2002 and tried to convince me that property T was interesting. He convinced me it was interesting, but I had no idea how to do anything about it. So I wish I could be standing here right now telling you the proof that out of FN has property T, but you have to invite those guys instead. So, yeah, so the exciting things are happening in the world of out of FN. Excuse me, what did you say about property T? The outer automorphism group? Yes. So does the automorphism? Yes. For N at least six, and at least five, and at least five. So does the automorphism group? I just, since I'm talking about outer automorphisms in this, I mentioned out. So those are properties, that's just a small part of the list of properties that these groups share, and there's lots of other things like they have finitely many classes of finite subgroups, there's homology stability theorems, and the list goes on. But they're definitely not the same group, and there's a lot of ways in which they're different. For one thing, GLNZ is a linear group. Out of FN is not. I mentioned that they both have finite virtual co-homological dimension, but there's a big difference. For out of FN, it's linear in N, and for GLNZ, it's quadratic in N. Another difference, big difference, between out of FN and GLNZ is that every solvable subgroup of GLN, out of FN, is virtually abelian, and in GLNZ, it's definitely not true. You could say it's virtually polycyclic. Property T distinguishes the two groups, at least for N equals 3. For N equals 3, of course GL3Z has property T, but out of FN does not. So that's been known for a long time. It has a subgroup of finite index that maps on to Z. N equals 4 is open. Right. Other things that distinguish these, kind of related to the ... Yeah, so the Dain function, which measures how hard it is to solve the word problem in a group. For out of FN, it's exponential, and for GLNZ, it's polynomial. Actually, there's other big news in out of FN that is not so ... hasn't maybe received as much press as property T. So there's something you can define for a group that has torsion-free subgroups of finite index, called the rational Euler characteristic, which is just the usual Euler characteristic of the subgroup of finite index divided by its index. For GLNZ, Burrell, I believe, proved a long time ago that the rational Euler characteristic is zero. I think of N as at least three. And it was just proved, it's actually not even on the archive yet, that for out of FN, the rational Euler characteristic is always negative and it grows more than exponentially with N. The rational Euler characteristic? Yeah, yeah, I'm sorry. This is greater than three. No, but for N equals three for GL. Yes, it is exponential. Yes, GL three is that you're right. It's GL four and up. It's it's polynomial. This, well, I have to ... so this is not the subject of my talk, but I have to say this. This is proved by somebody named Michael Borinski. He's a physicist and he proved it. So a long time ago John Smiley and I made this conjecture that the Euler characteristic is negative and grows more than exponentially with N. And we did some work on the Euler characteristic. In particular, we just we used a certain function which we called tau to do a calculation and we found some sort of a generating function. But we couldn't tell whether and we generated lots of numbers. We generated the Euler characteristics for rank up to ten and then Don Zagie simplified our generating function and got it up to a hundred and they seemed to do this so we made a conjecture. But what Borinski realized is that this function tau can be thought of as a character on the con-crimer hopf algebra of graphs which physicists have been studying and using to calculate Feynman diagrams and so he used some things he knew about this, the number theory associated to this hopf algebra to prove this. Okay, I'm done. But lots of exciting things are happening in out of FN. Right, so the general question that I wanted that I want that I'm curious about is how does the shape of gamma actually affect the group of out of automorphisms and its subgroups. In particular these properties, you know, which are true for all out of a gamma. How do you tell when one property holds in some set of graphs and not in others, etc. So what I wanted to address today, what's in my title, is the virtual co-homological dimension. So I want to study that. So in order to study this group, I need to know like what's in it. So we have to start by, I'm going to start by talking about some basic elements of out of a gamma. So let's start with a graph, any old graph, I just, I'm going to use that one as an example throughout the lecture. So there's a couple of obvious kinds of automorphisms. If I take a generator V and send it to its inverse and send everything else to itself, then that gives me an automorphism. All I have to do to make sure I've gotten an automorphism is preserve the commuting relations are satisfied. So if I just invert a generator, it still commutes with everything it used to. Another obvious type of automorphism is a graph automorphism. So if I have, for instance, this graph has an automorphism that kind of flips along the diagonal and it changes V and B, C and W, U and A. Again, if edges were connected before, they're going to be connected afterward. So the graph automorphisms actually induce automorphisms of a gamma. The subgroup generated by inversions and graph automorphisms is finite. So that's just a little tiny bit of the group of, in general, of the group of automorphisms of a gamma. So how do you get infinite-order automorphisms? Well, you think about z to the n. How do you get an infinite-order automorphism of z to the n? You take an elementary matrix, right? You send one of the basis vectors to EI plus EJ. So those are elementary matrices and they have infinite order. For the free group, you do something that looks almost the same. You take a generator. So this is a1 up to an. You can send ai to ai times aj. Call that rho ij. That's an automorphism. You can undo it by multiplying ai by aj inverse. And you don't do anything to the other guys. But notice that that's different from multiplying on the other side. So those are two kinds of automorphisms, right and left. Those are called right and left Nielsen automorphisms. Okay. So, so that's really easy and extremely well known. But for a gamma, for a general graph, you need to be more careful. You can't send Yeah, you need to preserve the commuting relation, right? If you do something to a generator, you can't just arbitrarily multiply it by another generator. If you do that, you better make sure that the result still commutes with everything it used to. So what do you do? How do you get infinite order automorphisms of a gamma? Well, here's the general idea. You choose a vertex. I'm going to choose this one. And I'm going to look at the star of this vertex in the graph, which means the full subgraph spanned by everything that's by it and everything that's a distance one. So here's the star of M in this picture. And then I'm going to look at the component. I'm going to take the star out of the graph and look at the components of what's left. So there's one component. And there's another component. So I'm going to look at these components. In the first case, you can really see that. Okay, kind of. Should use a darker color. Never mind, I'll stop playing. Okay. Right, the component on the left, it's a singleton. It's only got one guy. Everything that commutes with you also commutes with M. So I can actually take you and multiply it by M and do no harm. I've still preserved all the commuting relationships and I can do that on either side. Okay. On the other hand, if I've got a component with more than two vertices in it, like C2 over there, then I can't do that. I can't multiply A by M because then it would, it used to commute with B and it no longer does. So, but what I can do is conjugate the entire component by M and the fact, the rest of the graph won't notice that I've done that because it's kind of isolated from M by, as far as it knows I, yeah, I haven't done anything. So in fact, that also gives me an automorphism of gamma. So I can't get away with just these multiplying one generator by another. I have to either, sometimes I can multiply a generator by the other, sometimes I can conjugate a component of this gamma minus the star by the generator. But anyway, these types of automorphisms, they're all in infinite order and they're called, whoops, I didn't want to highlight that. I wanted to highlight this. They're called gamma-whitehead automorphisms. I should probably call them gamma-neelson automorphisms, but and then the theorem is that the group of all automorphisms and therefore the group of outer automorphisms, too, is generated by inversions, graph automorphisms, these elementary gamma-whitehead automorphisms that I just told you about and one more type of automorphisms called twists. So what's a twist? Well, it too multiplies one generator by another, but in this case the generators commute. What I did up here, I multiplied u by m and they don't commute, but if I multiply, so the twists, yeah, I'm multiplying v by m, but v and m commute, so that's different. So notice that if I started with the free group, then I don't need the twists. In fact, I don't have any twists because new generators commute. On the other hand, if I have a gamma z to the n, then I only need actually one in inversions and twists. I don't have any of these gamma-whitehead automorphisms. I conjugate stuff by an element of z to the n, nothing happens. But in general, this is what you get. You really need all those different kinds of automorphisms. So for general agamas, the twist subgroups is actually very well understood. So the answer is that it's the subgroup generated by those twists is actually injects into the general linear group and you can say exactly what its image is. The image lies in a parabolic subgroup that you can write down specifically and you can, anything you want to know about this, you can just read off from this representation, including for instance, its virtual co-homological dimension. So the twist subgroup we understand, so what I'm going to talk about today is what we call the untwisted subgroup. So it's the subgroup generated by everything except twists. So a couple of remarks about these two subgroups. First of all, every automorphism can be written as a product of a twist and an untwisted subgroup and untwist, and yeah. Yeah, you can put all the, put all the twists in front of all of the, of the untwisted guys if you like. So you can write this as a product. The intersection of these two groups is very small, it's just inversions, the subgroup of inversions. It's an interesting group. It really kind of measures the difference. Well, the kernel of the map from out of A gamma to GLNZ that you get by abelianizing A gamma, kind of measures the difference between out of A gamma and GLNZ and that, that group, which is an interesting group, is contained in this U of A gamma. And of course, if there aren't any twists, then it's equal to U of A gamma is actually, actually equal out of A gamma. So this is a group we're going to study. We're going to study this untwisted subgroup. So to explain what I, how I do this, I want to go back to the case of the free group. When we wanted to study the group of outer automorphisms of the free group, we built a simplicial complex called case of N. What are the vertices? Yeah, what are the vertices? How can I say this efficiently? These are graphs, oops, G, together with isomorphisms from the free group on N generators to pi 1 of G. No, so I haven't put in a base point there because I don't care about base points, so this is right. But I have an isomorphism from the free group to pi N of G and what's an edge? I get an edge from G to G prime. So these are the vertices of my simplicial complex. I get an edge from G to G prime. If G prime is G and I'm going to collapse some edges. In an acyclic subgraph. So you call an acyclic, so that's a subgraph with no cycles, so we'll call that a forest. So edges are, we call them forest collapses and a k-symplex is a chain of k forest collapses. Okay, so the group, that's a simplicial complex. Easy to describe. And how does the group of outer automorphisms act? Well, one vertex comes with this isomorphism from the free group to the fundamental group and the out of FN just acts by changing the isomorphism. So I've got an isomorphism with FN to pi 1 of G. If I take an automorphism, that gives me a new isomorphism from FN to pi 1 of G. So that's, that's a simplicial complex. The group of outer automorphisms acts and the theorem that Mark and I proved in 1986 was that this the simplicial complex is contractable. The action of out of FN is proper, meaning it has finite stabilizers and co-compact. So let me just draw some pictures. That there is a picture of one of the vertices of KN. It's called a rose because it's supposed to look like a rose and the edges are marked with elements of a basis of the free group. That gives the isomorphism with the free group. Okay, so that's a point. That's a vertex. What does a neighbor of this thing look like? Well, here's a neighbor. Okay, there's another graph and that's supposed to tell you, you can see some loops in there. They go up an edge and down the tree and that gives me, yeah, that's a point. And I claim that these two are connected by an edge because if I just collapse this edge, I get that. On the other hand, okay, so another, here's another neighbor. Basically, I can draw any graph I want, draw a maximal tree in the graph and label the rest of the edges by these A's. Then I can collapse one edge to get that picture and I can collapse two edges to get this picture. This is what, this is E and this is F. Et cetera. Right? So there's a little picture of a neighborhood of a couple of vertices in this complex, in this simplicial complex that are next to my to my rows. So what's the precise construction when you say you take all the graphs? Of course there are. Yeah, yeah. So I've been- Both of them classes or you have to rigidify them in some way or do you take- I take, I've been a little cavalier here. I take, I only take graphs, all of whose vertices are at least trivalent and they're connected and I take isomorphism classes, yes. Right, I guess so I've been talking about this since 1986 and it always surprises me that everybody doesn't, I mean it's like when you teach calculus. You kind of think they ought to know this by now. So I'm sorry if I'm a little bit glib. Right. So that's, that's this, that's a space. I want to give another kind of a description of what the neighborhood of a rose looks like in this complex and to do that I have to move to partitions. So there's a very well-known correspondence between trees and partitions, namely if I have a tree and I have an edge in the tree, then that naturally gives me a partition of the other vertices. So for instance, this edge in this tree gives me a partition of the vertices of the tree into two pieces, the vertices that are in here and the vertices that are out here. If I have two different edges, that gives me two different partitions and they're compatible in some sense. The sense is very precise. They're two, so the partition has two sides and I can choose a side of one and a side of the other so that they're actually disjoint. So enough or another way to say that as you can draw circles representing the partitions that don't intersect. And in general I can describe my whole tree as a set of partitions. I have a partition for every edge in my tree. Okay, so there's there's a well-known correspondence between partitions of sets of elements and finite partitions and finite trees. I guess you don't even have to say finite. Okay, and the nice thing about this is, yeah, I already did this, I can actually reconstruct the tree from the partition. So if I have a partition like that, then there's a tree. I just put a vertex in every component of the partition of the complementary sets and connect the dots if there's a circle between them. Okay, so trees and partitions. Now, when I was talking about the neighborhood of my rows, I was talking about graphs together with a maximal tree. So if I have, if T is actually a maximal tree in a graph, so I've got, you know, edges. I don't know, I have too many edges. You don't have that much time. So there's a maximal tree in my graph. Then, and all of these edges, remember, were labeled AI. Then if I take one of these partitions corresponding to an edge, whoops, I wanted a blue partition. It actually, not only partitions the vertices, it partitions the vertices of the tree, but I can also think of it as a partition of the half edges of my generating set. Right, and I look at the, maybe the thing, the way to do this is cut all these half edges into two pieces. AI and AI inverse, and put AI and AI inverse in the same piece of the partition if they end at the same, same vertex in the tree. So what am I saying? Not only could I construct this tree from this set of partitions, I could also reconstruct my marked graph from the set of partitions. I could, right, I know, I know how to glue in the extra edges if I know these partitions. So for instance, in the two graphs that I had in my, the neighborhood of my rows, the first one, I have this one edge and the front, actually in this one the front edge of all three generators is on one end of the edge and the back edge is there all at the other end. So that gives me a, this graph corresponds to that partition and the second graph, I've got two edges in the partition, two edges in the tree, two partitions, and that tells me how to reconstruct that graph. So, yeah, and the punchline is that I can reconstruct the graph from this partition, this set of partitions and each PE partitions, the set of generators. Okay, so what this boils down to in the end is that I can describe the link of a rose in my simplicial complex as actually just the geometric realization of the partially ordered set of compatible sets of partitions. A compatible set of partitions gives a tree.  If I throw out all the partitions, I get the rose and so the dimension of this space is the number of partitions in a maximal collection of compatible partitions. Okay, so that's a picture. So why did I go all through all that? Well, I claim that these gamma-whitehead automorphisms I was talking about, things that are actually automorphisms of a gamma, can also be described in terms of partitions. In fact, partitions of the generators of my right-angled art and group, which remember the vertices of the graph. So how do I do that? Let me remind you of the kinds of automorphisms I was talking about. For instance, I had this picture and I said I could multiply u by m. Well, the link of m doesn't play. So I've written down the the vertices, which are the generators and their inverses in a list and they kind of separate into sets. There's... I shouldn't don't actually want this part in the set. There's the link of m, which just consists of v and w and their inverses and then there are these... there's m itself and its inverse and then there's u and its inverse, which I treated separately, and then there's these components, c plus or minus. So how do I draw a picture of... how do I draw a partition that represents, for instance, the white-head automorphism that multiplies u by m? Well, I just partition u and m from the rest of the components. How do I draw the partition that... Yeah, so that was... you goes... yeah, what about if I want to do... I want to multiply on the left instead of the right? Well, I claim that this does that and I want to think of that as multiplying u inverse on the right by m. So it multiplies u on the left by m inverse. And what about a picture of this partial... this conjugation? Well, I just take m and m and separate it from n inverse and put c inverse in the same way. So these are examples, as I said, of elementary gamma-white-head automorphisms. There is a much more general thing called a gamma-white-head automorphism. So it's a combination of these basic ones. So it multiplies some generators on the right, some generators on the left by u inverse, and some components it conjugates. So here's the general picture.  And then you partition that set into two pieces. You have to separate m from m inverse. So those are the kinds of things I've done. And then you define the automorphism by you multiply something on the right by m. If it's inside, if it's in one piece of the partition in the side containing m and you don't do anything if it's outside the side containing m. So let me just do one more example. So there's a partition. It separates m from m inverse. It contains two guys, one of the singletons and one of the components. And what do I do?  And a is in p, so I have to multiply it on the right by m, but a inverse is also in p, so I have to multiply a on the left by m inverse. So that gives me a conjugation. Okay, so it's a fairly simple rule. There's a partition. The partition has to be the right sort of... it has to keep these components together. And it has to separate m from m inverse. And given any such picture, I get a gamma-whitehead automorphism. And I call the partition a gamma-whitehead partition based on m. Okay. So now we get to how do we study this group? So Ruth and student of hers Nate Stambach and I in a paper that just came out in 2017, we defined a simplicial complex, like the one I defined for a free group. But now the vertices, instead of being graphs, they're they're certain special cat zero or NPC, locally cat zero, cube complexes. So a graph is just a locally cat zero cube complex. The cubes are one-dimensional, but they're cubes. Yeah, but they have to have with the right fundamental group, and you have to have an isomorphism of pi one with a gamma. And what's an edge? You get an edge between x and x prime. Well, for graphs, we collapsed an edge. Here we have a higher-dimensional thing. Instead of collapsing an edge, we're going to collapse an eye bundle. So a product of a graph with an interval. x prime obtained from x by collapsing a certain type of eye bundle. And again, I'm being a little vague. They're they're details here. So what we did is we defined this complex, and then we proved it's actually contractible, and this subgroup of untwisted automorphisms acts properly and co-compactly. The mineral vertex, so for the free group, it was this rose. So what's the analog here? It's a so-called salvedi complex. So it has a generator for a loop for every vertex of gamma, and it has a torus, t to the n, for cliques in gamma. So for instance, if two vertices are joined in the gamma or joined by an edge, you have two generators of the a-gamma, and you sew in a torus to make those two generators the meridian and the longitude, and you do that in higher dimensions, too. So that just by construction gives you a space with the right fundamental group, and it turns out to be, and it's locally cat zero, non-positively curved. Okay, but we actually don't need to understand what kind of spaces these are because we have a description of these spaces in terms of partitions, just as we did for the free group. In fact, if you take one of these minimal guys, these salvedi's, and decide what's around it, it's exactly the same as before. It's every vertex in this link is given by a compatible collection of partitions. Now you have to be fairly careful about what you mean by compatible here, but there's a definition which works. So you got this cube complex, and it's, sorry, this is a simplicial complex, and the vertices are collections of compatible partitions. So as before, the dimension of k-gamma is the number of partitions in a maximal collection. Okay, so where have we got? I said I was supposed to be talking about virtual co-homological dimension. Well, I have a proper action of a group on a contractable space, so the dimension of that space gives me an upper bound on the virtual co-homological dimension. And actually when we wrote this paper, we conjectured that this would be exactly the virtual co-homological dimension. But story's not quite over. It'll be over in five minutes because that's how much longer I have. How do you get a lower bound? Well, an easy way to get a lower bound is find a free abelian subgroup rank R, of some rank, rank R, then R, then the VCD of u of a-gamma is at least R. And of course, it's less than or equal to the dimension of k-gamma, which as we've seen is just the number of partitions in this maximal collection. Okay, so where do we go from here? We have this nice dimensional space. We would like to find a free abelian subgroup of the same dimension as the space because then we would have shown that the VCD was exactly that dimension. So the idea is I'm going to be very sketchy now. You take one of these compatible collections and so given any of these partitions, you've seen that they correspond to automorphisms, these gamma-whitehead automorphisms. So now you think about, well, when do the two of these automorphisms commute? They don't always commute, but sometimes they do and it turns out you can decide exactly when they're going to commute and if there's a partition in your set that you don't like, you can often get rid of it and replace it by another one, which will commute with more things. So this requires lots of sort of cute combinatorics. Yeah, which I shouldn't tell you about. And if you're lucky, you can replace all of the partitions in your biggest collection by ones corresponding to commuting automorphisms. So let me just state the theorems that we can prove. Not yet on the archive. We can find, we can tell you the the biggest possible free-abilian subgroup you can build that's generated by these gamma-whitehead automorphisms. We can tell you precisely, we can calculate it, give me a graph, I can tell you what this dimension is, what the, this rank of this free-abilian subgroup is. And, so the next question is, well, when is this free-abilian subgroup exactly equal to the dimension of your k gamma, and we have a condition? So here's a theorem. Yeah. So we say a vertex is principal if its link isn't in any bigger link. So, and then we look at the, here's the criterion. Supposing I have a vertex that's not principal, so its link is in a bigger link. Here's the link. Suppose it's in some bigger link. So, that guy has a bigger link than that guy. And supposing there's also something else in this bigger link. If it's true that whenever I have this situation, then these two m's are actually in the same component somehow of gamma minus the star of u, then it's always true that the VCD is exactly equal to the rank of this free-abilian subgroup. So, I'm pretty much, right. Okay, so that's nice. This is something that's, here's an example of a graph in which this is true. There are lots of examples. But here's the theorem, too. Sometimes it's not true. Sometimes the dimension of this space is strictly bigger than the rank of this free-abilian subgroup. It's strictly bigger than the rank of this free-abilian group you can build. If, in addition, there's another condition that these non-principle guys, almost everything within distance, two of them, is bigger than them, then, in fact, this K gamma has an equivariate and invariant deformation retract of strictly smaller dimension. And, in fact, you can, in many of these cases, you can retract this space down onto a space of dimension equal to the rank of this subgroup, this free-abilian subgroup you can make. So, this is a condition under which this happens. And there's an example where it happens. The dimension of the space is six and the VCD is only five. So, let me just state some conjectures from everything. So, for out-of-fn, the rank of the biggest-abilian subgroup you can build inside of out-of-fn is exactly the VCD of out-of-fn. And my feeling is that should be true for this untwisted subgroup as well. So, that's the first conjecture, that the VCD is exactly the rank of this abelian subgroup. Right. So, it's conceivable that you could find some other free-abilian subgroup that wasn't generated by gamma-whitehead automorphisms. But I don't think, I think the second one is just a true conjecture, so I won't say anything. Another thing, as I mentioned, for out-of-fn, all the solvable subgroups are virtually abelian. And I can prove, well, Ruth and I have proved for many classes of graphs that this is true for these untwisted automorphism groups as well. Every solvable subgroup of U of A gamma is virtually abelian, but it's not a theorem yet. It's only true in lots of cases. So, those are some conjectures related to this. What is the second conjecture? The rank is just the rank of the largest free-abilian subgroup inside of U of A gamma. So, this guy M of L is the rank of the largest free-abilian subgroup in U of A gamma that's generated by these gamma-whitehead automorphisms. But there could be some weird other free-abilian subgroup somewhere in there. I don't think so, but there could be. So, let me just say, in summary, maybe this is the point. If I want to study this group, in particular the untwisted subgroup, which is the part of this group that I really don't understand, I should replace finite graphs as in the study of free groups, the outer automorphisms of free groups, with finite locally cad-zero cube complexes with the right fundamental group. And that will give me, well, will give you then a contractable space with a proper co-compact U of gamma action. And, right, and most of my talk was about trying to use that to get a better handle on the VCD. That was the rest of my talk. But I should say that there, as I said, there are many properties shared by, I listed at the beginning, some properties that are shared by fn and out of z to the n, right? And it turns out that many of those properties are also shared by all out of A gammas. And there's a list of people that have proved theorems, some people, some of the people who have proved theorems in this way. So here's a question for Alan. When does out of A gamma have property t? So maybe this space, I mean, we've got a geometry now. So it's conceivable that could help understand this question. And that's my last slide. The conjecture about standardly subgroups, it depends for GLNZ, right? Right, I was talking about the untwisted subgroup. So, of course, for GLNZ, it's generated by twist. It is the twisted subgroup of itself. So, yeah, I guess it's not quite true to say that it's a parabolic subgroup in that case. But, yeah, no, I'm just talking about the untwisted subgroup. Can we expect that every solvable subgroup of out A gamma is fanatic generated? Yes, I think that's true. I think it's in a paper by day, matte day. Yeah, so we know a fair amount about solvable subgroups. We know lots of interesting examples. And as I said, in many cases, we know when the solvable subgroups are either solvable subgroups of GLN, a little GLNZ inside of out of A gamma, or they're virtually abelian. So, yeah, we know a lot about solvable subgroups in general, but this question we don't know. And can we expect that the cohomological dimension is always achieved by a need port and subgroup? That's a good question. I would think so. But based just on examples, evidence, evidence of examples, I think that's probably true. But I can't prove it. Maybe you can.