Hello and welcome to the Digital Freethought Radio Hour on WOZO Radio 103.9 LP FM here in Knoxville, Tennessee. We're recording this on Sunday morning, October 9th, 2022. I'm Larry Rhodes, or Daughter 5, and as usual we have our co-host Wombat on the line with us. Hello Wombat. Hello, it's me the Wombats. Nice to meet everybody. Our guest today is John Richards from England. Welcome. Hello. Digital Freethought Radio Hour is a talk radio show about atheism, free thought, rational thought, humanism and the sciences. Inconversely, we'll also talk about religion, religious faiths, gods, holy books and superstition. And if you get the feeling that you're the only non-believer in your town, well I'll bet you're just not. In Knoxville, in the middle of the Bible Belt, we have over a thousand of us in the Atheist Society of Knoxville, or ASK. And we'll tell you more about them after the mid-show break. Wombat, what's our topic today? We're talking about design, and I can't think of a better group with a better design name than Ask for an Atheist group. Isn't that wonderful? That's right. You should ask. Keep asking those questions. I still remember that business card I found, and I was just like, this is just the coolest thing possible. Okay, but Atheist Society of Knoxville, definitely check them out. Where did you find that card? So you had given me that card the first day we had met when I went to the Meetup Group. And I had, whenever I accept cards, I remember I didn't look at the back of it until like I already got home. And I was just like, oh, Atheist Society. Ask! That's fantastic. I love that. Back in the early days of ASK, I printed cards on my own computer and left them everywhere. So the people would find them. And I was just wondering if you'd found one of those somewhere. Yeah, I put it up on our bulletin board at work when I was in Knoxville. Oh, pretty good. So guys, I want to catch up, see how everyone's doing, and then we can delve into the topic of design and what we mean by it. Because it means probably different things to different people. So how about this? We'll open it up. Larry, tell me how you've been over the last couple of weeks. And what do you think design means to you? Well, last week I wasn't available for the show because I was on vacation. And I spent most of the week just playing computer games and just generally taking it easy. But on the weekend when we do the show, I was in West Tennessee visiting my niece. And that was very nice. So it was all good. Cool. And what does design mean to you, my friend? Design. Yeah. Well, when something, someone, an entity, a person generally lays out a plan to build something and then they follow that plan to create the thing that they're going to build. It's pretty straightforward. Pretty straightforward, you would think, right? We'll see. We'll see. John Richards, you're all around the globe and anticipating even more spots of globe trot. But how you've been, don't show off too much. And tell me what design means to you. Well, I've been okay. Thank you very much and doing my usual scheming and, and wheeling and dealing. Love it. And having fun. This is the advantage of being retired. You can, you can, you can do what you want pretty much. So what does design mean to me? Well, it's, it's the first part of making something. You can't make something without having an idea concept of what it's going to be. And that coming up with that concept and creating the detail of it. That's designing. Yeah, it's sort of like setting out the outline or a goal for something, right? Yeah. Making intent. The foundation intent. Yeah. The interesting thing about it is for agents like humans, it can be done from blank. I mean, you can start with a clean sheet of paper, nothing on it at all. And that's where you make your design, which is very different from evolution, of course, because evolution doesn't start from a blank. It, it's the opposite. It starts with something that exists and then tries to modify it. Now, every Christian will tell you every scientist says that evolution says the world came from nothing, but that doesn't make any sense. But what are you saying? Well, evolution, of course, doesn't deal with how the world began. It just deals with how the diversity occurred. We've got a good explanation for diversity, but we don't yet have a good explanation. We've got some hypotheses, but we don't have a, a, an agreed theory for how it all began yet. Right. But the thing about evolution is it's like it would be like in, in sort of design terms, it would be like going into your designer's shop, your studio where he does a design, giving him a tank, you know, as a military vehicle and saying, I want you to turn that into a jumbo jet. That's what evolution does. Right. Yeah. That's not, that's not what creation does. I love the way how you said it at first. It's just, it's the first part of making something, but along with that comes an intent to make a particular thing. It's not just, hey, anything that works is, is fine. It's more of like a varied, you're trying to get to a defined point of creation or, or a product. And it's sort of like in my head where if I gave that sheet of paper and I gave it to like four people and I said design something and there's at the end of the day there's just scribbles all around that piece of paper. There's like screws on one corner because they didn't want to work together. There's like a bird on one side, someone drew a tree on the other side. I'd be like, you didn't design anything. Sure, you try to make something and this paper is different than when I gave it to you, but there's no coalescence of like intent. You know, you have to design something together or make a singular thing as a group, but you didn't do that. There's no intent for what you guys are planning on making. And I find like, what are you, what are those four kids called? That's evolution. It's sense because evolution is very much a I'm throwing everything I possibly can on the wall. I'm going to see I don't even care if it works or if it doesn't work, but if it does work fantastic. That's great. Now we have some biodiversity.  I don't know what I'm doing. I'm just trying to be different at every opportunity. And the mutations that come about through evolution are not designed or planned out ahead of time. They are literally random changes in DNA that cause slight mutations and offspring and some diversity. Larry, what do you think? Well, absolutely. It implies intent, but also don't forget, I'm sure you don't that there are rules involved.  All of the design, I mean, all of the evolutionary changes have to follow those particular rules. Even from the very start, or we couldn't get where we are. Nothing would work if it didn't follow those rules and they are enforced by the laws of nature and laws of physics. The way I think about it is instead of saying as rules because it implies it was a rule maker. There's simply limitations. There's physical limitations. I like that. Yeah. And it's not like I can put marshmallows into DNA like that's not going to work, but like I can work with certain base groups. And the sad thing is the sad thing. And this is an actual thing is while there are chemical limitations, there are there can be cases where the chemical limits are pushed too far. And the thing that is produced through evolution is not capable of sustaining itself through life. Not viable. Right. Not viable. And life is filled with a plethora of these non viable forms that either suffer or are stillborn or never make it to a point where they have a fair chance of survival in a cutthroat universe. And so it's really unfortunate because we do have this appreciation for, you know, the world as if it was created by a grand designer. But unfortunately, I would say like a lot of this doesn't seem like it was intentionally made. It seems like we have a scenario where we're just operating through trial and error physically and chemistry, chemically wise. John Richards, what do you think? Well, I want to say a bit about constraints and the laws of nature because the laws of nature. They're not laws in the sense of this is what you can do and this is what you can't do. They are what we have observed nature doing. Right. And they don't actually restrict nature in any way. There's no sort of barriers to the ends of them. In fact, they're just models that we have noticed happen. And in fact, we've changed them periodically for better models when we discovered that they don't really fit. Right. Yes. And I like to think of it as well as it's not a it's not a lot. It's more of a prescription. The laws of the universe are more prescribed by just observers of the universe at best. And and we come up with not proscribed. Right, right, right. There's always this hunt for intent by the by dogma or religious minded people when they look in the universe. Yes, they need that intent because they needed intent or they needed a creator or designer layer. I think you just posted something you want to talk about that real quick. Yeah. Many times I'll be talking to this and they'll say, when I'm talking about evolution, they say yeah, but that's, that's designed by accident.  And that accident implies thwarted intent.  No, it's, it's, it's designed, like I say, by the laws of physics and the laws of chemistry, working together. The laws of physics, the way they were, there wouldn't be a world to have life on. Right. Didn't have the chemistry, the way it is, you know, you wouldn't have beings on that on the world. But language is a very persnickety thing, particularly English language, no, no offense, John, but like the English language man it's so rough. It's so rough if only we could have something more less, less baggage with every word because when we say the laws of physics are right. A theist can hear that and be like well then who made the laws, right. Yes, yes. We're the ones who described the laws and created the laws, and sometimes the laws need some tweaking we don't always get them correct. With the worldview of there is a creator there is an intent or there is someone who designed all this a law is a very appealing term to describe limitations that we found in the physical world and prescribe to certain rule sets right. By saying a lot you think to yourself well I know how laws are made they're made by a person who has authority that in that pans them down to other people, and that could be my God and what better analogy is therefore creator of the universe is humans decide how humans live, but God decides how reality works. And those are both as that makes sense to me I'm really to go out of here I pass physics right. The English language any language really it's not just English has ambiguity and what I say goes into your head has a different connotation. Very unfortunately, the word law is one of those very ambiguous words because in the legal sense. If I was speaking to a lawyer, he would know what he means by the word law. That would be an edict that has been decided by authorities, and that there are sanctions for disobeying. But that's not what we mean by laws in science not we just observe something so frequently we think it's likely to be true. That is such a salient point because it's just a question of what your background is what your education is, and I can tell you this as an engineer as a scientist and an engineer right, I wear both hats. We design a lot of things in our labs, but design the word has become a very controversial term I've noted, because when I try to talk to people about the work that we do. And then we maybe transition into more of a religious philosophical conversation. I find myself using the same word design in both cases where it's like, well the world's design like blah blah blah oh you just said design. Therefore there must be a designer it's like well I don't know a better word that I can think Lee. Oh I'm totally open to it. I'm totally open to it. Well, the whole point of the show is to figure this out. Okay, for a long time, I assiduously avoided using the word design in connection with life, and any living thing, because I knew that it would go into the ears of creationists, and they will assume that it was their designer what done it. And I even had an argument, well a disagreement with one of our national icons national treasures, and a broadcaster and scientists called Dr Alice Roberts, who up until recently was the president, the honorary president of humanism UK. I met her some time ago, and I said, I watched your television shows. And every time you said this has been designed to do that. In relation to some fossil or something. I threw my slipper at the screen. So she's like, I will eat only two times. Why are you getting so upset. I've only had to. I said, no she's had a whole series. She's a number of a number of series she's a very great. How many slippers do you have, or do you just sit with slippers next to you. There it goes again there goes again. All right. Really. That's design. That's so great. The thing is I said to her that, you know, you annoyed me by saying that word why didn't you say adapted. That's a perfectly good word. They adapted. And she said, listen to this. She said, we've got to reclaim language back from the creationists. I like that idea to honestly. Larry. Oh, one point I always like to make when I hear these. I'm on them. I'm on Facebook a lot. I do a lot of arguing about theism and atheism. And whenever I see someone post a design argument, I always post a meme, because I don't want to type in all the stuff every time. The points out that design doesn't get us any closer to a God than deism. It doesn't point to any particular God that we've ever worshipped in the history of mankind, or some job, some God that we don't know anything about it, even if all of the design claims were true. He gave up and said, yes, okay, it was a God doesn't mean it was your God doesn't mean it was a God. It could have been a simulation designer we could be living in a simulation. It doesn't get you to your God. My favorite God is uncle uncle Lou. To her God. Okay, go on ahead. No, that's what you've mentioned there is my favorite God deaths. Oh, my bad. They don't qualify. Okay. Not judge you at the bottom of the sea I would think since you guys, I like the idea of using adapted. I want to throw out a story of what prompted this show in the first place to when I was just or let's see Friday I was doing a seminar on how we design things in our story. And we, I brought up a really great high modification picture of a fiber that we're producing. It's like a hollow tube that has to be stronger to high pressure. So the walls of the tube have this very porous like material because we designed it to be structurally rigid and and have a very high structural integrity and tensile strength and all that stuff. And when you do a cross section of it, it looks just like a bone. It looks just like that spongy material. And a girl who was watching the show or watching my seven I was like, that looks just like a bone. Right. And I was like, yeah, it kind of does. We, that's not by accident. We were doing when we were making this fiber was we asked ourselves, what was the most structurally stable and resilient kind of form fact that we can develop. And we found like this very poor structure was a great way to handle stress from any sort of direction. So that's right. We didn't stumble in it through a bunch of trial and error steps we looked into nature. And this is where I made the mistake. I said we looked into nature to find what had the best design. Oh, no. I made the fiber and in my head I'm like, Oh, I said the D word. Oh, I just kept going. Thankfully, though, the people that are talking to are both atheists. They're all atheists. My head I'm like, I need a better word for this. I feel like I do. You're absolutely right because not only has nature, open air quotes, designed clothes air quotes, everything to fit a purpose. But also, it's so your spongy bone and your hollow bones, they are the best structures for rigidity. That's why that's why tubes work and you can save all the material that you would have had in the middle if it was a rod, make it lighter by taking that middle out and the outside is still as strong. So nature has come up with that air quotes design, but not only that nature has designed things like that several times. So it's redesigned and then re redesigned and often comes down to the same design because that's the best. Yeah, yeah, Larry. And if you'll notice that if you look at things that artificial intelligence have designed, they tend to follow the same type of thing. It's, it's open and that is a lot of air pockets in it, but it has a lot of structural connections in there that don't seem to they seem willy nilly. They go in every different direction. But when you look at the overall thing it has the outside purpose design is is correct for the function, but the inside is just mostly air but with Chris crossing supporting structure. So you brought up, you guys both brought up really great points. John, as an as an amendment to saying design maybe I could have said, if you look at the nature for what's best adapted for structural stress. Then you'd see like we just basically pinpointed our design towards that. And when we, and we could have used, for example, artificial intelligence, because we do have something called generational development, which is sort of like a program that designs things through iterative process on a computer. And it will typically design things based on trial and error and stimuli that we program into a model, and it'll build the most structurally resilient model it will probably look exactly like the tube that we already have. The problem is is that it's a program that was designed by people, but the method that it uses is almost identical to evolution where there's millions of drafts that just don't make it and only one iterative process that keeps getting improved on. The tube that we designed, we were just like, what's a good fit here.  Yeah, we're going to design it kind of like bones in like three steps. We were there in and we made it in like about a month or so. So I find like what design does is, we had the plan. We, we had the intent to make a very particular thing. We designed that specific thing, we made the process to build that thing and then we made that thing. And that's fantastic, but there was no those very little scrap behind very little money and time wasted. And that is the value of design, when it's actually an operation, because there's just so little waste as a result it's very lean process when you use it properly. I want to revisit the story I was telling about meeting Dr. Alice Roberts and talking about the use of words and how they are perceived. Because although she made the point, which is a good point that we ought to be able to use language to mean what we wanted to mean without it being polluted by these creationists who wanted to mean what they wanted to mean. That is a good point, but we're never going to do it, you know. Hold on, hold on. Is it like 50% growing 51% of non believers now like this is the time to strike why give up now. Well, that's, that's true. But nevertheless, it's still too big a job, changing the meanings of words is a mountain of a job that. So I'm going to stick to using adapted. And I want to give you an example of how difficult a job is.  Yeah, yeah, yeah. Either of like every established group is like why are we changing changing. You make up new words every four hours.  Yeah, yeah. But the point is that we didn't have control of that. It was the population, the culture that made that happen. And me going out there and saying, when I say design I mean adapted is not going to cut much mustard. And to give you an example of that. We had a prime minister called Margaret Thatcher a few years ago, who she introduced a tax that she called the community charge. The idea was instead of charging buildings you charge everybody. And the opposition referred to this as the poll tax because it, it charged everybody who was on the list of poll people you know the people who had a vote. And she kept saying community charge they kept saying poll tax eventually got the country adopted poll tax for as the name through the newspapers and so on. And eventually, she stood up in parliament and referred to her own community charge accidentally as the poll tax. And you should have seen I'm sure it's still a clip that you can find. You should have seen the hilarious reaction in parliament when she said poll tax. So the American version of that would be Obamacare, because when Obama came out with hey we don't have health care as a nation this kind of sucks. And everyone was like we just going to disagree with whatever you say because that's our job is to be the lawyer. And I was like, okay, well I'm just going to try to make a government Medicaid, you know, that's really regulated supported so that you can afford health care can get health care. You wanted to widen. Right, you wanted to widen Medicaid. That's Obamacare. They're like, don't call it after me don't call it after me gave it four years next thing you know it's like it's Obamacare guys is just like, okay we know what that is. This is this is language being weaponized. That's what that is. Yeah, but the context of it can flip by the culture to so like words that mean met like words that meant bad things, or use in a in a prerogative prerogative prerogatory manner can flip to very good things and be embraced. And I imagine like, yes it's not controlled by any one person. But we have a culture right now that is moving towards this non believing position and I think if we were just to clarify what we mean when we say certain things that are ambiguous, but still be firm with who we identify as and and and maybe even use other country words along with that. I feel like that could be a really good way of just continuing the, the trend that we're on right now where more people are, you know, I think we have more critical thinkers now today than we've ever had in the past. I hope I live long enough to see design being dis an entity. Yes, that would be fantastic. No, see the thing is, here's the problem with Christianity they change words to, and I know we're getting closer to the half but it's not only that they change words faster than the the the non believers can go through changing it so like when design came up, there was no Christianity concept of it. And then when science established that like listen, here are the limitations of the universe, blah blah blah they said Well, now what's intelligent design is there's design, and now there's intelligent design, and that's us, even though you disfigurized and tell designed to mean no creator, we've now re implanted a new version of it with intelligence, the hat to come from a higher I got some stuff to say about that. Let's take it after the break though. Yeah, after the break. This is the digital free thought radio hour and w o z o radio 103.9 LP FM here in Knoxville, Tennessee. Stay tuned for the second half we'll be right back after this short break. Welcome back to the second half of the digital free thought radio hour. I'm doubter five and we're on w o z o radio 103.9 LP FM here in Knoxville, Tennessee. Let's talk about the atheist society of Knoxville for just a moment. ASK was founded in 2002. We're in our 20th year and have over 1000 members. We have weekly in person meetings at every Tuesday evening at Knoxville, Old City at Barley's Taproom in Pete's area. Look for us inside at the high top tables in the woods of it. Pretty weather outside on the deck. We also have weekly on Tuesday night, zoom meetings. If you'd like to join us on zoom email us at ask an atheist at Knoxville atheists or or let's chat se at gmail.com. You can find ASK on Facebook meetup.com or go to the website at KnoxvilleAtheist.org, or you can just Google Knoxville atheists it'll take you to us. By the way, if you don't live in Knoxville, you should still go to meet up and do a search for an atheist group in your town. Don't find one star one. Guys, we're going to be talking about listener comments and I'm sure we're going to delve into intelligent design. How about we meld the two together and we'll start with one of the comments from first aid man 87 Thank you so much for posting to our thread with a very thoughtful comment. His comments on intelligent design and his, his comment is intelligent design is just selected by us. If our planet was made of lava and humans drink that for whatever reason, religious folk would say that some that somehow was designed for us. It was so unlikely. It seems to me that whatever unlikely thing results would be called design, when really any result is probabilistically really unlikely to happen, just because we are one of them doesn't mean that one of them was predestined. This seems like an adequate response to any intelligent design argument thoughts. What gets me is that they, they use the watchmaker argument like you're walking along along the beach or in a fork you see a watch you know that's designed. And they say, you know, but by the same thing everything else in the world is designed and the cosmos designed. Well, then why would you notice that a watch is different. I mean if everything in the world designed by man or by God was all designed they would all look the same wouldn't they. Yeah, so what really sucks is, there's so much circular thinking here because like you need to compare you need a frame of reference to make something claim like that and everything's designed, then you don't have a frame of reference of what's not designed. No, but if you talk to Christians sometimes they'll be like well God's not designed was like you haven't seen God. Nope. He never shows up. What God looks like and you're like well he's invisible and you have a relationship with like, well, you're, you're literally just at this point you could have just said pixie magic. Right.  Yes, and every other religion in the world would say no, it's our God. Right. Yeah, and that's how in God we trust made it on the money. Every religion can point to inside our God. And the truth from the real frustrating thing is it's not so much that I'm saying that well your God's not the product of design. I'm just saying, if you don't have way to test that claim. You still don't have a frame of reference with literally everything else other than God is a product of design. You still don't know what something that's not a design looks like. So you can't come out with complete justification with the claim, when you don't have any frame of reference to even make it. That should be one of the red alarms in your head being like, whoa, whoa, whoa, I have a problem here, unless if you want the conclusion to be true. And if that's the case, then yes you do have a select bias. Yeah, what you're saying, what you're saying is what characteristics do they look for in order to establish that something has been designed by their God. Very nice. Yeah, that's a good one too. I like that. All right, another one, because this feeds off of Larry Big Brown House commented, you know, intelligent design is an old argument. Christian say that the universe looks like it was designed, which implies there's a designer. The starting point of the argument is to establish some means of distinguishing design from chaos they'll talk about how we can investigate whether certain archaeological funds or natural formations versus ruins of a civilization or something like that. But then the argument concludes by saying that everything in the entire universe is designed. So the original premise of their own argument is refuted by the conclusion. So when we look around, we have no way of distinguishing design from chaos, because they just concluded that there is no chaos at all anywhere. Has anyone else noticed this other than it's so frustrating. It's very true. I've noticed it, I've noticed it. You need to have a frame of reference you can't be like every can of soda is sprite. By the way, I don't know what's what things that aren't sprite look look like. My clothes drawer is a sock by the way I don't know what anything that's not a sock looks like everything in my utensil drawer is a fork. Anything that's not a fork though I don't know what that looks like though it's just like you you're literally making no sense. It's cancer by the way I don't know what things that aren't cancer look like I wouldn't go to that doctor. Right. So why are you to say that everything's by a project design come on guys come on Christians. It's that easy. Yeah. And of course, intelligent design is a peculiarly American thing that was brought about by the laws, the federal laws that forbid the teaching of creationism as a science lesson. So they had to come up with an alternative way of getting their ideas into science. And that's why they came up with the phrase intelligent design. Right. Got round the law. Right. So we have to remember that, yes, words can change and we can come up with new words too. But so can Christians so can religious people and the problem is, Christianity has a great marketing team. Because they are selling basically a product that costs nothing for them to make, which is essentially false hope. There's no production there's no inventory. They can sell it. They can distribute it over any line of communication immediately and people want, people want the product, because everyone's afraid of dying. And their complaint department is pretty much empty, because after you find out that the product doesn't worry we all you're in no position. Yeah.  And it's almost as disconcerting as being pulled out of the matrix is like, wait a second, I had a good time in the matrix, I could eat I can learn kung fu.  It feels like you've lost something but you've never really had a true thing to begin with it takes a deeper appreciation for the truth to realize that Christianity is false not necessarily getting a perfect argument to realize that you're in that your reasoning is invalid. It takes a deep appreciation for knowing true things and false things. That's what gets you out of it, the critical thinking criteria. Larry, what do you think? Well, I was just gonna make a point you were talking about it's really hard to get out of it because you don't know you're in it and it's really hard to pull somebody out of it. If they they're thoroughly brainwashed. I was gonna make a point that the only time a congress a US congressman was ever killed in the line of duty was trying to get one of his constituents out of Jonesboro. The cult of Jonesboro. Wow. It went down there to get him get the congregate. And Jonestown sent him a Yeah, a contingent and killed him. Yeah, and the saddest thing is is the daughter of that Laman is also now in a cult right now. And think about that in terms of like one of the most you infamous cults in the world that killed the person's father, the the offspring of that person who was like a young adult at the time is now in a cult herself. It's not a fact that bad things happen to you that you get critical thinking, or that you're born with it. It's that it preys upon people who think they don't need it. And so you don't develop it. And truly appreciate it to the point where you're willing to disregard or let go of falsehoods in the search of true things even if you don't have them yet you can at least take the position of I don't know if you can't do that you make yourself very vulnerable to those who want to take advantage of you. And what's really bad is that religions tend to use two things that most people want. They want love and they want truth, and religions, you know, will tell you that they own pretty much both of those terms. Yeah, you know, we are love God is love. Right. And the Gospels are truth. Yes, the capital T No witnesses don't even call their religion jovo witnesses and they just call it the truth. Right. Yeah, that's right. Let them trademark that. Speaking of which, you know, we had a comment from classic got, I'm sorry, let's see I read this. Classic got to me giddy says design also applies to religion. Take Buddhism. You should be happy without owning anything. Be nice and docile or else you'll be reincarnated into a life of suffering. All the basic principles of Buddhism enable the ruling class to take advantage of the common people. Like most religions. And while I consider Buddhist values noble due to some of their inherently humanist principles. If you think about it from this perspective, it's still disgustingly obvious what this religion was designed to achieve. And Larry you make a great point. Yeah, that is part and parcel of every single religion up there. You know suffering this world and have a paradise in the next. And that really helps an oppressive ruling class. Yeah, John Richards I'll let you make a go for it go for it. Well, you, Larry's just reiterated it but you mentioned false hope selling false hope and Larry's given the example of offering paradise after death. Yeah, and this country I may have told this on the show before but in this country. A couple of years ago we had a group of churches in the city of Bath, who clubbed together, printed some leaflets and started standing on street corners handing them out. And the leaflets promised that if you went and worshipped in their churches, you would have all your diseases cured there's all list of diseases from a to Z at the bottom it said, and any other condition. But in this country we have something called the advertising standards authority. They were reported by a couple of skeptics to the advertising standards authority who instructed them to stop giving out these leaflets because they offered false hope criminal Larry go for it. We do have truth and advertising laws here. However, religions have never ever been held to those laws, and generally because 90% or 8% of lawmakers and law enforcers are all part of that religion. The other part was the point I was going to make is that the one thing that theists say that atheists take away from them from people is hope. And there's no reason in this world that you just, you can't hope for a good afterlife if you want to do you don't have to join a religion of a structured practicing religion to have hope in an afterlife you want to hope for an afterlife do it.  We're not taking anything away. We don't have any options. Right. Right. It's guys we don't believe in we don't. I mean, a lot of us don't also believe in souls, but you can believe in soul if you want to design your own heaven. It's a great genre of music. What else. Yeah, nothing to sell. No. Right. John, Larry, you had made the comment that most religions have the idea of being docile and not rebelling against authority and not wanting to have your own positions owned to you and just being nice and only concerned with what you're going to do in the next life. I know of a religion, and we've had guests on the show who practice Satanism. And not like the, not like the, the sense of, well, who cares. I know there's two different versions of Satanism, but I feel like in both cases, the idea of rebelling against dogmatic authority, valuing your possessions valuing who you are making a point to I'm sure that you aren't docile in the face of administrative changes on you. And I'm like, Why isn't the case that the only one religion where you're fighting for your personal rights and freedom is the one that's demonized by Christians left and right. And it feels like, huh, there's, there is something to that. Anyway, we're going to go to one of our last comments today. And this one is based from an anonymous commenter messaged me personally and said, Actually, I'm still an atheist but I want to come up with a justification for intelligent design. The proponents of intelligent design claim that the entire universe is designed for humans. And a common rebuttal is that humans cannot naturally exist anywhere in the universe. I mean, as far as we're aware, except for a small planet on earth, you know, a small part of Earth on land in But perhaps the people who claim ID or intelligent design as a thing, they mean that the universe can be conquered by humans, due to us having the highest intelligence of all known species. Unlike other species, we can access all parts of the universe. I know it's an assumption, maybe some of it. But as we can understand the world and create solutions which other animals cannot do maybe this is what they mean by intelligent design. Wow. That's stretching. What. Well, John, what do you, what do you got to say to that. Well, I think he's casting a very wide net and trying to catch and everything in it. There's no justification for that. And he started out on the right foot by saying that we can only survive in a very tiny part of the universe. So, in that case, surely, the description, unintelligent design should apply to the rest of the universe. After all, it's a failure, isn't it? If it was intended for us. Yeah, all this black space and radiation. Oh my gosh that you kind of overdid it on that side. Yeah.  But according to the holy book, you know, the earth is supposed to end with Jesus coming back and starting a thousand rain, a thousand year reign of Satan rolling the earth for a thousand years, and then it's going to be destroyed. There is no intent to go just to the rest of the universe. And why the heck would he create even create the rest of the universe. In the first place, if we're just going to live for a thousand years and die after, you know, pretty much the Bible comes out. Right. It just makes no sense. I found this. Oh, gone in. When's the next rapture guys. Right, right. There's a website time for it. There's a list of upcoming rapture events. We didn't get after nobody that we know about rapture. So last couple of weeks. Yeah. So my idea is this goes back to the docile nature that's not necessarily enforced, but it coerced, perhaps is the better term or encouraged in the most fair sense by religion. They want to have docile followers. They want to have docile rebuttlers or people who disagree with them, because that light enables them to have more authority and power. And when you make a desperately incorrect claim, targeted towards trying to continue to sell your false hope. You want people to be like, well, maybe they got a point to maybe we can all be right. Maybe they are making a sense if I stand on my head they do kind of have a point. So when someone says ID, it's important for you to speak up because it's in being quiet that you give them more confidence to be loud about it. And what we found, historically, is that the confident loud voices tend to be the ones that people listen to the most. Silence implies consent. And in many ways, science can even be betrayal and in a situation like this and the stakes are too high. The stakes are simply too high when we have, as Larry pointed out, majority of congressmen and senators and politicians all caught in this fold that we put ourselves in where they believe in their own separate dogmas they actually have authority to control other people's lives, and they can work in Congress together, both in the word and as their job title, we have a problem, especially when we elect them into like, Living in the south, it's, it's the worst. It's rough. It's so rough. So I say living's not here can be basically traced directly to the religious right, keeping our rights down our personal rights down in deference to the religion. What they have privileges, they don't have rights, they have privileges. Right, they do. I'm also going to throw this out to don't make an argument up for them. It would be my other argument to like don't try to rationalize a bad argument for someone. Leave that to them. It's their job to do that for them. Don't be like, well, this is a way how it can make sense. Like, no, you still don't make sense until you make sense. I'm not going to do it for you.  It's not up for me to post ad hoc rationalize nonsense as is given to me.   That's just me recognizing that they have accountability for the things that they claim to be true. Let them come up with a method to determine if that's true or not. And in the meanwhile, they are in the, I'm not considering them as a viable option until they come up with some sort of reasonable credit to put me on the list of things that I should be doing. They have the burden of proof. There's no need for us to act as advocates for them. Right, right. And we should be willing to speak out when some and you know atheists have a bad reputation for, for being adversarily argumentative, but truly if someone is making a case that is not true. It is worthwhile to speak up or at least let them know, hey, until you have a better criteria to know if that's true or not. I'm not going to believe that or I disagree with that, based on the fact that you haven't met your standard of evidence for it. And what else are things the same, feel free to have a position up. I don't know if that guy's telling the truth or not. I'm not saying that you're wrong. I'm just saying you haven't made a point yet. So please establish that with some evidence and I'll be happy to describe it. It seems if you're saying an intelligent designer made it, you still have this big gap of proving that an intelligent thing exists. And where's your criteria for that you can't look at trees and be like well that's proof of it because that's just proof that a tree exists. Can't look at a rock or a sponge or a bone and say that's proof of my God, therefore my intelligent God exists like no that's just a bone. That's just proof that a bone exists. And I can tell you how that bone came about with better methodologies through tests and practices designed that was actually or adaptations through life that we can track through a record.  What they're doing. What they're often doing here is saying, I can't understand how that could have come about that tree without there being a God. Well that's commonly known as the fallacy of personal incredulity. Right. Right. Yeah. Yeah, argument from incredulity. Yeah, Larry. We can't be talking about intelligent design without talking, at least mentioning the Dover trial. You may be familiar with the monkey trial. The was it was the name of the scopes trial. Thank you. They took place a little bit south where I live down in. What was it? I can't remember the name of the town. Anyway, it's about 50 miles south of Knoxville. Yeah, in 1925. However, in 2005, there was another evolution trial in America called the Dover trial and Dover Pennsylvania. It was a movie made on it by, excuse me, Nova called intelligent design on trial. I encourage everybody to go out and if they're interested in the subject, go find that and find out how ID did not win that case. So design failed and mostly because they lied. Under oath to try to protect the fact that they claim. Because they put their faith, their faith above law, because they think they have. Now, here's a weird thing.     That's constantly putting making birds with three wings or kids with only half their hearts or like tails. Yeah, or tails and just like, you know, I think I'm going someone with this. Oh, by the way, I got some, I got some other things to do and he's just constantly distracted. I'm like, there might have a better argument down that road than what we appreciate in design. Well, I'm offended. I'm offended. I'm offended now because you've just blasphemed against Uncle Uncle Lou. Oh, no, my bad, my bad. I do have one last thing I'd like to say I'd be remiss if I didn't say it but this is an example I bring out all the time but a lot of people imply that the complexity of the universe is is proof part and parcel of intelligent design. I think we know for a fact that if I had to flash bulb or I had to light bulbs, and one took one step to screw into a hole, and one took 1000 steps to screw into a hole, but made the same light. I think we can argue that the one that's simpler in design is the better design. And that's not just for light bulbs. It's true for bicycles is true for car engines is true for anything that simplicity is the hallmark design. And I'm looking at a room full of guys, and there's six nipples across those. We don't need any of them. Yeah, we have so many extra body parts that we got that we don't need. There's so many extra parts to the universe that exists that are far more complex and they need to be. And as john Richard says, small tiny miniscule part of the universe that we're in, surrounded by all this other stuff. It seems like yo you could have simplified this so much more than it was now to get to more or less the same test or trial that we're under the complexity that's been added to the universe is not an indication of intelligence design, if anything, it's just proof that we are on our on our own capable of coming up with what we have now, through our own understanding, through our own trials and adaptations. And because of that we don't need to give credit to a God we can say hey we're here we're in control. Let's make this better. Let's use real design, make this society and tools that we have available better and stop wasting time and all these old books and dogmas think of what we could do if we all billions and billions of minds, put our minds to improving the lives that we have here on this planet this life this life we make this life better. We can do that. How much, how much more so we're alike than we are different. Right. We keep concentrating on differences. Yeah, we need to make a better world just for us as a human species. We need one less God. That's it. Going back to our earlier conversation about the ambiguity of words, you used the word own a lot in your little speech just now. You wanted to form our own opinions, having critically examined the evidence rather than just take somebody else's downloaded view. The trouble with that is, own has another meaning, because it means that something belongs to you as well. And a lot of people possess their religion, as though it's part of their identity. Yeah, and that they do that because they don't have any evidence for it. They just accepted emotionally.  Yeah, my boss used to say, I was a programmer, and I used to get upset if he if he what just my program if he disrespected it if he said something bad about it. This is all I understand your program is your baby. Right. And, you know, their religion is their baby, identify with it. You have to get to the mindset where it's like the personal ownership is different from the accountability, or you want your, you want to, you want your identity to be separate from the you might be nearby or possession. That's hard thing to do. It really is. Yeah, I've got a, I've got a four word expression for that. Got it. Ideas can't be your baby. Oh, it's five words. All right. I love it. I love it. We'll make that the title of today's show. How about that? Larry, why am I taking this out? I think we're near the end. We find your stuff at right. That's where it's at. And I'm focusing on taking down Islam more from now on because a lot of people have complained. Are you only targeting Christianity? Oh, no. No. I want to take out Buddhism because a lot of when I was in California, a lot of people who are Christians is Christians too cool for me or too bad. I'm now a Buddhist. It's like. They have the exact same. My cat's shaking scratching himself. That's why I'm shaking. Taking the table. Oh, no, it's an earthquake. Larry, why are you getting me out of here? Okay. My content can be found at digital free thought.com. Be sure to click on the blog button when you go there, though, for we have our radio show archives, atheist songs and many articles on the subject of atheism. You can also find my book atheism. What's it all about on Amazon?  The time to worry about it is when we prove that heavens and hell's and souls are real and we haven't until then don't sweat it. Enjoy your life. And we'll see you next Tuesday. Take care. Everybody say bye. Bye. Bye. I think so.


Day three of the school, so we start with Yifan's third lecture, right? About non-invertible symmetries. Fourth? Oh, sorry, please. All right. Good morning. Recording in progress. Well, back to everyone. So today will be the last lecture from me, non-invertible symmetries. So in the previous lectures, we have been focusing on the big picture, the general structure of non-invertible symmetries, and especially we spelled out a lot of this general structure in detail in two-dimensional CFTs. And in this lecture, we'll apply the knowledge we have gained to identifying non-invertible symmetry in the very simple CFT, just to, you know, get our hands dirty. That is in the case of this one of the standard first non-trivial CFT that you probably encounter in any CFT class, the Ising CFT in two-dimension, okay? As I explained, this very simple CFT already gives an interesting instance of a non-invertible symmetry generated by a topological defect line, okay? So let us start with a brief reminder about, well, a brief review of the CFT, okay? So first of all, the CFT has a center charge equal to one-half, okay? So it's one of the simplest CFT, and the operator spectrum equivalently, the hubris based on S1, contain these primaries, okay? We subscript, you know, in the scaling dimensions, identity operator, the spring operator of dimension 1, 16, 1, 16, and the energy operator of dimension one-half, one-half, okay? And together with, because we are talking about two-dimensional CFT, the operator spectrum organizing two-dimensional primaries and descendants, here I'm listing the primaries, and then the rest of the states in the hubris space are generated by the verisoral descendants. This CFT has a famous symmetry, a very simple symmetry, that is the Z2 splint flip symmetry. The symmetry act on the CFT, this symmetry acts on the CFT in a very simple way. All of the operators in this hubris, corresponding states in the hubris space are even under the symmetry except for the sigma operator and its verisoral descendants. The sigma operator and their verisoral, its verisoral descendants are odd under the Z2 symmetry. And in terms of the notation that we have introduced, let's call this symmetry generated by a topological defect line, eta, okay? And in terms of the picture we have been drawing, this means that with eta acts on the operator sigma, okay? By enclosing it, whenever we encounter this kind of graph in your correlation function, we are free to shrink this graph and obtain just the sigma operator by the way it's opposite sign at the same location, okay? As I've told you in the very first lecture, a hallmark of symmetry is that it gives rise to selection rules. In particular, in this case, because sigma operator is odd, this implies immediately any correlation function that involves odd number of sigmas. In particular, the case with three sigmas, in terms of arbitrary locations, better be zero. But this CFT is very simple. It's so simple that you can actually compute all the correlation functions of these operators. I will not explain the technology, but you have to trust me that you can compute all the correlation functions. And after you compute them, you will discover that in fact there's some other kind of hidden selection rule that says any correlation functions that involve an odd number of epsilon operators inserted at arbitrary points is again zero, okay? So if you try to extrapolate between from this picture down to here, you want to say that there may be some hidden selection rule that could be explained by some hidden symmetry, okay? And that is the symmetry that will be identified. It turns out that will be a non-invertebrate symmetry. Just a historical remark. So there is a non-invertebrate symmetry. The kind of the signal there, this non-invertebrate symmetry, goes all the way back to Cranbers-Wanier. There's some already suggestion of such a non-invertebrate symmetry in this simple model. Since the work of Cranbers and Wanier, I believe in the 1930s. So back then people studied a lattice version of the CFT, Icing lattice model. You can think about as the statistical model in two space dimensions, and it's described by a Hamiltonian normalized by the temperature in terms of Nier's neighbor coupling of the sphinx on the square lattice. Imagine you have some square lattice, and on each side you have this sphinx, know by Si, and it can take two values, plus minus one. And this notation means that you introduce this kind of Nier's neighbor coupling for each pair of Nier's neighbors, okay? And K is the dimensionless coupling constant. As I said, I was briefly saying, the same model, there's a very similar model related to this. That's described by one-dimensional transfer sizing model. That's the quantum version of this statistical model. This model is so simple that you can actually study its entire phase diagram as a function of K. And because we have observed the temperature over here, you see that this is equivalent to, to tune K is equivalent to tuning the temperature. So in particular, high temperature will correspond to the small K part of the phase diagram. And low temperature will correspond to large K. And in this limits, it's very simple to solve the model, okay? I will now solve it here. But you find that high temperature, you have some non-degenerative vacuums, okay? And on the other hand, you have a low temperature, you have a doubly degenerative vacuums. They correspond to spontaneous breaking of the Z2 splint flip, okay? As a consequence, you expect there to be a phase transition between these two different phases. This is usually referred to as the disorder phase. This is related to, referred to as order phase because the spontaneously symmetry breaking, okay? There's some phase transition over here, which happens at a special value of K, which is denoted by Kc. That's a critical C, a critical value of K. And over here, the description is given by, there's a second order phase transition. And the phase transition is described by the Ising CFT, which is the CFT we reviewed over here, okay? In particular, the sigma operator, the spin operator, is the CFT version of this individual spins that live on individual lattice sites, okay? What is the statement of the Kramer's Wernher duality? The Kramer's Wernher found, when they studied this Ising model, okay? As a function of K, there's some mysterious duality between the high-temperature and the low-temperature phase of the theory. They find, what is the duality? They find the following equivalence relation, okay? That under the identification between a dual coupling, which I call K-dual, there is relation, okay? Ising, and you already see that if one is small, the other is large. And correspondingly, the duality relates to the low-temperature and high-temperature limit of this phase diagram. And the more detail, it was found out that the precise statement is that Ising at a low-temperature is equivalent, or is dual, to Ising at high-temperature in the infinite volume. But to be precise, you also need to introduce another D2 gauge field. The reason being that if you don't worry about the global issue, sorry, if you care about the global issue in particular, like the number of the ground states, obviously, these two phases will not match, okay? But introducing this additional D2 gauge field, which gauges the Ising's D2 symmetry over here, fixes the problem, so that it's actually an exact duality. And because this duality relates the low-temperature and high-temperature Ising model, and I should also say that in terms of the CFT, this phase diagram can be captured by the CFT, the Ising CFT, couples to a relevant deformation, well, deformed by a relevant deformation, figured by precisely this energy operator, okay? Which essentially dual to the Hamiltonian over here, where m squared is the coupling. And translated into this phase diagram, this point corresponds to m squared equal to zero, so we are at the fixed point, and the high-temperature phase corresponds to m squared bigger than zero, and the low-temperature phase corresponds to m squared smaller than zero in my convention. So you may have different conventions for your definition of the action, and there could be an opposite, these two phases could be flipped, okay? But this is my definition. In any case, this duality can be written more explicitly as a transformation on this couplings from m squared going to minus m squared, okay? Because it goes from low-temperature to high-temperature and the vice versa. And correspondingly, because how it couples to the operator epsilon, your Ising CFT, this is equivalent to sending epsilon to minus epsilon, okay? So this is already some hint that the Kramer's-Wende duality may be related to this hidden symmetry that explains this lecture rule at the fixed point. While the duality relation doesn't end here, there is also the famous duality relation that relates the sigma operator to the mu operator, okay? So we call sigma is the outer operator, okay? It corresponds to this spin-degree freedom on the lattice. When it takes a non-trivial expectation value, that corresponds to the spontaneous symmetry breaking phase of the Ising model, okay? On the other side, this is the desoldered spin operator, okay? This is the operator that takes VEV on the desoldered phase or high-temperature phase of the Ising model, okay? So when I draw this diagram, okay, this is in terms of this other parameter, sigma. All right. Then at the critical point, which in this case coincides with the self-dual point of this relation, meaning that sinh 2Kc is equal to 1, this duality first implies, sorry, this duality implies that the Ising CFT is equivalent to this Z2 over fault. This operation of coupling quantum field theory to Z2 gauge field is essentially implementing the Z2 over fault, okay? And as is common for dualities, duality typically relates two descriptions of the same system, and if there are some parameters you can tune, then typically what happens is at a special point at the parameter where the duality becomes a self-duality, the self-duality can be described by a symmetry. For example, you see this happens a lot on the modular space, conform manifold of two-dimensional CFTs. One typical example is the duality of a compact boson. Two duality maps the compact boson radius R to 2 over R, in certain units. That is not a symmetry in general, but at the self-dual radius, which is described as Z2 level 1, the duality becomes a very special Z2 symmetry in the Z2 level 1 WSW model. So we're expecting something similar here, and you will discover that it's indeed the case, but the difference is that in the case of Z2 level 1, from the compact boson special radius, that symmetry is invertible. Here we'll discover the corresponding symmetry would be non-invertible, which is correlated with this very special feature. So this is a question we want to ask. So there's many ways to pin down what this symmetry is. Okay? So let me give you one argument that uses this very simple picture that we draw many times. That is the modular invariance. For different perspectives, you can, two different perspectives, you can adopt to view the torus pattern function twisted by insertion of some putative topological defect line. So this is again the object we were considering is simply the torus pattern function of this CFT twisted by this topological line. So right now we are not assuming what this topological line is. We're agnostic about the details of a line, but we'll deduce constraints from this very simple equation. And once again, this is the same object, but with the topological line oriented in a different way. Sorry, the other way around. And as we said before, this equality leads to the following relation between a pattern function that's twisted in the time direction by the line defect insertion weighted by the Hamiltonian associated with the CFT generated by L0 and L0 bar. And on the other hand, we have the trace with no other temporal insertion of the hubris space twisted by the insertion of the topological line. And the astral version of the torus modulus enter into this expression. So I'm writing this for general C, but here C is equal to one-half in this specific example. And the fact that the topological line preserves the stress sensor means that the right hand side and the right hand side will have decompositions into the basic building block of 2D CFT, representation theory building block of 2D CFT, namely characters of the erasoral algebra at center chart equal to one-half. That is very constraining because unitary representations of erasoral algebra at center chart equal to one-half only comes in three families. There are one-to-one correspondence with the operators that we are talking about in the Ising model for the chiral representation. So that means the left-hand side let me call it is a linear combination of the character associated with the identity operator, okay? Let me call it alpha one, okay? Alpha zero, sorry. And the coefficient multiplying the character associated with the 116, 16 representation, okay? And the character associated with the h equal to one-half representation, okay? And they correspond to physically the three operators, identity, sigma, and epsilon, as well as their descendants. And these coefficients, which we are being agnostic about, determines how this operator acts on, this putative line operators acts on those operators, okay? The line operator acts on those local operators, okay? There are too many words about operators. Hopefully there's no confusion. And we can do the same thing for the right-hand side, okay? But as we said before, the right-hand side in some sense is more constrained. So even though we are, because we are agnostic about the detail of the line, we don't know much about this defective cube space. But just from the verisoral symmetry, we know whatever this defective cube space is, it must be built from the basic building blocks, which involve these chiral representations with weight zero, one-half, and one-sixteen. Okay? So you have a sum over two numbers. Each of these numbers can take value in a set of three possible representations. Okay? And the summand involves this coefficient, which is a positive integer, a non-negative integer, that comes for the degeneracy of the representation in the given two-state hubris space. And they are multiplied by these characters. And this very simple relation, so we have this equality, this very simple relation weighs the constraint that this coefficient of positive integer is surprisingly strong. Okay? So I'll leave that as a homework to show that there are three independent solutions to this equation. Okay? Meaning that all the other solutions have the same positive integer combination of the solution I'll write down. Okay? The first solution is such that three solutions, the first solution is when they are both equal to one. The second solution is one minus one and one. Okay? And the third solution is for two zero minus square root of two. Okay? So this corresponds to the identity sigma and epsilon means that this is nothing but the trivial line, the identity line. The second one, X non-triviality, triviality on everything except for the sigma operator as well as the sentence, identifies this operation generally by this punitive line as the Z2 flip symmetry, Z2 spin flip symmetry. So this is the object that will give rise to this duality defect. Okay? So this is the only other possibility and as you'll see, this is indeed a consistent solution, a consistent symmetry operation. Okay? In the sense that we will give an alternative description, a deterioration of this result that does not rely on any assumption. Okay? So here it's like we assume the line exists, this is the most general form it can take. The line exists. Okay? Is it okay that some coefficient is negative? So this coefficients appear on the left hand side. Okay? What's important, what's not true about the equation is that these coefficients are always non-negative. So it's your homework to see that having certain coefficients being negative is fine but for example you cannot have this coefficient being negative. The coefficient function is a... That's right. It's twisted in a temporal direction. Okay? So this left hand side keeps track of how symmetry acts on the hyperspace with no twist. Sorry, and what are the corresponding value of the coefficient n? You are keeping it arbitrary. Sorry? Come again? The coefficient n i j are arbitrary. Totally arbitrary. So to solve this equation all you need to know is that this coefficient has this property but you leave it in general and you will find the solutions will be in general a positive integer linear combination. Sorry, non-negative integer combination of these guys. But once you fix the alpha the n is going to be fixed? Yeah, so once you fix alpha the n is obviously fixed but if you are forming alpha you don't need to make assumptions apart from what I have said. Sorry, just one other clarification why in the left hand side you are assuming that this is diagonal? Right, so this is what we know from something we just erased. Right, so we know that the way this to what a defect line acts on the operators will be such that it cannot change its scaling dimension in particular it maps a varisoral multiplet to a varisoral multiplet. In the IC model there is no degeneracy in the hubris space without twist. So for a given varisoral representation there is only one operator so there is no other possibility than having just an overall number. Alright. Okay. And we can learn a bit more from just this very simple table. From this how it acts on the operators in the untwisted hubris space you can already infer the fusion rule. In particular the fusion rule obviously of eta squares identity that's what we expect for z2 symmetry. Moreover when you fuse the duality defect with eta in either way you will recover the duality defect. That is because this entry is 0. Okay. Furthermore if you square the duality defect you get 1 plus eta. So these rules are uniquely determined just by postulating the most general fusion rule with non-negative fusion coefficients and consistency with this table. This defines what's known as the icing fusion rule which is not so surprising. Okay. And as I said before once you have a set of duality defect lines and you have specified the fusion rules there's the consistency condition just coming from locality of the theory says that they should furnish to this whole fusion category structure. Meaning that it should have consistency solutions to that symbols. So there's a consequence of locality essentially the isotope invariance. Okay. In other words the f symbols associated with junctions formed by this topological defect lines would have to satisfy the Pentagon equation. And that has been solved. Okay. So here I'm listing the solutions. This was actually this problem was solved in generality that generalized this particular fusion rule in the case when the Z2 is replaced by a Zn by the work of Tambara and Yamagami Okay. So in general we call it Tambara and Yamagami fusion category associated with the general abelian symmetry. They generalized the case with just eta. Okay. But here I'm listing the full data of the fusion category in the case of this particular icing fusion rule. Okay. So in particular your simple objects are these three topological defect lines that satisfy this fusion rule which I showed before. And there's only one non-trivial junction where none of the three lines involve the identity. So whenever three of the external legs involve the identity that correspond to a trivial junction as we said before that comes from just bringing the identity operator in the bulk to the defect line. This is only non-trivial junction in this game. Okay. And then non-trivial junctions enter into various non-trivial F symbol associated with this fusion category which I've listed here. So the important thing is about this sign. Okay. Which is similar to what appears in the complex symmetry case. Okay. The fusion symbols, the F symbols are faces in general. But the characteristic of this non-invertible symmetry case is that F symbols are in general not just faces. It will involve these matrix elements. Okay. Which are not not faces. Okay. And we'll use there's a question. Sorry. But we know that Tambara Yamagami's fusion categories are not uniquely fixed by diffusion rules. Very good. Very good. So here I jumped over one small subtlety is that if you just use this particular fusion rule for the Z2 case, there are two solutions up to gauge freedom to the F symbols. Here what I'm writing down is the F symbol that will be relevant for the Ising CFT. Okay. And there is some physical meaning to the choice of... Sorry. There is some physical meaning for the choice of one of the two solutions. Ah, it's because the CFT actually realized just one of them. I think CFT realized one of them. The other is realized by the SU2 WZW model at the level 2. And there is a way to see that. That's right. But I'm afraid I don't have time to explain that detail here. Okay. But thanks for the question. Okay. And just from how this solution looked like, okay, and it tells you how the duality defect acts onto the hubris space, we have these diagrams, okay, which we have been drawing before. So acting on identity, which is equivalent to inserting nothing, this gives you square root of 2. We're just copying down the table over there into the diagram we have been drawing. This means that whenever you have this duality defect encircling nothing, you can just shrink it and the cost is to include additional factor of square root of 2. If you have instead the epsilon operator inserted in the interior of this loop generated by the duality defect, you have the cost of introducing extra minus sign. Okay. And similarly, instead if you have the sigma operator inserted inside the loop, you will just have zero. Okay. It's completely annihilated. And this is another signature of this this duality defect line being non-invertible. So it annihilates certain operators. Okay. But there will be in a sense where this operator will be recovered. Okay. But it will recover in a way that will be consistent with this duality relation. And this is what we will see next. Okay. So instead of as we said before a feature of this non-invertible duality defect is that it doesn't just give between the, you know, the hubr space without twist to itself. Okay. It also gives maps between defect hubr space twisted by a given line to defect hubr space twisted by a different line. Okay. In particular, gives maps from defect hubr space without twist to defect hubr space with twist. Okay. And such linear operations are represented by again this kind of diagram. So this is a diagram that we call lasso diagram. Okay. When we discuss the generality, but with potentially with a non-trivial junction so I'll be using the red to represent eta and using the, okay. This is not very red. The red line to represent this eta symmetry defect and the white circle to represent the duality defect. Oh, I should also have said that here the defects that's involved in the icing fusion category they're all self-dual. So I do not need to keep track of the arrow. Okay. Just in case you worry about this. Question. Again about the f-symbols it's not true that you always have the solution with trivial f-symbols. Come again? Is it not true that you always have a solution with trivial f-symbols? No. No, okay. So as I said before f-symbol what f-symbol is doing is giving you the change of basis between different representations of the junctions associated with four external legs. Because of the change of basis it will always have to be invertible so it cannot be trivial. But I... Yeah, I don't mean zero. I mean that essentially you have no anomaly. Yeah, so well, trivial so trivial could be zero, trivial could be one, identity matrix. Yeah, one, let's say one. So that would not be consistent because you have multiple fusion channels. That would be okay for that's the case for non-anonymous group like symmetry. But because you have multiple channels you cannot put one here and here to be consistent. So for some fusion rules you necessarily have anomalies. Come again? What you're saying is that for given the fusion rules there are fusion rules that imply automatically that you have tough anomalies. I'm not sure I get your question. Maybe it's better to ask that again in the discussion. Okay, good. So what I was saying here is just that there's additional actions linear actions of the symbolic defects, the duality defect represented by these white circles acting operators and sending operators not to the hyperspace without twist but to a hyperspace twist. In this particular case twisted specifically by the eta line. So once again because every junction is topological so you can shrink this diagram. So this produced for you an operator that's attached to this eta line. And this is precisely the operator mu that's relevant here. How do we see that? So once again because the theory is simple enough you can actually specify the entire hyperspace. So every state that lives in here is a state in the hyperspace twisted by eta. So similarly to the IC model without twist here the hyperspace is completely fixed. It consists of the operator that corresponds to the remnant of the fermion before you bolonize the size of dimension one half on either side. And just one other operator of dimension one sixteen one sixteen. And for the same reason as before this topological operation of shrinking this diagram encircling this operator does not change its scaling dimension and because there is a single operator of dimension one sixteen one sixteen it has to be proportional to this guy and the coefficient can be fixed by asking this operator to have normalized two point functions. And what you find is that the coefficient with that particular choice of normalization is square root of two. And similarly just to be consistent with such a duality operation another thing that you may wonder if it is this kind of diagram, this again a lasso diagram but encircling instead the mu operator so like this. So for this to be consistent this better give you something similar to this. So it should be zero. Why is this zero? This is why I draw this over here. This minus sign is crucial. So look at this region apply that as move because this operator scalar you can freely rotate this red spoke all the way around and because in the process of moving all the way around it crosses this point once at which you use this operation it give up a minus sign. It will say that would mean that this diagram is equivalent to minus times itself that implies this diagram vanishes. And furthermore a similar exercise what we did over here tell you that if you have this diagram again shrink it so what this diagram means is that it's a map induced by the top of defect line on the hubris space twisted by eta into the hubris space without twist. So because when you shrink it there's no dangling line defect. So this better produce the state in the hubris space without twist and what you find is that indeed you recover this operator the spring operator. So what we see from this diagrams is the following if we just focus on how the duality defect acts restricted to the hubris space without twist it looks invertible it looks non-invertible because the spring operator. But somehow this non-invertibility can be recovered once you realize there are other non-trivial maps that max one defect hubris space to another in particular the hubris space without twist to the hubris space with twist. So there's a sense in this particular non-invertible symmetry that once you include once you take into account how the duality defect acts on all the defect hubris spaces it is really invertible and not losing information. And that is why it makes sense to talk about it as a you know as a remnant of the duality of the duality. So there's another picture that is helpful to represent the way the duality defect acts on local operators is to instead imagine that you have the duality defect over here and some local operator inserted around it. This diagram we draw when we discuss the topological feature of these defect lines. And as we know as we have drawn this many times you can deform the duality defect line as a consequence of topology invariance these diagrams produce the same observable when inserting correlation functions. But because because of this diagram this implies and you apply the fusion rule over here so the fusion rule here is important so let me So you apply the fusion rule for these two corners sorry you apply the f-mool for that two corners using that rule what you find is 1 over the square root of 2 times this diagram plus attached to the eta line and then further attached to the duality line. And then you use what we have already got over here so there's one diagram I didn't draw which is the case when you have this line attached to the epsilon I'll leave that exercise to convince yourself that this is 0 from a similar argument and this implies combining with this fact that this is equivalent to flipping the sign of epsilon so the cost to move across this energy operator to move the duality defect across the epsilon operator to flip the sign you can do a similar analysis and this is okay and this explains this selection rule so we have achieved in explaining the selection rule using this symmetry and the way you do that is to put a duality defect line at one end and move it all the way you pick out all the faces and you get a contradiction if this is down to 0 and that's how you argue the selection rule a similar exercise in view of time let me again leave as homework by doing the same procedure again using the f-symbols we wrote over here what you will find is precisely the expected relation that says that when you move the duality defect across the sigma operator which is charged on the Z2 you will get instead all the operator which lives in the hyperspace twisted by the Z2 line this explains this duality mapping between sigma and i mu and you can do it also inversely move the mu across and you bring the sigma so combining this picture this explains the Kramer's winding duality at a self-dual point with this non-trivial transformation rule that sends this basic operator in Icing CFT which naturally are local operators in the Icing CFT after the dual operator so the mu operator is not a good operator it's not a good local operator before you do the dual operator because it is attached to a non-local line but after you do the dual operator this becomes a local operator and this operation explains in what sense this is the precise symmetry so let's not discuss a kind of explicit example of how non-invertible symmetry works in motion let's now given this example let's not deduce some consequences so the main point here is that this symmetry just like a Z2 symmetry we discussed it in the very simple CFT like Icing CFT but the structure of the symmetry it shows up in a very interesting system and it can be used to deduce non-trivial consequences for example on RG flows so this is what we will discuss now the dynamical consequence for RG flows so what is the general picture for RG flow so you have some we focus on the case when you have some quantum field theory which we will call TUV which is the UV description for some potential RG flow you can trigger some RG flow for example by some relevant deformation or by gauging this will end up with a non-trivial IR face in general if the theory is strongly coupled and there are several possibilities for what the IR face may look like so possibility number one is trivially gapped meaning that there is a unique vacuum that is gapped only massive excitations about the vacuum possibility number two is vacuum degeneracy or in other words a multiple discrete because it is gapped this corresponds to the case for example when you have some discrete symmetry that is spontaneously broken in two dimension context RG is gapless in other words described by a non-trivial CFT so these are the three general possibilities for RG flow so let's focus on the two dimension case from now on and for example consider RG flow trigger by a CFT in two dimension perturbed by a relevant operator that's the meaning of being relevant and also to preserve the Lorentz symmetry okay so symmetry that's preserved by RG flow generally leads to constraints on what the IR face diagram may look like and here we want to consider this non-invertebrate symmetry so we first need to introduce in what sense is non-invertebrate symmetry preserved by RG flow of this form a non-invertebrate symmetry generated by the Vodger defect line called L is conserved and L is transparent to the deformation operator we can move it across the operator without introducing any face factor that's the meaning of transparent just like how stress sensor is always transparent to the Vodger defect this ensures the Vodger defect remains topological under this deformation okay and then there's a very simple theorem once we have defined what it means for a symmetry generated by a non-invertebrate Vodger defect to be preserved on RG there's a very simple theorem we can state the theorem the very simple theorem states the following if a quantum field theory admits a Vodger defect line L such that its quantum dimension is there on the cylinder is not integer positive integer but preserved then IR theory IR phase cannot be trivially gapped okay so the only possibility will be a non-trivial TQFT which is described in multiple vacuums or a gapless CFT and this is a very simple theorem there are refined statements that constrain how precisely the symmetry is spontaneously broken let me just quickly give you the argument for this theorem which is very simple to prove so the proof proceeds by contradiction essentially the same steps that you will go through in solving that homework problem will lead to the proof of this statement and the proof actually only uses something even simpler okay so assume because we are proving my contradiction we assume the theory close to a TQFT or a gapped phase with one vacuum there is only one operator of dimension 0, 0 in this TQFT okay and while it preserves the topology of defect L so we can simply consider this again the corresponding function twisted by the topology of defect in the time direction in temporal direction and which is related by a modular S transformation to the configuration with the topology of defect L inserted in the twisting the spatial direction okay but in this TQFT we can compute the differential function very simply on the left hand side we have a trace of this line weighted by twisted by this insertion because of the TQFT the Hamiltonian trivial you literally just get a trace there is no non-trivial Q dependence and because there is only one state in the super space there is only one state in the D by R this just give you the number and that's nothing but the depth of this line operator but using the right hand side on the right hand side instead you have a trace over the defect that's punctured through by this defect line and there is nothing inserted because there is no more twist and it just corresponds to one and just because you have a super space this has to be a non-negative integer so we arrive at the contradiction to the assumption in the theorem thus we have proved the theorem so if the number of states in the twisted sector is bigger than one would you still call it a trivially gapped phase so it could be that in the twisted sector there are more than one state as long as there is only a trivial vacuum in a single state in the untreated sector I would still call it a trivial gapped phase according to this definition that's the circumstance where the theorem applies but it can be refined does this also apply to higher dimensions then the very same argument applies in higher dimension and indeed that is how the higher dimensional version of this dynamical constraint is taking this form having derived in higher dimension you have more choices for what you call a torus depending on the choice of the space d-1 dimensional slice so now use the other side the other table that I wrote before to apply this dynamical constraint to another less trivial example what is the simplest simplest next non-trivial CFT is the tri-curializing CFT so let me just write over here for example the application of this theorem so here I've written down the operator content of the tri-curializing CFT this is the the next minimum level of 7 over 16 it has 6 primaries and because the theory is so simple you can actually solve the entire you can actually identify all the topology factor line is theory and there are 6 of them the detail is really important there are two distinguished sub-categories this is one called the Fibonacci category it is also called the Lyon category it is generated by a single topology defect line W and it has this very interesting fusion rule it squirts to not quite itself but with an additional identity line also appears and this line is also same as its dual okay and the Ising category appears also in this tri-curializing CFT and this is correlated with the fact that similar to the Ising CFT the tri-curializing CFT also have the Cremers-Wanier type duality its self-stool under Z2 gauging okay but what's important about this particular sub-categories generated by the topology factor line W and N is that this W and N they have the common feature that their VEVs are non-integral in particular the quantum dimension of this duality defect line is square root of 2 on the other hand the quantum dimension associated with this W line because they have to solve the same polynomial equation given by the fusion rule you can find out is a golden ratio okay and so if you have any RG flow that preserve the symmetries and from the general theorem we just discussed then it's guaranteed to land on a non-trivial IRF space so we just have to go through the table to find out which operators if there are preserving these lines okay and as we said preserving means that you have this line over here and you can move it across without introducing any factor okay so this is the equivalent to to that this diagram is equal to the VEV of the topology defect line multiplying this operator so in term of this diagram this will be the equivalent relation so we just have to go through this table and look for operators phi when L is either the W line or the duality line that this equation is satisfied and it's easy to spot that for the duality line the relevant operator so you're looking for h because h is equal to h bar you're looking for operators which are smaller than 1 the relevant operator will be this one so this is the operator that preserve the duality preserve the duality defect and if you look for operator that preserve this W line then the only option is the sigma prime operator that is relevant so what this means is that the tracheonol we have the immediate prediction that the tracheonol ising deformed by sigma prime okay and deformed by epsilon prime okay in this case we preserve the Fibonacci category okay in this case we preserve the ising category okay so they cannot be trivially gapped so if gapped there has to be non-trivial vacuum degeneracy okay and you can actually derive a stronger result which I did not explain that you can actually show the minimal number of degeneracy is 2 and here the minimal degeneracy from a similar argument is equal to 3 okay but there's no other symmetry for this deformation there's no other symmetry if we don't know about this non-inverbal symmetry having some degeneracy typically want to interpret as something being spontaneously broken that leads to this degeneracy just like the d2 degeneracy in the ising case in the low temperature phase by here there's no if you don't have this non-inverbal symmetry there's no other symmetry that's responsible for these degeneracies okay instead these degeneracies are enforced by non-inverdible symmetries in particular this is a prediction and one can go ahead and check if this is actually the case given the tracheo-dual ising model okay this rg flow is integrable and you can check this statement so if it's gapped indeed which corresponds to one particular sign of deformation indeed you have 3d degenerative vacuum this side is not integrable but you can check numerically and you will find out that indeed has a 2d degenerative vacuum it turns out that for this deformation there's another possibility as I said the general theorem would solve the possibility of having a single vacuum a single gapped vacuum there's another possibility of being a non-trivial CFD saturating this symmetry and that is nothing but the ising CFD with the opposite sign of this deformation okay so this is just a very simple application of the general theorem we derived and this is a similar theorem can be applied in higher dimensions to deduce similar statements I think I'm running out of time so let me just summarize these lectures by listing some other aspects which I did not discuss but you are free to ask me afterwards so let me just summarize so in these lectures I've spent a lot on the basics of diagonal symmetries and hopefully through these lectures I'll convince you that they are as good as the usual symmetries in particular they give rise to selection rules and leads to constraints on RG flows IR phase diagram of some UV description what I didn't discuss is that in these lectures I focus on the bosonic theories and to watch with the effects in the bosonic theories there are extensions to the fermionic case just like the extension of bosonic group-like symmetry the fermionic case including the fermion parity and that story can be tied together with what I discussed using the bosonization duality in two-dimension and higher and as I just discussed this non-inverbal symmetry similarly to usual symmetries can undergo symmetry breakdown and it can be used to explain the generacy of the vacuum and something I also didn't discuss is that this non-inverbal symmetry if they are not anomalous they can be gauged so there is a precise way to gauge some sense non-anomalous non-inverbal symmetries and this is the way to produce other CFTs starting from CFTs with non-inverbal symmetries and the list goes on essentially the list contains all the nice things we like about usual symmetries and it's a more general it's kind of a more general richer framework and lastly let me just try to connect to the other lecturers the very nice lecturers by the other lecturers at the school just posing some questions for you to think about the obvious question in relation to Laura's lectures the non-inverbal symmetries in the context of celestial CFTs and the potential applications of these non-inverbal symmetries on constraining the asymmetrics of massless particles and in relation to Matias and Kevin's lectures a puzzle, current puzzle is to understand these non-inverbal symmetries in the context of ABS CFTs and in relation to the notion of all global symmetry in quantum gravity so in particular in the context of this non-inverbal symmetry in the context of the ABS3 tensionless strength which is a very nice explicit pre-glound to discuss the non-inverbal symmetry in the quantum gravity in that case describe some explicit string theory which we will hear more from Matias and similarly in higher dimensions perhaps in the twisted horary the string theory in the bulk is much more complicated perhaps one can make some progress using the twisted horary so that is the end of my lectures but hopefully this will not be the end of your journey in the world of non-inverbal symmetries so sorry for going over time I'll take questions