But I also don't know if it's unjust. That's the definition of unjust. It's completely unfair for someone to choose who lives and who dies. You're saying there's a certain point where murder is justified for you. I'm challenging that because, like, well, you know. I still don't know if it's. Could I kill old people? I still don't know if it's my disease. Yeah. You're firing at me, basically. Well, this is this case. This is similar. You wouldn't do that there for this. Would you still eat meat if they had better conditions? Depends on my level of conditions. Would you still eat, like, free-range pigs just cruising around? They lived to a fairly old age, and, yeah. So it wouldn't bother you the killing of them so much? It also depends how they kill. They felt it was literally within a span of 30 seconds, and it was almost like a guillotine. A happy animal has more of an interest in living, yeah? You would assume. Assume, please? Yeah, they've had better well-being, and they want to continue that well-being because they're in this amazing condition. On the presumption that animal minds are equatable completely to human minds, we are just sophisticated animals, aren't we? We don't have to equate minds, say that they're equal, but we can compare them and say that they are sentient. We don't really compare them. If there was no meat, being the key word, worldwide for meat, then I'd happily give up meat forever. However, and certain poor villages are not permitted access to certain resources, so they have to catch rats and stuff and eat meat. I've heard about that. In order to not just survive, but have any decent chance of nutritional input for themselves and their family, they have to eat meat. I get what you're saying, but that would be a case for people in a survival situation where they have to scrounge for rats and things like that. That wouldn't be a case for you. Oh, no. You said I would only stop eating meat if this cultural issue was solved and this issue was solved, but that's got nothing to do with you. So let me ask you this. Do you still think murder is justified as long as they've had a long enough life? I think it's actually better. I would agree with you.  Why? What's your definition of murder? Murder would be the ending of life of a conscious being. You don't think animals are conscious? What do you mean by conscious first? That's the thing, I don't know. So let's talk about the species of animals that you eat, because they're the ones that are concerned. Pig, I'm concerned with those, but pigs.  It's not sure.  Can I agree with that? I'm going to play devil advocate and say, do they? OK, well, if it was one or the other, you know, you could start making a case for who's going to be the best choice for society to exist. Maybe it's the genius who's going to create this. I get you, but it's not. We're just talking about, like, not in these crazy one or the other situations. We're just talking about just generally in society. I agree. They should have the same basic human rights. Exactly. That's what I'm talking about. Fundamental rights. The fundamental ones. Yeah. Yeah. So why don't we have that same concept for these non-human animals? You're saying there's a certain point where murder is justified for you. I'm challenging that because, like, you know. I still don't know if it's. Could I kill old people? I still don't know if it's murder, though. Kill someone that. It's against their will. They've got an interest in living. I come along and I rob their existence from them. I call that murder. Taking their existence away from them against their preference to live. So right now, you've got a preference to live. I'm trying to agree there with preference to live. I can't get off and ask, but I'm going to agree. Yeah. As an individual, I don't have a pragmatic or logistical justification or excuse not to eat meat. I don't think I have an excuse. Based on my moral principles. I'm basing this on people's subjective morals. Like, because most people, they are against killing a dog for meat. They're against killing, you know, marginal case human beings for meat. But they have this massive inconsistency for these species of animals. I think a lot of people from Afropomorphize their pets and they give them human attributes. Whether they do or not is irrespective. They project a sense of, like, family and human characteristics. So I do think it's easy for people to do that to non-traditionally domesticated animals as well. They do have human attributes, though. Like a brain, a heart, eyes. They have consciousness. They have pain. So I don't even know what that means in a human. Oh, well, they experience reality from a subjective standpoint. So they don't have a brain. You don't have to have a brain. Are you saying a brain, in terms of its anatomical structure, is essential in order to have what you call consciousness? Because firstly, I'm not sure what you mean by consciousness. And secondly, I'd argue you can come across hypothetically as a thought statement. You can come across in any species that does not have a brain anatomically similar to a mammal, but can still have what we class as consciousness. If we found out there was an entity that was sentient conscious experiencing the world, that would, whatever that was, would need rights. Do you have a plant? Experience world, but I wouldn't say they're conscious. No, no, there's no one in there. There's no one home. So there's no subject inside of a tree experiencing they're rooted into the ground and just, they're like a biological computer that is intelligent and alive. But there's no one in there in that tree. No one home, you know what I mean? Like if you were in a coma right now and your body would, if I cut you, your body would heal and you would react to stimuli probably. Let's just say they're brain dead completely and there's no, but their body is still functioning. That's how I would consider a plant. There's no need for them to have rights because there's no one in there that is suffering or has needs or desires. But in a pig, it's very clear there is. So it comes down to suffering? No, no, not just suffering. Suffering, well-being, experience. They're experiencing the world. I mean, you could technically take away all their pain receptors it's to be wrong to rob their sentience from them to essentially take their experience, their only experience they'll ever have away from them. It's, I don't think that's justified.  I don't know if it's justified but I also don't know if it's unjust. Unjust? Well, unjust. That's the definition of unjust. It's completely unfair for someone to choose who lives and who dies. It's the definition of injustice. There's no fairness in that. It's, it's difficult because my personal preference is mostly aligned, well, based on conversation with what I can only presume are your sort of moral principles. Yeah. But morality, it's not so clear cut. Why don't you just put it simply? Like you have eggs and dairy here which we know establish that you eat when we have a bunch of industrialized suffering and things like that. Or they all get slaughtered anyway even if you get them from a smaller farm they all go to the slaughterhouse. So you've got that choice here and then you've got the tofu, the beans and the rice and the, you know, the vegan burgers from wherever that, you know, there's plants on the other end of it. There might be some, some issues with the plant farming but none that aren't magnified through feeding crops to animals anyway. So you've got these two choices.  Pleasure? Yeah. Pleasure with meat? Yeah, we know it. Pleasure with dairy? Pleasure as a... But you're using pain as justice. It's not just pain, I'm saying it's, it's unjust. It's unfair. You're stating it's unjust but you haven't proven it's unjust. You're convinced. But if you're gonna... Convince you. Convince me or someone else that is even less inclined to a very fake nation of animal ethics. You can't just start with the presumption that your conclusion is always justified. Yeah. You're coming at me basically, well this is this case, this is similar, you wouldn't do that there for this. You're coming at it already with a conclusion just fine in your head but if you're gonna convince anyone you need to prove to them with logical premises or should I say foundational claims that they themselves logically don't need just fine and then build up a case. Yeah. So what I usually establish first is if they believe animals matter morally and go off of that and most people do. If they don't then I don't even bother.  Some species they think matter morally and these species they don't care because they've been conditioned. So that's where I would start from. And we started, we kind of started from that with you in a way because you already told me that you're vegetarian for ethics. I didn't stop eating meat because I don't know the taste of meat. It's because it's called to be the object. You really, really? That's why I'm already... Building a bridge is similar. Yeah. Established common ground. Yeah, that's fair to know. I think it comes down to pleasure. Not a justify though you would say. See that I disagree with. It's a where, it's in pain, it's not instant on a microsecond where it can't even register pain. Of course, it's worse. I would say it's worse. Oh it's worse. I would still... The quick killing is still murder. You don't get points with the judge because you didn't torture them.  Yeah, but they're not sentient, I don't, yeah. They're like a little biological. I think it comes down to what I mean by sentience. I am inclined to think most animals, if not all animals, are quite croaked. There's ambiguous animals like mollusks, some mollusks, some mollusks, there's more evidence. Some insects, it's a hard case, that some insects, there's good evidence to suggest they do feel pain in our sentient. They definitely experience. Something is... I don't think pain and sentience need to go hand in hand. There are human beings, no pain in sentience. Of course. Yeah, that's why I don't, it doesn't need to be pain. But in order to feel pain, you have to be a subject, don't you? There has to be someone in there to feel that pain for it to matter. Yeah, so you need to be conscious to feel pain. I think if it was literally instantaneous without premeditation on the animal's part, I think it would be okay. You think it would be morally fine? Because we did establish quick killing of happy animals and I thought we got to this... Just put it this way. So let's just say there's no need for me to kill this random person, right? And I come up with them and they're not going to feel this and they're not even going to know and they've had a happy life up until this point. Let's just say they just got to raise at their job and they've got everything going for them. I come up and go, bang. And you know what it's for though? It's for a cheeseburger. And yeah. So you know, do you see how unjustified and irrational it sounds? To just kill someone for a sandwich, even if there was no suffering and they were happy and free-ranging, it's murder. Do you agree that it's bad to kill animals even if they are not aware? Of course. Yeah, yeah. In the context of eating a food when you have a auto. Yes. I'm trying to agree with you. If it was survival and it's like a line in a wild... I would kill anyone if I was in danger, my family was in danger or survival's a different... Morality doesn't exist in places where they're surviving. Anyway, my point being is that we have enough to share, but it's not shared because a lot of waste, a lot of feed is wasted. Don't forget that all of this cropland, you know like 83% of the farmland on Earth has been used for animal agriculture. Oh yeah, yeah. It's because of the grazing. It has to be the size of Brazil. Yeah, and then they're growing all of these crops and they're feeding to these animals so we can have a little bit of... It's an incredibly unjust way we are distributing our resources as well. And then you've got obviously environmental problems. Problems of like loss of biodiversity, the harm on the life forms in that original habitat. Of course. Animal agriculture itself is one of the most destructive... Well, it is the most destructive in terms of resources, water use and other crazy environmental destruction that happens because of animal agriculture. Also the cruelest thing we do... Well, you certainly made a good point. It's really good talking to you. What's your name? Jordan. Jordan, good to meet you, Jordan. I'm Joey. Nice to meet you, Joey, and yeah. Good thinking. Good philosophizing. Philosophizing. Cheers, mate. It was interesting, wasn't it? He was quite pleasant, wasn't he? I really liked him. He was really honest, too. He enjoyed that, too, didn't he? He was great. I quite enjoyed it, too, actually.


Hello, all.  I am just providing some quick context for our land acknowledgement before we head into our performance by stage seeker. So as I mentioned earlier during our first land acknowledgement kicking off the event, we are going to make sure to acknowledge the people's lands and histories of each of the territories we now know as the Stick New England State. The next state represented by the fabulous ensemble of stage seeker is Connecticut. We are honored to have collaborated with a Connecticut based ensemble heartbeat ensemble for the in person portion of our convening last week. The land acknowledgement with grace from stage third stage seeker is actually going to be their land acknowledgement because both organizations do share the space known as Hartford Connecticut, as well as other Connecticut areas. So I am going to share my screen and I am going to present a prerecorded acknowledgement from God three Simmons, who is the artistic director and a founder of heartbeat ensemble. Let me make sure I can do that now. I'm sorry to interrupt play Lonnie. This is Derek speaking. And I just wanted to mention that we do have live captions available. You can open those by clicking live transcript on the bottom of your zoom screen, or clicking the link that I just posted in the chat. Thank you. I don't know where the sound went, but I have the actual file because you all will give me just one second I will pull that up and play the actual file from my computer instead of delay. I'm having a hard time with the sound specifically it's also not playing right from the file. Fortunately, the ensemble does have their landing knowledge on their website which I will paste into the chat and we'll also read. And I will be happy to post the recording once I have the sound figured out in Hoover for this performance session so that you all can see God free offer it as intended. So this is from the heartbeat ensemble in Hartford, Connecticut. We live, work, learn, and commune on stolen land. This land on which we gather is the occupied, unseeded, seized territory of the Mohegan, Pequot, Eastern Pequot, Golden Hill, Pugsucket. And I'm not actually sure how to say this people's name so I'm going to post it, rather than mispronounce. Skaq to Coke. Thank you, Peter. We also acknowledge the tribes with us in spirit and ancestors, the Podunk, that I'm going to post these names again so that Peter can help me with pronunciation. The Skaq, the Podunk, and the tenexes. We acknowledge the grave harm that colonialism brought to these lands, in particular the erasure of both indigenous and African identities, not only under slavery, but the erasers laws that segregated all people into binary classification of white and black. We honor the spirit and ancestors who have lived and do live now at these intersections of identity and experience. This acknowledgement is the very beginning of a process of learning, our obligations as guests in this territory. We invite you to ask yourselves, as we are these questions, what are the indigenous protocol involved in being a guest. What are our responsibilities. Please do our host tab toward us and are we making space for those responsibilities to be exercised. How will we incorporate what we learn from our host. To what extent are activities and events benefiting our host. I want to ask for a moment for us to contemplate those questions. And thank you all for grace in the face of showing up for the work, even if it's messy and in pieces. Guide me, my each breath, my each movement, to clear this space, unnecessary pain. To cleanse this space for those of us who come here willing, willing to share our stories. Guide me, Great Spirit, as I prepare this space with protection, with certainty and kindness to give them this rare moment in our violent world. To release their grief and admirations that we may all have the heart to bear witness to each other, to see each other in spirit beyond our bodies. I thank you, Great Spirit, for your guidance with this amethyst. I open myself to your divinity and me and may this provide my invited story shares and fellow curanderas to open themselves up to their greatest connections to you. With these dead flowers, I thank all of you, our ancestors, whom have lived and laughed and loved and grew food and medicine, who gave life to generations, the curanderas of our past lives, who lived fully and wholly through hurricane and volcanic eruption, through colonization and attempted genocide, through enslavement and rebellion, through rape and torture, through it all. You came together, great ancestors, surrounding each other with love. In your times of deepest wound together grew infinitely like Jed Babrua. And we thank you, for we knew you had to live and love and dance and fail and triumph and die so that we could live with great reverence to you. We call your names as you appear in our dreams. We call your names in poor water for you, hydration for our souls. And we say, Ibae, bae, intonu, Ibae, bae, intonu, we light this candle in memory of you. Your radiance shines in us vibrantly. May we never forget your light. And with that, as I bring you fresh flowers. Letter to self, I did not solely inherit the intergenerational trauma. My hands were also passed down to me. The same hands that will mend wounds time and time again. Hands that bind up every seen and unseen gash of inferiority. And what matters most is that I don't have to do this alone. The healing part, the crossing onto the other side. What matters most is shame and guilt do not belong to me. Those are two old friends that cannot join me on the rest of this journey. I will have to leave them behind. They just don't fit for where I'm going. I have resistance, my resilience, and the audacity to heal. Have you ever wondered just where our mutual liberation can take us? What will I leave behind? Cut off, burn down to get there. What wounds will turn into wisdom? How will I choose to lighten the load? These are decisions we must all make. Because the thriving of lineage unknown depends on it. I will never meet the man that saved my mother's life by the tree. I find peace that he would be proud of the fruits that blossomed from the seed he unknowingly saved. What will you leave behind? And what will you take with you when it is your time to choose? Keep me whole, keep me strong. Feet shaved, my knees ache. I walk so far through the valleys and peaks of these mountains, through the deepest of sea rifts. I've climbed and swam and ran and wandered, all to return back to you. To return back to me. Where I go, when the highs like 25, too cold to cry outside.  Broken guns and dead roads, they tried to bury me. Earth requires a sacrifice, sacrilege, take it in blood. They expedite and extra eyes sits in my belly. Just let me grow in your light. How extra white, attempting to tame nature. Uniform confuses taser for gun, that gun was really a pager. A paper, a CD, a cigarette, a blunt wrap.   Don't beg a cop, please. You grew from concrete. They tried to pull you from your roots and hang you like strange fruit. While you were reaching for the sky, showering you with hate.  Nature is my journal. It's been a lifetime and a verse somewhere you dispersed you can return to. As flowers bloom beneath you, bequeath blue skies and sunlight. May your ancestors receive you, lead you in life towards safer roots. Furrow soil you on songs of truth. Surrender, like spells to words. I once spelled the bird and witnessed her come to life. After freeing her from a cage, I watched her take flight. Surrender, like suspended belief. Surrender, like a falling autumn leaf. Surrender, like the tides to the moons. Surrender, like the ocean to Oshun. Surrender, like the waters to the winds. Surrender, to this spiritual hymn. Surrender, like fire releasing embers.  And remember, desire for control renders you powerless. Surrender like sand slipping through an hourglass. Taking a moment to ask folks to take a breath and sit with the performance we just got to witness. Inviting our guests from Sage Seeker to turn on their cameras and be present in the space with us. And I am going to turn things over to the folks from Sage Seeker to contextualize this performance and share whatever information they'd like and invite you all in addition to listening to this informational session to think of any questions you may have, reactions you may want to share, et cetera. I will be monitoring the chat and I defer to our guests and the artists if they would like to take questions via hand raise or other function. Awesome. Thank you all so, so much. My name is Jasmine Augusto and I'm the founder and lead curator producer. I go by different types depending on what I want to do for that project of Sage Seeker Productions, which is based in Hartford, Connecticut. And for many years we have been, I'll be inviting two of our collaborators from this project on really shortly but I wanted to just give a brief introduction to contextualize this project and then invite Habin and Machario on and ask a couple of questions. So Sage Seeker Productions has been a company that I started in 2018 but I've had over 15 years of experience curating, producing cultural events, festivals, working with many different folks, elders, teens, really from Hartford, Connecticut but also branching out and collaborating with artists across the state. And in from 2018 to the February of 2020, we did a series called La Salafem that really centered black women, women of color, queer folks of color, their stories and centered around these collaborations between artists who had never worked with before, would never worked with each other before in the state, bringing together live music and dance, poetry and choreography into these intimate duets. And in when the pandemic hit, it was like, holy shit, right? All of us were trying to figure out how to do performance. And Longworth Theater had been in New Haven, Connecticut, had been an awesome collaborator in the past and we've been talking about what was possible with collaboration. They were going to host my first ever New Haven based La Salafem and we tried a virtual one in the May of 2020. And then by the fall, they were like, look, we would love to essentially commission you to do a project of your desire. And it was kind of this open-ended thing. They were like, we have a budget, you know, I think it started with 10,000 and ended up being 15,000 but it was kind of like, what do you want to create with that? And you can have our theater space and our team to support you. And I took a while to marinate on what I thought could be important for this moment where we're in a space of isolation, going through a lot of reflections. And I had come across this book called Remedios by Aurora Levin Morales, who is Jewish Boricua and I'm Boricua myself. And she had talked about this plant, Jerbabruja. And the plant, despite harsh conditions, even like the puncturing of the plant, it literally would just survive and thrive throughout anything. And even in the puncturing, the plant itself would protect itself and grow around that puncture. And so she uses this as a metaphor for the history of Puerto Rican women through time, through generations. And I kind of took that concept and I use that as kind of, as a prompt and as a kind of question, as kind of an invitation to a number of collaborators to kind of get into this. So how could they share their own stories, their own, you know, how did they connect with that in terms of their own stories around the lineage of folks in the African diaspora surviving and thriving throughout time. And my projects have always been experimental, have always been collaborative. So it's kind of like, here's some resources, here's some ideas, and then let's go with it. And so this is kind of, this was a 15 minute excerpt of a larger film that was about 40 minutes. And so I want to invite Haban Maria to come on and Machario Brown. Haban was part of that first. So I did the introductory kind of blessing at the beginning of the film and then Haban and worked with Colleen on a collaborative piece. And Machario actually was the lighting designer and helped capture sound throughout the piece. So I want to invite them on. And I don't know if I can see you guys I don't know why I'm not seeing everybody but we're both on with cameras on and Haban at least is unmuted. Okay, awesome. So I just wanted to start with if you guys could intro do yourselves really quickly. I think the reality is to that we're all we all have day jobs we all like have multiple ways that we survive and live in the world. So just like a brief introduction and then, you know when you first receive the invitation to be part of this project what major you say yes, to be part of this project. Well, hello everyone. My name is Haban. I'm actually a licensed therapist and a vocalist, and at times a painter. One of the reasons that I can say I said yes and which is ironic about this particular project because Jasmine has asked me to do past projects she's invited me a number of times to do other projects. And I always was just like you know I don't know I don't think I'm ready you know I haven't really been doing my art and keeping up in that way and, you know, I think life has a very interesting way of snuffing joy out of us. And I'm constantly reminded that art is there to replenish that. And so for some reason I was kind of just like overwhelmed by this invitation and I immediately said yes, and didn't know what I was going to do exactly but I knew I was at a time where release had to happen. And I took this as an invitation to let this be the release of that. Yeah. So thank you. Thank you. I work with Jasmine. I don't even, I can't even count the time so anytime Jasmine calls I know it's something that I already said yes before I even know it. It's just the entity that you bring to anything that she's a part of it always positive always. My spirit so I've always loved working with Jasmine. Anything she calls me for. It's going to be something good. And as far as being a part of project and what I got out of it. It just showed me a different perspective to people's lives and the people's stories. I'm from the Caribbean and the stories coming out of pretty much any immigrant communities always the same and just to see that perspective and connection. It was really I that's kind of what I took out of the show. Participate and match what is your, like, like your work because I know that you like what, you know what is the gamut of. I mean, I do production work I do sound and like, kind of getting more into live, live music, spear and recording, but I really do everything that anything that has to do with sound lighting and production that that's where my interest. I'll jump on any project, as long as it's around that scope. Thank you so much. So I have one specific question for have been one specific question for mash. And then if we if we have a little bit of time I would love if anyone who's watching with us this afternoon to ask any questions that you have. If we have time. So, so have been. What was it like to work with a collaborator you didn't know prior to this project and you know how did y'all end up creating together and forming a story that focused around sharing your mother's stories. So, our experience I would say was a very special one it was it felt very healing in itself like meeting for kind of like rehearsals and like the planning meetings that happened before the actual performance leading up to that. And both of us coming from African cultures also played an interesting role, even though we're from different countries. The similarities of experiences, the struggles of African women and and where that conversation kind of led us to building up our actual performance. It's always kind of kind of like how much Ariel touched on the similarities right that we can all share, even though it may seem we come from separate worlds. And we really wanted to sort of illuminate that part throughout the performance as well. It's always kind of nerve wracking because I had not been in the performance space for a while. So it was an interesting component where Colleen is like constantly creating constantly performing, and, and there was really a beautiful sort of invitation to, you know, do what you feel, you know, do what feels right there was still this, there was this kind of rigidity to it which I think is what helped the both of us collaborate in the way that we did and have it be more of a positive experience, and a learning experience. And then just a, it wasn't just a space to vent right or just talk about trauma it was, how are we actively healing this in this performance, what does liberation really look like if we could design it ourselves. It just opened up a beautiful collaborative space, and the goal seemed, we seemed united on a goal. And I think that's what made all the difference in feeling more comfortable collaborating with someone I've never met before. So I want to let folks know that, you know, I only got to do a short excerpt of y'all's performance. Oh, right. Yeah. And, you know, what you could see this was kind of like the, the conclusionary piece, which I thought was really beautiful. Like the lessons that kind of came out of this. But the, the, it was probably the most like theatrical of the three duets. And, you know, can, I don't know if you can kind of describe, you know, some of the elements that y'all brought in and why you guys brought those elements in, especially because you have the most. So for those that don't know, it was a giant altar that was that was designed by our homey Mercury and then split into four pieces so there was a large central piece and then each duet kind of had a smaller altar that they were able to use if they so chose. And it was an invitation. And y'all really had the most items. You know, all these different elements that were added and can you talk to us really briefly about some of those pieces that you brought in and why. Yes, so we really wanted to highlight like different fabrics, for example, in, you know, in our cultures different fabrics, they have different symbols associated with them, even tribes or demographics are attached to certain fabrics in your clothing as well. So that was a component that we did use you'll you'll notice Colleen is wearing librarian pieces and I was wearing Ethiopian pieces. So being very specific to our lands in that way as part of our representation was important for us to bring in. You know there was elements of a certain type of dance that Colleen was also doing. She was completely connected to her culture, I believe there's even a harvest connection that was attached to the dance that she was doing. And the element of storytelling so my major piece in the beginning was, I'm basically telling the story of how my mother escaped Ethiopia during the dictatorship.  Not just coffee as like a product right but the, the, the beauty and sacredness around ceremony and how coffee is used to honor people that come into your home. It is one of the highest signs of respect if if a homeowner sets out a coffee ceremony for folks. So that was the setting of our particular scene to pay homage to multiple pieces of our cultures. And the and what we grew up in right so even though we're far from home. I came here when I was very young from Germany. But I definitely grew up in an Ethiopian household that was not a secret to anyone or anyone that will come over you know my home was a very different space and and I appreciate the fact that that was part of my lived experience in being here. And obviously the symbolism behind the way we left the scene, leaving things burning you know there's incense burning there's coffee still being made was to speak to sort of the unexpected kind of turn of events and things that can happen when people are fighting for their liberation or needing to escape and the things that we leave behind as a result. Thank you so much I just feel like all of those details are really important. So thank you so much for sharing all of that. We do have like five minutes left before they close this off so I just wanted to ask you I know this was such a short thing. I wanted to ask you, you know, how did you determine how to light each segment, and how is this different from previous projects because I know you talked about doing lighting and sound in general. But I know, you know, I know because we talk and stuff that you do, you know you throw a lot of parties you throw different kinds of events that are not necessarily theatrical or in a theater type space. I want to talk a little bit about what that was like for you in terms of being able to play with their lighting system why you chose what you chose and how it changed over the course of the production. So, most of our lighting design is kind of collaborative for the most part, when you're having those pre meetings and rehearsals. I drew off of the stories and kind of like that fear that the story said, for instance, having stories traveling through a desert almost so kind of try to recreate that type of. And we just kind of took that idea and kind of worked with what looked good on camera and what looked good on the set and what could basically bring the whole performance together. It was really collaborating with the storytellers and the performances to make sure that what we were what I was doing what everyone else was doing was complimenting their story and compliment. And just really kind of have a keen eye and focus on really what was being said and how the performance is flowing. You know what what you almost almost imagine what it was like to try to recreate that if that mission with their idea that comes to mind. It's really about color. He did mash. Freeze on you guys to. Okay, okay, okay. I know we have two minutes and we're gonna we're closing off now. I don't I don't see any questions in the in the chat but I wasn't sure if there were any comments or questions I do see the comment from the ensemble of color. So they said, beautiful from one African to y'all feel so great to hear folks talking about who I am. Thank you so I really I really appreciate that comment and that comment is really, you know, for Hobbit and Colleen. And I just, I just wanted to kind of reiterate that, you know, a lot of like black and brown Connecticut artists don't have. You know, we don't have a lot of the opportunities to work with major theaters to be able to work with, you know, very kind of like professional settings of things. A lot of my productions have been like, like mash will bring in all the lights bring in all the sound will create something out of the space that isn't particularly a theater. So I just want to shout out long war theater and for theaters that are interested in collaborating with folks in their in their cities and their states that may not, you know, be traditional folks in theater to kind of create these really these experimental pieces to be able to have the freedom to do that. I think was really important for this project to be produced for everybody to get paid. And, you know, the fabric the fabricators at our feeder, we were able to design and they helped to actually create to build the altar. You know, we worked with their head of production and tech folks to like be able to access the lighting system and the sound and all of that. So I think, you know, those are really important when collaborating with folks in your community and thinking about that for those of you who might be in the audience that are presenters as well. So just kind of want to want it to put that out there and thank you all so much for joining us with this and we look forward to connecting in the future. Thank you. We do have a tight time schedule just as we tried to make sure that all of our artists and panelists and presenters have the opportunity to tech tests and such. So we are going to have to shift here to our next panel. I did want to encourage folks to look in Huba at the performance page and at the agenda there are materials from Sage Seeker Productions. We also will have in our networking time one of the spaces is a debriefing space to discuss the performances and panels and of course Sage Seeker is invited to that. So opportunities to connect the goal is connection. Thank you all for your time and we will see you at what is it 1pm for our conversation about community theater theater in community professional theater, etc. Thank you all.


twos that I need and then from that I craft the threes it is expensive and yes I have to that's the thing I have to cultivate it takes time though to cultivate all those nuts that's what I'm saying I have to I have to like build up all the nuts and cultivate them and I have like right now I've cultivated let me show you um I have like nine I have a thousand blast nuts almost a thousand blast nuts just from cultivating and I got like 150 dragon strike I think I was growing those and then I got the the stuff to make the gun powder the blaze nuts I got a thousand of that all from cultivating so that's the main way I do it uh and dung let's let's actually update this what that just do screamer pod now I don't want that let's update this uh this build a little bit I just need demon powder can I craft a lease enough to update this loadout let me see hardshell powder too yeah let's do hardshell powder um where's that that's life powder hardshell powder any demon powder I feel like I always pass it but I think it's further down yeah so I don't have any might seeds they're being grown right now all right ready let's do this I spent most of my first 120 hours only playing gunlands and charge blades so I just kept collecting crafting ammo in case I ever wanted oh man that's cool that's actually really cool like I started on on hbg they love put me in the wrong spot chat I think I already ate though yeah I already ate so I'm good I just need to get some cool drink or whatever but I'm gonna tell you guys are looking for if you're interested in heavy bow gun dude let me tell you it's incredibly fun incredibly fun oh oh that's cool after the fact okay okay I didn't mean to that oh he's on the weird frog yes walk out of it that's right there we go good I hate that you dodge one and the tail comes back around and gets you oh I got boost how did that miss we'll never know chat I hate how sometimes they just don't run when you poop them ah walk right into that I don't want to come out of that swinging thank you this is bad just missed everything because I just started in the middle of its model are they that's cheaper I'm gonna tell mama stop it I gotta stop making stupid mistake oh hello we're gonna poop one of these I will add some more poop somehow I got stunned there nice dragon piercer not what I wanted to do is this a spot we don't want to be in uh this is pc dude yeah pc man am I having fun with this charge blade this is disgusting I don't want him to come out of there where's my uh my mantles I don't want to be in here or at least I got the charge off barely dodged that didn't dodge that one no it doesn't have crossblade dude this is I'm pretty much at this mercy now like I'm focusing I'm focusing so much on offense now mainly just doing these combos you know is he getting up no he's not okay sometimes you derp when you hurt would you sir let me tell you about that look what just happened right there chat you're gonna enjoy this okay so in order to to have a good symbiote relationship between the melee controls and the range controls on pc okay on the range controls you can set up right click to do aiming right um but when you go to when you go to um crap I didn't bring the things I'll hide any more traps I can go get some yeah let's just beat it up um so when I go to melee now I don't right click anymore to shoot stuff for the uh for the slingers I have to press C the thing is when you press C it locks in I can hold down V too I should hold down V when you lock in C nothing else works so you just sit there clicking buttons and then it's just like uh you know that'll actually do some damage feels good man feels good man okay why would you quit that so I have to remember to take the C off otherwise it's sad days you know that's just one dude dude that's just one of them all right where is he I lost the I lost the giant body there it is well I'm gonna go back I'm gonna go back and get the I actually bought some trap kits but I didn't put them in my inventory actually let's reset everything first and then we'll do okay the traps are in there all right um but the dunk pods which I don't think I need whatever we don't need us yeah it depends it depends um where it stops okay so I got traps and trap kits right just trap kits black morale welcome dude how you doing wait is this gonna take me back to the other one hold on let me let me mark these flies got a minor oh man they'll take me back to the trap one I'm spoiled as a streamer I get a lot of people that know what they're doing to come and join me so I don't have to I don't have the experiences you guys have having equipped you guys probably go through a lot more crap than I do all right here we go let's get our charge back oh it's already up hold on oh good timing yeah I just got the fart I got the full yep just all up in this just went all up in the nose and everywhere yep I got the full whap yep oh I'm gonna be out there for a little bit thanks palico all right so let's do this I always walk into that chin thing I'm trying to roll but I keep sidestepping this is a weird thing with this probably the same idea though oh it's so satisfying it comes right out with this oh good this is so good oh I love it when the plane comes together there's a tail over here and I got a gem from it wow what a delicious tail this one is look at this guy okay dude I'm loving I'm loving this freaking this is ridiculous I didn't know I like it this much it just just like resonates on every everything that's the most we've gotten that's the most I've gotten that's eight armor shards from that geez my goodness Anna and palico is when nuts do that's a good amount of HR there oh zeno's up all right I need some help chat I need I need zeno's tail who wants to help I need a zeno tail for my honey horn I think it's my honey horn it's on my wishlist so whatever it is it'll uh I don't know if I know I don't need those you can run zeno thank you yeah that's so makes your point session in chat uh if you want to join the session this is gonna be interesting I'm gonna I'm gonna fight him with this I've only fought I fought him with bow I fought him with hunting horn and I fought him with hammer so I'm just gonna beat up on his toes um and I'm gonna make sure I got all my powders and stuff let me see I think this this this hammer loadout is missing stuff yeah I need to put I need to put a life powder back on here I got the trap kits well we don't need it with him hard shell powders life powder and demon powder which I don't have yet adamant seas mega armor skin bringing that as well as the do I have normal armor skin let's see I used to have it in my loadout but I think I need to craft it armor potion armor skin yeah I need catalyst so I'm short on bitter books all the armor upgrade your charms please and then buy another set of charms the inventory charms that is wait you can do that buy you can upgrade the inventory charms how how do you upgrade these these right here power charm and armor charm how do you plus b-52 talon you have to do that at the uh at the armor at there at the and crafting menu oh drop them in your stash first then use the crafting menu what are they called very last on the list I don't have I have these here they are I'm just redoing my hammer loadout now


This is something that we have on any system upon which rotation operators act. The general logic is that if you have rotation operators that act on your quantum mechanical system, by restricting to infinitesimal rotations, you can extract their infinitesimal generators, which are the vector of permission operators, J. And then from there by diagonalizing the finding the simultaneous eigenstates of J squared and J z, we get the standard angular momentum basis, which we denote by gamma J m. The gamma here is an extra index which is needed in case J squared and J z by themselves don't form a complete set and therefore it would be necessary to introduce an extra index to resolve the generalities. Gamma in fact can often times be an extra, the eigenvalues of an extra set of observables, which are unique to add to J squared and J z in order to get a complete set of commuting observables. In any case, once we've got these standard angular momentum basis, I mentioned by the way that it's more of a normal basis like this, once we have this then it's easy to see what the action of the angular momentum operators is on this basis. J squared and J z are particularly simple because by construction the basis is an eigenmesus of the amount of those operators, so J squared just brings out its eigenvalue, which is J j plus one, and J z brings out its eigenvalue which is m. By the way here today I would set h bar equal to one, this is just a safe writing really for simplicity. Likewise, if you apply J plus and minus, what you get is the famous square root, which I assume you had to memorize in other graduate schools, so I've been seeing it before, multiply times the basis vector in which the m-value has been raised to lower, these are the raising and lowering operators. And then finally one thing to notice is that the J x and J y, the remaining two components of the angular momentum are linear combinations of J plus and minus, so if you know those matrix elements or if you know the action of J plus and minus, then that's easy to obtain the action of J x and J y, and therefore you get all three components of J acting on this standard angular momentum basis. Alright, so that's the basic setup of this. Maybe a further remark about this is just to remind you that the magnetic quantum number, even being the quantum number of the operator J z, is something that depends on the orientation of the system. So if you change the orientation by applying a rotation operator, for example, you're going to expect that the different m-values will get mixed up amongst themselves, you get linear combinations of different m-values. We'll see in a moment that's exactly what happens. Whereas J is the eigenvalue of an operator J squared, which is rotationally invariant, and so that actually doesn't change in the rotation. So this is a point I'll reiterate later on in a few moments. Anyway, this is the structure of these actions of these angular momentum operators on the standard angular momentum basis. One of the things you can notice right away from these formulas is that these angular momentum operators don't change the values of gamma and J, gamma and J on one side. It's the same as that on the other side. In fact, some of them don't even change the value of m, as you can see here, the m is the same on both sides, but the raising and lowering operators certainly do change the value of m. So we can say in general that angular momentum operators leave the gamma and J indices alone, but they change the m-values. Again, this is related to the fact that they change the orientation, but not the values of any rotational invariance. All right, another way of looking at this is to construct the actual matrix elements of the angular momentum operators in the standard angular momentum basis. I mean, the significance of the angular momentum basis is that first of all, it exists for virtually any physical system because you can apply rotations to anything, no matter what it is. And so you can construct the standard angular momentum basis, and it's particularly convenient for studying properties of rotations and other issues. All right, in other words, it exists for essentially any physical system as basis. If making more or less useful is particularly useful in metallic molecular and nuclear physics where we have typically isolated systems where the energy is not as independent of the orientation, not always, of course. It depends on whether the system is interacting with external fields. But even if it is, this is still a useful basis to consider. All right, so to go back to what I was saying a moment ago, let's now look at the matrix elements of these angular momentum operators. To do this, allow you to take a bra, which I'll call gamma prime, j prime, and m prime, like this, and sandwich this on the left of these operators to create matrix elements. And if we do, let me put it on the list of the subreddit classes and the last time, so we could do work on them before. If we do, we get this. For example, for j squared, gamma prime, j prime, m prime, and then sandwiched on a j squared, gamma, j and m on the right-hand side, an arbitrary matrix element of j squared with respect to the standard angular momentum basis. This is, first of all, a chronicle of delta, gamma, gamma prime, a chronicle of delta, j, j prime, gamma, gamma, this is a gamma prime, gamma, a chronicle of delta, j prime, j, because the prime is on the left here and the n prime is on the right. And then what's left over is j times j plus 1 times the chronicle of delta, and the magnetic quantum numbers. Likewise, if I do this for a gamma prime, j prime on the left, m prime, and then jz in the middle, and then gamma, j, m on the right, this is the same, delta, gamma, prime, gamma, delta, j prime, j, and then we get n times delta, n prime. These are diagonal. These are diagonal in the n quantum number because they're, because they're eigen, they're, they're, they're the, they're letting the operators act on their own eigen, eigen states. If we finally take the case of the raising and lowering operators and sandwich these two states on the both sides, like this, gamma, j, m, we can write it this way as delta, gamma, prime, gamma, delta, j prime, j, times the famous square root, j minus plus m, and j plus or minus m plus 1.  If we take the raising and lowering, these are the main matrix elements that occur here. And as you see, there's a common factor of delta, gamma, prime, gamma, j prime, j in all of these cases. This is again the way of saying that these operators don't change the values of either gamma or j. The matrix elements are zero if the m and j are not equal on the two sides. All right. Now, the, this gives a general structure of the matrix elements of rotation of, of negative momentum rotation operators in, of any generality. To be general about this, let me make this following notation. Let's let x be equal to any function of the angular momentum operators, which is j vector here, like this. And just to give you a whole list of examples, this would include the components of angular momentum, which is j x, j y, and j z. I called them j 1, 2, and 3 in last lecture, but it's the same as j x, j y, and j z. Also the raising and lowering operators, j plus and minus, also j squared, because we are an operator. But in addition, let's not also forget the rotation operators, which are e to the minus i theta times n hat dotted into j, which is another important operator that's a function of j. Those are the rotation operators. Did I say this earlier? I can't remember. I'm going to set h bar equals to 1 here in lecture today. This is the same writing. It's easy to restore the h bars. Anyway, let's let x have, have be any one of these, any function of j, and these are the main examples here. And then if we look at the matrix elements of x in the standard angular momentum basis, so I'll put gamma prime, j prime, m prime on one side, and gamma, j, m on the other. The general structure of it is this, is that it's diagonal and gamma, delta, gamma prime, gamma, diagonal and j, j prime, j, delta. Then what's left over is that it's multiplied by times the function of j and m and m prime. And so it's this final function that contains the essence of the matrix elements of the operator in question. Now as far as this final function is concerned, allow me to write this in the following way. I'll write it as j prime m prime, excuse me, I'll write it as this way, j m prime on the left, and x in the middle, and then j m on the right. So the two j values are the same. Here the n prime are a lot to be different, and there's no gamma pairing at all. This is just notation if you like for this function, but of course I've written down the difference in matrix element and the question is, can we interpret this quantity here as a matrix element? There's a couple of different points of view on this and I'll try to explain them. In the first place, just to write j m does not specify a vector of the standard A to M basis because I wrote the gamma here. The reason for doing that is that in the first place the right hand side is diagonally gamma, but moreover the answer that comes out here doesn't depend on the value of gamma. So if you like I could just say j m here is the abbreviation for gamma j m in which I drop the gamma because the answer doesn't depend on it anyway. That's one point of view on this. Another thing to say is that since the answer is diagonal in j, I might as well make the two j values and the two sides equal as I've done here and the more of a possibility of them being different. So this is what I mean. This contains the n prime of the matrix element that remains. These matrices that you see are even sometimes diagonal in n, but not always. So sometimes we're going to say that in general angular momentum operators are not diagonal in n and this is certainly true for the rotation operators as we'll see in a moment. All right. Now, there's another point of view on this as well. This has to do with the concept of invariant subspaces. Let me remind you that if you have an operator that's acting like you're over in space, then a subspace is invariant if the operator takes any vector in that space and maps it into another vector in the same space. Well, since these angular momentum operators don't change the value of gamma and j, it means that the subspace in which gamma and j is fixed is an invariant subspace. Let's look at that subspace. Let me call this e sub gamma and j. This is the subspace of our entire Hilbert space. So this is the subspace to write it out in words with fixed values of gamma and j in our original Hilbert space. Now, it's easy to write down the basis in this space. The basis in this space is just the collection of vectors in the standard angular momentum basis, gamma and jm, in which gamma and j are fixed and m is allowed to take on any value you want. The values that you can find possible are invariant ranging from minus j to plus j. Like this, if I put a brackets around this to indicate the set of vectors, that's the basis vector of the standard space. And you can see how many basis vectors there are with 2j plus 1 of them. And so the dimensionality of e gamma j is equal to 2j plus 1. Is that dependent to gamma? All right. So another point of view on this final notation here is that these are the matrix elements of the operator x inside one of these invariant sub-spaces e gamma j in which we just suppressed the gamma index. By the way, there's another point of view on this as well. Let's just say that these matrix elements here and here could be the matrix elements of the angular momentum operator on any of these e gamma j's for any system whatsoever, not necessarily one you started with. It could be, for example, a spin system where you don't even need the index cannon. And the reason for that is is that these things depend only, the matrix elements depend only in angular momentum commutation relations and not otherwise on the physics of the system. And the reason for that is is that ultimately this all traces back to the rotation operators which describe the geometry of the Euclidean space. And that's why it's independent of this particular physics of the physical interpretation of the angular momentum. And any other kind of angular momentum one. These are, in fact, universal matrices that apply for all problems involving angular momentum. Now, as I mentioned, this space e gamma j is invariant under the action of any rotation operator or any function of j which includes the rotation operators but also leaves as well. This is an invariant subspace. And these invariant subspaces are particularly important in angular momentum theory. Roughly speaking, the reason for this is that if you take your system and you rotate it, you're changing its orientation but you're not changing the value of any of the observables inside their rotational invariant. For example, in an invariated system the energy is independent of the orientation so you don't change the energy eigenvalue if you rotate it. What you will do is you'll mix up that's a say you'll take some linear combination of these basic vectors in this in this subspace and transform them into linear combinations of themselves to create a new vector inside the same subspace. So that's why this is an invariant subspace. The subspace is something else. It's also what's called irreducible. And so a longer name for it is an invariant irreducible subspace. Do you have questions somewhere? This is a name for it. If you ever study rotations and group theory in more detail you'll certainly hear a lot about this terminology, irreducible subspaces. For our purposes, I'll just use it as language to describe these spaces. I'll call them for sure irreducible subspaces. And when you hear that word what you should think of is a subspace that is created by taking some stretch state operators to create all 2j plus 1 spaces that can be created out of it. These are also subspaces that contain the vectors that are obtained by taking some given vector and rotating them in the same plane. You see the original hope space indeed composes into a actually direct sum of these irreducible subspaces for different values of gamut j and they're orthogonal to one another. That's the effective rotations. Now the so the result is is that if you want to make a abbreviated presentation of the matrices, the matrix elements of these operators it's best to do it just in this form and more fully you can put it in one of the deltas and then you get the full form of the matrix elements for accessing any of these operators. Allow me to actually present some of these matrices and represent these operators for different examples. The simplest case is a case where j is equal to 0. If we do this then the basis vectors which I'll just write as jm is suppressed in the aminel there's only one possible value for either j or m is namely 0 and 0. j is equal to 0 and n has only one value. And the dimension of the space is equal to 2j plus 1 which is equal to 1 in one dimensional space. In this case for example if I take jc and let it act on 0,0 which just brings out 0 so the answer is 0. If I let j plus or minus act on 0 of course that raises or lowers the m value but the only m value possible is 0 so it annihilates both of them and you get 0 again and this implies that jx and jy acting on these when this takes 0,0 is also equal to 0. All three components of angular momentum act on act on the vector 0,0 just giving 0 as an answer. So if we want a sandwich on the other side of the bra which in this case has to be 0,0 there's only one of them on any of these. What we get is 1 by 1 matrices and what we have to say then is that jx,jy and jz are just given by the 1 by 1 matrix containing 0 it's pretty simple for a spin or a system that has a total angular momentum of 0 angular momentum of matrices and so on to call 0s. Now let's take the case j equals 1 half and I don't have both here in this little box this is the next value of j up in this case the vector's jm there's two of them there's a 1 half, 1 half and there's a 1 half minus 1 half and jz is diagonal in the magnetic quantum number and it just brings out the m value so right away you can write it so well let's see first of all the dimension of the space is equal to 2 as you can see the dimension is 2j plus 1 so if j is a half the dimension is 2 so we're dealing with a case we've dealt with before it's been a half systems and so the matrices that represent the operators are going to be 2 by 2 matrices but the case of jz is particularly simple because you just get the magnetic quantum number of m and the diagonal which is either 1 half or minus 1 half times 0 that's the matrix for jz as far as the matrix for j plus is concerned well here's what we do to find that let's take the the stretch state which is 1 half 1 half if we apply j plus to that you get 0 because you can't stretch it anymore and if you take the anti-stretch state 1 half minus 1 half apply j plus to that and work out the famous square root in that case you'll find that it's 1 so this converts into it raises it the m value up to the stretch state of 1 half 1 half the result of the matrix j plus that's the square root is zero zero 1 zero if you see not symmetric it's not a matrix but it turns into that anyway once we've got j plus then j minus is easy because it's just the transpose I mean it's really the revision conjugate since j plus is real then j minus is just the transpose of it but then from that it's easy to get jx which is 1 half of j plus plus j minus so that's 1 half of 0 1 1 0 and j y is equal to 1 half 1 over 2 i excuse me minus j minus 0 1 minus 1 like this and the effect of this is that is that the j vector is the matrix form is 1 half sigma this is the same identification between negative momentum and poly matrices that we made earlier in talking about spin when it has systems so those are examples for about j equals 0 and j equals 1 half of the matrices for negative momentum operators if you go into the case of j which is 1 then there's 3 there are 3 states so the states jm now there's there's a stretch state which is 1 1 there's a middle state 1 0 there's an anti-stretch state 1 minus 1 like this the dimension of the space which is 2 j plus 1 in this case is equal to 3 so the matrices are 3 by 3 matrices you see each time you increase the angular momentum by half unit the matrices goes 1 dimensional, 2 dimensional now 3 dimensional jz as always is easy because it's just the magnetic quantum numbers on the diagonal and this makes 1 0 minus 1 and otherwise it's 0 is everywhere else if you work on j plus what you find is that is that if you lower the anti-stretch state you get square root of 2 times the middle state so this is this column if you lower the middle state it's square root of 2 times the stretch state so the center column is this and then the first column is 0 because if you try to raise the stretch state you can't stretch it anymore so you just get 0 so this is j plus or spin 1 or angular momentum 1 system j minus is going to transpose of that to that you can get jx and jy by taking linear combinations so this is that an example of the matrices representing angular momentum of various values of j now what about the rotation operators up here those are functions of j2 so we're particularly interested in the matrix elements jm of a rotation operator which I'll write let's say at this angle 4 and I guess I'll put the prime right hand side now either way of course let's consider this matrix element because this is a a function of j I made the 2j values the same on both sides because if they weren't the same the answer would be 0 but I love the m and m prime to be different so this is going to be a function of j m and m prime obviously and it will also be a function of the axis and angle of rotation it's really a matrix and there's a standard notation which is given for this matrix which I'll show you now it's given by the symbol capital D with a j superscript and an m prime subscript and then we label the rotation by axis and angle like this the difference between d and u is that u is the operator and v is the matrix and v is the standard angle of minimum basis in some cases I'm sloppy and I don't distinguish those two but here I'm making a distinction between the matrix and the operator the operator is the matrix and the operator is the same axis and angle this is just a definition of what they call the D matrices sometimes called the bigger rotation matrices in the literature D here by the way comes from the german Dreyon which means rotation and it's now a standard standard notation for rotation matrices if the rotation is about the z axis the D matrix is particularly simple because in this case if I've got so let me turn it around and let's write this as dj m prime of n hat comma theta let's make it z hat let's consider a D matrix for a rotation by the z axis by definition this is just jm and jm prime sandwiched around the rotation operator in the z direction so that's the same thing as my angle theta but that's the same thing as e to the minus i theta times jz and the reason this is simple is because jz is diagonal the standard angle of minimum basis jz acting on this kind of the right hand side is just going to bring up even prime but even what's left over is a chronicle delta and even prime so the answer is that this is even the minus i theta m times chronicle delta and even prime there you are that's an example of the D matrix for rotations about the z axis particularly simple this comes about of course because we chose to diagonalize jz in creating the standard angle of minimum basis so for example in the case of a a case of a spin one half particle this would turn into e to the minus i theta over 2 on the upper diagonal e to the plus i theta over 2 on the lower diagonal 0, 0 is on the two sides so this is for the cases of j equals one half for example a spin one half particle this is the D matrix in that case I hope you recall that when we were talking about spin one half rotations we encountered the fact that if you rotate an electron by 360 degrees it doesn't return to itself but a phase change of minus one and that's because when theta is equal to 2 pi each of these factors in the diagonal becomes minus one well this is just the case of a rotation of z axis but it's actually true for rotating by any axis you get minus one if the angle is 2 pi so one thing you can see now is that the same thing actually applies for any half integer value of angular momentum because here's the general components of the D matrix the rotation of the z axis and it has the m up here if j is a half integer such as one half, three halves, five halves, etc then the m values and the magnetic quantum numbers are half integers also they go for example from minus five halves up to plus five halves and so if you put theta equals 2 pi in here each of these diagonal matrix elements is going to become minus one so the result is is that the D matrix for a half integer angular momentum with an angle of 2 pi is equal to minus one it's the same minus one phase factor that the solve in spin one half particles on the other hand if the angular momentum is an integer 0, 1, 2, 3, 4 then the m that occurs here is an integer and so you just get e to the i integer theta on the diagonals and if you set theta equals 2 pi then all these diagonal elements become plus one so for systems with integer angular momentum if you rotate by 2 pi it returns a system to its original state in other words you get what they call a faithful representation of the classical rotations that's the same pulse the same rule as classical rotations it's only for half an integer spin that you get these double-valued or half an integer angular momentum in general that you get these double-valued angular double-valued representations of rotations alright anyway this is just the definition of the D matrices and I've only worked it out in a simple case in which the axis is is the z hat there's another just a slight variation in this notation when one is interested in the Euler angular representation of the matrices rather than the axis angle representation so let's take our basis states Jn and Jm prime let's sandwich them around a rotation-operated written in Euler angle form and alternate again well this is a definition we'll call this again D matrix with Jn and Jm prime indicating the J value of the matrix of the matrices of the matrix of the magnet prime of the alpha, beta, and gamma instead of the n hat and theta this is a very slight modification of the notation it turns out that there's some simplification that can be made in the case of of D matrices in the Euler angle form and that's because I'll remind you that this U alpha, beta, gamma is the product of a rotation about the z-axis by angle alpha times the rotation about the y-axis by angle beta times the rotation of the gamma this is the z-y-z convention for Euler angles which we discussed earlier and so this rotation operator here factors into a product of three rotation operators and we can insert resolutions of the angle between the pairs of rotation operators and if we do again an expression like this let's call the N1 and N2 the indices of the resolution of the identity so we get an element J him and we get Uz of alpha and then J him 1 we want to make it solid excuse me and then you just hear z and 2 of it are you at z-y-z? no it should be z-y-z z-y-z take a look at the notes on the Euler angles and you'll see why it is, it's a z-y-z convention I think I mentioned that in classical mechanics books they usually use z-x-z but Fignan is responsible for N2 and z-y-z in one mechanism that we use it for why it's more convenient for quantum mechanics anyway I'll tell you in a minute why so these three rotations factor by inserting resolutions of the identity the second factor is J1 and M1 and Uy and beta J2 and J it's not J, it's J1 excuse me on the left, Uy beta in the middle Jm2 on the right and then the third main consultant is Jm2 on the left Uz gamma times Jm prime on the right just writing as a product of three matrices here however as we've just seen rotations of the z-axis are diagonal from the largest above so the first factor becomes e to the minus i i-alpha m times prong of a delta m in one but the final factor becomes e to the minus i-gamma m prime times prong of a delta m2 m prime and the result of this is the sum can be done because you've got diagonal matrices on the right and the left and then we've got the and the only non-trivial part is the y rotation which appears in the middle so people make a special notation for this y rotation here which is the non-trivial part my definition is written this way it's another D matrix but they use a lowercase D because it only depends on one number angle not in three it's written this way lowercase d to the middle Euler angle. And if you like, this is the same thing as e to the minus, this is one of the matrix elements, jm e to the minus i, e to the minus i theta times jy jm prime. That's the definition of the law of case D matrix. Anyway, the result is the capital D matrix written in Euler angle form, capital T jm prime of alpha beta gamma is able to e to the minus i alpha m times e to the minus i gamma m prime times more case D jm m prime of theta. And so as I say, the alpha and gamma Euler angles are trivial and it's only the middle one and the beta Euler angle that takes some work. But that's because matrices for jy are not diagonal. So computer exponentials have got to do some work here to get to this. In any case, the result of this is that if you look at tables of rotation matrices, they never tabulate the capital D matrices, they just tabulate the lower case D matrices. And they're considerably simpler because they only depend on one parameter, the beta. There's formulas for them. Maybe I'll just mention a couple of them. If we take the case of j equals 0, then we have prime of beta, the lower case D matrix. Well, if j is 0, then m and n prime can only be 0, 2. So this is going to be a 1 by 1 matrix.  Well, an exponential of 0 is 1. So this matrix is equal to 1. So j equals 0. Once again, in fact, more generally, if I take D0 and n prime of any matrix, any matrix, let's say 1 by n form the answer, it's just 1. Any of the rotation matrices of a system of 0 angular momentum are just 1 by 1 matrices containing 1 because they're exponentials of 0. And what that means is that a system that has 0 angular momentum is rotationally invariant. If you apply this matrix to a vector, a one-dimensional vector, this whole plus of 1 does nothing to it. j equals 0 systems are rotationally invariant. That's an important thing to keep in mind. If you talk about wave functions, they're called S waves. That means 0 angular momentum. But it's true in general as well for spin. The total angular momentum is 0. The whole thing is rotationally invariant. So that's the case of j equals 0. If we do the case of j equals 1, we worked out the rotation matrices. Excuse me. Let's go on to the next case, which is j equals 1 half. For j equals 1 half, we already worked out in the last lecture, I think it was, or two of them, two ago, the rotation matrices for spinally half systems. And in particular, if you want to rotate about the y-axis, here's what you get.  This is the same thing as e to the minus i beta over 2 times sigma y. And if you work it out, it turns into a cosine of beta over 2 minus sine of beta over 2, sine of beta over 2, and cosine of beta over 2. Like this. It's a non-trivial rotation matrix. I can tell you why Degner decided to use the Z-Y-Z convention for Euler-Engels instead of the Z-X-Z. The reason is because the conventions we're using here for the matrix elements, the matrix elements of the raising of lowering operator is real. And that's why we have this famous square root of it with no other face at it. And if you do that, then you can see that the matrix elements of Jx are going to be real, too, because it's J plus plus J minus over 2. But that means the matrix elements of Jy are going to be purely imaginary. You know this already from the standpoint of polynomial matrices, but it's true for any value of angular momentum, not just J plus a half. And so when you exponentiate these J matrices, you get these rotations. For example, a rotation about the y-axis can be either the minus i theta times Jy. Well, the matrix for Jy is purely imaginary, multiplying by i's, and that can be purely real. So the result is that these rotation matrices will be purely real matrices, as you see in this example right here for spending half. Whereas if you use the X convention, then they'd be complex matrices. It just simplifies things, and it means that these lowercase D matrices, which are the essence of that, are purely not to be purely real with this ZYC convention. That's the reason it's done. Okay. Okay, I think that's all I want to say about rotation matrices. I did just the 0 and 1 half case. I'll leave it as an exercise for you to look at the J equals 1 case. There, as I say, the essence is to do the y rotation. So what you need to do is to work out the matrix elements for Jy, and you do that by adding those matrix elements for J plus and minus and dividing by 2i. And then you need to exponentiate the series, and you can do this by the means that you've done already for exponentiating matrices. You try to express higher powers in terms of lower powers. It's easy to do. You collect the terms together and get a trigonometric series. Anyway, the calculation is summarized in the notes that's also done in a stockerized book. And it's similar to other such calculations that we've done in the past. When you've done, you'll end up with this 3 by 3 matrix, which is used for rotating systems of angular momentum that equal to 1. Del. There's one final topic on this. There's some limitations which I want to mention, and that is the story of adjoin formulas. And I'll be fairly brief about that because we've seen two different versions of adjoin formulas already. When we did the case of the special case of a spin line path, the adjoin formula was this. It's that if I have a rotation that can access any form where I use it to conjugate tolerance to these inverse clusters, they're unitary, then this is the classical rotation actually with an inverse multiplying on the singular. So this is how it worked out for the case of a spin row path. Now, of course, the spin one-half signal is proportional to the angular momentum that j is equal to 1-half signal against h bar equals 1. Well, then, in view of this formula, it won't be surprising to learn that for general angular momentum, we have an adjoin formula that looks like this. It's that if you take the rotation operator and use to be conjugating angular momentum itself, what you get is the classical rotation inverse multiplying on the angular momentum vector. And I think I will spend class time proving this. The proof is in the notes and it's straightforward. Actually, there's several different proofs that you can construct, but it's such an obvious generalization of the spin one-half case that I'll just leave it at that. But as I said, these are very useful formulas because they allow you to take a rotation operator and pull it through an angular momentum, which is something that you end up doing quite a lot in practice. Now, in the remaining 10 minutes, then I want to turn to a new topic which we'll take up further next hour, which is the subject of spins and magnetic fields. I'll just give you an example of real problems there. There's a whole host of issues which are typically glossed over and ignored in the introductory courses, and I'd like to pay some attention to them because they're connected with a fundamental understanding of what's involved with spins and magnetic fields. I'd like to begin by just reviewing some classical electromagnetism regarding multiples in magnetic moments and things of that sort. So for the time being, I'm going to do classical mechanics and it will be classical E and M. So hopefully this is just a reminder for you. If we have some region, some localized region of space that contains a charged density and a current density, maybe functions of position. Yes? Is this also in your notes or is it in the magnetic field? No, there's some notes on this. I've got to say I'm not very happy with the notes and I won't have time to rewrite them, I apologize for them. They really need to be reworked. But anyway, I'll try to give the most logical presentation of material in lectures. I think it's a little better straightened out from the notes. But there's a set of notes on this that's coming up. So anyway, talking about classical electromagnetism of multiple expansions, it's not something like this. We have a localized charge and current distribution and here J is the electric current now, not angular momentum anymore. Then this, of course, produces electric and magnetic fields and the electric and magnetic fields can be represented as a sum of multiples, multiple fields. And the first term is the monopole field and the second term is the dipole field and then the next term is the quadruple field and so on up. Next one is octopole and so on like this. And these fields are, this is an expansion of the electric and magnetic fields and they're characterized by the manner in which they fall off at distance. The electric field falls off as one of our, excuse me, the monopole field falls off as one of our squared. The dipole is one of our cubed and the quadruple is one of our fourth and so on like this. The result is that if you're at a large distance away from the localized current distribution and it's the first non-managing term in this series is the one that's going to dominate. For example, if the total charge is non-zero at large distance, it's just the electric field will be dominated by the monopole field which is basically the Coulomb field but it'll look like all the charges concentrate at a point. Now in the case of magnetic fields, however, there is no monopole field because as far as we know, magnetic monopoles don't exist. So the leading term for the magnetic field is the dipole term and that's the term that will dominate at large distances. Of course, if you come into short distances near the charge of current distribution, you'll require multiple moments to become important and you won't take them to the top, too. So it's really in large distances where the leading term is important. All right. Now, I mainly want to concentrate on the magnetic dipole term because I want to talk about spins in magnetic moments. So the magnetic moment the dipole magnetic field of the localized current distribution is described, quantified by the magnetic moment. The magnetic moment view is defined this way, the Gaussian units. It's one over two C. It's an integral over space which is the current distribution of the position vector crossed into the current band bar like this. This is just the definition of it. For example, if you take a current distribution, which is a current going around the wire loop, like this, then you'll find the magnetic moment view as a factor which is perpendicular to the loop. You can take calculations like this, like so. Now, let's suppose we take this current loop or this magnetic moment to lead in general. We put it in this couple of magnetic moments. Then just by calculating the V cross B force on the current, in the words J cross B, you can calculate, for example, the total force on the current loop and other things too. Calculating the force, here's what you find is the force is the gradient of U dotted into V. The magnetic moment view is not a function of space. It's just a property of the current distribution, but it may be a function of time. For example, the loop is moving around. So when you do this gradient here, the gradient can only act on V, which itself may be a function of space. In particular, if the V is uniform, then this force is zero. There isn't no force on a net force on a magnetic dipole in a uniform magnetic field. That's why you need non-uniform fields in the Stern-Gerlach apparatus in order to get the particles to move. Actually, this result which is obtained here is obtained on the assumption that V is varying slowly or the dipole is a small spatial extent because you're really expanding the magnetic field about, let's say, the center of the dipole. If you could be more careful about this, I should hire over terms of this. This is a leading term. For a small dipole, this is true. There's also a torque on the dipole which you can calculate, and this is a mu cross V. The torque is, of course, since this is classical mechanics. The torque is the same thing with the time derivative, the angle of the dipole. Now, the torque brings up the question of what is the angle momentum of the dipole. And this is still new classical mechanics. The, you see, the magnetic moment is clear from the formula. It is dependent upon the charge, the current distribution. In other words, the charges of how they're moving, distribution of charges of how they're moving. Whereas the angle momentum, of course, is dependent on the distribution of mass and how it's moving. Those don't have to be the same. You could have neutral particles that are moving around in a circle and creating angle momentum, but they wouldn't create any magnetic moment at all. So, that one, that one, the mu are different vectors in the classical problem, and in general, the L vectors are going to stick them off like this in some particular direction. Nevertheless, there are some simple examples in which the, in which the angle momentum and the magnetic moment are proportional to one another. Simplest one is the case of a charged particle in a circular orbit. This is still classical. Let's say the orbit, as a radius of r, the particle's got a velocity b like this, and let's say it's moving with constant velocity in a circular orbit, and let's say the charge is q. Well, in this case, the angle momentum L is, of course, 10 times r cross b, and that's a vector which is perpendicular to the orbit like this. And if you use this formula to compute the magnetic moment, you find that it's in the same direction also, and that mu is equal to q over twice mc, charge over twice mc, both by terms of the angle momentum L, so mu is in the same direction like this. So mu and L, the magnetic moment in angle momentum, are in fact proportional in a similar example like this. All right. Now, the question arises is whether mu and L are proportional to one another also in quantum mechanics. And the answer to this is so much complicated, I may have gone into too much detail of this in the notes, so let me try to just simplify it here by saying that in many important cases in quantum mechanics, they're also proportional there too, although not always. In fact, to be a little more general about it, you can say that in quantum mechanics, mu and the angle momentum, which now may include spin angle momentum, the magnetic moment in the angle momentum are proportional if the applied magnetic field is small enough to quantify that later on. But in any case, let me give you some important examples. If we're talking about an orbital angle momentum in quantum mechanics, so for example, considering the orbital motion of an electron in an atom that has an orbital angle momentum, then it turns out that the classical formula that comes from this simple current loop can be carried directly over in quantum mechanics with no modification. We get mu is equal to q over 2 mc times l for the orbital angle momentum. One thing I meant to point out from the board of above, which I failed to do, is that this is a vector, let me write it down again. This is a vectorial relation between these two vectors. They may be pointing, they may be parallel to or anti-parallel to one another, but there's a coefficient in here and it involves the charge. And so in particular, if the charge is negative, then the magnetic moment is the angular momentum pointing in different directions. You see, these are physically two different things. Magnetic moment can be technically experimentally by interacting with a magnetic field. The angular momentum is a mechanical thing. You can measure that, for example, by using conservation of angular momentum and having an interactive load system. They're very different things. They indicate for a negative particle they will be pointing in the opposite directions whereas for a positive particle, they'll point in the same direction. This carries over in quantum mechanics as well as far as the orbital angular momentum is concerned, you have the same relationship with the orbital angular momentum. Now, particles, whether they are so-called elementary particles or so-called composite particles, have a property also of angular momentum which is generally called spin. And in the case of a particle with spin, there is still a proportionality between the magnetic moment particles generally have magnetic moments. And there's a proportionality between the magnetic moment and the angular momentum except notationally we write the angular momentum as s just to indicate spin. And we split off a factor of q over 2 mc which gets the dimensions right but then in general it's necessary to put in a fudge factor or a scaling factor called g and I'm sorry my q looks like a g I'll try to make it as different as possible. There's a g factor here which is a dimensionless factor which needs to be introduced in order to quantify the proportionality between mu and the spin s. And so these are the g factors of particles, the various particles one can consider. Let me just make one more remark before I let you go is that the spin which occurs here in our particle, in the case of a composite particle the spin is regarded as a total angular momentum of the particle of all of its internal structure added together. For example, the proton is made out of three quarks and what we call the spin of the proton which is one half is really the sum of the spins of the three quarks as well as their orbital angular momentum all added together. For another example, the proton is a composite particle made out of a proton and a neutron. And what we call the spin of the neutron is the sum of the spins plus orbital angular momentum of the proton and neutron regarded as a two-body system orbiting around each other. The same applies for more complicated nuclei which have larger numbers of protons and neutrons. Yes. And why don't we see the protons and the quarks? I mean why couldn't we go to an excited state where you've got a different orbital? Well that would change the energy so you'd be talking about an excited state of the proton and in the sense you do see that these are the baryons in some sense the baryons like the lambda particles and so on. These are the sigma particles. These could be regarded as excited states of the proton neutron system. Actually in the sense you do see that. All right. That's all for today. If you want to pursue that next time ask me again because that's just a question.


Jeroen, thank you very much for the TH Council Europe to be such an active partner of Green Digital Action here in COP28. Why is it important for you? It's important for the TH Council because we want to lower the negative impact of the ICT sector and especially the optical fiber sector in Europe and we want to increase our positive impact by using our technologies and the green technologies we have to decarbonization of the complete world, you can say. So that's the important thing we want to do. Thank you very much. It's so great to have industry with us on this. Thank you.


Hey everybody, welcome back to Magic One Thaloxie. My name is David and this is a Magic Review. Hey, today we're going to look at the DVD Any Shuffle Deck from Liam Montier and Big Blind Media. What is Any Shuffle Deck? It's a DVD, completely self-contained, doesn't have any gas or gimmicks or anything like that. Liam is going to teach you 10 killer card tricks that you can do with any shuffle deck, any deck of cards at a moment's notice. Sounds pretty awesome. Want to see the trailer? This is it. Hi there, my name is Liam Montier and on this DVD and project we're going to be showing you all of the tricks that I do that are self-working and from a borrowed shuffled pack of cards. We've all been in the situation where you've been totally called out, you get introduced as a magician and you've got nothing on you or nothing set up. But by the time you finish this project you're going to have 10 absolute stone cold killer tricks that you can do literally any situation where you can beg, borrow or steal a deck of cards. So let's get started. So that was Any Shuffled Deck from Liam Montier and Big Blind Media. A couple questions we always ask about all of our Magic Reviews and the first of which is what's in the box? What's in the box? You're going to get a DVD. The DVD has about 10 tricks on it, okay, 10 tricks. Each tricks between I'd say five and six, seven minutes long. You get a performance, you get an explanation and then you get Liam's tips, advice and credit where credit is due. Is it what I thought? Absolutely. I have a couple of these collaborations between Big Blind Media and Liam Montier and pretty much, you know, they all go the same way. It's just a wonderful Any Shuffled Deck DVD that has tons of really solid, well hard-hitting card tricks and Liam is a great teacher. What's the overall quality and production value of the video? Like I said, BBM, they make great videos. Everything's well-miked. Everything's well shot. Beautiful locations. They always have stunning spectators to do their tricks with. Like I said, Liam's a great teacher. He's very patient. He always gives credit where credit is due. I think he constantly comes up with great effects to teach you without throwing in any filler tricks, you know? And so all around, I think it's a great DVD. What's taught on the DVD? What are the effects you're going to get? You're going to get a trick called Interstellar Out of This World, which is an Out of This World routine that you can do without any prep. Well, you do the prep right in front of the spectator, but it's pretty cool. You're going to get another trick on there called Mates. Mates is a selected and revealed reverse card trick. You'll get another trick called Gemini Location, which is a variation on the Carl Fulves Gemini Twins effect. And that's a wonderful trick, solid, well-working classic of magic. You get another trick on there called Silly Questions, which is where the magician just goes through a series of silly questions and then ends up finding the spectator's card. You'll get a Wheel of Fortune trick, which is basically a clock wheel effect. Another trick on there called Jack's Poker. It's a poker hand effect, but the spectator cuts to and finds the exact card they need to make a winning poker hand. Another trick on there called Salto Triumph. It's a self-working triumph effect, I think, worth the entire price of the DVD. And then there's a trick on there called Last Turn Up, where the spectator will actually deal to their own card. This is a great trick. But the trick on there called Invisible Dice is one of my favorites. It's a card stab effect with the magician's prediction card. And then lastly, there's one trick on there called One Over the Eight, which is a math trick. Positive. What are the positives to any shuffled deck? You just can't go wrong with the combination of Big Blind Media and Liam Montier. Every magician needs a strong repertoire of self-working effects, and this DVD delivers. Is it worth your money? It's $30, so you're $30 for 10 tricks. That's only a couple of bucks a trick. Plus the combination of Big Blind Media, plus the combination of its self-working card tricks, plus the combination of its Liam Montier. You can't go wrong. Well worth your money. Who would like this? I think fans of self-working card tricks, I think magicians are looking to add a few more self-working, hard-hitting card tricks to their repertoire. Fans of Big Blind Media, fans of Liam Montier would definitely love any shuffled deck. All right, so that is my review of any shuffled deck from Liam Montier and Big Blind Media. I want to thank Murphy's Magic for allowing me to have this trick so that I could do the review for you. And if you would like to purchase this for yourself, you can find it from your very favorite Murphy's Magic retailer. Thanks, bye.


The World Cup in Brazil is less than a month away, and workers are still scrambling to finish construction on stadiums like this one. Spiraling costs and delays have meant that half the 12 stadiums that will host matches throughout the country miss the deadline for completion at the end of 2013. But those are only the beginning of Brazil's problems. Nine workers have died so far, including Mohamed Ali-Maziel, who was electrocuted earlier this month at Arena Patinal. That figure pales in comparison to the hundreds of migrant workers who have already died building stadiums in Qatar for the 2022 World Cup. But this one death is no less a tragedy. Masiel leaves behind two sons. Brazil has other problems, and they are serious, as workers describe unsafe conditions and late wages, and the larger population protests against the billions of public funds used to host the event. Brazil is a sacrament nation, but some Brazilians are just becoming angry.