Hey Virgo, welcome back to my channel. Hope you all had a wonderful weekend. This is Kelly from House of Virgo. If you are new, please do hit like, share, and subscribe. You guys, I'm going to do on Sundays now, Sunday singles. I'm going to do a Celtic Cross. So we're going to try this out, see how it goes for Sunday and see if it goes well. And we'll just keep doing that. Okay. So yep, this is a Virgo channel. Please do click, like, share, and subscribe if you're new. And Virgo, let's get into your reading. All right. So what does Virgo need to know? Virgo singles. Singles are those of you who like you're either married or you're not. You're either long term committed relationship or you're not. Singles could be dating, but this is just about your energy. The recent past. I'll take a look here. Okay. So you have the 10 of ones that reach the recent past, your situation. Okay. You have the magician in the reverse, the block, you have the moon, the root of the problem in your life. You have justice, the possibilities before you are up ahead. You have the sun. Okay. Direction that you're heading. We have the 10 of pentacles. How you view yourself, the world in reverse, others and your environment that's around you. You have the high priestess and I will clarify the major arcana, your hopes and fears. You have the four of wands and the outcome and where the energy is heading the three of swords and the two of swords. Okay. So the bottom of the deck of ergo, you have the two of wands.  Maybe travel, making some plans. Currently, I feel like, you know, some of you are just you're resting, you're taking your time trying to figure out what you want to do. Some of you might be really just withdrawn, might be doing a lot of praying or trying to manifest in your life, doing some meditation work, not really talking, listening to your dreams, making these plans according to your dreams and what you want to do in your life going forward. Now the recent past here, there's some kind of struggle, an end to the struggle. Okay, something came to an end, something that you were pushing and pushing and carrying the weight of the world, carrying everything in your life, carrying a relationship. It felt just an energy of labor, labor, all this hard work, like physically exhausting or some type of situation that made you feel like it affected you physically.    That doesn't really, it's too, too much work. So currently you have the magician in the reverse. So I feel like your situation right now is kind of hard for you to put all or lay all your cards out on the table. I feel like you're having a hard time manifesting things in your life right currently, at least the situation around you with that card, it feels like, hmm, it feels like you're, I'm feeling an energy of trying, I feel like you're, you're working on something. I don't, I'm not picking up like depression or hopelessness or anything like that. I just feel like at this current time, you are as a single person, the block is the moon. So it's like, there's not enough, your dreams, it's your dreams. You're, I feel like you're trying to connect with your dreams or connect with your wishes, your desires, the things that you want in your life. You have some kind of an idea, but it's difficult for you to turn this, turn this thing into reality. And even in the case of, you know, wanting to have a relationship or meet someone, it feels like it's, it's difficult for you. Maybe you don't know where to meet people, or you're not sure how to meet someone or make yourself available, or if you're ready for that. So you kind of have, you know, a difficult time here. Like I feel like you've dropped some kind of a burden, but you're not quite, it's not black or white. You're in a very gray area right at this time, I feel. And that's all right. Cause I feel like there's some kind of transition that you're going through. Let me just get a clarity on the magician in the reverse. Okay, so you're the queen of wands. So as an energy, this is you kind of like taking some bold steps in your life, male or female doesn't matter, it's energy, becoming more confident, more in control, right? That's that I feel like that's what you're trying to do.   Some of you might be having trouble remembering them when you wake up, or there's only bits and pieces or portions of them. Some of you were trying to remember and write things down, or there's just these wishes, but the block though, I feel like that is kind of what the block is. Like when we have the block as the moon, this feels kind of like what's preventing you from getting to where you need to be or where you wish to be in your life on the love front. The block is the moon is disillusioned or I'm sorry, is illusions. There's a lack of clarity. Okay. And so I feel like you can't manifest the things or the type of relationship you want in your life until you are clear about what it is you want. Because if you are not clear and you're, you're, you know, sending those desires or half desires or certain just bits and pieces to the universe, the universe is going to respond that way. You have to be clear and direct with yourself and with your hopes and wishes. Okay. As far as like manifesting a person, I'm not, I'm not like a believer in manifesting people because imagine that kind of feels like spell work. Imagine if someone that you weren't interested in was trying to manifest you, you would be like, I'm blocking that. No, I don't want anybody trying to pull me in that I'm not interested in, right? So I, you know, how would you feel? I don't, I don't like the, I hear people talk about, oh, manifest the person.  So I feel like the block here is there's a lack of clarity as far as like, if someone were to say to you, Virgo, okay, well, what type, what are you looking for? If you were like really, really wide open, you're like, I'll just take anything, universe is going to be like, okay, we're just going to bring anything. And then, you know, Virgo was like, wait, maybe I should rethink that. I feel like you need to like somehow find a way to sort that out about what it is you want and then start trying to manifest. So for example, I'll give you an example, if you're new to this whole thing, if you are looking to date someone who, for example, okay, say they have a career working in the corporate world, okay, the way you manifest that type of energy is you need to surround yourself in that environment. Okay, so it's kind of starting with the environment of these type of people. Like if you're looking to meet someone on, for example, and I always say this like on a dating site, you're going to surround you're going to surround yourself in an environment, different kind of environment. If you're looking to manifest someone who has a similar lifestyle as you, you want to be in that environment, that's a process of manifestation. Okay, so this is a strong message for you singles about getting clear about what type of person you would like. If you are someone, for example, who you're very artistic, or not, I don't want to say artistic, like say one specific thing, like say you're someone who likes to run marathons, you're not you're certainly probably not going to want to have a connection with someone who sits on the couch and eats chips and soda all day long, right. So this is a message of clarity. And I feel like I keep repeating myself here. So let's move on. The root of the problem is justice. So this is about getting truthful with yourself and but being fair. So if you're going to try to manifest someone and get clear about what it is that you want in your life or what type of energy or person you would like in your life. I don't think it's I don't think making a list of 100 things to be so super specific because then if you're too specific with like 100 things, I mean, you're going to really narrow it down. I feel like there's going to be probably some things that you're going to have to ask yourself, hmm, well, this I might forego but this I definitely not like so make your list of 100 and then, you know, keep making it shorter and shorter. What is this like House of Virgo Kelly's dating advice? I don't know, you guys just the messages that are coming through here. So be fair and be balanced.  Once you get that all together, and you figure that out for yourself, because in order to know what type of person you would like to be in alignment with, you have to know where you are and where you stand and what will work for you and what will not. Okay.  All right. Yeah, so five of cups energy. So the block is maybe a little bit of hopelessness as well. It's interesting with the five of cups is I've been saying for years, you see this person is looking down at all that they have lost rather than seeing those two cups that are still upright. This is kind of like some of the block might feel a sense of regret or remorse or somebody saying maybe I was maybe I was too picky or maybe I should not have let somebody go for others. This could be like a message of like sad that something didn't work out. You know, but once if once this person is able to turn around and see that there's two cups, that's the two of cups. There is love out there. There is someone who will be in alignment with you, but I feel like you have to get in alignment with yourself and get clear if you're not about what that is, what that means for you. Okay. Let me just take a look, clarifying there's a lot of major arcana here, clarifying justice. Okay. Being fair, honest, truthful with yourself. Okay. Yeah. And the three of wands. So planning, looking out onto the horizon here, looking out to see that there is more threes always represent communication to me as well. So this is also the root of the problem is maybe you're not talking to yourself. Are you not being truthful and honest fully with yourself? Maybe you think you are. Maybe there's a little more digging you need to do. So for example, um, here's something you can do to practice. If you, if you're kind of like not sure, try to write your own personal bio like for yourself. What would you say about yourself? What do you like to do? That's one way to kind of get an understanding of yourself, of who you are. If you're not fully sure, or if there's more to be discovered, or if you're just on a path of discovery. Okay. So crowning is the possibilities here. You've got the sun. So yes, it is possible for you to have everything that you want. You're in control of your destiny. So let me see. Joy, happiness, success. Okay. Yeah, look at that. I always feel like when I look at this card, I always feel like this is you. This is the Virgo card.  If you had to put a monetary value on yourself, how much would you be worse? How much do you think you're worth?  Ask yourself that. I feel like that's, you know, the possibility for success is here, but this is really about positioning yourself to reattract or to attract someone into your life based on your self worth, your self value. Okay. And this is related to your self esteem. Okay. It's related to your self esteem as well. Are you even ready for dating? Do you think that there's more you could do? Are you ready to come into commandment with someone? Do you think you have some more work or some other things that you want to manifest in your own personal life? Other plans or projects or goals? Are you working on those? Do you want to start working on some? Write that stuff down and ask yourself like, what else do you want? I keep hearing that or seeing that Noah from, what was that movie? Noah and Ali. What do you want? What do you want, Virgo?  Okay. So the direction that you're heading, okay, you have the 10 of pentacles. So this is good. This is kind of like you're heading in this, you know, secure, safe kind of position, if that makes any sense. And the best and most efficient way for you to achieve your goals here, as far as your single life or meeting others or meeting someone in particular, is to keep your eye on the absolute price.  Okay, so I feel like with the 10 of pentacles, some of you, you know, this could be about a career, about a job, this could be about meeting someone also. Remember, I was saying, like in a particular environment, surrounding yourself with like-minded people. This feels like security and safety and long term relationship. So you're like, that's what's before you. As long as you are following through with these things, I do see that this is before you know who that's going to be with. We shall see if someone is coming in here for you. But I feel like this mostly is like your goals and your plans and what you're seeking. Okay, so I feel like manifesting, getting clear on what you want, what you will put up with, what you will not instead of settling in love just so that you could have a partner or someone comes in and they seem to be everything that you want. But then there's these red flags that some of you may have had a tendency in the past to just kind of overlook because if you're feelings of attachment to someone, I feel like that's a big no-no if they're huge red flags. Okay, so I see you heading in a really good direction at this time. This is representing your future. So I do feel like you are going to have some type of long-term success with a relationship. I do see that. How you view yourself is the world in the reverse. Okay, chapter's not finished. Something here that you are your goals, your success, your dreams, the things that you wish to have for yourself. You're still working on that. And I feel like that's just as good as being successful because it's still moving. So I feel like some of you might be viewing yourselves as you're not really where you want to be just yet. Some of you want to relocate or travel and it's not possible at this time. Some of you may not even view yourself as being able to do that. And these are just about how you're viewing yourself right now. Okay, let me see. I feel like it's not really negative. It's not overly positive. It's just transitionary. Like you are so close to getting what you desire at this time. And I feel like it's just a matter of you got to keep pushing. You know, it's like being, I feel like if you were running a race, and the one thing I want to tell you Virgo, it's not a sprint, it's a marathon. Okay, so don't get discouraged if you have yet to meet the person of your dreams, or the person that you want to be with for a lifetime. Don't get discouraged. It's a marathon that requires self discipline, patience, perseverance to keep doing what you're doing. I know some of you are like, I've been doing that, I've been doing that. Well, I feel like you might be hitting like a goal marker here where there's something spirits trying to tell you, hold up, there's another thing here that we need to take a look at. Mostly it feels like your environment is you're not really clear, or you may find yourself like, wait, what am I doing here? Is this really what I want? A lot of questions are going to start popping up here for you. Okay. So the devil energy is here. Okay, there might be some past energy that you're still trying to clear out, you might view yourself still stuck on someone, or obsessed with someone, or still very physically attracted to someone whom if you look here, if you're female, you're looking at that person, and that person's looking away from you. So it's like they're not interested, yet you're still bound to them in some way. The new word I'm going to use here is maybe there's a bit of limerence. So there's a little bit of obsession possibly. Okay. Or there is another person in your life who is still kind of in and out, and it doesn't feel like it's officially like finished.  So there hasn't been an ability to complete a final chapter to move on. Okay. And if you're male, yeah, you might be looking away and trying to like, you may still feel stuck on someone, but you may be trying to look in a different direction in this person, but still looking at you, right? So there's the energy is kind of mutual, I feel. And I feel like you might be viewing this like you're trying to move yourself forward. Now for some, this might not exactly be like a person. This could just be energies from the past. Perhaps there was some addictions or some trauma or anxieties, or stress or struggle and past relationships that you were trying to heal from.  That's not a message for every single one of you, but somebody here might relate to that in some way, you know, so you might be viewing yourself. Now, let's take a look and see what is external to you. So this would be the environment. And you do have the high priestess. So there's a lot of secrets and hidden energy. That's external to you, whether this is helping or hindering your situation, there could be somebody in your environment who may be psychic, or you might be listening to psychics trying to get clarity, you could be speaking to someone like who is very wise, full of wisdom as well. I kind of feel like this doesn't feel like a friend. This feels more like maybe you're listening to terror readings. This feels more like your environment. If you're listening to terror readings, it seems like it's all that's around you. It's your go to. And maybe that's helping you. So I feel like that that would be great. There's somebody or some people around you who are very wise and have a lot of like intuitive knowledge. They keep secrets. Maybe they're this could be someone who's very religious as well. Now, they may you may be communicating with these people or this person right now, or that may be showing up throughout the rest of this month into October. Let me see here. Okay. So all right, I'm just going to say this straight out.  Some of you might be stuck on a particular person and wondering if anything's going to change. Right. So when the chariot's in the reverse, this is kind of like you get in the car, you got the gas, the tank is filled, car is clean, wheels are good, and then you go to turn the ignition and nothing happens. That's the that's a chariot in the reverse or it's like driving down the road and you run out of gas. Like I feel some of you might be in this situation where there's way too. All right.  There's no action here. There's no action and the environment surrounding you in some ways there are things that are helping you with this intuitive information you're receiving that's external to you or these aha moments in regards to, you know, what you need to do moving forward in your single life. But at the same time, it's hindering you because there's too much reliance for some of you on the readings. Okay. And I feel like that's maybe that's part of some kind of an addiction. Some of you might be like, Oh, I need to give this a break. And if you need to give it a break, give it a break. It's fine. I know I'm still going to be here. So come back whenever.   So your hopes and fears, you have the four of ones. So, you know, it's good. I feel like you're hoping to have that. You know, some of you might want to reunion with someone. Some of you want that family that happily ever after that, you know, structure the 1111 energy. Some of you want that long term commitment marriage. And these are your hopes, maybe to have a family because this is the family card.  Oh, goodness gracious. I'm so sorry. So yeah, I feel like you are hoping for this, right? But there is a fear that the foundation, right? The foundation has to be built first before anything else. There is a fear that it might not happen for you. But you know, look, the 1111 upside down is still the 1111. Okay. Four structure and balance. So, and you know, I feel like there's a fear that this isn't going to happen. But these are just basically, you know, it's hopes and fears. It doesn't represent anything that I feel will actually happen. It's just kind of maybe your outlook on the situation here. So just take that into consideration, be mindful of your hopes and fears, which one is like directing your path, your fears or your hopes? Okay, so we have the outcome here. And this just kind of for me, it's not a hard and fast prediction, but to tell you where the energy is heading. Okay. So you have the two of swords with the three of swords. So I feel like there's a decision here, right? I feel like you're going to come upon an actual decision of blocking out any kind of things that hurt you. Okay, this is kind of like turning a blind eye to either a sword is all about intellect and thoughts. I feel like this is turning a blind eye to the negative, right?  Like this is all negative thinking. And you know what, Virgo? Everybody has their pains, right? Okay, we have the number 23, very significant 23. I'm just seeing that right now. I feel like Virgo, turn a blind eye, forgive, let go of the past and open yourself up to allow love to come into your life and even love for self. Okay. So yeah, the two of swords is kind of like going within and making a decision and making a compromise with self, you know, yes, I've had my heartbreak. Yes, I had a divorce. Yes, I had that breakup. That doesn't mean that that energy is going to happen again. Okay, those were your experiences learn from them. The energy is heading in the direction of you kind of, you know, putting your swords up there and blocking that, right? Not being in fear of that happening again. I mean, love is always a risk.  It might be a decision that you're making going forward. Maybe it's time to block so that you can heal and move on or reblock someone or just kind of look at the situation and say, you know what, maybe somebody was a third party or there was, you know, other involvement of some sort, maybe Virgo, it's time for you to take those two swords out of your heart. Okay, use them to protect yourself and just move forward in your life. Right. And I feel like the energy going forward is going to be a decision for you to do something along those lines. Now, all right, I want to see, let me see here, I'm going to get a couple more messages here for you. What are the island time messages here for Virgo? What else does Virgo need to know going forward? Okay, the butterfly, beautiful. Can't see it, but that's all right. Relationship is evolving to the next phase, healing the inner child and growth. Some of you, this is relationship itself is evolving, which is beautiful. That is so beautiful. For others, you could be connecting with someone or dating right now while you're going through this process. I do feel like that relationship is going to evolve as time goes by.  You could be, right? If you're not dating anyone and you're just solo and single and on your own, this is relationship with self evolving, which is beautiful, okay? And healing that inner child's stuff, right? Parenting yourself again, kind of parenting yourself, healing the inner child is becoming the parent to the child within that didn't get her or his needs met and meeting them. Okay, all right, you've got love, unconditional love, self love, oneness, passion, affection, and attraction.  Okay, just when I said that lightning sudden change, okay? Shocking news, surprise and epiphany upheaval and a transformation is occurring in your life. Yeah, wow, you guys. This is amazing. I do want to ask though, for those singles, if anyone is coming into your life in October, I want to take a look at October, if there's anyone coming into Virgo's life in October, let's see, Virgo going to meet anyone new in October. Okay, now the seven of pentacles, let me see. I do feel like, yeah, there will be an opportunity that will come to you in October here. But you know what, Virgo? I think you are, and this is for the complete singles, okay? I don't know that you're going to really be interested. I feel like someone will kind of reach out to you. But I do feel like your energy, whoever this person is, I do feel like the energy is going to be, I'll think about it. I feel like that's going to be kind of your response. Okay, we have the queen of cups. So this could be a water sign, cancer, scorpio, Pisces coming in. This might be someone, for some of you, if this is someone you reconnect or you're reconnecting with, this could be someone that was blocked in the past, or they blocked either one. For others though, I feel like it's going to mostly be about like, oh, I'll think about it. I have other opportunities or other things that I'm trying to manifest in my life. Okay, now for some of you, there you are. For others, there's also, we're getting court cards now. So it could be Virgo Taurus or Capricorn. Yeah, okay, that's what I feel like. There might be some shocking news.  If you're reaching out to anyone at this time, anyone new, I would advise like even up until October 2nd, between 2nd and the 9th, not reach out to anybody yet, just keep doing you because during that retrograde is never a good time to start a relationship. And some of you might actually tell someone like maybe in a couple weeks, or I'm not sure, or I'll think about it, you know, just because it's at retrograde and you're going through some changes, I mean, that's as far as like going into dating for the purpose of to have a relationship, like if you already started that, then that's different. But maybe go have a few dates or have dinner or drinks and just as a friendly thing, that's fine. But to start any kind of a relationship during this time period, I don't know. I mean, you do what you want. Some of you might just, like I said, just kind of say, put on the back burner for now, not yet, or something along those lines. Now let me say, you know, as always, Fargo, you have free will. You can change your approach. You can change the energy in any situation that you're in and achieve a different outcome. This is just some type of guidance message for you to try to give you maybe some pivotal markers for you to bounce off from. If it helps, great. If not, don't worry about it. Let's see what the romance angels have to say. Okay. All right. Some codependency. So you may have to take a look at some codependency issues, addictions affecting your romantic life. Look and see are there any addictions or things that you need to, I mean, we're talking addictions, it could be, you know, addicted to anything. It doesn't have to be the typical drugs and alcohol thing. It could be some could be addicted to smoking. Some could be addicted to cheesecake. Some could be addicted to a person, a place, or a thing, you know, some things that interfere in your ability to have a healthy relationship or may have had that in the past. You know, it's not for all of you and all of you have codependency issues or could have been issues with family members or a parent that was an addict and that has caused codependency in you. Right. So there could be stuff like that to take a look at during this retrograde as well. Okay. Past life relationship. Also something from the past that brought on some type of codependency. I feel like you're being asked to take a look. This is a really deep like therapeutic read. Some things you've got to heal that stuff fur go if you want to have that healthy, happy relationship. If you have codependency or addictions, your addictions might be the one who's making all the decisions in your romantic life.  I am. I'm in control of my destiny, not my addictions, not my codependency, things like that. All right, I'm gonna get a couple more messages here from my Moom Pitero deck as usual. Let's see what else this Virgo needs to know. Okay. Yeah, non committal. So I kind of feel like for you Virgo, it's like, for some reason, you're doing, you've got something ahead of you here that you're trying to sort out or that you will want to be sorting out. This could be in relation to a person, place, or a thing. This could be your spiritual, mental, physical, emotional health, okay, which might be at a position right now where you're like, you know, I can't commit to someone at this time.  I feel like you're some of you went through something that was really difficult in your past. Okay. And I feel like you're some of you're exhausted. Some of you really do want to meet someone, but at the same time, you're like, I don't know if I want to get involved with someone and then, you know, feel that burden again. I don't feel like you will. I just feel like that might have been a unique situation, but there is responsibility to committed relationships. Some of you might just want to enjoy your single life a little bit longer. Okay. And kind of reposition yourselves so that you don't attract that same energy from the past that you attract what's in alignment with you. Okay. All right, so you're going to get a sweet text message from someone. I feel like, okay, so sweet text message is kind of like sweet nothings, make you feel someone thinking about you, someone wondering how you are, someone that maybe you haven't heard from or someone a long lost friend. It could for some of you, it could be a past person. It really just depends. It might make you feel like give you a little bit of goosebumps. I'm just getting goosebumps, right? For some, it could be. It could be coming from a person who is noncommittal. You know, some of you might not feel anything at all.  I'm not committing to this. Why? Because I'm busy putting an effort in my life. And some of you have goals, you're trying to finish. That's what I said here, right? This is not yet complete. This is almost completion. So whatever you're working on here in your life, I don't even know what it is. Okay, I know some of you are in a position in your life where you know what, you've got it all together. You have your money, right? You have your physical self, right? You've got everything you need. And you're doing well. And you feel like there isn't anything else that you need. But maybe there isn't. But there is something here with this devil energy that I feel like you need to this is the one last thing that needs to be dealt with whatever this is who person place or thing that represents the last the last train on the track. Okay, the last train on the track that still has yet to dock. Okay, let me get some numbers and signs. All right, so we have Pisces here, Aquarius, Virgo, Pisces twice. Okay, 111, I just saw that right there. Okay, Pisces Aquarius, Virgo, let's see, we got a couple more, Sagittarius twice, Pisces again, and Libra. All right. Okay, I'm getting the numbers 203. My stomach's growling. Can you hear it? Oh my gosh. 116 and 124 and also the year 2000 seems like it was significant for some of you. Okay, let's see what other numbers are showing up here. Let's look at September birth date, August September birth dates. Okay, so September 18th, September 9th, September 3rd, September 1st, September 9th, we have the September 2nd and September 4th. We also have August 23rd, 24th, 29th, and the 31st. Okay, so if any of those birthdays resonate for you, it's definitely a reading for you. If it doesn't, it's still your reading. Okay, if the message is resonate, it's still your reading. I want to get your Chinese signs to see if anything else we can pick up here for you. Also, someone has just turned 40 or is turning 40 years of age. Okay, we also have 42, age 31. Okay, let me see here. Chinese signs for Virgo. Okay, year of the tiger. Look, it's the year of the tiger. This is the year where you need to like pounce and get stuff down here. The year of tiger is like very aggressive kind of year. It's like a cat. Okay, or that's the person. Okay, year of the goat. So this could be you or your person or both of you or neither. Okay, take it as it resonates. Year of the ox. We have a rooster. We have a rabbit. Year of the pig. Okay, year of the snake. One, two, three, four, five, six, seven, and one more double pig. Double rabbit. Did I say a rat? I thought I did. I didn't. Okay, so year of the rat. All right, so if that's you and your person or both of you or none of you, just take it as it resonates. All right, let me see what your charms are here. Let's get all this out of the way and check out your charms. All right, so snowflakes. Okay, snowflake. You have a seahorse. Two stars. Beautiful. Oh, silver and turquoise. I feel like silver and turquoise might be significant for someone and something connected to stars.  You know what, you guys? Okay, I'm just seeing, oh my gosh, every time I see this charm, I'm not intuiting this message, but I'm just every time I see this charm. My grandmother used to have these little flower petal stickies on the bottom of her tub from like the 70s. Every time I see this, I don't know if that resonates for any of you or you're like, yes, my grandmother had that too, or maybe your mom. I don't know, these little flower. Okay, so interesting thing here is that if you look, these are all pointed. There's something going on here, something going on here with all of these points. So we have two stars, which are five points. And then you have a snowflake, which is six points. But yeah, and then even this little flower petal is five and six. I'm feeling like five and six or 56, five and six. Okay, five to six. Okay, they're just saying, okay, they're saying, all right, there's something that you're going to look at or see, maybe you see it now, or you will, that's like in a group of five to six. And I'm also picking up this snowflake thing is very important as far as like uniqueness. I feel like this represents your energy. There's something very special and unique about you and others can see this. Okay, don't think that you are just another donut in the donut box. You know what I mean? Like each one has unique abilities. There's something special and I feel like for some of you, I want to ask you, what is so special about you? What's unique about you? What sets you apart from others? If you're doing any journaling or you're writing your bio or you're trying to figure out, look, I had a conversation the other day and somebody said, yeah, he's, he's gone out there and he's seeking or he's looking for himself or other people are saying like, I'm seeking myself. I'm lost. I'm trying to find myself. Listen, you will never find yourself until you first accept yourself.   Okay, cultivate and work with what you have and build upon that. That's what makes you unique and special. So understand who you are. Okay, you don't have to go out and copy another person, copy what everybody else is doing. You know, be a sheep, be a part of the crowd. Be what is so unique? And if you can't answer that, then, you know, what sets you apart? What makes you because there's something we all are set apart. There's something about you very unique and special. If you're not sure, ask people, ask people who are close to you, what ask them, what, what do you think? Like, if they tell you that you're special, or there's something about like, ask them, what do you see that I'm not seeing, begin identifying and cultivating self and this seahorse, some of you, there might be a connection to seahorses in some way, you know, some of you are males that really want to have babies. You really want to have a child and maybe you never had a child or you wish to have a child at some point in your life, right? And that's just one small message that I'm getting here, but there is some kind of connection to seahorses for you. And if that resonates for you, then obviously that's a message for you. And if it doesn't, don't worry, it's for someone else. But I feel like the strongest message here for Virgo for you singles is really start working on self, you know, whatever that is, persistence, consistency, self discipline, perseverance, success, keep every day, do the grind of whether it's journaling, whether it's your physical health, whether it's like, it's meditating every day, putting things into practice, getting that stuff done. Listen, I got to tell you, if you guys, there's certain some of you here who are like, I've done all that. Where's my person? My answer to you is it's not time yet. There might be something else you need to take a look at, but it's just not time yet. But don't be discouraged. Your time will come.  But you have got to, you might just need to put yourself out there more or get more social. Listen, if you're at the top and you have done every single thing, every single thing that you could possibly do and you haven't met someone yet, it's just a timing thing. And just be patient. Okay. All right. I think that's going to be it. I think that was like your Sunday singles 45 minute plus reading. I hope that that was enjoyable, at least to some degree, or that it helped you in some way. So again, if you want to get a personal reading, there's a link in the description box below this video. Definitely click that link and book a reading with me. You can also join my channel. There's two options there to join. So go check that out if you want to become a member of my channel here. And I think that's it. That's all I got to say. So I'm going to leave your reading. I hope you guys have a wonderful Sunday. Happy birthday, Virgo. Today's your birthday. And I will see you guys tomorrow. All right. Take care.


So first I'll thank the organizers for giving me the opportunity to come and give these lectures. So the title of my lectures was Gravity and Entanglement. And so the context of that is trying to understand gravity quantum mechanically. So this is the major challenge for theoretical physics for the last several decades, trying to understand gravity within the framework of quantum mechanics. And fortunately by now we have at least some examples where we think we have some complete description of theories of quantum gravity. And the examples that I'm talking about are in the ADS-CFT correspondence.  I'll just mention as we go along, I'll mention some of the things that I'll need. It won't be all that much. But the basic idea is that we can define certain theories of quantum gravity starting with non-gravitational quantum systems, just ordinary quantum systems on some fixed spacetime backgrounds. The simplest ones are actually just, they don't have any space at all. They're just quantum mechanics, matrix quantum mechanics models. But mostly I'll be talking about quantum field theories. So some, for example, certain conformal field theories on some fixed spacetime background B. And this actually, it could be Minkowski space or a sphere times time or actually anything you want. But it's fixed. OK, so we consider different states of the CFT on this fixed background. And the idea is through this magical equivalence that Maldesena taught us about, then this theory somehow describes non-perturbatively completely a theory of quantum gravity, first spacetimes with certain asymptotics that are determined by this geometry B and the UV behavior of the field theory. OK, so mostly I'm just going to be talking about ADS CFT where we're actually talking about a CFT. And in that case, the geometries that we're talking about, the states of the quantum gravity theory that we're talking about are asymptotically anti-decider spacetimes. And the boundary geometry of those is the same geometry that the CFT lives on. So let's just mention a few examples. So maybe the most common example would be to think about B to be equal to Minkowski space. And then, for example, if we take the vacuum state of the field theory on Minkowski space, then this is supposed to describe in this dual picture, pure, the state of the gravity theory has a spacetime, which is pure ADS spacetime. If I need to use a specific metric for that, I'll often use this Pfeffermann-Gram description. So I'll write down the metric. So there's some dimensionful parameter that sets the curvature scale of this ADS spacetime. There's a coordinate Z, which starts at zero at the boundary and then increases as you go away from the boundary. And the metric for pure ADS spacetime looks like this, but then you could consider some excited states, so I could add some excitation to the vacuum. And this would correspond to then not just pure ADS, but perhaps pure ADS with some gravity waves in there. I could do something which is a larger excitation, so for example, if I considered a thermal state, so now I think of my field theory at finite temperature, so then there's lots of excitations. It's understood that this would correspond to, again, an asymptotically ADS spacetime but not pure ADS, actually a spacetime that includes a planar black hole. So at some value of Z, we reach a horizon and then we have this black brain. So incidentally, all of these excited spacetimes, we could also describe at least close enough to the boundary in the same gauge where we take Z as some special radial coordinate, and then the difference would be instead of just this Minkowski metric in the directions orthogonal to Z, then we have some general metric. Okay, so the black brain would be some particular choice for this tensor, and other geometries that would correspond to other states would correspond to other choices for that tensor. Another example that will come up, so in understanding quantum gravity, one of the most interesting types of states that we would want to study would be black holes. Okay, so instead of considering the thermal state of a field theory on Minkowski space, we might consider the thermal state of a field theory on a sphere. And, okay, so then it's quite similar to this example, except that now we have a spherical symmetry instead of a planar symmetry, and you end up with a black hole. So you can have an asymptotically ADS space whose boundary is spherical, and if you look at the thermal state of the field theory on the sphere, then you get a black hole geometry as the gravity side of that correspondence. So that was a lightning review of just roughly how ADS CFT works. I mean, the important thing is that you have different states in the field theory. These correspond to different geometries on the gravity side. And this is now, well, 18 years old. But there are many big questions that I think we don't really understand. So these questions are what will motivate many of the things that I'll talk about. So some of the questions would be, well, why does this work at all? How is it that we start by considering some, say, a field theory system? And, okay, so I should mention, I think I mentioned that the field theories for which this works, they tend to have large numbers of degrees of freedom. So if there's a Lagrangian, often at some matrix, field theory, a UN gauge theory where n is very large, or in one plus one dimensions, we would have large central charge. And often these are strongly coupled theories. So they're somewhat difficult to study. But somehow out of this strongly coupled dynamics of large numbers of degrees of freedom, there's some interpretation that emerges, that's equivalent to a spacetime geometry, a classical spacetime geometry. And somehow from the dynamics of this field theory, you end up with the dynamics of gravity. So how and why does this work? How do you get, how does spacetime emerge, how does gravity emerge? One of the things that I probably should have, that you're surely familiar with, but I should mention, these spacetimes are higher dimensional than these ones. So because that's the boundary of this spacetime, really an entire extra dimension has emerged from the physics. And so the recent work that I'm going to be talking about is giving some answers to some of these questions. And it's quite surprising. So there's various recent work that suggests that in order to understand how spacetime emerges here and how gravity emerges, you actually have to think of, so even to understand just the classical level on this side, classical spacetime and Einstein's equations. To understand that, it seems that you have to think about intrinsically quantum mechanical things on this side. And specifically what we are now seeing is that the structure of entanglement, so how different parts of this field theory system are entangled with each other, that seems to be crucial for understanding the spacetime structure or the spacetime geometry. And we'll also see that just various constraints on entanglement, things that quantum information theorists had come up with in just understanding fundamental properties of quantum systems. So these constraints on entanglement seem to be fundamentally related to constraints on spacetime, or in other words, the dynamics of spacetime. Einstein's equations are sort of a constraint on what possible spacetimes that you can have. Okay, so that's roughly an introduction. I'm gonna start by mentioning that all of this recent work, there were actually hints of it starting in the 1970s, okay, so even before ADS CFT, there was this really interesting work in the 1970s where Jacob Beckenstein and then later Hawking and other people started to realize these connections between black hole physics and thermodynamics. Okay, so that's actually going to be intimately related. All this recent work is in a sense a generalization of that. Okay, so let me remind you of some basic statements there. The observation of Beckenstein was that if you consider black hole horizons and you think about the area of those horizons, then the horizon area of these black holes actually has various properties that are quite similar to entropy in thermodynamic systems.  The 4G Newton is for some quantitative reasons, but to get something dimensionless, so the horizon area has the same dimensions as G Newton, and so to get something with the dimensions of entropy, then we have this ratio and the 4 is for some detailed quantitative agreement. So the idea is if you look at this quantity in the context of dynamical gravity, then it obeys various relationships, very similar to laws of thermodynamics. Very similar entropy appears in laws of thermodynamics. So there's a first law that says if you consider some black hole of a certain mass and a certain horizon area, and now we make a perturbation. So we maybe add some matter so that the mass of the black hole increases. Then there's a first law that says that the change in mass is proportional to the change in this horizon area. So that's like the statement that the change in energy is proportional to the change in entropy of the system. What's playing the role of temperature is this quantity called surface gravity, which is related to how much curvature there is at the horizon. And then there's a second law, so in classical general relativity there were results that the area of horizons should only increase with time. If you consider general dynamics or throw things into the black hole, this should be increasing. And again, this sounds like a property of entropy in thermodynamic systems. And so Beckenstein suggested that this horizon area of black holes actually should be interpreted as an entropy of the black hole, an entropy associated with some degrees of freedom of the black hole. By that time, this was very mysterious because we're talking about a classical theory of gravity. It's not really clear what the microscopic degrees of freedom are or how you would count the number of states of a black hole. Okay, but 30 or 40 years later we now have examples of quantum theories of gravity where we talk about black holes. And we know that what he was saying is exactly realized in ADS-CFT, okay? So in ADS-CFT, I mentioned that the black holes, so say a spherical black hole in anti-dissidus space, this corresponds to a thermal state of a conformal field theory on a sphere. Okay, so think about a field theory on a sphere. This has a discrete spectrum of states. Actually, in the previous lecture, there was a discussion of the spectrum of operators in a CFT. And so many of you might know that the spectrum of energy eigenstates for a CFT on a sphere is actually the same. It maps over to the spectrum of local operators in a Euclidean CFT. So there's this discrete spectrum of states and just like any other theory we could consider the thermal ensemble. I'm talking about you, so here we're you, Lorenzian, okay? So this is the CFT on, right? So it's, I'm talking about this example, again, okay? Okay, so it's a black hole in ADS, Lorenzian, CFT on a sphere times time, a thermal ensemble. And so what that means is I'm considering this ensemble of energy eigenstates with probabilities given by the usual Boltzmann. Okay, so when I said before that the thermal state corresponds to the black hole, this is precisely what I mean by the thermal state. This particular mixed state of the quantum system, this ensemble corresponds to the black hole. And now we can understand exactly what's going on. Why does this horizon area on the, on the gravity side have properties that are like entropy? Well, it's because in this fundamental description of the black hole through CFT degrees of freedom we actually have a microscopic theory. And it's true in that theory that the horizon area on the gravity side maps over to the thermodynamic entropy in the CFT side. So in ADS CFT, the statement would be that, yes, this area on the gravity side does have a microscopic interpretation. It's counting some states and it's precisely the usual formula for entropy. So if you take those probabilities given by the Boltzmann factors, then this is the standard formula for entropy. And this corresponds to the area of the black hole horizon. Okay, so, so now if I, if, if I consider, you know, going to a larger black hole, then I'm, I'm, I'm taking this ensemble and I'm changing the temperature and I could tell you exactly how much the entropy changes and just tell you how much the mass changes. And you can just verify all these things. Yes, right, so, yeah, so we can consider more general kinds of, of black holes with charges and so forth. And again, the idea would be that, so if, if I start from, if I start from this one and, and say, add some charge or some spin, then we should still, this type of formula would still be understood to hold in the CFT. And sometimes in the limit of, you know, for certain very special black holes, you have limits where the area goes to zero. And in this case, this is understood as that you're, you're taking a limit where the ensemble of states in the CFT is, is a sort of a small number of states. So that the entropy also would, would go to zero. I should say when, right, sometimes it's important to distinguish these CFTs often have a parameter like the central charge or the N in a gauge theory, often when we're talking about classical things on the gravity side, we are really talking about these being equal to the leading, the leading contributions to the field theory quantities in an expansion and one over the large number. So, so sometimes there could be zero classical area, but then there could still be some small entropy, which is instead of going like N squared or like the central charge, it could go like some smaller power. All right, I'm going to, so that's, that's how we understand this connection between black hole areas and entropies in this modern context of ADS CFT. The entropy of the CFT in the thermal state maps over to the area of the black hole. Yeah, oh, yeah, wait, so not talking about entanglement entropy yet. This is just thermal entropy. Yeah, this is ordinary entropy, yeah, but that's the next thing. So I'm going to jump right to the most important, the most important formula or development in, in the recent, in all this recent work. So there's a generalization of this. So 35 years after this, this work in the context of ADS CFT, it was understood that there's an amazing and massive generalization of this connection where instead of just considering thermal states, we can consider any state of the CFT that would have some kind of arbitrary gravity dual, so it, it could be not just a black hole, but any kind of, any kind of space time, even, even empty space. Okay, so we're going to generalize to the case where the CFT is in some much more general state. And we're going to generalize to the case where we're talking about the entropy, not of the entire CFT, but of an arbitrary subsystem of the CFT. And then what these guys Ryu and Takiyanagi did was to say that, that much more general kind of entropy, so the entropy of a sub, an arbitrary subsystem of an arbitrary state. They said that also has a geometrical interpretation as some kind of area in the, okay, so, so now this is an arbitrary state. We consider some arbitrary region. And here's the dual, okay, dual space time. And this entropy has some interpretation as some kind of an area in the dual space time. But I have to, I'm going to, I'm going to wait a little bit. I have to tell you more about what I mean by the entropy of a subsystem. So we need to understand that better and, and then we'll understand exactly what the statement is. But this is, you can think of this as just, you know, one, one particular tiny example of this much more general statement, which has kind of opened the door for a huge leap in our understanding of, of this ADS CFT correspondence. Yeah, well, it's, yeah, I'm going to, I'm going to talk a lot more about this. But so far just think of, there doesn't have to be a double. It's just a mixed state. We can talk about entanglements without actually purifying. But, okay, so I want to review what, what do I mean by subsystem entropy? So people, by the way, people talk a lot about entanglement entropy. It's really just the entropy of a subsystem. It's not, it's not a diff, it's the same notion of entropy, but just applied to subsystems of general quantum systems. So that's what I want to remind you of now. So the context of this is that I want to say, consider any quantum system with, with multiple parts. Okay, so I consider a quantum system where the Hilbert space factorizes into a tensor product. So this would always be the case if I have individual, like, different degrees of freedom. If I, if I can isolate some, some degrees of freedom, which are a subset of the whole system, then according to general rules of quantum mechanics, the Hilbert space has this tensor product structure. And we're going to consider a subsystem, I'll call it A, of a quantum mechanical system. And so we'd ask the question, if we have a state of the whole system, let's say we have some general state of the entire quantum system. What is the state? How do we describe the state of just the subsystem? We're only interested in, say, expectation values of operators that act on the subsystem. What is, what is the description? What is the most efficient description of just the subsystem where I don't have to worry about the entire state? And, you know, in the classical world, we just say, well, okay, this is the configuration of sub, of the A part. This is the configuration of the B part. In the quantum world, it's not possible. There's no, there's no state psi A, which reproduces all the expectation values for that subsystem, starting from some general state. So what you need to do is actually consider an ensemble. So, okay, so there's no, well, let me just write down the statement. So the state of the subsystem is an ensemble of pure states. So if I consider all of the operators O, A acting on that subsystem, and I wanted to try to find a state psi A such that the expectation value of O in psi is equal to the expectation value of this full operator in the full system, then I would not be able to find it in general. Okay, but what I can always do is find some ensemble, some set of states of the subsystem, and some probabilities so that, so that this is true. Okay, so I can always find, I can always find an ensemble of states where the calculation of the expectation value in the ensemble, according to these usual rules, would reproduce the calculation of that expectation value in the full state that I started with. I'll tell you. Yeah, so I'll just write it down explicitly. So the question is, how do I write down this ensemble? And so this is the procedure. You start with a system, the state of the original system, you can write in terms of the basis elements of the tensor product and then you calculate what people call the reduced density matrix. Okay, so I'm going to write down now an operator on the subsystem A, which is people describe this mathematical operation as tracing over A bar or the partial trace over the subsystem, the complement of A. Okay, so I can take these coefficients, I can just write down this operator and then you can always diagonalize this operator. So it's Hermitian. I can always diagonalize it so I can write it in this form. And then the ensemble that I'm talking about is actually just this one. Okay, so it's probably more familiar to you to say, the state of a subsystem is described by this reduced density matrix, which I get by this procedure of tracing out the rest of the system. But I want to emphasize that when we talk about density matrices, we're really talking about, it's equivalent to be talking about ensembles, just sets of pure states with certain eigenvalues, with certain classical probabilities for being in those states. Okay, so in particular this calculation that I did over here, where you calculate the ensemble average of this operator, this is the same as just taking trace of row A times OA. So this is the more familiar thing. Take the density matrix and evaluate the trace of the density matrix times the operator. Okay, so given any quantum system, you choose a subsystem and you can always either calculate the density matrix or find this ensemble of states, which completely captures the state of the subsystem. Now in very special cases, you might just find a single state with probability one. So that would be if the subsystem is itself in a pure state. But in general, the set of these probabilities is not just the set one. There are multiple probabilities. And this is the definition of what it means for something to be entangled. So when you have your subsystem and you find the ensemble of states that describes it, and it's not just a single state, if it's actually a number of states with probabilities less than one, this is what we mean by saying that A is entangled with the rest of the system. So A and A bar are entangled. The fact that you have these probabilities, where it's not just one and zeros, in the thermodynamics context, we would say that's saying that we have some classical uncertainty about what the state is. So there exists classical uncertainty about the state of A. And so then we're back to the situation, exactly the same situation that we have in the thermal ensemble. When we talk about the thermal ensemble, you have a set of energy eigenstates, and you have a set of probabilities for those eigenstates. And when we talk about the thermal state, you compute expectation values exactly by this procedure. In that case, we quantified the uncertainty, the classical uncertainty about the state by using entropy. So in this case also, when we realize that our subsystem is now not defined by a specific state, but actually by an ensemble of states with these probabilities, then again it's useful to characterize, to quantify this uncertainty. Are we very close to this case where you have a pure state describing the subsystem, or do we have a large amount of uncertainty? So being entangled is not, you could be very entangled, or just a little bit entangled, you could have just a little bit of classical uncertainty about which state your subsystem is in, or a lot. And we quantify that by entropy. So quantify. And it's exactly the same formula as I wrote down before. This is the formula for entropy. It works just as well for these general ensembles as it does for the thermal ensemble. In the quantum context, we can write down an equivalent formula in terms of the density matrix that I guess was written by von Neumann. So sometimes you'll see this as a formula for entropy, but it's the same as this, and it's the same as the usual formula for entropy. So this is just the ensemble describing the subsystem. What is the entropy of that ensemble? And it's called entanglement entropy, but it's not really any different than the other entropies that we talk about. It's the same definition. And so this is really the same quantity that we're talking about. And this I think motivates more this Ryu and Takenagi formula that we're going to write down later, that if the entropy of the whole CFT corresponds to some geometrical quantity, the area of the black hole horizon, and now we look at the entropy of just a part of the CFT, well maybe that should also correspond to some similar quantity. So summary. If you start from the state of a whole system, you can define this density matrix or this ensemble, and then you can characterize how much classical uncertainty there is using this entanglement entropy. But there are actually a few other quantities that come up. This is one very useful combination of the set of probabilities that characterize the ensemble. But sometimes we're interested in more detailed information. So if we have a thermal system and we calculate the entropy, I could find another system which is not thermal, which has exactly the same entropy. I could have a different distribution of probabilities. Or I could have the canonical versus the micro-canonical ensemble, and I could find two ensembles with the same entropy, but they could be different. So sometimes you want to look at in more detail how do you characterize what are these probabilities. And so just the set of probabilities in this entanglement context is called the entanglement spectrum. And then the other thing you'll hear about are some other combinations of all of the eigenvalues. So this is the entanglement entropy, but in the literature often you hear about Renye entropies. So this is a quantity that you can compute from trace of the density matrix to the nth power, or the alpha power. So if I have a density matrix, the trace is always one, but if I take some power of it and then I take the trace, well this is some quantity which is given by the sum over the probabilities raised to that power. And then this particular, if you take the log of that and divide by one minus alpha, this defines the Renye entropy. The reason for all of this is that if you take alpha to one, then you get the entanglement entropy. So if you take a limit. So in some, in a lot of context, the main reason why people talk about these ones is that in a lot of contexts it's easier to calculate these Renye entropies. And so if you can calculate these and find some analytic formula as a function of alpha, often you can calculate it for integer alpha, but if you can find an analytic formula, then you can take the limit where alpha goes to one, and this gives you a way to calculate entanglement entropies. So we've talked about going from a big system and describing the state of a subsystem, but you can also think about going the other way. So say you start from a density matrix. So given rho, we can ask is there a state, is there a larger system, and can I find a pure state of a larger system where the state of the subsystem is rho? Yes. So if, yeah, I mean it's considered to be some more generalized measure of entanglement. You see that if all of the probability, if there's just one P and it's one, I guess you get zero, it's more of a formal quantity, but it's often described as a more general measure of entanglement. It doesn't have some of the nice properties that entropy in general has, but so I'm not sure if it has a really nice direct interpretation. It's more used as a calculational tool, but I guess you can consider it, I mean you can consider anything that you build from these probabilities as some measure of entanglement, because if it's not entangled, then it's just one, zero, zero, zero. So any other quantity that you compute from those probabilities, it's sort of some measure that will tell you are you entangled or you're not entangled. Okay, so given a density matrix rho, we can go the other way and try to find what are called purifications of rho. So generally, I can describe the most general purification. So say I start with a Hilbert space for a system. So what I can do is take some other Hilbert space, I can consider this tensor product, and then starting with my ensemble, I'm assuming these are orthogonal. So if I take another Hilbert space whose dimension is at least as large, then I can write down the following state. So I choose some orthogonal states in the other Hilbert space. So again, these are orthogonal. So I need a dimension of the other Hilbert space to be at least as large as the number of states. Appearing in my ensemble. And then I can write down this state. So this is a state in the larger Hilbert space. And it turns out that any purification can be described in this way. So anytime where you have a state in a big Hilbert space and you find that the state of a subsystem is equal to this, then the whole state you can write in this way. You can always find sort of orthogonal states in the two subsystems where I can write the full state as this kind of the superposition of the product states. So you can check if you start with this one and then you calculate the density matrix using the procedure that I described. Remember I had these coefficients c and then we had the c and the c dagger. So the square root of p will appear twice and then we'll end up with just getting the p i and the states appearing. So you can check that starting from this state calculating the density matrix and getting the ensemble you get exactly this. So this is sort of the general way you can go from a density matrix to a pure state of a larger system. This particular way of writing it is known as the Schmidt decomposition and you can prove that it's always possible to do that. So not... Actually generally not unique. So once I fix the larger space I'm actually able to choose any orthogonal say I have 12 different states appearing in the ensemble. Just choose any 12 orthogonal orthonormal states here and it gives you a purification. So it's very nonunique actually. One of the interesting things that you realize though an interesting thing is if you were to consider the other part of the system so instead of looking at A look at B and calculate the entanglement entropy or the spectrum of the density matrix for B you're going to get the same answer. So this formula is completely symmetrical between A and B. If I find a purification and I say what is the entanglement spectrum for the B subsystem what is the entanglement entropy for the complement it's exactly the same. So it implies row A and row B have the same... row A and row B have the same entanglement spectrum the same entanglement entropy and so forth. So that will come up later. It's a little bit counter-intuitive. Yes, that's a really good question. So I was going to talk about that specifically. Let me postpone the answer to that. But just for two minutes I'll postpone the answer to that question. So let me just do an example. If you take the thermal state so you have some general thermodynamic system in the thermal state with temperature T well we actually often think about a purification of that when you're learning about thermodynamics or statistical mechanics you say the thermal state is really the state where you have your system and you have it coupled weekly to a heat bath. And then you say the whole system is in some pure state and we have if you just consider the subsystem then it's in this canonical ensemble or this thermal ensemble. So in that context we think about the purification as being the pure state of the system plus. And in that context also the thermal entropy of the subsystem is the entanglement entropy between the system and the bath. So the thermal. So again this entanglement entropy is considered all the time when you were thinking about thermodynamic systems as systems coupled weekly to a heat bath. Okay yeah I should hat or something. So yeah the well oh so good B could be much larger but I've only chosen I'm only summing over the non-zero probabilities. So I guess I should say PI is not equal to zero. It's a special case of this purification that comes up a lot in these discussions. So one nice choice that I can make which is rather different here we normally assume that the heat bath is a much larger system but if I want to I can write down a purification where the other system is exactly the same system. So if I take B equal to A and I take the state of the combined system as this is for a thermal state instead of considering a big heat bath I'm going to write a purification where the other system is exactly the same and I choose these states to be exactly the same as these states so then I've defined this state where I have the square roots of the Boltzmann factors and it's symmetrical between the two sides so this is called the thermo-field this is called the thermo-field double so this is an example where you start with a thermal state and choose a particular purification where the other one is this the B system is the same as the A system actually when do I start do I have five minutes? okay so in the last five minutes what I want to do is go back to ADS CFT now answer your question and motivate what I'll do in the next lecture this afternoon okay so back to ADS CFT so I said earlier that the CFT in a thermal state on a sphere is equal to is dual to the black hole and that the entropy is equal to the horizon area but I wasn't very precise when we talk about black holes in general relativity there's the part of the black hole outside the horizon I'll draw these conformal diagrams so in ADS that corresponds to this so there's a part of black hole outside the horizon but then you can sometimes extend the geometry past the horizon so you can do that and actually maximally extend it there's a canonical way to do that and you find that there's this two-sided black hole that has a Schwarzschild geometry on the outside in both sides and two different asymptotic regions in ADS this would be asymptotically ADS with some spherical boundary this side is asymptotically ADS with some spherical boundary if I look at a time slice through that it looks like this wormhole geometry with two asymptotically ADS regions so when we talk about the thermal state what is it dual to is it dual to this or is it dual to the whole thing it's not totally clear but Maldesino wrote a paper in 2001 with a specific proposal that ties into what we were just talking about so Maldesino said the maximally extended black hole because it has these two asymptotic regions and therefore two different boundaries which are spheres he said that should correspond to something which is not just one CFT but actually two different CFTs and in this in the case where we're talking about a thermal state of a CFT we just realize there's a canonical system and state where you start from a thermal state you double it you double the whole system and you write down this symmetrical state so there's this very natural thing from the point of view of quantum mechanics where it's a symmetrical system with two copies of your original system and each side looks the same just like this extended black hole from the geometrical prescription so Maldesino said conjectured that this thing was dual to the thermo-field double and I'm just drawing the spatial this is the spatial slice and he says this is dual to this specific state where you take two CFTs which are not interacting at all with different systems except you put them into this particular state and this hints at something really dramatic what we've really done in the context of what I've been talking about the rest of the lecture is we've taken two different systems and we've just entangled them in this particular way so I took two completely different CFTs just two copies of the same thing no interactions the only connection at all that says that those are related in any way is that we've added we've gone into this thermo-field double state which is a particular purification of the thermal state on one side so it's entangled between the one side and the other side in this symmetrical way and apparently doing this entangling on the gravity side according to Maldesino what it's done is it's taken your two empty ADS space times that you might have thought you had if you had to say the vacuum state of those two CFTs and it's provided some kind of connection geometrically between those this wormhole going from one side to the other okay and so this is I think the first suggestion that and this was before we were attacking everything this is a suggestion that somehow entanglement just by adding this entanglement you've connected the two sides up and the next lecture I want to argue that even in the context where you just have one CFT we'll see that entanglement between different parts of that CFT is kind of intimately related you might say it's the reason why you have some connected space time that's emerging as the gravity dual okay but we'll get to all of the details in the next lecture


Okay, good morning, exciting session. And I'd like to acknowledge my collaborators in this work. It's led by Adeline Bichet, who you hear from in, I guess, tomorrow. And other collaborators include Lawrence Moudric, who is working with me at the University of Toronto, Leontanet and John Fife. So this is work that I think dovetails nicely with Matt's talk to some extent. And I'd like to kind of go over what is really kind of a simulation protocol, and we're just, we're developing it now. This is work in progress. And so over the course of the talk, I will talk about the use of prescribed SSTs, AMIP type simulations, to predict continental hydroclimate trends, and a pattern scaling-based method that we've developed that we're still working on, that we'd like feedback on to extract the force component of climate change, the long-term global warming. And I'm gonna show you some applications on past recent climate trends, and Adeline will share with you some results related to projected climate. Okay, whoops. That seems, that seems rather, rather abrupt. Yeah, all right. All right, so to start with, I just wanted to take us back to a basic point that if you feed an atmospheric general circulation model, observed oceanic boundary conditions, so observed SSTs, and also throw in sea ice as well, that you can do a very good job at reproducing trends that have been observed over the continental region. So this is a figure taken from a paper by Shun and Sardish Mook showing in the top panel observed temperature trends over land in the second half of the 20th century. And then the ensemble mean from several AMIP simulations where all SSTs are prescribed globally from the CMIP3 generation of models, but these are atmospheric GCMs. So if you, and you can also get the same kind of result or at least part of it if you prescribe just tropical SSTs. So a way to quantify that is using a Taylor diagram, which we're introducing in the last talk, but so a Taylor diagram shows the, on the polar angle here indicates the degree of correlation with some target. So the target here is observed land surface temperature trends, the pattern of that and this is, these are three observational estimates. So the target here is the mean of these three observational estimates.  So this is the CMIP3 generation of models. In green as well, there's ones in which only the tropical SSTs have been prescribed. But if you look at coupled models, you can see that a couple of models over the same period have had a really difficult time at reproducing the pattern of observed trends. And so there's no, this is kind of a ruling out internal variability to some extent as a cause of this disagreement because none of the coupled models from that period were really able to capture it to the extent that any of the ones with prescribed global SSTs. So because of that connection, we know that there's a lot of useful information in the ocean for continental climate. And the dynamical causes as Matt was saying, I'd say it's unclear to me, but I think if you take a long enough time history of ocean SSTs, you can get kind of good agreement with OBS over land. So exploiting that connection is an interesting idea, I think, and so what we're trying to understand is whether we can get additional insight from the observed history of SSTs. Okay, so one of the challenges in this and then one of the interesting points is to try to separate out internal and short-term variability that's driven by anthropogenic forcing from a long-term trend. So what I'm gonna explore here today are two questions about whether we can estimate the long-term variability associated with the global warming, so just taking the global radiative forcing as kind of a target, try to extract that from observations, and then whether we can use that information to gain insight into past trends and maybe use it to predict the force component of climate change in the future. So our method here, it's a somewhat complicated slide, but basically the idea is pattern scaling. So in the top equation here, what we do is we take an SST field or a sea ice field and we decompose it notionally into a long-term, slowly varying part which we call GW for global warming and a short-term part which could include internal variability and also any response to short-term forcing such as anthropogenic aerosols, volcanoes, and ozone, for example, ozone-depleting substances. And the very simple idea here, the simplest idea is that there's a stationary pattern which we call H as a function of X and that stationary pattern is scaled by the global mean temperature, an estimate which we call GFT. And you can make various choices in how to carry out these estimates and I'll show some evidence that we're on the right track, but basically we've done two things and in a publication that's out in Journal of Climate, we estimated GFT from observations, from a long-term observation, SST observations, so that's the global mean surface temperature and in the recent work we're actually using the estimate from CMIT five because we're going into the future. And H of X is just a simple regression, basically a trend pattern that's taken from your observational data set of choice. So in the previous work, we looked at the sensitivity of our results to various estimates of this global mean surface temperature, but basically we hit on a simple, slowly varying, slightly non-linear trend that goes through the global mean SSTs and that's what we're calling GFT. So in this sense, H of X, which is the pattern of SST and CIS is the regression of this curve on observations, its projection. So I claim that this is actually a method that we can quantify to some extent how well we're doing. And what we do is we turn to a large initial condition ensembles. We have a few of those at our disposal to test the idea of whether we are actually extracting the long-term force component of climate change. So we have the ensemble mean of a large initial condition ensemble to use as a kind of filtering of internal variability. And from that, we can compare the patterns of H of X from that ensemble mean to the individual H of X that we get from this method. And this shows the pattern correlation. It's one test we've applied is the pattern correlation between individual H of X is extracted in this model setting to the ensemble mean. And this is testing the sensitivity to model types. So we do it here over a 45 year period with CCSM-4, with CES-M1, the next generation model. Then we extend the period here and you can see that as you increase the period, not surprisingly, you get a better agreement between the estimate and the final result. And we've done a bit more of this in a more recent work where we've extended the period further to 2012. We've done some other adjustments to the method. So we have a sense now that we can capture about 70% of the observed pattern if we believe that there is some correspondence between the coupled model test bed and observations. However, we're not using the coupled model for those patterns. I just wanna emphasize that, that the pattern is coming from observations. Is that clear, by the way? I don't wanna, because this is important. If you don't, it's important to kind of understand it at this stage, all right. So what we actually get then is shown, the most important result I think is shown on the right. So on the left, I'm showing 30 year trends of sea surface temperatures from the recent period, 1980 to 2010, okay? And on the right, I'm showing the, what we're calling SGW, okay? It's a global warming pattern. And this is the long-term trend, basically, in SSTs, predominantly warming, smoother. There's no AMO, there's no PDO signal. It's just taking the 70, the long-term record, this is from the Hurl SSTs. So you might ask what happens when you vary SST data sets, but this is what we're using for convenience for now. And a lot of the structure that we associate with internal modes of variability or with short-term responses to short-lived forces is smoothed out, okay? So we think that this is an interesting pattern. It's a much broader pattern. There's much less structure in the tropical Pacific. And we wanna use this to drive AGCMs and see what happens. So before I show you that, this is the similar pattern from sea ice, okay? So we take the sea ice product that's contained in the Hurl data set, which is conveniently in our model. We're using the NCARA-CAM model, and so this is easy to do. So this is the sea ice that's coherent with that pattern-scaled, so with that scaling factor G of T. And you see that the recent, large sea ice loss that's seen in different seasons, particularly in the summer, Arctic summer, is reduced if you just draw basically a long-term trend line through that rapid sea ice loss. So that's what we're using to force the sea ice in this model. Okay, so now we're gonna apply and practice this pattern of warming and this pattern of sea ice loss. In CAM-5, we run a course resolution, two-degree model. We've done 10 ensembles of two types, okay? So these are 30-year runs. We have an AMIP run, which is observed SSTs, the time-varying history of the SSTs in sea ice. And then we set of runs we call GW, which is our estimate of the forced SST change. And we're using that to force the full AGCM. And we're looking out over the continents at what's happening there. Okay, and so what I'm gonna show you is a few results from these simulations. And we're looking at, we're cherry picking here. We're looking for variables and seasons where there's agreement between the AMIP runs and the observations. And so AMIP runs are not guaranteed to reproduce observations in all cases. So we're gonna focus on those regions. And also, none of the trends we find in these short runs, the 30 years, most of them tend to be insignificant because we tend to focus on mid-latitudes, although I'll show you one tropical result. But if we do these runs over and over again, we find that we often get consistent responses. So in regions that are not shaded in gray and the figures that follow, that means that we have 10 runs and the signal-to-noise in those runs represent it, which is the ratio of the response to the standard deviation of the 10 members is greater than one. Okay, so I'll start with surface temperature. Always a nice reliable field to start with. So this is wintertime surface temperature trends from CRU, from these AMIP runs that we've done and from the global warming pattern we've imposed. So what's interesting to us here is the correspondence between AMIP and CRU. And it looks like the AMIP runs are getting a pretty good match in several of the features to what we've seen in observations. This is not too observationally dependent or observation set dependent. And what you see, a pattern of warming, cooling over Northwestern North America, warming here in the Southeast in the winter. And in this GW run, we're seeing basically that this cooling spot is removed. So this has been reasonably attributed to the PDO trend that I showed in a previous slide. And this GW run helps quantify that. And then in this warming run, you see the warming has shifted into the central Eurasia from where it's been observed more or less. And so we can attribute some of this to internal variability, to the PDO variations. And then of course, cause and effect is hard to get out of these runs, but it is a kind of, I think it does give us insight into a separate part. What you can attribute to short-term variability versus to the long-term inexorable kind of warming that's been going on. Okay, now we're focusing on winter precipitation. This project has actually been largely funded by a Canadian network called CanSICE, where we focus on snow and sea ice variability and modeling in the Canadian setting. And so I'm gonna show you a couple of figures related to that. This is wintertime precipitation, okay? And I think the AMIP runs actually here do a pretty nice job of capturing what we're seeing in observations. And so there, you can get a sense that we can attribute the recent trends to the SSTs, SST variability. And the global warming run that shows very, very weak trends over this period. And there's a little bit of drying that's seen in the west coast of North America. And so the difference here is really highlighting that. So much of what we're saying here is that much of these trends are represent the result of short-term forcing and internal variability. This is a picture of a snow cover fraction. As I said, CanSICE is really focused on that. And so up here, I'm showing a couple of observational estimates of recent trends in snow cover, which is highly observationally uncertain. This is a satellite data simulation-based estimate called globe snow. This is the mirror reanalysis. And you can see there's quite a difference in the pattern. So it's worth showing this before I show you any results from our simulations. So I know there's a lot more gray shading here indicating that there's less agreement among the models as to exactly how the snow cover fraction will respond to these changes. However, what you see is that there's this reduction of snow retreat over Scandinavia, Northern Europe, over this marginal area here. And some of that is also found in the same global warming run. So we can attribute much of this pattern to what is an externally forced signal. And the residual shown here is kind of a very noisy pattern. Now I'm gonna switch, this is a sort of final results slide. This is a global, these are global simulations, and I thought it would be worth sharing this results as well. So if we look over Africa, which is an region, so this is summertime Africa in precipitation, okay? So July, August, September. This recent recovery of precipitation that's been observed over the Sahel is really captured well in the same upfront, which is certainly something that's been seen before. And I think just for, as a point of information, when we put in this global warming pattern in which there's no AMV signal, there's no PDO signal, this is the response over that 30 year period to just that broad warming of SSTs. And we see a drawing in West Africa, okay? And the difference between these patterns is showing you the result of how internal variability and short-term forcing might be compensating what's going on over the very long term with global warming. Okay, so I'm gonna summarize, I'm gonna show you one more slide, and then I'll conclude. So we've tested and extended it, I didn't give credit here to where it was due to, it was an idea that was proposed by Hurling and Hurl and Terrain and others to actually do this as a method of climate prediction in the near term to predict the force component of climate change using this kind of pattern scaling method. And so we thought to test this method first, and we have a couple of papers that we're working on with that. And so what I've tried to show you is that we have a reasonable confidence that we can actually estimate this pattern from observations given a 70 year record of SSTs, we can do a reasonable job. It's a very broad pattern, so we might not need a lot of spatial detail to get the general idea. And it seems like there's a good evidence that what we're seeing in North America, there's a lot of the precipitation changes are related to PDO variability, and that we can also apply this to other regions such as Sub-Saharan Africa, where we're seeing a global warming signal that's counter to the recent trends. A question that you might ask is, well, why didn't we use coupled models to do this? Okay, and it goes back to a point I showed earlier indirectly. Okay, if we try to estimate H of X from coupled models, this is kind of an unsolvable mean of what we tend to find, but we tend to find that, this is H of X estimated directly from Seaman 5, and we tend to get a lot more tropical warming and also a lot of North Atlantic warming that we don't see when we do the same estimate and observation. So the difference between these patterns suggests that we should at least try to do this with observations. And so the idea of near term projection with this is to persist this pattern into the future, and that's what Adeline will be talking about tomorrow. Okay, so the key points are that we can reliably estimate the observed pattern of long-term sea surface temperature response to radiative forcing from global warming. This pattern allows us to attribute the related component of past hydric climate trends, and we're able to use this for future projections, and we're still working on those results. And it's really different from what you'd get if you did the same exercise in current coupled models. So I would just argue that there's a lot to be gained on understanding forced decadal climate variability from looking at existing SST observations. Thank you.


So people, we have something amazing today. The reveal of the DLC4's trailer. Now I won't hold you back in watching this thing, hit that like button and let's check this thing out. People, this is DLC4, Cyclocreague and Fantastic Foster Clock. Now how's it going guys, my name's DPJ and today I bring you another BL3 video. If you do enjoy living a life, really helps out and subscribe if you do want to see more. So how amazing was that trailer people? Doesn't it look just great? Now I have a few more details on this DLC and what it's all going to be about so let's check those out. So the DLC drops September 10th, which is literally right around the corner, not far away at all. And what else will this DLC offer? What will we venture into? Well a small description we have is, Cyclocreague and Fantastic Foster Clock dares to ask, what makes the BL3 of Borderlands so uniformly deranged?  So naturally Tannis is sending new unemission into Krieg's chaotic mind in search of clues. Only by surviving the perils of Krieg's twisted inner world can you reap the rewards of Vault Halla. Help both sides of Krieg's dual-psych process his traumatic memories by blasting his inner demons to bits and try not to succumb to lunacy inside Krieg's fractured mindscapes as you journey through the many demented vistas of Krieg's psych where anything is possible and likely very violent. Experience the world as Krieg sees it including his perception of fan-favourite characters like Maia, the light of his twisted life. Overcome a vast array of life-threatening manifestations that Krieg's mind conjures up. Expand Krieg's mind and Tannis' research in surreal side missions and crew challenges. Score power for legendary weapons and gear that will still work outside of Krieg's consciousness according to Tannis that is. A quite a brain-busting cosmetic item including Vault Hunter heads and skins. But people the details on what comes as DLC doesn't end there. We also get a new level cap increase with going up to 65. Five more extra levels are being added on September 10th with this DLC and Gear Bucks do state this will be the final increase for the foreseeable future. So actually I think we have some amazing times ahead. Now this DLC and what it stands for is really something I predicted a while back and knew we wouldn't get Krieg back as a playable character although that would be amazing. I just knew wouldn't happen I said in the past I actually feel this DLC would be on the basis of us playing out his memories. Now although this isn't an exact description of what we see it is along the lines as we go deep within Krieg's mind and experience what life as a psycho was all about. Now I know we saw Maia within their trailer but yeah she isn't back I don't believe she is a part of Krieg's mind and we will meet Maia again but Krieg's perception of her which will be pretty epic. I also don't think she'll be the only character we've come across within the mind of Krieg which will be interesting as these characters will be portrayed as Krieg himself sees them which could be hilarious and terrifying at the same time. Also I wonder who the main story bus will be will it be Krieg himself or the giant version we see within this trailer kind of makes sense if you ask me but yeah this is a DLC I'm super looking forward to Krieg was by far my favorite character up until Zane so it's going to be an amazing DLC an amazing addition to having back and to actually see where this next venture leads and in general learning more about him so what do you think about this DLC what do you think about the trailer and what do you think this DLC will behold let me know down below within that comment section are you hyped like I am because I am super looking forward to this Krieg like I said it was my favorite character before Zane I know he's a fan favorite across the board a lot of people in the Borderlands community absolutely love this dude and are super hyped about him coming back so let me know your thoughts down below within that comment section but I know guys we have come to the end of the video this has been the review trailer of DLC 4 for Borderlands 3 so called Krieg and a fantastic foster clock guys I hope you enjoyed the video if you did leave a like really helps out if you're new around here want to see more BR3 be sure to subscribe and if you never want to miss a video upload you can turn notifications on by hitting that bell button but guys thanks as always for stopping by hopefully you enjoyed the video and hopefully I will see you on that next one


if someone say accused someone of sexual assault, you would have to discredit their claim. Do you agree there's a difference between saying, I got a pet puppy and I got a pet fire breathing dragon? Yeah, there's a difference.  You would essentially have to discredit all history, by the way. If you actually don't think claims are true, then you would have to discredit history. The moon splitting in two is not in a history book. It's not verifiable. It's not scientific. It's not supported by any evidence. It's just a claim. And the claims aren't in and of themselves sufficient to believe the claim.