is Lucy and I, Lucy Ricks is my guest. And just as I was gonna push the button, go live, my phone rang, and Lucy's co-collaborator for the book. Here's the book, gotta put it up here. 50 years of miracle, Jason called in and I thought, oh, this is very, very synchronistic. So welcome Lucy and welcome Jason. Thank you. Very nice. I like it spontaneous. So I had talked with Lucy last week about having your on just because I thought this book was, was such a fantastic expression of parables and many of us relate to the parables. But before I get into the full interview with Lucy, what do you have to say for yourself, Jason? Lucy first proposed this book to me. I thought it was a great idea. I didn't know, like many things that are sponsored by the spirit that actually meld a long time community member a while back actually had written and saved hundreds of parables as if the book had already been written. And so just in our collaboration, it was almost like Francis had heard with the movie. I'm just gonna step outside here. Francis had heard with the movie, it's already done. That, yeah, this would be very, very simple. And then as I was reading these parables, you know, I've heard you speak David over the years, all these parables and sometimes I think, okay, I've heard that one before, but I heard all of these in such a fresh way that I was so inspired every morning to just get up and read a parable or two or even at night because something about it being written in this way. I don't know, it was just really inspiring for me. Beautiful. Wow, I'm just glad that you were inspired and I felt inspired. That's how they seem to all come because I was just following my happiness and my joy. And I remember at the beginning, I did say to Jesus, I said, am I gonna have to come up with parables? Cause I don't know if I can. I don't know if I'm a good parable writer and Jesus laughed and Jesus told me, don't worry, you just live your life in an inspired way and there'll be plenty of parables. You don't have to worry about making them up or generating them. So that's kind of the way it went. So, well, Jason, thank you so much for playing your part and also for this spontaneous call. Just as I literally had my finger onto the go live button and that's when you called in. So I know you want to talk to me about maybe a few other things.  That's good, I guess. Thank you. It's so nice to see you, Jason. Love you. Love you. Beautiful. So blessed. That is amazing. Well, that is kind of a good lead in because yeah, Francis was just talking yesterday at the online retreat about how she felt that she was told by Jesus that she would be making a movie and she said when and basically Jesus told her it was already done and then basically the question that she had was to Jesus, well, how will I know when it's supposed to start? And he said when the film team shows up and then when the film team showed up, that was basically at the beginning of a mystery school, a month long mystery school and that's when the whole most of the movie got shot there and then I did have a beautiful idea and inspiration that I knew Francis and her partner J.P. wanted to go to Iceland. So I told him there was a contest where they could enter wow airlines contest to put a blog out and do some posts and everything. And if they won the grand prize they would have an all expense paid trip to Iceland.  And on the way back, Francis said I had a mystical experience in the plane on the way back from Iceland and it was all everything was worth it just that mystical experience. So maybe we can talk. Maybe you can just share a little bit about your healing journey kind of leading up to your encounter with the Course in Miracles and then the beat goes on collaborating to pull together the parables in this book. And then I know it wasn't too long ago Kenneth Clifford and Anna Paola came up I saw these beautiful smiley happy faces on Facebook.  So just tell us about your healing journey. It's hard to know sometimes where to start because where do I jump in on this? Yeah, it really does. I think the whole thing so quantum it doesn't really matter where I start. So I could say the Course came into my life at a point where I was really at my lowest, like desperate, like I finally got what I thought I always wanted, the special relationship and it went from, I don't know I thought we was walking off into the sunset and but it turned out to be the flames of hell. I was, I think I'd ran away at this point because the relationship got very violent and confusing and I just didn't really know what to do. I was at my mom's, I think at the time and I was, I just read another book which was very fearful. It was about how to run away, how to escape all these things steps you've got to take to get out of a situation. And I was like, there's got to be a better way. And in my mind, I heard a Course in Miracles, like very clearly. And I'd heard of the Course many years before that I was very into self-help books and all this sort of thing. And I always used to read the bibliographies at the end of books, just to see what else I could read. Excuse me. And so many of them referenced a Course in Miracles it must have kind of got lodged in the back of my mind. And so I heard a Course in Miracles and I had a Kindle, one of those Kindle tablets at the time. So within like a couple of minutes I downloaded the course onto this Kindle and it started, I think it skipped a lot of the beginning just started right at the introduction. So I had no context at all about how it came or anything like that. And I started reading and it was like I recognized Jesus' voice and it was just, I kept saying, it's a shoe. It's a shoe. It sounds like you. And then finally, something definite happened. I think he was talking about the crucifixion or something. I was like, it is you. And then it kind of like reeled back in time all the books I'd read that had that same voice in. I mean, there was many like, because I read all kinds of books, even Harry Potter is like, I heard your voice in so many places before. And so I began reading and reading and reading. And I also didn't know how long it was. So it was going on and on. And it was like, it had immediate effect in the, it was like I had a choice between this fearful perspective which was also true according to how my mind was at the time, very logical. And then there was this course in Miracles and it was like I made a choice to do the course. And it just had an immediate effect. Like something inside started to like stare and like it was like getting my best friend back really like, when I was a little girl, I used to be, I was quite a little miracle worker. I started off good, very close to Jesus. And I was just doing my little miracles and all this. And then like I was about seven, I decided I wanted to be cool, you know, and it was not cool at that time in my school to be in my mind to be a Christian and all this. So I was like, right, Jesus, isn't in the playground. I was like, I can't be your friend anymore. You know, like maybe one day I'll come back and like I'll carry on. And in my little girl mind, I thought he actually went away. It just sort of like up and down our like for many years. And then I think I was about 18 where I had to, it was like, I was with a group of friends and we had, we started talking about God and we all had this like joint mystical experience together. And that ended up becoming a rasta for a few years. Like I found a lot of teachings in the reggae music which was very biblical at the time, you know. And like the philosophy of I and I, meaning like the oneness, I just loved all that. But there was also a lot of guilt in me which suited being a rasta because obviously it was very like Afrocentric at the time. It wasn't really the place for a little white girl. It was like, there's a bit of like racism and stuff I was experiencing but also many, many, many like mystical experiences. And so that kind of started me back on looking for the truth really. And what I found was like, I seem to spend a lot of my time in this mind fog. And I thought it was because I smoked loads of weed, you know, like I thought it was the marijuana. So it got to a point, I think, when my third child, Maria was born, I was like, all right, I'm stopping smoking weed. I need to be clear. So I stopped smoking weed, but the mind fog was still there. And so my prayer just came for clarity, for clarity, for clarity. And then my sister was getting into Buddhism and I did a bit of chanting with her and I was doing Namiroho and Gekyo. And then one day I was just had this huge prayer. I just wanted the truth. And it was probably the truth about a particular situation that I was praying for, but this prayer for the truth is like, when I come out for meditation, it was like it had gone in. The prayer had landed somewhere and I got a bit scared. And I was like, oh, what did I ask for? It just started to kind of like just unfold. And so when this special relationship came, I don't know, I just thought I was gonna ascend in a load of clouds with this holy partner and it was gonna look like that. And it didn't look like that, but it was still the most rewarding relationship I could ever imagine because we're not together now, but I still, he's become like my forgiveness muse because there's so much juice in that kind of relationship for forgiveness. So I'm just so completely grateful actually, not every day I have to admit, but most often it's become very rewarding. So yeah, and then I think I came across your teachings somewhere along the line, like the memory doesn't hold it all anymore because every day is so more joyful than the one before. It's like, I don't really need to go remember. I don't need the time to remember that. Yeah, but at some point I found your teachings and there were so many stories that stuck in my mind. I think one of the first ones I heard and loved was that Jesus with the purse. And it just stayed with me. And then after, I think the sound quality wasn't so great with some of those videos. So I kind of, what happened? Oh no, I got to a lesson in the course where it was one of the first lessons to go within and look for the light. And I think I kept doing up to lesson 50, then starting again, then I got to like 70, then I'll start again. And I just had to keep doing that. And I could just never find this light that was being talked about. And I was like, I think this is important. I don't know how to meditate. Like I didn't even have a clue where to go once I was going inside. So I was kind of guided to go onto YouTube and I saw Muji and straight away, I felt an affinity because I saw the dreadlocks and the accent, it was very familiar. And it just happened to be day one of his Rishikesh, like a month long satsang. So I just did the whole month and he does an invitation to freedom. And when I did that invitation to freedom, it was literally the invitation to freedom. I felt like I found that place, you know? Yeah. And it was just so profound. And I think my boyfriend even called me after I'd done the first one and I was so peaceful. Like he was ringing to shout at me, but like I was just like, no, just like, let him just speak. Just like, I was just like laying there all blissed out. And it totally changed the whole tone of the kind of broke that cycle a little. So that was amazing. And then yeah, things continued for quite a long time, got worse actually, a lot worse before it ever got better. And then I began to see that this was a reflection of my mind. And I think some of the worst days, because he would have these episodes where the personality that I was having a relationship was like totally gone.  But to me, it was like he was stepping out. My ego was stepping into his body like just showing me all this hatred. And I remember reading in the course, like you don't know the depth of your own self-hatred or something like that. He put it much better in the course. And that's literally how it felt like that's what I was seeing. Because some of the things he was saying were so personal. I hadn't even told him that before. You know, that had these feelings. So it was, yeah, it was extraordinary. And eventually, like the relationship kind of the violence stopped. And we kind of went into a peaceful sort of a situation a bit during lockdown. And then on just a normal Tuesday afternoon, I heard in my mind, it's done. You know, it's complete. So, and I just went down and told him and that was kind of it. Really, we haven't seen each other since. It was a bit sticky at the end, but yeah. And it just happened to be when I'd started, I think I'd done, I might have done a retreat with you. The Jesus our beloved elder brother was my first retreat. And then there was the free celebration of illumination. And it was really that retreat there where I was so touched by, I think it was supposed to be a skit, but it was the one of the most serious, most beautiful expressions I've ever heard with the, what did they call it? COVID, COVID. So Emily was expressing her miracle. Susan, what Susan said just touched me and it was just incredible. So I tried to volunteer like twice and then I just kept like, I can't do any of these things. Like, I'm not pressing the button. And then in the middle of the night, one night, it just got, I just knew I was being called and I was just trying to ignore it. Like, I was like, anything else you want me to do? And yeah, in the end, I just put yes to everything. Yes, I can do animation. I can do that. Check all the boxes, hesitate, hesitate, check them all. Send. And the response came back so quick. I missed Linda's first email for a call, but then we had our chat and then next thing, you know, she gave me to Ken to be in the social media team and to work with Lilo on the Big Wash magazine. So it just happened so quickly. It was like, there was no time. It was like, yeah, you've asked for healing. Here it comes and it's, then it's happening. And Ken, I call it the Kenneth Clifford finishing school social media, because it really, it just, when you're, when you're doing it, it just washes everything away over and over again. And all the remnants of ego that was still there, Ken just kept, bucket of water for you. Bucket of water like the evangelist and the pilgrim's progress. Yeah. That's beautiful, Ken was so uncompromising, leading the social media. And then I think I remember seeing you on a lot of the time to get real, on the get real show that I would show up a lot of those that Ken was doing. And I remember seeing you and there was, oh, a number of people that have kind of even gone on and are really shining and sharing around Europe and other parts of the world, as well as Ken and Anna over there now, shining over around Europe and Spain. But it seems like once you say yes, like you said a big yes, you checked all the boxes, you sent it away, and then things just opened up and accelerated, I know with our ministry and all your extensions that you've done, it seems like we have to go through a bit of a trial period where the ego is still kicking and screaming a bit, like it doesn't wanna come along for the ride and wants to bail and tries to convince our mind to bail. But yeah, so you just hung in with that, stirring all that, you just really hung in there. Yeah, yeah. I had a lot of help, like so much help. It was beautiful. Like I said, there was so many people pouring out, just pouring themselves out in the expression sessions and Ken himself set such a beautiful example of that. And it was like, wow, because I always thought my safety lay in, keep in private thoughts, don't upset people. If you think it, don't say, whatever you do. So it's just, that was such a turnaround for me, and I still have trouble expressing what I call dark thoughts, even though they're the ones that should be expressed.  So it felt like I was being taught by everyone I met how to do this, you know?  Yeah, it's amazing how the best definition of teaching is to teach is to demonstrate, and Ken was such a great example of being transparent with everything, that that's like a great witness or an example that it's safe, it's okay. I had another friend, Kenneth Price, who I did a show, I think it was called Escape to Freedom where I read a letter from a prison friend of mine, Dale, who's been in prison for many years and is still in prison. And he was in prison for murdering a man named Frank, but he had been a boxer, a very prolific boxer, even boxed on ESPN, but he became such an example of in prison, of practicing the principles, of forgiving that other prisoners around him became more and more aware of it, and then a whole prison ministry started up in Chillicothe in the prison, and then they were able to get movies in and do like some version of like movie gatherings, and it just took off. He's been transferred to another prison now, so now he's starting again to light up. And, but my friend Kenneth Price, who I had on recently on a live, he was so touched by the emails, he became a pen pal with Dale, and then he collected over 100 emails that he received and he put them into a PDF file. So what you've done with this book and the parables, it seems to be replicating itself in different ways where people are feeling the same inspiration to put them all and compile them into a book, a PDF file, and then Kenneth was taking it down to Mexico to share with friends in Mexico. So it's like the gift just keeps on giving when you have the breakthrough and you feel the joy and are lifted up, then the spirit just says, okay, we'll just keep the seeds being planted, keep spreading the good news, and wow, amazing, just amazing how those miracles work. No, it really is, it really is. And I never expected any of this, at least a word to it, because I never finish anything, like I've done so many different things in my life and I do it for a bit and it's like now, this isn't it, so I've got like a multitude of skills, but writing a book wasn't one of them. I mean, I may have written a small book like 10 pages, but so when it came, it came complete and it was like, I don't know, I was just like, my main memories from the time was, I was just sitting at my computer watching these hands fly over the keyboard, like Lucy in the movie, it was just like.  I was like a Kirtland turtle, and yeah, it was just, it was phenomenal to watch and such a privilege. It was almost like, so I'd be typing something, also listening to a talk and then the words that I needed to type next, you would be saying in the talk, so type that in it was, and it was more like sewing than writing because I was like sewing these stories and having the framework of the 50 principles was really helpful, because I never, I always kind of like rushed through that section of the book and I'd be like, oh yeah, I'll come back to that, I don't really get what that is all about. So, Marguerite, that was me for most of the book to be honest, I was like, I really wanna figure this out. And there's something about, I felt Bill Thetford's presence very strongly at the beginning as well. It was almost like I could hear him singing and all kinds. It was like, oh, Bert, oh, way.  Right, and we were calling everybody in, even the spirit of Bill Thetford was right there with his singing. There, Nate, you on. I sort of realized that there was, it was 50, oh, because I was also born in 1972, which is why I noticed it was gonna be 50 years this year since the course was finished, not published, but finished writing. I was like, oh, that's interesting. I'm 50, the course is 50, and then there's these 50 principles of miracle. So it was, it just seemed very given. And then one day I was on Facebook and I saw this painting Marguerite had done. It's actually in the back of the book now. It's blue, it's like coarse, color blue, but with these bright, bright splats. That's it. Yeah. And when I saw that painting for the first time, I heard very clearly, this is our front cover. So I was like, wow, okay, it's happening. Because before that, he'd just given me the title. Didn't know what it meant, 50 Years of Miracles. I put a thing on base camp. Like, I thought maybe it was gonna be a party, you know, like another celebration of remuneration. It's a party of art. Isn't that lovely? That's kind of very abstract art. 50 Years of Miracles, the art, the painting by Marguerite. Yeah. You can share too it. Because Marguerite was a huge collaborator in this. Jason was there, I think Susan Houselac. It was interesting how everybody seemed to have their part to play. And then even when I saw the PDF file and everything, and I was like, wow, this is such a great book. I would love to have it be, and somebody could have it in their hand and carry it in their purse, or just carry it with them in their car, their backpack. So then I started getting activated to, yeah, contact a man in Pakistan who could reformat things and bringing in Lisa and saying, I think this is coming through. And she said, I'm not a book publisher. Why do you call me? And I said, I don't know. I just didn't feel like Jesus meant to call me. So it's like it grew and grew into a collaboration. And I think people who have done books know it's quite a collaborative effort to put together a book, plus when you have paintings, graphics, formatting, miracles, principles, parables, and then try to make it cost effective. I think Jason had one printed on a print on demand, but it was like, I don't know, over 60 euros. And I said, it's a great coffee table book. It's spectacular with all those paintings by Marguerite. I mean, I could just use it as a meditation, but I said, not many people are gonna be able to pay 63 euros for a book. So it's amazing how it's just like a huge collaboration. And we're doing it for Jesus. We really feel the joy of Jesus in our hearts. Yeah, yeah, totally. It was such a blessing to get to talk to Lisa. And then Francis was in the background on one of our calls. I was just like, I was like, excuse me a moment. Ah! They're gonna come back.  Like the whole time I was just lit. It was incredible. And I think one of the things I really wanna share is when I was seemingly doing all this, it was like I was in this golden place. Like, very hard to describe. Or like I think it was golden. That's all I could think. That's why there's so much gold in the book because it was like being immersed in liquid gold, you know, totally safe. And there was no sense of giving or receiving or anything like that. It was just, it was like the zone. But for nine months, it was like nine months of zone. And everything in my life was also in that zone. I mean, I'm a parent. I don't know. Sometimes I'd look up, there'd be like eight kids running around. Like so many boys. And I was just like, just so focused. But yeah, it was that connection that, I mean, Jesus called it the emergency room, which I thought was really beautiful. It's like I was merging. And we're merging together, really beautiful. Yeah. It's interesting too. There's a part in the course where Jesus talks about, you know, this arc of golden light that surrounds everything. And then the edges fall away and you see that there is only this light. It's an interesting verbal way of Jesus taking us into this vastness. And you were like in that, during this whole process. Yeah, I was just looking at the goldenness on the top and the goldenness across here. And even the flowers are kind of golden. So that kind of golden glow that you were talking about, that you were in, it just kind of extended all the way in and through the book. So it's come, it's everywhere. It's got a crisp blue persuasion. This was a golden persuasion that was surrounding you and carrying you. Yeah. And it seems like the message for me was, he'd never left. Like even though I thought I'd finished with him in the playground, like through your parables, he was taking me through my parables. I was like, that happened to me. Oh, that happened to me. And I was like, he never left. And there's, I mean, so beautiful. Like I thought I'd done something, you know, like I'd gone, I'd come back or like, and it was like, no, he just wanted to show me he'd never left. And like, that's the most incredible miracle of all, I think, is that realization. Yeah, your dear, dear, dear's friend had never left you.  But like, yeah, if you put yourself back in your shoes of being this schoolgirl and on the playground and we love our friends when we're children, you know, they call it peer pressure, but at the time our friends are very important to us and what they seem to think and believe and feel is very important to us. And it's part of this world where we, our identities kind of frail and volatile and we look outside ourselves to friends and family to inform us, am I okay? Do you still love me? Am I enough? And yet I had another friend many years ago who when she was 14, she was part of the Catholic family and she went into the convent when she was 14 and she was in the convent from 14 to 22. And you're in the vitiate and you have to go through all these stages to ultimately to marry Jesus. You have to go through like six or seven stages and then in the end you take your vows and you marry Jesus. Well, she got from 14, left school to go into the convent 14 to 22 and then when she came to take her final vows and marry Jesus, she couldn't do it. She just bailed and she left the convent and after that she was searching and then she married a man and, but the thing was she always felt like a regret like, oh, I just, I left Jesus at the altar. I had to make your courtship with Jesus. I had to take the final vow, you know put the wedding dress on and be married to Jesus and I couldn't do it. I just told Mother Superior, I can't do it. But, you know, I remember telling her when she told me that story, I said, well, Jesus always comes back to you and she was saying, she'd worked with me 10 years before in an office and when she read met me she said, you are not the same person. You're so happy and joyful and you were so shy and timid and introverted and now you're just so beaming and happy and joyful. And she said, what on earth happened to you in 10 years that made you change your whole personality? And I said, well, there's course in miracles. What's that means Jesus, he's back for you. No one leaves Jesus at the altar. He's gonna never give up. But he's always there. Ivan wrote a book called Quantum Forgiveness, Physics Meet Jesus. Yeah, science initially with Newton and a lot of them tried to divorce Jesus. But then in the end, he's there in quantum physics too. He's been right there with us in everything we've tried. And even when we thought we were wandering, he's like, no, no, I'm here, you didn't leave. We're right where we always have been together. And isn't that a wonderful feeling? I know you must feel just so joyful with that. Like, wow, I've never really loved Jesus. Yeah, it feels amazing. I think you were saying yesterday, when the beginning meets the end, it's like everything else in between is gone because there was never was a middle bit. And that's, it's incredible. Another one with a clip in the middle. Yeah. Still trying to like, I don't know. And it really feels like sometimes there's so, what I realized when Ken and Anna came to stay, I think was that it's his love that does it all. I kept thinking I had to generate love somehow.  And I just thought I had no emotions, like love. So I used to like fake love through using guilt a lot of the time. It's like the more guilty I felt, that was what I thought love was. But when I was getting ready for Ken and Anna to come, basically this room I'm in at the moment used to be my work shed. And it was filled to the brim with all things which I've tried and stopped bits of equipment. And he got me on a mission, like a 21 day mission to clean out this shed and put some beds in. And that was Ken and Anna. Your shed became a guest room. Yeah. Now it's a guest room. Yeah. We're broadcasting all over with it. Yeah. And it was the same as doing the book. He had me on a mission. I was doing six trips to the tip of day. Massive fires was going on. And, but all I could feel was this huge love that was coming through me for them and also for me and Jean. And it was like when I thought I was finished, he was putting these beautiful little touches, like really thoughtful touches. And it was, again, it was just incredible. And it was really relaxing for me to realize that I really can just step that, there was just no need for the ego. You can do nothing for me, like at all. And it was just beautiful. And then when they came, there was no sense of there was people. It was like sitting with myself or sitting with Jesus. It was just beautiful. And everyone that came, they met my family, my neighbors, you know, people from all different walks of life just came. I didn't invite anyone specifically. And it was just so peaceful and blessed. It was wonderful. And we, I think the pictures you saw on Facebook was us, we went to the garden center, we bought plants and they planted themselves in the garden of my heart. It was just blessed. That really reminds me, like just the online retreat we just had at the very end, there was Johnny Jax and his wife, Fay. And they had a long stretch. They knew each other, then they were apart for 56 years and then they're back together and now they're selling their house and going out in a motor home just to bless everyone that they meet. And I think that's so beautiful because that's the answer right there. If we just see it's always our own lesson and it's a lesson in giving the blessing, giving the miracle, extending the love, letting Jesus come through us, then it's really simple. Once you try to take a course of miracles and you try to put it in a box as if there's teachers and students when he teaches us in the manual for teachers that teaching goes on all the time because you're teaching with your thoughts, you're teaching with your attitude. It's taking it away from the roles, teachers and students. And when I would travel around, I loved going around wherever I was invited, staying with a host for as long as they, I felt guided and they felt guided to have me there and meeting the family, meeting the neighbors, meeting the friends. I had a friend, Jim Worderman in Georgia and I went down, he was a retired pilot. He had been a priest and a pilot and he lived in a suburban neighborhood where all these retired pilots were all in the houses together and they had a runway strip in their backyard. They shared the runway and would for fun take their little bus and the planes up. But when I went to meet Jim one time, he said, David, I wanna take you around to every house in the neighborhood. I want you to meet all the people. And he was like, I don't know, about six foot nine. And he would take me and he'd say, come on, let's go in one house. Hey, knock, knock, knock. Hey, want to meet my friend, David? Da, da, da, let's handle something to drink.  Then the next time, hey, knock, knock, knock. This is my friend, David. I thought, wow, this is Georgia hospitality. This is Jesus coming through Jim. And that's what I think when Ken and Anna were coming and you just felt like you were just sitting with yourself and Jesus was there. It's so different than thinking of a course in miracles is like a profession where you've got to go from hotel to hotel and city to city and course in miracles, gathering to course in miracles, because you miss smelling the roses when you can stay with the people and meet their family, meet their neighbors. Like Kenneth is always talking about too, just, wow, I got to meet so and so and so and so and so and you never know what you're gonna walk into when we were talking on the live the other day. He said, yeah, one time they were upstairs and two people were arguing downstairs in the living room. He just walks right down into the argument and sits down and before you know it, through kindness and friendliness and Jesus just pouring through, everybody feels grateful. The argument ends and to me, that's what living in course in miracles is. It's not just books and seminars and here and there and conferences in hotels. You miss the joy of the flowers. You don't see all the flowers. You don't see the whole rainbow unless you really put your heart into it and meet everyone with the blessing. And so there it was, you guys. I mean, I could see it on the photographs. Gene from Paris and just happy, happy, happy all over the place. Yeah, it was just amazing. I went down to Devon to meet them again just before they went. And that was another, it was like my first road trip. And I got like, it was another like huge heart opening time because I had this image that I was gonna, cause it was in Devon right by the sea. I was like, oh yeah, I'll go down a good day early. I'll sit on the beach and I'll feel all peace. You know, planning how I was gonna feel on this beach. Yeah, it didn't work out like that. I ended up getting a migraine because I just drove straight through. It was supposed to be like four hours. It took me six and a half hours. Drove straight through, nothing to eat or anything. Sat on the beach, started throwing up on the beach basically it was a mess. And then the next day with the gathering, that's when the peace came. And it was like another lesson. Like it's not in any place. It's not anywhere. It's right here in the mind. In the joining, something about, yeah, when you join with something, that's where it is. And yeah, so it's another beautiful experience. And it just keeps on coming. And that kind of led me to really look around and think, hold on, all these images that I've made, they don't love me back. You know, I love the beach. The beach doesn't love me. You know, this must be the same for all the images I see. And I started looking at like even my family. It's like, these images I've made, they're not gonna love me back. And then what came to mind was the two pictures Jesus talks about in the course. It's like, when I look at a person, I can see the ornate frame with the drops of blood and all that, or I could see the frameless picture that is real. So that's kind of where I'm at at the moment is just really, I wanna feel that connection, like for real, not my imagination, not anything else, just reality and truth. Yeah, that's beautiful. I do like that two-picture analogy because yeah, the frame is really, in that analogy is the body. And then the other one is just lightly framed where the body doesn't draw your attention and you feel just the love in the connection which is in our hearts and in our minds. And before I came on with you, I happen to see an article and it was an article about Dolly Parton and meeting her husband, Carl, she was in a laundering net and Carl was just driving by in Tennessee, probably some little town in Tennessee, which was driving by and he looked in and saw Dolly Parton, a very young Dolly Parton in the laundry mat and he stopped his car, parked his car and went in there and he just, he said, your skin is so light, you have to watch it. You can't be out in the sunshine. You could damage that beautiful white skin that you've gotten. But she said, she noticed that the whole conversation he just kept looking at her face, looking right into her eyes and she felt this deep connection and she didn't really know what he was thinking but she felt this deep heart to heart connection and then later he said, well, actually what I was thinking that this is the woman I'm gonna marry. That was what was going on in his mind as he's looking right into the eye and now she's like 75 years old they've been married all these years and to me that's kind of a symbol of the picture, the frame, if people are too focused on the body, on the behaviors and everything, they say the windows are like the eyes of the soul. There was this contact in a laundry mat between two people and it's gone on and I would say a very holy relationship. There's lots of light that has come through that relationship that really blesses the whole world. Even people that I know were actresses were dolly pardon doubters or haters. Over time they say, what a blessing she is, what a wise woman, what kindness, what sweetness comes through dolly. So in the end it's the sweetness wins out, the kindness wins out, the honesty wins out, the heartfelt experience just wins out and that's just where we're at. I think that's why we just pray every day and we just say, okay, here's a new day, show me what I'm supposed to see and let me be an instrument of your love and like you're saying, you don't have to figure it out as a person, how am I gonna love? Like Jesus, it's more just stepping out of the way and saying, use me, use my heart, use my spirit, my mind, my thoughts, use me in a way that brings a blessing. So it's so nice that it's so simple and sweet. Yeah, yeah. It ends up simple.  It's hard to get out of your own way though, I think that's, I think you were talking about that recently as well. It's like when you're still valuing something of the world, like this, you're in your own way really basically, aren't you? And it was really just this last week when I was looking at the relationships I have with everything. Actually, it's not just a relationship in terms of people. I was like, oh yeah, there's relationships with food, there's relationships with all different things and I wanna see what's truly there. Actually one like the table finally told me what it meant and then I woke up and I'd forgotten. I woke up and I'd forgotten. I woke up and I'd forgotten. I woke up and I'd forgotten. I woke up and I'd forgotten. The table told me what is the universe is all about, but then I forgot. Can you tell me again, table? I think it's beautiful though, how for everyone it comes in a way that can reach them like you were saying, you talked for a few minutes before we started about how the parables were so important for you because reading the course wasn't always just click, click, click, it was like, hmm, what did I just read there? And then the parables kind of like lit you up, like really touched your heart. And it was the same for me. I mean, I used the course as an oracle during the first two and a half, three years just praying and opening the book and it was very helpful to me that way. It was like an oracle. And then I got to a point where, let's say probably about four years after I had the book, after I found the course in California, I took a road trip up to the Catskill Mountains where Ken and Gloria Wopnick had their foundation for course and miracles. And I would go up there a few times and once when I was up there, I was just in this, they had the sunroom with all the books, library books and they had Krishna Murdy videos, which I watched. Sometimes I couldn't sleep so the door was open. I'd go in there two in the three in the morning watching Krishna Murdy feeling all this sparkle in my heart. And then I remember pulling up a little thin book about as thin as this one. And it was like, I pulled it off the shelf in their sunroom and it was called The Peace of God is My One Goal by Barbara and Robert Varley. And I opened it up and there was a nice little handwritten note from Barbara to Ken and Gloria. And then I started reading it, chapter one. And it had a workbook lesson and then it had a parable. And then a workbook lesson and a parable. Well, I was probably three in the morning, I was reading it and I thought, oh my God, I never heard of this book before, but this is so touching. I was so moved by the parables. They were really showing the meaning of the workbook lesson. So I just got a little cassette tape recorder that I had and I read the book a lot. I did my first audio book for myself, of course, because I wanted to, as I traveled around, I wanted to play and listen. So I listened to that little book, The Peace of God is My One Goal on my own little cassette recorder over and over while I was doing the same thing that they had been doing, traveling around to basements, backyards, churches, bookstores, anywhere, the spirit guided me. So I think with the book that you really helped compile with Melanie Doyle, she kind of compiled some parables and then you dove in and then you did writing and then everybody played their part. That's what I heard from Jesus. It was like Jesus was saying, remember how touched you were back in like 1990 when you came across that book of theirs and how it propelled you, it propelled your confidence, it propelled your trust, it propelled your faith. And then you went on to share it. Later on, when Barbara passed away, I contacted Robert, who was at the time in Praxis, married to Shaka. And so it was Robert and Shaka Varley at that time. And then I said, what, that book was so helpful for me. That was so transformational. And he said, well, come on out here. Look in my garage, see all those boxes of books. I said, yeah, he said, those are the books, The Peace of God is My One Goal. I said, what are they doing in this garage? They should be all over the world. So I had my friends, Resta and Kathy transcribed the book. I put it online as an e-book, kind of a PDF version. And then he kept sending me boxes of books. And I was like the traveling mystic with it going around in the little car. So I would load up boxes of The Peace of God is My One Goal, put it on the internet and take it around and just hand it out at course gatherings.  That book, you have no idea, David. So that's kind of one of those reasons. That's why when you had done this book, it started off as just the EPUB I think we had and the PDF. And then I just, Jesus, it was like, come on, David, you know how helpful that book of parables was for you. Why don't you help get this one extended more? So that's when you got to meet Lisa. Francis was in the background. You see, Jesus has fun bringing in all the collaborators just to carry the original gift.  It's still there, I think on livingmiracles.org for free if people wanna download it for free. But now some people, they like to have something in their hands. They like to park it up and get there. Highlight it around and, you know. And then the free paintings, you know, you, that's another, that's like the bonus of this. This is just one, but there's, oh my gosh, there's so many that are even the backdrops for the principles. There's a beautiful painting and then you've got the principles. And that's not so easy to see, but you can see there in between, this is kind of a sparkly artistic parable book. It's kind of what it seems to be. Yeah, yeah. And Margaret's journey with the paintings itself, I mean, if you're a reader of art, like her journey with that, I remember seeing Margaret on a couple of expressions on the retreats and she was just having this huge experience that she didn't understand. It was just like just all howling out of her onto this canvas and they just were so beautiful. I mean, she started like just painting everything she felt and I don't know that every single painting is just stunning. Like even the printed versions don't do the justice. And she's been a wonderful, it's funny like a couple of months after we started joining, we was doing regular joining and expressions together. I found her name written in one of my journals where I'd seen her on screen expressing about this art and I'd written her name down. And yeah, it's just really, so it's almost like there's many stories in one book with many stories. Yeah, yeah, yeah, yeah. And how painting could be a whole pathway to God because it's just another opportunity to surrender. And I know with Slava, my friend, Janie, a lot of times the painting, like my friend Janie, she basically wasn't a painter until she had this really deep mystical experience. And then after the mystical experience, the spirit just started painting these amazing paintings through her. It's almost like channeled art. And I think I feel that with Marguerite, that I know that's been with everything she's dealt with in her life, the paintings have been a means of communication and a means of expression and healing and clearing. So it's really appropriate that they ended up in this book for what, I mean, the original book that you did was very big and that they printed for me for 63 euros and as a coffee table book. And I would just sit there with the big print and the spectacular paintings, like full paintings, color paintings, I would, whoa, and then, whoa, it's another one. It was like a deep experience to go through that. It was because it was so big. It was in my hands, a hard cover, you know. So I still have a copy of that at the peace house. It's lovely, it's the adventure. It was almost like each painting was, reminded me of somebody, like the painting I used for Kerstin's Parable, for example, just reminded me of her. Like it was all gold and blue and so peaceful. And the way she talked about diving into the water, it was just like, oh, it's okay. So everyone's painting with their story just had, it was, yeah, I don't know, just very deep. Yeah, it is a collaborative book. I mean, we have parables in there from the original founders, some and parables from my experience and Kerstin and Lisa and Francis. And you know, it's so beautiful as you go through because it's, you can see the miracles are kind of just like cascading out. And there's nothing really personal about it. You know, we experience it through what seems to be persons, but then we feel the essence. Like you even have the colors, the yellow and the blue when you have Kerstin and sharing the pair. And then you put the colors and the painting and everything in there together. So it's like a really felt intuitive extension of what you were feeling in that golden light is what comes through in this book. And then I'm sure for the reader too, you know, it's felt, it's very, very felt. I hope so. Because it was also the year of, there was so much extension coming from the community. We had the CASA program. Francis was doing the Francis show, Francis Zoo show. I was out of the blue and Ken had to get real. It was just, there was so much, so much coming out. And I was just so inspired by the stories that I was hearing. And I realized there's no separation. Like you can't just talk about David Hofmeister without talking about everyone that you met, that thousands of people were in prison. And yeah, and that's how it kind of felt. And even Jason was, I said to Jason, he was like the gold running through the book. Because so many of the parables, he was like there witnessing as well, like in the background or, you know, just, yeah. It's just so, so one. Funny, he was in the background. And then as we started this broadcast, he called at the very moment where I'm ready to press the go live button and my phone was on, which I usually have it off and I'm like, ooh. So, he got into this one too. The way to get in. It's a classic. It's a classic. Jason moved. Well, I'm just so grateful. Yeah, I felt it would be so wonderful to talk to you about this because I think it's just something that comes from your heart. And then, like you said, you felt all the extensions that the community was doing. And then you just jumped right in. It's like, if we were all in a swimming pool, you went running and glee and just jump. I'm in there too. I'm coming. I'm coming. I'm coming. I'm coming. It's hilarious. Big pinball into the pool. But it's, it really is an honor and a treat to be together like this and share this joy. And they say the Holy Spirit is the spirit of joy and the Holy Spirit's curriculum is the curriculum of joy. So, I feel that really comes through. That's like the spirit behind everything we extend. And yeah. And so, thank you for your part in this golden book that came through. And I know it will bless many, many, maybe we have no idea for generations even because that's what one of the things I liked about reading the New Testament. I always was, I get the Bible with the red letters and Jesus was the red letters. And then a lot of what he taught was within parables because it was too deep for the people, the consciousness of the people, but he would like throw out a parable and preface it with just a few words for those that have the ears to hear, let them hear and then tell this parable which is really just illustrating something even much more deeper than the parable. And I think what this does, the paintings and the words are just helping people get in touch with the joy in their own heart. And that's the most you can do as a book or as anything in this world, a painting is just help people remember the love, the truth. Yeah. Yeah, and that he never left. Yeah. He was your second. Never left, you didn't do what you thought you did. Jesus was there, still is there all along. Well, thank you, Lucy. And thank you to all of you who tuned in today. And if you enjoyed this, just share it with your friends and that's how it works. Spread the seeds. Okay, lots of love. And lots of love. Thank you, David. Thank you.


The board has before it, for consideration and approval, a draft host-state agreement between the IAEA and Kazakhstan, establishing the IAEA-LEU Bank, as well as a draft transit agreement between the IAEA and the Russian Federation. The conclusion of the two agreements represents a significant milestone for this important project enabling us to proceed to full-scale implementation.


bookstore is by Professor Kim of KAIST on first passage dynamics of primary parties. Thank you. Thank you. Good afternoon. First of all, I'd like to thank professor Jeong Yeo Jo for all the effort, preparing this nice program. Today I'll talk about some recent work on the first passage dynamics. 이선셜 아이디어로 이동할 수 있을 것입니다. 너무 많은 디테일이 있습니다. 첫번째 문제는? 지난 5년에 코스프인 덱스에서 피해의 불쌍한 불쌍, 높은 흥미를 보였습니다. 최근에 흥미를 보였습니다. 그래서 한 몇 년 정도의 스톡을 보셔야 한다면, 오리지널의 비용을 알 수 있을 것입니다. 이 상황에서, 아낌올을 흘러내리기 위해 식물을 찾을 수 있을 것입니다. 이 시기에는, 간단한 모델을 설명할 수 있습니다. 이의 흡수의 흡수는 흡수의 흡수의 흡수의 흡수의 흡수의 흡수의 흡수의 흡수의 흡수는 어떤 가능성이 될지 모르고, 그 후에 그의 흡수는 좀 더 흡수한 것입니다. 물론, 비코스코픽에 우리의 이유로 인해 기술과 정보, 예를 들은 바퀴리오키모 택시, 특정 DNA 시퀴스타일, DNA 바퀴리오키모 proteins. 모든 이 문제는 다른 지역과 다른 길을 보입니다. 하지만, 사실은 스태트스크류 피지컬 프로듀스에 첫 번째 문제입니다. 이 문제입니다. 이 문제입니다. 우리는 previous slide, this is a universal problem, we experience this kind of problem every day, right? Then sometimes the searcher can be a person or can be an animal, microscopic organism, molecules, even mathematical index, such as a cospy index, right? In this business, one of the central question or key question is how long does it take for a searcher to encounter a target, which is usually referred to as a mean first passage time, right? And this is the central quantity of general interest and which we want to understand here. Okay, let me begin with the elementary stuff. First passage dynamics is the classical subject in stochastic theory, originally formulated by Smolochowski and Cramer's almost 100 years ago. This is a typical setup. We have a metastable potential like this, and a particle escapes from this metastable region to reach here, and here the potential suddenly changes into negative infinity, right? So this position can be considered as the location of a target, right? And we want to estimate or calculate the mean first passage time or mean exit time, the time required to from this metastable region, right? Okay, it can be calculated using focal plane application in general. For example, for diffusing particle, the transition probability to find a particle position at r' at time t, given initial condition at r, satisfies this focal plane application, right? And this is the survival probability that the particle is not observed until time t, and usually slowly decaying function of time, and given by the positional integral of the transition probability. It is a first passage probability that the particle absorption or barrier crossing occurs for the first time at time t, right? Then the mean first passage time, the original quantity of our interest can be calculated by average time with a rate of this first passage probability, right? Then simply integrating by part, you can see that this mean first passage time is given by the time integral of the survival probability, right? And also given by the spatial temporal integral of the transition probability, right? And then the transition probability is expanded using the eigenfunction and eigenvalue lambda of the focal plane co-operator, right? Then this is the mean first passage time according to the previous definition. Then applying the backward focal plane co-operator on both sides, and you can easily see that this mean first passage time satisfies the backward or joint focal plane co-occasion. This is the second differential occasion. So given boundary condition, it can be calculated, right? As a simple example, consider a one-dimensional simple diffusion without any external potential, right? And we put reflecting boundary here and observing boundary on the other side and integrating this equation twice with this boundary condition. Then you can calculate the mean first passage time as a function of the initial position of particle, right? In this simple case, everything just as expected. The mean first passage time is given by the time scale to diffuse over the length scale of the system with the diffusion constant D, right? Very simple. Okay, this is the picture I'd like to show when explaining a random in the classroom. This is a load in our campus called endless load, Y. It leads to a marketplace, nearby marketplace with many bars and puffs, right? So after drinking a lot at night, you have to take this load to get back to your dormitory, right? But sometimes you drink too much with too much of C2H50H, you become like this, right? And you feel the load is winding and never ends, right? So next morning, you don't remember anything sometime, but interestingly, you always find yourself in your room, right? How is this possible? You can actually prove it mathematically. I can show it. Okay, this is the starting point called linear relation. User starting point of first passage problem in many cases. So this is the previous occupation probability in discretized version, right? So this is the probability to arrive site X after n step. Given started at X0. F is the previous first passage probability to arrive site X for the first time in j-step, right? It's decomposed like this, which means that you arrive at site in the previous j-step, right? And for the remaining n-j-step, you just simply make a returning work, right? So this occupation probability can be expressed in the form of a convoluted summation. Therefore, it is useful to introduce a generating function or discrete Laplace transform, right? Then this p can be expressed in the form of a convoluted integral. So simply product of respective generating functions, right? Okay, then now focus on the long-time asymptotic behavior. Then this discrete summation is replaced with continuous time integral and also sharp cut-off approximation can be used. Which means that we neglect this integral after this upper bound of the time scale. So the long-time behavior, long-time asymptotic behavior of the function can be studied by considering the limit where this z approaches 1, right? Then this t star goes to the infinity, right? And then now suppose that we have a simple isotropic diffusion, right? Starting at the origin, then we know that the PDF is given by the simple Gaussian distribution and then the long-time behavior of this function can be considered from the generating function with z approaching 1, right? So given like this. And due to this linear relation, then generating function of f is related to the occupation priority, right? Also this define the survival probability. The probability that particle is not observed until time t, right? And following this scheme, you can actually calculate the long-time asymptotic behavior of s and you can find that this s has interesting dependence on the spatial dimensionality, right? In the low-dimensional system, this s becomes always zero but in high-dimensional system, it remains finite, right? And this long-time behavior, long-time behavior of survival probability depends only on the spatial dimensionality, not on the details of random law, right? Therefore, the probability to find your home with random steps is always one in two-dimensional system. So even if you are completely drunk, you don't have to worry, you always find your way back to home. But this is not the case if you are wandering in three-dimensional system, okay? Okay, this dimensionality dependence can be understood by a simple scaling argument. So consider a d-dimensional random walk, then the radius explored by this random walk is given by the time to the 1 over walk dimension. And the total number of sites within this volume explored by the random walk is determined by the fractal dimension. And the total number of visited sites by this volume within this random walk will be proportional to the time. Therefore, the fraction of visited sites in this volume will be given by the id time with the power of 1 minus d over 2. Therefore, in dimensions higher than 3, this fraction of visited sites becomes vanishingly small, right? And walks become very transparent, okay? Right. So this classical subject of target search or first path dynamics has regained a growing interest recently. This problem consists of four elements, first searcher, target, searching domain, and underlying dynamics, right? And these four elements have been extended in various directions. For example, you can consider a target search problem in complex environment such as scaling the network or crowded intracellular medium, right? And also, you can think of different dynamics other than simple diffusive motion such as leviflight or fractional Brownian motion. You can also bring up with many interesting ideas such as the motility of searcher's target, okay? Right. So these problem has been studied widely and extended in various direction. However, most of them considered a single particle, single searcher, right? So it is natural to extend to consider the presence of multiple searchers competing for the same target, right? Suppose that we have n searchers instead of 1. Then in this case, one interesting question will be is your search time still given in this way? I mean in terms of the single particle, search time renormalized by the number of searchers. If so, what will this exponent alpha? Is it 1 or any other value, right? Okay. When you have searchers more than 1, then the problem becomes already quite complicated even in the case of non-interacting particles. Why? Suppose that you have n non-interacting particles, right? With different initial positions, then they will record respective first passage time, right? And from the point of view of first passage dynamics, only minimum value among n first passage time should be counted, which means that we need an order statistics, right? So this can be done only through a full distribution, first passage time distribution, right? So this is the problem we considered. We considered n non-interacting or independent searchers in a finite domain of volume v with dimension d, right? And I'm going to skip the detail rather focus on more recent works, but you can actually solve this problem analytically. This is possible because for non-interacting systems, the trajectories of particles are statistically independent, right? So therefore the probability distribution function of n particle can be decomposed into the product of a single particle distribution function, right? So that's the reason. And also assuming a uniform distribution of searcher, then you can show that when properly rescale, this search time or mean first passage time shows a universal behavior. When the number of searcher is small, then the gain in the search time is proportional to the number of searcher. But when n is large, then the gain is more enhanced. So it is proportional to one of n squared, right? And using extensive numerical simulation, we confirm our theoretical prediction and the simulation here are performed for different systems with different sizes, different number of particles in different dimensionality, right? And as you can see here, all the data points nicely collapse on a single curve as predicted by our theory. Okay, in the previous example, we considered uniform initial distribution of searcher, right? But you can think of different strategies employing different initial distribution, of course, right? And as I said, important question in this business is to optimize the system parameter to reduce the mean first passage time, right? Then in that case, one important question is what is the optimal distribution of searcher, right? That minimizes the mean first passage time, right? Okay, so this is the question we would like to answer here. Now, the target position is given in the form of a probability distribution function. What does it mean? Suppose that we have a missing child who was lastly seen an hour ago here, right? Then you may guess the current position of the child as a Gaussian distribution centered around here, right? Like this. Then how should we deploy the searching squad? You can think of different strategies, right? row the distribution or narrow wall or the same as the target distribution, right? What will be the best one? So in that case, the formulation almost remains the same as before except that the target position is given by the probability distribution function. And then you want to minimize this mean first passage time as varying this probability distribution function of searcher position, okay? Okay, let me consider a simple case to get some idea. Here we have a target position as a truncated Gaussian in a finite domain, right? And the target is most probable at the center and we have a single searcher. Then what will be your choice for the starting position of search? Natural choice will be the center, right? And this is actually calculated mean first passage time as a function of initial position of searcher, right? And as expected, it is minimized when you start your search at the center. Then what do you expect if you have two particles, two searchers? Still is the most efficient to put two searchers together at the center where the target is most probable or not? The answer is no. Actually, the efficient way is to put two searchers separated from each other with a certain distance. Why? This can be understood by collective searching efficiency. If initial positions are identical or too close, then searching domain tend to be largely overlapped, right? Lowering the searching efficiency, okay? So anyway, the exact answer of optimal searcher distribution is a highly collate problem and it's quite difficult to obtain general answer. So in this sense, we propose an alternative approach which makes sense when, for the case of large number of searchers, when you have large number of searchers, like a thousand or 10,000 particles, then it's not so practical to deploy each of them precisely in a highly correlated manner even if we know the exact answer of the optimal distribution, right? Instead, we consider independent deployment, placing particles according to a prescribed independent distribution, which is u here, right? Then our question becomes things like that. So what will be the optimal distribution of u that minimizes the mean first passage time, right? Then, okay, so this is the question we would like to answer and it's equivalent to taking the functional derivative of the previous quantity with respect to u. And after some calculation, we can find that this optimal distribution is given by one-third of the target distribution, little bit broader of the original target distribution, right? So using the Langebaum dynamic simulations, we checked our theoretical validity of our theoretical prediction. Here, for example, we considered Gaussian target distribution, which means that we generate target position according to a Gaussian distribution. Then also generate many searchers according to this distribution with different value of gamma, right? And this is inverse mean first passage time renormalized by the searching time when gamma is equal to 3, right? So as you can see here, these solid lines are our theoretical prediction and the symbols are numerical result clearly you see that the searching time is minimized when the gamma is equal to 3 as consistent with our theoretical prediction, okay? Okay, let me skip this. So far, we have considered the target search by multiple searchers, but they are still not interacting, right? However, in many cases, rather usual cases, some form of interaction certainly exist between searchers, right? For example, think of predator such as wolves or whales. They communicate with each other to locate or hunt down a prey, right? More importantly, the first passage dynamics was originally proposed to describe chemical reaction of molecules, and we know that molecule experience various kind of interaction, right? Renaissance potential or DLVO potential. Anyway, so this is the question we would like to answer or understand here. How does the mean first passage time depend on the interaction, right? And actually in many of the system, rigorous consideration of interaction is always non-trivial and has been one of the fundamental questions in theoretical study, right? For example, let me remind you of how we describe the effect of interaction on the equilibrium pressure of real interacting gas system in graduate statistical mechanics course, right? So we know that for real gas, it is given in the form of a variable expansion, right? So in order to derive that simplification, what we have done like this, we consider canonical partition function for n-particle system where the Hamiltonian is given like this. p is a momentum, u is an interaction potential. Then the momentum integral and positional integral can be done separately. This is the configurational integral, which is further expressed using moment expansion and u0 here indicates the average with respect to non-interacting system, right? Then to calculate the thermodynamic potential or thermodynamic function, log of partition function should be considered which is expressed in terms of cumulant expansion, right? All right, but this cumulant expansion or moment expansion, still, perturbative approach, which means that they are valid only for weakly interacting system, not so practical for strongly interacting system, such as a system with hardcore potential, right? So in order to consider general form of interaction, you have to do some kind of a partial resummation, right? Summation of all two point clusters, for example, in low density limit. Then you can see that all reducible clusters subtracted out in the variance and only irreducible clusters remains in the final expression in the variable form, right? And this kind of expansion is a little bit complicated to do in a canonical picture, so usually we consider this cluster expansion in a grand canonical system, right? That's what we learned from the textbook, right? And at the end, then you can show that the equilibrium pressure of interacting gas system is given in the expansion in powers of density, right? Okay. Then, so this is a kind of a brief review how to deal with the interacting system. Now, let me get back to our original problem. So, we have an interacting Brownian particle searching for a single target in a finite domain. So this is a dynamical problem, right? So in order to estimate or calculate the mean first passage time, then you have to solve the focal length occasion for this n-interacting particle, right? Which is, of course, a nontrivial task, right? So our problem corresponds to the generalization of the previous example of equilibrium pressure to the n-body dynamical problem, right? So I'm going to I'm going to skip the details of mathematical derivation. Actually, we have tried, actually we solved this problem using three different methods, right? And then we obtained every time identical result. So anyway, we found that kind of a partial resumption similar to the previous example is also possible for the solution of this focal length occasion, right? And as a result, the searching time is given in this way. So the correction to the mean first passage time for the real gas system is given in the form of a virial expansion, right? And as expressed with the virial coefficient this is a universal result valid for any kind of potential. And we have demonstrated this universality by performing a Langebaum Dynamics simulation considering various potentials such as exponential, hardcore, Sutherland potential, Renaissance potential of different number of particle interaction strengths and system size, right? And as you can see here all the data points numerical results nicely collapsed on a straight line as predicted by our theory, okay? Right, so this is summary. We have considered target search by multiple searcher and when they are non-interacting and initially uniformly distributed then we have universal scaling behavior with respect to number of particle and when you have a degree of freedom to adjust the initial distribution then the optimal distribution is given by one third of the target distribution finally when they are interacting this dynamical problem still can be solved giving the answer in the form of a virial expansion. Okay, most important part this work was done by my former PhD students Dr. Seung-Hwan Lu currently at MIT as a postdoc and in collaboration with Professor Ju Hyun-hee sitting over there in Busan National University so I'd like to specially thank these collaborators and of course I'd like to thank you all for listening. This is the last result for the search time in the Interactive Particle Number 3 Is this for 3 dimensions, right? Actually, the dimension doesn't matter Actually, the dimension doesn't matter It doesn't matter It's a general result for arbitrary dimensions because it doesn't matter Okay, thank you What if the searchers are obstructing each other or what if the searchers are obstructing each other Suppose this is a treasure hunt and physical interaction or However, you want to phrase the interaction so that one searcher wants to get to the target before the others That is already included because we have to do some kind of order statistics The first one is meaningful So physical interaction these kind of order statistics among the N first passage times are already taken into account in this study Thanks In the summary slide, you presented three results Results No. 1 and 3 Can they be connected? For instance You showed that time decreases with a number of searches without interaction and you presented the results for the case of interaction So for instance, in the weak interaction limit can you reproduce No. 1 from No. 3? But you have to be careful because it is the video expansion so that makes sense only in the dialogue limit So in order to check this kind of crossover or universal scaling behavior with respect to N then you have to take into account the next order term or actually infinite order term in terms of the density So maybe another approach may be useful or will be better I don't know the exact answer how to extend to consider this large N system So every assumption applied to the equilibrium pressure calculation in the textbook should be also applied here except that this is a dynamical problem So can you apply this kind of idea to real situation like small child trying to find many people people are intending each other so can you calculate B2 kind of thing and you can give a consultation to the police So that's an interesting point but you have to be careful because it is based on still smaller chopstick occasion or focal plant occasion so underlying dynamics is very random of but in our scale search we make a kind of directed motion and we have also long distance communication method so in real life search maybe you can apply that to the some kind of searching algorithm for drawn something like that but not for human I guess I have a question for your number 2 Can you intuitively understand why the linear distribution should be broader than target distribution Actually that's partly can be understood by this collective searching efficiency so it is a diffusive motion it is highly there is a high non-negligible probability that the searching domain can be overlapped so on the one hand it is better to minimize this searching domain and on the other side you want to put your resources at the target position where the target is mostly expected so this is kind of a balance between the 2 different opposite behaviors so the exact number of 3 I don't know the precise argument but the qualitative argument is just like that I also have a short question So this are expected time for search condition no success in higher dimensions there is always a probability of failure Is that correct? in more than 2 dimensions 3 and above there is always a finite probability of failure that you don't find the target If you are working in the infinite space without any boundary in finite system Thank you for the clarification So just a technical question So this video coefficient So this result was obtained for without any boundary condition just free space in 3 and 2 and 1 dimension Actually we have in order to get some numerical simulation you have to put boundary otherwise there is a certain probability up to infinite time Right So then the video coefficient itself is actually boundary condition dependent it is known that if you assign some boundary then it's like you are applying some sort of potential field so your whole particle is actually not only interacting actually interacting particle actually feel the potential to each other but if you set the boundary potential field such that you have to reformulate your VR coefficient P2 this is known for the engineers as far as I can tell Yeah, but actually we are looking at very dilute limit and small number of particle in very large system so thermodynamically this boundary condition shouldn't be so relevant in cases otherwise an isotropic space then it might be true very long cylinder something like that or some space between the plate then boundary condition can be relevant but if you think of very isotropic space then I think it will be very difficult to detect any boundary effect in the video coefficient so that is usually the thermodynamic limit we consider so volume and number of particle both of them go to the infinity with a finite density Okay, let's thank Professor Kim again Thank you