Okay, I am so excited. I live for this stuff. I live for these kinds of stories and I'm so glad I stumbled upon it when I was researching for a week of stories based out of Rome, Georgia. I also feel a little bit validated over some feelings I had when I was a child living in Rome about a particular piece of property. And I do want to acknowledge that I did change the set. I guess you would call it for today. I'm still having a little bit of some issues with my ears and my eyes and if anybody who also has ear issues, you know, it makes you a little bit dizzy. So I wanted to make sure I was sitting on the sofa versus sitting on the stool. I typically sit in while filming. So I do apologize if the set's not as exciting, but you'll deal with it because the story I have today is, I think in my opinion, pretty exciting. And before we get started, remember to hit that subscribe button, give us a like, tell your friends, pass it on. And if you are from Rome and you have some really spooky story or really interesting place you want me to talk about, please message me on our Instagram that's at Esoteric Atlanta. The same goes for anybody else who is in Georgia. If you have any stories you want me to cover later on, please don't hesitate to reach out to me. Okay, here we go. Welcome to Esoteric Atlanta. My name is Bryce and today we're going to be talking about CCC Road on Berry College in Rome. I knew it. I knew it. When I was a child or a teenager or whatever, I, I knew that there was satanic practices happening on Berry's campus. I knew it. And now I feel validated because obviously I'm not the only one who knows about this. And to be honest with you guys, I've had so many freaking paranormal experiences in my life starting from being a little child. I now know at 37 years old that a lot of what I've experienced does apparently have to do with my blood type. I did tell you guys in a past video that my blood type is the blood type that the global elite, the cabal, the Illuminati thinks is just very special. And there are side effects to this blood type. There's a lot of physical side effects to it. For example, I have an extra bone. I have an extra organ. I struggle with autoimmune issues. There are some downfalls too, but there is this element of being very susceptible to paranormal activities and being able to see beyond the veil. Now, if I had grown up with one of these powerful families, then maybe I would have been able to learn how to use this for nefarious ways. I'm glad because I would never want to use anything for nefarious ways, but you get what I mean. And I don't think that just because I carry a particular blood type that I'm better than anyone, it's just the makeup of a blood type. In the practice of yoga, we talk about something called prana, which prana means life force. And in a lot of cases, your blood is part of your life force in your natural form, not in your spiritual form, but your natural form. And all blood types have specific side effects. And with my particular blood type, again, it is very, very common for people who carry this blood type to have certain abilities to be able to see beyond the veil, to be pretty empathic. So you get what I'm talking about. And maybe in future story time videos, I'll tell you guys more stories of some crazy things that have happened to me in my life. I definitely think that being exposed to certain sides of our reality that a lot of people can't see is what has pushed me down the path that I have taken, where I've spent a lot of time in India. My whole life, I've been trying to figure out what the meaning of life is and what God is. And I'll tell you, I'm very, even though I grew up Christian, I'm very anti- church. I'm no offense to people who go to church. That's awesome. If you have an accountability, if you have something that helps you find, that helps ground you with God, that's great. But my experiences, because of what I've seen, what I've experienced, I found that when I would go to talk to a preacher or a priest or whatever, if they had not experienced what I had experienced, if God had not allowed them to see what I had seen, then how the hell were they going to be able to guide me or help me? And I started to realize that in the Bible especially, basically Jesus is like, do it yourself. You do it, you do you. Like you have your own relationship with God, you don't eat anybody else. And that is part of the reason why I have dedicated my life to this particular practice of yoga. My teachers in India and the teachers that I've had here in the United States with this traditional form of yoga, if you were to ask them a question pertaining to spirituality, usually they answer you back by asking you another question. And they're asking you to think for yourself. They're asking you to figure it out on your own. And I love that. I really, really believe that most of this world has been heavily manipulated by religions and by people who want to control you versus help you. And part of my opinion on that is going to get into our story regarding this particular road on Berry campus. And so before we talk about what happens on this road and why this road is so weird and why there is so much folklore around it, we have to really go back and look at Berry College as a whole and its history. So Berry College is a private university style college, four year college that is located in Rome, Georgia, obviously, it is so large that it is kind of its own little town. I know that sounds weird. It's kind of like a town within a town. Now Berry is a beautiful campus. I will give them that it is gorgeous. And when I was a kid, Berry was very open to the public for people in Rome to come on the campus to use it to walk to run. They hosted a lot of road races. They have a mountain campus where they have a lot of camps in the summertime, lots of hiking trails. From what I understand, it's gotten a little bit more regulated now. I'm not sure. I haven't been on Berry's campus in probably 20 years. So that's just what I've heard. And normally, so if we weren't under quarantine right now, what I would have done is I would have actually gone to Berry and driven or walked on this road before filming this video so I could really give you my opinion. But obviously right now that can't happen. So if you further down the road and we're able to join society again, we will be going down and trying to get on this road and experiencing it for ourselves and maybe doing a follow-up video on that. Berry College was founded and started by a woman named Martha Berry. Now Martha Berry was born on October 7th, 1865 in Jackson County, Alabama. Her father was a man named Thomas Berry and he was a veteran of the American Civil War. Now shortly after Martha's birth, the Berry's moved from Alabama to Rome, Georgia, and Rome, Georgia is right by the Alabama line FYI, but they moved to Georgia because Thomas Berry, again, her father co-owned Berry's and Company. And Berry's and Company was a company that owned grocery stores and they also owned cotton gins. And then in 1871, Thomas Berry purchased an old plantation house called Oak Hill. Now if you can remember from our first episode on Rome regarding the clock tower, Rome has three rivers in it. Back in the day, it was a hot spot for a lot of travelers, a lot of steamboat engines. It had a lot of huge potential to become a very, very huge city. It's kind of funny. We were laughing about all the hashtags with Rome because one of the hashtags is all roads lead to Rome, which again they get from Rome, Italy. But at this point in current times, Rome is a very hard town to get to. When they were building I-75, apparently Rome decided it did not want I-75 coming by Rome. And so it's made it really complicated. You have to get off the freeway and you take all these back roads, you have to go through different towns to get to Rome. It's not easy to get to like it was back in the day when people used the rivers for transportation. And I do think that for Rome, not having I-75 that close and not wanting it that close has really hurt its ability to grow now. But back then, gosh, with all those rivers, there was so much prosperity and so many trading posts and a great place for industry to boom. And so Oak Hill, the plantation that the berries bought, the old plantation, was right on the Usternala River. Now today, Oak Hill is a museum. And a lot of you who are not, who are watching, who are not from Rome or have never heard of Rome, you might have seen Oak Hill before. It was used in the movie Sweet Home Alabama, which was shot in 2002 with Reese Witherspoon. In fact, they used a lot of the town of Rome to shoot that movie. Even some of the New York scenes were shot in Rome. Oak Hill was the Carmichael's plantation. And in fact, Berry College itself has been used for many movies, like Remember the Titans. The Titans was shot in the year 2000 or put out in the year 2000. It was with Denzel Washington, Ryan Gosling when he was a lot younger. And when they go off to their football camp, that is on Berry College's campus. Now going back to Martha Berry and her childhood living at Oak Hill, she was educated privately by tutors. And she was sent up to Maryland to attend the Edgeworth School, which was a finishing school. So those were very common back in the day. I talked about this a little bit with our werewolf of Georgia that a lot of times girls, especially women from high society, were educated to a certain extent, but most of their education came through what would be a finishing school where they learned how to be proper ladies of society. Now Martha Berry never married. She gave her life to educating underprivileged children who came from local Georgia farmers. And around Oak Hill, this is where we get the start of Berry College. Oak Hill is now on one side of the street and Berry College is on the other. So back in that time, this whole property or most of the property, not all of it that we see today was owned by her father, Thomas Berry. So in the 1890s, Thomas Berry gave his daughter Martha 83 acres of land so that she could build a little log cabin, a little small school to start working with these children who otherwise would not have the chance at an education. And reading about this actually like hurt my heart. Berry College now is one of the more expensive schools that you can go to. In fact, I looked up their tuition price and their tuition price for the 2019-2020 year, including room and board. Okay, so that includes if you live on campus was $50,316 for one year of school. So basically $50,000 for one year of school. And the University of Georgia for in-state tuition for the 2019-2020 year was $11,500 where out of state tuition was $20,600. So huge difference between the University of Georgia and Berry College. Now, granted, yes, Berry College is a private school now. But I mean, it's painful to see that this woman started teaching children who could not afford to have an education. And now it's turned into this huge, very expensive school. Now, granted, they do have work-study programs. There are programs where you can work for the school and get the deduction from your tuition and of course they have scholarships and all sorts of stuff. But that's beside the point. It's just really like, I wonder what Ms. Martha Berry would think about the fact that her project to what she dedicated her life to helping these children. And now it's turned into this huge money-making establishment. And I have absolutely nothing against private schools. I am private school born and bred. I don't know much about like public schools here. I really only went to private school. So that is where I'm coming from. I am coming from a private school education. So I'm not, I don't, I don't have anything against private schools. I just have, what my problem is is I have a problem with the intention of what Berry has done. What it started out as is so different than what it is now. At least in my opinion. But anyway, let's continue. So over time, obviously Ms. Berry's little school started to grow. She did start to incorporate a boarding facility for some schools.  And in 1926, Berry became a junior college. So a junior college would be a two-year college. I know for my friends, possibly watching in Europe, we have different terms. Like I know that you guys call a four-year school university and maybe more of a college being more your upper sixth form for England, especially, which would be the last two years of high school for us. So I know that might sound really confusing. So a junior college. So our upper school or our high school years are ninth through 12th grade. And then after that, when you go onto your continuing education, you can go to like a vocational school if that's your calling, where you can learn how to do hair or all sorts of really great stuff. I think vocations are fantastic. I think that people who have vocations are laughing at everybody else all the way to the bank.  A lot of people will use a two-year college and then transfer after to their final two years at a university, which is the full four-year college. So for my friends overseas, college and university pretty much mean the same thing. So when someone says they went to college, that means that they went to university. And then in 1930, so four years after it was given its two-year college to be a junior college, it became a full four-year college in 1930. Martha Berry actually passed away on 5 February 27, 1945. So she did get to see a little bit more, she got to see her school grow. And that must have been a pretty nice feeling to start with such a small little school and see it grow. And then in 1962, it became Berry Academy. And in 1983, the year that I was born is when it incorporated as Berry College. Again, it was already a four-year college, but it incorporated as Berry College. That's when I believe from what I studied it became like this expensive school, which had the work study programs and scholarships and all that kind of stuff that I talked about before. But that was in 1983. Berry College is a liberal arts college. It is a Christian school. We're going to get more into that later on. It is 60 miles from Atlanta, Georgia, and it has 80 miles of trails that again, like I said, when I was a kid, these trails were open to the public, although I have heard that perhaps that's not necessarily true now. And I have my own little conspiracy theory around that regarding the story we're going to talk about. They also have the Winship Foundation. That's a camp that was started by the founder of Chick-fil-A. Most of you guys are very aware that Chick-fil-A is a very Christian organization as well. All right. So now we're going to get into our story regarding CCC Road, which is one of the roads on Berry's campus. Now a little side note, like I said in the beginning, Berry to me, it's gorgeous. Like I absolutely would go hiking on Berry. We go out, we're very, we seek out adventures. We like to go out into the mountains. We like to do fun activities. And I would definitely go back to Berry and hike again. I have suspicions around Berry. Now, when I was a kid, Berry was a dry campus. Because it was a Christian campus, I'm assuming it probably still is. So yeah, very strict in a lot of ways. And you know, some people like that. I don't know. I think that, you know, college is definitely a time when you're kind of still a kid, but also like an adult at the same time. So I definitely think it's like the safe space for people to test their own boundaries and kind of learn a few things about themselves. So I have a problem with that much restriction. But again, to each his own, some people like that. And I, that's why I didn't go to Berry. I don't want to be under that much lock and key, you know? But interesting, a lot of people, I didn't know this, but I guess a lot of people call it scary. Berry. There are apparently a lot of hauntings on Berry's campus, which I just kind of skimmed through that because what I'm interested in is more interested in is the satanic element to Berry College. Now, Berry College is, again, famous for a lot of things. It also has a lot of chapels on its campus. And like I said, I'm going to reiterate again, this campus is huge. It's so big. And a lot of the schools that I went to for higher education, they were in cities. And so they would have campuses kind of all over the city. It was a little bit scattered. But Berry is all together on the same flight of land. It's big enough to be its own zip code, its own little area. And there are so many chapels and churches on this campus. And one of the chapels that they have on this campus lies at the end of CCC Road. And this church is called the Mountain Spring Church. From what I understand, where Mountain Spring Church sits at the end of CCC Road was not its original place. From what I read, it sounded like they actually moved the church. I could be wrong about that, though. I was having a little bit hard time following some of the old paperwork. The church was deeded by a man named John L. Cook on September 23 of 1889. And this church has gone through a lot of reincarnations. It looked like it was a Methodist church at one point, and an Episcopalian church at another point. Side note, I like both Methodist and Episcopalians. I know Episcopalians are called Wiscopalians, and I think that's fantastic. And I think the Methodists are the least cult-like of all the Christian faiths. Seriously, if you look at the Bite Model, the Methodist church falls very low on the Bite Model. That means that they don't try to control their members or congregation at all, which I think is fantastic, because I really, really, really cannot stand religious organizations that try to turn their faith and the vulnerability of their congregation into a manipulative cult. That's wrong. Don't do that. And there are a lot of churches that do do that, but the Methodists seem to be pretty cool people. Now, the church also has a graveyard around it. And like I said, for the most part, I, besides our Oakland Cemetery graveyard, I don't really think graveyards are that spooky. I wouldn't want to hang out in a graveyard unless it was Oakland, because again, Oakland was a very social spot. But other than that, I wouldn't want to hang on the graveyard. I would want to go to my house or to where my loved ones are hanging out. So normally, graveyards don't really, like, catch my eye that much. But the church that stands at, so this Mountain Spring church that stands at the end of this road, apparently, according to what I read, is that it still functions as a church like once a month during the summertime. I'm not sure if there is any air conditioning at this church. When I was a little girl, I remember going back to South Carolina with my mom, my grandmother Maxine, my mom, and my Aunt Mary Jo, who is since she's since passed away, well, both my grandmother and Mary Jo since passed away. I remember going back to South Carolina with them and we went to a wedding of some cousin, some distant cousin. And the wedding was held on the Bryce, one of the old Bryce properties. Again, for those that this is your first time watching Bryce as my mother's maiden name, I'm not being egotistical. It's her family's last name. So when I say Bryce property, it's my mom's family's property. And there was an old family church that the wedding was held in and it didn't have like air conditioning or heat. And I remember wearing this red sweater and being miserable. It was horrible. Oh, I think I have PTSD. I was so young. I was probably like four or five. I was so young. But yes, I just can't like I, oh my God, and Lord have mercy on our souls. It is so damn hot here in the summertime. Why the hell would you want to go praise the Lord in an old rickety building without air conditioning? It is 2020. Go sit in a church with air conditioning, please. But anyway, this church is legend has it that this church also works as a satanic church. I'm serious. Don't laugh. I'm serious. And this isn't uncommon. Just this happens.  Now Barry has a lot of places. There's a lot of wilderness in Barry. There are over 80 miles of hiking trails. Like I said, there's a lot of different buildings there. And it has a lot of folklore that a lot of people will say there's specific places at Barry where satanic rituals happen or SRA happen. And when I was a kid, I believed it. Like you feel it. It feels so freaking creepy. And one time I was with a friend, it was in high school and we were driving out to the mountain campus. And there's this really long patch of road when you go from the main campus to the mountain campus. And there are these like dirt roads, or at least there were back in the 90s off the side. And we pulled off and we were my friend was so intrigued and wanted to try to find some of these satanic churches. So we went this was at night. It was evening. It was dark. We went back into the woods and we did stumble upon this what appeared to be an altar. And there were like voodoo dolls. And it was really creepy. And my my friend started picking them up, which of course I freaked out. I was like, just leave it. Don't touch it. I my family's from South, a little country, South Carolina, like this stuff is real, like just leave it, leave it, leave it. So I have seen with my own two eyes that this is not just folklore. This is not just legend. There are legitimately satanic practices happening on this campus. Now again, if that's what you want to do, if you want to like praise the devil, then you that's that's your prerogative. You have freedom of religion in this country. What irks me and what makes me mad is when there are sacrifices involved that involved killing an innocent animal or killing a human being. I just are casting negative stuff out towards people. That's crossing a line. But if you want to like hang out with Satan by yourself them, you know, whatever, but just I just don't like the whole sacrificial part. Now sacrifices are necessary in positive polarizing positive faiths as well. For example, for me to be able to participate in the yoga practice that I do, I have to go to bed very early when we're not under quarantine. I typically get up at 330 in the morning to do my practice and teach my mice or program. I follow extremely strict diet. I don't eat any animal.  But that's a sacrifice for me. I am doing something just that just affects me. It doesn't affect anybody else or anybody else's life. It's just mine. Does that make sense? And yes, I have seen places up in that Rome area near Barry where there have been goats that have been sacrificed. I've seen it and it's real. This is real. Now it's also, I don't know if I can explain this well, but I'm going to try. Like I said earlier, Barry is a Christian campus. There's nothing wrong with a school being a Christian school, but they take it to like a whole other level. They're like evangelical, you know, dry campus. And for me, that gives me the heebies. I don't see Jesus in that. I don't. There is so much like I, the church I grew up in was evangelical. And I know for sure that there was a lot of spiritual manipulation. There was a lot of narcissistic abuse that was happening. I've had to talk about a lot of things that happened that the church I grew up in that have caused me that have contributed to CPTSD or complex post-traumatic stress disorder. And I again, am very skeptical of these big organizations that claim to be Christian. I don't believe them. Like I don't, I don't believe you. I don't believe that you're doing anything holy. I think you're trying to control people. I think you're trying to manipulate people. I think you're trying to abuse people. If you literally want to help somebody, you're not going to behave in the way that these big Christian organizations behave. And if you do get deep into studying Luciferian cults and satanic cults, there are again online, some people who have been interviewed where they talk about infiltrating the Christian faith. They send people, Luciferian are satanic people into these Christian churches, and they manipulate the churches and they turn it into something it's not, it's not.  Who is this preacher? Where do they come from? And what is it they're manipulating me to do? Where is, is there mind control happening? All sorts of stuff. So I know some people are going to think that's crazy, but I will do not trust the faith that very college says it has. I don't trust it. If you are legitimately a Christian school, I don't, I think you would loosen your reins of control over people or over your students. I understand the legal drinking age in the United States is 21 years old. So I understand that you have to abide by those legal, legal laws. But I think you exert too much control for you to be considered Christian in my opinion. I don't think Jesus would approve in my opinion. Again, strictly my opinion. So with that being said, I don't think that these satanic churches, these satanic practices that are popping up all over Barry campus are not like polar opposites of the campus itself. I don't. I think that because of the way the campus is set up, because of the way they're running their programs, these satanic practices are able to flourish because they're coming from the same seed. Now I need to step back a little bit because I do know that there are people who work at Barry college that teach at Barry college that go to Barry college that have really good hearts and that are truly trying to be good people and really are very Christian and follow Jesus and are amazing, amazing human beings. I'm not talking about those people. I feel like those people are very good people and they're just maybe have the wool pulled over their eyes a little bit. I'm talking about the powers that be. And again, this is all just my opinion. This, you're free to have your own opinion about it as well. The truth is though that there are satanic practices happening on Barry's campus. I've seen it with my own eyes and people typically believe that this church at the end of this road is used for nefarious purposes. It's not just one person is a lot of people that believe this. And I think that you have to start to look at things that if there are a lot of people that are having the same opinion over something, maybe where there's smoke, there's fire. But anyway, let's move on. So the road itself that leads out to this satanic church allegedly has a bit of a mystery too. It says that once you start going down the road, west down the road, you will drive over seven different bridges. But when you turn around and come back the other way, you will only go over six bridges. Weird, right? And I actually believe this. I have this feeling that as time goes on, I believe that we're in the middle of a great awakening right now. And I think that we're going to start to understand consciousness and how it more deeply how it actually works. And I do think that there's some weird kind of space reality and very much, but Tesla was studying and Einstein was studying. And I believe that people are literally counting seven bridges going one way and six coming back the other. And as I mentioned before, there are a lot of hauntings on Barry's campus. And I'm not really going to get into all of them except for one. There is the green lady. And I looked up, so I was curious. So I got online and I researched different colors of spirits and what they represent. If you see a green spirit, according to some of the websites, it means that the spirit is happy. It's a good ghost and it's pretty attracted to nature. So this ghost that is on this road seems to like being there. And it doesn't seem to want to do any harm to you if you see her. Apparently the ghost that lives on this road is the combination of two spirits, two little girls who died in one of the creeks, which CCC stands for like Cold Creek, something I couldn't get the full name of the road, but it does mention the word creek in there. So I'm assuming there is a creek by the road. Apparently they drowned in this creek. And if you stand on a particular spot on the road and spin around three times, apparently this green lady will appear to you. So it used to be that you could drive down this road. Well, now they've blocked it off. You can't drive down the road. You can only walk it. And like I said earlier, it seems that they're doing that with a lot of trails. I don't know if they're trying to control the amount of SRA that's happening on campus or what. But it sounds like there was way more freedom to go about the campus back in the 90s when I was a kid than maybe there is today. But for CCC, apparently you can walk down it. You just can't drive down it anymore. Well, when I was researching this, I did find a few Reddit chains. And I'm going to read one of the responses to the Reddit to you, because I think that this person, it's better to tell the story in her own words. So here we go. Yes, I have been there once. My parents talked about it and some older friends and I decided to write out one day and check it out when I was 14 years old. I am now 51. The bridges did actually count seven and six going out. When we made it to the church, we got out of the car and you could see a huge tree that had been cut down with a small axe drove into its side. All of us except one talked about the evil sadistic feeling of being there. Judging from the side, it looked like a sacrificial area. The door of the church was open and you could see most of the pews were gone and things were thrown about over the floor. It was very rundown. Everyone walked on ahead of me. We were laughing and cutting up. I kept hearing something walking in the woods but saw nothing. When I began to walk and maybe took eight to 10 steps, a tree that was approximately 12 to 15 inches in diameter fell right in front of me. It came to rest about two feet in front of me. The only sound of the tree fall I heard was when the tree hit the ground. There were no limbs except in the very top of the tree.  It was overwhelming like time stood still. It scared me and my friends very bad. When I got myself together we left and as far as I know, none of us have ever been back. I have a police scanner now and over 20 years ago there were quite a few calls to go out there in reference to devil worshipers and sacrificial events taking place there at the church. It is sad that these things happen in our world but the Bible does speak of demons and spirits and the state of the dead. It is very interesting and has helped me put today's life into a much better perspective. I don't know about you guys but when I read that on Reddit it gave me chill bumps. This woman remained anonymous on Reddit. So if you are from Rome and you're watching this, thank you so much for sharing your story.  Hell yeah, there was satanic stuff happening in 1995 out there. I 100% believe you. I felt it. I saw some remnants of it and I believe you and I would not be surprised if it's still happening today. I mean what's that saying the devil's greatest trick was convincing the world he didn't exist? So yeah that story of CCC road and the whole of Berry College anyway and it's supposed a connection to satanism is stuff that I could literally talk about all day long. I, this stuff especially the whole bridge thing, driving out and seeing seven bridges going one way and six bridges coming out the other. I mean talk about a mind scramble. I mean have you experienced that? I, when we're able to drive up to Rome and walk this road, I literally, I can't wait. I can't wait to see to try to figure out what's happening coming back to take a bridge away. I don't know. Do you have a logical explanation? Is it a time space continuum sort of thing? What about the church? Have you been out there? Do you get the heebie jeebies? Do you feel that way? When you're on Berry's campuses, did you graduate from Berry? Did you see anything? Please let me know in the comments. I really, really, really am so curious. Again, I'm gonna say this all the time.  Really don't. My only concern is how you treat other people and other living things. So all right guys, thank you so much for sitting on this story. That was our second Rome Georgia story. I'm gonna go ahead and film the next Rome Georgia story for the next day and again, thank you to Josh McCabe for doing our music, for Todd Fraudrich for doing our editing and thank you to you guys for joining in in the fun. I hope you're enjoying these videos. I am having fun making them. I'm learning things. So I thank you guys so much. Be safe. Be well. Use your critical thinking skills. You own your mind. You have sovereignty over your body. Nobody should control you. No one. All right, I'll see y'all later. Bye.


Hi, it's Bridget. Welcome to Above Life Channel. The purpose here is to inspire your spirit and to fill you with hope today. Kind of a serious topic I want to talk to you about because I want to hopefully bring some comfort to you. You know that if you've been watching Above Life Channel that I'm a psychic and a medium, and I've been doing this work for over 15 years now, so I've had a lot of different experiences talking to many of you who have lost loved ones, whose loved ones are in the afterlife, and one of the common things that I have heard over time has been this feeling of curiosity and needing to know if their loved one, how they felt at the time of their death, or if their loved one was lonely or felt alone specifically. I think that as humans, as part of our healing process ourselves, when someone dies, we feel sometimes a lot of guilt or regret or naturally wonder and think about how we could have done things better. I think that's just naturally human, that's just human nature to think that way. And I get asked often about time of death, especially for some who weren't able to actually be there at the time of their friend or their loved ones passing, it can be just a very incredible heavy thing to carry or a burden to carry because there's a lot of questions that some of you will ask yourselves about, again, why wasn't I there? Why did I leave and second guess yourself and question if your loved one, if the person who died is angry at you or upset with you or how did they feel when they died? So I want to talk to you today about how how it feels from the spirits that I've talked to in the afterlife and their perspective of things. I can assure you that no spirit, which is all of us, we're all spirit.  You have spirit, an essence, an energy, whatever you call it, your intuition, your higher self, you have spirit in your body.   And when you die, your spirit does leave your body. The spirit transcends its life eternal. And so it doesn't cease. It doesn't stop. The body does because it has a has a limitations, but the spirit of you, it does not.   So your mother, for example, who who may have died in the hospital, you know, that that time when your brother called you and you didn't get there in time before she died? Does that sound familiar to some of you? You couldn't get there in time or you didn't know how serious it was? Did I touch some of you there? Yeah Your mother, your loved one does not have any kind of anger or resentment or judgment. There's no judgment, specifically the judgment part. There's no judgment about you not being there, about them being alone if they were alone because some people do transition alone into, you know, why they transition alone because it's easier for them. So often I have stories of as soon as the loved ones leave, go home to take a shower, go get something to eat at the cafeteria, then grandpa takes the exit and he's gone. And even if he's in hospice and there's like this constant vigil by the bedside, I know I can relate to that because I've done that in two instances for my father and for my grandfather. And so as a human person I can relate to this too and that person sometimes they just wait. It's easier. It's easier to just leave. Check out when nobody's watching you because there's so much attachment to us who are here and the loved ones who are here to try to even though you're saying with your mouth, your words are saying it's okay to go. You can let go now dad. It's okay to go. You can go now. It's okay. We're going to be okay. We're going to take care of mom. We're going to take care of things that will be okay. You can go now. Dad probably didn't even listen to you in human life. Why would he be listening to you now? And the reality is is even though you're saying that your heart is breaking and the feeling of what you're going through is one of the ways energetically that we connect spirit to spirit, heart to heart. And so you're not keeping your loved one here. I don't want you to hear that. That's not what I'm saying. But I am suggesting that sometimes it's easier for someone to cross over when they are alone, when there's quiet and they can have that conversation with their spirit guide or an angel that comes to help them and it's more clear. It's not as confusing when they see the human person, the people they love and then they see the angel or the guide. It can be much more clear for them and then they can choose to make their transition. So don't feel like they're lonely. Don't feel bad like oh that person was alone. They suffered alone even if you guys, even if that's a debilitating illness or a disease and someone has to be isolated or kept separate and you can't see them or you can only see them through a window or they're not even conscious because they're in a medical induced coma or they're in some kind of a state where they're not not with it at all and have no idea who you are or can't see you. You do not have to worry. You don't have to worry about how they feel. The whole shift in the narrative when someone is dying is they're letting go. They're slowly releasing, they're working through their own stuff to help them to release their body and move into their spirit form and that has nothing to do with you really. It's not about you but as humans we're like oh it's all about us and we think we're doing the best things we can do and we do. You do. You're well intended. You do the best that you can do. You're trying to heal yourself. You're trying to be strong for your family. You're trying to be strong for yourself. You're trying to be honest with yourself. You're praying.  They are your own. So in these times of uncertainty when people are separated when they're forced into isolation or they're separated and they have a medical or health crisis and they end up taking a turn and going down a path where they're going to transition I want you to understand something. I want you to try to reach in to the core of your being and know that what I'm saying to you is true in your heart and in your soul as your heart is aching and breaking for humanity when families are ripped apart and not able to hold physical hands when their friend or their loved one crosses over that the spirit transcends that and the connection lives on in the afterlife. The spirit so often will tell me but I'm not they're not like they feel no distance to you. They still feel connected to you. They don't feel like they've gone anywhere. The only difference is it's not a tangible human touch or experience in that way. For you there's a deep loss and an incredible disconnection feeling but for the person going through it they are not suffering as much as you are. You are suffering even if they're it's horrible or it's painful or you know that it's hurting them. The physical experience is traumatic for the body. The body is built to manage it. The body is built to to work through and move through the process and just like birth is not so pretty especially if you've had a couple like I've had a couple you know like four of them is a tough process so too can death be. It's not always peaceful and quiet. It can be loud and chaotic and messy but that doesn't mean the person is really in pain or trauma. It's not a trauma. It's an expression. It's a release and they are close close to totally releasing from all of it and then they don't really remember like they don't they don't hold a body that has pain and remember the pain. Most often from my experience is again 15 years of sessions thousands of people that I've talked to in my psychic and medium work. Human people and former people afterlife. I can tell you that they don't cling to the pain. They may share with you in a context when we're having a dialogue or you talk to a psychic or a medium in a context where you can understand that it's them and you can reference them because they will go back to where you can recall things if it is essential for your healing because that's what they want is your spirit to heal but the only thing that can heal your heart is you and that does take time in human context it takes time to do that. So I don't want you to feel it's so hard not to see stories especially now people dying without being near their family without being able to say goodbye but you all please understand it's a human thing to saying goodbye because in spirit there's no goodbye there's just forever there's really no goodbye it's different yes 100% is it easy for us there are left here no it's not easy and the spirit in the afterlife knows that they know it they know it and when they show up for you in session guess what it's not to help them 99.8% of the time it's to help you heal it's to help you understand this whole process of afterlife. I thought it was a really poignant time to have this discussion with you today here at above life channel on youtube I know there's a lot going on in the world and a lot going on in our individual lives I wish your family health and wellness during this time well being throughout and lots and lots of love in these moments these very precious moments I'm Bridget thank you so much for watching above life channel if you like the channel make sure you subscribe so you never miss my weekly channeling videos I also have a vlog at fairy grasshopper on youtube where I do multiple times a week sometimes daily vlogs with card readings and other psychic topics thanks so much for watching remember the purpose here at above life channel is always to give your spirit inspiration and to give you some hope some seed of hope because it's your life now it's on you to live it just live it thanks for being here


We are live. Hi everybody, this is a regular Google Summer of Code meeting in the Jenkins project. Today is April 17th, and we just have a regular sync up between mentors, org admins, students, and whomever is interested in JSOC. I believe we don't have a specific agenda for the today's meeting, but yeah, let's check. We have Jeff and Martin on the call, the JSOC org admins. We have Nisart, who is one of the students, and we also have Rick, who is one of the mentors for the GitLab ACM project. I'll share my screen. Do you see it? Yes, yeah. OK, so we have a Google, it's just empty. OK, so what do we have? OK, so regarding current status, currently we are reviewing the proposals received from students. The design for slot number applications is next Monday. So by the next Monday, we need to agree how many project slots we are going to request. There is a lot of private meetings and discussions happening between the mentors and org admins. This phase of JSOC is not public due to various reasons. But once we have everything set by May 6, they will be announcements of the projects we accept. So everything is going OK. We had some discussions. We already had one meeting with mentors. And yeah, Martin wanted to say some words to other mentors participating in the project. Yes, so I would like to remind mentors that we are expecting active participation at this time for all mentors to review the applications because we're trying to form potential mentor teams. And we need their participation before the slot application deadline. Yeah. That's what I had to say. I'm trying to work on some emails to get those discussions started for those mentor teams that have not had a chance to look at the applications yet. Yeah, we have quite a number of such mentors. So in some cases, we have preliminary feedback from mentors. We got before the final applications got received. But we still need to get more information and more confirmations, especially because some student proposals have changed. We also want to know about mentor availability. Because in a few weeks, we need to decide what will be the student projects we accept. And it's not only about student applications. It's also about mentor availability mentor teams because we want every project we accept to be successful. And it means that if there is a high chance that the project is not successful, then we would like to avoid accepting it, even if the risk comes from the mentor side. We disable sound from notifications right now. And from the check, we just disable a Gitter for a while. So yeah, regarding other activities, we also need to do something about swag. Yeah, we will be doing it, I believe, in the next few weeks because now we have information about the active participants this year, including students and mentors. And of course, we need to just do the distribution because this topic got delayed significantly. It's mostly my fault. Yeah, so something like that. And I guess there is no major activity that is happening right now, except the reviews. So do we have anything else to discuss now as a part of the project meeting? So we have Nisar, we have Supurna on the call. So if you guys want to ask something, just go forward. Yeah, so like I have only one question to ask that if there is a project and if no mentor is interested in that project for mentoring, like any mentor haven't given the feedback on that proposal, then what would be done with that particular project or proposal? Yeah, so in this case, it's a responsibility of all carmenes to try finding mentor teams. So if we think that the proposal is generally OK and that we would be interested to have it in GSOC, in such a case, we try to reach out to potential mentors outside from the original list. So if we are successful, then we can still have the project. If we are not successful, then unfortunately it happens sometimes because, well, mentors are just potential mentors. Some mentors may decide to go to other projects. And sometimes it happens that we cannot accept projects because we finally just cannot find mentors for this particular project proposal. It happens. It happens not that often. So as Orca means, we will do our best to prevent it. OK, thank you. Thank you, Tom. OK, anything else? If not, we can probably just stop the broadcast and then spend some time with Martin, Jeff, and Supun on another call to do some scrap of the mentor applications. Yes, I'm in favor of that. OK, Justin, somebody is interested. In one hour, in 45 minutes, we will have initial meeting for Google Season of Dogs in Advox, Sianandri, Outreach Special Interest Group. So if any of the mentors are interested to join, feel free to do so. But yeah, right now, I'll probably stop the broadcast unless Praspeak, Nisarkovs will have other questions. So here you go, Justin. Hello, sir. Yes, sir. So actually, talking about documentation, I just wanted to know if there's a certain sort of blog that is dedicated to Jenkins. If I wanted to write something about Jenkins, some sort of plug-ins. So is there any special type of blog that is dedicated to Jenkins? Yeah, I can show it to you quickly. Yes, yes. I can just post my articles related to the software. OK, this is my screen? Yes, I can see. OK. OK, creating a blog, so I'm creating a blog post. We have a Jenkins website, Jenkins.io, the same site where we had all of the JSO resources. And here you may see that there is Jenkins.io slash blog or slash note. There is a list of blog posts. And there is a lot of blog posts happening now. If you want to contribute your blog post, actually, everything is powered by the configuration that's caught on our website. So there is a project called the Jenkins, and Jenkins.io. So it's a configuration that's called for our site. And it includes contributing guidelines. So these contributing guidelines explain how to propose a change, how to test changes for the website. And they especially include an entry for creating a new blog. So if you want to post something technical or something community-wise about Jenkins, it would be one of the ways to do that if you are interested. Otherwise, just post on whatever your blog post, a blog, and then Jenkins, we can use our community resources to post your blog post, to tweet there, et cetera. But if you want to have something on Jenkins.io, there is an opportunity for that. OK, and before posting that, would there be some sort of editing or that I should be showing to the mentors, showing to the maintainers? Should I show them before releasing? Yeah, so blog posts, these blog posts actually, they're just being created as pull requests. So here you can see some examples. So open pull request, you may see that there is a template in Jenkins plug-in blog post created by Steven Tirana, something like two days ago. So here you can just remind me. So here you can see that it's just a pull request. There's one file in a ski dock, which includes all the information. OK, I need to submit it as a PR. Yes, everything is submitted as pull request. OK, thank you, sir. Thank you. OK, you're welcome. OK, anything else? No, sir. OK, thanks for the interest about your blog post, by the way. So if you want to share something, it's something we will definitely welcome as a project. OK, OK, I'll surely do that. OK. So if there is nothing else for today, I'll stop the broadcast. We will have another meeting next week. But in my case, I will be traveling. So Martin, Jeff, would you be able to run the meeting? I'll be here. So Martin's not. I'll be second. Have you got permissions to run YouTube recordings, Jeff? I don't think so. I'm good for next week. I can be there next week. That's perfect. So I'm not sure whether we will have much things to discuss. We probably need another meeting with mentors for the next week. I think that we can submit initial application for project slots without additional meeting with mentors. But once we have project slots communicated by Google, we definitely need something. We can just chat about it later in private. So I wanted to run something by you. I had sent out a couple of posts looking for a backup mentor for my project. And I got one or two people that I didn't know saying that they were interested in being a mentor. I don't need them for my project. Would we be interested in having them? I guess my only hesitation is it's somebody I don't know. I don't know if they'd be a good mentor. But do we want to give them a shot anyway? Yeah, so if I recall correctly, you got a response from Christian and from Keith Rosento? Yeah, there was another guy too. Sagar Uttakar. He says he'd like to mentor Jusak students. Yeah, so my advice would be to talk to them directly. So Christian is an experienced mentor. Keith, he was also mentoring community activities because he works for CloudBees and we had some projects. So I'm confident that he can be a good mentor, especially in JavaScript and React world. But if you want to have a mentor team, it's still something for all of you guys to just chat with each other and to agree how you would approach in this project. So yeah, just reach out to them and maybe set up a short meeting to get introduced with each other and it would be a good first step. So I've chatted with Keith and Kristen already, but there's this third person that said they were interested in mentoring. So I don't think I would need them for my project, but would it make sense to encourage them to find another project? I think we can discuss it in the mentor menu, please. Okay. Yeah, so definitely it won't hurt to have more mentors. I mean, organization-wide. But yeah, it's hard to say whether all people would be interested to mentor many projects. We have a lot of mentors who are interested in just one project idea, which is perfectly fine. But yeah, that's why we have work meetings. We will do this coordination. We will do this mapping. And yeah, for us, right now the main objective is to get an approximate number of projects we can have because we need to send a request to Google. So maybe I should ask them to see if there's another project that's interested in that? That's one of the options. Another option is to just see how it goes because we still need to coordinate projects. I'm not sure whether it would be a first choice for Chris, for example. But yeah, it's something we should really discuss in private. So let's start the discussion in the mentor menu, please. And then let's just press it from there. Sounds good. Okay. Anything else for today? If no, thanks everybody. And see you next week. And again, if you are a mentor, please spend some time to review proposals in the area of your interest, provide feedback, and respond to our mentor forum which we sent on Monday because we really need your insights about the projects you would like to take and what would be the priorities for you. We will use this information to draft the mentor teams and then to send out these drafts to mentors so that we can continue the discussion. Okay. I have kind of a question. So I'm not sure that even... So none of the students that I kind of was hoping to write a proposal wrote a proposal which I think there was some confusion, but it's fine. I think I'll be doing more school summer of docs stuff or season of docs. But what if there's no proposals that need additional mentors? I mean, I'd be fine with mentoring, but I'm kind of more helping out any of the other mentors who are already mentoring. And I don't know if there's too many people on one student if that's overload for the poor student. But I really don't remember a year when we had enough men, to be honest. Okay. And yeah, even if... So this year we have not only mentors, but also a technical advisor. So people who are not directly involved in mentoring students, but are more able to answer technical questions, maybe provide some reviews, et cetera. So maybe if you're interested it would be also an opportunity. So if you don't want to strongly commit to one particular project, but if you're still interested to participate somehow, with your experience with Jenkins, it may be a reasonable approach. Okay. Great, yeah. I would love to be involved and I would help out any way I can. Yeah, thank you. So anything else to discuss today? Martin, you have to drop in a few minutes, right? Yes, I have to go in two minutes. So probably there is no need to have a private meeting right now after this call then. But we can just discuss everything in the meeting, please. Okay. Let's just do the meeting, please, the discussions. Okay. So yeah, thanks everybody. Thank you, Oleg. Yeah, thank you.


Welcome back. So, last class we were discussing the probability generating function which is the transform which is typically used for integer valued random variables. So, I there was the small clarification I had to make. So, the region of convergence of the PGF I said. So, it is a they are discs for non negative integer valued random variables. And if the random variable potentially takes negative values they are generally annular regions right. And, but the region of convergence always contains the unit circle right. So, this is one clarification I want to make. Today, we will study the moment generating function which is actually defined for defined in general for any random variables not necessarily discrete or continuous or otherwise. And the reason we will see the reason it is called moment generating function because it generates the moments the nth powers of the expected nth powers of the random variable MGF is a function m x from r to 0 infinity by n by m x of s equal to expected value of e power s x. The domain or region of convergence of m x is the set d x equal to the set of all s for which m x of s is finite. So, the moment generating function of some random variable x is like an exponential moment the expectation of e power s x where s is the parameter. And it obviously this may not exist everywhere and the domain in which or the region of convergence where this guy is finite is called the domain or the region of convergence of this moment generating function. Now, notice that so there is so I have defined it as a function that maps r to 0 infinity right. So, what I am essentially saying is that this s is something real some real number right. So, again so strictly speaking moment generating function ought to be considered a function of a complex variable. So, strictly speaking that it is analogous to the Laplace transform in a so we will see that very soon right. So, strictly speaking we should allow s to be complex right, but throughout there will be little bit sloppy about this part of the reason is that we have not really defined the expectation for complex value random variables right. We only spoken of expectation of x where x is some real value random variable not really spoken of. So, e power s if s is complex e power s x will be complex and we not really described complex random variables in any detail right. So, ideally we should have s is complex, but I am kind of pushing it under the corporate I am not going to be very serious about this. And for this reason even for the many theorems and results on the moment generating function which really require a fair amount of complex analysis to prove and understand properly right. So, many of in that sense I will only be quoting results and using some properties from complex analysis without being very serious about deriving them or you know proving them. So, this is expectation of e power s x. So, if x were to be discrete this is you would just sum up the p m f right. So, for example, if x is discrete with p m f p x of x then m x of s will be sum over x e power s little x p x of x right.  So, just to be clear let me just write d x all right. So, it is in this sense that. So, for continuous random variables this moment generating function is exactly analogous to Laplace transform except for that little minus sign you use for Laplace transform right. Usually you put a minus here for Laplace transform, but otherwise it is the same thing and just like in Laplace transform you in Laplace transform you consider s as a complex number right ideally that is what you should do here also to be precise. But we will just we will not do that. So, just to keep things simple and to avoid contour integration and so on. So, any questions on this? So, let me give you some examples we have an exponential random variable with f x of x is equal to mu e power minus mu x for x because now is equal to 0. Then you have m x of s is equal to integral mu e power minus mu x e power s x d x right this is from 0 to infinity this is equal to.  So, if you can just for now s we are treating s as a real number right. So, we just do this integral and you can see that if s is less than mu e power minus mu x. So, if you just take this up you will get this just simplify this. But if s were to be bigger than mu this e power s x is growing faster than e power minus mu x right. So, you will get infinity right in that case the moment generating function is plus infinity. So, again so there is one remark I want to make here if you had. So, again right. So, if you if you were doing this as a Laplace transform right. So, this will become a integral of a complex function right. So, technically in order to be rigorous you have to do this as a contour integral some of you might have studied complex analysis. So, you would have to do this as a contour integral the thing is you will get the same answer and the answer will be valid for real part of s less than mu. So, I am ignoring that bit here I am just treating s as a real number and blindly integrating it this clear. Second example let us do a Gaussian. So, let us do a standard Gaussian 1 by square root of 2 pi e power minus x square over 2 for x in r. So, I have to write out now m x of s is equal to integral minus infinity infinity 1 by square root of 2 pi e power minus x square over 2 e power s x d x right fine. How do you do this integral is a very standard trick to do this integral you have to you have to square I mean you have to complete squares in the top right you remember that it is an old trick. So, you have to multiply you have to I think do that s square over 2 and then you do. So, then multiply by e square e power minus square minus s square over 2 and then you will have a perfect square in the top right you will have e power minus x minus s square over 2 right correct with me. So, this is just algebra right this is standard trick and then this integral is your is a standard Gaussian integral right. So, this integral become 1. So, the answer will be e power s square over 2 and this is valid for all s I will say that for all s in r actually this is in fact this is the moment generating function for all complex values of s also it is valid in the whole complex plane. So, this is not value in the whole complex plane it is valid for real part of s less than mu if s were to be complex. So, I am so far I am just doing all this as real integrals which is not technically speaking the full means fully correct actually when we do Fourier transform this issue will bite as even more when we do characteristic functions right which is like a Fourier transform will this will bite as even more. So, that is exponential this is Gaussian and finally, let me do Cauchy. So, if you have f x of x is equal to 1 over pi 1 over 1 plus x square x in r. Now, you try to do this integral m x of s equal to integral minus infinity e power s x over pi times 1 plus x square d x right. Now, what happens in this case if s is equal to 0 you get if s is equal to 0 you get 1 right you are just integrating the p d f itself right. So, by the way I mean if s is equal to 0 anyway you get expectation of whole thing will become 1 right. So, it is always 1 that is one of the properties I am going to state right. So, this will become 1 for s is equal to 0, but if s is again pretending s is real if s is greater than 0 you have a growing exponential competing with the decaying 1 by x square type of a term right. So, that will be infinity right, but if s is negative what happens you have the opposite problem because on the negative side it is growing right and 1 by x square is the decay on the negative side as well. So, what you can conclude if s is not is equal to 0 this is not 0 this is always infinity right infinity otherwise right with me. So, as if you are restricting s to real values only for s is equal to 0 is it defined otherwise it is infinity it is not. So, the region of convergence in this case will be just s is equal to 0 on the real lines only for s is equal to 0 is the m g f finite. But s is equal to 0 is always a part of the region of convergence because as you can see the moment generate m x of 0 is always equal to 1 right by definition. So, for this particular so there are 3 different cases right. So, here there is a certain range where it is finite certain range where it is not in the region of convergence here for all values of s then m x of x exist. So, the region of convergence is the entire real line in this case and here there is only 1 point in the region of convergence only the origin right. But origin is always in the region of convergence and that is all there is in this case no further there is no further points in the region of convergence is that clear. So, that brings us to the question is it enough to specify the moment generating function in order to specify. If I just tell you this is the moment generating function and this is the region of convergence is it enough to specify the random variables distribution of the random variables density in this case completely right. So, if I were to give you this is my moment generating function with this region of convergence is it necessarily true that. So, for the exponential this is the moment generating function, but is this true that if I only give you this can you conclude that the can it can it uniquely say that it is this p d f or for the further matter for the Gaussian. If I give you this is my moment generating function e power s square over 2 for all s can you tell me that the random variable is the standard Gaussian right. So, more generally if I give you the moment generating function and region of convergence can I tell you can you tell me the distribution uniquely right. So, that is the what do you think yes or no no who says no yes. So, suppose I give you this suppose I tell you that the it is equal to 1 for s is equal to 0 and everywhere else it is undefined or infinity right infinity actually. So, then what you say does it have to be Cauchy. So, in fact I can have 1 over 1 plus x cube right you get the same answer correct. So, if this were to be not 1 over 1 plus x square, but 1 over 1 plus x cube with some other constant in front by the same argument you can conclude that or 1 over x to the 4 for that matter right. So, you will you can easily conclude that it will be the same moment generating function will be defined only for s is equal to 0 and undefined or plus infinity for s not equal to s not equal to 0 correct right. So, what do you think. So, generally the answer is no. So, I just prove that the general answer is no if I give you the moment generating function just like this for example, there is no way you can figure out the distribution, but it seems like I mean if you tell me something like that or something like this it seems like you can uniquely identify what the distribution is right. So, the complete answer to this turns out to be very interesting, but in order to appreciate it you have to you have to know some well it requires some tools from analytic theory of analytic functions. So, the answer is the following if you specify the if you give me the moment generating function not at one point, but in some tiny neighborhood of the origin of s is equal to 0. If you specify in any tiny neighborhood around the origin then that is enough to specify the density uniquely the distribution is uniquely specified by specifying the moment generating function in any tiny interval right. The interval can be very small or very big does not matter. So, you do not even have to tell me for example, that e power s square over 2 is the moment generating function in all of real line. If you just tell me this is the form for a tiny interval around the origin then it has to be Gaussian in this case in that case it has to be exponential and so on, but if you just give it to me at one point it is clearly not enough right. So, I will just state this as a theorem without proof this again goes back to the this goes back to the theory of analytic functions analytic functions are these you can think of them as the very nice functions which get completely specified if you specify them in a small interval m x of s is finite for all s minus epsilon epsilon. So, this epsilon is greater than 0 epsilon is any positive number it can be very small also as small as you like it cannot be 0 can it has to be strictly positive. Suppose you tell me that m x of x is finite in that little interval around the origin then m x of s uniquely determines the c d f of x if x and y are two random variables such that m x of s equals m y of s for all s in some tiny interval minus epsilon to epsilon again epsilon is positive then x and y have the same c d f. So, this is like a uniqueness of moment generating function. So, it is if you it is not enough to specify it at a point or a few points, but if you specify the moment generating function in a tiny interval right no matter how tiny it is if you specify it in an interval the c d f is uniquely specified. Furthermore, if you have two random variables let us say you know nothing else about them, but you do know that they have the same moment generating function not necessarily everywhere they have the same moment generating function in some very tiny interval around the origin. See all moment generating functions are I agree at the origin right because m x of 0 is equal to 1, but I am saying that m x of s and m y of s do not just agree at the origin with they have two they agree in a tiny interval around the origin. Then it is necessarily the case that the moment generating functions have to agree in their entire regions of convergence and the random variables have the same c d f. So, this is the. So, this is this kind of a result is possible because these so called analytic functions this moment generating functions whenever they exist in a neighborhood they are analytic functions of s of the complex variable s actually. And these analytic functions have some very they have some very tight properties. So, you cannot have two analytic functions agreeing on an interval and then differing elsewhere because you cannot make analytic functions by stitching together right because they have some very tight structure. They cannot stitch together functions and make them analytic it never works that way. So, that is why this theorem holds this proof is beyond the scope as I said because requires machinery from complex analysis which one there is no further conditions right. I mean I have not said anything else here right. If they agree in an interval they agree everywhere actually that has nothing specific to do with moment generating functions is true for all analytic functions. It just so happens that the moment generating functions whenever they exist in an interval they are analytic. So, if you take that let us say s is equal to 0 m x is always all moment generating functions have the value 1. So, what I what I require is that the function b function agree on some interval that interval can be anything right. If it agrees on minus epsilon 1 to epsilon 2 it necessarily agrees on some minus epsilon to epsilon right. So, I can take a there is no loss of generality in taking a interval like that. Generally if an analytic function agrees on any interval whatsoever it will that is enough it is always defined right. Zero it is always defined, but it is not clear that it will be defined in an interval around 0 as in this case right. But if it is defined it is uniquely specified no matter how tiny is epsilon is yeah you can have minus epsilon 1 epsilon 2 if you like there is no there is nothing very sacred about keeping the same epsilon right. So, is that clear. So, to go back to this if you give me a function like that and specify an interval in which it co holds then I am unique I am sure that this is an exponential and that is a Gaussian without even specifying it for let us say the whole of real line.  But here you cannot specify it for an interval right it is 2 bar it is only defined for 1 point in that case it is not unique. So, that means so at some level I must be able to if you are giving this kind of some functional form to me in an interval I must be able to invert the moment generating function and get back my c d f or p d f 4 as the case may be right. There are actually explicit formulae in terms of the moment generating function to get back here. So, to get back here in this case density let us say right these formulae are basically similar to the inverse Laplace transforms. But again we will not go into it because it requires. So, what is the inverse Laplace transform like it is a contour integral right it is an integral of a complex function over a certain contour right. So, because that is a little bit beyond our scope we will not actually perform contour integration to inverse invert any transforms. After all if I tell you that the m g f is 1 over 1 minus s you can just do some pattern matching and figure out what the random variable is right. So, what the approach we will take is somewhat more what I what I might call practical rather than very mathematical just that if you just pattern match if you see a transform like that you know it is Gaussian right. So, we will just figure out some transforms for some popular random variables put that in your keep that in your mind or put that in your formula sheet for your exams. And you just do pattern matching we will not worry about contour integrals.  So, in the case you can pattern match if you have not that type you put it in your formula sheet no problem right. So, properties properties of m g f m x of 0 is equal to 1 right that is the most trivial property that is by definition second property moment generating property which is why the function is called the moment generating function in the first place right. So, this I will put as a theorem suppose m x of s is finite for s in minus epsilon epsilon is positive then the derivative with respect to s evaluated at s is equal to 0 equal to expectation of x. And generally the m th derivative d s m at s is equal to 0 is equal to expectation of x power m. So, what this is saying is that if you take the derivative of the moment generating function with respect to s and set s is equal to 0 you get the expectation which is the first moment. And generally the n th moment the m th moment is obtained by evaluating the m th order derivative and taking s is equal to 0. So, this is again. So, if you want to prove this theorem. So, there is a I mean there is I will just at a very hand wavy level this is what is happening right you are taking d d s of expectation of e power s x right. So, if you tolerate me taking the derivative inside. So, if you do expectation of d d s e power s x then this will be expectation of s times e power s x correct I am differentiating with respect to s right. So, x times e power s x correct. So, this is equal. So, and then I set s is equal to 0 then I get expectation of x right.  I am essentially taking the derivative inside what is this expectation after all it is integral right it is an integral x d e power s x d p right. So, this requires a somewhat serious proof not a difficult proof, but this will be in your home work it is a I will put this in your next tutorial. This requires a proof it I believe it is you have to invoke dominated convergence theorem somewhere in order to yeah it requires invocation of the dominated convergence theorem that is your hint. And similarly for the m th derivative again if you are willing to buy this step you can differentiate this m times and you will get x to the m th here right. So, you will get the m th moment. So, the only real mathematical thing is in the taking in the you are essentially differentiating inside the integral that requires the justification it is not always true it requires justification after all the derivative is. So, let me give you one more conceptual hint. So, the derivative is some kind of a limit correct limit h tending to 0 of something right. So, you have an expectation is an integral and what is outside is a derivative which is like a limit. So, you have limit of integral and if you have to integrate interchange it you have to have integral of limit right. So, you must invoke either m c t or d c t you know only two ways to do it in this case it turns out that d c t will do the job. So, I will so I will not say anything more about the proof because you will supply this step and then you are fine. So, that is property number 2 property number 3 if y equal to a x plus b a and b are real numbers. Then m y of s is equal to e power b s m x of a s is actually a fairly simple change of variable fine. So, in particular so as an example if you have x is your standard Gaussian and we have y is equal to well sigma x plus mu y is equal to sigma x plus mu. In this case then y will be you can easily show that y will have mean mu and standard deviation sigma we varying sigma square right. So, then y will be n mu sigma square and in that case m y will be e power mu s times e power sigma squared s squared over 2. So, you know the m x of s for the standard Gaussian is e power s squared over 2 right. I am just using this result to compute the moment generating function for non standard Gaussian as well n mu sigma squared right. I can compute the moment generating function yes I am saying that this is valid. But, it is not always valid it is valid in this case you cannot arbitrarily interchange derivatives and integrals. Now, you need an you need to in work dominates convergence theorem this is not a this requires may be 4 steps it is not 1 step it is a you will do it in your home book it is a guided proof that you will do. Now, finally property number 4 you have z equal to x plus y x and y are independent then you can show that m z of s is equal to m x of s times m y of s. And this is because expectation of e power s z. So, e power s z is equal to expectation of e power s times x plus y that is equal to expectation of e power s x times e power s y. Now, you know that see you know that x and y are independent therefore, any functions of x and y are independent. And since then therefore, these 2 are independent e power s x and e power s y are independent and independent random variables are uncorrelated right. So, this will become e power s x times expectation of e power s y. So, here is where you need and you are using independence here. And similarly, if you have n random independent random variables you will just multiply all the moment generating functions in order to get the moment generating function of the sum. So, this is valid for this great continuous any kind of random variable right you have not assumed anything in particular. So, this is exactly like in signal in systems. If you are instead of convolving functions you multiply Laplace transform when invert back right that is exactly what you doing here. So, if x and y had let us say they had densities then you would convolve the densities, but that is convolution is an awkward operation. So, it is better to take transforms multiply and transform back right. So, if you want to example, if x 1 is exponential of mu 1 and x 2 is exponential mu 2 and x 1 and x 2 are independent. And then if z is equal to x 1 plus x 2 then you have m z of s will be the product of the 2 moment generating functions right which will be mu 1 mu 2 over mu 2 minus s times mu 1 minus s right I am just multiplying the 2 moment generating functions. And this will be valid for s less than this more than of the 2 is not it minimum of mu 1 comma mu 2. So, this is the moment generating function of the sum correct. Now, how will you find the if you want to find what the distribution of z is you will have to invert this moment generating function right. So, now you can use some of your Laplace transform tricks what you are used to in Laplace transform right normally if you have something like this you write a partial what is it called partial.  So, that is fairly standard I think you can proceed from here. If mu 1 were equal to mu 2 you will get mu minus s whole square. And that will be the transform of your second order Erlang because you are adding 2 exponentials. So, good then finally, let me just state the final property before finishing. If you had a sum of a random number of random variables let say z is equal to sum over i equals 1 through capital N x i where x i's are i i d with m g f m x and n is independent of x i's with p g f g n and m g f m n then. So, this is a situation you considered before I am just trying to write it as write its moment generating function m x of s is given by g n of m x of s are equal to m n of log m x of s. So, g n is your p g f from the previous class the proof of this is using the law of iterated expectations is very similar to the proof we derived in the previous class is fine. So, the most the this formulas most useful in an example of this following kind where you have x i's are i i d exponential with parameter mu let us say and n is geometric with parameter p I think we consider this example earlier did not we where you had a geometric sum of exponentials right. And I think what we did that is just brute force did wrote out the whole thing and figure out that there is some answer right here you will get a very explicit answer. Because here you have m x of s is what mu over mu minus s right where s is less than mu and you have g n I know right. So, g n of s g n of if you like g n of z is what I used right what is the p g f of this from previous class I had p z over something like that is not it 1 minus p z is that right correct. And this is valued whenever the argument is less than 1 over 1 minus p. So, if I were to blindly substitute here. So, my m z z is of course, my geometric sum of exponentials m z of s will be equal to p. So, I have to compose so I have to take g n of m x of s. So, whenever I have g n of z in place of z I have to write this whole thing right.  So, I have to take care of the regions of convergence of course, just do that.  Remember the taxi example or the word is a taxi or alpha particles either way either example will do right. You are waiting for taxis which arrive like with exponential durations and with probability p they are occupied may be probability 1 minus p they are occupied. So, you have to wait for a geometric number of taxis each of which takes an exponential amount of time to come. So, the total time you wait is exponential with parameter mu p. So, this is very easy right this is like three steps rather than doing the big summation in the previous case I will stop here.


What are game engines and how do they work? Ever heard of a game engine like Unreal Engine or Unity? Well, I thought it was a literal engine on your PC. They're actually a software framework that game developers use to create games. Without them, games would not be as advanced and game devs would have to work thousands of hours more to create a game. Some game engines are free and some aren't. So basically, there are three main parts that game engines do. The first main functionality is to house the logic of the game, which will be everything from what you press to what your character does. They have a rendering engine, which like the name says, rendered graphics for the user. The audio engine would generate the sound and when the sound gets played, this will cut back time for the developer and it will help them with different parts of making the game. It also helps with networking and logic and physics.  Another reason it saves time is because it has pre-made scripts, so things like moving would be implemented in a game without the developer having to write a whole script about it. Even bots are made by scripts nowadays and they're getting more and more realistic thanks to game engines. Of course, it can help a ton, but you still have to do some work. Game engines are just a tool for making games. In games a few decades ago, developers had to design everything from the physics to the sound along with the little things that game engines take care of like memory usage. It wasn't until 3D games that game engines became popular and skyrocketed. It was way too complicated to create a 3D game by just starting it from scratch. Like think about it like this. Where else are you going to customize the lighting and the character models without an engine? Some developers still make their own game engines, like me due to their idea of a game not supported by the tools out now. Even things like mobile games can be made with game engines. Finally, learning game engines might seem like a big deal, but just watch a tutorial on YouTube and search up problems you might have later on. That's how I learned many things like video editing. I wish I watched this video when I got into games, so if this helped, great. If it didn't, well, I'm sorry. What do you think about this topic? If you want to learn more about gaming, or you just want to know more about games, subscribe. I post videos weekly and you'll be missing out on a ton of things you might want to know about gaming. Thanks for watching, and let's have a discussion about this in the comments below.


And in sports, the German Olympic soccer team will leave on Tuesday evening for Tokyo. Coach Stefan Kantz has contacted over 100 players, as he said, but for various reasons many of them gave him a refusal. Mostly it was the closeness to the euros in which Germany intended to much further that it did, with only 18 instead of the 22 players. Kantz's team still aims to do well in the Olympics. Besides the many newcomers amongst them, seven of the 21 European champions are also old hands like Max Cruz, the Maximilian Arnold. There are 16 nations competing in the next tournament.


What's going on Chris from justice case breaks calm? This is part two of that immaculate 55 break Which show you our teams here? The first part was the randomizer series our teams from Nick and the Hawks down to Nick in the Wizards This is our original randomizer from Bjorn and Nick With the rockets into the Wizards same things already put them in order. I have the sheet in front of us as well Sorry about that y'all so 55 Nick in the Hawks All the way down to Nick in the Wizards. Sorry about that again y'all Let's uh, let's get to it though immaculate break number 55. No spots given away just another rip Let's hope this last immaculate is a banger. Yeah And last box for a while. I didn't see any more in the back That's a more fun stuff. We can leak it some more in soon. I have redemption. Let me get you at this back Incredible All right Good luck everyone. Thanks again for getting this break filled out Let's get to it All right first card Kevin Porter jr For the houston rockets 66 out of 89 Going to Bjorn The standard Carl anthony towns big blue jersey patch 27 out of 99 Series tied at one here now with minnesota and menfess Cat had a nice first game big poster on jaren jackson jr. That was cool to see next card Looky patch three out of 99 onyeko kong will go into the hawks go into nick They may be done. It's hard any hawks friends out there next up Passive presence signatures lefonzo ellis 19 out of 99 go into the denver nuggets go into david g I have not thought about lefonzo ellis in a long time We'll throw back there Next card Another old school guy three out of 10 Harold signatures chris mullen hall famous for the gold state warriors another one. Let's go into david All right, and our last card is a redemption our last box of immaculate. Good luck everyone. Thanks again Talking once again They have the worst cold ps in all the baseball rookie patch auto Card 117 Cole anthony nice nice one for the alando magic had a nice second year canard Congrats canard Nice from the filler 239 gets in there. It's a good way to nice rpa. Cole anthony rpa Very nice. All right, that is our last immaculate box of her The current moment. Thanks again for getting this all filled out in no broken jaspy's case breaks.com. Thanks again