Tiger, thank you. Thank you. Thank you so much. I love you and um, yeah, take care take take care of my Alan for me I'm doing my best. Yeah Handful, yeah, I bet he's uh, he's chill though. No, he's chill Yeah, his handful isn't a physical handful, it's like a other dimensional. Yeah, I understand I understand we worked closely together for you know good two years Back in the day and I learned a lot about myself and um And us you know collectively I'm so grateful for that experience with that I had with Alan It's the it will be the highlight of uh, you know, if I die tomorrow It will be the highlight of my existence, but if I go forward, you know, I'm sure Yeah, we may Surpassed me again. Yes. Take care All right, once again, we're talking with Atlas He's a thought-provoking interviewer and producer of multidisciplinary shows in which he has interviewed some of the most creative Scientist entrepreneurs and educators of our time. He has an overall mission to rebirth the public intellectual and inspire people to build I know he's doing other things is also the co-author of what is I it's a book that investigates I are into most sense of self and He's involved in a few other things Psycho Plastigens, which is the new word for any drug involving mind expansion. I guess, you know, it's no longer psycho doubt is psychedelics, but Plastigens and um And among other things is there anything else that you know, you know the word Polymath comes to mind, but you know, you're so much more than that a lot of people don't understand what that with that word means and He's just a very ease of ease You can't even say smart because you know in even in your awareness You know that there's so much you don't know on top of what you do know He's just a wonderful human being trying to get ready for Humanity 3.0 and he's gonna talk to us about Dow a project that he's involved in Homedow, which is like what's your what's your role Alan in in home Dow and Tell us a little bit about it. It's it's it's you know, I'm gonna say words like blockchain and NFTs and Sustainability and People want to know more about that. There's many things that are cooking to share right now One of them is that Ron and I spent several years together blossoming a Really beautiful show called simulation and I learned a tremendous amount of the directing and producing skills that I have today from him and I've taken those and continued moving forward carrying the torch into whatever else is being created through this of SLS projects Ron listed a bunch of them in addition to simulation. There's home Dow Which Ron has asked the question about There's the books that I've authored or co-authored which have been super fun There's the role that cycle plasticians have an ego dissolution and ego expansion and The best protocols for human development in general now home Dow is the Mechanism that enables the planet's basic needs infrastructure so water food energy housing both residential and communal and It's owned by nobody and everybody so That's the beauty of a Dow. So Ron asked about what some of these web three technologies are about and That's really at the essence of them is that they're They're oriented around The nature of consciousness, which is that consciousness isn't nobody and everybody and That's another topic that has been very interesting to me as My pursuit of truth has ended in my own awakening Which means awakening out of the separate false self and Into the true Source self Which no longer see separation and no longer sees any duality So there's no more Difference between a subject and an object. There's no more difference between self and other There's no more difference between inner and outer and there's no more difference between God and human So all those things Were perfectly together with the exploration of what web three technologies are and Will enable us to do as we feel the desire for the planet to be in perfect harmony with Humanity and with all these next generations that want to come to play and to actualize creative gifts and all that good stuff Which is something that Ron and I have been beautifully envisioning Sense the time that we were working together. And so this is just the downstream manifestation of that But we're also in this particular Timeline which is extremely frightening this transformation this division Among us this intellectual Division among us and I also feel That you know this timeline in particular although I'm hopeful I'm not very optimistic because You know, how is the change? How are we comfortably going to establish a more cooperative sense of humanity With this division among us or is that is that question? You know because where you are I'm sure it's you don't care You it is what it is. I listened to your talk with Colette Davies earlier today, which touches a little bit on you know one aspect of you know, what what we're trying to achieve in and in self and I as One a lot of the answers were in that film Everything everywhere all at once that I saw last night it but it's so complex. It's so mind-boggling It's it's all as if you know this what we are experiencing right now is a dream state That just has a little more glue to it. So it doesn't necessarily Feel like a dream. However, it's a dream It's it's it's here today gone tomorrow whatever today and tomorrow means so What what can you say in regards to? You know those that understand and surrender to this process and those that are just gonna go out fighting Literally fighting You know with finance Or is doesn't matter it doesn't matter You Yeah, what do you have to say cut just because you have Grappled with your With with inner peace and you have that and I have that too. I'm very grateful for that I do still get triggered a little bit. I told you I'm in a romantic relationship and that does trigger You know because we're two separate people or two individuals and we're trying to come together and even within that It's it's it's it's you know, I have a little I have a little more to go, but we're intellectual enough to discuss The things that are you know, legitimate problems with combining with each other. So I mean I have that to work with and But I'm still gonna wonder why how everybody else that isn't even where I am at I'm gonna achieve this state of awareness and collective consciousness and You know loving loving thy neighbor as you know, thyself your thoughts well This is the best movie of all time and It doesn't Have a manifest in any specific way and so if there are those that Desire Harmony and basically needs to be met then those will be and if there are those that Do not want that Then those will be and that's just what will be What is We're in 2023, you know, we have we have 2023 To look at and I understand that this a More harmonious existent involves time travel And time travel is already among us as We're trying to create time travel. We're not necessarily, you know we're gonna I told you before that this is already virtual reality all we're gonna get to is discover that You know as we try to make time travel machines We're gonna we're gonna be informed that there already is a time travel machine and that's how we We grow Happening all at once. Does it make sense to you? Am I you know, just do you when I when I tell you these things? Am I am I hitting the nail on the head is is my head in the right place of this? Understanding because a lot of people will say that I'm batshit crazy You know, but I take the concept of past present future happening simultaneously Very seriously. I wake up every day with that understanding Every day and this timeline is a rebirth for for me and to Shed as much skin from the day before as possible and only focus on what's really important You know for me and Everybody else, you know, and when I say what's important for me I'm inclusive of those that are around me and that includes this community that I live in And it's it's hard It's hard, you know, I'm not gonna say I'm advanced But I've been working a lot on this I you know, I I selfishly Work on it while including those around me Including, you know, my loving relationships a deeper deeper loving relationships romantic relationships. I'm so glad we have I'm just so good to see you Alan And I want to I you know as much as I want to help others Get to a better humanity You know, I still the bottom line is it's it's all within me. That's all that's all I can do for Collective consciousness Is not be the liar the cheat and the thief among us and be true to myself and True to others and what is truth? You know, what is truth?  I'm you know that game of risk. I'm getting tired of nations I'm getting tired of flags in my Overall existence. These are the things that I'm tired of is you know, is there any other way? Yeah Do you want to talk a little bit more? What's an NFT? Did you hear what I said? Earlier. Oh I said let go. Oh Let go. No that I got blocked out. Yeah, I've let go of a lot of things.  Yeah Thank you, but I want to help this someone close to me too, you know, cuz I'm close to him Start with yourself and with fully putting on the oxygen mask Yeah And so letting go what does that feel like I get back to get yeah, I guess it's safer less anxiety Had anxiety preparing for the show because I knew a lot of it as much as I you know, it's gonna be it's gonna help me You know, whatever wherever your head is out, you know, you're somebody I trust You know, I can trust you all the people that we spoke with from you know, 2018 to you know, was yeah 18 18 18 months Yeah, all those different people working on different things that are now coming to the surface, you know We had access to them a lot of them before their work, you know, propelled them even even To higher levels where people are now interested in what they're saying It was such a It put things into perspective for me Made me be grateful that I was privy to other people Working on other things beyond the political arena If anything You don't made me lose faith in politics completely not that I had any faith in them before But so we're to kind of gather as much of your Energy as you could and declare one Thing that you desire One thing that you seek. What is the thing that you seek or that you desire just to be the best? possible version of myself in This timeline the best possible version the most strongest the the the wisest and The stillest Peaceful not bothered not no trouble not fretting not sad not angry You know and I'm doing pretty good, you know, I get I get Close to that version, but like I mentioned earlier I don't I'm not ready to be a Buddhist monk, which is not a bad idea for everybody to just get into as We go forward to this collective Consciousness of humanity and however that may look but that's what how do you become the best version of yourself Meditation helps the first thing I do when I wake up is to be mindful of to be to be grateful here. I am and To breathe to move to focus Immediately when I wake up immediately first thing on My mind is that understanding and stay with that as much as possible as My day unravels however long that may be if it's 16 hours whatever an hour is Before that period of slumber and I die and I wake up the next day and do it all over again How is meditation helping you be your best self? It stills it stills my mind and in quiet Quiet's down versions of me that no are not serving me And that's you know, I have a I have this ball I have this ball this No, they're singing balls Yeah, that frequency I want another frequency that helps that those, you know music You know helps the the lyrical content of some of our more poetic What if what you're looking for is your own Emptiness and wholeness. I'm aware of my emptiness I'm aware of my emptiness and I try to And wholeness well Because they're two sides of the same coin they come together. Yeah, you know, I love me and I hate me You know, I want to find that balance What's gonna work best in this timeline how to be most effective for myself first What is what is the eye that is loving or hating the me? Like if you slow that down and go to the source of that the eye the eye that is loving me is The div the divine a More or a more divine source and the eye that is hating me is Possibly just a just a program that I need to delete Mmm an ego of sorts, you know, I'm me that I created to What's at the root of that program running well, I was born into a Man and you know through a woman and there was man involved and I have those genetics That I needed to you know, you talk about the program. We're programmed from birth To the bleep well, even birth is an assumption well And birth as I mentioned tomorrow, I will be reborn. I understand that birth but also there's the the from infancy birth where you're at the mercy of Parental units that believe some some believe and just some, you know, it's not for me to say But you know a lot of things that you know that my my my parents believed in It just seemed like they didn't necessarily serve me and it did They were trying to work on a collective best interest, but that collective like the best of us right now Alan The best example of us, you know, how good is it is the question People that are leading and people that are following keep the keep the focus as much as you can on your inner escape And that like you said earlier that that's where the change happens and then that's also how perception has changed so it's less Directed outward at All of those stories and narratives and it's a more directed at its own source. So how do you feel when you're Not aligning with that ego program But instead you're aligning with the divine source program. How do you feel? well, I'm still comfortable in the ego source in this timeline I'm still the star of my own movie and what are you getting out of the ego program come come for familiarity But I'm also aware of the process that the ego does want to evolve the ego in me still wants to evolve and it's gonna deal with I Uncomfortable realizations appropriately I'm not gonna, you know, I'm not gonna go You know going out kicking and screaming. That's a lot of a lot of people are afraid of that including myself I imagine, you know, I don't want to be a mindless zombie. I don't want to be an alien gray That's but maybe I got no choice. I Got no choice So It's I like me for the most part Mm-hmm. Yeah, especially the one that That feels like it's truly you Well, who I truly am is are those rocks at the end of the film Everything everywhere all at once in a sense You know, I would who I truly am Now is not who I truly am I know where who I truly am is that you know the source the source That's who truly needs to come out That source but you also Yeah, well one of the Most important things about this style of quote work or approach of the inner with the inner is that There's nothing to change and there's nothing to do and so the inner Gets to be whatever it wants to be forever So if the inner wants to be nothing and Therefore everything infinite space consciousness if it wants to be that it can be that it's seriously just a change in identity If it wants to be it's false self and if it wants to keep playing those games It's totally free to do that and the crazy thing is that neither one is better or worse than the other and That's the nature of reality Then I should then I should just go start killing people You know, I know I Know but I really don't I think that's still gonna cause problems, although it's Because there's something deep inside of you That plays with the game of killing people and Then it makes that okay because it's actually important to make that okay it's important to make okay the idea of Death and destruction and annihilation and then By making that idea okay instead of off limits what we do is we Very clearly see within ourselves that that's the false self that wants to play with those ideas and that the true self Just wants to be it just wants to play it just wants to live in harmony It wants to see all these different expressions of itself in its dance infinitely and so that's what is happening but if we put the little death and destruction button in a corner and Put it in the cage and never look at it and never touch it. We're actually more likely to be monomaniacal and Egotistic So so that's sort of how that game is played You have to feel free to look at everything Including your own deepest shadows and the deepest shadows of the collective and therefore be free That's what you are it's just pure freedom So freedom to be whatever you want There's people among us that are having a difficult time With others expressing that freedom within a big concern amongst You know more adults than the generation dealing with it is the whole Transgender process and what do you what can you say what can we say to those who aren't Realizing it's just life expressing itself, you know, there's a there's a there's a there's a there's a structure among us That wants, you know, it's not too much room to move And it doesn't like that it's not normal What can we say what can we say to them that are having a hard time with that? not understanding Or does it as we there's nothing to be said well, there's only There's only boxlessness There are no boxes so everything is already Infinite space and it doesn't matter if the person that's listening to this message is able to right now fully understand this message Because eventually given the evolutionary trajectory more and more of the collective will be able to hear the message and they'll be able to look and see at how silly the idea of of Resisting identitylessness You can't resist a natural cosmic progression So it's a natural progression for consciousness to be boxless and It's just doing that. That's what it's doing Consciousness being boxless. That's what it's doing And it's great It's liberating for That understanding it's liberating It's fun. It's radical. It's revolutionary but for others it's threatening and What is it threatening but the false self? The false self loves its box and it loves pretending like there are others that are also in boxes and so the only thing that boxlessness or truth is Threatening is the false self Nothing real can be threatened nothing real can be destroyed and That's where true comfort and true safety and true fearlessness lie and You know in order for me to get a better grip on that, you know, I have to lose the whole life death paradigm And not be afraid of that frighten that and know that whatever influence I have on this process is a Fraction of a you know, nothing What if right now? What was looking out your eyes? Wasn't Ron and Atlas But what if it was death? What if death itself was what was talking to itself right now and that it was exploring life What if the nature of source is death? Being life How would that change Your fear of death of what you truly are and how would that make you feel that at any time? the idea of death Would it actually change nothing? freedom Well, you know me Alan, you know, there's no fear There's no fear Alan, you know, I'm still cautious, but there's just no fear and it opened it is liberating It is you know, it is liberating and that's good for me You know, is it good for us? so everything is perfect exactly as it is and There is only one thing that's happening and that one thing that's happening is infinite space infinite space without any identity being all identity and There's no difference between being in the illusion of separation and chasing after matrix pleasures Versus being a monk There's no difference and that's truth. That's reality. That's peace and so whoever is able to hear this message Whenever they're able to hear it We'll create exactly the catalyst that's needed for that entity to see that truth But this here is no longer Shapeshifting itself This year is communicating this Clearly from now on because it ended its own seeking you have to end your own seeking by Dying your false self into the source self and then You can end seeking because you'll know yourself and you'll know there's no difference between a monk or being in matrix pleasures and then You are free and you can communicate that freedom and live and be that freedom Fearless of death because you are death being life. You've transcended the death life paradox and Found that there was none the whole time. It was just your own imagination creating a paradox between the two and This is freedom and it's your birthright and you were never born Consciousness never births and never dies. It's just a persistent illusion That there are separate people that born and dies called relative reality and as long as you in As long as you entertain relative reality as Something that is more important than absolute reality you will be in its Illusions and games and delusions and puppetings and all kinds of stuff, which is also fun.  There is only water flowing Infinite space is water flowing and that's the only thing that's happening and if you go and sit next to a waterfall and Just be in the presence of a waterfall and Die into the flow of the waterfall That is the end of the story. That's the only thing that's happening. It's endless stories Source being endless stories And so just relax and just be that flow Whatever it is if your character if your dream character is destined to be part of The worst atrocities There that's what it is if your dream character is destined to be part of the greatest Ecstasies and blissfulness is then that's what it's destined to be. That's what I want That's what I want the last one Well, then if those that want that they really Need to take the inner work seriously Because that's where the blissfulness is found. It's found by Dissolving the false self in its games. That's the way that it's found and it's not found any other way the moment that attention is turned outward That's the moment that All of illusion begins Attention has to be turned inward and it has to be turned on a very deconstructive process if you're if you're if you're deconstructing Your false self on a daily basis you are doing the work Anything that's not that is not spirituality. It's just not So it's all everything else is just spiritual materialism Your only work is to deconstruct your false self, which is an inner game that you're playing with yourself That's the only work I'm devil's advocate here There's people among us that have come to conclusions and think they're right and they're gonna die that way And they don't think there's any work that needs to be done with them at all. It's the other person It's these there's these other problems among us that are causing the havoc the mayhem I'm Good with what I've learned You know a lot of people come to that these conclusions at such a young age and they have children and they teach their children these conclusions and It's it's it's a vicious cycle that of learning and unlearning and It's hard Alan The ego is it's hard for a lot of people. There's a lot of people that believe in themselves He and themself and Their friends to believe in the same shit, you know that sense of community where that's within the box There's communities among us that are in the box that are comfortable with that Mm-hmm Can we see that as Beautiful because the moment that we see ego as Simultaneously beautiful at the same time that it's a virus That's when we have truth Because ego is your greatest creation the illusion of ego is your greatest creation and yet at the same time you being on a an Violation path with your own ego and with all other egos is one of the most beautiful ways that you can manifest yourself So this is the this is the game. That's why it's like a mobius strip reality is unorientable You can't orient yourself in a way and That's the point of directionlessness and lostness and That's why when people talk about I feel Directionless or I feel lost or I feel Depressed or whatnot a lot of times they're just recognizing that the nature of consciousness is empty space And that there's nobody inside of them and a society is so brainwashed into thinking that that's a Mental illness and that we need to give them pharmaceuticals and all kinds of crap But in reality in an awake Collective you would be taught that the nature of consciousness is empty space and that you can be whatever you want to be So do we have to wait for people to just get tired of being this? Limited human of Ego and destruction, you know, how many how many lifetimes do they have to go through?   Why why would Why would I Come on to the stage and Then focus exclusively on On Being a character on the stage and Have blinders on and only be focused on being the character on the stage and then spirituality the spark is the Complete tearing apart of everything that is the character in order to recognize that holy fuck. I'm actually the stage itself So the question is why if the whole game is about going into the character Then isn't technically those that are very brainwashed into being the character only Aren't they technically doing their very part and isn't it technically perfect the way it is and those that are Spark to be the stage instead of the character to deconstruct that It's just what it is It's just source wanting to know itself, but source also wants to know itself through its false self characters Yeah, that's why it's unorientable. You can't say one is better than the other You can't say that waking up from the dream is better than dreaming and that's why it's all fucked up And you can't understand it and maybe we can't We also can't say we've got a long way to go because that doesn't make any sense either You know, we've got a long way to if this is who we are right now We have a long way to go where There's only it's only going one way What what is what is time? What is directionality all of those things right? And then there's peace and if we can let that be like right now around like that feeling inside of ourselves Where it's like wow Okay, I can I can like really give up Like I can give up All of my like seeking energy and I can just be okay with that lostness Like not able to orient towards waking up or towards staying asleep and just Being nothing and there for being everything and just like just feeling it inside of yourself more than anything And just seeing how that brings you peace if it doesn't bring you peace and you want to Continue being in Maya's amusement park of delusion Go for it if that brings you peace through Experiences and Substances relationships all kinds of delusions then go for that if that's what you think brings you happiness I'm feeling pretty good about the convo though Ronnie like that's a pretty good Oh, you were great Alan. This is you know, it does You were great. I don't know it was it's all I'm glad we had this talk because it's helpful It's helpful for me too you know I to see your progress and To you know be happy with my own at my own pace And yeah, if you watch me like a clock, you'd see the change and you know may not appear that way in my 56 years But are you 30 yet? Yeah, I just heard happy birthday Thank you 30 it doesn't mean anything I'm perpetually 12 and that's the bottom line That's that's that's the way I feel that you know child You know, I'm you know if they say oh, we must become like children, you know, I am so Yeah, yeah, but these these are machines and You know, this is all my brain knows Even if we I've mentioned this before if we swapped souls You know, we wouldn't know We because we'd be living off of each other's brain and that's what our brain tells us and you know You'd get a little bit of sensation of you know, how I roll and I'd get a little more peaceful From your end, but we wouldn't know Even if we would do different entities with each waking day what was still living off of this machine's brain You know trying to bring the mind the body and the spirit together Mm-hmm. All right. It's it's three o'clock Alan. Is there any do you want to um, let's let's let's let's bring people to home Dow Yeah, so let's let's um if you feel like your burgeoning in any way in your human development and You feel like you're Connected not only to what exists outside of the egoic frameworks that society is embedded in but you're also interested in the basic needs infrastructures of earth being in perfect harmony and For people to be free of their need for basic needs So they can be creative and they can be playful and they can travel all around the earth And we can be in perfect harmony then go to the home dow.com and You can join the discord there. That's the best way to get involved and we have our A Couple other things that are available. They're the white paper. There's there's other things that explain the mechanism there which is great and Besides that I would also suggest Following up on you know the show that Ron and I developed simulation and just keeping Focus on that channel and the way that that channel is going to grow and Pro and produce more content around the things that we talked about on today's show and then You can always check out What is I or the other books that I've written and they're available on the website and another thing that I would suggest What website are your other? Oh Alan's hockey on comm and there's other books on there. There's other books I went to Alan's hockey dot-com and all I saw was What is I high-level perception? Okay? Is there? That's the first book I wrote And then there's another book called riffs on the ineffable that is on Amazon So Riffs on the inevitable riffs on the ineffable ineffable Mm-hmm. Yeah, how's that spelled? I any ff a b le? uh-huh and What does that word even mean ineffable? unspeakable unspeakable riffs on the ineffable Mm-hmm. Are you are are you co-author of all those books? Just one what is I but high-level high-level perception and riffs on the ineffable are you know You're solely the author of the book and they can find those both on Amazon or just On Alan's hockey on comms the easiest way and then they'll link you to wherever you want to go and then So getting involved in that way and then one more way I would suggest to get involved is that if you desire ego dissolution Which means to just basically be your true source self that doesn't see separation.  I have an obsessive compulsive disorder with my desire to do things endlessly your Lee and so Learn how to not Okay That non-doing I want you to learn how to journal.  Okay?  Have I been a suit I have a name and so in this way you're gonna deconstruct your false self by Writing what's happening inside and then externalizing it and looking at it. So non-doing writing and Then Yes, meditation is good. I would say cycloplastogens are also really good. So taking plant medicines of sorts so anything that is In a facilitator network is usually pretty good So people that have extensive training with running these circles is pretty good And then you can go and sit and begin looking at things that are unhealed in your life Because those are the things that contract you Anything that's unhealed in your life meaning your mom trauma your dad trauma your lineage trauma your childhood trauma Anything in your frames of life of your previous experience that you fear to look back at is Typically where your little diamonds and gems are that are creating the contracted energy inside of your body That are not allowing you to feel infinite space So I would say those are your homework assignments if you actually want to feel Infinite space and wake up and if you don't I love you equally Loving your enemies Which are just yourself. Yeah Yeah Yeah Atlas, thank you so much for coming on our program and sharing your insight Keep up the great work. We're all counting on you I'm here to support you a hundred percent Best of luck with Best of luck to you best of luck to Tiger. It's great to meet him as well And again if you want to learn more Go to Alan Saki and calm all the links are there. It's a wonderful journey of A man's quest for truth And um, he's He's Not like everybody says he's not dumb. He's smart and he just needs respect Love you Ronnie. I love you. I love you too. And um, you know stay in touch and now I'll continuously see you and the continuum You know so grateful for this experience in this timeline And and and I love you and take care And I'm so grateful for the foundation that we established together, right? It helped it helped me Alan I I'm so glad that I had that that there was that was allotted in my journey that's you know I'm glad I'm very glad about that It helped me It gave me better It gave me some some hope speaking what all these other people outside of the mainstream narrative People And thanks everyone for tuning in Thank you guys


In this video we provide the solution to question number 12 for practice exam number 1 for math 12-20, in which case we have a work problem, specifically we have a water pumping problem of a tank. So let's first talk about the shape of the tank. The shape of the tank is in fact going to be a solid of revolution itself. A tank has the shape of the surface generated by revolving the parabolic segment y equals x squared on the interval 0 to 3 for x about the y-axis, and all of this is measured in feet. So before we even talk about the pumping problem, let's make sure we understand the shape of our tank. So we're going to have our x-y-axis as illustrated right here. I'm going to draw a parabola, like so, yeah that looks pretty good, in which case we might do something like we should label things. We're going to have x equals 0 right here, and then let's say that this point over here, and then not that far, we'll go like let's go I guess to the edge right here, this would be x equals 3. This thing does not have to be perfectly drawn to scale or anything like that. This point right here for future reference would be the point 3 comma 9, because after all this is the curve y equals x squared. We're going to take this curve from 0 to 3, and we're going to revolve it around the y-axis. So I'll draw the other side here for like completeness sake, and then I'll also draw a line at the very top of this thing. And so while this is not perfectly drawn to scale, this region over here is the thing that is our tank. But of course you have to think of that parabola and spin it around in three dimensions. If the tank is full, and it's full with a fluid weighing 100 pounds per cubic feet, then let's notice that's not water right, but I mean it is, it's something. But notice the units here, we're using feet, we're using pounds. We don't need to multiply our results by 9.8, because with scientific units, you often measure this with mass, mass is not a force, you have to multiply by the force due to gravity. With standard units, pounds is already a force, it's already a weight, it already has that built into it. So it's going to be 100 pounds per cubic foot in that situation. So that'll come into play later. So we need to set up an integral to find the work required to pump the contents of the tank five feet above the top of the tank. So I want to make mention, like we mentioned over here, the top of the tank is happening at y equals 9. We need to then go five more feet up the line here. And so in the end, the top of the tank, sorry, we have to pump the water to the point y equals 14. That'll be important for us in just a little bit, okay? So we need to set up the integral to calculate this work, but we are not going to evaluate it. So our strategy for doing this is to look at a typical cross-section. If we were to cut our tank into little slices, they would be circular slices, cylindrical slices, and then we have to move these to the top of the tank. Now let's do it in steps. The first thing we're going to do is we're going to calculate the volume of one of these slices. Because it's a solid of revolution, each slice is going to be a disk. And so its volume will be pi r squared. The thickness here is going to be a dy, because the thickness of one is a small change of the y-coordinate. So we get that the volume will be pi r squared dy. R is not a very good one if I have to integrate with respect to y. So how do we get rid of the r? Now the r is the radius of this cylinder, of course, but it's also the distance from the x-axis to this point on the very edge of the circle, whose coordinates are going to be x comma y. So in particular, the radius of this disk is going to be the x-coordinate there. So we can improve upon that, pi x squared dy. But remember, we want to integrate with respect to y. So I have to rewrite the x's in terms of the y's. But as this point lives on the parabola, the relationship y equals x squared comes into play. So since I have an x squared, I can rewrite that as a y. And we get the integral pi times y times dy. That gives us the volume of that slice. I didn't need to compute the weight. Weight is the force due to gravity. Although w makes sense, because w might also mean work. I'm going to actually write this as ff for force. To find the force that is the weight of the object, we're going to take its density, which is pounds per cubic foot. And then we're going to multiply it by its volume. So we have this constant rho times volume. That gives you the weight of the object. The rho is 100 pounds per cubic foot. The volume we just did, pi y dy. And so then we're ready to talk about the work here. The work is the integral of force times distance. I guess there is one other thing we haven't considered yet. What is the distance that has to be traveled here? Now if you take a typical slice like this, this has to move to five feet above. So the distance that a typical slice has to go is it has to go from y equals 14 to that has to go up to there from the location of the slice. This slice is happening at the address of y. So the distance we have to travel is going to be 14 minus y in that situation. So then if we apply that to the work that we were doing just a moment ago, we're going to end up with a 100 pi that came from the force integral. I just put those coefficients in the front. We have y for the force. I'm going to put the dy at the end. So then I'm going to put a 14 minus y right here, dy. That's the integrand. Then the next thing we have to consider is the locations of the disk. That is, what are the bounds of integration? Our disk can range anywhere from the very bottom of the parabola. That's going to happen at y equals zero. And they can go all the way to the top of my parabola, which actually was bounded above here at x equals three, aka y equals nine. So the upper bound is going to be nine. So even though the disk will be pumped up to the level y equals 14, the integral's bounds are the locations of the disk, not where they end up, but where they are. And these disks live anywhere from y equals zero to y equals nine.  You can see why I changed the font color. This is the very final answer. This gives us the integral to measure the volume of this thing. I confess it's not a very hard integral to compute, but the instructions did say do not evaluate it. All of the points here are for setting up the integral, not from its evaluation.


The United Nations Children's Education Forum, UNICEF, stakeholders and civil society organisations have advocated for six-month paid maternity leave and establishment of crutches at workplaces in both the public and private sector. They made the advocacy at the one-day strategic dialogue aim to encourage early initiation of breastfeeding within an hour of Beth, exclusive breastfeeding for the first six months of life and continued breastfeeding to two years of age. UNICEF Nutrition Specialist, Indy Kaduna, fuelled our fishing ways, a face said, breastfeeding within one hour after birth and during the first six months reduces infant life-threatening diseases and mortality of children. UNICEF Nutrition Specialist, Indy Kaduna, fuelled our fishing ways, a face said, keep that child alone on breast milk for the first six months. You find out that it will help to reduce child mobility and mortality. The rate with which they fall sick and if not controlled they may die. So breast milk is really something we must encourage women to do and doing it properly. We want to show the commitment of government as to the issue of the six-month paid leave that we have and to continue to have this kind of arrangement not only in the businesses but other departments and agencies of government so that Kaduna will remain number one by the time we have all the crutches everywhere. The crutches are good. Children have a very young and sharp brain. By the time they come to the office they see what is happening they will grow with that mentality and they also want to participate in governance. The President of Medical Women's Association of Nigeria Kaduna Brand says zero water and extensive breastfeeding improves a child's cognitive and keeps the child healthy. We are talking about zero water so that our children can have the full benefits starting from that early initiation and once that happens we expect that that child will be positioned to be on the journey of a lifetime that is benefiting and at the end of the day will help the child to grow to become a productive adult. When a child is well breastfed and provided that opportunity to grow and thrive they stand a better chance of survival they are better protected and at the end of the day their cognitive function in terms of their intellect becomes stimulated. They do well in school. Our message really is for mothers for fathers and the entire communities to understand and embrace this breastfeeding practices and other maternal infant and young child nutrition practices that are very healthy for the entire family and society. Nutrition advocating from the state government of Kaduna State to ensure that every MDE have a crutch where our breastfeeding mothers after the six months maternity leave they will now come back to the workplace with their little children to continue breastfeeding as we have said the breastfeeding continues after the exclusive breastfeeding even up to two years and beyond so with the crutches made available the mother will have a conducive atmosphere to work and also to breastfeed her baby without anyone wanting to be put into law so that not only the public facilities are going to adhere to the law but even the private sector. August 1st to 7th is set aside as the World Breastfeeding Week the 2023 campaign is to increase awareness on the health and well-being of infants young children mothers families and the society at large hello hope you enjoyed the news please do subscribe to our youtube channel and don't forget to hit the notification button so you get notified about fresh news updates


Hey, AJ, how did you feel for the unit to be able to close out the game here? Y'all had to get off the field there a couple times late. Just going out there and just playing a complete game and just getting it done in the fourth quarter, just weighing our hat on that. What are some of the keys to Trevor Lawrence's number one pick? You know, it's one of them that's just keeping them under control. Just hats off to Trevor, you already know that. Great quarterback. But defensively, we just played as a unit this week. Just came together as one, everybody just did their job and came over to W. When you went out briefly, what happened that you just kind of felt? Just something happened with my shoulder, just came down on it.  Did it feel good? Yeah.  Yeah, just being ready, next man up, next man mind set, and he was ready. He had a good practice all week and just came out and did his job, helped us get to W. Has the unit grown over the last few games? Looks like things are starting to all be playing as a unit better over the last couple of games. Yeah, just something that we focus in on every week, just not being ourselves and winning situations in football and just playing as one. Like I said, just playing as a unit. Does that help you early on in the game potentially or at all? Me and Trevor, we had our battles at Clemson, whether it be in practice or whatever. But yeah, like I said, good quarterback, very instinctive and just decisive with all his passes. And you know, the ball gonna get rolling over here, so he good.  Well, I ain't played him in so long. I've never been really against him for a real live situation. So that was my first rodeo. So, you know, it is what it is. What for you guys are feeling? Just the heart of the team, you know, just everything we do. You know, we try to be meaningful, just come in, whether it be in meetings, in practice, just trying to focus in on details and understand that we still gotta, you know, race for the playoffs and just not getting complacent, just staying on 10 toes the whole time. Anything else? All right, thanks, AJ. All right.


Hello people of the internet, my name is Johnny and welcome back to another FNAF News video. We've got some news about the books, a lot of news about the books. We have a cover for FNAF Fazbear Frights Into the Pit and then we also have the title, description, and cover for the second Fazbear's Fright called Fetch which introduces a whole character to the franchise so who that is? We don't really know and we're going to find out when it releases, I believe sometime March 2020. So we've got a while to wait, but for now let's check out the Book Manager page. It's not Amazon, it is Book Manager. That's for both the Fazbear Frights. Link down below, you can check it out for yourself. And yeah, just gonna jump straight into it, starting off with Into the Pit. So before we read the description, we're gonna start off with some information about the book. The title is Into the Pit, FNAF Fazbear Fright number one. Paperback, it's made by Scholastic, Scott Cawthon, and Ellie Cooper who is a new person working with Scott to create these books. It's the first in the series, again Scholastic. The categories are young and old fiction, horror, monsters, and ghost stories ages 12 and up. It releases the 26th of December this year. So we still have a few months to wait, but it's not as long as the other one, which is Fetch. I don't remember their names, it's new information. Yeah, this is the cover. Oh, that's the wrong button. We're gonna see a better close up image of it later on. It's also in the thumbnail so I'm sure you guys took a few minutes to look at that and if you didn't, don't worry because we're gonna look at it right now. And this is the cover. The top reads from the number one New York Times bestselling author, which is Scott in the new edition of Ellie Cooper. Five Nuts at Freddy's Fazbear Fright number one into the pit. And the cover is a lot different from what I expected it to be like. I believe when we first made a video about Into the Pit, I thought it was going to be about the twisted animatronics with their little pits that they did, that they dig in the daytime so people don't see them. Apparently it meant ball pit. As we can see, it would appear to be spring bonnie just kind of looming around in a ball pit.  It is flesh, it is skin, muscle, all that stuff. So this is most likely spring bonnie, which is spring trap, before he got all messed up, tear it apart and everything. And probably the purple guy is in here. I wouldn't be surprised if in the book William Afton is in here or if it's this Fazbear Fright's version of William Afton. It definitely is someone wearing this suit on the cover, who it is. We don't know yet all that we know. All that we can say right now is that it is probably going to be William Afton or this book's version of him. Where this ball pit is located, I don't know. The only time we've seen a ball pit in the franchise is for NAF 6. Pretty fast, but it's a pizzeria simulator. It's one of the objects that you can buy and put it in your pizzeria. I don't know if this is going to be in the FNAF 6 location. I don't think it will be, just because spring bonnie did not exist during the FNAF 6 time period. So maybe there was a ball pit in Fredbear's Family Diner, or maybe this is an entirely different animatronic aside from spring bonnie. Or maybe it's just some other option that I can't think of right now. Who knows? The description reads, Five Nights at Freddy's fans won't want to miss this pulse pounding collection of three novella length tales that will keep even the bravest player up at night. What do you wish for the most? It's a question that Oswald, Sarah, and Miley think they know the answer to. Oswald wishes his summer wasn't so boring, Sarah wishes to be beautiful, and Miley wishes she could just disappear from the face of the earth. But in the twisted world of Five Nights at Freddy's, their hearts' deepest desires have an unexpected cost. In this volume, horror master Scott Cawthon spins three sinister novella length stories from different corners of his series's canon. Each story comes complete with accompanying artwork from fan-favorite game artist Lady Fizzy. I think that's how you say that. Who brings the horror to life in startling new ways? Readers beware this collection of terrifying tales is enough to unsettle even the most hardest Five Nights at Freddy's fans. We've seen that title before in the last episode, but in case you missed it, there it is. Author Scott, obviously, here's some background about him. Product details. Paperback, again, 208 pages. Series is FNAF, publisher Scholastic. The release date, ages 12 and up. Subjects, we've seen all those. And then some other stuff like dimensions and shipping weight, which is zero pounds. I'm guessing that's rounded down? Because I don't think that a book should weigh nothing. Anyways, let's move on to Fetch, which is the Fazbear's Fright book number two. And this is a little bit of information about the book. Again, Fetch, FNAF, Fazbear's Fright number two. Paperback, Scott, and then two new writers that we've never seen before again and are different from the other person. I think the name was Ellie Cooper helping Scott write into the pit, which is very interesting. We have Carly and Andrea. Yes, Andrea. Scholastic, all that stuff, blah, blah, blah, blah. Release date, March 3rd, 2020. Yeah, so it is quite a ways away, unfortunately. Now this cover is super interesting because it features a character that we have never seen before. Some people are saying that this is the, that this is Sparky, the doggie straight from FNAF one that was a hoax. I don't think it is. It's really not. Someone on Reddit, oh god, I wish I had the post up. In the twist ones, apparently there was a closet which had, it described having a character or at least a suit that resembled this. They didn't leave a page number and I didn't, so I couldn't double check it. So I kind of just have to take that word on it. But I'm not sure about that because again, I can't double check it. But maybe this is that character. But needless to say it is definitely a dog, as you can tell from the word Fetch. Usually that's what dogs like to do. They like to go fetch a stick or a tennis ball or something like that. So this is a dog character. We've never seen a dog character in the franchise. And really this character just resembles the nightmare animatronics and the twisted animatronics. I'm guessing they're going to maybe act just like them. Like the nightmare animatronics in FNAF 4 or the twisted ones in the twisted ones. But who knows, this is entirely new character. We've never seen them. I have no clue what they're going to do. And then the description. The Fasbez Fright series continues with three more bone-chilling novella-length tales to keep even the bravest FNAF player up at night. After years of being kicked around, Greg, Alec, and Oscar are ready to take control of their lives. I think that's Alex or Alec. I'm so bad with names. Greg decides to put the controversial science he's been studying to the test. Alec launches a master plot to expose his golden sister for the spoiled brat he knows she is. And Oscar, even the miniature grown-up his mom needs him to be, decides to take something he wants even though he knows it's wrong. But as these three will learn, control is a fragile thing in the sinister world of FNAF. In the second volume, whoremaster Scott Cawthon spends three sinister novella-length stories from different corners of the series' canon. Each story comes complete with a cump- a cump-bending cump-b- fan art. Not fan art. Artwork from fan-favoured game artist Lady Fizzle who brings the whole to life in startling new ways. Read as it be where we read all that. Read all that. Author, again, nothing about the other authors, which is very interesting. This is slightly longer than the first one at 224 pages. Again, March the 3rd has all the same subjects. Ages 12 and up. Some more dimensions. And then all the weight and dimensions and stuffs. So these books are going to be very, very interesting because, again, they are entirely separate from- oh, you can't see them. They're below these books. From the mainline FNAF books of the Silverized, Twisted Ones, and Fourth Closet. This aren't gonna have Charlie, John, Jessica, all those people. It's going to be all the new characters that we've said. Like Sarah, Oswald, Oscar, and all those- wait, no. I thought, wait, their names. Do they all start with the same letter? But they don't. That was wrong. I'm done. Yeah, these are gonna be super interesting. December 26, March the 3rd. Pretty far away, but I'm really excited for them because they are going to be so different. Like I said, there are pages on Book Manager, a link below. So you can go take a look at their cover, their description, and come up with your own conclusions about the books. Anyways, mark the calendars, and thank you everyone so much for watching, and I will see you all on the flip side. Goodbye.


The federal lawmaker representing Isukwato Umunechi, federal constituency of Abia State Honourable Amrubi Olga, has condemned the brazen attacks on indigents of Isukwato and Umunechi local government areas of Abia State by kidnappers, assassins, bandits and other criminal elements and these have lingered for more than half a decade. Honourable Olga says the activities of these bandits and criminal elements have forced the Nigerian military to close traffic on the Iwobe Iswachi Road at the Lumara military checkpoint for a long time. He called on the federal government to intervene and take urgent action to curtail the dangerous trend stating that the primary function of government is the protection of lives and properties of its citizens. The security in Nigeria is the issue and which federal governments have no power on the issue of security. But we agree on that. Even if we have a plan to see how we can engage with workers, to form like the Nigerian groups, to see because it is very hard for foreigners to secure the indigents. Using the indigents as a little help, but the issue of this is not only my position, it is all over the country today. On the south and the west, security is becoming a business. So if you look at up to 20 nations, move today that the security has made up for safety of it. So I think it is a mission that one might need to look into. So you get notified about fresh news updates.


Diversion of diaspora remittances is the reason for Naira Crash, that is according to the CBN Acting Governor, and on the show today we'll try to x-ray the statements by the CBN Acting Governor. Also, a risk of SMEs being crippled by current economic climate is area of concern as well on the show this morning. We're going to be looking at the headlines that made it to the front pages of our national dailies. Good morning and welcome to the break fast. My name is Nyam Gul Aghaji. Every Thursday we think business, we think entrepreneurship, we think how to make our lives better by being innovative enough in our business world. We do hope that wherever you are you've been able to reach your office or if you're about to leave nowadays the kind of traffic we used to experience is not more as much as it used to be. For whatever reason it is, we thank God for small messes. So we go straight to our top trending for this morning and the first one is the implementation of student loan to begin in 2023-2024 academic session that's according to the federal government. By the way, we sincerely apologize for starting a little bit late. The federal government has announced the implementation of the student's loan scheme. They say it will commence during the 2023-2024 academic session. The permanent secretary of the Federal Ministry of Education, David Adejo, made the disclosure in Abuja during a meeting with the House of Representatives Committee on Student Loans. He said President Bola Atinogu had directed the completion of necessary work on the modalities for the student's loan implementation with a target start date in September 2023 and according to the permanent secretary the president had established a coordinating committee with the chief of staff Honorable Femig Bajabia Mila serving as the chairman. He added that the committee comprises key entities such as the Central Bank of Nigeria, the Federal Budget Office, the Ministry of Education, the Ministry of Finance and others. Adejo also described as untrue that the signing of the Students Loan Act had prompted several federal universities to increase their charges while saying they recently increased their charges by federal universities in the country was unfortunate. He explained that no federal university in the country was allowed to collect tuition fees from students at all. In his words the charges are not to cover anything else but the cost of accommodation, ICT and power among others and it is the governing council of the university that have the power to approve such charges. He explained that the only federal university that increased charges after the signing of the Student Loans Act was the University of Lagos who got approval from the ministry after submitting a proposal to increase their charges because all governing councils were dissolved and this was followed by a resolution from the House stopping the increase of fees in the president and the president gave a directive stopping any increase in fees with other federal universities also having submitted proposals. So if Lagos will be given the opportunity to do that maybe in time other universities will also be given opportunity to do that and that's the worry of everybody. Now even if the tuition is not charged in any institution and other charges have skyrocketed then what is the difference if you say that fees are not going to be charged in school? Sometimes it's just like having a basic salary and having allowances. Sometimes the allowances are a lot more than the salary so you can even forfeit your salary and say okay let me just take only the allowances which will be a very very lump sum. So if you're saying that the charges or the charges it's appropriate for the governing councils of every university to see as they're going to, if they want to raise it, it is their prerogative to do that and you just leave it for every university to do that. Will that not be cutting corners to get the same thing that we're trying to avoid by saying that there should not be tuition in any federal university? So maybe the government should look into that. When we saw the report on the student loans we saw their responses from the people. A lot of people were not comfortable with it and they said that they were not going to take these loans and they would not encourage people to take the loans maybe because of the kind of experiences they've had. I don't know about that but the comments, there were not many supporting these and saying that it's a good thing that it's going to happen. Some say that you're going to pay this loan for the rest of your life and so many other pessimistic comments that were given when we read those things or when that thing was posted on X. That's a new name for Twitter by the way. So we do not know what the new modalities are because the first ones that were given, people were not comfortable about it. The people who were qualified and how much will these people be getting and then how do they plan to recoup this money from the people that are going to collect this money. These things should be laid bare for people to see and decide whether they're comfortable collecting the loans or not. Then very worrisome news, that's the second trending, is that the terrorist group claimed responsibility. A terrorist group claimed responsibility for NAF helicopter crash. Remember that the helicopter crashed and notorious terrorist Abdulahi Abubakar, popularly known as Dogo Gide, has claimed responsibility for the shooting down of a Nigerian Air Force helicopter on a rescue mission in Niger State on Monday. In a 2 minute 17 seconds video, Gide's fighters were seen celebrating the shooting down of the helicopter with a voice in the clip narrating how the helicopter was shot down. There's a video for that but we cannot play that for obvious reasons and even the pictures we are showing, viewer discretion is asked for is needed. Military authorities said the helicopter crashed while on a casualty evacuation mission near Chukuba village near Shiroro and the helicopter was on its way to evacuate some of the soldiers killed by the terrorists urging or during an ambush in the state. Dogo Gide rose to prominence in 2018 if you remember after he reportedly killed Soho Buhari who used to be the most ruthless and most feared terrorist in the region. Gide who used to be a protégé of Buhari Daji allegedly killed him after an argument ensued between both men after Mr. Buhari reportedly rustled the cattle of Gide's in law. Now it's unfortunate that we lost our garland soldiers there in that unfortunate plane crash. Whether it was a crash or it was shot down, the fact is that 20 lives have been lost. Those are fathers, those are brothers, those are friends that have gone in the course of duty to our nation trying to keep us safe and may their souls rest in peace. And a final thing that is really, really trending is the fact that the president has finally given us a portfolio that has put a name to every minister. There would be ministers, now there are ministers and then this is what we got. So let's take a look. Okay, that was the ministerial list as it is and their portfolio. We're glad that we've seen at least one new face or a few new faces and every other one is, you know, you are either one-time senator or one-time governor or something, something, being in the corridors of power for a very long time. For example, the minister of finance and the economy, Walidu, has been there forever. He was also the commissioner of finance in Bola-Tinobu's time as governor in Lagos state. So he trusts him so much and has taken him to the national level. So he's now the minister of finance and the economy. Okay, but we also have the minister of humanitarian affairs and poverty alleviation in the person of Dr. Beta Edu. I think she's like the youngest minister on that list. It's just in her 30s and she has made the list. She is the current women leader, APC women leader, so national APC women leader and she's now been made the minister. I don't know if someone else will take that position or it's going to still be her holding two portfolios. One in the party and the other one in the cabinet. Well, whatever it is, we do hope that these ministers will deliver. That's the point in all this. We do hope that they will deliver and we do hope that all geopolitical zones will be satisfied with the nominations and everything because we saw a breakdown of where the ministers come from. Some people had or some geopolitical zones had six, others had four, others had five and all that. The least geopolitical zone was I think the southeast that had four ministers and the rest had five or six, as the case may be. But whatever it is, we don't care as Nigerians where anybody comes from, if we can get the job done. If Nigerians will see a new lease of life, if Nigerians will have it very rosy from now on, nobody will care where you come from. For instance, when we look at our football team, if they are playing, nobody says that is a Euroban man passing to an Igbo man or passing to a Hauser man or passing to an Iqbal man. They don't care where they come from. So long as they are Nigerians, we applaud them all. So the team should play as a team and then deliver the dividends of democracy to Nigerians. That's all we care about. We'll just take a short break right now and when we return, we're going to be looking at the headlines. Stay with us.


Yes, the answer is correct. So let me, so someone answered in the chat. I don't know how to repeat. Yes, two times, that's right. You compute, what do you do?  So, let me see. So the degree of, that's what they say, 16, that's correct. And then moduli count is 16 minus three. In any case, it's bigger than 12. So you also have a five-year-old dimension, one dimension. Okay, so we are now in business. Let's see, let's see how, yes, yes, please. The thing is, the first thing, okay, for this, when you write this exact sequence with a normalization, I guess you have a Jacobian of normalization. So I assume that if a normalization is disconnected, you just, you take the product of too, too many smooth components, yes? So that's just the first thing. Okay, and the second thing, when you write those for loci, yes? I guess you need to show that the image, that the restricted prem map is still dominant on those things, yes? Because they are not generic, yes? In a sense, in the whole... Yes. Yes. So this is not trivial, I think. No, no, no, no. So first of all, the list itself is not trivial. Actually, the list itself is bigger, but there are some cases we are not considered because they go to a smaller loci, so the smaller dimension, they doesn't cover, is less than 12. And as you said, the restriction has to be, has to be proper as well. So it has to be, yes, so, yes. So how do you compute, so here's the question, how do you compute the degree? So what does it mean the degree over a fiber, which is half the whole city dimension of the fiber?  So I think it's worth to spend time on this lemma because I think it has, yes, let's answer that question. Okay, so how to compute the locality? Okay, let's do a little bit. How to compute a locality? So let's consider a proper map. First, you start with the proper map and don't mean it. Between same dimensional varieties, same dimension, oh, yeah, n-dimensional varieties, n-dimensional varieties, x, x, y. So in particular, f is generically finite. So take an irreducible, irreducible two-variety of co-dimension k and then take the inverse of this variety. So this breaks out in, finally, many components, many components, the set E of different co-dimensions, l, i, n, x, okay? So you can compute the local degree of, local degree, the i of f along every component set i, yes, by localizing x at the set E, then you compute the local degree this map. So it's such a way, so let's say the local degree of z along set E, so the degree of the map, the degree of f is the sum of all these values. Okay, so I have to do it. Okay, let's analyze, take one of these components, and then look at the diagram after blowing up.  Let's call it is x tilde over x, set. So it has a sectional divisor called set tilde, that maps to z, sectional divisor, and then goes, you have f goes to y, you have the image here, and you blow up on this side, v of y, this is the blow up, and let's call it w tilde, the sectional divisor here. So you can, you have a map between the blobs, f tilde. Okay, now, you have an induced map, so that can use a map. Actually, you have induced map f tilde between the sectional divisors, and this is the degree you want to compute. Yeah, actually, let's call it in the Nagas notation. Yeah, this is f tilde, just take z tilde. So with what is this set tilde? So from the definition of blow up, set tilde is the projectivization of the normal bundle, normal bundle of, I don't know what this said over x. Yeah, this is the definition. So you have a tangent space to x, so in each, yeah, tangent space. So the composite tangent space to z plus a normal bundle, z over x. Okay, good. So take a z, a small z in z, w the image, and look at the differential of z at the point. So this is a map between the tangent spaces at the point, and then these maps here inside, you have a tangent set of x set goes to the tangent of w, small module, okay? So these set induces, so you have induces, you have a map between the fibers, so actually a map between the normal boxes at the point, small set, with the normal bundles, what, okay? So here is the lemma, this lemma follows from the universal property of blown ups, that this map f tilde, so you want to extend this map in such a way that is now regular, f tilde is regular at the generic point in z tilde, if and only if this map at the level of the normal bundles is not identically zero, zero, a generic z in z, okay? Ah, well, that's actually didn't, I didn't really need this, but now if tilda is regular, I wanna actually need more, I don't know exactly, for every z tilde in the fiber, as of the blob in the fiber over this small set, if only if, actually it's what I need, this map is injected on the normal bundles, on the normal space, oops, oops, oops, oops, on the normal space to z, so here, where, here, this one, yeah, I wanted to be injective, so this map is injective, that's equivalent to say that actually the f tilde is regular in this case, and in this case, in this case, you can f tilde restricted to the fiber over the point set is the projectivizer of the linear map, so you projectivize the linear map f tilde, so the computation of the degree of the f tilde goes through the compactificate, through the, to the degree of this f tilde, so let's assume, so here's an important lemma, it's not so difficult to show, but I'm just gonna give you, assume that this map is injective, so this is an extra on the normal bundle x over the point set at each set in set, and that's gonna be very, very important, I was playing y, you have to, you have to guarantee this, this map is injective on every point of set, then the local, the local degree of f along this component set equals the degree on the sectional devices of this at the level of special devices, which are of the same dimension, now I have equipped both our devices over the same dimension, so here's the warning, why we need that warning, if, so you need this, this condition, if you have a point where it's not injective, that means that it's not regular, so if it's not injective at set, then you have, then, the map is not regular, because it was if only, it's not regular in any neighborhood, on a neighborhood, on a neighborhood of, of, of, of the fiber, c tilde, so c tilde is over c, it's a point in the fiber, so what happens at, so it's not regular at this point of the fiber, so in order to define it, you have to blow up again over this point, yes? So you have to blow up, yeah, for some, in some smaller dimension there, you have to blow up again, and if you blow up again, you get more components, so you have a super IT, you have super IT, another super IT, another super IT mapping to, to w tilde, yeah? So in that case, so c tilde is not the only, yeah, it's only one of several components, of several components mapping to this, so, so yeah, so what happens is that possible, so it might happen, might not, but the possible, the degree of the f tilde, when you compute the degree, it might be smaller of the actual degree you are looking for, also the degree on the fiber, or in a neighborhood, neighborhood of the point set, around this fiber, which is, that was, it was the local degree, the degree of this component. So yeah, you are computing something, something small, and you are missing some other components. So this is why, this is why, in the computation, one has to check this condition, that for every c, z, this map is tilde set, it is actually injected, and the good, that is very general, but the good news is that in our example, this is all computable, and it's going to be essentially, as we mentioned the other day, in terms of multiplication of sections, in terms of quadrics containing the canonical embedding, and so on and so forth. It's very, very specific. Okay, let's me, okay, let's, let's start with the plain quintics. Quintics. I didn't say what the data characteristic is, right? Well, I don't know if I need it, but let's, let's, let's start with the curve in M6, the smooth curve, or plain quintic, plain, plain quintic, Quintic. So you have a map into P2, given by G25, yeah. So actually this is given by a completely linear series to have L. So it's going to be both data characteristic. Let's see. So there is a natural, a natural line bundle, data characteristic, L, given by the hyperplanetized. So, so it's essentially take the, I'll give a name. So the pullback of the hyperplane class, phi pullback of OP2. Okay. So data characteristic means that the U square, the line model is can, is isomorphic to the canonical model. Let's see. So in particular has a, this guy has degree five. Okay. So here's the picture. So usually there are more pictures, but so you have the embedding. And then as a plain. Yeah. And then plain Quintic, you intersect with a line, the class of a line. Let's see. Yes. So you, you, let's just give name to the, this is the Donagis notation in Donagis Smith, but then in the other paper, change of notation, but I will keep the notation of Donagis. So it's later, you want to read that paper carefully. So. Yes. Let's put it like this. See. All the double corbrings. In our six, such that C is a plain Quintic. So maybe I'm going to fast, but this, remember that this Etta is, is the two torsion point associated to the local code. Okay. This one is isomorphic. You see, you can, you can give an isomorphism from, from here into, you tensor by, by L. So you have a naturally, you have always, since you have a plain Quintic, this L, this degree five, this Etta characteristic. And you can tensor C, hit the tensor with L. And now the difference is this, this line bundle now lives in, in peak five, in G minus one. So you can, you can check the parity of the, of the space of sections. So essentially what I'm saying here, I'm going to, I'm going to, I'm going to, essentially what I'm saying here is that this equivalent to, to, to, to the pairs like this, such that C is plain Quivic. So I, is the couple of a plain Quivic plus a data characteristic, plain Quintic. And we say that, yeah, I see a zero of, you have two types of such data characteristics is one of us. And then we use this, it is, we say that data is called, well, then we said, it, sorry, it is called. And with this congruent to zero, it is, even, but it depends on the choice of, of, of embedding on the plain Quintic. Yeah. So then you can stick with it. This is the so called the spin course. But you have plus a minus. And this is another story. So this, this distinction between, between all then even gives you at a composition of this space. It has to, to connect the components, the old part. And I will use Q for, for, for what? For Quintic, Q for Quintic. And with C, that's a story. This is notation for, from the Nagismith, but it has a reason. So this is the even.  The even. Well, as we, we know under, under the data map, they want to map to Jacobians. And the others. We, I hope to see later, maybe in the last lecture, they are going to cubic truffles. So cubic truffles, they are another nice example of. So the intermediate, I mean, I mean the intermediate Jacobian of a cubic, cubic truffles define it as a, in terms of a whole story, gives you naturally and principal price, a million variety of dimension five. This is another nice locals that they expect. I hope to say a couple of words about that. And one can compute also the degree there. Okay. So where am I? So, so let me tell you some, some, so it looks a little bit aside, but we have the following result. Give me more fun. Oh, maybe it's not so relevant, but yeah. You have a double covering in R6. Oh, an RQ prime. So double cover and a Quintic, such that the Bream. So we say that the Bream is in the Bream. Sorry, I'm changing notation all the time, but you take the Bream of this double covering, is in the, and wrote in major loss. I look us in one. I will tell you what it is. If only if the associated data is even. It's another way of characterizing. Yeah. So that means, that means if you're covering actually was seen in the, in the RQ without, without alkystroph. And what is N1? This is, this is the Android, Android remain major. We say that the principle polarize a billion variety. A theta lives in the NK. This is, and the O.T. Mayor. No, sorry. This mayor is mayor. So probably. Sooner. If the dimension of the singular locus. So the singular locus of the data divisor. Yes. At least K. So he is. In general, you take a general, a generic, a billion principle polarize a billion variety. The data divisor has no singularities. Okay. The general one, but you are interested to understand the, the geometry of the model space of a G, you start to look for a special law size inside there. And one natural way of distinguishing special law size is to looking at the, at the places where the data divisor has singularity. And then you have all sorts of. So the first case is when the data divisor has at least one singularity. And it turns out that. And. The prems of quintics. They have all. Actually the Jacobians, they will have also singularity. So where it comes from. Okay. So more and give you more precisely. So. So if you have the Jacobian. Of X. Is the brain. Of discovery. Okay. With the generic. So, okay. Maybe here I need to say more precisely this is non-hyperliptic. And North. She is going to be pretty one. But the start mix is not. Okay. So. You can look at the singular locus. So. Of, of, of the, of the data divisor. Maybe, yeah, sorry for the notation, but okay, singular locus. So. By the Riemann singularity theorem. The singular locus of the data device. It can be identified with the line models of degree. Four. Onyx. Which have more section as expected. Namely, at least two. And it turns out. Well, that is one dimensional. Actually is a curve. This, this gives you a curve. So. This is. And these curves come with a natural. Involution. Yota. Which is just take L. K minus L. It's an evolution. And it's going to be an evolution. Of, of. Free. Without fixed points. Because. Well, because the curve is generic. So it has no financial. But. Okay. To have. Mm hmm. Okay. Now. The generic. Also tells you that. For instance, The canonical map is an embedding. So it's not hyperliptic. Goes into before. Okay. Canonical embedding. And as you know, this is a classical. Geometry. For a generic. Genus five curves. In the canonical embedding, you can describe as a complete intersection of three. Quadrics in general position. Small quarks. Okay. Mm hmm. So, actually any, any, any G14. On, on X is cut out. By one parameter family. Of planes. So there are planes. Swiping. Swiping out the curve. Swiping out. Okay. So you have, you have a family. A family of planes inside. Inside the aquatic. And when you caught. Yeah, you caught the. Yeah. Your, your, your curve. It defines four points on the curve. This is a G14 analogy forms comes in. And the quadrics are actually singular quadrics. So they have. Could be ranked. Three. Or four. Before. Of course. So quadrics. So the three dimensional quadrics. Containings. Okay. So, okay. So you can always define. You can parametrize all the quadrics containing your curve. Your canonical curve. By a plane. Let's call it P. Generated by this. Two one. Two. Small quadrics. So it's a P two. Mm hmm. And. Mm hmm. Mm hmm. Three dimensional quadrics. Containings. Okay. So you can always define. You can parametrize all the quadrics containing your curve. And so P comes with a discriminant log size locals. The discriminant locals of P. Is. Of P. Is, is the set of all the quadrics or all the points. Representing a quadric which is single. Let me correct. So. So. So let me be more concrete. So every element here. Right. You can describe it as. So for instance. Zero. Zero. Just. Make concrete. Two. And the lambda zeros are. Parameters is lambda. The points on P. Two. Two. Two. Two. And the lambda zeros are. Parameters is lambda. The points on P. Two. The points on P. Two. Okay. Mm hmm. Okay. So. Mm hmm. So this is the discriminant locals of. Of this net of quadrics. Is. It's a Quintic. It's a Quintic we're looking for. Quintic. Because it's given by. The banishing of the discriminant. Of all. Of all these. Yeah. The. The banishing of. Yeah. The determinant where the entries are, are the partial. The partial derivatives of this. So it's linear forms inside. So there are two planes. So for each. For each lambda here. So let's call it that C. For each. For each lambda and C. So we have a singular quadric. The singular quadrics. It comes with two, two, two families of planes. They are two. Two planes. Of cool lambda. Two families. Cutting the. The G14. All right. G14. Okay. So this way you can construct. C tilde. To see. Two to one. Covering. So the C tilde parameterizes. So you can. Yeah. You can associate it also to. All the G14. Coming. Coming from the singular quadric. When you cut out the. The families of the singular. Quadrics. Yes. Two. No, two planes. There are two systems of planes. Systems. Two. So there are two systems of two planes. Two systems. Of two planes. Mm-hmm. Mm-hmm. Okay. Right. So this is the construction. So, uh, from the singular locus. You recover. You recover. C tilde. Plus the data. Plus the data of the G14. Yeah. Mm-hmm. Okay. How much time they have. Um. Is any question. Here. It's a lot of. It's a lot of. Okay. Okay. Right. So this is the construction. So from the singular locus. You recover. You recover the city. Plus the data. Plus the data of. Of the G14. Yeah. Okay. It's a lot of. Around 10 minutes. Okay. Right. Okay. So. When you say plane quintics. Okay. Let's let's talk about the trigonal curse. So. Mm-hmm. So this is going to be trigonal. Trigonal curse. So I'm going to tell you the residual construction. Construction. Mm-hmm. And it works in arbitrary G. Yeah. So I start with the curve. X. With G minus one. Such that the extra. Okay. So it's going to be applied for a genus five. When X is of genus five. Because all, all the, all the genus. The general X. We'll have a tetragonal. We'll have a, actually we'll have a finite number of tetragonal. Maps. So G one force. So it's the first case you can apply it. In the generic generic way. And to, to every extra diagonal curve. You can associate the double, double covering. So let's say. Let's. It exists a double covering. Such that the pre-modus double covering is a size. So. To the top of the two.  To see. To every extra diagonal car. You cannot see the double, double covering. So let's say when it. It exists a double covering. Such that the BREAM of this double covering is isomorphic to the, to the Chaco. And this is a, this is a bijection. You can go up. Okay. So let me let me tell you all the city. So pairs of points but unordered points is why put some on the symmetric product of X such that they are in a fiber. So P1, P2, P3, there exist all the two points, so such that this is in the G14. So what does mean the G14 is that you have P1. And that's right. So C tilde is going to be a map 6 to 1 to P1 because you have six ways of taking pairs of points among four unordered ones. And so it's taking some little drawing. So you have four points. Yeah, P1, P2, P3, P4, and they're all mapped by the G14. This is a G14. So what you're choosing, you're just choosing pairs, one, two, three, four of the diagonal. So but it comes also with the natural involution, namely the P1, P2 points you map to the order two. So it comes with an involution that I think I call it Sigma. It's not your anymore. Sigma natural involution. And the quotient of this we call it C. So this is 2 to 1. This is without fixed points. Sigma is free of fixed points. So I said that, and this is 3 to 1. So you get naturally a trigonal curve C. And when you, in also the branch locus of the diagonal curve, the branch locus of the trigonal is the same. Yeah, this branch locus are in the same points on P1. So when you do the computations, you get that, okay, first, as I said, this is trigonal. This is tal. And H has, which is H, I call it H is this. The branch locus has, as I call it F, same branch locus as F, which is equal to 2G plus 4, I think. In any case, when you make the computations, the genus of C is one more than the genus of X. This is the diagonal construction, has an inverse construction. Yes, so now you consider a double covering C in the trigonal locus. So they are CT, let's see. In R6, such that C is trigonal. And how do you go? So C is trigonal. So now it's a C who has a map 3 to 1 to P1. So I'd like to give this diagram. So you have a G13. So this G13, of course, is isomorphic to P1. In G13, you can embed it in the third symmetry product of C. Yes, just take three points over one on the fiber. And the double covering pi here induces a double, no, it's not double, but you have the induces a covering from CT to 3. Which degree? Well, from over each device or degree 3 here. For every point you have two choices of the covering. So the degree is 2 to the 3. So this is a degree 8 to 1. Okay, and then you take the restriction of this map to P1. And just call it X tilde, which is embedded here. So this is just P3 restricted to, this is the restriction to do this to P1. And it comes also with an evolution, sigma, which means because induced by the evolution here. So C tilde has an evolution so you can exchange the points, so you exchange the points over each point of the device. So that gives you also is fixed point free. And you get the quotient, X, 2 to 1, so it's 2 to 1, then you start with the 8, so from here you get degree 4. So you get an tetragonal curve. X. Okay, so maybe I don't have, let's see. Where am I? My notes. Yes. Yes, maybe I should stop because there are now, now we are interested was it was a question. So using this trigonal construction, I'm going to show that there is only one exactly only was not so difficult now to show this is only one, only one double covering over three one of course and not to the jackpot. And some point we need, we can study also the degenerations of the trigonal construction. So which generations can happen. For instance what happened when, well, in principle, the tetragonal covering is generic so it's simply ramified, but you can have points where double ramified, triple ramified, and the double covering looks different. And in some cases though this double covering is going to be in the boundary, it's going to be disconnected and some cases you know, so what has to analyze all these cases. So what I'm going to do tomorrow, and I think is for the theory is very important is to give you a proof of the fact that I mentioned that the preem of this double covering is isomorphic to the jackpot. This is the proof that I can give it. And it's a very nice argument by the generation actually. Yes. Do you have any questions. While we wait for questions there is something I would like to say for those who are still with us, and we're not giving a talk. It would be since tomorrow we have a free morning we should all be a bit less tired. We, our aim is to meet that 130 on gather so that those who are not giving a talk can introduce themselves. There is a podium where you can speak to everybody. And you just say your name where you are what you're working on, so that we have a little bit of the knowledge of each other we would have if we were at an in person conference. Angela, please. I just had this announcement to make anyone has questions. I've had one, one question. Oh, yeah, so but I think that you already somehow answered it, because you said that in your tetragonal construction, yes, that trigonal construction that the sigma is free of fixed points yes. I think that in order to, to, to have the sigma free of fixed points you have this tetragonal this g14 to be as general as possible yes because I can choose probably x the g14 such that you have fixed points yes p1 plus p2 plus p1 plus p2 somehow. Yes. Since you assume that x is generic in G in a five in J five yes in the Jacobian in M five. You will, you will assume you will get it somehow for free that the g14 is as general as possible. You can still have funny cases where you have more ramifications but yeah you can still have them. Yes. But, again, they are not going to be general inside of the, of all g14. And, and when you made a modeling count. And so in the end is, we can just reload out because they are going to map to something smaller. But funny things can happen for instance you can get singularities on the city that's not something that we don't like so much, or, yeah, but we can talk to more of you want more so thank you. A larger picture of what happened on the, you can happen. Yeah, for for the. Cannot have for the form to be the feed there is. That's right. Yeah, some of the answer. Yes, it's what I mean. So she in the case for him because you have a fiber to two p plus to two, or do you still have those are precisely the cases where the Associated Corp is singular. Yeah. Let's see how much singular and yeah. Yes, Angela, and I also that there are some problems if the, the foregone series is not simple so the 41 covers stock factorizes as two to one to two. I think that the trigonal construction does not. Because. It's also commented in the chat. I don't know if you saw it is something is called. No, no, this is was no you mean something else you mean. That's right so. But I think in that case you will get something hyperliptic. Yeah, they will do will have a you factorize this x to some double covering. Well, you will get some special curve in any way. So you have the factorization them is a exist is special in some way. I think that you don't get a curve you get a rule surface because there is also another approach, but maybe we can. That's interesting yeah okay. Uh huh. So if I understand correctly, if this you mean if this map for two one actually factorizes to something else. Yes. I don't know. Yes, yes, through a hyperliptic curve that has to be hyperliptic. And this is well depends on the genius political bio elliptic. But if you get an elliptic one, why hyperliptic yes, my hyperliptic right you have an if that's right. And so my understanding is if you can factorize you have a special course in some sense. So it's not that general. You have an extra out. Yeah. You may have extras automorphism there. Yes. Yes, so. Yeah, yeah, but yeah, that's nice. Okay, this is another way to consider the trigonal curves, trigonal construction on this. You get something different. Yeah. Yeah, true. Okay. Another comment. If the tetragonal map factor is then it necessarily has to pick up two in the fiber. I think. Yes, but then you need it through in every fiber. Yes, so this is again the game. And then, and your answer is that you take the generic X and generic X is not of this. No problem with that. But, you know, since you said that the trigonal construction works, you know, more generally. No, that's then you have a problem of sometimes if you have problems sometimes. Yes, but I think it is still war war to look at the generations, maybe for all their problems for all the things, but it's too war to look at the generation of the construction. For the degree will not going to be important but you get the interesting things. And this is when you allow ramification on points and yeah, you can you can play with that. Yes, but depends depends what you are looking for. Don't dismiss the specific case is very important. Yes. Okay. No more questions. Okay. Continue tomorrow and the plan is just finished the computation with more more geometrical arguments. I'm ready to give you the answer. And then I will talk a little bit about the other specialist side cubic triples and Yeah, and then why you have this 27 more. Yeah, let's discuss about this 27 more precisely. Okay. Thank you. Thank you. Thank you very much. And as you all in gather very soon. Bye bye.