Today on the breakfast, 14 of the 18 registered political parties in Nigeria have threatened to withdraw their participation from the election forthcoming general elections of the Nigerian federal government and the Central Bank of Nigeria Council also spend the ongoing cash withdraw limits and the Naira redesign policy will look at the implications of this for the election. Also on the breakfast report says one in four Nigerian women and girls have been caught. How can we partner with women, men and boys and policy makers to end female genital mutilation? As usual, we'll take a look at what the papers are saying this morning, enough to press. Good morning to you. We're back with a breakfast on class CV Africa starting with them. My name is Kofi Bartels. And I am messier before. We don't look like what we're being going through, Kofi. I just wanted to say that, you know, the whole drama that's going on, you know, trying to move around, getting petrol to power your house, because there's no pass-up light. Anyways, you live in a different environment where there's constant pass-up. No, I live in a heavenly economy, a heavenly economy. Before we get into the main, you know, training stories, we will not be doing justice if we don't. Let's keep spirit thought for what's happened in Turkey. I'm sure, you know, you saw the videos and images of the Turkish earthquake that we hear several persons have been lost, several buildings collapsing and all that mess. It's really sad, you know, where they're still looking for the survivors, but what is compounding the search and rescue effort right now is that Turkey is in the middle of winter, you know, so it's snowing over there. And it's really, really cold. And the part of Turkey where this occurred, it's really cold, you know, it's really cold. So that's a sad one. I mean, yesterday also, Ghaniel Futbola, Christian Atsu, you know, also was so straining because he said he was missing and he was part of a football team in Hatta Espor in Turkey. And they were in a building, when this nine-story building, sorry, a high-rise building, when this thing occurred, he was on the ninth floor. Of his teammates and some of his teammates and I think the football teams, football clubs manager or something like that, I think, assistant CEO is also missing as well. It's really sad. But I think eventually for him, he was found alive. The report of him being found, because I tweeted that late last night, Ghaniel, journalist by name Sadik Adams, put that out. But report of him being found, actually, people have to draw my attention for that. It's not being confirmed. I haven't checked for the latest, but this was as at maybe 2 a.m., you know. But you know how that's a crisis situation. I mean, it's very intense. It's also possible that people are carried away by others going on. And the updates might just almost be impossible. But fingers crossed, we're definitely praying for them. We were praying. I mean, you never can tell. You will never understand what it is to experience a natural disaster. And that's exactly where we are at the point where we don't even experience that. So we probably might not be able to relate in local or street words. Will be I can't relate because I don't know what that means. It's sad. You know some. Yeah, sorry. Yeah, so it's very saddening. And our hearts and prayers are with those who are going through this. So we're definitely praying that never one comes out alive. But that's not going to be. So far, according to CNN, last result, I saw about 4,000 people have lost their lives. And it's really, really unfortunate. The Ghanaian football is there. There were three Ghanaian female footballers who were also said to be missing. But they've been found to play for, I think, Hata Espoir. The female football team of Hata Espoir, one place for Fenerbahce, the female team of Fenerbahce. So for a lot of people who know this football, I played in the Premier League. Christian Atu for Chelsea. He was bought by Chelsea after playing for the underage team in Ghana. And Chelsea put out a tweet saying that they're praying for him. Including Newcastle. He also played for Newcastle United as well. And they put out a tweet saying that they're wishing him, you know, he'll be found and all that. So it's sad. But let's move on to the current one that we want to talk about here, which is about Nigerian musician, Thames, who has won a Grammy. Yesterday I saw Shade Adu trending. And I wondered, what is Shade Adu trending for? Only to see that, and people are saying that Shade, the last time Nigerian female won a Grammy award, it was Shade. We need to check that, you know, but that's what some were saying. But Thames goes by the name, she goes by the name Thames, but she is officially called her government name. She's a Tamila de Ocbeni. And she bagged another international award. This is not the first time she's won an international award. The Grammy. It was held at the Crypto.com arena in Los Angeles, and you had the most respected and revered musical artists in the world in attendance. She won her Grammy award for a part in Future's Hit Single, Wait for You. All right. Yeah, I think we're thinking that she won a Grammy, a whiskey to win a Grammy for that song, you know, that's been trending all the while, that Thames sang with Whiskey, and I think just essence, Justin Bieber, I love that song, you know. Yeah, but it didn't work out for Whiskey, and I think Thames is second time lucky, because she was featured with Future, and that's a big name. Future and Drink. Yeah, and she won that Wait for You, Future and Drink. You know her hip-hop. You know her hip-hop. I've been into doubt today. So this category under which they won that award is Best Melodic Rap Performance. So she's also, apart from being the second Nigerian female to win a Grammy, she is the first non-mixed Nigerian, according to what they're saying. I like how you do it. They're calling the first non-mixed Nigerian. I don't think we should have a disparity between the first and non-mixed. So you're not a couple here. You're meant to be the first non-mixed Nigerian, a female musician to win a Grammy. Shadiadu won a Grammy in 1986. And yeah, before I forget, Cynthia Erivo, backed Best Theater Album in 2017. Cynthia Erivo is a British Nigerian. A lot of people don't know about Cynthia Erivo. In 2017, that's just about seven years ago, or six years ago. So congratulations to Tepes. I think that that's the right word. I mean, that's the thing to say, congratulations to her. It's great. It's fantastic.  I mean, this is for the culture. This is for Nigeria. I like to be you say, this is for the culture. This is for the culture. Yeah? This is for Nigeria. This is for Africa. And we are super excited about it. Now I also know that there are conversations around not being a single win. It's a collaborative effort. That's a win because you have a future. You have Drake on that. Not like... Does she have the Grammy Award? We can't say, but I don't think that that's the case because I don't think that, you know, okay, why are you making me feel like this? Because she received an award. She's going to get one, right? No, she's got... She got one. Did she get one? Yes, yes. She did. Okay, that's fine. So... But you know... It'll be in her house. It'll be on record. Her name is on it. So this is what we have to say. We're not trying to... I mean, this is me not trying to be not here, you know? But we have to state it to waiters. Like I said, it's a win for the culture. It's a win for Africa. It's a win for the women. Which culture are you from? Because... Let's... So what culture are you from? Have you also done that? Have you also done that? All that hip-hop jaggon. All that hip-hop jaggon. What culture are you talking about? I don't know if you've listened to this song. Wait, have you even listened to it? You need to see that she did great. I mean... Oh yeah, yeah. We know the song. Thames has, you know, she's gifted and she's got this very powerful vocals, if you like to put. Her vocals are really, you know, we... Like very, very outstanding and we really have to give it to her. But that's what it is. The argument whether Shadia Adu, you know, was the first musician, but I like how you put it and it should be known that, yes, Shadia Adu... They say that she's the first musician of Nigerian origin. She's of Nigerian origin, right? But of course, she's British. Excuse me. In 1986. But you can't take it out. I mean... No, no, no. The fact that she... You see, you can't pick and choose. It's a messy search intro. You can't pick and choose. You know... I'll take this one out. If you take something, you have to take it in its entirety. I'm just putting out what people are saying. You know, not you. Not you. I'm not referring to you. I'm talking about them. They now... People are saying, OK, Shadia Adu. But when Shadia wins? We say, oh, Nigerian, right? And we celebrate her as our own. And when people say, said... They say, no, it's not said, it's Shadia. So if that's the case, then we should leave it at that. That's what I'm saying. That's exactly why, you know, all of this has to be put out. Because there's a conversation. I'm sure that a lot of peasants have not been able to... This information might be needed to many peasants right here, right? So I'm not sure too many people know that there was a certain Shadia who is of a Nigerian origin. But of course, she's British. And she won this award the first Grammy she won in 1986. That's a long time. I'm sorry for those who don't know. It's not Shadia's fault. But I mean, as a kid, I knew about Swilester. If you don't know, you don't know. No, no, no. You know Sabi, you know Sabi. Don't be false. Say you know Sabi. So I don't want to say this. You know, we knew about Swilester Boa's kids growing up. I'm sure you know about Swilester Boa's kids.  But the point is, if you don't know already, which I think that a lot of peasants are on this table, not knowing that once upon a time, we had someone who won the Grammy in 1986. And it was not her first Grammy. She's had a couple of them. I mean, she's an amazing singer. But you want to put it at the fact that of course she is a British singer with an Nigerian origin.  However, you want to look at it, it's a win-win for Nigeria. Okay? Shadeh, Thames, any other person, like I would say, it's blessed for the culture. It's blessed for Africa. But there's also one thing that has also been of a conversation around social media space and office social media space is, hey, should we be part of this conversation? Don't forget, it should be emphasized. Thames rose to prominence after the future. You know, when Whiskey featured her in that song Essence. And unfortunately, just like last last, everyone that selected the last last of Bonoboi was going to take it, right? Also, everyone also expected that Essence was going to take it at that time. And I know a lot of peasants who tweeted that Whiskey was robbed. The likes of Naomi Campbell tweeted that. A lot of peasants, I mean, you could look at it, if you look at Essence, it was a global music. It was that sound that was accepted. So, but however, we're very appreciative and we're saying that Nigeria is making us proud. Yes, I mean, I don't think for me, I feel that the debate about whether Shadeh was the first Nigerian female or not How does she identify herself? British Nigerian, we need to find out. But I think for Nigerians, the fact that, you know, this country identified with Shadeh and called Shadeh their own means that they should live like that. You know, I mean, if Thames had not won anything, it would still be saying Shadeh is our, we have a female who has won. I don't think that that would have been the conversation. No, no. I think if we can say that, you know, Thames is the first non-Mix Nigerian, that's fine. But like I said, since everyone won a Grammy after 2017, that's another person to look at. But as to whether Shadeh was the first Nigerian or half Nigerian Mix Nigerian, whatever you want to call it, or some Nigerian origin to win, that's not the case because King Sonia, they won a Grammy in 1984. No, we're not talking about males now Kofi. So the conversation is about the females. I'm just saying that first ever, okay. For those who are saying first ever will be King Sonia, they're not saying first ever male. I know, I'm just saying first ever is first ever. You know, just listen to me, what I mean is first ever. In 1984, I'm just saying that he won it in 1984. Nothing serious about that. And if we even want to talk about the Grammys. So a list of Nigerians who've won Grammys in the past, I'll just go over some of the names. And it's quite a long list. I think Nigerians need to be proud about it. So these are Grammy nominations we're talking about here. Not awards, nominations. King Sonia had a nomination in 1984. And of course he didn't win. Baba Tunde Olatunji won a Grammy nomination in 1998. He didn't win. King Sonia, they got a nomination in 1999. Femi Kuti got a nomination in 2003. Femi Kuti got a nomination in 2010. He got a nomination in 2012. Another one in 2014. Sheo Kuti in Egypt 80 got a nomination in 2019. Borna Boy got a nomination in 2020. And then in 2021, finally, he won. In 2021, that's twice as tall. And then we have Whiskey having a nomination in 2021. Femi Kuti and Madi Kuti 2022. Whiskey reaching 10. That's the one you talked about, Mercy, in 2022. Femi Kuti still had another one in 2022. And then you had Borna Boy in 2023. So the point I'm trying to make is that from this, this is an official list on Wikipedia. It seems that they are not including Shade and Cynthia on this list. So it is interesting. But what I'm saying is that if we claim people, it's just taken out like that. So I think it's very important that we put out... I don't think we should dwell on this. We probably have to move on. But it's also important to put out the statistics and put out the facts, the argument that people are having. Those who are saying, oh, Shade is not...  It's a mixed breed. So she's Nigerian. She's British. And she's been claiming that she's Nigerian. But like I say, I mean, it's a win for the culture. But I have, but I'm full. However you want to look at it, one quarter, the fact that you have a Nigerian winning is a win for all. It's a win for the culture. And we're super proud. I probably might not just be a single-handed win just like Borna Boy, but it's a win. A win is a win. And we're really proud. Essence was one of the collaboration that brought, you know, Thames. Probably she's been on, but you just need that. Just one kick. You just need one collaboration. You just need one phone call. That's exactly what happened. And we're saying, hey, if Whiskey didn't do all of that, I mean, probably the problem would be here. So yes, a big shout out to Whiskey, by the way. So quickly, let's move on to another of our top trending. Niger and the Republic of Niger have signed a bilateral agreement in Abuja for a coordination of frequency utilization along their borders to ensure seamless deployment of services around and within two countries, Nigeria Republic and Nigeria. The agreement signing ceremony was one of the highlights of a two-day digital economy regional conference also stood by Nigerian government and it was facilitated by the Federal Ministry of Communication and Digital Economy. Issa Pantami would be part of it. And I just missed off communication and digital economy. Professor Issa Ali Ibrahim Pantami signed on behalf of Nigeria while his Nigerian counterpart, you know, the Minister of Post and New Information Technologies, Musa Barzer signed on behalf of this country.  I mean, that's the conversation Nigerians have been having. The Executive Vice-Chairman talk about the weaknesses and the Chief Executive Officer of the Nigerian Communication Commission Professor Uma Danbata and Nigerian Public's Chairman of the National Council for Regulation of Electronic Communications and Posts Were Witnesses to the Agreement which applied to the coordination of frequencies existing in Nigeria and Nigeria Republic trans boundary areas between 87.5 megahertz to 30 gigahertz. That's what it is. We understand that there's so much I mean, Nigerians will say about this collaboration when you look at the Nigerian Government and our relationship with Nigeria Republic so it feels like we always are suspicious of every move of the Government. Well, Merci. It's an interesting involvement and I really have nothing to add to that. I think that it is what it is. We will keep watching this space as we always say. But quickly, because of time, go to the last training story which has to do with the Yoruba Nation agitation and what we hear is that the police have arrested 10 Yoruba Nation agitators. They also set their camp on Blaze and for setting camp rather to launch a massive protest and Yoruba Nation has been the news recently especially with the protest planned in Ojota I mean, people thought that okay, it was had been nipped in the board. Let me say a bit dead because of the arrest of the leader of that group Igboho who has been in Kotunu by the Republic in detention for some time. But these members of Yoruba Nation were setting up camp at Alaosa planning to use that camp to launch a massive protest you know. They had another one at Ojota where the police intervened. Remember we talked about this time on this program. And the suspicion was that some lives were lost after the police fired some bullets but the police said they didn't fire bullets and there was an altercation between two groups who mentioned their names. But yesterday the police arrested 10 Yoruba Nation agitators in Alaosa Alaosa is where the seat of government in Lagos is that's the seat of government. So you have government offices, the governor's office I believe and a lot of ministries, departments and agencies around that area. From all the NSAS protests as well that was one of the bases where protests were held. So the spokesman for the Lagos State Police Command Benjamin Hounday who tweets a lot put out a tweet again on his handle at Benjamin Hounday on Sunday two days ago where he said the suspects were arrested when they started setting up camp. They planned to use as base launch a massive protest and he said in his tweet quote the camp was promptly dislodged while agitators were arrested and they're still continuing their investigation. He said quote this is words lawlessness will not be tolerated. So that's that I'm sure that if there's any further involvement he will test. You can see some pictures of those who were arrested, you know the holding flags of your abomination and all that you know. So that's that I mean I don't know what you said, well it's messy but well you probably might want to understand the concerns of the Nigerian police just like yesterday making reference to the fact that protests is a tool that has been used over time in different countries by citizens of this country to demand change of policy but usually for climbers as people take advantage of the protests and begin to truncate the entire and it should be peaceful when you become a threat to national security we can't explain all of that. You should go ahead and protest but not you know being violent and whatever you will just move away for the winter time we'll take a break. When we return we'll be looking at the pictures of the national dailies we call it off the precipice with us. Good morning.


In this video we're going to look at how to balance chemical equations, and while we're doing that we'll discuss one of the primary laws of chemistry, and indeed the universe, the law of conservation of mass. The law of conservation of mass states that matter can neither be created nor destroyed. It can be changed from one form into another, and mixtures can be separated or made, and pure substances can be decomposed into other pure substances, but the total amount of mass remains constant. This means that whenever a chemical reaction occurs the total mass of the reactants must equal the total mass of the products, since mass cannot be gained or lost. And the reason the mass remains constant is that the atoms cannot be created or destroyed, only rearranged. So another way of looking at this, a way that helps us in balancing equations, is that the number and type of atoms in the reactants, which are written on the left of an equation, must be identical to the number and type of atoms in the products, which are written on the right of the equation. All that can happen is that the atoms are rearranged. This law came about from the work of many early chemists, but it was the Frenchman Antoine Lavoisier, along with his wife Marianne, who most conclusively showed it to be true in the late 1700s. And it was only by some excruciatingly precise and careful lab work and the use of the best technology of the day, in particular accurate balances, that they were able to prove this law conclusively.


Hey guys thanks so much for joining me again. I wanted to answer a couple questions on these earrings that I had on in my last video that I uploaded. In that video I had filmed it last weekend and I said that I was going to film three videos hopefully that day to get uploaded at a later time. Well I did actually film those videos but they did not come out. So needless to say I'm filming my evening routine all over again and I figured I'd take the opportunity to talk about these earrings. These earrings that many of you commented on they're all different colors they're little like round little very light medley pieces very dangly I love these earrings. I mean these are really awesome awesome earrings but these earrings are old. When I was in high school back in that timeframe in the late 60s early 70s it was very common for a big furniture company I think it was called Lane Furniture to come and talk to the high school girls that were getting ready to graduate and talk about having a hope chest and they gave us little tiny small hope chests cedar lined hope chests and as an example of what a larger hope chest was well of course the whole thing was you can this is your hope chest you're going to fill it with china with pillowcases with certain things that you want to keep for that hopeful day when you get married. I don't think do they still do hope chests today I don't know I don't have any girls in high school and my boys wouldn't have been aware of that but anyway so back in the day we did have that and they gave these three little mini hope chests out to everyone and for some reason I used mine rather than my little my mother and dad they were not going to buy me a big hope chest so that was out of the picture but I used my little one as a way to collect my jewelry and at one point I don't know whether it was late 60s 70s and into 80s I put that away and I packed it away forgot all about it until one day I came across it a couple of years ago and inside that little hope chest were all my old earrings so I don't really know how old these are I'm guessing early 70s but it could be mid 70s could even be late 60s I don't know because all of the earrings I had in there were all vintage pieces that I actually wore you know and some of them I had I did see a couple of pictures you know that I had earrings on so it was really really cool so wanted to share that with you because I had some of you asked where did I get the earrings and how awesome they were yeah they're just old earrings that I saved from way back way back in the day so now on to my video this is a very highly requested video by many of you and that is for me to update my evening skincare routine and to be very honest with you I have had not so much I've not had a whole lot of changes I am definitely creature of habit but I am not an expert I I do listen to my skin I do go to a dermatologist I do follow their advice anyways my skin is an experiment in progress so what I do for my skin in no way am endorsing that you should do it or saying or recommending I'm just sharing with you what I do for my 64 year old skin in the winter time when it changes when my skin is super dry when the air changes heat comes on all the time it can be a real nightmare dealing with dry flaky awful skin and so my routine I have bought a few different devices skincare devices and I'll talk about those in the end if I have time if not it'll be separate video but my routine is pretty well consistent I come home from work and I can come home from work 5 36 o'clock at night and I usually leave on a normal day when I'm not having to drive travel anywhere other than my office I usually leave 8 a.m. in the morning so I get up fairly early I go to sleep fairly early but when I get home if we're not going out if nothing is happening I will stop the process of removing my makeup and normally what I do is I use if it is a if it is a night that I am going to be putting my eyelash serums on my eyelash growth serum which is right now I'm even using the blink product if it is that type of a night I use a oil-free cleanser and it's usually I just buy the equate you can get the new string to Gina show you the one I have I usually just buy the cheap equate oil-free I put it on my fingers I don't put it on a cotton ball and I just gently massage it into my eyelashes and then after that I will take some water and I will rinse it off so because it's a night of using that kind of a treatment I don't want to have any kind of oil residue around my eyes at all I was told way back when that the secret to these serums I know if they're true or not if you use any kind of an oil product any kind of oil based cleanser if you don't remove it all and inhibits the serum from actually doing what it's supposed to do for your eyelash growth so I've always believed that and I've always done it that way whether it's true whether it works for you that's up to you but that's what I do so on that type of a night I use a non oily cleanser to clean my face and then I normally will go in now I use it I usually do double at night double cleanse at night because at night your skin is is full of makeup so I might use a makeup remover wipe I got it at sans club in a big box I happen to like it I'll use that sometimes I'll wet it down with warm water and I'll just put it all over my face gently and just kind of remove a little bit of a first layer but it the key is gently then I take and this is what I usually use I have used other cleansers and I am experimenting with other products right now to but this is what I normally use in both in the morning and the night so I'll take my Cera V I'll put it all over my hands and then I will gently massage that into my skin usually use my Foreo or my Foreo dupe and I wet this with warm water and it kind of vibrates I'll wet it with warm water and I have the Cera V and I was just gently gently go over my skin down my neck all over the place then I've rinsed this off and then close it you know shut it down and then I'll take some warm face cloth and I will just rinse off the rest of my makeup and then once I do that if I'm still feeling that there is a huge residue I will go back in and I might use a different cleanser but if I have to go in a second time after I've done the two cleanses and then I will take a cotton ball and I will use either my witch hazel after I've done that and this is really gentle for me this is alcohol free this is a great toner I use it at night especially on a night I'm using my Retin A so I will put that on my cotton pad and that I can tell by how clean that pad is how good I did on my skincare so and this is again this is going to be something that switches up depending on what I'm going to be using so I'm talking to you right now that this is going to be an eyelash serum night in a Retin A night so I would then do this and I make sure I have that all over the all over my skin I let it absorb into my skin currently I'm using the niacinamide still from the ordinary I am looking into another niacinamide I haven't made my decision yet but this is what I currently use every single night I don't use it in the morning I know there's some you know back and forth about how you can use it in the morning in the morning I use vitamin C do I want to mix my niacinamide in the beginning I was I was told no don't mix them I just don't mix them I use my niacinamide at night and it's usually after I've toned my skin and lately I have been using an essence and this is the essence I cannot pronounce it I believe this was I've mentioned this in the previous video in advanced snail 96 so it's just a power essence this is I believe I heard from Natalie the beauty diva but then I will do my niacinamide I will put that all over and when I pat it in I don't know maybe 10-15 minutes I mean sometimes I'm doing this in shifts and layers I will come back and then I will take the ordinary's buffet this is what I will then put into my my skin I let that absorb in I'm usually not in a hurry at night so once I've done that that is kind of the last step before I get into my retin A then hopefully it really all depends on the time sometimes I've done a mask sheet mask sometimes not sometimes they do sheet mask in the morning so it really switched that up a little bit but if I'm doing a mask I'll do the mask you know before I put on the the serums but on the serum night when I've done that after I've done my niacinamide and my buffet I let it dry I'll go in with my retin A this is my powerhouse I don't think it's gonna make you stop aging I think it will help you control the wrinkles you have to a certain degree over time so to me this is a powerhouse so I would not be giving up my retin A for anything in fact when I get approached from skin care companies I say listen I use retin A I'm not willing to to not use retin A to try test your product if your product is something I can't use with retin A or whatever they're not interested in trying a retin A alternative because I use the big guns these retin A so I use the 1% and I do put it my forehead down my nose I go all around my cheeks down here on my upper lip I use a good amount of it and I get it cheaply from my novices pharmacy so I use a good amount of that amount of it at the same time I take my eyes my eye treatment so I've been using the Olay pro retinol eye treatment this is the UK version the US so somewhat identical same name US is a red version the ingredients are somewhat the same but they're in a different order and I think the different order of intensity as well meaning you know how much of the amount of that product is in here there is a new US version out that I'm really excited to try but I'm not going to try until I'm done this so I normally take a tiny drop and I put a drop here and a drop there and you could actually see like two white drops then I just tap them in and I tap them in focusing on my lines right here and I tap tap tap tap tap tap now I must tell you that I've washed my hands after my retinol application so I no longer have retinol on my hands because I don't want to be putting it transferring anything left over on my fingers to appear of that powerful so I do I tap that in at this point in time and then usually at this point in time I take my eye serum and I'm using the blink eye serum which is the same thing as the care post this is what the container looks like and there's a little tiny indent here I take a drop and I put it in there and I just do like eyeliner on both sides of my eyes that's that's how I do it and I usually do that about four to five times a week at night so now I have everything on I the last step that I usually put on is I will take my B venom cream I use this B venom cream religiously this is the B venom cream I buy at TJ Maxx or Marshalls it usually cost me about $5.99 if you're lucky enough to see this in your TJ Maxx or Marshalls and you're not allergic to bees I would consider trying it I find this to be a super super moisturizer I put this on at night all over my face and literally it does sting me it absolutely does sting but that is usually my last step on my skin two other creams that I really like one is now I've done my eyelash serum I've done my my Olay pro retinol for the deep wrinkles at night I take the note via skin firming and soothing concentrate this and I will take a tiny little jab of it and I will put it on the inside corner of the eyes now some mornings I use it as well it all depends on how early I get up I don't want this will sit on your skin for a while it does not sink in on my skin anyways so if I'm going to if I don't have enough time for this to dissipate or whatever this won't play nice with my at least not my makeup my eyeshadows so usually this is an at night process or on weekends or when I don't have to get ready or I'm not gonna have eyeshadow on I'll do it in the morning just a tiny bit right on that fat pocket and that's it and then I take my timeless eye cream this is what I'm using currently although I'm gonna be checking out another one I take my timeless eye cream and I will dab that on and I will go all around up top now I avoid my eyelash area because I don't want to have any issue but since I put my eyelash serum on early enough this shouldn't interfere at that point in time if I feel that I need a little extra moisturizer around my smokers wrinkles will take my it secret sauce I love this cream this is really really expensive at the time I bought this it was the most expensive cream I bought myself but I do like it I still have plenty and I use it and it's expensive and I am more of a affordable type of products that I like to use so that's really my nighttime routine in a nutshell and I now have a couple of tools that I use so my retina use which I was using retina five to six times a week is now more like four times a week in some cases three times a week really depending on what else I'm doing to my skin I bought the I bought the the Lobel ultrasonic skin spatula I'm just bringing the empty cover in here because it's easier for me to carry that in the bathroom but I bought this and this actually cleans out my pores beautifully I make sure that if it's a night that I'm using this or in the morning that I've used it I would end up and I'll do a video on how I use this if there's an interest but I probably use this three to four times a week and I love how it cleans out my pores it is it's amazing to me I love it so I'm really glad that I bought that I got it at QVC I pay it like those monthly payments that makes it so much easier the other thing that I bought on QVC that I love because the and I've mentioned this before this is the trophy skin microdermat abrasion and I love this absolutely love it so my gadgets that I bought this year these are the two gadgets that I bought this year that I'm like freaking out and so so enjoying so this to me is the like a once every three weeks this is a deep deep deep exfoliation you don't want to over exfoliate your skin you want to be really super careful about that because you can over exfoliate your skin you don't want to do that so currently right now and their website said don't use this when using retin A well I'm gonna do it my way doesn't mean you need to do it this way it's up to you but this is how I'm doing it so every three weeks or so currently I am using this and I make sure that I use this either two or three days after my last application of retin A so if I know this weekend I'm going to be using this my trophy skin derma derma abrasion MD if I know that I'm gonna be using this this was a week in which I'm not but next weekend I will I will make sure that I don't use if I do this on a Saturday morning or a Sunday morning the last my last application for my retin A will be Thursday night every two weeks I am currently doing the derma rolling I still use gin amber I love her derma rolling system I am going to be trying a product that's sent that's gonna be sent to me on derma stamping you know that's the right way to word it I haven't got it yet so I'm not gonna show it but rather than the actual rolling is actually like kind of stamping on your deep lines your deep wrinkles I'm gonna be using that I'm doing this about once every two weeks I'm perfectly content doing this once every two weeks I use a face numbing system I make sure I numb my face before a derma roll and perfectly content doing it once every two weeks I hope I covered everything because you guys all wanted to know about my nighttime routine my products stay basically the same I don't have that you know huge product turnover so yeah that's that's what I'm doing so anyways thank you all so much for spending some time with me and watching this video I know it might be on the long side and hopefully I explained my routine well enough I don't think I left anything out I hope so next up is gonna be my morning skincare routine and then those people that have asked for my diet update as far as what do I actually consume in a day I'm working on that as well and I'm also working on some of my year-end favorites which probably wouldn't get published until January anyways so I've got a couple of video ideas but I would absolutely love it if you guys in the comments below leave me suggestions on some of the things you'd like to hear about you'd like to see me cover in my videos so I would really love that and I appreciate every single one of you and I know I can't express that well enough but I truly truly appreciate every single one of you your support has meant the world to me thank you all so much guys I hope you all have a wonderful day


We heard a lot of names of elements already. We heard outward bank corner. We heard lift hill. We heard Micro bunny and now I heard some names step up under flip. Can you tell me what is a step up under flip? What I can tell it's just a barrel roll. It loads you up. You're gonna be Flipping this way and then you kind of preload into this bottom part You go this way and then where do you end there because I see another element over there Well, when you're coming down, you're gonna be banking hard on this outside I believe 97 degrees outward bank. So should be pretty cool. What feeling does that give our guests? I think you're gonna be floating through there. I'm not too sure. I really haven't experienced this aspect So should be good. Can you tell us the difference between an element and an inversion? So an inversion would be like this where you go upside down continue or stall out and then flip back the element would be a bunny hill or a Bank like that You don't have to go upside down and in the version you always go upside down When I see you guys working on the coaster and screaming at each other for fun It seems you're so passionate about your work. Is it is it your passion roller coasters? Yeah, it's definitely a passion of mine You know, it's not all routine that you think it would be at this point But building a coaster from an existing coaster. There's always gonna be something we're gonna run into a problem We're trying to build around it. It makes it it makes it interesting. Are you going to ride on the tank? I hope so, you know, well at times they ship you out to the next job right when you finish it. So I'm hoping Alrighty, we have a really awesome update out of wallaby. Howland for you guys So definitely go check out their YouTube channel, which I'll link down below As you can see they are moving along with construction at a rapid pace and this coaster is looking absolutely Absolutely amazing. It's giving me like some twisted timbers vibes, but twisted timbers like on steroids almost That's the kind of vibes I'm getting from this coaster. It looks absolutely insane. It's got five inversions Okay, we found out about I'm gonna guess like three weeks to a month ago that this thing was gonna have five inversions And I just couldn't fit it into my schedule to react to that So first of all, that's awesome that this coaster at Wallaby, Holland Is gonna go after steel vengeance's inversion record can't wait to see all the inversions after they're done being built But from what we're hearing it will have five inversions that basically means the most inversions on any RMC yet We have a 40 degree left hill with an 80 degree drop a 45 degree outer banks corner It will have a micro bunny hill right after the drop like steel vengeance a 97 degree outer stall right after the first inversions released A 97 a 97 degree outer Outdoor stall a step up under flip a track length of 1,085 meters and it will go 92 kilometers an hour So they're also people predicting that the last couple inversions will be a zero G stall And it'll have some sort of roll rate before the break room again. Those last two are predictions. They're not final A huge thank you to Renz on Twitter for giving me some information on this huge Thank you to adrenaline thrills for giving me a ton of information and having this video ready for me But this is looking absolutely insane and they still have a lot more to go So I'm not sure if this is gonna open early spring. I don't know when whole wallaby Holland opens Or if this footage is maybe slightly delayed for editing purposes and all that Maybe we're like actually two weeks behind seeing this footage But it's they look like they have a lot of work to go But this thing looks like it does a lot of sharp maneuvers. It looks like it's very almost like Sharp turn sharp turn sharp turn and it's gonna have go 92 kilometers an hour. That's insane So can't wait to see the final product can't wait to see the footage from opening day This is gonna be a powerhouse RMC. I can't believe it's across the pond But definitely super excited for anyways I want to hear from you guys comment down below what you think of untamed at wallaby Holland And are any of you gonna be making a trip to go ride it? Anyways, hope you really enjoyed this construction update out of wallaby Holland Don't forget to hit that like button subscribe You haven't and share this video for others to enjoy. Thanks so much for watching guys. Have an amazing weekend. Bye


One of the reasons some studies haven't shown more impressive results tying disease reduction to the quantity of fruit and vegetable consumption may be because of the quality of fruit and vegetable consumption. People are more likely to eat bananas than blueberries, more likely to eat cucumbers instead of kale. Friday is also important, though. If in one of these studies you ate a whole cantaloupe, you would be recorded getting eight servings of fruits and vegetables. One head of iceberg lettuce makes 10 cups. We know that whole foods are better than eating individual nutrients. For example, a carrot is better than a beta-carotene pill because of what's called nutrient synergy, where the whole is greater than the sum of its parts, as many of the nutrients interact, work together, compliment one another. But what about synergy between foods? Check this out. I've talked about the wonders of the spice turmeric, but the key component of turmeric has very poor bioavailability. Just a tiny bit gets into our bloodstream after eating a nice curry. Unless we add some black pepper. The phytonutrient in black pepper boosts the level of the turmeric phytonutrient 2,000%. That's why dietary diversity is so important. Not only may the variety of fruit and vegetable consumption decrease disease risk independent from quantity of consumption, sometimes variety may even be more important. Check this out. No difference in inflammation at C-reactive protein levels between those eating six servings of vegetables a day and those eating two servings, but those eating the more variety, even if they didn't necessarily eat greater overall quantities, had significantly less inflammation. This supports the American Heart Association's latest dietary guidelines, which for the first time added a recommendation for also eating a variety of fruits and vegetables.


The panel that we're starting with today is the Crisis in Pediatric Immunization. I'm Laini Ross, one of the associate directors here at the McLean Center. Our first speaker is going to be Rick Kodish who is the F.J. O'Neill Professor and Chairman of the Department of Bioethics at the Cleveland Clinic Foundation and a professor of pediatrics at the Lerner College of Medicine of Case, Western Reserve University. Rick was here in Chicago doing both his He-Mong Fellowship as well as his Medical Ethics Fellowship and then he joined the staff of Rainbow Babies and Children's Hospital where he was the founding director of the Rainbow Center for Pediatric Ethics. His areas of expertise include childhood cancer and blood disorders, pediatric ethics, end-of-life issues, and research ethics. Today he's going to be talking about the problem with parental autonomy, implications for pediatric immunization. Really nice to be with you. I'm not sure there's a crisis in pediatric immunization. We were just talking about that a little bit. It's certainly a good name for a panel. There are some disturbing trends in pediatric immunization and I'm going to launch into a talk that will, I think in the first part, talk about some fundamental ways I think about pediatric ethics and then get to the issue of immunization around that and a lot of what I'm going to talk about focuses on language. I don't think I need to convince this audience that language matters in both an efferent and an afferent way. That is, language is a reflection of what we're thinking but even more importantly I think language affects how we think and just to start out with I would say that autonomous parents are not the same as parental autonomy. The latter term implies a lot of untoward consequences which I'll go through while the former is compatible with autonomy as exercised in one of many moral roles, the role of a parent. My barber Danny has autonomy to some degree in how he cuts my hair. He's got barber autonomy I guess but more importantly he's an autonomous barber. So we play these many roles in life, barber, parent, ethicist, you name it I think the language is important here in parental autonomy as language gets us confused from the perspective of moral psychology and I'll say more what I mean about that in a minute. The Academy of Pediatrics core value statement this year is really consistent for many years and the most important thing is that we believe in the inherent worth of all children they are our most enduring and vulnerable legacy and that's a core vision for me also I think as I think about pediatric ethics remembering that children are vulnerable and thinking about the legacy aspect of it. The principles of pediatric ethics are no different than the principles as articulated in the Belmont report and I tend to think that beneficence which is highlighted here is the dominant principle but certainly respect for persons is incredibly important in pediatric ethics and as you'll see as I go on I'm going to distinguish that from respect for autonomy or autonomy I think those are derivative from respect for persons. Another way of thinking about respect for persons if you sort of move from the philosophical to the theological is to take this phrase everybody is made in God's image right you guys have heard that phrase before everybody is made in God's image at a secular institution like the Cleveland Clinic where I work or like the University of Chicago that can be probably not a wise way to frame it but I think personally for me that captures something about respect for persons that I have trouble in philosophical language conveying to you why respect for persons is so important and certainly I buy into this idea that everybody is made in God's image but certainly all children I think we would agree if we have a theological perspective never met a child that I think is not made in God's image so this is a long way of saying respect for persons is important in pediatric ethics beneficence is arguably more important though and justice certainly will talk about some justice issues with regard to immunization problem of the free rider and that sort of thing so as I said I think what's happened historically is that autonomy or respect for persons has become the dominant principle for adult medical ethics beneficence has become the dominant principle for pediatric ethics the phrase the best interest of the child carries a lot of currency and resonance to refine it a little bit in these next two bullet points the concept of basic interests is I think preferable to best interest I think best interest is a bar too high and the harm principle which our colleague Doug DeGama has written about very eloquently I think in some ways is the converse of basic interest I'm not going to go into the harm principle in detail today for this analysis but wanted to be sure that I mentioned it so we move from respect for persons and beneficence to the operationalizing of that in informed consent and there's this very important difference which is going to relate to immunization between informed consent and parental permission the autonomous authorization of an adult on her own behalf for something is more ethically robust than parental permission for a child and the AAP again says the pediatricians responsibility to his or her patient exist independently of proxy desires or consents that second statement is very interesting when it comes to immunization a pediatricians obligation with regard to immunization is the parental desires are not primary it's about what's best for the kid so the problem of parental autonomy happens this way I think there's downstream consequences get back to this language the interests of children are put at risk because of the shift in thinking from questions of what's the right thing to do to a focus on who gets to decide and in our ethics practice at the clinic we do about 325 consults a year very busy busy practice and we've learned I think to help people focus on those two questions and toggling back and forth between who gets to decide what's the right thing to do and looking at each case to try to see the extent to which those two framework questions pertain so the downstream consequence of parental autonomy is it really focuses on who gets to decide substituted decision making which is a cornerstone of adult clinical ethics is of really limited help in pediatric ethics especially in this age group children younger than 5 before school that we're talking about with immunization the historical considerations arguably would say that we need an affirmative action kind of approach here and the parental autonomy is the wrong language to do that there's even a compensation model for past wrongs if we think of children as a class that says that children are not the property of their parents and we need to begin treating children in a way that is respectful of them and interested in protecting their interests so this does not imply a state sponsored takeover of proper parental authority I want to make clear that that's not what I'm saying here there's a latitude issue that I think is important there are some important a-words here and just quickly to go over them Dan and John Lantos published a paper recently on autonomy that I would recommend highly to you that talks about agency and authenticity has two sort of sub-components or ways of thinking about what autonomy really means but as someone interested in pediatric ethics I'm going to say autonomy is not that important really so I'm not going to spend time on that a I think authority is what's at issue here and parental authority with regard to the immunization decision and that latitude about how much latitude we give parents to accept or reject vaccination so I have no data in this slide except for this and I am an empiricist the source of all truth is Google I did a Google search based on the thing I learned at University of Chicago it's axiomatic that one cannot claim a right without attributing to someone else a corresponding responsibility I'm interested in responsibility and not just rights so parental rights on Google there were 199 million hits parental responsibility 5.3 million hits what does this say about the ethics of parenting in the age of Google I'm not sure I'll leave that for you to think about informed consent in pediatrics is kind of the wrong language too it's parental permission and assent to the child the recommended schedule for most childhood vaccines precludes a major role for assent so I'm not going to get into that component of it now permission is not the moral equivalent of informed consent because kids are not the property of their parents and I'm going to talk just for a minute about the clinical context the research context and the public health context because I think immunization belongs mostly in the public health context what's the proper obligation of parents in this public health context in the clinical context parental latitude is more constrained I would say in the research context because it's a super erogatory phenomena we give parents veto power in almost all cases but what about public health should public health concerns count in a parent's assessment of a risk-benefit ratio that they're doing regarding immunization and I would say that a responsible parent with appropriate education should decide in favor of vaccination without a need to invoke that public health benefit so it's kind of a moot point if the safety profile of the vaccine is good it's low risk and high benefit to the child the public health concerns don't need to come in it's almost like a piling on that a pediatrician could do if she wanted to in framing the risk-benefit balance so what are some of the factors to consider with immunization the safety profile as I mentioned each vaccine is different and I want to stipulate here that this is not a talk about the specifics of different vaccines each one is different but in general the safety profiles are excellent the risk of acquiring infection at any particular time depends on the prevalence of immunization in the community and the prevalence of the infection in the community the severity of the infection involved I saw kids die of age flu meningitis when I was training here in Chicago bad disease, immunization has wiped it out we don't see it anymore but I think we're going to start to see new outbreaks of diseases and the younger pediatricians who have never seen diseases are going to start to see them and that's going to change how they talk to parents about these issues the reason for parental refusal may or may not be important I don't want to weigh in on that but maybe on the panel we can talk about that I think it's an interesting question and changes in these and other factors could alter the risk-benefit analysis parental refusal of therapy I think I ripped this off from John Lantos at one point if it looks familiar John age matters the rule of sevens kind of thing here acuity matters you have time to negotiate about something or not morbidity and mortality both matter parental reasons in refusal to therapy may not matter but immunization I would argue we probably don't want to think of it as therapy it's a public health intervention it's a prevention and not a treatment so what is a good pediatrician to do I'm going to wrap it up here I think there are three approaches there's a hard line approach which says you cannot be in my practice if you do not immunize your child there's a parental autonomy approach which says it's their decision it's not mine to make they're fine and then there's the middle road which I advocate and it says good pediatricians should coax cajole patiently persuade do not coerce and importantly educate parents about these issues to counter much of the nonsense that's out there on the internet educate parents about the benefit to their own child educate parents about benefits to other children educate them about benefits to society and give them honest data about the risk I would highly recommend to you the academy's clinical report on responding to parental refusals of immunization I was privileged to be on the committee when the work was started and Doug Deacon again took the lead I think on this it provides very practical guidance it emphasizes responsibilities and relationships not rights and it reiterates the AAP supportive immunization requirement for school entry very important one one minute alright gonna be done on time so conclusions pediatricians should advocate for the health of both individual children and for children as a class and I think we'll be talking more about that as the panel goes on I think parental autonomy is not a good basis for accepting immunization refusal but prudence suggests that the wise pediatrician pick her battles carefully and in most situations it makes sense to be patient to invest in strengthening the clinical relationship with the child and patients trying to keep your eye on the ball thank you


Let us talk a bit more about the dual function. So what is the dual function? What is the geometry of the dual function of the Lagrangian? What is the geometry of the Lagrangian? So now here is one way of so the Lagrangian or and so on all of these appear they make an appearance in problems that are unconstrained. But we can convert these sort of problems that are actually constrained to problems that are unconstrained in the following by doing the following thing. So I have suppose a problem that I mentioned before which is minimize fx subject to over variables x subject to gi of x less than equal to 0 for all i from 1 to m and hj of x equal to 0 for all j from 1 to p and then I defined this as my Lagrangian lambda of x L of x comma theta as f of x plus right. So this was my lambda L of x lambda theta. Now suppose I did the following I decided I want to express this constrained optimization problem as an unconstrained optimization how would how can I do that? So to do that let me introduce this function this function let us call this the function i plus the function i plus of t what does this do? This function is 0 minus infinity it is greater than for t greater than equal to 0 it is 0 and for t strictly less than 0 it is minus infinity right. So i plus of t how does this look as a function of t? So here is suppose my t for t is strictly less than 0 this i plus is equal to 0 change the color and first it is this for t is less strictly less than 0 it is sorry for t is strictly less than 0 it is equal to minus infinity right. So for all right and for t greater than equal to 0 it is actually equal to 0. So this is my function i plus so it takes value minus infinity when t is less than 0 and 0 onwards it takes value 0 let me define another function related looking function i 0 of t. i 0 of t is defined in this way i 0 of t is equal to 0 if t is equal to 0 and it is minus infinity otherwise. So how does this function look? This function looks like this at 0 it is 0 and everywhere else its value is minus infinity okay. Now these are obviously very ill behaved functions they are taking value minus infinity and so there is obviously a huge discontinuity and a non-differentiability here but in terms of these functions if I include minus infinity in my calculations I can express an unconstrained problem in terms of the I can express this constraint problem as an unconstrained problem. So how do I do that? So notice that this optimization okay this problem let us call this problem p, p is actually equivalent to minimizing fx now what do I need to do here okay let me just change this a little bit I will just change this definition a little bit so actually let me make a slight change in this definition because that will be convenient for us so let us instead of taking defining i plus and i 0 in this sort of way let me put these as using this as plus infinity okay and also I will change the range so it is plus infinity so define i plus of so let us so define these functions so define i plus of t as is in this sort of way at so for t for so whenever t is less than equal to 0 it is equal to 0 and when t becomes positive it shoots to plus infinity alright and i 0 of t is 0 when t is equal to 0 and whenever t is not equal to 0 it again shoots to plus infinity alright so what is this look like what sort of function does this look like let us draw these here so i plus of t as I said it is for t less than equal to 0 it is for t less than equal to 0 it is 0 and for t greater than 0 this it shoots to plus infinity so this is my i plus of t and i 0 of t looks like this at 0 no problem it is equal to 0 and whenever t is not equal to 0 it shoots to plus infinity this is i 0 of t alright now using these functions i plus and i 0 of t I can actually express express my I can express my the optimization problem p I can express in the following way I can I can write this as minimize fx plus summation lambda i i plus of gi of x sorry I do not need the lambda so using these these these two functions i plus and i 0 of t I can express my optimization problem p in the following way I can write it as minimize fx plus summation i plus of gi of x I going from 1 to m plus summation i 0 of j of x j equals 1 to p so now what does this do what does this do well it says that look at I look at the definition of i plus whenever gi of x is less than equal to 0 I plus is equal to 0 alright so in that case this this term here the term here this this term actually is equal to 0 whenever gi of x is whenever gi of x is less than equal to 0 in particular when all the gi of x is less than equal to 0 this entire summation is actually equal to 0 similarly look at this term whenever h j of x is equal to 0 this term is equal to 0 right this term is 0 so whenever so whenever so in short if I take any x that is feasible for p then each of these terms the i plus terms as well as the i 0 terms each of these terms should would end up being exactly would become exactly equal to 0 so in short on the feasible region this new function that I have defined you know this new non-differentiable infinity value taking function this function is on the feasible region is actually nothing but f x now outside the feasible region of p outside the feasible region of p what is what is this function well if you are outside the feasible region then it means that at least one of these terms is going to be not 0 so at least these if either one of the at least one of these i pluses or one of these h j's i 0's one of these is going to be non-zero and when it is non-zero what value does it take whenever it is if it is not 0 if these these things are equal to plus infinity remember so this they take value plus infinity so which means that once you are outside the feasible region this this here this this expression here actually takes value plus infinity so what does this mean it means that this this function here let me write it like this this is equal to f x for all x feasible for p and plus infinity otherwise so which means that if you have to minimize this this if you have to minimize this this function that is that is mentioned here if you are minimizing this particular function what are you doing you are effectively just minimizing f x over the feasible region of p which is nothing but solving p itself right so all so this problem although you are minimizing this over all in an unconstrained way over the entire over all of r n what you are effectively doing is minimizing just f over the feasible region of p right so that is that is actually an incredible incredible simplification because you you you do not really need to care about the geometry of what is happened in the constraints and so on but it is also very deceptive because what you have done all that geometry has actually been absorbed into these complicated i 0 and i plus functions which if you have to analyze you would need to understand the geometry of of the g i s and h j s in the first place all right now what has this got to do with the Lagrangian so if you look at this the Lagrangian function here that is less that is mentioned here and if you look at the function that I am optimizing here there is clearly a close resemblance because here is your f plus a summation of something right and and some other terms with with the here they have inequality constraints and then here you have your equality constraints right and likewise here you have f plus something that involves inequality constraints plus something that involves equality constraints so now what is the connection between these two that is something that we can see we can see now so what I have you can think of you can think of it this way that what I have done is actually in place of the i plus and in place of the i 0 I have put in some new functions here which are actually linear functions so in place of i plus of g i of x what I have done is put in lambda i times g i of x and likewise in place of i 0 of i 0 of h j of x I have placed theta j of theta j times h j of x now what is that what is that actually doing so let us come back to this figure see remember i plus has this sort of form where for t less than 0 it takes value 0 and for t greater than 0 it shoots up to plus infinity now if I want to approximate this linearly in a if I want to do a linear lower approximation to i plus of t what sort of function can I choose well the kind of functions that I can choose have to be of this sort of form so I have not drawn this very well let me draw it again so the kind of function that I can choose has to be of this sort of form so what does this mean what kind of form is this it is a function whose slope is like this it is positive because if I take a function just this was for just for you to see if I took a function whose slope is negative then it would at some stage for some value of t it would go above 0 above this line here and then it will not be a lower approximation anymore so for it to be a lower approximation it is necessary that it must have a slope a positive slope like this it must have a positive slope like this moreover for it to a since it must have a positive slope I can look for the best lower approximation amongst the guys that have positive slope and it is clear that it there is no use having an intercept here so taking a lower approximation like this is of no use I might as well get a better approach better lower approximation by taking the intercept by making sure it passes through the origin in short the intercept should be 0 right so it is of no use taking this kind of lower approximations so what we can take are approximations like this we take a lower approximation that is we take a lower approximation like this which is passing through the origin all right so what does this mean the in short a lower approximation to i a lower linear approximation to i plus is takes the form it takes the form lambda i times t okay so so this this one here is a function of the form lambda i times t okay where lambda is is lambda i is greater than equal to 0 likewise a lower let us look at now i 0 so if I have if you look at i 0 if i 0 has this is it takes a value plus infinity everywhere except for 0 so if you want to take a lower approximation to this now that you can take a linear function like this you can also take a linear function like this so long as the intercept is is is below 0 there is no problem right because everywhere else the value is plus infinity and you will be okay you will be all right so so long as the intercept on the y axis is negative you can continue you can take any kind of linear function but again if you want a tighter approximation if you want a better linear approximation why even bother with an intercept you might as well take a linear function that passes exactly through through the origin and that gives you that means that the function should be of the form theta j times t either this or this whatever right this these are functions of the form theta j times t where theta j is any is any real number right okay so what does this mean this now these are both linear approximations all right so which means that point wise that means for every t they actually take value less than the corresponding i plus or i 0 respectively right so which means that if I look at what is here if I look at what is in this optimization what I just put in the bracket that can always be lower bounded if I if I replace these the i plus and i 0 by their respective linear approximations so I can I can get this is always greater than equal to write like this so p is the optimal value of p is is always greater than equal to the minimum over x in R n of minimum or infimum whatever over x in R n i going from 1 to m j going from 1 to p theta j times j of x what is and what is this this is actually nothing but the inf you are doing effectively the minimum of the Lagrangian and this is equal to your dual function so so long so the greater than equal to here this required that lambda is greater than equal to 0 and any theta. So for all lambda greater than equal to 0 and for any choice of theta we have that we have that the optimal value of p is is greater than equal to this which is which is nothing but the dual function and now so what is the what is effectively the dual function doing the dual function is taking a linear approximation to these i 0 and i plus functions okay and and solve the dual function is the optimal value of that linear approximation so or in other words the Lagrangian what the Lagrangian is actually doing is is taking a linear approximation to these i plus and i 0 functions and the the minimum of the Lagrangian is basically the minimum value of this linear approximation and that is what we are calling the dual function and why is it a it is a function of what it is a function of the slopes that you choose for making the linear approximation. So as a function of these of the slopes you could have we remember we we said there is no need to take the intercept and that is why we took the intercept as 0 and we and we got these linear functions passing through the origin but we did not say anything about the slope the slope is up is still up for grabs it can it is still to be decided so as a function of the slope the gap between the actual optimization and and or and and this can can still be fine tuned the actual approximation as actual optimization and the lean and its linear under approximation can still be fine tuned in any case the linear under approximation is giving is is captured is captured by the dual function which gives it to you in is a function of the slope so maximizing the dual function so maximizing this which is your dual problem maximizing this which is your dual problem is basically asking for what does this ask for it is asking for the best linear under approximation and see basically asking for the best linear under approximation. So in this class of under in this class of approximations you can what is the best you can do right so you you so so the sequences you have you create your you write your actual problem like this you write your actual problem like this create a family of linear approximations using this using this logic you look for the best value of the minimum of those linear approximations and then you ask what is the what is the best I can do amongst amongst my entire family what is the largest value of my what is the tightest lower bound that I can get using this linear approximation all right. So that is what that is what the dual problem is doing now this if you think about it this way it is actually nothing short of a miracle that that in the case of linear programming the primal and dual actually end up being equal. So the the optimal values of the primal and dual being end up being equal which means what I mean by that is see you see how grossly inaccurate this entire linear approximation is so what you wanted to actually approximate was this sort of function something that 0 here and shoots to plus infinity after that likewise what you wanted to approximate here was this function that is plus infinity everywhere and 0 here and you are approximating it by what an extremely benign function you are just taking a linear function like this and then you are saying okay amongst this class of approximations which is the one that is giving me the best possible value that is by that is what you are solving by solving the dual problem right and it is incredible it is actually really incredible that you can in fact get get back the same value as of the primal that means that there will be no gap between this one which involved is i plus and i 0 functions and this problem that has been found by looking for the best value of the linear approximation okay. So in the case of linear programming that is exactly what we get with the linear programming duality theorem taught us that the primal optimal and the dual optimal are whenever there is a solution to the primal there is a solution to the dual and the values are equal and that is what we are finding here okay. So this sets the stage now for convex optimization duality and so we will do that we will do that in the next lecture okay.