I want to be in bed at nine o'clock. I want to be rested. I want to spend time in my room. I want to go to sleep. Okay. Give me all the stuff that was punishments when you were the kid, right? Keep watching to find out what that has to do with today's book. I'm Kyla Denaya and we are talking all about the book. Rest is resistance, all right? And a festo and that's for real because this is an evidence-based book. You hear me as full of all kinds of facts and quotations and all the good stuff. But this book is written by Trisha Hersey. The genre of the book is nonfiction. The theme of the book is growth, self-improvement, okay? So I know y'all are busy. I know you're busy. Let's get straight into the most important examples of rest that I could find.  So literally rest. Meditating, resting your eyes, showing through the park, praying, deep listening to a full album, okay? Not just music playing in the background, but like Beyonce, what are you saying in Renaissance? Rest is all of these things, okay? And the entire point of the book is that we have to take care of ourselves. We will not be here to fight the fight, to do the work, to be entrepreneurs, to record the videos if we don't rest. So that is off jump. So let's get into the first way that I am resting, all right? Can you see that? You see that? Y'all, I've been trying for months to stop wearing my digital watch, okay? I have a ton of analog watches. I read physical books. I'm an analog kind of girl, but oh, I like to get these little alerts and the notifications when I'm doing stuff. Ma'am, if you run a flight of stairs, it's good for your heart, not your watch. If you jump rope, it's good for your heart, not your watch. My first way to get rest is to cut no more digital watch. So did you know that rest is not a reward for you working hard? To me, I'm working, whether it's editing, whether it's writing, whether it's reading, whether it's typing, whatever it is, let's take a five minute break as a reward for being productive. I never caught it a reward, but it was a reward. I'm a big fan of the Pomodoro method, which is work for 25 minutes, take a five minute break. Or in my case, I work for 65 minutes and take a 10 minute break, because 25 minutes is too short. So for me, this book told me that I had to reorder things. It had to say, I am taking 10 minutes to myself because I'm taking 10 minutes to myself. But that also means if there's a day that I just am not feeling the work, I can also just take that day off. Or I can decide one day to not do the Pomodoro, right? Like I tend to commit and dive in. So now I'm like, if it's not Pomodoro, it's not working. Kyla, you can also just go and work and take a break if you need to. Now, if you're not good with taking breaks, which I'm not, that's why the Pomodoro method works for you. So that leads right into the next point, which is rest is intuitive, okay? So I'm gonna talk all about rest being intuitive, but speaking of intuition, go on and subscribe to the channel if you're enjoying the content, okay? I talk about books every single week and I would love to see you again. I struggle with this one, okay? Trisha was getting me together and I don't know if it's the lawyer background. I don't know if it's the entrepreneurial hustle, but I needed some net ministry and Trisha got me together, okay? And intuitive rest means you need to listen to your body and you are allowed to rest, okay? And we're not talking about you becoming a slacker. It doesn't have to be that extreme, okay? If your body is telling you you have been burning the candle at both ends and it is time for a break, you can take a break. My life, I've been waking up at five in the morning to get work done. Now my daughter wakes up at seven thirty in the morning, packing lunch, having breakfast with the husband and the kid, talking, all of this stuff, right? I know the time has been official, I can't get up. So you know what that meant? I started going to bed at nine forty five, okay? So our lives are busy, busy being professional troublemakers, busy running businesses, being all the things. So go on and check out this video here. It's all about how to be a professional troublemaker, all right? So I'll see you in the next video.


The fewer than 70 registered hotels in Adamawa State risk fizzling out of businesses if they fail to install CCTV cameras. The State Deputy Governor Carla Tapua-George of Farota gave this indication at an emergency meeting with the hospitality business owners at Government House Yula. The directive came following a recent killing of a lady in Happy Day Hotel Taggart Junction Yula. And we will not sit as a government and watch citizens, you know, being decimated and killed one by one. And in our hotels where we think once we all do have guests, and we take our guests to your places, most of you are our customers, once our guests arrive we take them to your hotels.  But if this is what is happening, even us, we are not safe. Not just to talk about governance but also for our guests and relations who come around and we cannot accommodate them, then we need to go to your places to accommodate them. We will not be safe ourselves. Therefore, after going back and forth, government has agreed for six weeks. And that means six weeks and I assure you it is six weeks. So after six weeks, if you don't have the CCTV in your hotel, motel, lodge, whatever name it is, the government will have the right to take its decision because the service is your runway, you are doing it on behalf of these government and citizens and we would ensure that the right is. The Deputy Governor stressed that protection of life and property of the citizens is the fresh air government top priority. A lot of our hotels and hotels that are in small, small areas were into short service and I'm sure we all have got to understand what I mean by short service. A man bringing in a woman and they sleep there after two hours. He paints maybe half the rates or half the whatever and he walks away. That can be your daughter. It can also be my daughter. And in our hotel, she will read of such activities because that young lady will be the mother of the next president of Nigeria. Why would you allow her to be wasted in your own hotel because you're looking for money? And the drugs, they push through your places. Those drugs can reach the house of your own son and my own son. So why would you allow your hotel to be the place where those drugs are pushed through? If you put yourself as a parent, as your hotel owner, you have your children, you want to send them to the best school, you want them to be the best they date. So why do you allow your hotel to be the place where other people's children, especially their lives will be wasted because you're looking for money? I'm sure that can be called low money and that is not fair and that is not acceptable to us as the government. In his own remark, the State Police Public Relations Officer, SP Suleiman Guruje, asked the public to give timely information to the police to enable them to take action immediately after an incident, as the police is committed to ensuring peace and stability in the state. We really appreciate the vision of the government. Our excellency, on behalf of the hotel in the state, all your contributions, your observations are noted. I'm sure that you will put your heads together to see a way forward and to protect this public situation.


to taking your health back on Think Tech Bahi. I'm your host, Wendy Lo. Today on my show we have a dear, dear friend and her name is Susan. Thus the title of our talk today is Susan Scott starting the conversation. What are the wounds in society and how can we heal them? Susan wants to share this thought with you. Healing starts with starting the conversation and changing the vocabulary. So just listen to those wise words because it'll make a world of difference the next time you want to talk to somebody. So let's get started. Susan, I've known you for many, many years, but I know our audience, they want to get to know you too. So can you just share a little bit about yourself with us? Absolutely, Wendy. Thank you so much for having me and yes, many years. That would be 29 years since we've had the product. Yeah, it's amazing. I'm here today. I do this great talk and it's called Start the Conversation and for me this work started back in my 30s when I had experienced some life-changing events and it was then that I started to really pay attention to those around me and becoming a little bit more aware of their needs and also their behaviors. As a society, it's human nature. When we see people acting out or we're walking down the streets and someone's talking to themselves, it's very natural for us to attach that label crazy or to keep a distance because we just don't understand what's going on and it looks weird, it sounds weird and we attach all these negative again labels and then the conversations we have about it, it just perpetuates this energy that could be very hurtful to our society. So it was then at that point where I started sitting down and I just started asking questions and listening to people and really developing a space where I could listen with an open heart and at that point I just decided from here on out I'm going to work on my labels. I'm going to work on how I have conversations when I talk about others and just being a little bit more responsible about that energy. Wow and you know you hit it right on the nail. I mean speaking to someone taking time to just saying hi and how are you and really wanting to know and not just another phrase you pass out loosely like hi how are you and then you're walking away. Hey how are you and when they start engaging they want to talk story too and that's what we're really desiring the most especially. We really saw that going through COVID and the need for people to just have human relationships again and what is the best way to have a relationship communicating and starting a conversation. So you've hit it right on the nail Susan. So please share a little bit about your need to start the conversation. Absolutely. There was a time where that I was just surrounded by a bunch of individuals that I could just feel that there was a lot of hurt. I could feel that there was a lot of masking, some pain and often at times when I would hear conversations and I would just hear a lot of vulgarity. I would see these behaviors and so I just wanted to just spend some time with them to see where it was coming from and at this point I started meeting some really and again I have to be careful with these labels because society would call them nuisance to society offenders but I found them to be some of the most beautiful and incredible individuals I've ever met in my life and I like to tell the story about this young woman that her name is Christina. Beautiful beautiful girl and when she was 11 years old her parents had passed away. They had both died in a car accident and her uncle became her guardian and at the age of 11 she went to go live with them and instead of being a parent or taking care of her he exploited her. He put her in the sex videos and in order to get her to comply he would give her crystal methamphetamine and by the time she was 12 years old her whole life has now changed. She's an addict and she just lost her whole childhood. By the time she was 17 she had four daughters and she didn't know she had not developed life skills. She had really not had much of an education but she knew enough to take these girls and take them out of this home and somehow protect them so the only place that she knew to go was up an accountment and she set up a tech and the only way that she knew how to provide for these four girls was through prostitution and the only way that she knew how to get through that was by taking drugs and all of a sudden people started paying attention to her and these four girls and they started attaching all these labels that she was a hoe, that she was an addict, that she was homeless, that she was a bad mom. So you know instead of anybody at any point ever like sitting down with Christina learning what her story was it was all this negative conversation and energy going on around her. Eventually CPS was called and these four girls were taken from her and it just had this bigger hole in her life and she didn't know how to fill it except with all these unhealthy behaviors and she delved into even more of her addiction and the only way she had to keep that up was now getting into criminal behaviors where she was breaking into cars and breaking into homes and eventually she ended up in prison. After she did her time she was now released but nobody wanted to hire her because now on top of it being an addict, being homeless, being a bad mom, she's now a criminal, a thief, an offender and she's just really really struggling so she was in the system for quite a while going in and out of the prison system but there was never a time where anybody ever sat down with her and just let her know like I'm here from you and basically just validated her loss, right. So eventually she got into a shelter in a woman's program where she started addressing her trauma and her abuse. She went through drug rehabilitation, learned some employment skills, actually went through the KCC culinary arts program and is now doing her best to reintegrate and hopefully do so with integrity. So it was then after hearing her story that I needed to start having this conversation hopefully at this point we can sit down and we can have this conversation where it's with compassion and with an open heart. And again that word, that term open heart, that's all they need, that's all they want and that's pretty much what will be the beginning of a start is someone listening to their story and their heart and not labeling them or condemning them but really having a compassionate heart to who they are and they are human beings just like we are. They have a different story, we all have different stories but the fact that you took the time Susan to sit down and hear her heart and then she felt your heart and that's where healing comes from and I know that's exactly what joy gives you because you know the impact that you're making with these ladies. So I commend you Susan for taking the time to make the relationship and the conversations with these women and men as well. I know that you also speak to a lot of veterans and I know that that's very difficult as well, another difficult journey that you're on but you're the right person and you have that compassionate heart and the desire. So where did you meet? You have a bunch of photos with veterans. Where did you meet these veterans that are presently unsheltered? So I have a really dear friend, her name is Nani Medeiros and she is the Executive Director, right? She's my beautiful soul ever meet, not just on the outside but her heart is just gorgeous. She's the Executive Director of this great organization called Homemade Hawaii and this non-profit is comprised of basically all these developers here on the island, whether it be Castle and Cook, Stanford, Carr, Howard Hughes, they all come together and started addressing our needs in our community and addressing homelessness, those that are living on the streets. They're building these homes but yet a lot of the individuals here in Hawaii unfortunately cannot afford it. So they took it upon themselves to provide funding and contractors and even supplies to either build shelters or assist the existing shelters that are in place and refurbish them, renovate them, put on new roofs. They also worked like with Koala Dukua out at Sunset and they put on the roofing for the safe haven that is now open for young children that have been sexually trafficked, sex trafficked. And they have this great construction site out at Kalimua that they're building 36 tiny homes that will lend homelessness for their veterans that are experiencing homelessness. It's not a temporary shelter, it's not where they could own their six months or two years. If they choose to live there for the rest of their lives, they can and it's such a cute little community out there. It's really, really special. I'll go a little bit more because I think I have some pictures of them. Wow, that's I mean I just got to again thank you. I got to thank Nani, give her a shout out for doing this Hawaii homemade homemade Hawaii and her heart and fact that you're her buddy to just encourage her along as I know she must have had some you know roadblocks and stumbles but that she has a buddy partnering with her and her heart to make this happen for the veterans out there. So congratulations to all the partners that have made this possible and I know it's a whole tribe that makes that happen for these young men and women. So Susan in our next slide I need to ask you where was this taken and who are you with? Awesome, so I pre-COVID I was able to go to preschools and talk about recognizing the needs in our conversation in our community and again it was starting the conversation because it's this generation that's going to be going forward and addressing those societal wounds that we're experiencing right now whether it be domestic violence, whether it be homelessness, whether it be you know kids that are presently being trafficked here in Hawaii. So I walked in and my first question with them was you know what are the needs in our society? What have you recognized and it was basically again just getting them talking and thinking and one of the things that I asked is as we start this conversation let's shift our vocabulary a little bit. So it's very easy to use the word homeless however it has a negative connotation when you use that word. It takes away from the fact that these individuals are either veterans or former teachers or mothers, fathers, sons, daughters. So I started asking them hey let's use a different word because these members are still part of our community therefore there still are neighbors and if you were to look up just the definition of the word neighbors it means someone who lives next to us or close to us which is them they live close to us. So that's just a shift in vocabulary that has a little bit more of a compassion approach. I also asked them when I challenged them that when they go out and when they hear the people use that word homeless say hey you know let's change the vocabulary here. I also have taken upon myself that every time I'm in a Reno and close to a politician that I also asked them to start shifting their vocabulary too. It wasn't too long ago where I was with Lieutenant Governor Josh Green and I had just read this article and the media kept using the word sweeps. So when we're at home what do we sweep with the trash? So now we're using this word sweep when we're out on the street so when they're doing these community cleanup projects that they're sweeping these individuals who are unsheltered. So why are we using that word? It's hurtful to our society right? It inflicts even more wounds and it it even puts on more labels to people who really that's not what's needed. So I addressed this with the kids and they were really really great. I encourage them to participate in different community projects whether it be starting a canned good drive at their school whether it be participating at beach cleanup down at their beach there at Kailua Beach because I was at Kailua Colohale High School in this picture and I also asked them like you know when you are starting your career in college and starting your careers and going out professionally use your voice when you recognize these needs use your voice and also start developing some mental and emotional intelligence and that's going to be through lived experiences. So go out and experience what these people I didn't encourage them to go and like start experiencing what homelessness is like but just to go out start having conversations with them and sharing the meal and you know again starting the conversation. Wow so Susan you're absolutely right you know I mean just changing the verbiage that we're using and that we're so used to using and then like what you're doing you're starting with the young people the students the younger generation so that they start off you know with the right terminology and we don't mislabel our friends our neighbors in the street and so again I commend you for that continue to do that you sharing that with the politicians and the people of influence in our community powerful because they are on tv and they make an impact on so many people so of course you're you hit it right in the head man just keep going with that message and I think a lot of different outcomes will occur because of just changing the verbiage so I'm so excited. Yeah me and by the way just to let you know Lieutenant Governor Josh Green was so receptive but he's been really on the forefront and addressing that. He has I've seen him on tv I'm trying to resolve the problems you know some of the situations on the street and again commending him for his efforts as well so on our next slides is if there's a gentleman and you guys look so happy what you guys so happy about. So I know there's a few pictures which what does this gentleman look like does he have one of the white beard and you guys are hugging and he looks happy. Yeah well his name is Michael and he's so special so Home in Hawaii had a construct or they still do they're still building that the Kalei Loa um that the Kalei out at Kalei Loa of the 36 tiny homes and prior to the construction I would go out and I would meet with those that were living in the tents in the encampment out there and Michael was is 72 years old he's a Vietnam vet and I'm born in Vietnam I was born in Vietnam in Saigon and so we just sat started talking story about Vietnam and and how long he was there and and a sense of loss with his buddies that he basically grew up in Vietnam in his 20s right and then when he came back life was actually very different he wasn't well received back into the states because he was a soldier of Vietnam and number two because he was African African-American so he struggled quite a bit but in the picture we're smiling because one of the things he just asked for he goes can I just have a hug and I said sure I would love to hug you and he just gave me one of the biggest and one of the best hugs I had I've ever had it was just he gave me such a gift that day and he just walked me around he said he wanted to be my escort and chaperone around the encampment and just introduced me to everybody it was just a really nice day without and you know Susan you know we go to these locations these communities and we're going there and we are thinking we're going to make an impact and make a difference in their lives but the the gifting part of it all is when you go there and you receive something like that that you've not experienced in a long time I tell you that's the continues I'm sure and it continues to propel you to want to do more just having that hug and making a positive impact in someone's life that day I mean that's so powerful so again thank you yeah it was so much fun right I know you advocate for women in need I know that that when I saw you you know the first time in a long time that was your passion you were driving that course and men and women but I know the women in need is close to your heart so please share with us their mission and why you are so passionate about that so women in need have three shelters here on the island of Oahu and also a shelter on the island of Hawaii and they take women in that are that are removing themselves and their children from a domestic violence environment which takes a lot of courage women in shelter also work with women that are coming out of the penal system and that are taking their time to reintegrate and to do so again with integrity which is really really imperative women in need number one provides safe shelter number two provides a place to where there's healing there's an opportunity to be vulnerable in a safe place and what I mean by be vulnerable they have to get to the point where they can share their stories and our stories are gifts by the way Wendy when we share these stories we are the ones that get to choose who we share that story with and that person should be able to hold the space for our shame stories our hurts our pain and still just love women in need it's really special they also help women get back on their feet reunite with children that have been separated through CPS and also provide employment um rehabilitation to where they get skills and they they help them with their resumes and get them back working and employed um they're really really amazing and this is a critical part of their journey where all the hearts come together and just love on them and listen to them and really help them to just get back you know to what they where they want to be I should say um very critical and so all these components that you're putting together and not just loving them and hugging on them but also just spending the time to listen to them and and feel their hurt because they've felt it for so long alone but you're there now with them as well as all these support groups so again I'm very aware of many of them um I'm so excited that you're working directly with them as well and it just feels that big puka in our hearts because we want to make a difference a positive difference so Susan we talk about this open heart and I I love the term open heart that's my favorite term of all so why is it so important to listen with an open heart it's so easy when we're having a conversation we're only not completely present right because we've got so much going on so we're thinking about many other things and we're not just really just absorbing what is being shared with us and again these stories are gifts so to listen with an open heart and just be there with no judgment no opinion but just to be there with love and again it requires you to open your heart to do that so what's next for you Susan I know you you've done many things you you we didn't even talk about what you do professionally um but if you want to dive into that we have some time for that just share with us what are your your goals and your dreams that you want to make happen so I have a couple things I'm writing a book right now and the whole premise is to talk about what happens when abuse goes untreated so that's on my plate but I'm working on a really really neat project that I would love to even come back and maybe share with your your viewers a little bit more but it's for whole ala nopua whole ala nopua is a safe haven that is providing housing and trauma care for young girls that have been trafficked and in sexually trafficked and it's prevalent here more in hawaii than it is anywhere in the united states and we are preparing to have a celebrity auction that will go live in january and we want viewers to come your viewers or any supporters to come and bid on celebrity experiences for instance like golfing with marcus mariota um having chef chai come to your house and teach you how to make a really nice gourmet meal and all the funding that will be raised will go towards the trauma care for these young girls wow so um any celebrities out there listening we need you whether it's for a luncheon or dinner or just whatever you can't was this because the the need is great and we always think that this situation is not in our state but we're definitely wrong about that and I think more knowledge and information has been coming out that it's right here in our backyards in our front yards and so we better be made more aware of it once the awareness is there then of course the need to support and help these women and men through this time of their lives I mean it's so critical so if anyone can reach out and help we are going to have some information where Susan has her um direct contacts that you can get in touch with her and um just reach out as she's taking all her time and her energies and I think even your professional life uh Susan you can talk a little bit about that what do you do I mean like if you don't mind I know you're writing the book but there is also another way that you reach out to people you want to share a little bit about that sure I have a company called the social touch which is a social media marketing agency I specialize in branding and rebranding on social media however when people really ask me what is it that you really do well I uh I collect stories again I sit and listen with an open heart and I collect stories of your service and your products and I highlight them on social media I think that's so powerful you know um as I was building another business after I retired I would sit at Kahala mall and you'd be surprised I would sit at the mall and just mind my business and look like I'm busy and for some reason um especially the seniors they would come and sit down with me and they would just talk and they would tell me everything about their kids about their ailments medical issues all these things and I'm like an hour has gone by and I'm still talking story and I'm like so involved with their conversation and you know I would say to them before they had a go or before I had to go so what does your son or your daughter say about all these things and they said I can't tell them I said why not and they said she says oh because they're too busy to hear me so it's so so important Susan what you're doing you know when they especially when you see a young person like yourself going out and reaching out people really want to feel this and experiences and it's not just the elder community but it's everyone the young generation right now especially they need to just fill that void especially with the last year that everyone's experienced so I mean I'm so grateful to you Susan for reaching out is there another story that you would like to share with us that has made an impact in your life up to this point there's so many so yeah so just by the way let me update you guys on the story on Christina that I had shared earlier so this woman has earned her degree in culinary arts and she has now opened a food truck and it is out in Waianae so I just wanted to give her a little props I don't know the name of the food truck but where is she parked I don't know I just know it's one night it's just been in the last week that this has okay that's important because you know I'm always out on the west side and I want to go and support anytime I can support a great part like this and a great story I'm gonna go there and then I'm gonna say I want to order a hug I love it I'm gonna ask how many oh can I have two hugs please super strong and never stop so come on and give me a hug and then I'll order my lunch later but I love that so what we'll do guys if you do want to support this young woman as well get in touch we have Susan's information you have mine and then Susan you have some homework now that you leave the cat out of the bag you're gonna get us the location of the name of her truck and we'll go give her a hug and give her something and enjoy her honor food because those are the stories that we really want to support and I just yeah thank you so much and also before we sign off which is coming up soon I do want to mention that how long has I have I known you Susan 29 years at least 29 years right yeah a long time so I met Susan when she was a contestant in our Miss Hawaii international and that was in the year 1992 we crowned her in 1992 and you know what if she puts the crown on right now you think she still is a rainy queen because she's kept her youth her vitality her beauty and her heart which is even more beautiful and I think that's the secret to what you're doing your heart is beautiful and your heart is open so you're wearing your heart and your species and so never stop being in that pageant just allowed you to open the doors that you never thought were going to be open or was open and now you're in the door and you're going to make such a difference to more and more people that you come across so never stop doing what you're doing all right thank you and me you're just out you're just you're more beautiful you're amazing I love you I love you and I'm so glad you're still our friends after all these many years so I'm grateful thank you right now we've come to an end of the show I'm gonna have to leave us for now but as I said and as you mentioned you'd like to come back and when you have more information about the whole of the poor then of course we want to know about that and anybody that wants to donate or volunteer please it's not coming up until is it August is that correct so the the option will go live in January January oh so we have some time we have some time but I still need to get those donations in right and I know that you spoke to our dear friend chef chai and uh he's kind of thinking about it or he's going to do it he said he'll do it yes and you know another big free thing about chef chai's he's willing to employ these individuals that have gone through these programs yes and any employers who right now they're looking for for employees you do get a $2,000 tax deduction yes for employing individuals right but I'd explain that goes through these programs and chai he's right on the on on the mark with that he's always had that hard whether the 2000s yes he and that's the kind of heart that we're looking for right now so a shout out to all of you out there open heart you know open heart so you've been watching Taking Your Health Bath on Think Takawaii Mahalo to Susan from Social Touch thanks for talking story with us and Mahalo to all our viewers for watching I'm Wendy Lowe and we'll be back in two weeks with another edition of Taking Your Health Bath. Aloha everyone!


Hi, I'm Chef Robin. Welcome to Hands in the Kitchen Workshop. Today we're going to be speaking about sugar. Sugar is a spice that we all have in our kitchen. We're going to find out what is sugar. Talk a little bit about the history of sugar, how it came to be in those packages on the grocery store shelf. The benefits, if there are benefits to table sugar, the harmful effects of table sugar, then majorly speaking a lot or directing our attention to eating less sugar, sugar alternatives, and then natural sugar in fruit and vegetables. So what exactly is sugar to begin with? Sugar is a soluble, and that's a really important word, soluble. It's a soluble, sweet, crystalline substance that comes from plants. The two plants that we get the majority of our sugar from are sugar beets and sugar cane.  Soluble means that it dissolves in a liquid, and that's going to be important when we talk about how sugar affects us in our body. So I have some sugar here. I have just a little bit of plain water right here, and you're going to see that without heat, without any kind of motion other than a little turbulence with this chopstick, the sugar is going to dissolve. So not all spices do that, not all substances do that, but because sugar does that, we really need to bear in mind how it affects us once we get it into our body, so we'll talk about that after a while. But soluble sugar, crystalline structure. We also want to discuss added sugar, because in addition to sugar being present in all fruits and vegetables, added sugar is usually a sugar carbohydrate that's added to food and beverages during processing or at the table. Added just means more sugar coming in. So that should give you some idea of what sugar is, where it comes from, where it comes from, and what we need to give attention to. So if we talk about the history of sugar, just give us a little background. Pavement, we're probably eating sugar. Sugar cane grows like bamboo. They probably were snapping it off and chowing it down to get some energy to go to that next mammoth hunt or whatever they were up to. But cavemen were probably eating sugar. Thousands of years ago, the Greeks and the Romans in ancient times were using it to take care of stomach ailments. The Crusaders brought it back from India, where it was being cultivated, and they called it sweet salt. That's how it came to Europe. Once it got to Europe, the country of Spain started to cultivate it and manage it as a trade product. When it became a trade product, then it came to the New World with the Portuguese. First it went to Brazil, then it went to Barbados, the Dominican Republic, those islands in the Bermudas. And really, that's where our slave trade came from. Our slave trade didn't start in the Americas because of cotton, although that's what sometimes we think of slaves on cotton plantations, but actually it was sugar because sugar is very labor-intensive to grow, and at that time it was also very labor-intensive to process. So it was called white gold because it was just valued so much, but it also had implications for that part of our dark part of history, the slave trade. Sugar began to be processed and cultivated in Louisiana in the 1700s. Then in the 1800s, domino sugar, which is still on our shelves today, was developed by two brothers in New York City and started to be refined in New York. Sacrine was introduced in the later part of the 1800s as the first sugar alternative. And then just last year, dominoes created a new product on the shelf called golden sugar. And golden sugar is in response to people being alarmed about the health effects of white sugar. Golden sugar is not quite as refined as white sugar, but less refined than brown sugar or molasses. So golden sugar is still sugar, still has all the qualities of sugar. It just has not been bleached white. So just to be aware, even though they're saying it's a little bit better, it may not be better. Let's talk about the benefits and the harmful effects of sugar. So sugar, as we know it on our shelf, that white soluble crystalline structure gives us energy. It's really all it does. It has no nutrient value whatsoever. It has zero minerals. It has zero vitamins. It has zero good stuff, fibers, anything else that we might need that our body could make use of other than this little fuel that goes into our bodies. When we talked about it being soluble, when we do ingest white sugar, say we put it into our coffee or our iced tea or on top of our cereal, it immediately becomes available to every single cell in our body. Our body is not particular about which cell it goes to. All of the cells in our body absorb this sugar, immediately get a fuel burst from this sugar, and then almost as immediately dissipates, and we crash from that sugar. That's why we're on this cycle of early sugars, mornings, snacks, more sugar at lunch, sugar, sugar, sugar, sugar, sugar, trying to maintain that energy burst that we got when we first had. So it's a dangerous product because it kind of controls our mind into what we think we need, and it controls our body by craving more and more and more. It's an addictive product, actually. Too much of it, as we know, can lead to obesity, can lead to heart disease, because our bodies are also, our systems are older and aging. It has a hard time regulating in our blood, so we might get high blood pressure from too much sugar, and we can, with too much, become diabetic, which is a big problem. So where we get that energy burst is a good thing, but all these other items that sugar brings when we have too much are not good things. And the thing that we want to remember, most of all, is that every plant and vegetable has natural sugar in it. So adding more table sugar is just sugar on sugar. So just to remember that. Let's talk now about too much, how much is too much? And this is the value that people are always like, really, that's all I get a day, because the value of sugar, fat, salt is almost always microscopically smaller than we think we need. And for women, six teaspoons is the recommended daily allowance of sugar. That translates to 25 grams and 100 calories. And the reason I have grams and calories on this chart is because when you look at nutrition labels, usually they're in grams or calories. So you can't always look for teaspoons on that label to tell you how much sugar is in that product, or how much sugar is added to that product. So I have measured out for you six teaspoons for women, and six teaspoons and nine teaspoons for men, just so that you have some idea of how, and to me, it seems an incredible amount of sugar. But when we start looking at grocery store products, and we see how much sugar is actually added in, it's not going to be that much. So this is six teaspoons for an adult woman. This is nine teaspoons for an adult man. Looks like a lot of sugar, correct? That is what our body asks of us every day. Remember, we get sucrose natural sugars from every plant and vegetable that we eat. So we don't necessarily need this white crystalline granular substance in addition to other sugars, but most people do, or do use that in their diet. If we try to think about coming away from so much sugar in our diet, we want to start at the very get-go, right at the top of the day, and avoid that sugary breakfast, because if we start with that sugary breakfast, it kind of sets the tone for the rest of the day. Saying that, if you make a change in your diet, do it in a moderate fashion. It's very important that you don't all of a sudden cut out all sugar, cut out all salt, cut out all fat. Your body's going to be like, what? What's going on? You need to take time, be deliberate, be disciplined, and moderate in your changes. Dramatic changes affect your body dramatically, and also, more often than not, that dramatic change is not going to be successful. You're going to get lightheaded, you're going to be tired, you're not going to feel good, and that will not encourage you to keep pulling back on sugar, salt, fat, whatever it is that you're trying to use less of. Again, be disciplined in your approach, follow doctor's advice, but you can take control. Avoiding that sugary breakfast, instead of having that heavily sugared cereal with more sugar on it, or the lactose sugar in a dairy product, have oatmeal and berries, have a whole grain toast with jam, have plain yogurt with whole fruit, or poached eggs. The farther we get away from the raw product, the farther we get away from this apple right here with its natural sugars, to this apple juice, or to this granola bar, the more and more processing that this product goes through affects the benefits that we get from eating it. So when we eat this, our sugar comes with fiber, it comes with vitamins, it comes with nutrients, it takes our body longer to digest it, it takes our blood cells longer to make use of that fuel, the availability is timed out so that we get our energy boost over the time of that digestive process. When it's diluted in a liquid form, it's almost again like putting sugar right into your drink, right into your cereal. If you see this word right here, apple juice from concentrate, again, anything that's concentrated means the total amount of that sugar is just high because of a concentrated nature of something.  And then when you get to this for breakfast, and you look at oats, which is a good thing, because this is an oat bar, the very second ingredient is sugar. The second ingredient on a food label means that that is second in size of ingredients of all of the ingredients in there. So that's a pretty high level of sugar in this product. So have a healthier breakfast to start your day. So if you don't have your healthy breakfast, by 10 o'clock you want a ho ho. So instead of a ho ho, go for something that's a little bit healthier. You can have trail mix. Even trail mix with chocolate chips in it is a healthier alternative than a ho ho. Have harbore of eggs. Fresh fruit, again, is the best. Every plant, every fruit, every vegetable has its own natural sugars available for us. We need to take advantage of it. Grapes, popcorn, harbore of eggs, nuts, all manners of healthier snacks than just maybe that granola bar. One of the healthiest things that you can do is to swap out that soda. The soda is just another, it's just a vehicle for immediate transference of sugar into our system. And it gives us that immediate boom bust of energy. But again, then you will just crash again. So instead of a sugary soda, enjoy just water, put mint in your water, put lemon slices in your water, orange slices, cucumber slices, anything that can make it a little bit more exciting for you and flavorful for you. Have seltzer water if you like bubbles. It's fun. It's enjoyable. Seltzer waters come in all kinds of fruit flavors as well. Or herbal or fruit peas. So just try and delegate your sodas to a smaller number every day until you're not drinking or reliant on soda. When you get to the point where you're ready to just toss that table sugar but still want other sweet in your diet, again, everything that we eat that's in a fruit or a vegetable form has its own natural sugars. But if they are not enough for you, there are sugar alternatives. Honey, maple syrup, seed oil, molasses. All of these are sugar alternatives that still provide calories. They do have some trace amounts of minerals and nutrients to give our bodies as well. But you still need to be moderate with their uses. Apple sauce, if you're baking, is a good replacement for sugar. A lot of bakers will do half sugar, half apple sauce in their zucchini bread and their banana breads and are delighted still with the end product. Extracts also are tasty and an alternative to use instead of just straight sugar in baking. Stevia is relatively new. Stevia comes from a plant. It's in a powdered form. It dissolves in water so it's soluble as well. It is very, very sweet but it has zero calories. So it is a product that some people are finding to be their sugar replacement. Just be aware that it also can have that jump, that spike in energy depending on how much you use but it is a little bit healthier for you than just regular table sugar. This is a new product on the market called agave nectar. It's relatively expensive. It comes from the agave plant. Nectar is like a concentrated syrup. Some people are using this. It does have some health benefits other than just being sweet. It does have calories. It does have some small amount of fiber so whereas sugar has none of those, it is a slight bit better for you than just regular table sugar. Again though we really want to concentrate on eating plants, eating fruits and vegetables that have a high level of fruitess in them to get our sweetness from them. So let's talk about that for a moment.  So for example, there is the sweet potato. There is the sweet bell pepper. There are sweet vedalia onions. There are sweet sugar snaps. So it's just another reminder of the fact that from eating a varied diet with various fruits and vegetables you are going to get the sugar that your body needs for energy. It's just going to be in a better delivery system because it's going to bring you minerals, it's going to bring you nutrients, it's going to bring you fibers and it's going to bring you that delayed timeline of the energy being relegated out to your system to use instead of just immediate boom with the table sugar. So fruits as well, apples and pears and peaches, high in fruitess, a great sugar alternative for and also fiber, vitamins, nutrients, sweet grapes, grape for snacking, the banana, very high in vitamin K which is also good for you and then berries which are very adaptable for snacking on for having with breakfast. So all in all, there are all manners of different food items that you can obtain sugar or sucrose in your system or for your system to benefit from much healthier than just using table sugar. The statistic that I read that was incredibly alarming when I was doing all this research on sugar was that Americans tend to eat 60 pounds of sugar a year. The average adult American eats 60 pounds of sugar a year and to put that in perspective that is six 10 pound bowling balls. So just or six 10 pound bags of sugar, that is just incredible to me. So it is out there and it's kind of blind and wait for you. We're going to talk now about grocery shopping which is so difficult actually if you're trying to eat a clean diet. It's incredible catch 22 to me that by the time we get older and we've worked hard and maybe we don't want to cook everything for ourselves every day that the package on the shelf that we can afford is not healthy for us to eat. It's really hard and it's so pervasive in our food system. I just want to show you a few examples of things that really were surprising to me as far as containing sugar and now you really have to become a label detective. Okay this is a big chart I understand but the FDA which is the Food and Drug Administration has allowed food manufacturers 38 different ways of saying sugar on a label. 38 different ways. So you may see the word sugar but you may see something else that's completely different and yet it is sugar. It's just a different name for it. You really need to be aware of any word that ends in O-S-E. Dextrose, maltose, lactose, glucose, fructose, sucrose that is all a form of sugar. I fructose corn syrup. I fructose right there corn syrup. We know that corn on the cob sweet corn on the cob we love it. It's been developed into a syrup and it's almost used in so many products and it's not good for you at all because they use too much of it. It becomes something that our taste buds get used to we want it we would do more of it it's not it's an alarming thing that it's in so many foods. Fruit juice concentrate again anything that's concentrated fruit is full of sugar so if you concentrate it more it's just another way to get sugar into that product. Modified corn starch again it's just another term for sugar and there are more and more and more I didn't list them all but believe me so many products on the shelf if they don't say no sugar sometimes are going to or more times than not are going to have some kind of sugar added to them they feel like the American palate is just demanding it and possibly we are um when you become a food detect a food label detective you're going to want to look at the list of ingredients the ingredients are labeled or the ingredients are in line of the largest amount to the smallest amount so if sugar is in the first five ingredients it's going to be an issue for that product or it could be an issue if you are sugar sensitive that maybe you will want to look for something where it's down farther. If you look at the nutrition facts label which almost every product is required to have now the first thing they're going to tell you is the serving size this is not an RDA determined figure this is figured on what people typically eat so saying we are talking about crackers and on this one it says six crackers is a typical serving size on this one it says 16 crackers are typical serving size the reason that's important is because every other value is determined by that serving size how much sugar how much fat how much protein is determined by that value that they think is a serving size so on the cereal boxes they say a serving size is two-thirds of a cup it's really not a lot of cereal if you typically eat two cups of cereal you will have to take those values and change them based on two cups serving so that's just something that you might want to keep in mind if the doctor or your health professional is telling you to be aware of how much sugar you ingest every day it needs to be determined by what the serving size is and then what the value is we're going to talk about it gives you three numbers for sugar on a nutrition label the total sugar is the value of the sugar that's in the product organically like if we talk about an oatmeal raisin bar or an oatmeal blueberry bar it would be the sugar that's already in the oats it would be the sugar that's already in the blueberries or already in the raisin that's an integral part of that product but then it has another value of added sugars so you have the value of sugars total that's in each product itself each ingredient in shell itself but then the value added sugars are more sugars that might be added during processing or preparing that product so the total value of sugars for these if we were eating two crackers is 16 percent or 16 grams so if you remember before we talked about the number 25 or six teaspoons for a young lady and 37 for a gentleman 16 is pretty high up there it's only nine less than 25 and that's just for that product right there so it is astounding to figure out the total grams of sugar if you they don't have grams listed or to figure out how many teaspoons when we talked about six teaspoons for a young lady nine teaspoons for a gentleman we're going to take four grams that's listed 16 eight plus eight is 16 grams divided by four is going to give you the number of teaspoons so two of those crackers is still four teaspoons of sugar that's amazing it's amazing to me that that would have that much sugar and it's so difficult to get away from sugar it's incredibly difficult so we're going to talk about some grocery store products and being a label detective honey nut oats so with honey I think that's great that's you know going to be a major ingredient if you look on the label whole grain oats whole grain barley that's what the oats are made out of third ingredient sugar third ingredient sugar just be aware label reading no added sugar so this item is sweetened by the apple that's in it but it is less harmful in your diet because they didn't add sugar as the second ingredient in the cereal to start your day just to be aware maybe you like crackers I'm sorry guys wheat thens second ingredient sugar trisks only three simple ingredients it really is important if you want to become in control of what you eat that you take the time you take your little magnifying glass with you and you look at those ingredients this the third ingredient in this product is salt so if you're on a salt restricted diet it may be something that you need to be aware of you may need to find a no salt no sugar cracker they're out there sometimes they're more expensive it is kind of discouraging to spend all of your time having to investigate what's on that label but if you don't how incredibly quickly you're going to go over those six teaspoons or nine teaspoons that are recommended for you and how quickly it's going to lead to added weight gain heart ailments diabetes all of those things that were red lighted because of too much sugar so disturbingly enough big source of sugar simple marinara sauce big source of sugar peanut butter you think peanut butter why can't peanut butter just be peanut butter peanuts are sweet they have their own sugar but you really have to look for on-natural vegan no sugar because on the less expensive sugar I'm afraid what we could afford second ingredient sugar after peanuts it's really distressing two cans of corn I have fresh whole corn whole kernel corn and I have sweet corn cream style guess what first ingredient corn cream style second ingredient sugar so this one has no sugar cream it yourself guys it's just a matter of being a smart shopper it is like I said it is distressing that you have to take the time to do this but if sugar is becoming an issue in your health and it will become an issue if you just continue to ingest sugar on a daily basis too much unknowingly until you're sick then really take the time and look for sugar and sweet things or look for sugar that's been reduced in products you can find them you do have to search for them this is an apple sauce if you're unable to eat the whole apple and get the fiber from an apple because of a tooth issue or you just can't finish a whole apple look for something that doesn't have sugar added to it they are out there you do need to kind of try and search them out but make a list keep a food diary it sounds kind of I don't know like I'm not a teenager I don't keep a diary anymore why would I do that too much trouble make it easy on yourself if you keep a list to go to the grocery store right beside wherever that list is however easy it is to put something on that list make it easy to write down what you ate that day and if you ate something that was low sugar and you enjoyed it make a note of it go back to it make it part of your diet include it more if you ate something that was high sugar and you had an effect from that make a note of it and then after keeping that food diary for a month or so or maybe even a less amount of time you'll see patterns in your diet that you might want to either make reinforce and make a standard way of eating or just do without completely but it will be kind of like a little eye-opening experience for you just to see exactly what your body is making use of every day or not making use of so we covered a lot of information I hope you learned a little bit about sugar and are able to maybe take a little bit more control of sugar in your diet and just go from here to a healthier time in the kitchen I'll be seeing you in the kitchen


Hello everybody, my name is Wolfgang Fichtbauer and I will now be giving my talk on automated report generation using the metaphor package. So to start, let me say a few words about the metaphor package itself. This is an R package for conducting meta-analyses. It grew out of code that I wrote from my dissertation research. Eventually this turned into a full R package in 2009 and I've been updating the package ever since. Hello here are some relevant resources related to this package. Now what is the usual workflow when you're conducting a meta-analyses? Well first you need to search for the relevant studies, collect them, extract information from these studies and then eventually you can compute effect size estimates which you can use as input to some meta-analytic model like a random effects model and then you can do some further analysis steps like checking for outliers, drawing some pretty pictures, maybe checking for publication bias and eventually you need to write this all up and then the very last step is to send your paper to science or nature and get it rejected. Okay, so let me give you an example. BCG is a vaccine against tuberculosis and if you want to find out if this vaccine is really effective you can do a study where you vaccinate one group of individuals and not another group and then you check for the infection risk in the two groups. So here are the results from one of these studies. So we have four TB cases in the vaccinated group out of 123 people, 11 cases in the not vaccinated group out of 139 cases. We have the infection risk in the two groups. The risk ratio which indicates that the risk of infection was quite a bit lower in the vaccinated group, the log risk ratio which we really need for the meta-analysis and the corresponding sampling variance. Now in total 13 studies have been conducted on the effectiveness of the BCG vaccine. So if you want to do a meta-analysis of these 13 studies, we first need to compute the log risk ratio and the corresponding variance of these 13 studies which we can do using the ESCalc function. And then we can use these log risk ratios and variances as input to the RMA function which is one of the main model fitting functions. And by default it will fit a random effects model and then we can look at the output. So we see here our estimate of tau square. So the amount of heterogeneity I squared, we get the Q test for heterogeneity. We get the estimated average log risk ratio and the corresponding confidence interval. And then we can do things like forest plots, funnel plots. We can check for outliers and we can run the rank or the regression test for funnel plot asymmetry which may be indicative of publication bias. So that is the usual workflow but the metaphor package has a function called report term that can automate quite a bit of this process. So what it will do is it will write a report for you describing the statistical methods used and it will provide the results in terms of natural language including a forest plot, a funnel plot, it will give references for all of the methods used and then you either get an HTML file, a PDF or a Word document. So let me demonstrate this, how this works. So we first load the metaphor package, then I'm gonna again compute the log risk ratios and variances and then I could fit a random effects model and then look at the results. And then instead what I could do is I could run the reporter function. So if I do this by default, you will get HTML output. So I get this analysis report. So what does it tell me? Well, it will tell me what kind of effect size estimate was used for this analysis, log risk ratios, a random effects model was fitted. How was tau square estimated using restricted maximum likelihood estimation? Then it provides references for the Q test for I squared. It describes how the data were checked for potential outliers or overly influential studies. It provides information, how the data were checked for publication bias. And then you get the results. So 13 studies were included in this analysis. We get the range of the observed log risk ratios. We get the estimated average confidence interval. We get the funnel, the forest plot. We get the Q test, I squared. We have no indication in these data that there may be outliers. And we get a funnel plot and we get the results from the rank and regression test for funnel plot asymmetry. And then some notes down here and references for all of the methods used. So this report is dynamically generated. So if the results, of course, were different, then it may indicate that they are outliers and whether there is heterogeneity or not, while you will get different output depending on the results. So that is what the function can do. Now it's not complete yet. So right now the results are given in terms of the effect size measure that you use as input. So if you meta analyze log risk ratios, then you will also get an average log risk ratio. But usually we want to back transform this to risk ratios. So in the future, it may be nice to add the option to sort of transform the results. Also, at the moment, the reporter function does not work with meta regression models. So this is something that I would like to add. And also to extend this function to work with other model objects, like the arm a dot h function, which uses the mental Hensel method. So right now it only works with the arm a function and maybe some more customization, maybe an option to include explanatory footnotes. So to make this even more useful. But already right now this function is quite useful for teaching purposes, learning purposes, and just really for automating report generation. So that's all. Thanks for your attention and I'll be happy to answer any questions.


So, what I am going to do is I am going to use something called unit quaternions as a better or perhaps the best representation of 3D rotation. So, I will use Q for quaternion it will look like a 4 dimensional vector I will give it 4 very simple coordinates A, B, C, D not going to use x, y, z just to avoid confusion with the ordinary Euclidean space that we are in, but nevertheless you can consider this as an element of R4. So, there is nothing strange going on with each of the components they are just for 4 real numbers, 4 real parameters and I am going to impose a constraint they are called unit quaternions which is going to mean that A squared plus B squared plus C squared plus D squared equals 1. Hey that is not bad that gives us how many degrees of freedom? 3. So, that is good. So, I just want to make sure that is a sanity check right just make sure we are always keeping the degrees of freedom right. What is this geometrically? What kind of shape is this? It is the equation of a yeah hypersphere or let us just say a sphere hypersphere that is right. So, it is 1 dimension higher than the 3D sphere it is a 3 dimensional surface right the ordinary sphere is a 2 dimensional surface that sits in R3, this is a 3 dimensional surface that sits in R4 right. So, you know you do not have to completely visualize that. So, the set of all Q that we are allowed to have here the ones that are unit let me even say it I will say unit quaternions is a hypersphere. In mathematics it is called S3 if you are curious. So, yes you can do it in higher dimensions you can have S n in n dimensions. It is 3 because it is a 3 dimensional surface. So, the standard sphere that you know is S2 and a circle is S1. I should point out that I am going to use this A, B, C, D representation and in unity 3D and in game engines they tend to use a different representation which is x, y, z and w. So, even without being sorted alphabetically correctly and in terms of my representation which I am going to use the one that is consistent with mathematics and most of engineering as well which is B, C, D, A. So, if you want to go back and forth between what I am doing in class and what you might see in unity and other game engines then you have to take the first element and put it at the end. I do not want to tell you how many bugs I had in my code because of this this extra change. So, it is very easy to make mistakes with this. So, it is be very careful. Very commonly you will see quaternions especially in math written like this instead of writing it as a 4D vector you have A plus B I plus C J plus D K perhaps with little hats on these, but not necessarily. So, so maybe with or without the hats. In fact, I am going to take the hats off let me sorry. So, very often you will see it written like that if I look at it with just this part A plus B I that reminds you of what complex numbers right maybe you put a J there if you are an electrical engineer because somebody used I for current right. So, and so very often people say that there is a real part of the quaternion which is the A and then three imaginary parts which are I J and K and then this leads to lots of fear and confusion among students right. So, when you deal with complex numbers and you have the real and imaginary parts those were invented because people wanted to find roots of polynomials right. The polynomials have real coefficients and if you want to find all their roots you need to invent complex numbers to have a kind of algebraic closure. This does not correspond to the algebraic closure of some kind of polynomials. So, there are some reasons for referring to these as imaginary parts because algebraically they behave similar to complex numbers and become a kind of generalization, but they do not correspond to roots of polynomials and we are not going to do things like that. So, in this class I prefer not to make a big deal out of real and imaginary I do not think that is important here. It is important for you to just think of it as four parameters it is a 4-D vector and we are going to normalize them so that they are on a sphere. So, I would say avoid this kind of you know let us say fear of something perhaps nightmarish and algebraic does happening here. If you find these things interesting go and read about it and learn about it it is quite fine I find it interesting, but we do not need to go down that path and so it is important here just to keep in mind that there are four parameters ABCD and if you treat it as a 4-D vector the length is 1. The next thing I want to tell you is how to encode a 3-D rotation using our ABCD parameters. So, here I gave you an example of how to encode rotation using exponential coordinates I just took the theta and multiplied it by the v. I am going to do some other transformation or operation to do the encoding as a quaternion. So, I am going to have v and theta and convert it to a quaternion.  So, I have four parameters that I am using. So, I want to go between v and theta and I am going to have this representation cosine theta over 2 that is the A part I just going to be a 4-D vector here that is the A part the B part is going to be v 1 times sine of theta over 2. So, that is the B v 2 sine theta over 2 that is the C v 3 sine theta over 2 that is the D alright. So, all I did was write cosine theta over 2 here and then for the remaining 3 components I just took the v vector and did a scalar multiplication times sine theta over 2 correct that is all I did. If I square all of these and add them up what do I get right. So, I get cosine squared theta over 2 and then these 3 well I get a bunch of sine squares to add up, but I know the length is going to be 1 because the v's when I square those and add them up they all add up to 1. So, the entire thing is going to when I square all of these is going to add up to be sine squared theta over 2 by the simple trig identity I get 1. So, this is a parameterization that puts points on this unit sphere in 4 dimensional space right. So, what I want you to get comfortable with is just being able to move back and forth between these 2. So, that when you see this a b c d vector somewhere in the code maybe you are looking at unity or you are reading the code except remember that it is x, y, z, w there, but whenever you whenever you see it you should be able to look at it directly and understand how to extract the angle theta and the axis v. So, it should be very natural for you do not have fear about imaginary parts and other kinds of strange things going on and visualization of 4 dimensional spheres and spheres in R 4 and things like that. So, 3 dimensional sphere in R 4 do not worry about that just worry about understanding that there is an axis and an angle that is encoded in here and it is provided by this simple formula. So, if you understand that let us try to go over some simple examples. So, these are some useful examples useful examples. So, what does that quaternion do if I apply this formula what is it what does it correspond to what is that? Yes. So, this is this should do this should be the identity rotation right it should not do anything. If theta equals 0 then all of these components becomes 0 b c and d and this component becomes 1 correct. So, this one means the identity rotation it is very interesting that in that case I cannot even tell what the axis was anymore right because they all became 0 does that matter? No it is the perfect case it did not rotate anyway. So, there is no axis. So, it seems like the the axis just vanishes exactly in the place where there was no rotation occurring. So, very nice feels good does not it? Let us see well let us try some other very obvious patterns here what does that correspond to? So, that is right 180 degree rotation about the x axis right because the axis here for this case must be v equals 1 0 0 right for this case. So, this is pitch am I still being consistent with my definitions pitch is rotation about x correct ok. So, pitch by pi 180 degrees well if you know that case should be able to fill in these this one is yaw by pi right because it is rotation about the y axis. See how you can look at the last 3 components and if it is simple enough you know the axis of rotation. In fact, this is just the axis of rotation, but not correctly normalized right. If you just take the last 3 components and renormalize them you will get the axis you cannot renormalize it in this case, but that is ok because there is no rotation anyway. So, the axis does not matter, but the other cases if you test for being non-zero then you can figure out the axis very easily with your eyes not even writing code all right. The last one is roll by pi right. So, these are very simple examples. So, there really should not be fear of quaternions I see a lot of fear of quaternions these it is quite simple once you understand what to look for. The first coordinate is the amount of rotation which is inverted right the smaller the number the bigger the rotation and then the last 3 coordinates are giving information about the axis of rotation. Let us try another one 1 over square root 2 1 over square root 2 0 0. So, suppose I see that what is the axis of rotation. So, again that is a perfect case where now I have to renormalize it, but it looks like it is about the x axis how far have I rotated yeah very good. So, that is good. So, you are doing you are doing great here. So, 45 or 90 90 because in the formula here we divide by 2. So, that is how some of you got fooled right. I make the mistake a lot myself. So, it is no problem. So, pitch by pi over 2. So, I should be able to very quickly go with the other cases 1 over square root 2 0 1 over square root 2 0 1 over square root 2 0 0 1 over square root 2. So, this is very nice if you are debugging your code you just want to make some simple transformations and try them out. It is very nice to be able to just immediately specify some simple transformations like this or if you are debugging and you are not sure you got the code correct. So, it is very nice to be able to to read these quickly. So, this one is yaw by pi over 2 and roll by pi over 2. Questions about that? I am going to give a little more information as we as we go along here, but I just want to make sure that is clear right. So, no questions see there means it is very clear or very confusing. So, I know hmm. So, here is something else to think about inverses and multiple representations in other words non uniqueness multiple multiple representations. So, if I have if I have a quaternion ABCD now Uniquaternion that is being used to represent a rotation I should probably write back the conversion formula.  So, remember that right that is how we got the ABCD components. So, what if I have minus a minus b minus c minus d can anyone tell me how the two of these are related. So, if ABCD corresponds to some 3D rotation what is minus a minus b minus c minus d going to correspond to? Is that the inverse rotation? It is the same rotation is not amazing it is the same rotation because if I take the v and I twist it in the opposite direction right I just flip it around I will negate the BCD components and then if I negate the theta as well that will negate the a, but it will not force another negation here. So, that will negate all four components. So, that means that these two are equivalent. So, that is something very interesting to pay attention to. So, that means that when we travel on this sphere right. So, 3 dimensional sphere in 4 dimensions if we go to the opposite side of it right it is called the antipodal point right the opposite point what anybody know where the opposite point on the earth is from here maybe it is a good guess I do not know it has to be in the southern hemisphere right. So, you have to change hemispheres in all cases right. So, anyway you go to the opposite point on the earth and that corresponds to the antipodal point. So, on this quaternion sphere this unit sphere of quaternions unit hypersphere of quaternions the opposite point is always equivalent is that interesting just to add an extra layer of confusion all right. Let us think about what this one does what if I have a, but I decide to negate the BC and D parts. So, I keep a the same by negate these three what does that correspond to yeah I decided not to now yeah. If I take what do I get if I do cosine minus theta it negates right or it stays the same oh it should stay the same ok I see. So, if I move the axis backwards let us see ah. So, these should stay the same right. So, let me let me think about this if I let us go back here let us go say I have v I do rotation by theta I want to now do minus v and the question is let us see I want to make this correspond to the exact same rotation see if I am going in the opposite direction yep yeah it is a very it is a difficult problem of orientation you have to visualize it we have to remain going counter clockwise right. So, if I want to continue going counter clockwise and apply the exact same rotation is it going to be theta or minus theta was that 2 pi minus theta thank you. So, it is 2 pi minus theta. So, we go in the opposite direction it is 2 pi minus theta alright. So, if I go 2 pi minus theta what sign do I get over here negative a alright good. So, let us keep we keep the trig going ok alright. So, we are fine now what if I decided to do it this way instead and I did not negate the a how are these two related. So, if I say by Euler's 3D representation theorem that every rotation corresponds to a single rotation about some axis then if I want to undo that rotation I just twist it back the other way right. So, that corresponds to the inverse does that make sense. So, if I have some axis v and I rotate it by some amount theta if I now rotate by minus theta it will just undo that rotation. So, in this case this should change the sign and I leave I yeah this should change the sign. So, I end up getting the opposite right. So, if I keep the axis the same, but I just negate the theta then I will negate these three components, but the a will end up being the same. So, here if I relate these two it is inverses is that fine. So, if you are looking at a quaternion ABCD and you want to figure out what its inverse is what do you do just negate the last three components is that interesting it is that easy to compute the inverse rotation. If you want to do it with a matrix what do you do you have to compute a full matrix inverse maybe except if it is a rotation matrix it is just a transpose turns out. So, it is easier it is also reasonably easy in that case. If this is the case here then we also can have another case where I just negate the first coordinate I negate a and I leave B, C and D alone and these two should be equivalent right does that make sense the same rule is up here. If I negate all four components I should end up with these being equivalent and these two being inverses that seem all right. So, again just to summarize if I negate all four components it is the same rotation. If I decide to negate only the first component or I decide to negate the second third and fourth components together, but not the first one either one of those corresponds to an inverse is not nice. So, that is one very quick way many times in programming in these kinds of systems it is easy to make a mistake where you should have the inverse rotation and you have instead calculated the forward rotation. In that case you just perform some simple sign changes you should of course go back and check all of your math carefully and make sure you understand what you are trying to do, but for debugging purposes it is very helpful to know you can very quickly spot that you are off by an inverse if the signs are wrong. So, that is why I am telling you this trying to give you this extra information all right. Any questions about that? There is a direct formula for multiplication of quaternions that do not that does not require you to convert back to rotation matrices. I am not going to make a big deal out of it, but I at least want to quickly give it to you. So, just so you know multiplication, so let us suppose that again we have a b c d for a quaternions and I will say let p equal just a b c d part. So, I can treat it as a 3 d vector let us just suppose that is a 3 d vector called p and now if I want to calculate some quaternion q 1 multiplied by some quaternion q 2 to get some third quaternion q 3 there is a very simple formula just using 3 d standard vector calculus. I say q 1 multiplied by q 2 is equal to a 1 a 2 that is the scalar part the the first components of each one minus p 1 dot product p 2. So, that gives me the first component now this is actually a 3 that we are calculating and then the remaining 3 components are given by p 1 standard cross product p 2 plus scalar a 1 multiplied by p 2 plus scalar a 2 multiplied by vector p 1. So, this gives me the b 3 c 3 and d 3 components I am not deriving this at all there is a whole algebra of quaternions there is a reason for it coming out this way, but what I want to say that is very interesting about it couple of things one of them is that if you go through this you will find out that it is not commutative this product is that a good thing it is a good thing because if you are using this to represent 3 d rotations and 3 d rotations are not commutative it would make sense that this algebra of multiplying quaternions also ends up being non commutative as does matrix multiplication of rotations encoded that way. The reason why I put this and you usually you will find this inside of a quaternion library you know that you do not have to really worry about the details of it, but one of the reasons why I put this is so that you know that you can do the following you could have rotation matrices R 1 and R 2 and you might want to multiply them to get some third matrix R 3. The thing you could do is you could represent the first rotation as a quaternion q 1 you can represent the second rotation as a quaternion q 2 and if you do this and you apply this product that I have given here and you get a result q 3 the interesting thing is that these two results here end up being the same if I go and convert back. So, the arrows here correspond to the standard conversion formula to convert rotations. So, if I go and I convert from rotation matrix to quaternion another rotation matrix to quaternion I do the quaternion multiplication and then I convert that back to rotation matrix I will get the same result and you will actually get it with fewer algebraic operations. So, people tend to prefer to just stay in quaternion land the whole time let us say right. So, you do not ever have to convert back to matrices if you do not want to if you are using a library that forces you to in your code then so be it, but I just wanted to point out that because of this nice algebra you can stay entirely inside of quaternion representation. So, it is another reason why people like using them in computer graphics and in virtual reality in addition to this property that I mentioned, but I did not prove formally in any way which is that small changes in your in your quaternion parameters correspond to the same small changes in rotation of the rigid body regardless of where that rotation is occurring at in the space of rotations and that is very important. Another way to say it is that if I were to pick a an orientation uniformly at random what would that mean? If it is a 2D orientation you just pick a number between 0 and 2 pi at random and you would be fine what would I pick at random for 3D rotation? If you pick Euler angles you all pitch and roll at random you will not end up with a uniform covering of orientations. If you pick a unit quaternion at random a random point on the sphere you will in fact have perfect uniform coverage. So, if you do probabilities over transformations as well it is very important to have this. If you are interested in a lot further detail on this subject it is called Har measure. If you want to study the mathematics of these things.