As a doctor, I know the value of good therapy. So, dear friends, may I prescribe two activities to help us experience the healing power of gratitude. During my 96 years of life, I have seen a great depression, a world war, the rise of terrorism, hunger and poverty throughout the world. I have also witnessed the advent of space travel, the Internet, medical advancements galore and countless other discoveries that delight me. Prior to my ministry, I was a cardiovascular and thoracic surgeon and spent many hours in operating rooms. As a surgical resident, I was one of the research team that developed the first heart-lung machine to be used in a human open-heart operation. Subsequently, I had the privilege of helping to save lives of hundreds of patients and, sadly, I watched other patients die despite my best efforts. As a man of science, and as a man of faith, the current worldwide pandemic has been of great concern to me. As a man of science, I appreciate the critical need to prevent the spread of infection. I also honor the devoted service of healthcare professionals and grieve for the many whose lives have been upended by COVID-19. As a man of faith, however, I view the current pandemic as only one of many ills that plague our world, including hate, civil unrest, racism, violence, dishonesty, and lack of civility. Skilled scientists and researchers are laboring diligently to develop and distribute a vaccine against the coronavirus. But there is no medication or operation that can fix the many spiritual woes and maladies that we face. There is, however, a remedy, one that may seem surprising because it flies in the face of our natural intuitions. Nevertheless, its effects have been validated by scientists as well as men and women of faith. I'm referring to the healing power of gratitude. The Book of Psalms is filled with admonitions to express gratitude. Here are just three of them. It is a good thing to give thanks unto the Lord. O, give thanks unto the Lord, for he is good. Come before his presence with thanksgiving. Jesus Christ frequently expressed gratitude. Before raising Lazarus from the dead, before miraculously multiplying loaves and fishes, and before passing the cup to his disciples at the Last Supper, the Savior prayed and gave thanks to God. No wonder the Apostle Paul later declared, In everything, give thanks. Over my nine and a half decades of life, I have concluded that counting our blessings is far better than recounting our problems. No matter our situation, showing gratitude for our privileges is a fast-acting and long-lasting spiritual prescription. Does gratitude spare us from sorrow, sadness, grief, and pain? No. But it does soothe our feelings. It provides us with a greater perspective on the very purpose and joy of life. Nearly 16 years ago, my wife, Dancil, and I were sitting on the sofa holding hands while we watched television. Suddenly, she collapsed. Despite being well-trained to treat the very thing that ended her life, I could not save my own life. Dancil and I were blessed with nine daughters and one son. Tragically, I have lost two of those daughters to cancer. No parent is prepared to lose a child. And yet, despite these and other difficult experiences, I am incredibly grateful, eternally, for so very many things. I'm grateful to God for the nearly 60 years Dancil and I shared together for a lifetime of love and joy and cherished memories. And I thank Him for my wife Wendy, whom I met after Dancil's passing. Wendy now fills my life with joy. I'm grateful to God for the years I had with my two departed daughters. This father's heart melts when I see attributes of those girls in the precious faces of their children and grandchildren. We can all give thanks for the beauties of the earth and the majesty of the heavens that give us an inkling of the vastness of eternity. We can give thanks for the gift of life for our amazing bodies and minds that allow us to grow and learn. We can give thanks for art, literature, and music that nurture our souls. We can give thanks for the opportunity to repent, start over, make amends, and build character. We can give thanks for our families, friends, and loved ones. We can give thanks for the opportunity to help, cherish, and serve one another, which makes life so much more meaningful. We can even give thanks for our trials, from which we learn the things we would not know otherwise. Most of all, we can give thanks unto God, the Father of our spirits, which makes us all brothers and sisters, one great global family. As a doctor, I know the value of good therapy. So, dear friends, may I prescribe two activities to help us experience the healing power of gratitude. First, I invite you, just for the next seven days, to turn social media into your own personal gratitude journal. Post every day about what you are grateful for, who you are grateful for, and why you are grateful. At the end of seven days, see if you feel happier and more at peace. Use the hashtag give thanks. Working together, we can flood social media with a wave of gratitude that reaches the four corners of the Earth. Perhaps this will fulfill, in part, the promise God gave to Father Abraham, that through his descendants, all families of the Earth shall be blessed. Second, let us unite in thanking God through daily prayer. Jesus Christ taught his disciples to pray, by first expressing gratitude to God, and then petitioning Him for the things we need. Prayer brings forth miracles. In that spirit, I would now like to offer a prayer for the world and everyone in it. As I pray, I hope you will feel inspired to do the same. Pouring out your heart in gratitude for the countless blessings God has given you, and petitioning Him to heal our hearts, our families, our societies, and the world at large. Our Father in Heaven, as fellow passengers on Thy planet Earth, we humbly pray unto Thee. We thank Thee for life and all that sustains life. We thank Thee for the beauties of the Earth for order in the universe, the planets, stars, and all things of eternal significance. We thank Thee for Thy laws that protect and guide us. We thank Thee for Thy mercy and loving watch care. We thank Thee for our families and loved ones who fill our lives with joy. We are grateful for all who are striving to combat the COVID pandemic. Please bless them with protection and inspiration. Help us end this virus that has plagued so many of Thy children. We thank Thee for the leaders of nations and others who strive to lift us. We pray for relief from political strife. Will Thou bless us with a healing spirit that unites us despite our differences? Will Thou also help us repent from selfishness, unkindness, pride, and prejudice of any kind so that we can better serve and love one another as brothers and sisters and as Thy grateful children? We love Thee, our dear Father, and pray for Thy blessings upon us. In the name of Thy beloved Son, Jesus Christ, amen. Thank you for listening. May God bless you, one and all.


Welcome, welcome, welcome. This is the day the Lord has made and we will rejoice and be glad in it. Welcome to Hope Today. This is a place where we are inspired to bring you hope and I'm so excited that you have tuned in. It's gonna be a great day. I'm J. Anthony Guild. I'm here with Tom Hollis and Corey Langford. And you know what? It's gonna be a great day today because we've got a phenomenal subject to discuss, don't we Tom? We do, I wanna know where the women are. Okay, I got these guys sitting here, they're fine. Pretty ladies, I mean, we got these men here. It's gonna be a man's show actually. That's why we're all guys up here today. We're in desperate need of strong men in society today. Strong masculinity, you know what? It's rapidly disappearing and that doesn't really speak too well for the future of our society. Well Owen's strong, but he'll be with us in just a minute to talk about God's design for men and what true masculinity is and how the women in our lives can help us in shaping and empowering the men in their lives. It's gonna be a great conversation, Corey. Absolutely, and this is very important for people to understand because in society there is an expectation of what man is supposed to be and then there's the expectation according to the word. And so there is a dichotomy that is happening a lot, especially when it comes to finances in men, when it comes to physical attractiveness in men, when it comes to the intuitiveness of how a man should think in his family, in business. And I think it's causing depression in men and they are also repressing because that's one thing about us as men is that we won't speak about it but we'll repress deep inside of us that causes us to become depressed because we don't express because we don't think we have the right to express that kind of vulnerability. So I hope we talk about vulnerability today because that's a big topic for men.  Listen, I want you to contact some men. Listen, this airs at different times throughout the day at 1 p.m. It'll air again at 8 p.m. tonight. I want to encourage you to get as many men and women. This is gonna be a phenomenal subject. We are in a day and an hour where men are being emasculated, Tom. Like we've never seen before. We're seeing men being stripped of their ability to lead. They're being stripped of their ability to be men. And it's actually considered being toxic nowadays. And I think there's a war. And I'm so glad that we've got a great guest that's gonna help us with this today. I think there is a thing that is toxic. There is a toxic version of masculinity but what about the biblical version of masculinity? And that's what we're gonna be talking about in just a minute. But Corey, we've got something else coming up in a little bit. Listen, listen, as you know, it's the holidays and so there are wonderful experiences and movies coming. Listen, later on we're gonna show the trailer for the journey to Bethlehem, which is a phenomenal movie that is coming out about the story of Jesus like you've never seen before. So we're excited to show that to you pretty soon. That's right. Well, hey, there's no doubt that today's society is in desperate need of strong, courageous men of God. That's right, men of God. Unfortunately, the current view on men has been rapidly declining and it's not only affecting men, but it's affecting the women in our lives as well. Owen Straughn is our next guest and he's the author of the book, The War On Men, Why Society Hates Them and Why We Need Them. Owen, it's great to have you with us on Hope Today. Thank you, man. It's great to be with you today. Well, let's talk about that. Let's dive right in. What is the war on men? What are you seeing? How is society attacking manhood? Yeah, fundamentally, I think we've got to recognize that men are in the penalty box today and our woke society tells men that they're bad because men have historically been leaders and they've had influential roles. And so we're really in a kind of leveling moment where 40 or 50 years of feminism eroding our culture and reaching into all aspects of entertainment, politics of the church and more has caused many men to be tentative and halting about their roles. So many men want to be strong, boys are wired to want to be strong by God, but instead, men are encouraged to lean back today and to be passive and they're told that if they act in a strong or aggressive or assertive way that they're toxic. What I wanna say very clearly is that we're all sinners. We need the grace of Jesus Christ every single day we live. Every man does, every woman does. We need the cross of Christ to wash us clean of our sins. But fundamentally, manhood isn't toxic. The American Psychological Association literally released a 2019 report that labeled risk-taking behavior, assertive behavior, aggressive behavior as toxic. And you've gotta recognize, of course, those dimensions can go bad in a man, right? You've gotta either be channeled for good or you're gonna be channeled for bad. But fundamentally, it's not toxic for a man to be assertive or aggressive. Men have to step up and be leaders in the home, in the church and in society, but all that is under fire today. Well, what's the results then? What's the results of men not being willing to do that for fear of being labeled toxic? What's the result of weak leadership? Great question. The result is a society in flames. We've got a crisis everywhere you turn. You look at education right now. For every woman who drops out of university or college, seven young men drop out. For every one young woman who commits suicide in those 20-something years, six young men commit suicide. Boys are doing terribly in terms of physical fitness. Men are entrapped in pornography. Men aren't going to church. Women are now vastly outnumbering men in church. You look at one metric after another, Tom, and men are doing badly in it. And you survey all those metrics together and you just have to recognize, as I say in this book, we're in a crisis right now and we see it, but very few people are speaking up about it and building into young men with the gospel of divine grace and trying to reach out to them and help them. Our culture is actually still telling them they don't really have the same value as a girl. We don't really want them in positions of leadership. If they act up, they're toxic, they're bad, they're evil, and we have to say something very differently. We have to go to a text like First Kings 2,2, where David says to his son Solomon on his deathbed, be strong and show yourself a man. Be strong and show yourself a man. Then he defines that strength as primarily spiritual strength in God. We've got to give young men that foundation today or things are only going to get worse and worse. Well, and you're not just saying this as just something you made up in the book. There's a lot of examples you give about where this very thing is being promoted as just general masculinity is being promoted as bad. Yeah, you've got this kind of language all over the place. I mean, you think about how a Canadian university a few years back set up a confession booth for toxic masculinity. There's no confession booth for toxic femininity. So again, the message that boys and young men get over and over is that if they are aggressive, if they break something, if they want to play contact sports at recess or whatever, then they're bad. That's something bad in them. And so society really isn't set up for the flourishing of young men anymore. And we have a lot of work to do in the church because we've just got to recognize our boys are in peril, our boys are in trouble. A lot of young men, they don't have a strong father. That's what boys and young men need desperately. But instead of a strong father in the home across all sectors of society, across all classes too often today, you've got a harried mother, a mother who may not even have the man still in the house.   And they end up on medication and then they're not doing well and they're not wired well. And then they end up suicidal a good amount of them. And what we've got to say as Christians is we know what boys need. Boys need a father and a mother. They need a husband and a wife in the home. They need shepherding. They need training. They need discipling. They need a lot of love. I mean, I think back to how my own father, he wasn't a man of many words like I am, but he would take me out, when I was getting a little hot under the collar some of those evenings and he would say, all right, it's time to play some catch. Nothing fancy, but if a boy doesn't have that, he's in peril. He's in a not good place. Well, listen, I'm excited that I was just getting ready to ask you a question about fatherhood and you went right into that. Let's talk about that when men don't have that identity of a father in their home, they're reaching for something. How can you speak to men who may have to step in as fathers for boys and for men, even older men who haven't had fathers and don't understand what it means to be a man like many who have had fathers to show them? Yeah, I loved what you said a few minutes ago about vulnerability. So the strength of biblical manhood, the authentic man in your life, you need an authentic man in your life who models an appropriate conviction. He's like, here's where we're going. I'm gonna lead this family. I'm gonna crack open the Bible. We're gonna pray at mealtimes. You need that strength in that sense, right? When there's a threat against the family, you need a man who says, all right, I got this, I'm on this, but then you also need a man who says, hey son, dad doesn't get everything right. Dad spoke too strongly to you there. I'm sorry, would you forgive me? And so you need that balance. If you don't have that though to your question more specifically, if you don't have a father in the home, oof, that's a tough situation. What's gotta happen then is that there's gotta be a church and there have to be other institutions that step up and that fill that place of that dad. So you need a strong pastor, you need elders, you need coaches, you need teachers to help. And that's what we desperately need today. Oh, and let's talk about the definition, the proper definition, the biblical definition of masculinity, what is that? And how does that differ from society's definition? Yeah, I think being a man is being strong for the good and strong against evil. Strong for the good, strong against evil. And I'm trying to work biblically, as you said, that's based off of 1 Kings 2, 2, be strong, show yourself a man. That's based off of 1 Corinthians 16, 13, where the apostle Paul says, act like men. So you gotta recognize the Bible thinks there is a way to be manly. Our culture hates that. You say that even in a church context today, you get laughed at, you say the word manly, people laugh at you now. There's nothing funny about that word. But we need to recognize that that strength against evil and for good, it's all grounded in the gospel. So what men most need is not fitness tips. What men most need is not how to spit game at a girl, what men most need is not ice baths in the morning or something like this. You can do different things, you can do different practices as a man, but what men most need is the gospel of divine grace. We need to be forgiven. And there's just a lot of lack of that in our world today. And so you've got a lot of young men going to the internet, for example, and they watch videos of Andrew Tate, the former kickboxer. You know, he's coiled, he's muscled, he's got a Bugatti behind him and his Instagram slo-mo videos. And boys and young men want that. They want to be strong, they want to be impressive, but we've got to be very clear. Men, you're never stronger than when you're repenting of your sin and you're trusting Jesus and then you're striving in all areas of your life to lead out as a man. And you're not seeing your strength, honestly, is a bad thing. You're seeing it as a gift that has to be stewarded for the good of others. I think of my dad going to work, just going to work every day, just consistently, consistently, consistently going to work. And he didn't have a Bugatti. He would have probably liked one. And it was just that thing of him going, talk to us a little bit about, we've talked about fathers, talk about the role of the Christian husband. Frankly, and I've said this already, I'll say it again, Christian men have been not always the best even, and men in society, but Christian men have had difficulty in many areas that have hurt their wives, porn or other things that have hurt their wives. How is a Christian husband the proper role? How's that defined? Yeah, we want to be a husband like Jesus Christ, his husband to his church, Ephesians 5, 22 to 33. We want to be a Christ-like husband. And that means laying down our life for our wife. Now, that doesn't mean anything your wife says she wants, you do, you have to lead her, you have to shepherd her. You're the authority in the home. Dad, you're not supposed to be on your phone. You're not supposed to be watching sports all the time.  You're exactly right, Tom. There are plenty of ways that we husbands have been married for almost 18 years myself. There are plenty of ways we fail. We stumble, we falter, and our culture encourages that.  That culture is affecting all of us, that pulls at all of us, but there's a higher call. And that's the call of Jesus Christ. And the call of Jesus Christ is for us as men to die to ourselves. You think of 1 Peter 3 to live with our wife in an understanding way. So a godly man is like Christ in that he's tough against evil, but he's tender with his wife. He's tender with his children. He's the kind of man, you saw a picture of this in Afghanistan with the withdrawal over a year ago where there was this stone cold killer who had his machine gun propped up beside him on the wall, but then he had a baby in the crook of his arm. And you could tell this guy was a dad the way he was holding the child. That's who we have to be. We have to pick up the machine gun against the devil and his demons that want to take us down. But then we got to lay it down when we go home. We're not shooting at home. We're coming in and we're tender and we're on the floor with a tea party with our daughter and we're wrestling with our son in a loving way. And man, we got a lot of work to do in the house, but we love to do it. We love to do it. Wow, and I love that you started talking about this specifically with men and even being romantic. I can't stop thinking about David, how David was a man of war, but he was also a man of worship. And there's that, we don't hear that a lot. Some men, be strong, be strong. But here is David being a man who's saying, creating me a clean heart and a new right spirit within me, but he would go kill about 400 men in a second. So understanding this as well, the significance of men being able to tap into the heart of God and be vulnerable and sensitive to God that when they may not have had that opportunity to be sensitive to God, how would you coach men in learning to see their worship also as strength in their families? Yeah, there's a sense with worship, with men that it's not a manly activity. And we've got to just reframe that for men and we've got to say, sure, there's activities that men might like and all men are not the same. All men are not an athlete. All men are not a public speaker. There's men who are gifted at music. There's men who are gifted at being a chef. So we don't want to say being a man means one vocation, for example, every man works with his hands or something like this. But we do want to say that being a man is fundamentally about knowing God. You're made to know God. So I've seen football coaches even recently, one prominent football coach out there who put a prayer up of him praying to God. And it was one of the strangest moments I've seen recently in my little Instagram perusal of my reels. You just don't see, what I'm trying to say, Corey, is you don't see men praying anymore commonly, like cool men. It's like seeing a unicorn walk across the highway. Like what, a cool man praying? A guy with a chain and with swag and he's praying and we just want to restore that. I can't hit a button and change all our society and our culture. What I can do in my little corner of things is I can model to my son, hey son, I'm striving to be a strong man by the grace of God. I'm trying to pray. I'm trying to read this Bible. I'm trying to love your mother. I'm trying to repent of my sins and I'm trying to follow the Lord. And that's what God wants. That's how God has set the home up so that manhood isn't just son, do this. No manhood is modeled and it's developed and it's lived out day by day. Well, I know at least three cool guys that pray. Okay, I mean, they're all sitting at four, four. I know four, okay? Let me just ask you, we only have a minute or two left here but I wanted to touch on this subject of the whole subject of gender confusion and the kind of the gender roles being all skewed all over the place in our society today. Just what is the biblical place we need to be with all of that? No, my word. Wow, talk about confusion. Talk about madness. Talk about a culture that lives in lies and denies reality. That's where we are. And what we as men, that's the strength part. That's where we are stepping back into that public square and we are drawing a line in the sand and we are saying no further. And we are saying to, you know, disturbed young men who wanna enter the restroom of our daughter or whatever it may be, we are saying absolutely not. You are not coming in here. Brothers, we have lost fathers in the society. We have lost strong men who speak up and say, no, you can't do this. Don't you see this all around you?  You're not coming in here. And so we've gotta say there's only two sexes. There's men and women. They're made by God. You can't make up your identity.  You can't change your gender. You're made who you are by God. And we've gotta stand for that. And we've gotta help our boys and girls understand they're growing up into manhood and womanhood. Owen, thank you so much. Owen Strawn, the book is called The War on Men, Why Society Hates Them and Why We Need Them. And I recommend this book. There's a lot in there that is positive towards building biblical manhood. Owen, thank you so much for being with us today. Thank you man, appreciate you very much. Wow, guys, that is, I mean, first of all, there are three here who are manly people who like to pray. But Jay, that's such an important subject that is getting so skewed in society today. Yeah, it really is. You know, there's something about the men standing up to lead. That's just why you go to a lot of churches and see a lot of women that are in church because the devil recognizes the authority starts with the man.  So if I am the devil, I'm coming after the man because the man is the seed bearer.  So if he can break down the man, he can also break down the family and then ultimately the gospel of Jesus Christ can't go out. So that's why all the confusion is coming.  Wow. And also the man is able to handle a level of pressure that God built us to handle. And sometimes when a man gives that pressure over to his woman, you'll find how she's just filled with anxiety because it really wasn't for her to carry. It was for us to carry. Listen, Christmas season is just around the corner and there's a fantastic new movie coming out about the birth of Jesus. Check out this new trailer for the film Journey to Bethlehem. Your father has always known you're special. Nothing will change that, Mary. Tell Mary, we are ready. The music, play. You're getting married. It's about to be the best day of your life. I'm Joseph. I feel like we're already friends, no? God has chosen you to have a son. The king of all kings. This wasn't a dream. An angel came to me. It's hard to have faith. It's hard to believe. Look at the star. The future holds more. This is it. Let's go. There are too many. But divine king is to be born in your land. It's a mountain to hide a... Hell, fine. A new king in my kingdom. When you put it that way. Perhaps we should go. What is the exit? It's going to be the worst. My crown! I won't let mother found me. Herod must know of the prophecy. He wants my child. Joseph! I'm not the only one who's chosen for this. You have a choice. You can say you believe me. And that you love me. Will you still marry me, Joseph? I do. I will. Yes, of course, yes. You truly believe that this child is the chosen one. What is his name? Jesus. I think even Fig is beginning to tolerate you. This is something for everyone. Journey to Bethlehem hits theaters nationwide beginning tomorrow, November 10th. Go to JourneyToBethlehemMovie.com for tickets and showtimes. Listen, this has been a powerful conversation. And we just want to talk about this a little bit more. Specifically about that attack on men and how the enemy gets in to separate us, to shrink us, to just cause confusion within the man because he understands that when a man is out of position, the entire home, the family, the city, the nation, and the world gets out of order. I feel like, Pastor Jay, you have something that you want to share about that attack on men. Go ahead and just let the Lord use you. Well, you know what? I believe there's some men there watching right now. And even some ladies, it's very important ladies that we're going to be real right now. Nothing encourages us more than when you build us up. Man is so much like God, not that he is God, but he's so much like God that if you begin to praise him, he'll start flexing his muscles. Even if your husband's built like olive oil, just tell him how sexy he is. Tell him how strong he is. Build him up and it will encourage him to lead.  Be a person that praises that man and speaks into his life. And man, it is time for us to rise up. You are going to get hit with titles if you lead like a man in this generation. But you have to be strong. I love what Dr. Owen said, Tom. He talked about the importance of David telling his son, go and be a man. There's ever been a time that we need men to rise up to pray, to love, to be tender, but still to be strong. It's today in this hour. I think David is a great example of that. I mean, here's someone who was strong, was a warring leader, was a leader of a nation, but stumbled and fell and repented and repented and realized that God is the one that he's accountable to, that it's not just whatever he wants to do. It's that God has called each of us to a place of authority in our homes, in our churches, in what we do. And he's called us to be that godly person right there. You know, just wherever you find yourself, be that man of God right there. Ladies, wherever your husband is, build him up into the man of God that he is going to succeed in that place because God's called him to be there. Listen, I know one thing that women, you can do specifically for men is be intercessors for them. There's more you can do in prayer than can be done sometimes in talking. Cause I'm gonna tell you, as a man, we're stubborn. We could be stubborn. And sometimes we have a way of how we see things going and say, you know what, baby? This is how it needs to be. And then that's what it is. And I'm the man and I'm speaking all that and that could cause a lot of tension. But let me tell you something. There is nobody that can speak to the heart of a man like the spirit of God. And that prayer, that time, if you feel like this man has a stronghold, whether it's addiction, pornography, pride, ego, whatever it is in his life, he's dealing with need for affirmation, not having a father, trying to compensate it with money, trying to compensate with muscles, trying to compensate with achievements, speak to God fast and lay down before the Lord. And I'm telling you, the presence of God has a unique way of getting into the heart of a man and almost like the in Troy, there was the gift that came. But in the middle of the night, all of these warriors came out. God will come out into that heart and spew his word all over that man and his mindset, his attitude will begin to change. Pastor Jay, go ahead and just share what I feel like the Holy Spirit is sharing with you right now. Well, I believe right now it's time for men and women to come together. There's ever been a time that we need men to rise up its right now. You may be battling in some way. Just pick up that phone, dial<PHONE_NUMBER>. There are prayer partners that are standing by that want to pray for you.  Go ahead and pick up that phone as well. This is the time there is an attack on men. If men rise up and become the best version of themselves that God has called them to be, there'll be nothing impossible for any family to overcome. So let's rise up, let's defeat this war on men and let's go forward in Jesus name.


Hey guys, this is Rich from Rich to be live and I want to talk to you today about pure extracts, which has some big news First and foremost pure extracts uses CO2 extraction technology to drive full spectrum oil from cannabis biomass Says here. We are an emerging leader in the extraction space offering only the purest quality oil and they're also in the psychedelic space and If you see the chart here, especially in America It looks like just pure consolidation and typically that's what we get before we see a move in the market That's the American symbol PR XTF for pole pure extracts and in Canada. It just looks like this It's like up and then down and up and then down. So right now. We're in this zone right here and to be honest with you this is kind of like This zone right here, we're at It's kind of like, you know a pretty decent dip. You can see every time it does this It's a pretty decent dip That was a good dip and right around here This was a good dip So you can see like I'm marking like all the areas where I consider by zones. So you can clearly see that Pole pure extracts is kind of in a by zone and then these tops are where I would consider cell zones So whenever I look at a stock, I'm always looking at the by zones I'm looking at the cell zones and I'm trying to make good decisions to determine when to get in for the win and this right here To me the tops are the cell zones the bottoms are the by zones and you can clearly see that pure extracts is Probably in an area of a by zone. Maybe it goes a little bit lower But I also see some good upside here Like if you get in around 60 cents and it goes to 80 or a dollar The upside is pretty good, especially considering it's a tight float stock just getting started And they had some big news. So let's go into the news Here's the news right now pure extracts emits application to health canada For sales license big big news for pure extracts technologies corp Pull in canada prxtf in america a to q j a g j a j sorry in frankfurt germany a to q j a j A plant-based extraction company focused on cannabis hemp Functional mushrooms and the rapidly emerging psychedelic sector It's pleased to announce that its wholly owned subsidiary pure extracts manufacturing corp has submitted an application to health canada to amend its license To permit the sale of cannabis extract products to provincially authorize distributors and retailers nationwide Big news the company the company recently announced a distribution agreement with a large canadian licensed producer To distribute pure extracts vape and edible products through their established provincial distribution channels and thus Pure extracts expects to have significant sales momentum for its pure polls And pure chews branded products by the time the company receives its sale license Amended from health canada pure extracts is continuing to develop its portfolio of cannabis 2.0 products With emphasis on its 34 proprietary formulations of pure polls branded full spectrum oil fso vape products and on our new line of pure chews edible gummies Being produced under license from the taste t l l c the manufacture of fireball cannabis gummies Pure extracts co ben nikolevsky remarked this milestone Dovetails perfectly with our recently signed distribution agreement We have all of our bases covered now and we will quickly and efficiently Get our vape and edible products to retail buyers across canada And that means sales and that means revenue and revenue is always the key driver for any stock About pure extracts technologies corp pure extracts features an all new state-of-the-art processing facility located just 20 minutes north Of world famous whistler british columbia The bespoke facility has been constructed to european union gmp standards In me towards expert sales of products and formulations Including those currently restricted in canada into european jurisdictions where they are legally available On september 25th 2020 pure extracts was granted its standard processing license by health canada under the cannabis act And the company stock began trading on the canadian securities exchange on november 5th 2020 only been a few months Just getting started and the news keeps coming I think that the upside is tremendous for this company and it's really just getting started Only just begun and you can go to their website at pureextraxcorp.com Learn about their business Learn about their facility Learn about their equipment And learn about their advantage So you can see right here The business model extraction formulation and brand development Those are the three pillars our unique business model is founded on three pillars So this is a company that's got their hands involved in a lot This is their extraction business Formulation business And brand development You can see their business lines the functional product And emerging psychedelic compounds market represent outstanding growth opportunities In uncrowded sectors two of the hottest sectors in the world psychedelics and cannabis extraction And this is a company that is heavily involved in both These are some of the upcoming catalysts focused on growth So you can see fully funded expansion of existing facility to 10,000 square feet Completed health canada high level review. So they're definitely on track For bigger and better things and the news keeps coming. Love to know what you guys think about the news today Remember risk to be live is strictly for education and entertainment purposes Always do your due diligence always do your research before you invest in anything that we talk about here in risk to be live If you like the video, please smash the like button comment down below share the video everywhere and subscribe Let me know what you guys think pure Extracts technologies corp poll in canada prx tf in america With some big news and of course, we'll bring it to you again first Pure extracts submits application to health canada for sales license. Let me know what you think Is your border rich from risk to be live bringing the news?  Let me know what you think And comment on the video is your border rich from risk to be live and i'm old peace


I should I'm a fellow Canadian first of all all right cool man you go back to get back home Peter board You go back to Toronto haven't been there since before the pandemic Tell me about the news a single a new album. What do we looking forward to here? Well, I got a an incredible day for me because 35 years ago today My first album skid row Was released to the day Yes, it is So not only am I inducted to the Hall of Fame, but I Have a new song That's on the radio now Like today they have this FM radio the power drive at five across the country Yeah, and my song is number six on the top 20.  I couldn't be happier That's my dream is to get another song on the radio. It's happening So I'm very happy just quickly. Tell me about the musical direction of the of the new album It's all one big song. I always do the same thing when I make an album I just try to make an album that I love because I love albums. I collect albums So I know what I like So I've always just tried to make albums that I love Starting at 18 in life youth gone wild. I love that then and I love what do I got to lose now? Last quick question. Yeah, how many times a day do you get asked about a reunion with skid row? You'd have to ask them Thank you


This study found that male students had better knowledge and attitudes towards physical exercise compared to their female counterparts. However, both genders did not put in enough time in physical exercise. The study also revealed that girls participated more in physical exercise, but this was not reflected in the amount of time they spent doing it. To address this issue, school curricula should be modified to include more physical activities and allocate more time for physical education classes. This article was authored by Ida Jifabunmi, Ibigoni Jumbo, and Martin Zoloid.


Uploading files into Moodle. There are two ways of adding documents such as presentations or word processed files to your course. One way is dragging and dropping, as we've seen in an earlier video. If you can't use drag and drop, this next method uses Moodle's activity chooser and file picker. To upload files this way, we need to turn on the editing by clicking the link in the gear menu top right, then in the section where we'd like to upload the document, we click the link Add an activity or resource. This brings us to the activity chooser and we scroll down to resources. A document is a resource and we're going to add a file. So we click file twice to go straight to the setup screen. Name is important because the name is what the students will see on the page when accessing it. The description is also important. You may or may not want a description, but if you do and you want it displayed on the course page, tick the box. Then we arrive at the file manager and again if your browser allows it's possible just to drag the file straight into here. But we are going to click Add and this takes us to Moodle's file picker, which we will explore in another video. We just want to upload a document, so let's ignore for now the other options. We can choose our browse for a file and then click to find the file we want. We can change its name if we want to, we don't have to. We can change the author name, change the license if we're not happy with the default license, and then click to upload the file. It's worth exploring some of the other settings, such as in appearance, we can display the size of a document, useful if your students have poor internet connections. And we can also display when it was uploaded, so let's do that. If we now save and return to course we can see our file displayed on the page with its upload date. And note too that like our presentation file above it, it has a useful icon which also shows students what type of file it is.


Okay, so we're going to start a new topic today, reading the low codes. Man, it's okay, we're reading the low codes. Okay, so before we do that, I want to emphasize once again that what you've seen so far is...  So what would be your choice? There are two possible choices. One is to have a... What are the two possible choices? You have a read-solving code, or you could have a VCH code. There are some advantages and disadvantages with either one. VCH codes have better performance for the same rate, etc. But read-solving code has better lower implementation complexity in terms of field involved. So that's the point where we are, and that's a good thing. So in a way, one ready-made solution we can always provide. So this is quite competent, it's not going to be very bad solution. So the read-muller codes are in a way codes that were replaced by read-solving and VCH codes. In a way, in case of read-solving, read-muller codes are slightly older. You might wonder why are we going to look at it. We won't look at it in great detail, but we'll see enough things there. Of course, the decoder for read-muller codes has some constructions which are very interesting. So it's not like a T error correcting boundary distance decoder. It's a different kind of decoder. For instance, I've been mentioning how when you want to get to capacity and such things, like we'll see in the next course, if you take a course, you'll see that it's not important to just correct up to the error correcting capability. You should correct a large fraction of errors beyond that also. So read-muller codes have decoders which at least correct a non-zero fraction beyond the error correcting capability. And that is a big interest. For that purpose, we'll see it. It also has a lot of nice coding theory ideas and we'll see the construction is very nice. So that's one thing which is good about this. So those are the reasons why we're saying it. Talking about it, so when I talk about the decoder, I think it would be good to pay more attention. The way we derive the decoder and look at the properties would be very interesting. Read-muller codes. Okay, so let's begin with the RM codes. So read-muller codes are a popular abbreviation of codes with the RM. So read-muller codes have a block length which is 2 power M of 1. So it's very trivial to start with 0 and 1 and all that. So if the block length is 1 and 2 and 4, you can pretty much distort all possible codes for blocking one. Similarly, if you start with 3, I mean nothing starts here depending on the problem. 0, 1, 2, 3. So usually I'm equal to 3 onwards is where it will become the I3 non-privileged. Otherwise it will be just a real set of codes. And this is the block length. And the construction, so far for each RM and BCH code, are always motivated with the parity check matrix. So you'll see for decoding read-muller codes, we'll go to the parity check matrix. But before that, the construction is usually described in terms of the generator matrix. And this is an interesting construct where you can guarantee a minimum distance based on the generator matrix construction. So far if you look at minimum distance property, the solution property we used was the random on-structure. And we said if you take, the matrix will be in full rank, so we cannot have any independence. What can I say? I have nothing. They have a job to do and they have to do it. So that's what we've seen. So coming back, this construction is using a generator matrix. And even through that, you'll be able to guarantee a minimum distance. So I'm going to give you the parameters first just to get loose to it. And then we'll see the I3 construction. So the read-muller code has usually two parameters, R and M. Length will be 2 power M. M will go from 0, 1, 2, etc. And R will take any values from 0 to M. So the read-muller code itself has two parameters, small R and small M. M is some non-negative integer, 0, 1, 2, 3, etc. R is, again an integer, but it takes values only from 0 to M. So if M is 3, R can take values 0, 1, 2, etc. So for every R and M, you have dimension 2 of R and M. So this is the dimension. State of R and M is basically M2 is 0. What is M2 is 0? 1, of course. M2 is 1, so R and M2 is R. So the block height is a power of 2, 2 power 3, 2 power 4, etc. And the dimension is this binomial coefficients added up to R. So if you say R, so this such a code is called the R-powder read-muller code of length N equals 2 power M. So you say R is the order of the read-muller code. M is the state 2, stands for 2 power M. So you see the R-powder, RN, the read-muller code, you can also say as the R-powder read-muller code of length 2 power M. So this is called the R-powder read-muller code. So that's the dimension. So it turns out minimum distance for this code is 2 power M minus R. So I think that probably got caught in the, let me just change this to 1. So you can see that. So the minimum distance for the R-powder read-muller code is 2 power M minus R. So that's the powerful nature of this result. So you have some good properties of this. So that's the parameters. If nothing in the parameter itself, we really need to know about the encoding and decoding and the construction, etc. That's what plays a crucial role. So the construction, like I said, is through the generator matrix. It also uses ideas of Boolean functions. So everybody here, I'm sure, have met Boolean functions at some point in their life. We may not have thought of Boolean functions in this way. So we'll think of Boolean functions in a certain way. And so we'll worry about what are Boolean functions? What is the Boolean function? So Boolean function is some function which takes you from 0, 1. So specifically we'll be interested in 0, 1, M to 0, 1. So we'll have M variables. So we'll denote as V1, V2, Vm. So this is standard notation. So there are M variables. How many possible values that these M variables can take? 2 power M. So you can make a truth table if you like through Boolean function. So Boolean function, if I call it F, I can make a truth table which would list V1 through Vm like this. And then if you have F of V1 through Vm here. So I can put all possible 2 power M possibilities here. So you start from 0, 0, 1, go all the way to the 1 fellow. And write the value taken by the function here. So this will be like 0, 1, whatever. So that's what we'll do. So this is a Boolean function, I think. Quite a few properties of this Boolean function. So I'm going to use some of those properties in the construction. The first question I'm going to ask you is, how many different Boolean functions are there in M variables? 2 power 2 power M. 2 power 2 power M, is that right? So how many different Boolean functions are there in M variables? 2 power 2 power M. How do you get to this? How do you get to that answer? 4M. So don't think of it in terms of whatever, min term or max term, form. You'll get really confused. Let's think of what it is. Here is a vector which represents the Boolean function. Every vector of length 2 power M can be a Boolean function. There's no problem with that. So you have a function of length 2 power M, a vector, binary vector of length 2 power M. It can be a Boolean function. How do I make it a Boolean function? You put the vector vertically in this way, and then write all possible Boolean through VM in this order from top to bottom. You change this vector, the function changes. So every vector of length 2 power M, binary vector, is a Boolean function. So how many different vectors, binary vectors do I have of length 2 power M? 2 power 2 power M possibilities. So what we'll do is, we'll think of the set of all Boolean functions as a 2 power M dimensional vector space. So this single vector is a Boolean function. I'll think of every single vector a little bit. So if you think about it, then when we do a NK code, we are dealing with N-bit vectors. Vectors of length N. Here I didn't read any reports. I want N equals 2 power M. So 2 power M nicely fits into this Boolean function framework. If I don't have 2 power M, then I can't quote things of it as a Boolean function. Only when I have power of 2, it becomes a proper Boolean function of N-variable, some variable. Otherwise, it just doesn't have the rich state. So that's what we'll do. We'll take the Boolean functions in N-variables. N-variables. Think of them as 0, 1, 2 power, set of all vectors, and 2 power M dimensional binary space. That's the first one. The next thing that I'll invoke is from your knowledge of Boolean functions, you might know this. So if I write down a table like this, this gives me a 7-form for the F. So I can go through and see every single place where F is 1. Then look at the V1 through VN that gives me that. Whenever a VI is 0, I will put a VI bar. Whenever a VI is 1, I will simply retain VI. So I can write F of V1, V2, VM in this form. I can write F of V1, V2, VM as some summation where each term will be 1. So if you want to be careful about V1, V2, VL, and it may also be a bar. Is that correct? I can also say it puts a bar there. What do I know about V bar? V bar is what? 1 plus V. In binary, V bar is the same as 1 plus V. Remember, plus is what? Modular pre-addition. Is that correct? Is that okay here? Maybe yes. So I can do that here. What is this plus? What is this summation? It's R. So I have to think of R here. What happens when I do R? Remember, this plus cannot be, it's not the same as Modular pre-addition. So what is this? This is some R. What do I do in the R? R is what? Can I write R in terms of itself? Maybe not possible. Let's see a simple example, and then we'll go to the case. I think if I write in general terms, it's very confusing. So let me take a simple example. I'll appeal to this example and show you a general form for the Boolean function. Which is always possible. So let's say I make this 3. I have 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0. So this is Vp, V2, V1. So it's common to write V3 on the left side. It's a convention for read miracles. So here I wrote it differently. Usually people write it in reverse. We'll start with Vm on the left-hand side. And let's say a function that I want, but V1, V2, V3, perfectly. Let's say I'll come 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0. Okay, suppose I do this. Okay, can I do that? Is that fine? Okay. So... Okay, so... Okay. Alright. So how can I write this function now? Okay, so I can write this function in that form. Yeah, V3, V2, V1 plus V3, V2, V1 plus. Okay, correct. Okay, so here this plus would be R, right? So let me replace with R. I think it's not a very good thing to say anything else there. So let's say R. We're okay? We're okay? Sorry? Is this correct? Or is this wrong? Did I make a mistake here? It's fine, right? Okay. So... Okay. So... So each term here, what is each term here? I think of each term here. It will have a rate of... So it's okay. So let me combine this. So what does each term have? This is also a function, right? This is also a Boolean function. Am I right? Okay. That's fine. This is also a Boolean function. In terms of a vector, what will be the weight of that vector? So if I think of this Boolean function... See, this overall Boolean function has a weight of 2. Now if I take this Boolean function alone, what will be the weight of that Boolean function? 1. What about this Boolean function alone? It's also a weight 1. So when I have 2 weight 1 vectors which are not the same, R becomes the same as XR. That's fine. So keep this duality in mind. So you are always used to thinking of min terms as not vectors. So you think of it as just the expression V3, R, V2, V1. So you don't think of it as a vector. So I want you to think of every single term in this R sum also as a vector. So that becomes a vector. You put all possible values of Boolean to V3. But if you have only a single one, that's clear. You'll be happy about it. What is the vector corresponding to V3, R, V2, V1? 0, 0, 0. 1, 0, 0, 0, 0, 0. Is it okay? What is the vector? 0, 0, 0. 1, 0, 0, 0, 0. Is it okay? Okay. You tell me. Okay. Let me ask you a question. Okay. So you are all very happy with the correlation between vectors and Boolean functions. You tell me the vector corresponding to V3, R, V2, V1. What I wrote here, right? Yeah. It's like, yeah. You write the truth table, say V3, R, V2, V1. You'll get a long vector, 2-param length vector. That is the vector corresponding to that. Okay. So what is the truth table corresponding to V3, V2, V1, R? 0, 0, 0, 0. 0, 0, 0, 0, 0. Now, in terms of these vectors, it doesn't matter whether I'm or XORing. Or XORing. Why is that? Well, you know, if this is one, that cannot be one. Right? Is it okay? It's okay. Okay. So what can we do next?  I want to replace this R with XOR. So I can do this here in this form. Okay. So I can take any function. S of V1, V2, V3. I can write it as wherever it is one. I put the mean term corresponding to that. And then instead of R, I can replace it with XOR. That is fine. So it can be replaced by XOR. Okay. So let's look at, let's say V3 bar, V2, V1. Okay. And suppose I want to write V3 bar as 1 plus V3. Okay. So what happens when I write 1 plus V3 there? Okay. So let's just look at that equation. What is V3 bar? I'm going to write 1 plus V3. This plus is XOR. XOR is not R. Okay. So I can take this equation here and replace V3 by V3 bar by 1 plus V3. And then do multiplication. Multiplication is perfectly. Okay. So it is here. V1 bar I can replace by 1 plus V1. And the plus would still be XOR. And I have an XOR only in the middle. Okay. So when I write F in terms of this momentum expressions, the R that you are used to can be replaced with XOR because I'm interpreting these functions as vectors. Be very careful. I mean, don't do this in the binary world that you are used to. You can't replace the R with XOR. You get a completely different value. Okay. In the vector sense, I can do that. It's okay. Right. Because I'm thinking in terms of the vectors that are XORing there. Okay. When I write a function F of V1, V2, V3, I'm thinking of the entire vector, not something else. Is it okay? R cannot be replaced with XOR and then done. But when I have such a situation, special situation, I can do it. Okay. So every bar can now be replaced with 1 plus without the bar. And then I can now multiply it out. So finally, a claim I can make is any function. So we proceed and proceed like this. And you will see that the function therefore V1, V2, V3 that I had bar becomes, becomes what? If I put 1 plus V3 here, I will get V1, V2, V1, V2, V3. Remember, what is this plus? Plus again an XOR. Okay. Sorry. Again an XOR. I will get V3, V2, V1 plus V3, V2. Okay. So once again V1, V2, V3 plus V3, V3. Is that the same? So this will cancel V1, V2 plus V2, V3. Remember, this plus is not XOR. Okay. Vector XOR. Can we check this V1, V2 plus V2, V3? Is that the same as the function I had? You can go back and check that. Okay. So if I do V1, V2, what will I get? So V1, V2, 0, 0, 0, 1, 0, 0, 0, 1. Okay. What is V3, V2? 0, 0, 0, 0, 0, 0, 0, 1. Okay. So if I do the XOR there, I get back to the same. Okay. So this is another expression of the same function except that in terms of R, I have XOR now. Is it okay? So be a little bit careful about what I mean by this, but it's a valid statement. It's not a wrong statement to make. Is it okay? There are various other ways of proving it. It's not very hard. You can replace R with XOR, but you have to do the corresponding changes there, and you can get to this formula. It's not given in the binary. Well, this is true. Okay. Maybe it's simple. You may not have thought about it, but it's very important. Okay. So now I can do this through every single function. Any function I come up with in M variables you can write the truth table. You can write the minterm form with R. Since each minterm does not have any problem with these. So that's only rate one. I can replace it with XOR. Then go into each minterm. Wherever I have a bar, put one plus. Remember when I say one, what is this one? I'll think of this one as the all one's vector. Right? Okay. I'll think of this one as the all one's vector. V3 is, wherever V3 is one, it will be one. Okay. So you can go back and look here. V3 will be this vector. V2 will be this vector. V1 will be this vector. Okay. So those are just real by themselves. Okay. Okay. So when I do that, I get rid of all the R's. They all become XORs. I get rid of all the bars. They just become product, except that in some cases I might have the degree, the number of terms might have gone down the one. So I have V3 bar, V2, V1. I might have gone to V1, V. Okay. A lot of cancellation might occur, except why I'll do all that. But finally I'll be left with the form that each term is a product of some subset of the V1 through Vm. And then I have XOR. Okay. So that is the result I want to make. I don't want to be able to prove it. But it's not clear how to do it. Okay. So finally I want to claim that any function V1 through Vm can be written as, this is true for, in general, for, in the case, can be written as some zero times one. Okay. So I put a big one into the bar where to denote that it's actually the all one's vector. Okay. So I can also think of a vector function. Plus A1 times V1. Okay. Remember, the V1, I'm thinking of it as a vector now. Okay. So if you want to solve this thing, this function is now a vector. One is a vector. V1 is a vector, et cetera. A2 V2 plus one, two. Some, I don't know. I mean, it's a bit painful to count this. So I'll say some A question mark. I'll put a question mark here. Just, we'll come back to the count later. It's not very difficult to count it. Plus, what else can I have? All possible products of two at a time. Right? So I could have that. Okay. So some A question mark, V1, V2, all the way through. Question mark, Vm minus one, Vm. And then what can I have? All possible, three at a time. All we have to, the last one will be a question mark, V1, V2, Vm. Is that okay? Right? And the plus is an XOR. You can write any Boolean function in this form. We're okay. So you can also think of it as a Boolean identity. It's very much a Boolean identity. And all the pluses are XORs. You can think of it as a vector. Just put one there, V1, V2. You substitute the values here and take the XOR. You will get the function. So it's kind of an identity. You can think of it in that form. You can use some other Boolean identities if you want and show this. It's not very hard. So we will think of it as a vector. I mean, so the vector is useful because the vector is, it will go back to the code we had eventually. So that's what you got. Okay. So any Boolean function, remember, Boolean functions, I'm thinking of it as belonging to 0, 1, 2, 0, n, right? So that's the vector. It's a vector. XOR, XOR. Is that okay? So each of these gates is a vector. One is a vector. V1 is a vector. V2 is a vector. Vm is a vector. So if I have to select this question mark, I can go through what will be the last question mark that's of interest to me. 2 power n minus 1, right? I'm starting at 0. Is it okay? Or will it have to be 2 power n? So set of all subsets of V1 through Vm, right? So you can have one at a time. See nothing, the null set, and then one at a time, two at a time.  So you have 2 power n. Terms in this. And what about each of these vectors? 1, V1, V2, Vm and all that. What about each of these vectors? Can I make some statement about linear independence here? Can they be linearly dependent? Can any two vectors in this XOR to give you 0? It's not possible, right? See, you will never get a Boolean identity like that. Two of them. See, any two terms here have a different form, different set of subsets of V1. For instance, it will be V1, V2. Another will be V3, V4. Why will V1, V2 ever be equal to V3? So that will never happen, right? So there can be no identity, linear relation involving any of these things. Because they're all independent variables. They're all linearly independent. Think about it for a while. There are various ways of convincing yourself that they have to be linearly independent. But it seems easy to think about a Boolean function. If it is not linearly independent, there should be an identity linking all of them. And how can that happen? Right? Nowhere that for all possible V1, V2, V3, you will never get an equation being equal to this. Okay? So each of these gates is linearly independent. And any function can be written as a linear combination of those things. Okay? So what does it mean? So this is a basis. Okay? So this is from 1, V1, V2, Vm, V1, V2, Vm, minus 1. All these gates, these two param vectors, form a basis for this space of Boolean functions. Then you view it as a vector space of two param dimension. Is that okay? So this guy has a basis, which is 1, V1, V2, Vm, then V1, V2, so until Vm minus 1, Vm, all the way down to the last row will be V1, V2. Is that okay? Okay? So these are all relatively simple statements about Boolean functions. But you may not have thought of Boolean functions this way. So first time you see, it will give you a bit surprise. Okay? So it's not very hard, but a bit confusing. Okay? All right? So remember, each of these basis vectors are length two param vectors. Okay? Right? Remember that. So I'm going to ask you more difficult questions. If you think you understand it, there will be more difficult questions coming. We'll see in clear. If you have any question, you can ask this. What is the question? V1 plus V2 plus V1 V2. Hmm. What is that question? Why will that be zero? See, it's XR, no? V1? It's XR. V1 plus V2 plus V1 V2. They're not the same. You have a one in the first row. No, it's bar, no. It's a bar. Be careful. Be careful. Don't use a Boolean entities. XR is different. What is AXR, A bar? A or A bar is one of them. What is AXR, A bar? A. A. It's not cool. So be careful with XR. So you're doing entities, usually you have with R. Be a little bit careful. A plus A bar is one of them. So that's R is the linking factor. Right? Okay. Alright. So maybe that's what I wanted to say. Why are you saying, okay, so you're saying what? V1 plus V2. Why is this V0? V1 has a one in the first version, and the only one is V1. V2 has a one in the second version, and V1 is zero. No, everything else is zero. Okay. Sorry. I think that's where the confusion comes. Okay. So V1 is this guy, man. V1 is this guy. V2 is this guy. Okay. So I take that back. So AXR, A bar is one, right? A or A bar is also one. So I got confused there. Sorry for that. So let's just come back to this. So when I say V1, so V1 is a Boolean function, which is one. Every time V1 is one. Okay. So it is actually, if you write it in this, in this minterm form, it is a very complicated expression. There will be like four terms. It will be V3 bar, V2 bar, V1, plus V3, V3 bar, V2, V1, plus several terms. Yeah. So every time it cancels, it will get V1 alone. Okay. V1 is basically this guy. Okay. So this linear independence is, maybe it's not very trivial to see, but we cannot have any identification value in these things. Okay. That's something that cannot happen. So basically, I think about it as, well, I'll tell you a very simple way to think about it. Think of SFV1 to VM as polynomials. Okay. Polynomial is the best way to think about it. Okay. So think of these guys as polynomials. Okay. And the way they take binary values is that they are polynomials. Okay. So when you want identities, you have to look for polynomial kind of identities. Okay. There's no way V1 plus V2 plus V1, V2 and V2 will be zero for all of you. So that's something that won't happen. So don't think of it as a Boolean function with R and XR and all that. It's a bit confusing if you do that. Okay. Even I got confused. But everybody can get confused by these things. So it's totally different. They are thinking about it. The best way to think of these things are polynomials. Okay. They take binary values, the polynomials and binary variables. Okay. They are thinking about it. So if you want an identity, you will have to have a polynomial identity. The only thing you can have is like A plus B in square equals A square plus B square. Something like that you can have. That's okay. But such things won't happen yet. If you have distinct monomial terms, there's no way they are going to give you any information. Is that okay? But also, other ways of arguing the linear independence, I'll just leave it at that. So the linearly independent, they form a basis for Boolean functions. Is that okay? Any other question? Okay. The next question I'm going to ask is what is the weight of every single vector on this basis? Okay. What can you say about the weight? Be a little bit careful. Okay. What is the weight of 1? 2 power m. So what is the weight of these guys? 2 power m minus 1. What about the weight of these guys? 2 power m minus 2. 2 power m minus 2. Is that okay? Did you get that? Okay. Every way, V1 is 2 power m minus 1. Okay. So it has only V1. Right? V2 through Vm are brain curves. Okay. As long as Vm, V1 is 1, I can have 2 power m minus 1 possible values assigned to V2 through Vm. But all of them, it will still have a value 1. So the number of places where it will be 1 is 2 power m minus 1. So what do you think of V1, V2? So V1, V2 to be 1, V1 should be equal to 1. And V2 should be equal to 1. What about V3 to Vm? It can take arbitrary value. So you have 2 power m minus 2. Okay. What will be the weight of this day? Okay. Weight is 1. Is that okay? Is that okay? All right. So one statement that I can make very easily is, out of these 2 power m vectors, only a single vector has odd weight. That is weight equal to 1. Everything else has even weight. Okay. I want you to remember that. That's quite important. Everything else has even weight and they are linearly independent. Okay. So what do you think of V1, V2, Vm, Vm, Vm, Vm, Vm, Vm, Vm. Okay. But there is one way, it says odd weight. So together, they can make a basis. It makes sense. If you all of them are even, then it cannot be a basis. It is wrong. All of them. There is one way, it is odd, it can take a basis. Is it okay? So another way to think about it is, if you forget about Boolean polynomial is, all those nonsense. So, 0, 1, 2, power m, there are many different bases. This is just one interesting basis. It is just an association with the Boolean variable. So, you can have the canonical basis if you like, it is not very exciting. This basis is a little more exciting, I will show you one. But ok, different basis for 0, 1, 2, param, but it also has a relationship with the binary polynomial terms, all right. So, if you want, let us look at one more example. So, maybe we will look at the example I make and slightly more detailed, ok. So, I have, I have 1, I have b1, I have b2, I have b3. So, let me write it down, ok. So, it is very common like I said to write b3, b2, b1, let me do that. So, it is going to be right there, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1. And 1 is going to be what? Oh, 1 is to go. So, remember our letters are this way, ok. So, in many bits you will find people write it roll wise. But, I think people are not very comfortable with 2, 3, 2, written roll wise. So, it will be like column wise. So, let's try it again. So, you have b1, b2, b2, b3, b1, b3 and then you have what? V1 V2 V3 okay so what is V1 V2 you can write it down it's not very hard so you see it's not V2 okay what is V2 V3 okay did I make a mistake here it should be a one comma okay V2 V3 is what I wrote before right 0 0 0 0 sorry yeah I'll do that I'll do it this should be 0 right we're okay what is V1 V3 0 0 0 0 0 1 0 1 okay and what is V1 V2 V3 all zeros last two alone V1 okay so it's probably not the best presentation possible but you can see the pair are how many vectors here eight vectors okay eight functions and they are linearly independent you can check that they are linearly independent if you like or you can believe what I said linearly independent and they form a basis for the eight dimensional binary vectors so it's just a different basis think about it okay it's a different basis and I have a some peculiar way of indexing each element of the basis instead of saying E1 E2 to all the way to E8 I'm calling that as 1 V3 V2 V1 V1 V2 V3 so it's just that's one way of thinking about it is it's a polynomial in three variables with binary values so the only possible monomial terms are V1 V2 V3 the constant term V1 V2 V2 V3 V1 V3 V1 V2 V3 they cannot be any other term for instance you cannot have V1 square V2 part serve why can't you have that V1 square is equal to V1 in binary well that's true so V2 part 4 is also the same as V2 so it come back to V1 V2 it won't give you any new vector okay so to think of binary value polynomials these are all the terms that you can have okay so that's how it works okay I don't even have to appeal the boolean functions I can just say binary polynomials okay so given you binary polynomials now we're ready to see the definition of read the records okay so the read the record R and R comma M is generated by okay so you can guess it's not very hard generated by one V1 V2 Vm V1 V2 V1 V2 V1 minus 1 Vm okay so think about that one okay all the way up to V1 V2 VR okay so let me do the all the way up to this side the last case will be will be taken R at a time okay so it will be M minus R plus 1 well okay so this is just one term this is another term okay so remember if I have n variables this base is right we'll start at 1 it'll have Vm Vm minus 1 all the way to V1 then it'll have V1 V2 V2 V3 all those things and it'll have 3 at the time then it'll have 4 at the time so on till R at the time right I will stop there I go all the way from 1 to products of V1 through Vm taken R at the time and stop there okay so take only those vectors and make that the basis of my code okay what do you mean the basis of my code they are the reverse of my generator matrix okay they're all linearly independent so clearly dimension will be equal to the formula ideal okay 1 plus M choose 1 plus M choose 2 so on till M choose okay so this is one way of defining read molecules there are so many other ways I'll give you one more way soon okay so is this clear okay right so I'm going to take the basis vectors corresponding to more or more terms having product of up to R Vi okay so V1 V2 Vr or Vm Vm okay very equal in destination is the following Rm of Rm equals f of set of all Boolean functions Boolean polynomials such that degree is less than or equal to okay so previously I gave you the basis and I said you combine the basis in any which way you want and you combine them in arbitrary ways what will you end up getting you will get all possible Boolean polynomials of degree less than or equal to R what do you mean by degree now okay so degree of Vi1 Vi2 ViL will be basically L okay and what is the degree of the of the function itself what is the degree here to a maximum degree maximum degree over alpha okay so for each term I can define a degree which is basically the number of variables occurring in the term and for any del Boolean polynomial I can have a maximum degree in fact there can be multiple terms which have a maximum degree what's okay I have no problems with that but the maximum degree itself will be unique okay we have just one value which is okay so why are there is this definition equivalent to that definition yeah both of them are the same which if you have degree less than or equal to R each term has at most R terms so clearly it can be written as a linear combination of vectors I gave you to take linear combination of arbitrary vectors there it will definitely give me only a Boolean polynomial of degree less than or equal to R so both increase okay so it's very convenient to think of an arbitrary regional code word okay so code word as R comma M it's very conveniently type of a function like this degree less than or equal to R which is what I wrote down there but that's all we think of a code word of a regional code okay so if you think of code words of strictly codes we found it very convenient to think of it as a polynomial right c of x it has some roots that's what controls it here for regional codes it's very convenient to think of them as polynomials with binary variables and the degrees are significant degrees less than or equal to R okay so everything adds up in this nice little bit okay so let's say examples for n equals 3 okay so let me take this guy here okay so what happens when R is equal to so let me just copy this guy then take it to some other page and then we'll see this okay so this is what we had for M equal to 3 so if I have R equals 0 okay what are the dimensions so R equals 0 has n equals 8 of course k will be what 1 right and what will be the code yeah so it will be the 8.1 repetition code do you see that okay the basis is only this guy so let's say alone and that is just a repetition code so clearly the minimum distance is also 8 and it agrees with our formula right so 2 bar M minus R if I use the function what happens when R equals 1 it will be an 8 comma 4 code okay so it's a more complicated code I don't know how to how to describe it so in fact you can describe it in a nice way so if you think of this think of these guys okay I mean there are various things thinking about it so let's forget it so 8 comma 4 okay so you can show the minimum distance will be 4 that's okay so what happens when R is equal to 2 I'm sorry 8 comma 7 but what code is that can you identify the code it's the even weight code how do I conclude that this is actually the even weight code yeah so first of all these seven guys are linearly independent and each of them has even weight you have the each of them has even weight so any combination you make will still have even weight okay so that will be all the even weight vectors of length 8 okay but 8 comma 4 I don't quite know what it is right so let me just leave it as a question mark it's the first part of each molecule of length 8 okay it's a very nice code it has some good structure we'll see it later on but one thing we know is d is equal to 1 so if you have these two we know that what happens if R equals 3 I get the entire 8 comma 8 identity code and d will be 1 okay that's also okay we can take code word yeah it is also a code word yes it's got 8 only this guy is weight 1 everything else is even weight this is 8 weight 8 no yeah 8 possibilities all right no no no this guy is already given me to be three is already all is odd weight all one was I mean I'm looking at 2 par n right so it's always even no problem okay there are 8 so some of these statements are in general true okay so R equal to 3 is the 8 comma 8 identity code okay so you'll notice once again the codes are appearing as dual paths so R equal to 0 and R equal to 3 are actually duals R equal to 1 I don't no no no R equal to did I get that right I'm sorry okay I'm sorry I'm sorry R equal to 0 and R equal to 2 are duals yeah R equal to 1 we'll turn out to be a self dual code okay so we'll see later on that it's a self dual code okay R equal to 3 is a real code but anyway it's it's 8 comma 0 if you think of a not including anything okay it's like the null code or something okay so you can take up it also as a par if you like that R equal to 0 and R equal to 2 are duals and like you said R equal to 1 we'll do a self dual code okay so we'll see that later on okay so these statements are in general true and we'll try to prove that but one more thing is this property of minimum distance d equals 2 par m minus r okay so so I'll urge you to look at the example of m equal to 4 it's not very hard try to look at that write down all the bases what does see what it looks like it's again you'll see some interesting observations okay so let me one observation which I'll make which I'll write down right now r m of 1 comma m is the repetition code sorry 0 comma m sorry the repetition code the other observation I want to make is r m of n minus 1 comma m is the even rate okay repetition code 2 par m comma 1 even rate 2 par m comma 2 par m minus 1 okay these two statements are in general true for any n how do I prove this is again the same proof only the last way is add weight everything else is even right it's linearly independent so it has to span all the even weight okay so these two statements we'll keep what I'll show in the next class is the minimum distance property in fact the minimum distance is 2 par m minus r that's what makes it interesting right so guarantees of minimum distance and the next thing we'll show is the dual property also so after that we'll try to go towards the deeper this will stop here


One of the concept of the show was that we would have five women on the panel, but we decided that we wanted that if that woman was busy, that she could take the time off and be with her family due to things she needed to do. And what that said is that you'll hear people say, oh, Yolanda's created the show and she's the executive producer. But Madison Gray also co-created the show. And there came a point in her life that she needed to concentrate on. She wanted to have babies, and so she had to leave the show. And then she came back, and she had babies, and she came back. So that really is what the show is about. As the show grows, women grow, and their lives change, and the show change. And it's okay. It's okay as women that we change. We don't have to be fixed into this one identity. And it was important for me to say, it's great that Madison left, had our babies, but now she's back. And that's why she's an every-way woman. And I'm an every-way woman, too.