In chapter 8, we're going to be looking at verses 41 through 46, but I'll begin reading here in chapter 8 at verse 41, and we'll read to verse 48, and we'll get into our study. Luke chapter 8, beginning at verse 41, reading to verse 48, Luke writes, Behold, there came a man named Jairus, and he was a ruler of the synagogue, and he fell down at Jesus' feet and begged him to come to his house, for he had an only daughter, about twelve years of age, and she was dying. But as he went, the multitudes thronged him. Now, a woman having a flow of blood for twelve years, who had spent all her livelihood on physicians and could not be healed by any, came from behind and touched the border of his garment, and immediately her flow of blood stopped. Jesus said, Who touched me? When all denied it, Peter and those with him said, Master, the multitudes throng you and press you, and you say, Who touched me?  No, Jesus said, sometimes you want to. Jesus said, Somebody touched me, for I perceived power going out from me. Now, when the woman saw that she was not hidden, she came trembling and falling down before him, she declared to him in the presence of all the people the reason she had touched him, and how she was healed immediately, and he said to her, Daughter, be of good cheer. Your faith has made you well. Go in peace. Jesus is returned to the city of Capernaum. He had just been on the eastern side of the Sea of Galilee in a region called the Gadarenes, and while he was there, he had delivered a man, actually two men, who were severely demon-possessed. And as he had done that, the people there on that side of the lake had actually asked him to depart from their shores. Remember what it says in verse 37? It says the whole multitude of the surrounding region of the Gadarenes asked him to depart from them, for they were seized with great fear, and he got into the boat and returned. And so he had been asked to depart from one place, but according to verse 40, when he returned, the multitude welcomed him, for they were all waiting for him. So on the one hand, he is asked to leave, on the other hand, he is welcomed back, and now we're going to see from this sentiment, Please go away, we're going to see someone now saying, Please come. And that's what's taken place here through a man by the name of Jairus. Now Jairus is called a synagogue official, a ruler. As a ruler, he was really what we would today call an administrator. He was one who oversaw the order of service, and he invited people to come up, and they would read the scriptures or speak in the assembly. And as a ruler, he was more than likely aware of the growing opposition against Jesus Christ. There's no doubt about it. But also, he was more than likely a Pharisee. And so as a Pharisee, and also one who's aware of the mounting opposition, he still comes to the Lord Jesus Christ, and he still asks him, because he's in desperate need, he's at the end of his rope, and he needs help. And so what happens here, it says in verse 41, there came a man named Jairus. He was a ruler of the synagogue, and he fell down at Jesus' feet, and he begged him to come to his house, for he had an only daughter about 12 years of age. She was dying, but as he went, the multitudes thronged him.  Now when it speaks about him falling down, that is in the gospel of Matthew. Matthew chooses to use the word worship him. He fell down and worshiped him. The word worshiped in the original language in the Cornei Greek is proskoneo. Proskoneo speaks of somebody not only just falling down, but it speaks as an act of worship, of basins, and it could carry with it a humility. It involved kissing his feet. It would speak of him touching the hem of his garment. It would speak of him just laying on his face before the Lord Jesus Christ with humility. And what he's doing is he's throwing himself down on the mercy of God. He's asking God for help. And he's humbling himself to do so. The Bible in Proverbs 3.34 says, he mocks proud bakers, but he gives grace to the humble. And this is what he's doing. He is humbling himself before God. He's humbling himself and saying to him, I need your help.  It's the girl of his heart. It's his only baby. She's 12 years old, and she's now dying. And he loved this little girl. He loved her with such a great passion. He loved her with such intensity that he was beside himself with worry. I've shared this with you on a number of occasions, but it bears repetition as an illustration.  There's just something about them that just capture your heart. That's just the truth. And when my little girl, Corinne, was very ill on one occasion and she had a very high temperature and the doctor said we needed to put her into a tub of ice water in order to bring her temperature down. And I still remember she was less than a year old. She was a few months old, and so it's very critical that we bring that temperature down as quickly as possible, save her from damage and all. And as I've shared with you before, we filled that tub with water. And I had her in my arms, and she was so hot she was making my skin warm as I was holding it, and she was crying and clinging to me, and I still remember having to peel her off of my body as she would just hold tight to me, and she didn't want to let go of me.  And I put her in that tub, and as I did, I couldn't let her go. And I climbed in the tub with her, because that's what dads do. I thought, if someone's going to be cold, I'll be cold with you. That's just what dads do. You love them. You pray, and you say things like, God, if you could take that fever from her and put it on me, I can take it. Give me that pain. You know, my mom used to say that she'd get mad at the son when it was burning me. And I thought, well, that's a nice thought, mama. But you know what? I used to get mad at the son, too. If it was hitting my children, and they were in their car seats, and I'd hear them, you know, getting uncomfortable, and I'd turn around, and I'd see them sweating and hot. And I'd actually have this anger. How could you be hurting my, it's just a crazy thing, I know. But there's this intensity, there's this passion, there's this love that goes beyond anything that you could imagine. And that, I am sure, Jarvis had for his little girl. She's 12 years old. You see, in the Hebrew system, when a child reached the age of 12, she was moving from being a little girl into womanhood.  And this is something that he just wasn't ready to accept. This wasn't something he could deal with. And he comes and he asks Jesus for help. I'm sure that he is aware that Jesus Christ has been performing tremendous miracles throughout the north and into the south of Israel. According to Matthew chapter 4, verse 23, Jesus went about Galilee teaching in synagogues, preaching the gospel of the kingdom, healing all kinds of sickness, all kinds of disease among the people. And so he knows that the Lord Jesus Christ can heal, and also it's worth taking the risk. What more could he lose? And so he moves, he believes that Jesus will move on his behalf, and he comes and he humbly makes a request. And the request does have faith involved in it. Now, the Bible tells us without faith it's impossible to please him, and undoubtedly he does have faith as he approaches him. But as we look at this, I want to give you three thoughts about it, three things that you can see, three lessons you can learn from this. One, a first lesson that I'm going to glean from this, as I look at this man named Jairus, a man who is a religious individual who is well respected in his community and all, a man who undoubtedly has a love for God and all. Well, the first thing I want to point out is sorrow comes to all people on earth regardless of their station in life. Just because I'm a believer doesn't mean I'm going to be excluded from pain. Just because I'm a Christian doesn't mean that I'm somehow going to be taken away from the things that other people go through. We all go through pain and we all go through sorrow. So his advantages don't exempt him from pain because both the rich as well as the poor suffer loss. According to Ecclesiastes chapter 9 verse 2, all things come alike to all. One event happens to the righteous and the wicked, to the good, the clean, the unclean. To him who sacrifices, to him who does not sacrifice, as is the good, so is the sinner. He who takes an oath as he fears an oath. Whether you're good or bad, things occur to you and it happens to Jairus regardless of whether or not he's believer or not. You see, some people come to Christ because they think he's going to exempt them from the pain of life. That does not happen. He doesn't exempt you from the pain you go through. He just goes with you through that pain, but he doesn't remove you from it. That's part of life. Life is filled with pain. A second thing we note though is that he waits until the last minute to approach Jesus Christ. It's only when his daughter was at her worst that he approached him. You see, when you compare Luke's gospel with Mark, you get some insight in Mark chapter 5 verse 23 because in Mark 5, 23, speaking of the same incident, Mark says, he begged him earnestly saying, my little daughter lies at the point of death. Come and lay your hands on her that she may be healed and she will live. So he waits till the last moment. This child didn't have an immediate illness. It's something that probably had been, she'd been dealing with for a little while at least, and he waits till the last minute. And then third, the third thing we can see is in our time of sorrow and pain, we can come to Lord Jesus Christ and we can ask him for help. The Bible tells us in Psalm 50 verse 15, call upon me in the day of trouble. I will deliver you. You shall glorify me. Call on me. And so even though he's waiting till the last minute, even though she's now lying at the point of death, at least when he initially comes to see the master, well at least he came to him. He came to Jesus, he fell before him, he made his request of him, and he's gonna trust him. Jeremiah 32, 17 says, all Lord God, behold you have made the heavens and the earth by your great power and outstretched arm. There's nothing too hard for you. And so he comes to him, asking him for help. Now notice verse 42 it says, but as he went, the multitudes thronged him.  Now as this is taking place, verse 43, a woman having a flow of blood for 12 years who spent all her livelihood on physicians and could not be healed by any, came from behind and touched the border of his garment and immediately her flow of blood stopped. One, you see a little girl who's 12 years of age. Two, you see an older woman who's been suffering for 12 years. This woman had a blood flow for 12 years. You see, as Jesus is moving with Jairus towards Jairus's home, there's an interruption.  She may have had a tumor, she may have had a diseased uterus, but what has happened in her life is she has been rendered ritually unclean for 12 years. You see, according to Jewish law, whenever a woman was in her menstrual cycle, she was exempted from any physical contact with other people. Leviticus 15 verses 25 through 27 says, when a woman has a discharge of blood from any days at a time other than her monthly period, or has a discharge that continues beyond her period, she will be unclean as long as she has the discharge just as in the days of her period. Any bed she lies on while her discharge continues will be unclean as is her bed during her monthly period and anything she sits on will be unclean as during her period. Whoever touches them will be unclean. He must wash his clothes, bathe with water, and he will be unclean until evening. This woman has had no physical contact with other people because if she contacts him physically, they become ritually unclean and can't offer sacrifice and all, and so for 12 years she's been isolated. There she is in this throng, in this crowd. And here comes the Lord Jesus Christ. Now the Bible tells us that she didn't go quietly. I mean she actually had been working on trying to get healed. Notice verse 43, it says she spent all her livelihood on physicians and couldn't be healed by anyone. She had spent every penny she had to try to become well but medicine had no known cure for her and she's declining in health. Not only has she lost her health but she has also lost her wealth as she's been seeking healing and so what does she do? Well verse 44 says she came behind and touched the border of his garment and immediately her flow of blood stopped. I wanna share with you something that I think you might find pretty interesting about this passage here. Touching the border of his garment. I'm gonna spend some time looking at this with you. I actually have something I wanna share with you in a few minutes that goes beyond this but this is kind of like an introduction to that thought. To him of the garment. Why is that significant? And what garment are you speaking about? And why would she come from behind and touch him in that particular way? Now Mark 528 says that she came behind him, touched his garment and she said this within herself, if only I may touch his clothes I can be made whole.  Why is that significant? Well every Jewish male wore a rectangular or square shaped outer garment that today we would refer to as a prayer shawl. And on this rectangular or square shaped shawl, on each corner were tassels. The tassels had a blue thread in them. This was according to Levitical law. This is according to the law rather of Moses. In Numbers chapter 15 verses 38 through 40, God had said, speak to the children of Israel, tell them to make tassels on the corners of their garments throughout their generations, to put a blue thread in the tassels of the corners. You shall have the tassel that you may look upon it and remember all the commandments of the Lord and do them. And that you may not follow the harlotry to which your own heart and your own eyes are inclined. And that you may remember and do all my commandments and be holy for your God. Jesus was a Jew who observed the right understanding of the law. He would have worn that garment as it was appropriate for him, especially as a rabbi. So that's the garment that this woman is reaching up to touch. Now, when she comes up and touches the hem of his garment, that hem is in the Hebrew word, it's actually the word border or corner, and it's the Hebrew word kanah. And what she's doing is she's reaching to that particular region where the tassels are. Now, what makes this interesting is in the book of Malachi. In chapter four verse two, Malachi makes an interesting prediction about the coming Messiah. He says in Malachi chapter four verse two, to you who fear my name, the Son, S-U-N, the Son of righteousness shall arise with healing in his wings. The word wings in Malachi chapter four verse two is the word kanah, which speaks of the corner or the border. And so, during the time of Christ, a legend had already grown and was accepted that when Messiah came, he would have special healing powers in the hem of his garment. That's the reason why this woman is seeing him as Messiah and is thinking of the Levitical Law and Malachi's prophecy, and she's thinking of the hem or the border of the garment, and that's the reason she goes to Jesus and she reaches up to that border area because she believes that that is symbolic of Messiah who is to bring healing. And so that's the reason, very often I've wondered, why did she reach down to his garment? Why did she want to touch him in that way? The answer is because during the time of Christ, they believed that that symbolized the place of contact where Messiah who is bringing healing will perform healing on their behalf. We're gonna look at this a little deeper and take it a second, a little further on in just a moment. Moving on, what happens in verse 44 is immediately her flow of blood stops. When all other help has failed, her trust drives her to reach the one who can help her. You see, she had said, if only I may touch his clothes, I shall be made well. And then immediately the fountain of her blood was dried up and she felt in her body that she was healed of the affliction. Now, when she says I will be made well, the word well in the Greek, and I'm hoping I'm able to communicate this, as the Lord has spoken my heart about this, the word well in the Greek language is sotso, s-o-z-o. The word sotso is a word that is used for health, but it is also a word that is used for being made whole or complete. And salvation, as we'll look at it in just a moment, is more than simply being delivered from sin. Salvation is going to include a wholeness that takes place in your life. And I wanna develop that in a moment, but in verse 45, Jesus said, who touched me? Now, people are denying it. So Peter says, look, you see this crowd around you? Now, it's not as if Jesus is unaware of who touched him. He's doing something else. What he's doing is he's noting that somebody reached out in faith and touched him. So what he's asking for is a confession of praise. Because when blessings descend from heaven, we have to take time to give thanks to the one who gave us those blessings. Now, the people are denying it. And Peter is saying, look, you see this multitude here? These people are gathering around to receive a touch. They're pressing upon you. It may be that Peter's a little anxious to say, let's just keep moving and get out of here so we can get to the little girl and all. But Jesus is in no hurry and he wants to wait so he can minister to this woman more completely. Now, verse 47 says, when the woman saw that she was in hidden, she came trembling. He's looking at the crowd. She knows that she's been detected. She comes forward. Jesus doesn't want to scold her. Jesus wants to bless her. So he says to her in verse 48, be of good cheer, your faith has made you well. Now, this is what I want to talk to you about for just a moment. And he goes on to say, go in peace. She's become an evidence of the grace of God. She has become somebody that is an evidence of the works of God being worked in somebody's life. And so he encourages her. But here's something the Lord has been speaking to me about this last couple of weeks that I want to share with you. I want you to see that he says to her, go in peace. And I want to speak about that for a minute here. The word peace in the Bible is used in a variety of ways. When you use peace, you can speak about peace between nations. You can speak about peace between people. You can speak of peace between God and man. It often speaks of a cessation of antagonism. It speaks of a ceasing of hostility. And when you're at peace with man, at peace with nations, at peace with God, there is no longer hostility taking place. But the Hebrew word for peace is the word shalom speaks of more than simply an absence of conflict. It speaks of the presence of God's goodness. It speaks of wholeness. It speaks of completeness. So Jesus was blessing her in her entire being and not her physical health alone. You see, peace speaks of being reconciled to God. It speaks of being brought into harmony with him in the whole person. Salvation speaks of an immediate reconciliation with God. When you speak about salvation in the Bible, on one hand, it can speak of a legal process because God is a judge. We have broken his law. And so when I have peace with him and I have been reconciled to him, God deals with that through Jesus Christ in order that I might have a relationship with him. Jesus took my place. He died on a cross. He paid my penalty and he gets what I deserve that I might receive what he really deserves. And so when that takes place in salvation, when I understand that I have a relationship with God through Jesus Christ, I've been reconciled to him. I can now have peace with God. I am no longer in hostility. He's no longer in opposition to me. And because that warfare is over, I can walk in peace with God. I can enjoy fellowship with him. And as a result of that, I am ceasing from hostility. And as a result of that, I am now being blessed by God. But here's the problem. And this is what the Lord has been laying on my heart recently about people that I know and ministry as I see it. I think that sometimes people think of salvation only in legal terms. For them, salvation has boiled down to having a relationship with God.  I have a personal relationship with Jesus Christ. And what happens is very subtly, salvation becomes something that is really all about me. It's all about what I have with God. It's all about the blessings I have with God and all of that. But what happens is if I remain there, I am gonna remain self-centered. I'm gonna be unhealthy. I'm not gonna be healed. I'm gonna remain a broken person because I haven't understood that when Jesus is saying to this woman, go in peace. He's saying a lot more to her than simply saying your blood flow's dried up.  What he was saying to her is you have been cut off from God. You have been cut off from man. The reason you have been cut off is because of your blood flow, which is symbolic or typical of a relationship that has had a cessation because of something creating an obstacle. And so what I have done is I have taken that obstacle out of your life. But that isn't so that you can continue on and just live as a broken woman who suffered for 12 years being ostracized and ignored and isolated. I didn't heal you so that salvation is all about you. I healed you so that you can become a whole person so that you can take what I've done in your life and actually communicate it to somebody else. What we live in today is a generation of people. If it's not entertaining, I don't want it. If it isn't something fun, I don't want to do it. If it requires me to actually change or see something about myself that isn't healthy, I don't want to change. You have to accept me the way that I am, but that's not salvation, you see. That's not what God called us to. God didn't call me to please myself. God didn't call me to live for myself. God called me to realize that I am broken, a broken vessel that he has healed so that now I can carry within me his spirit and live in such a way that his gospel is permeating my life and the lives of others as it pours out of me. And so what I have to be is I have to be healed completely, not just say, well, I've got Jesus in my heart. I have a personal relationship with God, but I want to take that and give it to other people and that happens when I take my eyes off myself, when I stop looking at just me and my problems and my sorrows and my pains. You know, I was in the gas station a while back now and a young man in his early 20s pulled up and began to put his paycheck in his gas tank. And he had a beautiful car. I happened to like cars, so I know what it was. It was a Lexus, a black Lexus and nice wheels and it's just a very nice ride.  And very handsome young man, I might add, very good looking guy, dressed very nicely, driving a nice car and his music's bumping and all of that and I can hear it. And I'm listening to the words of the music that I could make out and the words were saying things like life is bad, things are terrible, everybody hates me. And I'm looking at this kid and I'm thinking, kid's driving a Lexus. The guy's as handsome as they come. You know, he's dressed nicely, but he's got that, yeah, yeah, life is bad looking. I'm thinking, whoa, man. You have, you know, you want to see bad.  You want to see a bad ride. That was bad in the literal sense. It was bad. I had an AM radio with one speaker and it was busted. I mean, now that's a bad car. And I didn't run around saying, life is bad and I'm so miserable. I mean, I just can't get into that. And I trip on, it blows my mind. I said, whoa. What's, you know, what are you so mad about? What are you so upset about? You're living better than I ever did at your age. You're so much better than I ever did at your age. And yet, I mean, you talk to people, you ask them how are things going, oh man, you're not that good, they're not that good. They're not that good. Man, what happened to you? God wants to take that self-centered mentality and break it. This woman had every reason to say, I've had it tough. 12 years of isolation. I haven't been able to be touched by anybody for 12 years. Now, some of you say, you know, that sounds pretty good to me. I wouldn't want anybody. I don't like people touching me.  I don't wanna hold that person's hand. You know, I don't like being touched by people. But that's because you have a choice as to whether or not you can or cannot be touched. What would happen if you simply could not be touched, that nobody could reach and touch you, not just for a week, not for a month, not for a year, but for 12 solid years. See, human beings need touch. We need to be touched. Years ago, I was a behavioral science major in college. I read about a study that was done in the Middle Ages, actually, through a particular king who ignorantly wanted to know what kind of language babies would speak if nobody ever spoke to him. And so there was a nursery with babies that were there and were never spoken to and never handled. The only times these babies were handled was when they were fed and when they were changed. And he wanted to see what language, if there's some kind of innate language within people, he wanted to see what language they would speak, but he never was able to discover that because every one of those babies in that nursery died. Every one of those babies died because none of those babies were health. None of those babies were ever held by anybody and loved by somebody. And as a result of that, they just languished until they finally just expired. And so the experiment was not a success because they never even lived long enough to make sounds like that called language. We need to be touched. We need to be held. We need to be loved. And that makes us whole. And when Jesus was speaking to this woman, he was saying, your faith has made you well. Go in peace. He wasn't simply saying to her, go in life now in an absence of conflict with God alone. He was saying the absence of conflict with God is good, but I'm touching you in every element of your life. Your emotions can be healed as well as your physical. Your spiritual life that is broken is now being made alive by my spirit. I'm doing a work called salvation. And so when she had said, if I but touch him, I can be made whole. She was actually getting something she didn't bargain for, something she didn't really understand. Yes, you can be healed, but you can also become a real person, a whole person, somebody who's put back together again. You know, Humpty Dumpty had a great fall, and nobody could put Humpty back together again. But we're not Humpty. We're not Humpty Dumpty. We're not eggs. As a matter of fact, it's interesting. We don't even know that it's an egg. Does it ever say Humpty Dumpty the egg, but that's something else, you know? We always think it's an egg. I don't know what it was. All I know is he fell down and was broken. But nobody could put him back together again, but you wanna know something? God can put us back together again. And that's what the Lord has been teaching me and has been trying to remind me of. He's saying to me, listen, David, when I say to you, go in peace, I'm not simply saying look at your sin question is forgiven so you can continue to be a broken person, running around still trying to get people to satisfy every women need that you have. I'm saying I'm healing you so that you can carry my spirit and my message to people who are broken so that they can be healed too. It's not all about you. And when you talk about your personal relationship with Jesus Christ, that's true. You have a relationship with him, but God didn't intend us to have a personal relationship all by ourselves, but we're to be inviting people into the kingdom of God. And so when she goes out in faith and all and goes in peace, he's going in wholeness. And that's what God wants to do in your life too. He wants to make you whole. Now, verse 49, while he was still speaking, someone came from the ruler of the synagogue's house saying to him, your daughter's dead, don't trouble the teacher. But when Jesus heard it, he answered him saying, do not be afraid, only believe, she will be made well. When he came into the house, he permitted no one to go in except Peter, James, and John, and the father and mother of the girl. And now all wept and mourned for her, but he said, do not weep. She's not dead, but sleeping. And they laughed him to scorn knowing that she was dead.  Her spirit returned and she arose immediately. And he commanded that she be given something to eat. And her parents were astonished. But he charged them to tell no one what had happened. He's frantic. There is this interruption. Jesus wanted to bring the master to his house immediately. He had originally said, my daughter is at the point of death. She's about to die, you need to come now. Jesus is coming and you can almost see Jesus as he's wanting the people to get out of the way so that the master can get through so I can get him to my house so that he can do something for my little girl. But the crowd is thronging and pressing and there's no way he can get through. And now this woman has the nerve to reach and touch him and then Jesus stops. What do you think you'd be feeling like? What if you were in an ambulance and your child is in the back there and it's a traffic accident and there's no way around it. You can't get past it, it's just stopped. What would you feel like? Would you be so tense and so anxious, angry? Would you be looking at the door thinking maybe I can just get out of here and run? I would be going through 1,001 emotions at that time. How am I gonna get there in time? How am I gonna make it in time? She's at the point of death. We've gotta get out of here. I ministered to a woman years ago who told me how her nephew had had a serious accident. He had been in a lake and drowned and they had pulled him out of the lake and they threw him in an ambulance and off they went through town and as they were trying to get through town there was a traffic jam and the baby died in the back of that ambulance. Never made it to the hospital. Never made it to the hospital. Jerus is there and he's seen this take place and he's gotta be anxious. And as he's there frantically waiting he hears words that are gonna stagger him. Your daughter is dead, do not trouble the teacher. And when that comes, imagine what you would feel like. Jesus obviously overhearing it as they're whispering to it. Verse 50, Jesus heard it and he answered to him saying do not be afraid, only believe, she'll be made well. Fear, fear is the opposite of faith. And as Jesus speaks, he only has two options, either believe him now or don't believe him. But Jesus has spoken a word to him because he knows that he has to encourage him and so they finally make it to the house. Verse 51 says he came into the house, permitted no one to go in except Peter, James and John, father and the mother of the little girl. And as he enters in, verse 52, all were weeping and mourning for her. You see, this was a man who had had status in the community and so there were people who were there, more than likely professional mourners.  It was to reflect emotional grief and confusion and all. And so there's all this sound going on in there when Jesus walks in and as he walks in, he says in verse 52, do not weep, she's not dead but sleeping and they laughed him to score and knowing that she was dead. They derided him, they humiliated him. So what's he do? Well, he kicks him out. He kicks him out and he begins to minister to the little girl. Notice verse 54, he put them all out, he took her by the hand and he called saying little girl arise. Oh boy, wouldn't you like to have been there? Wouldn't that be incredible? You know, I've performed a number of funerals, quite a number of funerals. And I've attended the death and I've seen that monitor as it, the heartbeat stops and it flat lines. And you stand there and you just see that and it's gone. It's over, it's nothing else you can do. Been there, I've seen that, experienced that. My mom tells me how my grandmother who was born and raised in Mexico, the little girl went to a funeral as a little girl and in the chapel, they had the coffin and the person who had died and the coffin was open, the lid was open but they hadn't embalmed the person they were burying and rigor mortis hit in such a way that there was a muscle contraction as my grandma was there in the church, the person in the casket sat up. Can you imagine? The whole church was emptied in a moment. They were out the door man. I'd have been leading the parade.  Ooh, I don't know. Well, in this, that would be scary. In this case here, Jesus has only three witnesses along with mom and dad. He's ministering to the inner circle, Peter, James and John and he's teaching them lessons of faith and he speaks to her and as he says arise, she regains life and it says that she arose immediately and he commanded that she be given something to eat. She's brought back to life. Her parents are astonished. They wanna tell people exactly what happened but notice verse 56, he says, tell no one what has happened. Of course they're amazed. Of course their minds are blown completely by this but he's charging them to tell no one what had happened. Why? Well, because he had a lot of work to do and such a startling miracle could cause miracle hungry people to follow him. And so to prove that she was alive, he gives her a meal that demonstrates that she's alive and reminds them that she has needs that still need to be met. And so they're rejoicing. They're rejoicing. Their 12 year old is alive but I wonder, I wonder if they were rejoicing when she became a teenager. Now that's another question, right? They're happy. They're blessing God. They're excited because God broke into their sorrow and healed them. So Jesus Christ touches a woman and he brings her to wholeness and he touches a little girl and gives her life demonstrating that he's capable of giving us life and a wholeness if we trust in him.


So in these excerpts we'll see Kant trying to do two things, he's trying to answer two questions. The first question is, how should I live my life? Pretty much the topic of the whole semester. The second question is really in response to the answer to the first question. So Kant is posing this question, how should I live my life? And his answer is that you should live a life according to duty. The second question then, it follows very quickly from that is, well then what is my duty? So for Kant the answer is going to come from rationality. It's not so much allegiance to one's country or even to a set of moral principles or anything like that. Rather what your duty is, is going to be determined by rationality. And rationality is determined by the will. It's also important to remember something about Kant's theory. What it's giving us is a conception of morality where more rules are absolute. That means that these rules have absolutely no exceptions. You must obey the rules no matter what else follows. This is contrasted to what we might call Ketter's paribus laws or Ketter's paribus rules. But Ketter's paribus means in the Latin it is all other things considered equal. So the idea, and this is pretty typical, we can see from morality as a set of rules all other things considered equal. So all other things considered equal, you know, you don't lie.  Now suppose something more important, what we think is more important is at stake, say people's lies. Then we think it's perfectly fine to lie. So Ketter's paribus rules, Ketter's paribus laws, which pretty much encapsulates a lot of what we've been dealing with so far, are rules that you follow all other things considered equal. But when you travel outside normal circumstances or typical circumstances, you have to re-evaluate the rules. That doesn't mean anything goes, but you have to re-evaluate the rules. Kant strenuously disagrees. Morality is absolute. Morality is without exceptions. For Kant, the only thing that's good, the only thing that matters, what is good is the will. This means that whatever decisions you make, it doesn't matter what the consequences are. As long as you willed in the right way. It doesn't matter what you will. Only matters is how you will it. It doesn't matter what you decide. The only thing that matters is how you decide upon it. It doesn't matter what happens as a result of your decision. Something dreadful happens, something wonderful happens. That doesn't matter. If you will in the wrong way and something wonderful happens, you haven't done something moral. If you will in the right way and something terrible happens, you have done something moral. Now the consequences are unimportant for Kant. The only thing that matters is the will. You might be tempted to think what Kant means here by how one wills by something along the lines of what were your motivations. What did you intend to happen? That doesn't matter.  That doesn't matter. The only thing matters is how you will. Not what you will, not even what you intend to happen, but how you intend, how you make a decision, how you will. You might wonder for Kant at this point what's supposed to determine how you will, what's the important relevance. If it's not consequence, if it's not character, it doesn't matter your intentions or motives or the results of your actions. What is it that matters when you will? For Kant, the way that matters how you're supposed to will is by conforming your will to duty. You might ask yourself how do I know what my duty is? Is it to country? Is it to some moral value? That's not it for Kant. Remember, for Kant the only thing that's good is the will. What does the will do? It makes decisions. It's rational. Your duty, then, is to rationality. Rationality is self. Not to any particular will, not to any particular person, but to rationality itself. Now, to illustrate what Kant means by rationality, I'm going to start with a notion, self-defeating actions. Now, this is important to remember. Self-defeating actions is not a concept that Kant describes, at least not explicitly. But I'm going to use this idea of self-defeating actions in order to illustrate the kind of rationality that Kant's getting at. Again, I want to be clear that the concept of a self-defeating action is not Kant's concept, at least not explicitly. This is something that I put together to help illustrate what Kant means by rational. He doesn't mean rationality in terms of truth. He means rationality in terms of practical reason. Now, what it's getting at here is that every action, at least the intentional ones that we perform, are for a purpose. So, it's a matter of practical rationality that if you want to be healthy, then you should eat, write, and exercise. That's practical rationality. Performing those actions achieves the purpose. A self-defeating action is an action which actually defeats the purpose for which you're performing the action. So, considering health, we might think of something silly as, oh, I don't know, eating nothing but Milky Way's candy bars. So, the idea is, well, I'm going to have Milky Way candy bars and just have just enough to reach my calorie limit, but I'm not going to go over that and that's going to be healthy. That's a self-defeating action. Because there's all kinds of things that you're not getting with those Milky Way bars from vitamins to proteins, well, you're getting proteins, but vitamins and certain minerals, all you're getting is a bunch of empty calories and fat. Okay. So, that's perhaps kind of a trivia example of a self-defeating action. There's lots more. There's lots of examples of self-defeating actions. We kind of tend to do these a lot. So, suppose something like this. You and a friend are having a discussion and you're trying to reach a point of agreement. Say you're debating politics and you're trying to reach a common ground with this friend of yours. You're trying to reach a point where something that you both can settle on and then move from there. But after a while, you aren't able to do this. So, what do you say? You say, well, let's just agree to disagree, but that's a self-defeating action. You're trying to say, well, we can agree to disagree as in saying this is the common ground upon which we will start from. But you haven't reached a common ground. All you said is we're going to, our common ground is the fact that we don't have a common ground. That defeats the purpose of the discussion. You might have ended the discussion, okay, but you haven't ended the disagreement. The point of the discussion was to find the common ground. The point of the discussion was to find an agreement from which you two can begin and move from there. There are other examples of self-defeating actions. As I say in the text, or I wrote in the text, you have often heard people say question everything or question authority. Well, an imperative is what's given by an authority, and that's what that command is. It's an imperative, question authority. Well, that means that you're supposed to question the very authority that's supposed to question the authority. Supposedly changes bait, question everything, including that command. Somebody says question everything, say why? Or they say question authority is like including you. You're not the boss of me. So self-defeating actions, again, are actions which defeat the very purpose for which you're performing the action. So this brings us to imperatives. Imperatives are these obligations or principles upon the will. That's what's demanded by practical reason. And remember for practical reason, the idea is that you perform these actions to achieve this goal or to achieve this purpose. So for con, imperatives come in two kinds, hypothetical or categorical. Now, hypothetical imperative is an action or was demanded of you by practical reason to fulfill some further good, some further purpose. So as an example of a hypothetical imperative, if you have the goal or further purpose of health, you ought to eat, write, and exercise, including pull-ups or walking. For another example of a hypothetical imperative, suppose you're good or your purpose is education or completing a particular course. In order to do that, you would have to study, you'd have to read and take notes and take tests. Now that might be narrowed down even further, right? Hypothetical imperatives for a chemistry class might be different than an English literature class. For a chemistry class, hypothetical imperatives would involve going to the lab and carrying out experiments. But that hypothetical imperative would not be the same for an English literature class. Now these hypothetical imperatives are hypothetical and the said said, if you were to have this goal or if you were to have this good that you're pursuing, then you'd perform these actions. That doesn't sense the wish of a hypothetical. Categorical imperative is different. A categorical imperative is an imperative you follow regardless of what good or purpose you have. This is what's good, what Kant calls good in and of itself, performing the action in and of itself. Now that's the definition of a categorical imperative. Kant thinks that this definition of categorical imperative leads to only one categorical imperative. We don't have a set of them, we just have one. This brings us to Kant's argument then for the categorical imperative. Now for Kant, the categorical imperative is that you must act in such a way that what you act, you can will into universal law. In universal law he means that anybody can do it and you're even more to the point that anybody does do it. So that's kind of extreme, right? Everything that's moral is what's rational. And what's rational is that you act in a way that can be made into universal law. Now it's got some reasons for this. So as we saw from the beginning, he's just starting with this idea that rationality is what matters morally. So pretty much maybe quite simply or stupidly it was like if you're acting irrational then you're acting morally. That's kind of the first major step. Well say you suppose or if I act or one acts in a way such that what and what acts, the acts and what performs cannot be made into universal law. Well if you're doing that, if it can't be made into universal law then you're acting in such a way that a person's decisions can be obstructed or stopped or hindered. So if you're acting in a way that can't be made into universal law then you're acting in a way such that somebody's decisions, somebody's will can be obstructed.   Okay. Well, if you're acting in a way where somebody's will can be hindered, you're acting in a way where the will, anybody's will, can be hindered.  Well, remember what matters for Kant. It's the will, not your will, but the will, its rationality itself. All wills are created equal in Kant's eyes. It doesn't matter whose will it is. Just like it doesn't matter what is being willed, only how it's being willed. It doesn't matter who is willing, it only matters how the will is willing. So if you're acting in a way where somebody's decisions can be hindered, then you're acting in a way that can hinder your will, that can hinder your decisions. Well, if you're acting in a way that can hinder your decisions, you're acting against your own will. You are making the claim anybody's will can be hindered, including mine. That's not going to work, right? That's contrary to rationality. That's contrary to practical reason. If you're acting in a way where your will is hindered, that is contrary to reason. Okay. So that's irrational. And as we saw before, if it's irrational, it's immoral. And at least Kant, since what started this whole deal is the idea that you can act... What started this whole deal is acting in this way. If you're acting in this way where it can't be made to universal law, that's what's immoral. Well, if that's what's immoral, then acting in a way such that your action could be made to universal law, that's what's moral, that's what's rational.


The value of an option contract can be determined if an investor buys such a contract well before the expiration date. The value of a call can be determined using its upper and lower bounds. By lower bounds, let's see an American call which is in money prior to its expiration. An example is that we have a stock price of this American call at $60 and the exercise price is $50. This option cannot sell below $10. If the option, let's say, sells at $9, then there is an arbitrage profit of $1. Means that buying the call at $9 with the exercise price of buying the underlying stock at $50 make a total cost of $59 and then selling this stock at $60 will yield the profit of $1 to the holder of this contract. So this $1 is termed as an arbitrage profit. Now we will see that the access demand for this option contract will quickly rise the option as the option price goes to $10. So which is the difference between the stock price of $60 and the exercise price of $50. In this contract, the option price is likely to go above $10 and the rational investor will pay over $10 only in a case if the price of the underlying stock goes above $60 before the expiration date. For example, if the call sells for $12, then the option's intrinsic value is same as we see it is $10. The $2 will be termed as a premium and that is a time premium because this remaining $2 in which is called as a time premium. This is the extra amount that the investor is willing to pay due to the possibility that the price of the underlying stock will go higher. So far as the upper bound is concerned, the question arises does this upper bound exist as well? By upper boundary, we means the price of the underlying stock or the PS. There is no higher value for the option to buy stock at a price of the stock itself. A call option can be used to buy a common stock with a payment of the exercise price. It is better to buy the stock if we can buy it at the price below the price itself. In the graph, we see two bounds colored in red. The value of the call lies between these two bounds. What are the factors that determine the value of a call contract? These factors can be grouped into two classes. The first class is the features of the option contract. In this class, we have two further factors. The first is the exercise price and the second is the expiration date. Any increase in the exercise price will reduce the price of the call. For example, for a given stock price of $50, the exercise price of $50 will reduce more value of the underlying stock if then the exercise price of $40. This means that any rise in the exercise price of $40 beyond this value, the value of the call will go down. So far as the expiration date is concerned, any increase in the expiry date will enhance the value of the call with the other call having similar rights. For example, an American call with maturity of 9 months and the same rights will worth more over the same call expiring in 6 months. The second feature is the characteristics of the stock and market. And we have two further classes in this class that is stock price and the interest rearsome. So far as the stock price is concerned, keeping other things remaining the same, the higher the stock price more valuable will be the call. This means that any increase in the stock price will increase the value of the call. For example, at a stock price of $150, a call with the exercise price of $100 will be more worth than at a stock price of $80. And so far as the interest rate is concerned, the buyer of a call does not pay the exercise price until he exercises the option. And if he does so, this means that delaying the payment worth more valuable during the higher interest rate periods than making payment during the less interest periods. There are factors that can be used to determine the value of an option contract like the calls contract. Now, the effect of three factors on the value of put are the opposite of the three factors that determine the value of a call contract. For example, puts market value declines as the stock price increases because the puts are now in money. When the stock sells below the exercise price, the value of put with a higher exercise price is greater than the value of an otherwise put having the lower exercise price for the similar reason that is happening in the first case. A higher interest rate also adversely affect the value of a put contract. The effect of other two factors on the value of put are now similar to the factors that affect the value of a call contract. Like the value of an American put with a distant expiration date is greater than the identical put with an earlier expiration date. And the value of a put increases as a result of volatility of the underlying stock.


Our lives began with resisting staying in a space that was too small. We yearned to breathe. We are a revolution, a necessary part of our evolution. It starts with our hearts, is expressed through the arts, it feeds our souls, it nurtures our lives when we are the love we seek.


Welcome back to our lecture series math 1050 college algebra for students at Southern Utah University. As usual be your professor today, Dr. Andrew Misseldine and this lecture 43 also in lecture 44. I want to talk about well basically story problems involving exponential functions. How do we model things using exponentials and why should we model things using exponential functions? It turns out that many natural phenomenon have been found to follow the law that an amount a varies with time according to the following formula you see right here. The amount a is equal to some initial amount a not times e to the k t where t is some measurement of time and k is going to be some growth rate so different things might grow at different rates. So we have that initial value and so this right here is often this formula is often referred to as exponential growth or sometimes called uninhibited growth in contrast to some other growth models we'll see a little bit later exponential growth. It turns out we've seen this formula before we wrote it in a slightly different way a equals p e to the r t pert right continuously compounded interest is an example of this type of exponential growth that interest grows exponentially. Okay, and when we talked about compounded interest, we gave some idea of where this number e came from as the number of compounds was allowed to go towards infinity, we are able to pull out this number e. That is there was no break in growth, right. So when it comes to like population growth that often is a good model right that they're when you have a certain species that you're watching whether it's humans or bacteria or bunnies or whatever. If you know if there's like seasonal type birth right like you know bears only have their babies in the spring or something like that right then this wouldn't be an appropriate model at least not from a month to month but maybe from year to year that would be appropriate. But and so the idea is if there's no like noticeable break in the growth right there's no like seasonal growth or something like that then this idea of continuously compounded growth is appropriate and that's where this exponential growth comes from the basic idea behind exponential growth. Is that the growth rate is proportional to the current population the bigger the population is the faster the population will grow and that's that's the main idea behind this exponential growth. We can use that to grow talk about population which we'll talk about we've already done some financial examples, and we'll see also later this example that we can use this this growth model also to represent decay models right. So when you have this expression e to the K, like we see in this formula right here, if K is a positive number that means e to the K will be a positive base that is a base greater than one, and therefore it will represent a growth model when K is positive. On the other hand when K is negative, you're actually going to be taking e to a negative power right that to give you a reciprocal your exponential will have a base less than one and that causes it to be a decay model. So when K is positive, this means growth. When K is negative, this means decay. And so sometimes it's appropriate to have a decay model we'll see that if you have a hot object and you put it in a cold environment, the temperature actually will decay over time it gets cooler that we can see that with Newton's law of cooling. We'll also see later in this lecture, the idea of radioactive decay that the mass of an object goes down over time as atoms fall apart in the with the radiation there. Again, those are all some examples we'll see in this lecture so for this current video. Let's consider a very basic exponential population growth problem. So we have an initial population count of 500 in a culture so culture just means a collection of bacteria right here. So we have 500 the initial bacteria count in a culture is 500. A biologist later makes a sample count of the bacteria and the culture and finds out the growth rate is 40% per hour. Okay, so our first question is can we come up with a formula to model the growth of this bacteria right here. So let's notice some observations we made. So the initial bacteria was 500 so our initial amount is going to be we can call it the initial population that turns out to be 500. Okay, because our goal for a formula is going to look something like the population is going to look like an initial population times e to the kt that's what we're trying to figure out here. So we have the initial population is 500. The bacteria is growing at a rate of 40% per hour so this tells us two things. One T is going to be measured in hours right so we're going to talk about hours, hours since, whoops for a letter there, since the start, whatever that is. So the 500, the 500 mark, and then our growth rate k is going to be 40% so 0.4 per hour. When you talk about your growth rate rates are always ratios right it should be something per whatever right so it's going to be per hour in this situation here. So when we put that together we see that our our model is going to be the population with respect to time is going to equal 500 e to the point 40 and we're going to measure their growth in hours so that's our formula. We're going to be using to model this and so then we can ask questions like okay what is the estimated amount after 10 hours. So after after 10 hours how many bacteria should we expect to have well essentially what we're trying to do is we're trying to compute p of 10 right so we're trying to figure out 10 hours here would mean that T equals 10. So that's where we need to compute what's p of 10 so we would take 500 times e to the point four times 10, which point four times 10 of course just before, but we're going to get e to the fourth right, you know, given e is some irrational number 2.7 etc etc right. I'm not going to bother doing this without a calculator so use a calculator to help you out here. A consoled your calculator is going to tell you that e to the fourth is approximately 54.5981 try to have a lot of decimal places here. It kind of depends on what you're trying to model here if in this case we're talking about bacteria bacteria are organisms you can't have a fraction of an organism it's either alive or it's dead right you can't just take a fraction of it. It's like oh we're going to count the kidney of this person or we're going to count the. I don't know the nucleus of this bacteria know you got to count the whole thing so you got around to the nearest integer, but add a couple extra decimal places to keep track of things right. Because of course if you multiply this by a big number that's going to cause the decimal to move over a couple we need to have a lot of decimals here in a scientific setting we might be paying attention to significant digits. We're not going to worry about that in this mathematical setting right here 500 times this approximation is going to give us 27,300. Right if we round to the nearest decimal and again I should probably mention that these of course are approximations that we were exact up to e to the fourth. But after that one started console console dinner calculator these are approximations so we should expect about 27,000 bacteria. After 10 hours of growth assuming their growth rate remains constant throughout that duration and so again this is just the typical example of how one does calculations with exponential growth.