Well, I invite you to turn in your... Actually, I don't invite you, I command you in the name of Jesus to turn in your Bibles to the book of Psalm, Psalm 102. We're just going to read two verses as we look tonight at another attribute of God, the immutability of God, or the fact that God never changes. Psalm 102 verses 25, 26 and 27. Of old you laid the foundation of the earth and the heavens are the work of your hands. They will perish, but you will endure.  There are other texts to which we might have referred in in Malachi 3, God declares, I am the Lord, I do not change. James 1.17 says that there is no variation with God, not even a hint of his turning away from what he is. And this is the doctrine of God's immutability. God does not change. In fact, God cannot change. Now that's only logical, you will agree.  He cannot be any greater than he already is in any of his attributes. I mean, there are no degrees of perfection. You can't say, well, he's kind of perfect. No, if you're perfect, that's it. If God were to change, it would have to be one of two things. It would have to be an upgrading of his nature, and that would mean that he's defective now. That would mean he's not perfect. And if it's not an upgrading of his nature, it would have to be a downgrading of his nature, and that would mean he wouldn't be perfect then. So God were to change at all. He wouldn't be God anymore. It's the mutability of man. The fact that man is capable of change that explains how he could sin. This is the question that's perplexed theologians for thousands of years. You think of Adam and Eve in the garden. Perfect man, perfect wife, no garbage to take out, no arguments about anything. They had everything they could possibly have wanted, and they did not have a sin nature. How could sin look good to them? I mean, when Satan comes along with his temptation, what in the world appealed to them? So everybody asks, how could man have sinned? It's because, as the Bible tells us, he was created holy and upright, but capable of change. Any change from a holy state would have to be to what? An unholy state, right? It could only be a downward slide, not an upward one. If you're created in holy and upright, and you're capable of change, and if there's any change at all, it would have to be to an unholy and sinful state. Now only God is immutable. God has no beginning. Every other being is a created being, so that's a mutation to go from non-being to being. To restate the doctrine, God, with all the perfections of his nature, is without any variation. He is now what he has always been and what he always will be. God is the same as he's always been. He will not change. Again, he cannot change. Now let me spend some time explaining this, because it is very important to our doctrinal foundation. God sees all things in continual motion beneath him, while he remains fixed, constant and unmovable. His wisdom and power, his knowledge and will are always the same. There's nothing greater than God, so no external forces or causes could affect change on him or in him. And he will not change himself, because that would mean he thought he could improve somehow. Which he cannot, or that he would desire to be less pure than he is, which he will not. God is eternally the same. Now immutability itself, and if the word immutable throws you, your kids know what that means, because they know about teenage mutant ninja turtles. That's the word mutation, change. Immutability itself is not a perfection apart from God's other attributes. For example, it's the greatest misery and imperfection of the fallen angels that they are immutable in their malice towards God. But God is infinitely good, and infinitely wise. He is infinitely holy, so it is a perfection necessary to his nature that he's immutably good. Immutably wise, immutably holy, along with all of his other attributes. God is immutable in all of his attributes. What I mean by that is this, God is as wise as he can be, and he'll always be exactly that wise. And this is why God never changes his mind, because God will never get new information that if he'd had before, he'd have made a better decision. And that's why we waste so much time praying as if God needed more information. I was in a church service in Pittsburgh some years ago where they asked one of the elders to pray before we took the Lord's Supper and he stood up and this is what he prayed verbatim. God, you may not know this, but my neck whipped up. I thought I was going to need a neck brace from the whiplash. You may not know this, but Mrs. Brown is in the hospital. He may not know. Who are you praying to? You may not know this. Who does he think putter there? God is as good as he can be and he'll always be that good. He's as holy as he can be and he'll always be that holy. He's as loving as he can be, etc., etc., etc. And this is true of all the divine attributes, his sovereignty, his self-sufficiency, his omnipresence, his power, his knowledge, his faithfulness, his anger towards sin and sinners, his grace, his goodness, and his love. The New Testament tells us that he is the ever-blessed God. In other words, God can never be anything but happy because that's what the word blessed means. God ordains everything that comes to pass and everything he ordains pleases him since he has ordained it. God obviously could never be displeased with something he had ordained to come to pass. Any theology that has God mad at himself is bad theology. Well, yeah, I ordained it but I wasn't happy about it. No. Now if you were to ask about the passage where it says, I take no pleasure in the death of the wicked and ask how that can be reconciled with the eternal happiness of God, here's how I would answer that. Sometimes when we go to a passage in the Bible, we can't always say with certainty what it does mean. Not every passage is as clear as every other passage. And sometimes we just have to go to the continuum of Scripture to make sure we know what it doesn't mean. Well, what does that passage mean? Well, I don't know but I can tell you what it doesn't mean because the Bible doesn't say one thing in this verse and another thing three chapters later. Not the opposite.  No sinful pleasure in the death of the wicked.  There's some people we all know in our lives that they go to hell, that'd be okay with us. And we won't mind watching them squirm. That's not God. You can't have God at odds with himself. Someone else asked me one time how could God be eternally happy when it says he's angry with the wicked every day? The answer is it makes God happy to be angry at sin. God always is happy when he acts like himself, which is all the time. He never acts like anybody else, couldn't be otherwise. Any other response to sin would be a complete betrayal of his holy character. If God didn't hate sin, he wouldn't be loving his own purity. You can't hate A and non-A at the same time, at the same place. You can't love this and its exact opposite. You can't love fruit cocktail and steamed broccoli at the same time in the same place. Those two are exact opposites. If God changed for the better, he couldn't have an eternal pleasure in what he was before the change. If he changed for the worse, he couldn't be ever blessed in himself after the change. Because according to the diminishing of his state would be the decrease of his pleasure in himself. He could only then be the temporarily blessed God. Of course, then the Scripture is suspect, but God cannot add to his perfections because that addition would have to come from some external source. But God is the source of all that is, so there is nothing external for God. That is the doctrine of the infiniteness of God. God is everywhere and everything is in him. There's nothing outside God that could possibly affect change on him. And God can't decrease. Because any decrease would have to come from something contrary to the nature of that which is decreased and something that is more negatively powerful. That's why it's important to understand that God has all power. Now sin is powerful, yes, but it's not as powerful as God is. So sin can never detract from the perfections of God. So God cannot have anything added to his nature and he can't have anything subtracted from it. We have to be careful with the language we use in Christendom. You'll hear people say, well I want to give God glory. You can't. God is completely glorious in himself and he was completely and infinitely glorified before you were ever here. God receives glory from himself. You can't add water to a full glass. All you can do is pour it in and he keeps running over the top. What you and I can do is put his glory on display. But you can't give him something that he already possesses infinitely. Let's just run with that thought. If God is immutable, his word is immutable. Scripture itself testifies to this in Isaiah. The word of the Lord abides forever. Now its meaning does not change. The application of the meaning might. God's standards don't change as much as our politically correct society would like to think to the contrary. If adultery was wrong on Mount Sinai it's wrong in Oviedo. If homosexuality was a sin in the Old Testament it's a sin today. Regardless of what the president, the congress, whoever likes to say something to the contrary. I just read a quote from somebody. Why are we bound to standards by a book written 4,000 years ago? Because that book does not change. Well we need to make that book conform to our society. No, we need to make society conform to this book. God's law doesn't change because it's an expression of his character. And the immutable God has an immutable character. There are many things that we can see from this doctrine. For example, if God determined in his wisdom that the preaching of the gospel was the power of God for salvation, that's still the case. It's not puppet shows. It's not dramatic dance. It's not emotionally laden music. It is the preaching of the gospel. That is the power of God for salvation. You can't add to that. You can't alter it. You can counterfeit it, but you can't change it. That's why if someone you know needs to be saved, you need to bring them here to hear the preaching of the gospel on a regular basis. I have a dear friend in Scotland. He's a retired minister. His name is Eric Alexander. If you look up Gracious Faithful Minister of the Gospel in the Dictionary. It's pictures right there. And he told me a story one time. He was preaching expositionally through a book. And this particular Sunday, the scripture text was all the bigots. And before the sermon, one of the elder ladies in his congregation came to him and said, Reverend Alexander, my unsaved daughter is here. I sure hope we're going to hear a gospel message. So and so beget, so and so, so and so beget. And he just went through that. And afterwards the woman came up and just gave him the, Hey man, I told you man, man, man, man, man, all you did was look at him. The daughter got saved. You know, it's really not what we do with the text. It's what the Holy Spirit does with the text, right? I have preached wonderful sermons, magnificent sermons in my own estimation. Like I said, one of the first times I was invited to preach was in a Christian reform church in Warren, Ohio. And I gave, I knew it was a good sermon because I know how much I liked it the first time I heard RC Sproul give it. And so as full of myself as I could be, I went to the back of the church afterwards. And this little old lady comes up to me on a walker and she sticks out her hand and she says, Nice try, son. And then I've preached what I was sure were what I called dog meat sermons. And people fall all over themselves. That's the best I ever heard. It's what God does with it. Our job is to be faithful to it. His job is to make it work. And I don't want to do his job and he's not going to do my job. It doesn't matter if we live in a post-modern world or a prehistoric world. God still saves people by the preaching of the word. I get the biggest kick out of that word, post-modern. Can anything have less meaning than that word? Post means after. Modern means right now. Some people want you to believe that you're living after the world that you're in right now. I mean, talk about words that have no meaning. How about government intelligence? Government intelligence. Jumbo shrimp. My favorite. Rap music. Non-existent entities. If God inspired Paul to give us the method and the message which was to preach the word, preaches the method, the word is the message, then preaching the word is what we're still to do with it today. Ministers are not called to share. We're not there to give our opinions. We are not here to put our political views into the pulpit. We are here to be the mouthpiece of God to his people. God saved people by faith in the Old Testament and he saves people by faith in the New Testament and nothing but faith. And that's how he does it today. If works couldn't save anybody a thousand years ago, they can't save anybody today. I mean, how could God have made it any clearer in the book of Jude when he called it the faith that has been once for all delivered to the saints? There's nothing that needs to be added to it. You don't need any new special revelation. You need to find out what the original revelation is. True doctrine doesn't change. What was true then is true now and it's a once for all thing. So our job is to learn the old paths not to be seeking new revelation. Again, application may be new but meaning is not. There was a cartoon some years ago in Christianity today and for some time the cartoons have been the best part about that magazine. There was a group of people sitting in a semi-circle and it constitutes for most people what a modern Bible study is. Somebody reads a verse or two and then everybody gives their opinion about what the verse means. As if it mattered what your opinion about what the verse means is. And so the verse the leader read was this, Paul said, I am in chains for the sake of the gospel. What do you think that means, Frank? Frank says, well, it makes me think of Aretha Franklin. Chain, chain, chain, chain of fools. I don't know. How interesting. You can't say you dimwit. Then you might offend somebody. Mary Ann, what do you think it means? Well, it makes me think of my addictions because I'm in chains. So they go all the way around the half-circle and then the last person says, well, Pastor Bob, what do you think it means? And he says, well, I think it means exactly what it says.  He's in chains for the sake of the gospel. And one person leans over to another and says, I told you he wasn't relevant. No, no, no. The application may be different, but the meaning never changes. I mean, if in Leviticus 16 the atonement was for the people of God and not for the people who were not the people of God, then the atonement today is for the people of God and not for those who are not the people of God. If God said in Leviticus 10, by those who come near me, I will be treated as holy. Then today when anyone comes into his presence, he will be treated as holy. So worship is not a common, ordinary, casual thing today any more than it was not a common, ordinary, casual thing a thousand years ago. This also means that God will never change his decrees because those decrees are based upon his eternal purposes and those will never change. I mean they are his eternal decrees. What God has determined to do from all eternity past, he will do it and it will come to pass. This also means that God is never reacting to circumstances. Rather, God has already decided what his will is and will carry it out without changing his mind. God could never will himself to change. Before anybody changes, they have to want to change, right? I mean wives, you know that. You've got to give your husband some reason to want to change. So don't do this one. Don't give him the silent treatment. That's not punishment for men. I mean if he says, well honey, what do you want to watch tonight? It's Independence Day. But whatever you do, like writing Bible verses and limb stick on the mirror or John 3.16 on the refrigerator, you might make him want to change. But until he wants to, that won't happen. It's a famous skit of Jack Benny and only a few of you are old enough to know who that is. He's standing in Central Park waiting for the bus and a man with a gun walks up and puts it to Benny's head and says, your money or your life? And Benny just stands there. And he said, I said, your money or your life? I'm thinking, I'm thinking. Now, the will cannot be forced. It is your will. But the will can be changed. It's impossible though that God could ever be dissatisfied with himself at any point in his existence. He could never find anything in himself that needed improvement. And he could never wish himself to be less than he is now. Now the implications of this doctrine are staggering. For both saint and sinner alike. Although those implications are alike. To the saint, to the believer, this doctrine should be of the utmost comfort. For the impenitent sinner there, this doctrine is of the utmost misery. Let's look at the sinner. For the impenitent sinner, it means that God's hatred is unchangeable as long as the sinner remains impenitent. And it's not degrees of anger. John 3.36 says, if a person does not believe in Christ, the wrath of God abides on him right now. And the word wrath, the Greeks had seven words for anger and this is the most intense one. It is the word orge from which we get orgy, which means unbridled passion. If you do not believe in Jesus Christ right now, God's hottest anger is not coming down the future. It's hanging over your head right now. Perry Miller was a scholar who taught at the Yale Divinity School, which was ironic because he was an avowed atheist. But he had a great respect for Jonathan Edwards. And in 1953 they started the Jonathan Edwards Project which had as its goal to have everything Edwards ever did republished by 2003, which was the 300 year anniversary of his birth. They didn't get anywhere close. I mean they had to stop with about half the material. Well, in fact in volume one, which was the freedom of the will, in his preface to the book, Perry Miller said, I'm so glad we no longer live in a day when people believe this stuff. My mentor, the late John Gerstner, was working in the Beinecke Rare Book Room at Yale, which is where all the Edwards manuscripts are kept. And they were working and talking about sinners in the hands of an angry God. And what brilliant imagery that was. The arrow with the archer with the arrow pointed at the sinner's heart. And Dr. Gerstner says to Perry Miller, Perry, if Edwards is right, that arrow is pointed at your heart. To which Perry Miller replied, I know. And Dr. Gerstner says, I don't know how you sleep at night. And Miller says, sometimes I don't. I just hope to God he's wrong. You're going to stick with that? That's your hope? Your hope is wrong? What if he's right? But as long as the sinner remains impenitent. It's not God is just displeased. It's not God is annoyed.   And get this. An infinite God is capable of. And get this. And then Paul warns sinners in the New Testament to flee from the wrath to come. You're not only under God's abiding wrath, His hottest anger right now. Wait until your father gets home. I never understood double punishment for sin.  There's no double punishment for sin. That's God. This house is different.  The sinner will not be annihilated because that would be to end the eternal, which is an impossibility. And the scripture speaks of eternal punishment. Punishment that ends can't be eternal. So to annihilate a person under eternal punishment would be a contradiction of terms. That would be like speaking of temporary eternal life. You know there are evangelists who tell people, come forward, walk the aisle, sign the card, pray the prayer, and receive eternal life. But they also believe that salvation can be lost. It should be sued for false advertising. How can you get eternal life if it can be lost? Jonathan Edwards once remarked that it was this attribute of God, his immutability, that made sinners hate him the most. They hate him because he's holy, but they hate him more because he will always be holy and he'll never be anything but holy. Another thing that the immutability of God means is this. It means God will never lower his standard just so more people can get saved. We have a tendency to think that God would receive more glory if more people got saved. So we make it as easy for them as we can. The problem is that God's way of saving people is unchangeable. So if God requires repentance and faith, we have absolutely no right to take repentance out of the formula. We have no right to tell them they don't have to give up their sin. When God tells them, they do have to give up their sin. We have no right to tell them they can have Christ as Savior now and make him Lord of their life later. That's not an option the Bible ever offers. Nowhere in the Bible are the words Savior and Lord used in that order. Nowhere. 631 times the word, phrase Lord and Savior is used. 631 to zero. On anybody's scoreboard, that's a slam dunk whitewash. In the history of college football, the greatest victory was in 1925 when big, powerful Georgia Tech played little Cumberland College of Kentucky in football and beat them 222 to nothing. How about 631 to nothing? How dare we offer Christ to people in a way that God never did. So whatever God was, he must always be.  If Christ was ever the only way to God, he will forever be the only way to God and that will never change. Mary can't save anybody. Now with regard to the sinner, if God is immutable in his holiness, the sinner is immutable in his sin. Even God can't change himself and the sinner cannot change himself. No one has the power of self-creation and no one has the power of self-alteration as far as the essential nature is concerned. I mean, Jeremiah says that when the leopard can decide he doesn't want spots anymore and that happens and when a black man can decide simply by an act of the will that he'd rather be a white man then you can do what is right, oh man. Now don't bring up Michael Jackson to me. That was not an act of self-alteration. But either change would have to be the act of a greater power. For God, that's impossible. For the sinner, it's an absolute necessity. On the other hand, God being incapable of change, the sinner can rest secure in the unchanging love of God. He says, I have loved you with an everlasting love. How long does an everlasting love last? Forever. It lasts forever. And if that's not enough, the Bible keeps using this phrase forever and ever. Wouldn't you think forever was good enough? Well, when forever runs out, we've still got ever to go. A Christian can know that his salvation is secure because the God who loves him does not change, cannot change. In other words, God cannot but love the saint whom he has once chosen to love. And for salvation to be lost, God would have to stop loving the believer, which means he would have to change, which means he would no longer be God. It means after saying in the Bible in Isaiah that he would see what Christ did on the cross and be satisfied, that's not enough anymore. What Christ did was okay for the first 2,014 years. I'm not satisfied anymore. You're going to have to do something better. You're not God anymore. God's immutability is seen in his statement that his covenant is an everlasting covenant. He says that his faithfulness endures to all generations. He is unchangeable in his love. His love is everlasting. We looked last time we were together in the book of John that he loved his own to the end. To the end of his infinite ability to love. The life that he gives is eternal life. His kingdom is everlasting and shall have no end, Isaiah says. Isaiah 26,4 says, Trust in the Lord forever, for in the Lord Jehovah is an everlasting strength. In the Hebrew it is literally a rock of ages. In other words, God's strength is perpetually unchangeable. Ultimately all of our hopes rest on the unchanging nature of God. What if tomorrow he could change and that what Christ did was no longer enough and we had to make up the difference? What if our standing with God no longer depended on Christ's righteousness but on our good works? That frightens me. We can rest all our hopes on him because he's the same yesterday, today and forever. If he's trustworthy, he is eternally trustworthy. He is forever the same. That should terrify sinners. Well, I'm just hoping that God will chill out and he'll be more merciful by the end. It's impossible for God to be more merciful. He'll never be more merciful than he is this minute. And while it should terrify the sinner it should give the true believer every reason to smile and to thank God that he's exactly what he is and he'll always be just that. God never changes. You and I might. You and I will. Thankfully he won't. He cannot deny himself. You know God's got a lot more at stake in your eternal destiny than you do. And he will always be true to himself, his covenant and his nature. That's security. People mistakenly say, well, women need security. So do I. I need to know that I can trust God that even though I mess up tonight, tomorrow morning his mercies are new every morning. I need to know that every morning I start with a clean slate that the sins of today will not be piled up as the sins of tomorrow. You know there's no rollover sins like there are rollover minutes with your cell phone. His mercies are new every morning, the slate is wiped clean and that will never change. Pretty nice being a Christian isn't it? Let's pray. Father we thank you for being secure in your unchanging nature and may our confidence grow leaps and bounds because of it. We thank you in the name of Christ. Amen.


Three Barriers to Improving Poverty Rates in America by Abin McDonald, an Audio Mises Wire narrated by Michael Stack. As the election is well underway, the United States political discussion has intensified about the living standards of the poorest in the country and the solution to their poverty. The Democrats as usual have proposed extended welfare benefits and greater government aid to poor families. This experiment began in the 1960s when President Lyndon Johnson initiated the War on Poverty Programs. As he signed them into law, poverty levels were already plummeting, according to data collected from the Census Bureau, thanks to substantial increases in productivity and wages. Since the 1960s, although approximately $20 trillion has been spent on the programs, poverty levels have basically flatlined, often ticking up due to the occasional recession. There's a fundamental reason for this. The War on Poverty Programs lowered the relative cost of single parenthood in terms of poverty. Under the War on Poverty, subsidies to single parent families became greater than two parent families. This is why, since the programs were initiated, rates of single parenthood have ballooned. In 1960, less than 10% of all children were born out of wedlock in the U.S. In 2008, it hit 40%. Single parenthood is a potent predictor of poverty. According to the Census Bureau, in 2019 the poverty rate for two parent families was estimated to be 5.2%. The estimated poverty rate for single parent families, however, was 25.9%. The Heritage Foundation puts the numbers at 6.4% and 36.5%. It is also well documented that children who grow up in single parent households are much more likely to suffer psychologically and when they grow older commit crime, as documented by a study published in the Journal of Political Economy. Getting single motherhood to drop or at least stop rising would require reforming the welfare system, either by withdrawing welfare benefits from single parent families or increasing them for two parent families. But either way, the message is clear. One of the side effects of welfare is high rates of single parenthood which can be very damaging. Take a look at Europe. As described in the 2012 report conducted by the Institute of Economic Affairs, single parenthood levels are very high in Europe as well, a symptom of welfare. Another strong predictor of poverty in the U.S. is a lack of full-time work. According to the Bureau of Labor, in 2016 the percentage of full-time workers who were working poor was only 3.1%, compared to 12.2% for part-time workers. As the report itself notes, quote, full-time workers continued to be much less likely to be among the working poor than were part-time workers, end quote. This problem is once again attributable, at least in part, to welfare because workers might lose incentives to work full-time. This happens when welfare payments are reduced or withdrawn when the recipient obtains full-time work. Here reform would be vital. It is why benefits should never be more profitable than a full-time job. The implementation of work requirements for recipients would also make a difference. Reforms like this were made during the 1990s under President Clinton. As a result, in 1994, 40 million Americans lived below the poverty line. By 2000, it had approached 30 million. Of course, it is not always easy to find a job, but this can be improved through the removal of policies that hinder hiring, such as high taxation rates and high regulatory burdens for employers. Many will suggest that raising the minimum wage will alleviate poverty for those with jobs. This is wrong on every level. The people hit hardest by this policy will be the very people it intends to help. Low wage workers. According to a 2016 analysis conducted by the Heritage Foundation, a $15 minimum wage, for example, would cost the economy up to 7 million jobs. Minimum wage jobs are merely a means to an end and are at the bottom of an ascending socioeconomic ladder. It is why over 76% of all minimum wage workers are between the ages of 16 and 34. Cutting these off would inevitably cause poverty because it would become increasingly difficult to climb the wage ladder up to prosperity. A third reason for poverty in the U.S. is, like in most countries, the high cost of living in many areas. This often comes as a result of the government imposing regulations on basic, necessary commodities which drives up their costs. Housing is an notorious example. A 2019 study showed that housing regulations limited aggregate U.S. growth by one-third between 1964 and 2009. A reduction in regulations would increase the rate of construction, which would lead to a decrease in costs. Just compare the housing costs of California and Texas. The difference is that while California's housing market is heavily regulated with zoning rules and rent control, Texas is relatively free. A similar phenomenon was witnessed in Britain in the 1930s. During the Great Depression, the housing market was dramatically deregulated, which led to a boom in construction. It was one of the reasons why the U.K. economy had only two consecutive years of negative GDP growth. To put this into context, last year for every thousand people in the U.K., three houses were built. During the Depression, the rate was almost doubled. Housing deregulation will increase construction and therefore lower costs because of an increase in supply of housing. Lower costs will take burdens off working families and free up their purses. When it comes to housing, though, at least the U.S. is at an advantage in terms of housing cost. The U.S. ranks highly in terms of housing affordability, with the average American family spending 19% of their expenditures on housing, lower than in most European countries. Most houses also enjoy basic facilities such as indoor flushing, etc. Only .1% lack them. America ranks highly in terms of rooms per person, 2.4%. The only country which is higher is Canada, with 2.6 rooms per person. However, there is still clearly room for improvement. If we want to lower poverty in America, we ought to adopt these three policies. Reform the welfare system so it encourages intact family formation. Reform the welfare system so it encourages full-time work and lower the cost of living through the deregulation of important commodities like housing. For more content like this, visit Mises.org.


What is that by everybody? Jason here for jazby's casebase.com. We just sold out 2024 tops chrome black baseball PYT number six And here we go guys There's everybody that bought in guys. We did have to sell eight teams via a serial number. So we did do that There's the eight teams there with the team and customer names and Fresh case. Oh, I feel like also baseball is the only sport you could actually play double headers. All right Imagine like hockey players and football players have played double headers Basketball, I feel like we've seen tournaments where you do play multiple games, but even then All right, lead-off lock for Otani Still the still a fourth inning. I guess there's still plenty of time Freddie Freeman has been struggling. I will say though man. His batting era is now down to 273 which For him, that's pretty low. And last 11 games hitting below 200 Freddie Freeman That is not Freddie Freeman like Adam bro Three straight off-speed pitches and Freddie Freeman swung at all of them All right, well, you've been much better That's a pop fly. We hit Otani in the head Dude, Otani just got smacked in the head. Nice. There you go.   Brera, Dominguez and Blake Rutherford for Washington 299 and David's dropping some knowledge. I think I seen this that earlier Gave a two home runs in 171 in Japan last season and he gave up three home runs in his first 17 Yeah, no for real. That's what I'm saying. Like it's a whole different ballpark so far For Yoshinobo, you know, Mocho Like I said, it's not like he's done terrible. It's just I think a lot of people expecting him to just like wow everybody And just probably have a no-hitter by now Out of 50 Like and like I said, it's not gonna help when your team it doesn't give you run support either Darius Vines out of 150 Austin Riley Yeah, John, they want two no-hitters, right right now Nick Gonzalez Even Aga and then Jose Altuve and Byron Barson Mason Wynn the Cornels Aaron Judge to 75 And Evan Carter is that Gallop as well as your rookie Variation Texas Ranger that one that's gonna go to Adam Kelly. I couple more packs you guys Still no still no Dodd Christian Yelich to 75 and Nolan Chanel All right, also too. I haven't been paying attention to the R&B teams. Hold on. I know the angels are part of that 54 I don't want to deny So angels 54 Four is Jason Get three straight braids right there so far Just that known Chanel There might be some base, but bases base people Armstrong and Calharris and good Oh, we'll see. Let's see. Oh Come on John.  Oh, so funny someone called this dude the Great Dane 71 out of 99. I don't think that's his real nickname, but Marlon's though that is part of the R&B 91 Out of 99 spot one's going to Eugene gold rookie It's a pitcher Quinn preister for the Pirates David with that one to 50 gold mini diamonds Pajas Cade Marlowe for the Seattle Mariners Mariners part of the R&B. So that's actually a non-numbered card So we're gonna have to randomize that Dbacks Jordan Lollard very nice Richard There you go rich on the board there buddy About some more Slade For the Diamondbacks backs back diamondbacks Forced wall for the Braves To 150 Braves is big dog and Christian and Karnas on strand Another teaser there for the Reds EA Nolan Chanel for the Angels very nice again a non-numbered one. So everyone would get a shot at that To 99 Colton Couser For the Orioles EA with that one 32 out of 99 Superfutures and we have Kyle Harrison to 50 for the Giants Giants is so men Alright two more hits guys Raffaella Raffaella the Raffaella Raffaella Red Sox going ahead No Pranerik and Jared triolo David M. Alrighty there guys so Again some nice stuff Couser you know Lawler R&B to get a couple numbered cards there, then we get two non numbered our autographs. So we'll have to randomize those And then if there's any base More on space there Mariners base Mets Audrey's Blue jays All right cool. So yeah, there is some base. So this is what we're gonna do guys So these ones obviously went to the customers All right We'll give out this Nolan Chanel to number one Number two. We'll get the Cade Marlowe And just as added bonus because these are nice base cards to have some good players We'll we'll give away the base to number three.  So that's a little added bonus for you guys I'll print out the sheet too So there you go. Thank you guys. I appreciate it again guys Obviously, I want to continue to do more top chrome black guys Let's try to get this one in single digits that way we could put it in a serial number again I think people like that and like I said also to for the customers that bought in straight up I know I didn't show in the last video, but don't worry guys. You guys are in for number five Number six customers are also gonna be part of the giveaway now. Remember obviously the R&B names are not so Like I said, that's kind of the only downside So that's why I suggest guys baby buys full spot But doesn't mean don't get to the R&B because you can still save some money and get some really big hits for some Really big teams, but what we'll do is we're gonna take out the R&B's here so delete delete delete delete delete and delete and delete so that should make it 22 right there perfect, and then there's the full list and like I said guys only need to sell what? Four more cases figure team seven through ten So let's get it going guys that we can give away that case Jaspis case breaks calm


Hello everyone and welcome to our session managing your cluster, the GTOPS way. We'll introduce ourselves. My name is Nishant Kumar and I work for Microsoft as a senior software engineer and I'm a developer at the Azure Operator Distributed Systems Product and I have with me. Hi, I'm Uday T. Kumar. I work for Zeta Technologies where we are revolutionizing the world of banking. I'm an engineering manager heading a team of DevOps engineers. Thank you, Uday. So talking about the agenda, I'll talk about what is GTOPS. Why do we use GTOPS? What are some of the benefits? GTOPS principle and then Uday is going to talk about a specific tool, Argo CD and talk about this architecture features and provided demo and then I'll be talking about some of the GTOPS challenges and then we'll end up with the comparisons with some other open source tools. So what is GTOPS? It is a way of implementing continuous deployment for cloud native applications and it was a term which was coined by Weaverworks in 2017 and the core idea of GTOPS is having a Git repository that contains declarative descriptions of the infrastructure currently desired in the target environment and an automated process to make the environment match the described state in the repository. So if you want to deploy a new application or update an existing one, you only need to update the repository and an automated process handles everything else. So it's like having a cruise control for managing your applications. And Kubernetes specifically enables GTOPS by fully embracing declarative APIs as its primary mode of operation. And why GTOPS? Because you can deploy faster and more often since all of your artifacts are stored in your Git repositories, you could be sure that there are no manual changes or any random script that is running in your environment. So it's really good that you go into the Git repository, make your changes and just click the button and you're sure it's going to match the desired state with the current state. And also you have faster error recovery for free. So let's say the production environment is down a big deal, but with GTOPS you have a complete history of how your environment has changed over time. And this makes error recovery as easy as issuing a Git reward and watching your environment being restored. And the Git record is then not just an audit log, but also a transactional log. And you can roll back and forth as many times you want. Yeah. If you don't mind, can we take the questions to the end? Yeah. Thank you. So it also makes our deployments secure. So GTOPS allows you to manage deployments completely from inside your environment. For that, your environment only needs access to your repository and image registry. And that's it. You don't have to give your developers direct access to the environment because, you know, the QC tells the new SSH. And then you have self-documenting deployments. So have you ever logged into environment and wondered what's already deployed here? So that's really a pain when you really log into some environment. But with Git repositories, everything is declared there. You just log into a Git repo and you want to find out what's deployed in the environment. You don't need to even log in. You just check the Git repository and everything is out there. Some principles of GTOPS, the entire system must be described declaratively. So with GTOPS, one example is just one example of many cloud native tools that are declarative and can be treated as code. And with your application declaration version in Git, you have a single source of truth. So your apps can then be easily deployed and rolled back to and from Kubernetes. And even more importantly, when disaster strikes, your cluster infrastructure can be independently and quickly responded. And that system is then versioned and immutable. So as I mentioned earlier, everything is stored in Git and serving as your canonical source of truth. So you have a single place from which everything is derived and driven as well. And then approved changes that can be automatically applied to the system. So once you have declared state that is stored in Git, the next step is to allow any changes to the state to be automatically applied to your system. So what's significant about this is that you don't need cluster credentials to make changes to your system. And then your systems are continuously reconciled. So once the state of your system is declared and kept under version control, software agents can inform you whenever the current state is not matching the desired state. And the use of agents also ensures that your entire system is self-healing. And by self-healing, we don't just mean any nodes or pods failure because those are just handled by Kubernetes. But even some manual errors, like if someone comes into an environment, deletes a deployment which is by mistake or not intended, then the reconciliation loop will actually check what is there in the Git and it's going to undo all the changes which was done by a human. And then there are two ways of how you deploy a cluster, either via pull-based or push-based system. So with push-based, you use a CI-CD pipeline to push changes to your environment, and then the pipeline is triggered by the code commit or merge. And with pull-based GitOps and agent running inside your environment, continuously pulls a Git repo or container registry for changes. And when it detects a mismatch between the defined state and the running state, the agent pulls the defined configuration into the environment. So pull-based, first of all, it increases the security because the agent is running inside the cluster, so there's no need to store your credentials in your external CI, and it makes more of an environment more consistent as push GitOps typically only works in one direction from Git repo to your environment and pull-based deployments work in both directions. It actually pulls from a Git repo into your environment. So this can detect and remediate configuration drift in the event that changes that are made to the cluster manually or from other sources. So here are some of the popular open-source tools, Argo CD Flux, Junkins, Weave, GitOps Core, Pipe CD, and there are many more that you will find out in the internet, but in this talk, Uday is going to specifically focus on Argo CD, talk about its architecture and provide a demo, and then I'll talk about some of the challenges and comparisons, so I'll hand it over to Uday. Thanks, Nishant. So Argo CD is a very widely used tool, one of the many open-source tools that we try to contribute to, customize and use at Zeta Tech. It allows one to use any Git-based repository, whether it's GitHub, GitLab, or BitBucket. Specifically with respect to Kubernetes, the manifest can be specified in any number of ways, customize, helm, or just plane, vanilla, YAML, or JSON manifest as well. It also supports any custom management tool which can be configured as a plugin for the purpose of config management as well. Argo CD can work with many of the commonly used ingress controllers, including Ambassador, Nginx, Contour, Traffic. In fact, if you go through the Argo CD documentation, it has sample manifest files, which act as a quick starter reference, and I suggest you do check the documentation out. Argo CD supports two major deployment types, multi-tenant with UI and CLI, and the core, which only comes with the CLI. Multi-tenant installation is the most common installation type where multiple dev teams can access it and collaborate, and it is basically why the API servers, which uses the web UI as well as the CLI. Now, this further has two modes, the HA and the non-HA. The HA is basically a kind of version of the non-HA, but it supports the HA and resiliency, as the name suggests. Now, the non-HA is strictly not for production use. It is more for demo or evaluation. No prizes for guessing what mode I'm going to be using in my demo today. Now, when it comes to both of these modes, there are two ways or means in which they can be deployed. There is an install.yaml where Argo CD is installed in the same cluster as the rest of the applications, and there is a namespace.install.yaml file where Argo CD is installed in a completely different cluster as compared to the applications. The difference is whether somebody wants it in the same cluster or not, and for various reasons of security amongst other things. The last mode, of course, is the core. Core, as mentioned earlier, does not include the API server at all. We'll discuss a little more about the components in the next slide, and therefore does not have a UI. So this is essentially if the cluster admins want to have an independent setup, and they want to run a specific instance of Argo CD, this is a more preferred way because it's lightweight, it does not have the HA components built-in, and everything is done via CLI. Let's look at a little bit of the architecture, which will help you understand what we were talking about earlier. Now, there are three major things, API server, repository server, and the application controller. So API server, as most of us would guess, is what enables the communication, most of the communication with the rest of the world. The API server is basically a GRPC or REST server, which exposes the API consumed by the web UI, the CLI, and also the CI CD systems. It takes care of a couple of things, application management and status reporting, then invoking of application operations, including rollback and any user-defined actions that might be put in repository and cluster credential management, that is, which are stored as gates, secrets, or can be delegated to any of the external or third-party authentication or IAM management tools, then authentication and delegation, as I mentioned, RBAC enforcement, and in case somebody has Git webhook events, it can also act as a listener or forward for them. The next one is the repository server. Now, as the name suggests, this is basically an internal service, which takes a local cache of whatever is present in the Git repository itself, and it holds the application manifest. Now, it is responsible for generating and returning any Kubernetes manifest when certain inputs are required. Now, what are those inputs? It's your typical Git-based inputs such as the repository URL, any revisions, application path, template-specific settings like parameters or environment variables or Helm values.yaml. And finally, there's the application controller. Now, it is basically nothing but a Kubernetes controller which monitors running applications and compares the current life state with the desired target state, as specified in the repo. It detects any out-of-sync applications, what actually happens, you will get a better idea when we go through the demo. And now, what I mean by out-of-sync application over here is that suppose we've made a change in the GitHub repository, and it is not what is deployed currently. So that's where it says, okay, that this is the desired state and this is not currently what it is. And it can sometimes optionally take actions as well. Optionally, why? It will manual sync or auto-sync as well. That's something, again, which you will get a better idea during the demo. It is also responsible for invoking any user-defined hooks for lifecycle events. This is for any advance deployments when you have canary or blue-green deployments in place. Now, here's some of the major features. Now, when it comes to the features, I tend to categorize them into five major category and try to remember them using an acronym. S-A-L-A-D, SALID. Yes, guys, it's a post-lunch talk. So I had the option of using Dallas or SALID, so went with SALID. S stands for state. So automated configuration drift detection. When an application moves away from its desired state, as I mentioned earlier, it finds that out and it syncs it. It also provides visualization. There is a big yellow icon which comes up saying this is out-of-sync. And as I mentioned, for any advanced or complex application rollouts, it supports hooks for precinct, sync, and post-sync. Then there's the API part for A where as we've already discussed, there's a web UI which provides any real-time view. There's a CLI for automation or CI integration and webhook integration for GitHub, Bitbucket, or GitLab. The L is for logs and metrics. It can always look at the health status and give an analysis of what is going on, audit trails, and also supports Prometheus metrics. Then S stands for auth. There's an SSO integration via various methods and third-party tools. OIDC, auth to GitHub, GitLab, LinkedIn, Microsoft, et cetera. It supports multi-tenancy and RBAC policies for authorization and access tokens for automation as well. And finally, the D stands for deployment. Automated deployment of applications to specified target environments, rollback, or roll anywhere to any application configuration committed in Git repository. Multiple config management templating tools are supported, as we said, customized Helm, or even plain vanilla JSON files. And it has the ability to manage and deploy to multiple clusters. Let's now talk, go through the demo. So we tried to do a live demo, but the demo gods were not with us. So you can see how the installation is done. Basically, a namespace is added, and we need to do a Cube CTL apply of the GitHub account. So I've done that already over here. And when we do a Cube CTL get-all in the namespace for ARGO CD, we can see a whole bunch of things that are deployed. So we can see the services, the deployments, the pods, and the replica sets, and a stateful set. We'll grab a hold of the load balancer IP, and this is already deployed. So in case we were to, it's already deployed, but just for the sake of the demo, I'm putting it out there again, and you can see it comes up. I've already configured the GitHub repository. All we need to do is go to repositories and click on connect. So you can see that I've set up something specifically for this demo.  And now what we are going to do is I've already configured some YAML files, which we will use. I'm creating a new app on ARGO CD itself. I'll give it a name. This is going to be a simple Nginx application. So just Nginx test. The project will be default. The sync policy, we'll keep it manual for now. Repository URL, since the repository is set up, the repository URL comes in as a prompt. The path I can put in any optional directories I want, I've just put in a dot for now. The cluster URL will be the Kubernetes default URL. I've used microkits over here. And I've put in the namespace as GitOps, which I've specified as well. It could be just as default in the default namespace as well. You can see it's healthy and synced because currently in the repository, there's nothing, absolutely nothing except for the readme file. Now, as I mentioned, there's Nginx YAML file, which I've already set up to save us some time. I'm going to copy it into the GitHub repository and then push it on to GitHub. And I'll open it up in a bit and show you what we've done. We're just going to push this, you may have and run some commands, which you may have seen a hundred times. We've kept it just for the sake of the demo to show that it's not some pre-baked, pre-configured things. You can see the YAML file over here. The containers have been set up. The port has been set up. Notice the number of replicas was just that in now. You should get ahead, get commit, and get push. And there we are. So while that happens, let's go back to the application and you can see that it's just showing Nginx test. If I were to do a refresh, it now shows out of sync because the manifests have been pushed into GitHub and it is saying that the desired state and the current active state are not in sync. So we can click on app diff to see what the difference is. We can see that the services and the deployments are showing whatever I had earlier shown on the YAML files. Now we hit a quick sync. Sync has a couple of options, like prune. Prune is when you have a certain application and you want those pods to be killed and have new pods created. For example, we are upgrading from one Nginx version to another . You can see that as soon as I have synced, the services have come up and two new pods have come up as well, which are getting created. I will now just do a Qubectl get all and we can check what is the status of that on the CLI. And we can see in the namespace GitOps, the status of the pods are container creating. That should come up in a minute. Now we can see it is in running state. Let's go back to the UI. Yes, it's in a running state. And if we pick up the cluster IP and we are to enter it, voila, Nginx is up and running. Now this is where we get to see what happens when there is a drift in the current state and the desired state. So I'm going to modify the YAML, change the replicas from two to four so that we actually create a drift in the current state and the desired state and the usual Git based commands, Git add, Git commit and Git push. So let's again find out if the status has been synced. But before that, let's take a look at what is there on GitHub. You can see that the file has been updated, the number of replicas is four. Let's do a quick refresh to see if everything is hunky-dory. It's not because it's again out of sync. The app difference this time clearly points out that the number of replicas is the only factor that has changed from two to four. And we can hit a sync and again the number of options are still the same. As soon as we hit sync, we should see two more pods coming up. There we see one has come up and the fourth one. Let's quickly check on the file. We can see that two new pods have come up. Both the statuses are container creating. The app difference or the app details rather shows us various options. One of them is to enable auto sync where Argo CD would do the job of refreshing it, checking every now and then and then doing the actual sync. We can delete the application as well which will allow us to see all the four pods are up and running and in a healthy status. With that, over to Nishant. Thank you, Uday. I will talk about some of the GitOps challenges. So far what Uday has shown is you have a Git repository and then within Argo CD you provide a source and then Argo CD would ensure that whatever is the desired state is then available to you. So the second one is how do you create those manifest file which resides in your Git repositories. That's one of the challenges and then the second one is how do you do secret management. I will talk about both of them. There are two popular open source options for managing your manifest files which is building blocks for your applications. One of them is with the help of Helm you can actually package your applications, its dependencies and it has a templating language so you can use that to deploy, upgrade, install your applications on your environment and then the second option is customize. So customize uses purely Kubernetes YAML files and with Helm what you get is you have a values.yaml file, you can substitute all of the values that you want to let's say update. If you want an image to update you can go and change in the values.yaml and then it will reflect in all the other places that image has been getting used. It could be in your deployment or any other files. Similarly in customize it also it has a customization.yaml file. Again it's a single yaml file where you can provide your substitutions. If you want to use a custom yaml file the only benefit that I see with customizes you don't get the complexity of Helm templating language. If you really want to do some complex logic then Helm templating language can be very overwhelming but in case with customize since it's just pure Kubernetes YAML file it's pretty straightforward so if you understand a Kubernetes manifest file you already understand customize and something else you can do is you can do a lot of overlaze. If you want different configurations for your different environments let's say a dev or production environment then it is natively supported within customize. It's really a good tool and I would recommend you go and explore that. The next thing is secret management. You might be aware there are multiple open source secret management tools like hashikap, vault, external storage and so on. If you want to know how to store your secret in your Git repositories I mean right now without GitOps or without a good solution you need you can't store your secrets directly in your Git repositories because it's just base64 encoded by default in Kubernetes and it is not encrypted. So either you have to use some third-party solutions where in your environment or you can use another tool called bitnami seal secret. So the special thing about that tool is you can actually store your secrets along with a manifest file in the same Git repository. So seal secret is a one-way encrypted secret that can be created by anyone but can only be decrypted by the controller that is running inside the target cluster. And once it is encrypted it can then be safely uploaded to your Git repositories. And it has a seal secret is composed of two parts. One is a cluster side controller and operator and that is used to decrypt your secret and then there's a client-side tool called KubeSeal. So in the example you can see on the right-hand side you have a normal Kubernetes secret and using KubeSeal you can actually encrypt and on the right-hand bottom side it creates a seal secret. The client is sealed secret and the data section is completely encrypted and now you can upload that secret into your Git repositories. And then the controller, once you apply that secret in the environment the controller would already be running and that controller will decrypt the secrets on the fly and make it available to your pods. So again an interesting tool that you can explore. And here are some of the comparisons for different tools in upstream. This might be a little bit outdated since the open-source community is continuously evolving but yeah, like Flux, Flux, V2, ArcoCD, PipeCD, Junkinex, these are some of the really popular tools that I think you can go and explore. And I would like to thank all the awesome blog posts available on the internet because it was really useful in putting the content out for this talk. So thank you for attending this talk. Any questions? So as I said, for the cluster admin you can always have a separate CLI-based deployment.  So there are a lot of charts which comes in Helm which is what we typically tend to use. And in fact in OpenStack itself this project is one such project where all the charts are written where you can deploy OpenStack on top of Kubernetes, have the Kubernetes itself deployed and that entire set of manifests you can have it in a GitHub repository, you can have ArcoCD and you can choose what mode you want and have the entire thing deployed. Do you have the same production? Not in my current organization but in a previous organization we have done that. I think we may have just crossed time. So if there are any questions you can come to us. Thank you.


The narcissist never wanted a future with you. When the narcissist first met you, they love bombed you. They told you whatever they thought you wanted to hear. They showed you whatever they thought you wanted to see. They sold you a dream. They gave you wanted scenarios that could hypothetically come true. They gave you false hope. They lied to you about something about your possible future. While knowing that it wasn't true. While not taking any steps to make it a reality. Because the truth is that the narcissist never wanted a future with you. From day one, they saw you as something that was temporary. You were disposable. You were readily available for their use as required. You were intended to be thrown away after use. But they had to make you believe in something. They had to make you believe in something good about your possible future. In order to keep you around. Which may make you wonder. If they want something temporary. Why didn't they target someone who wanted the same thing? The narcissist cannot target someone who desires something temporary. Because then that person wouldn't be willing to invest everything they have. Then that person wouldn't trust and believe in the narcissist. If you know that something is going to end. Why would you give everything you have? Which is why the narcissist has to target someone who is thinking about the future. Someone who has goals and dreams. Because they sell that dream to you. They can future think. They can give you a detailed vision of the future to facilitate bonding and connection in your relationship. Because they know that if they can simulate bonding and connection. You're going to be more willing to invest everything you have. Because you think you're going to get something in return for what you give to them. You think you're going to get your desired outcome or result. But although the narcissist may have fed this dream to you. They had no intentions of making it a reality. They never took the steps to bring it into fruition. It was just something they used. To string you along. So that they could get what they want from you in the present. Because the truth is. Regardless of what the narcissist said to you. They never wanted a future with you. The evidence of this was there all along. But we overlook it. We believe in what they're saying to us. We don't assume that we're being deceived. But the reality is that they never consider what lies ahead. It was never a concern to them. When a person is in a relationship. And they're thinking about their future with that person. They're going to take the necessary steps to ensure that everything turns out okay. It's like preparing for a storm. They're going to do everything they can to prevent destruction. To prevent anything from going wrong. But the narcissist never took any steps to protect your future with them. And although you could argue that there are storms in every relationship. The narcissist also never took any steps for recovery. They never took any steps to make things right. When you look back at your relationship. You will see that the narcissist is the storm. They caused destruction in your life. They broke you down.   They destroyed you financially. If they were considering a future with you. They would never have done any of that. If you have a laptop and you plan on using it in the future. You're not going to grab a bat and start smashing it up. Because that will affect its functioning in the future. It's not going to be able to perform in the way that it used to. It's going to be destroyed as a result of your actions. You're not going to intentionally damage something. If you have a purpose for it in the future. And it's the same thing with the narcissist. If they have a purpose for you in the future. They're going to treat you with dignity and respect. They're going to protect you from danger or harm. They're not going to abuse you. But that's exactly what these narcissists do. They abuse you to the point where there's no going back. Where you're not going to serve any purpose for them in the future. Because those are their true intentions. They want to break you down. They want you to be no good for anyone after they're gone. Because they know that the relationship is going to end. They know that at some point you're going to leave them and move on to something else. Every narcissist knows this. They know that they're not meant to be loved. They know that you would not willingly desire to remain around them. Which is why they use false promises and future faking. They promise something in the future. But they always withhold what you need in the present. Because if you had everything you need. You would have no reason to remain around them. What keeps you stuck with them. Is when you're holding on and waiting for a return on your investment. You're waiting for a possible future. But there is nothing in the future. They sold you a dream. They never took the steps to make it a reality. But by the time you figure this out. The narcissist has already done their work on you. They've already ran you through the mud. To the point where you no longer possess the qualities and abilities. To just move on on your own. Because the narcissist knew that at some point you would figure this out. At some point you would desire to leave. They knew that you would take everything that is valuable about you. And move on to something else. They knew that you would leave them in the pit that they created for you. Which is why they stripped you of everything that made you who you are. Everything that otherwise would have given you power and strength. They never invested anything into you. Because they knew that would have given you strength. That would have given you the strength to move on. But they need you to be weak. They need you to feel like you're not good enough for anyone or anything. As though this is as good as it gets for you. Because then you're not going to try to leave. Then you're going to continue to invest all of your time and energy into the narcissist. Which is building them up. And making their life more convenient. It's recharging their battery. But it's draining you to the point where you begin to feel dead. You begin to feel like you have no purpose in life. And that's where many of you become the cause of your own destruction. Because the narcissist has already primed you for this purpose. Many of you start doing destructive things.   Because they've already primed you to be this way. They don't even have to do anything anymore. You're doing it to yourself. And now they can say that it's all you. They can hold you responsible for everything that happened. They can say that you were the cause of it. That's when they start their smear campaign. They turn everyone against you. They must lead people into thinking you're bad or crazy. When if they had wanted a future with you. They never would have done that. If you're thinking about what lies ahead. You're going to practice the proper maintenance and recovery. You're going to treat it with dignity and respect. You're not going to run it into the ground. But that's exactly what these narcissists do. They're intentionally trying to destroy you from day one. Thank you for watching. I hope this video resonates with you. Please like, comment, share, and subscribe. If you would like to donate, my PayPal link is in the video description. Coaching inquiries. You can email me at coaching.narsviver.uk. Thank you for watching, and I'll talk to you soon.


Mathematically, I mean that as you take, see f is defined on delta d which is an open set and there is a boundary. So, as you take the limit of the value to approach the boundary from any direction, the value of the, as you follow any path. So, essentially it is a continuity that you have, you take any path approaching the boundary and look at the value of f along this path and look at the value of f on the boundary. So, this limit converges to that value, it does not matter which path you follow. So, that essentially the value of f on the boundary does not behave strangely, f is continuous in d well that is hard to say because that would mean that if you are approaching from outside also then it should be continuous, that you cannot say, f is continuous on d bar as long as you approach it from inside then it is fine. So, that is why one cannot say there is continuous on d bar, but one has to say it this way. So, that is the theorem and proof is a pretty straight forward almost directly by Cauchy's integral formula and we do induction on. So, for m equal to 0, this is just the Cauchy integral formula. So, that is the starting point. So, let us assume this is holds for some value of up to m minus 1 and now we want to prove it for m. So, now what do we know? We know that m th derivative of f is defined as and of course, this limit should exist and all things should be around only then this is. So, let us just because now we know that m minus 1 is derivative not only exists is given by that formula. So, let us use this.  So, finally, subtract the 2 and now let us use binomial theorem to expand these 2 or well not we want to expand these 2 or we will expand this out as splitting it as w minus z and delta z and expanding this out we get j equal to 0 to m m choose j w minus z to the j. Let me write it as m minus j and minus 1 to the j and delta z and if you look at this the first term for j equals 0 is w minus z to the m that cancel with it. What is the second term? m choose 1 which is m times w minus z to the m minus 1 times minus delta z and second and higher terms will have delta z square or higher powers of delta z. So, I will write it as m minus 1 factorial over 2 pi i plus. So, this is the first term that survives and the rest I will just take as delta z square times something some expression in w and z and that is a polynomial expression. So, if we just split these 2 integrals out what we get is take the sum as 2 different integrals or sum of 2 integrals we get the first term would be m factorial over 2 pi i delta d f w over 2 minus z minus delta z to the m times w minus z delta z d w that is what happens to the first term. And the second term is in fact delta z is can come out the integral is over w and for the second term let us just notice that it is whatever it is it is some delta z square times something and now knowing that this is the quantity we are looking at the difference divide by delta z let us divide the right hand side by delta z and take the limit. And as you take the limit delta z going to 0 this vanishes and what happens to this again delta z is independent on integral. So, at delta z goes to 0 you get the m z is this goes to w minus z and so it is pretty straight forward. And it all follows from this Cauchy's integral formula directly essentially which in turn follows immediately almost immediately from the Cauchy's theorem about the contour integral. So, analytic functions have this really nice property of being infinitely differentiable. So, there are no discontinuities or any kind anywhere as long as the function is analytic on a domain. Of course, it is quite possible that the function is not analytic at some point and where there will be a discontinuity even at the basic level. So, we will look at that aspect as well that the function being analytic at most of the places, but there will be points where it will not be. In fact, that is the kind of function we will mostly be interested in because zeta function is one of that kind. But before we try to understand that we will let us you know clean up the basics of analytic functions. So, fine. So, analytic functions are infinitely differentiable they have this property that in any domain where the function is analytic its value on side a point of the domain is determined by the integral along the boundary of the domain and they satisfy this Cauchy's integral Cauchy's theorem that integration along the boundary of the domain of an analytic function is 0. Now, what one can may ask what about the converse an analytic function has this property of Cauchy's theorem what if a function is 0 when integrated along the boundary of a domain then is it analytic that would be the converse of this theorem that converse of Cauchy's theorem and actually a very strong form of converse actually holds which is a Morera's theorem. This is a very useful theorem when we try to prove some further functions analytic. So, we start with a continuous function on a domain because that is a minimal we will need anyway and if this function the integral of this function along the boundary of an excess parallel rectangle. So, r is an excess parallel rectangle. So, it is the sides are either parallel to x axis or y axis. So, if for every such excess parallel rectangle inside the domain t this integral is 0 then f is analytic on t. It is a strong converse because if f is analytic on d then for any closed curve inside the domain d this integral is 0 whereas, here we only require it being 0 on along the excess parallel rectangles is that clear why this is a strong converse we do not even need it the assumption to be that f is 0 along every closed loop. So, the proof is quite simple but this is a neat trick. So, what we do is suppose this is domain this is a domain d pick up a point any point in the domain call it z and let us call it static point z 0 and pick up any another point here let us call it z and pick up yet another point which is very close to z call it z plus delta z. Delta z will as the expression says will eventually go to send it to 0. Now, let us define a way of integrating between two points say between z 0 and z. So, we will how do we integrate between this I am going to since f is given I will integrate f from z 0 to z but whenever we try to do it we have to define a path of traversal from z 0 to z and the path will choose is very simple this is probably the simplest possible move around in move parallel to x axis from z 0 until the point we reach just below exactly below z and then move vertically.  So, whenever I am going to integrate from z 0 to z 1 where 2 point z 0 and z 1 are given it will be this kind of a path to be followed and let us define f of z to be this integral from z 0 to z of f w. So, this integral is well defined since f is analytic f is continuous it is a finite integral. So, it is well defined now similarly f z plus delta z is the integral z 0 to z plus delta z f w and now the path followed is this one then what is f z plus delta z minus f z is this integral or the difference of these two integrals where this is following this path and this is following this path and now we use the assumption let us complete this the second one is negative which means that in the first one we are going from here do not have a colored show we are going from here to here in the second one since it is negative. So, the sign is the direction of traversal is reversed. So, there we are coming down from here to here and then here. So, I can split this integral that is easy to split this integrals first one as going from here to here then here to here and then going up there the second one is coming down from here to here and then going from here. So, these two parts cancel each other out. So, what is left is coming down from here to here then going from here to here and then going up now we use the assumption that along the any closed any along any excess parallel rectangle the integral of f is 0. So, look at this rectangle the integral of f on the boundary of this rectangle is 0 in the integral there we already have covering three sides of this rectangle fine. So, let us add the fourth side also add and subtract fourth side the fourth side would be addition would be going in this direction and if you add that then this whole thing is 0 that part and you subtract it which means integrate from here to here that survives and then this from this point to this point also survives. So, that is all the and that is all there is survives. So, which means that this expression on the right hand side is equal to z to z plus delta z f delta 2 and remember this important thing here is that whenever I write integral from point 1 to point 2 it is in that mode of traversal horizontal then vertical which is indeed being followed here from z to z plus delta z I first go horizontal and then go vertical. So, all these things cancel out and ensure that we get this integral divide by delta z what is this equal to. So, if I just take this f z and integrate from z to z plus delta z of d w that will only give me delta z I will take that later. So, I am just writing it in this fashion and then I just integrate this part if you just look at this part f z d w integrated from z to z plus delta z that will give you delta z f z delta z and that will divide by this and then you get z plus then you is continually write then take this on the left hand side and take the absolute value. Now, this by continuity this value is bounded by a small amount right. So, let us say for small enough delta that this is bounded by epsilon and where epsilon will go to 0 as delta z approaches 0. So, this is epsilon and then this integral now this is in absolute sense z to delta z will have at most contribute most two times absolute value delta z what is that this right this is this is less than epsilon I am just saying about the rest of the this will come out and then the just the integral z to z plus delta z of d w because that is now inside the modulus. So, I cannot say that it is exactly equal to delta there, but is bounded by two times delta and therefore, this is less than equal to 2 epsilon and now take the limit. So, the derivative of capital F is small f that was the whole idea of showing this. So, capital F is a function which is differentiable on d it is straight forward to see that it is also continuous on d by its definition actually since small f is continuous on d it just translates this property to the integral which is capital F. So, capital F is both continuous and differentiable on the domain d therefore, it is analytic on domain d since capital F is analytic is infinitely differentiable. So, its first derivative which is small f is also in both continuous and differentiable and therefore, small f is analytic. So, now we get this characterization of analytic function in terms of there in contour integrals on a domain z was arbitrary point in on domain d. So, naturally because it is a domain and z naught I can choose and which is a it is an open set d. So, any point z I can always by nature open set there is a disk which is entirely contained in d and within disk I can pick my z naught and z plus delta z because anyway delta z has to be very tiny and then let me prove one more very interesting theorem for analytic function today which will which is actually again quite remarkable it allows us to extend definition of functions on real to complex numbers. Instead let us look at some examples of analytic I think we already saw all the polynomials are analytic by the very nature e to the z is analytic continuous and differentiable right. We can define of course, you have to do it by first principle you cannot just extend the definition of differentiability over reals and plug just assume that it is differentiable here. So, you have to just look at e to z plus delta z minus e to the z and take the limit of delta z going to 0. What is the definition of sin z y z is a complex number right. So, that is that is a way to define sin actually e to the i z minus e power minus i z to y. Similarly, cos z e to the i z plus e to the minus i z divided by there the fact that they are analytic follows essentially from the fact that this is e to the i z is same as e to the z it makes no difference it is only a. In fact, that is also interesting point to note that if you look at the plot of function e to the z it is actually a 4 dimensional plot because z has two parameters x and y and this will also have two parameters being this being a complex number. So, it is a 4 dimensional plot, but without worrying about the values of this if you just look at the z plane the x y plane which defines the complex number z and look at the corresponding e to the i z this plot of this is just 90 degree rotated from this right because if you z is like i x plus i y this is i z is i x minus y. So, x goes to minus y y goes to x. So, that is the just the coordinate shift that happens between these two. So, which clearly shows that all continuity differentiability these are all maintained is just a simple rotation. Now, sin z cos z therefore, all naturally defined and differentiable and therefore, analytic this is going to be a very interesting function for us log z. How do we define log z? Well, in the real world it is the inverse of exponential function. So, can we define it as log z is w where equal to e to the w that will be a natural definition for log z, but there is a problem with this definition. It is a one to many map log z if you define this why because e to the z is not a one to one map it is many to one map. If you look at the x y plane and see what for any z on this plane what is e to the z let me just mark out 2 pi 4 pi. So, in this strip between 0 and 2 pi e to the z is 1 to 1. However, in this strip which is between 2 pi and 4 pi e to the z values are identical to this strip. Similarly, in this strip the values are identical because the e to the z is e to the x plus i y and as y takes value of y from goes from 0 to 2 pi is a cycle back. So, e to the z function itself behaves please differently I mean the exponential function on real in real world you just assume it just keeps on growing that does not happen here. In fact, exponential function in real world can never take negative value it can take negative values if value of y is between pi and 2 pi its value would be negative. In fact, if you think about it for a minute e to the z maps this strip to the entire complex plane except 0 I think it will never hit 0, but every other value is mapped to. And so, if this is mapped to then again this strip again maps repeats the same set of values with maps to again. So, it is e to the z is a map which is many to 1 in fact maps infinitely many points to the same complex number. Now, when you divide the inverse of this which is log z the question is there are infinitely many w's which are for which this holds. So, which w do we assign this we can say that there are infinitely many log functions one for each particular strip right we can say that first log is when z is mapped to w where the y coordinate of w is between 0 and 2 pi. The second log is when it is mapped to y coordinate is between 2 pi and 4 pi third log and there of course, we have to do something about the negative side also here which is not a very nice view to have infinitely many log functions that make sense. The other alternative is to say forget about the other strips we just say that focus on one range of values and this seems like a the main strip between 0 and 2 pi seems like means naturally we are in more inclined to think about this strip as the right strip for us. There is mathematically there is really no difference between these strips but for us somehow between value between 0 and 2 pi seems more natural than a value between 2 pi and 4 pi. So, we say that log z is always going to refer to this strip then it is one to one there is no confusion about the definition of log z, but then this view is also somewhat arbitrary of course and there is which is fine I mean we can be arbitrary if we are defining a function we can define it the anyway which we want. But there is another problem that this function is no longer very nicely behaved what do I mean by that even the continuity of this function is not present everywhere because suppose you are mapping this e to the z maps this coordinate system to this coordinate system and log z being the inverse reverses that. So, let us pick up a circle of radius 1 in this coordinate system and let us start traversing from let us start from this point and traverse this circle counter clockwise and let us see what happens to the log value there when we adopt that log z is this corresponds to this strip. So, what is this point this point is 1 0 what is the corresponding log value to this y would be 0 here and x would be 0. So, it is this point 0 0 actually we cannot include both ends of the strip also. So, we just have to say take this line and throw out this line because otherwise 0 and 2 pi will also have a conflict fine. So, we start at this point and let us start traversing it counter clockwise as I said. Now, as it traverse the modulus of the radius remains 1 which would mean that here the x coordinate will be always 0. And as we increase go this. So, the angle goes up which means that we start traversing up y axis. So, you rotate go keep on going keep on going keep on going come all the way up to here. So, you reached somewhere here and now in this plane I can just loop back, but what happens here you from here you have to jump back here. So, a continuous motion on this plane leads to a non continuous motion on this plane which is a not a very nice property. So, we will see how to fix this. In fact, there is a very nice way of fixing it and the way it works is that as you move there the you keep moving up the y axis and as you traverse cross this x axis here you will move from this function to the function which maps this plane to this one. In a very natural way if there is no we do not have to introduce any artificiality while moving there that is called analytic continuation and we will see exactly how that happens. So, I mean this. So, it would bring in this infinitely many different possibilities of log set which I earlier first called define, but instead of making them any arbitrary choices it would tie them with certain ways of traversing the plane here and that will bring in this all these copies of or different types of log set functions and passion together. So, but by the way why is log set and analytic we have not figured that out. We have not shown that inverse of an analytic function is analytic. No, no inverse is one over the function is analytic, but this is inverse of it. That is that is probably the simplest way of doing it that you have to show that this satisfies Cauchy Riemann, but to do that also we have to z we have to substitute a z equals x plus i y and then you will separate it out into complex and non complex parts other imaginary and real parts. You can write it in polar coordinate that is probably a better idea. Yes, use Cauchy Riemann polar coordinates and then you write in polar coordinates and then check it out. So, that will ensure that this is analytic which I will leave to you to verify and as I said this function is going to be really really important to us and the reason we will for that we will see later.