This is a super cheat. I don't care what you're afraid of, right?  Bring up your own weaknesses. Are you short? Well, cup to girls and be like, hi, you ever hear that short guys are best in bed? Well, I think you should find out, you know? How you doing?  It's true, we're rich. Hi, what's going on? Whatever.


Okay, yeah, we'll just pray and get started. I just wanted to just remind us about the Lord's instruction in Matthew chapter 6. Matthew chapter 6 verse 25. Okay, so now this is something that we do on a daily basis. You know, if you're not careful, we can slip into this, which is Matthew 6, 25, yeah. So this is something that we, you know, sometimes we slip into this and then we think we say that, okay, it's normal. Like a lot of things are normalized in life. And just because we see everyone doing it, or you know, everyone says it's normal, doesn't make it normal. Very important, especially some of the values that we see. So we think, okay, it's normal. Why? Because that's the popular culture. That's what everyone indulges in. That's what everyone does. So I guess it's normal. If it's normal for others, it's normal for me as well. Right? So we see here a very specific instruction and it's, we can say, you know, we can say it's a command, right? The Lord is saying, you know, therefore do not worry. That's how it starts, right? Verse 25. And so which means that he's everything that he shared before comes and bears on that word therefore, right?  So he's talking about everything.  And then no one can serve two masters, God and money. And then he comes and says, therefore do not worry. Okay. And he's talking about very legitimate needs. Okay. Which means that these are needs and these are not luxuries or wants. Okay. He's talking about basic things, food, clothing, shelter, three very basic necessities in life, three things. And then he says that, you know, these are all things your father knows, your heavenly father knows that you have need of these things. So he's saying, you know, he's saying, he's not saying don't work for it. He's not saying don't plan about plan plan for it. Don't pray about it. But he says, don't worry about it. Right. So, and also other things, you know, we can say, okay, at least three things, he's very clear, food, clothing, shelter, I should not worry about. Okay. But what about other things in life? You know, can I worry about it? But the thing is, the Lord is saying, do not worry. And the reason is this, that he is the provider and he will make things happen. And when we seek him, his kingdom, his rule and reign in our lives, that all the other things will fall in place. Okay. And I just want to add, you know, he just said, you didn't say you don't worry, you know, you don't work for it. Right. Didn't say you don't work for it. Because one of the ways in which God provides for us is through work. Right. He didn't say don't plan for it or don't dream, you know, big things. He never said that. He said, don't worry because worry cannot help. He says, you know, how can, you know, why do you worry about clothing? Why do you worry about these things? What shall we eat? What shall we drink? After all these things, the Gentiles seek, your Heavenly Father knows that you need all these things. So that's the assurance. My Heavenly Father knows that I have need of all these things. Right. And he he will make sure that he'll provide and he'll provide those avenues through which these things can come into my life, what I'm going to seek him. Right. Okay. Let's pray. Let's pray and and just, if we have been worrying, we can just say, Lord, I just want to let go of that. Okay. So what is it that's worrying you today? Can we just place it, bring it before God? Maybe it's about your future. Maybe it's about your present. Maybe you're worrying about what happened in the past.  Bring it before the Lord and say, Lord, you said, do it. Therefore, do not worry. And therefore, I will not worry. No, we can just make it a simple prayer. Therefore, Lord, I will not worry because you said it, Lord. And Father, we thank you because you're our Heavenly Father. We thank you that, Lord, that you know our needs even before we ask of them, Lord, and Master, even as we, Lord, you asked us to bring our needs to you, Lord, to ask and seek and to knock God. And so we do that, Lord, and all do all that without worrying. Lord, yes, Master, Spirit of God, lead us, Lord, so that we don't fulfill the desires of the flesh and some of the desires could be to just worry and to be in that place of not making any progress. But Lord, I pray today that you will release us from that and maybe, Lord, move forward, Lord, let not worry, cripple any of us, God, in that particular area, God, and let not worry, paralyze any of us. We pray that there will be momentum, there'll be movement, there'll be breakthrough in those very things, God, even as we release these to you, cast these onto you, Lord, and cast these burdens onto you, God. We thank you in Jesus' matchless name, we pray. Amen. Amen. Okay. Inner wholeness, how's your garden? Yeah. The internal garden. Is it being nurtured? Is it full of weeds? Is it thriving, flourishing? Yeah. Okay. So we looked at some of the lifestyles of that we need to put in place. Lifestyle changes, right? And the last one we looked at was practicing the power of forgiveness. Okay. So chapter seven, we're looking at another important aspect. We've studied it before, the conquest of the mind. Okay. Just want to encourage us, conquest of the mind, the publication, the book, maybe some of you have read it. And maybe in your first years, you must have also written a review of it, have you? Conquest of the mind? No. Okay. So if you've never read it, I just want to encourage you to get a hold of it, read it. And it's a very good book on the mind. Okay. The fact that our mind is something that sometimes we neglect what goes on in our mind. So things like worry, for example. And how our mind is, that's the first thing that we're going to see that how our mind is a battlefield. Okay. A battlefield for what? Battlefield for who? Right. Battlefield where the enemy wants to really take a hold of and rain. Okay. So, you know, we can do one of the two things we can say, okay, you know, all this talk about the evil spirits and powers of darkness.  We don't factor that in. But the fact is that our mind is a battlefield, and it is for the enemy to work on. It is for our unrenewed flesh to be even enthroned, our unrenewed flesh to take hold of us. And, and, but it is also something to be renewed. And the renewed mind is, is a, it's a powerhouse, right? A renewed mind is something that, that would just, you know, just grab a hold of whatever instructions that come from the Holy Spirit, whatever proof that is quickened by the Holy Spirit, a renewed mind is so, so powerful in the life of a believer, right? Just imagine just, you know, there is a suggestion from God, there is a whisper from the Holy Spirit, and your mind does not negate it, but just goes with it, right? Just grabs a hold of it, and, and, and it's so wonderful, right? Okay, so, so what is, what is it that come, you know, to our minds? We use our minds to, I mean, to process a lot of things, right? We analyze with our minds. We, there is sometimes even, you know, our imaginations are in the realm of our, in our mind, right? Our soul. So, what happens is that whoever has our mind has us, okay? So, so that's the thing, you know, in the sense, like, for example, if you look at advertisement, okay? So, right now, you know, if I'm thinking of clothing, you know, one thing comes to my mind, that is the recent store that I went to, which is Zodio, okay? I found that, okay, things are not so expensive. There's a good range of clothes and things. So, that is, you know, when I think of clothes, I'm thinking of Zodio, okay? So, that's been in our mind. When you think of whole drink, what do you think of? Limca, Thumbs Up, anyone else? Fruit juice, there's no soft drinks. Okay, that's a healthier option. See, but the reason we think of Limca or Thumbs Up or Coke or no, Fanta, is there's a reason, okay? Of course, you like the product, you enjoyed it. But also, there's an advertising which reiterates and reaffirms that, hey, you know, go for it. Whenever you think of a soft drink, whenever you think of, you know, you are thirsty, go for it. It's summer, you need a cold drink, go for it. So, that's why it's in our minds, right? So, that's why, you know, I said whoever has our mind has us. You know, therefore, we see that there is, you know, so much invested, every company pumps in so much of money into advertising, so much in advertising, right? And wherever we turn, you know, it need not be just the billboards, but whatever we see on social media, you know, on YouTube, there are some videos which come, advertisements which come, and of course, you have those two seconds of whatever, how many seconds to skip it, but those ads come. Why do people spend so much?  And some of these ads are not meant for you, right? Because that's why you find it boring.  You know, it's for a different age group. It's for a different season of life. But they want to put it there because they want to capture the mind space. So, when you think of maybe housing, when you think of vehicle, when you think of it, a holiday, when you think of clothes, whatever, you know, you're thinking of this thing. That's what, right? So, a mind is a powerful thing, right? It's, this is what James says, you know, when James, you know, in James chapter one, he's talking about the whole breakdown of our thinking or breakdown of the process of temptation. Okay. So, what does he say? He says that James chapter one verse 13, let no one say when he's tempted, I'm tempted by God, for God cannot be tempted by evil, nor does he himself tempt anyone. Verse 14, but each one is tempted when he is drawn away, led away. Okay, that's verse 14, drawn away, we're on page 40 in the notes, drawn away by his own desires and enticed. Okay, so there is this whole place of desires, our own thoughts, our own imagination, our own desires, and we are drawn away, drawn away from what? Drawn away from maybe some decision that we, right righteous thing that we decided, he said, okay, I'm going to live like this, I'm going to live for God, I'm going to, you know, delight God's heart. This is what I'm going to do, that's the thing that you've decided, that's the thing that you're focusing on, but one is tempted when one is drawn away from that, right? What does it mean to draw, or draw away when you're drawn away, to move away? Yeah, what do you say?  He says there are some, some desires and you're pulled away. Now, these desires need not be bad desires, you know, it's just that these desires, the desire is to satisfy those desires in a way that is not appropriate, or in a way that is not God ordained, right? All these desires, right, they need not necessarily be wrong, but to satisfy those desires in not God ordained ways, now that's the wrong, right? Okay, so each one is drawn away, pulled away by their own desires, thoughts, imaginations, you know, and enticed, and that word used there, you know, I think it's candle on, which means that in Greek, which means it's a trap, it's a snare, okay? So entice, which means, you know, it's like, literally means a snare that is used to catch an animal, like how you can use a rat trap, right, to catch a rat, so an enticed.  Verse 15, then when desire has conceived, it gives birth to sin, okay? So it's really talking about thoughts, imaginations, desires, everything being stirred up, we've been pulled away from doing what we have actually decided not to do, or even, you know, desired the right thing to do, you're drawn away by that, and we are trapped. Then he says, verse 15, when the desire has conceived, it gives birth to sin. So he's using that whole analogy of a woman giving birth and the baby growing in a woman, right, in the womb. So when desire has conceived, it gives birth to sin, and sin, when it's full grown, brings forth death. So do not be deceived, brethren. So we see that, okay, everything, this whole thing we're talking about till that person actually sins, right? Is everything is in the realm of the mind, if you look at it, right? Desires, thoughts, thoughts, desires, imaginations, drawn away again by desires, trapped along with our desires. Then, you know, there is this passage of time, or it could be very quickly, but then when desires conceived, it gives birth to sin, which means that the actual act of sin takes place, and then when it is full grown, meaning when the sin becomes a lifestyle, right? It is something that's on and on and on, and it's full grown, it brings forth death, okay? Death in various form, you know, it can be, if it's a substance abuse, if it's, you know, it can be a physical death, if it's any other thing, you know, draws away us from God's separation realm, from the source of life itself, God itself, right? So he's saying, do not be deceived. So the thing is this, that our thoughts are powerful, our mind is powerful, okay?  And I kind of agreed because I didn't know about all these things, right? But the fact is this, that yes, it's powerful, and yes, James one talks about, you know, the mind and in a powerful way, but in a negative way, right? It's powerfully negative to do the negative things, but the reverse is also true, right? The same way in which it can be drawn away, it can be drawn to, the same way it can be trapped, it can be actually set, the mind can be set to do the right thing, the same way, you know, even it's full grow, it says it brings death, well, it can be a lifestyle of righteousness with brings life and righteousness and so on, okay? So it's James one, you look at it in a positive way, yes, that can happen, okay? But the practice is this, you know, mind is a battlefield, so which means that certain things we need to be aware of certain things we need to do, okay? So the Bible says 2nd Corinthians 10, right? Three to five is talking about spiritual warfare, okay? So he says, let me just read that, right? Verses three to five. For though we walk in the flesh, we do not war according to the flesh, right? For the weapons of our warfare are not carnal, but mighty in God for pulling down strong holds, casting down arguments and every high thing that exalts itself against the knowledge of God, bringing every thought into captivity to the obedience of Christ, okay? Okay, so verse three, okay, though we walk in the flesh, we do not war according to the flesh, okay? So what does that mean, though we walk in the flesh? Is that what it means? Right? Though we walk in the flesh, we do not war according to the flesh. So here in this context, flesh does not talk about undone mind, flesh does not, flesh just talks about our humanity, our natural life, okay? We live as human beings, we live in the flesh, natural human life. So he says, though we walk in the flesh, you know, this is how we do it, we live as human beings, we do not war according to the flesh, which means we do not employ natural human methods, okay? Why? Because first of all, that war is not, it's not a natural war, it's not a physical war, it is a spiritual war, right? Because, you know, where does he say we do not fight against flesh and blood, but against principalities and powers, right? So we know that, okay, it is not against a human being. That is why I walk in the flesh, but I do not war according to the flesh, right? And the weapons of our warfare are not carnal. What does carnal mean? Romans 8 talks about that, right? Correct. Yeah. So Romans 8 talks about, we're going to look at that, you know, Romans 8 and verse 6 says, for to be carnal minded is death, but to be spiritually minded is life and peace. Carnal mind is enmity against God, right? It is not, yeah. So it means that it is a fleshly, so when we say here carnal and fleshly, we're not, you know, what we're saying is it's given to, you know, human fleshly appetites, it's given to, you know, things that are not of God, not righteous, right? So we're saying, okay, the weapons are not carnal, but these are mighty in God for pulling down strongholds. So he's making that distinction. What are the weapons, these weapons, which means that these weapons are spiritual weapons and what are they used for? For pulling down strongholds, casting down arguments and every high thing that exalts itself against the knowledge of God, okay? So every high thing that exalts itself against the knowledge of God, bringing every thought into captivity. Okay, what does that mean? Bringing every thought into captivity to the obedience of Christ. Yeah, bringing every thought, it's like a, it's like bringing every thought as a prisoner, captive is a prisoner. Yeah, so bringing everything as, it's mainly like, when somebody is a captive, you cannot do anything else, right? So you're bringing thoughts, imprisoning the thoughts to the obedience of Christ. Okay, that's what he's saying. Okay, but if you look at it, what are these weapons used for? Pulling down strongholds. A stronghold is a, and it's another word, which describes a fortress or a fort. What is a fort? In olden days, the people, Jericho is a wall, the city, we read about that. It's a highly safe, very protective, I mean, very strong thing, structure, right, built of stones and et cetera, you know, and the kings, usually the rulers would be there and inside the fort. Okay, so he's saying the weapons of warfare, which are not carnal, a mighty in God for pulling down strongholds. Okay, and where are these strongholds? Where are these forts? Yeah, because he's saying, you know, if he's talking about strongholds, he's talking about arguments, what are arguments? Yeah, I mean, like, normally if you say argue, it's something that you, it's a strong, it's a strong case. Not necessarily, you can argue for something, right? It's a strong set of reasoning, it's a statement and no, not wrong, not our own understanding. When you say an argument, you know, it's a statement or a set of statements that you present for or against something, in a simple way, that is what it is. So, in our own minds, there could be arguments, you could be arguing, right? Should I do this, should I not do this, right? Should I wear this, should I not wear that, which is the a lot of argument. What should I eat today? What should I cook today? They could be, you know, these are simple things, but there could be arguments against the knowledge of Christ, right? Against the word of God. This is the argument saying, oh, yeah, no, it's actually okay. It's okay to do this. It's fine. It's okay, you know, it's okay. Just this one's, yeah, God forgives anyway. I'm the grace of God anyway. I deserve it anyway. I'm entitled to this. I'm entitled, right, to relax once in a while and, you know, I'm okay. Hey, they do it.  You know, so anyway, it came with the, it came with the lunch. I didn't order it, but they brought it, right? It can be arguments, reasonings in our minds. So stronghold, we know it's a fort. It's like a strong structure in our mind. It is set, it is set about a particular matter. It is just set. And here Paul is talking about a stronghold, which is not of God. Okay, it's something that is off the flesh, something that is energized by the enemy, maybe, you know, some imagination, some thought, something which is a stronghold, resulting in maybe behavior, maybe the way we think about certain things, right, which is not of God, right, pulling down strongholds, casting down arguments, again, a set of statements, which are for something very strong case, right, we build a strong case against the truth, right, and every high thing that exalt itself against the knowledge of God, bringing every thought into captivity to the obedience of Christ, because that's where the actual problem is, right, thoughts, reasonings, arguments, imaginations, strongholds, right, all these. So he's saying that, so the thing is to bring every thought captive to the obedience of Christ, because that's the problem. When the thought is not captive, when the thought is not brought captive to the, or it's not subject to God, then there is a problem, because thought can easily go get into the reasoning, it can get into an imagination, and it can be that desire which James talks about, because it's not a subjected, you know, it's not subject to the word, it's not subject to Christ, it is just going wild, right. So he's saying, you know, bringing every thought captive to the obedience of Christ, and here he's talking about, you know, spiritual warfare and the battlefield being the mind itself, right. Every high thing that exalts itself, where is the knowledge of Christ? You know, I have it in my mind. I know that this is what God wants, or these are the standards of God, but something is exalting itself, you know, this is where it is, the truth is, but something is trying to lift itself up above the truth of who, what God wants, etc., that needs to be brought down, right, and he says, you know, bringing every thought captive. So strongholds to be pulled down, arguments, reasonings to be cast down, bringing every thought to the obedience of Christ. So, you know, we need to be mindful of ideas, thoughts, reasonings, our imaginations. We need to be mindful because it can take us captive. It can bring us to a place of captivity. Okay, so is it easy or difficult? What do you think? Why is it difficult? If it's easy, why is it easy? Okay, everybody said difficult, so why is it difficult? So is that the method? So that's the thing, you know, once I tried, I tried, okay, I need to take every thought captive. So I'm just, you know, constantly thinking, is that, is that, you know, is that something righteous? Is that unrighteous? And by the end of the day, I was so tired, so tired, right? And that's not the way to, I don't think that's the way God wants us. So, I was constantly thinking, okay, it's not something that means convenient. When you all go to some institution, there's already more to come out of some, or something. It's not something you just say, what is it? It goes, you have to constantly think about it. Yeah, so a couple of things, right? One is our understanding that our thoughts cannot be controlled. Or maybe that's, that's what we think. No, we're saying, okay, our thoughts seem to have a mind of their own. It just seems just like a never-ending flow. I cannot control it. I cannot manage it. That's something that we think. Second thing is that, okay, it's too tiresome.  But, you know, when they measured it, they said there's some 30,000, 40,000, 60,000 thoughts that actually go through our minds. What timeframe is it like for one day? And one day, of course, we're talking about, you know, even when we are at rest, there are thoughts going through, right? So you can just think of, you know, on an average, this is what it is, right? So, yeah, you can, you might think, okay, it's too tiresome. It's not possible. Okay, but then when scripture says, you're taking every thought captive to the obedience of Christ, which means it's a possibility. Okay, that's the first thing that we need to kind of come to a conclusion in our minds. If the Word of God declares that we can take every thought captive, that means that it is possible. Okay, and it is a key or it is crucial, first step, to bringing down strongholds. It is a key to cast down arguments, reasonings, right? It is a key to not to be drawn by our desires and to be enticed. So, so that's the whole, that's the thing, you know, so that is the first step. Okay, we have a question, a question, I don't know, Jackie. So when we try to avoid an argument, because we choose to obey God, others at times think we are silent because of pride. In that case, we have to explain ourselves politely, because we, when we try to explain, there's a possibility of taking defense, and we get into another argument. Okay, so we actually, Jackie, when we say arguments, we are casting them arguments, we're talking about our own selves, right, arguments in our own minds, where we have reasoning for and against something. Okay, so you're talking about argument with another person, trying to avoid that argument. Okay, so yeah, that's a, that's a very real scenario, when we avoid an argument. And so maybe my, my, my, my suggestion could be, you know, yeah, maybe in that moment, because of emotions being stirred up, etc. Maybe you can choose a time when it's appropriate to explain.  Maybe at that point, when you're silent, I mean, it's good to be silent, because the person is not in any frame of mind to receive that, whatever you say, you know, that the person is not able to receive it, not in the frame of mind to receive. So it'd be best to, to pause and say, okay, I'll defer it to another time. I'll put it another time, explain, choose that time, and then I will explain, right, when the person is in a better frame of mind. Yeah, so that is what I would suggest. Yeah. Okay. Right, so, so what is the solution, right, to bring every thought captive? What is the solution? So the Bible talks about, you know, different kinds of minds, you know, which, which are actually, you know, what, what we saw just now, you know, a natural mind, a carnal mind, a spiritual mind. Okay. So let's look at that. Romans chapter eight. Romans chapter eight was five onwards actually. Okay, so it talks about those who live according to the flesh, set their minds on the things of the flesh, but those who live according to the spirit, the things of the spirit. For to be carnal minded is death, but to be spiritually minded is life and peace, because the carnal mind is enmity against God. For it is not subject to the law of God, nor indeed can be. So then those who are in the flesh cannot please God. Okay. So, so it talks about a state of mind, which is carnal, a state of mind which is not subject to the law of God, because it's focus, it's on the things of the flesh all the time. Okay. Now a carnal mind could be an unbeliever who has this kind of frame of mind, or it are, you know, the sad thing, or the worst part is it can be a believer, right? It can be a believer who's having a carnal mind, right? So the person is saying, okay, you know, I'm a believer, but then my mind, I'm setting on the things of the flesh, and it's the pattern of the world, it is not subject to the law of God, which means, you know, it's a very frustrating thing for the believer, right? Here's a person who loves the Lord, here's a person who wants to follow the Lord, who wants to do the things as laid out by the Lord, but the mind is not subject because the mind is set on carnal things. Okay. And so it says, it's, you know, to be carnaly minded is death, which means that eventually, because the thing is to be carnaly minded, it is so filled of thoughts, it's so filled with imaginations, reasonings, right? Strongholds maybe, and it results eventually in death, right? It leads, the path it leads to, because whatever you think in your mind is what you actually live out, what you decide or what you think is what you live, right? Yes or no?  So fast, right?   And it happened. So it's such an important function. So all these things are happening to be carnaly set, means it results in such kind of behavior, such kind of action, okay? So a carnal mind results in death for this reason, it will result in a lifestyle of carnality. And, you know, one Corinthians 3 and verse 3, Paul is talking to the Corinthian Church, which is, you know, there's so much of division and strife and so on. So he's saying, for you are still carnal. So is he talking to believers or unbelievers? Believe us, the Corinthian Church, he's talking to people who are filled with the Spirit, right? He was talking to people to whom he said, you come short in no gift, right? And you come short in no utterance, knowledge or anything. Yeah, that's what he says, right? First chapter, right? That you are enriched in everything, by him in all utterance and all knowledge. Verse 7, you come short in no gift, eagerly waiting for the revelation of our Lord Jesus. You know, that's the state of the believer. But look at the state of the mind of such a believer.  So that's the danger. We can be split-filled believers who come short in no gift, very gifted, right? But our behavior can be carnal because our mind is carnal. In our mind, there are these strongholds, there are these arguments, there are these imaginations, which are not being dealt with, right? Okay, so let's look at Romans 12. Okay, Romans chapter 12, verses one and two. So Romans chapter 12 is an important scripture, important key that Paul gives the believers for transformation, okay, for change, change in behavior, okay? So for change in behavior, he's not saying, okay, don't do this, don't do this, don't do this, do this. But change in behavior, he's saying, you need to be renewed in your mind. Okay, that's what we see, right? Romans 12 and verse one, he says, I beseech you therefore, brethren, by the mercies of God, that you present your bodies a living sacrifice, wholly acceptable to God, which is your reasonable service. Verse two, and do not be conformed to this world, but be transformed by the renewing of your mind that you may prove what is that good and acceptable and perfect will of God. Okay, so several things we see here. First of all, he says, you present your bodies as a living sacrifice, right? Just give your whole body, your whole self to God, wholly acceptable to God, which is your reasonable service. Verse one, verse two, do not be conformed, what does conform mean? Do not be conformed, C-O-N-F-O-R-M-E-D, conformed, what does that mean? Molded, don't align, sorry, don't copy or don't follow, right? It just means don't follow and the picture that is of, you know, fitting into a mold, like suppose you have, I'm sure, you know, all of us have played with clay at some point in life, right?  And whatever shape of the vessel is, it retains that shape, you know, because it's clay, it's wet, moldable, so on. So suppose saying, don't conform yourself, don't be like that, see, the world has a mold, the world has a certain value, certain standards, now you don't put yourself and conform to that, be molded like that, right? So don't follow, don't set yourself, so don't conform to this world, but instead, what does he say? Be transformed. So again, there is a, you know, if you see what is common in the English language, you see that formed is there, that word that phrase formed is part of both those words, conformed, transformed, conformed, transformed, like be transformed, what does transformation mean? Change. So what kind of a change is it? Yeah, but what, yeah, that's what we want, but then it can be used negatively also, you know, like Satan transforms himself like an angel of light, right? So it can be a negative thing also, but transform, what does that mean? It means, it means a drastic change, like use the word change, but it's a, it's a very drastic change. And the Greek word used there is metamorphoo, okay, that word. Yeah, metamorphoo, which means from where we get the word metamorphosis, right? A caterpillar changing into a butterfly, going through those different stages, and the first stage and the last stage are unrecognizable, right? Caterpillar, you're saying, we're wondering, wow, is this what it is that will become this beautiful butterfly? Yes. So you're saying that can be the change, that can be the drastic change that can happen. How? By the renewing of your mind, okay? So when you say mind, we are talking about thoughts, we're talking about imaginations, right? We're talking about reasonings and everything. We're talking about, you know, what is there in our mind, goes on in our mind. So we be transformed by the renewing of your mind, okay? To renew is to make new is to renovate change, okay? Renew, make new again, change again, right? Okay, look at Isaiah 55 verses 7 and 7 to 11, okay? Isaiah 55 verse 7, let the wicked forsake his way and the unrighteous man his thoughts, okay? Ways, thoughts, behavior, thoughts. Let him return to the Lord and he will have mercy on him and to our God and he will abundantly pardon. What are the words, Lord saying verse 8, for my thoughts are not your thoughts. So he's talking about the unrighteous man who needs to forsake, unrighteous person who needs to forsake his or her thoughts and the Lord is saying my thoughts are not your thoughts, okay? So which means his thoughts are thoughts of righteousness. The unrighteous man's thoughts are maybe carnal unrighteous thoughts and he's saying, nor are my ways your ways says the Lord, for as the heavens are higher than the earth, so are my ways higher than your ways and my thoughts than your thoughts, okay? So we get, we understand something here, God's thoughts and man's or the unrighteous man's thoughts are totally opposite. God's thoughts are different, the unrighteous man's thoughts are very different and the Lord says, you know, you need to forsake that, okay? So we need to forsake those thoughts. Forsake means what? What does forsake mean? God will never forsake me, but I'm called to forsake those thoughts, leave, abandon, right? Completely just leave and abandon and go. So the Lord is, you know, the instruction is that, that the unrighteous man has to forsake his thoughts, okay? So again, the question, is it possible to forsake my thoughts? It's a very practical thing, let the unrighteous man forsake his thoughts, okay? Forsake is abandoned. So abandon a way of thinking, abandon that analysis, abandon that imagination, that's forsaking, right? So is it possible? The answer is yes, it is possible, yeah?  And that's the key to a renewed mind and a renewed mind is the key to a transformed life or a transformed behavior, right? Okay, we'll stop here and then we'll come back again.


Hi, I'm Zor. Welcome to Indizor Education. Well, it's time to solve a few trigonometric inequalities. I did have some introductory lecture about basic trigonometric inequalities like sine effects less than a. So now let's just solve some problems using certain methodology which might really be very helpful. So I have three problems. They're not really difficult, but there are certain calculations which I hope I will not get lost in. Okay, the problem number one, tangent of x plus cotangent of x less than or equal to a. Alright, so the first complication which strikes our eye is that it's not just simple tangent less than something. It's some of two different trigonometric equations. Some of them, each part we can actually solve. Tangent is less than something and cotangent is less than something. That's okay. How about their sum? And what kind of a function is the sum of tangent and cotangent? Just to better understand what this is all about, I prefer to draw a graph. So let me just think about the graph of this particular function. So this is, let's say from minus pi over 2 to pi over 2. I know the tangent is monotonic and it looks like this. That's our tangent. Now the cotangent is monotonic on 0 to pi, right? So it's like this and it's decreasing. And similarly, here we will have minus pi, so it's this, right? Now, I would like to have some common period of periodicity, interval of periodicity. So I will choose from minus pi over 2 to pi over 2. So let me just wipe this out so it doesn't disturb us and this. And let's sum them together. Now, obviously the minus pi over 2 and 0 and pi over 2 are asymptotes because in this point tangent is going to infinity. At this point cotangent goes to sum infinity, whatever it is. And at this point, again, tangent is equal to infinity. So these are asymptotes minus pi over 2, 0 and pi over 2. Now, at this point, they're both of them the same. And what happens then? Then one function goes to infinity and another goes to 0. So basically we are adding something to this and it will go to this way. And on this side, from this point, it will be exactly the same, but it's the tangent which will go to infinity. So the function goes to this.  This is my sum. Now similarly, on the left from the 0, this both are negative. So the sum will be like this. And then it goes to negative infinity. So my graph would be like this. Now, these are points. They are right in the middle, by the way, between 0 and pi over 2. It's pi over 4, actually, which is 45 degrees and cotangent are equal to 1. So their sum is equal to 2. So this looks like this is 2 and this is minus the corresponding one. But this will make sure actually this is really true. But in any case, I wanted to have a feeling of what actually the graph of this function represents. Now, if I would like to have less than or equal to a, well, it depends. If a is between these two, then the bottom part will be completely inside this interval. If it will be below 2, I will have two different intervals, left and right, and it will be above 2, I mean below minus 2. But if it will be above plus 2, I will have the whole branch of these guys and piece of this plus piece of that on the other side of the intersection. So it all depends on where y is equal to a straight line intersects this graph. So in this case, like I just drew, it's greater than 2. Now, all this part would be part of this solution, well, except 0, of course, where it's not defined. And on the right, from the right part, it would be on this side. Again, not including the pi over 2. So that's basically my general approach to solving this particular inequality. Now let's do it analytically. Now, again, we have the problem, tangent and cotangent, and we don't like it. However, we do know that cotangent is 1 over tangent, right? So what I have here is tangent of x plus 1 over tangent of x less than or equal to a. Now, that's a little bit easier, but not that easy yet. Now, obviously, I have to exclude from all the solutions where the tangent is undefined or the tangent is equal to 0 because the cotangent is undefined. So basically it goes to x not equal to 0, pi over 2, pi minus pi over 2, et cetera. So basically we can say that it's pi over 2 times n, where n is any integer number. So these are prohibited values, and we should really exclude them from all the solutions. Now, after this is excluded, I can multiply by a tangent of x because it's not equal to 0 now since we excluded these values. And what I will have? I will have tangent squared x plus 1 less than a tangent of x, right? Or tangent squared of x minus a tangent of x plus 1 less than or equal to 0. Let's call tangent of x by some letter b, some variable. Now, this is, in terms of v, this is a quadratic equation, a quadratic inequality. And we know how to solve this quadratic inequality because, practically speaking, any quadratic inequality can be represented as a parabola. In this case, it's this way. So depending on where exactly are solutions to the corresponding inequality, where the whole left part is equal to 0, solution to this are all these values of argument in between these two points, right? Because that's where the whole parabola goes below 0. So let's solve this equation. We will find what these are representing the solutions to the corresponding equation. So if I have equations equal to 0, v squared minus a v plus 1 is equal to 0, and solutions are 2 a plus minus square root a square minus 4, right? That's what v first and second are. That's the solutions. And our condition when it's less than or equal to 0, it actually means from that with a minus to that with a plus. So in between these two values, my quadratic polynomial is less than 0, right? So we have solved the corresponding equation, find solutions, and in between these two, since the coefficient of v squared is 1, so the parabola goes upwards, and in between these two solutions, it's below the 0 level. So what we have actually reduced our original inequality is that tangent of x should be basically greater than this particular expression, but less than this particular expression. So we have reduced one particular trigonometric inequality, reduced to a combination of two, to the union of these two conditions, right? Well, that's easy because we know what to do in this case because we can solve each one of them and then take the union. What I would like to add, it's very clearly visible here that a should be at least 2 by modules. It should be either greater than 2 or less than minus 2 because otherwise my expression under the square root would be negative and there would be no solutions. So solutions exist only if a is greater than 2 or less than minus 2, which basically corresponds to whatever I was just talking about, right? Okay, now how to solve these guys, okay? If I would like to solve this one, the left part, so tangent is greater than some value. Now, the tangent is this. So if somewhere is wherever it is, it's greater than, so it should be greater than arc tangent, right? So solution to the left part is x is greater or equal than arc tangent. This is minus. That's solution to this one. Now, solution to this one is x is less than or equal to arc tangent of a plus minus 4 divided by 2. Now, and obviously in both cases we should not really go beyond our interval where we are looking for solutions. So if x is greater than this one, then it should be less than or equal to pi over 2 and in this case it should be greater or minus pi over 2, right? So whenever a is greater than 2 by absolute value, we basically have this particular type of equations of inequalities and we have to combine together into some kind of a solution, right? So what we can say is the following. If a is somewhere here, then above 2, then we can say the following. These two points represent arc tangent of a minus square root of a square minus 4. Let's call it p and q. This is p and q. So this is, it's not really p, it's arc tangent of p and arc tangent of q, right? So in this particular case, so what we have is our solutions are all these guys, all the negative except minus pi over 2 and minus and except 0 because that's where it's not defined. And then from 0 to arc tangent of this particular expression of p. So let's call it p. So we will have from minus pi over 2 x to 0 except we don't have it both obviously. And then we have from 0 to including arc tangent of this expression, which I call p, but anyway it's a minus square root of a square minus 4 over 2. And in addition to that, we have another interval from arc tangent of a plus square root of a square minus 4 over 2 to pi over 2. So that's what we have, right? Completely this thing, that's this. And this is, oh, no, no. It's not before that, it's in between these things, so I'm wrong. So we have to combine these two together. So it's not to the left and to the right, it's in between, actually. So it should be from minus x to plus arc tangent of a plus square root of a square minus 4 over 2. We have to combine these two together, right? So that's what we have. So this is exactly the same as whatever I put here except I applied these particular restrictions. No pi over 2 and no 0. That's why we did this. Now, if it's less than minus 2, I will have correspondingly from minus pi over 2. So this is for a is greater than or equal to 2. Now, if I have a is less than or equal to minus 2, I will have two pieces from here. The one from minus pi over 2 to arc tangent. So minus pi over 2x to including arc tangent of this thing. And this piece from the intersection to 0 from arc tangent of a plus square root of a square minus 4 over 2x, not including 0. I'm not sure which is plus and which is minus. Let's just think about it. If a is negative, then this is more negative, right? Then this. So that's correct, right? So it's two intervals here. Now, what if a is in between? Then the whole solution actually is not working because this square root cannot be extracted. But if a is in between, all you can say is that for minus 2 a plus 2, you have x from minus pi over 2 to 0. So all this part, if a is in between these two values, then it doesn't really intersect the graphs, which means everything below is this whole piece. So that's what we have as a solution. So these three cases. Now, how to get the complete solution? Add pi and to each one of those, basically, because you have to add the period. So this is a complete solution. Depending on a, we could come up with different formulas, different intervals, and then we added the period. But the principle is basically the same. So if I would like to find out where some expression is, let's say, less or equal to a, I try to graph this expression more or less approximately. I'm not saying it's exact. And then intersect it with y equals to a and see on which side values are located in this case. Okay. That's mobile. Well, as you see, it's not really very difficult, but it's involved. There are certain calculations and you have to consider certain cases. It requires certain accuracy and I'm not sure I'm perfect in this, but anyway, trying. Okay. Now, next one. Six cosine square x plus five sine x less than or equal to seven. Again, the problem is we have a mixture of different trigonometric functions. However, it's obvious that cosine square can be converted into sine square and then you will get a situation which is relatively similar to whatever was in the previous problem. We have a quadratic inequality, so it's six minus six sine square of x plus five sine of x less than or equal to seven. So it's a quadratic inequality which we know how to solve. We will call sine of x v and what I will have is it would be minus six v square plus five v minus one because this is seven, this is six less than or equal to zero. Or I like to have plus at the square, so I will have six v square minus five v plus one greater than or equal to zero. I reverse the sine of the left part and reverse the equation to the opposite one. Now, what is this? This is a parabola, right? Directed upwards. So all we need to know are two values where it intersects the x-axis. So it's basically the solutions to the equation, to this equation. Alright, so what are the solutions? Twelve, five plus minus square root twenty-five minus four times twenty-four. So this is five plus minus one over twelve. So I have, if it's minus it's four, so it's one-third. And one-half. One-half and one-third. Two solutions. How can I use this? Well, basically if I'm looking for something of this particular polynomial to be greater than zero, it's quadratic polynomial, it's parabola. Greater means it's left from the left solution and to the right from the right solution, right? Again, parabola. So it goes to the left and to the right of this. So that's where my parabola is positive. So what it goes to is the following. It's sin of x is less or equal than the smallest one. That's one group of solutions and sin of x is greater or equal than one-half. That's another group of solutions, right? Now let's go to the graphic. Now it's easier. So from minus pi to pi, sin goes like this, right? This is minus one. This is one. And we're interested in one-half and one-third. So one group of solutions is less than one-third. Now this is one-third. This is one-half. So less than one-third is everything from minus pi to this point and from this point to pi, right? So from minus pi to this point, this is obviously arc sin of one-third. That's one interval and the second interval greater than this particular point. Now this particular point is pi minus arc sin of one-third and ends at pi. By the way, I specify the interval as two numbers, the left and the right part, and the square bracket means it's including the endpoints. If it's not including, like in case of tangent, I use the round parenthesis. Now what about one-half? That's yet another solution. So here we have greater than. So it means it's in between these two things, from here to here. So this is obviously arc sin of one-half and this one is pi minus arc sin of one-half. So these three intervals within, so it's this one and then the middle one and the small one, these three intervals represent the solution on the interval of periodicity from minus pi to pi. So to get the complete solution, you have to add two pi and two each one of them. Both ends of this. Well, that's it. By the way, in this case, as in the previous case, what I did, I have reduced my original inequality which involved different trigonometric functions to a quadratic inequality in terms of one particular trigonometric function. In case the first one was tangent, the second one was sine, but in both cases I have obtained, from analyzing the quadratic inequality, I have obtained the condition, a very simple condition in this case, on the original trigonometric function, on tangent or sine. And that I have converted into the interval for x, which was supposed to be. Next one. It's kind of similar, by the way, so far. This was also be similar. Now, as usually I don't remember the formula for sine of three-x, but I do remember it's something like some number multiplied by sine x and some number multiplied by sine of three-x. So I'm going to obtain this formula right now, but why am I talking about this? Well, because if this is a combination of sine and sine cubed of x, multiplied by sine, it will be sine square and sine to the fourth degree, which brings me to the point that it will be almost a quadratic equation, but instead of having just an independent variable, I will have sine square as an intermediate variable. So let's see, first of all, I don't remember, as I said, sine of three-x. Let me just derive it. So it's sine of x plus 2x, right? So it's sine of x times cosine of 2x, which is cosine square x minus sine square x. Plus cosine of x times sine of 2x, which is 2 sine x cosine x.  So I have here 1 minus sine, minus 2 sine square. So if I multiply by sine, it will be sine x minus 2 sine cubed x.  So it's minus 4 sine cubed. That's where it is. Okay, so I will use it here. I will use this. This is completely invariant transformation. So I will have sine x times this, which is this, which would be 3 sine square x minus 4 sine to the 4x less than minus 760 by quadratic equation, right? So what I'm doing here right now is quite obvious. I will put sine square equals to v. And what do I have? Minus 4v square plus 3v. Let's put it here. Plus 716 less than or equal to 0, right? That's my equation. Well, again, I prefer to have the positive coefficient at v square. So I will have plus 4v square minus 3v minus 716. Greater than or equal to 0. So I reverse the sine here and I reverse the sine of inequality. Okay, first what we have to do, how to determine the points where this particular parabola is greater than 0, it's left to the left solution when it's equal to 0 and to the right from the right solution, right? We need two solutions of the corresponding equation. So it's 8, this is 3 plus minus square root of 9 minus, it's plus because it's minus, 4 times this times this, 4 times 4 is 16, this is 16, so it's just 7, right? 9 plus 7 is 16, square root is 4, so that's what I have, which is minus 1 eighths and 7 eighths. And this is sine square. Now, when this particular parabola is greater than 0, when v is less than or equal to minus 8 and v is greater than 7 eighths, right? Now, can sine square be less than 1 eighth? That's positive thing, or 0, but not less than minus 1 eighth, right? So this does not bring us any solutions, this one does. So we have to analyze basically the very simple inequality, sine square greater than 7 eighths. That's what we have reduced our problem to. Now, how to solve this? Well, there are many ways. Obviously, you can extract square root. Actually, I prefer to do something I think a little smarter. Remember, cosine of 2x is equal to cosine square minus sine square or 1 minus 2 sine square x, right? So sine square x is equal to what? 1 half, 1 minus cosine of 2x. Cosine square minus sine square. Cosine is 1 minus sine, so it's 1 minus 2 sine squares. And if I resolve it for sine square, it will be here. Cosine will be there. 1 minus, yes, so. And that's invariant transformation, so I'll do this. 1 half, 1 minus cosine of 2x greater than 7 eighths. Well, that's easier because there is no square here, right? OK, so it's 1 half minus 1 half cosine 2 x greater than 7 eighths times 8, right? So it's 8, no, that's 4. 4 minus 4 cosine of 2x greater than equal to 7, 4 cosine of 2x. It's here. It's less than or equal than minus 3. So cosine of 2x less than minus 3. And this we know how to solve for 2x, and then we'll just divide by 2, right? All right, so let's solve it, and that will be the end of it. Now, when is cosine of 2x less than minus 3 quarters? So let's say this is my cosine, 0 to 2 pi. This is pi, this is pi over 2, this is 3 pi over 2. Now minus 3 quarters is here. We need less than minus 3 quarters, right? So it's from this point to this point, this interval. Now, this is arc cosine of minus 3 quarters, right? Because arc cosine is defined on this. It's angle cosine of which is equal to minus 3 quarters. Now, I can actually do it this way. So it's from arc cosine of minus 3 quarters to this point. Now, if this is arc cosine of minus 3 quarters, this is 2 pi minus, because these are symmetrical, right? So 2 pi minus arc cosine of minus 3 quarters. So that's the solution, and adding 2 pi to both sides will give you the complete solution. Well, that's it. Was it difficult? I don't know, it's a little tedious, I would say, because you have to really first transform your original trigonometric inequality, which contains multiple trigonometric functions, into something more bearable with one trigonometric function, but not the simple one, but something like a quadratic inequality, where the one and only one trigonometric function is the argument. The first problem, there was a tangent. In the second problem, it was sine, and in the third problem, it was sine squared. And then, after you solve the quadratic inequality, basically by obtaining some kind of a condition on the argument, and argument is not original x, it's like tangent x or sine x or sine squared x, et cetera, you basically analyze the second wave of inequalities and the third if it's necessary, whatever. So by substitution, you reduce the problem further and further down to the elementary basic level of style like sine of x less than whatever. So that's the methodology. Hopefully it works. And all which is required for you is to see what kind of transformation you should do with the original inequality, which is a mixture of God knows what. How to transform it into something more palatable, more understandable, which can be resolved in steps. So you reduce your complex problem to two, three, four, whatever number, more simple problems. And that's basically the approach to an entire world. Whenever you have a complex problem, reduce it to a combination of small ones, and that would definitely do the trick. Well, that's why mathematicians are the best people who can solve the problems when nobody really knows what to do, because they're trained to think outside of the box. They don't know the algorithm, they come up with algorithms. And that's what this course is supposed to teach you, I hope. All right. Don't forget Unisor.com is the website which allows you to register, pass exams, enroll into different topics, basically to do this controlled educational environment. I definitely encourage you to register and to take exams, etc. So thank you very much. Try to repeat these calculations, these solutions yourself. That's very important. So you'll go again through the same problems. If you can do it by yourself, great. And good luck. Thank you.


In this final example for section 4.5, let us try to find the complex roots of the polynomial function, which is the same thing as writing it factored with a complex factorization. So we have g of x equals x cubed plus 13x squared plus 57x plus 85. Some things to note here, that if we do the rational roots test, we have to look at factors of 85. 85 is 5 times 17, and therefore our rational roots would look like p over q.  I hesitate to do the bigger factors, try the smaller ones first. But also notice, look at the variation of signs here, positive, positive, positive, positive. This tells us that the variation of signs is 0. The negative variation is going to turn out to be 3, so you get 3 or 1. But in particular, if your variation is 0, this means that there are no positive roots. That is a very helpful statement. So now I'm not going to be looking for the positive roots whatsoever, because there are none. So what I'm going to do is I'm going to amend my previous list and emphasize that I'm only going to look for negative numbers. Negative 1, negative 5, negative 17, negative 85. I don't really like looking for the bigger ones, negative 17, negative 85. They're just so big and it's not as likely. So I'm going to try something in the middle. I'm going to try negative 5. It's kind of in the middle of this, not too big, not too small. Sort of the Goldilocks of my potential rational roots right now. So if we go through some negative division, 1, 13, 57, and 85. If we try negative 5, we bring down the 1. 1 times negative 5 is negative 5. Plus 13 is going to be 8 times negative 5 is a negative 40. Plus 57 gives me 17. This is helpful here. Negative 5 times 17 is negative 85, which gives us the root. So my Goldilocks guess was actually a pretty good guess right there. So g of x can then be factored as x plus 5 times x squared plus 8x plus 17. As this polynomial is now quadratic, the quotient, I'm not going to try synthetic division whatsoever. Factors of 17 that add up to be 8 is not going to happen. 17 is the prime number. So my only option was going to be 1 plus 17, which was 18. That's not enough. If there was like a extra digit of 1 right there, we'd be good, but no. We can't factor this using those techniques whatsoever. So instead we got to try the quadratic formula. Because we can't factor it using the reverse foil technique. So we're going to use the quadratic formula. x equals negative 8 plus or minus the square root of 8 squared minus 4ac all over 2a. Like so. And so let's see. 4 times 17, that's a 68. So we get negative 8 plus or minus the square root of 64 minus 68 all over 2. That gives the radicand as a negative 4, which then the square of negative 4 is going to be 2i, negative 8 plus or minus 2i over 2. Fact around a 2 from the numerator, we get negative 4 plus or minus i over 2. This 2 cancels. And so we see that the non-real roots here are actually going to be negative 4 plus or minus i. That actually shows up with what Descartes-Rouls says. Descartes-Rouls said we'll either have 3 negative roots or 1 negative root. We actually only had 1 because 2 of them turned out to be non-real. And so therefore our polynomial will factor as g of x looks like x plus 5 times x minus negative 4 plus i. We're also going to get an x minus negative 4 minus i. If you don't like the double negatives, you can distribute the negative signs right here. And this would give us g of x equals x plus 5.  This would be the complex factorization of this polynomial into linear factors. And in terms of the roots, the roots turned out to be x equals negative 4 plus i and negative 4 minus i. So we can find the complex roots, we can find the factorization. Finding the roots and the factorization are one and the same thing. And combining these techniques of Descartes-Rouls signs, upper and lower bound theorems, the factor theorem, the remainder theorem, it meshes together to help us very effectively solve these polynomial equations by factoring these large polynomials.


Okay. We're going to move on. Our next speaker is Rick Lifton from Yale University talking about genes, genomes, and the future of medicine. Thanks, Eric. I'm delighted to be here today to have a chance to speak to you. I want to start with the proposal that many of the goals of biomedical investigation revolve around four major prospects, understanding the pathosesiology of human disease, with the expectation that this ought to contribute to the ability to make early diagnosis, enable prevention, and enable new and effective treatments. Genetics clearly has had profound impact on our understanding of pathophysiology. And going forward, the one thing that I think we can safely say is that we have great tools to understand pathophysiology, where that will ultimately lead us in the ability to diagnose, prevent, or treat disease will really depend on what the actual pathophysiology is of each disease. And until we know that, we really can't speak, in my view, coherently about what the prospects are for any of these alternatives. I do want to reflect on this anniversary that we've been through, I believe, three distinct eras of gene discovery in this explosion, and I want to make the point that each of these has been driven by saltatory changes in technology, and all of these technological advances have been driven by NIH and NHGRI. And I don't think there is any doubt that without the focus and the commitment to build tools, that we would not be where we are today. And I think it's worth reflecting on, there are so many ways that this could have gone off the rails and not happened, that I think it's just miraculous and a real testimony to NIH's and NHGRI's commitment that we have come to where we are today. So those three, these three eras, in my view, have been the development of complete genetic maps, the development of complete lists of variation of sequence, and now the rapid advances in the technology for whole genome and whole exome sequencing. And so when one thinks about how this has transformed our thinking about disease, as has been discussed, there are thousands of diseases that have been figured out now at the molecular level, and you can't open any textbook of medicine and not find organ systems and pathways that have been profoundly changed by genetic contributions to these disorders. And this is simply a list that I was thinking of last night. Without any particular goal beforehand, I recognize that all of these have come out of the three different eras that I was just alluding to, some from the early Mendelian era, some from genome-wide association and admixture mapping, and some from whole exome sequencing. And all of them, I think, hit my list of favorites because they have pointed to potential therapeutic applications or diagnostic capabilities that have profoundly changed the way we think about these diseases clinically. BRCA1 in cancer has obviously had profound impact for the early diagnosis and prevention of adverse consequences of breast and ovarian cancer. We've changed fundamentally our view of obesity from being a matter of personal strength and character to one of biology with the recognition of the impact of leptin and mutations in the MC4R receptor to have profound effects on body weight. Our understanding of Alzheimer's has been dramatically transformed from thinking, well, maybe these amyloid plaques and the proteins in them have something to do with the disease and maybe not, to recognizing that there's a causal relationship between mutations in gamma secretase and Alzheimer's disease and similarly rare families with Alzheimer's with mutations in APP. New insight into sleep-wake regulation from discovery of the gene for narcolepsy, a recent finding that I don't know how many of you have, it's really percolated through. If you walk into any dialysis unit in the United States, you will find an excess of young African Americans on dialysis. This has been hotly debated over the years as to why this is, it's simply a matter of access to care, explaining why they end up on dialysis. We now recognize from the work of Martin Pollock published just this fall that there are common variants in APOL1 where the heterozygous state protects from infection with the particular tropanosomes in Africa. Homozygous state as a pure recessive increases the risk of going on dialysis by a factor of seven. This will profoundly change the way we think about this disease. Eric has mentioned IDH1 and glioblastoma, multi-forming, gain of function mutations with large effects for glioblastoma and we've also heard about innate immunity and autophagy in inflammatory bowel disease. And lastly, NAV1.7, if you're missing this channel altogether, you're ostensibly normal except you're insensitive to sensory pain, which obviously has interesting therapeutic potential. In my own work, we started for years with an interest in hypertension for the primary reason that this is one of the major contributors to death on the planet. The major risk factor for death from the number one and number three cause of death in the United States and worldwide and its treatment is far from optimal. Most patients are not adequately controlled and most of those who are require three or more drugs and its pathogenesis has been unknown. The reason it's been so hard to understand from physiologic analysis alone is demonstrated here in this working model for the regulation of arterial blood pressure by Arthur Geithner. And you can see that this, I think you'll concede that this is a pretty complex wiring diagram and as a consequence, it's been hotly debated as to whether this is a primary disease of the brain, heart, kidney, adrenal gland, or vasculature. And this struck us now some 20 years ago as an ideal place for genetic investigation with the idea that perhaps we could identify single lesions that would have large effects on the trait. And my one minor disagreement with Eric in thinking in his beautiful talk was he mentioned GWAS as the analog of drosophila mutagenic screed. That would be like Yanni Newsline going out to understand development by taking a collection of millions of flies and identifying subtle differences among them and then trying to understand development. That of course is not what was done. Mutagenesis was done looking for mutations with really large effect that you could pin your hat on and pin down and identify the molecular basis. And so the analog in human is to look for the extreme outliers that would be what you would get from a mutagenic screen if you could do one, which of course you can't, but the fact that there are six billion individuals walking around on the planet, virtually every base that can be mutated that's compatible with survival is walking around somewhere on the planet today. And if we cast our net wide enough and are observant enough, we can find these extreme outliers in the human population. And we have done this repeatedly. And instead of finding genes that are distributed all across the physiologic landscape, the genes we have identified that drive blood pressure to the either the extremely high or the extremely low end of the distribution all converge on a single final common pathway that regulates how the kidney handles salt. And these mutations are distributed both along the nephron, if this is one of the million nephrons in our two kidneys. There are mutations that alter salt reabsorption along the nephron. There are also mutations that lie outside the nephron in endocrine systems that regulate the activity of salt reabsorption in the kidney. So for example, there's an epithelial sodium channel that if you have loss of function mutations in that channel, you have a profound hypotensive disease that typically causes death in the first weeks of life due to an inability to maintain a blood pressure due to a profound intravascular volume depletion. Conversely, if you have activating mutations that increase the activity of that channel, you have the opposite phenotype. Severe hypertension manifest from births onward. In addition to finding genes that we already knew something about from prior physiologic analysis, there are a number of genes that were previously known of entirely unknown functions such as the wink kinases, which we've demonstrated by subsequent physiologic analysis. Our master regulators of many of these diverse salt and water retaining pathways. Importantly, these effects are not subtle and they point to a single vector. There are diverse effects on potassium, magnesium, and calcium. But if you know what is happening to sodium and chloride, you know what is happening to blood pressure. Increase net salt reabsorption, blood pressure goes up, net salt reabsorption goes down, blood pressure reduces. And these effects are individually large. So we think perhaps one of the most telling features is that there are five genes in which loss of function mutations drive blood pressure to the extreme low end of the distribution in the human population, whereas gain of function mutations in those same five genes drive blood pressure to the opposite extreme. The entire spectrum of blood pressure encompassed by the 6 billion people on the planet can be found with variations in a single gene going from loss of function to gain of function, telling you the power of the salt homeostatic pathway to regulate blood pressure. This has been turned into predictive medicine by applying diagnostic methods to identify individuals who have these mutations regardless of their family history or blood pressure. And prospective screening is quite successful in identifying these. And this is clinically important for getting these patients on the right treatment. And also in mitigating some of their consequences, many of these mutations result in cerebral hemorrhage at early ages. In this family alone, there are six people who died from cerebral hemorrhage before the age of 45. And we now prospectively screen these families for intracranial aneurysm. And in this family alone, there are two individuals who have been clipped based on this idea. So if salt is so important, why aren't the diuretics that are the most commonly used anti-hypertensives worldwide more effective as single agents? And why is the epidemiologic data relating blood pressure and salt intake so weak? This is a nice example where finding the gene suggests environmental interactors and these extreme outliers can be used profitably to understand basic aspects of biology. So this is a kindred segregating mutations for the thiozide-sensitive sodium chloride co-transporter. And if you're missing both copies of this, you have a syndrome called Gittleman syndrome, which is the most mild of the blood pressure-lowering mutations. And in this kindred, we identified 200 descendants and identified those individuals who had two mutant copies of the gene, those who had one mutant copy of the gene and those who had none. And that's a very simple question. By measuring 24-hour urinary sodium excretion, identifying how much salt these patients are actually eating on their own normal ad lib diet. What we found was that compared to their wild-type brothers and sisters, those with two or even one mutant copy of the gene are eating a lot more salt. This is not a subtle finding, and it makes a couple of important clinical points. One, when we give patients a thiozide diuretic and a gentle pat on the back and say, don't eat too much salt, we're ignoring the fact that the drug we are giving them is actually driving them to engage in the behavior that we're encouraging them not to participate in. Well, this suggests that if we really want to get where we want to go, we shouldn't be driving thiozide use to higher and higher levels without intervening with something that might blunt the drive for, to increase dietary salt consumption. And this is one of the bases for combined use of inhibitors of the renal angiotensin system, along with diuretics, which is becoming a standard of care. The second point that it makes is paradoxically, in families such as these, the individuals who eat the most salt have the lowest blood pressure. Of course, this is not a paradox when you understand why that is. They have a primary salt wasting problem, and they're compensating by eating more salt. This makes perfect sense in the light of the molecular understanding, but obviously indicates the confound in trying to simply relate dietary salt intake to blood pressure in the general population. In addition to these rare Mendelians, for diseases that we have not been successful in identifying rare Mendelian forms of disease, we have done a number of genome-wide association studies. One of these is cerebral hemorrhage, a devastating consequence frequently interacting with high blood pressure. And with Murat Gunnell and others, we have done two genome-wide association studies comprising 6,000 cases and 14,000 controls, and have a list of genes that are coming out of these that I'm very interested in. One of these is the same variant that contributes to myocardial infarction on chromosome 9. And there are others that are beginning to emerge as a pathway, as Eric was suggesting, in endothelial repair. And a lot of work will remain to prosecute this, but this is the direction that it's pointing. Others have done genome-wide association studies for hypertension, and these have been among the largest disappointments in the field. Studies of nearly 100,000 individuals have explained about 0.2% of the variation in systolic and diastolic blood pressure, and these will prove difficult to prosecute. There may be interesting genes under there, but this remains to be established. In our case, we asked a very simple question. We had three genes that, in which homozygous loss of function mutations caused extreme lowering of blood pressure. And we asked the basic question, what is the prevalence of loss of function mutations in the heterozygous state in the general population, and do these affect blood pressure? And to approach this, we sequenced 3,000 members of the Framingham Heart Study and identified likely functional variants based on variants that occur at positions that have been conserved from invertebrates to humans. And we subsequently confirmed virtually all of these biochemically as loss of function mutations. So first, about 2% of the population is heterozygous for mutations at one of these positions. Importantly, all of those that are inferred to be functionally significant are extremely rare. There are no common variants with frequency 1% or greater. These are all 1 to 2,000 to 1 in 40,000 in their prevalence. And as I indicated, we've now demonstrated that virtually all of these are biochemical loss of function mutations. Turns out that these actually have quite large effects on blood pressure. They reduce blood pressure at age 60 by about 10 millimeters of mercury. And this is sufficient to reduce the overall prevalence of hypertension by about 60% in the Framingham cohort. So these are rare variants with relatively large effects. So we're now entering into this third phase of discovery, which I'm particularly excited about because of the ability to identify rare variants with large effects and to identify previously unrecognized Mendelian traits. In our own group, Muram Choy shown here developed the whole exome sequencing approach, which is about 95% sensitive and greater than 99% specific for identifying novel variants. And the cost of this is coming down. It's about $2,500 last year. We'll likely be about $1,300 this year. So to take advantage of this, we've established a new sequencing center at Yale based on a different model. It's an open access facility. We didn't know what the demand would be in the first year of operation. 60 Yale faculty have used the high throughput sequencing facility. And our throughput has grown from virtually none to about three and a half terabases of sequence per month. So the applications will be to identify previously unmappable Mendelian loci, dominant reproductive lethals we've had almost no ability to find, recessive traits with high locus heterogeneity, somatic mutations in tumors, and then rare mutations with moderate effect in common disease, and finally clinical diagnosis. Our first proof of principle was simply a simple clinical diagnosis. A boy who was referred to us for one of these renal disorders, we simply sequenced his entire exome and nine days start to finish, identified a homozygous mutation in the gene SLC26A3, which was particularly satisfying because this is not a gene that affects salt reabsorption in the kidney, but instead affects the colonic absorption of chloride. We went back to the referring physicians, suggested a diagnostic test that confirmed the diagnosis, and this enabled institution of treatment that has been sustaining for this infant. Secondly, Murat Gunnell has a wonderful cohort of patients with arising from consanguinous union with structural brain abnormalities. This is a natural for this kind of application because novel homozygous variation is likely to be of interest. And in the third exome that we sequenced, identified a very interesting mutation. This is the MRI of a three-year-old boy. You can see the profound loss of the cerebral cortex, despite having normal cerebellum and brain stem. And you'll also note the complete loss of cortical folding compared to a control individual, a normal three-year-old subject. So this boy has a forebase deletion in the gene WDR62 of previously unknown function. And then going back to this cohort, it was interesting without the MRIs, the diagnoses were all over the place, but once you had the mutations and you got the MRIs, it turned out to be quite monotonous. They all had loss of cortical mass and loss of gyro folding. And these patients all had homozygous loss of function mutations in WDR62, which turns out to be expressed in neural progenitors and somewhat later in the maturing neurons. As an example of a new disease with a dominant de novo mutation, I'll give you this. Keith Chote came to the laboratory with these two photographs of patients with a disease called ichthyosis with confetti. The ichthyosis is the bright red skin. The confetti are all of these white spots. And when I asked him what's the genetics, he said there are seven cases in the world, they all arise from unaffected parents, no consanguinity, and they're all singletons who typically do not reproduce. And I asked about the spots and he said, well, we just biopsied one spot and it appears to be normal. So that led to the thought experiment that what could this be? Perhaps this is a disease caused by dominant gain of function mutations and all of these spots are somatic revertents. And how could you have high frequency somatic revertent? It would have to be some kind of recombination mechanism that we speculated. So we went on and demonstrated that this is in fact true, which is what's so wonderful about the technology. These patients have de novo mutations in the gene keratin 10. Interestingly, all of the mutations, although they occur from exon 6 to exon 7 and in the intron, in between, they all lead to frame shifting into the same alternative reading frame. And all of the white spots are independent revertents that have arisen by mitotic recombination having lost the mutant allele. Well, this is an example of high-frequency reversion by the mirror image of the well-known tumor suppressor mechanism and why this occurs with a keratin mutation is interesting but presently unknown. I'll close with a story that is just published in Science today. One of the major causes of severe hypertension on the planet is aldosterone-producing adenoma. This is found in 5% to 10% of patients with severe hypertension and hypertension clinics all around the world. These are interesting tumors. They are benign. They virtually never invade local structures or develop distant metastases. And this poses the question, like other endocrine tumors, is there a fundamental mechanism that links the constitutive proliferation in the tumorogenesis and the constitutive hormone production? This was, of course, a very difficult question to answer prior to the ability to do high-throughput sequencing. So we started with a very simple experiment. We thought, well, we'll start sequencing tumor normal pairs and we'll go as far as we need to go. We didn't need to go farther than four tumors to find a very interesting result. Of the first four tumors, the first thing we found was that these were quite bland tumors. They're on average two protein-altering mutations per tumor. And in the first four tumors, one gene was hit twice, the potassium channel KCNJ5. That was not uninteresting for reasons all explained subsequently. And we consequently went on and sequenced another 18 tumors. And in the first 22 tumors we sequenced, there were eight mutations in KCNJ5 and they were all one of two variants in the gene, G151R and L168R, and the likelihood of that occurring by chance is exceptionally low. So these mutations tell you what they are actually doing. The potassium channel has a selectivity filter shown here from the crystal structure by Rod McKinnon. And the reason these channels are selective for potassium is that there is a gatekeeper series of amino acids, GYG motif, that is conserved in every potassium channel from archaebacteria to humans. And Rod McKinnon back in the 1990s had demonstrated this selectivity filter and it demonstrated that the key residue G151 and this tyrosine that 152 were key to the maintaining selectivity. And these two mutations in adrenal adenomas, aldosterone producing adenomas, mutate this residue directly and residue in the second transmembrane domain that interacts directly with the adjacent tyrosine residue. So this predicted that these mutations would directly alter sodium handling. And this indeed is the case, not shown here, but we've done electrophysiology which demonstrates that indeed these mutant channels conduct sodium as well as potassium. And the consequence of this is readily understandable. The normal adrenal glomerulosa where aldosterone is made, these cells are hyperpolarized owing to constitutively open potassium channels. Aldosterone gets made normally by either closing these channels in response to angiotensin 2 or by extracellular potassium increasing, depolarizing the cell. This activates a voltage gated calcium channel raising intracellular calcium channel, calcium levels. Acutely, this causes increased secretion of aldosterone. Chronically, it causes cell proliferation. So these mutations do this by simply opening the channel, making them permeable to sodium, allowing cell depolarization, raising intracellular calcium, and leading to both chronic aldosterone production as well as cell cycling. Now, you might have argued that this is actually, may not be the complete story. There might be other mutations that contribute, and that could be the case. However, we now have five families that have inherited mutations in a Mendelian form that are associated with congenital aldosteronism. In this family, for example, this individual father who was investigated here at NIH in 1957 had profound aldosteronism at age five, needing both of his adrenal glands to be taken out. He had two daughters, both of whom had their adrenalectomy in childhood as well, and they have inherited mutations in the same potassium channel that also make the channel permeable to sodium. So past views on salt and blood pressure before the genetic era, the Salt Institute and Industry Lobby like to say one thing we know for certain, salt does not cause high blood pressure. That view has changed. The WHO and NHLBI now recognize the essential role of reducing salt balance in the treatment of hypertension. Early use of combinations of diuretics and inhibitors of the renin-angiotensin system are now recognized as a key combination. Prospective trials have shown that if you reduce dietary salt, you reduce blood pressure. This has been modeled by Lee Goldman this year in the New England Journal to show that if you reduce salt intake by 25%, that you'll have a profound effect to reduce the number of strokes, heart attacks, all cause death, and reduce healthcare costs in the country. As a consequence, the Institute of Medicine this year released a study on strategies to reduce sodium intake in the United States focusing on the fact that a very large fraction of our dietary salt intake comes from processed foods, and if you intervene there, you might be able to make progress. Lastly on therapeutics, we've identified a number of potential targets, and the most interesting thing is to find targets that have large effect on blood pressure but are neutral on the adverse effects. And for reasons that are clear from physiology, patients who have mutations in the potassium channel, ROMK, have profound reduction in salt balance, but no discernible effect on net potassium balance. And this has led to this being a very promising target for pharmaceutical development that is now in clinical trials in humans and shows great promise. So as we think about going forward in using sequencing in clinical practice, there obviously are tremendous capabilities, many potential liabilities. Who should we be sequencing and why? We should likely be using this to identify mutations that either establish diagnosis or markedly change our estimates of the susceptibility or that dictate therapy. They're already good examples as to where we might apply this. My own view is that in the near term, we will have the greatest traction when we focus on patients who are likely to have mutations that are pathogenic, but we'll see how this plays out. When should we be doing this? It depends on what the utility is. In Connecticut, we do 40 neonatal tests for about $40 on every newborn. One can imagine as costs come down, one can imagine that this might become cost effective, but a lot needs to be worked through. How do we deal with incomplete understanding of what every variant we see means? We know from the exome data that we will find handfuls of novel variants that are not present in anybody else that we can find to date. How do we communicate these results? These have profound implications for the education of healthcare professionals, patients, and social policy. And then lastly on therapeutics, we need to really help our industry colleagues to focus on the best targets and to prosecute them with passion. I think it's safe to say that the core strength of industry is medicinal chemistry and they have been late to the game in understanding the meaning and how to prosecute biology. There's an awful lot that we can contribute from the academic community to industry and without that we will fail to close the loop and with that I'll stop. Thanks very much for your attention. Time for a question if anybody wants to go to a microphone. I will then ask Rick, what's been your experience in your clinical realm with all these stuff as you're making the more general community or even non-community doc taking up the diagnostic side of what you're finding in hypertension? Yeah, so I think we spend an awful lot of time persuading people not to get molecular diagnosis because once you know enough about the molecular, about the relationship of genotype to phenotype, you very frequently can state categorically that if you have the following 10 clinical findings that everybody always collects, that that's pathognomonic for the disease and there's no need to pursue a molecular diagnosis. Interestingly, many patients want molecular diagnosis regardless and one of the areas that we are not very good at is inexpensively sequencing single genes and I think that's an area that we would clearly like to see improved. On the other hand, for the dominant traits in families, our experience overwhelmingly has been that families are interested, want to participate either in research studies or for clinical purposes and one of the barriers has been finding inexpensive, clear certified validation of these. Certainly for many of these dominant traits, that has been very important. I think in particular with this aldosterone producing adenoma, one can imagine the possibility of having a diagnostic test from the blood since there appear to be two mutations. If you can get a sensitive enough test, that could actually be very important clinically. We now spend an awful lot of resources evaluating patients by very invasive methods for these tumors, adrenal vein sampling being the dominant method and I think there are great opportunities there. All right, thank you Rick.