I just want to read from Isaiah 66 and a couple of verses there, maybe verse 2 verses. It says, Thus says the Lord, Heaven is my throne and earth is my footstool. Where is the house that you will build for me? Where is the house that you will build me? And where is the place of my rest? For all those things my hand has made and all those things exist, says the Lord.  So as we read these scriptures, the Lord is just explaining about physical structure, what we as human beings see on the outside, maybe a big place and he's just contrasting and especially in the light of what is happening, what was happening yesterday and what is happening in our country. The Lord is saying, Heaven is my throne, I'm beyond any physical structure. Where is the place that you will build me? Heaven is my throne, earth is my footstool. And he's saying, Where is the house? Where is the place of my rest? And he's saying, all the physical things, everything that you see, my hand creates all nature and everything I create. And the Lord is saying that on him who is poor and of a contrite spirit, on that person will I look. So the Lord is, man looks at the big structures, grander structures, big monuments, etc. But the Lord is saying, Isaiah 66 was this one and two. The Lord is looking at the heart of the person. And it's like saying that I will inhabit the person who is of a contrite heart and one who trembles at my word. So for the Lord, this is what is precious. This is what is important, that he makes man his holy habitation. And thereby changing, transforming and making something beautiful of that person's life. And he's saying one who's humble, one who's of a contrite heart and contrite spirit and one who trembles at my word, one who reveres God's word, one who honors God's word to the point of literally awaiting and literally trembling at the word of God. So he's giving the priority, this is what is my priority or this is what is important, precious in my eyes. So may the Lord give us discernment in such ways that we will also consider the things that he considers, that we will also esteem as precious, what he esteems as precious, that we will not be swayed or moved by external things that contradict the word of God, that goes away from his point of view or his perspective. So let's pray. Father, we thank you for this day, Lord. We thank you, Lord, that you are awesome, you are greater, you are bigger, Lord, than anything that we could give credit for. We thank you that you are all-powerful, that you're all-knowing God. We bless your name, God. We acknowledge, oh God, that you are the Lord, the all-powerful one, all-knowing one and all-seeing God and nothing escapes your attention, God.  Whatever things that we might be, Lord, experiencing, going through struggles, challenges, Lord, everything, God, you are aware and even as, Lord, you've said, oh God, this one, you will look, that you earn your attention, Lord, to each one of us, God.  We thank you, we come with ourselves into your mighty hands. In Jesus' name we pray, amen, amen. Okay, so we've been looking at the Lord Jesus as an example of leadership, right? So you've got the notes you've received, yeah? Okay, okay. So we looked at three things, right? Three of these points or four maybe, that as the Lord served, so must we be. So we're looking at all these things that the Lord showed us as an example so that we can learn and we can follow. Okay, so let's look at the fifth one. Okay, so that as a leader, this whole aspect of sacrifice. Okay, so the Lord Jesus as a leader, he was willing, ready and he also sacrificed himself, right? So that was an example for us to follow. Hebrews chapter 2 verse 10 says, For it was fitting for him, for whom are all things and by whom are all things in bringing many sons to glory to make the captain of their salvation perfect through sufferings. For both he who sanctifies and those who are being sanctified are all of one, for which reason he's not ashamed to call them brethren. Okay, so he says, just described that for whom are all things and by whom are all things and we know that he was before all things talking about Jesus that through him were all things made that was made. Hebrews 5 verse 7 says, Who in the days of his flesh when he had offered up prayers and supplications with vehement cries and tears to him who was able to save him from death and was heard because of his godly fear. Though he was a son, yet he learned obedience by the things which he suffered and having been perfected, he became the author of eternal salvation to all who obey him. So he talks about his earthly ministry or his walk on the earth and how he talks about the Garden of Gethsemane and he offered up prayers and supplications with vehement tears and cries but he submitted and he was willingly ready to let go of his own life and give his own life as a sacrifice and he suffered. So as a leader, this was something that he came prepared for the Lord. He knew that this was how it was going to be and so he did not deviate from that. He did not move away from that. So what does it mean to sacrifice? One aspect of sacrifice is to give up. That's something that we are familiar with. A sacrifice is something that belongs to you or something that is rightfully yours. It could be a material possession. It could be you have a right to it, a privilege or maybe it's something of a comfort, whatever. So you have a right to it. You have a right to, let's say, live in a certain way. You have the means to live a certain way but you willingly give that up for the sake of the life that you want to live. You willingly give it up for the sake of serving the others because you are a leader. You willingly give up. That's one aspect of sacrifice and the sacrifice which is tied to leadership. So it means maybe we can talk about it. What are some things that we might have to willingly give up to be a leader? You have a right to your time and privacy but then you give that up maybe a little bit because you want to serve others. Maybe you have a right to your rest maybe but sometimes you give up a part of it so that you can serve others. So you willingly give up certain things so that you can serve as a leader. Now the other aspect of sacrifice is also to take on. Now that is something that we may not have considered. Sacrifice is always like letting go. It's about death and giving up. But sacrifice also means that you willingly take up certain things. You maybe take up a responsibility. You take up a task. You take up some work because you are a leader. So we understand that leadership comes with that, comes with sacrifice. So as we are serving as leaders, calling as leaders, we might be called to sacrifice and give up certain things. So I'm just thinking in a small way maybe when some of you were leaders at the short-term Bible college. I'm sure you had to sacrifice certain things. You could not go on living your regular schedule or regular things. You might have wanted to sit and listen to this music or sit and listen to this message or I just want to sleep for some time. But you had to willingly let go of that because of the responsibility.  I need to get this done. I need to maybe in terms of purchases, in terms of whatever. Instructing people or looking after monitoring them, whatever. So you saw, you experienced that in a small way. So similarly, in Christian leadership, we see that this is part of being a leader to be able to sacrifice. So it should not come as a surprise because the Lord Jesus himself set an example for us that a sacrificial living is something that we are called for. See, the thing is there are different levels of sacrifice and depends on the call, whatever. So there's no point in us comparing. Anand comparing with Princeton saying, but his level of sacrifice is, I don't know, it's less or more. There's no point in comparing because when we compare, then it's pointless when we compare. For example, even if you look at believers worldwide, for some, especially those who are hearing some testimonies of those who are living in very difficult places like Afghanistan and so on, to be a believer, to be a witness for Christ. It's a high call. It involves a life of sacrifice to be able to worship, to be able to read the Word. It takes a lot. And there are some, even in our own churches, we hear as I'm saying that for them to come to church, it's a big sacrifice. It's a big thing because they're not allowed. They're not permitted. So they need to work out something. I know of some girls who are living in Mangalore who took up additional work so that they can get out of the house at an earlier time so that they can finish that work, either in the hospital where they were serving or where they finished that and then come or some course so that they could finish and so they could come to church after that and they could go. So for them, just attending church, being part of church itself was a big sacrifice. It was a big thing that they had to take on. Now for some others, that may not be the issue, but it could be something else. So it doesn't matter. We don't have to compare, but we just need to know that in our call, in our role and responsibility that the Lord has placed us as a leader, there will be sacrifice. So we don't have to oppose that. We don't have to be surprised by it, but we just need to understand that yes, the Lord set as an example for us to live a life of sacrifice as leaders. The next one is to be an example. Now as a leader, we are, in a sense, we are called to live our life itself to be a pattern for others to follow. The Lord Jesus set an example like we read about in John chapter 13, about the fact that he, in a way he just explained how he had come to serve and how the disciples ought to serve one another as leaders. And so he washed everybody's feet and he said, you need to do the same thing for I have given you an example. So that word example, it just means a pattern for others to follow, that others can observe, that others can learn about and others can follow. So he says, I have given you an example that you should do as I have done to you. So our life, as leaders, needs to be an example that others can follow. Because in our life, there will be instructions as leaders, there will be instructions, there will be certain things that we need to instruct, command, etc. But never forget that our life is an example for others to follow. Our values, our decisions, our lifestyle, the words we speak, the things that we do, how we live our life, it is an example for others to follow. So that doesn't mean that you always go around thinking, okay, now people are watching, people are watching, how do I live? Am I doing the right thing? No. The thing is that you change your life. It should just flow out. So it's not that I'm in fear or I'm being observed. So I need to behave in a certain way. I need to do a certain way. No. The thing is that let the life of Christ in you completely change, you transform you. We are aligning ourselves to the Word of God and we are led by the Spirit. So we are totally liberated and free to live this kind of life, aware, being aware that we are examples. Okay.   If you are of the world, the world will love its own yet because you are not of the world, but I chose you out of the world, therefore the world hates you and so on.   And so the Lord was making it very clear, you know, even though people persecute, even though people reject, you continue to be an example. You continue to be a pattern of life that others can follow.  But your good works, they will be put to shame, okay? And the other words that we see is in where Paul writes Timothy and he says, maybe in 1 Timothy 4 and verse 12, like he writes about what are those areas in which you can be an example. 1 Timothy 4 verse 12, let no one despise your youth, but be an example to the believers. And he talks about all those areas in word, in conduct, in love, in spirit, in faith, in purity, okay? So in all these areas that we can be examples as leaders, okay? Right. Then the last one here is that as leaders, you know, we are called to trust the team or, you know, trust the core people whom you are leading, whom you are giving leadership to, right? The Lord Jesus again as an example, right? The Lord Jesus appointed, sent the twelve, he sent the seventy others, right? He appointed them, he sent them, okay? So he spent time with them, he taught them, he instructed them. These were people with whom he had conversations. These were people to whom he explained the parables, right? And they went, they did amazing things in his name. And so they came back, you know, we looked in 19, I think the Lord gives them the authority. They came back with good reports saying, Lord, at your name, you know, even the demons are subject. We saw that the demons just leave. So at your name, in your name, you know, they left and so on. So they recognize the power of Jesus' name. They used the name of Jesus as they prayed and commanded the evil spirits to leave. So they saw all that, that was the experience, right? Yet when it came to the Lord being persecuted, they all left, right? No one was around, they all left. And around the cross also, we see John, the mother of the Lord and a few others. But the others had actually left, okay? And we also read about Peter. Peter denied the Lord three times and vehemently and in ways that you would think, okay, maybe this man didn't even know the Lord, you know, the way he was vehemently denying and saying, I don't know Jesus, okay?  And everybody else says, okay, I will also come. Then they all go fishing, right? So he's still a great leader. But the fact is that the Lord forgave and restored and also gave him that responsibility, okay? So which is, I don't know, for the human reason and logic, it seems, you know, why would anyone do that? How can someone do that? How can someone entrust that huge responsibility of the Kingdom of God to such a person, right? But obviously the Lord saw beyond what anyone, any human being could see. He saw beyond their failings or limitations and he saw their heart, okay? Obviously the Lord saw that. And so we see something very courageous that he does. He forgives, he encourages and he restores, right? So this also we see as an example, okay? Which means that as we lead, there will be moments when, you know, maybe, you know, the kind of trust that we are placed on people is broken. So I want to ask, you know, is it easy building trust or rebuilding trust? It's difficult, right? Once trust is broken, you know, every time you are guessing, you know, is that person saying the right thing? Is that person saying because they want me to hear it? Will the person do it? They're saying they will do it, but will they actually do it, right? So you're always thinking about that. So trust, rebuilding trust especially takes a long time to rebuild, right? Bring it back and to heal and so on. But the Lord did that. The Lord did that. The Lord entrusted them. The Lord again gave back that responsibility. And let's, if you read John 21, you know, we see that, right? John 21 verse 15. So when they had eaten breakfast, Jesus said to Simon Peter, Simon son of Jonah, do you love me more than these? He said to him, yes Lord, you know that I love you. He said to him, feed my lambs. He said to him again a second time, Simon son of Jonah, do you love me? And he said to him, yes Lord, you know that I love you. He then said to him, tend my sheep. Now the third time, he said to him the third time, Simon son of Jonah, do you love me? Peter was grieved because he said to him the third time, do you love me? And He said to Him, Lord, You know all things. You know that I love You. And Jesus said to Him, Feed my sheep. So we see this whole restoration of the task and the Lord encouraging Him and really His heart being reconciled and the Lord doing that. So as leaders, you know we will face this will be a reality. So for us to, and it will take a lot out of us, for us to trust the Lord, for us to draw on His strength, right? And for us personally to receive healing, wholeness and also to extend that forgiveness and trust to others. So that it will definitely be something that we will face and it's something that we need to do as leaders. So any questions? We looked at just three. Any questions here? Anything that you might want to add? Online students, anything? Nothing at all? Okay, so just wanted to add some things here. Regarding trust, the example of Peter stands for us in spite of who he was, Jesus chose and trusted, built him up. But they're not the case with Judas when we see others especially while building them up. When we face a situation, how do we see others when they break trust and move further in building them up just like the Lord? Okay, so if you see the difference, of course Judas was not around. He took his own life and that was it. So there was no opportunity to further restore or restore him. So we see that in Judas' life. So when we see others, when they break trust, your question is how do we see others and move further in building them up? Okay, so of course, it requires the response of the other person to whom we are extending trust, to whom we are trusting. So are they repentant and are they willing to work at their life? Which was the case with Peter. So the Lord asks him that question, do you love me? He says yes. And then the Lord says, okay, feed my sheep. And so it's a question of willingness on the other person's part. It's not that we cannot force ourselves to, or force that person into getting back to where they are. It's actually the other person's will, other person's decision and choice. So we extend forgiveness. We extend trust. But is the other person willing to receive that forgiveness? And it's the other person, by virtue of us extending the trust, is the other person willing to work at their lives in order to get back to living a trustworthy life. So that's the thing. So from our part, we extend what we need to extend. In the sense we love, we forgive, we honor. But we need to see that willingness in order to, let's say in terms of responsibility and task and so on, we need to see that willingness. And we need to see that effort to be able to entrust those tasks, entrust those projects or entrust whatever, you know, plus we want to rebuild. We need to be able to see that and then do it. Yeah. Hope that helps. I understand what you're saying. I think somebody's saying something. Sorry. I didn't get anything. Pastor, can you hear me now? Yeah. Yeah. So I understand what you're saying, Pastor, but while we pray for others, especially God has put a burden within us, maybe our relatives or our friends whom we have, who we are praying for. We are praying for their salvation and growth in the Lord. And we don't see that change in them, even in spite of maybe we'll advise them or counsel them as in how the Lord leads. So in our heart, should we keep on praying for them? Or is there a point in time that we give up on them? Okay, God, I'm not able to invest in their lives. Is there a point there or it's a personal thing, Pastor? So the example that we have is that, and the scripture also says that when it comes to saving our salvation or even transformation of life, that he's able to save to the uttermost, which means that because the Lord does not give up, we also don't.  So we don't give up on them. We continue to pray for them that they will change. And of course, we know that it is their decision, it is their choice, but we can continue to uphold them in prayer. That's the least that we can do.  And so it becomes a little more difficult to keep on extending, and we need the grace of God for that, right? So that's a reality. But the fact is that we can continue to extend grace, we can continue to extend forgiveness.  Yeah, that's okay. Okay, just a few comments on, you know, being as a servant, right, as a leader. And we need to understand it correctly because sometimes, you know, we, I don't know, this whole thing of serving, we sometimes do it to the point of really letting go of the role to which we have been called as a leader. So we need to do it right, you know, at the fourth point we saw that the Lord served, you know, He Himself said, I came to serve and not to be served unto, right, to receive this, you know, service or honor from man. So He came to serve. But at the same time, you would see His life in ministry that He went about doing what He was called to do, like He taught, He preached, He instructed. And then, you know, in some cases, you know, the disciples, He would tell them, He would rebuke them, He would correct them. He did all that, right. But in all this, He was serving. Okay, so which means that sometimes we think, okay, maybe you've been appointed as a leader, maybe a leader over a team or leader over an organization, or a particular organization, we have responsibilities. Then we think that, okay, if I need to serve, then I need to let go of this leadership, let go of this thing, you know, sometimes. So we think that, okay, I should not instruct them anymore, because I'm serving, right, I should not correct them anymore, because actually I'm, you know, I'm serving. So sometimes we think in those ways, right, let go of our leadership or let go or compromise on the role and the responsibility that we have called to do, right. So we need to be careful, you know, our heart is a heart where we are saying, okay, my heart is, I want to serve these people or this, whoever the Lord has appointed me as an overseer, I want to serve. At the same time, I need to fulfill that responsibility to which He has called, you know, whatever it requires, if it needs leading, if it needs correcting, if it needs, you know, appointing and all that, instructing, I do it to the full ability with the heart of a servant, right. So I just wanted to state that. Do you have a question? Pastor, one more thing like being servants, like some of the people, some of the pastors will disciple some junior pastors. So what is the level that we can go and their leadership? So this, this, this serving is commander, everything like to serve the pastor also, whatever he says, and his personal works, is that we can take it as a learning or how much we can go in that perspective. You know, as a leader. As a servant, okay, the other side, okay, how much can we do? See, the thing is, okay, you want to do it willingly, and it's not really commanded of you, right. Thank you. For example, you were talking about some personal work, doing some personal work, buying some vegetables, buying, you know, getting this done, etc.  I think it's fine, you know, out of your own free will, out of your heart, you want to do it, you want to serve the other. It's fine, but if it becomes something like a controlling thing, we don't see it in the life of Jesus, right. He doesn't do that. So we need to ask ourselves, you know, do I need to do this? Yeah, I'm respecting, honoring and all that. But then, you know, has this crossed that boundary? Has this crossed that line of free will? And is it become a control? Is it become something like a manipulation? Then we need to be careful. Yeah. And so as a leader, if you see the other side, that also we need to be careful, you know, am I, you know, just using their mess? Am I really serving them or am I using them to serve me in all these things? We need to be really careful. Yeah. The thing is also the sixth point, leader be an example.  Everyone have their own weaknesses. So if someone is pointing out on our weaknesses, like how much extent we have to be an example in other things? Like there will be some weaknesses for us also. That doesn't mean they should not, they should point each and everything, what we are doing, our personal works, or any personal business or character in few things. And it should not affect we as our own self, right? Yeah. So the thing is, let's say somebody gives a feedback and then or review or something. And then they say that, you know, they point out, you know, pastor, this is like this, it should be changed, or this needs to be corrected. And you see, you check, you know, is it valid? Is it really, first of all, is it true? Okay. Because sometimes it can be an assumption on the other person, it can be, you know, whatever, you know, it could be their own, their own mind that they, like, for example, I'll tell you once one morning, I walked into church and then I think something was on my mind. So I, I just went and I believe this person wished me, I did not wish. Okay, so I, I just went, I just, I think we were late or something, this happened many years ago.   So something was, so I, after the service, I asked him, you know, like, is everything okay?   So, you know, so then, and I apologized, I corrected myself. But the thing is that, that's a valid thing, right? It's not that you wanted to dishonor them in any way, and you intentionally, but it was a mistake, a genuine mistake. But you didn't, you didn't see it, and your mind was thinking of something else. So these things happen, the people point out and say, and then we willingly receive it and they say, okay, I'll, you know, I'll change, I'll correct. And this kind of thing is good. But then some people might also, you know, just want to poke holes, just say, you know, you should not have done. I also remember one person saying, and, you know, you, while praying for, I think I was a leading worship and I said pray for this, pray for that. And I was, and I was listening around different, different languages in different states. It was just end of a worship time.  I think we were singing some song about the nation. That person was very upset. You didn't, you didn't say pray for Karnataka. You know, you're living in Karnataka, you're staying in this thing and you're ministering. Yeah, you didn't say. Then, you know, I think you have a bias about, you know, that kind of thing. So you just take it, you know, you take it with a pinch of salt. Okay. It's a, it's a mistake. Oversight. I didn't even realize how many other languages I listed, how many other states I listed. I didn't even realize, but then this person obviously noted and said this. So sometimes people might, I don't know, because of their own insecurities, because of their own hurts, they might say, so just make that distinction and just go with it. Yeah, just need to be discerning. And yeah, that's all we can say. Okay. Okay. We still have some more time. So let's, let's just kind of change. But so that is what we saw about the life of the Lord Jesus, life and ministry of the Lord Jesus and how he was an example in all these seven things. So we can, we can also do the same thing. Right. So, you know, in looking at these examples, we saw that he was very clear about his purpose. Right. For this purpose I had, so he would not be deviated from the purpose, irrespective of the difficulty of the environment or the situation. Right. Despite the pain, despite the difficulty of the situation, he would not be discouraged. He would not be distracted. He would not be very focused because he knew this was the purpose. And so, you know, we're just going to talk about this word vision. Okay. It's different from visions and dreams, something that we, you know, supernaturally see by the work of the Holy Spirit. You're looking at vision being something that is, but that communicates purpose. Okay. So a vision statement. Okay. So you all know the minister, the vision of APC as a church and ministry. Right. So what is that vision? Being salt and light is one part of it. Come on. Okay. Let's, okay. Online folks also, you can actually list down. What is the vision? So I think during the announcements, we all switch off. When we watch the service, anyone wants to take online, you can post it and let's see if we get it complete. So no checking. Okay. Online students, somebody is checking. Okay. Okay. So vision of all people church is to be salt and light in the city of Bangalore and and a voice to the nation and to the nations. Okay. So that's the full or what? Excuse me. So that's the vision. So what does it tell you vision? Let's just analyze it. Salt and light to the city of Bangalore, voice to the nation and to the nations. Okay. So what does it, when you read that, what does it tell you? What do you get from it? What do you understand from it about the church, about the ministry? What does it tell you? That we should be an example.  That we as in the church. Okay. The church community. Okay. Okay. Francis, we'll just pass the mic. So there is that mainly two things, light and salt. Salt and light, yeah. It is like showing the light of the Dalmas and salt. It's a taste of the Jesus to the city of Bangalore and to the nation, the India and the, all the world. Okay. Okay. Right. Nikhil. Nikhil say. Okay. What do you understand from that statement? Like about the statement itself. Okay. That's one part of it. What else? Like, as Nina Chetty said, like first, for this Bangalore, not to that be an example for this world also. Okay. Okay. Prince. Like just communicating what it will do, like what is the purpose of the church is to be your flavor and also to guide and show to the place that Bangalore at the first and also to speak to nations and also to nations. Okay. So communicating what we will do, what purpose. Okay. Shri Radha. It's like APC, what APC stands for, the purpose, the, as a community, as a team, all the believers from APC, their vision, their purpose is like they will reach out to the people, to the nation, to the nations, to the Bangalore. Okay. So what the church will do? Yeah. Okay. You saw it online, so you tell. Little more depth. It's me being silent and let Jesus, Jesus spoke about that. And I mean, APC's the main purpose is to be a silent and like APC want to show the path. And it want to extend its influence over all the Bangalore city. And being as a voice, as a spiritual community, as a Christian, as a, all people search. And to be, to extend that influence to all the nations. Right. How to, like, how the spiritual world focus. Yeah. Right. Right. So, so, yeah, thank you. So everyone, I think I see Jack in response, we are called to live as examples, a testimony. Yeah, and do what large urges us to do great change agents influence Bangalore. Right. So yeah, so that is the, okay, description of the vision. And I think we got a couple of responses where, you know, just saying that, okay, this vision, which means this is something that is the big picture of all the services, all the conferences, all the youth events, all the everything that we are doing. You know, this is the big picture that we are aiming at. That is what a vision is. This is the big picture. In all that we're doing, right, in all the rostering, scheduling, planning, you know, all these events where we are spending the money and all those LEDs and everything, you know, this is the big picture. This is where we are going. And this is what who we want, who we want to be, to be salt, meaning that we will be an influence to be light, meaning that we will have impact in our city. First of all, wherever, you know, geographically, you know, we are placed there as a church as the body of Christ. So where we are and the nation and to be a voice to the nation. So which means a voice of truth, voice of hope, voice, carrying the message of the gospel of Jesus, right, gospel of the kingdom to the nation and to the nations, right. But this is the big picture. This is where what we are aiming for as a church. So that's why you said, you said purpose and what did you say, this is what we want to do. So all our doing, all our being, everything comes because of that. Okay, so that's the purpose. So which means that that defines who we are called to be as a church in everything in our planning, scheduling everything. This is the big picture. This is the target. So we know that, okay, we are going in one direction. You don't have to deviate from that. Okay, so we'll stop here and then we'll talk more about it next class. Thank you.


Missing Link, next question came from my guy George. He said, what's up in Greenville team? Keep it clean fam. I hope you and your family are doing well. Yeah, I appreciate it, George. He said, so after the heartbreaking loss to the Chiefs, I believe it showcases a huge need for the Ravens organization. You may have never heard this before, but the Ravens need a wide receiver, LOL. I know you and I have agreed a lot on the wide opposition. Zay is gonna be a playmaker. And I still have faith in Bateman through this upcoming year, will determine his future with the franchise. I know that you won at DHOP last season, as I did too. I was Zay being here for the foreseeable future and bait with us for another year. Let's say we re-signed Agalor to a modest extension as a debt piece and go and get that big buy to receive a free agency and sign Mike Evans. We are gonna need a running back as well, but imagine lining up with Andrews and likely at tight end with Zay Flowers, Mike Evans, Bateman and Agalor and Evans replacing Odell Beckham Jr. That will give us an option we don't have on the boundaries. I know that's when the wide receiver in the off season will be a new concept for this organization, LOL. But I believe we will finally get it right. And then we will have the best receiving corp this franchise has ever seen. Get a tackle early in the draft, another running back to Pamela Keaton in a corner in the mid rounds and I believe we will have an AFC championship rematch next year versus the Chiefs. Sorry for the Ravens' need to why I receive a question, but what seems ongoing for a decade now, but I truly believe he would put us over the top. Oh man, Mike Evans would, that would be amazing. Because Mike Evans is, yeah, he's liked that. Now, with his 1,000 yards being Jeopardy, being with the Baltimore Ravens. No, I think he could get it. He's somebody that's worked with Todd Munkin before. Couldn't remember, offensive coordinator's name for a second. But he's somebody that's worked with him before so there's that familiarity. And Mike Evans is just productive, straight up. He's a producer, he makes plays, makes catches, gets yak, gets yak in a different way. Not does they flowers kind of yak? I mean, really, who gets it like that, really? Maybe not even Tyree Hill does the same thing, but then this is in a different way. Tyree Hill uses more speed. Agility's there too, for sure. But Tyree Hill uses more speed, they flowers like that. Agility is crazy, it's like through the roof. But anyway, Mike Evans would be amazing because if you have, and with all the guys that you mentioned too, with Mike Evans and his eight flowers, and Rasha Baby, and still Nelson Aguilore, and still likely he got Mark Angus too in the running band. So yeah, Mike Evans would do great for the Baltimore Ravens. He would be a great piece for the Baltimore Ravens and he would just, he would make them that much more powerful. New Year, same problem. Next question came from my guy, Evan. He said, I ain't gravy, I hope you and the family are well amidst this day, but here's my thoughts. There's a lot that goes into the loss against the Kansas City Chiefs. Number one, there were lack of calls on KC side. That could have been taunting from them and maybe two PIs that should have went our way. Number two, there were a lot of fair calls where we showed a lack of discipline, all the roughing calls, unnecessary roughness, et cetera. Number three, there were a lot of mistakes with our turnovers. He was very upset because in that part of the question, he did not keep it clean. Come on now, man. Anyway, number four, bad offensive play calling is what killed us. Number one, Russian offense against the bottom 16, Russian defense, and only eight running calls played. Only eight running plays called, excuse me. Biggest takeaway this game was very much given to the Chiefs we threw. It's just like with peak Brady era, we know they're gonna get calls their way, but we have to stay disciplined and true to our game. Can't set up a defense without setting up the run, which we've had ample opportunity to. But nope, bad play calling and lack of discipline lost this for us, yeah. Made it easy for the Chiefs. We beat ourselves that game by not utilizing the run game in which we had a very clear advantage and love my Ravens, love team keeping clean, but we got to be consistent with our strengths. Can't play the way the media wants us to. We have to play our game. Shout out to Nyan, the great, and yeah. Ravens didn't play that game, and they got beaten bad. Was everybody right about Lamar? Next question came from my god, Jair. Is this Jair Alexander? Could it be? Anyway, they said, I ain't great, I'll be doing well after this heartbreaking loss. I'm questioning if everyone was right about Lamar Jackson after this game. I'm puzzled by the repeated playoff struggles, especially when comparing to Mahomes, Allen, and Burroughs, amazing and sustained performances in the postseason. I know it's not solely Lamar's fault, but I can't grasp why he faces pressure differently. Is it coaching, play calling, or the need for perfection? We had better weapons than the Chiefs offensively and still lost. The playoff losses feel frustratingly similar each time, making me wonder if Lamar can't progress like his peers. I'm lost. Is it Lamar coaching or organizational factors? The uncertainty is getting to me. I'm starting to believe the doubts about Lamar might be valid. The losses feel the same and I can't pinpoint the common denominator. What do you think it is? Lamar coaching, hubs, or culture? I think it is a mix of all of it. All have certainly had their struggles in the playoffs, but in my opinion, I think it starts at the top. Who are your leaders on this team? Who runs this team? If I ask you the question, who runs this team? Who runs the Baltimore Raven? Would you say it's a player, or would you say it's a coach? I'm assuming, just assuming that your answer would be a coach and that answer would be Jonathan Harbaugh. And if that is your answer, then I would think somebody who runs the show, somebody who calls the shots, somebody who makes the decisions, they would realize and recognize what's going on and what's not going on, what's working and what's not working. And they would address it right then and there, especially come playoff time. Now I know John likes to let his coordinator coordinate and I get that. But sometimes if you don't wanna be a micromanager, that's cool, but you still gotta step in at times. And then with Lamar Jackson, Lamar Jackson, you gotta make some better decisions in playoff times. If you're talking about how some of the playoff games are eerily similar, you think about the Bills game from 2020. You think about the pick six that was thrown, cause they call the same play two times in a row. On the previous play, I think either Hollywood was open, I think, or Mark Andrews, or one of them two was open. But Lamar got pressured. And then later in completion, they ran the same exact play back to back. Then he threw the pick six. And that's points right there. That literally takes the minimum of three points away. And of course it could have been seven, but it changes it into zero. And it actually is a seven point swing because it's a pick six, cause they scored a touchdown off of it. And then you think about that Isaiah likely, or the interception with that one. While it should have been passing the fans, it should have been. It was not a good decision. He threw it into one to triple coverage on that one. So that's the part that's on Lamar Jackson. And when you talk about coaching, I mean we talked about that already. Culture, it's weird because the Baltimore Ravens culture, it is and has been based off of defense. It's obviously been a lot of offense now recently too, especially under Lamar Jackson, but their culture is also running the ball. It's running the ball. So the Ravens, they didn't even use their culture in the playoff game. Next question came from Brandon. He said, I know that's a lot of people been saying Lamar is not capable of winning a playoff game or anything. Do you think this is true? No, he literally won a playoff game this year. He literally did. So I mean that X is that out already. He's won a playoff game before. He's won another one this year. So no, that's of course that's not true. There's some people within my family state that also, how do you believe 2025 will go for the Baltimore Ravens? Oh, you're already thinking two years ahead. We got to get to 2024 first. Well, you already think it, but I'm sure you meant the 2024 season. He said, will we come out on top next season? What are your thoughts there? I would hope so, but it's gonna be one of those things we're seeing as believing. I'm with a lot of Ravens fans. I'm not the most confident in the Baltimore Ravens moving forward. I would love if they won a Super Bowl, of course, but my confidence for them, especially playoff time, especially in tough games, especially against the Chiefs, my confidence for them is not through the roof right now because of what we've continued to see. It's very hard to be confident in the Baltimore Ravens moving forward. They're not the most confident in the Baltimore Ravens moving forward because of everything. So, if they change stuff like in regular season, we could see them make adjustments. We saw it this year. We saw them make adjustments, but we saw them not give up leads. We saw them fix stuff. We saw them go through all these positive changes in the regular season this year. We're like, oh yeah, let's go. Then even in the playoffs that first game, it was like, oh yeah, they continue to do it. But then against the Chiefs, against Patrick Holmes, against Andy Reed, yeah, they did that. They did the exact opposite of everything that worked. So, and it was frustrating. It was frustrating to watch. It's frustrating to sit there and sit through that. So, I would hope they come out on top, but my confidence ain't through the roof right now. Next question came from Sebastian. He said, 2023 playoffs, RB1, JK Dobbins, let out his frustrations of not getting the ball more in the run first offense versus the Bengals. 2024 playoffs, different offensive coordinator, six carries for the running backs versus a D-line with a Hopper Chris Jones and no Willie Gay. Oh, I forgot that Willie Gay was out too. This, he said after they just ran, after they just got ran over for over 200 yards a previous week, this isn't an offensive coordinator problem. This is a hardball problem. I'm sick of hearing, yeah, we could have done this that every loss.  If Steve Barshotti can't do the move because he's buddy buddy with him, then we at the end of the ball will just have to watch years of regular season success and wait for the inevitable coaching collapse in the playoffs. See, that's what I was saying too. It's, again, regular season, we're not scared of that. We're not worried about that. Regular season, we're like, oh, yeah, regular season, we got that, we straight. It's the playoffs, man. Playoffs, it just, because again, we could have the nicest teams like we had this year. Got the nicest squad, got health on our side and then they go out and do that. If they go out and do that with a great team, how can we really have confidence that things won't be different or things will be different moving forward? It's really hard too, man. It really is. Oh, and to tag along with the previous question, this was obviously something before this move was official. He said, P.S. promote Mike Mack to head coach. He actually has a brain. Zero points allowed on the second half against Mahomes, sheesh. Then he said also playoff Kyle Hamilton is slowly reaching playoff Ed Reid status. Kyle Hamilton is just amazing. He just, he's amazing at everything. He's just like, I can't call him a perfect player because like he'll have his hiccups because he gave up that touchdown to Travis Kelsy. Even though like Mahomes put that in a perfect spot, man. Cause Kyle Hamilton was all over Travis Kelsy. But when Mahomes put it, only Kelsy could get. Oh, man, that was like, I couldn't be mad at Kyle Hamilton for that one. Cause he was all over Travis Kelsy but Patrick Mahomes put it perfectly. Then he said also it looks like our overconfident rookie got humbled. Yikes. I mean, just try to make a play. Got the ball knocked out and that was that. Next question came from my guy, Jack. He said, do you think we should trade? Come on now, man. What are we doing? What are we doing? He said, do you think we should trade Lamar to a bad team and draft the rookie quarterback? No. Wow, wow. Come on now. We not, we not going back to these. We're not doing this. What are we? Let's continue though. He said, the reason I say this is because Lamar has had so many chances to win it all 2019 blew it. 2020 to 2022 seasons taking uneasy hits and this year he was finally healthy again and blew it. I am done with Lamar. I think we have got to keep mad at BK and coordinators at all costs. In addition, we will probably lose so many pending free agents or honestly, depending on who we lose, we need to draft and sign the wide receivers. O-line secondary D-line edge rushers as well as running back. Anyway, I think the blame pie starts with Lamar. Safe flowers, Todd Monk and John Harbaugh and then the defense to add on. This was probably the easiest chance to win it all. Obviously, winning it all is never easy but so many teams and quarterbacks were having up and down seasons. Next year, so many teams are gonna be better. We will have a harder schedule. Anyway, sorry for the long question. We'll have to hear your thoughts on this. And no, no. Trade Lamar Jackson, no. Just signed him to a big deal, no. He has been the most amazing quarterback in Raven's history. No. And look at, that's not a shot at Joe Flacco. Can I know somebody? Can I say, not a shot at Joe Flacco. Joe Flacco, obviously the most accomplished Baltimore Ravens quarterback in Raven's history. Well, with the Super Bowl, he's the most, he has the most playoff accomplishments. I gotta say that, because Lamar individual accomplishments as far as the two MVP's are the million records, but Flacco playoff accomplishments because all the playoff wins Super Bowl and Super Bowl MVP too. So it's nice that our most recent two quarterbacks, they've done that thing. Now we're waiting for Lamar to just get over that playoff hump, but by trading him, no. I don't think that would be a good idea for the Baltimore Ravens at all. At all. For them to start from scratch, I just do not think it would be a wise move.


This coming Thursday on Winner Home, having completed both spare rooms in the first challenge, the design viewers are briefed on their second challenge and realize that the competition doesn't get any easier. Plus, stand in line to win amazing weekly prizes and your chance of winning the grand prize, your very own home. Tune in for all the design inspiration with Winner Home, Thursday evenings at 7.30pm on SABC 3. Proudly brought to you by Capitech and Private Property, with Samsung products designed for your connected lifestyle. Grand Prize Luxury Penthouse Apartment by Bowen Properties.


I came up with this iterative view of instructional design and developing our open education resources. It's a clear adaptation from Kent Beck and his book Extreme Programming Explained. It's about agile software development. I thought in looking at this approach that it was very appropriate to course design. It was not just limited to an approach for programming. This extreme programming or agile approach came about because 85% of computer projects fail. What the agile approach does is it works in short iterations of two weeks. So every two weeks you have something that works. It's like an onion you build in a layered approach using modules. That software program today is more about assembling modules than it is about creating computer programs from scratch. In fact, I remember about a year ago a speaker from Microsoft was saying that they're looking at assembling. They don't consider themselves to be software creators. It's assemblers, so they take all kinds of modules and you put them together. So I thought this is particularly appropriate for people who are developing OERs. You take the OERs from all the different places, assemble them, and you have a course. But before I really get into that I'm going to do a very fast preview on mobile learning because the other point I want to make today is that we need to be designing for mobile devices. You should stop designing for print, stop designing from a PC on your desktop, and start thinking in terms of mobile devices because when you design for mobile you can easily port it to print, you can easily port it on a PC, but the other way around is quite difficult. And the reason I'm pushing that is right now there's 1.6 billion internet connections in the world. Out of a population this Halloween it will be 7 billion people. There's 3.4 billion mobile devices, 1.3 billion mobile internet users. One third of the world's population, sorry, one third of all the people who access the internet only access it using a mobile device. And here's an example, all over the world the smallest villages have mobile devices. And if you look at web usage worldwide and how they reach the web, you can see Asia. It's mobile devices more than anyone else, Africa, in the developing world. So it's a huge share of total web usage by region. And what you've got to do when you're developing for mobile devices is to take a tip from Ken Anderson and you've got to balance usability, the features, the accessibility, functionality, performance and what bandwidth people have. And you need to have it all in balance to ensure that it's workable on a mobile device. So you need fluid design to then make it flexible. Design it so you don't have horizontal scrolling in particular. And it's easy to do if you just think that way from the beginning. So again I'm going to say design for mobile first. Now extreme programming or agile development, it goes from the philosophy of Randy Paws. One good thief is worth ten scholars. And what it means is there's all kinds of stuff out there that we can use and we don't have to create it ourselves. So what is XP? It's extreme programming and approach to be adapted for web-based course development. And you take the requirement to design implementation, verification and maintenance. And the key to using extreme programming methodology is when the requirements are vague or changing. And all the time you find if you're developing a course where things change, the subject matter expert, what you're using, the technology, different things change and you need to be able to adapt to that. So you meet the goals of XP if you use simple design, unit testing. They use pair programming so they have two programmers working on it. And the key is the iterative development. So you build it like the onion. So you always, even after two weeks, you have something that works and that's the key to it. And there's too many, it's sort of the bizarre approach rather than the cathedral. So why do 85% of these projects fail? Why do we overrun in our course development costs? It's because we build a huge program and then in the end you find out it doesn't work and you're trying to fix it and debug it. With an iterative approach you make sure it works right away. Every little module, every tiny part of it. So you do a review, testing, design, simplicity. These are all principles of XP architecture and integration. And the key again, keep saying this, short iterations. So with the review you have two people watching it. And that's quite common in course design anyway. You have an SME and an instructional designer. So it's nothing that we can't do. Functional testing, when you build a module you test it right away, make sure that it works. Refactoring is you go back and test it again. And when you build a second module you go back and test the two of them together. And you pick the simplest possible design. And you go into a major project, you find out what is the minimum requirement for me to succeed in this project. Not the big project with all the bells and whistles. What is the minimum requirement that we need in order to complete? And you build that and make sure you have it and do it right away, do it in two weeks. And then you start adding on the other things. You use a metaphor as architecture. So you're building it and you use storytelling techniques as part of that. And integration is continuous. So when you don't sort of plan at the end you're going to integrate it into something. You do it all the time as you're working. And again I'm going to say it again and again. Really, really short iterations. So as you've always got something that works. Proven techniques. Early concrete feedback between the subject matter expert and the developer. Continuous feedback. Incremental evolving planning. That is you don't build the big and say we're going to build this big thing. You work at it as you go and you change it as you go. Flexible scheduling. Testing all the time. Testing to make sure it works and continuous collaboration. So how is this innovative? All the practices are under one umbrella of extreme programming. Practices thoroughly as possible. Ensure that the practices support each other to the greatest possible degree. And you have a mentality of sufficiency, not scarcity. And that's important to realize that with Infinite Bandwidth now and all of this. I mean we don't have to start thinking we have to design it and let it fit into one little box. So good practice. You have all of these. The review, architecture testing, design, short iterations, integration and simplicity. And we sort of always are adjusting. We adjust these things in all different ways. But with X speed you turn everyone up full volume. You really review the architecture, the testing, etc. You have that full capacity all the time. Because when you're doing short iterations you can do that. If you do a big one then you have to adjust. I'll do the review later. I'll be doing testing later. The design now is done up front. With extreme programming methodologies we can do that all the time as part of our course design. So a problem, your schedule slips. The XP solution use short release cycles. So why would your schedule slip? It means you're trying to do too much in too little time. Maybe you can do less. A project's cancelled. Solution, the smallest release that makes sense. So as if you're working on a project and the funding ends, if you've done it iteratively, you'll have something that works. You won't have to throw it away. Because you've been doing it in short iterations. So every step of the way you have something that works right from the beginning. Problem, the system goes sour and there's too many defects. Continuous testing, you've been testing all the time. So you know what works. Misunderstandings by developers. The content expert is part of the team. So you keep them into it at all times to eliminate any misunderstandings. The course changes shorten the release cycle. XP is perfect for somebody who says, and you always get this, the content, that's not just what I wanted. I said that, but I really wanted it this way. And with these type of changes, if you do it in an iterative way using an XP methodology, you can incorporate that in right away without it unduly affecting your project. Big problem, rich in features you don't need. Address only the high priority tasks. So as you've got something that works, and then you build something else that you need, something else the high priorities, and then at the end you'll find out, hey, we've got lots of time to put in the bells and whistles and features that may not be needed but are good to have. Staff turnover, people leave. You make people accountable for their own work. And we're talking about short iterations, so if somebody goes, they're accountable up to that point of what they've done. And we can be fairly sure that it's working. Control variables. You've got cost, time, quality, and scope. And we've all discussed the iron triangle. If you decrease the cost, it affects the quality, et cetera. And in a project, if you change the cost, if you have too little money or too much, it causes problems. And a lot of people don't realize that, but if you have too much money, it can cause real problems in developing in any type of courseware development. Time is a terrible control variable. You can have short-term gains, but it can be costly. Sorry, yeah. Time is a terrible control variable. You want to do short iterations. If you start stretching the time out, you're going to get yourself in trouble. Quality, you get a short-term gain, but it's costly. So if you sacrifice quality, there will be a little gain, but then you're going to get yourself in trouble. The key is the scope. The less scope equals better quality and less time. So you have a project like this. Reduce it down to its minimal of what you need. And then you've got it built. You have something that works great. Then add the other things on. Build the scope on after that. So in traditional projects, as they go further and further down, the risk goes up. But with agile projects, the risk leads down as you go on because you have something behind you that works. You've tested it, you've made sure it works, and you can be pretty sure you'll have something that works at the end. So the cost of change does not rise over time. So you build these big cathedral projects and channel, we can't change now because it's too much into it. But with XP, you can change at any time. Change is cheap using XP. You can charge ahead. You can defer decisions. You only need to implement what's needed. And quite often a lot of the dollar costs that you think are going to happen don't happen. You already made it. So the values are there. Simplicity, right at the top. Courage, go for it. Feedback, get feedback all the time. Communicate regularly with the people who are accountable and respect for each other. And the values are all there.  And work on symbol of a design and design it like an onion and have it out like that. The agile manifesto, highest priority is early user satisfaction. So get something that works up as soon as you possibly can and test it. Continuous delivery of valuable coursework. Welcome changing requirements, even if it's late into development. You know, don't panic when the subject matter, well no, I'd like to do this a little bit at the end. You can do that with XP. Deliver the working coursework frequently. Every two weeks have something. That's your goal. Every two weeks you have something that's working with testing. The faculty and developers must work together. Use motivated developers and faculty. Well, that's in anything that is always key. Support them and have face-to-face conversations whenever possible. Working coursework is the measure of progress. So, yack, yack, yack, I've done this, I've done that, and I've heard that from all the time. Oh yeah, I've got it. This is it, but it doesn't work. Yeah, I did exactly what you said, but it doesn't work. So you get working something that works. Sustainable development. You have continuous attention to excellence. Simplicity. Maximize the work that's not done. So pick the work, that kernel of work that needs to be done, and maximize the amount that hasn't been done, and then slowly you build on it. Self-organizing teams. And regular reflection on effectiveness and adjustment. So, the value. There's more value in individuals and interactions over the process and the tools you're using. Working software is more valuable than documentation. And you see some projects, people are very eager to document it. But customer collaboration is more important than negotiating contracts with them. And you see that all the time. Well, the contract said this, and you said that, and I meant this and I meant that. No, work together. Responding to change rather than following a plan. So you don't have a strict plan that you follow. You start responding to the changes as they're needed and come along. So that gives you my introduction to it, and I'll open it up for comments and questions. And I'm not saying that this is the only way you should do course design, but I think it's a good way. It's one good way you can do it. And I don't think that enough of a position doing it that way. I still see too much of the cathedral mentality in course design. Yes, sir. I'm going to ask you this directly. I mean, you work in an institution, which I helped create problems in years ago. And you inherited those. You've got a whole bunch of people that are wedded to that traditional way of doing things with major course teams. I remember our early courses cost over a million dollars each to produce. They were producing beautiful forms so that nobody wanted to even write on them. And they were like PhD thesis because faculty were worried about what they would look like for their peers. There's been a lot of evolution since then, but we all know that these things get quite embedded in our organization. So what happens when you introduce something like XP, the concept at a place like that? I'm going to turn the answer to that over to Cindy. Oh, that's not fair. We're not there yet. I can say that. But Cindy, where are we? We're better than what you're talking about. We've come a long way. We have come a long way. And Ross and I talked about this yesterday, but we are not doing agile development like you're describing it all. I think some of our projects could in fact benefit from something that's closer to that. The problem I have with your methodology is it's not in learning terms. And one of the things that we've found is beginning to work really successfully in working with professors is that we're talking to them in learning terms. So if we were to use this kind of a methodology, we would have to adapt it further so that we would talk about it because what we're really talking about now is a learning design approach. And that has resonance. Faculty are really concerned about what students are learning. And they're also... And they're less concerned, of course, at Athabasca about the teaching piece. And I think now, Ross, they're less concerned about their credibility because of the persistent offer for such a long time. So we need to embed the notion of learning design approach that speeds things up. Some of the resistance is not among the faculty though, I need to say. It's in the administrative systems that supposedly support the design and delivery of courses. And so we need some language that they can also understand. Anyway, it's an interesting idea that they take back and start working on it. But we're not doing it yet. Yeah, and I must say our computer services department say they're doing it. And they're not doing it. There's a few people there who are committed to it. And then you find out it's not really being done maybe partially or something. They're not really getting into it. But your point about it, this has to be described in learning terms. I think it can. I think we can. I think this can be very effectively put into terms of, you know, you get your module, one module, you get it. You don't think of the whole course going, do what I terribly change it as it goes along. I think we can do that. But you're right. And we need to do that. Yes.


In previous videos, we've talked about how derivatives relate to problems that arrive in physical science, particularly in physics. We've talked about how derivatives are used in the motion problem with respect to velocity and acceleration. We've talked about how derivatives relate together the idea of mass, length, and density of maybe like a rod of some kind, the linear density of that rod. The examples do not stop there, of course. Derivatives occur all over the place in physics. Other examples include the idea of power. Power is the rate at which work is done with respect to time. You have ideas about the rate of heat flow, temperature gradients, that is the rate of change of temperature with respect to position. But it's not just physics, right? We can also do other physical sciences like chemistry, which we're going to see in this video right here. Some examples that you could see in chemistry would be about the rate at which a radioactive isotope is decaying over time. You could talk about, for example, the chemical idea of reaction and concentration, and how this introduces the idea of instantaneous rate of reaction. In this video, I want to talk in a little bit more detail about the idea of isothermal compressibility. So what does that even mean? So one of the quantities of interest in thermodynamics, thermodynamics is about essentially the physics and chemistry of heat and temperature and related topics, right? Thermodynamics, among other things, is concerned about the idea of compressibility. I like to imagine in the movie, the Studio Ghibli movie Ponyo, which is kind of like a Japanese anime version of Little Mermaid, right? At the beginning of the movie, Ponyo, who's the fish, she wants to turn into a human girl, and her dad is trying to squish her back into a fish. So you see her in this magic ball, and she's going to squish, squish, squish, and she really doesn't want to do it, but her magic's not powerful enough to resist her. Her dad compressing her back into a small little fish, right? I mentioned if you haven't seen the movie, this dialogue might not make any sense right now, but the compressibility is the idea of how, given like say a gas, how easily we can compress the gas into a smaller volume. So we have the same amount of mass, but we want to compress it down into a smaller volume. How easily can that be done? Is the ability to compress hydrogen the same as oxygen, or nitrogen, or argon? I don't know. I'm not a chemist, but these are things that a chemist would be interested in, or people in thermodynamics would be interested in. How easily can a substance like a gas, or other fluids, how easily can we compress downward? That seems to be something that's a property of that substance, of that gas. So if a given substance is kept at a constant temperature, then its volume V depends on its pressure P. So this is a very important principle from chemistry here, that the volume, pressure, and temperature of a gas, we'll just say gas here, is they're all related to each other, but it's not exactly the same thing. So if we take our, for example, our gas, and we decrease its volume so we compress it down, then these little particles inside are pushing back, right? That's where the pressure comes from. If we decrease the volume, the pressure will increase. That is to say that the volume and pressure of a gas are inversely proportional with each other. On the other hand, if we take our gas right here, and we add a little bit of heat to it, so this is my flame going on there, very clever here. If we heat up the gas, this is going to excite the particles, which then they'll vibrate more. This will then cause an increase of pressure. Let's say that the volume is restricted. We have a rigid container of some kind. It's not flexible at all. If we increase the temperature of the gas, then that'll increase the pressure, right? The object will get, the particle could get more excited. That's to say that pressure and temperature are directly proportional to each other. If we don't have a solid container, like maybe our gas isn't an expandable container, like a balloon, if we increase the temperature, then these things are going to expand so the volume will increase as we increase the temperature. There is a direct relationship between temperature and volume. All of these things are related to each other by direct or inverse proportions whatsoever. When it comes to isothermal compressibility, the idea is isothermal means that we keep the same temperature. Iso means same thermal, kind of like your thermal underwear, it means temperature here, so the same temperature. If we keep a gas at the same temperature, how does the change of volume affect the change of pressure? That's the question we're trying to consider right now. We can consider the rate of change of volume with respect to pressure because if we increase the pressure, if we take our gas and we start increasing the pressure, we're squishing it, we're compressing it, how does that change the volume? We do know the volume will decrease, but how rapidly does the volume decrease? We're asking about the derivative of volume with respect to pressure. As pressure increases, volume decreases. We know that the derivative is going to be negative. This is again given by the fact that pressure and volume are inversely connected to each other. The compressibility is going to be defined with an extra minus sign in it. We know the derivative is going to be negative. The compressibility quantity we're going to come up with, we want to be positive, so we're going to slap a negative sign in front of it. Isothermal compressibility, which is commonly denoted by the Greek letter beta, this is the quantity negative one over the volume times the derivative of volume with respect to pressure. The negative sign comes from the fact that we know the derivative is going to be negative, so we want a double negative to be positive. We're optimistic here. What's with this one over volume right here? The amount of pressure it takes to decrease a gallon of say atmosphere by one. Let me say that again. Let's say we have a gallon of just regular air that's on here on planet Earth. If we want to decrease that from a gallon to a half a gallon, that takes a certain amount of pressure, increase of pressure to do that, but what if we take a half gallon of air and we want to decrease that to one fourth of a gallon, right? So you cut the volume in half. Well, the fact that you have so much more over here versus here, that original volume has an effect, right? And so to make this thing comparing apples to apples, we divide by the volume here so that everything is, it's not based upon the specific size. We actually get a quantity that's resemblant of the molecule, the element that's in play right here and not on the volume of it whatsoever. So what this tells us is that beta is going to measure how fast per unit of volume the volume of a substance decreases as the pressure on it increases at constant temperature. So that's the idea behind isothermal compressibility. This is a valuable quantity to measure how easily one can compress a certain gas. So let's look at a, for instance, so for instance, the volume V in cubic meters of a sample of air, if we keep it at 25 degrees Celsius, which is a normal temperature for air to be here on planet Earth, let's say that that's found, let me read that again, the volume V in cubic meters of a sample of air at 25 degrees Celsius was found to be related to the pressure in kilopascals by the following equation volume being measured in cubic meters is equal to 5.3 divided by kilo by something the amount of kilopascals. So this is an inverse proportion between the two, the two quantities of volume and pressure right here. So Pascal's is a measurement of pressure, which is honestly not very large. And so oftentimes you have to measure pressure in kilopascals like so. Well, the derivative of volume with respect to pressure when the pressure is at 50 kilopascals is given by the following. We can compute the derivative of this by using the usual power rule, right 5.3 divided by P, we can write that as 5.3 times P to negative one. You could use the quotient rule if you prefer, but the power rule is going to be a lot easier here. Taking the derivative of 5.3 times P to negative one, you're going to end up with negative 5.3 over P squared or P to the negative second power right there. If we evaluate the derivative at 50 kilopascals, you're going to end up with 50 squared in the denominator, which is 2500. You can negative 5.3 over 2500, which is going to compute out to be negative 0.00212 cubic meters per kilopascal. Now, as these are scientific questions, we probably should be worried about significant digits, but this is a math video. I don't care about significant digits. Sorry, everyone, we're just going to crunch numbers and not worry about measurement error and things like that. So we get that. We get that the derivative at 50 kilopascals is going to be this negative 0.002. Okay, so we plug that into our formula for isothermal compressibility. So the volume is, what is the volume? It never actually tells you what the volume is here, but we do have a formula that relates volume and the pressure together. So volume is equal to 5.3 over P, which P we know to be 50 kilopascals. So we see that volume is going to be 5.3 over 50, or more importantly, one over volume is going to be its reciprocal 50 over 5.3, which we see that right here in the formula. So we get negative 50 over 5.3 times that by negative 5.3 over 2500. And so when you simplify that, you end up with this number 0.02. And so this gives you the isothermal compressibility of air, just standard earth air at the temperature 25 degrees Celsius. And you can compare that with other quantities of isothermal compressibility to show you how easily 25 degree air compresses compared to other gases at other temperatures.