Well tonight, we're continuing our study here in the book of Joshua. We're almost at the conclusion of our study We only have one more chapter to do and I plan on closing the book of Joshua next week And then we'll embark on another study in a different book, but tonight. We're looking at Joshua chapter 23 and We're looking really at a history lesson Because that's what you're gonna see here as we go through Joshua chapter 23 He's going to rehearse for the children of Israel some very basic things that as we look at together We can learn from he's going to say some things to them That by way of application will help us to live our lives as Christians here in the 21st century And so what we have is a reminder from history We have a history lesson in which he's going to be Communicating to them some things that they already know with an Exertation for them to put into practice those things that they've already been taught and those things that they remember so let's begin reading here in Joshua chapter 23 at verse 1 and I'll read to verse Verse 8 and we'll get into our city Joshua chapter 23 beginning at verse 1 reading to verse 8 Now it came to pass a long time after the Lord had given rest to Israel from all their enemies roundabout That Joshua was old advanced in age and Joshua called for all Israel for their elders for the heads for their judges and for their officers and said to them I'm old advanced in age You have seen all that the Lord your God has done to all these nations because of you For the Lord your God is he who has fought for you See I have divided to you by lot these nations that remain To be an inheritance for your tribes From the Jordan with all the nations that I have cut off as far as the great sea westward and The Lord your God will expel them from before you and drive them out of your sight So you shall possess their land as the Lord your God has promised you Therefore be very courageous to keep and to do all that is written in the book of the law of Moses lest you turn aside from it to the right hand or to the left and Lest you go among these nations these who remain among you You shall not make mention of the name of their gods or cause anyone to swear by them You shall not serve them nor bow down to them But you shall hold fast to the Lord your God as you have done to this day Now as we've been looking at Joshua remember with me that Joshua has divided up the land the land of promise amongst the tribes and He has found a place for himself to settle and it's mentioned in chapter 19 verses 49 through 51 Where that place was and so he has found a place to settle and he's been living peacefully now and has done So for a number of years Now a great amount of time has passed as we enter into chapter 23 a great amount of time has passed from the initial entrance into the land We know that as we've studied through Joshua It took some time for them to conquer the land and it also took some time for them to begin to settle within it and so It's been estimated that when he distributed the land amongst the children of Israel that he made it been around 95 years old We know that according to chapter 24 verse 29 at the time of this riding. He's a hundred and ten years old And so he's lived a long life Which is why he's going to make reference to the fact that he's an older man now and he's he's nearing the close of his life and Because he's nearing the close of his life He feels led to gather the leaders of the nation of Israel. He's going to have a final meeting with them So his life is nearing its end and he's compelled to give them a final and a heartfelt exhortation Now you can sum up what he's going to say and we're going to look at this in some detail in a moment and find some practical Application but the final thing he has to say can be summed up in this Remain faithful to God. That's basically what he's going to say. That's the best advice he can give at his age Remain faithful to God Remain faithful to God's word and remember the things that God has done in the past because remembering the things that God has done in the past and Remaining faithful to his word is going to be the guarantee that God will remain amongst you and working on your behalf And so his exhortation is very simple. It's very basic a simple reminder what God has done and an exhortation to remain faithful to him to remain close to him and To follow him So what he's doing is he's giving them a final exhortation If you will he's giving to them a final piece of advice Advice that comes from the mouth of an experienced old man a man who has remained faithful to the Lord a man who has seen who has seen God's faithfulness to him and Because he's remained faithful to God and because he has experienced the faithfulness of God That gives to him the ability to be one who communicates advice to other people He's nearing the close of his life But he has the ability because he's lived consistently for the Lord He has the ability to communicate to them an exhortation that they ought to listen to because he's proven By the kind of life that he's lived That what he is saying to them would be effective to them because it's been effective in his own life Now when we look at our own world today, we live in a world with no shortage of people who love to give advice We live in an advice-giving world There's no doubt about it a nation that is filled with so-called experts who can at the drop of the hat Give to you the advice that they think you need we hear these advice givers on talk radio. We we Read their magazines There are professional counselors. We have afternoon TV programs filled with people who want to tell you how to live You know people as famous as Oprah and Alan you don't even need to give their last names really You have dr. Phil and dr. Drew you have so many different people who are out there as advice givers Who are telling people you ought to read this book you ought to have this diet you out of vacation in this place You ought to drive this car You ought to do these things you know it and I know it the afternoon TV talk shows are filled with advice givers Or when you leave today all you need to do is go and go to a.m.. Radio And they have a whole lot of people in there wanting to talk sharing their advice with you. That's just the way it is You can get on the net and the net is filled with sites that offer advice and information All you need to do is type in your question. What should I do about my gray hair? And then for you know it you just open up page after page after page of people who are going to tell you Exactly how to do that and they'll give you advice about everything that that you could possibly even question They give you advice about things you've never even thought about. I mean it's filled with advice Or go on Facebook. So many people are on Facebook and you'll see people who are giving advice all the time on their page Well, you need to do this and you need to do that We're living in a in an era of advice and so we have people who are wanting to distribute their wisdom to their friends so The bottom line is is you can find advice in many places Now Solomon who wrote the book of Ecclesiastes Said in Ecclesiastes chapter 12 verse 12 Further my son be admonished by these of Making many books there is no end and much study is weird some to the flesh He's saying there are so many books out there that you can read with so much advice and so many things that people want you to know So experts on life abound the question has to be asked.   Who's going to be the primary advice giver in your life now? Joshua was a hundred and ten years old and He's exhorting the people and he's advising them. How do you find somebody who is going to give to you? Expert advice concerning life One of the best things you can do is look for those who have faithfully followed the Lord over a lifetime look for somebody who has a lifetime kind of Devotion that you can look at and you can say this person here has obviously Been doing the things that are being blessed by God and therefore I'm going to listen to them When we have men's conferences as we had recently I Like to it. I like to have some of the younger men come and share with us You know John Randall who's not really a young man, but a younger man David Zamora for example and others who are younger men. I like that because I enjoy their exuberance I enjoy their fire that they have and and they give great studies And I love these men and the ones that I've had for a conference Isn't the younger men that I brought up here in this pulpit and turned them loose on you are great guys And I love them to pieces But I have had a habit for the last 17 years of bringing Pastor Chuck to come and share with us as the first speaker Pastor Chuck is turning 86 years old and in a few days 86 years old now somebody to say why do you have that old man up there talking? Well, you need to put it into perspective the first time I heard Pastor Chuck speak. He was 43 years old and I was 20 and I looked at this old man Who was 43 and I thought with it myself What does he have to say to a younger man? And so I began learning early in my life to listen to the men who've gone before you to listen to the one Who's gone before you has the experience has the knowledge who's followed God? Because they're the ones that I need to follow and listen. They're the ones. I need to seek advice from They're the ones who who have a knowledge of the things that I need to know So how do we how do we find the person to to listen to if we are looking for counsel? Well, again, we look for those who have faithfully followed the Lord over a lifetime in Psalm 71 verses 17 and 18 It reads oh God you have taught me from my youth and to this day. I declare your wondrous works Now also when I am old and gray-headed. Oh God do not forsake me Until I declare your strength to this generation your power to everyone who's to come When I've grown old and gray-headed that's kind of hard to grow gray-headed today because you can just well if you hate that gray What do you do you wash it away, right? You can always I mean these commercials where these guys are in a bar trying to pick up a younger girl And she doesn't even look at him. So he goes into the bathroom and dabs this stuff on his face comes out He's a check magnet automatically, right? Amazing Amazing still ugly, but at least his hair is not gray We don't want to grow older We don't want to admit That we're growing older and unfortunately for us for those of us who are growing older and Instead of becoming the leaders that we should should be instead of taking life's Experiences and wanting to communicate to those who would be hungry to hear sometimes we try to be young and Act just like the younger crowd and lose the ability to communicate to them because we lose their respect What we need to do is we need to act our age Because I believe that that the generation that is younger than ours those who would belong to my generation The generation that belongs to my children's generation and grandchildren's generation are not looking for buddies They're looking for mentors. They're looking for examples They're looking for people who can demonstrate with their life that the things that God says are true And and they actually impact and when putting to practice They're a blessing and you can be a blessing. So I encourage all of you who are growing older, but don't admit it I'm encouraging you To just grow in the Lord and be willing and ready to share your wisdom wisdom often follows Experience like it says in Job 12 verse 12 wisdom is with aged men and with length of days understanding So it's important for us who are growing older in the Lord to be willing to mentor others and to give advice and exhortation It is also important for us to be careful whom we allow to influence our life by their advice You need to be wise when you select somebody to speak into your life Like it says in Psalm 1 verses 1 and 2 Blessed is the man who walks not in the counsel of the ungodly nor stands in the path of sinners Nor sits in the seat of the scornful But his delight is in the law of the Lord and in his law he meditates day and night So blessed is the man who doesn't walk in the counsel of the ungodly The the new living translation says it like this all the joys of those who do not follow the advice of the wicked Or stand around with sinners or join in with mockers But they delight in the law of the Lord meditating on it day and night Those who do not follow the advice of the wicked and so the Lord has called us to follow the exhortation and advice of those who are walking in his ways and so advice should be sought from those who have Approven life and they should it should be sought from those who have a genuine concern for you You see there are people who are willing to give you advice You may be contemplating doing something and you go to somebody and ask for advice and and they don't love you They don't have a concern for you. And so they're not going to really give to you the best advice that is possible Sometimes they'll give you advice that is poor. It's an advice. It's advice that that they they they think is valuable for you But in reality is going to be harmful to you And so advice ought to be sought from the ones who have a proven life and have a love for you in Romans 15 verse 14 Paul said it like this. He said now. I myself am confident concerning you my brethren That you also are full of goodness filled with all knowledge able also to admonish one another so goodness and knowledge and a willingness to encourage others Makes for a good counselor Now they should always have a desire to advise you to follow the proper path They should always be the individual who directs you to the Lord By his word. I have a picture. I'm going to show you. I believe we have it. I'm not sure I had asked if it could be put up And I don't know if they have it ready or not. Yeah, I just wanted to point this out to you That's my mom who went home to be with the Lord about three weeks ago. This is a Short time before she went home to be with the Lord I want you to see what I'm doing because it's a picture of the advice. I'm giving you right now in my right hand What do I have I?  No, I have a Bible I have a Bible that I carry in my back pocket I've told you before one of my friends said always carry your sword and and he lifted up his Bible He said you because the Bible is called the sword of the spirit and then he said to me Look at David if you can't carry your sword and he pulled out his pocket Bible He said then carry your switchblade so I always so I always carry this with me wherever I go I've always got a Bible on me. I've got a Bible in my heart because I've memorized scripture But I carry a Bible in my pocket so I can pull it out and give advice and counsel from it That's what the Lord has called us to do You ought to listen to the one who has the Bible ready to give you God's advice and not simply their opinion I am telling you that is exceptionally important to understand Because when you have a situation that you want your footsteps directed properly You don't want to go to somebody who doesn't have an understanding of the ways of the Lord You don't want to go to somebody who doesn't love you and have a concern for you And you don't want to go to somebody who's not going to direct your your your steps in the proper path Ecclesiastes once again chapter 12 verses 13 and 14 Says let us hear the conclusion of the whole matter Fear God keep his commandments for this is man's all For God will bring every work into judgment including every secret thing whether good or evil This is the conclusion fear God and keep his commandments His word is what directs us its word is what directs our footsteps And so Joshua is beginning to advise them and he's doing so by reminding them of the Lord's faithfulness to them Over the years. That's how he begins and he gives to them a brief history lesson calling on them to remember He's stirring their memory. He's reminding them of what the Lord has done And and that's a common practice by the way in scripture for people to draw your attention to what God has done in the past It's something that is important. You see it in the writings of paul in philippians chapter 3 verse 1 When he says finally my brethren rejoice in the Lord For me to write the same things to you is not tedious, but for you it's safe I'm reminding you. I'm writing the same things to you so that you know these things I want to rehearse these things to you so that they're embedded within you It's like second peter chapter 1 verse 13 where the apostle peter wrote Yes, I think it right as long as i'm in this tent to stir you up by reminding you Or jude verse 17, but you beloved remember the words which were spoken before by the apostles of our lord jesus christ And so what joshua is doing is he's reminding them He's reminding them of the history. He's giving them a history lesson And he's reminding them of how god has been in the past and Encouraging them to remain faithful to him so that god can continue moving on their behalf So he's old according to verses 1 and 2 He's advanced in age He calls the leaders of the nation that they might meet with him And he begins to remind them As a matter of fact he begins by reminding them first and foremost i'm old That's what he says in the opening statement Well proverbs 16 31 says a silver haired head is a crown of glory if it's found in the way of righteousness And he's saying i'm old and i'm experienced And i have something to communicate to you You see i've guided you in times of war And i've guided you in times of peace And now i want to guide you into your future And so in doing so verse 3 he says to them You have seen all that the lord your god has done To all these nations because of you for the lord your god is he who has fought for you And so he begins by saying you remember god's goodness towards you You remember god's protection You remember his deliverance It is wise to consider god's steady presence on our behalf And it's wise for us to remember how faithful he's been to us And the past victories that we've had in him It's wise for us to meditate on the works that god has done and perform because Those things that he's done in the past he can continue to do in our present And the things that he is doing in our present We'll prepare us for the things he wants to do in our future And so there are times in your life that you may have to look back and remind yourself Has god ever forsaken you has god ever left you behind has god ever done harm to you Has god ever intentionally hurt you has he ever done something that has caused you so much pain And the bottom line is no he has actually seen us through all of those times He's never left us. He's never forsaken us. He never abandoned us He always was there to protect and be with us. And so it's wise to remember the things that god has done in the past You see they had fought to take possession of this land, but he's reminded them listen Yes, god was with you as you fought But it is god who gave you the victory So even though you participated in the battles Remember who is the one who gave you the ability to win and remember who is the actual one who won and fought that battle on your behalf Like it says in psalm 44 1 through 3. We have heard with our ears. Oh god. Our fathers have told us The deeds you did in their days in days of old You drove out the nations with your hand, but them you planted You afflicted the peoples and cast them out For they did not gain possession of the land by their own own sword Nor did their own arms save them, but it was your right hand Your arm and the light of your countenance because you favored them And so the victories they had came because of god The blessings that I have and the blessings that you have Are not earned and deserved They're graciously given to you And when we understand that well, we'll serve him with humility and thankfulness So he's reminding them god has done this. He said the lord your god is he who has fought for you Verse 4 c I have divided to you by lot these nations that remain To be an inheritance for your tribes from the jordan with all the nations that I have cut off as far as the great sea westward And the lord your god will expel them from before you and drive them out of your sight So you shall possess their land as the lord your god has promised you So they have nations that are remaining And the conquest is being is is gradual They're in the process of settling But god is promising to continue expelling their enemies And though there were nations that still remained israel remains separate from them And that's what god has called them to do remain separate So he goes on in verse 6 and says therefore be very courageous To keep and to do all that is written in the book of the law of moses Lest you turn aside from it to the right hand or to the left And lest you go among these nations These who remain among you you shall not make mention of the name of their gods nor cause anyone to swear by them You shall not serve them nor bow down to them But you shall hold fast to the lord your god as you have done to this day And so what's going to safeguard them what is going to make the total conquest of this land possible Notice how he begins by saying you need to be very courageous be exceedingly courageous You need to live out your faith You need to be people of faith is what he's saying You need to trust god with all of your heart And you need to obey him You need to consistently remember the things that he's done in the past because there are still things to do in the future And as god has been with you in the past So he will be with you in your future And he says be very careful to not be turned out Of the right path do not be turned out of the proper path remain faithful to god and avoid the temptation to abandon him For other gods You see god's word will protect you From doing such a thing as you obey him In deuteronomy 28 14 it says so you shall not turn aside from any of the words which I command you this day To the right or to the left to go after other gods to serve them So don't be turned aside from the right path verse 7. He said don't even make mention of the name of their gods Let them be totally forgotten Let them be as if they had never had their names mentioned in this land May it be that they will be like those that have never ever even been heard of now. Why is that so important? Well, because if you remember those gods You may become curious about those gods When you become curious about those gods you may begin to investigate those gods as you begin to investigate those gods You may be tempted to follow those gods By remembering them you're going to give an open door for them That you might be drawn away tempted And even led to worship them Be careful You may begin to swear to them As if they're the judges of your motives and your actions You may begin to serve them in the religious rites that the pagans practice You may bow down to them as your creator and preserver And then what you'll end up doing is giving your worship to idols instead of the true god And so what you're supposed to do is detach yourself completely and finally 100% From those things forsake those things have nothing to do with those things don't even mention those things And pursue the lord with all of your heart, you know as as I read the bible and I've been reading it for a while now As I read the bible I never find any indication from the old to the new testament anywhere That god ever says to me, you know, I'd like you to follow me half-heartedly I never see that have you ever seen a verse where Jesus says if you're going to follow me That's cool. Follow me on a couple days out of the week, but the rest of the week is yours All I'm asking is just a little bit. I've never seen that You when he when he calls his apostles He calls them to leave everything behind and follow him The call of the disciple is for a person to to change the direction of their life So that they instead of pursuing the things that took him away from god The call of the disciple is to turn them around so they'll pursue the things that are of god And so you find that through scripture Pick up your cross daily. Jesus said deny yourself pick up your cross daily and follow me And so you never see an indication in in scripture that god has called me to partial Worship of him. It's always complete and he's even gone so far as to say no man can serve two masters You're going to worship one or you'll worship the other, but you can't worship both of them So what we have to do is as christians is we have to make a determination that i'm going to follow god Now some people see that is so heavy that it scares them. They're they're afraid to do that But I I discovered a long time ago that that I cannot be a hundred percent committed To to two things I have to be a hundred percent committed to one And i'm a hundred percent committed or should be to my faith in christ and my following of my god That's what i'm supposed to do and then everything else follows after that I used to teach a bible study here in uh inchino back in 1975 At a house that's right up just up the street from here off of uh About two blocks up off of east end and um Philadelphia It's a rock. It's it's a house that's made out of rock.  I was 25 years old I had a man who was coming to the bible study at that time his name was charlie and um charlie had just committed himself to the lord and uh And he started coming to the bible study there and and grew in in that ministry under me for for a while Then I hadn't seen him for some time And then I was teaching here as the pastor of this church. So years had passed and And and charlie came to visit us and he came and spoke to me one day and he said, you know David he said when you would teach because I was taking him to the gospel of mark He said when you would teach and you read the scriptures that said love god with all of your heart all your soul all your strength He said when you would when you read those scriptures and you exhorted us to love god like that Now remember I was 25 years old at that time And I was already saying we have to love god like that because that's what the word says He said what I heard you say that He said I I could not grab hold of that. He said I just I couldn't buy into that He said I was christian. I wanted to follow the lord, but that sounded so demanding especially when you said To love god with all of your heart more than you love anything else And he said and I would argue with you in my mind about that And I would say I can't because I have children. How can I love god more than I love my my son or my daughter How can I do that? He said and I would feel so bad within me because the bible says to love god with all that's within you And yet he said I loved my kids so much and this is what he told me I'll never forget. He said and then I realized after following the lord for a while That my source of love for my children really sprang forth from the love I had for my god And the more that I grew to love my god He said the more I learned to love my children And the more love that god poured into my heart in my relationship to him More love I was able to give to my son and my daughter And he said it took years for me to finally realize what had transpired As I was becoming more devoted to my god it didn't take me away from my family It made me a better man in my family Because the love that I started to have for god began to pour over into the love that I have for my kids He said so now I understand what you were trying to say And that's what the word would say you see if you love the lord god with all your heart Which no human being really has ever been able to do that Even the one who was commanded by god to pen those words Moses himself didn't love god with all of his heart because he didn't even make it into the promised land And as I've shared with you before men like david who god himself speaking of david said This is one who's who's his heart is completely after me And yet even david himself Could not claim to have loved god with all of his heart because when you mentioned the name david King david There's always another name that's associated with his name, and that's the name bathsheba and so even david who couldn't go outside and And just watch the sheep without looking at the stars and thinking of how great god is Even david could never make the claim that he loved god with all of his heart So I understand that because of the limitations of my flesh of our flesh That there will still always be An awareness of my own weakness and frailty and my capability Of of really understanding that to the depth that god would have me to understand it and yet at the same time I know that if you pursue the lord on a daily basis and you say god today I want to seek you more than I did even yesterday That you begin to mature in the things of the lord you begin to grow in the things of god And it's more of god and less of the world through a lifetime And that's how maturity occurs in your life by simply seeking him on a daily basis By pursuing him and by holding fast to him Now instead of clinging to and holding fast to false religion He says in verse 8 you shall hold fast to the lord your god As you have done to this day They're to hold fast to the lord. How do you do that? Well, it begins by holding fast to his word in deuteronomy 13 4 We read you shall walk after the lord your god and fear him and keep his commandments and obey his voice And you shall serve him and hold fast to him We saw in joshua 22 verse 5 But take careful heed to do the commandment and the law which most is the servant of the lord commanded you To love the lord your god to walk in all his ways To keep his commandments hold fast to him serve him with all your heart with all your soul We see paul in second timothy 113 equine that when he says hold fast the pattern of sound words Which you've heard for me in faith and love which are in christ jesus You hold fast to the lord as you hold fast to his word Because god god's word reveals god to us and therefore we cling to the one who's been revealed And so by holding fast to the lord and holding fast to his word Well, that will make it possible for them to be in the midst of evil but not be part of it Because there are still there are still tribes that and peoples that have yet to be Taking care of they're still there. They're living amongst the evil Well, even as christians live in the midst of those who do not believe We can still remain separate We're in this world. There's no doubt about it. God hasn't pulled us out of it We're in this world, but we don't have to be of it It doesn't have to dictate the way that we think it doesn't have to establish our morals It doesn't have to establish our our ethics. It doesn't have to establish those kinds of things in our life We can actually be livers Those who live in this world not livers as in your body, but those who live in this world We can be those who live in this world without having to be those who are letting the world conform us into its image When jesus was praying in john 17 verses 14 and 15 he said i've given them your word And the world has hated them because they are not of the world Just as i am not of the world I do not ask that you take them out of the world, but that you keep them from the evil one Don't remove them from the world because they're salt because they're light because they have work to do because they're Going out there as a rescue crew to to to give the word to save people and draw them out I'm not saying to to pull them out of the world.  Did he lose his voice and then somebody says my prayers have been answered? No, I haven't lost my voice I'm just wrestling as to whether I can share this with you whether it's understandable When I was 20 and I gave my heart to the lord I've shared with you how God Radically transformed my life I've shared with you how that Some of you have been around for a while you've heard this forgive me for repeating myself and I'm going to make a point in a second How that I didn't know how to love people I didn't know what love is some of you have heard me say that before and you've never really understood exactly What I'm trying to say so I'm going to try and explain something right now to you and it's difficult to say this but I have the freedom now to be able to I've shared with you how when I grew up That it came from a certain background But I've never shared with you that my mom when I was a little boy For many years was an abusive mom That my mom abused her children that there were times That I heard the words I hate you much more than I ever ever heard. I love you And one of my memories is when I was about nine years old my mom throwing me on the ground and kicking me And I hate you because I had opened a door To look at some Christmas gifts That we had received because the year before we didn't have any money to get gifts And that year we actually got some gifts and my brother Frank and I were very excited And we looked in just to see just to look at the packages because the year before we hadn't received them And my mom discovered that we had looked and my mom used to get very angry and She threw me on the ground and was kicking me in the ribs and screaming.  I didn't know how to love Because When the people that you love the most treat you like that You don't know what that word really means now. I'm not speaking ill of my mama Everybody in this church knows how deeply I love my mom. I'm just telling you the truth So for me Love what is that? Women you can't trust them That's the fact. That's why I grew up. You can't trust them. They hurt you And so I didn't have good relations because I didn't know What a woman's love really was because when the word love is used It could be associated with all kinds of craziness So At 15s when I finally said I've had it. I'm checking out And that's when I began the alcohol. That's when I began the drugs That's when I said I don't care how you feel about anything. I'm not doing this anymore. I'm not taking this anymore It's a lot of story that I can tell you about that But when I got to be 20 And I'd gone through all the garbage and the nonsense and I'd Ruined relationships and I didn't know how to care for people and I didn't know how to love And I didn't know how to even say it and I was afraid to use that word That's when Jesus saved me And when Jesus saved me I brought this love of God Home to a family that didn't know what love was And I brought my mom to faith in Jesus christ when I was 20 And from that point on my mom's life began to change because mama needed to know what love was to you see I understand some things through experience That I have never been able to communicate to you I've never been able to open up because I didn't want to do and do not want to do my mom a disservice by By causing her name and reputation To be sully amongst you because you have known those of you have known my mom have known her as a woman who loves the lord I have always seen my mom as a woman transformed by the power of god That's what happens when you cling to him That's what happens when you say god. I can't take it anymore. I don't want any more of this life I don't want to be this way anymore I need your help god forgive me because of the bitterness and the anger the hurt and resentment Because of all of those things that were in my personal life Because of the the betrayals and the hurts that that our whole family had endured But god has said to us that that that we can be in this world, but we don't have to be of it I don't have to use the world's model of relationship. I don't have to use the world's model of love I don't have to use the world's model of forgiveness and reconciliation I brought the gospel to my mom And I shared you need jesus christ And I brought the gospel to my dad And I said daddy you need the lord And I saw god transform my parents My dad was a man who never said the words. I love you. My dad didn't say those words to us My dad was a man who didn't show affection at all until he got saved And when my dad got saved some of you had the joy of knowing my dad He was the most sweet and the most tender man That you'd ever meet My dad was a kind and loving man That was the gospel power to transform a life Because my daddy never showed affection to me At the age of three or four I went to kiss my dad good night and he pushed me away Stuck his hand out and said men don't kiss men shake hands My dad never showed affection to me until after well He was when I was 17 he showed me it once he said I love you when I was 17 He just wasn't cut from that cloth When I got saved I brought a gospel of transformation to the family And my mom who was abusive and angry My mom changed because she finally came into connection with the one who transforms lives That's why you'll there have been many times When I in this pulpit have begun to weep And you haven't known why It's because I'm remembering Of the transformation that God has done in me and my family and his goodness And I can sometimes remember the things that were not so good And then I compare them with where they are they're at now That's why I could stand up last week and I could eulogize my mom as a gracious loving caring woman Because she became that through the gospel of jesus christ It's the clinging to it that changes you You see and that's what god has called us to do We can live in the midst of this evil world, but god has called us to cling tightly to him We can live in the midst of a world that rejects him, but god can transform us And that's what he's saying. He's saying it's the lord who fights for you Even as he prays but take heed to yourselves love the lord your god That's what changes everything guys. It's learning to love the lord And letting him love you and receiving his love and then giving his love to other people Now he says in verse 12 Or else if indeed you do go back and cling to the remnant of these nations These that remain among you and make marriages with them And go into them and they do you know for certain that the lord your god will no longer drive out these Nations from before you but they shall be snares and traps to you and scourges on your sides and thorns in your eyes Until you perish from this good land, which the lord your god has given you behold this day I am going the way of all the earth And you know in all your hearts and in all your souls That not one thing has failed of all the good things which the lord your god spoke concerning you All have come to pass for you and not one word of them has failed Therefore it shall come to pass that as all the good things have come upon you, which the lord your god promised you So the lord will bring upon you all harmful things until he's destroyed you from this good land Which the lord your god has given you when you have transgressed the covenant of the lord your god Which he commanded you and have gone and served other gods and bowed down to them Then the anger of the lord will burn against you and you shall perish quickly from the good land Which he has given you so he closes with an encouragement and a warning You see outside of their failure at ai israel had moved from victory to victory by just simply trusting in the lord The lord had fought on their side and he had given them victory and he is now giving them rest The bible tells us in romans 8 31 what then shall we say to these things of god is for us who can be against us The psalmist in psalm 44 verses 4 and 5 said you are my king.  We will trample those who rise up against us So the lord has given you victory against these great and strong nations cling to him But if you don't verse 12 and 13 if you go back, well, what's going to happen? Well, you're going to end up Being judged it's interesting how in verses 12 and 13. He speaks concerning inter marriage Notice how he says in verse 12 Or else if indeed you do go back and cling to the remnant of these nations These that remain among you and make marriages with them and go into them And they to you know for certain that the lord your god will no longer drive out these nations from before you They're going to be traps and scourges. They're going to be Things that are harmful to you, but it's interesting how he's saying be careful that you do not inter marry with unbelievers I can't tell you how many christian people who claim to love the lord Um Have gone out and gotten married to those who don't know the lord at all You see there's no other relationship as intimate On earth as intimate as marriage So nothing is more certain to draw a person away than for them to Fall in love with and marry an unbeliever as a matter of fact When somebody has approached me and has said to me that they want to marry And the person that they want to marry doesn't know the lord There's hardly anything I can think of that more clearly Exposes their lack of faith in christ than that decision When you speak to somebody and I have to tell you I've done it more than once Over the years who will come up and say i'm going to get married I can remember one conversation in particular with a young lady years ago now Who spoke to me and I said You know what the word of god says concerning this this man that you want to marry is not a believer And she says yes, I know And I said you know what god's word says concerning that She said yes, I do And I spoke to her with with with the heart of a father for a young woman And I said to her you know that this is not the man that your father prayed for you to marry And you know that on your wedding day It's going to break your father's heart that you're marrying a guy who doesn't love jesus christ You know that She said yes And a while later she got married to the guy And that if there's anything that reveals your heart More than that. I don't know what is Possible to reveal it even more the one you choose to marry demonstrates your faith in christ The bible says be you not unequally yoked together with unbelievers asked the question What is this light having common with darkness? What is the devil having common with jesus? and so This is this new testament forbidding Believers from intermarrying is not just a new testament, but it's an old testament And there's hardly anything that is more In is is more sure to help you to walk away from god Then for you to be hooked up with get married to somebody who doesn't know the lord in in first kings chapter 11 versus 1 Through 3 it reads King Solomon loved many foreign women As well as the daughters of pharaoh women of the moabites ammonites Edomite sydonians and hithites from the nations of whom the lord had said to the children of israel You shall not intermarry with them nor are they with you surely they will turn your hearts After their gods salomon clung to these in love He had 700 wives princesses and 300 concubines And his wives turned away his heart That's what happens Now he's saying in verse 13 if you do intermarry you're going to lose my protection god's protection will be Moved and it's going to bring great pain to you And then he finally says this I'm going the way of all the earth. I'm about to die You've seen and you've experienced god's faithful keeping of his promises These are experiences that you cannot deny So continue trusting him and continue keeping his word And then he basically closes in verse 16 with not only a warning But also a prediction He says when you have transgressed the covenant of the lord to god Which he commanded you and have gone and served other gods and bowed down to them Then the anger of the lord will burn against you. You shall perish quickly from the good land which he has given you They'd already been told what would happen if they turned away from the lord But in spite of god's faithfulness They eventually did turn away And they did go into captivity in 722 Before christ the assyrians came And took the 10 northern tribes into captivity And then in 605 The babelonians came And three different campaigns against israel until they removed the majority Of the people of judah the southern tribes Till they removed them and then the land became barren for those 70 years as they were in babelonian captivity God's word was fulfilled God said if you Fail to keep my word. I will judge you If you remain faithful to my word, I will bless you So this was not only a warning But it was also a prediction a prediction or a prophecy That was fulfilled Not that long afterwards when the assyrians came and the babelonians came So god's word has promises and god's word has warnings We need to receive both Not only the promises which are so wonderful But also to walk in the warnings Which were surely will surely come to pass because god's word is sure and so he's saying to them You need to understand this remain faithful to god But i'm telling you what is going to happen in your future You will turn away from him. You will be judged as for us. Let's remain faithful to god


What's up, guys? Welcome to SPM Buzz. My name is Liz Jackson and this is Buzz. It starts with the one and only Telepak Brahabariya Kukofiti. Kukofreshi. Yeah. Good to see you. I appreciate that. Tumiwa na umekwa Spain for a while na ukwa pa. Are you back officially amu me kujatu kidogo for a few weeks? I can say I'm back officially. Okay. And how is Matina and the babies? Everyone fine? And are they going to come? Wana kujapia, ama? Ya, ya. Kusawa hote. I will bring them soon. So, tu kwa pa tuko eventi akote? Umekuja hasok fanyani. Do you have a close relationship with akote? Not really a close one, but just work-related. Yeah. And how is it that spark, bro? Tuna kujwa ulkuna ishima. Ilikwa kibera? Right. Kibera. In a very good suit. Driving una filaji. Well, I mean, it's not like nili lala anka amuka ewe, you know. It's been about three years of hard work. So, ya. Is that the reason why you are so... Like mituwa kikujwa kukulizi ya, do you like... Ata mimiseti nili amuka nika jipata pa, like work hard? Ya. Actually, I help a lot of people. I just, I am very picky with it. Ya. You don't really expect someone to just... I took it to kwa kumbe bro nili pi rent. And then I just send them and, you know. But mostly we wanna say the... Like watu enyoku kwa very, very tough situations, you know. Situations enyu mostly as in alternatives, you know. Like for me rent, I feel like it has an alternative. If you can't manage your rent, just look for a better or cheaper house. Like an advice that lady, I literally say, there's no shame in going back to your parents. It's only that tukulia muaku twist my words. Ya. But I will do the same. Kama ngekwa na shidi rent. I didn't really come out there too. Bilas to a remake. But I actually do help. I especially singo mazes. Wangekwa na type easy way to you would have been surprised to be honest. Ya. Because for someone who is a single mother that doesn't have school fees for the kids. Akuna alternative. Akuna alternative. So that's where now I come in. But I do a lot of good diligence. I go to the school, I pay school fees. The staff like that. Ya.  How has the dance industry been in Kenya? Ulu kwa kama payo. Nia kwa za tukotunona watua kifanya dance for a living ime kwa je? Well, the dance industry, when I started, it wasn't so good. But for me, I put in the work and they showed a lot of people that you can actually make money through dance. Nani kwa motivate a lot of people. I'm glad that it's picking up. Ya. When you were in Spain, how were you able to handle it? Ulu kwa na other dance classes going on on Spain? Ya. I had a lot of work in Spain because I was teaching in about four or five schools. Including dance studios and like school schools. Na, they pay well. That's the thing. Like they appreciate art to be honest. Ya. What do you think is different in the dance industry in Spain compared Spain and Kenya? What is different? Well, I can talk much about Spain because it wasn't like in the whole of Spain. But the only difference I can say is that art has more value in Spain than in Kenya. Like here you tell someone, someone at a kujaku akumbe and toko fanyekazi. But then they will start arguing with the rate saying that it's too high because you'll be dancing for like three minutes. But in real sense, it has taken me seven years to be able to dance in those three minutes. Ya. So in Europe in general, they do appreciate that. Ya. They take dance as a career. Ya. Here mainly, I don't know if I can say it. Me na kufanya waka waka ruka ruka. Ya.  Me nili kwa kichungumu tango kitambo. So I don't know if I can say it. But my mum literally trusted in me all the time. So I didn't really say it. Because I was actually in university. So I was doing computer science for the second year. But I didn't know much. She does cool things. I was straight and have two guys on the corner. Isomia kambiles me baki. I think I can do something different. Ya. And how has your wife been instrumental in your career? Well, I don't know. She has played a very big part. Very, very big part. One of the things I can attribute to her is her backup. So with her being behind me, I had the power to set my value and stick with it. Kini tia shuwa taw, sasange kata. Nkwa nbi aabuda tawiyuezi. Tawiyuezi. Kwa sababu. Ili time nili kwa solo. Sina backup ya ni. Yota on kiki kata, I'm brisking a lot. Because yota hondu rentia angu sas. But sasatiki kia wili. Nkwa na. In case ni seime, yota hositu kuya lafu artista katae, kana zani akole ya maali. Ya. And you being a young person and a very successful person, let me say that. How have you been able to keep yourself grounded? Raja truna nga vidya nawa, me putea juya madawa. How is Pakbro still rooted? Neshida. Neshida na juya ku guide munt. I was born without anything, so I don't have the luxury kumesa round nakidogo enye na me manage ku get. And also I've done a lot to be where I am.  I work a lot. Trust me. Kuna sayengia na se ma gaudia mani pesa ham zungu. If I put them in my shoes, I'm sure. Miki mojia. Raka misha kata yo kaz. Alright. Thank you so much for talking to us. We appreciate. Guys, that was Buzz. It starts with Tile Pakbro. Make sure you like, share, subscribe to his channel. Jipla Gavo. Well, Tile Pakbro, basically, I am among the most subscribed to dances in Africa, so it will be so easy for you to find me. Cheers. See you on the next.


Hi, I'm Isla, I'm a part of the Ellisburgam Bristol team, and when I'm not working I'm helping run the University of Bristol Snow Sports Society. I'm here to talk to Dom from Protect Our Winters, a charity that we at Ellisburgam have been working closely with for a while now. I'm very keen to understand from Dom what I can do to protect our sport and the environment. Let's go chat to Dom. Hi Dom, would you like to introduce yourself and say a little bit about Pow and Eurovision's emissions? Hi there, I'm Dom, I work for Protect Our Winters UK, so Protect Our Winters or Pow is a climate charity. We help passionate outdoor people take effective action on climate change, and it was first founded in the United States by legendary snowboarder Jeremy Jones. It's now lots of chapters worldwide following in the footsteps of that first chapter doing really well and helping progress climate action. So we do things like run campaigns, we're also delivering courses like carbon illiteracy training, which are delivered to the Ellisburgam stuff. So does a typical day involve talking to Jeremy Jones? Yeah, not the typical day, but he's definitely really involved still in the States in particular, and we have our own athletes and ambassadors in the United Kingdom, so yeah, I work with them to train them, and it's working with the athletes is a key part of how we can achieve our mission. Being a skier, I'm passionate about the environment that I love, but the two are odds because I'm not ready to hang up my boots, not just yet. Yeah, so this is what Protect Our Winters is all about, is people who are passionate about snow sports or climbing or whatever it is that gets you in the outdoors, and they don't have to be at odds, right? We have the opportunity to make this industry sustainable, and we also have the opportunity to use our voice to make the wider world a better place. So that's what we have to do now, and I'm passionate snowboarder and also a surfer, and yeah, being out in the outdoors is what's made me want to protect it. I have been skiing since I was in school, but then it was more recently, I did two ski seasons just after I finished university, and there I was seeing weirdly late seasons. I was lucky because I was in a high altitude resort, but the Dolomites were just little strips of snow. There was a snow gun that was pretty much it, so that was what was really opening my eyes to the issues in the mountains, and that's what makes me want to protect it, so harnessing that is what it's all about. The snow sports industry and mountain sports aren't perfect, but very little is in the way the world is set up. We have the opportunity to change that. So, is it too late for our winters? We've seen that the glaciers are melting, and in the past few weeks felt the temperature rise. Is it too late? It all feels a little out of our hands. Yeah, so definitely we're already feeling the effects of climate change and global heating. Certainly in the last few months, as we're filming this, there's been crazy heat waves across Europe, but yeah, this is also being felt in the mountains, and the IPCC, the Intergovernmental Panel on Climate Change, which is sort of the leading scientific body on climate change, says that it's definitely already impacting the operation of the lower elevation ski resorts. Ski seasons are already about a month short, and they were 50 years ago in the Alps. At every degree, the temperature increases, it gives you sort of a best part of 150 metres snowline increase. So, we've already seen a couple of degrees average in the Alps, so it's already shifting hundreds of metres where the snowline is. These sorts of impacts, impacts local communities and economies massively, and that's why communities are keen to have snow cannons to provide backup. The snow is not as good, but also adds environmental impact because there's a lot of water use, a lot of energy use, and it's actually cited as a bad adaptation by some of the top scientific bodies because if the temperature gets too high, you won't be able to snow cannon it just won't work anymore. And yeah, it leads to some scary impacts. It's like this is safety in terms of avalanches, and particularly some of the summer rock climbing. There's routes you just can't do anymore because of these impacts. So, yeah, it's really causing issues in the mountains, but the more we do now, the less that that will be impacting the future, and that's already recognised by the top level scientific bodies that there is a chance still to protect what we do. Skiers, snowboarders and outdoor enthusiasts, what can we do to help? So, there are changes that you can make within the sports you mentioned and those interests. So, travel is one of the biggest causes of greenhouse gases. If you look at a mountain trip, it's probably at least two thirds or more travel if you fly. So, if you can get to the mountains, not by flying or by flying less far, so even just the Alps rather than Canada, you know, that's making a massive difference to the impact of your trip in terms of climate emissions. There's also the choice of resort and some resorts have moved to renewable electricity or have certifications like Floc on Veur in France, which is sustainability certification. So, you can start to choose these places and shop well when you're buying equipment and make it last. But yeah, there's also the case of like what can you do outside your trip and your everyday life or influencing the biggest systemic change. So, we also need to make sure that politicians are taking responsibility for this issue. So, just supporting campaigns from charities is really powerful and that's what's going to get us really to net zero at the end of the day, which is where we need to be. And how do you find these resorts that have the better, more eco-friendly side? Yeah, if you look on the resort pages, they'll often have a sustainability page that tells you all about it. You can look in France for the Floc on Veur, Green Snowflake, Lager. But yeah, particularly on the travel side of things, just some resorts are just easier to get to by train, for example. So, if you go to Lezac, you get a free transfer from the train station. So, the overall cost is not bad compared to flying at all. What is the bigger solution to global warming? Well, fundamentally, it's fossil fuels causing the problem and we need to leave those in the ground. Like we can add all the renewables we want, but if we don't stop using coal, oil, gas then it's not going to solve the problem. Yeah, so we've got to make sure this happens and commit to an end date on fossil fuels. How can people take action via Pau? Yeah, so you can learn a lot more about the problem of climate change, how it's affecting the outdoors and the wider world through our carbon illicitly training. And it also teaches you more importantly what we can do about it, how to take that effective action that will stop climate change. You can also support our campaigns. So, current campaigns include Save the Ski Train, trying to bring back that direct route from London to the Alps and Devest the Dirt, which is helping move money out of fossil fuels. And there's big campaigns coming in the future, so keep a look out for that. Sign up to Newsletter to find out more. You can also help companies take effective climate action with the Pau Pledge and you can also donate to Protector Winters to help us take more effective action ourselves. The pledge is something we at Ellis Programme signed up to and have started our journey towards Net Zero. How many other organisations do you have signed up? Yeah, so the Pau Pledge is really there to help organisations take that effective action to stop climate change, as you mentioned, by getting to Net Zero. And we've got well over 100 organisations working on the Pau Pledge and it really brings out eight of the key steps that everyone as a company can take on climate change. What are the eight steps of the pledge? So companies can increase their resilience to the impacts of climate change, move to 100% renewable electricity. There's also stopping using fossil fuels for heating. Then there's using zero emissions transports or electric vehicles. Then you've got to identify what some of your top causes of greenhouse gases and really focus on cutting them, committing to cutting them in the next few years.  Where do we need to be is Net Zero. So pledge six is about reaching Net Zero and that needs to be before 2040. Number seven is about helping the topic of green finance, talking to your natural service providers about taking money out of fossil fuels. And then the final one is influencing others. So partners you work with and your customers telling them about your journey and influencing the wider world positively on climate change. At Ellis Brigham we've been working with you guys at PAO for a while now and we've been donating 1% of our ski sales. How is that money being used? Yeah, this money is hugely important to protect the winter's UK and it really helps support us delivering our missions. So particularly underpinning our campaigns and attending events like going to COP26 and going into other areas of the community and being able to talk about these topics and deliver information that's really important to us. So what's next for PAO? We've got big campaigns coming up so definitely keep an eye out for those. We'll also be expanding our carbon literacy training further and adding new athletes and ambassadors to help us grow our reach. So yeah, big things to come. If you could go back 40 years what would you change? So 40 years ago there was already the opportunity to start taking action on this and if we had then we'd be having a much easier transition in dealing with this issue and because we've left it quite late we now have to take quite urgent action this is why we're talking about it as a climate crisis. So yeah, just making sure we got started earlier but to make sure that happened I think it would be potentially an issue of communicating the science clearly and particularly how we talk about it and the impacts of it. There was a lot of focus early on about sort of the Arctic and places that are a long way away for people so if we can talk more about the impacts on people, wildlife and more direct and near-term impacts I think that would be more effective so I'd probably change that. And now fast forward to 20 years what will the world be like? So hopefully we'll see a lot more electrification particularly heating and transportation. If we're lucky by then we might even be seeing some net zero short-haul flights but key to that is mass rollout of renewables and stopping use of fossil fuels so that we can power these newly electrified systems in a low carbon way. So where is your favourite place to snowboard and why? I think it's got to be VT in the French Alps. I love Whistler but it's a bit far away to go on the regular. And why is that? Well I did a season there so I just know it. I couldn't find the good snow. High altitude too so less likely to be bad snow. So Dom thank you so much for meeting up with me I've personally learned a lot. Do you have any forward thoughts for viewers? Protect Our Winters we're really dependent on people getting involved and supporting this issue and we all need to work together to beat climate change so please do come everyone and follow us on Instagram sign up to our newsletter you'll find out all the latest information what's going on on this topic and particularly things you can do about it so you'll find out about our campaigns our opportunities to learn more so yeah come support us and Protect Our Winters with us. Thank you.


Metallic biomaterials used in medical devices are primarily chosen for their corrosion resistance and biocompatibility, with the body environment posing challenges for corrosion control. This invited review paper analyzes the effects of corrosion on biocompatibility, discusses the kinetics of corrosion, passivity, breakdown, and regeneration in vivo, reviews commonly used metallic biomaterials and their corrosion performance, highlights principles of implant failure, retrieval, and failure analysis, and describes common corrosion processes in vivo. Approaches to control the corrosion of metallic biomaterials are also highlighted. This article was authored by Melmeleus.


We analyzed reports for 59,073 contacts of 5,706 coronavirus disease, COVID-19, index patients reported in South Korea during January 20 to March 27, 2020. Of 10,592 household contacts, 11.8% had COVID-19. Of 48,481 non-household contacts, 1.9% had COVID-19. Use of personal protective measures and social distancing reduces the likelihood of transmission. This article was authored by Young Joon Park, Young Joon Cho, Ok Park, and others.


So, I am going to talk about a theory of equilibria. So, game theory, what does it do? It does analysis and design of a system where people are interacting, rational, let us call them rational agents with their selfish rules. And so, let us take an example, it is called game of chicken, where on a single lane path, two cars are heading on to each other. Both of them have only two choice, only one car can pass. So, either both of them head on and collide or they can change their course and go into a field or a side path or whatever and then they cannot go forward where they were heading to. So, if you look at the payoff, of course, both of them want to go straight, but then they are going to collide and that is an accident that is a really bad outcome for both of them. If both of them change their course, then nobody is going forward, nobody is happy. In the other two cases, one of them is happy, whoever goes straight is happy and the other person is not happy. Immediately you can see that these two outcomes are undesirable and these two are ok outcomes, at least one of them is happy. And so, this is kind of an analysis of a game scenario and traffic light is a mechanism which achieves one of these two outcomes and that is kind of a design part of it. So, in particular I am going to talk about games today. So, in our games there are going to be players and players have strategies. Rock, paper, scissor is one example. So, everybody knows the game Rock, paper, scissor or do you want me to explain what the game is? So, there are through other play Rock, paper or scissor and once both the players chooses their strategy, the payoffs are decided. Let us say it is a win-lose game, the loser has to give 1 dollar or 1 rupee to the winner. If you are playing this game, do you want to choose a strategy deterministically? Do you want to play Rock or paper or scissor? If you want I am I really want to play with you. So, no we would like to randomize right, we do not want our opponent to guess what we are going to play right. And so, randomizing, randomization is essential not only in this game, but in many important games. And Nash proved that once you allow randomization not in only two player games, but many player games a stable state exist. What does that stable state mean? That no individual player wants to change their strategy and they can improve no unilateral deviation that is the stable state. And the way Nash proved this theorem is through a fixed point theorem by Brauer. So, the fixed point theorem says that if you start with a disk by disk I mean a compact convex set and the function is continuous and, but it is still over the disk. So, it takes every point from the disk to itself to the disk itself. Then there is the point which is fixed by the function f of a is a. And this essentially fixed points will be the Nash equilibrium that is how we constructs the function. But what about computation? This is completely existential theorem. It does not tell us how to compute this fixed point. And the computation question is not only like CSV started asking this question. Immediately after Nash's theorem people started asking this question how do we compute the Nash equilibrium even before actually this Nash equilibrium for special cases of game. Nash proved it in more generality. And there were many, many algorithms, but for the algorithms for the most general case are. So, these are economics mathematicians they never cared about running time of the algorithm. And for the most general game the algorithms we have are through fixed point theorems and so they suffer from numerical instability on all these issues. Within CS when we started asking this question first thing we saw was that it does not seem easy. So, then we think of complexity classes can we so show hardness of this problem for some complexity class. And the first thing that comes to mind is NP. But for NP there always exists a solution. For Nash the solution sorry for NP we ask whether there exists a solution, but for Nash the solution always exists. So, this question is irrelevant in that sense because the answer is always yes. So, then we are in the regime of total function problems within NP where existence of solution is guaranteed. And Megiddo and Papadimitru showed that if Nash is NP hard then NP equals co-NP because Nash is both in NP and co-NP. So, the later Papadimitru defined this PPAD class and showed that it is kind of between P NP and P and PPAD is short form of Papadimitru. It is a polynomial parity argument for directed graph although it resembles very well. So, the problem in PPAD canonical problem is this. You have a graph every vertex has at most one in degree and at most one out degree. So, you can imagine this graph is essentially sets of set of paths and cycles. You are given one endpoint of one of the paths and ask give me any endpoint of any path. You know there exists one because this path which has a starting which is given to you has an ending. So, you know that there exists a solution, but give me any solution I am fine with that. Now, you can say that oh I am going to check every vertex no, but there are exponentially many vertices and graph is given by a circuit succinctly. So, there are two circuit predecessor and successor that tells you given a vertex it tells you who are the who is the predecessor and who is the successor. So, you cannot just do enumeration and showed that Nash is in the PPAD. Now, our focus is two player game. So, let me describe how we are going to represent the game. Let us say our two players are row and column it will be clear why we call them row and column briefly. So, we are going to represent when they play we cannot think that the row player is choosing a row of some matrix and column player is choosing a column of that matrix. The corresponding. So, there are two matrices corresponding entry in the R matrix is the payoff of the row player and corresponding entry in the column matrix C matrix is the payoff of the column. So, that is the representation of the game is this clear because I am going to use this part again and again throughout the talk is the representation clear. So, now, the problem of two Nash is finding a Nash equilibrium in a two player game which is represented by two matrices R and C. If the number of strategies of the players are m and n then these are m by n matrices. Now, what about algorithms? So, we have from 64 a very nice path following type algorithm which is kind of simplex, but not essentially simplex is a pivoting is complementary pivoting. It always finds a Nash equilibrium, but worst case is exponential. Now, for complexity it was shown that it is PPAD complete in 2006 and the same time even approximation one over poly an approximation was shown to be PPAD complete. On a positive side constant approximation we have a quasi polynomial algorithm. So, QP does rank 0 that is 0 sum game your loss is my win and my loss is your win. So, some of the payoff of two players is always 0 then you can just solve it through LP which was known even before Nash proved his theorem by von Neumann. And then there has been a lot of work for special cases ranks rank of the individual matrices are constant rank of a R plus C is low for this we know approximation or sparse which is work by Siddharth and so on and so forth. And there is a lot of work on query complexity communication complexity which Yako will talk about which I have not listed here. So, this is just for communication. And then we know that the constant approximation we cannot beat this if we assume exponential time hypothesis for PPAD. And similarly, if we now try to optimize something over the Nash equilibrium like give me a best approximate Nash equilibrium in terms of payoff or give me a Nash equilibrium where this strategy is played with non-zero probability and so on. Any such decision is cannot do better than quasi polynomial assuming exponential time hypothesis, the standard exponential time hypothesis. So, in all of these algorithms that we know are kind of enumerative using the properties of the game you restrict the search space and then enumerate. So, whenever they are solving for one Nash equilibrium essentially they are also solving the decision problem whatever you want. So, the first question I want to ask is are there efficient non-enumerative techniques to solve this problem. And the second question I want to ask is can we get some kind of hardness that are kind of unconditional. And I have my talk is divided in two parts. First part I will kind of talk about the first question, the second part the second question. So, the first part I am going to describe a method which is based on a linear program and one dimensional fixed point and it solves the game when rank of r plus c is 1. Remember rank of r plus c is 0 that is a 0 sum that is L p, r plus c is 1. So, 0 sum has convex set of solution because it is L p, rank 1 can have exponentially many disconnected Nash equilibria. So, immediately the complexity goes like a while, but still we can solve it, rank 2 and beyond is hard. So, this is threshold that Kavita was also mentioning about K equals 1 to K is 1. Somehow you could just get it. And then the second part I will talk about this another algorithmic framework which is sum of squares which I will try to convince you that is pretty strong powerful framework and then prove some lower bounds against this algorithmic framework yes. So, you can ask this question and there has been a recent very nice work on finding equivalent games. So, if you are give me a game can you tell me is there a rank 1 game which is equivalent to this and that is a very valid question. Rank is fragile in that sense, but this is basically motivation was because we can do rank 0, can we do rank 1 and there is a fundamental difference between rank 0 and rank 1 convexity with opposite versus exponentially many disconnected equilibria. And that is a separate question that is very valid yes. So, the first part, so again back to our game. Now as we just discussed that players would want to randomize. So, let us say the randomized strategy for the row player is x and randomized strategy for the column player is y. So, this x is m dimensional vector whose entries are non-negative and they sum up to 1 because it is probability distribution over the rows and y is a probability distribution over the columns. In this case the expected payoff of these players is this vector matrix vector multiplication right you can just see this. And then the Nash equilibrium is just no unilateral deviation. So, once they play x and y individually row or column player does not want to change their strategy. So, what does this mean? So, let us fix column player to playing y. Now row player will think if I play my ith strategy what is the payoff do I get? Now remember why column player is playing y. So, she gets Rij the ijth entry of R matrix with probability yj because that is the probability yj is the probability of playing column j for the column player right. So, this is the expected payoff from playing the jth cell right. So, if you take the summation then that is the expected payoff from playing ith strategy against y right. So, let us this is just ith coordinate of this R y vector ok. So, the maximum payoff she can achieve from playing an individual strategy is this quantity right. So, E i is just the unit vector with ith entry 1. And if she wants to achieve this maximum payoff with any randomized strategy she cannot achieve more than this maximum individual maximum right. If you have a set of numbers and if you put a probability distribution over that number you cannot achieve more than the maximum in that set right. So, the maximum she can achieve is this. So, checking whether x gives the maximum payoff is equivalent to just saying that it is better than any individual strategy pure strategies right. And this can be done only if she is playing a strategy with non-zero probability whenever it gives maximum payoff. So, the strategies that are played with non-zero probability then must be giving the maximum payoff right. You have to put non-zero mass only on the maximum numbers then only you can achieve that maximum right ok. So, this is the characterization and this is kind of a complementary slackness type of condition and the variable is non-zero only if some constraint is tight right. So, using this let us define this polytope that capture the maximum payoff. So, let us say pi r is the variable that captures maximum payoff of the row player and pi c is the captures the maximum payoff of the column player. So, to see that pi r will be only more than the maximum payoff for any fixed y right and pi c will be more than the maximum payoff for the column player right ok. So, now suppose I take the a point in the product polytope of this P and Q and look at this objective what is the first term? This is the sum of the payoffs of both the players. What is the second term? The second term is the sum of the at least the maximum payoffs right. So, this can this quantity be positive? This can never be positive because this is more this term is more than this term always right. So, this is at most 0 and this is exactly 0 when you are at the Nash equilibrium. So, this gives us a nice simple quadratic program which is maximizing this objective over this product polytope and now you see why you get an LP for a 0 sum game. When r plus c is 0 this bilinear term the difficult term vanishes everything else is linear and you get an LP right ok. So, this is the problematic term if your game is rank 1 then again this simplifies is to product of two linear terms right ok. Still it is a rank 1 quadratic program which is in general NP hard. So, we cannot just rely on existing techniques for solving QPs ok. So, what we do is let us first use minimum information we need for representing the game. So, if we have r u and v I can reconstruct the matrix C right because that is just u v transpose minus r. So, u and v is just rank 1 matrix it is a u matrix column matrix multiplied by a row row vector right. So, that is a rank 1 matrix and do this replacement at both places in the objective sorry in the in the polytope ok. After that I am going to look at not only one game, but a space of games where I allow any vector instead of u ok. So, instead of u I have star. So, I do that replacement in the objective and in the constraint. Now, this is more complicated because now this is like three variable in some sense right because star is also a variable in that sense. So, I replace that difficult term with a lambda and now you see this is kind of a parameterized linear program where lambda is the parameter. Once I plug in some value of lambda it is a linear program right ok. And what can I show for this linear program? If you look at all the solutions of this linear program for all possible values of lambda they exactly nothing less nothing more exactly capture all Nash equilibria of this game space for all of these games ok. And we can show this through complementary conditions. Complimentary sickness condition of this linear program matches with the complementary condition of for the Nash equilibrium characterization ok. In particular what can we show is that if you plug in lambda you get some solution for this LP then corresponding x and y is a Nash equilibrium for all c. So, instead of u I have a vector c such that x transpose c is lambda. So, instead of finding solution Nash equilibrium for one game I get a Nash equilibrium by solving one LP for a space of games which is m minus 1 dimensional space right because this is m variables here. But I am after this R u v and not any R c v right. If u belongs to this space then I am done. So, now what we have is we have this parameterized linear program where we plug in lambda we get x and y. If lambda then I am done right. So, what should I do? Just put a box around this think of it as a function which is inside is a single parameter function takes a lambda inside solves the LP commutes x and y outputs x transpose u. If x transpose u is lambda then we are done that is a fixed point of this function right. And fortunately we know how to solve one dimensional fixed point that is just binary search. So, if you have a function from a 0 1 to itself then you know that if you do not have a trivial fixed point at 0 and 1 then 0 will belong to this upper half and for 1 the function value will belong to a lower half right. So, this give you two pivots between them the function is continuous I know that right because it is a solutions of a parameterized linear program and then you just do the binary search. And we know that the precision of a Nash equilibrium is finite actually polynomial in the bit length of the game. So, we are going to be done in polynomially many iterations and that is it that gives us the algorithm. So, it would be interesting to see if this can be applied to we did apply this technique to other Nash equilibrium computation problem in other games, but can be applied to other quadratic programs let us say which are coming from some different domain it would be interesting to see that. So, that second part is some bad news. So, I am going to focus on applying sum of squares algorithmic framework on Nash equilibrium what is sum of squares it is basically SDP based hierarchy based method and many state of the art algorithms for optimization problems has been using this powerful technique. It has helped break into integrality gaps it has helped get state of the art approximation algorithms and so on and so forth for really classical important problems. So, we were hoping that may be something can be done using this and we really honestly started with a hope of a positive result not a negative result, but we ended up with a negative result. Again when we try to apply this framework to Nash the first road block was NP versus PPAD. So, far it has been applied to optimization problem the formulation was like that how do we kind of get rid of optimization and just want to kind of solve a search problem. So, here is our attempt we try to define this algorithmic framework. So, this is the definition of Nash equilibrium right you want to find vectors x and y such that they satisfy these inequalities and now these are polynomial inequalities they are not linear because of this bilinear term on the left hand side and what is an approximate epsilon approximate Nash. So, it says that a player can deviate and gain, but no more than epsilon that is an epsilon Nash. And now if we do linear relaxation of this that means, here we have a quadratic terms here right x i times y j if we replace those x i times y j by y j by variables say p i j then we get a linear relaxation of the system which captures correlated equilibria if you know about it if you do not know about it do not worry, but you do not get Nash equilibrium, but you get something which is correlated equilibrium. Now, we want to do more we want to build this hierarchy on top of this by doing this relaxation, but higher order. So, what is I am going to define degree D pseudo distribution it is not a distribution it is a pseudo distribution in the sense that it is going to be defined by its expectation operator. What do I want from this expectation operator that it is linear it has a variable for these higher ordered monomial terms. So, instead of just replacing x i and y j x i times y j by p i j now I am going to replace x i times x j times x k by say p i j k and I am going to look at all degree D monomials and introduce variables for them. And on top of that I have to make sure that everything makes sense. So, I have to introduce all the symmetry constraints and whatever the other important constraint is that the normalization constraint that the expectation is of 1 is 1, non negativity constraint that if you take any polynomial q of degree less than of course, d over 2 and take a square of it then the expectation of that has to be non negative. So, that is why some of squares in some sense and then this expectation has to satisfy my important polynomials by this. If you want that p greater than equals 0 polynomial p greater than equals 0 then you introduce all of these constraint that expectation of q square times p where degree of q square times p is less than equals d is non negative. So, this is how it is defined this essentially captures up to degree D movements of your the final distribution you are after. So, degree D pseudo equilibrium is degree D pseudo distribution that satisfies say Nash equilibrium or epsilon Nash equilibrium constraint whatever we are after. And you can see that if you just take d equals 1 you get or it should be d equals 2 sorry it is a type of if you take d equals 2. So, degree 2 monomials if you only replace degree 2 monomials then you get collated equilibrium polytope if you go all the way to degree n and higher then you get back the Nash equilibrium. But you can see the size of your this program exponentially increases with d right if you have let us say degree d then your size is n to the d if n is the original set of variables right. So, you do not want to go all the way to n. So, the algorithmic frame where we work with is kind of oblivious is information theoretic. So, you have you get your system gets this degree D pseudo equilibrium you never get to see the actual gain. Somebody computes this degree D pseudo equilibrium and gives it to you using this you can take as much time as you want as much space as you want. And whatever resources you want you do some kind of rounding, but you can only look at this distribution and not at the actual gain. After that you generate set of solutions or let us say one solution and then verifier will tell you whether this is actually an equilibrium or not. So, that is how it is information theoretic instead of and then we also allow partial solutions where you do not have to give like entire equilibrium you can give one of this player strategy and we can complete the other player strategy that is fine. And not only one solution, but an array of solutions ok. So, degree D query Q oblivious rounding with verification oracle algorithm will take degree D pseudo equilibrium do whatever rounding it wants in whatever time and resource it wants generates Q queries for possible solutions gives it to verifier. And if any of them gives you a Nash equilibrium I am happy. So, the framework is clear because I am going to prove lower bound against this framework. This system never gets to see the game that is important because if I give you the game this part will generate the solution right because there is an exponential time algorithm ok. We observe that many or most algorithms that we knew for S O using S O S fit into this framework. So, it is strong enough in that sense ok. So, first because we were aiming for some kind of positive result we could reconstruct the Q P task and we were not the first one we realize that just before us somebody had use S O S framework to come up with a Q P task which we already knew from Lipton metamarcha is that Tim mentioned using they actually gave a Q P task the first Q P task for Nash. So, what the main theorem we show is that if you are aiming for a 1 over poly n approximation then either you need D to be omega n or you need the queries to be exponential. So, either way you are going to hit the exponential running time and if you are looking for a constant approximation then D has to be either the D has to be log n or the query has to be n to the log n ok. So, we cannot beat using this framework we cannot beat the state of the art. So, here this you once you get the pseudo equilibrium this oblivious rounding algorithm not only generates one solution, but let us say Q solutions and this is the query part. Yeah, you can generate 2 to the n if you wish. So, these are the final theorems and essentially saying that this particular framework does not allow you to beat the state of the art ok. So, high degree pseudo equilibrium does not give you any information about actual equilibrium that is what we want to achieve ok. So, let me go to the proof I have 15. Yeah, we prove for 1 over n to the 4, but I think we can bring it down to 1 over n square, if you do more optimization into the analysis that we did, but it would be interesting to see if we can do say 1 over n to the c for any c greater than 0 that is the hardness result for P P A D hardness of natural equilibrium it says that any given c greater than 0 getting 1 over n to the c approximate natural equilibrium is P P A D complete. Steps like classes that are data like in the ethers for log n that is an open and super interesting to me because I am trying to look into that yeah. So, there is a queue for this. So, the queue is one way. Sorry, sorry yeah. So, the queue pitas we have does not need to enumerate it is just the SOS solve SOS and then generate the solution queue is 1 yeah otherwise you just do LMM structured classes like let us say rank of R plus C is constant or let us say it is a sparse game where. So, this is general games right. So, let us go into the proof. So, the main idea is to construct a family of games we will have to construct a family of games because we want to also have hardness against this enumeration. So, we are going to construct a family of games that all share a common pseudo equilibrium, but all of their approximate equilibria are disjoint actually they are far apart and that is our goal. So, essentially the pseudo equilibrium contains no information about Nash equilibrium and we know such instances for classical optimization problem like 3 set K click and so on. And another thing we know is that once you have such a problem if you can map that problem to another problem that has a low degree mapping of solution sets as well then the hardness also carries forward yes sorry yeah. So, I will just say that Nash equilibrium sets of any two games they are they are disjoint and they are there is some gap between them. I am going to restrict them to a nicer set and they sets are disjoint. High degree pseudo equilibrium it is not. Yes. It is not a click. No, no I do not allow you to do equilibrium, but I allow you to choose whatever Nash equilibrium you want. So, Nash equilibrium sets are going to be disjoint it is not as if these games have different set it is one Nash equilibrium no it is all Nash equilibria are disjoint kind in both of the player strategies. If you are going to use the SOS framework as a black box then you will have to allow to be any pseudo equilibrium to be used right unless you do some more tweak to it. So, this game construction we will first talk about the meta game construction before we go into the details of the two theorems. It has two parts one is the SOS hard game which has what we want from this game is that it has a degree D pseudo equilibrium with very good payoff, but all of the epsilon Nash equilibrium payoff not only Nash equilibrium epsilon Nash is the bigger set than Nash equilibrium right. All of its epsilon approximate Nash equilibrium has really poor payoff the sum of the payoffs. D degree D pseudo equilibrium has the payoff delta for both the players while all epsilon Nash equilibria has the total payoff of both the players at most two times delta minus epsilon. And then ennume hard game which is a family of games which are defined by subsets of the strategy set such that all of their Nash equilibrium set are disjoint basically. So, we make sure that each of these games so if you take a subset of these numbers then their Nash equilibria are around the uniform distribution over that set US stands for uniform distribution over that set of strategies. So, all their epsilon Nash equilibria are constrained in this epsilon, tau epsilon ball around this point. And so they are essentially this make sure that they are disjoint. And then you construct this combine these two games where you put there are two blocks first block and the second block red block and the blue block. Red block contains the information about the pseudo equilibrium and the blue block is this ennume hard game. And the way we constructed it is important that what you put here because what we want is that this part the red part does not have any equilibrium. Whatever equilibrium are there in R and C we want to kill them. So, we show that this game has degree D pseudo equilibrium in the red block, but all its epsilon Nash equilibria are in the blue block. So, the red block the first block does not contain any Nash equilibrium or any approximate Nash equilibria. And then the theorem we can show is that if you have this subsets S 1 through S q through which you construct these ennume hard games. And then you have this one S O S hard game then you construct this family of games using these two where you have common first block which is this S O S hard game. And then using ennume hard game you construct this blue blocks. So, these games just differ in the blue blocks not in the first red block. Red block is common over all of these games. Then all of these games have a common pseudo distribution or pseudo equilibrium in the red block, but all of their Nash equilibrium are in the blue block and they are distant. So, this essentially gives us the hardness right lower bound because I am allowed to give any pseudo equilibrium. So, if I give a pseudo equilibrium here and then this does not give you any information about the blue block. It could be there yes, but nothing about it. So, the pseudo equilibrium essentially will tell you set all of these strategies corresponding to the blue block to 0. All of their moments will be 0, but still your equilibrium are in the second block itself. There is no equilibrium in the first red block. So, for the exponential lower bound we construct the S O S hard game using the k independent set. So, there is a reduction from independent set to game by Gilbo-Wenzemel and we extend it to get hardness not only to like mapping solutions to Nash equilibrium, but also to approximate Nash equilibrium also gives you independent set and so on. The property is that if there is an independent set then there is a Nash equilibrium with payoff 1. If there is no independent set then 1 over n square approximate Nash equilibrium has payoff less than this whatever we wanted. And then we have a new hard family. This we do using matching penny. We basically have to restrict that the players only play this strategies from set S. You set really bad payoff for the rest of the strategies and then it is basically like that only identity matrix for the this part and then they will have to really randomize even if they just care for approximate solution. Yes, this one. No, so it is that is the gap right. So, if there is an independent set. So, this is the payoff of both the players individually is 1 and this is the total payoff of the. Thank you. So, I am rushing through the details, but essentially this is an extension of Gilbo-Wenzemel reduction from independent set to approximate Nash equilibrium and this is a construction through matching penny extension of a matching penny game. And for the quasi polynomial lower bound we did have to do more work. So, there was a result by these guys. I cannot pronounce the first name for Lee and Savani assuming strong exponential time hypothesis order 1 approximate max payoff n is hard to compute. And so we extended it to get what we wanted that if basically using this. So, they start with this what they call free games. So, from there you want to construct a two player game where omega log n pseudo equilibrium there is a omega log n pseudo equilibrium with payoff at least 1 for both the players individually, but actual equilibria have payoff at most 2 times 1 minus epsilon for epsilon some constant epsilon. Again the constant is not too great it is I think 1 over 500 or something. So, it is not nice. And then for the enum hard game we extend the construction of the Scalakis in Papadimitru which is much more complex I am not going to introduce, but essentially we show that we can construct this n to the log n many games such that for every game USI it is Nash equilibria are restricted to 8 epsilon ball around the uniform distribution over set S I. And the for any 2 games their uniform distribution corresponding uniform distribution are at least 17 epsilon apart. So, these 2 sets have to be destroyed and combine them to get the final game. So, essentially I showed you this very nice technique this is an old result this actually I did this here during my PhD. And this is a relatively new result I am still working on this. So, we define this oblivious framework we using SOS of oblivious surrounding with verification oracle which is kind of information theoretic. And we using this we could find essentially just using pseudo equilibrium not even enumeration part of it a non enumerative cupitas, but show lower bound for the actual questions of finding one over poly and over constant approximation. And as a consequences we extended the results of Bilbova Zamel and the Scalakis in Papadimitru for some certain things. And open questions so somehow we are stuck for constant approximation I guess we are stuck at still 0.3393 right I have not seen any improvement after that. So, we know a polynomial time algorithm for epsilon equals 0.3393 no better than that polynomial time algorithm. So, that is it would be really interesting if any kind of SOS framework or SOS algorithm gives you better than 0.3393 approximate natural equilibrium. And let us say can we do some kind of beyond worst case type of analysis using this framework or maybe special classes can we do better than the state of the art algorithms. That is it thank you questions.


I spent a portion of my childhood living overseas in countries such as Saudi Arabia, Thailand and Taiwan. You really realise just how lucky you are and I do think that I have a duty to get back to the community, particularly to those who are less fortunate in our world. It's very confronting to actually see statistics that you read and get taught about in real life and that's because suddenly these numbers become real people with families and I think I was well equipped to work in this environment with the knowledge that I had gained from Griffith Medical School. I just realised how big this concept of health is, one of the most effective ways I think to target it is through promoting public health measures and that's a way to actually create a sustainable change within a community. When I found out I received the Queensland Road Scholar, I was speechless, it was completely surreal and still pinching myself. I'm travelling to Oxford on a road scholarship to study a Master of Global Health Science in Epidemiology. The founder of Road Scholarship, his vision was to enable young people to fight the world's fight. The ultimate goal would be to work in the global health space. My vision is to help to reduce health inequality.