I want to dive into a topic that is not rarely discussed in church, and especially even by me, the topic of the fear of God. I want to title this today, Don't be afraid, fear God. I know it's a contradiction, but don't be afraid, fear God. The idea of fear of the Lord is very confusing for some people, because some people are saying how can you love God and fear Him at the same time? The Bible says love casts out fear. Why does Bible expects us to fear the Lord and love the Lord? It's very simple. How can you fear someone you deeply love? You can understand that when you get married, how you would love this person deeply and be terrified of them at the same time. Fear of the Lord is not being scared of God. It's living with the awareness of His presence that causes us to change how we live. If you've ever seen a police officer on the road, how many of you know that if you're not aware that the police officer is on the road on the side, your driving is by grace? The signs are there, but they're for other people. They're not for you, because you're in a hurry, because you have your own rules. And the police officer doesn't change anything until you become aware of the police officer. Then quickly, grace goes out of the window and the law steps in.  Father God in the name of Jesus, Mary, anybody out there, just kind of Lord, I promise. And then you begin to make vows. You begin to make promises. You're driving changes. You go from a reckless by grace driver to a person who obeys the law, your heart begins to beat. You're not scared that the person is going to do something bad to you, the police officer. You're just simply scared.  Now God is not your police officer. He is the Father. But when you live with the awareness of His presence, you're driving changes. You're talking changes.  You felt like you were walking on water after that. Your spouse was nicer. You were nicer to them. That you didn't beat the dog, didn't curse the cat. Everything around you seemed a little bit better. You walked out with a different attitude. Why? Because when you live with the awareness of God's presence, you will always live, speak and have a different attitude. And my friend, that is the fear of God. Come on somebody. Fear of God is an incredible respect and reverence growing out of the greatness and the power of God. Young people especially always ask this question of me and they probably ask of you, how can I have the fire of God? I just want to have a fire of God and I hope they don't mean by have a hype for God but have this burning desire for God. I always tell young people this, don't seek the fire of God. Seek the fear of God. Any time you have a fear of the Lord, you will always have the fire of God. The fire of God is not emotionalism. The fire of God is not hype. The fire of God is not having an outburst of passion for God that lasts for the weekend. The fire of God is not having a one night stand with God. The fire of God is not having a weekend custody where God has a weekend custody of you. And then the rest of the week you live as you own the fire of God. It comes out of the fear of the Lord that causes you to run from sin and run after Him. Can somebody say amen? I'm going to have four points today. I didn't preach for a few weeks so it accumulated. The first thing if you have your notes or if you're watching us on live stream you can write below is this. The fear of the Lord is not the same as being scared of God. Being scared of God is not the same as the fear of the Lord. You don't have to read very far into the Bible. Third chapter of the book of the Bible and you will see a man scared of God. Adam hid because the scripture says, I heard your voice in the garden and I was afraid because I was naked and I hid myself. My friend, that is not fear of the Lord. That is being scared of God. Because the one who is afraid of God hides from God. The one who has the fear of God hides in God. And there's a world of difference. John Bovier said the fear of God is not being afraid of God. It's being afraid of being away from God. That will preach. The fear of God is not being scared of God. It's being afraid of being away from God. In Exodus chapter 20 verse 18 and I'm going to read the four verses. I want you to listen to these verses very carefully as I read. Now all the people witnessed thunderings, the lightning flashes, the sound of a trumpet and the mountain smoking. And when the people saw it, they trembled and stood far off. Verse 19. Then they said to Moses, you speak with us and we will hear.  Verse 20. And Moses said to the people, do not fear for God has come down to test you. That his fear may be before you that you may not sin. So people, the Israel were scared because who wouldn't be? When Almighty God came on the mountain and the mountain is shaking and not two smoke machines. I'm talking about real smoke. Not controlled behind a sound booth by a man like Ryan Fink. But a smoke controlled by angels in heaven. And the mountain is shaking. There's a lightning and the people are standing far on the thing. Moses, go talk to God because we don't want to hear. When he starts speaking, imagine what's going to happen. And I want you to see what Moses says. He says, God is doing that. But don't be afraid. Why? So you can have his fear. They were scared. But that's not the fear of God. You know who had a fear of God, Moses? Because he went into that thundering. He went into that scary place. Because the fear of the Lord always draws you close. He's scared of God, pulls you away. Verse 21, it says, The people stood far off. But Moses drew near the thick darkness where God was. And I'm going to coin a quote by John Bovier. He said, the one who is afraid of God stays at a distance. The one who fears God stays close. The big difference between the fear of God is it draws you close. Being scared of God keeps you at a distance. Being scared of God is one of the first signs you don't have his fear. Because his fear pulls you in. And I'm going to explain that a little bit. So for those of you who are like, man, I grew up with an abusive father or maybe I grew up with an abusive authority. And now the fear of God, the last thing I need is to hear about that. It's actually really good for you. Stay tuned. My problem personally that I see among Christians today, myself included. Many of us have a relationship with God. We lack reverence for him. We're going to heaven, but living in hell. We flirt with sin instead of fleeing sin. We can speak in towns 300 miles per hour. And our lives many times, they don't resemble any different than the people we work with and the people that we hang out with. And it's not that we don't have a relationship with God. It's that we lack reverence for the God we have a relationship with. Who we revere is our governors. Who we revere is our doctors. Because when the doctor calls you and they said, you got positive COVID, you don't even think second time is it true or not. Yes, I'm sick. When God says you heal, you're like, nah. We don't tremble before his word. We tremble before sin. And I'm not saying to doubt doctors. I'm not saying to disrespect the authorities. What I'm saying is that we have reverence for everything that moves. Except God. But the God we have relationship with. It's lovey dovey thing. Oh, I love him. My friend, that is awesome. But your Christian life can really have an upgrade if you go from having relationship with God and take a step higher and have a reverence for him. You will tremble at his word. You will honor his presence.  My friend, your view of sin is going to change. Your view on the immorality is going to change. Your view on the world is going to change. Having the fear of God is not the same as being scared of God. Having the fear of God is a good thing. You're drawn to him. You have a reverence. You have a deep respect. You have an awe. You tremble before his word. What his word says, that settles it for you. It brings calm to you. And you are then number two, free from every other fear. Fear of the Lord removes every other fear. Fear of the Lord gives you freedom, not to panic, not to be timid, and not to be terrified. Fear of the Lord is amazing because fear of the Lord, especially at this hour, freezes.   Every person watching us right now and sitting in this room will have fear in their life. We just have to choose which fear we're going to have. You will never be able to live without fear, my friend marked my words. You will just have to choose which fear you want to have. You can have a fear of the Lord or fear of being single all your life. You can have fear of the Lord or fear of bankruptcy. You can have fear of the Lord or fear of cancer. You can have fear of the Lord or fear of COVID. You can have fear of the Lord or fear of being rejected. The fear of never utilizing your dreams. The fear of not being accepted. You can choose your fear, my friend, but it's not possible to remove fear. You can only replace it. And it's time to put fear in its place. Put the right fear in our life so that we walk with the fear of the Lord. Does that mean that all other things don't matter? Does that mean that we are reckless? Does that mean that we walk through the valley of the shadow of death with a smile on our face? Sometimes no, but we fear no evil. That's why the Lord says 365 times do not be afraid, do not fear. But the same God says, the reason why we can not be afraid of everything else around us is because we have a greater fear that consumes all other fears. Consumes all other fear. Every other fear is consumed by the fear of God. The fear of death is consumed by the fear of God because, you know, life will end.  The fear of failure is consumed because, you know, in Christ you're more than a conqueror.  The fear of my life will mean nothing. Allah have no significance is consumed when, you know, for I know the thoughts that I think of you, the Lord, the thoughts of good and not of evil to give you hope and the future. The fear of the Lord consumes all other fears.  If you're consumed with the fear, I'll never get married. Everybody else is getting married. If you're consumed with the fear that, you know what, my business will not take off because I got for load and that I'm going to go bankrupt. I want to give you another fear, a good fear today. Swap fears. Replace fears. Don't just try to remove it because some other fear will come in. Put another fear that will push everything else out. My God. Now all the people in Exodus chapter 1 verse 17, it says, But the midwives feared God and did not do as the king of Egypt commanded them, but saved male children alive. And those of you who, maybe it's a little bit harder for you to swallow, how can we have service and defiance to the governor's orders? This is just our collective, maybe not every person's inclusive in this place, but we're not scared. We have a fear. I have a fear that beats in my heart. And this is not a fear of a governor and even COVID. Midwives, the Bible says they feared God and they saved children against the governor's orders. Because at that time, what we'll be honoring the pharaoh would be to kill children. And so today I want to let you know that God wants you to live in the fear of the Lord and you will be free from the fear of man. You will be free from the fear of failure. You will be free from the fear of disappointment. You will be free. You won't feel that fear. You won't be paralyzed by that fear. Because the Bible says in Proverbs 29-25 it says the pharaoh man brings a snare and whoever trusts in the Lord shall be safe. See because when I fear God, I trust in God. I trust in God to provide for me. I trust in God to protect me.  I will honor your presence and I just refuse to be paralyzed by man. I don't want to be ensnared by a man or by my past or by my future because he who fears God will be safe. Somebody say amen. My friend whoever you fear that is truly who you revere. Who you fear is who you revere. Many believers have a relationship with God but they only revere man. Because if somebody sends them a call if they see that person texting shortness of breath your palms are sweating and you become scared your boss, your ex or maybe your present your spouse your child your employees, your coworkers while we have relationship with God but truly we revere man I want to love men and revere God I want you to love God and revere God so then you can be free to serve men without seeking to please them because whoever you revere you will always seek to please and God never called us to please men he called us to love them. You can't love someone you depend on you can't love someone like that be free to serve them if you need constantly something from them and their approval you're bound by them you're a slave not their servant God wants us to revere God not to be afraid of man not to be afraid of the future not to be afraid of the past and not to be afraid of other people the best way to overcome fear is not to remove it but to replace it William Gurnel said we fear men so much because we fear God so little we fear the future so much because we fear God so little that we will be reckless I am not saying we will be without concern without caution but when you fear God you can look boldly in your future people have went through worse my friend people who followed Christ before us have faced very uncertain things right now they're facing very challenging things all around the world what caused these people not to deny their faith when they looked at 20, 30, 50 year prison sentence what caused them to not still deny the Lord it was one quality my friend and it's not a relationship with God it's a reverence for God because believers today have a relationship with God on Sunday and they go to a nightclub on Saturday they live sin they come in all kinds of things and they come and say Jesus loves me this I know you just don't have reverence for him and God wants us not just to have a relationship with him he wants us to have reverence for him number three the fear of the Lord causes me to flee sin having relationship with God only causes me to flirt with sin the difference between someone who has a fear of God and someone who has only relationship with God is in how they react to sin and temptation we all get tempted we all fall into sin and Satan has access to every single person in a sense to cause us to feel tempted if we only have relationship with God we will flirt with sin if we have reverence for God we will flee sin when I say flirt with sin I mean this it's when Christians us we say things like how close to sin can I get without going to hell it's kind of like me coming to my wife and say hey babe how close to cheating on you can I get without committing adultery what do you think she's going to say it's like oh yeah just as long as you kiss but don't do like french kissing hold hands but don't like interject with the fingers just like like this and then if you go for a coffee make sure that it's not after 9pm other than that I'm fine how many of you know that woman if my wife don't say that we have a problem in a marriage because real marriage the man should be afraid to bring that question up there should be a fear of your wife to think that question and that's exactly why when a Christian comes and say things like hey how close to sin can I get without committing sin that tells me there is no fear of God there already because when you are in love with God you understand God doesn't want to be the first out of many lovers he wants to be your only one God doesn't want to be the first among many idols he wants to be the only one in your life and therefore the question to God is Lord how can I be closer to you that I don't have a desire for sin that I run from that thing that I don't have an appetite for that thing God how can I be closer because man with a relationship has a reverence for God come on somebody Proverbs 166 it says in truth atonement is provided for iniquity and by the fear of the Lord one departs from evil one of the reasons why Christians practice sin indulge in sin and feel no remorse whatsoever is for this reason no reverence for God no fear of God and if you mark those Christians closer you will see they are consumed by inferior fears they are living in fear just the wrong one they are still bound by fear that controls their decision that paralyzes them keeps them in a snare that leads them that fear is still there oh they are not fear less they still fear something except not someone who is worthy to be revered and last thing I want to share is lack of fear of God brings lots of foolishness lack of the fear of God not only it causes me to flirt with sin lack of the fear of God causes me to commit a lot of foolish decisions Proverbs 1 7 fear of the Lord is the beginning of wisdom beginning of knowledge but fools despise wisdom and instruction most of us learn somebody said he said that wise people learn from other people's mistakes smart people learn from their own mistakes and foolish don't learn at all I would like to paraphrase that wise people learn from God's word smart people learn from their mistakes and foolish people don't learn at all to avoid foolishness in life you don't need to have a degree you just need to have humility to avoid foolishness in life if you are a teenager right now listen very carefully it's very simple read book of Proverbs every single chapter has this thing listen to your mom and your dad stay away from bad friends and don't have sex until you get married and have only sex with one person these four rules will keep you away from jail even if you don't have a degree you will have money in your life you will stay away from heartbreak there's gonna be no need for child support there's gonna be no need for divorce lawyers there's gonna be no need to buy things you don't need with money you don't have to impress people you don't even like why because your parents in the beginning will steer you in the right path that only when you and I become 35 we're like they were right I wonder how much money I would have saved if I would have not done this, this, this I wonder how much all my heart would have still been intact if I would have not dated him hang out with them and my parents were telling me that and the reason you and I don't obey our parents is because we are too busy wanting to be smart but in order to be smart you have to make mistakes God wants you to be wise don't make mistakes but how will I learn God simple, very simple and trust me, you live long enough you will have many of your friends to learn and spy on and I was tempted to death so glad I listened to my mom and dad I look back in my life I have a high school diploma don't have anything above that I'm not the smartest kid on the block people still make fun of me for writing a book writing books and they're like you write books I'm like yeah I think exactly the same I'm amazed at myself sometimes because I'm like that's not me I'm not smart kid on the block but I avoided a lot of foolishness in my life not because I was smart it's because very simple practical things that a lot of teenagers did not do one of them is I listened to my mom and my dad for a very long time I'm talking about don't hang out with her be at home at 9 and I'm 20 years old and I'm a youth pastor but I'm gonna tell you one thing those years passed quickly and I look back I didn't have heartbreaks I didn't have debts I didn't have those things and other friends who then tried to go and get a master's degree and compensate I overpassed them, surpassed them because I'm smart not because I'm better not because my IQ is better in fact I'm the slowest the only difference is this is what I found is that God will give you wisdom beyond your years if you fear Him and the reason why young people don't obey their parents it's not because your parents are demanding and not because your parents are hitless siblings it's because you lack the fear of God and because the culture tells you be smart my friend, you don't have all of your life to make all the mistakes your heart is too precious to break it into a million pieces you're not Bill Gates to be able to waste all of your money on all of your wrong decisions you don't have your only God short period of life you can't learn from every mistake people have went before you and God has documented in His Word and if you choose the fear of God yes, you might not be the smart in the beginning but wisdom trumps smartness wisdom trumps smartness because you will see a person who is maybe very very exrespected in the community have a particular cleverness in this one area but you see, they can't put marriage together you see them, they're even maybe doing a heart surgery on people or they're a lawyer and attorney went to so many years for college and you're realizing six four relationships already children from different countries why is this person so smart here because being smart and being wise are big difference because wisdom comes from the fear of God smartness comes from university and smartness comes from experience and smartness comes from watching youtube videos smartness comes from taking online courses smartness comes from, oops I did it I'm not gonna do that again that is where smartness comes in but wisdom comes, God says don't do it you're like but I want to my friends are doing it, everybody is doing it I trust you, you're not trying to hurt me you're not trying to steal my fun you're not trying to destroy my life, God I trust you, God I fear you God I will place my life in your hands God I want to follow you and God says I'm gonna protect you from this dumb mistake that dumb mistake, that crazy person that crazy person I know you don't have this and you don't have that but God I will add as a bonus what other people are seeking as I go, ah my God Jesus my God God will add as a bonus what other people seek as a goal that's wisdom you know Joseph was a man who was very smart in the eyes of the world Pharaoh called Joseph, whom can I find who has a spirit of God in him Joseph had a gift of translating dreams but I want you to notice one thing that Joseph used to describe himself when his brothers came Joseph said this this is your day do this and live for I fear God the secret of Joseph's wisdom the secret of not flirting with Porifer's wife when he had no accountability partner no software on his computer and his phone to track his purity life no Bible teacher to remind him that immorality leads to poverty and leads to bad things how could a teenager a young man, good looking young man who was rejected by his family who had appetites that you and I have who have the same urges that you and I have he had the same flesh but he ran from sin instead of flirting with sin how can a man do that and he didn't have the Holy Spirit like we do did not know the blood like we do did not have a church like we do and there's one thing Joseph uses to characterize himself I fear God in jail I served other people because I fear God when I had opportunities to commit immorality someone who actually wanted to sleep with me not like some of you who are trying to beg another person to sleep with you never mind that was for not for us not for you guys on live stream that was for somebody who will be rewatching it 20 years down the road Joseph actually had a woman who wanted to sleep with him and Joseph said no where does he get that I fear God and that's why when he had the power and his brothers came in who caused him harm and pain he didn't destroy them fear God my friend the secret of your blessing is to have wisdom and the secret of wisdom is to have the fear of God maybe you were born on the wrong side of the tracks maybe you were never handed anything that was good you may feel maybe you feel like man but so many things are against me fear God you will have wisdom you might not be the smartest but you will be wise you will protect you from foolishness and that alone will give you peace prosperity and protection generally speaking there are exceptions yes but generally speaking that alone will give you that in the conclusion I look over my parents' lives my mom and my dad they don't know I'm going to mention this but I'm the oldest so I'm going to say it I might not be going home after church my dad and my mom they don't speak very good English in the United States we moved 20 years ago I've watched them they're quiet people most of you don't know about them they're sitting right now here with us they raised 5 children my dad was never allowed to go to college because he was a Christian when they found out he was a Christian they didn't allow him to go to college when he came to the United States he didn't test because he didn't speak well English so he started to work for post office and that's where he works my mom works fixing and assembling wheelchairs both of them are the most generous people I've met in my life the top 10 givers in the church my parents are one of them I have not had a birthday where my parents did not give me a large sum of money we just had a birthday a week ago my mom brought a gift with my dad and then they brought a seed into the online school they do that every time in the church for over 15 years when we needed to fix anything in the church after work while my dad was building his house he would come here work here and manage finances for 15 years when we offered to pay him he always declined we have a lot of people today who won't come to pick up a rock if they don't give you an invoice and I've seen that in my parents they just finished building a house and this is just me being proud son of my parents and they build that house for cash my mom drives that red Tesla it's hers she doesn't know electronics and she drives a Tesla they don't have education English is their third language because Russian and Ukrainian and I look at them and I said what is the secret if I could use one word to summarize my parents and that would be this I've seen them they're very minimalistic people they don't watch movies they don't go out to eat they're very simple, they focus on God they focus on the church, they focus on their family and they focus on each other never seen my mom and dad raise voice against each other never seen them threaten each other with divorce they stayed as one couple for over 30 years they focused on giving to church they focused on serving and I've seen God this quiet, simple couple God bless, God raise and I watched that and I said God I said God I have so many more gifts I have so many more opportunities but God I want to have that that they have because I've seen people with opportunities and gifts who will fall flat on the ground who will end up in jail who will do all of these things their marriages fall apart they only maintain a relationship with God and they lose reverence for God and I said God no matter how big the ministry gets no matter how much you enlarge my territory and influence God my prayer is God I fear not to fear you I've seen it for 30 something years and for 20 years living in the United States going to school and kind of watching over people's lives I see where the fear of God brings and I see where education cleverness, good looks, connections everything on the outside without the fear of God where that brings and I said God I fear not to fear you you can be impressed with my gift the world can be impressed with my anointing but I know one thing longevity and God's blessing rests on those who fear the Lord for as heavens are high above the earth so great is His mercy toward those who fear Him He will bless those who fear the Lord both small and great if you feel small God says I will bless you if you fear me those of you who are great God says I will bless you as well He will fulfill the desires of those who fear Him He will also hear their cry and save them the angel of the Lord encamps all around those who read their Bible and come to church on Sunday no it's just those who fear Him and He delivers them can somebody say amen my desire church is not to belittle anybody it's my cry it's my prayer I turned 34 a week ago and I prayed to God I said Lord help one characteristic to stay with me until I die and it's not my speaking it's not my writing it's not a large church it's the fear of God if I have His fear I'll be wise I won't be doing shady stuff if I have His fear even with nobody's watching I will walk under His eye the blessing amen I pray that over you today that God will give you His fear if you lost that if you're living a shady, loose life I pray to God He's going to convert you right now I'm going to tell you one thing life will punish you life in America will punish you sin will punish you but God has a way of leading people away from those foolishness things He takes those people who are small they seem like you're looking at them they're not going to make it and God just guides them through that and then you're like I'm surprised myself those who fear Him He blesses them with wisdom even if they lack smartness cleverness they'll never lack wisdom it's not about material things it's about the issue of the heart if you lost the fear of God if honestly like you have no reverence for God whatsoever God is not trying to guilt trip you He just wants to wake you up today and I know this message has woken you up and I know that I just want you to just pray this prayer I know you prayed before God give me a husband give me a saved my children God give me a house give me this but I want you to pray this prayer right now say God fill me with your fear God give me your reverence God I fear not to fear you God bless you


For some reason, this particular bridge, which is 12 feet high from the bottom to the top, gets an awful lot of wrecks from men, women who are driving trucks who have not paid attention to the sign. The average height of some of these trucks are about 13, 13 and a half feet, and they will not fit underneath this bridge. Now, we see clearly who's going to win. Going up against an immovable object is going to cause a lot of problems for who. Not the immovable object, but for you. Similarly, the Bible says that he who has an ear, let them hear. We are given these different warnings, often times for us to obey, to hear God's word and to avoid danger. So guys, make sure that you spend time in God's word, that you hear what he's saying, and the different warnings that he offers. Please listen. Amen.


Hey guys, welcome to Video Friday. So it's November and it was actually snowing outside the art resin studios this morning and it made me think the cold weather is coming, I can't deny it any longer. So you might not know but epoxy resin and cold weather are not friends and what happens is you can get a lot of bubbles in your epoxy resin if it's too cold. So I thought I'd share some of my top tips, my top seven tips for reducing bubbles when you're resining. Okay, so first one. Now depending on your substrate, if you're using wood or paper or any other natural object that can really contain a lot of trapped air that might off gas, sealing first before you apply your resin is always always a good idea. That will create a barrier, it's going to prevent that trapped air from releasing into your resin in the form of bubbles. So sealing your artwork first is my tip number one. Okay, tip number two and as I said, if your resin is cold, it's always a good idea to bring it up to room temperature first before you resin so you can do that in the form of a water bath which I have here. Now also a water bath, you can warm it up and you'll get even less bubbles. It's going to be a thinner consistency and you're going to have next to no bubbles in it but always, always make sure your resin is at room temperature. If you do use a water bath, make sure you thoroughly dry off the bottles. So I always put my bottles in with the lid on so there's no chance any water can get mixed in with the resin but always dry them off thoroughly before you open the cap and pour. Okay, so dry it off, open the cap and then pour. Okay, so that's my second tip. My third tip is to stir slowly, okay, so just stir slowly and steady and scrape the sides and bottom as you go. Now I am really guilty of this, sometimes I really whip my resin as if I'm beating egg whites and I'll show you what happens when you whip, okay, as if you're beating egg whites. I mean you can already see as I'm whipping here, you're just incorporating more and more air, more and more air means more and more bubbles. So remember, when you're stirring, slow and steady is the name of the game. Okay, so tip number four, just as you don't want to whip it too much to incorporate more air in, you also don't want to pour from a really high distance. You want to pour close to your artwork and you want to pour slowly, okay, so just like this, right, compared to pouring a pie and just dumping it out, you're going to get way more bubbles, way more friction bubbles in there, so pour slowly and pour closely. Okay, so tip number five, always make sure you pour in a one-eighth of an inch layer. Art resin was meant to be poured in a thin application, an eighth of an inch, self-levels to an eighth of an inch, so if you're pouring into a mold where you have the opportunity to pour a thicker amount, always pour in a one-eighth of an inch layer and the reason for that is if you pour thicker, bubbles aren't going to have a chance to rise to the top to get torched out, so if you want to pour thicker or pour, make sure you pour in multiple one-eighth of an inch layers. Tip number six is to always use a torch. It's the only method we use here at our resin to get rid of bubbles. Nothing else beats the intensity of a flame to really zap those bubbles, so you can see here, see, it just absolutely incinerates those bubbles, so using a torch is tip number six. Okay, so tip number seven is sometimes you just want to babysit your work a little bit. Now, this is particularly true in the case of resigning wood and paper and those other objects I mentioned that can off-gas, trapped air, any other natural objects.  If you do happen to find a bubble that's popped up, you can just pop it with a toothpick. And that's it, those are my top seven tips for eliminating bubbles and stay warm guys, keep your resin warm and we'll see you next week on Video Friday. Video Friday with our resin. Ah, thank god that's over.


Hey guys welcome to training and reviews. Today I'm going to be looking at the Sennheiser Momentum 2 headphones. Now these are the Bluetooth on-ear headphones they cost around 220 pounds and I'm going to be covering the design the build quality, the buttons and ports that come with it, the sound quality and I'm going to be looking at how to pair it with your phone or your laptop as well. So let's get straight into it. Okay so let's open up the pouch and see what's inside. So you can see the headphones they're pretty compact. They fold right in. It comes with the wired headphones as well as the USB charger and you also have an extra little pouch that you can carry it in. So let's have a look at the headphones. Now they have a all-leather headband with a stainless steel band here to connect the actual on-ear headpieces. It's got a very nice gold stitching as well along the headband there but I reckon it would probably look a little bit nicer if it had dark stitching in black as well.  Now the actual earpieces it has a very soft leather earpads and if you're going to be wearing the headphones for a long time, two hours, maybe on long journeys, you expect the earpads to be really comfortable and I think they do an actually a really good job. Sometimes you don't even feel that they're on, that's how soft it is and it does fit nice and cozy onto your ears. You have to pull up from the sides with the circle outside of the earpad there and push it along the stainless steel band and then it will get tighter and tighter. So if I push it down, make it taller like that. So that's one good aspect. Now the earpads, the thickness of this is a little bit thicker than the predecessor which allows you to actually wear this for hours. So before it used to be a little bit thinner than this, the previous momentum headphones. So this makes it a little bit easier for you to wear for extended period of time. It does a really good job. Okay guys, if you wanted to pair the headphones with your phone or your laptop, all you need to do is hold down the power button here for about seven seconds and the light should start blinking alternating red and blue. Now you do hear audio confirmations, it says pairing, the light is now flashing red and blue as you can just see there. Now it is searching for the headphones and we can try and connect to it. Now I'm just going to try and pair this, go to pair new device and it will start searching for the headphones. As you can see, Momentum M2 has come up so you just select that and now it's connected and it tells you the battery percentage as well. So I can now listen to my music using the headphones. I can connect it to my laptop. You can see how quickly it connected. It had no problems picking it up and it was very easy to do so. To turn off the headphones, you just hold down the power button for about four seconds.  Now just on the ports, we have the on off button which is also the pairing button as I just showed you. You have the volume button here which is a slider. If you slide upwards, it will put the volume up, downwards for the volume down. It also allows you to skip to the next song by double pressing and if you wanted to view the previous song, you can triple press that as well. One thing to note about the triple press, if you're not listening to any music, if you triple press, you'll get confirmation in the audio about how much battery percentage is left which I think is a really good feature which is something you can't find on a lot of headphones. And then finally, you have the charging port and then the headphone jack port there. If you wanted to use the wired headphones, you can do that from the pouch that comes with it. In terms of the sound quality, it comes with noise guard, hybrid noise cancelling sound. Now I think from all the headphones I've tried in the past, it does a really good job in cancelling out outdoor noises, transport noises and so on. If I had to give it a rating out of 10, 10 being I can't hear anything outside of the headphones, I would probably give it a 9 which is very high and I think Sennheiser have done a really good job being able to cancel out so much noise. Now I take the train in the mornings to work and the train is very noisy. Putting these on, I think it's done an excellent job. I can't hear anything outside of the train tracks and I can't hear the people in the train talking next to me and I can just concentrate on my music whilst I'm playing on my phone and it just allows you to blank out from the rest of the world and it's a really good job there. Now I haven't tried this on planes, I would presume it wouldn't block up to 9 hour 10 on an airline. I think it would probably do maybe 7 hour 10 but again that's very good compared to other headphones out there. It also comes with voice max technology which dynamically cancels out external noise for intelligently allowing you to have conversations with other people when you take calls on this. Now one thing I've noticed is if you're walking outside, you've got your headphones on and you get a phone call and there's too much background noise and the other person can't hear you properly. With the voice max technology that comes with the Sennheiser headphones it's crystal clear. I can't hear anything else around me. I can hear the person clearly and even though there is a lot of noise outside the person on the other end of the call can actually hear me through the voice max technology a lot clearer than other headphones or the wired headphones that have mics in or into them. In terms of the music I think it's got a very deep rich bass to it so if you listen to loud music, rock music and so on you really hear the basses but even if you want to listen to just mellow music, calm, relaxing sounds it does an excellent job. So I would give the sound quality in terms of the bass, treble, all the different types of audio variations and frequencies that you get. A very high 8 out of 10 and it's kind of like having a mini nightclub in your ears. You really feel the sound quality coming through. You can never get the sound quality like this in ear headphones and I'll try some other over ear and on ear headphones as well and the quality on this is far better than all the others I've tried. Now in terms of the battery life, Sennheiser mentioned that it comes with 22 hours of battery life if you want to get an example of how much that actually is. If you listen to this one hour a day for just the weekdays the battery life will last you a whole month. Now it depends obviously on your usage if you're going to listen to it while you're working and you listen to that maybe four or five hours of your working day then of course your battery is going to run out fairly quickly maybe just over a week but in terms of the quality that you get in response I think the charging time it takes about two to four hours depending on how low your battery is to charge fully and that will last you for weeks on end and it does a really good job in that. I have used on ear headphones previously which have a longer battery life but again with the quality build the sound quality that you get if you're using bluetooth compared to the white version then the battery life varies in different aspects like that. Overall I would give this a seven out of ten only because there are other headphones out there with a much better battery life so for example the Bose QuietComfort 25 headphones that has a battery life of over 35 hours the Plantronics Backbeat Pro headphones has over 60 hours of battery life so that's a big difference here that's almost three times as much as this one so there are ones with better battery life but again that's one of the reasons why I give this a seven out of ten on battery life but the sound quality is far better than some of the others that I've listened to in the past. Now coming on finally the price it's a little bit expensive it is 220 pounds you can find that on Amazon and on the Sennheiser website I'll put a link in the description below if you look at it from the US this costs roughly around three hundred dollars but I'll put a link to that one in the description below as well it's not the cheapest of headphones but if you're going to be using this for minimum three years for example I would definitely recommend buying it because it is worth the high price tag but if you're going to switch up the headphones maybe every year I probably wouldn't go for it at this price I think there are other headphones that come close to it which are half the price I have another video where I've reviewed the Marshall 2 major 2 Bluetooth headphones you can click on the little gray box up here to view that video now and I think that is half the price with almost the same quality and sound and you can probably go many years with that headphone as well and it just depends on you on what your preferences are so guys thanks for watching the video I hope you liked the review if you did like it please give it a thumbs up if you have any questions about the Sennheiser headphones here then do drop me a comment below I tried to keep track and answer all of your questions and do check out some of my other videos here and I will see you guys at the next video take care


The Indus River basin faces many challenges related to population growth, rapid urbanization, industrialization, environmental degradation, unregulated resource usage, poverty and climate change. These factors have led to increasing abstraction of water resources, which must be reassessed. In addition, the basin's current water supply and demand management systems must be improved. Options for improving these systems include reservoir management, water quality conservation, alternative water sources such as wastewater treatment and desalination, land use planning, flood management, and the rehabilitation and modernization of existing infrastructure. Additionally, water demand management strategies such as conjunctive use of surface and groundwater, rehabilitating and modernizing existing infrastructure, increasing water productivity for agriculture, crop planning and diversification, and changing food demand patterns and limiting post-harvest losses must be implemented. This article was authored by A.N. Laghari, D. Vannum, and W. Rouch. We are article.tv, links in the description below.


I'm happy to listen to you. Great. Thank you so much for organizing such a wonderful conference. Appreciate it. The title of my talk today is the same as the title of a paper I've been working on with Thomas Barrett, but really I'm going to talk about a larger body of work that I've done with Hans Halverson and Jim Weatherall along with Thomas and some of the papers leading up to this one and some papers that have come after this one and some that we're working on now. Okay, so in the second chapter of his book, World Enough in Spacetime, John Ehrman constructs an elegant hierarchy of classical spacetime theories. And the hierarchy tracks both the geometric structures involved, but also the associated spacetime symmetries. And he finds that as the spacetime structure becomes richer, the symmetries become narrower, and the list of absolute quantities increases, and more and more questions about motion become meaningful. Following Ehrman, I will present a hierarchy of spacetime symmetries today, but instead of comparing the symmetry properties of different, excuse me, of different spacetime theories, I'm going to restrict attention to general relativity and compare the symmetry properties of different spacetime models within that theory. So the hierarchy turns out to be analogous to, say, the hierarchy of causal conditions that's long been used in the foundations of general relativity. And I'm going to highlight a few connections between this symmetry hierarchy and a hierarchy of causal structure. Let me just say that there's many levels to the symmetry hierarchy. I'm only going to, because of time, I'll only be able to focus on four today. So here they are. These are the four that I'll be focusing on. And I'd like to emphasize that as we move up the hierarchy, the symmetries decrease, and so the structure increases. And it turns out that with this additional structure at each level, one is able to prove various types of things. And so again, this is kind of analogous to the hierarchy of causal conditions. So I'll take one example. Somewhere up at a certain level on the hierarchy of causal conditions, one is able to prove that the causal structure of spacetime is rich enough to, say, determine the topology of spacetime. This is a classic result by David Malament. It's actually going to be coming up a bit later in the talk, but that gives you an example. So as you move up the hierarchy, one is able to do more and more. And in just the same way that with globally hyperbolic spacetimes, one is able to prove an awful lot more than if one is just considering chronological spacetimes. Each of these four levels corresponds to a recent paper that I've written with either Hans or Thomas or Jim, and here they are. I'll also be talking about some future work with Thomas and Hans. Okay, so let's start. Let's consider some preliminaries concerning isometries. I just want to make sure that we all have a good idea of the definitions. There's only a few definitions, but I think being very, very clear about what one is saying is important. So here's my definition of a spacetime. It's a pair mg, where m is a manifold, g is a Lorentzian metric. The usual background assumptions concerning the manifold are in place. It's smooth, it's Hausdorff, and so on. We say that spacetimes mg and m prime g prime are isometric if there's a diffeomorphism from m to m prime such that when you push forward g, you get g prime. And let's say that the collection of isometries from a spacetime to itself are the global cemeteries of spacetime. So again, one could possibly explore many different types of definitions of a global cemetery of spacetime. I want to be very clear, this is what I mean by a global cemetery of spacetime. And it's the one that Wald uses in his book. It's very influential within that literature, Garrosh, Penrose. It's also the one that Erman uses when he's constructing the hierarchy of cemeteries in classical spacetime structure. So again, been very influential within the philosophical literature. So I understand there might be other definitions of cemeteries out there. I'm focusing today on this one. Now let's consider a very influential construction used in discussions of the whole argument. So let mg be a spacetime and let h and its complement have non empty interiors. Well, we know there is a whole diffeomorphism from m to m, which is non trivial in the whole, but acts as the identity outside of the whole. That's what I mean by a whole diffeomorphism. So a trivial proposition one can prove is that let mg be any spacetime and let psi be any whole diffeomorphism. Then the spacetime mg and the spacetime m where you push forward g, those models are isometric and the isometry is realized by psi, the whole diffeomorphism. So here's the picture. I think we're all familiar. Okay, now for the quiz. Erman in his second chapter has a quiz at the end. Here's my quiz. And yeah, I'll just say that in the past few years, I've had many email discussions, many discussions via referees, many discussions in person, where I come across people holding views consistent with A, B and C. I'd like you to think about the question for a minute here. A whole diffeomorphism is blank, an isometry from a spacetime to itself. Is it always an isometry from a spacetime to itself? Is it sometimes an isometry from a spacetime to itself? Or is it never an isometry from a spacetime to itself? Okay, the answer is C, never. So a whole diffeomorphism is never an isometry from a spacetime to itself. Trivial doesn't count, I take it. Trivial doesn't count, yeah. But a trivial would be not a whole diffeomorphism, because by definition, I have to move something non-trivially in a whole diffeomorphism. This follows from a very general uniqueness result that's been around since 1969 from Garrosh. And a simple corollary is that a whole diffeomorphism is never a global symmetry of a spacetime. Okay, let's now consider the hierarchy. Let's start with the bottom and move our way up. So the weakest condition in the symmetry hierarchy draws on the whole construction just considered. So the condition essentially requires that when the global symmetry of spacetime are fixed in an open region, however small, then they're fixed everywhere. So following Garrosh, we'll refer to these spacetimes as rigid to avoid confusion with the whole argument. So we say a spacetime is rigid. If for any open set in the spacetime and any isometry from the manifold to itself, then if psi is the identity on the open set, then it's the identity everywhere. And so we show that every spacetime is rigid. Now, despite the fact that every spacetime is rigid, you might get the sense that this is an extremely weak condition. I think it's fruitful to explore situations where spacetime is not rigid. And so here's another proposition that's related. Non-Hosdorff spacetimes always fail to be rigid. So here's the picture. Consider Minkowski spacetime. And you've got two origins that are non-Hosdorff-related. These are the witness points witnessing the non-Hosdorff-ness. And now just consider a bijection, which takes each point into itself, but exchanges the witness points. That bijection turns out to be not only a diffeomorphism, but an isometry. And so fixing the global symmetries outside of a hole, which contains the witness points, will not fix what happens inside the hole. So the spacetime is not rigid. Or you could say that non-Hosdorff spacetimes have a certain type of symmetry holes that standard models just don't have. Okay, now let's talk about the next level. So the next condition in the symmetry hierarchy requires that the global symmetries of spacetime just be completely fixed. One doesn't have to fix an open set somewhere to fix it everywhere. It just comes already fixed. So we say spacetime mg is giraffe if the identity map is the only isometry. So here's a way to think about this. David Malament suggested one way to construct a giraffe spacetime.  So here's a giraffe spacetime. Here's another giraffe spacetime. This one can work with it. It's easier. It's a portion of two-dimensional Minkowski spacetime.  Now you've gotten rid of all global symmetries. The only isometry from this spacetime to itself is the identity map. Of course, any giraffe spacetime is rigid. Every spacetime is rigid. The other direction does not hold. Minkowski spacetime is a counter example. All sorts of symmetries, global symmetries. So it's not giraffe, but of course it is rigid as we've seen.  And yet everyone knows that giraffe spacetimes are actually generic among spacetime. I think that tension is something interesting to just meditate on because I think we're accustomed to thinking about spacetimes with symmetries when our universe probably has none. But the meaning of generic in this context is never made precise and in general proof does remain elusive. Partial results are available namely on compact spacetimes due to mountain. All right. Time for the next level. The next condition in the symmetry hierarchy requires that the local symmetries of spacetime be completely fixed. And I'll say what I mean by that here. So we say that a spacetime is Heraclitus. If for any distinct points P and Q and any open neighborhoods around these points, there is no isometry from one neighborhood to the other, which takes P into Q. So in other words, we see that since any neighborhoods of distinct points fail to be isometric, we have a sense in which each event is completely different from every other event. And so you might say that in such a world it's impossible to step into the same river twice. Okay, one can show that any Heraclitus spacetime is giraffe, of course. The other direction does not hold. So back to this example, we see that of course it's giraffe, it is not Heraclitus. This is a flat spacetime. So every point is exactly like any other point in terms of there is a local isometry there that one can set up. So not only does this spacetime fail to be Heraclitus, it sort of maximally fails to be Heraclitus. One can show that Heraclitus spacetime does exist. So let me say a bit about this. It's good to have a feel for what a Heraclitus spacetime looks like and feels like what a concrete example certainly helps me. So start with a portion of Minkowski spacetime and standard TX coordinates and call it MG. So this is the portion I have in mind. It's back to that triangle. Down here at this point, this is the origin in a standard coordinate system from Minkowski spacetime. So I'll be referring to the origin, but the origin of course is not included in the spacetime. We've deleted it. Now what you do is you consider a scalar function, which is the Euclidean distance from the origin. And then a conformal factor where the conformal factor is just one over that Euclidean distance from the origin. Now consider this conformally flat spacetime. The claim is that it is Heraclitus. So how do we know that? Well, we use scalar curvature invariance to do this. So one can show that the Ricci scalar has this expression here. And it follows from that that any local isometry must map P to a point Q with the same Minkowski and distance from the origin. And so the picture is that if I'm considering a point Q and I want to map it, even locally map it to another point in the spacetime, I'm constrained to map it where my Ricci scalar is the same. And the Ricci scalar is the same only on that blue line. Now I construct a different scalar. I'll call it Q, where I just take the covariant derivatives of R and use the inverse metric to form a scalar function. And one can show that Q takes this form. It's proportional to both R and F squared. And so you can work out the details. It follows from this that any local isometry must map P to a point Q with the same Euclidean distance from the origin. So here's the picture. The point must be mapped somewhere on this red line if the F values are going to be preserved. And so taking these two constraints together, then if you're considering a point, you are forced to, if there's a local isometry, you have to map the point to itself. And that's true for every point in the spacetime. And so there you get that the spacetime is Heraclitus. So you're actually proving something much stronger than the Heraclitus property there. I'll say a bit more about that in a moment. But I have a question, which is, do four-dimensional Heraclitus spacetimes exist? We've constructed a two-dimensional one. Man, I've tried. I really have tried. I can't figure it out. There doesn't seem to be any reason why you would have a block here to be able to do it. It's just things get really complicated. Presumably one would have to find four different scalar curvature invariants and play them off of each other like coordinate systems like I've done in the earlier example. So really what's going on there is that my curvature invariants are, yes, playing the role of coordinates. And so I use those coordinates to prove this Heraclitus property. And yeah, so can one do this in higher dimensions? But Heraclitus spacetimes are highly structured at each point. So this allows for some pretty crazy uniqueness results. Remember, as we're going up the hierarchy, the structure is increasing. This allows us to prove more and more results. So here's something that you can show at this level of the hierarchy. Let's start with a couple definitions. A pair of spacetimes are locally isometric if, for each point in the first one, there's a neighborhood around the point that you can embed into the second one and vice versa. And then we have to define what a local property is. Let's say a property of spacetime is local. If given any two locally isometric spacetimes, one has the property if and only if the other does. So then you can show that Heraclitus spacetimes are locally isometric if and only if they are actually isometric. That's kind of crazy. So a corollary there is given any collection of local properties, there is at most one Heraclitus spacetime with exactly those properties. There's a uniqueness result here. It's telling me you don't have to tell me what the global structure of your spacetime is like. You just tell me the local structure at each point and I'll be able to put the puzzle together in a unique way. If it's possible, of course, it may not be possible. So one could rephrase this by saying for Heraclitus spacetimes, local structure just determines global structure. And of course, we have the other way around global structure determines local structure. And therefore, these two structures are kind of similar in this way when one can recover one from the other. Here's another uniqueness result. So consider a spacetime MG with any property P. We say that this spacetime is P maximal or P in extendable if the spacetime cannot be properly and isometrically embedded into some other spacetime with the same property. And it would seem that Leibnizian metaphysics would demand that spacetime be maximal with respect to various physically reasonable properties. And now consider this definition of observational indistinguishability. One spacetime is observationally indistinguishable from another. If for each point in the first, there's a point in the second such that their causal paths are the same. There's an asymmetry in the definition here, which will be important in a moment. But there is a general underdetermination problem when one considers the class of all possible spacetimes. But you can show that if one restricts attention to Heraclitus maximal spacetimes, so these are spacetimes with the Heraclitus property, which are also maximal with respect to this property, then these spacetimes are observational indistinguishable if and only if they are isometric. So we have Heraclitus asymmetry, Leibnizian maximality gives us no underdetermination problem. Or another way to put the point, for Heraclitus maximal spacetimes, the observable structure determines the global structure. Okay, and now finally to our highest level of the hierarchy. This condition requires spacetime to have maximal curvature structure. So for any manifold, you can consider the collection S of M of smooth real valued scalar functions on M. And associated with each spacetime, MG is a collection CMG, which is a subset of S of M. These are the smooth invariant scalar curvature functions constructed from the metric and its associated Riemann curvature tensor and covariant derivatives. And now we can consider the following definition. Let's say that a spacetime is maximally structured if the collection of invariant scalar curvature functions just is the collection of smooth functions. In other words, every smooth function you can possibly imagine on the manifold corresponds to some invariant scalar curvature function. So one can show that any maximally structured spacetime is Heraclitus. Question, does it go in the other direction? I don't know. It would be cool if these two conditions were turned out to be equivalent. But yeah, this question is open. Now maximally structured spacetimes do exist. And so here's a sketch of the proof. Consider the Heraclitus spacetime that we already took a look at in the previous section in standard TX coordinates. This is just, again, conformal Minkowski spacetime. Use invariant scalar curvature functions R and Q that we already took a look at to define invariant scalar functions T and X where T and X are, they mimic the coordinate maps, the global coordinate maps. So then you consider an arbitrary function on M. You put that function in coordinates T and X, you can reconstruct that same function by using the invariant scalar curvature functions big T and big X in place of the coordinates. And so you can build your smooth invariant scalar curvature function, which just is whatever F you gave me to start. So at this highest level of the hierarchy, some even stronger uniqueness results are available. We know there are a number of senses in which the scalar curvature invariance can be used to determine the local geometry of spacetime. There is a literature on that. But in general, one finds that such functions do not determine the topology of spacetime. For example, one finds that local invariance cannot distinguish a plane from a flat torus. So let us make this claim precise. Let Mg and M prime G prime be spacetimes and let Mg and C of M prime G prime be their collections of invariant scalar curvature functions and let them be indexed by a set I to generate the respective families of functions Fi and Prime I. And we do this in such a way that for each I, Fi and Fi prime, they correspond to the same metric construction. So however you're constructing your scalar curvature function from G, do the same thing with G prime. Now we say a bijection from one manifold to the other is a curvature isomorphism if for all, for any I that you choose, when you pull back the F prime, you just get F. So F prime of I pulled back just is F of I. And so you can show that of curvature isomorphism, it need not be a homeomorphism, let alone a diffeomorphism. So in this way, the situation is completely analogous to the one concerning the malament result. You set up a I'm sorry, a causal isomorphism and you show that at low levels in the causal hierarchy, a causal isomorphism just isn't a homeomorphism, but that at some level it is. So to show in this case that the result doesn't go through, just consider any bijection at all between any pair of flat spacetimes with different topologies. So for example, consider Minkowski spacetime and Minkowski spacetime with a point removed or a torus of some kind. One finds that when one pulls back any scalar curvature function from the one spacetime to the other, you get that the functions are the same. So you have a curvature isomorphism, but you do not of course have a homeomorphism since by construction, these spacetimes have different topologies. Well, you can show that if you're willing to go all the way up to maximally structured spacetimes, a curvature isomorphism not only is a homeomorphism, it has to be a diffeomorphism. So the result is completely analogous to the one from Malamint showing that sufficiently rich causal structure is going to determine the topology of spacetime. But I want to emphasize a very important difference between the cases. The causal structure of spacetime is encoded in a particular relation between spacetime points. Relations come to the fore. On the other hand, the curvature structure of spacetime is not encoded in a relation between spacetime points. Instead, each scalar curvature function gives rise to an invariant property of each spacetime point. And the scalar curvature structure of spacetime is encoded in the collection of all of these properties of all of the spacetime points. And so what I'm saying is that maximally structured spacetimes have so much structure that even the properties of spacetime points determine the topology of spacetime. You don't need any relations to do this. What justifies the label maximally structured? Here's some current work with Hans and Thomas. So given a maximally structured spacetime MG and any tensor field whatsoever, T on M, one can explicitly define T from G. So in particular, any global coordinate map that you might be interested in is explicitly definable from the metric. In addition, any other metric G prime is explicitly definable from your original metric G. And so we can say that for maximally structured spacetimes, all structures curvature structure and any structure can be explicitly defined from the local metric structure. Okay, let me just close by with a brief review of where we've come. We've looked at four conditions of a symmetry hierarchy or asymmetry hierarchy. As you move up the hierarchy, symmetries are reduced and structure increases. There are a number of levels in between, but there's nothing lower than rigid and there's nothing higher than maximal structure, at least that I have considered. Maybe there is. Of course, there is. Whether it's of interest is another matter, but at the lowest level, rigidity, this is the condition that holds when fixing the global symmetries of a spacetime in a little open set fixes them everywhere. And what we saw was that every standard spacetime in general relativity is rigid, but that you can find non-rigid examples of spacetimes if one is considering non-Hosdorf models. Then we bump up a level to giraffe spacetimes. These are the spacetimes where the global symmetries come already prepackaged fixed. There's only one isometry of a spacetime to itself and that's the identity map. And these spacetimes, of course, are rigid. The implication does not go in the other direction. These spacetimes are or it is thought to be generic in some sense. And yet most of the standard examples that one sees in the literature, whether that's textbooks or research literature, these spacetimes are almost always giraffe spacetimes. Then the next level we bump up to Heraclitus. Here's where we not only fix the global symmetries of a spacetime or the global symmetries come fixed, also the local symmetries come fixed. Heraclitus spacetime is one in which one can't map distinct points into each other even locally. And at this level, now there's tons of structure both globally and locally. And with this, especially the local structure, one is able to show that certain claims follow that didn't claim lower down on the hierarchy, but now follow. And one that we highlighted was you give me the local properties of spacetime and I'll give you the global properties of spacetime. We also highlighted another uniqueness result which essentially says that the observable structure determines the global structure. Finally, we jump up to maximally structured spacetimes. These imply the Heraclitus spacetimes, the other direction is unknown. So these top two levels perhaps may be equivalent.  You don't tell me anything about how they're related at all. I can use that internal structure to give you back the global topological and even the manifold structure of spacetime. And moreover, one can use maximally structured spacetimes to explicitly define any structure that you're interested in as long as that structure comes in the form of a tensor field. Okay, that's it. Thank you very much. Thank you. Yeah, it's a technical material, but you explained it very clearly. And now we have Brian Roberts, which is your respondent and he has up to 10 minutes to tell us something interesting about this. Well, I think JB has said all the key interesting things. I'll try to be really brief just to allow maximum discussion here. Thank you, JB. Wonderful. Wonderful. Lovely to see these things all tied together. I've been following these papers, of course, with interest. And so the hierarchy is just, I just want more, really. So my first comment is, there's another interesting work that wasn't mentioned here by JB and Jim Weatherall from 2014 regarding conventional, conventionalism about spacetimes. And so my first sort of question is, I wonder if you've thought about whether a relation of conventionality might fit into the symmetry hierarchy in some interesting way. Their thought, for those who haven't read this paper, first, you should definitely read this paper as well, amongst all the others, wonderful piece. Their thought is when one says things like I can buck you to like these two spacetimes, you know, you can't really tell which one you're in, because there might be funny forces which make you think there's a certain metric which there isn't. And then JB and Jim very reasonably respond, what do you mean by forces, my friends? And you ought to have some minimal reasonableness constraining what you mean by forces. And that would mean something like F equals MA or in a relativistic sense, you'd want a two form characterizing the force tensor field so that you have F equals MA in a relativistic sense along every time like frame. So and then the result shows that for the class of conformally equivalent spacetimes, there basically is no conventionalism. But of course, this condition can be relaxed, you can look, you know, for conventionalism and more general spacetimes. And anyway, I just sort of wonder how this could potentially some note, they also point out that depending on if you know how rigid you are about what you mean by force, there could be lots of other you know, interesting notions of conventionality you could identify, you just have to tell me why you think that notion of a force is interesting if it's not a rank zero to a symmetric tensor. So anyway, just looks to me like some room to play here. I don't, to be honest, see how they would be related by implication to many of the things you said, but I wonder if you thought about this. Some other very brief comments. The original Geroch stuff was about limits of spacetime. So I mean, I think one of the things that's being revealed here is interesting tension between these, maybe two research programs, research programs involving non house dwarf spacetimes, which you sometimes use for reasons of branching among other things. I mean, people sometimes appeal to this when they want two points to get really close, just closer than you can get in an ordinary spacetime. So branching could be a reason. But then, you know, these limits of spacetimes, of course, we have different options, but that rigidity result was used by Geroch is a key step in showing the existence of so-called Geroch limit spacetimes. And these are crucial in certain sorts of stability results, which, you know, help motivate what it means to be a generic spacetime. So I wonder, does attention between these two sorts of research programs, does that adopt the Geroch approach to limits? And people who might try to use non house dwarf spacetimes for interesting modeling and physics. Gosh, there's lots of other things to say, but I don't want to just carry on. Maybe I'll just leave it at that. And I mean, I'm sure other people have things to say about the whole argument. JB already knows what I think about that. So I'll leave it there. And thank you again, JB. Wonderful, wonderful talk. Yeah. Thanks, Brian, for your comments. I really appreciate them. I'll sort of try to give a response. Concerning the conventionality stuff. Yeah, you know, that I have never given that thought. That's intriguing. I do know that, you know, we're just piecing this structure together. It's a very big structure. You know, like I said, I think it's analogous to the hierarchy of causal conditions. One, one thinks about just all of the results that one finds there. I'm not on that level. I can't prove, you know, I'm not on the level of I'm in guzzy, for example. And so I'm very, very slowly working my way through this stuff and hitting mainly the really simple stuff. That sounds a bit complicated, but there might be something there. And with as the structure kind of builds out a bit, more and more results presumably will be collected. But I appreciate the heads up because I never would have even thought to put those two things together. About the limits of space time paper by Garrosh. Yeah, that's the context where this general uniqueness result shows up. And as you emphasize, Brian, you're absolutely right. This is the result that sort of forces the uniqueness of limits. One could take limits in all sorts of different ways. And it just turns out that the rigidity of space time in the sense that I've been talking about, which relies on the Garrosh stuff, picks out a unique kind of limit to look at. But you mentioned some tension. And so that's the part I'm still, I don't know what exactly tension, I want to get a better grip on that part. As I see my project, of course, it's no surprise. I just have these definitions around. And I prove things with these definitions. And so, of course, the mathematical theorems are true. And so there can't be any tension concerning the results, of course. So I guess I'd like a better picture of what that tension looks like. I sort of had a mind, sorry, if I wasn't clear, maybe the idea that if you take yourself to be modeling physical phenomena with non-Hausdorff spaces, and you want to say things like my result is robust under perturbations in the sense that there are nearby space times that all share the same property. That in non-Hausdorff spaces, I take it the lack of a rigidity theorem means there's a lack of a well-defined limit here. So it's not clear how long we get. Yes, absolutely. So I guess what I would want to say is we already had reason to be suspect of the non-Hausdorff thing. I have in my past work, I guess I've been playing that kind of open. I haven't come down one way or the other where I think, for example, a non-Hausdorff space time is physically reasonable or not. I've sort of left that door open. And to be honest, I've kind of emphasized the other side, which is probably what you're referring to. Now I can kind of see the tension. So I do have certain writings where I say, well, if you look at something like an initial value formulation, and it's in Misner space time, you can take a surface, put some data on it, evolve it to where you can't evolve it anymore. You have a maximal Cauchy development, and you see that in the Misner context, that maximal Cauchy development is extendable. And so then you're thinking, well, we can consider various extensions. And it just turns out that in that context, the maximal, maximal extension, when you're really thinking about it, what Garrosh calls the natural extension is non-Hausdorff because it sort of branches. And so exactly like you said, Brian, it branches in some sense. It turns out that that particular model doesn't branch in another sense. But it doesn't matter for this context because it is non-Hausdorff. And all you need is the non-Hausdorff property to show that the rigidity result fails. And so taking a cue from what you said, once you have that rigidity result failing, then now you don't have a good sense of limit. You don't have a good sense of generosity maybe. And so then how are you going to be talking about nearby possible worlds when you're considering a non-Hausdorff model? So I think you're absolutely right that these mathematical results are now coming down on the side where it's like maybe non-Hausdorff space times aren't as reasonable as we might have thought, right? And this is a reason why. Or to put it in a slightly different way, fixing global symmetries outside of a hole which contains these witness points, it's not enough to fix what goes on inside. And so there's a type of indeterminism that just is not in play in the standard models. And so if people are worried about certain types of indeterminism, then that's a type where you've got something going and you might become worried about that. And so I think you're absolutely right. This counts against non-Hausdorff models for sure. So thank you very much. Okay. Just thanks for the talk and for the response. And we can still take some questions. I wanted to ask about this issue of generosity. And as you correctly say, too much any space time you write down, he's going to have some symmetries, but we can regard that as non-generic. I mean, here's the sort of physics intuition reason to think that that I've done with would be something like, well, you know, take the solution, linearize around it, look at small, you know, for the gravity, for a little pulse of gravity radiation pretty much anywhere, and it's going to break the symmetries. And so the, you know, I can think in a kind of intuitive sense of the topology. I get an arbitrary small distance from any symmetric thing, and I'll find a non-symmetric thing. I expect the symmetric points to somehow be topologically sparse. What are the problems in rigorizing that way of thinking? Is it just the infinite dimensionality of it that becomes troublesome? Yeah, what comes into play I think is what troubles all sorts of foundational results concerning generosity and general relativity. One can put, well, first of all, one would like to be able to take the entire collection of all space times and put a topology on that collection. That turns out to be really, really problematic. And so instead what practitioners do is they'll focus on collections of space times having the same manifold, and then they'll put a topology on that. But the problem is, is that there are a number of different topologies one might consider, and none of them seem completely satisfactory. So that's a point that Garrosh made very early on when the topic of generosity was brought up, when one had to prove things that were generically true. It's also something that Sam Fletcher, I mean, that was kind of his dissertation, is to pull out reasons why there just isn't a, you know, a canonical topology to work with. And it just turns out that if one works with the compact open topologies, then results, of course, are easier to find in terms of stability results. But the physicality there comes into question. When one moves to the open topologies, the Whitney topologies they're sometimes called, then it's much harder to get results. And I think that's the problem here with trying to prove that giraffe space times are generic. The compact case is easy because in that case, then the two different topologies actually coincide. So the physicality of the compact topologies there. And so one can prove this result. My sense is, and this is not really something I've looked into much, I know Sam was interested in this question of proving generally that giraffe space times are generic with some interesting topology. I don't know of any work that's done other than this result that I cited from Mounend in 2015. Thank you. Okay. Any other questions? Yes. I don't see. Thanks. That was really nice. I actually just wanted to hear, I find this hierarchy of space time structure intrinsically interesting. But I'm wondering if you could say, do you think there are sort of philosophical upshots to be had? Do you adhere to various methodological principles involving relative amounts of structure? Or do you think there are some theoretical virtues that come from considerations of comparisons or structure? Or I'm just wondering where you go from here within philosophy of physics? Yeah, yeah, you're trying to get me to say stuff that I don't want to say. I want you to say it. That's the thing is that my project is one in which, yeah, I'm considering these very clear definitions and seeing what followed. There's already so much to do there. Of course, there's all sorts of interesting topics that are related to this stuff. And I'm certainly interested in that. But I just keep my cards pretty close to my chest. And I just see no need to wait into those waters when I've already got so much to do here. Sorry to sidestep your question. Okay, other questions? I would like just to continue this. Maybe you don't like, but you are speaking about space but what about matter and what about equations? What do you mean what about matter and what about equations? Yes, so for example, matter should determine the metric. So is this somehow represented in your case? Or for example, some Oxford persons, they think that the symmetry of matter determines the symmetry of spacetime. But you are speaking about the symmetry of spacetime as if matter was not there. So what do you think of these kinds of dependencies which seem absent in your talk? Yeah, let me say something about that. But before I do, I want to push back on something that you said. You said that matter determines the metric. That's just not right. The metric determines the matter, but not the other way around. There's an asymmetry there. Yeah, but if you have a massive thing, then it will have a curvature. If you have no matter, then you can have a flat spacetime. Yes, but you can have two different vacuum solutions on Rn, different metrics. So without matter, you can have differentiation. But if you have matters, then you have a curvature. No, I still want to push back on that. I'm sorry. Where is that theorem found? Maybe I'm not as specialist, but you're speaking about generality. It's not true that as soon as you have a massive matter. Yeah, so I guess what I want to say about matter is in the background, of course, one has Einstein's equation. If you give it a metric, then I can trivially define via Einstein's equation a matter field, a TAB field, the stress energy field. And so every spacetime is a solution of Einstein's equation in that sense. And so if one is considering a more restrictive sense, then you have to say what that means. So sometimes folks talk about exact solutions, or sometimes one might use energy conditions and so on to kind of limit what you're calling a solution there. But my results here hold generally. And then if you want to impose any constraints like that on top, everything will go through. So nothing I've said here will be contradicted by that discussion. It's a sub discussion of this one. Yes, okay. But you can have different distributions of matter, but you mean they will be the same metric? Will they be compatible with different spacetimes? I guess I'm not sure what you're asking. I mean, Einstein's equation is one in which if you give me a metric, I can come up with a curvature tensor. And I can use that to define one side of Einstein's equation that contains the curvature structure, a certain type of curvature structure. The other side is the matter structure. And so I can look for solutions in a variety of senses. Like I just said, every metric is going to produce some matter distribution via Einstein's equation. Whether one wants to count that distribution as reasonable or not is a question that you can check out. But at this level, I like to think of Einstein's solutions as coming in levels. I'm working on the most general level so that my results are the most general. If one wants to impose any kinds of constraints on matter, like it seems like you might want to do, then I invite you to impose those constraints. And then you'll have a limited discussion. But everything I've said will carry through. Yeah. Just in some discussions, matter is supposed to be primary. And what you tell would be coming afterwards. You have a reverse direction. Yeah. But I don't want to let this go, because it really is important to recognize the asymmetry of Einstein's equation. So you can have whatever opinion you want about matter and the geometry of spacetime. But you're not allowed to have the opinion that the TAB field determines the metric. It just doesn't. It's just a mathematical fact. But the other direction does hold. You give me a metric, it determines a TAB field. So there can be no disputing that fact. Yeah. You mean just there is a freedom about vacuum. So when there is no matter, you have different options. Yes. But it's not just the vacuum, though. So do you think that there's a mathematical theorem that says, you give me a TAB field that's non-vacuum? I can construct a unique metric from that. Because I do not know of that theorem. Who proved that theorem? No, I'm not a specialist in such theorems. But what I'm saying, as soon as you have matter, you cannot have a flat solution. Well, that is true. Yeah. Okay. We can call this a weak determination of matter. Okay. As questions, debates. Okay. Thank you for the talk. You guys have combined different works in it. So with this, we should finish. Someone has the last remark, but it's already quite late. So thank you all for being here and the speakers and the respondents and the public. We will continue these discussions and some further questions. Thank you so much. Thank you very much. Yeah. Thank you.