The final item of business is a member's business debate on motion 5, 7, 0, 9, in the name of Christine Grahame on Brexit's impact on inflation. This debate will be concluded without any questions being put, and I would ask those members who wish to speak in the debate to please press the request to speak buttons. I call on Christine Grahame to open the debate around seven minutes, please, Ms Grahame. Thank you very much, Presiding Officer. Let's start at the very beginning. The EU referendum vote in 2016. The vote across the UK was close. Rounded up to 53 per cent voting leave, to 48 per cent remain. In Scotland, the figures were 62 per cent remain, 38 per cent leave and interesting by waving aside, Northern Ireland voted 56 per cent remain. In Scotland, every constituency voted remain, including, of course, Scottish Warders and Midlothian. This was in the face of an aggressive and ill-informed campaign, blaming the EU for all ills and promising not just the infamous side of a bus, £350 million a week for the NHS, but being tariff-free, bureaucracy would be cut. But was it? Increased paperwork, for example, truckers need import and export declarations, security declarations and other paperwork for their shipments. New infrastructure reports to deal with queues and to check loads of vast lorry parks. The trading world was to be our oyster, despite the fact that I believe that the Umbaric Obama said that the UK would be at the back of the queue, which is where it is and has stayed. There were no favourers waiting for the UK. The one that you deal with Australia has infuriated farmers and was even criticised by George Eustace, then the Environment Secretary. The reality is that most British traders with Europe and Brexit has crippled it. Migration would be under control as the UK quotes took back control more of that later as it impacts on our economy. The UK then cut itself off from its biggest trading partner, the EU, where 40 per cent of its exports went and for what. The answer is for the highest inflation of the G7 countries, running currently 11 per cent with food inflation at nearly 17 per cent. In terms of how UK inflation compares to other nations, recent analysis from the Financial Times shows that the rate of consumer price inflation, CPI, is higher in the UK than in other devolved economies. It rose to 11.1 per cent in October 2022 in the UK compared to 10.4 per cent in Germany, 7.7 per cent in the USA, 6.2 per cent in France and 3 per cent in Japan. A member of the Bank of England's Monetary Policy Committee noted that Brexit has added 6 per cent to UK food prices, and he said that at a recent appearance at the Treasury Select Committee. Yes, Covid had a price tag. The war in the UK does impact on the UK economy, but Brexit is why it is doing so badly. Even before Brexit, the economy was weak after nearly a decade of Tory government. Add Covid, Ukraine, Trusonomics and it is a heavy mix for failure, bad enough. When you add in the basic ingredient, the Boris Brexit, it explains much more. Do not take my word for it that Brexit has had a devastating impact on the UK economy. The Office for Budget Responsibility predicts that the UK will suffer the sharpest decline of any European nation with a drop in growth by 1.4 per cent in 2023. That compares to small independent countries similar to Scotland, such as Ireland, who will see their economies grow by around 3 per cent next year. Can you take an intervention? I can, yes. Kenneth Gibson? Thank you for accepting an intervention. Does the member agree with the OBR that Brexit will actually cost the United Kingdom £80 billion this year in lost trade, whereas Rishi Sunak said in 2016 that we would actually be £20 billion a year better off? Does that not call into question the Prime Minister's economic judgment? I do indeed accept that. The OBR has also said that Brexit's impact on the economy is now adverse over the medium-term to tune a 4 per cent of GDP. That is massive self-harm, not a weak passage without cries of protests from traders, truckers, farmers, hoteliers, care homes, scientists and even performing artists. Trade bureaucracy has soared. Every exported cow needs a vet certificate. Unskilled labour has dried up, all impacting on the UK economy. Now public opinion has swung dramatically against Brexit. With just 32 per cent still in favour and 56 per cent regretting leaving, rumblings in the Tory ranks about swiss-style deals muttering from the CBI about the needs for changes to rules for migrants to work here. You know that even the Tories wedded to the ideology of Brexit and Rishi Sunak is right up there can no longer delude us that Brexit is just the ticket. Rishi has to keep his party together and foremost especially the Uber Brexiteers including himself and to pop with the rest of us. The Bank of England in the November monetary policy report, while saying that the major contributor to current levels of inflation is the global increase in gas and therefore energy prices, it also highlights the impact of non-energy tradable good prices. These are partly driven by global factors such as the bottlenecks in international supply chains since the pandemic disruption linked to the Russian invasion of Ukraine but also costs associated with Brexit. To quotes from the Guardian, to stately obvious, the war in Ukraine and pandemic-related supply issues are sending prices soaring across the world but what gives Britain a particularly pronounced problem which forecasters say will endure into the immediate future while inflation in the Euros one starts to fall is Brexit. Our departure from the EU has weakened the pound, increasing the prices of imports, adding to companies' costs. Post-Brexit limitations in foreign workers are also hitting firms' bottom lines as our problems with the UK European supply chains. Adam Ponson, the American economist and former member of the Bank of England's monetary policy committee, said that 80 per cent of the explanation for Britain's higher inflation was bound up with Brexit and its endless complexities. It amounted, he said, and I quote too, a trade war the UK declared on itself. So, while living standards are under immense pressure around the globe this year due to record inflation, particularly in food and energy prices, the officials said that Britain would suffer more as a direct result of leaving the EU. More bad news. Even before the economic disaster, there was trust. Between 2016 and 2021, it is estimated that Brexit cost the UK £31 billion, the equivalent for Scotland is £2.5 billion. For Scottish Borders Council, that's £53 million and for Midlothian, £43 million. Care of the Starmars, no help. Battered by its past flip-flops and the subject rejecting any easing for a single market is not in line with public opinion. Neither are Lib Dems. For them all, Brexit is done and dusted and we must make what we can of it. We were told in 2014 that a vote, yes, were independence who see us thrown out of the EU. Ironic, is it not? That we were dragged out despite 62 per cent voting remain and by a party which today only holds six Scottish seats. That lie won't fly again. Already support for independence is on the rise as the Scottish people see the inadequacies of UK economic policies. Tomorrow we will learn of the Supreme Court judgment. However that goes, I know that sooner rather than later Scotland will regain its independence. Brexit was the final straw. I now call Stuart McMillan to be followed by Edward Mountain around four minutes. Thank you very much. First of all, I may have to leave just prior to 6 p.m. as I'm cheering across party group later. I also like to congratulate to Christine Graham for securing this important debate, highlighting the catastrophe that Brexit has brought upon her midlodian South, Tweeddale and Lauderdale constituency. As her motion indicates, the Brexit shambles has also affected elsewhere in Scotland, and that's obviously where I will focus my comments. Nobody with any credibility can state that Brexit has been positive. So-called Brexit opportunities have weathered in the vine and the false dawn of a trade deal with the US, much heralded by the former, former Prime Minister Boris Johnson to the mission by the former Prime Minister, Liz Truss, that a deal will be years away, as negotiations are not even taking place, proves that the Tory's Brexit crusade has left people in Ms Graham's constituency and my own Gynon Cynwbrachai constituency worse off. I voted remain and I would do so again tomorrow. I look forward to the day that we in Scotland can rejoin the EU as an equal partner when we do secure our independence from Westminster. The economic climate that Scotland faces at the moment is driven by a variety of factors, and that is undeniable. Once again, what no one with any credibility can deny is that Brexit has been a major contributing factor to rising costs, rising inflation and also a reduction in opportunity. The Trusquarteng shambolic budget has also played a huge factor in the current economic crisis, leading to the extension of the cuts agenda that we saw last week from the current chancellor. The filling of the budget black hole is going to lead to yet more austerity, family struggling, kids going hungry and food banks facing unprecedented demand. Some in the chamber will argue that inflation is high elsewhere, so the cost of the living crisis is not solely down to the Tories and the UK Government. The Financial Times reported that the CPI rate of inflation in the UK is higher than in any other developed country. At the 11.1 per cent, Germany is at 10.4 per cent, the US is at 7.7 per cent, France is at 6.2 per cent to provide just some other examples. The fact that a member of the Bank of England money's repolition committee has stated on the record to the Treasury and State Committee in Westminster that Brexit has added a whopping 6 per cent to the cost of food in the UK tells a story. Even worse, a former member of the Bank of England money's repolition committee, Adam Pozen, suggested earlier this year that Brexit was responsible for up to 80 per cent of the increase to prices in the UK. That truly was a remarkable statement that once again highlighted the folly of a Brexit Scotland that didn't vote for and how the right wingers of the Tory party have led to a level of poverty many of my constituents and no doubt others across the chamber haven't suffered from before. Decisions by politicians matter. Policy decisions and legislation that politicians and Governments progress have a real life effect upon our constituents. I don't have much time, so I'm sorry. That's why the complete disregard the UK Government had when pursuing Brexit legislation through the Westminster Parliament ignoring legitimate concerns from many across the political spectrum, but also from those with no political allegiance has led to the situation that we face. No matter how many cost of living surgeries I do in my Greenock number of Clyde constituency, I know that I will just be scratching the surface of the support that my community needs and deserves. The Tory obsession with Brexit is increasing poverty and the fact that both Labour and the Lib Dems who acknowledge that there's only one Labour member in chamber today and there's no Lib Dems, the fact that both Labour and the Lib Dems wouldn't reverse Brexit speaks volumes about them and how thrilled they are to be part of a Westminster system that helps the richest and punishes the purest. Thank you, Mr McMillan. I now call Edward Mountain to be followed by Fausal Chowdry. Around four minutes, please, Mr Mountain. Thank you, Presiding Officer. During this session, Christine Graham has used members' debates to highlight non-overtly political issues such as the men's sheds movement and the miners workers pension scheme. We've seen other MSPs follow the same convention with debates such as Gas Safety Week and Cancer Card initiative. Sadly, Presiding Officer, this motion does not follow that recipe. It is overtly political and I believe goes against the unwritten conventions of the Parliament. That disappoints me, Presiding Officer, and I believe is unworthy of Ms Graham. Mr Mountain, sorry, but is your music just very second if you don't mind to resume your music? It was just to point out that the procedure for the selection of members' business is well known to members, and that is what the decision was. I don't know if the member is calling others into question. I hope not. That was the business motion that was selected according to due process. I would just point that out for the member to reflect on. Please resume, Mr Mountain. Well, thank you, Presiding Officer. Let me say that I've never been one to stray away from the subject of a debate, so I'm going to address some of the issues that Christine Graham has raised. Christine Graham makes much—by the way, if there are people who want to intervene, Presiding Officer, finding you let me have the time back, I'm very happy to let them intervene. Christine Graham makes much about this Parliament responding and respecting democracy, and I agree with her, and I'll always defend democracy, but it cannot be on the basis of agreement when it seats her views only. In her motion, she states that the solution to the issues that she highlights are twofold, becoming independent and joining the EU. The voice of democracy spoke in 2014 and again in 2016, and the answers were indeed clear, no to independence and yes to Brexit. As a Democrat, I respect both of those results, and I believe that every Parliamentarian should, too. Sadly, however, it appears that because Ms Graham did not get the answers that she wants, she wants to rerun the debate and the vote. Let's be clear, ever since the votes and decisions of the majority have been made—sorry, was there an intervention? Have I had a good time back? Yes, absolutely. Christine Graham? Yes, thank you. I apologise for not taking in mind, I actually cut my speech considerably. Will the member and I respect what he is saying, address the issue that has Brexit contributed to high inflation across the UK? Edward Mountain? Indeed, I will. I will keep my speech short and to the point. Specifically on the European Union, I think that most people will accept that forging a new relationship with the EU and other countries would, after 47 years of membership, be challenging, and it has been. However, the suggestion of separating from a 300-year-old union would be easier is pure hot air. We have seen flimsy pamphlets produced to support this argument. What they haven't done is deal effectively with the issues, and specifically, fiscal issues such as currency, pension issues, national debt to mention but a few. You cannot gloss over these or play fast and loose with answers in the hope that no one notices.  What about the border that you will create with our biggest trading parter, if you were, God forbid, to get independence and join the EU? The First Minister has said that it would lead to a border crossing point, which no business welcomes. Indeed, I am sad that the member who I am about to mention has already left, but the only person that seems to welcome border crossing points is Emma Harper. Goodness knows why. Perhaps she wants to establish a bureau de Champs. We are better together. Take the pandemic, for example. The figures speak for themselves. Scotland received £14.4 billion in barn consequentials from the UK Treasury. On top of that, hundreds of thousands of Scottish jobs were saved through the furlough scheme. In Christine Graham's constituency alone, which both reaches into Midlothians and the border councils, nearly 34,000 jobs were saved. If I can just finish this point, and then if I get the time back, Presiding Officer, I'm happy to. Even during this energy and inflation crisis brought about by Putin's illegal war in Ukraine, the UK continues to step up and provide support to Scotland with the energy price guarantee and an extra £1.5 billion in funding announced in last week's autumn statement. I can give you up to six minutes, speaking time for reflecting the interventions. Thank you, Presiding Officer, and thank you, Mr Mountain, for taking the intervention. Can he recognise that last week, the Paris Stock Exchange overtook the London Stock Exchange in terms of financial trading in the European Union and that Brexit has been an utter disaster financially and people can't pay their mortgages right now? I would answer that question if I have more time, but I don't, so I'm going to continue along the line, and it's not in the motion as you well know. Turning to the cost of food for which Christine Graham suggested is due to Brexit, as a food producer, and I refer you to my member of interests, I can tell you the following. Fertiliser has gone up by 450 per cent, sprays have gone up by 30 per cent, tractor fuel has doubled, electricity has almost doubled, the result for wheat is, for example, which is a basic staple for human food construction and animal feed, has gone from £200 a tonne to £290 a tonne, and might well be trading post Christmas at £320 a tonne. None of this is due to Brexit. All of those increases are down to Putin's illegal war. Presiding Officer, pursuing another divisive independence referendum is not the answer to today's problems. The impacts of war and inflation and the resultant energy crisis are not just local to Scotland or the United Kingdom. They are global challenges and are better addressed with Scotland remaining part of the strong United Kingdom that it's in in the moment. Thank you, Presiding Officer. Thank you, Mr Mountain. I now call on Foisal Chowdry around four minutes, please, and Mr Chowdry will be the last speaker before I ask the Minister to respond. Mr Chowdry. Thank you, Deputy Presiding Officer. I would like to thank Christian Graham for bringing this important issue to the chamber. Christian Graham's motion mentions the scenic and beautiful area of Midlodian South to Dill and Lododill, but Brexit poses challenges in Midlodian North across Lodian and across Scotland. So, there is much to agree with in the motion being discussed, but it will not surprise Christian Graham that I cannot support its conclusion. Last week in the debate on the Constitutional Europe External Affairs and Cultural Committee report, my colleague Sarah Boyack said many of us did not want to be here dealing with the consequences of the UK's departure from the EU, and she's right. But Brexit and the levels of inflation being faced today lie squarely at the door of the Tories. The EU referendum was a political choice by David Cameron to try to unite his party. The Brexit deal was firstly negotiated by Theresa May and voted against by Boris Johnson, only for Boris Johnson to renegotiate parts of the deal. The former Prime Minister described it is an open ready deal, only for him and now his two Tory successor to seek to uniliterally change that very deal through the Northern Ireland protocol bill. Now the Tory party are very keen to point out that there are inflationary pressure everywhere, which is true to an extent. But the UK finds itself in a far worse position than many comparable countries because of two factors, the recent political instability and the fact that the Tory party is held hostage by an internal function which will only accept the most extreme from of Brexit. But I think many across the United Kingdom are tired of government by internal Tory drama. We need a Labour government in Westminster to provide solid leadership and move the UK forward. So I cannot accept the conclusion of the motion that independent is the answer to this problem. As Mark Blyth, one of the economists appointed to the First Minister's own panel of advisers, sorry I'll just go ahead, adviser has said independence would be Brexit times 10. The answer to the disruption caused by separation from our biggest trading partners is not to repeat the process. It is a change of direction in Westminster with a new constructive attitude to our friends on the continent and a commitment to revitalising our economy. Only by doing this will we deliver an economy that works for everyone across the UK. This better future is possible and I want to see it for Christian Graham's constituency just as much as for the Lothian region and the rest of Scotland. I thank Christian Graham for bringing this debate to the chamber. I recall that we debated Brexit many times in the last session. It strikes me that so much of what we said then has come to pass. I think that this debate, amongst reminding us of what we said then, also serves the useful purpose of puncturing the conspiracy of silence that seems to have taken hold in many quarters with regard to the material impact that Brexit is happening in concert with other factors that are impacting on our economy and indeed our way of life. We did warn repeatedly and we did so emphatically that Brexit and particularly the variety of Brexit, the hub Brexit imposed by Westminster, would cause huge damage to Scotland's economy. To add to the harm caused economically, socially and culturally from the loss of horizon, erasmus, free movement and also environmentally with plans now to remove high EU standards from our statute books. It was not just the Scottish Government at saying so and it is not just the Scottish Government saying so now. Sadly, this is reaffirmed by the sort of statistics in Christian Graham's motion and reported almost weekly with each new economic forecast or trade statistic. Recently, the Governor of the Bank of England, Andrew Bailey, linked to current financial predicament to Brexit and Mark Herney, a former Governor of the Bank of England, believes that Brexit acts as a break on economic growth and increases the rate of inflation. The UK's rate of inflation hit a 41-year high in October, accelerating to 11.1 per cent. The sharp rise was caused by higher gas, electricity and food prices. Annual food price inflation rocketed to 16.5 per cent, the highest for 45 years. Those figures mask a bleak reality. They mean hardship for more individuals, families, businesses and communities. The people paying the highest price for this are those on the lowest income. The people paying the highest price for Brexit are those on the lowest incomes, despite Scotland voting to the main. I recognise that there are other factors, but Brexit is a significant contributory factor. Of all the factors that we face now, it is the one that was the result of a clear political choice by a Government in these islands. The Office for Budget Responsibility has forecast that UK GDP will be cut by 4 per cent as a result of Brexit. The Financial Times reported that £100 billion has lost output and £40 billion in less revenue for the Treasury each year. Brexit is contributing to fueling inflation and is making Scotland and the rest of the UK poorer. As a consequence of Brexit, the UK is facing a worse cost of living crisis than it otherwise would be, partly due to the loss of free trade. Analysis in April from the London School of Economics showed that post-Brexit trade barriers resulted in a 6 per cent increase in food prices in the UK. A report by the Resolution Foundation in June. I thank Mr Arthur for giving way. As a food producer, I know that the majority of costs come down to the cost of fuel, because that underpins all costs of production. It is not actually down to Brexit. Will you accept that fuel prices drive food prices? If so, everyone will gain to affect it. I suspect that others will be catching up across Europe shortly. I have not said in my remarks that Brexit is a sole cause of the situation that we face. I recognise that. I recognise that inflation across the economy is going to ultimately be a reflection of energy price inflation. That is just a reality and an economic fact that we cannot accept. However, the point that I am making, and those are independent statistics, is that Brexit has had a contributory factor. A report by the Resolution Foundation in June found that, even before the UK left the EU, currency depreciation linked to Brexit increased the cost of living in the UK by £870 per year for the average household. The trade barriers that we now have are causing real harm. The OBR now expects trade volumes to decline over the medium term, falling to 8.3 per cent below present levels in the final quarter of next year. A food and drink sector in Scotland has borne the brunt of the harbregs that was imposed by Westminster on Scotland. Exports to the EU and key food products have fallen by 52 per cent in fruit and vegetables, and 25 per cent in exports of dairy and eggs in the first half of 2022, compared to the same period in 2019. Scottish businesses have seen record increases in input prices in 2022 and saw Brexit as a factor according to SNP global statistics. That has fed through to the 21st monthly rise in prices charged by businesses as of July. Brexit has ended free trade and also free movement, hurting key Scottish industries and contributing and creating labour shortages. It is now more expensive and time consuming for employers to recruit from overseas and for people who want to come to Scotland to live and work. Food processing and manufacturing, hospitality and agriculture are particularly affected, harming rural Scotland in particular. As of July 2022, a range of key economic sectors in Scotland were experiencing worker shortages, for example 43.4 per cent in construction and 43.8 per cent in accommodation and food, but that economic harm is also a social harm. We are poorer as a result of Brexit and we are risk missing out on the cultural benefits of having more people of working age from a range of backgrounds and contributing to our common will. We are doing everything we can within our limited powers to support people and businesses. By the end of March next year, we will have invested around £3 billion in a range of measures to support households. That includes supporting energy bills, childcare, health and travel, as well as social security payments that are either not available elsewhere in the UK or are more generous. For businesses, we have an existing package of non-domestic rates relief worth over £800 million, which includes the UK's most generous small business bonus scheme. However, we are doing all this with, I do not just say one, but at times it feels like two hands tied behind our back. Inflashing is eating away at the Scottish budget, which has already fallen by 10 per cent in real terms between this year and last. Due to the lack of additional funding in 2022-23 and the financial restrictions of devolution, we have had no choice but to make savings of over £1 billion. The announcements in the last week's UK autumn statement do very little to address the damage that is done to the Scottish budget. I recognise that we face a series of global challenges and that the situation that we find ourselves in today lends itself to no easy solutions. However, I recognise that, many of the issues that we have, Brexit can be cited as a contributory factor. Brexit was ultimately a political choice. I dispute anyone who would wish to argue that it has democratic legitimacy in Scotland. Scotland comprehensively rejected Brexit in 2016, and every election since then to this Parliament and to Westminster, parties opposed to Brexit have been overwhelmingly returned. However, there is another reality, Presiding Officer, and it is this as well. The hard Brexit that we have inflicted upon us was not a necessity. There was a moment in June, July and August of 2016 when the UK Government could have listened, they could have engaged, they could have heeded the warnings of this Government, of this Parliament and many other stakeholders and sought to pursue an arrangement for European Union that would minimise damage. However, rather than focusing on what was best for the United Kingdom, the United Kingdom Government focused on what they thought was best for the Conservative Party. Unfortunately, and as a consequence of that, we are all paying the price today. Thank you Minister. That concludes the debate, and I close this meeting.


Again, Tony you don't get it This life this Sucks Seems like you're blind like I mean I don't want to be here Me either. What are you doing to fix it though? Huh What are you doing to fix it because your current plan of just getting drunk every night is obviously not working Whatever, I'm going outside Tony drunk again. It's just so frustrating, you know I wish I could get him to see that we could still have all the things that we dreamed of. I mean this This is never supposed to be permanent Supposed to be temporary You know In the three years that I've lived here. I've never known either y'all to be quitters. Okay? Don't give up on each other now Hmm Drunk again Tony. I just had a few of the boys come on. That's some serious It's not about how many you had Look, I'm working really hard. Okay, I go to work all day I take classes at night and it would be nice if you would show like some interest in moving our life forward I don't know why you blame me. Okay. I didn't ask to get injured. It just happened.  I love you And I'm committed to having a life with you But not like this. I need you to try Okay Hey, Tony, what's going on?  Hey? I'm just trying to be nice man. You know you You got a good woman there never mind man Tell me what's going on? I had grand plans you know Gonna show the world And I got hurt And it all came crashing down. Just yeah, this is it. Hey, I mean That's the thing about life man. You know the more we try and control it more chaotic it appears I Mean you just gotta embrace it and appreciate it all Come on, man. That's easy for you to say.  You could be anywhere in the world right now And this is what you come up with Truth you may be right But you got choices too Except you choose not to see those choices You have a good night, man Hey, babe, can you sit here, please? Can you come sit here? I know it's been really hard for you since you got hurt But I want to take a trip down memory lane with you, okay? Do you remember when I first got this place? We never let the fact that we were stuck in this temporary situation make us lose gratitude Do you remember when you used to come in singing and dancing all the time?  I miss my partner And it's my best friend. I can't change how you're choosing to think about our life Really think about your next set of choices They could change everything Otherwise, I might not be here for the end of the story I'm gonna go to bed though night Hey, babe This is for you Look, I'm I just wanted to say that you were right last night I've been really stopping myself from just progressing because I've been afraid and There's no excuse for it. I've really been letting what could have been Stop me for what could be with you and It's not fair and I want you to know I'm gonna be better a better partner. I'm gonna get back to physical therapy I'm gonna look for a job. I'm gonna do all the things that I promised. Just I want to thank you for not giving up on me Sure, you couldn't have got me a smaller flower though Where am I gonna put this? It was the last one. Sorry Thanks so much for watching this video if you want to help us change the world Please hit that share button so that more people can see more messages like this


odd. Hi, it's Bridget. Welcome to above life channel. The purpose here is to inspire your spirit and fill you with hope. I'm like, hi, this is so odd. So I'm in, I'm in the living room at, let me just move some stuff behind me because it's going to bug me. All right, I'm in the living room in the office space. Whoa, just a minute. Oh, loud, loud, loud. And it's an unusual day because my sister rescued a dog yesterday.  She's only like seven pounds and she is very, very anxious, very timid, shy. She's hiding under the couch right now. And so there was some drama with her this morning. I wasn't here. I was actually with my kiddo and I ended up having to come here and help out with the dog today to help get her acclimated because she went on the run this morning. Tiny little dog didn't know where she was like to thought my sister found her. So that's good. But oh my gosh, it was so much drama at like six a.m. So here I am connecting with you all this morning. I'm just gonna, I have my laptop in front of me. I want to make sure I can check the sound quality here. And I have to work tonight too at the community center. So I got some stuff going on, but I was really, really, really, really excited. I knew who I wanted to channel with you today. I knew last week who I wanted to channel today. And so we are going to channel Liberace Lee. Yeah, we're gonna have a conversation with him. And how this came up was, you know, you guys know right that I like to chat a little bit first before I start the channel.  Hello, welcome in the chat. If you're watching and you say hi in the chat, I'll probably say hello to you later on or at some point during our our live stream today here on Monday. Thank you so much for your patience for my regular crew and the community who usually shows up earlier in the morning. However, because of the drama this morning, I am just now getting to the point where I can channel. You might hear the dogs by the way, because there's two, there's a little a little one sleeping here, who is going to be the big brother of the little girl Charlie. So Tucker's here. You've seen Tucker before on my other videos when I visited my sister in Washington State. And now that she's back home, and I'm here. I am also then with Charlie as well. And she is hiding right now, which is fine. She's okay. She's actually come out a lot and we've hung out. She was hanging out with me in the bathroom and I took a shower and she loves to be outside. And she even grabbed a toy and tried to play with it, which is a really big deal for her. So yeah, so it's going okay. So but I want to channel Liberace, which is absolutely perfect too, because the dog situation because Liberace had a ton of dogs and rescued a lot of dogs. I don't know if you know that about him. I didn't know that. And how I decided to channel Liberace or get involved with wanting to channel because I need to feel connected to the person somehow or interested or curious about the person that I channel in the afterlife. And so with Liberace, I hadn't really felt like a pull to him or draw to him, except one of the vloggers, that old school vloggers I used to follow like five years ago, Daze, D-A-Z-E with Jordan, The Lion. You might remember that because in the early time of Above Life channel, I watched, I was watching this daily vlogger who lived in Hollywood and I was so inspired because I had remembered being there. I'd remember he'd go to the cemeteries and he'd go to like movie locations and things like that. And he was an actor himself. And I used to just watch his videos just because he was walking around Hollywood. And I knew, you know, Hollywood a bit because I grew up going to California. And so I've been there many times when I was younger. And so I knew like, you know, the stars and little bits and parts of West Hollywood. And at that point, I think it was a man's Chinese theater. I can't remember. It's been so many names, but the big theater, the famous places, you know. And so I now going through all the changes and things that I've been going through with my move and new jobs and new job and stuff like that.  And so I went back to like my old Disney vloggers I like to watch, except I can't go to Florida right now. So that's kind of a bummer. And then I thought about when I was on looking at my subscriptions on YouTube, which I haven't done for a long time, when I was walking, I realized, oh, here's one with days with Jordan the Lion. I haven't watched Jordan for a long time. I wonder what he's up to. And so I went to look at it, it just turned out that so he moved out of Hollywood and moved someplace else has a house and all that regular life and he's focused on like travel vlogging. And it just so happened that he happened to be back in SoCal and was doing videos of in part some of them of famous the famous cemeteries and some famous spots and things. And I'm like, Oh my gosh, one of the things places that he went to was in, was it Palm Springs? So Liberace had a house in Palm Springs. He also had, I think, maybe one in LA, I'm not sure, but I saw him, I saw Jordan do one about his house in Las Vegas that actually has been bought by someone and is being restored. So I'm like, wow, that's cool. So I watched him do the tour of the house. And I thought this is fascinating and beautiful and it's super extravagant. And so I felt so connected to his energy. And I was like, wow, it was crazy. And in that video that Jordan Jordan was talking about him on, I think, Johnny Carson or something like that, like one of his last television appearances, not the one with Oprah, but one with Johnny Carson. So I thought, I'm going to watch that. So I did. And then I was like, super connected to him, like I could feel him. And it was like just this beautiful entertainer, just this really jovial energy. And I thought, okay, I want to, I want to channel him. And I could hear him really clearly. So then I went on this walk and then I could hear him. And I was like, after like, after I watched the Johnny Carson thing, and I'm like, oh, okay, I'm connected now. I'm like, I'm gonna have to channel him. So I must have watched that like a week and a half ago. And so now I get the chance to channel Liberace.  But it's totally poignant with the dog thing. So and it was really sweet this morning, because I actually said that out loud. It was just me and the dogs here. And I said, Oh, makes sense that I'm talking to you with this new dog. And he says, I know a thing to chew about dogs. Yes, I do. And so we're going to have a conversation. You have a seat Lee. There's a beautiful leather couch in front of me. And so I'm going to just kind of visualize his energy there.  She's such a sweet. She's just scared. She's just scared. He says, she will calm down. She's just scared. She's such a sweet thing. Yeah, she is a sweet thing. Isn't she? She is very sweet. So little dog, I wish I could show her to you guys, but I can't because I'm not going to I'm not going to touch her. I only pick her up if I need to. Like when I needed to put her collar on, I only put my hands on her when I have to to do that or to hook up a leash, because I don't want her to be uncomfortable. I want her to come to me when she's comfortable with me touching her. So he says, that's exactly what you should do. He says that's exactly what you should do. That's exactly what you should do. So I understand that you had that there's a movie somewhere about you and your life and I'd like to see it. I haven't seen it isn't on Netflix. It must be on Netflix or something, the candelabra or something about the candelabra. Yeah, yeah. Yes, yes, he says yes. So a golden candelabra is something that's very connected to you kind of like a symbol and in the work that I do, I talk a lot about symbols and metaphors and signs and things like that. So can you share with us first out what does that mean for you? What does it symbolize for you? Oh, he says, oh, thank you for asking. That's so sweet. He says, thank you for asking. Well, first of all, I prefer gold. Gold is the, it's like the piece of resistance, like the most beautiful, the most beautiful metal, the most precious. And he says it's very elegant and it has this feel of being very special. And he says, I would like whoever is listening, whoever is in the audience to feel special, sort of like getting out the fine China when you have guests, just really to make people feel special. Like this is a very special experience. It's very special. And that they are included in this specialness of it. Okay, I would say vibration because gold is a very high vibrational frequency. And it's when I, when I communicate or talk with people, it's sometimes I'll see a gold circle around their crown chakra. And that's like this kind of passage portal energy. And it feels like to me that they are working on some really high stuff, high level stuff, or they have just this very acute attunement to spirituality. It might be somebody that's a medium. It might be somebody that does healing work at like a level that is so high and vibrational frequency. So that golden energy is that's how kind of it depicts for me. And then we often see archangels with halos over their heads in pictures and things that are gold. He says, yes, yes, you're right. Yes, you're right. And so I feel like there's a lot of things we could talk about your family. We could talk about your loves. We could talk about your music, your performances. What would you like to talk about? He says, Oh, oh, he's very sweet. He says, Oh, whatever you would like, what would you like to ask? Well, let me tell you, Mr. I don't know what to call you Mr. Liberace. Oh, call me Lee. He says, call me Lee. All my friends call me Lee. Okay. Thank you. You remind me of the kind of energy that Prince has had from like my generation. Prince Rogers Nelson and very he says very talented guy, very talented guy, quite like quite different genres, all that kind of stuff, very different presentations and everything. But you remind me a lot of him as far as this, this, this, this deep appreciation or savoring of the music, like the piano for you and for him, it's the piano and the guitar. So he did both. Yeah, he, yeah, he was a good piano player. He says, yes, he was a good piano player. And he says self taught, self taught piano player. Yes, he was. Yes. So were you a fan? And he says, not, not quite. I wouldn't, I wouldn't go that far. He says, you know, people used to, to think that I didn't maybe keep up with the times or the, the rock and roll. And he doesn't say energetic, but the rock and roll scene, and he says, which isn't true. And he says, apparently he, I don't know if he hung out with Elvis, but he's referring to Elvis Presley. And then he says something about Jerry Lee Lewis, a fantastic piano player. He's a fantastic piano player, had some troubles as a person, but personal troubles, but fantastic piano player. And he says, you know, well, yeah, music wise, like what kind of music genres did you connect with? And like, I feel like performance wise, like Freddie Mercury, that's kind of how you're kind of like this, people are going to string me up by my toenails if they don't like this, which is fine, whatever, kind of like this Freddie Mercury, Prince kind of vibe kind of thing. I don't know what to explain it, but you feel like such this, like this desire to just really have a show, just put on a show and just have it be spectacular and just that. He says, thank you, thank you. And the only time I've seen you play is on the Johnny Carson show, that clip that I saw. And to me, that's like, wow, like just beautiful, you know. And he says, well, I sing too, you know, I sing. Yeah, I know, I know that. I heard that. But what do you prefer? Like what do you like as far as genre and music and rock and roll and that kind of thing? He says, oh, I could. He said, I could rock. I could rock. He says, yes, I might surprise you to know I could rock. Yes, yes. And he shows me like a glass of brandy, like sitting on the piano. Not sure if that's his drink of choice, but it looks like brandy or it's a brandy glass and the dark liquid. I was known to partake, yes, yes. And he says, the Hollywood scene was complicated, rather complicated, he says. But I enjoyed the company of movie stars and had had some great friendships from people who were actors and actresses. And he shows me like going to Hollywood parties and things too. And so, okay, there's so much. He's like, he's like a storyteller. He talks a lot just like me. Do you have so so genre and rock stars and stuff like that? Like when I say Freddie Mercury, how do you feel about that performer? Very much a performer. His voice. His voice, he says. He could play the piano too, he says, but his voice, really his asset, his voice. And okay, so I'm bringing up Prince, but he's not really responding much to that. And Elvis, what about Elvis? That young man had quite a bit of challenges. He said he had a very difficult time in his life. And he says, he was a bit wild. He says, I'm not going to say, I'm not going to say, I'm in no place, he says, to judge other people's behaviors. But he's a bit, he was a bit wild. He had a lot, a lot of energy about him. And I'm feeling like, almost like, and there's kind of an Elton John vibe too. I mean, with the, oh, he says, he says, well, Elton is in the UK. He's more of the British type. And he says, and much more rock and roll, as far as his presentation.  Sort of like, almost like musical theater slash, like a kind of like a Broadway show. It's kind of the vibe I get with the piano. Thank you. He says, thank you. That's very, that's a classic. He says a classic. Thank you. He says, thank you. I appreciate that. Thank you very much. And he says, you know, I played in Vegas. I had shows in Vegas. Well, I could assume that because the, you had a house there. Yes, I did. And is that the home you died at? I can't tell if it's a Las Vegas house or if it's the, it's not Santa Barbara, but it's the Palm Springs. I can see, I see the desert in the mountains. So I don't know. I think you were in Palm Springs. Does anybody know on the chat? Can you clarify for me? I'm just going to look. This is why it's helpful to have the chat. Oh, hey, I'm just going to shout out, thank you Patty, my moderator for being here. So late in the day. He did not die in Las Vegas. Okay. So then it must have been Palm Springs. It must have been. It looks, yeah. Okay. Cause I can see what looks like the mountains. It's kind of hazy and it's hot and it's like desert-y. So I don't, I think that may have been California. Um, and is it true that you died of AIDS? He's saying like arc or something. Yeah. See, like AIDS related complex or something like that. Oh, and he says, yes, like your dad.  There's such a stigma. Yeah. There was and there's now there, there is also like in the gay community right now, there's just a lot of incredible, like there's a lot of targeting happening and a lot of stuff going on. That's just not, he said, it's such a shame.   It's, it's hard to believe really. He says, it's hard to believe so much time has passed and sometimes you roll back the clock. He says, it seems, it seems that it seems as though that, that, that tends to happen. So I'm feeling into, so you didn't have any children. No, no. Did you want to have children? Well, I had several dogs. You know, I do know. He says, I wasn't quite suited for that type of life. And he says, from an early age, I was very much pointed in the direction of becoming who I was to become, you know, a piano player, a famous piano player. Okay. So is that, did you really know that that's what you wanted to be? There was no question. He says, there was no question. That was just, that was the way it was for me. Is there anything you would like us to know or would like to share with us about the afterlife itself about, about being a spirit? Because I think you died in like the 80s, late 80s or something like that, right? You died before Freddie Mercury. I'm pretty sure of that. Oh, that's what they called it back then, ARC. Okay. Good. 1984, the home springs, California. Oh, you were born in Wisconsin? Somebody just posted that. You were born in Wisconsin. I live in Minnesota. He says, yeah.  You were a cheesehead. It feels like Milwaukee. Is that right? It says West alias or something. It feels like Milwaukee. Is that near Milwaukee? It feels like it. For some reason, I just literally heard Milwaukee. All right. So is there something, anything that you would want, think it would be beneficial for us to know about the afterlife, about being a spirit in the afterlife? He says, it's like, he says, it's like looking at, he's like showing me rings of a tree, like multiple circles, like a circle, a circle, a circle, a circle, a circle, a circle. And he says, it's a bit like that. He says, there's different layers and you would call it energy of energy. And in a way, if you think about it like the solar system and things are laid out and there's all these different planets, and he says, it's sort of like that. And as a spirit, as an energy, you can take on different forms and you can become and enter into connect with whatever layer you desire you want to be connected with. And it's part of your soul plan or soul path journey. Are you talking about reincarnation? Or are you talking about like dimensions? And he says, as you would call the D's, so the dimensions, so like 3d, 45d, he says, like 11d. He says 11, like that. Okay. And he says, it's very much like light or how some people would say sound, like the speed of sound, it's not like sound, it's different than that. It's more like light. That's the best way, I think, to describe it. He says, it's really hard to describe it in terms where conceptually where the mind can understand it, except for in the things that you would relate to, he says, like the solar system or the planets or the rings of a tree, or he says, or light. So vibration, though, sound is something that you can use as a human to calm the level of your system, he says. So what I would say, not just about like the afterlife or being in what someone referred to as heaven or in spirit form, he says, I would say one of the most beneficial things for you to know as a human is that you are spirit. You are spirit. And so sound like music is vibration and that supports your spirit and the health of your spirit, he says. And so you can move between these different levels or these different rings based upon how much you are comfortable with the vibration of what that ring offers to you or the environment in that ring. It's like stepping into a room and turning the light on like a dimmer switch like bright light or not bright light like that.  So, okay, so would you recommend that we use music or singing bowls or meditation? He says, all the above, whatever you can do for yourself to keep yourself, he says to keep yourself. He says the really important thing is the health of you as an energy, the health of your energy is very, very, very important because as you've seen with many of us, our bodies cannot rebound. It cannot bounce back. He said, I thought I really believed that I could heal myself in my body. And I'm like, well, why couldn't you do that? Why wasn't that possible? I mean, why not? You know, and he says, it was too late. It was too late. It's a sequence of events. Things get set into motion and then it's, you can't stop the speeding train. It was far too advanced in my body. He said, and back then we didn't really know much about what they considered a gay cancer. He says, people didn't talk about it. It wasn't discussed. And when you were perceived to have had it, then it was like you were a sinner and it was something you got from the devil. And he said, so it was very much riddled with judgment. And that's not to say, he says, that's not to say I didn't believe in Jesus, Jesus Christ and in God. Yes, I did very much. Yes, I did very much believe in God and Jesus and Mary. And he shows me like the statue of Mary with all these flowers on it. So it feels very aligned with Mary and the divine mother. And he says, things are so much different now, but they're also not different at all. He says, so the thing that people need to understand is that you have the power consciously over what and how your body feels based upon what you choose to ingest and take in and expose yourself to energetically. Okay, he's literally saying because energy can make you sick. So interesting. Okay, I see a lot of green energy now. Archangel Raphael steps in and if you guys are dealing with anybody that's watching is dealing with physical ailments, there's always a an energetic side to a physical manifestation in your body. Nobody I don't believe anybody causes or creates their own disease or anything like that. I believe that there's a whole levels, multiple levels of complications, circumstances and situations. Nobody's to blame. There's that doesn't help blame is just a toxic energy that creates more poison in the body. It amplifies the negative and it overshadows the light. And so we're going to arc you with beautiful green energy, no matter what it is. If it's an immune disease that you have, if it's a cancer that you have, if it's a mental health challenge that you have, we're going to arc over the body through the circle of over the head and then through the circle of the heart space to really just amplify this energetic space with the crown, the third eye, the throat chakra and the heart chakra just breathing in a beautiful green circle around this part of the body that really helped to use this energy to embody you and encompass you and enfold you with healing energy. Healing is not about a one-time event or a miraculous fix. It's not. Healing doesn't mean fixed. Okay. Healing is your ability to receive the support that you need, the inspiration that you deserve to have, the motivation to receive the love from yourself. And if you can't from yourself from the higher sources of your spiritual teams, your angels, your guides and God source creator, whatever that is to you, whether it's Gaia or the land or the earth or the wind or the sea, whatever that is for you, you deserve that. That is just a baseline standard. Okay. So nice breath in, kind of nice exhale out. And he literally says, that was very nice. He just says to me, that was very nice. He says, you know, I could have used someone like you to work with. Oh, you're so sweet. You are really sweet. You are very kind. Oh, he says, oh, thank you. He says, you have a lovely, you have a lovely soul. Oh, thank you. Was he charming? He had to have been charming. He feels very charming. Let me just say. Okay. So I'm going to check the chat. If there's more questions or things that come up, I'm going to, I'm going to share with you. Okay. Oh, shout out to Elizabeth and her mom, who actually adored you, who is in the afterlife. She loved you very much. Her mom. Oh, they're talking about illness. Oh, and that West Alice, Alice, Elise is a suburb of Milwaukee. So thank you for that affirmation and confirmation. Oh, I'm surprised there's so many people in the chat. I'm going to say hello to Rebel, Patty, Project H, Elizabeth, Anna, Anna, Patricia, Lisa P. Let's see who else I've got here in the chat. And Jeremy, nice to see you. You are very talented. Hello, Juliet.  Ah, he says, not everyone, he says to me, not everyone would say that, but thank you. I thank you. He says, but I thank you. I thank you. Lots of hearts coming through here. Oops, there goes the doggie. He says, what a sweet heart.  Just making sure. All right. Okay, my beautiful friends, thank you so much for being here for this channeling. Come here. Come here, honey. Tucker, you want to come here? Want to come here? Come here, buggy boo. Let's see this little cutie pie. This is Tucker. You guys have seen Tucker before? This is Tucker. Maybe I'll be able to bring Charlie in the future. Hi, you're so handsome, aren't you? You need a haircut, though, don't you? We're all new to hard cut.  I mean, I do have, I've had little mini docks since I have one now, right now. And, but I've also had big dogs. I've had a Wymer Anner, who I love so much. She was my heart. That was Mimo Molly, my Molly. And then Riley, she has moved into the afterlife a couple of months ago, our red lab that we rescued.  So I had like four dogs and they were all about the same age. So now I have a couple. I have two left out of the four. And Louis is 16 this year. And Toby is 12 and a half, I believe, maybe 13. Toby is a schnauzer. So yeah, so I love dogs. My whole family has had dogs. And obviously my sister too.  All right, thank you so much for being here on a Buff Life channel on YouTube. I so appreciate you showing up for our weekly channeling sessions on Mondays. And also join me for Sunday Morning Coffee, the podcast here on Sundays as well.  This is your life after all. And you get to live it. Just live it. Thanks for being here. Bye for now.


Welcome back. We have proved this theorem in the last lecture it took the whole of our lecture that if you have two reduced forms which are equivalent then those two reduced forms have to be one and the same. And I also told you that while proving that we actually computed the set of all possible transformations which will take one reduced form to itself. Depending on of course the conditions that you have on the coefficients a, b and c. We are now going towards proving the we are now going towards determining the set of integers which is sums of two squares. And for that we will require a small criterion of a number represented by some form in the terms of the discriminant of the form. So, the statement is here in front of you that an integer n, so of course this is in natural numbers it is properly represented by some form f of discriminant d if and only if we have that x square congruent to d mod 4n has a solution. Let us make sure that we understand the statement clearly. There is one condition which says that d is a square modulo 4n. This is something that we understand quite well by now. We have understood the theory of congruences very well. We also know how to compute squares modulo given integer using Chinese remainder theorem and then using the quadratic reciprocity laws. So, we will understand this thing quite well when a certain d is a square modulo 4n. This is equivalent to sum form of discriminant d representing n properly. So, we have some pair of integers m, n which are coprime or since you have taken n already we will take some pair of integers p, r which are coprime and f of p, r is equal to n. This is the statement that we have that this integer n is properly represented by some form. We will begin with some form f of discriminant d representing n and we will show that x square congruent to d mod 4n has a solution. And in the other direction we will assume that x square congruent to d mod 4n has a solution and we will construct some form. The form is not fixed. The statement therefore is very liberal. We are allowed to choose any form of a given discriminant which represents the number n properly. So, let us assume first of all that x square congruent to d mod 4n has a solution. b square is congruent to d modulo 4n for sum b in integers then b square minus d is 4nc once again for sum c in integers. Or this also implies that d is b square minus 4nc which reads something like our formula of the discriminant b square minus 4ac. n is taking the role of a then the form where I will just put n instead of a nx square plus bxy plus cy square represents plus minus 1 comma 0. Of course plus minus 1 comma 0 is a co-prime pair of integers and therefore we have that n is properly represented by some form f of discriminant equal to d. This is the formula for the discriminant. So, we have proved one way of this statement. We started with assuming that x square congruent to d mod 4n has a solution and we have constructed a form which has discriminant d and it represents n properly. Now, we will prove the other direction which is where we will start with assuming that f represents n properly and we will need to prove that the discriminant f which is d has to be a square modulo 4n. Now, represent properly then p comma r is n with the GCD of p and r is 1. But whenever we have GCD to be 1 remember that the GCD is a linear combination of your two integers with integer coefficients. So, then there are these q and s coming from integers such that pq minus rs is equal to the GCD which is 1. Then f prime be the form by changing the variables by x going to px plus qy, y going to rx plus sy. So, let prime be given by a prime x square plus b prime xy plus c prime y square then we know that f a prime has to be the value of the original form taken at p comma r but we had assumed this to be equal to n. We had assumed that f of p comma r is n. So, the new a prime is equal to n we also have that the d remains the same that means the discriminant of f and the discriminant of f prime are the same and from this formula we can compute the value for the discriminant of f prime which is b prime square minus 4 a prime c prime which is b prime square minus 4 n c prime and it shows that x square congruent to d modulo 4n has a solution our b prime is going to give you that solution. So, we proved that whenever our form f represents an integer n properly then modulo 4n the discriminant of the form f has to be a square. This is a very important and very useful criterion. Note that here we do not have a control on the form f but we can we have that the there is some form of discriminant d which is going to represent our integer n and by using the equivalence we can show that there is a reduced form of the given discriminant d which represents n. Now if you happen to have that h of d is 1 then there would be a unique form unique reduced form of the given discriminant and that would mean that any form of the discriminant d represents n properly. We will soon see an application of this result but before that we have to think about the form x square plus y square. We are going to study all integers represented by x square plus y square but this form in particular x square plus y square has a very peculiar condition. It has a very nice property and we are going to see this property in the next slide that the form x square plus y square is multiplicative. What do I mean by this? I mean that if I take a square plus b square and multiply to that by c square plus d square then this is again a sum of 2 squares. This is a very remarkable property it says that the form is multiplicative that means if I take 2 numbers which are represented by the form take the product of those 2 numbers that product is also represented by the form. This need not be true for all forms but for this form this is true and the proof is very simple.  I said in the beginning of the lecture course that I am not going to use any advanced techniques but I believe that the notion of complex numbers is a very basic concept and therefore everyone would know that I will assume this and we also have that c square plus d square is mod c plus i d whole square and we know that if I take 2 complex numbers take their modulus and take the product this is same as taking the complex numbers taking their product and then taking the modulus.  So any 2 numbers which are represented by x square plus y square their product is also represented by x square plus y square. This is a very useful fact because if we could determine all the primes which are represented by x square plus y square then we are essentially done. It will tell us a big set of numbers which are represented by x square plus y square. And before going to do that we will also need this important result that if you have n which is a square plus b square and p is a prime factor of n with p congruent to 3 mod 4 then p square should divide n. In the introduction I had listed out some primes which are not sums of 2 squares and I had listed them out as 3, 7, 11 and so on. These are all the primes which are congruent to 3 mod 4 and if you should have so assuming this result we see that whenever prime congruent to 3 mod 4 divides a sum of 2 squares then the square of that number should divide. It would then follow that such a prime p congruent to 3 mod 4 cannot be a sum of 2 squares.   So a square plus b square is 0 mod p. If p does not divide a then p does not divide b that is quite clear because if p divides b then a square plus b square is 0 mod p therefore b square is 0 mod p would tell you that a square is 0 mod p and therefore p will have to divide a. So whenever p does not divide any of the a's a and b it will divide none of them. Then a square congruent to minus b square mod p gives a solution x square congruent to minus 1 mod p. This is because since b is not divisible by p you can simply cancel out b square and write this namely x equal to a b inverse the b inverse being computed modulo p. So we have that x square congruent to minus 1 mod p has a solution but this would imply that p is then congruent to 1 modulo 4. We have computed precisely when minus 1 is a square modulo p. It would then imply that p is congruent to 1 modulo 4 which is contradiction because we have started with p congruent to 3 mod 4. So this contradiction says that something that we have assumed on the way has to be false and the thing that we have assumed is this that p does not divide a. This was the assumption that we started with it then said that p does not divide b and then it gave us a solution to x square congruent to minus 1 mod p. So this assumption has to be false which would mean that p divides a. So p divides b and then we have a by p which is an integer its square plus b by p square is n by p square. This is an integer and clearly a natural number which implies that p square divides n. We had that a square plus b square is n and we proved that if p divides n then p should divide a and p should divide b.  So you get that n upon p square is an integer has to be a natural number then p square divides n. So what we have proved is that whenever we had a prime p congruent to 3 mod 4 dividing a sum of 2 squares then square of that prime should divide the integer n. After that we have one very small cute result which is that the prime 2 is represented by x square plus y square. I believe that all of you can prove this we have that 2 is nothing but 1 square plus 1 square. So we have dealt with p congruent to 3 modulo 4 we have dealt with the oddest of the primes which is the prime 2. Now the only class of the primes which remains is the prime is the set of primes p congruent to 1 modulo 4. We will prove that every such prime is a sum of 2 squares. Every such prime is represented by x square plus y square. This is our next result. Na prime p congruent to 1 modulo 4 is represented by x square plus y square. Recall the criterion which we did in the beginning of this lecture that is represented by some form of discriminant if and only if. Here we have the criterion for proper representation x square congruent to D mod 4n has a solution. We are looking at the form x square plus y square. Our form is and its discriminant if you remember is minus of 4 discriminant if you remember is minus 4. So we want to see where we have this congruence where n is now our prime p congruent to 1 modulo 4 x square congruent to minus 4 mod 4p has a solution. Observe that 4p so then here 4p must divide this solution x square plus 4 which implies that x has to be even say x equal to 2 alpha. Any solution if there is a solution we will actually we are actually going towards constructing the solution. So we have to see what properties the possible solution should have and that will help us constructing the solution. So we observe that such an x has to be twice of an integer because 4 divides the number 4p which divides x square plus 4 and therefore 4 divides x square. If 4 divides a square then by unique factorization of integers the fundamental theorem of arithmetic which gives unique factorization into prime of any integer will tell you that x also has to be an even integer.  Now I hope you see the thing that we are coming to which implies that y square congruent to minus 1 mod p has a solution. We started with minus 4 being a square mod 4p and we have reached minus 1 being a square modulo p. Our p is congruent to 1 modulo 4 so we do have such a solution. We do have that minus 1 is a square modulo p and once we have this solution since p is congruent to 1 mod 4 we do get alpha in integers such that alpha square is congruent to minus 1 mod p. This gives a solution x square congruent to minus 4 mod 4p namely x equal to 2 alpha. So by the criterion there is a reduced form discriminant minus 4 that represents p it represents p properly but certainly it represents p and I would now like to recall this to you that we have computed h of minus 4. h of d for any integer d was the number of in equivalent reduced forms of discriminant d which we also proved to be the number of reduced forms of discriminant d. We proved that h of minus 4 was 1. There is only one form which is reduced and is of discriminant minus 4 and that form is nothing else but x square plus y square. Here we have proved that there is a reduced form of discriminant minus 1 which represents p that implies that x square plus y square represents our integer p our prime number p. So let me just recall this to you once again that any p congruent to 1 mod 4 is represented by x square plus y square 2 is represented by x square plus y square p congruent to 3 mod 4 is not represented by x square plus y square but the square of these numbers should divide the integer x square plus y square whenever p divides it and using this in the next lecture we are going to determine the set of all integers which can be written as sums of 2 squares. So very interesting thing to see I will see you then. Thank you very much.


I think they're doing well, I mean they have come a long way since they jumped in here on the 5th of October and this was the first airborne operation of its type for this organization since essentially since they jumped into Iraq. Again because of that tempo and that pace of deployments they haven't focused tremendously on kind of the large package, tactical airborne operations that we saw on the 5th of October. So just the fact that they were able to put that all together, jump in this environment, really when you think about where they're based between three different locations with the heavy drop platforms, bundles and then almost a thousand paratroopers I think was pretty incredible. It was synchronized, it went pretty much in accordance with their plan so I think it went extremely well. There's been learning points all along since then, we found ourselves initially in an analog environment so again we were doing things that we were not used to doing, tracking on maps with pushpins and markers and most of us are used to falling into an environment that's very mature with digital systems where one guy gets up out of the seat and the next guy sits down so again kind of going through some old skills that some of us that have been in the Army a little longer were used to but they've come a long way with that and they've done an impressive job in getting their systems up and they're certainly a learning organization, they've taken a lot of the lessons learned throughout stuff that's been brought up in the AARs and they really find it and they are truly getting better.


Welcome back everyone to BC 213, our second lecture today on the end times. We're looking at the signs of the end times. There's a question on the chat. How do we understand 2 Thessalonians 2 verse 3 in the light of what we are learning? It goes right in with the point that we were just discussing about the great deception that would take place, false spirituality. Paul did mention 2 Thessalonians 2 verse 3 that there will be a falling away. He said the falling away comes first, so there's going to be a lot of people and he wrote about that in 1 Timothy 4, 1 and 2. There's going to be a lot of people who will depart from the faith and he describes the condition of man. So it's in line with this sign, number 11, that we just spoke about the falling away coming first, people departing from the faith, giving into deception. Point number 12, the 12th sign. This is Gabriel, Angel Gabriel. He spoke to Daniel and Daniel 12 was 4. He said, Daniel, you keep the words of this book and he said, in the time of the end, many will run to and fro and knowledge will increase. Many will go to and fro. They'll be traveling a lot. Many will travel a lot and knowledge will increase. So both these signs are so apt or relevant to the times in which we live. We are living in a day and a time when people are going to and fro. Every day literally hundreds of thousands of people traveling. We are living in that time and knowledge is increasing. The amount of information that's being put out and the access to knowledge has exploded. On our device, we literally have huge amounts of information available. We can search, we have access to it. So we're living in a time where Daniel 12.4 is being fulfilled. It's happening. And of course there are some articles that you can read and these are a little old but you can look at a lot of information where it's constantly, constantly information is exploding. A few other sciences and we are familiar with and these are taken from Matthew 24 and Luke 21. There will be wars, national rise against nation, kingdom against kingdom. Now it is true that wars and fighting has been going on through the centuries. It's not something new. So and in fact all the next few signs, they have been happening all along. But what we can expect to see is things happening in a much larger scale and in a larger number. More nations, more countries, fighting is happening. So there's unrest, there is fighting happening just about everywhere nation after nation. You will be hearing about that and which is going on and it's increasing. Similarly, number 14, fear, hate, terror, men's hearts failing them from fear. I mean there is going to be so much distress, there is going to be fear, hate, that people's heart are gripped by fear. What's happening? The hate, the violence, people are living in fear. And that's again increasing, increasing more and more. And so even in places where what once used to be very peaceful, now it is becoming a, be careful where you're going, what is happening. You never know, some bomb threat here and this, that and all. But these used to be peaceful places, peaceful cities. There's fear coming because of hate and terror that's happening. Similarly, there's weather conditions, there's great earthquakes, famines, pestilences. Again, these have always been happening but there will be an increase in these things happening more, more widely. Earthquakes, famines, pestilences, plagues, epidemics. Again, we are, we under-recognize that. So these are things that will happen. Jesus said these will be things happening. And the moral condition of man, number 17, the last one. Jesus said lawlessness will abound, lawlessness. People will not care about the law, lawlessness. I was just reading, I think Haiti or some country that is now taken over by some other country, I forget. Gangs are running the country. It's no longer government. Gangs, we are running the country, taken over. So lawlessness will abound. Love of many grow colds. People no more love, no more love, no more compassion. That's all gone. So as in the days of Noah, they were just eating and drinking and there's immorality and violence, these things. So even the moral condition of man becomes very bad. Sin was always there from Adam's time. But in this time, just before the end of the day, end of the age, this is going to reach its peak. So these are some of the signs that we keep looking at and we say, okay, whatever the Lord Jesus said, these things are being fulfilled. It's happening right before us. And then there are some of the bigger signs. I mean, major, major things about Israel, Jerusalem, the church, the alignment of the nations and other things, which are all telling us we are very close to the end. We are reaching the very end of things. So for us as believers, I think we should be students of scripture. That means we understand what the scriptures are telling us. At the same time, we should be informed. So read the news, be aware of what's happening globally so that you can look back and say, hey, the Bible said this. It is happening. But we're not alarmed. We're not preoccupied with that. Our main responsibility now is to take the gospel to the nations and to help bring the church to a place of maturity. So two things. On one side, you need the gospel to reach people. On the other side, the church has to be brought to a place of unity and strength and maturity to be a glorious church. That is our work. That's the work we have. That's why he has put us here. That's what we're working on. Why are you here? Well, two reasons, right? We have to reach the worlds. We have to reach the nations with the gospel.  While we are doing that, that's our work. We keep ourselves busy with that. And while we are doing that, we're also looking at the signs. This is what is happening. We can see that everything is aligning towards the coming of the Lord. And so we live in a state of readiness that with the Lord Jesus comes, he will be ready to be taken up to meet the Lord in the air. So let's take some time for questions and some discussion. Go ahead. Faster. This is a general question like the many pastors and preachers depends upon the seasons that had happened. There are any situations like something global issues or like tsunamis or some political reasons. So there are many preachers have been preaching depending upon these things that Lord is coming. So this is the sign. This is the sign. And there is no particular proof for that. Just by observing something happening, they're preaching what is coming from this is the sign. Like because of that, there are so many confusions happening and the people who are speaking against us about Christians and preachers. Can we do that in our, when we are preaching like, like do we have to take it as important things? I understand what you're saying. And I will just share my approach. So one of the things that I would also encourage all of us is not to be alarming. Like, you know, don't, oh, something happened. Then immediately one, oh, Jesus is coming tomorrow. Like, you know, like that. Yeah, you know, like maybe some volcano erupted. Maybe there was earthquake, maybe there's a fighting happening. Or, you know, for example, last October, when there was this fighting that broke out between the Palestinians and Israel. So many people are preaching sermons on Israel and thing. I purposely never did anything. Just kept quiet. Why? Because I don't want to be an alarmist, right? So these battles, these things are happening all the time. Right? It's always happening. You know, so there have been so many incidents between the Palestinians and Israel. It's not like this is the first time they're fighting. It's always happened. Yeah, maybe on a scale like this, it hasn't happened before or in recent times. But these things are happening. So we don't want to be alarmists. That means take advantage of some situation and, you know, build up the emotion of people. No. Preach the truth. Paul said preach the truth in season and out of season. That means we'll talk about the end times when something happens and even when nothing happens. Because the word of God still reads the same. Right? So our approach should be, you know, my approach is don't unnecessarily take advantage of the situation. Yes, people will have questions. You address the questions, but at least in a very calm way. Don't, you know, create a lot of emotion and hype. And just because something happened, we do want people are having questions and we do want to address the questions, but don't do it in an alarming way. Don't, you know, create hype and emotion and all those things. Otherwise, just for example, we talk about the end times, but even we talk about the end times, even nothing seems to be happening. This is what the scripture says. Right? So that's a better approach because then we're not building something based on the emotions of people, but rather saying, telling people, look at the truths, look at the word of God in season, out of season. This is what the Bible says. So that's our approach. And sometimes intentionally, I don't say anything. Is it okay? You know, we don't want to build on the hype. Just because of using the situation. Because like in normal sermons also, there are people who are using the situations, what are happening? Listen, there is a video I just went through. Like this, someone is married. So he told like in a video, my life is not like a rose petals. I've also gone through so many struggles. So there is one pastor who was telling, see the richest man of Asia is also gone through a situation because there is no Jesus in his life. Because there is no? No Jesus in his life. So there are pastors who are preaching like this today. So we should not better not to use the situation. Yeah, I would avoid. Just because of some people's experience. Yeah. I would avoid that. Instead we just preach the words. Yeah. Any other questions? Friends, you have a question? Go ahead. First of all, we are seeing about the age scale chapter 7 and chapter 37 sorry. Chapter 37 and 38. And like how we can be sure like it is for now, but not for them in the Old Testament. Because even if we see in the during this time, even people were scattered. Right. So how we can take it like even this applies now. Yeah. So after 38 we are seeing nations were coming. My it can be for that time also. Right. So how we can be sure like we can take it now also. Yeah. So there is what we say a near term fulfillment. So there's a like many of these prophecy there will be a dual fulfillment. There's a near term and then there's a long term. Now the reason we say is equal 38 37 37 we know. Okay. The nation is was regathered. The reason we say is equal 38 is in the future. Two reasons. One at least two or three times in chapter 38. He says in the latter days. So he's using a phrase which of course we cannot give a day and time, but it's speaking of in the latter times in the later days. God will do this. That's one thing. The second thing is that this itself has not been fulfilled of even in the past because he mentions dog in my God mentions Turkey. He mentions Ethiopia, Libya and some other tribes. These will come and attack Israel. Right. So we know the Babylon, I mean, we know the Assyrians came. We know the Babylonians came. We know later on Israel was displaced by the Arabs or the Ottoman Turks. They're all from Iran or from the neighboring place. But he talks about from the far north. He talks about Rosh Meshach Tubal. He talks about Ethiopia and Libya joining them and Persia joining them. So that in itself we haven't seen yet. So two reasons is okay. We know there is a near-term fulfillment. Israel was dispersed from its land and they have been gathered. We know that. So there's a near-term. But there are some elements in Ezekiel 38 which are yet in the future because he says in the latter times and this is what's going to happen. So that's why it's okay. This is going to happen. Then we also say, okay, let us see what happens in the book of Revelation. So even in the book of Revelation, God says the river Euphrates will dry up so that the armies from the east will begin to come against Israel. Again, we see in Daniel chapter 12, actually chapter 11, I think. Let me just point out to you. We will study this next year. Yeah. In Daniel 11, he talks about, I'm looking at basically verses 40 to 45. When he talks about the king of the south, the king of the north coming against him and he will enter the glorious lands. Verse 44, news from the east and the north will trouble him. So this hymn that's being referred to is talking about the king and we will read the context. Look at it. It's talking about this king, this man who will speak blasphemies against God and when we compare it with earlier chapters of Daniel, Daniel 7, 8, and 9, we know that it is this antichrist who speaks blasphemies against God. And so he says here in verse 44, Daniel 11, 44, news from the east and the north will trouble him. So it goes along with Ezekiel 38, it goes along with Revelation 16. So we put it all together and say, okay, yeah. So there are certain prophecies, parts of Daniel 11, which is yet to be fulfilled and it goes with what we read in other passages of scripture. Yes, go ahead. Pastor, the whole world knows that the Israel belonged to Jews and there are archeological evidences also. Then why they want to divide the land? Everybody want to divide the land of the Jews but the truth is that this was theirs before. The world knows about it. Then why is that so again because God intended that? So the question, why do people want to divide up the land of Israel? So we go back in time. So we know that God promised Abraham, said, from the river Euphrates till the river Nile in the south, from the Mediterranean Sea to the river Jordan, that whole land I'm giving to you and your descendants. So God spoke, that is what Abraham believed he came. But when they came, they had to dispossess or displace the tribes who were already living there. And again, we can't prove this, but some people say that the Palestinians were the Philistines who were living there. So remember when King David came and Saul, I mean, not before even Saul, I mean, Saul was there and they had to fight against these Philistines, many tribes. Philistines is one of the tribes. So they came, they dispossessed, I mean, they conquered those other tribes like Jericho or all those and they had to conquer, meaning there were people living there, they had to fight and conquer and they dispossessed the land. So God promised them the land, but the Palestinians are there. Some people trace them back to the Philistines. So they also say we were here, right? So and they are there right now, the Palestinians are there. So they also are looking for a land or a place for them to live. Where will they go? So the whole question is how are we going to resolve this?  Right, so that's the conflict going on. Any question from those online? Okay, another question on chat, in Matthew, referring to the days of Noah, it is talking of total disregard for the things of God and totally involved with themselves. Is this talking about the world in general or the church as well? So that we would take to refer to the world, right? So Noah's time, Noah feared God. So there was him and his family who feared God. But the people around, they mocked him, they laughed at him and they were living in total disregard of anything that Noah was saying. So when Jesus said, as in the days of Noah, is referring to the way the world would be, that they would be just living like that as in the days of Noah. This also is in line with what Paul wrote in 2 Timothy chapter 3, where he describes the condition of people in the latter times. Like he says, they will be without, let me just look at that. 2 Timothy 3, he says, verses 1 to 9, he says, in the last days, perilous times will come and men will be lovers of themselves, lovers of money and so on and so forth, basically describing the condition of people in the last days, the people in the world. So that would be whom Jesus is referring to as in the days of Noah. For the church, the warning is, people will depart from the faith, giving heed to seducing spirits and doctrines of demons. There will be a falling of it. So that's what we will see in the church, people falling away in the world as in the days of Noah. Any other questions? So we're going to stop here for today. Next week, I'm just going to do a full revision. I will start from the beginning, go through everything. So we may take one class or maybe two classes, full revision. So again, we'll be open to asking any questions. And then after that, I'll just give you one final exam. That's it. One exam will have three parts, as usual. One exam, which I'll put up after the next week's class, which will cover the whole thing. As usual, it's an open book exam, open Bible exam. But it's like a review. It'll start from beginning to end. Just check everything. Basically, be clear in your understanding of the end times and the sequence of events. So next week is going to be full revision. So please come prepared to ask any questions about the end times and what we have covered in this course. What we will do next here in the third year course is we will go into detail of Daniel and Rebellious. We'll read verse by verse. We'll explain everything. But that connected to what we learned in this course will give us a clear picture of the end times. We'll be very clear both. This is an overview course. That one is verse by verse. We will look at Daniel and Rebellious and other scripture passages. But next week, any questions, come prepared so we can take those questions. It is going to be, I think, will be our last lectures. After that will be on final exam. Let's close in prayer. Anyone can close in prayer, please. And we will dismiss. Father God, we thank you. We thank you and bless you for this time. You have given us a lot. Lord, help us to be very watchful and help us to cling more to Jesus and your word, Lord, in these last days. Father, we thank you and we bless you. In Jesus' name we pray. Amen. Amen. Thank you, everyone. Enjoy the rest of your day. God bless. Bye.