Gwaith yn y tîm ff commodity bywyd y gwaith bywyd yn Gwyrryd Cwyrryd Rydw iiden ni. Mae'r Gwyrryd Rydw i'r gwaith yn gwybod wedi cael mynd i'r gwaith, mae ydych chi fyddai i gwybod i'r ffordd o gweithio? Mae'n gwybod i'r Gwyrryd Rydw i'n gwybod i'r gwedd an og yn 10 mae gwahol. Rydw i gymryd i'r gwaith y Plyguedd mewn ffórdigolion o y gwaith y Pw quality bywyd yn Gwyrryd Cwyrryd Rydw i'r gweithiad I will announce a new chair and an amendment that will be made to the inquiry's terms of reference. I begin by repeating my condolences to those bereaved during the pandemic. I also repeat my conviction that the Scottish Covid-19 inquiry must help to provide the answers for which those individuals and others affected by the pandemic's search. In fulfilling our commitment to establish a public inquiry into the handling of the pandemic in Scotland, the Government took time to meaningfully and openly engage with the public on draft aims and principles for the Scottish inquiry. I again express my thanks to everyone who engaged with me and my officials during that important work around the design and scope of the inquiry. On 14 December 2021, I announced to Parliament the establishment of the Scottish Covid-19 inquiry under the Inquiries Act 2005. Under the 2005 act, ministers have the power to establish an independent public inquiry to set terms of reference and to appoint a chair and panel. In my December statement, I announced the terms of reference of the Scottish Covid-19 inquiry and the appointment of the Honourable Lady Poole to be its chair. On 9 June 2022, I announced to Parliament three amendments to those terms of reference. The amendments were designed to clarify the scope of the inquiry following a period of reflection. My statement in June was intended to be the final word from Government on the establishment of the inquiry. In particular, I expected that statement to be my last word on the terms of reference, thereafter they move over to the inquiry itself. Section 17 of the 2005 act gives an inquiry chair alone, rather than ministers, responsibility for deciding how an inquiry should operate. It was and is for the Scottish Covid-19 inquiry itself to comment on its work. On 30 September, I was given notice by Lady Poole that she intended to step down from the role of chair of the Scottish Covid inquiry for personal reasons. The Scottish Government was not given any indication before 30 September that Lady Poole had intended to resign. However, ministers fully respect Lady Poole's decision and I accepted notice of her resignation. The Scottish Government is grateful to Lady Poole for the work she has undertaken since the establishment of this inquiry. I thank Lady Poole for her work and wish her well. The Scottish Government has always been clear that we want the inquiry to be delivered at speed and to address the range of questions that people have, the bereaved in particular, so that we can learn and benefit from those lessons as early as possible. I am acutely aware from recent discussions with bereaved families representatives how important it is that there be no delay to the inquiry arising from the resignation of Lady Poole's chair. That is why arrangements for identifying a new chair for the inquiry have been taken forward as a matter of urgency in order to ensure a swift and successful transition. To that end, I have liaged with the Lord President regarding the appointment of a new judicial chair in line with our previous commitment to having the Scottish inquiry led by a judge. I would like to thank the Lord President for his engagement and his co-operation on the matter. I have benefited from the insights and reflections of bereaved family groups about what they would want to see from a new inquiry chair and I am especially grateful to them for their engagement at this time. As a result of this work, I am pleased to be able to announce that the Honourable Lord Brailsford, a sitting senator of the College of Justice of Scotland, will be the new chair of the Scottish Covid-19 inquiry and will assume the role of chair of the inquiry tomorrow. I am confident that Lord Brailsford will bring his extensive experience as a long-serving senator of the College of Justice to the role of chair of the inquiry and will approach its work in a way that properly addresses the need for answers to questions posed by those who have suffered through the pandemic. From my interactions with Lord Brailsford, I know that he is keenly aware of the need to ensure that the inquiry progresses and delivers at pace in order that the lessons can be learned within a timescale which will make them applicable and useful. I am also assured that Lord Brailsford will undertake the role of chair in an inclusive way with sensitivity, empathy and compassion and I am confident that Lord Brailsford will see that full scrutiny is applied in all directions that are required to ensure that this inquiry provides the answers that it has been established to find. I have asked Lord Brailsford at the earliest opportunity to meet with bereaved families so that he may hear at first hand their perspective about the inquiry and its approach. Lady Poole undertook in her resignation to support and assist with the transition to her successor. It will now be a matter for Lord Brailsford to determine how those handover arrangements will work in practice to best support continuity within the work of the inquiry. The Scottish Government in its role as sponsor of the inquiry will provide operational support as the chair considers necessary and appropriate in order to enable the inquiry to continue its independent work and ensure the progress made so far by the inquiry is maintained. I can also announce today that the terms of reference for the inquiry will be supplemented in one important respect. This amendment has been discussed with Lord Brailsford and is designed to provide absolute clarity of the Government's desire that the inquiry be taken forward in a way that supports our commitments to a person-centred and human rights-based approach. The terms of reference for the inquiry currently set out 12 areas of investigation each covering a strategic element of the handling of the pandemic. In investigating those 12 strategic elements, the terms of reference ask the chair to consider the impacts of handling of the pandemic on the exercise of convention rights as they see appropriate and to create a factual record of the key strategic elements of the handling of the pandemic. In my June statement we amended the terms of reference including to expressly highlight the consideration of disparities by way of amendment to the terms of reference which encompasses unequal impacts on people. Today I can confirm that we will make one further addition to the reporting requirements in the terms of reference effective from the formal appointment of Lord Brailsford as inquiry chair. Specifically, this change will require the inquiry and I quote, to demonstrate how a human rights-based approach by the inquiry has contributed to the inquiry's findings in fact and recommendations. This will coexist with current references in the terms of reference to convention rights and to considering unequal impacts on people. The operation in practice of a human rights-based approach will still and must still lie in the hands of the inquiry chair. But this amendment reflects a joint commitment between Scottish ministers and the new chair that the inquiry take a person-centred human rights-based approach to ensure that every person and organisation taking part can meaningfully participate, be treated fairly and be empowered to take part in the inquiry. I'm grateful to Lord Brailsford for supporting this amendment, the announcement of which I hope gives confidence to bereave families and to others about the future direction of the inquiry. Presiding Officer, the inquiry operates independently of government which is a key to its integrity and within the legal regime under which it has been established. The 2005 act sets out a clear framework for the independent functioning of the inquiry. This statement fulfills my duties under the act to inform Parliament of my intention to appoint a new chair. I've also set out today my intention to change the inquiry's terms of reference and how this will be done. An inspired parliamentary question to be answered tomorrow will fulfil the duty under the act to set out the terms of reference as amended and confirm that they have taken effect. I should also note that no panel members will be appointed today and that will be for Lord Brailsford to consider whether to appoint any assessors to provide expertise on particular subjects or any other assistance to the inquiry. From my own and the First Minister's interactions with Lord Brailsford, I'm left with no doubt that he is fully qualified for the demanding task put in front of him. I express my gratitude and that of the First Minister to Lord Brailsford for his agreement to take on this important role on behalf of the people of Scotland. I reiterate that the Scottish Government undertakes to engage fully to support Lord Brailsford and the inquiry in the vital task before them. Thank you, Mr Sonny. The Cabinet Secretary will now take questions on the issues raised in his statement. I intend to allow you around 20 minutes after which we'll need to move on to the next item of business. I'd be grateful if members wish to ask a question and we have not already done so. Press the request of big buttons now or as soon as possible. I call Dr Sandra Scullhoney. In the gallery today is Caroline MacDonald. She is a long Covid sufferer and is here at personal cost to her health and well-being tomorrow. Long Covid has devastated her life, but we know that it's also devastated the lives of over 200,000 other Scots, all long Covid sufferers. Everyone in Scotland will be dismayed by the resignation of Lady Poole. And there are still many unanswered questions regarding the resignation of Lady Poole, and I hope the Cabinet Secretary will explain these in due course. I welcome the appointment of Lord Brailsford. In the past, the tram and hospital inquiries have been besets with delays. With the resignation of Lady Poole, can the Cabinet Secretary guarantee this will not happen again and can he commit to long Covid being included in the inquiry? First of all, can I express my good wishes to Caroline MacDonald in the gallery today? I understand and fully appreciate... Well, I actually can't fully appreciate the impact of long Covid personally because I have not experienced it, but to individuals I understand the suffering and the endurance that is involved. And the Government, of course, is entirely focused on ensuring that we address the clinical needs of individuals who experience long Covid. In relation to the conduct of the inquiry, as Dr Gohani will know, inquiries, by their nature, particularly those set up under the Inquiries Act, must operate independently of government. So the operation of the inquiry is a matter entirely for its chair. As I have indicated to Parliament, I very much regret the fact that Lady Poole felt it necessary to tender her resignation. She did so, I respect those reasons and that is the end of the matter. I have moved swiftly to replace Lady Poole with judicial leadership of the eminence of Lord Brailsford who will be able to start his activities in leaving the inquiry tomorrow. I am very grateful to the Lord President and to Lord Brailsford for the substantial amount of information that has been involved in enabling that to be the case. Of course, the issues that Dr Gohani raises about long Covid are all legitimate issues to be raised as part of the inquiry, but it is wrong for me to prescribe beyond the setting of the terms of reference what should be discussed in the inquiry. That is a matter for Lord Brailsford to determine within the scope of the remit. Jackie Baillie. I thank the Deputy First Minister for advance sight of his statement of the appointment of Lord Brailsford as the new chair and wish him well as he undertakes this incredibly important work. It is essential that there are no delays to the work of this inquiry in order to retain the confidence of those who lost loved ones to Covid. I do note, however, that the Deputy First Minister makes no mention as to the appointment of new senior counsel given their resignation at the same time as Lady Poole. I wonder whether he can advise of the likely timescale that the chair will take this forward. When I raised this matter earlier this month, the Deputy First Minister was keen to quote section 17 of the Inquiries Act at Me as an attempt, I think, to avoid comment on the resignation of senior counsel, but it is true in the same act that there are other sections that permit him to engage with organisational matters. Let's be clear, he must not interfere with the evidence-finding activities of the inquiry, but he has a responsibility and indeed a duty, quite frankly, to support the chair and ensure that the inquiry can function well. As such, can he tell me what delay will there be for the work of the inquiry? Will he ensure that the chair has all the necessary resources required? And should he wish to, that the chair can appoint people to staff the inquiry who are entirely independent of Government and finally, will he confirm in a follow-up to my colleague Sandish Gulhane's question that consideration of the impact of long Covid is actually within the scope of the terms of reference of the inquiry? Presiding Officer, there's a lot in there, but I shall endeavour to work my way through. First of all, I welcome Jackie Baillie's comments in relation to Lord Balesford's appointment. When I spoke with Lord Balesford on Tuesday to advise him of my intention to appoint him, he indicated to me and he has said this in his public statement this afternoon that he believes that to be anhonored to be invited to lead this inquiry and I think that speaks for what Lord Balesford will bring to the inquiry. He realises its significance. The other thing which I've said in my statement I asked Lord Balesford to do was to engage with Bury families and he has agreed to do that as an early priority because I totally accept the importance of ensuring continued confidence and indeed just before I came into Parliament this afternoon I have three separate discussions with Bury families groups to advise them of the contents of the statement. In relation to the conduct of the inquiry and the appointment of senior councillor, it's not a pedantic point about section 17. There are very good reasons why the Government is not close to these matters and should not be close to these matters. Those are questions for Lord Balesford and he isn't engaged on those questions and will be tomorrow when he assumes his formal responsibilities. I unreservedly give the commitment that the Government will provide whatever support Lord Balesford considers necessary and I've made that offer to him. In relation to the delay to the inquiry I would want to reassure Jackie Baillie that since Lady Poole's resignation she has remained engaged, staff have remained engaged and the work of the inquiry is going on. The Government is undertaking work to support the inquiry and to request for information that we have been asked of us and that is all under way. In relation to the question of resources as I indicated publicly before, there are already over 60 members of staff in the inquiry so there are resources in there. If there are more resources required, Lord Balesford will be advising me of the requirements and the Government is subject to ensuring that we are able to protect the independence of the inquiry will give all operational support but Lord Balesford will be the judge of that point as he is the custodian of the independence of the inquiry and I am very confident that he will exercise that. Fulton MacGregor to be followed by Mordo Fraser. Thank you, Presiding Officer. Can I say in response to the previous two questions as well, I welcome the Deputy First Minister's commitment to the long Covid issues that I have also been having raised. In terms of my question Deputy First Minister, I believe families should rightly be at the forefront of all their minds as the inquiry progresses. How will the Scottish Government ensure that their voices are kept central to the inquiry's work and their testimonies handled with sensitivity and respect? Come in, Secretary. Presiding Officer, I apologise to Jackie Beaillie that I omitted to deal with the point on the long Covid. I am not in any way avoiding the question but we have set out the scope of the terms of reference. In my judgment long Covid issues are certainly within the scope of the terms of reference but fundamentally it is a matter for Lord Prylshford to determine as he leads the evidence in the inquiry and I hope that addresses the first point that Mr MacGregor raises with me this afternoon. On the bereaved families, I cannot stress to Parliament more the importance I attach to the voices of bereaved families being heard in this inquiry. The one thing I have asked of Lord Prylshford, apart from asking him to cheer the number of things, to cheer the inquiry to follow the terms of reference, I've asked him specifically to meet with the bereaved families groupings as an early priority because I think it's important. As I said to the families I have done my best to convey to Lord Prylshford what the bereaved families have said to me about how they feel about the inquiry. I think it's critical Lord Prylshford hears that from those families himself and he's given me the undertaking that he will do. Murdo Fraser to be followed by Rona Mackay. Thank you Deputy Presiding Officer. Were any of the four council who resigned from the inquiry required to sign a non-disclosure agreement and if so was there any payment associated with that? I don't know the answer to that question and it's not appropriate for me to know the answer to that question because these are operational matters for the inquiry. If Mr Fraser wishes to pursue that issue it's an issue he could raise with the secretary to the inquiry. Rona Mackay to be followed by Pam Duncan-Glancy. Thank you Presiding Officer. Nobody's life has been untouched by the pandemic and people from all the areas of society will rightly be invested in this inquiry. With this in mind how will the Scottish Government ensure public confidence in the inquiry and its new team? I think there has to be very active engagement with those who have an interest in the inquiry and the inquiry needs to make progress at an early stage to ensure that we address these questions. Covid has not disappeared from our lives it is still part of the fabric of our society unfortunately and there are many decisions as we go into a very challenging winter that will have to be taken that will be affected by the presence of Covid. Understanding and learning those lessons as quickly as possible is a critical part of the work that we must undertake to ensure the inquiry fulfills its purpose and has an impact on public policy within Scotland in relation to Covid. Pam Duncan-Glancy to be followed by John Mason. Thank you Presiding Officer. The Deputy First Minister will be aware that Scottish Labour, Amnesty and other civil society organisations pressed for a human rights based Covid inquiry and that, as part of their letter, we and they were concerned that the terms of reference relied on the chair's professional experience in equality and human rights and personal commitment to look at rights breaches. We were unconvinced then that the chair's professional experience should substitute embedding human rights in the inquiry's terms of reference and so I am pleased to hear today the commitment to do so. A human rights based approach needs participation and accountability and disabled people felt left out of the response to Covid in the inquiry. So can the Deputy First Minister set out whether he would agree to commit to supporting their active participation in the inquiry and signal that their involvement and others' involvement is key by being explicit about what the human rights means in the terms of reference, including to give explicit reference to a panel approach in the terms of reference. Cabinet Secretary. I welcome the comments that Pam Duncan-Glancy makes in our recognition of the steps that she has taken today. I think what she invites me to do now is to prescribe to a degree not envisaged in the inquiry's act, how the inquiry should operate. I have to be mindful of the, I have to have a legal basis for all the actions that I take as a minister. In section 17 of the 2005 act, as I read it, it gives the sole responsibility to the chair to decide how an inquiry should operate. If I did what Pam Duncan-Glancy invites me to do, I would be acting inappropriately within that section of the act. Pam Duncan-Glancy has, of course, put her comments on the record. I'm certainly the official report of today's proceedings will be studied by Lord Balesford, and I'm sure he'll be interested to read the particular proposition that Pam Duncan-Glancy has fairly put on the record today. John Mason to be followed by Alex Cole-Hamilton. Thank you. I noted Cabinet Secretary's statement that he used the words at speed, but I do just wonder sometimes if the words at speed mean something slightly different to the legal profession from the rest of us. Therefore, can he give any assurance to families that this inquiry will not drag on as I'm afraid the Edinburgh trams one has done? Cabinet Secretary. I think the point that I would want to assure Mr Mason about is that the issues of Covid remain very present in our society. Indeed, Mr Mason is a member of the Covid-19 Committee of Parliament is engaged in all of these questions. So the inquiry in Lord Balesford come to me or strike me has been entirely seized of the importance of that point. I would say to Mr Mason that there are other inquiries that have taken a different approach to the trams inquiry. I've cited before the Scottish child abuse inquiry where Lady Smith has taken a modular approach and indeed has reported on, I think, at least six modules of that inquiry. So the findings of the inquiry are already in the public domain with evidence having been heard and further evidence being taken. And that is indeed the approach that's been taken by Baroness Hallott in the United Kingdom inquiry. So there are ways of making sure that the issues of concern in this debate can be heard early and swiftly and the point that Mr Mason raises can be satisfied to be addressed by the conduct and structure of the inquiry. Alex Cole-Hamilton, to be followed by Jackie Dunbar. I congratulate the Deputy First Minister on the swift turnaround of the appointment of Lord Balesford. He carries with us the good wishes of this chamber. I can also say that I'm gratified to hear that in his judgment the committee should look at the inquiry because there are 200,000 Scots while all of Scotland wants to know how we handled our nation's response to Covid. We need to know how we handled our response to what Covid can become as well. Can I ask the Deputy First Minister given the length of time that this may well take and we know that inquiries like Iraq like Penrose, like the Trams can take many years. Whilst he can't direct the inquiry does he share my desire to see some kind of interim report that answers some questions as we have the answers to them? First of all, let me welcome the points that have been made by Mr Cole-Hamilton and I think they are encouraging in relation to the conduct of the inquiry. I think the structure of the terms of reference are deliberately designed to enable Lord Balesford to take a modular approach. There are 12 different sections of the inquiry and they are all reasonably compartmentalised so it would be possible to do exactly what Mr Cole-Hamilton says and as I've reflected in my answer to Mr Mason, I think the experience of Lady Smith's inquiry is a good experience I've been able to give people timely conclusions based on the hearing of evidence rather than waiting sometimes a very long time for some conclusions to materialise. So again I think the points that Mr Cole-Hamilton makes are valid ones. The operation of the inquiries for Lord Balesford but he will hear the points that have been raised and will understand the seriousness with which they've been put forward. Jackie Dunbar to be followed by Gillian Mackay. Thank you, Presiding Officer. With the listening project still scheduled to go ahead later this year does the Deputy First Minister feel confident that the inquiry team has the capacity to conduct this activity properly by recent staff changes? I think that that is possible and I think that the point that Jackie Dunbar raises with me is a good example of how the inquiry has been continuing to proceed with its activities whilst we have had the issue around its leadership and I pay tribute to the staff of the inquiry who have continued that good work and I think that it gives us the basis upon which we can ensure members of the public can engage with the inquiry through the listening project and their contributions can begin to be reflected within the conduct of the inquiry. Gillian Mackay to be followed by Brian Whittle. Thank you, Deputy Presiding Officer. I welcome the decision to put human rights into the terms of reference. I appreciate the inquiries independent but given the public interest in any outcomes of the inquiry how will the Scottish Government ensure that its conclusions including any interim conclusions if appropriate are in accessible formats in order to provide all families who have lost a loved one the answers they deserve? I think that the requirement that I am placing on the inquiry to demonstrate how a human rights based approach has contributed to the inquiry's findings in fact and recommendations would place that very obligation on the inquiry to ensure that it reports and it engages at all times in an appropriate and accessible way to make sure that the needs of all interested parties are properly and adequately met as a consequence. Brian Whittle to be followed by Jim Fairlie. Thank you, Deputy Presiding Officer. Is there just a point of clarification for the Cabinet Secretary if I may? Can I ask if the Scottish Government's civil servants are directly involved with the inquiry and if they are would you not recognise that that might be a significant conflict of interest? Cabinet Secretary. There are civil servants who have been seconded to the inquiry. That is a standard practice within public inquiries because they bring with them a great deal of expertise. However, it is absolutely critical that those civil servants exercise their professional responsibility which in my experience of the civil service is an absolutely consistently delivered proposition. When I entered Government in 2007 I had spent many years as a political activist as a member of Parliament as an observer of politics been told that civil servants could one day support an administration of one colour and in the next day the self-same people could support wholeheartedly a people of another political colour. I wondered if it was correct I had no experience before early May 2007 and on day 1 I found out it was correct because those civil servants operate in an entirely professional manner where they act in relation to the the remit that they are following and the accountability that they follow that is part of their professional contribution and I am grateful to them for that. I thank you David Deputy Presiding Officer. First of all I will give you my apologies for being waiting in the chamber colleagues. I have listened carefully what the Deputy First Minister has said and I do hope that Lord Baresworth is listening today to the genuine concerns about the long Covid situation that a lot of our constituents keep coming to us with. It is unfortunate that the inquiry has been delayed because of the resignations but I am sure once the new appointments have been made and finalised the work will resume quickly but regardless of the loss of time can I ask the Deputy First Minister how the Scottish Government is going to ensure that the inquiry and that the work will continue to be a high and thorough standard? It is briefly responsible cabinet secretary. I think that Lord Baresworth will bring his experience of many years in the Court of Session to bear and leading the inquiry and we have had a period where the leadership of the inquiry has required to be changed. I have addressed that as colleagues across the chamber have recognised as swiftly as humanly could have been the case and I am grateful to the Lord President and Lord Baresworth for their engagement on this question and I am very confident that the inquiry will proceed in a professional manner to address the issues of vital importance to members of the public and members of Parliament. Thank you very much Deputy First Minister there will be a brief pause before we move on to the next item of business.


We've got classical, we've got rock, we've got blues, and we've got a little country. So we've got a whole wide range of stuff for you for ten weeks. There's a balance that you're trying to catch. You want to get folks out that people are familiar with and excited about. You want to get some things out that folks are not so familiar with. So, you know, on the one hand you have your meat and potatoes that everybody's going to go gun hoe for. Then on the other hand you have a little bit of vegetables that are good for you and everything. So I think we have a good balance of the folks that are out there making good music that is very popular and people really love to see. And then folks who are making great music that people aren't so familiar with but will really like when they hear it.


So, last class we have discussed that linear quadratic regulator problems and we have proved that linear quadratic regulator problem has a good robust I mean properties gain margin is infinity or you can say LQR LQR problem gain margin we have seen it is a infinity and greater than equal to half. That means, what are the present gain is there of this system we can increase the gain up to infinity and still the system is stable if you design the controller based on the LQR. And also the gain you can reduce to half what are the present gain is there that gain you can reduce to half of its value still the system is stable at least it may be less than half also it is stable, but this range is granted if you design a controller based on LQR then system will be stable this is the gain margin and phase margin phase margin will be at least the phase margin is 60 degree. So, this LQR design if you do the LQR design again based on the what is called performing index minimization then you will get this gain margin and phase margin is greater than 60 and gain margin infinity half greater than half and less than infinity. So, today we will discuss that is what is called linear quadratic Gaussian problem in short it is going LQG problem. So, in LQR design problem there is a restriction while we are designing the controller first restriction is there the system is deterministic systems. Again in real practice or real world the what is called system is under stochastic environment. So, we have to design a controller under that environment. So, more general control problem you can say the more general problem is LQG problem LQG that deals with optimization of a quadratic performing index performance measure quadratic performance measure for the stochastic systems. In LQR what you did it deals with the optimization of quadratic performance under deterministic systems system is deterministic that means the system is not corrupted with noise in state is not corrupted with noise and measurement equation also not corrupted with noise. But more general problem you see that what is LQG problem deals with the quadratic minimization quadratic minimization under stochastic environment. So, first we will state the statement of the problem so LQG problem statement LQG problem statement. So, consider the our consider the stochastic systems x dot of t is equal to a of x t plus b of u t plus gamma w of t and x initial state is given which is in stochastic in nature that random in nature. So, this is Gaussian with 0 mean x 0 is Gaussian with 0 mean. Now, let us call the state of the number of the states in the system is n. So, number of inputs is m and number of the noise corrupted the state equation corrupted with noise through gamma channel is dimension let us call small r into 1. So, once you define the state of the dimension of the x w u t and w of t w t is the noise and this noise is 0 mean white noise Gaussian process agree the w w mean 0 mean white noise Gaussian process and once you know this dimension immediately you know the dimension of a a b and gamma. So, and this is the state equation you can say this is nothing but a state equation state equation and our output equation y of t is equal to c of x t plus v of t and again this w of t sorry v of t is 0 mean white noise Gaussian process whose characteristics is known means noise covariance matrix is known to us before that. So, this is called measurement noise this is called input noise w is input noise v is called the measurement noise their statistics is known to us mean and covariance is known to us w and v as I mentioned it they are 0 mean white noise Gaussian process and they are uncorrelated. So, there are few assumptions are made before we what is called get the solution of controller solution in under stochastic environment. So, input stroke output statistics are like this way first is e expected value of omega of t input noise is equal to expected value of v of t is 0 mean both input and measurement noise input measurement in 0 mean and not only this they are white noise that mean e w of t into w transpose of tau that equal to q delta t delta tau is operator when tau is equal to 0 tau is equal to 0 then this value is 1 other than 0 this value is 0. So, this indicates that t is equal to t is equal to small t is equal to tau then their covariance matrix is the q and d this is the delta operator again this is the delta operator. Similarly, this indicates that this input noise covariance matrix is q and they are independent different because at t time what is the noise and t plus some other time or t 1 time they are uncorrelated that means noise and t 1 time is no way related to noise at t 2 time. So, this indicates this is the noise covariance input noise covariance matrix input noise covariance matrix agree. So, in place of this one when tau is equal to t when tau is equal to t this value value is 0 sorry this value is 1 when tau is not equal to t this value is 0 that means it indicates they are uncorrelated and this w of v of t into v transpose of tau this equal to r delta of tau and this is the noise covariance of measurement matrix noise covariance of the measurement noise covariance of noise covariance matrix of v of t and this is of v w of t these are this indicates that w is w and v are what is called white noise with 0 mean and v and w are also that uncorrelated you can say that v and w you can just say then v and w w and v are uncorrelated and uncorrelated how will you define w of t v tau transpose of t this equal to their different initials or v of t is equal to 0 they are uncorrelated of t and also we assume that initial state has a 0 mean and their covariance is equal to s which is known matrix that each noise covariance matrix q and v are this is a this matrix this matrix is positive semi definite matrix and this is your that we use the v because we have used if you recollect we have used the r when you are discussing the linear quadratic regulator problem that r is the weightage in the control input. So, we should not use the same symbol here. So, we are using the noise covariance matrix of the measurement noise covariance matrix is v. So, this is this is also we will not use q. So, we will use this value is w capital W capital W is the noise covariance matrix of w because q you have used it l q r problem in state weighting matrix. So, in order to avoid a confusion we have used the w and this is v. So, then this is the noise covariance matrix and this matrix is positive definite matrix and this is positive semi definite matrix and the measurement noise covariance matrix is positive definite matrix we made a sense and they are symmetric. So, this matrix is positive definite matrix and symmetric. So, and they are uncorrelated this initial state is uncorrelated with w of t of this 0. Similarly, there is initial state uncorrelated with the input noise as well as it is uncorrelated with the measurement noise. So, this for all t. So, these are the assumptions is made it before we solve the l q g problem. There are further this characteristics assumption or characteristic as input noise covariance matrix output noise covariance matrix and also initial state what is called covariance matrix is in initial net variance is known to us. Then our made an assumptions a and b pair is controllable because then we will able to shift the all the poles of the system open loop poles at desired location by l q g problem also as just like l q r that must be controllable. Then a and c is controllable pair a and c observable pair and we assume that all the state variables are not measurable that is why we need an estimator to estimate the state of the systems. So, our quadratic the objective function the quadratic objective function first we define the j is equal to limit t time t tends to infinity 1 by 2 t expected value of that performance index minus t 2 plus t and it is nothing but 1 by t I am taking the average of that one x transpose q x transpose q x of t plus u transpose r u of t whole d t whole d t agree. So, this we want to minimize this one the now our problem boils down to like this way the problem is to find is to find the optimal control u of t capital u of t that minimizes the above performance index that minimizes the average cost function. Let us call this is the equation number two and our basic equation what we given describe this two is a equation number one. So, state equation and measurement equation we have given the name equation number one and the performance index what we are assume agree in stochastic environment this is equation number two we are taking the expected value of this just like a quadratic function that means we are giving weightage on the state and as well as on the input vector u. So, this q and r is same as before one when we have discussed the what is called l q r problem the q is positive semi definite matrix r is positive definite matrix and they are symmetric as early as possible. So, now next is we will just solution of l q problem solution of the l q g problem via Kalman filter. You see we have consider that system is corrupted with newton that means state equation is corrupted with noise of measurement equation also corrupted with noise. So, when we are implementing the l q g problem that u is able to minus controller gain into because states are not accessible we have to estimate the x hat of t we have to use. So, first we have to find out what is called that how to estimate the state of the system under stochastic environment that one. So, details of this one I will not discuss about the Kalman filter here again. So, I will just tell you how to design a what is called Kalman filter here briefly. So, first step is control law our control law u of t is equal to minus x hat of t. So, let us call this is equation number 3 this is dimension in n cross 1 and this dimension since it is m cross 1 the dimension of k must be m cross n. In l q r problem we have assumed the all the state variables are accessible to us which will be used for implementing the control law. Whereas, in stochastic environment or l q g problem the states are not accessible or measurable. So, what we did it we have estimated we have to estimate the states except to this x hat of t. So, how will we estimate the state that we will discuss step by step now. So, here is if you see here is the k is the controller gain and the controller gain is designed same as what is called the l q g problem. And we will prove it here that estimated or the Kalman filter estimated and the controller design. Estimator design and controller design they can be done separately or independently because they are varied separation theorem is valid in order to design controller as well as the estimated separately. So, let us see this one where k is equal to minus r inverse b transpose p let us call this is equation 4. As I mentioned earlier that k is designed same as l q r problem. So, I am not already we have discussed how to get we got this expression. So, since k dimension is m cross n and n dimension this immediately other one dimension we know it. So, that is equation number 4 where the p is the p is n cross n is the solution of our solution of algebraic Riccati equation.  So, this is an infinite regulator problem we know already how to solve this one different techniques. So, let us call this is equation number 5 next is once we design k because I cannot implement u of t until and unless we estimate the states because our system equation are corrupted with noise with a known statistics. That means, we have used the conventional that noises are statistic is known means they are 0 mean white noise Gaussian process and some other assumption also we made it. So, now next is how to estimate x of t x is the estimated state estimated state obtained form Kalman filter in short k f. So, what is the Biffler and Jettling? So, ultimately in Kalman filter they are minimizing a performance index and that performance index is the error covariance matrix trace of error covariance matrix. So, minimize the that means minimize my is the performance index performance index. What is this performance index considered for estimated that J e is equal to expected value of x t of x hat of t. So, this is nothing but a error between actual state and estimated state. So, that into transpose x of t minus x hat of t. So, that will be a scalar quantity that means we are doing the sum of the errors squared over the period of time and then we are taking the expected value of that one. This is same as if you see summation of component wise of state if I write it there are n states are there i is equal to 1 to n then expected value of x small x of t or small x i of t into small x hat of t. So, this is state error square the same as that expression or minimizing the trace of error covariance matrix. So, one can write it this also like this way minimize J that means J minimize the trace of e e x of t minus x hat of t this into x t this is capital X capital X minus x hat of t whole transpose then this and this take the trace minimize that trace of that one that means your problem estimated minimize the performance index that either you write expected value of the error square or you write it trace minimize the trace of this is the error covariance matrix trace the error that means all the diagonal elements of this matrix is nothing but a that quantities. So, this you do it the so this way we have to estimate the state of the parameter. So, I am writing directly that what is the estimated equation the Kalman filter of this equation is same as what we did it for the deterministic case structure is same, but only the implementation wise we have to do in different way. So, this plus L into Y capital Y of t minus C x hat of t look that one this L is the Kalman gain and this is the error. So, this third term is the error correction each iteration or each time this will correct the error. So, this is the error term again. So, this dimension Y dimension you know this dimension p cross 1 the beginning I just mention it just see the dimension of p is not mention it here dimension of p dimension of y is p cross 1. So, similarly immediately we can find out C this dimension of a number of outputs is p. So, if it is this p immediately you know the dimension of this one will be n cross p L Kalman filter gain is n cross p. So, now how to obtain the L in the next question is how to obtain the L. So, this if you can simplify I can write it a minus L C this into this L C x hat of t plus b u of t plus L Y of t. So, let us call this equation last equation number is what we have given it 5 then this is the equation number 6 you give it this is equation number 7. So, the estimator design is the dual of controller design agree. So, how L is computed this Kalman gain is computed L is computed as follows. So, you write the expression for L Q R controller or L Q G controller controller design expression you write it there you put it in place of A you replace by A transpose. So, you replace A by A transpose B by C transpose and Q by W and R by R replace by V and then L replace by K transpose or K replaced by K transpose replaced by L. So, let us call how it is. So, our expression for L and whose dimension is n cross p is equal to what is the if you see side by side I am writing what is the controller expression R inverse B transpose P R inverse B transpose P. So, I will replace the because our K is what K will be replaced by L transpose, but I want to find out L transpose sorry L then it will be K transpose L is K transpose. So, it will be a P first will come P let us call for estimator I am denoted by P E then B transpose and then transpose is B B is replaced by C transpose. So, C transpose then it will be coming R inverse R is replaced by V. So, V inverse again. So, this is the our Kalman gain you have to find out for you know C you know V is the noise V is the measurement noise covariance matrix, but we do not know P E P is the error covariance matrix P E is the P E is the error covariance matrix of dimension n cross n. So, that we do not know look here how I am a final computing the Kalman gain Kalman gain I am finding out what is the expression for controller gain that K is equal to R inverse B transpose. So, take the transpose of K if you take the transpose of P transpose, but I am writing is P is symmetric matrix P. So, P is replaced by P E my error covariance matrix and then B B is replaced by C transpose. Then R inverse transpose is R. So, it will be a R is replaced by V. So, this is the Kalman gain expression. Once I get, but here is unknown is P E error covariance matrix of dimension n how to solve the error covariance. The way we solve algebraic equation for L Q G problems or L Q G problem when we are designing the what is called the L Q G controller we have used this expression if you recollect that one. This expression is used to calculate the L Q G controller gain. So, in this expression I will replace A by A transpose and P by P E B by B will be replaced by C transpose and Q will be replaced by W that we what we have mentioned in the beginning. So, if you do this one that L is that P E is completed P E is completed by solving continuous filter algebraic equation. Algebraic equation what is this continuous filter. So, filter expression design of filter and design of controller is dual of each other and how we are doing it dual replacing controller whatever the A is there replaced by A transpose B is there replaced by C transpose and your Q is replaced by noise covariance matrix and R is replaced by measurement noise covariance matrix. This are replaced by in their original Riccati equation. So, if you replace by this one it will be coming A P E plus P E A transpose then P E C transpose B inverse. Then we will see P E then gamma transpose gamma W gamma transpose. What is this one because it is the expected value of gamma into W of t. So, this is nothing but this term I am getting from this one expected value of gamma W of t into this into transpose W of t. So, transpose of that gamma this gamma Y of t whole transpose and that will come gamma that is W noise covariance of this one into gamma transpose that one is right this one. So, anyway this equal to 0 and that is equation number.  So, A is replaced by A transpose. So, A transpose and its transpose A P is replaced by P E error covariance matrix and in this way B is replaced by C transpose C transpose R is replaced by measurement noise covariance matrix V and so on. This Q is now I have shown you this Q is what noise covariance matrix that one this Q. So, this is equation number 8. So, now if you see the our LQG controller structure how it is then the detail diagram that what block diagram of block diagram of LQG controller. So, we have a this star then B this then integrated I am just writing the block diagram from actual system this is X of t then C and this is our output actual output, but it is corrupted with a noise V of k and then we are getting the Y of t measured output. So, this output from this output and this is our B and it is corrupted with here you see this is the W, W is coming it is passing through the gamma this block is gamma and it is coming here this is W of t input noise input noise entering through channel gamma, so this now again you can see here that from here this is reference input let us consider 0. Then we have a B the structure of control by estimator is same as the structure of the actual plant structure I am talking about. So, this equal to this one then integrated and here is not completed. So, here from here from here the system matrix A is there system matrix A and it is coming here plus here is X dot of t this signal is X dot of t. So, this then it will be coming is X hat of t. So, this is a integration this is a integration so X dot X hat dot of t then c then it is coming here Y hat of t this is minus this is plus again. So, this signal is coming and from here this A this and the if you see this is one this is the Y hat and from the estimated state the controller I am telling the estimated state will go to the controller k minus k and that is the control law that is the control law agree U of t and this signal is plus U of t. This is B this. So, now if you see the observer what is your estimated equation A X plus this is the correction term correction term we have not build up here. So, now this is the this signal is Y minus Y of t minus Y hat of t again. So, this will go to the Kalman gain l. So, that l that l will come ultimately it will come that l or you write it here instead of showing here this is the Y hat of this one I will show you in the red one this is the Kalman gain. So, that will come this Kalman gain will come from here plus that one. So, this is this I am now showing you this block this red with this block this is your plant this is your plant this is your plant and this is your controller again and this part from here from this part from here to here part is your Kalman filter Kalman filter which will estimate the state of that one. So, this is the this block I am indicates the controller along with the Kalman filter where the states are not available.   So, this is the your Kalman filter best controller is design now we have to see we will see it in the LQR design we have observed that if you design the controller based on LQR that we have a gain margin is infinity and the present gain you can increase to infinity. At the same time present gain you can reduce to a half in this region the system is stable from as well as you can save the phase margin of the system when it is controller is design based on the LQR the phase margin will be at least 60 degree that is we have a gain, but when you are using the estimator along with the controller that properties is totally lost that means robustness is of the LQR LQG is compared to LQR is much less of this one. Then we will see this one how to that. So, first we have see we will see the LQR LQG separation principle. So, since we have done earlier so I will not go separation property since separation property for LQR we have derived it will not go in details in this. So, recall the equation number 7 this equation number 7 you recall that one this equation putting u is equal to minus k x hat. So, from 7 we can write x dot of t is equal to a minus l c and b k because b u k u k is replaced by minus k minus x hat of t. So, that is why it is x hat of t plus l y of t.  So, with u of t we replaced by minus k x hat of t let us call this is equation number 9. Now, we will find out the trans function from this is just a from y to that u what is the trans function of that one y to u if you see the trans function from y to u. So, now find out the trans function from y s to u s why you are finding out the trans function to show that our loop gain is different from the loop gain of LQG is different from the loop gain of LQR. And there we will show it that we are the properties of LQR nice properties of LQR is lost when we are designing a LQG problem. So, can be derived as so take the Laplace transform from both side if you take this one I can write s i minus a minus b k minus l c this into x hat of s is equal to L y of s which I can write x hat of s is equal to what is this s i minus a minus b k minus l c whole inverse into L y of s both side I multiplied by minus k x both side I multiplied by minus k x k minus k. So, both side I multiplied.  And we denote this one when there was no observer s i minus s i minus bracket a minus b k when there is no observed that we have denoted by phi s if you recollect in the LQR design problems. Now, this whole thing I am denoted by phi r of s agree this part s i minus a minus b k whole inverse this one. So, now from system state equation and from 9 one can write it from 1 and 9 with gamma I just consider is an identity matrix again whose dimension will be a r cross r because noise w of t noise we have considered the dimension is r cross 1. So, now it is a that one dimension gamma let us call it assume or in general you can keep it gamma gamma also in the expression. So, we get x dot of t and x hat of t x hat dot of t is equal to a minus b k l c a minus b k minus l c from 1 and 9 only gamma you have replaced by identity matrix plus. So, this but from this thing we cannot come to conclusion that whether the estimated design calmer filter design and the controller design can be done independently or not we cannot say that means separation principle is applicable we cannot say. So, what we have to do let us call this equation is equation number 11 what we define that error equation now. So, you define the error e of t is equal to x and x hat of t is equal to x and x hat of t minus x hat of t this you define and then you express x hat in terms of error equation. So, I will get it finally, x e of t is equal to a minus b k b k 0 a minus l c plus i i 0 minus l w of t that will be v of t what I did it x hat I express in terms of e. So, x hat is equal to x minus e in this if you manipulate this expression equation you will get this one. Now, see the structure of that x dot and a e dot expression there is upper triangular form the Eigen values of t that will be v of t what I did it x hat I express in terms of e. So, x hat is equal to x minus e in this if you manipulate this expression equation you will get this one.  So, they are decoupled when we are designing this one we do not need any information of Kalman filter gain information and when we are designing this one we do not need any information of the controller design information. So, this and both the matrices that means a minus b k and a minus l k both the matrices are stable matrices are stable again. However, you see the how do you design the controller gain or you observe gain l. So, you have to design it is better you did the Eigen values of observer Eigen values of estimator a minus l c should be at least 5 to 10 times of the Eigen values of the controllers agree. In that way we can get better performance or the better closed loop behavior of the system that means Eigen values of this one should be 5 times 5 to 10 times more distance from the Eigen values of that controller Eigen values. And that will give you the what is called good closed loop system behavior this is. So, now let us investigate our loop gain loop gain of the l q g problem. If you look at the l q g problem our basic structure it is a system the Kalman filter then controller. So, this what is our loop gain of this thing we can make it in simplified form. This is the estimator equation a of minus b k minus l c x hat of t plus l y of k y of t. Now, take the with u of t is equal to minus k x hat of t this is the with u of t is equal to minus k x hat of t. This is the controller gain and this is the Kalman filter gain. So, if you take the Laplace transform both side of this equation u of s u of s is equal to minus k x hat of s. And you know the x hat of x expression in details from equation number that is what you have given it x hat of s equation number that is 10 we can get it this one. So, I will discuss this that expression that how to find out the loop gain of the l q r and compared with the l q g how to find out the loop gain of l q g and compared with l q r that we will discuss next class. But l q g when you will see there are different loop gain you will get it and that will show that we are losing the properties of excellent properties of l q r when you are using the Kalman filter along with the controller.


To Allah is your return, and He is most capable of everything. Alright guys, welcome back to the channel. If you're new, my name is Bobby. Guys, it has been quiet around Hamza Yusuf. However now, finally, he pops back up on the scene and talks on the current situation in Gaza. Today we're gonna check out the channel Kim Iverson, I never heard of her before, interviewing Hamza Yusuf and they're gonna find out what Islam really says about Jihad. This should be a pretty interesting watch. I'm very curious to hear what Hamza Yusuf has to say about Jihad. I already hear the Christian apologists in the background screaming. First and foremost, Jihad does not mean automatically war, it means struggle and it can be a variety of struggles. Back in the day in Africa during the colonization of the French, you had a phenomenon called the Jihad of the pen. So essentially Jihad can be any type of struggle that a Muslim goes through. But no, we're not here to deny that Jihad can mean war as well. And what is so bad about it?  One of the 99 beautiful names of Allah is al-Hak, which means the absolute truth, the absolute reality. And if we reflect upon reality, what is reality truly? Reality is what it is. You cannot change it, you cannot impose your will onto reality. If you are for example a vegan and you go into a forest and now you see a bear. You can take your vegan ideology into that forest, but you're not going to take it out of it. You can believe that oh, that is such a cute teddy bear, I want to pet him. But the reality is that probably, highly likely, that bear will attack you. So your delusion, your fantasy, your ideology cannot stand against reality. And that is the whole point. In Islam, we are realists. We are realists. We see how the world works in accordance naturally to the world. We act, of course. This is what a true religion does, of course. A true religion cannot go against human nature. And by that standard, we realize that war is a reality. This is what humans have done. This is what humans do. And probably this is something that humans will do till the end of times. War is a reality.  That will solve the situation. But meanwhile, America, a Christian nation, is bombarding Arab countries. So this is hypocrisy and Islam clearly stands against hypocrisy. Alright guys, I'm going to keep the rant for later.  Subscribe to the channel if you haven't already and check out the links in the description box to further support the channel. And now, with no further ado, let's have a look. What is jihad? And what does that mean? Jihad in Arabic literally means struggle. There's no holy war in Islam. There's nothing that says war is holy. War is actually the absence of holiness. War is the failure of holiness. And that's why in the Quran it says whenever... That's pretty disappointing. I didn't expect this whatsoever. Mentioning that jihad means struggle, I did the same thing. That is great. However, then to claim that war is the most unholy thing, that it is the lack of holiness, is actually pretty close to kufr. Because first we have to establish who Allah is. Allah revealed the Quran and one of his 99 names is Al-Qudus, which means the most sacred, the most holy. So now that we established that Allah is the most holy and he revealed the Quran after all, therefore we cannot say that anything within the Quran is unholy. Let's read Surah Al-Bakara. We read, fighting is ordained for you, though you dislike it. You may dislike something, although it is good for you. Or like something, although it is bad for you. God knows and you do not. So we can read very clearly that the most holy one, Allah, God ordained fighting to us. So he ordained war for the most slims. And now you're going to say war is the most unholy thing. That's a very dangerous statement, man. God works to put it out. The fires of war. Whenever the fires of war are ignited, God works to put them out. And that's through people raising people up that are peacemakers. One co-wrote another book, he edited a book on the peace movements within Islam. There are many, many great peace movements in Islam. People forget that Gandhi's main supporters were Muslims. One of the closest people to Gandhi was Abu Qadam Azad, who was a scholar of Islam born in Mecca. Yeah, and absolutely have no issues with this whatsoever. We had many peace movements throughout the history within Islam, in Africa, in Senegal. We had tremendous peace movements led by Senegalese leaders such as Amadou Bamba. But nevertheless, to solely focus on peace and in the same breath, disregard war completely even goes so far to say that war is unholy, is yet again against the Koran. And he was with Gandhi. He was with him in jail. He worked with him and was one of the closest people to Gandhi. And Abdul Ghaffar Khan was the great peacemaker from the Pathan community. Yeah, that's fantastic, but Islam is not just a piece of history. There's been a belligerent element within Islam and I would never deny that. And Jihad can be misused. So Jihad, when the leaders say, you know, this Friday we're going to have a night of Jihad, what does that mean to the average Muslim? Nobody said a night of Jihad. I don't think they would use it that way. Like I said, Jihad, Dushimi struggle, there's two Jihads according to our tradition. The Prophet Muhammad, peace be upon him, famously was quoted as saying, when they came back from a military expedition, he said, you're leaving the lesser Jihad to the greater Jihad. And they asked him what that was and he said the struggle against the ego. So the real Jihad is against the ego and fighting the impulses of vengeance.  This is pretty annoying to watch, to be honest. He's just trying to nullify every single thing that has to do with war. Yet again, there is nothing wrong with war. It is mentioned within the Koran. Of course, we're talking about just war. Moreover, we actually do have just war rules within Islam. You cannot say that about any other religion. You find things such as, do not cut a tree. Which other religion is promoting to leave nature alone?  The same cannot be said about the occupier Israel.  Again, the same cannot be said about the occupier Israel. Do not destroy a temple or a church. I don't want to repeat myself. Do not destroy any building.      Don't disfigure the dead.  Be good to the prisoners and feed them. And do not enforce Islam. Which means there is no compulsion in religion. So Islam has beautiful rules for conduct in war. As I said, no other religion has that. But it has to be emphasized that yes, in Islam there is an aspect of war. A defensive war, expansionist war. All of those rules are found within Islam. Why? Yet again, because it is reality. Islam is not only a religion, but a social construct, a political construct. Islam has a system for everything in human life. This is why we believe that it is directly from God. Because it is applicable in any sense. And therefore, yet again, war is a reality. And therefore Islam shows us how to deal with this reality. You know, I think about even the prime minister, Netanyahu. People forget that his brother Yoni Netanyahu, who was a national hero, was killed by a Palestinian in the raid on Antebe when he was young. And Netanyahu said it was like the heart was ripped out of his chest when he lost his older brother. And so fighting that hatred of the other and being able to forgive, being able to get beyond that, to try to see the pain also of where that comes from. You know, W.H. Auden wrote that extraordinary poem September 1939 about Hitler. And he said to go back and look at what happened in Linz in Germany. Where did this monster come from? And then he said, I and the public both know what all school children must learn.  You know, that's a terrible lesson. But fighting the self to overcome that. You know, we have a default setting. They are a great fantasy story. What evil has been done to Hitler. We get angry easily. Somebody cuts us off on the road. Suddenly we're in road rage.  That's all because there's no spiritual work. You know, we have to be vertically aligned. We're upright creatures. God put the head on the top. He could have put it on the stomach. But the reason should rule the human being, not the heart, the thumos, what the Greeks called, you know, the irascible. Yeah, he now goes into Greek philosophy. I do not know where he has this from. Ultimately, your heart has to be opened up to Islam. And therefore it's not only your rationale. It's not only your logic.  You ultimately have to act out of your heart. And this is exactly what the Quran says as well in Surah El-Hajj verse 46. We find Allah gives this warning. It is not the eyes that are blind, but their hearts which are in their breasts. So no knowledge, no logic in the world can set you on the straight path. This is done through the heart. It should be controlled. It should be mitigated. It should be constrained. And if it's not, the world could be horrible. And I'll tell you, I mean, I work on myself. I have to work on my own self. But I know like I, you know, I pray five times a day. I read a good deal of scripture. I pray a lot. I do occasional prayers throughout the day. And yet the modern world drives me crazy. So I think about people that don't. There's actually a very wild statement for a man in his 50s or 60s that the modern world is still driving you crazy. So then you really haven't learned anything, man. According to the Quran, this dunya is nothing but the enjoyment of delusion. If you haven't learned that by 50 or 60, nobody can truly help you. This change that you're talking about, this energy, heart, you still haven't completed that. How can you get angry at the world? This is just temporary anyways. Spiritual practices. And I can understand why there's so much mental illness out there. Very striking. Because if you don't have a spiritual practice to remind you about patience and about virtue and about working on the self and struggling with the self, I can see why people lose it. With these groups, these really violent groups like ISIS, al-Qaeda, are they getting Islam wrong? Or are they just taking the Quran to the extreme? So the things that we know, like martyrdom, if you die, you'll get like 72 virgins or something along those lines.  Or take sex slaves, I should say.  There's a variety of ideas that seem to be still very much... There's a lot of ideas in the Bible where Christians are like, Yeah, okay, but that's, we don't really... It's just like old time talk, right? Nobody really does that. But it seems that in Islam, there are factions of people who do actually take... Most Muslims actually believe that scripture. I've never read the Quran, so I don't know. Are they taking the words literally and they're practicing it? Literally, are they perverting the Quran? Are they reading an entirely different book? No, I think the Quran has... There are passages in the Quran that could be easily taken out of context and misapplied. There's no doubt about that. And the same is true for the Bible. Less so. I mean, I think the New Testament probably arguably less so than the Old Testament. But Christians traditionally did believe in the Old Testament, although they do believe in abrogation as well. So a group like... The Muslims are 1.7 billion people. So our extremists are probably numerically... Statistically, not that different from say the Jewish extremists or the Christian extremists. But because our numbers are so great and they're far more practicing Muslims than they are practicing Christians. Okay, where are you going with this, bud? Europe has seen it as a Christian country, but people don't go to church in Europe anymore. I mean, the churches are empty. Even in the United States, the churches are beginning to empty in many places. I mean, the blue states have a much lower rate. So you're saying that even though Christianity is the dominant religion in the world, because there are more Christians at this point on earth than there are Muslims, there's just more practicing Muslims than there are practicing Christians. So there's more religion. I think... Yeah, he's just deflecting, deflecting, talking about all kinds of things, but not really answering the question. How about martyrdom? For example, can we find anything like that within the Koran? The answer is, of course, yes, we can. And Surah Al-Baqara, again, we read, never say that those martyred in the cause of Allah are dead. In fact, they are alive, but you do not perceive it. And here we can see the tafsir of Ibn Kathir. It explains further what happens to the martyr. Their souls are inside green birds that have lambs, which are hanging below the throne of Allah. And they wander about in paradise wherever they wish. Then they return to those lambs. Allah looks at them and says, Do you wish for anything? They say, what more could we wish for while we go wherever we wish in paradise? Allah asked them this question thrice. And when they realize that he will keep asking them until they give an answer, they say, Oh Lord, we wish that our souls be returned to our bodies so that we are killed in your cause again. Allah knew that they did not have any other wish, so they were left. So yet again, instead of deflecting here, Dear Hamza Yusuf, why don't you show those verses?  And the same applies to Christianity or Judaism. This is not an extreme stance. This is simply what the Koran teaches. The vocabulary is theocentric.  People don't say those things anymore. Even secular Muslims say those things constantly. Insha'Allah, Masha'Allah. We also pray for the dead. If a dead person's mention, we say, God have mercy on your soul. So I think it's just a much more... You didn't answer the question at all. Extended family, you know. Alright, this is it for today. It's a very disappointing video. I don't know what I expected of him. However, I expected a little bit more of course. The question was, what is Jihad? His answer at first was correct. It means struggle, sure. Then to go on this rant of deflection, of talking about peace, yadda, yadda, yadda. We're finding ourselves in a very dire situation. Palestine, Gaza has been occupied for 70, 80 years by now. People are dying on a daily basis. Innocent civilians, children, women are being slaughtered on a daily basis. Nobody is coming to help. The Arab world has closed their eyes. Nobody is supporting our brothers and sisters in Palestine. The only thing that we can do here is spread the information.  Truly, I did not know that this would await me once I revert to Islam. To sit here, to speak on behalf of the people and to not be able to do anything. If I could, I would go to war right away.  Not one Muslim government, quote unquote, is standing up for our brothers and sisters. And then we have those great sheikhs like Hamza Yusuf here. Instead of taking a proper position, explaining what is going on. No, he's going to tell you about peace and how much he loves to do spiritual work.  Truly, I have to repeat this. It's really on my heart seeing this dire state the Muslim world is in.  The only hope that I have is Allah, because Allah will punish and judge all of those corrupt leaders that have done absolutely nothing and stayed silent. Alright guys, but this is it for today's video. If you liked it, leave a thumbs up, subscribe to the channel if you haven't already and check out the links in the description box to further support my work. And as always, may God bless you all. Much love and peace. Thank you.


Hello friends, welcome back to another episode here on the channel. I hope you're all doing great and as always for anyone new to the channel, my name is Lee also known as Osiris in today's episode. We're going to continue on with our Pokemon VGC series 10 content and play a team that's on your screen right in front of you now, which is the Ternitus. So Ternitus, a Pokemon that I haven't really featured too much on the channel before. But I'm looking forward to diving in with it today. It's got a really unique typing, obviously that dragon and poison typing as well. So really high base speed, decent special attack and has some good defensive bulk about it as well. It can be kind of even further extended with something like cosmic power, which we're actually playing on this build today. Obviously, though, the rest of the teams made up. We've got a nice firewater grass court in there as well, no incineroar. But we do have it intimidated on the lander. And I know a lot of you have been kind of crying out recently for teams where we're not featuring so much really boom and incineroar. And I am going to be doing that. Obviously, it's hard to not incorporate some of these Pokemon sometimes because they're such underpins of the format at the minute. And that's why you see them on so many teams. They kind of pull a lot of kind of builds together. And that's why they're so successful. But in line with what you would like to see, we will be kind of innovating and playing a few different calls going forward, especially into this week and next week and keep the suggestions coming. We've had some great suggestions about formal teams that you'd like to see featured and particular some restricted Pokemon as well. But I feel like we're touching on a Ternitus today. It's kind of one of those fringe Pokemon that's doing kind of good, but it's not doing amazingly well. But I feel like it could become one of the top kind of restricted options that the players do jump on. But it's an interesting Pokemon. Hope if you do try the team out, as always, I mentioned the poker face is down in the description. We'll throw the rental team up at the end of the episode that you do enjoy the team if you do try. And if you've been playing around with the Ternitus already, do let me know down in the comment section what your what your opinions are on on or because I love to hear and always interested to hear what what other players' perspectives are on some of these lesser used restrictives. But without further ado, friends, hope I can say you enjoyed today's episode and we'll jump into our first match of the day. First up today, we have a treat. We've got an evolution theme. I can't believe this. OK, so we've got Jolteon, Flareon, Espion, Umbry and Glacion and Sylveon. There's always, you know, this is like throwback to back in the day on the rank ladder where you'd always get one Japanese player who would be piloting just a full EV team. And it's kind of nice to see, again, how we're going to approach this. I feel a Ternitus does pretty well against the majority of stuff here. There's not really a ground type to give us any real issues. Obviously, the Espion gives us a few problems, so we need to to deal with that. But outside of that, I think a Ternitus has a really nice time against this team. OK, do we lead a Ternitus or do we kind of just deal with the Espion and then a Ternitus kind of has that wincon, right? We could get a cosmic power pretty quickly, though, with the fake out and then just cosmic power and then just kind of go to town on everything. I think anti is pretty useful here. Do we want some speed control? Regi Alecki always going to be good. But I feel like stability of Suicune can kind of come in and fire water, grass core against something like an Espion. All evolutions build is good. I kind of want these these episodes to kind of be more against common archetypes. I always like to kind of play things that are like relevant in the format the minute, but you do sometimes just look at the draw, obviously bump into some some archetypes that aren't as as common as others. And sometimes it's kind of fun to go up against these sort of teams as well, you know, so we've got the Sylveon and we've got the Espion. I wonder if there's like a round. Sort of a theme going on with the team because we can nuke the Sylveon here. But like I say, I think the best thing overall is probably try and get like that cosmic power up as soon as we can here. Just go for the fake out into something like Espion.   And once we've got one up, I think we're going to be in a pretty decent spot. So see the Sylveon retreat here. Umbrian going to make its way onto the field. We do have to worry about something like yarn from the opposing Umbrian, because that can be a little bit annoying to get around, especially if it yawns us this next turn. And we're not really able to to get the full kind of use out of a turn is this while we're sleeping. Right, do we just go after the Espion? Or do we kind of concentrate down on the emerald? It's going to be an end game of Umbrian, I think. So we'll sludge bomb and more grassy glide into the Espion. Get rid of that big threat and then and then we can just work around everything. It's beside the Umbrian while Espion is so weak for Espion. I love Espion. Don't get me wrong, but. OK, the sludge bomb. Do a nice work. And as they yawn, we knew it was coming. We knew it was coming. We knew it. I knew it. It could double up into the Umbrian the next turn. I guess it's unlikely that Umbrian has protect. But it's always these kind of, you know, like in a common set, Umbrian never really has room for protect. But it's always these kind of builds that you see as a protect. But I would say it's more likely that the Sylveon protects here gets away from the potential sludge bomb that's that's really kind of looking like it would go into that slot. So OK, we get the battle cancel, which is which is excellent, excellent news for for me for you guys, because we don't really want to see that. We want to see some more meta teams. Anyway, good game to my opponent. We'll jump straight into our next match of today's episode. OK, next up today, we have a Reggie, a lekkie and Togekiss, Ferrethorn, Sableye, Enti and Kyoga. So an interesting kind of Kyoga build, not kind of common Kyoga build that you've seen with like Tornadus, but you do have another prankster user here in Sableye. It's got Faker, got Qash, big things to kind of note here. Obviously, taunt as well to kind of shut down as be controlled. Got redirection with that Togekiss, which is going to be another kind of layer to protecting the Kyoga, especially from something like Rillaboom, where the Togekiss has a really kind of good matchup against us. Enti as well gives us a few issues. I think probably here we want something like Reggie, a lekkie, Rillaboom, like a Tornadus is good here. Kind of really doesn't care too much about what's on my opponent's team. I mean, the only ground type attack that potentially could come out here would be from something like Enti, Bulldoze, Stomp and Tantra, maybe. But I very much doubt it. I think we want Rillaboom for the Olga and then maybe our own Enti as well, you know, because it gives us that double kind of layer against something like Ferrathorn and with the dragon typing on a Tornadus, we don't worry so much about Kyoga, especially if we get like one cosmic power up or kind of, we're kind of good to go. Tornadus gives us cover against the Togekiss as well, which is nice. And we've got the Flamethrower, which helps us against Ferrathorn, which could be a little bit tricky otherwise. So, let's see what my opponent brings. Okay, Togekiss, Sableye, what are we going to see here? Well, we led pretty well here. I think the thing that we need to be like a little bit mindful of is like that the Sableye does carry Fakeout and it could potentially Fakeout turned us this year. It could stop us going for something like a cosmic power with Tornadus. So, it's got a lot of ways where it could shut us down. I think we, did we just Volt switch out onto the Togekiss and just get a cosmic power while we can, I think, because then kind of gives us that stability going forward in the match. Fakeout coming out into the Red Jaleck, which is fine because, yep, that's that's all right. Get the cosmic power off, which is great. And that'll just weaken the the Dazzling Gleams that are potentially coming out from this this Togekiss here. Oh, throwing out the Yorn already. Okay, well, that's not ideal for us. But we can we can manage with that. I think we get another cosmic power up rather than attacking here because, yeah, it's going to give us just a little bit more longevity when we do eventually go to sleep. And you've got powerhouses that could come in, like Kyogre, and we want to be able to just kind of soak those attacks up a little bit better than when previously. And we're seeing a protect here, unless we get taunted. Not taunt coming out. We're going to see what we're going to see if our play. What's this Sableye doing? We're getting another cosmic power off, which is good. Our play, yeah, into Eternatus, but yep. I mean, it's just it's just tickling, tickling us right now. And we will go to sleep. But I mean, we kind of set ourselves up well to kind of deal with this sleep. Like I said, I think now, did we see the quash come out? Potentially. I'm just going to sludge bomb and vault switch into the Togokris slot. Be interesting to see if it's got Dazzling Gleam or Air Slash, or if it's got both of those, you know, I wouldn't have thought so. Because you think like it's probably got Yorn, Protect, follow me. And either Dazzling Gleam or Air Slash. Makes sense to have the Air Slash. There's the ally switch coming out. I mean, I don't really mind this too much. We'll get some nice damage onto the Sableye, which is always going to be something that we want to try and get rid of anyway. And I think probably want to get, we want to get, I don't want to get really booming just yet. I think it's a good way for us to deal with the Kyogre in a late game. So that end time makes a lot of sense here. I'm going to be able to come in and disrupt with things like Snarl if we need to. And yeah, if it is a Dazzling Gleam, I mean, we take that.  Two cosmic powers, nothing's taken this Eternatus down. It's ridiculous. All right. Well, we go for a Sacred Fire into the Sableye and then we'll just sludge bomb into the Togokris. It's likely that the Togokris, well, I mean, it's pretty hard. My opponent's got like quite a passive like combination out on the field at the minute. You know, you can see the damage that they're going to be able to do with something like Dazzling Gleam. It's not really going to be kind of cutting the mustard here. So they really want to probably adjust their bold position. I think even a Sacred Fire in the rain will take down that Sableye. So if Kyogre does come in here, I think we're not in a terrible spot anyway. And if we get the wake up with Eternatus, that's a bonus. We get the sludge bomb into the Kyogre. So that damage would be really useful. Okay, Sableye just got nothing better to do, but go for those ally switches, I guess at the minute. Sacred Fire, the burn here would be nice if we can get it. But Eternatus is like on the ticker. It's going to wake up at some point. We don't really want to sacrifice anti-just yet. So I'm going to go for sludge bomb into Kyogre and just switch into the boom. Because then we got Gracie Glide. We can go after the Sableye, just get rid of that because it's a bit annoying that it's just sitting on the field. We know it's got stuff like File Play, Fake Out. I don't know what else it's got. Do we? Do we? Ally switch, of course. Yeah, that's the only button it's been clicking. So let's see. Let's see what happens here. But we're probably going to take a walk spout, I would imagine. Maybe. Is it got Qash, do you reckon? Maybe? I don't know. Sableye is such a hard Pokemon to play against because it is especially in a best of one. It is just, you know, you're just guessing a lot of the time. And the Togokis comes back in. Okay, well, that's all right. We take three turns of sleep. The Blizzard. Nice play from my opponent. Scouting out the Rillaboom coming back onto the field. Yeah, really nice, really nice play. But the turn is just taking that pretty well. We do have the active fake out this next turn. So that kind of helps us out a bunch. I think what we'll do is fake out into... I mean, the Dazen Gleam is a bit annoying. But I mean, the Togokis probably protects here. Fake out the Kyogre. We don't really want to have to contend with another Blizzard, especially on Tarilla. Even though that we've got like Regi Alecki in the back, I think Eternatus wakes up here. We get the Sludge Bomb. Yeah, they're going to go follow me anyway. Okay, well, that's all right. I mean, Rillaboom dodges a bit of damage. Yeah, we've got the wake up. So two Sludge Bombs should get the... Yeah, and we'll get the... Yeah, so this is... We kind of want the Grassy Train to go away here because we want to be able to get the Togokis and then the Grassy Glide into the Kyogre the next turn. But I guess we can just protect Rillaboom here and then just get rid of the Togokis because they have to follow me, I think, to protect protect the Kyogre here from the Grassy Glide. I think it makes the most sense. And then once we've removed that Sleep Threat, we're kind of all right. But just Cosmic Power is just a ridiculous move.  So we'll protect. We'll see the follow me, I think. Yeah. And the Ogre probably goes for another Blizzard. And it's got the chance to miss, you know? So get rid of that threat. And we've got to contend with... Fake Up from the Save Light coming in the next turn. Another Blizzard coming out. But these Blizzards are going to run out of PP because, you know, unless a Max does hit, though... Are you kidding? Are you actually kidding? Are you kidding? Are you kidding? Are you kidding? Are you kidding? It was going to happen, wasn't it? Inevitable. All right. Well, the Freeze comes out. It's always a bit harder to take, you know, when the Blizzard's not got its 100% accuracy. What is it? Like 70% out of Hill? And to get the Freeze as well. Okay. Well, oh, Entire comes in. That's interesting. Are they going to... They're not going to allow us. They're not going to allow us to go for Grassy Glide here, surely. I mean, we don't... I'm going to just click the Grassy Glide button and Sludge Bomb. Sludge Bomb into the Entire. Probably see the Kyogre protect here, walking into this. And then Sacred Fire. But Sacred Fire can miss as well. It's not 100% accurate. Do we thaw? You know, that's where we need to get our Entire onto the field. And Sacred Fire... Yeah, they take us down. But I mean, it opens the door for Regi Alecki to come in. And then I think we're going to have to end the game by Sacred Firing our own... No, I think what we could potentially do now is get Entire in, Sacred Fire our Attornitus just to thaw ourselves. And then Regi Alecki and Attornitus can kind of clean this game up for us. Yeah, let's just thaw ourselves right now. Because it's kind of annoying that we are frozen. So let's Sacred Fire our own Attornitus. Let's go for... Well, we can't really do anything because we're going to move after our Entire. But I mean, if we thaw, that's great. Be the case here where we thaw out and then we Sacred Fire ourselves for unnecessary damage. Okay, well, we're thawed, so it's all right. Snarls aren't great. We're going to take a water spout and it's probably going to kill our Entire, but... Oh, it's Origin Pulse. That'll kill us, I think. Maybe not well in the rain. No rain. Yeah, it takes us down, whatever, regardless. But we've got Regi Alecki to come in. The Free's definitely not ideal, is it? Like, not in the slightest, you know? But what can you do? What can you do? You could just deal with it when it comes around. So, Alecki going to come in. I think we need to kind of protect Regi Alecki a little bit, you know? I think we go for the Sludge Bomb into the Entire, protect. Because I think they'd probably protect and snarl in this situation. And we'll Sludge Bomb into the Entire. God, Eternatus has not had a great time in this battle. How's it the status effect? I've been terrible. Right, well, what are we going to see? Like I say, the Kyogre is going to... Like, the thing is, like, you can just pee-pee stall with Eternatus. And I don't think my opponent's got a way to actually take Eternatus down now, even if they keep snarling us, you know? It could always get a crit, though, couldn't it? Critical hit is always a thing. Let's see.  Click some buttons. So, we protect with Regi Alecki. Oh, the Entire reveal and protect, which is interesting. And a double protect. Okay, Kyogre. Okay, well, we know it's not Soldves, so we can probably just double into Entire this next turn. Because I think the Kyogre switches out here. Is this a Kyogre switch out? It has to switch out, right? Yeah, we Thunderbolt and we Sludge Bomb. And hopefully that is enough to get it. It'd be interesting to know what items on the Entire. So, I'll be full of regret here if the Kyogre stays in and just Origin pulses, but it's just a knockout bait at this point, right? So, my opponent really should switch it out to the Sableye, and then you can get the rain back up. So, it makes so much sense to do that, yeah. Here we go. And if we can get the Entire here, we're minus one after the Snarl with Attentus, but we are Magna Boosted. Yeah, it should be in range. Yeah, okay, that's perfect. Now we're in business. Now we're in business. And now the Kyogre can come back in. But we're all right, we're all right, because we can Sludge Bomb the Sableye. I think there's a turn. Do we, do we, do we worry? Yeah, I mean, it's just annoying because we know they've got ally switch, right? So, that makes it a little bit more frustrating to have to deal with, I guess. Protect because there is a fake-out pressure there. Sludge Bomb into the Sableye. And hopefully that's enough to take it down. It's not got a lot of health left. And then we can just T-Bolt. T-Bolt, well, won't T-Bolt be enough for the Kyogre at a margin from this range?  It's kind of a good example to show, like, when your opponent hasn't got that ground type stab to kind of really, really go nuclear on something like Attentus. Wow, you fake-out into Attentus. Predict in that switch, that's good. Please don't freeze us again. I can't cope with another freeze. Can't cope with it. Can't cope with this. What is this? What is this? We know we're going to see ally switch. We could play the game of just electro-webbing. Oh my God. Oh my God, I can't believe this. They're going to, they're going to, they're going to ally switch. They're going to ally switch. Let's thunderbolt into the Sableye slot. And even if we don't, we can try and recover. We should throw out at some point, right? Oh, they're cautious. Okay, well, that's their last move. Yeah. Oh God. What is this? Let's see what an Origin Pulse does. Yeah. Okay, well, Quash coming out.  My opponent hasn't missed a single attack yet. So, you know, it's, this is brutal, brutal. What have we done to deserve this RNG today? It's not like we've been, well, I mean, the turn is this, you know, there's always an argument when you play builds like this, teams like this, you know, you're sitting on the field for a lot longer, you're taking a lot more attacks. So naturally you're going to take a lot more RNG. It's going to come into effect, you know. So that is one of the drawbacks with this sort of, with this sort of team. So, oh man, we need the, we need the recover. We need to throw out. Come on to two freezes. And three turns of sleep. I thought this would be like a really short match, but obviously not. Here we go. Come on. Let's, let's, let's do this. We kind of need an Origin Pulse to miss. It'll be, it'll be handy, handy if an Origin Pulse missed. We need to, we really need to, oh my God, I think we go down to the next Origin Pulse. This is going to be a tragic way to end this, this episode. But sometimes when the game doesn't want you to win, you do not win, do you? So, I mean, we thought out, we get the recover. We're back in this. There we go. That's what we want. Okay. Justice. No miss though. Origin Pulse. Come on. Right. There we go. Justice, Justice has been almost served up. We need to get rid of this save line next. And then that Kyle, there is not an issue. The rain stops so that Origin Pulse is not going to be as powerful or potent. And then we can remove the save line. Looks like we're only going to get one this game in today. You know, I mean, at least we've got the evolution team, right? But it's, it's going to be, I don't want to put up a 40 minute video today. Um, now I like to try and keep the videos around 30 minutes. Bloody allies, witch. Come on. It's a must for strain game.  No poison. Skulled. I want to get that burn, I think. I'll probably get it. No, unless they've got every other status condition. Go on, you know. Um, let's just, let's just go for the save line. I won't rid of the save line. I'm not, not your friend today, save line. There we go. No ally switch. Get rid of you. Ah, it doesn't even. But we get the poison. Okay. That's what we need. I knew it wasn't. It's not very effective. There's ghost typing. Kyogre is going to be, okay. There's the burn. We knew that was going to happen. We knew it. We knew it. Um, we probably want to recover this next turn. Just to, uh, to see out this game. Save like gone. No more ally switch. No more shenanigans. And then, yeah, we just recover off and then we can, we can go for this. I mean, this is a, it's a good thing and a bad thing. I mean, do you want games where you've got a Pokemon that is like near impossible for Pokemon like Kyogre to, to deal with? And in that respect, it's great. But in the other respect, if you're playing the ladder and you're like every game, every game is not going to be like this. Let's, let's admit that. Like this game should have been over a long time ago. The multiple RNG hiccups that we've had make this a little bit frustrating. Three minutes left. Let's see some, uh, protecting coming out. I think from my opponent. So let's, we've got plenty of time left. We can just recover this off and the battle was canceled. Finally, finally. Good game to my opponent. I guess, I guess. Anyway, friends, that's today's episode. I'm going to jump over now and get us a rental team for today's team. And, um, we'll be right back. Friends, here is the rental for today's team. I hope if you do try it out, you have a way better RNG than what we had in today's episode and you have a great time using it. I think it turned out this is an incredible Pokemon. I think it's a lot of fun to use. And I think if you do try it out, you'll enjoy the team. You can see that we didn't really get to feature the lander today, but it is. You kind of standard set with the scarf, the earth power there, earthquake and rock slide you turn. And then the rest of the teams pretty self-explanatory. You've got speed control there on the Suicune. So you can really disrupt teams between that and the entire with the snow support there. You've got the tailwind, icy wind as well for just that extra speed control support. It comes out against Kyogre. I mean, this team does really well against stuff like the kind of standard Kyogre teams. You've got to be careful against opposing kind of landerists. Because obviously it will give the turns just a little bit of a hard time, but the beauty about a turn it says it's going to have to be the majority of things in the format. So it's going to normally be able to get that cosmic power off before an opponent can attack. So at least you've got that kind of buffer to help you out.  It can give you a few issues, but you do have the fake add support with the roller boom that can kind of mitigate that to a certain extent. Anyway, we'll wrap it up there. Like I said, it's been a little bit longer than what I thought it would be today, and I thought we'd get a few more games in, but two freezes of whatever it was in the end. Who knows? Hope you've enjoyed today's episode. Have a great rest of your day. Take care of yourselves more than anything. I'll catch you all again for another episode very soon. Until then, take care. Bye-bye.