Good afternoon. Today is October 5th, 2020. How can it be October already? It's crazy this year is just flying by the year of COVID. We are so delighted and honored to have a very special guest on our show about and about today. A title of our show is Bear vs. Lewin, Marriage Equality Case, and our tagline is LGBTQ rights, pre and post Bear vs. Lewin. We are honored to have Justice Stephen Levinson, who's retired from the Supreme Court of Hawaii, who wrote the opinion of the court there, and I would just like to read a little bit about that so our viewers have an idea of what's going on there. In 1991, a lawsuit Bear vs. Lewin in the Hawaii Supreme Court held the denying access to marriage to same-sex couples amounted to sex discrimination under the Hawaii Constitution Equal Protection Clause. At that trial, the Director of Health would have the burden of demonstrating that the state had a compelling interest in the otherwise prohibited sex discrimination clause. This ruling created an enormous shift in the cultural landscape, setting off a series of events that culminated in the US Supreme Court's 2012 Windsor and 2015 Obergefell decisions, recognizing marriage equality nationwide, and it's had impacts worldwide in the LGBTQ rights movement. Today, we're going to discuss some of the background of the case, the rulings involved, the backlash, and the progress we find ourselves today. If time will look at some current climate forefront challenges to equality on the edge here for LGBTQ folks and elsewhere, we are not going to have time to do that because there's so much to unpack here, but Justice Levinson is a graduate of Stanford and then University of Michigan Law School, where he received his JD in 1971 and came to Hawaii shortly after that, worked in a couple of private firms and then served on the Hawaii Supreme Court from April of 92 until retirement at the end of December 2008. Justice Levinson authored 271 published opinions of which 231 were published opinions of the court, and he did write the lead decision in Bear versus Lewin, which was the first appellate court decision in American history to hold that a state's marriage laws were presumptively unconstitutional or discriminatorily prohibiting same-sex couples from marrying. At the time, let's remember, this is not that long ago, same-sex marriage was legally recognized nowhere in the world, the bear decision catalyzed the push for marriage equality in the US beyond, and it is now the law of the land of the US, virtually the entire Western hemisphere, most of Western Europe, South Africa, Iceland, New Zealand, Taiwan. Justice Levinson has authored numerous opinions addressing the application of statutory constriction, lawful limits of government intrusion and private affairs of individuals, legitimacy of police interrogation, searches, seizures, and other matters, and he has very storied record and serving on many different law-related and non-related entities, and most recently the Honolulu Police Commission. And so thank you so much for joining us today. I'm sorry for that long introduction, but it's a pleasure and honor to have you here, Justice Levinson. Well, it's a pleasure and honor to be here and to have been asked, and I'm really looking forward to this discussion. Well, you know, it's here today that we're, it's 2020, so when was, tell us about the, what's the background of the case of Bear versus Lewin? What was the situation that led to that case going to the Supreme Court? Okay, so this is the Bear story. Toward the end of 1990, three couples, two of them, woman, woman, one man, man, appeared at the Department of Health on Punchbowl Street and asked for marriage license applications. The clerk of the, of the, at the Department of Health was flustered. That had never happened before. So the three couples were told to come back later, and they came back later. They were handed letters that had been signed by the director of the Department of Health, Jack Lewin, a very fine guy, but probably written by the then attorney general for Hawaii, Warren Price, also a very fine guy, telling them that they couldn't have marriage license applications because they were ineligible to marry being same sex couples, and therefore there wasn't any point in giving them applications. They looked around for a lawyer, had some difficulty, lamb to legal, turned them down, didn't think they could win. The American Civil Liberties Union of Hawaii turned them down, didn't think they could win, but they found Dan Foley, who had been previously the legal director of the ACLU of Hawaii, and he agreed to take their case. So they filed a lawsuit in early 1991 in the state circuit court, the trial court, and they claimed on two grounds, one under the state's equal protection clause and two under the state's due process clause, that denying them access to the legal status of marriage was unconstitutional. And therefore they were entitled to receive marriage license applications. They were otherwise eligible to marry, but for the fact of their genders, and therefore they asked for judgment in their favor and against the state. The Department of the Attorney General representing Jack Lewin, the director of health, rather filed an answer to the complaint denying any obligation to give the three couples marriage license applications. But then immediately after that filed what's called a motion for judgment on the pleadings in the circuit court. And what the motion basically said was that assuming that every factual claim that the plaintiffs lay out in their complaint is true, even then they can't win under any legal theory, and therefore judge you should enter judgment in favor of the director of health and against the plaintiffs. The circuit court judge happened to be Bob Klein, a very old friend of mine who came up to the Supreme Court with me from the circuit court, and he was persuaded by the state's argument. And therefore he entered judgment in favor of the state and against the three couples. The three couples then filed an application for a writ of certiorari in the Hawaii Supreme Court. And that's the way normally in the course of a regular lawsuit, the losing party at the circuit court level seeks further review either in the intermediate court of appeals or in the Hawaii Supreme Court. Our court granted the application for further review. And that's basically when I came on to the court. I had been on the court for about four months when a staff attorney circulated the calendar for the next week or the next months oral arguments. 15 different cases. And either number seven or number eight on that list was Bear V. Lewin. I had never heard of it. I didn't know what the issues were. I two days before the oral argument was scheduled, I got the file out, I read it, thought the issue was exotic. It had never, the matter of same sex marriage or the idea of it was something that had never occurred to me. So I hadn't thought about it one way or another. My law clerk or one of my two law clerks submitted a memorandum working the case up for me analyzing it and making a recommendation. And based on her memo and my reading of the record, I was persuaded that denying these couples marriage license applications probably violated the state's equal protection clause by way of sex discrimination. Because if John and Jill apply for a marriage license application and are otherwise eligible, they get one. If Jill and Jill apply, they don't. If John and Bob apply, they don't. Why? Not for any reason having to do with their sexual orientation, but purely because they are not a potential groom or a potential husband and a potential wife. Dan Foley was sophisticated enough in the complaint that the three couples filed in the circuit court not even to allege his client's sexual orientation. So nowhere in the record that came up to us on appeal from Bob Kline's order denying or granting the motion for judgment on the pleading was there any claim of the sexual orientation of any of the six plaintiffs. But the fact that they were three same sex couples was claimed. And that then made it easy to decide the case based on sex discrimination under the state's constitution. Fortunately, the only issues that were involved in this matter were state law questions, not federal questions. And so there was really nothing that the United States Supreme Court could do about our opinion. So that's how it came up and that's how it was decided. The court was very, very divided on the question. Initially, I wrote the lead opinion, but it was joined in by only one other justice. Initially, Associate Justice Ron Moon, by the time that the package of opinions was filed, Chief Justice Ron Moon, for reasons of his own, the Chief Judge of the Intermediate Court of Appeals, James Burns, who was assigned to the appeal by reason of vacancy, concurred in the result of our decision, but for different reasons. Intermediate Court of Appeals Judge Walter Heane, who was assigned temporarily to sit for oral argument on the case, dissented, disagreed with our opinion, agreed with the decision of the circuit court below, and retired Justice Yoshimi Hayashi, who had been assigned to sit as a substitute judge, had turned 70 years old by the time the decisions were filed and therefore was prohibited by law from signing any opinion, but he insisted on a Roger Maras sort of asterisk appearing on the caption of the opinion after his name, which said at the bottom of the page that if he had been allowed to decide the case, he would have joined in Judge Heane's dissent. So it was basically a 2-1-2 decision, which became a 3-2 decision shortly after that, when the state filed a motion for reconsideration of our decision, or in the alternative for clarification of what was supposed to happen next, and by that time Justice Paula Nakayama had joined the court. And so CJ Moon replaced Judge Heane with Justice Nakayama, Justice Hayashi was out of the picture by then, and on reconsideration we clarified that we meant what we said, but that what had to happen next was that when the matter went to trial in the state trial or circuit court, the burden would be on the state to demonstrate a compelling interest in the sex discrimination that would justify what would otherwise be unconstitutional, a very, very, very difficult burden to meet.  We have an interesting Equal Protection Clause. The Equal Protection Clause that appears in the 14th Amendment of the United States Constitution basically says everyone's entitled to the Equal Protection of the Laws, and that's it. That's all it says. Our Equal Protection Clause basically says that all people are entitled to the Equal Protection of the Laws and the enjoyment of their civil rights and may not be deprived of them based on race, religion, sex, national origin, and the like. Sexual orientation was not mentioned, but there's a story about that too. If we had had to reach the issue, at least in my opinion, we would have ruled that sexual orientation is a subset of sex and lives within it, inside of it. The history of the Constitutional Convention of 1978 bears that out, no pun intended. If I need to get it, I can walk over to my bookshelf and get it, but we didn't have to reach the issue of sexual orientation because it wasn't alleged and it wasn't at issue, at least in the record before it's on appeal, but sex very much was. That argument's been used very recently, I think even last year at the federal level. Last June, that's right. In the Title VII, employment discrimination on the basis of the fact that someone was a homosexual and someone else was in the process of transitioning from woman to man, there was a third. The funeral home case and it was based on gender or on sex. It was an interesting strategy, which you employed, obviously, successfully. I was overjoyed at Justice Gorsuch's opinion because if I had had to write the opinion, I would have done it exactly the way he did. And it's interesting because it was in a theoretically more conservative court that that came up. A lot of these questions about the state and the arguments for the state, what were their arguments that they put forth to try and have you rule in another way or the court to rule in another way? Well, on appeal and remember that this was on a very minimal record. No evidence had been gathered at all. It was simply what was alleged in the complaint, period. And so the state's main argument was that there's no discrimination involved because by its very nature, marriage is a union between a man and a woman. And so there's no sex discrimination when you deny access to marriage to a same-sex couple because by its very nature, marriage can't be a union between two people of the same sex. That was the first argument. And the second argument was that assuming that they at least get to first base on that issue, there is a compelling interest in restricting marriage to opposite sex couples. And that is that children are optimally raised in an environment where there is a mom and a dad. And therefore that in itself justifies the state discriminating against same-sex couples. Those were the two primary arguments. Among some other smaller ones, which had been then as evidence poured out then, which we saw again and again and again, especially on the national stage, I thought, by Theodore, who was the fellow that took the cause of the brilliant lawyer. Oh, Ted Olson. Ted Olson and David Boyes. David Boyes. It was wonderful to watch that. And I think that people need to understand that your ruling and the court's ruling here set off this chain of events. It didn't exist before this ruling. And it had an effect on society. So what happened? What happened when your ruling came down? What happened in society? What happened in America? I should say that I was fairly naive in approaching the bear appeal. I wasn't thinking beyond the state because the issues were purely questions of state law. And I imagined that the decision was going to attract a lot of attention. Around the country and probably around the world. But I really didn't think a whole lot about what immediate effect the decision would have on the rest of the country and not to mention the rest of the world. But it didn't take the United States Congress very long to hear about our 1993 bear decision. And the question then began to arise, what are we going to do if same-sex marriage actually becomes the law in Hawaii? Same-sex couples are married in Hawaii and they move to the mainland. And for people that may not know the Constitution, why is that an issue? Because ordinarily, under the full faith and credit clause of the federal Constitution, one state has to respect the law of another state and defer to it when there's a clash between its own law and the law of another state when a dispute arises initially in the other state. So that if a same-sex marriage couple had moved, say, from Hawaii to Missouri and Missouri didn't recognize same-sex marriage, what was supposed to happen then? And the United States government at the time did not recognize same-sex marriage. Dan Foley, in his briefing on the appeal, listed every single federal law that dealt with the rights and benefits of marriage and all of them referred to the man and the woman or the husband and the wife. And how many rights and benefits were there? Do you remember? There were over a thousand. And so in 1996, around three years after the bear decision came down, the federal Congress enacted the Defense of Marriage Act, otherwise known as DOMA, which consisted of three sections. The first section was essentially devoted to the bear cake and it recited legislative findings. And in effect, what section one said was this might happen in Hawaii. And if it happens, same-sex married couples may come to the rest of the United States with their contagion, their contagious marriage and infect the rest of the country. So we have to do something about it. And so the Congress did two things about it. In section two of DOMA, Congress decreed that if state A recognized same-sex marriage, state B was not required to. Oh, okay. State B would not have to recognize the same-sex marriage consummated in Hawaii, even if the married couple moved to state B. And what section three of DOMA did was to say, and not only that, the United States government does not recognize same-sex marriage so that even if Hawaii says you're married, we say you're not for purposes of federal law and the rights and benefits that flow from federal law. Like getting Social Security or anything else. Survivor benefits, yes. That kind of thing. Or as in Edie Windsor's case, having inheritance rights when your same-sex spouse dies. Right. Like you said, over a thousand rights and benefits. And then many states enacted their own DOMAs, including Hawaii, which must have been pretty bitter pill to see that happen. It was. And that, so when Bayer came down, the Hawaii legislature went into a tizzy. And there was a lot of sackcloth and ashes and rending of garments over what to do about it. But ultimately what happened was that the legislature proposed an amendment to the Hawaii constitution. This was after a lot of negotiation had taken place. Some of which involved Dan Foley very centrally. And we now know in retrospect we can thank Dan Foley for the amendment to the Hawaii constitution ultimately being presented to the electorate in the form it was. But what it said in effect was not that Hawaii does not recognize same-sex marriage. Didn't say that. What it said was that the legislature shall have the sole prerogative or shall have the prerogative to restrict marriage to opposite sex couples. Which basically sawed off at the knees the court's equal protection analysis basically said the equal protection clause no longer has anything to do with the right to marry in Hawaii. At least when it comes to the sex of the couples who want to get married. We the legislature say whether marriage is restricted to opposite sex couples or whether it isn't. And that amendment went on the ballot in November 1996 and was overwhelmingly ratified by the good people of the land of Aloha by a margin of roughly 70 percent to 30 percent. Which was the rate the national rate as as determined by various polling in terms of who favored same-sex marriage and who opposed it. And so everybody assumed at that point that that was the case was closed. That there would never be same-sex marriage in Hawaii because obviously the legislature would never change its mind and allow it. Well little did they know. A lot of water went under the bridge after the amendment to the Hawaii Constitution and we can talk about that if you want to. You know I would love to talk about it and I think we're going to have to wait for another show on this because this is so unbelievably this has been a half an hour already that's gone by. But I think that's a teaser for our next show and if you would if you would be so kind as to join me and and continue the story I would be honored to pick up here. Well let's make it a series. Okay let's make it a series because this is so important for us to understand this ruling and where we are today and the importance of the courts and of and and how we are have become a more perfect union and how our rights have been expanded as a peoples and it's not just gay rights but it expands our all of our rights and your role in this was so critical and and just the story is so interesting as well. So when we come back without without being arrogant I mean it's simply a fact that the bare decision changed the history of the world. It changed the history of the world and I think that is a absolutely fair thing to say and so we're going to find out more about that when we come back for the next installment of this because we didn't get through two of my questions that I got a ton of them but I will just give a spoiler alert that we can get married today in Hawaii and probably that ratio of the 70-30 has flipped and it's probably 80-20 now in the opposite direction. That wouldn't surprise me at all. I don't know but I will try and find that out. So Justice Levinson I would like to thank you so much for coming on today. I'm looking forward to of continuing this because it's it really is a series so that we can understand you know what's happening right now what's continuing to happen. We had a ruling about Kim Davis today or maybe not a ruling but a denial to hear her case at the Supreme Court. There's a lot of issues right before us right now. And some very interesting thoughts expressed by Justice Clarence Thomas. Very interesting. We'll definitely want to talk about that later. Yes and and I would say disturbing thoughts but we couldn't we'll pick those up next time and anyway for our viewers out there if you have questions about this please send them along because we're going to continue this discussion. So for today I would just like to thank you for being here Justice and we will look forward to our next installment of this Bayer versus Lewin and your impact on it and where we're going from here. Thanks so much. It was a pleasure. Thank you. Aloha everyone.


Acceptance is not finding a way to turn off your fear or even to turn it down. That's not a thing. You might be working overtime to try and find a way to feel less afraid of your anxious sensations or anxious thoughts or just the state of anxiety or fear itself. So acceptance has nothing to do with finding a way to turn off your fear magically. Acceptance isn't figuring out some sort of special method for hating your anxiety any less. You are totally allowed to hate it as much as you want. So don't worry that you have to somehow find a way to stop hating your anxiety so that you can accept it. That's not the way this works. Acceptance is a precursor to less fear. Acceptance is not the result of less fear.


So this video isn't particularly related to anime Shaden, but it is something the patrons overwhelmingly voted that they really wanted to see. So here we go. Now, for the record, I absolutely hate retopology.  So I went on a life journey to find the most efficient, fastest retopology workflow possible. And that's what I'm gonna share with you today. So if you're sculpting in Blender, there's an add-on that you should really invest in called Quad Remesher.  J429 has created an excellent tutorial, explained it in depth, but the gist of it is, after you finish sculpting, vertex paint any areas with related geometry, then decide how many polygons you want and press the remesh button here. You're done. Usually it does 90% of the work for you automatically. Now if you're using ZBrush, it's actually even easier. Instead of vertex painting, just use polygroups to highlight areas of geometry you want to preserve the boundaries between. Then under geometry, go to ZRemesher, usually the defaults are just fine. Make sure to keep groups checked on and decide how many polygons you want. This number is usually in thousands, so 5 equals 5,000. I'm doing a game, so 1 to 2,000 should be more than enough. Hit remesh and you're technically done. From here you export the model as an OBJ and import it into Blender. Now Quad Remesher and ZRemesher are awesome, but they're not perfect. Very often you'll get point clusters that make absolutely no sense. I'll have to manually clean up a few areas and usually it's not too bad, but because of this, usually what I do is I go to edit mode, delete half the object, export it as an OBJ, then bring it into Maya. Then go up to mesh, remesh, again to mesh and this time read to apologize. Set the amount of polygons you want, I'm just going to pick 1500 and if you're having trouble, I recommend uncheck and preserve hard edges and read to apologize. Now because we split the model in half, it's going to work a lot faster than normal and you're done. So automatic topology. And those weird point clusters that sometimes appear in Quad Remesher really almost never appear in Maya's remesher. You can make additional adjustments if you want, but usually it's good to go from here. So that's my workflow, simple, fast, with decent results, which means that you don't have to spend your life read to apologize. So hope that helps and as always hope you have a fantastic day and I'll see you around.


So, we will continue with the one-dimensional flow. So, the governing equation that we had was this and we basically said that we could discretize it using FTCS, right, discretize it using FTCS as Qp at Q plus 1 as being Qp at Q minus delta T by 2 delta x, Qp, Q plus 1, Pp, Q, P plus 1, Q is E p minus 1 Q. I am using central difference, okay, just to recollect what we did in the last class and then we said that if you look at two grid lines, this is at Q, this is at Q plus 1, these were the boundary points, right, I will draw a few interior points just to, I am not going to draw a whole lot of them just for the sake of this discussion, I will draw a few interior points. So, it is clear that we can do FTCS, right, using that stencil, no problem. We have everything at Q and we can determine the value at Q plus 1. The difficulty is when we get to determining the value, right, one shot of the boundary on both ends, on both ends determining the value one shot of the boundary requires values at the boundary, right, it requires values at the boundary, fine. And this clearly in the way FTCS works since we are going to do this and we are going to use them to determine the interior points, this clearly is a problem we have to solve because when we take the next time step, when we go from Q plus 1 to Q plus 2, we are going to have the same difficulty, we are not determining these points, okay. We are not finding out what these values are and what do we need at these places? We need the Q, I need Q at this point, I need Q at that point, I need all, okay. So, because we were in the situation, we decided that we look at the physical problem, actually because so far we have just been dealing with the Choctas, we have been working only with the theory. So, we said the physical problem just to recollect because it is a one-dimensional flow, I remember, right, I took a pipe of length L, right and there was a valve on one end where you place the valve will only determine the initial condition, right. I should not say we will only determine, it will determine the initial condition. So, if you have the valve here, then whatever, this is open, right, on this side to the atmosphere, typically you would have P ambient described on that side. So, the initial condition would be whatever the ambient condition is, right, since the valve is on this side, valve is on the other side, it would be whatever is in the chamber, right. And here, we have total pressure and total temperature. These are typical conditions that you would use, right, if you are performing an experiment and making sense in a gas dynamics lab, okay. And it is not a very exciting, even that experiment is not a very exciting experiment, but still for our purposes, it is simple enough that we can play around with it. So, the physics of the problem requires, as I pointed out in the last class, three conditions, right. Physics of the problem requires three conditions. Describing T ambient here does not really do anything for you, unless of course you need it, the T ambient here you require in order to determine the initial condition, but as the boundary condition, it does not do anything for you, okay. You understand. It is a pressure difference that is going to drive. See, this is just like normally when you say that you have, let me think of a situation. So, if you think of all the sources of power that we have, the most sources of power that we have, where we compress the fuel, air mixture, and we add energy, right. We ignite it, there is combustion, and then there is expansion. The process always involves compression, expansion. You understand what I am saying? If I were just to create a fireball in the open and raise the temperature of all the air, we are ignoring gravity here, all that will happen is the temperature of all the air will go up, right. In order in this room, if I were to raise the temperature, the temperature in the room will go up. There is no change in pressure, nothing of that sort. You actually need, so I need a lower pressure at one end, a higher pressure here, and the pressure drives the air and we extract the energy from the fluid. That is why we always in thermodynamics deal with enthalpy and not directly with pressure or temperature, right, because you need the pressure gradient in order to drive to start the motion, so that you can extract the energy. Having the temperature alone through mechanical processes is not enough. Am I making sense? So, in that sense, it is the pressure difference that is going to drive the flow. It is the pressure difference that is driving the flow. Is that fine? So, in this side, we can measure the total temperature and this total temperature will basically do what? What is that total temperature? Does it determine anything? Do we need it? You go back to your gas dynamics and see why I need to prescribe the total temperature there. So, a P ambient, P not, T not and this problem can actually work using gas dynamics, fine, okay. From the mathematical point of view, we have already said that because we have a time derivative, we have a doh q, doh t term, because of the doh q, doh t term, at t, for some given t, we will take t equals 0, at t equals 0. I need a condition, so I need, I have an initial condition for all spatial locations and I have a doh e, doh x term, right. So, for all, I have a q at t equals 0 and I have a doh e, doh x term, I have first derivative. So, integration in my mind will give me 3 constants of integration, which have to be determined and P not, P not and P ambient are given. So, both physically and mathematically, well determined, okay. It is just that our FTCS requires that I need a q at this point and the q at that point, fine. And consequently, I need to determine something here and something there, is that okay, right. The experiment, thought experiment we are running yesterday was if P ambient was P not, P ambient was P not, as I just indicated, there would be no flow. And if I started to lower, there are some mechanism by which I could lower P ambient, right. If I have another pressure vessel here or something of that sort, I start to lower P ambient, then a flow field will be set up. So, the effect, if I look at the first, if I look at the, this interface, if I look at this interface, valve is open. So, if I lower the P not, P ambient, the effect will be that there will be a u set up here because of the lower P ambient, right. So, presumably this boundary condition communicates itself here through an increase in u, fine. I am just giving you a hand-waving argument.  I am saying here is a way by which we can do it. So, what we do is, from the first interior grid point, maybe I go back here, from the first interior grid point, so whatever I have here, I copy the u to this point, I extrapolate the u to that point, is it okay. So, this is a very naive way of doing this, but this is the first cut. We will see whether, how we can improve, we can improve, right. I copy the u here. You could also copy rho u if you want it, but I will copy the u there. So, what does that give me? At this grid point, I have prescribed P not and T not and now what we need to do is a little gas dynamics, right. Given u that I have extrapolated u, I use energy equation, what does it tell me? One-dimensional energy equation, not the differential equation that we are using, Cpt plus u squared by 2 and if you give me the u and you give me the T not, this tells me that T equals T not minus u squared by 2 Cp, is that fine. And once I have T by T not, I can find P by P not, right. So, from T by T not, I can find P by P not and consequently, I can find P. And given P and T, I can use equation of state, I can use equation of state or I can, I guess I might as well write P equals rho over T for example and find rho. Now you have set, now you have everything, you have rho, you have rho u squared, right. You can calculate everything, you have q tilde and therefore you can find q, right. Is that okay, fine. What about the right-hand side? I have only prescribed at this point, I have only P ambient prescribed at this point, right. I only have P ambient prescribed at that point at time level q. Remember this is not the initial condition, initial condition we knew everything. This is at some time level q, just in case you are wondering what is the deal. That is why it is at time level q, right. So, we have only P ambient at that point. Clearly not enough, I need 3 quantities, right. So, I need to extrapolate 2, fine. What can I extrapolate? The different variations now that you can do, right. There are so many possibilities. Even upstream, there are so many possibilities. You could have extrapolated P instead of u. Am I making sense? So, these are things that one can try out.  So, one possibility is that for example, you say that there are no sources and heat sources, energy sources in between, right. Maybe I extrapolate T0, possibly. I could extrapolate T0 and u. I could extrapolate T0 and u, possibly. I am just making a suggestion, right. The point that I am trying to make is that you need to extrapolate 2 quantities. See, these are boundary conditions that I have to generate. They do not exist. The physics does not provide them. The mathematics is not right now giving me a clue. We will look at it to see whether we can use the differential equations somehow to generate these. Is that fine? So, if I extrapolate the T0, if I extrapolate the T0 and u, what do we get? Again, if I extrapolate the T0 and u, I can find the static temperature. And given the pressure and static temperature, I can find the density. It is the same game. Then you can go through, right. Is that fine? Everyone? Okay. It seems like a rather arbitrary thing to do. It seems like a rather arbitrary thing to do. So, this is something that you can try out. As I said, it leaves scope. So, you can try it, let us say, to extrapolate density and rho and rho u or rho and u. There are various quantities. The thing that you want to make sure you do not do, these are things that you have to be careful with. You already have T ambient here. You do not want to really extrapolate density and temperature, for instance. Because potentially you could violate equation of state at that point. Am I making sense? If the pressure here is different from the pressure here, by extrapolating the density and temperature, you could potentially violate equation. So, you have to be very careful what quantities you are extrapolating. But you could try out various quantities. Some of them may be totally unstable. You may not work at all. You could try out various quantities. But these are something that I thought, okay. We can just start with. Is that fine? Is that okay? Can I justify that? Is it possible for me to justify that? Maybe I will stick with this. Is it possible for me to justify that? Justify extrapolating these quantities. Okay. So, the question is, when can I do this? What are the conditions? Is there any inherent assumption that I have made? I am saying there are these quantities. Can I always extrapolate? Will it always work? Okay. So, let us go back. Let us go back. Remember that this could be written as dou q dou t plus a dou q dou x equals 0. And this could be further decoupled into three equations. I am going to write now component form dou q i carat dou t plus lambda i dou q i carat dou x equals 0, right, where q1 hat, q2 hat, q3 hat are the characteristic variables. We are not going to solve the equation in this form because multiple dimensions anyway it is not going to help us, right. So, that it does not make sense going there. But it is useful to look at. So, what are lambda i? Lambda 1 is u, lambda 2 is u plus c and lambda 3 was u minus c. This is what we found. Is that fine? Okay. Now, we will actually investigate these equations. So, if you look at one equation, if you look at one equation, you have dou q1 hat dou t plus u dou q1 hat dou x equals 0. That says that q1 hat is being propagated along a characteristic. I will just draw a small figure here first. So, at this point, q1 hat is being propagated along the characteristic whose slope is 1 by u. What about q2 hat? q2 hat is being propagated along that. And this is, this corresponds to, so I would not write the 1 by u and so on. I will just write out what characteristic this corresponds to. So, this corresponds to u.  This is u minus c. That is u plus c. Remember, this is x. So, it is travelling faster. This is u plus c. So, if this is u minus c, u, u plus c and all the slopes are positive, what does that tell you about this slope? u minus c, u is greater than c. So, this actually corresponds to supersonic flow. So, this actually corresponds to supersonic flow. That is u greater than c. So, if you are talking about subsonic flow, if you are talking about subsonic flow on the xt plane, you would have u plus c there. You would have u here and you would have u minus c headed out in the other direction. Am I making sense? Because u minus c will be negative. This is for u less than c. This is for u less than c. So, at a subsonic inlet, at a boundary condition, go back to those boundary conditions. So, if this happens to be subsonic, if that boundary happens to be subsonic or if you look at what happens to the first interior grid points, if the flow is subsonic, these are the grid points. If the flow is subsonic, if the flow is subsonic, what happens at this point? So, you have one characteristic which is u minus c. Maybe I will use a different color here, u minus c. One characteristic which is u and one characteristic which is u plus c. Is that fine? Actually, a sort of deliberately drew this characteristic this way. This, if you go think about your stability condition, the grid size is too, the delta t is too large. All of these characteristics should be above that. Just go back, think about your stability condition. But we are going to look at the stability issues in this seriously anyway. But I thought I would just sort of stick that there. I could resist the temptation to have that. So, you could have a u plus c that is going there. Is that fine? So, what this basically says is there is one characteristic that is propagating q1 hat or q3 hat in this case. It is propagating q3 hat in that direction, outward direction. And if I look at the boundary itself, at the boundary itself, at the boundary itself, since the flow is subsonic, I have one characteristic that is propagating q3 hat out. And I have two characteristics that are propagating q1 hat and q2 hat in. Is that fine? And if it is a subsonic exit, I would have the same situation. So, I draw at the last but one point. So, I would have u plus c here. I have u there. I do not know why I am putting arrowheads. And I have u minus c here. I guess I am looking at it. I am putting arrowheads because instinctively I am looking at it as being propagated along that direction. So, in which case then you have q1 hat going out, q2 hat going out, q3 hat coming in. Now, when I look at the problem, when I look at the physical problem that we prescribed, we prescribed p0, p0, two incoming characteristics, two quantities prescribed. That is nice. And I prescribed p ambient, one incoming characteristic coming into the domain, one quantity prescribed. So, the mathematics and the physical, the experiment that they are the same. I am happy with that. We are happy with the way that worked out. And we are extrapolating two quantities. We should be extrapolating q1 hat and q2 hat. Obviously, that would be the way to do it. And we will see how we go about doing that. So, there are two quantities that we are extrapolating that correspond to in our mind now the characteristics u and u plus c. And the one quantity, say I am giving you a rational. It is a hand waving argument. I should what is being propagated or q1 hat, q2 hat, q3 hat. That is what are being propagated. But I sort of say, well, I will extrapolate the u. It is easier to extrapolate the u instead of going through all these characteristic variables. Fine. If it works well, I am willing to live with it. But as I said, we will also look at the legal way to, the proper way to do it. Is that fine? Are there any questions? Okay. So, this is one mechanism by which we can apply boundary conditions. As I said, we will come back to, we will revisit boundary conditions again. It does not end with this. But this is something that you can definitely implement and try out. But before you do that, the question that we have is, is it going to be stable? Is it going to work? Right? Or do we need to do something? It is FTCS. So, is this going to work or do we need to do something? So, we come back to our original equation. How can we, what is the, how do we do the analysis? How can we do the stability analysis for this? Now, we have a system of equation. Earlier, we had only one static situation. Now, we have system of equation. What do we do? Any suggestion? Well, there are different ways to do this. Maybe we will, I will cheat a little. There are different ways to do this. One, you could write it in terms of delta Q's and so on. But let me just, I will just do a little cheat here. So, first, we will use the shift operator, right, and get this E out. So, Q, Q, P, Q, P, Q plus 1 equals Q, P, Q minus delta T by 2 delta x E, P, Q into E power i n delta x minus E power minus i n delta x. Obviously, there has to be a 2 pi by L and so on, right. I am acting as though that I am going to wave my hands a little and say that, okay, L was 2 pi, okay. And I do not know whether you check this out, right. The reason why I said I will do a little cheat is because in this particular case, it turns out that E is, E can be actually written as AQ, right. In other words, you have tried it out but E can actually be written as AQ. It so happens. E can be written as AQ, right. So, consequently, this is going to turn out to be Q, P, Q plus 1 equals Q, P, Q, okay. So, what I will do is, I know I am going to replace an AQ here. I am going to have an AQ here, okay. I am going to have an AQ here. Oh, I mean, okay, minus delta T by 2 delta x.  What is e power i n delta x minus e power minus i n delta x? 2i, 2i sin, I will call it theta where theta is n delta x. As earlier, the 2s go away. So, I can write this as Q P Q plus 1 equals i minus delta T by 2 delta x. So, I can write this as delta x i sin theta A P Q, Q P Q, which of course is a very familiar looking. The only difference is that they are all matrices. It looks familiar but they are all matrices. What now? There is one way to decouple it. We could pre-multiply the equation by x inverse, right, okay, where x is the matrix of eigenvectors. If I pre-multiply the equation by x inverse, and of course I can choose x inverse so that it is normalized in some sense, right. It does no stretching, only rotation. I can take unit vectors, right. x inverse Q P Q plus 1 equals x inverse minus delta T by delta x i, I have that right, x inverse A x x inverse. This is i minus delta T by delta x, little i lambda into x inverse Q P Q, sin theta, oh, sin theta. Very important. How can I forget my sin theta? Remember, x inverse Q is not, they are not the characteristic variables, right. X inverse Q is not, they are not the characteristic variables. Characteristic variables are related through the idea of a derivative. D Q character is x inverse D Q. Characteristic variables are related this fashion, right. This is some strange map. We are just doing some kind of a transformation. Am I making sense? So in a sense this gives me some, I will just give it a name S so that you do not confuse it with Q character, right. I will just give it some name, Q P Q plus 1. So I want you to be careful here, right. Yes, now I just take the, I take the norm. I take the norm. I want the norm of this divided by the norm of that, norm of S P Q plus 1 divided by norm of S P Q equals norm of, this we have seen as an iteration matrix before when we did Laplace's equation, right. System of equations, think back to the example that I did with Laplace's equation. I had a scalar equation. I performed a rotation, right. I had two scalar equations. I performed the rotation and showed that they became coupled, right. Two scalar equations. I made them into a coupled system by performing a rotation. I am doing the opposite here, right. I have a coupled system of equations and I am trying to undo the coupling. I am trying to undo the coupling. So we might as well take the spectral norm. What is the largest eigenvalue is what determined, right. The largest eigenvalue is what determined whether that sequence of iterations converged or not. I could have just used that argument directly but I just wanted to tie it up with this. We have actually done this before, right. We have actually done this before. So what is the largest eigenvalue? U plus C looks like the largest eigenvalue but you do not know the sign of U. You understand what I am saying. So the largest eigenvalue are U plus A. If I use C throughout it does not matter. C and A they are the same, okay, right, fine.   In general mod U plus A would be the largest eigenvalue, okay. In this case it is clearly going to be unconditionally unstable, clearly going to be unconditionally unstable just like it was for FTCS applied to any one of the equations, scalar equations. So I could add, I could add, what do I want to add? I can add artificial dissipation. It will make it upwinding, right. What was the term that I wanted to add? What is the term that I want to add? I can add a mu2 dou square q dou x square, right, and subtract out a mu2 dou to the 4th q by dou x to the 4th. Is that fine? Okay, fine. I usually prefer to write this in terms of, because if you think about the term that we added to eliminate, I prefer to add a delta x square but it does not matter. You will see as you go along here. I rather make it the mu2 delta x square dou square q by dou x square or you can try this delta x to the 4th, right. See if you think there is any difference. And of course the minute I give you two options like this, one of the, one thing, one possibility that catches, I can see a few smiles out there. It is obviously that you can try a mu2 delta x. See what happens, right. See what happens. What are the, right now I am not going to give you any helpful hints on what possible values of mu2 may work, right. You try it out. You see what it is. You already have, remember what we have done for the one dimensional flow, right. You already have enough, you already have enough of a background to figure out what you need to add, fine. The only difference there is there you had only one propagation speed, a. Here you have three propagation speeds, right. That is the problem. You have u, u plus a and u minus a, right. And after adding these, this dissipation term, if you do get a stability condition that corresponds to the CFL less than, CFL condition that is sigma less than 1, which sigma do you use, right. Because there are three sigmas actually. So for the wave equation you only had sigma, right, one sigma but here you have sigma u plus c, sigma u minus c or u minus a, u minus a and sigma u. There are three possible sigma because there are three propagation speeds, right. And all of them have to be less than 1, even if you do this, even if you do this, right.  You add the right amount, it goes back to up winding. Which one do you add? Which one do you, which is the most constraining one? Which of these is the most constraining one? That would seem to be u plus a, right. It would seem to be u plus a.  Is that fine? But remember that you can actually define three of them. So there are three propagation speeds. You can actually define three of them. Are there any questions? Is this fine? Okay. So you can ask the question why are we bothered with FTCS when we know that it is unconditionally unstable, right. Why are you wasting our time when you know it is unconditionally unstable. Fine. I know that we can add this, right. We can do something with it. Let us go to a more sensible scheme that we had. But the only problem there was, what was the problem? BTCS. BTCS, the advantage was, BTCS you may also see it as backward Euler centered space, whatever. BTCS unconditionally stable, it gave you a system of equation, right. And here we already have a system. So now we have to be a bit careful. We have to see what does that mean. So what does we did a semi discretization? If you remember when we did this, delta q by delta t plus dou by dou x, I am going to write this in the delta form E at delta q by delta t at time level pq. And this is at time level pq plus 1. I want to write dou q dou t at time level q plus 1. This equals 0. Okay. And just like we did last time, Eq plus 1 is Eq plus dou E dou t at q by delta t. Times delta t plus higher order terms. I am going to truncate the series here. Anyway I am planning to do only backward, right, backward Euler or backward time, backward step. And again I will use chain rule. E is a function of q. So dou E dou t, I will write as dou E dou q dou q dou q dou t. Okay. So that this equation becomes delta q plus delta t times dou by dou x of a delta q equals minus delta t into dou E dou x. This is at q. We are all at q. Is that fine? Everyone? So dou q dou t plus dou E dou x equals 0. If I am looking only for the steady state, seeking steady state, I will tell you what we will do when we are going to look for a transient. But right now we will look for only the steady state, seeking steady state. So this tells me that dou E dou x equals 0 is the equation that I am actually trying to solve. Okay. So that equation can be written as i plus delta t dou by dou x a acting on delta q is minus delta t into some matrix R. Just like we got for the wave equation, the generalized wave equation. But there is little difference here. What is the difference? Each of the delta q's, each of the delta q's is a matrix, vector. So each of these entries is a vector, is a matrix. So what does this equation look like? If we write it for an arbitrary pq, if we write it for an arbitrary point p, what does this, and if we use central differences to discretize that, this is going to give me delta q pq.  So you will get a tridiagonal system. You get a tridiagonal system. But the point is that each entry in the tridiagonal system is a block, a matrix block. So the general equation will turn out, so you will get a tridiagonal system. What I mean by that is you will get something, so this will be delta q p. So this is the equation p going through. And what you would get here is, what is on the diagonal? There is an identity matrix on the diagonal. There is ap minus 1 delta t by 2 delta x on the sub-diagonal. And there is an ap plus 1 delta t by 2 delta x on the super diagonal. You understand what I am saying? That is the diagonal, that is the sub-diagonal, that is the super diagonal. Everyone, is that fine? And each of these entries, each of these entries is a matrix. Each of these entries is a matrix, ap minus 1 delta t by 2 delta x. Just to make it clear, ap plus 1 delta t by 2 delta x. Those are the entries. These are the entries in the matrix. So if you decide for example to do Gaussian elimination, if you decide for example that you want to do Gaussian elimination. So where in Gaussian elimination you will say divide through by the pivot element, here you have to pre-multiply by the inverse. Am I making sense? Pre-multiply by the inverse. If you are planning to do this, if you are planning to do that, it is better that you factor this ap minus 1 using LU decomposition. There is always this question when you do numerical linear algebra, you know that LU decomposition and Gaussian elimination are essentially the same. LU decomposition and Gaussian elimination, operation for operation you can actually show that they are essentially the same. Am I making sense? You do the elimination part of Gaussian elimination, you end up with a upper triangular matrix. You do LU decomposition, you have a lower triangular, upper triangular, you do a forward substitution of the L, you end up with an upper triangular matrix. You would expect that you can map the two operations together. You actually can. You can show that they are equivalent. You can show that they are operation for operation, you can actually identify that they are equivalent. Fine. So then the question always pops up, why would you choose one over the other? Well if you do LU decomposition, if you factor it as L and U, then you only have back substitutions and forward substitutions. If you pre-factor this as L and U, if you are going to multiply through by, right, the inverse, you could actually do back substitutions, forward substitutions and back substitutions. That is the idea. Fine. That is if you are using, if you are using Gaussian elimination. Even if you want to do Gauss-Seidel, you are doing an iterative method, you may still have to do something of that sort. But of course Gauss-Seidel, the big advantage is the diagonal matrix here is I, right. So Gauss-Seidel is not that bad. Gauss-Seidel it is not that bad. Am I making sense if you are using an iterative matrix, it is not that bad. There may be consequences but it is not that bad. Okay. Is that fine? Everyone? Okay. So then we have only one question left. How do you apply boundary conditions here? You have a system of equations. How do you apply boundary conditions here? In this problem, how do we apply boundary conditions? Let me see where is the best place for us to discuss that. Maybe I will do it here. How do you apply boundary conditions here? So in the application of boundary conditions, we need to maybe look at it a little more carefully. Again, I will draw two timelines Q and Q plus 1. Like I did the first time around, I am not going to choose, I am going to just choose a few grid points. I would not choose a lot of grid points. So it does not become too messy. And what I had indicated at that time is you need a value here that you can extrapolate some quantity from the interior. Say for instance t0 or u or whatever or we said that from here you can extrapolate to u. It need not be from the current time level to the current time level. Right now what we want is we want the value here. So actually you could instead of extrapolating from the current time level to the current time level, you could actually propagate. Now that looks more like, that looks more like our characteristics. You could actually propagate from the previous time level to the current time level. You could extrapolate both in space and in time. There are so many different ways by which you can do this. You can extrapolate both in space and in time. Another value goes from the last but one grid point at the previous time level to the time level to which you are stepping. It is possible. I mean if you are going to do it hand wavingly that is possible. So in a similar fashion even here you could do the same thing. By the way this is just, I am suggesting this suggestion comes to mind only because we are looking at an implicit scheme. But even in the case of FTCS we could have done that. Even in the case of FTCS, even in the case of FTCS you are going to use this stencil. Even in the case of FTCS you are going to use this stencil. You assume at the initial condition this is known. You find all the interior points then you can ask the question what do I do at the boundary and you can actually extrapolate from the current time level to the next time level even in FTCS. Am I making sense?  So the minute you start this, so it is this, we needed the conditions. The conditions were required because of the scheme that we came up with. We have no physical basis by which we can justify this. Right now the only mathematical basis that we have done is though the characteristics are propagating in that direction. So that rationalizes why I am extrapolating. That is all we have done. The question that we can ask is cannot we just directly use the characteristics themselves. Why not just use the characteristic equations? Am I making sense? Why not just use the characteristic equations directly and say that at all of these interior points we use the regular equations and at the boundaries we will do something with the equations. Say in characteristic forms we will allow, we will use the equation in characteristic form to determine what is the boundary condition, what is the equation that is solved at this point. Am I making sense? We will admit that only p0 and t0 is provided here which means that from the differential equation we need one differential equation for one parameter to be solved at the boundary. Am I making sense? And it is the same thing at the right hand end. That is you have p ambient and p ambient provided. You have only one condition given. So two of them should come from the interior. Is that okay? Right? So in the next class what we will try to do is we will try to determine how do we apply these boundary conditions using the equation governing equations themselves. Is that fine? Okay. Thank you.


The first chapter of my book is without death, there are no ashes to rise from.  And you can't do that without ceremoniously.  Breakups have left me suicidal, physically suicidal, spiritually suicidal, emotionally suicidal. And it wasn't until I realized that killing myself would accomplish nothing.  The people pleasing, the insecurity, the internalizing of other people's behavior, stuff like that.  Well, love yourself. You know, do this. I point out exactly how you go about doing that. Write out everything that it is that you are no longer willing to tolerate. Forgetting other people in yourself. And use that as fuel. Sometimes it's the only way to get through to people in that position. And you have to smack them around for them to start looking at things in another way and to give up on the pity party that they're having with themselves, looking to dull the pain that is going on. And we want to help people, but they need to be able to lift themselves up or they're gonna continue that relationship in another form with somebody else. Or worse, how they were treated, they might end up treating their next relationship, the next person they're with in that manner as a sort of revenge, thinking that they're getting better with themselves. To make those changes where they can be a better person and then finally be in relationships that are healthy, change is going to need to be made and growth needs to happen. And I just got a big dose over the weekend of just how people fear change. I had two friends over the weekend that I was hanging out with who both complained of the same thing. We're now all getting older, I'm 48. So they're complaining about how they feel in the morning, not thinking clearly and not being as productive. And both of them, I know don't have good diet. So I mentioned, hey, have you ever thought about taking sugar from your diet? Maybe giving up the soda, the pushback that I had gotten over just that. I didn't tell them to reconfigure their diet and they hit the gym and I was like, if you take sugar out of your diet, I will guarantee you will feel better, you'll look better and you'll think clearly. And that was too much of a change in a task. They both looked at me as if I was out of my mind and then cast me off is a health nut. Well, you have to be a health nut because that's the only way they can continue on with a habit that they know deep down is not really great.  And I talk about this in the book. These are people, whether it's relationally or it's in their diet, they're focusing more on the high of satiation than the shame of starvation.  And we wouldn't believe anyone that said it was moldy. We'd say, there's no way mold could make me feel this good. We're focusing more on the high of satiation than, oh my gosh, how starving did I have to be for that piece of moldy bread to bring me back to life? Life is messy, it's complicated. And the one thing that I always try to be, especially in my line of work, I see so many people and they're like, I got it all figured out. I went through a bad breakup. I lost all my money, I Uber drove, and now I'm doing a TED talk. And you should listen to me. It's not about that. Not only do they set themselves up for never being able to make a mistake because then they get crucified when they do because inevitably we all will, we're human. They're not on the journey with their people, with their community. And so they're creating a dependency. It's like they're creating almost like a cult or a religion. They want people to be dependent on them. They want people to follow them, so to speak. I still get insecure. I still get very defensive when someone says Natasha, put down the ice cream sandwich because I love it. I still get very scared and have times where I don't feel like I could carry on. But the difference between me now and when I was highly toxic myself is that those very normal human emotions no longer permeate to the point of paralysis. That's where you need to get. And I can take criticism, whether it's constructive criticism or it's just fueled in hate or whatever it may be. And I can take compliments too and understand that this isn't about me. This is actually a gift into looking into a window of the relationship someone has with themselves. So when people get defensive about sugar, they're giving you the gift of what's going on between the relationship that they have with themselves. And no one is going to be in a relationship with anyone who treats them any worse than they are already consistently treating themselves.


My name is Chishara Loizel and I'm in Rifle, Colorado. I tried to double up Food Bucks because my son is five and he's on the autism spectrum along with ADHD and combating preservatives is a main way to keep his levels of anxiety down. My experience at the market, the first time I went there, it was very different for me because where I was actually born, we have a market all the time and in Colorado there are seasons and when I went there and I utilized the manager station, I got informed of Double Up Food Bucks and then I got the experience of going there and getting the fresh fruits and vegetables that were local instead of from somewhere else. The impact that Double Up Food Bucks has made in my life is I'm able to give fresh local fruit and vegetables to my son and myself on my extreme limited budget. What would I tell someone who's considering it? Don't guess, just do it. Try it one time and taste the freshness and then you're not going to go back to a can. My favorite Colorado grown produce has got to be the Palo Sate Peaches. Coming from Florida they compare to Georgia Peaches and that is so nice because I am far from Georgia.


The narcissist turns your life upside down. They disrupt or overturn everything that you know and are familiar with. It changes completely. Making you confused or upset. But you always have a choice. You always have an option. But what keeps you enmeshed with them is that when you've been with a narcissist for so long you've been manipulated into trying to adjust to them rather than adjusting to your own needs.  You've been programmed to focus on and attend to them at all times so you don't have the time to look at your own situation and how it is becoming progressively worse. This is why you need to determine where you are now. You need to assess the damage that has been caused already to then be able to accurately predict how bad it will be in the future because it always gets worse with the narcissist. You think you have it bad now. You think you've been through a lot. But just imagine what it will be like in a few more months or a few more years.  They do things in such a subtle way where you don't really notice it at first. They use clever and indirect methods to get what they want until you begin to notice parts of your life falling apart or fading away, which is why you have to focus on getting out of these relationships. You cannot stay in relationships with these types of people. The longer you stay, the more damage you will be doing to yourself. The longer you stay, the more you will lose your happiness and enjoyment in every aspect of your life. You will develop health problems, stress, anxiety, depression, CPTSD, adrenal fatigue. You will develop problems with focus, learning and memory, social communication and interaction issues. You will develop financial issues, sexual problems. You will have all of this to deal with when it is finally over, when you stay with a narcissist for long periods of time.  It will take you a very long time to recover, a very long time until you finally begin to enjoy the little things in life again. You feel like you need to hold on to this relationship. You feel like it's going to be worse if you don't trust your gut instinct or intuition. You don't need to think it over or get another person's opinion. You just know what is right and what you need to do. Trusting your intuition is the ultimate act of trusting yourself. All of the answers you need to get out of this situation are within yourself. Your intuition has been trying to tell you what you need to do. That's why you've been experiencing stress and anxiety. That's why you've been getting depressed. It's trying to tell you that this is not the right situation for you to be in. If it was, you would be happy. You would be at peace with yourself. Your intuition has been trying to pull you out of this situation but you've invested so much into the narcissist.  You come out lacking all of your good qualities, lacking everything you established and worked for.  After you have lost everything that you worked so hard to establish and you've given your life away to someone who didn't even value or appreciate it, you lose motivation and ambition. You don't want to try anymore.  Just like narcissists are and once you've become depressed, it's very hard to get out of that state. The manipulation, gaslighting and mind games will be very damaging to your health and happiness. This is why you have to stop yourself, just to think about what you're getting yourself into. Think about what it's going to be like in a few more months or years.  Don't focus on how you're going to be losing the narcissist. Because in the process of staying with them, you're only going to end up losing yourself and that is the greatest loss you will ever experience in your life.  But the narcissist will move on.  They've messed your life up so they can move on and be completely fine because they know the damage that they've done to you. They leave you in a state where you're no good for anyone else after they've gone. So what do they have to worry about? They don't have to worry about you finding someone else, moving on and being happy. That's how they look at it. They know exactly what they did to you. They know the effects of what they did. They are aware of the mental suffering that you are now experiencing and they know just how difficult it will be for you to compensate for their faults or bad aspects after they have turned your life upside down. The longer you stay with them, the more difficult it will be to reverse the effects of their abusive treatment. Some people never recover from this, but you can recover from narcissistic abuse. And it all starts by removing yourself from this situation. You have to get yourself out of there. Before it's too late, you need to plan how you are going to do it and where you are going to go. You need to put yourself in a situation where you are able to focus on your healing and recovery. A situation where you finally have the time and energy to focus on yourself. There may be a period of isolation, a period of time where you just want to keep to yourself and that's okay. It's completely normal. Just as the caterpillar builds a cocoon and then transforms into a butterfly, you will soon be a lot stronger and wiser and more able to protect yourself against these types of people. You can't change the past, but you can certainly determine your future. Thank you for watching. I hope this video resonated with you. Please like, comment, share and subscribe. Click the bell icon to receive notifications for my future videos. If you would like to donate, my PayPal link is in the video description. Culture and inquiries you can email me and ask for my coaching at gmail.com. Thank you for watching and I'll talk to you soon.