Peak number four, round number three in the world, championship on the way we go. They've all behaved, and gate number two is working the treat. Once again, Martin Vassalik fires himself to the front. Anders Thompson round the outside of Dudek, powers his way into second place. Martin Vassalik out in front, looking good. This is good for Martin Vassalik. Needs a confidence booster. Peak number four is stretching away out in front. Front's good to see Martin Vassalik just settling down. He looks his own self plenty of speed.  He is indeed, he's powering on nicely here. This is a nice ride from him. Not too much overtaking at this stage of the night. The track will evolve, and I'm sure it's going to improve. But for Martin Vassalik, he's not worried about that, because he wins heat four in fine style. Us tonight, away we go. And Bartos Vassalik, wow, that is something special from him. From the inside gate there, Jack Holder coming through on the inside of Martin Vassalik, Vassalik responds and gets his nose in front into second place. Religates Jack Holder back into third place, and that might not be enough for him. Oh, I've got to say, Martin Vassalik did have a lot of speed out of gate turn number four. All of a sudden, very untidy there, through the first and second corner for the second time of asking Bartos Vassalik was very wide indeed, but that was all of a sudden. Vassalik's just about got enough pace there. He's working hard. It hasn't been a straightforward night for him. He really has battled really hard for his points, but he wins heat 20. Three points for him, moving nicely along, comfortably through to the semifinals. Disappoint for Mikkel, Mikkelson this time. Come on, semifinal number two, away they go. Martin Vassalik makes a really good start. Really gets to the first corner in front, Jason Doyle alongside him, and a stop, son. Oh, he's gone down. I thought for a moment he was going to run in the back of Jason Doyle. He picks the bike up, the race continues. It's going to go on now, and Martin Vassalik will move on to the final if he hangs on out in front there. Looking good for Doyle now, Bartos Vassalik running too wide. Going to miss out on the final for the second consecutive Grand Prix. Martin Vassalik, right in out of his skin, through to the final. Chased home hard by the former world champion, Jason Doyle. Green line is on, away they go. Martin Vassalik, what a start from him. He fires himself to the front. Tyre-Wiffen, and now slots into second place. But Martin Vassalik down there, back straight on the opening lap. Absolutely will perfect away from the start. It was a textbook start there from this little action. Jason Doyle back in third. They have indeed, but for Martin Vassalik, that was a stunning start. It's been a terrific night of speedway, right through all the evening for him. He's out in front, he's got this final really wrapped up. Just needs to keep it going. One last turn for Martin Vassalik. As it comes out at turn number four, the crowd are on their feet. Martin Vassalik wins in fine style here in the Marquette tonight. What a performance from him. He'll be absolutely overjoyed with that. 20 massive world championship points for him. Good result for Tyre-Wiffen and back in second place, and Doyle in third for him. Martin Vassalik has come into this meeting and found some fantastic form. I've never seen him ride better, I don't think.


Hello everyone. Welcome to the fifth lecture of this final week of our course on non-linear control. We have been looking at sliding mode control in the last sort of couple of sessions. Now what was sliding mode control? We introduced sliding mode control as a particular kind of variable structure control and we understand that this sort of variable structure implies that the control structure tends to change across the sliding surface and we have seen an example of that. So we have been introducing the whole material on sliding mode control using motivating examples and the example is pretty straightforward. It is just a double integrator with some non-linear disturbance. The non-linear disturbance is assumed to be uniformly bounded for all time and for all values of the state and what we do to begin with is to construct what is called a sliding surface. So the sliding surface is like a one-dimensional for this two-dimensional system.  So essentially what we want to do is we want to send sigma to 0, the sliding variable sigma to 0 in the presence of disturbance. So this quantity is the sliding variable. So that is what we want to do. We want to send this quantity to 0 in some finite time. That is the M in some finite time. So it is actually a kind of finite time control. So we use some finite time ideas as well. So since we want to do that, we construct a Lyapunov function which is exactly in terms of the sliding variable itself. Notice that this is not in terms of the entire states of the system. So it is rather interesting that way. So it is actually something only in the sliding variable. It is almost like saying that I am looking at the dynamics of the system on the straight line. Basically we want to make sure that the dynamics of the system goes to this straight line in finite time. And what we want to do is we want to make sure something like this happens because we remember that this exactly gives us finite time convergence. So we simply compute a v dot just like we are used to doing. And then of course we know that we use the signum function property. We use the signum function ideas. We prescribe a v which is something like this which is something similar to this. So basically we first prescribe a u which cancels out this guy. And then we are left with another knob v. And we choose that knob v in a way so as to compensate for this non-linear disturbance by choosing this gain rho to be larger than L. So once we do that, we get something like v dot is less than equal to minus v to the power half. And therefore we have our finite time convergence. So our entire control looks like this. Now the important thing to note is that that is where we were last time. That is where we finished last time. Is that the control across the sliding surface is rather big switch. Depending on how big my, if you notice on the sliding surface you have x2 plus cx1 that is equal to sigma. And that is exactly equal to 0. And on one side of it you have the control to be minus cx2 minus rho. And on the other side of it you have the control to be minus cx2 plus rho. So depending on the size of this rho, notice that this x2 may not change too much if you just move across the sliding surface. The states are not going to change much because I mean it is not like we are going to move too much in the phase plane. But the point is depending on how big we chose the value of rho, there is a significant discontinuity in the control. There is a jump in the control. And this is what obviously leads to this non-smooth control idea of course. So what happens is because we are not exactly cancelling the disturbance at every instant in time. We are not exactly cancelling or simply dominating it. What happens is that the, even after the system reaches the sliding surface. So this is called the, you know this is called the reaching phase while it is reaching the sliding surface. And then you have the sliding phase when it actually moves on the sliding surface. So what happens because of this disturbance and the fact that we do not exactly compensate for it is that you tend to oscillate around it at very high frequency. Why?   Go back to the other side, big control to compensate and so on and so forth. And in fact, even the control plots start to look like this, where you have large chattering kind of control. We have large fast changing control. So however, the aim was to send the sigma to 0 in finite time and that is achieved. So the sliding variable goes to 0 in finite time. And this is what is called and of course, this is called first order sliding mode. Why? Because the sliding surface that we chose was a first order system in fact. So for the second order system, it reduces the dimension. The system starts to evolve technically in the absence of disturbance. It starts to evolve on a one-dimensional surface. So you reduce the order of the system by 1 beyond a certain finite time regime. So this is called the first order sliding mode. And on top of it, this is also called an ideal sliding mode. Since reaching phase is finite time, that is why this is called an ideal sliding mode. So that is what we were discussing last time as to how to alleviate this issue of chattering. So that is what we want to do next. So the question is how to alleviate the chattering. So one of the methods, we discuss obviously one method right now where multiple, but it has got to do with some kind of a higher order version of things in some sense. So what is it? Answer is add an integrator. So the system was something like this x1 dot is x2, x2 dot is u plus fx1 x2 t. Now we say we do not directly apply the control u, but we apply, we supply to the system the derivative of the control. So and we have some x1 0 equal to x1 0, x2 0 is x subscript 2 0 and the u we, now that the u variable has been made into a state, we just choose its initial condition as 0. That's in our hands. So that's what we do. So we start working with this higher order system. We start working with this higher order system. And then what do we say? We say that now I am going to construct new sliding surface. And what is it? We call this variable s and it's sigma dot plus c bar sigma. So sigma dot plus sigma sigma and remember that sigma was x2 plus c x1. And now we say that you notice that now our new sliding surface has been constructed using sigma itself no longer using x1 and x2, but directly using sigma. And you still see that this will now start to contain the derivatives and the disturbance itself. The sigma dot will contain the disturbance. So that's the interesting thing. Now the sliding surface itself starts to contain the disturbance terms. So what happens? Now if we say that s goes to 0 in finite time, what do we have? We know sigma, sigma dot go to 0 asymptotically. Just like before, before we proved that if sigma goes to 0 in finite time, we have x1 dot and x1 that is x2 and x1 go to 0 asymptotically. And that's what we'll have. So we just prove that sigma, sigma dot goes to 0 asymptotically, which means that the earlier sliding variable is no longer going to converge in finite time. So we are in fact working with an auxiliary sliding variable s. But this sigma now goes to 0 only in asymptotically, not in finite time like before. So we have weakened the requirements. We have weakened the requirement. We are no longer requiring that sigma go to 0 in finite time. Now how does that help me? How does that help me sort of get rid of the chattering? So let's construct the dynamics of course. So let's see what s dot is. s dot is sigma double dot plus c bar sigma dot. And this is, let's say, I have to take derivatives now. So this is x2 double dot plus cx1 dot. So I'm going to do this carefully, plus c bar sigma dot, which is x2 dot plus cx1 dot. And this turns out to be x2. So first I write the c bar x2 dot, which is u plus f. I'm not going to write the rest of the things, plus cx2. Notice that I've not written the arguments here, but I hope that's evident that it's a function of x1, x2 and t. And now this quantity will be x2 double dot, which is u dot v plus f dot is the derivative of this guy. Because we have prescribed the dynamics of u now. So u dot is v and f dot is just written as it is. So that is x2 double dot. And what is cx1 double dot? So cx1 double dot is just cx2 dot. Okay, it's just cx2 dot. So what is cx2 dot? This is simply c multiplied by u plus f. Okay, so I've just carefully written the derivatives here. I have not done anything more. So this is exactly this guy. Right? Okay, great.  And that accounts for all the terms. Now if I want s to go to zero in finite time, what would I do? I would take v as one half s square just like before and compute v dot s s times s dot, which is s times this whole thing. Right? So I'm going to write this. Remember now, well, I'm just going to write it like this as it is v plus f dot plus c plus c bar f plus u plus c c bar x2. Remember now that u is no longer the control. We cannot prescribe u anymore. We can only prescribe v and that's what we want to do. Okay. Now what are the terms we can, we know and we can sort of compensate for here immediately is c plus c bar u because now it's a state. So it's known. So I can compensate for it. And this is also well known. So I can compensate for it. The only issues are f dot and f. Now at this stage, we make another assumption because we already have an assumption on f on the uniform boundedness of f. So we make a similar assumption on the uniform boundedness of f dot. Right? So obviously this is true for all x1, x2, t. That's what we do. And we start off by choosing. So we choose v, the control now, v as minus c plus c bar u minus c c bar x2. And what else? We now take something like a plus a rho signum s. This is not very different from before. We are doing something rather similar here. Okay. And what does this leave us? Let's see if this works. We can, we may come back and change these terms a little bit if this doesn't exactly work. But let's see what happens.  This cancels with this. This cancels with this. So I'm left with only the ff dot terms. So I will get rho signum s plus f dot plus c plus c bar f. So this actually evaluates to again s and signum s multiplied to give me absolute value of s. So this is exactly equal to rho absolute value of s plus s multiplied by f dot plus c plus c bar f. Now, if I do the norm bounds, I know that this is going to be less than equal to rho absolute value of s. So actually, I apologize. This should be minus rho. This is what I knew that then we will need to do some change.  L bar is the bound on f dot, right? So this is coming from here using the bound on f dot and this is coming from here using the bound on f, right? And now it's pretty easy, right? It's pretty straightforward. I do what I've been doing until now. I will choose rho to be say equal to l bar plus c plus c bar times l, right? And I will add a factor now, right? Which is basically say something like a plus a 1 over root 2, right? So this will give me v dot as exactly less than equal to minus 1 over root 2 absolute value of s, which is actually equal to minus v to the power half, right? And then I'm done, right? I get my finite time convergence of s, right? This implies s goes to 0 in finite time, right? And therefore, we have what we went, what we wanted to achieve, right? We will have what we wanted to achieve. Now, this is essentially called since the actual sliding mode is sigma, actual sliding variable is sigma. Since sigma goes to 0 asymptotically, this is called asymptotic sliding mode and not the ideal sliding mode, okay? Not the ideal sliding mode, okay? So what is our control now? Our control that goes into the system is something like minus, well, I mean the control is already written here. So I don't need to repeat it. Let me just highlight it for you. Let's just highlight it here and that's what is the control, right? That's what is the control that goes into the system. But notice that v is not directly implemented, but the integral of v from 0 to t which is equal to u is implemented, right? Well, actually I should not say, but solution of, we should say solution of u dot equal to v with initial condition being 0 is implemented, okay? And that's a good thing, right? First of all, notice that u dot equal to v is a stable system because I have u dot, this is equal to minus c plus c bar u minus c c bar x2 minus rho signum s. So you see that this is a nice stable term, something nice is happening. And on the other hand, an integral effect happens, right? So when we do an integral action, earlier the control itself had a signum, right? In the previous case, if you see, the control had a signum function. In this case, the control has no signum function, right? The derivative of the control has a signum function, all right?  Actually, you can't expect it because you have employed some kind of finite time convergence for some variable, whether it be at one derivative level or second derivative level and so on. If you notice, this finite time convergence is sort of implemented on a second derivative level, right? So, but still because you implemented finite time convergence, you will not have smooth controllers. But the good thing is, the non-smoothness is pushed to one derivative below, right? So the control is actually an integral of the signum function, and therefore, what tends to happen is that you will have, you know, much cleaner sort of control, right? I mean, this is something that you can verify by simulations, right? But you will have much cleaner control, right? Control, so you has integral of signum function, hence no high frequency chattering, okay? And this is rather nice, and this is rather nice. I mean, it's not that it is still free of oscillations, it will still be oscillations, depends on how fast your signum function is moving. So, even if you integrate the signum, you will still have oscillations, but it will be significantly reduced, yeah, it will be significantly reduced. So, this is one way of sort of alleviating or attenuating this chattering, okay? And so, this is sort of nice, yeah, this is sort of nice. So, this is something that may be acceptable in a lot of circumstances for an actual application as well, yeah, right? Now, one of the concepts that we, well, in sliding mode control, one of the concepts that folks are interested in is the notion of disturbance estimation, okay? The notion of a disturbance estimation, right? And therefore, we sort of are looking at the, for disturbance estimation, there is a need to have a notion of equivalent control, okay? So, that's what we will introduce now a little bit, is the notion of equivalent control, right? So, what is equivalent control? What is equivalent control? This is sort of control as computed on the sliding surface, okay? So, this is the control as computed on the sliding surface. So, what is this? So, notice that when we started, we had the sliding for a surface, which was x2 plus sigma x1, right? And what we had, obviously, was it because of finite time convergence, we had sigma equal to sigma dot equal to 0 for all t greater than equal to some tr, right? Some tr, right? This is the finite time convergence time, right?  And if we say that this is exactly equal to 0 and it is on the sliding surface, then what you compute out of this, the control is u equivalent, which is actually minus sigma x2 minus fx1, x2, t, okay? So, this is what is called the equivalent control. Now, the interesting thing to notice is this is not the actual control, yeah? This is not the actual control. What was the actual control? You can go back. You can go back and actually get this back here, right? So, that's the actual control, yeah? Why cannot this be the actual control? Simply because it has this unknown quantity, right? Which is never being applied, right? Which is never being applied, yeah? So, that's the idea that even though you don't apply this control, right? Even though you are not actually applying this control, you do sort of get the effect of applying this control in a sort of averaged way, yeah? In a time average sense, this is exactly what you have, okay? So, what does this sort of mean, yeah? What does this sort of mean would be a good question and how does it help us, right? So, that's sort of the question that we ask ourselves, right? So, that's sort of what we ask ourselves. But before that, the important thing to sort of note here is this is the equivalent. This is not the actual control like I already said, but this is precisely the equivalent control, right? And how can we use it, right? How do we use it? So, the idea and we're not again stating this by carefully proving these things and so on and so forth, but the idea is that we can estimate the u equivalent as a low pass filter of the actual control. So, this is just minus cx2 minus rho multiplied by a low pass filter of sigma, okay? So, this is essentially just an acronym for a low pass filter.  It would be something like introducing a state tau z dot equals minus z plus signum of sigma and your equivalent control is simply minus cx2 minus rho times this new variable z, okay? So, what are we claiming? That there is this control that we can compute from the sort of steady state if you may when you're on the sliding, when you're sliding, right? So, notice in spite of disturbance, we are exactly sliding. So, sigma becomes exactly equal to zero. So, the idea is since sigma becomes exactly equal to zero in steady state or in fact, after finite time, so I mean, the steady state happens at finite time, we have an equivalent control which is different from the actual control, but can be obtained from the actual control by means of a filtering, like a low pass filter. And this is sort of expected because if that was not the case, then there is no way you would have been able to sort of cancel the disturbance and stay on the sliding surface, right? And therefore, there is enough logic here to understand that this idea of low pass filtering to get to the equivalent control actually works, yeah? And you can see this is a way of estimating the value of the disturbance and that is what we will do, yeah? So, this is actually a way of differentiator differentiating terms as well. And this is also a way of identifying this nonlinear disturbances in finite time, all right? That's what we look at in the subsequent lecture.


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What is an object in this? And so action Satisfy G If I had a point in a movie already, that should be the same thing as just moving it by the composition And if I hit it with the identity element of the group it should be the identity element should be the identity Symmetry. So this is all a G flow. So we just have some, we use an object, we have some group of symmetries It's moving around Well, there's some examples. Let's make it a little concrete. Four Itch examples running at all times. We can like think about how these examples relate to later notions Probably the easiest group to wrap our heads around is the integers The integers are a really nice group. What's a really easy space to visualize? How about the circle? S1 is literally just the unit circle unit circle Pretend that's a circle Action is going to be given by irrational rotation So in this case since Z is generated by Added to be generated by 1, I'm going to tell you what a one-step transformation is one step of the transformation is going to Rotate the whole circle alpha-many radians, that'll be some irrational Rotation You could think of a rational one, but we'll think about the irrational ones for reasons yet to come So this is a flow Since Z is a discreet group to check the continuity. You just need to know that each Group element acts continuously on the circle and these rotations are clearly The same space can admit many different Flow structures so I could change the group for instance. Let's change the group G is going to be homeo plus What is the little plus here doing so homeo S1? That's just all of the homeomorphisms of The plus means no flips orientation preserving This is not a discreet group anymore. This is going to carry the compact open to follow in this case It compact open to quality has a general definition, but since G is just this nice How far away is a typical group element from Doing nothing Well, I look at every single point every single point moves by some amount I Look at the supermum of those amounts and that'll be the distance of this group element from the identity And that'll be a nice right in variant. You declare that to generate a right If I want to compare G and H, I just say where does G send this point X where does H send this point X? compare those distances look at the look for the largest such thing So that that's a topological group and then X is the BS one and a is going to be just the evaluation so Not this two prime This is going to be the same as two, but I could have just kept a discreet topology. That'll be fine Same as to be discreet So the contact open to policy to be this is actually the courses It's one way to define the compact open to Paul G on a homomorphism space It's the courses thing that makes this evaluation continuous So it's the courses thing we could possibly need to get this to be a flow But I could take finer things and so just just the discreet topology would be a finer thing So that's one two two prime and then oh, maybe I'll put three we all know an action And I'm gonna put three above Just to have everything on that part of the board to keep and example three This is just to show I mean so the circle is kind of a it's a manifold It's a kind of easy to visualize object These things can be a bit more abstract So let's let G be the integers again Now the space is going to be the set of all by infinite zero one strings Just zeroes and one's going to the left and right forever I Give this the product topology, so that's gonna be nice And then what is the action going to do again since it's the integers I just have to tell you what The generating transformation doesn't see the shift a string of zeros and ones going in both directions forever I can bump it to the left and right as I want to do So that's a bit more Maybe a bit more abstract that comes from symbolic dynamics. All right, so these are four examples of flows I wrote a remark here Do I want to say this remark? Yeah, I'll say this I'll say a remark So we saw a little bit of We can mess with the topology of the group a little bit in general What is the thing that we need to get a flow? so So X say that X is a compact space and if G is topological group a useful thing to keep in mind G-flows Are the same thing from the group so by a so say that a a G flow a Need the same thing as a continues from the morphism 5a that'll go from the group to homeo X Where this is a tell if something is a G flow it should give me a What is 5a each group element is doing something to the space just Output what it does to the space that will be a homeo And so this this makes it a bit clearer that if I have some topology on G where this is a Flow I can make it finer But anyways, this isn't terribly central to what I want to do So what I want to do is I want to Discuss some properties the question Discuss some properties of the flow might have And then we're going to zoom in on one of those properties. I'm gonna we're gonna construct a universal flow with that So what are some properties we might be interested in some properties of flows call this a zero Because it's pretty rare For any pair of points there is a group element of these four examples Who can tell me which ones are point? Yeah, so homeomorphisms of the unit circle I can easily here's a point on the unit circle Here's a point on the unit circle. I can just rotate to get Another It turns out yeah, neither one or three are going to be point transitive so the irrational rotation Looks kind of promising because I can I can sure get pretty close, but The orbits here can be countable in the circle is uncountable And up here, I guess same obstacle works Transitive, but yeah, home OS is huge Well point transitive almost never happens, so let's weaken it a little bit Minimal so Zero is asking for one Everything is in this orbit is weakening that a little bit. I no longer require Everything to be in the same orbit But just that every orbit Sees most of the space so do we get any so two to two prime will still be Minimal do we get any new members in the minimal club? I see I see some heads saying yes. Yes irrational rotation is a good example of a minimal flow Here's a point say that I want to get into this Open interval I just have to I Guess I should compute. I just need to figure out some number of multiples of alpha that get me into here mod 1 and You can do that So this is this is This is this is not minimal. What's an easy way of seeing that?  You're going to have trouble reaching that If you only think about the AP here, I'll do Oh, so the eight that those won't be That won't be closed in general But we're gonna do one further weakening which will which will save a One said every orbit was dense So it's clear that that's a weakening of one which is internal weakening of zero two is the weakest of these notion So one two and two prime will still all be topologically point transitive and Now I claim that three three is also a weak point transitive. So How might you need to find some string whose orbit is dense? How do you do that? Don't take some string that just contains every finite. Yeah Neighborhoods are neighborhoods are gonna be described by finite patterns of zeros and ones and we have infinitely many infinitely much So I just need to type every possible That's exactly All right, so we're gonna do So those are examples What we're gonna do for the rest of the talk is we're gonna focus on number two so goal for rest of the talk construct the maybe one part of this goal is a definition But a definition I guess there's a group involved the GM X is just some G flow X will be topologically Point transitive as witnessed by this little point that's not though. I declared a point of interest with dense orbit So what we're gonna show? theorem greatest G and so what this means is that there's going to be a So there is some in it. It's usually to know that SMG for historical reasons Pierre Samuel was the person responsible for This stuff originally And I this point So this is going to be a GM it and then given other GM it There's going to be a Unique which what are the things we want our map to satisfy? I really should have I should have defined some sort of category of G and it's an amic math, but an amic map is continuous It respects the G action It respects the point I told you about so it should send this point to that point The uniqueness actually just follows from that last fact. I sent this point to this other point We know that it has to be G at covariant and they both have dense orbits, so if I Want to know Where I have some other point P in here. I want to know where Phi sends it Well The orbit of one is going to cluster around P. I know where everything in the orbit of one goes So I know I know where that's going to cluster Let's spend the rest of today constructing this Okay I don't have the intuition for why Especially this one because I would think of the initial object for the category as being the least thing Because we're Given if I had some other why why not in some map here I can complete the diagram What the reason that's not the right thing to draw is because all these maps are unique There's unique map between any pair of objects, which kind of simplifies the picture So so the simplest thing to say is that there's just there is an arrow from this object In what sense is a minimal flow That's just in a In a Zorn's Lina sense it contains no proper sub flows And here's another Annoying one so the universal minimal one It is unique up to G flow isomorphism, but not unique up to a unique G flow isomorphism That is an annoying wrinkle if you care about these things and this is a good stopping point Oh Yeah Each one of these things is an ambit Want to take the whole thing I'm going to take the orbit closure acting on the designated point so I have a designated point in each Coordinate that gives me a designated part of the product. I want that point to have dense orbit So I'm just going to pass it down to a sub space where it does happen This is this behaves like a product and so What's kind of cool is Is a set this is a bit of a logical bugaboo There's a set of representatives What this really amounts to saying is that ambits can't get too too complicated Why is that? It's really this dense orbit so you have your in particular that provides a map of your group into this a priori it could be a huge compact space But it can't be too huge because your group has a fixed size Say that your group has size Kappa works half of some cardinal We get a map with dense image So what does that tell us so if x is the ambit? so x has dense Subset can't be too too big Cardinaly back to less than 2 I mean, it's pretty large, but it's it's bounded Your amids aren't going to get bigger than this so I can with enough of a Initial fragment of set theory you can see all the ambits So what that allows you to do Let's take a set of representatives for all the isomorphism types of ambit. You take the amic product that is by construction by Absolute overkill construction a universal and it you just smushed all the Yes, well you use the what? Do you like this this connects to anything other category? Yeah, it's the product in the category The category of ambits is a little bit It's a bit easier than a lot of other categories because there's at most one arrow between any that's one way of Exhibiting this greatest GM, but it's not very useful like I'm joining what it looks like I want to actually construct this thing so I At least in the case of a discrete group, let's try to construct and as I Indicated in the abstract filters are awesome. So Without further ado, let X be a set collection of some sets of X So that it's non-trivial, which is usually these two Statements for clothes for a notion of a largeness if I have something I'm declaring to be large I make it bigger and that's still the way large if I have two large things and they intercept So it satisfies one two three and four so Look, there's a purely combinatorial way You So ultra filters are a notion of largeness that are very opinionated ultra filters have an opinion about everything Everything is either large or small Equivalent definition for crime is that you Is maximal to satisfy one That's sort of the non Abstract way of saying so ultra filters are maximal filters Ultra filters are really opinionated filters You may have seen ultra filters before They show up in like functional analysis. They show up in model theory But most of the time you think about like one ultra filter letting you take some sort of Like it's a it's a particular way of like I have some Countable set of things I want to grab a cluster point an ultra filter is a good way of letting you grab a cluster point So what we're gonna do today? I'm not gonna worry about one ultra filter. We're gonna worry about all of them in the space that I should remark that identify X as a sunset By taking principle If I have a point in X the collection of all subsets containing that point is an ultra filter But they there's gonna be a lot of other stuff Apology on this thing What we're going to do is A basic camera open set are gonna be over for filters that contain Over all subsets This notation might be a little bit Confusing at first because a bar kind of looks like the closure of a and that's not an accident under this identification a bar is the closure of it, so this is a zero-dimensional space It has a basis of clothing This is a I Don't think I have time to prove it This is a compact easy Compactness probably the easiest way to do it is through the finite Intersection property characterization of the practice so if I have a collection of basic closed sets The basic this basis for the open sets is also a basis for the closed sets Because a is also By this identification So basis for closed sets also If you have some Collections and with the finite intersection property Then the sets that you're mentioning form a filter Extended to a filter that's all right. So here is this is the key property about me to X the magic triangle Those of you who have seen me give GSS talk before have probably heard me Pontificated length about the magic triangle, but it's it's the best triangle So say that let Y be House dwarf everything is house dwarf function Exit just a set remember so there's no It's a discrete topological space So so any function So what are we gonna do? Here's X? Here's why you have here's the inclusion And then here is the last side of the magic Let's actually look for this I'm going to erase my the uniqueness Just follows I should remark that the principal the principal members dense just because if I have a basic open set like this and a member of a That's principal ultra filter a is a set containing So if this dense We know what's going on a dense subset of beta X So we just have to argue that there is an extension and How do we do this? Let's let let Why you know why consider That's going to be back here in X and He has an opinion about it. So let's Suppose that it's This is just a definition so P Thinks it wants to go why if this happens For every P this it's suppose not Why is compact and every point in why is a little neighborhood around it where something bad happens? So let's just grab a finite cover of the bad things So the union Every point has to somewhere so that's I Didn't spell this out explicitly, but this is going to be a problem in regards to four I guess one X is in there you Repeatedly apply that I guess came any times One of these has to be inside Way to If they are different Let's put little disjoint neighborhoods around them because everything is house door These have disjoint pre-images and so you're never going to have Disjoint things that P thinks are both large. That's bad So that's all right You have to do a little bit of fiddling to check that it is continuous, but I'm just going to say yes, it's continuous Why is it continuous because it's sort of the obvious thing that you wrote down That's kind of the way a lot of these proofs go filter spaces Like there's just one way to write down the possible function Let's get an ambit out of this. So if I have a discreet group So say G is a discreet group For you the G1 G Is an ambit what the flow is we have a space but where's the flow I'm going to send G It's pretty easy. So if A is a subset of the group G is a group element P is an ultra filter I need to tell you When a is a member of G dot P And it's really the only thing that can happen P is a collection of subsets group G is just going to move around This this works this It's continuous because I can ask about this basic open condition by asking about this Condition that's continuity G is discreet so to check continuity of the whole thing you just need to check So why is it the greatest and it well because of the magic charming wolf let's Be another GM it so let F Go from G to X G I'm just gonna look at what G does to the distinguished point That's sort of the only thing we could possibly write down And that's the only part of the map we could possibly know how to define ahead. We know what's happening on this orbit So the orbit tells us to do that and then we're going to extend To all beta G You have to check the magic triangle does not buy you G So that is that's the greatest Which is still I mean it's kind of abstract still but it's maybe a bit less abstract than just saying multiply all the emits together This is at least an object. We know what it is So yeah, I will not have time to talk about G not discreet, but you can speculate what would you do What's the problem maybe I'll say If G is not discreet you have to worry about joint continuity of the action So if G had some topology You can write down the same action it's just Beta G is the wrong Compactification to use so you can think of this This beta operation is turning In this case a discreet space into a compact space and the freeest way possible And so when G Has some of a topology that's you don't just want to regard the set You need to remember that it started off with a topology. And then there's a few extra All right, that's it. So is that any questions or comments? How simple is the simplest example you can think of for G that's Apologized. Oh, it's still easy to know No, but the subs is a counter example to this. Oh, any Not sure no topological group. Any no true topological group breaks this One one case where it's easy say that G is a compact then SG will just be the group itself That's kind of on the other extreme end of like Being trivial compact groups are Really really simple dynamically Anytime it acts on another compact space It has to be like a group like a group of quotients Oh locally compact groups are disgusting. You have Veatch's theorem that local compact groups admit free flows So that's gonna tell you that SMG is not matrizable, so SG is not matrizable So SG is gonna be a huge So they still like to see concrete description is If you were in the logic seminar today, that's sort of the like The hint is to where things we consider like nearness As far as I know


A report of a missing man early this morning on Upper Red Lake caused quite a stir as multiple law enforcement agencies pooled resources to locate the missing man who turned out was not missing. Around 4.30 this morning, the Beltrami County Sheriff's Office received a report that 68-year-old Michael Rostahl of Clearwater, Minnesota had gone missing while fishing with his brother. After searching on foot using drones and partnering with a helicopter from the border patrol, Rostahl turned up when he drove into Rogers Resort on Red Lake around noon. The Sheriff's Office says even though Rostahl was not missing, it's their policy to err on the side of caution. This is an example of people needing to communicate about what's going on, maybe watch the amount of beverages they consume, get along with the people they're fishing with and staying in the same small confined fish house. The Sheriff's Office tells us that Rostahl is okay and that no citations will be issued for the the false large-scale search. If you enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland PBS.


We continue today with Workbook Lesson 250 Let me not see myself as limited. Let me behold the Son of God today and witness to His glory. Let me not try to obscure the holy light in Him and see His strength diminished and reduced to frailty, nor perceive the lax in Him with which I would attack His sovereignty. He is your Son, my Father, and today I would behold His gentleness instead of my illusions. He is what I am, and as I see Him, so I see myself. Today I would see truly that this day I may at last identify with Him. Amen.


Hello and welcome back to the craft box my name is Brent and today we're in episode 207 of the wizard 101 death walk-through last time if you haven't checked it out already One you should what are you doing and two we entered the condo desert and had a whole bunch of fun And today we're talking to it. What luck Joshua seeds golden and fragrant So all the one who knows says we must fix Sir Alden drink It is a true honor reserved for hoppers coming of age Sir Alden must have powdered Jesper Saw the one who knows can grind the Jesper up the deep desert is home to death stalkers Who use Jesper for decorative bands get some and bring it to saw the one who knows Get up get in and know these guys are death. I believe In between episodes I had to defeat a whole bunch of these guys to collect Joshua seeds And now we basically have to do that for the Jesper seeds It was a struggle they effrate they're terrible they are nasty Those are all great words to describe them Luckily, I am not too worried about these guys. I had to put on Malastir stuff because All the other staffs that I have have death Wanted So yeah taking off the E free Minus 90s was not particularly easy in the first battle because I completely forgot that they were firing E free and They both effrated on the first round. So that was fun Yeah, that was west of a blade Okay, let's mass prism. Why is my mouse being weird today? Swear every second episode is just why is my mouse being weird? Who knows maybe by the end of this walkthrough we'll find out.  So that's cool Avenging hello, we still have divin Helping us so we get extra damage like a lot of extra damage and a whole bunch of extra exist as well So yeah, also my pets been on fire as well. It's been healing a lot, which is great He didn't heal that time, but I promise you he's been healing He's been a good boy or girl or thing. I know his name's Abby, but you know, I just prefer saying him Sorry about it Yeah Well, let's see another blade. Yes. Thank you We'll blade again and then hit. I know we should do a decent amount of damage, but sometimes you just don't know Things can happen and you just don't know what's gonna happen like that for instance. This is why I should have probably kept their melee wand on Mallyworn with all that pierce is just so handy It is really good to have. You don't have it. You should probably get it because it's actually really good That pierce is just Undeniably fantastic Yes, definitely. Oh Let's go for this one Let's see what this one can do that both past. Okay Um, let's go Fizzle, okay, maybe I should have gone the other one. Oh well Let's go for the Lulu We actually got the Shad. That's fantastic Didn't expect that but I am much appreciated much appreciated much appreciative good at England is great Dr. Von yeah, that's unfortunate because Sorry about it The spell takes forever. I forgot how long it took All three seventeen, that's so bad. Do you expect to heal off that? I didn't think so No fizzle yay. Lulu's obviously just the superior spell today Let's see if we can crit because that would be cool. I doubt it, but you know what oh we can look at that We can crit. That's fantastic We can even crit. Wow Now with your crit capabilities. Look at that. That's nice That was two blades That's crazy. Okay That's good None. Oh my gosh. This is a struggle I had with these guys. Oh Yikes, I'll be back in just a bit once I've defeated all of these Okay, I am back that took absolutely forever Sorry, I have to do that every single time that took ages. They have an abysmal drop rate So would not suggest doing that alone Let the soul try Barrow speak now it is time for us to make the soroldan drink Drink deeper the soroldan saw the one who knows made enough for two Barrow Knight Do not be shy By bastion, I feel like I've been brought back from the dead Speak to the elders to accept their head blessings Okay, don't get it weird but not gonna complain Presta warns you to be wary of power too easily gotten The arachna who took the shadow queen side without thought are lost in darkness Take my warning is your head blessing Okay You hi the legends that grow behind you are vast it when the arcane architect hopes They do not stack up your confidence too high That's it nerd you have done bright work in restoring the eclipse tower and radiance reborn I thought he said that said nerd not that said nerd. Oh My gosh, she's bad if you also restore the solar arc to the people It would be a day of joy and I would believe we would die another day Cool, bro. You are but dangerous. I do not want your sidequests Edwin the arcane architect saw the one Who knows welcomes you in the hopper tribe Yay Saw the one who knows grocks the solar arc the heliotrope key must be had to open it It is a powerful mystical hidden key The key is in a hush hush place listen close bloodstone cave Last we checked Bloodstone cave was empty. It's not going to be empty. Is it nope Why would you think it would be empty? That's way too easy, but anyway, yes those Those death people never ever ever Ever again and don't want to see them ever again their drop rate is terrible I went through about 10 battles just to get three like not even for which I had to do for this one Three and it took 10 battles of two each like what the heck that's 20 of them and they didn't drop up Like whoa, what okay Honestly, sometimes it is just absolutely terrible and this game hates everyone But I mean it took a bit of a bit of a time just to you know, just have to myself You know just put on some music. That's what I do and like I'm not recording I just put on some music and just chill a bit You know because sometimes you just got to have that moment in your life where you just got to be chilled Yep. Good job Brent. Okay. Look, I knew it wasn't going to be empty So blood comes through door gotten smoke for later Cannibal mice Okay, then these guys look super easy. I Mean most more battles nowadays are like really easy especially with them. He makes so much He just give brings so much to the table, you know, it's great Okay, let's do that and that and we will But yeah, that is good, I'm still waiting to get the Malastir robe. I haven't done rattle bones or Well, I've done a current Patrick So yeah, that's why I'm still wearing waterworks robe Thanks Malastir for your bad drop rate of things that I need Much appreciated But yeah, that's why I'm Holding off on making a new stitch as well. But as soon as I get that I will I mean, it won't be like my Kind of ideal go to but I mean the difference between Malastir Rattle bones and Crocker patria are basically one damage or one resist or one of something and I'm not gonna be too upset when I get Malastir I'll probably make a stitch for it. Just because one isn't like a big deal down the line like one is Okay, and I'll probably upgrade anyway because obviously I'm not gonna be going a full critical set So I'll probably be using the Kabbalist gear and at the end of Imperia. So I mean, it's not like Yeah, but for now as soon as I get that my stitch will be better, but I'll make a video On that when I get it kind of just go over my gear. I'm not I also need the I mean Yeah, there's a lot of things that I want to change about my Gear because at the moment, it's pretty bad like I mean it's doing the job, which is good, but it's also pretty bad I also need to work on pets as well. That's gonna be fun I need a wins wins and double PXP or double gardening rewards. I need that. I need that in my life, please Like please I should want it. That would have been a good idea Well, who cares but that that is something I definitely need in my life Double gardening rewards has been a while. It's been at least four weeks something Yeah, I need those pet snacks and I always get really nervous about harvesting Because you never know when it's gonna pop up and it all of a sudden it might pop up and then you don't have the you Don't have what you need to do, you know, like your garden is not finished So you can't just garden and then plant again and hope that you can get to in one weekend But I usually can't because I don't have all the likes because I'm bad, but you know, sometimes you just got a It's difficult, it's difficult. I'm gonna tell you that it's difficult Getting to max level is difficult and getting all the gear that you're expected to have is difficult Yay Have no key Run away. I will not run away. Lucky. They won't have found it yet Um, where are we going down here? This looks safe. Nope. We're not going down there. We're just going to here Nope, we're going over here to the wall. You search the bloodstone cave carefully Uh-huh under a loose rock. You find the sparkling heliotrope key. Yay. Good Let's go back to Saul.  Lord, please. Thank you. Please. Please Lord Lord Lord I haven't actually done a run of dark more than forever. I should probably start doing that again Because that is useful Like I actually haven't I haven't actually been playing this game for a lot recently Um I've got Yeah, I kind of ran into an issue where I just pre-recorded way too much With Finn all of the Road to 100 and Sky Bounds and what have you like I have I still have quite a lot of pre-recorded stuff So I haven't actually been actively on the game and recording. I've just been doing daily assignments every day because why not? That's basically the only time I've been on The heliotrape key beaut Someone was living in bloodstone cave. Not so good Telling me listen the spellbinder was led to the solar arc by the spider Magi where the Sun is brightest the shadows are darkest Once she grogged all there was she bent down the condor forest and sealed off the solar arc The solar arc lies in a hush-hush pass the valley of the dark Sun But the deep desert is too dangerous for hoppers The order of the beast tribes grogg it well You must find the tribal barbarians and convince them to help you those with a cannibal mice that just tried to eat us No, not cannibals, but only each other just everything else a great shame your fault. Do your best try not to be eaten Okay, then we're also level 102 still haven't leveled up in a while. I have 802 tickets I did a tournament the other day. I Actually lied. I have been on the game of it. I did a tournament and I I Technically Technically I won two and lost two But two of the two that I won with the The guy didn't turn up. So that was fun I got given the same guy twice and he didn't turn up forever And I think he was offline or something. No, how well this is going to go over. Do they look hungry to you? You want help we give you teeth Yeah, but so he didn't turn up so I got Two free wins for doing nothing. So I was very impressed with that That's the first time I've ever actually PvP'd in this game. That was kind of semi I Wouldn't say serious, but like Kind of mean something Instead of just oh, I'm just gonna one V1 you ha ha ha and not actually not what I'm doing when I kind of kind of Actually did make a sort of strategy and it didn't really turn out. Well, just gonna say that But then again, I was I didn't have the best gear and you know People crit on me a lot and I just bad, but you know that comes with practice Possible PvP in the future. Maybe who knows who knows not gonna be spoiling anything yet, but we'll see Yeah, these guys are really just bad, aren't they I've kind of realized that mobs are just really bad Like they're just bad, you know, like why Why why do they exist?  I'm just two op. I Won't like raw please one go away because you're a long-ass fellow. It should probably not be around and to it's bad still so Like what are we in Celestia? Geez 217 exactly. This is bad bad Really bad. Look at this bad. Oh wait. No, I'm good Dear night's actually really cool Dear night is probably one of my favorite spells in the game. Look at this.  It's big water here. This doesn't look good at all. The water appears putrid Smells worse. I can't see how even those cannibar barbarians drink here. Let's search for sign Okay Tracks lead off that way after them Um, okay, okay, follow my sign all the signs. You're giving me mixed signs my dude The tracks lead into that tent The biggest one of course. I hope they are friendly Well, let's go then I'm assuming that there's actually a boss here. That would be much nicely Which deck this one? Yep. This looks like a boss deck of sorts. We'll go with that go with this one I think One of my tc's like please please game. Please One of my tc's like trash. Okay Um ice Again, this is very very bad Bad bad bad um pronunciation Who dares the sharp teeth of queen jade eye I sniffed your sweat stinge from a hundred paces. I'll cut you into bug food They need to really work on their pronunciation Pronunciation they need to pronounce things slightly better. Um, I wasn't actually ready to go in thanks game But now that you're just dragging me and that's fine um I mean, let's just go for it. I suppose 23 easy Easy I can do that in my sleep Look at this that 50 blade you can't take that one away from me. Wait. Is he fire? No, he's balance. Okay I mean, there's nothing to worry about these guys are just so easy Like you get to a point where things are just Easy, you know Like there's literally nothing to worry about.  Are you good? Like what the heck why? I mean sometimes I do find this game just a bit easy, but then I also hate it when it's a bit too hard I'm a really I get really frustrated very quickly with games. I'm not going to lie.  I'm not going to lie pirate 101 is one of them it gets It's not difficult, but sometimes it's just So randomly Random that it's just not fun anymore And I I get that a lot in part two of pirate 101 Valencia part two that is I just Like people who can crit and do 1k on you followed up by another crit that does 1k on you followed up by another one in your dead Like well, how's that fair? There is no way to combat that Yeah, you can stun them, but So there's only a very few and none of Like companions that can actually stun properly and then still most of it There's just a chance that you're stunned.  Sometimes I'm not going to lie. I get frustrated easily as well So that doesn't help That's why probably shouldn't play games because I do find myself getting way too frustrated way too quickly But you know, oh geez that's a bit cheeky. What does that's peeve? Geez Set shield even though that's not my school. So that's unfortunately don't need two reshuffles Let us go for we've got like no perps either I like how we just blade up so much that we just have no perps We just don't have any perps. Usually you would have perps, but I just don't Like why why? Hello Why like seriously? Why don't I have perps? Did someone manabermen? I wasn't looking Oh, no, that's right. They did winter moon and that takes away perps I'm like why because I've Haven't done much. I've just bladed a lot. So I should have perps. We've already fainted Um, let's go for a blade, please Thank you Thank you very much. That is a four blades. Hopefully we can find a Lulu and an enchant and then we should be sweet And another faint as well. That would be even better. Rora What's this a blade? Can I have that blade, please? Seriously, can I? Well, we found that let's Yeah, let's go for avenging. Let's try and get avenging. Good. Lee um more pass strategic pass I mean, we're only half health. So nobody can kill us yet, which is good because balance does nothing And I still have to be pretty lucky to kill me at the moment Um, okay, you can be enchanted And you can be enchanted Kind of keen to hit with headless, but I mean Headless is really okay My strategy when I did that one tournament and I think I'm a little bit here now I don't actually But um, it was just to basically spam headless. You know how balance spam lawmaster I was just spamming headless and it like it did a lot Even with my bad pierce and pretty trash damage. It's still did a lot like no blades. It does a lot So yeah, that's like probably gonna be my strategy It's it's so OP couple blades and boom that that thing doing louts And it's better than a drain as well because drains don't have as much damages just solid hits And that's clear because you see vampire and you see headless next to each other and headless does like Like nearly nine 900 enchanted 800 to 900 and Vampire does what like four to five hundred five hundred enchanted like how? It's just okay, but we've got Lulu and now we should hopefully kill and if we don't I am sewing Kings Isle definitely If we crit we don't But I mean this does so much we should be fine, right? Right double. Yeah, we should be fine No, we're not fine. Okay, that's fine Uh, we will headless because we have pips. No. Yeah, we do it pips.  I will definitely do that because I don't like this place All it's going here And then I think we'll probably end off the episode there But we're able to talk to her first because why not? Why not? Where are you? You are just here. Hi queen Why do you still harrow me foul spellslinger spelled binders? Yeah spelled binder You beg the help of sonya jade eye queen of the orders of the beast We are fierce as fire beetles as dragons as tyron We will never serve you But you are capable We would train their favor for a favor The big water is poisoned by a creeping water Show him sharp and chase him out to save big water She sounds like she needs some medicine for her throat Just gonna leave that there and on that note Thank you for tuning in to leave a like and subscribe and if you've already subscribed press the little bell So you know exactly when I post another video and remember craft outside the box


Hi folks, I'm here with Sam Fieldman National Council to Wolfpack. Now, many of you have probably heard of Wolfpack if you've listened to the Young Turks or Secular Talk or the Humanist Report. We've talked about them quite a bit, but he is here to give us the breakdown specifically on how this one organization can save US democracy. And I know that that sounds hyperbolic, but their mission is absolutely ambitious and what we need in this country. So Sam, thank you so much for coming on the program. Can you tell us a little bit about Wolfpack for those who are unfamiliar? Sure. Thank you very much for having me. Wolfpack seeks to empower a mass movement to amend the US Constitution, one that shatters the corrupting influence of money and restores the Democratic Republic that represents us all. We have existed since 2011. We started in the wake of Citizens United to address not only that case, but the precedent that came before it. There were other Supreme Court cases that dealt with the issue of money and politics as well. That really overturned what had been for a long time a pretty effective campaign finance system. And I was a young lawyer at the time. I had twins who my wife was pregnant with who were on the way. And I saw a world approaching in which they would have absolutely no say in the government in which they lived. And I made a promise to my kids before they were born that I wouldn't let that happen. That I would make sure that they grew up in a world in which they had some say in how their government worked. And around that time, Cenk Uger was a new viewer of the Young Turks at that time. And Cenk kept saying, you know, I've got this plan. There's something coming. I've got this idea. Right at the same time, I was doing my own research. And I found that there is a method for amending the Constitution that does not require the ascent of the national legislature. Those were actually the words that James Madison used when he described the way the amendment process should work. He said that the ascent of the national legislature ought not to be required. And that method put into the Constitution by our founders is the Article 5 Convention. With that method, if you get two-thirds of the states calling for a convention limited to a specific topic, then a convention is called specifically for that topic, the proposed amendments. They then get sent to the states exactly the same way as an amendment proposed by Congress would get sent to the states and ratified through the exact same process. And I had found that in my own research. Meanwhile, Cenk kept saying, there's this thing that I've planned that's coming. And I was thinking, I hope it's that because we need all of us to do this together. I looked into how the Article 5 Convention process works. And there's simply no way that you can get an amendment to the Constitution through that process without a broad, popular movement. And I knew that I didn't have the audience that Cenk had to start that kind of thing. And sure enough, that's exactly what he announced. It was announced at Occupy Wall Street. There's a misconception that it comes out of Occupy Wall Street. That wasn't true. It was more of just a convenient place to announce it. And I signed up on day one. I had many roles within the organization as a volunteer. Now I'm paid as a contractor, as a national counsel. And I've been with the organization ever since. And you told me that you were part of the organization as well early on, right? Well, I tried. I did a couple of donations. I signed up to volunteer and tried to do a little bit of lobbying of my state lawmakers. I couldn't do it for too long because I was in grad school. And of course, that takes up so much of your time. But one interesting story that I told to Cenk was that my state rep at the time, Betsy Johnson, is now an independent gubernatorial candidate. And she was very open to the idea of sponsoring that resolution to get money out of politics, calling for that Article V convention. She returned voicemail. She was great. But now she has been a prominent independent candidate specifically because she's being bankrolled by GOP donors. So she's done a complete 180. So my activism with regard, my limited activism with regard to Wolfpack has been a catastrophic failure, given the way that she's done that term. But I've always really respected the organization because it's a very practical solution to a massive problem. Like nobody expects these lawmakers to pass a constitutional amendment to get money out of politics because it's like trying to convince them to do something against their own interests. But if we go the route of the states individually calling for these resolutions, that's the way that you can get it done. And look, normal Americans might not be able to articulate specifically why money is a problem in the United States government, but they know that something is up. And when you point them to these examples of, you know, Kirsten Sinema, for example, taking money from predatory companies, lobbying against closing the carried interest loophole, you know, Joe Manchin with regard to fossil fuels. I mean, the the examples are countless at this point. But when you explain it to people, they acknowledge that corruption is a bipartisan issue. It's not just a Republican issue. It's a Democratic Party issue. And so I think this movement is really clever in trying to make sure that you you limit it. You try to be explicitly nonpartisan and you make it a grass roots movement.  And to my understanding, the movement had reached five states to call or past resolutions calling for article five conventions. Since then, two states have rescinded. And part of this is in due to, I think, a lot of fear mongering over the prospect of a runaway convention, something that I think that Jeng Yuga, for example, has done a great job of dispelling that myth. But why do you think there was so much fear mongering in my this is my, you know, own, own guess is that before like an article five convention was never done. But whenever there was momentum, that's when constitutional changes were made. So I think that this is them kind of anticipating there's momentum, we've got to start fear mongering some way right now. But what actually happened? Like, what's the state of Wolfpack? And why was there some, you know, backsliding with regard to progress? Sure. First, before I do that, I just want to clarify one thing. We've both mentioned Jeng, of course, he founded the organization. He was never involved in the day to day. He's no longer a board member of the organization. Okay, I didn't know that years never taken any money from the organization. He's donated money to it before. But he is still, of course, a big supporter. And I know him a little bit. And I appreciate his support, just like I appreciate the support of all the other volunteers. But I know that there are inaccurate views out there. I about that. And I did want to just clarify. Okay, that's that's good to point out because, yeah, yeah, that's that's good to point out because I've always I didn't know that Jeng was always ever on the board. But I just kind of viewed him as like one of the people who helped get the ball rolling and like a promoter for which I was really valued because, you know, that that platform is really crucial, I think to getting the message out. But I'm sorry to interrupt you. He was on the board initially. But he never was active in a day to day manner. And he hasn't been on the board for several years. Okay. But yeah, to answer your question, though, when Jeng did found it, the philosophy that he, he espoused early on was, you know, give me 20 good activists in every state house, and we'll get these resolutions passed. And that was effective early on. We had we called the Mountain Army in Illinois, we had in a cadre of kids in high school like Walker Green and Selima Casio, who did fantastic work in New Jersey and Westchester. And we had, you know, the line up of people in California that were just going person after person after person, testifying. And that was really effective early on. It stopped being effective when we started getting organized and well funded opposition. And what we found was that kind of at that point, we kind of hit a wall, we had our first five states. And before we had well funded and well organized opposition, we were able to get meetings, we were able to explain the law, we were able to show them these legal things, we had numerous numerous counsel for legislatures and things like that, take a look at the law that we were showing them, and do their own research and check and see that what we were saying was true and come back and say, yes, what they're saying is accurate. That still happens today. Recently in Oregon, the council for the state legislature over there changed his view from being opposed to the convention to being in favor. We had nothing to do with that. He did his research entirely on his own. But he found that from looking into it, everything that we were saying was correct. The difference is that a lot of state legislatures now, that's not enough. Just being right is not enough. We have recisions in New Jersey and Illinois. In New Jersey, you may have heard the truck driver, Ed Durr, the sitting Senate president, President Sweeney. And a couple of days after that election, Senator Sweeney pushed to rescind our Article 5 Convention call in New Jersey. We had a similar effort and we mounted a very strong fight. They were getting a tremendous amount of pressure from the leadership there. And then we saw in Illinois, a couple of months later, they did it even faster. We only had about 24 hours notice or so. Wow. It had already passed the Senate for the notification systems that we had in place even triggered because it went so quickly. And then I heard from one house member who told me that she still wanted to vote for us in the house. And she still agreed with what we were saying. But she was being told by leadership that if she did, her bills would not get hurt. So they're getting now tremendous pressure from the leadership. It is still the case at the state houses that most of the state legislators listen to their constituents and want to help their constituents. Just like we've always said, the state legislature is not like Congress. They do still listen to you. The difference is they're also susceptible to pressure from leadership. So we've decided is that we have to be able to apply greater pressure on the other side. And that's why I want to explain what Wolfpack is. The very first thing I said that we need to do is empower a mass movement. I said that before even said to amend the Constitution. The reason is the mass movement is 100% necessary in order to have that kind of pressure that we can put on the legislators and put on the legislators so that they can once again actually look at the law, look at what all their voters are saying and be responsive. So we're starting to increase our coalition building. We've been going through a restructuring for the past year. And part of that restructuring is increasing our coalition building, giving our teams more autonomy to work in different ways and with different groups in areas where our team in Texas may not agree with our team in Massachusetts and they may do their own thing as long as what they're doing ultimately is ultimately in support of the same overall goal. That's how we're building a large coalition. And we found, you know, we've been able to have really good bipartisan relationships. In that way, I was at an event a few weeks ago called Academy of States where almost everybody there was a Republican and also all of them supported Wolfpack, which was not even I helped plan the event, but I did not only help choose one of the speakers and all of the other speakers I did not help choose also turned out to be Wolfpack supporters, which I love to see. Yeah, the story of Wolfpack is kind of bittersweet to me. I love the organization and I love the progress that you made, but at the same time to see it get rescinded, it's it's it's gut wrenching, right? Because that's so much hours of work that your volunteers did. But at the same time, it's a sign that they're afraid and they wouldn't exert this pressure money forces wouldn't get involved if you hadn't actually made a difference. So it's bittersweet, right? Where it's like you want to continue to make progress and you don't want to go backwards, but at the same time they notice you. And one thing to point out for my viewers who don't know, it's inevitable that at some point you're going to have setbacks in any movement. But the fact that you had so many organized, well funded opposition in each state come out against you, it shows you that you're on the right track, which is really encouraging to see. So I love to hear that Wolfpack is basically going to be better than ever.  I wasn't sure what the status of it was over the past couple of years. But you know, it's good to know that everything is still happening, you know, behind the scenes and whatnot. One reason for talking to you was because I got a little bit of pushback from Wolfpack supporters due to a video that I covered a couple of weeks ago. Now I've currently unlisted that video, but I'll link to it down below if people want to see specifically what I said. But long story short, so I talked about how Republicans are trying to emulate the Wolfpack strategy of getting an Article V convention called so they can ratify their own right wing constitutional amendments. Now what they want specifically, it's really vague, it's really broad, but it seems like a discombobulated movement. Now an article that I shared was from Grace Panetta of Insider. I also talked about an article written by the Center for Media and Democracy by Alex Koch, where he talked about, you know, a 2021 conference with Rick Santorum that became a flashpoint for the, I guess, Republican Wolfpack equivalent. That's maybe a bit of a misnomer, but the Republican movement to get an Article V convention, and it seems like the right is emboldened specifically because they've had so many dubs lately, you know, getting Roe v. Wade overturned and whatnot. But people who support Wolfpack and work within Wolfpack were mad or disappointed, I should say, in my coverage because by, you know, making this, you know, emphasizing the fear of this, perhaps, and you can kind of maybe describe the criticism better. I'm kind of inadvertently pushing this idea that a runaway convention is possible. Like, what did I get wrong specifically? Because I do want to make sure that I don't necessarily inadvertently push any messaging that could hurt Wolfpack, even if I am concerned with the Republican, you know, parallel movement in a way. Yeah, well, it wasn't so much what you got wrong. It's what that article from Business Insider got wrong. And I spoke to the other author of that branch for about an hour, giving an interview for that piece, although it does not appear that they used a whole lot of what I said, and I was not quoted at all in it. They painted a picture that was simply inaccurate in ways that I pretty clearly explained to them. And, you know, you're not the only one to have gotten that wrong. The channel owned by the Young Turks by John Iderola called The Damage Report, which I'm sure many of your viewers also know, also had a video, which they've since taken down that said many of the same things. And I spoke to Jessica Burbank, who was in that video about it, and we went through the article. And one thing that we noticed that that article had done was it mentioned, I told you recently, I told you that I was recently at the Academy of States 3.0, which the article mentioned that event. And they put it immediately after talking about Rick Santorum, which made it sound like those two were connected. It was a complete non sequitur. Rick Santorum has absolutely nothing to do with Academy of States 3.0. And by putting those two things together, which they did twice in the article, it made it sound like this is all part of the same movement. It made it sound like a big grand conspiracy. But the article, the way that Santorum's effort actually goes, and it's completely separate from all of the other groups, including groups that are filled with mostly Republicans. I basically, Mark Meckler founded an organization, it was founded around the same time as Wolfpack, I think a little bit after Wolfpack, but I'm not sure exactly when, called Convention of States. There's some confusion, because the phrase Convention of States is also sometimes used as a generic way to refer to the article of convention. I don't use that term specifically to avoid the confusion with his group. So he founded a group called Convention of States that was seeking an amendment on three different issues. One is fiscal responsibility, another is small government and another is term limits. Or limitation, the second one is limitations on federal power, something like that. I don't remember exact terms. And that group has kind of alternated through the years between a serious effort to try to get a convention specifically for those efforts, and something that's more of a right wing fundraising machine. But in recent years, I've kind of gone all the way toward the right wing fundraising machine. And they're not really taken seriously by the other article five convention groups anymore. The reason being it is impossible. There's a ceiling on how high you can go. It is impossible to get a convention by appealing to one party. And Rick Santorum in the quote that he had, which I believe you read in your video, and that was in that article, he made it very clear that they're trying to basically raise money to fund right wing elections to try to get so many Republicans that they will pass their convention call. Every other convention group out there recognizes the need for bipartisanship. And that includes ones that many consider more right wing like the balanced budget amendment, ones that many consider more left wing like campaign finance one and others like term limits as well. All those groups recognize the need to have that bipartisan appeal and work really hard to do that. More success than others. And that's why I was really glad to see so many Republicans supporting Wolfpack. Since we were founded by Cenk Yuger, who's obviously on the left, that most of our volunteers came from the left. So it has been a big process for us to demonstrate the appeal to those on the right. But I think we have been succeeding in that as well. But the effort, the convention of states project has simply stopped doing that. And we've gotten quite a few states, but there's a ceiling to how many they could possibly get. And that's seeing as well below the 34 needed to call a convention, and even farther below the 38 needed to ratify anything. So it's really just it's not a serious effort. They were not they were asked to be a part of a previous Academy of States, and they declined. When pretty much every other article five convention group from no matter what their issue is, joined that effort to study the process, even if they disagreed on the goal for why they're using it. They were not even asked to join Academy of States 3.0. So the article made it seem like Rick Santorum and Convention of States was a major part of Academy of States 3.0. They weren't there. They weren't asked to be there. I was a featured speaker there. Every featured speaker there was a supporter of Wolf Pack. So it was completely and utterly misleading. Yeah, it made it seem very nefarious. And, you know, that's why I covered the article because I read it and was horrified. But to be honest, I had to read it actually a couple of times because there was a lot that was there that seemed it was a very convoluted article. Like, I've covered stories by Grace Panetta before. I'm not familiar with the other author. And she's done great work. But it was difficult to get through and, you know, to learn that there was this intermingling of different conferences and like this implication that Rick Santorum was associated with Academy of States. It's a lot. And so what I was really fearful of was and why, unless the video ultimately was that, you know, if it is the case that this is this Republican art, you know, movement to get an article five convention is a thing. I don't want to play into this media narrative that a runaway convention is a possibility because I don't think that that's the thing. That's the case. And I think that you and Wolfpack has done a great job at debunking that myth.  Therefore, the conclusion must be that Wolfpack is also bad, which is why I thought, oh, my God, I have to bring on Sam so you can help correct the record because Wolfpack is a good altruistic organization. And it's literally not about partisanship, which is why actually, I think that having the movement overall, not necessarily be so at least aesthetically associated with the Young Turks is good because it gives it that veneer that it's left leaning when this really is not left leaning. And look, I'm leftist, right? But the goal, like this, the reason why this is nonpartisan is because this is beneficial to Republicans and Democrats, specifically their constituents and getting money out of politics allows them to better represent all of their constituents. So with regard to the runaway convention, can you dispel that myth just so that when we kind of have something to point to? Because I know that this will come up again if Wolfpack gains momentum. But I just want like a video that I could share with people and this, you know, a blurb from you explaining how that's not actually a thing with an article five convention.  Sure. Literally every single scholar, every single one who has published a peer reviewed article or the equivalent on this issue has agreed 100 percent that there is no way that a new limited article five convention call could possibly lead to an amendment on any other topic. When you see scholars quoted and op eds written by people who say otherwise, check the source. It's always either an op ed by a scholar who is has some other expertise within constitutional law or or it's a political statement there was testimony that has been printed in law journals, but it was political testimony and not a peer reviewed article. And those things are very, very different or a letter to Congress that was printed in a peer reviewed law journal, which is not the same thing as as an article. Every single article backs up that fundamental point that there is no way a new article five convention call could possibly lead to an amendment on another topic. And the reason why we know this for sure is the convention process is incredibly distributed. There are a few protections specifically written into article five. There's quite a few more protections that just come out of the structure of the Constitution because it gives certain it gives different roles to different entities. There is a role for the courts to play. There's a role for Congress to play. There's a role for the states to play. There's a role for the delegates to play. And I don't trust the courts and I don't trust Congress and I don't trust the states and I don't trust the delegates. But I do trust the process that puts them all together and distributes that power among those different places. And one thing that makes that process extra secure is that should it break down the possible result of one entity trying to run away and another entity failing to restrain them and then this or that happens in a worst case scenario like that, the result would not be an amendment on a topic that is not overwhelmingly popular and approved by the country. The result would be just nothing. My biggest fear out of a convention is not a bad amendment. It's no amendment. And that's why we need to work very hard to make sure that we have power. However, the same power that we need in order to get a convention, that's the same power we need in order to make a convention successful and the same power we need in order to ratify what comes out of it. So that can only happen if it's popular. There was James Madison is often misquoted here. He was involved in a lot of different types of conventions over the years. One that is almost always forgotten that he was involved in. And he was in favor of some and opposed to others for different reasons and never because of a fear of the Article 5 convention process. If you break down his quotes, there's all kinds of different reasons. But one that's often forgotten in 1930, I believe it was 1830 rather, there was an effort to amend the Constitution to allow states to nullify federal law. Madison knew that this was not a popular idea. And so he encouraged John C. Calhoun who was behind the idea to try to use the Article 5 convention process to get it rather than just declaring the power to nullify state law. He said, you know, if you think this is a power that the states should have, there's a process in the Constitution for getting the states to insist that they must have this power and that's the Article 5 convention process. And after working behind the scenes, he got South Carolina to go ahead and try to use the Article 5 convention to seek nullification. And he did that even though he was opposed to nullification because he knew that there is no way that an amendment can enter the Constitution through this process without being overwhelmingly popular. And indeed, he was right. Only two other states followed suit. One of them said that they agreed with South Carolina on the problems, but they didn't want nullification to be one of the solutions. And the other one was a little bit more vague overall. And the other states just completely ignored it and the effort to amend the Constitution to allow nullification simply disappeared because it lacked the support. You can't get an amendment to the Constitution without overwhelming popular support. There's no loophole in there. Article 5 is not one. It's simply misinformation that we see when people are afraid of a tactic being successful. They often find it more convenient rather than attacking the policy that they oppose to attack the tactic. And that's what we're seeing here. And that's what we've seen in the history of Article 5 Convention efforts that has led to this kind of misinformation becoming so commonplace that most people hear it from somebody who they trust. And that person heard it from somebody they trust. And that person heard it from somebody they trust. You heard it from a business insider article, the business insider article heard it from that of the Center for Budget and Policy priorities. This kind of thing is so in the zeitgeist because there have been efforts for decades now to fight the tactic rather than the policy when people disagree that now people assume the tactic is dangerous when it absolutely 100 percent is not. That's a really, really good point because when you think about it, how like what arguments would you even formulate against, you know, the Wolfpack amendments? That money in politics is good and politicians should be bribed? I mean to make that argument you sound like a clown. And I'm sure that there's some people in mainstream media that will do that, obviously. But you know, I hope brothers tried it in New Jersey. In New Jersey, that was the only time that the Koch brothers actually openly opposed us. They sent to a lobbyist from Americans for Presparity to testify against us in New Jersey. And we won. New Jersey passed and became one of our states. Then when we were rescinded in New Jersey, Americans for Presparity did not testify, but the head of the Provisional Policy Priorities, who I mentioned, did. And he testified about the Runaway Convention, which is not true. Interesting. Interesting. Yeah, that's it's probably more persuasive of an argument because it's complicated. A lot of people don't know these details. And as you said, you know, it can be something that was printed in a journal that was testimony from Congress. It's hard. So that's why I think that like your effort here is really important. Any lasting words that you want to leave us with? And also, can you tell us what we can do if we want to support Wolfpack? Yeah, absolutely.  I want to make sure, you know, this is not something that Wolfpack is doing to to help, you know, make our country what it should be and what it has been promised, what I promised to my kids. This is something that we are all doing together. I'm not Wolfpack. You are Wolfpack. We need help from everybody, whether it's donations or volunteers. We need both very much, especially as we're rebuilding right now. Wolfpack.com slash go or Wolfpack dashpack.com slash volunteer. We need everybody that we can get in this fight. It that's the only way that we're going to be able to put the kind of pressure to fight back against the larger interests. If you're part of other organizations and other volunteer efforts, that's fantastic. We need you to join Wolfpack also, not instead. We need you to join Wolfpack also because whatever pisses you off, the the root of that problem is the corrupting influence of money and politics. Think about why you can't make progress on environmental issues. Think about why you can't make progress in in regulation. Think about whatever the issue is that pisses you off most. Think about why you cannot win on that issue and it always comes down to the corrupting influence of money and politics. And that's why you need to work with Wolfpack and with that issue together in order to solve it. Yeah, well, we'll leave that there. Thank you so much, Sam, for coming on the program. I'd love to keep in touch to get further updates about Wolfpack because I think this is really important and the more people that we can get involved, the better off we'll all be. So I really appreciate it.