My name is Nate if you haven't met me already. A couple of announcements, there are solutions to the homework exercises which will be posted online I think later today. There are no official office hours, but I'll hang out after Michael Hutchings lecture today in case you have any questions. All right. So welcome to the polypholes discussion. The primary purpose is that I suspect that if you hadn't seen polypholes before Monday, then you're bewildered about at least part of what's been said. You know, like some piece of terminology that doesn't make sense, like maybe you think what the heck is this partial quadrant for or whatever else. So I'd like to take your questions and clarify whatever questions you have. So without further ado, let me turn the floor over to you. What questions do you have? It's not a question, but can we show some examples of any polypholes which are real? Yes. Yes. And yeah, I can do that right now. So here's a question for my quals. Where'd it go? Sorry. These are not my notes from quals. Okay, here we go. So this is a retract which is locally finite dimensional, but where the dimension varies within connected components. This is something that Joel alluded to earlier today. And this is also homework question number five. So the fact is that there exists a retract which is homeomorphic to the following subset of R2. So this is supposed to be the right half plane union with the x-axis, not including the y-axis. Does this, thank you, right? So does this satisfy your definition of weird umut? I can ask for weird, I think. This thing is like built up out of the union of things that are themselves magical. Fine, I mean it. Are there examples which do not perhaps like that? Can we first look at this all at the same time? This is the term when I need to say something. So if you built this from finite dimensional manifolds, you would take the real line and glue it into half space with this equivalence relation over the positive real line. And this is exactly what happens when you throw it into coronetial regularization. The topology, the quotient topology that you then get on this space is not good. It is not even first comfortable. In fact, so it is not metrizable. Whereas the topology that polyfoil theory puts on this is as a subset of a scale-bunner space, so it's perfectly metrizable. And it's absolutely key that we have a metrizable topology plane. So I must have been mistaken when I said homomorphic to this, or I guess. No, no, no, when it's homomorphic to that subset of R2. Okay, and you're saying that, for instance, coronetial structures would have put a different topology on it, which would have not been... The topology, again, is not the subset. All right, so the idea of this is that we're gonna fix some function, some bump function beta, and for T a real number, we're gonna write down a retraction on a function space, which is just projection to beta, but shifted by a certain amount depending on T. And I should have said, I'm sorry, for T greater than zero. And then for T less than or equal to zero, just consider the zero map. And so the funny thing that's going on here is that, so T is living in the x-axis, and as you come in from the right, so T's getting smaller and smaller, and E to the one over T is shooting off to infinity. So you're projecting onto this series of bump functions which are shooting off to infinity, and the interesting thing about scale smoothness here is that these maps behave sort of smoothly at zero. So something funny happens at zero, but we're gonna get a scale-smooth map. No, what is a bump function? I'm very convinced that your bump function is going from R to... You've got to try it. Where? I'll write it down now, but it's gonna go from R to R. But then where is this bracket thing? So this is the subspace in L2, R comma R spanned by that shifted bump function. Oh, so that's sitting inside. Yes, you didn't explain where that's sitting inside. That's sitting inside this infinite dimensional space, L2 of R, R. Yes, and I'll write that down. I'll write a precise definition down now. So let's set E to be the scale-bonic space, which is, well, the kth level is hk delta k functions from R to R, where we've chosen an increase in sequence of deltas starting from zero. And now the retraction or the candidate retraction, little R, goes from R times C to R times, sorry, R times E to R times E. And it's defined by sending the pair t, little e, to the projection onto beta t, when t is greater than zero. I'll write it in a second. Beta t means the shifted bump function. What do you mean, in the sort of t? It depends on the little bit. See the subtleties. See the subtleties. See the subtleties. But as either, is it? Oh, you have two e's. You've got two e's. It's not the exponential. But what is it the exponential? Oh, I'm sorry. I should call the function f, excuse me. Oh, that's inner product of the L2 inner product of that. Oh, it's not the exponential. So we've now set a world record for bad notation, so I'm sorry. Give yourself an R coordinate also. I'll show you the one that looks right now. Thank you, yes. So this is supposed to be mapped to R comma L2. So happy, good. OK, any other objections? Great. And so I think it's clear that the image of little R is homeomorphic, or maybe you don't believe the continuousness, but it's plausibly homeomorphic to the subset I drew above, where the x-axis is little t. And well, so the fiber living above any particular positive in the fixed point set is going to be the subspace in h0 is spanned by beta t. And the fiber over anything non-positive is just 0. Sorry, Nate. I'm going to be really, really annoying, and I'm sorry. But could you rewrite what you wrote in the bracket there? You mean right here? Yeah, did you wrote something just decided, I think? It has to be a retraction, so it's just the first coordinate to be 0. Yeah, so I accidentally written only the second component of this retraction. This is supposed to be t comma the projection of f onto the subspace spanned by beta t. It's the, yes, it's the L2 in a product. All right, so now before I move on to proving some amount of smoothness, any confusions about this definition? What does beta look like, did you mention? Yes, well, it doesn't really matter. It's a bump function with the h0 norm equal to 1. So why don't we just say it's, and let's say it's in c infinity. Do you need delta 0 to be 0 or kind of positive? I guess the delta 0 was positive as well. Do you really need it to be 0? I think probably if it was positive, and you also made this h0 comma delta 0, then it would probably work. The question is, if delta 0 were positive and not 0, would this still work? Delta 0 is the. There is a shift here. What? You can see that the h0 norm is not actually k. No, but if you replace to that by that. It's compact. So it doesn't, you can't forget the first one. You don't see the decay anywhere. Oh, but I don't know if beta doesn't 0. It should not be delta 0 if you work on anything that should be 0. Anyway, it really doesn't matter because it's an example. So let's just say that delta 0 is 0. OK. And let me just, before I prove that this thing is somewhat smooth, is everyone happy about this claim that the image of little r is this set that I drew in r2? I'll take your word for it. All right.  But I can at least show that the difference quotient condition is satisfied for proving sc1-ness at points of the form 0, f. I mean, but before, how would you even dream that this would be shown? You draw this, and how can you tell if it's a, is there a criterion to say it's a polyphonic, what type of polyphonic? How do you think about this? That smells really good. Does it come up somewhere? Yeah. I mean, this is actually an important example because it's not exactly the same, but it's related to the plus gluing. Because in plus gluing, well, you're not projecting onto some bump function, but you're multiplying by bump functions where something is shooting off to infinity. And you need smoothness of the retraction that corresponds to that. So the same reason that this is sc smooth is at least part of why the retraction, which is projection onto the kernel of minus gluing, is sc smooth. What's the significance of the axis or negative axis in that? Yeah, I guess it's not exactly analogous, but the idea is that in that projection to minus gluing, when a is equal to 0, you're doing nothing if you project to the kernel of minus gluing. Yeah, I would have to think about whether it's exactly the same, but there's something drastic happening at a is equal to 0. In that case, and when t goes non-positive in this case. You could, of course, take, yes, it's heavily beta 2. You could take identity minus beta 2, and then you would probably call it where you use one and it would be up to everything, the whole space, and then suddenly the hyper space. Great. So it turns out to be true that R is sc infinity, and therefore a scale smooth retract with the differential defined like so. So in the case that t is positive, this will be sigma, comma, negative sigma 1 over t squared x of 1 over t, then the quantity f times beta prime beta plus f times beta, and then plus var phi beta beta. Yes. I claim that it's trivial for t negative, but it's not trivial for t positive. But I think that the most interesting thing is happening at t equals 0. OK. So anyway, this looks horrible, but it turns out that it's not easy to come up with that candidate. But anyway, I'm not going to use this because I'm only going to be looking at what happens at t equals 0. So let's just show that if we write that R is equal to t, comma, p of tf, so p is just the second component of R, the component mapping to e, then p is sc1 at a point of the form 0, comma, f. So let's show that the difference quotient for that statement indeed goes to 0. Yes, sorry. So the difference quotient is uninteresting when sigma is negative because then it's just identically 0. So what you end up needing to prove is that if you look at the limit as sigma decreases to 0 and phi goes to 0 in h1 delta 1. And then the thing you're looking at is f beta sigma beta sigma plus var phi beta sigma beta sigma. And then you're doing h0 divided by sigma plus the h1 delta 1 norm of var phi. You claim that this limit is equal to 0. So what this thing is, is it's just p evaluated at sigma, comma, t plus f. And then the other two terms vanish. And then we'll say that this is less than or equal to the limit of following two quantities summed. Super good for you. Why does that pull up the expression you wrote at the top, not here, down here? It's because the differential that appears in here is the differential at t is equal to 0. Is there some way to calculate the differential in general? For example, can you actually differentiate something and gain the expression above? Or did you have to come up with this? You're asking, how did I get that candidate for the differential? I claim that if you pretend to be a calculus student who believes that everything is true, if you do the Taylor series approximation, then this candidate will easily pop out. If you just write down what the differential is supposed to approximate. If you're tired of this example, I promise that I'm almost done. OK, so we need to show that this limit is equal to 0. And let's just prove this for one of these factors, and then the other one is really similar. So let's look at this guy here. So the numerator is the product of f and beta sigma, and then beta sigma taking h0 norm. But the h0 norm of beta sigma is 1. So we just get the absolute value of this inner product. But because the h0 norm of beta sigma is 1, that's bounded by the h0 norm of f. So that means that this expression here is bounded by the h0 norm over absolute value of sigma. But then, right, we assume that, oh, I'm sorry. And when I say h0, I mean h0 only. Sorry, the only thing I'll use about the inner product is that beta sigma is a bump function on e to the negative 1 over sigma comma e to the negative 1 over sigma plus 1. And now we can bound this by some exponential. Yes, f restricted to this.  I see. So that goes with the h0 on that. So you're restricting after that sub-involve and taking some of this, and this, and this, and this. Right, right. So now we're using the fact that f is on the h1 level and therefore on the e1 level, and therefore it's an h1 comma delta 1. So you can bound this by e to the negative delta 1 times e to the 1 over sigma minus 1 fh1 delta 1 over absolute value of sigma. And then you know that this is just some constant. We're not, you know, this is fixed before we take the limit. And this quantity goes to 0 faster than sigma does. So therefore, this quantity is quite interesting.  OK. Yeah, so what I was saying is that beta sigma is supported on this interval, right? I'm OK with the second and last one. Adjust this one here. If you write down the definition of h1 comma delta 1, then this just pops out immediately. Because this norm is the h1 norm of ask xp negative delta 1 mod s times f. So if you just write down the definition of this weighted so-called of space, this pops out. I think you have to say that f has to be, in order to take the differential on the first level. Yes, that's right. So I didn't write it down. But in order to, we only need this difference question to go to 0 for f in the first level. And therefore, this norm is finite. OK. And this sort of raises the importance of the fact that we chose this particular gluing profile that our functions were shooting off to infinity like xp1 over sigma. If they've been going off to infinity much slower than that, this limit might not have ended up being 0. Faster is OK for this limit, yeah. Does it remain OK for all future limits? Or just to have? If you choose some gluing profile going to infinity much faster than exponential, would there ever be a problem? Well, it shouldn't us. I mean, I think if it oscillates a lot, maybe it's not so good. But if it grows rather fast in an oscillatory level in all derivatives, it's fine. So the worst case is minus 1 over 2 pi over root of sigma. That's the worst case, which unfortunately is precisely what he would use in gluing and delayed momfads. But that is, in some sense, in the general theory. And so, of course, from that point on. OK. Next question. Actually, could you reiterate the information about the typology of this thing? Because I think that is an important point. I mean, that's something, yeah. Yeah. I don't think I'll be able to say anything sensible about why this retract should actually be homeomorphic to the subspace of R2. But if you can, then. All right. Well, I mean, just like about, I'm not sure I could say anything, of course. But I mean, what's the typology of retract? It's like, it comes from? Well, by definition, it's inherited from the topology of the ambient scale, Bonach space, the zeroth level of that. But I don't know if that's the sort of thing you had in mind. Yeah. So presumably, it's some fairly easy exercise to show that this is homeomorphic to that subspace of R2. All right. No, so before we move on, what about three legs? Oh, you're asking. You're asking, could you get this as? No problem. I don't know. I can try that. So then I wonder, so the thing is look at retracts where the image should be in the smooth part, so it has a tangent space everywhere. Remember, that's the filtration. So look for a retract where the image is in the smooth part, which usually happens for low dimensional things. And so then you have a tangent space everywhere. And assume that the tangent space everywhere is one dimensional. So a one dimensional manifold would be the example. But it seems to be possible that things where you have bifurcating off branches sort of in this same derivative. So that could be like two things coming together, then have the same tangent space when they come together. So then I don't know. So there could be interactions which have this as an image. The exercise would be, I don't know, to take this thing and embed it into some bonus space and see if you can retract it. So it's possible that branched, something like branched one dimensional manifolds are actually retracts. But then it wouldn't be a problem still. Because now d squared equals 0 wouldn't be ruined by this, for example. Because in the end, we will actually get better results. So the thing is that the solutions of our Freton problems are strong retracts. Maybe the retraction goes into one level higher is a retraction. So the retraction which you get go from E into E1. And then there are actually really many problems. So if you would, yes, you're right. You could presumably do a Freton theory where you get, perhaps, this kind of things out. But then you would have this kind of issue. Unless you have some other structure like weights or whatnot. But the Freton theory, which Joel told you about, actually produces real manifolds. So that branching phenomenon doesn't exist. As the zero set of a transverse Freton. Maybe the last thing I can mention about this example is that it's a good exercise to compute the tangent space to this scale retract. In particular, you might wonder, what is the dimension of the tangent space at the origin? So I'll leave that as a mystery. Yeah, so any other questions? What are some things that are definitely not hand-pulled? What are some things that are definitely not hand-pulled? Non-measurable cells. I would catch yourself if that was hand-pulled. I mean it hasn't been really explored because in order to do SFT or so, the world isn't that bad. But I think it's bad enough, but it's not bad. But I think as far as the structure is concerned, I think there can be really weird stuff. So I mean you can have polyforge which look at some point, they look like a two. And the next point, they are zero dimension. Do you want to state what a splicing is in the retraction line page and how that guarantees that you can generally have a better structure in terms of what your own polyforge is? I don't know if that's helped in this case, but at least. So what Joel's referring to is that this particular retract that I've written down has this special structure, which is that it's a family of linear retractions. And there are certain things that are true for these special kinds of retracts which are called scale splicings that aren't true for general scale retracts. In all applications. Yeah, and in all applications currently, scale splicings are what appear. And I think my philosophical point of view, correct me if I'm wrong, Helmut, is that perhaps there are truly awful scale retracts like the Cantor said, I don't know. But I don't think we should worry too much about them. We should worry about what do we need for our applications and our polyfolds flexible to flexible enough to encompass them. So I think this one is relevant because it's really similar to the retract that you get coming from plus glue. And I don't need a great tangent space for the Cantor set. Is it not? Is there more something to settle on?  Or the mystery is whether the dimension of the tangent space at the origin of that space is it not just one mucus?  That's correct. And I guess you can actually see it very easily from the formula there. OK, if there are no questions, I can say something hopefully useful. If you ask sort of semi-continuity of local dimension, can it only go up, only go down, or it knows that property is true? In any rich direction, you're coming. You're always on those requests. You know of tangent space. Well, so OK, here's the answer to the dimension of the tangent space. For every point in there with t less than or equal to 0, it's 1. And for every point to the right, it's 2. So then so you could conjecture that you have what is it? Semi-continuity going down. So you can jump down. So I don't know the answer to that question. But there's some of this complementary solution. Right. Yeah, OK. But that is. Yeah. So the example that DUSA mentioned where you replace beta by 1 minus beta, of course, the dimensions would be infinite. But you can see that you'd sort of have the opposite kind of semi-continuity with that. All right. So last chance for questions or else I'll say something for the remaining five minute sub-lecture or discussion. Can I ask? I don't know.  But could polyphones, you think, just think, go beyond SFT, like, use them for something else? I think that that's a hope of HW and Z. But I don't know whether there are any particular examples they have in mind. Well, I'd be happy when I'm done with SFT for the moment. What are the ground species? Are we talking about J-hole? Well, I mean, I don't know if you would include Lagrangian flur theory in whatever notion of SFT you have in mind. But I interpret it as, can you construct things that are not modulized spaces of J-hole morphic curves as we're using? Right. Could you stand on its own, satisfy? Sure. I mean, it's actually, for a lot of bubbling up, you know, geometric flows and so on. It's precisely this kind of language which we need, if you want to describe it this way. So I think there are a lot of problems in nonlinear analysis where they have this bubbling up, but where they haven't actually, I think, because of the questions there are some steps, not develop a good language for a lot of the things. They are also non-generic. And you would like to do for some, some moxie. This minimal cell faces and such things hasn't been carried out. And all only under certain conditions are more geometrically and so on. Whereas I think there was, they never developed any abstract message to the top, which actually would at least allow you to count certain things. So I think there's actually a lot of possibilities for application of something like that. I guess in a strict sense, the answer to your question is yes, because Morse theory certainly could be framed in terms of polyfolds. You have a question? OK. All right, so the last thing I wanted to say is I thought that it might be mysterious to some people what the point of partial quadrants are. So I thought I'd say just a couple of words about that. So what's the point of looking at spaces like? Can everyone see this right here? And this answer to the question of why do we consider partial quadrants is what happens if we're trying to construct a modular space of j-hole morphic curves, and we want to construct a local chart near something with nodes? Yes, boundary nodes. So say we're doing Lagrangian flow theories. We're looking at holomorphic curves with boundary on Lagrangians. And we try to construct a local chart near something with the boundary node. So something looking like, and then the local chart near a map like this is going to be of the form 0 comma 1 times some space of functions. And the reason that this is the right local chart is that we, of course, want nearby maps to this guy to include where we've smoothed out the node.  And when the gluing parameter, which lives in here, goes to 0, you get actual nodal maps. So anyway, so that's where the partial quadrant definition is coming from, or at least it's one place that it comes from. And as a closing question for the audience, if you haven't thought about this question before Monday, let me ask you the following question. So say I take some map with an interior node. So something that looks something like, so a map like this is going to have degeneracy index 1 just because this is the local chart. And when you go all the way to 0, you get a nodal map. But the question is, what should the degeneracy, or what's the expected degeneracy index of a map like this? The question is, if you construct a local polyfold chart near a map like that, then what do you think the degeneracy index of this map is? And let me remind you that there are two gluing parameters, one necklake parameter, and one angular twisting parameter for gluing at that node. I'm going to take a vote between 0, 1, and 2. Yeah. 0? You can't vote if you knew it before Monday. 1 and 2. Do we all know which degeneracy index it is? I think here is the degeneracy index quickly, or is it not in the code system? Yes, so if you take a local chart, then for this particular chart, the degeneracy index corresponds to how much of the parameters living in the 0, 1, to the k are 0. And then to get the degeneracy index of a point in a polyfold, you take the minimum over all charts. Anyway, the answer is 0. And the reason that it's 0 and not 2 is that the gluing parameters for this node live in a disk. So the distinguished point at 0 corresponds to nodal maps. And if you move away from 0, then you're gluing the node. So in fact, this is an interior point of the disk, so the degeneracy index will be 0. Well, actually, also, we were just busy putting a chart there, a single chart. It shouldn't have any, right? So let me, with our retrack that we did with the plus gluing, we're putting a single chart on which had no quadric structure at all. Yes. Yeah. Indeed. All right. So I have a question as well. So when you find the degeneracy index, you take the minimum, right? Because you can have different charts, so it's the point that belongs to a different basic one or whatever. So even in this case, if you have a hypothetical chart which looked like, I don't know, 0, 1, 2, or something, then you can just say that the degeneracy index is at most completely correct. Yeah. So you would need to make some kind of proof in a particular situation that there wouldn't be some other chart where you'd have a lower degeneracy index. Sure. OK. I will stop there.


guys subscribe and turn notifications on leave a like and drop a comment down below get here first and win giveaway calls i will pin as first comment on some of my videos be fast and good luck what is going on guys welcome back to the channel and i appreciate you being here today i am back with another destiny 2 video and today have top five lucky some moments of the week but before we go any further people if you do enjoy the video leave a like and leave a dislike and help me out and if you are new lands here and enjoy daily destiny 2 videos be sure to subscribe but let's get straight into this top five in that number five you have a clip sent by brandy norton this clip was titled sleeper rex this clip proves that in number four we have a clip sent by barce raw oh sleeper you monster here we have a clip sent in by ikana kenken actually a decent clip shame about the ending though but damn he gets so so lucky here i have a clip sent in by civilize death from above quite literally place belongs to you now take the zone them fall you're unstoppable zone c captured you in number one we have a clip sent by game zero four two four hundred that collect though jesus people double down three opponents down but guys that is the end of this top five lucky moments if you enjoyed the video leaving a like really does help me out if you are new around here and enjoy daily destiny 2 videos be sure to subscribe and if you have any amazing clip to send in send it into the email i just linked at the top of the video the scourge but guys i hope you enjoyed the video and hopefully i will see you on that next one


I could tell I could tell dog did it did it did it By myself good morning blew up now. I'm still doing a podcast from my living room It's kind of like a little alcohol. What's good? Good morning.  I'm a little loopy went to sleep a little late. What's happening? So I went yesterday, and I did it and I didn't do it.  They're like Do you like avocados and they're like yes, and no, okay?  I went yesterday. I did it and I did it I went there, and I did it and I didn't do it. What that means is Signed up open mic, baby Orlando improv fish bar blue fish bar something like that It was not this it's at the Orlando improv, but it's in the restaurant open mic part Not the actual like Orlando improv stage, but it was awesome Signed my name dude that means I was ready to go I was gonna get up there, but they didn't have time they didn't have time so next week I'm bumped and I Performing next week 100% which means I'm gonna hone it in I'm gonna hone in my craft, and I was ready to go. I was in the right mindset I got a little nervous here and there, but most of the time like 99% of the time wasn't even nervous I was super excited which made me feel like I'm a performer and I'm ready and it was exciting and Then with all that excitement I was ready to go. They call the name Steven and it wasn't me It was a different Steven. I was like damn it I really because I wasn't expecting to go at that time because I kind of knew where my name was on the list and Nothing so there's that but it was a lot of fun And I met a lot of people there that were so cool that all the people of the comedians that were working out doing open mics That were practicing some people's just started some people have been doing it for a couple months So you're doing for a couple years got to talk to a lot of them and that was so much fun It was like it felt like where I wanted to be and I got to meet all these people and everybody was so supportive And there's a lot of funny people out there, and some people didn't do so great But that's also great I was ready to bomb bro And I was just thinking I'm made for this because all I wanted to do is get on the stage and fucking talk to Everybody because the people I talked to in the crowd since I got to know them a little bit All I wanted to do is make them laugh and it was like that's there's other people too But like if I'm up there making them other chances. I'm gonna make the rest people I just wanted to be up paper. I wanted to be in the spotlight. I wanted to be up there I can't believe I want to be up there. That's a crazy thought to me Welcome to dunk life daily where we we drag you into with dunks and we make you stay with the entertainment. Whoa Here we go. He's transparent. Um The other thing is that this is episode 50. I said yesterday episode 50, but it's not so happy half centurion Everyone this is the best episode yet because it's now and every the best part of every day is now right now So use this to your advantage. Am I a tony robins of comedy? You tell me what i'm saying is that you're getting a free show every morning I'm gonna be famous soon I almost did my first night mic. Oh, but my I almost did my first time. I'm famous soon What's happening, bro? Anyway, it's so much fun and I can't wait to do it again I can't wait to do it again because when I was there I was so excited having so much fun that it's it's crazy that I get to do that often It felt like a once-in-a-lifetime type of event even though it was just over mic If now I get to go practice and just go tell joes like I get excited for this podcast Because I know it's fun to do and I enjoy going nuts on and then yelling at you people in the morning so This free show i'm going to take on the road um But yeah, I get to practice and also just I love laughter so I get I get to go watch comedy too and meet all these people that are In comedy and just looking to have a good time.  It was just open mic So maybe there was more like strict comedy and a lot of a lot of new people too was so cool to see a lot of people's First time but I go up there. I don't I don't know I I know who I am is a huge advantage is like I know who I am I know how to get in the right mindset paradoxal intention I just finished the man in the man search for a meaning book. I have that in the back of my head So when I get up there, I'm nervous. Oh, no fucks. Oh god. I don't care. Oh, oh, you're nervous I'm not they're like more cringy than me the audience That's I was going to talk about my skin.  I was so excited and I was just gonna that's what I talk about I know how to be true to me and that's what I love. That's what I love about life And I love both sides.   That's that's the psycho mentality.  That would be really cool I'm like a real comedian. How did I get all this information in my podcast? God, I spit bars quick, huh? Whoo, um, so yeah, um That's what it's about. Um, and I wanted to bring up this Steve Jobs quote to be a little serious. Okay He said which I really love I love quotes. I love quotes I love words.  You got to make the dots yesterday. I made a dot. I went to the open mic signed my name Got over the fear got ready to go on stage And I was ready so now a dots been made next one dots made And you got to keep making dots bro and try not to make dots everywhere. I mean Try to know who you are so you can make the right dots But like you got to keep making dots and you never know which dots the one That's going to lead you in the dot path that you want to go So yeah, keep making dots. I've been putting off for you to for you to know I've been putting off going to open mic or going to stand up for Forever since forever. This is my first one I ever went to to watch.  I'm ready.  I'm gonna yell at people And I was in the right mindset I really was and I really think that it helps to know who you are because then you know to like Just be who you are and even if it goes wrong. I won't I won't be ashamed and I won't be mortified and I won't I won't try to leave the universe. I'll try to just sleep it sleep it off another night. That's it That's it. It was a lot of fun and I look forward to having my first open mic And recording it because I can record it. I was ready to record it And I'll be posting on youtube bomb or not, baby If you want to see bomb in a good fashion bomb's kind of good like you drop a bomb on the You know, it could be good, but Whoo, the word I mean, it might just be it might be really cringy But that's what we do and then I'll make fun of myself. How do we lose? How do we lose? Tell me how I lose. I want to know how I lose so I could do that now And then all I can do is win all we do is win win win win win win win win win skin skin skin skin What's good? That's the other thing you got to make yourself laugh. I know how to do that I'm talking to myself right now staring at the camera I just like was saying it like I was talking to someone because that's the mindset I go into and I'm looking at This thing and get a little fuzzy thing on top Whoo. Oh last but not least Breaking news in history.  So, uh, That's just the heads up, but I have a feeling it's gonna fizzle out But this storm Dorian's got everybody up in the frenzy We got the freaking water. I gotta get water now. I gotta get beans.   I might know how to swim.  So I need to swim I'll be swimming in Dorian If only I knew how to surf better. I'd be going to the beach and get my surf on my board anymore I sent it back to my sister.    I got plans Dorian Storms don't care about your plans. That's what I learned at his coffees perfect That's it.  Have a great effing day I'll keep you up to date with storm Dorian. It keeps getting pushed back now. It's supposed to land sunday night or something I can't keep up with the weather.     All right, I'm killing the character Let's go on this day in history.  Portugal recognizes independence of Brazil 1825. Oh, look at this. Look at this. Holy shit 2005 hurricane Katrina makes second and third landfall as a category tree Devastating me much at a u.s. Gulf coast from Louisiana to the florida panhandle kills more than 1830 chicks Causes over 115 billion dollars in damage.  Bro, I was born in the hurricane. My mama comment.  Okay. You already know. You know, this was common. You know what I know Today in film 1967 final tv episode of the fugitive Uh, the movie the fugitives talking about movies. We're back to movies I'm switching it up the movie the fugitive with Harrison Ford's one of the greats It's one of my dad's favorites. We got to watch that again. We haven't seen it forever. It's funny. It's hilarious. It's classic Today in music 1958 cliff richard and the drifters released single move it Canada's first british rock and roll song today in sport 1882 a australian beat england. I don't know why I got so serious Seven runs death of cricket.  Okay. Well, that works Oh, I think I forgot to record the drum roll. I'll put it in it. Oh my god.  It was I love rock and roll. I sing it so many times. My mom got scared. That's not a joke though We were all facing when I was losing my mind I was singing so much and my mom she was getting scared that I was like losing my mind She I wouldn't stop and the more she tried I know you're listening mom the more she tried to get me to calm down the more crazy I'd go So when you feed into it, I'm not giving in bro.  I think it's crazy Keep up the good work. Thank you so much, bro. And then my mom commented nine times and she wrote Uh 10 replies from me my passion do it Love you mom. Have a good day. Everybody love you all too.  They tried to get me in a frenzy.   That's it To the loot


This is TFNN the tiger financial news network Good afternoon everyone, this is the 1 p.m. Tiger financial news network market update I just got a message cannot turn the camera on So the camera was already on So all right well here we go the Dow is down The Dow is down 192 basil Chapman. Yes 34,281 of this one o'clock Tiger financial news network market update little Roman candle being formed right there We're looking at the S&P and after all the news yesterday You would have expected that the S&P would have been up 50 the Dow would have been up about 300 The comp index would have been up huge as well said the S&P's down 30 at 4053 that was just kind of a fake out yesterday the QQQ This is the NDX 100 trading Down 473 at 364 had a very big spike to 372 not on eight points from that level IWM the Russell 2000 the small caps we're looking at them at minus 183 at 183 94 down under the 200 period moving average goal. There's gold move up Gold steady is down to at 1946 had a fabulous move yesterday now. It's being reassessed me I think that this is the dollar is really interesting because the dollar is Action quite well. It hasn't taken out yesterday's high, but it's at 103 point 87 and It's getting closer to the 104s where there's a lot of resistance and looking at the crude oil Could all earlier was just kind of static up 22 cents at 79 But oh nine the pink 9p removing averages says that it has gone to a cell signal in the daily chart I don't know yet if it's a cell mode and we look at the TLT the TLT bonds Bonds are down 47 ticks at 9507. You'll keep going higher. So that said I will figure out why my camera isn't working Soon as I get oh, that's why there it is. Okay camera should be working right now, but I don't know why it you know technology Anything can happen at any point. So just to L if you can tell me if it's on me down back there I'll be doing the next hour Larry's voice is still Kind of problematic. He needs to rest it. I know with the whole thing with a voice It just needs time sometimes to settle in and everything comes back. So let me get well soon I'll be doing the next hour for him. It'll be trade what you see, but that it'll be his hour But it'll be my show. I'll be right back


Hello, welcome back to metals in biology. Today we are going to discuss control and use of metal ion concentrations. So, we need to control the metal ion concentration, not only we need to ensure metal ions reaches their destination, but if a lot of metal ions are getting accumulated at a given site, that could also be potentially extremely harmful. Of course, deficiency of metal ions can also lead to many disease states. So, it is essential therefore, to control and use of metal ion concentration for proper functioning of our biological systems. To maintain a particular metal ion in proper range, the term which is usually we use called homeostasis. Of course, one need to remove excess or unnatural metal ions otherwise it would lead to the toxification. So, detoxification is essentially an important process which removes excess or unnatural metal ions. Now, to remove these different metal ions, one can think of using extra cellular carriers. Of course, there could be passive transport, active transport in the form of ion channels and pumps which we will discuss in subsequent few courses. Now, there are metalloregulation that also are required. So, metalloregulatory protein will control the concentration of metal ion. Once again, homeostasis and detoxification are two important subtopic that we must understand. Detoxification becomes essential because otherwise it can metal ions can lead to different disease state. There are as I mentioned, there are different ways by which metal ions can be removed from a particular site. Active transport, passive transport, there are metalloregulatory protein that also control metal ion concentration. Binding and release of metal ions to receptors are controlled by pH and redox changes. So, for example, you know iron 2 plus versus iron 3 plus oxidation state change will control the binding of this particular metal with a particular ligand. For example, some of the sites are iron 3 plus specific because let us say too many anionic ligands are there. In that particular site, iron 2 plus is not a good fit. We will discuss one such case today, but once again the control of a metal ion and their usage must be done in a systematic fashion. Redox plays a crucial role to control any redox active metal ion concentration. Obviously, at given pH will be also critical for controlling the metal ion concentration. Well, we will discuss in subsequent slide the metal ion concentration control and how they are affecting different activities. In the last class, we are essentially discussing this cyderophore entrobactin where we have seen in bacteria how a particular metal ion we were discussing in particular iron centers, how iron centers or iron ions are getting accumulated inside bacteria by citric acid or by entrobactin. Today, we will see one such internalization process by mammals let us say, let us say in humans. So, how iron centers gets accumulated in our body that is what one of the subtopic we will discuss today. Now, these the transferrin is the protein that is involved in accumulating iron sites. Transferrin has 2 subunit, it is a huge glycoprotein it has 80 kilo Dalton molecular weight and it binds iron 3 plus very strongly ok. And what is found that the protein binding site of iron are also capable of binding carbonate CO 3 2 minus. Both iron 3 plus and carbonate CO 3 2 minus are binding to the transferrin synergistically. Of course, perhaps you know the metal containing protein when the metal is removed that is called apoprotein. So, apotransferrin is the one where iron site is not there and also cofactors such as in this case CO 3 2 minus is also missing. Now, this transferrin has 2 protein domains. In each domain, there are 2 subdomains that clamp down on the iron and carbonate ions. Once again iron 3 plus and CO 3 2 minus bind synergistically to the apotransferrin. Let us look at the transferrin structure. So, on the left we have the apotransferrin where iron is missing. Now, during this process of iron binding these are the 2 subdomain. This is one subdomain, this is another subdomain. These 2 subdomain are linked while iron is binding to this overall apotransferrin to give the iron transferrin protein, then essentially also carbonate comes into picture and they bind synergistically. Both iron and carbonate binds together in this whole protein overall to form a iron transferrin complex. Now, one thing you must have noticed the different the distance between these 2 subunits are decreased significantly during the iron carbonate binding. So, this is what is called the hinge motion. Hinge motion accompanies when iron carbonate binding are happening. So, this is similar to the hinges we know that it clamps down together ok. These 2 things are clamping down on the iron or carbonate indirectly overall iron and carbonate bringing these 2 subdomain closer together. Look at the distance between these 2 sides and look at the distance between here. Now, as we mentioned this is a huge glycoprotein. We are able to now see how iron and carbonate binds with each other. Now, these transferring active site geometry if we zoom in, if we zoom in here then we will be able to see perhaps the coordination complex inorganic metal complex that is forming when iron and carbonate is binding to the apotransferrin over here. Let us look at the transparent active site geometry. The crystal structure we have and that is fantastic to have because that gives you a crystal clear information about the active site. So, we find in the crystal structure that iron site which is over here iron site is binding with one histidine, one tyrosine and another tyrosine over there. So, 2 tyrosine and 1 histidine is bound with the iron site along with an aspartate. Over here this is the carbonate CO3 2 minus. So, both iron and carbonate are binding together with 2 tyrosine and one histidine and an aspartate bound iron center. So, this iron center is hexacoordinated. Quite interestingly and of course, this is a crystal structure obtained from lactoferrin. Quite interestingly you see that an arginine is present this is the arginine which is not coordinated directly with the metal center, but this arginine is present overall in this active site. An arginine active site forms a key hydrogen bond with the coordinated carbonate ion. This is the carbonate ion as you can see there is this hydrogen bonding with this carbonate ion. Therefore, overall it helps to effect protein folding around the metal coordination sphere. So, you have seen the iron center carbonate how carbonate is also hydrogen bonded with the arginine. Now, these 2 sub domain that we were talking about in the apotransferrin they bind with this iron and carbonate and both the sub domain comes close to each other as if they are clamping down on iron and carbonate. So, this crystal structure is quite informative in understanding how iron is binding with these apotransferrin to make the iron transferring and this gives us a overall picture crystal clear and very molecular level detailed picture how these are transporting or helping in internalizing the iron center in human. Of course, these carbonate that we have seen over there is not the only carboxylate ligase and present in metalloproteins. There are other carboxylate ligase and in metalloproteins and those are quite also interesting. So, let us look at the biologically available biologically available carboxylates, biologically available carboxylates. Well, one since we have seen carbonate another easy one would be the bicarbonate right. So, we have bicarbonate of course, another important one could be the aspartate one right. So, of course, I am not drawing the stereochemistry correctly here or CO2 minus and NH3 plus aspartate right. So, this is aspartate ASP aspartate and it also has these carboxylate ligation or it can provide carboxylate ligation in metalloproteins. There are other amino acids which are essentially of the similar type such as glutamate. You can also have once again the stereochemistry on this center I am not drawing. So, this is glutamate glue. We can also have lysine carbamate. So, where we have aspartate glutamate and lysine carbamate where we can also have the similar binding of this carboxylate ligation in metalloprotein. So, here we will have NH, CH2 and CH2, CH2, CH2 and then of course, carboxylate ammonia and H. So, this is lysine carbamate or carbonate is encountered in transparent as you have seen. This last one is found this carboxylate over here is found in urease, rubisco and phosphotryesterase right. There are different sites where different of these carboxylate ligation can be found. We might will be seeing quite often this aspartate, this glutamate and sometime even the bicarbonate. Well, it is also important to note that we are also having in addition to the carbonate binding that we were showing. Essentially other anions such as phosphate, arsenate, pyrophosphate, citrate, oxalate are all capable of binding with the metal center. There are different enzymes which can also bind or metalloenzymes that can also bind this sort of anion. Of course, ferric binding protein can also bind these phosphate, arsenate, citrate, oxalates, pyrophosphates. Those studies are done quite essentially quite a lot. What it can be concluded that not only carbonate various anions can also bind transferring in bacteria, which also have a transferring receptor. Well, another thing that becomes very clear that iron must bind as iron 3. This is iron 3 plus not iron 2 plus. So, this has to be in the ferric state. If it is reduced then of course, you need one need a bacterial reductase right. Thus affording the control of iron binding and uptake in the organism. So, this site for example, is very good in only specifically binding iron 3 plus, but this will not be a great binding site for iron 2 plus. Overall therefore, we can have control of iron binding particularly even iron 3 plus center right not for iron 2 plus center. And this sort of control binding and very selective binding also helps in uptake in the organisms. Now, let us look at how human transferring is actually involved in the iron release. So, how is overall process happening? So, the iron-free apotransferring that is the first step that we look at. This is each of the centers can load one of the iron. These are two different sub domain. Now, this iron-free transparent which looks like Peckman right. Now, it can pick up iron iron as you can see these are iron loaded transparent from outside the cell to inside the cell we are trying to see how iron is getting transported and what are the process involved. So, it starts with iron-free apotransferring. Once of course, there are receptor on the cell membrane and this receptor gets activated when iron ion is bound with the apotransferring. Subsequently, these receptors bind with this iron loaded transparent and they try to enter the cell. Overall a coated pit formation is happening. These are the clathrin which actually protects the vesicle formation or helps in the overall vesicle formation. Once this vesicle is formed, this is a coated vesicle as you can see from outside there was no such vesicle or protected information or protected apotransferring was there only after iron loaded transparent formation and getting activated and binding with the receptor one can then can see that this coated pit comes into the picture coated vesicle essentially it protects these are the fat layer right. It protects the iron center from getting misplaced so that it can reach to its target very reliably. Subsequently, once the target is kind of identified or target is reached, then uncoating of this you know of this coat that is nothing, but fat layer occurs. Now, this uncoating gives rise to a state where these iron can be released of course, it is going to be a going to be a ATP driven process and release of iron overall happens and then the rupture of this vesicle gives rise to the release of iron inside the cell and here in the ribosome so here these irons gets accumulated into the ferritin ok. We will come back to the ferritin in a moment. As you have seen transparent is the transporter of iron ferritin is the one which is responsible for storing iron inside the cell. Once it releases iron then remaining apot form of the transparent goes out of the cell membrane and from the cell overall again the catalytic cycle or the iron loading circle starts again. So, this is the human transferring mechanism how iron is getting released. Now, this iron release in cells by receptor mediated process is happening of course, as you have seen this is the receptor and this is happening you know in quite a reliable way it can be done again and again and again without any loss of activity as such. So, these are very effective process and that is the beauty of the biological processes. So, far what we have seen is how transparent is capable of internalizing or bringing the metal ions in particular iron that is iron specific iron is getting incorporated inside the cell. That is quite interesting it is a very simple process, but then understanding at a molecular level is quite exciting. As you have seen that there is a iron 3 plus ion not iron 2 plus and a carbonate that clamps down the 2 sub domain of apotransferring to bring them together. On top of that you have seen that the coordination site is quite interesting in these cases. We have 1 histidine and 2 tyrosine and 1 aspartate bound with the iron center along with carbonate. There is arginine is also patting or giving some sort of support through hydrogen bonding just giving the Koji feeling. So, that carbonate feels like welcome over there it binds with the iron strongly, but still further these secondary coordination sphere type of interaction through hydrogen bonding helps quite a lot in overall stabilizing these iron carbonate structure or the geometry in the apotransferring to give the iron loaded transfer. As you have also seen how these apotransferring are loaded and then they are getting carried inside the cell these are schematic diagram overall it helps in releasing the iron at a destination or it can be stored as a ferritin or in ferritin in multiple iron center can be seen stored. As you will see in this ferritin this sort of ferritin protein we can have even up to 1000 iron center that is quite exciting to note. And once again it is not only the carbonate that can bind with iron center or any other given center there are other carboxylate ligation in metalloprotein we have seen bicarbonate, aspartate, glutamate and lysine carbamate which are once again found in different active sites. Iron must bind as iron 3 plus in this transferring or apotransferring not in iron 2 plus state. So, the oxidation state plays a crucial role in controlling the metal ions and overall uptake in the organism right. Now, let us try to see the metal regulation of gene expression. As you have seen how metal ions is getting internalized in the cell now we need to also understand that we need to regulate the metal ion concentration inside the cell. Now, this metal regulation are governed by many different factor of course, without proper regulation of the metal ion concentration as we were discussing briefly that there are many consequences many diseases both higher concentration and lower concentration of metal ions can lead to many different diseases. Now, the principles behind these metal regulations are quite simple. Metal mediated protein structure changes affect transcription right. So, when metal is binding with protein the structural changes that happens by such metal binding with protein it affects transcription. Well as you know regulation of metal ion concentrations are going to be dependent both by transcription and translation let us just briefly mention what is translation and transcription as you all know perhaps. So, DNA is being converted to mRNA by transcription and the translation is essentially is the mRNA to protein formation right. So, overall so, DNA to mRNA formation and mRNA to protein formation these are the transcription and the translation and we will be seeing more of that in the next class. But let me try to tell you that metal regulation is quite an important topic which will determine the importance of metal and any milk malfunction in the regulation process can lead to the different disease. Metal mediated protein structure changes can affect transcription. Metal mediated protein structure changes also affect translation. APO versus hollow metalloproteins bind DNA and RNA completely differently. Of course, metallonegatory protein is a sensor just like what we have seen in different cases in inorganic chemistry everywhere metallonegatory proteins is the sensor. Metal induced protein structure changes also activate enzymes. So, if there is a metalloenzymes which does not have metal that means, the APO metalloenzyme. Now, once you incorporate the metal it is going to be active. So, metal induced protein structure changes during the metal internalization into the apoprotein. We are going to see the structure and changes and therefore, it participate also in activating the enzyme because these are metal enzymes we are talking about. Also metal induced protein structure changes are metal specific. Let us say there is a iron specific or iron specific enzyme it is not possible to induce the similar changes with any other metal. So, let me try to tell you once again that metal mediated protein structure changes affect transcription. Metal mediated protein structure changes affect translation. We will discuss this in little more detail. Metal regulatory protein is a sensor right, it senses what to do, it decides what to do or it tells what to do. Metal induced protein structure changes also activate the enzymes. Well we will see some of these processes in the next class. Let us keep studying and we will see how metal ions overall are involved in controlling the metal ion concentration as well as how they are getting stored in different places such as ferritin. Till then keep studying we will get back in the next class. Thank you very much.


The INCUS is a big data platform for monitoring net greenhouse gas emissions in the land sector. It uses a combination of the best available satellite and ground-based forestry data taken from across the entire country. The data is analyzed by an emissions modeling team to determine annual changes in carbon stocks in the landscape. From these changes, greenhouse gas emissions released into the atmosphere and carbon removed from the atmosphere due to new forest growth are measured. The difference between the two shows the total amount of greenhouse gas emitted by the land-based sectors in Indonesia. These results are then sent to emissions reporting authorities. The information can then be used to meet international reporting requirements and support informed decision-making on how best to reduce greenhouse gas emissions and more sustainably manage Indonesia's landscapes.


Ronald Coleman What's the trouble Oscar Otto? It's my battery Harlow water Why sure? But why not avoid that battery distress Oscar get an auto light stay full the battery that needs water only three times a year in Normal car use A fact that millions of cars and owners have proved for themselves Oscar and the auto light stay full gives longer life too Fiberglass retaining mats protect every positive plate to reduce shedding and flaking and give the auto light stay full longer life as Proved by tests conducted according to accepted life cycle standards. Where do I get this? No worry battery Harlow from your nearest auto light battery dealer to quickly locate him phone Western Union by number and ask for Operator 25 I'll tell you the name of your nearest auto light battery dealer where you can get an auto light stay full the battery That needs water only three times a year in normal car use and remember from bumper to tail light You're always right with auto light and now auto light presents a vision of death Starring mr. Ronald Coleman hoping once again to keep you in suspense If I speak too rapidly for your stenographer, you'll tell me won't you lieutenant no offense But um He impresses me as someone who has to sit on the floor to put on his shoes and stop me if I seem to wander away from the point Won't you I mean to say this is my first and I hope final appearance in a police precinct And I should hate to give a sloppy performance We were always known or aura and I for the smoothness and gem-like precision of our act as far as this murder Rap I suppose it's called is concerned and acquaintance with our act is the essential rabbit awfully good act smart informal Occasionally humorous and always mystifying Well the act always began with music never with the cliche fanfare of trumpets or a roll of drums I would saunter out to the center of the floor and say something like a good evening You're about to witness an exhibition of mental telepathy Ladies and gentlemen may I introduce Aurora my wife? They never fail to give her a hand What would they applaud? Why the vision she presented as she came toward me there has never been anyone as lovely as Aurora The most beautiful flesh in the profession Now Aurora would you care to tell the audience or shall I you tell them Judd while I tie the blindfold across my eyes Ladies and gentlemen all mind readers employ a gimmick a gimmick is a trick a device For example when the mind reader Threading his way through the audience says to the mind reader sitting blindfolded on the stage a lady has given me a small Object which I now hold in my hand What is it and the mind reader sitting blindfolded replies a silver coin the answer has not come through mind reading No, it has come through the gimmick a cue or signal Communicated through the very question itself, but we don't do that. We do not You will notice ladies and gentlemen that I never speak to Aurora at all now. Are you ready, Rory ready? Just here we go then now you sir you have something good Concentrate upon it like a good chap and the gentleman holds a coin in his hand It's a Mexican peso bearing the date one eight nine two That's very clever of you madam. I'll be surprised if she gets this one A sucker once born remains a sucker till death The audience never realized never in all the years We worked that although I was not speaking to Aurora directly my chatter nevertheless was loaded with signals and cues for her guidance By revealing the gimmick we concealed the gimmick and that lieutenant is the neat plus ultra of gimmicks Yes, it was as crude as that But it enabled us to work 50 weeks a year here and abroad at an average of over a thousand a week Of course, I always gave some credit for our success to to our agent Harry Arnold Although Rory was inclined to give him no credit at all Good knows Judt. I've managed to book the act into the college in in Chicago with a four-week guarantee It's not bad, huh? Get him. He managed to book the act. I suppose they never heard of us in Chicago I suppose we weren't held over there six weeks when we played the science who see in 1948 Well, you think it's easy to get a four-week guarantee these days money is short money is tight I have never yet heard you say money is long money is loose You have to sweat for your 10% don't you? Yes, you do and a pig's ear you do Agents they're all alike. There's gratitude for you.  You'll take it baby along with a 10% you'll take it You'll chew it you'll swallow it and you'll keep it down. How do you like that? I'm all in your kid Don't push me too far children children now on your way Harry and don't let it get you down I think a four-week guarantee is pretty good Thanks, Judd, but wasn't for you. I'd yeah, why go into what I'm going for a walk But aside from these altercations between Rory and Harry it was smooth sailing We wore the best ate the best drank the best Stated the finest hotels and every Saturday night after the performance Harry will bring us our salary. We bring it in cash thousand twelve fifty fifteen hundred I've the old performers distrust of checks been given too many with a high latex content Anyway, life couldn't have been more classic and then one evening About five weeks ago soon after we opened at the Grove here in town The frightening thing occurred. We just begun the act and I was out in the audience You will notice ladies and gentlemen that I never speak to Aurora at all. Now. Are you ready, Rory? Ready, Judd? Here we go then now you madam you have sold in her hand a Compact it is platinum it bears her initials are C You sir the gentleman is holding an engagement ring In it are three small diamonds Miss what would you be a young lady is holding? It's a small cameo brooch Rory Rory Maurice music I Picked Rory up from the floor and hurried with her to our dressing room almost beside myself with anxiety I placed her on the couch dampened a towel and put it on her forehead and began to chafer wrists Rory Rory honey Rory Judd Judd. I'm here Rory. Are you all right? I guess so. I don't know what happened. Well, you fainted away try to remember what happened I felt funny. I don't remember try Rory try try to remember. It's important. I can't Why is it important? You don't know Rory? You don't know You were calling out the answers before I even had a chance to give you the cues Do you believe in telepathy lieutenant? I don't mean the sort of thing Rory and I usually did I mean real telepathy I Never did either until that night I don't mind telling you I was badly shaken I mean after all I I knew we'd been using a gimmick and suddenly it began to happen without the gimmick Scared us to death. We didn't know what we were getting into but we went on with the act and in my mind I began to search about for the answer. I found it Of course, you'll find a gimmick in almost everything if you look hard enough. I Got it Rory We work together so long that you know what I'm about to say before I say it from my inflection my pauses even my movements You see oh Judd that has to be it. Oh, this is marvelous when Harry gets back I'll tell him about it and if I last told him I we can ask the management for more dough soon as he gets back next Thursday tonight How much more should we ask for? tonight What made you say tonight? Well, I don't know. Well, you were there when he told me he'd be in Palm Springs till Thursday. What made you say tonight? I don't know what difference does it make stop picking on me? So I made a mistake. So what I don't see how you can make such a mistake That's all just leave me alone I've been worried have crazy about really being able to read your mind. I've been under a strain So Harry's coming back Thursday and not tonight. All right. He's satisfied. He'll be here Thursday not tonight You just as a stone mister this dresser room a what is it telegram sign here sign for it. Will you Rory? There you are kid Judd I'm sorry. I blew up in your face. Judd. What's the matter? It's it's from Harry He's coming in tonight And he did too lieutenant Rory was so upset by it. She couldn't go on at all that evening. She had no explanation for how she knew none I don't know jet. I just don't know my mind seemed to go blank. I seem to hear a voice whisper in my ear Harry Arnold will be with you tonight. That's all When we got back to our suite at the hotel Harry was there waiting for us. Oh, what happened? Well, what happened you both look like ghosts Harry. I'll tell you some other time leave us alone. Will you all right? I'm going I just came to wish you a happy birthday to give you this birthday. Oh Thanks, Harry. Thanks. What is it? We'll open it. Why don't you? It's a bathrobe a red silk bathrobe with your initials. That's right. It's a red How does she know How do you know get out of here? I won't be talked to like that.  I wash my hands He kept his word lieutenant And that time on he kept himself to himself And I was prepared to let it go at that much as I liked Harry Until the night I was awakened by Rory Mourning in her sleep. No No, please. No, don't Rory Rory wake up. You're having a bad dream Rory. No, I'm here What Rory? the voice Whispering again. Yes. Oh Judd what?  Ronald Coleman in a vision of death tonight's presentation in radio's outstanding theater of thrills suspense Shoot Oscar Otto. I got it and I have it you've got an auto light stay full battery And now you have a power-packed Paragon that gives quick dependable starts and needs water only three times a year in normal car use Just what every driver should say when he needs a battery Oscar an auto light stay full with the fiberglass retaining mats Protecting every positive plate to reduce shedding and flaking and give that brawny battery longer life as proved By tests conducted according to accepted life cycle standards So friends choose the battery that states right on the case needs water only three times a year in normal car use To learn quickly where to get an auto light stay full battery Just phone Western Union by number and ask for operator 25 I'll tell you the location of your nearest auto light battery dealer the expert on all makes of batteries and remember from bumper to Tail light you're always right with auto light And now auto light brings back to our Hollywood soundstage Mr. Ronald Coleman in Elliot Lewis's production of a vision of death a tale well calculated to keep you in suspense Rory get a grip on yourself.    Stop it now It was just a bad dream.  Will you stop that? Will you stop saying that? Hold me.  You've had a bad dream. He hates me. He hates me. Oh He's gonna kill me I'm a rational man lieutenant I've always felt for example that when Hamlet says there is stranger things in heaven and earth than a dream Tov in your philosophy Horatio Horatio water reply tell that to Sweeney. I knew there was no such thing as mental telepathy I knew it as well as I know.  I knew it and yet the next afternoon I found myself entering a gun shop and purchasing a revolver and a box of bullets Determined that before Harry Arnold could so much as injure one hair of Rory's head. I would kill him. I Should have gone directly to the police first You're using hindsight lieutenant. I had all that out with Rory Please Judd, please go to the police. Tell them about this. Let them handle it. Tell them what?   Do you know when he's going to do it or how he's going to do it? No He hasn't decided yet Oh, Judd, isn't there anything we can do? Nothing Except wait I Reacted to the waiting as you might expect lieutenant sleeplessness loss of appetite growing irritability I flared up at everyone waiters Chambermaids elevator boys the manager of the club The manager of the club He finally said to me stone what the devil's gotten into you. I'd really like to know none of your business Well, I'm only trying to be nice.  Sure. I'll let you Alone, I'd let you alone right now if your contract didn't have another week to run But after that, I'll let you strictly alone. You'll never work this club again maniac I began to drink quite heavily quite noticeably I Was going crazy just from the waiting and then the waiting came to an end It was around three in the morning I was sitting up in bed in the dark smoking when Rory opened her eyes and said Judd Yes the voice Yes He is going to kill me here Right here in this room Rory Saturday the Saturday at midnight Rory Rory sweetheart.  He has a gun.  No Rory Rory. Listen to me. I want you to listen to me. You're mistaken.  You've been having another bad dream and that's all there is to it. No Judd.  No It's It's the bar over Tuscany Hotel. I See it's so clear You're wrong. I'll prove you wrong Get me the bar at the Tuscany will you over on Sunset one moment, please you'll see Rory He's not there at all. You'll see it's just a dream. Just a bad dream Hello, he's a Harry Arnold there at the bar No, I'm sorry. He's not he's not you're sure of that. I'm sure I'm sure He was here all evening left about a minute ago. I said good night to him myself. Want me to have Look look lieutenant my hands Just the memory of how I felt at that moment of my hands begin to tremble again Amazing, isn't it? Now there was last Thursday night or rather Friday morning Towards daybreak Rory subbed herself to sleep, but I was restless. I got dressed and went downstairs and Got into my car The long drive has always relaxed me, but when I got behind the wheel Oh, I don't know what it was possibly the fresh air, but but all of once I felt as though I couldn't keep my eyes open for another moment Simply had to have some sleep so I Crawled into the back seat Curled myself up in one corner pulled the rug over me and went out like a light I was awakened around noon by the sound of voices Don't slap at me you idiot. They may see us look business-like. Where is he? I don't know since he hasn't got the car. He must be out walking But he fought for it last night just like he fell for all the rest of it the red bathrobe Stooges you planted in the audience Even phoned the bar just after you left. Oh, I timed it beautifully Satin skin satin skin I can have it keep away from after tomorrow night will have all the time in the world for each other Harry You bought the whole story that it's going to happen at midnight tomorrow your place every word Just do what you have to do now. Remember to come to the dressing room before the 8 o'clock show Tell them you've set up a meeting with stamper the manager and stampers office at 12 Yeah, I want them to shake hands and be friends again I'll tell him yes, and don't forget when you come to our door at midnight keep talking to the elevator boy Don't let him go whatever you do you want him to testify for self-defense. Don't worry. I won't forget a thing You'll handle all the rest of it Just leave it to me. I mean about his gun That's pretty important. You know Don't worry. It'll misfire It'll be difficult for me to tell you what I felt as they walked away lieutenant One part of me felt the way a man ought to feel I suppose when he When he learns that the woman he loves is not only unfaithful, but plotting his death as well But another part of me felt only relief Relief at learning there was a gimmick in this tool They'd been fairly clever for amateurs Harry had a good excuse for carrying a gun to protect the cash. She brought me each Saturday My own behavior in recent weeks would lend weight to what he would probably offer in his defense that I must have been crazy But for no reason at all I'd opened the door pointed a revolver at him and threatened his life that he had a shoot in self-defense The presence of the elevator boy They could mean only that Harry would shoot just as soon as I opened the door I'd be found dead with a revolver in my hand and a heartbroken agent at my side Tableau I Found myself hoping as I never hoped before that they'd come to their senses before Saturday That they'd realize what a vicious inhuman thing it was they were planning But just before the eight o'clock show that night. There was a knock at the door of our dressing room come in Judd I've been talking to stamp of the manager. He's sorry. There's bad blood between you and wants to square it I told him you'd be in his office at 12 to talk things over all right with you Yeah, we don't want it. So this will never work here again. Do we I mean there's no reason we should no reason at all But my dress judge see you later judge Yeah, later We did the show and then went up to our suite. I Convinced Rory that I should meet Harry alone and then I helped her pack a small overnight bag I loaded the revolver and then there was nothing to do but wait The minutes passed nine o'clock ten ten thirty and I waited Judd Yes It doesn't seem right to leave you here alone Harry might know you go Things might not turn out as I planned am I not be able to stop him and if I fail to stop him No, no, it's best that you go just wait at the motel until you hear from me What time is it? almost 11 two minutes of 11 I I'm out of cigarettes This is mr. Stone in 1101 please send up a carton of players William right away. I want you to go now Rory Judd, let me call the police, please. It'd be useless. We've gone into it and it would be useless Well, then come with me. He won't find anybody here and he choose another place another time Here's your release. You have your gun in my pocket. You you won't take any chances I don't know what I'd do if you were hurt. I won't take any chances Let me help you on with your coat Oh John, I love you so yeah, I know and I love you Rory. I really do you know You ready?  Well, I find change. I shall always remember the look on Harry's face Lieutenant as she sank to the floor They'd concocted a bad dream between them and it had come true I'll bet he still doesn't know how it happened if you pass his cell you might tell him just whisper the word gimmick into his ear Yeah, that's what I said gimmick. I Gimmicked the clock while Rory was dressing set it back a full hour. It was 11 to her But 12 to him. I adore gimmicks. Don't you? Suspense Presented by auto light tonight star mr. Ronald Coleman This is Harlow Wilcox speaking for auto light and bringing back our distinguished star mr. Coleman Thank you, Harlow You know it's been over two years since I last played in auto lights theater of thrills But I've listened to suspense Attain new dramatic heights this season with such exciting fairs Edwin Drude and of course Othello Harlow my congratulations to our producer director Elliott Lewis and to water light for magnificent radio entertainment Thank you, mr. Coleman and friends You can always expect the finest from auto light the world's largest independent manufacturer of automotive electrical equipment Every auto light product is backed by constant research and precision built to the highest standards of quality and performance No wonder auto light serves the greatest names in the industry. Yes from bumper to tail light You're always right with auto light Next week we recreate one of the great mysteries of the sea a ship found drifting in perfect condition But with no human aboard the mystery of the Marie Celeste our star mr. Van Heflin That's next week on suspense Suspense is produced and directed by Elliot Lewis with music composed by Lucian Morrowick and conducted by Ludbluston a Vision of death was adapted for suspense by Walter Brown Newman from the original story by Jerry Hausner Into night story. Mary Jane Croft was heard as Aurora featured in the cast were high-ever back Benny Rubin Julie Bennett and Charles Calvert A full battery is auto light resistor or standard type spark plugs and auto light electrical parts at your neighborhood Auto light dealers switch to auto light. Good night. This is the CBS radio network


Hi, this video is called Practice Problem 1. I promise you, it will be a lot shorter than the video you just finished. But please, it's very important to go through these next four examples because the problems are all just a little different, and you will get good at these if you practice. So here, consider this. These next four videos, a chance to practice using what you've just learned. So this problem says find the exact area of a regular hexagon with a perimeter of 60 units. Well, we're told we have a regular hexagon. A hexagon has six sides. The picture proves that it has six sides. And since it's a regular hexagon, all six of those sides are the same. So since we have a regular hexagon to find the area, I'm going to use my formula of 1 half perimeter times a pothum. So my goal is to figure out what the perimeter is and what the pothum is, because once I have that, I'll just multiply the three things together. Well, the nice thing is that in the problem, they gave me one of the things I need. They told me the perimeter is 60. So I'll replace p with a 60. So this doesn't seem so bad. All I have left to do is figure out what the epothum is. Once I know that, I can just multiply everything together. One thing to note is that it says to find the exact area. That means no decimals are going to be allowed in your answer. So if you use your calculator, be careful. All right, let's get started. To find that epothum, when you do problems like this, always start by figuring out how many triangles you can make. A hexagon will have six sides, so it will have six radii. So it will make six triangles. All right? Let's think about what the length of these side lengths are. If the perimeter is 60, and there's six sides, 60 divided by 6 is going to be 10. End of the school day. 60 divided by 6 is going to be 10. So that's telling me that if the perimeter is 60, and all six sides are the same because it's regular, all of those sides will be 10 units long. So that's getting us closer to finding the epothum. Another thing to get us closer to finding the epothum will be to find the central angle. Remember the central angle is right here. Since there's a hexagon with six sides, there'll be six central angles. So we're going to do 360 divided by 6, which gives me 60 degrees. So all of these central angles will be 60. Now before I write the 60 in that bottom triangle, I want to think for a second. My goal is to find the epothum or the epothum. So let's drop that down. Well, what did the epothum do? It split my side length into two, five and five. And then it also split my 60 degree central angle into 30 and 30. So at this stage, it's a really good idea to take this little triangle and create it bigger so I can see what's going on. And one thing I forgot to mention, that epothum, it splits the segment. It bisects the segment to five and five. It bisects the central angle to 30 and 30. It also creates a 90 degree angle here. So that's nice. You've gotten a lot of practice with 90 degree angles. You know a lot about them. This is five. This is 30. Here's the epothum, which I'm looking for. What kind of triangle do I have? Well, if this is 30 and this is 90, this is 60. So you have to go back now and remember what you know about your 30, 60, 90 triangles. Opposite the 30 is n. Opposite the 60 is n root 3. And opposite the 90 is 2n. Well, this is pretty slick because n is five. So that would make my hypotenuse be 2 times 5, which is 10. And it would make the epothum, which is n root 3, it'll make it be 5 root 3. So which side do I care about for the terms of my problem? Can you remember in my problem, I'm looking for that epothum. And the epothum, we just found to be 5 root 3. So let's go ahead and replace the a with 5 root 3 in my formula. I'm feeling excited now because I can see I'm almost done because I filled in all the variables of my formula. All I have to do is solve. Since it is a multiplication problem, I can really multiply this in whatever order I want. I'm going to go from left to right. So first I'm going to do 1 half times 60. Multiplying by 1 half is the same thing as dividing by 2. So 1 half times 60 is 30. So then I have 30 times 5 root 3. Sorry, I don't know why it wrote like that. So this now, because it's multiplication, I don't need like terms. So I can go ahead and multiply the 30 and the 5 together because they're both outside of the square root. 30 times 5 is 150. I'll keep the root 3 there. And I'm going to put a label of units squared on my answer. Because it says find the exact area, I will leave my answer like this. I'm not going to do 150 times the square root of 3 in my calculator to see what decimal I get because my answer wouldn't be exact anymore, it would be approximated. So the area of that regular hexagon is 150 root 3 units squared.