Hi, I'm Zor. Welcome to Unizor Education. Today we will talk about Taylor series. This lecture is part of the course of advanced mathematics for teenagers and high school students. So it's presented on Unizor.com, so you can watch this lecture from from this website, which is definitely recommended because the site has very detailed notes for each lecture. Plus there is an educational functionality which you can get engaged with including exams, etc. The site is free. Alright, so Taylor series. Okay, now functions can be very simple, right? For instance, it's a simple function in terms of if you are tasked with some kind of calculation, you can very easily do it, right? Or functions can be really complex. I don't know, sine of natural logarithm of x squared divided by 2 plus e to the power of tangent x. Yeah, go figure and calculate this particular value. That's not really easy, right? So that's very important actually aspect of dealing with functions. If you know something about computers and how they work, basically you know that the processors, which are the heart of every computer, can perform four arithmetic operations plus minus multiplication and division on the level of commands. Basically, a processor command has these types of commands. There is no command, for instance, for calculating tangent of some value or power, logarithm, or whatever else. However, you know that if you will take, for instance, a calculator, you have some signs and tangents and logarithms. If you take any computer, there is definitely some way to calculate these values in just one stroke, right? So how is it done? Well, they approximate inside the computer. There is some kind of a program which basically is not calculating directly tangent or logarithm or anything like that. They use approximation of these functions using some much simpler operations. Now, what is much simpler operation, which includes only four arithmetic operations? Well, it's polynomial, right? If you have some kind of a polynomial f of x is equal to x cubed plus 3x plus 5. Now, it's easy to calculate it based on just four arithmetic operations. Well, I'm not sure about the power. Power can actually be a little bit more complex. You don't want to multiply x by itself three times, but maybe they do. I don't know. But in any case, this is much simpler than this, right? So any polynomial calculation is much simpler than something like this. So it's very desirable to be able to approximate any function. Well, not any, but most of the functions, at least nice functions, smooth functions with a polynomial. And then the calculations would be much simpler. Now, okay. So that's basically about why we are engaged in something like Taylor series. Now, let's talk about a little bit more concrete examples and requirements. Well, first of all, we are talking about functions which require this approximation, which are smooth and defined on some segment from A to B. Now, when I'm talking about smoothness of the function, I assume it's being continuous and differentiable and maybe twice differentiable, twice differentiable, maybe differentiable to any level of derivatives. So basically, my very short and not exactly mathematical answer is when I'm talking about smooth function and I'm talking about certain operations, I assume that these operations can be done. Now, in this particular case related to the Taylor series, I'm talking about infinite differentiability. And it's not such an unusual requirement for functions which we are usually considering in mathematics. Like, for instance, sine, it's infinitely differentiable. From sine, we have a cosine. From cosine, we have minus sine. From minus sine, we have minus cosine. From minus cosine, we have sine again, and it all repeats. I mean, if you talk about logarithm, if it's a natural logarithm, first derivative is one over x. Second one is one minus one over x square, etc.  So all functions which we will be talking about are smooth in that particular sense. So I'm not going to go into the details of this smoothness. I just assume that if I'm writing something, this is possible to basically to write and the function is really possesses the properties necessary for whatever the expressions, the formulas where it's participating. Okay, so that's first. It's done. Now, considering our function is relatively smooth, what I would like to do is approximate it with some kind of a polynomial. Well, again, I would like to be a little bit more precise. Not only I would like to approximate it with some kind of a polynomial, I would like to be able to approximate it as close as I want. So any degree of closeness of my approximation should be allowed. Now, it means my polynomial should be more and more complex, right? To incorporate all the different curvatures of my line. So let me be more specific. I would like to have a process which can generate for any function which is sufficiently smooth. It can generate basically not just a polynomial, but a polynomial series which is C0 plus C1x plus C2x squared plus, etc. plus Cnxn plus, etc. Infinite series. Now, infinite series must, number one, be convergent to my function f of x for any x in this particular interval from A to B. Now, if that is true, if the series is convergent, then I can basically cut it on any level, forget about detail, and say that, well, this is whatever I cut, let's say up to nth power of x. I'm saying, okay, this is approximation. How good is it? Well, for instance, I can evaluate how good it is.  Basically, the tail is infinitesimal as I introduce more and more into the main body. So whatever I'm cutting off, even if it's infinite number of members of this series, still their sum is infinitesimal if my n is going to infinity. So the more members I'm allowing from this representation, the more precise would be my approximation. I would like to introduce even more as a requirement because I know I can satisfy this more important environment. I would like this representation regardless of the number of members which I'm using as an approximation to be exactly the same as function f at one particular point. So there is one particular point where all these are true, et cetera. So at one particular point, no matter how far I'm cutting my series, I would still have exactly the same value. So I know I can satisfy both requirements. And this one actually makes me a little bit more assured that my approximation will not go too far from the function because I know that regardless of the number of members I'm using, so at least at one particular point, which is by the way called a center of this representation. So at the center of this representation, it always coincides with the value of the function precisely regardless of the number of members which I am choosing to retain and cutting the tail off. So these two requirements, at one particular point, it will be precisely equal to my function regardless of the number of members. Now at all other points, the more members I will have, the more precisely my approximation will be because this series is convergent at any point x it converges to this f. So these are two requirements. And now I'm going to basically try to satisfy these requirements. Here is how. Okay. First of all, let me satisfy this requirement. That's the easiest. Here is what I will do. Now instead of gauging my polynomial, I will use the sigma symbol for this polynomial because it's infinite. So n greater or equal to zero, that's index cnx to the power of n. So that's my polynomial sequence is a polynomial series. Now at point x is equal to x zero, that would be this obviously. Now let me express this slightly differently. I will express instead of this, I will use this representation. Now, is this a polynomial series? Yes, absolutely. Because any x minus x zero to the power of n is basically a polynomial in its own right, right? Of power n. So the sum of these obviously again is a polynomial series. So what this representation gives me is again a polynomial representation, a polynomial series which approximates my value of the function of the function f. But now I'm absolutely sure that no matter how many members I will choose, if x is equal to x zero, all the members starting from n is equal to one will just disappear because it will be zero, right? So the only thing I can say about polynomial series of x zero is c zero, right? Because starting from c one it will be it will be zero. So let me just choose c zero is equal to f of x zero and I can even represent it this way. p of x is equal to f of x zero plus and then I will start from one. Okay, this is a polynomial representation. This is a constant, right? Because this is the function value at one specific point which I have chosen as a center, right? So this is the constant, c n's are some constants, whatever it is, and this is basically the body of the whole polynomial. But again at point x is equal to x zero, all these members are zero and my regard, so regardless of how far I will cut my tail off, the value of the right side at x is equal to x zero will always be f of x zero, which is my requirement to have the polynomial representation exactly the same value regardless of the number of members at one particular point. Now let's talk about these coefficients c one, c two, etc. up to infinity. Now I don't know first of all if such a representation exists and even if I will find something the question is whether the series would be convergent. So what I will do is the following. First let me assume that this representation as a polynomial series exists for a sufficiently smooth function. So let's assume that there is such a polynomial which is equal to this from one to infinity. So let's assume that this exists. From the existence of this I will come up with certain values of cn. So these values are a necessary condition for this representation to be true. And then after I will find these concrete values for cn, I will prove that the series really is convergent for these particular coefficients. And that would prove basically that the whole representation makes sense. So how can I find my values of cn? All right, it's really very simple. Let me make the first derivative. Now this is the constant. So the first derivative would be, let me just explicitly start it from c1 x minus x0 to the power of one. What's the derivative would be? c1 plus the second member would be c2 times, it would be x minus x0 square. So it's 2x minus x0. Next would be c3, 3x minus x0 square, etc. So you remember that xn derivative is n times x to the power of x minus one. So from x minus x0 square it would be 2 times x minus x0. From x minus x0 cube it would be 3x minus x0 square, etc. Up to infinity. So this is a series. Now, what if I will put a derivative of x0? It would be this. So these members will just disappear. And what would be left? Just c1. Okay, good enough for me. So let me just leave this as this. And from 2 to infinity cn times n times x minus x0 and minus one. And, okay, now this member I can call it c0. I have already found it, right? Now, basically what I'm saying is that c1 is equal to first derivative of f at point x0. Now, let's do the second derivative. Well, this is a constant so it disappears. Now this would be sum of, well, let me again take the first member. So if n is equal to 2, so that's 2 times x minus x0 to the first degree. So it would be 2 times s2. And starting from 3 I will put cn n, n minus 1, x minus x0, n minus 2, right? So the derivative of x minus x0 to the power of n minus 1 would be n minus 1 times x minus x0 and I reduce the power by 1. So I had n before, cn before, so that's what will be, right? So what will be my c2? If I will put x0 here, all these will disappear, right? Because not starting from 3, so it will be to the first degree, x minus x0 to the first degree, which means if x is equal to x0, it will disappear. And then the second degree, the third, etc. And the only thing which is left would be this. So that's f second derivative divided by 2, right? Okay, third derivative. Okay, this disappears, it's a constant. And here again the one which as the n is equal to 3 I will just use. So it's 3 and 2 and c3. That's the coefficient at x minus x0 to the first degree, which means when I'm getting a derivative from this, x minus x0 disappears and I have only coefficient. Now starting from the next, I have n, n minus 1, n minus 2, x minus x0, n minus 3. And again, if I put a third derivative at point x0, this will disappear and I have just this. So c3 is equal to third derivative at point x0 divided by 3 times 2. Well, as you probably figure out that I can actually write a general expression, which I can prove by induction, but it doesn't really make much sense anyway, because it's obvious. It's n's derivative divided by, well, if it's 2, it's 2. If it's 3, it's 3 times 2. If it's 4, it will be 4, 3, 2, etc. So it's basically n factorial, right? So I can make times 1 here, times 1 here, divided by 1 here. And even with a 0, actually, I can put 0 factorial here. So this is for any n from 0 to infinity. So my function actually is equal to, let me return back to starting from 0, where n from 0 to infinity, assuming that 0's derivative is actually the function itself, then the first derivative is the first derivative, etc. And 0 factorial is 1 by definition, as we know. So this formula actually is just true for any n, right? Fine. I have found my coefficients. Now, question is, I mean, maybe it's not convergent at all. I mean, I found a necessary condition for my coefficients cn to be of this value, of this type. So x0 is that center, if you remember, which we have fixed in the very beginning. And as a function, it looks like this. But maybe it's not convergent for any x. So this is another piece of the proof which I would like to continue with. Now, there are certain conditions on these n-th derivatives, which we really have to impose, otherwise there is no talking about any kind of convergence, because this is unknown thing, right? We don't know anything about f. But let's consider for a second that the n-th derivative, no matter what n is, is bounded by some value. So let's just assume, let's just assume that we are talking about functions with bounded derivatives of any sort. So let's consider that fn of x, let's say by absolute value, is less than some value m, where x belongs to ad. Now, how important actually this particular requirement is? Well, it is important, because again, if you consider some function like, for instance, tangent on interval, which includes minus p over 2 and less pi over 2. Now, let's consider function tangent on some interval, which is greater than this one. So we have these points where, number one, tangent itself is not defined. And number two, in the immediate neighborhood of this point, derivative goes to infinity, right? Vertical, vertical derivative. So it's 90 degree basically, right? So the tangent is equal to infinity. Now, so what I'm trying to do right now is to say that we are considering only functions which do have certain bound on their derivatives up to any degree, up to any level of complexity. So for instance, on this particular interval, my tangent and its derivatives basically are bounded by some value. So I assume that we need this particular requirement for any derivative within the interval where we are considering our function, where we would like to approximate our function. I would like all these derivatives at any point of this interval to be bounded by some value. Now, why do I need it? Well, obviously, because now I can say that these are always less than m sigma n from zero to infinity x minus x zero n to the n factorial. So now I have to only prove the convergence of this series. Now, there are probably a little bit less strict requirements for these derivatives. For instance, I can ask that these particular derivatives are growing as n goes to infinity, but only as a power function, like this one. This is also fine, but it's a little bit complicated, and that's why I don't want to concentrate on this. I deliberately chose a simple restriction on all the derivatives just to be independent of it. So now I have to prove only the convergence of this. But basically, again, if I will prove that, then even if m is not a constant, but something like m to the power of n, which I can connect with this to the power of n, it will still be convergent. I just don't want to go into these details. So let's just concentrate on this thing and prove that this is convergent. Well, first of all, let's just think about this. As n is increasing to infinity, I am multiplying my denominator by greater and greater and greater number. But this, I am multiplying only by the same x minus x zero as n increasing. So next will be x minus x zero to the nth, multiplied by x minus x zero, and this will be next multiplied by n plus one. So no matter how big x is, this thing is always increasing this multiplier in the denominator. But numerator is always multiplied by the same number. So it's obvious that denominator is growing and significantly faster after a certain value of n, obviously. Now, that actually kind of makes us to believe that the whole member is infinitesimal and it is, obviously. But that's not sufficient for the whole series to converge. What I would like to do is I would like to prove that this thing is actually bounded from the top by some geometric progression with the quotient less than one, which means it's convergent. We know from the properties of geometric conversion that if the quotient is less than one, then the infinite geometric progression is converging. So that's what I'm going to do. And it's really not very difficult at all. So how can we prove that this thing is converging? So we don't need m, it's a constant. So this is the only thing which we need. But let me just do it even simpler. c to the power of n divided by n factorial, m from zero to infinity. c is any number. Basically, no matter what number it is, we're talking about some number, we're talking about convergence for any particular x, right? So it doesn't matter what I put x minus x zero or c, etc. So I would like to prove that this is convergent. Okay. How can I do it? Here is the way. Let's choose an integer. m is integer and m is greater than c. So no matter what c is, maybe c is 25.7. Then I will choose 26, something like this, right? Now, c to the power of n divided by n factorial. This is c to the power n minus m times c to the power of m, right? Now, n is growing to infinity. So after certain n, which is greater than m, I can write something like this. So n minus m is positive and m is also positive, etc. divided by n factorial. Now, n, again, is going into infinity. So I can just start from any n I would like. And obviously, if n is greater than m, I can represent n factorial as m factorial times m plus 1, m plus 2, etc., up to n, right? So far, I did not change anything. I just replaced n factorial, which is product of all numbers from 1 to n. I divided by the product from all numbers from 1 to m and then whatever left to n, right? Now, if I will reduce my denominator, I will increase the fraction, right? So how many numbers I have here from n minus m? So I have n minus m different numbers. All of them are greater than m, right? Because it's m plus 1, m plus 2. So if I will replace it with m to the power n minus m, I will decrease the denominator because each one of them is greater than m. And since I decrease the denominator, I increase the fraction. Now, what is this? Let's combine this and this. So it's c over m to the power n minus m times some kind of a constant q. Now, m is fixed. It depends on c. c is fixed. m factorial is fixed. So it's some kind of a quotient. It doesn't really matter. Some factor. As n goes to infinity, q is not dependent on n, right? q is a constant relative to n. Now, what is this? c divided by m is less than 1, right? By absolute value. We're talking about absolute value, of course. Which means that this represents a member of geometric progression with c over m being a quotient. And this quotient is less than 1, which means that this particular thing is less than or equal to some kind of constant a to basically bypass all the members starting from 0 up to m, whatever it is, some kind of constant. I'm not interested in the beginning because beginning is always fixed, right? We are interested in infinity. So after infinity, I mean to where it's infinity, this thing would be sigma of c over m to power n minus m. Again, some factor here. So this is basically a geometric progression. And obviously, since c over m is by absolute value is less than 1, my geometric progression has my infinite geometric progression can be summed up. And the series geometric series will have certain concrete value as a sum. So it's convergent. So basically, what we have proven is that this thing is converging. That's basically all I needed. Because in the very beginning, we kind of assumed that it's convergent. And then we came up with values for all the coefficients of this Taylor series. And now, so it's a necessary condition. And now I have proven that with these coefficients, my Taylor series is actually convergent for any value of the argument. And well, that's basically the only thing which I needed. So now I have proven this particular representation which we were considering the Taylor series. Let me just write it again. So f of x is equal to sigma f n's derivative at point x 0 divided by n factorial x minus x 0 to the power of n, where n is from 0 to infinity. So this particular representation is a converging series, which is converging to my function f of x for every x. And at particular x is equal to x 0, this series, not only this whole series is equal to this, but also every partial sum of it will also be the same as f of x 0. So these are two conditions which we have satisfied. We put it in the front of us in the very beginning. And it's called Taylor series, as I was already talking about. Also, if x 0 is equal to 0, I mean there are certain segments which contain 0 and people want 0 to be the center, then this Taylor series is called sometimes Maclaurin series, which is basically a different name because probably Maclaurin was the first one who kind of investigated this particular thing that x is equal to x 0 equal to 0. All right, so that's it for today. I do recommend you to read notes for this lecture on Unisor.com. Notes represent basically like pages of the text book. And try to think about this proof of convergence of this thing. There are actually very interesting researchers about how much we are losing by cutting my tail at certain points. So there is an variation of the error of the approximation, which I didn't go into. Now, in theory, I can always using my proof that members of this sequence are less than the corresponding geometric progression sequence, I could obviously summarize the tails of the geometric progression. And that would be a nice evaluation for how much we are losing by cutting at certain moment my Taylor series with a partial sum. I'm not sure if I will go into these details, but it's interesting researchers and there are more or less important articles about what kind of restrictions should be put on the derivatives of the function f. I just put a restriction that it's just always less than some constant m. You can actually be a little bit more specific and have a weaker restriction. Like it's growing, for instance, with the power of n. That would be probably the same thing more or less. All right, so all these are very interesting, obviously, elements of the research. But in any case, my purpose was to basically introduce you that any smooth function can be represented to any degree of precision with some kind of a polynomial. And this is most likely, well, maybe my information is obsolete, but that was the case long, long time ago when I was involved with computers. Most likely, this is exactly the way how in calculators and computers, all these calculations of some specific functions, which are not polynomial functions, are implemented. Okay, that's it for today. Thank you very much and good luck.


Okay, all right, all right, yes, I can see you guys. And yeah, that was a lot of fun. Now, gaming on the Apple Vision Pro is an interesting thing because it's new, because there are not many games, because there are many ways to game on this device. It's something that you have to actually decide what you want to play. So if you guys have joined us for the very first time, this is Thunder E on Board of Work, don't forget to smash that subscribe button and the notification icon to see more videos like this. Now, if you're wondering, I have done another video on the Apple Vision Pro, and I talked about one of my biggest scribes, which was, of course, comfort for me.  Now, the biggest thing to take away, especially in gaming, because when you regain, we like to gain for a long period of time, is how comfortable it is. So I switched away from the single loop band, that was really painful for me to use. This is much better, I still wish it was more improved, I wished it was more center support, but you get the idea, find the band that works well for you. Now, the second thing, of course, is the battery. Now, the battery life is roughly around two hours with the attached battery here, which you can, of course, plug directly with USB-C cable to charge, so you can actually sit down and play and game as much as you want. But you saw me earlier playing a game called Synth Raider. Now, Synth Raider is an AR interactive game, which is a lot of fun, I mean, it was great. And the one thing with Apple Arcade games like this is that you don't really need to map the area, as long as you have a clear area out. I do wish they did have indicators for this game, or maybe it's just a developer thing, I'm not sure, but I wish that was set like a boundary each time you want to play, just to make sure your environment is safe for you. But, again, gameplay was really fun. And that game, which is pretty cool, is called What the Golf.  I like that because it's just more relaxed. You can place it, you can play golf in different funny ways with What the Golf. I remember meeting the developers for that. That was actually a pretty cool, pretty nice game. But I like the way it works here in this environment. Now you're saying, okay, Thunder E, these are nice games, but what do they have in the App Store? What's available for me? Well, let's go ahead and take a look what games are available in the App Store for gamers, and what's also available on Apple Arcade. Okay, that was quite interesting. I didn't expect to find PUBG New States in the App Store because I couldn't find Call of Duty. So let's go ahead and download it and see how it is. Now, my biggest gripe here is that it just didn't work. I tried playing the game, I couldn't play it, it wouldn't start. It took forever to download by the way. So I don't know, maybe it needs an update and you're gonna find issues like this for at least the foreseeable future until things get updated. Again, this is a brand new platform, so not every developer has caught up yet and you can't blame anything. Now, one aspect that does work really well is using Steam Link. I have my PC upstairs, I can connect directly to it, and with Steam Link, I can play all my PC games as much as I want.  I've got a nice monitor, it's 144 Hertz, it's 1440p, which is cool, I've got a 65 inch TV here. But with this, I can go as big as possible. I was like 120 inches, playing Street Fighter, playing a shot of the Tomb Raider or Doom, you get the idea. Now, how about you take a look and see how well that actually handles. That's pretty dope, that is pretty nice. Plays really well and it was really fun to connect my Xbox controller and play that. Now, speaking of Xbox, Xbox Game Pass, I went ahead and tried to connect Xbox Game Pass by going through the browser, but because the Safari browser yet on the Apple Vision Pro does not allow you to pin websites to the home screen, yet I cannot play Xbox Game Pass, so there's just no way around it, there's no app, there's nothing. So your best bet to play more games is basically Steam Link, that's the biggest expense you have here. Now, another option that you do have is of course, basically connecting your MacBook to your headset and playing that way as well. And you can play whatever games available on your Mac, like Resident Evil Village, Resident Evil 4, Death Stranding, that kind of stuff, from your Mac to your Vision Pro. Now, the one thing I did notice is that it just ran a little bit slower. Again, shouldn't need an update because remember this has an M2 chip, same as my MacBook Air 15, so performance should not be an issue with that. But again, it's just one of those things where I think it's just the early kings. Now, there are a couple of arcade games that will play and work well, things like Teenage Mutant Ninja Turtles, that played really well. What you're noticing and seeing here is that gaming on the Apple Vision Pro is very early. There's really not much to play, there isn't a huge focus, which was very interesting for me because with a VR AR headset, I expected to see more of that because a lot of the interactive nature you found with its competitors like the Quest, you'll find that there. Now, that doesn't mean that it's not coming, it just means that it's slow. So that's where you have it. Now, when it comes to temperatures on this device, I've been gaming for a while with this headset and it's just a little bit warm. The battery itself actually has stayed pretty cool, so temperature-wise, both the battery and the headset have been nice. My biggest gripe is just the weight on your nose and around your face, just the way the headbands work. It doesn't hit the mark there, but the experience though, especially playing Steam Link and playing Street Fighter, oof, that was impressive. So let me know what you think about gaming on the Apple Vision Pro. Is it something that you would like to see more? I do what games do you like to see? I know this is not for everyone, this device isn't for everyone, but this is the first step in expanding that AR VR market that Meta had started over a few years back. So let me know what you think, guys. Don't forget to like, share, subscribe, leave your thoughts down below and always enjoy your entertainment. Okay, so more Street Fighter.


Non-government organizations and NGOs for global rights in partnership with KUKA Center, Kaduna has advocated the inclusion of women in peace-building efforts against violence extremism in Kaduna state and northwest region of Nigeria. The said women and children are more prone to violent attack and other abuses in the society noting that a voice in community peace-building process is a panacea to lasting solution in communities. Header farmers' clashes and a whole lot of crisis has made the north-west that used to be the most peaceful part of Nigeria become the most the most crisis within region in Nigeria and so we have thought how can we work together as people to begin to reverse the strength mobilized community to build community resilience against violent extremism but in all of this we have equally acknowledged the peace-building efforts going on in the region and we have seen the gap which is the the level of women inclusion in this peace-building effort and we realize that if we promote if we're able to promote small participation of women in this peace-building effort we will get better results. Also the permanent commissioner Kaduna state peace commission Rebekah Sarko say women have critical role to play in nation building to resolve and prevent conflict in communities. She added women, mothers and children are most affected by violence, conflict and insecurity challenges hence to engage to them in peace dialogue for lasting solution. In so many ways as women in the community as wives, as sisters, as mothers, they play very big roles after conflict because where there is violence they lose their loved ones, they are the caregivers they become the breadwinners or the heads of households prematurely and then they are also part of the people that will help to build the community back to assemblers of what it was before and so they need to be there on the table or at the dialogue session so that they bring in those views. These women have been neglected in communities and they need their own they need to be free to speak out because they have things they need to tell us that we don't know and things that they need to add for a community to move forward. Children have been neglected so based on my experience today what I learned is giving women the right and liberty to speak out. Women are very important in the society and if you look at the world we are in today everything you do with a woman you hardly achieve what you intended to achieve you see how the women even when the the men were called in order to make peace or how they can resolve the conflict but still they were unable to until when women agreed to gather and come and there was a peaceful resolution and if you can see it was a woman that make the peaceful resolution not given to me. Hello hope you enjoyed the news please do subscribe to our youtube channel and don't forget to hit the notification button so you get notified about fresh news updates


They had always said, you know, when you get a heart, this place will start going crazy and you'll start having activity and we started seeing that but it was all, you know, outside of my door and didn't know what was going on really and all of a sudden one of the coordinators walked in the room and we knew something was going on but we didn't know exactly what and quickly after Dr. Boe gave came in the room and said it's yours. And I remember asking her, am I still on the list, am I still a match or is it my heart? And she said, you have this heart, it is yours, it is 100% your number one, you know, you're getting a heart today. You know, I was so ill at this point that I remember Dr. Boe gave saying, you know, how fast can we get her son here, how fast can we get Carter because he was with my in-laws and they were about two hours away and I remember Carter coming into the room and I remember getting to see him and tell him I love him and my family, most everybody was coming in, you know, my brothers and my mom and dad and my husband Kevin were already there but everybody else was starting to kind of trickle in to see me before surgery and I got to say hi to everybody and just know that they were there supporting me. I remember going down an elevator and all of my family being in one elevator, there was probably 15 of us in the elevator and getting to say goodbye to everybody and you know, I'm gonna be great, no worries for me, just say some prayers and you know, everything's gonna be perfect, we're good and getting to do that and then I don't even remember going through the doors and I remember slowly waking up the next morning and you know, having that intubation tube still in and being scared to death of that, that was my worst fear was having the breathing tube in and getting through that and starting the recovery process knowing that I'm alive and my fingers and toes are warm, they hadn't been warm in a while and being able to breathe, I could lay down and breathe and that was unbelievable and couldn't automatically feel my heartbeat that I had felt for months and months and months and that was a good feeling to not feel your heartbeat which sounds absolutely crazy but it was a wonderful feeling to not sit there and count your heartbeats and wonder am I gonna feel VTAC, you know, have that fear and just know that it was success at that moment, you know, several hours later the surgery was a success, you have a new life, you've been giving a new life by an amazing family and an amazing person who decided that it was important to be a donor and to give somebody the gift of life when it was their time and it was not needed anymore and that's probably the biggest struggle through a heart transplant for me was the emotional side of loving this family and this person that I don't know and that I don't know anything about and praying for them at the same time that I'm praying for myself and my health to be given a peace for both of us for both their family and for me and my family that this all works like it should.


So, but I do want to get while it's fresh in my mind, I want to do this review of the movie Parasite. I think it's an important movie. I think it's very reflective of the time. It's stunning. It's a movie that has won all these awards. I mean, it's basically won everything. It won the Cannes Festival Top Movie Award. It won Foreign Film with all the various awards that are happening in the United States. Parasite won all kind of the foreign film awards. And then in Oscars, of course, it's the first foreign film, the first non-English film, to win the Oscar for Best Film, for Best Director. So truly, from a awards perspective, a stunning achievement. So I had to go see the movie. I had to find out what the deal is. And so I watched it on the plane coming home. And somebody warned me that I should really watch it on a big screen. And they're probably right. The movie has some stunning visuals. And I think the movie is very visual in many respects. It's got a really, really bad theme. But the movie uses visuals to portray the theme, which is really good filmmaking in that respect. It is, I think generally the movie is well made. I think it's well integrated. It took me a long time to figure out. It took me really chewing on it for two days to figure out what the theme was. But the more I thought about the visuals, the more the theme comes into focus, the more you realize what the movie is trying to say. And it's basically trying to say what the director, in this case, is saying it's trying to say. So in this case, an artist's metaphysical value judgments are coming across. And he can explicitly state them. So the theme is more political, but it's definitely a, the theme is, well, it's got a metaphysical aspect, but a theme is real. And, you know, so do I recommend watching the movie before we get into the review? So a few things. One, the review is going to have spoilers. Lots of spoilers. Because I can't review the movie without really telling you what the movie is about and what happens in the movie, including the end of the movie. The movie I'm talking about, for those of you joining late, is Parasite. So including the ending of the movie, because I think the ending of the movie kind of capsulates the theme and the whole sense, the whole sense of life and the whole perspective of the movie is encapsulated by it. So there are going to be spoilers. I warn you of that. We're going to go through a little bit of the storyline. And then I want to describe the visuals that I think are most significant in the movie. And again, I, you know, if you're interested in cinema, I definitely encourage you to watch the movie. It's got elements that are painful. And certainly, there is a climatic scene that is extraordinarily violent. It's short. It's short, but it's very violent and very shocking, right? Very shocking. You can kind of sense that it's coming or something like it is coming. I don't think I quite expected the rush of violence. But of course, the theme ultimately necessitates, ultimately necessitates that kind of violent climax. So do I recommend the movie? You know, if you're interested in movies, if you're interested in cinema, then yes, because I think it's a very interestingly made movie. I think, you know, the director here is very strong visually. He really has an understanding of space. He uses space really well. He conveys the fundamental theme of the movie through visuals, through visuals and people's movement through the scenes. So it's, I think it's very powerful in that sense. The theme is a negative one. It's not a pleasant movie. There's nobody, I mean, nobody good in the movie. There are no good guys in the movie. So there's nobody positive in the movie. It's typically modern in that sense. It has no heroes. It has no characters you can look up to. It has no positive message. The message is overall absolutely unequivocally negative. It's a very, at the end of the day, a very depressing movie. A very, you know, negative sense of life, depressing movie. But again, if you like movies, if you like cinema, then it's interesting to watch. It's an interesting how it plays out. It's interesting, again, what the director does with the movie. I've only seen one of the movie by this director. I didn't even realize it when I saw it. Only afterwards, when I was looking him up, did I realize, but I saw a movie years ago, a movie came out in 2013, called Snowpiercer, which is a science fiction movie that I saw. And what's interesting is the two movies are very similar themes. That is clearly this director is motivated by a particular view of the world. And that view of the world comes across in both Snowpiercer, which is a sci-fi movie I can talk about after we talk about this movie. And Snowpiercer and Parasite have very, very, very similar themes to the movies. Okay, so I want to talk about, let's first talk about, I'll give you a quick summary of the story, the story of the movie. And then I want to talk about the particular visual that if you're going to watch the movie, I would focus on. Now again, I'm going to give you a lot of spoilers to the extent that you like to be in suspense in the movie, then you should probably leave the podcast right now. And if you intend to watch the movie and not listen, if you've seen the movie, I think this will be interesting to you. And even if you're going to see the movie, but you know, mine spoilers, that is, it's not that important to you that you don't know where the movie is heading, then I would encourage you to continue listening to the movie. All right, so here's the story in short. So you've got a poor family, father, mother, son and daughter. They live in, I guess what's fairly common in Korea in the slums, they live in a basement type apartment with a window looking into the street and windows play. Windows are very important in this movie. Window looking in the street, but it's like, it's like on the top, right? There's a window she can look and you can see the feet of people, you can see the people standing up. But the apartment itself is underground with only this one portion of the window above. Again, very important that the apartment is underground and that it generally is underground and that they're looking up through these windows. Anyway, there are a lot of work. So you've got the son and the daughter they seem like post college. The son has also been in the army and they are out of work and a friend, a rich friend of the son, comes to them and says, look, I'm tutoring this girl of a rich family in English. You can take my job. I'm going off to study abroad. You can come and take the job. But in order to do that, you have to pretend to be a college student. You have to pretend to be wealthy. You have to pretend to be from a good family and you have to pretend to have a college degree. So the son, with the help of the daughter, forges all the documents necessary. He goes, does the interview and gets the job. Then he discovers that the son, oh, so he gets a job at this rich family. Now, the rich family lives in a beautiful modern home, right? A beautiful modern home, which we are told in the story was designed by some architect who used to live in it and is left. This beautiful modern home has big windows looking out into this amazing garden and then out into kind of the meadows and the hills and just a beautiful view, right? So it's just a gorgeous view and you can sit in the living room and look out into the spacious, beautiful thing. Again, big window looking out into this amazing garden. But in this home lives a wealthy man, CEO of some company, his wife, a son and daughter. Son and daughter are younger. The daughter is in last grade in high school, not very bright, needs help with her English. The son is a confused kid that they don't know what exactly to do with and at some point it becomes evident that they would like to get him some kind of art teacher. So the poor kid suggests, oh, I know an art teacher and he makes up the story about a girl that he knows was an art teacher, went to this art academy and goes to these schools and goes here and there and is really, really good. And the wife, the rich wife says, oh, you know, this is great. Let's get her. So again, they forge her documents and this is his sister and he brings the sister into the house as now the teacher for the young son. Anyway, they then manage to get the driver, the father's, the father, the rich father is, has a driver who takes him to work, takes him back, the family has a driver and they manage to get him fired and they get their father to replace him. And then they manage to get by again, creating havoc and lying and deceiving through deception, they manage to get the housekeeper in this house who's been in the house forever, including when it was owned by the architect and they get her fired and she is replaced by the mother. Now, in no, in none of the cases, they say this is my father, this is my mother. There are supposedly four different people who don't really know, who have some connection to one another but don't really know each other, certainly not all members of one family. So here, the poor family has been very resourceful, has come up with a plan of deception in order to get their jobs and the elements of this that are funny and it lead, indeed, the movie at the beginning of it seems like a comedy and seems like it's going to develop as a comedy. It becomes a tragedy very quickly but it is presented as a comic drama, a comedy tragedy kind of a movie and the beginning seems like this comedy where these poor people are basically deceiving the rich people and the rich people are portrayed as kind of naive, kind of childish, kind of silly, kind of empty and easy to manipulate, easy to manipulate. So not a very, not a very admirable family, very detached from reality, detached from the real world. So they're all in place, everything is running smoothly until one day the rich family goes off on a camping trip and the housekeeper comes back and the housekeeper comes back and she says there's something I have to do, please let me into the house. So they let her in and they discover that in the house there is inside the cellar, there is a secret door that leads down into this shelter, basically a shelter built by this rich family just in case of a nuclear war with North Korea. So there's a shelter underneath the basement and it's a secret door nobody knows about, the common owners and in the shelter the woman's, the old housekeeper that was kicked out's husband lives in there and he lives there and she basically feeds him off of the food from the rich family and he basically stays there and never goes out and he's there because he's lost the job and the whole thing is the poor family lost their jobs, they've worked and they've lost a job, the father has had many jobs over his career but keep losing them, the mother hasn't had many jobs but keep losing them. So it doesn't present them as people who don't want to work, they clearly want to work but they have no job, there is no option and this one guy is stuck in the basement and they have nothing, they have no property, they have nothing, she works as a housekeeper, she lives in the home and her husband's in the basement, really really really weird but basement, basement is important, really deep shelter you know bunker basement really really important again visually, we'll get to that. Anyway these guys the housekeeper and husband discover that the four people are actually related that they're not separate that they're actually one family, they threaten to tell the family so they can get, she can get her job back. Mayhem ensues during that mayhem basically the housekeeper is killed and then while all this is happening the family announces that they're coming back and so everybody's scrambling, they're locked down in the basement with a dead you know the guy and his wife are locked down in the basement with the his wife that's now being killed in this all this mayhem, the others scatter, they hide, the housekeeper's the only one who's there and you know everybody else is hiding and the family comes in and they have their clues, they have no clue that these people have been potting in their house, they have no clue that everybody's been there, they have no clue that all this is going on, they're completely clueless as to what's happening which is a continuation of this idea that these rich people are completely clueless and have no sense at all of what's going on. Anyway a bunch of stuff happens and we'll get to what happens in the meantime but the housekeeper stays, the other kids manage to escape the house. Now in the meantime massive rainstorm, a monsoon happens and the family, the two kids and the father walk back, they basically walk back from this rich family house to their apartment and when they get to their apartment, their apartment is completely flooded with water, of course the water flows down and floods their apartment, they land up going into shelter, anyway they're in the shelter, they get a call from the rich woman and she says oh I want to put on a party tomorrow, birthday party, I need you all to come and she calls them all back to the house to set up this party, okay so this party's happening and this is where the climax happens and the violent climax happens.  She's bleeding out, I guess the son of the kids got hit so they're they're kind of waving and the rich father wants, tells the driver who's the father of the girl dying that he wants him to drive the kid to the hospital, forget about the girl. So the rich guy shows complete disregard for anybody else's life, for anything else going on there, his kid just got hurt a little bit and he needs to rush him to the hospital. At this point and again another issue I'll get to in a minute, the poor father takes the knife and stabs the rich guy and kills him. He escapes, lands up hiding from the police in this bunker, they never find him, he stays in the bunker and the rest of the family, you know the daughter dies and the other two, they just, I'll tell you afterwards how it actually ultimately ends. Okay so that's kind of the outline of the story, pretty random, pretty crazy, pretty insane, pretty nutty action. So what's the theme of all this? What's the theme? Well let's go back to a few of the images.  They're trying hard, they're trying hard to the point of conceiving a plant to deceive people and finagle them but they're trying hard, they've been fired from every job they can conceive of, not because they were bad at the job but because that's the nature of the world, you know, businesses go out of business, jobs get replaced and people lose their jobs and they're just, they're just down on their luck.  The other family, the other poor family we know of, live in a bunker, the guy basically lives in a bunker under a rich people's home. So, and the rich people live in a house basically on top of a hill that has beautiful windows in which you can see the world and just gorgeous spread and they are sheltered from the rain and they are sheltered for anything. Their house never floods, their house is just beautiful, right, and it really is a beautiful house. It's a modernly designed house. They built the house, it's basically a set house, right? They built the house for the movie, for the purpose of the movie. So in that sense, every angle, every layout, every piece of furniture is thought out and this is one of the positive things about the movie. It's all really thought out. It's all figured out how it all lays out. So upstairs is where the rich people live. Downstairs is where the poor people live and it's clearly an upstairs downstairs, downstairs upstairs is a huge theme in this movie. We're constantly going down the stairs to the cellar and up the stairs and down the stairs to the basement apartment and up the stairs to the nice house. The house itself has stairs but less important but it's that rich people, poor people, poor people live down, rich people live up and the camera often spans up and down. Maybe the most illustrative, the two illustrative scenes of this, even, so when the rich people come back, come back after they've gone camping and everybody is hiding, well, they're hiding under a table, under. The rich people above them on the sofa, you'd think they'd see them but again, the rich people are clueless and portrayed as completely clueless. So they're under the sofa, on the sofa and under and they actually have almost sex I guess they make out on the sofa, the rich couple. The kid is outside in a beautiful modern tent while it's raining and the poor people are under the table. The poor people are always under the rich people are almost over. Then the scene where they walk in the rain from the rich house to their basement apartment which they find flooded is a beautifully filmed scene.  It's clear that you've got the class, class hierarchy, class positioning is central to this movie. That is the whole point of the movie is a illustration, visual and in the story of the relationships between classes, the relationship between the rich and the poor. It is striking how many times you see that up, down, rich up, the poor down. The rich are safe, the rich are warm, the rich are comfortable, the poor are in the modernity that they return to their basement apartment is it flooded but they're sewage spewing out everywhere. Nothing they can do about it. Nothing will stop it. They live in filth.  They live underground. All the poor people in the movie live underground. They're forgotten. They're unknown. Nobody cares about them. Now the movie doesn't romanticize poverty. The poor family are not good guys. They're clearly deceiving. They're clearly and in one case because they get the driver fired and they get the maid fired, the housekeeper fired. They're clearly hurting other people in the same economic class that they are. So it's not that they are good guys. It's that they have no choice. Class is beyond choice. Class is what it is. The rich family is rich. We don't know how they got rich. We don't see the father working particularly hard. There's one scene where he's at the work. It's not clear. He's sitting there making you know with a bunch of people surrounding him kind of I guess making decisions but there's nothing substantive about showing his work or showing the kind of decision making he's making. The poor families are poor and nothing they do. Nothing they do changes the fact that they're poor. They get the jobs. They've got money but they screwed up. They messed it up. They discovered bad stuff happens and back to poverty they go. So it's inevitable. The poor poor, the rich rich and there's a sudden appeal to a theme like this in South Korea because Korean society was very very what's the what's the term feudal really well into the 20th century. Clear classes. You're born into classes. You're born into a particular class. It's almost a caste system not quite but if you watched Mr. Sunshine which I highly highly highly recommended and you should have watched you could see the class structure of Korean society well into the 20th century and it's reflected now in the 21st century in Parasite at least that is the understanding that the movie conveys about the classes. The rich are rich because they just are the poor poor because they just are and nothing the poor do has any chance of bringing them out of poverty. They are doomed to that and indeed the conflict the primary conflict that happens is the conflict between the two poor families the housekeeper who comes back and her husband in the basement and this new that is the the the pie as the movie sees that the pie is so limited that the poor families are fighting over a very limited pie. They're fighting over the little crumbs that the rich leave them. The two poor families have to struggle to survive at each other's expense. They cannot both exist off of the little crumbs that the rich family sends their way. So not only the poor poor but they're all fighting against each other and eating each other up and damaging each other's chances of success. Yeah I mean somebody in the chat mentions one scene in the movie where the family before they get these jobs with the rich people they they're trying to fold pizza boxes to make a living. So the pizza company is willing to give them a pizza box to fold. So they're folding these pizza boxes the whole family sitting they're folding pizza boxes and they get 25% of them wrong. They damage them so they can't even do that properly. So these are not again the poor are not romanticized here.  The rich are portrayed as naive easily exploited easily taken advantage of. The rich are portrayed as suffering as ultimately suffering from the actions of the poor and from their own actions. So the father the rich father is killed in the end and that's important because I think the theme of it the theme of the movie is that inequality or class structure right the vast differences between the classes only results in horror for both the poor and the rich. So class inequality results in horror for both rich and poor. But class is also inevitable according to the movie class is inevitable according to the movie. So I think I think the movie is well made. It's well acted. The particular issues are well dramatized. The sense of the movie gives of the inevitability of class the inevitability of disaster then the inevitability of the inevitability of class. Well of the horror of murder of bloodshed. It's all inevitable. There's nothing to do about it. The movie offers no alternatives no options no out indeed at the end of the movie the son the poor son who's schemed this whole idea up in his constantly a schema it writes to his father who stuck in the remember in the in the you know bunker but underneath the house. He writes to the father he writes this letter saying you know one day I'm going to go down I've got a plan I'm going to go study I'm going to go work hard I'm going to make a lot of money I'm going to buy the house that all this happened in this rich house and I'm going to free you from the basement I'm going to free you from the bunker and there's this dream like scene where he comes into the house and the father comes out of the bunker and they hug and then the camera cuts away from that and brings it back into the basement apartment where the kid is writing and it's obvious that's never going to happen that's just a dream that's just another one of this kid's fantasies at some point the father the poor father tells the kid don't plan there's no point in planning everything sucks everything fails whether you plan or you don't plan failure is inevitable the unexpected always happens good stuff cannot happen to us so the movie is saying there is no mobility in the world doesn't matter if you're poor you're rich if you're poor you're rich in a sense you're born into that there's nothing really you can do about that there's no sense of mobility in this movie the richer rich the poorer poor they stay that way and to the extent that those classes exist everybody is going to suffer so yes it's very deterministic in there choices don't matter so if you could you could say inequality or class differences inevitably deterministically lead to horror for both the rich and the poor for everybody involved for people in every class so there you have it that is my review of the movie it is a terrible theme it is a depressing movie it is a depressing idea it's uh it's got nothing to recommend it and it but it's very indicative again of a culture particularly of Hollywood where inequality is they're they obsess about it the left obsesses about inequality this movie reinforces all of their most basic primary ideas and primary beliefs their idea and a kind of determinism their ideas of lack of social mobility their idea that you're born into a particular class and that is inevitable and their idea of a tragic a tragic the inevitability of tragedy the inevitability of tragedy so depressing horrible as social commentary really really bad but very well made and again I you know if you see the movie pay particularly attention to this idea of upstairs downstairs this idea of above and below the superiority of some to others and that that positioning that is very visual so it's it's this is a good movie for those of you who are studying cinema for those of you want to see how to use visuals how to use visuals in order to tell a story tell a story using the super chat and I noticed yesterday when I appealed for support for the show many of you step forward and actually supported the show for the first time so I'll do it again maybe we'll get some more today if you like what you're hearing if you appreciate what I'm doing then I appreciate your support those of you who don't yet support the show please take this opportunity go to your own book show dot com slash support or go to subscribe star dot com your own book show and and and make a kind of a monthly contribution to keep this to keep this going I'm not sure


Dear students, now we are going to talk about online gender-based violence. Before discussing the concept of online gender-based violence, let's see what is gender-based violence. Gender-based violence is a kind of violence committed against women, female or third gender group. And it is referred as an act of discrimination and injustice against women and female. So when we talk about online gender-based violence, online gender-based violence is a kind of violent acts committed online against women or female and against third gender group. And gender-based violence is considered as a criminal offense and online gender-based violence is also considered as a form of violence and crime. So what are the causes of online gender-based violence? The causes of online gender-based violence are similar to the causes of gender-based violence. The main difference between two is that it is happening online. So when we talk about the causes of online gender-based violence, the biggest cause of this is the patriarchal structure. The patriarchal structure of your society enforces masculine behaviors and reinforces feminine behaviors in society.  Along with this, there are social-cultural factors in which any social-cultural context of society is being reinforced and confirmed by patriarchal norms and culture and masculine behaviors. And in this way, it is becoming a cause of gender-based violence. Along with this, there are economic factors as well. In order for women to gain some kind of friendship from them. And psychological factors are also there when we talk about online gender-based violence. Some people are psychologically ill and they feel entertained when they perpetuate such kinds of acts in online platforms. So these are the main causes of online gender-based violence. And the research conducted on it tells us that the issue of online gender-based violence has increased day by day. And it is considered a crime. And cyber-loss has been created on it. And you can report it. As a form of offense in a relative country, and a perpetrator can be punished for this. Thank you.


All right, Maine New York City factory footage. Here's some footage from 8 fruit factory Be factory footage without a sunset. No, soon. There'll be more snow. Maybe


Freedom! Today I'm interested in seeing your YouTube setup. I want you to either make a new video or reuse an old video where you've already shown your YouTube setup.  As well as any other miscellaneous, maybe your fans, maybe your followers, whatever you want to call them, I want to see what you're working with. This is one of those community initiative videos that I was talking about. I want you to use in the title and the tags, hashtag my YouTube setup. That way, not only can we find those now, but also we can all tie these together. I want to see what you're working with, whether you happen to be working with an old craptop from 2004, or whether you're using like the biggest baddest mofo PC that's ever existed. Doesn't matter and I don't want to just see your PC. I also want to see your microphone setup, your recording setup in general. I want to see how you do whatever it is you do. Also bonus points if you can find a way to make it fun and interesting. If you click that eye, you'll actually see my old YouTube setup and you can see kind of how I tried to make it somewhat interesting. I did this as a celebration for 100 YouTube videos, if I remember correctly. For those of you who don't feel comfortable filming inside of your house this way, maybe you can also do this from a software perspective, showing us on screen how it is you produce the videos that you do and any other tips, tricks or anything like that that you can give us from a software PC type thing. Yeah, that said software PC type thing. Leave me alone. If you link your video in the comment section down below and if it fits exactly what I'm asking for it, we'll be placed into a playlist full of all of these so that we can see them later. Once this video is a few days old, maybe a week or so, I'll go ahead and compile that list and we'll go ahead and we'll link it on a card right about now-ish and possibly even reflect on those in a future video. So what do you say, Freedom? Are you up to the task? Well, if you are, that means you've got about a week or so before I compile everything so if you've already got one made, go ahead and link it to us. If you don't have one made, that means you've got about a week or so. This would be a really good opportunity to clean your room. So if you have any other ideas for these Community Initiative Challenge videos, let me know in the comment section down below and I'll entertain any and all ideas for you. Till next time, I'm Anthony. Like, subscribe, comments please. Also bonus points if you can find-


It's time now for Mr. Keen, Tracer of Lost Persons. Ladies and gentlemen, Anderson and Colonos present Mr. Keen, Tracer of Lost Persons, one of the most famous characters of American fiction in one of radio's most thrilling dramas. Tonight and every Thursday at this same time, the famous old investigator takes from his file and brings to us one of his most celebrated missing persons cases. Tonight's case is entitled, The Case of Murder and the Bloodstained Necklace. Believe anything you like about what this or that way to relieve pain of headache, neuritis, or neuralgia will do for you. But there's one important fact you can't get away from. That is, thousands of users of Anderson tablets have been introduced to this remarkable product through their own physicians or dentists. Anderson is like a doctor's prescription. That is, it contains not just one, but a combination of medically proven, active ingredients. Next time you suffer from headache, neuritis, or neuralgia pain, try Anderson. For most effective relief, use only as directed. I'll repeat the name, Anderson, A-N-A-C-I-N. For Mr. Keen and The Case of Murder and the Bloodstained Necklace, our scene opens in a corridor of a metropolitan hotel. A man with a briefcase in his hand has been knocking impatiently at one of the room doors. As a bellboy approaches with a pitcher of ice water and some glasses... Excuse me, sir. Was that ice water ordered for this room, boy? Well, yes, sir, for Mrs. Bradley. Well, I don't think she's in. I've been knocking for over five minutes. Well, it's funny, mister. She gave me the order herself over the telephone, told me to bring the ice water right up. My name's Orston. I have an appointment with Mrs. Bradley. Have you got a key to this room? Yes, sir. Well, open the door, then. You don't think there's anything wrong, mister? Now, don't ask questions. Just open the door, please, and let's have a look inside. There's nobody here, Mr. Orston. Mrs. Bradley must have gone out right after I talked to her on the phone. Put that tray down and get hold of the police, quickly. Why? What's the matter, Mr. Orston? Look, behind that screen. Holy smoke. It's...it's Mrs. Bradley. Yes, with a bullet through her throat. She...she's been murdered. And now, later, we find a friend of the murdered woman, a Mrs. Thornton, at the office of the great investigator, Mr. Keen, asking for his help. And she's saying... And that's how they found her, Mr. Keen, lying on the floor of her hotel room. My friend Grace Bradley had been murdered in cold blood. I read the details in the newspapers this morning, Mrs. Thornton. My partner, Mike Clancy, here, thought the case most unusual. It's a puzzler, all right, boss. That string of pearls they found in the victim's hand, for instance. That hasn't been explained yet. Yes, I was just going to ask Mrs. Thornton about that myself, Mike. Tell me, what theory did the police have, the string of pearls your friend, Mrs. Bradley, was clutching in her fingers? They had no explanation for it, Mr. Keen. And they were even more puzzled when they heard Mr. Orston's story. John Orston is a well-known jewel expert and appraiser. I remember reading about him in the newspaper account of the murder. He had an appointment with Grace Bradley to make an appraisal of some jewelry. But he said the string of pearls Grace had in her hand when he found her body were only cultured pearls and worth no more than $100. Mrs. Bradley would have hardly called him in for an appraisal of something that cheap. That's what the police thought. Well, maybe the pearls were switched and the killer took the real ones. I'm sure the police must have thought of that immediately, Mike. They did, Mr. Keen. But when I appeared to identify the body and they questioned me, they decided that perhaps it wasn't the right answer. Why, Mrs. Orton? Because I told them that, to my knowledge, Grace Bradley never owned any valuable jewelry. It's true her husband was wealthy. He died only a week ago. But Grace was a simple woman who hated ostentation. She often said she had no use for jewelry and she never wore any. Mrs. Orton, you say Mrs. Bradley's husband died a week ago? Yes, of a heart attack. The Bradleys lived in Louisville. He was a paper pulp manufacturer and very successful. After his death, Grace decided to come to New York to live. And she left right after the funeral. They had no children. When did you find out she was in New York, Mrs. Orton? The morning before she was murdered. She phoned me and told me she'd been in town for several days and was living at a hotel. Did you see her after she phoned you? No, Mr. Keen. When I arrived at her hotel room that afternoon, I found the police there and discovered that... that she'd been murdered. I see. Mr. Keen, I knew Grace Bradley for many years in Louisville before I married and moved to New York. A finer and more generous woman never lived. When times were hard for me, before my marriage, Grace came to my aid. She did everything she could for me. And if I could pay her back in some way, even in death, I'll do everything I can. I can see you were very attached to her, Mrs. Orton. I thought of her almost as though she were a younger sister. Mr. Keen, I could offer you money for your services, but I know your reputation. I know that no amount of money could make you accept the case unless you felt you were helping someone in need or working on the side of justice. In this instance, I feel that Mike and I will be doing both for Mrs. Orton. Then you'll do what you can to help solve the case, Mr. Keen. You can depend on it. Mike? Yes, boss. Get hold of the car and meet me downstairs in five minutes. I think our starting point should be at the office of Mr. Orston, the jewel appraiser, the man who discovered Grace Bradley's body. I'll give you his address, Mr. Keen. Good. I'll also need information regarding Mrs. Bradley's friends and acquaintances in Louisville, in complete detail. Mike, we got our work cut out for us. They won't be easy, judging by the circumstances. But we won't rest until we've brought Grace Bradley's murderer to trial. Well, here's the office, Mr. Keen. John Orston, jewel importer and appraiser. Now, let's go in, Mike. The ruby is genuine, Mr. Albright, but the ring isn't as expensive as you've judged. No. I'd say it was worth no more than $500. Oh, excuse me for a moment, please. Yes, of course. Yes, gentlemen, what can I do for you? Are you, Mr. Orston? At your service. My name is Keen. This is my partner, Mike Clancy. Mr. Keen, the great investigator? I'm very glad to know you, sir, and you, Mr. Clancy. Likewise, Mr. Orston. Perhaps you can guess why we're here, Mr. Orston. I presume it's in regard to the murder of Mrs. Bradley. Yes, I thought perhaps you might be able to supply us with some information, since you were the one who found her body. I only wish I could help you, Mr. Keen, but I've told the police everything I know. I was called on the telephone by Mrs. Bradley and asked to come up to a hotel suite to appraise some jewelry. Did she specify what the jewelry was? No, she didn't. As you undoubtedly know, a string of cultured pearls was found clutched in her hand. But it doesn't seem possible that she'd called me up to appraise them, Mr. Keen. They weren't very valuable, I take it. For cultured pearls, they were good, but they weren't worth more than $100. Would you say it was possible that Mrs. Bradley thought her pearls were real pearls? I wouldn't know, Mr. Keen. Isn't it true that cultured pearls do look like real ones? That is, uh... to people who don't make a profession of handing them? Yes, that's true, Mr. Keen. But if Mrs. Bradley originally bought those pearls herself, she certainly would have known their value. There's no question about that. Excuse me, gentlemen, but I couldn't help overhearing your conversation. My name's Albright, hollow Albright. Now, I knew the late Mrs. Bradley. You did? Well, we weren't close friends, but I was stunned by the news of her death. Have you been questioned by the police, Mr. Albright? Yes, Mr. Keen, but I had very little to tell them. I only met Mrs. Bradley about a week ago when she sold me this man's ring I just had appraised by Mr. Austin. Unfortunately, I was overcharged, but I'm certain Mrs. Bradley didn't do it deliberately. Did she try to sell you anything else, Mr. Albright? No, just the ring. She said it was her late husbands. Apparently she needed some money very badly or she would never have parted with it. The police have all those details, however. It was all perfectly above board. I assure you, and Mrs. Bradley's brother-in-law, Ralph Bradley, was a witness to the transaction. Uh, brother-in-law? I never read anything about him being in the case, Mr. Keen. Neither did I, Mike. You mean he hasn't even spoken to the police yet? Not as far as we know. Well, that's very odd. Do you know where this man can be located, Mr. Albright? I believe he was living in the same hotel with his sister-in-law, Mrs. Bradley. Well, that guest list has been checked four times by the boys' downtown boss. Sure, if they'd have found another Bradley, they'd have talked to him, sure. There's no question about it, Mike. That's a mystery to me why he didn't appear of his own free will after the murder, Mr. Keen. If I'd had any idea that he was deliberately keeping himself out of this, I certainly would have mentioned his name to the police. Mr.  Or perhaps you'll feel the same way when I tell you why, Mr. Keen. I don't know whether or not he was registered in the hotel under an assumed name or whether the room was someone else's. But when I first met Grace Bradley's brother-in-law, Ralph, he was apparently occupying the hotel room next to the one in which she was murdered. Here's the room Mrs. Bradley had, Mr. Keen and Mr. Clancy. I was the bellboy who found her body with Mr. Rostam. It's a corner suite I see with no adjoining room on the left. And according to the register, the room here on the right was rented by Miss Lola Smith. She's a good looker too, Mr. Clancy. I've seen her lots of times. Looks like a showgirl. Here you are, man. We won't need you any longer. Thanks a lot. Gee, wait till the guy's here. I met Mr. Keen, the famous investigator in person. All right, Mike. Now let's introduce ourselves to Miss Lola Smith. The girl who occupies the room to the right. Who's there? Miss Smith's certainly got a deep voice, boss. Well? I'm looking for Miss Lola Smith. Who wants her? Tell her... I told you to keep quiet and stay inside.  I have nothing to hide. Who are you to? What do you want here? My name is Keen. This is Mike Clancy. Keen? The investigator? I knew you'd drag the cops into this sooner or later. Okay, do as you like. I'll have no part of it. Just a second, mister. Not so fast.  Are you Ralph Bradley by any chance? No. Ralph, for heaven's sake.  Now, just a moment. Okay, you ask for it. Since preservatives. He's armed to the teeth. Look at the size of the gunnies toted around, Mr. Keen.  You stand on my way. Ralph, don't you see you're only making things worse for yourself. It weren't for you, Lola. I wouldn't be in this fix. But you can shift for yourself now. I'm playing this my own way. If anyone tries to follow me, I'll shoot to kill. Right, Mike. The phone. Give me the front desk. This is an emergency. Desk? There's a man on his way down carrying the gun. Get hold of the house detective and alert the policeman on the beat. Make sure he's stopped. I'll be right behind the boss. He won't get far. I'll be careful, Mike. He's dangerous. Well, I... I guess Ralph Bradley's in trouble. He's not the only one, Miss Smith. If that happens to be your name, which I doubt very much, you're in this too. Apparently we found the first link in the chain surrounding Grace Bradley's murder. And in a very short time, I hoped to weld the chain completely around the killer's wrists. In just a moment, we'll return to Mr. Keen and the case of murder and the bloodstained necklace. Meanwhile, beware of unpleasing breath that breathes between teeth. Get Colono's toothpaste with amazing dental floss action for a clean mouth and a pleasing breath. 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Mr. Keen, the famous investigator and his partner, Mike Clancy, are investigating the strange circumstances surrounding the murder of Grace Bradley, an attractive widow whose wealthy husband had recently died. In the hotel where Mrs. Bradley's body was found, with a string of inexpensive cultured pearls clutched in her lifeless hand, Mr. Keen has been questioning Ralph Bradley, the murdered woman's brother-in-law, who has just attempted to make his escape from the hotel room occupied by a girl named Lola Smith. Now, a few minutes later... Inside Bradley and behave yourself. And he never even got as far as the hotel lobby, Mr. Keen. I cornered him on the third floor as he was trying to open a fire escape window in the back. I see you put a pair of handcuffs on him, Mike. And he asked from Boss when he tried to get away. I'm not a criminal. If I haven't done anything, why don't you leave me alone? Bradley, your actions certainly place you in a suspicious light. Why did you try to get away, Ralph? Don't you see? Never mind the lectures, Lola. You're in this as deeply as I am, and don't forget it. I suggest you both tell the entire truth. Well, there's nothing to say, Mr. Keen. I met Ralph Bradley a week ago when he came to New York. And what about his sister-in-law, Grace Bradley? Did you meet her too? Only casually. She was murdered in the room next to this, Miss Smith. And you checked in this one the same day Mrs. Bradley occupied hers. That was just a coincidence, that's all. And is this a coincidence too?  What have you found, Mike? Well, you were right about her name, Boss. According to these cards in her pocketbook, her name isn't Smith any more than mine is. It's Cook. That's not the first time she changed it either. I wouldn't talk too much if I were you, Ralph. That's what I said to you, Lola. But since you've decided to leave me holding the bag, I'm going in for a little self-protection of my own. And what have you got to say, Bradley? I... I advise you to be honest. If I detect any trickery in your story, I'll have my partner, Mike Clancy, escort you to headquarters at once. All right. I followed my sister-in-law, Grace Bradley, to New York after my brother died. Why? Because I thought she cheated me out of my rightful share in his estate. Had his will been read yet? No. For all I know, she destroyed my brother's will and claimed his money and property as his closest survivor. What did you expect to gain by following her here? Information, maybe. I met Lola here and introduced her to Grace. I thought Lola might be able to get her to talk. But there was nothing criminal in what I did. I just... We'll decide that later, Lola Smith. Bradley, were you present when your sister-in-law, Grace Bradley, sold a small ruby ring to a man named Harlow Albright? Yes. I was there, Mr. King. The ring was my brother's. And you still believed your sister-in-law came into a fortune when she had to sell something like that to get a little money? It was a trick. She only did it to put me off the track.  I doubt it was a trick. But we'll settle the question of your brother's estate in a very few minutes. Do you happen to know the name of his attorney? Barton and Nesbitt in Louisville. Mike, put to a phone call to that law firm and inquire about the will of Grace Bradley's husband. Okay, boss. In any case, Mr. King, you've got nothing on me. Ralph's story proves that. Well, the contrary. It might make you an accessory to a murder, Lola. What?  And you were working with him in one way or another. But that's ridiculous. Do you think I'd do anything as obvious as outright murder, Mr. King? It's been done before, Bradley. Let go of me. That's what he works with, young man. Nothing. Let go of him.  Quiet. Hollow Albright. Inside, young fella. Mr. King may be interested in talking to you. Mr. King, I found this bellboy with his eye to the keyhole as I came up to the door. All right. I just wanted to see what was going on. That's all. The little spy. I caught him doing that once before. Don't you talk, girly. You're on enough hot water yourself. Well, stop your fish.  He's just trying to get back at me. He's been flirting with me for a week and I haven't even looked at him. Mr. King, I see you've put a pair of handcuffs on Ralph Bradley. Tell him I have nothing to do with Grace's murder, Mr. Albright. You know I'm innocent. On the contrary, Bradley. Grace told me once that she was afraid of you. It's something I forgot to mention to Mr. King. That's why I'm here. Did she say why she fears her brother-in-law, Mr. Albright? He followed her here from Louisville. Because I understand that they never got along. Incidentally, just how did you come to know, Grace Bradley? Why, we met here in the hotel. I have a suite of rooms upstairs. I recognized her as a woman of breeding almost immediately. A woman who was used to the finer things of life. I see. Well, when did you see her last, Mr. Albright? Three days before she was murdered. That was when I bought her ring. According to her husband's will, he died almost penniless. I offered to lend her money, but she refused. Instead, she asked me to buy a few trinkets from her. You're sure that was all the jewelry she had? As far as I know, Mr. King, she'd gotten a few pieces of costume jewelry from her brother-in-law, Ralph Bradley, here. But they had little value.  I know. He didn't tell me, Mr. Albright. Bradley, were there any cultured pearls in your stock of costume jewelry? You're trying to trap me, all of you. But I'm through answering questions, understand? I'm through. Boss. Just second, Mike, I'll be right with you. Mr. Albright, will you see these people remain where they are? It'll be a pleasure, Mr. King. Mike, keep your voice down. Did you phone the law firm in Louisville? Yes, Mr. King. And the will of Grace Bradley's husband was read the day she was murdered, according to the lawyers. They wired her that her husband had died in debt. He even lost his money because of bad investments. Let's begin dread up now, Mike. Come in here with me. Bradley, I'm placing you under arrest. You can't hold me, King. The whole thing's a frame up. We'll let the police decide that. What about me, Mr. King? Honest, I didn't do anything. Maybe I was snooping a little, but I'll lose my job as a bellhopper. Young man, I think you've learned a lesson on eavesdropping you won't forget too soon. You can leave and tell the house detective to get hold of a squad car for Bradley and his accomplice, Lola Smith. Anything you say, Mr. King. Then I'm under arrest too? I'm afraid you'll have to be detained, Miss Smith, along with Ralph Bradley. Oh, Mr. Albright, would you accompany us to the police headquarters, please? Not as a suspect, of course. But merely to give the police additional information. I'm glad to be of help in any way, Mr. King. Then I suggest we get started. Okay, Bradley. You and the lady walk out ahead of us. Don't try to make another run for it, unless you think you can travel faster than a bullet. Mike, one second. I just wanted to make sure they're all out of airshot. I've got some instructions for you. What is it, Mr. King? The case isn't finished yet, but it will be shortly. I think we'll all be due for a little surprise. Now, when the police have taken over, meet me downstairs in the lobby. We're going to find the final link in that murder chain. Have you tried that bureau yet, Mike? Yes, Mr. King, I went all through it. Well, you've practically gone through the entire suite. There couldn't be any secret drawers, not in a hotel room. And certainly the killer wouldn't carry what we're looking for all around with him. Well, let's go back to the living room. Oh, we've gone through everything in the place, Mr. King. Looks as though this time works to time, Ed. Mike, he's coming back, boss. He's opened the door. Yes, I was expecting him. Come in, Mr. Albright. You should have told me you planned to visit my hotel suite, Mr. King, I would have supplied you with a key. The desk clerk obliges us, Mr. Albright. I've spoken to the police. They're holding Ralph Bradley and his lady friend on suspicion of murder. They won't be held for long. Oh, no? You see, I believe that, uh, both innocent. Well, then why did you have them sent to police headquarters? I wanted to search your suite undisturbed. Then it was a convenient way to get you out of here. Did you find what you were after? Yes. That's very interesting. Mike, cut the covers off that sofa in the corner and go through the ticking. The sofa, boss? Yes, and thank you for your help, Mr. Albright. What do you mean? When I said I'd found your loot, you couldn't help glancing at your hiding place. I don't think we have to search any further. Search the inside of the sofa carefully, Mike. Leave it to me, boss. I must say you put up a very good front, Albright. Was this suite furnished by some of your past victims? Mr. Keen, look at this. Bring it over, Mike. It's a string of pearls, boss, and look at the size of them. That's genuine, too. Worth the King's ransom. They belonged to Mrs. Bradley and Albright murdered her to get them. Are you quite certain of that, Keen? You first aroused my suspicions, Albright, at the dual appraisers. I imagine you went there to find just how much Mr. Austin knew about these missing pearls. This conversation is beginning to bore me. But you made a mistake when you mentioned knowing Mrs. Bradley was penniless. She didn't learn the contents of her husband's will until the day she was murdered. You couldn't have known about it unless you saw her at that time and not several days before as you contended. She knew she was a pauper even before the will was read. She sold me that ring to get some money, didn't she? Yes. And you bought it as part of your plan. You learned she owned a string of fabulous pearls. You never had money enough to buy these pearls, so you decided to steal them. You asked to see them once more before Mr. Austin the appraiser came, then tried to switch them with a string of inexpensive cultured pearls.  So you put the cultured pearls in her hand, hoping it would implicate her brother-in-law. There's one thing you still haven't proven yet, Keene. How do you know these pearls were Grace Bradley's? I may be able to prove that even faster than you think. There. What are you doing? Breaking the string that holds the pearls together. Mike, take a look at this. Why, there's dried blood on parts of that string, boss. Yes. Mrs. Bradley was wearing the pearls shot in the throat. Hollow Albright wiped off the obvious bloodstains of the pearls, but he neglected the bit of string between each pearl. Is that proof enough, Albright? No, you won't, Mr. Not unless you want a taste of what your victim got. Keene, listen to me. Those pearls are priceless. We can share them and both be rich. They were collected in the South Seas in a shark infested lagoon. Grace Bradley told you that? It was all her husband left her. She never even knew he owned them until the day before he died. The story was dying broke, but he'd kept the pearls for just such a time. We can sell them for a million dollars and no one would be the wiser. Where you're going, Albright, even a million dollars wouldn't do you any good. Take him away, Mike. From here, Hollow Albright goes to trial for murder. And so Mr. Keene finds the solution to the case of murder and the bloodstained necklace. The next time you're suffering from heartache, neuritis or neuralgia, try Anacin. You'll bless the day you heard of this incredibly fast way to relieve these pains. Now, the reason Anacin is so wonderfully fast-acting and effective is this. Anacin is like a doctor's prescription. That is, Anacin contains not just one, but a combination of medically proven, active ingredients in easy-to-take tablet form. Thousands of people have received envelopes containing Anacin tablets from their own dentist or physician. And in this way have discovered how incredibly fast relief Anacin brings from pain of headache, neuritis or neuralgia. So next time such pains strike, take Anacin. For most effective relief, use only as directed. Your drugist has Anacin in handy boxes of 12 and 30 and economical family size bottles of 50 and 100. The name is Anacin. A-N-A-C-I-N. Mr. Keene, Tracer of Lost Persons, is based on the novel Mr. Keene. The radio sequel is originated and produced by Frank and Anne Hummert. Dialogue by Lawrence Clee. Bennett Kilpac plays Mr. Keene. It is on the air every Thursday at this time. Don't miss Mr. Keene next Thursday when the kindly old Tracer turns to the Yellow Talon murder case.