Kraft presents the Great Gilder Sleeve. Yeah! Kraft Cheese Company, makers of Parquet Margin, and a complete line of famous quality food products, presents Harold Perry as the Great Gilder Sleeve. Kraft brings you the Great Gilder Sleeve every week at this time, written by John Whedon and Sam Moore. We're from the Great Gilder Sleeve in just a moment.  And since there's only time to tell you a few, here goes. Serve baked potato with a golden Fab Steppe cheese sauce, melting into the potatoes' mealy goodness. Spinach creamed with Fab Steppe is another delicious treat. Dates or prunes stuffed with Fab Steppe make a grand nourishing salad and casseroles of macaroni or fish, what grand eating they make when you add the mellow cheddar cheese flavor of Fab Steppe. For a delightful between meal snack, serve graham crackers spread with Fab Steppe or combine Fab Steppe with jelly for a marvelous sandwich filling. Yes, there's simply no end of ways to please family appetites with the wholesome cheese goodness of Fab Steppe. So look for the familiar round, flat package on your dealer's shelf, and whatever you can buy delicious nourishing Fab Steppe. Come with us now to Summerfield in the merry month of May. For the first time this season, the sun is hot today, really hot, and life in Summerfield is slowed down to a walk. Birds are singing and children stop to listen to them. Flies are buzzing and people are thinking it's time to put up their screens, but not doing anything about it. There won't be enough business done in the whole town today to pay the overhead on Peabee's drugstore. And the great Gildersleeve, where is he? Well, the commissioner is in his office at the city hall with the door closed, his coat off, his feet up on the desk, the window wide open, the afternoon sun warming his back. Under his feet lies a stack of mail, still unread. What he's reading over and over is a note from his lady love. He knows it by heart now, every word, and still he reads it, because it seems to bring to him the sweet music of her voice. My dear, dear Throgmorton. Will you think it's silly of me I wonder to write to you this way when I could pick up the phone and call you, when I shall be seeing you again tomorrow anyway? Think it's silly, Eve, how could I? It's just that there's so much to say, darling, and when we're together it's so difficult somehow to find words to say it. I have the feeling at times that you too are tongue-tied, that you'd like to say things that you can't. Oh, that's so true, Eve. That's so true. Why, if I could say the things that are in my heart, I'd be a poet. Anyway, this is my little way of bringing you closer to me when we're apart, and I hope it will bring me closer to you. It's late afternoon now. I'm sitting at my writing desk, the little Rosewood one that mother gave me, and the radio's playing softly in the next room. It's a program that's on every afternoon called Tea Time Melodies. I wonder if you ever listen to it. Oh, I must make a note of that. Tea Time Melodies. I like to think that you might even be listening to it now, because guess what they're playing, darling? They're playing Tea For Two. Do you remember? Do you remember the first time I held my hand? Do I?  You held my hand, and you sang it to me softly. And so sweet. Upon my knees with tea for two and two for tea, it's me for you and you. What's the name of John Philip Susan? What's going on out there?  Where? Let me see. It's that truck down there with the flags all over it. See, it's got a sign on it. Vote for Ter Williger. Retain the incumbent. Vote for Mayor Ter Williger at the primaries on June 20th. He's given us four years of good government. Let's have four more. Vote for Ter Williger. Retain the incumbent. Retain the incumbents. Celebration of some kind? It's nothing. It's a plot.  Ter Williger paraded that truck past here deliberately. He did it to annoy me. He's just trying to get my goat. Well, if he thinks he's going to get my goat, he's mistaken. I'm just good and mad. That's all. Yes, sir. Parading past a city hall like that. Why is it disgrace? It's an attempt to corrupt civil servants. That's what it is. He's trying to sway him. It's an outrage. There's nothing else I can do, Mr. Gildersleeve. Yes, Bessie. If that truck comes by again, don't listen to it. Ignore it. Yes, sir. Mr. Gildersleeve, what is an incumbent? An incumbent, Bessie, is a political slug. A leech. You find them under rocks. Oh, I see. I'm joking, Bessie. An incumbent is anyone who's holding office. You mean like you're the water commissioner. So you're an incumbent. Well, they're good incumbents and bad incumbents. Well, how do you tell which are the good ones and which are the bad ones? Just come and ask me. I'll get out of here, will you, Bessie? Let me get back to my work. If you don't mind, Mr. Gildersleeve, I'll be out of the office for a few more minutes. I wish you would be. Now, my dear, dear, Throckmorton. My dear, dear, Throckmorton. My dear, dear, dear Eve. My dear, darling Eve. My dear, sweet, lovely, beautiful Eve. Hmm. And she sealed it with a kiss. Right here. Hmm. Hooker, who let you in? Nobody. The door was open. Oh, that Bessie. What goes on, Gildy? What were you... I just happened to be reading a letter. Is there anything wrong in that? Uh, it was from an old college chum. Oh, I see.  Hooker, what do you want? I've come here to give you a word of advice, Gildy. Keep your advice. I don't want any. You asked me to act as your campaign manager, did you not? In a moment of weakness, I did. In a moment of weakness, I consented. Yes. Now, as your involuntary campaign manager, I should like to call attention to the fact that I haven't observed any campaigning lately. Not on your part. I've been busy. I know. So has Mr. Williger. He's been very busy. Only he's been busy campaigning, not lollygagging. Hooker, I do not lollygag. Listen, did you hear that truck just went by? Yes, I heard it. Retain the incumbent. That's what's going on all over. Billboards throw away ads in the newspaper. The opposition is really going to town. They're spending money like crazy. What are you doing about it? I'll do something. Don't worry, Hooker. I'll do plenty when the time comes. I'm just waiting for the psychological moment. Kindly let me know when it arrives. Meantime, you may contact me at Dolan's pool room. Goodbye, lover. Goat chase yourself, you old goat. Bessie, Bessie, is that you? Do you want me, Mr. Goat, to see him? Yes. Bessie, do you ever listen to the radio? Oh, yes. My favorite's Red Skeleton.  Honest, I scream. Don't you think he says scream, Mr. Gilda Sleeves? But the program I'm interested in right now, Bessie, happens to be Tea Time Melodies. Do you ever listen to it? Oh, my mom does. She never misses it. Every day at 5.30, she does. 5.30? Oh, my goodness, I gotta go.  See the lights are turned off and the window's closed and don't forget to put the cat out. Going now, Mr. Gilda Sleeves? Yes, an appointment. I forgot it, but then I remembered it. Leroy, this is a community living room. Marjorie is just as much right here as you have. Oh, yeah? Does she let me stay here when Wally Hoff comes over and they want to sit on the sofa? Wally Hoff has now come near the place in three months. Yeah, but don't you wish he would? I do not. So, Wally, I never wanted to see him again. You didn't think you'd take you up on it though, did you? Leroy, sometimes I just... Stop at both of you. Stop fighting and quiet down. Eat God. Sometimes I don't know whether I'm a nuncle or an umpire. I came home to listen to a radio program and I wanted quiet.  Quiet. Quiet, Leroy. Ouch! Leroy? I never touched her.  I better go up to my room. Did you show your uncle what they went and did? Oh, no. What? Who did, Bertie? I don't know. Some men came and they put up a great big billboard. With a picture of a mayor on it. Where, Bertie? Look out the side window there. If I got to have that big fat incumbent looking at me every morning when I sit down to breakfast, by George, I'm going to see my lawyer. I think you should. No, that won't do any good. My lawyer's judge hooker. Besides, that billboard was just put there to get my goat. Well, ain't there something that can be done? They've gone and messed up the viewing hall. Yes, Bertie. There is something that can be done. Pull down the shape. Pull it down and keep it down. I thought you'd gone up your room. I did, but I came down again. You want to see a trick? No. All right, take a card. Any card. No tricks, Leroy. I have a radio program I want to hear. And by George, I'm going to hear it. Alone. A radio just... Leroy, too, my dear. I know. It's 5.30. Better turn on the radio. Pull up a chair and have a little piece for change. I wonder if Eve is listening. How bet she is. Two hearts that beat as one. Radio is wonderful. The U.S. and U.M. are Summerfield. Uh, just in time. At each time melodies, the program originally scheduled will not be heard at this time. Oh. Instead, we present at this time a talk by the Honorable Cyrus Peter Williger, Mayor of Summerfield. What? Mayor Joe Williger. I won't listen to it. Don't listen to it, Eve. My very... Well, I'll just listen a little. The time has come. The time has come, my friends, to face facts. You don't dare. That I have many times. Yeah, you bet you have. I have many times. You bet. But he will another vacancy. He's libel, Mr. Williger. That does it. You want action, eh, Mayor? All right, you'll get it. Why don't you answer? Why don't you stop saying hello? Listen, Judge. Mr. Williger just made a speech about me on the radio. I know. I'm listening to it right now. He called me a boondogner. That's nothing. Did you hear the other things he called you? Listen, you old rooster. Get busy.  Tell him I want to answer to Williger. But guilty. I want you to arrange for him to put me on the air tomorrow night. But guilty. Do you realize? Don't argue about it, Judge. Do it. I'm going to give the people of this town a near full. And by George, it won't be any tea-time melody. The Great Guilty Sleeve will be with us again in just a few seconds. Until the war is won, you homemakers won't be able to buy all the smooth, wholesome, fab stats you want because vast quantities of dairy foods are being sent to our fighting fronts. But remember, each package of gold and delicious fab stat cheese food you do buy goes a long way by lending its mellow, appetizing cheese flavor to other, more plentiful foods. You see, fab stat melts with such luscious smoothness. It's no trick at all to whip up tempting fab stat omelettes, Welsh rabbits, souffleys, and repair all kinds of grand macaroni and cheese dishes with fab stat. You can get delicious sandwich variety with fab stat, too, because it blends so smoothly with other ingredients. Fab stat is high in muscle-building milk protein, helps provide food energy, milk minerals, and important vitamin A. So look for, ask for, and when you can, buy this delicious nourishing food, fab stat. Now, let's get back to the Great Guilty Sleeve. He's had a night of dreams in which he's pursued by little demons screaming at him. I say demons. But he's followed it with a day of purposeful and fairly fruitful activity. Judge Hooker has arranged for him to broadcast a television WSUM. He's written a speech with which he's mightily pleased, and now he's hurrying home to supper. But what is this he sees in Pee-Vee's window? Oh, Pee-Vee, my old friend. He can't do this to me. Pee-Vee. Well, good afternoon, Mr. Gallagher. What can I do for you this fine day? Don't you try to soft-soap me, Pee-Vee. What's that Trewilliger poster doing in your window? That won't hurt Trewilliger. Ask me to put it in there. But I'm your friend, Pee-Vee. Trewilliger is just a stranger. I know, but he's a potential customer. Customer? You're money-mad, Pee-Vee. Oh, no, I wouldn't say that. Anything to get more customers. Anything to make a few more dollars. Well, there's two ways of looking at that. One is, I'm in business and I have to make a small profit. The other is, I'm performing a service. If I can extend a circle of my service, I feel I'm helping the community. You mean you're stealing a customer from the Atlas Drug Company? Mr. Gildersley, there's plenty of room for Pee-Vee's drug store and the Atlas.  Well, no, I wouldn't say that. I tried to be fair to all my customers, Mr. Gildersley. That's why I put your poster in the window and Trewilliger's. Confounded, Pee-Vee. Can't you see that politics is not the same as peddling pills? Politics is a matter of convictions. You've got to be for me or Trewilliger. You can't be for both. Now, which are you for? Well, there's two ways of looking at that.   Well, now, there's two sides to that question. There's only one. Are you for me or Trewilliger? Mr. Gildersley, I like to look at these things from several angles. Quit stalling. Quit stalling, Pee-Vee. Who are you for? I haven't decided yet. Pee-Vee, I demand that you remove that Trewilliger poster from your window. Oh, dear. Mr. Gildersley, really, I couldn't do that. If you value my friendship, you will. Oh, I do. I do value it only... Well? Well, I promised Mayor Trewilliger I'd leave him in there until the primaries, June 20th. But I'll tell you what I could do. What? I could put a war-bond poster in front of him. You're pretty cagey, Pee-Vee. I don't know, I wouldn't say that. There you are, Mr. Gildersley. Oh, that's fine, Pee-Vee. Not a trace of Trewilliger to be seen. A much obliged. If you have any doubts that you're doing the right thing, just listen to my broadcast at 9.15 tonight. You're going on the air? Yeah. Just tune in station WSUM at 9.15, and you'll hear me put the blast on Trewilliger, Pee-Vee. I'll pull no punches. Well, I'm certainly trying to hear that. Listen in and tell your friends to listen, Pee-Vee. Hello. Good-bye, Mr. Gildersley. Politics, politics, I wonder.  Throckmorton, are you sure you wouldn't like one of us to go down to the radio station with you? No thanks, Eve, I'll be all right.  I'd be glad to go along, Gildersley, if you want me.  Can I go on? I've never seen a radio station. Leroy, I can't think of any situation in which you'd be more of a nuisance. Oh, sound effects. Now, Leroy, you stay here and listen over the air. It'll be much more exciting that way. OK, Miss Goodwin, you want to see a good trick? What kind of a trick? Leroy, we'll have no tricks now, please. I've only got a few minutes before I leave, so just let us talk, if you don't mind. I wouldn't interrupt. Miss Goodwin could take a card, and you could just keep talking. Take any card, Miss Goodwin. All right. Are you sure you don't want the judge to look over your speech, Thracmorton? No, Eve. Just wait to hear it. Now, place the card back in the deck, please. Like this? That's fine. Thracmorton, I hope you won't be abusive or personal in your speech. Certainly not. I'll hit straight from the shoulder. Well, I don't mind that. Oh, I forgot to tell you. You have to remember the card you drew. No, no, Leroy, I don't. It was the Queen of Spades. Oh, for corn sake. Judge, you didn't have to tell. Now, you spoiled the trick. Take another card, Miss Goodwin. Leroy, stop that. It's impossible for us to talk with this confounded board of a lack going on. Okay, okay. Go ahead and talk. Politics, blah, blah, blah, blah. Cheerful young men. What I was saying, Thracmorton, was I see no reason for you to get personal just because Mayor Toboliger descended to the personal level. There'll be nothing personal about it, Eve. Just facts. What kind of facts, Gilly? The worst ones I could find. Thracmorton, that's the kind of thing you should be very careful about. Eve, it's my duty to tell the public the kind of man my opponent is. That's very low politics, Thracmorton. Well, Toboliger's a very low politician. I'll say that, too. I think that's all wrong, dear. Really, I do. Well, if I don't... Isn't it about time for you to leave for the studio? In just a minute, my dear, I... Take any card, Martin. Any card at all. Leroy, give me that deck of cards. Ah, please, huh? God, you think I was just sitting around the house? No, anybody realize I'm about to go in the air? We all realize it, Thracmorton.  But between Leroy and his card tricks and you and Hooker criticizing my speech, he goes... Now, Gilly, just keep cool. There's nothing to be nervous about. I'm not nervous. I just like to sit quietly for a minute before I have to go. All right. Now, let's all be quiet. Heaven's sake. Clear. Leroy, would you like me to cause you to disappear? Well, go ahead. That settles it. I'm leaving. By George, I don't see how politicians can stand. Stand for it, Thracmorton. Well, if they haven't got a family, they can't run. And if they have, they can't think. This way, Mr. Gildersleeve. The studio is right down the corridor. Quite an establishment you have here, Mr. Stagg. Oh, you're so right, Mr. Gildersleeve. Yes, WSUM has grown into a real institution. Oh, here's our announcer. Carl. Yes, Chief? This is Mr. Gildersleeve. He's making that political in Studio A at 9.15. This is Carl Crofit, Mr. Gildersleeve. Carl Crofit? Yes. Well, I've heard you on the air. Well, you must be a fan of teatime melodies, Mr. Gildersleeve. Oh, I never miss teatime melodies. Fine program. Well, we try to make it a little different. You know, the average program of recordings is sort of... Oh, well, you know. Yeah. I try to make our teatime hours say something to each listener. Great. We try to leave some lasting thought. Yeah, too willigar left some lasting thoughts yesterday. Well, I suppose I just leave you two here in the studio, and Carl can show you about the microphone and so on. Right. Yes. All right. Thank you, Mr. Stagg. Thank you.  What difference does that make? Well, we in radio have quite a few little tricks.  On the other hand, some get short of breath sitting down. I'll stand up. That's fine. Now, suppose you just read me the first line or so of your speech. What for? Well, so I can show you where to stand. We in radio consider that very important. All right. Now, just a second till I run into the control. These announces, you'd think there was something hard about this. All I do is stand there and read. All right, Mr. Gildersleeve. Go ahead, please. Oh. Fellow citizens, I can state my political philosophy very briefly.  Oh, too far? Yes. Well, I'll move in a little. That's it. All right. Try it again, please. Fellow citizens, I can state my political philosophy very briefly. You're too close now. How about here? Oh, that's just fine. Fellow citizens, I can state. Oh, that's perfect. Don't move now. Come out and mark it with chalk. Chalk? This is right where I would have stood in the first place if he hadn't been so. Now, before I mark the spot, Mr. Gildersleeve, I'm just dying to know what is your political philosophy.  Oh, I'm sorry, but you can't say that. Why not? Well, we in radio have little rules and regulations, you know. Now, if I could just glance over your speech first. On one condition, I won't change a word of it. Oh, now, Mr. Gildersleeve, I know you're joking. Why don't you just call the mayor a political opportunist?   Will you agree to that? If I have to. That's the spirit, Mr. Gildersleeve. That's radio. Teamwork is the big thing to we in radio.  Oh, just fine, Mr. Stagg. Mr. Gildersleeve being very cooperative. Oh, that's good. So good. Mr. Gildersleeve, you'll be going on in just a few moments now, but there's a little formality to be taken care of. Oh, what's that? The matter of paying for the time. Paying? Yes, that'll be $75. $75? Listen here, Mr. Stagg. Mayor Terwilliger insulted me over your two-bit radio station. I'm simply demanding an opportunity to answer his unfounded charges. Perhaps I can explain, Mr. Gildersleeve. We in radio have our little rules and regulations. And one of them is that political candidates have to pay for a time on the air. Well, I don't know anything about that, and I'm not going to pay a cent. Oh, but I'm sure Judge Hooker understood that you... Judge Hooker didn't say a word about money. Well, we have to have it. Well, you won't get it. And I'm going on the radio anyway. Now, Mr. Gildersleeve, we in radio... We in radio give we in politics a big pain, brother. I stand on my constitutional rights. I'll send for my lawyer. Uh, what time is it, Judge? Just exactly 9.14, but my gold-watching chain won't be long now, as the monkey said when his tail got caught in a lawnmower. Ashley Roy, we ought to turn it down. The judge's watch may be wrong. Hadn't been wrong in 20 years, but I'll turn it on anyway. Gee, I wonder how Uncle sounds. He'll sound just fine. We're afraid he'll sound like Gildersleeve. I do hope he isn't nervous. You're S.E.M., The Voice of Summerfield. Due to circumstances beyond our control, the political broadcast originally scheduled for this time will not be heard. We present at this time the music of Chuck Haslett and his ensemble. Their first selection, blow that. Judge, what on earth could have happened? Can't imagine, Eve. I'll go call the station right away. Stop the music. Stop it. Please, please, Mr. Gildersleeve.  I demand to be heard. Oh, Throckmorton. I don't want... Have you ever heard of Free Speech, brother? All right. You made a prime Jackass of yourself on the air. It was your fault, Hooker. Why didn't you tell me they wanted money? Well, I tried to. Maybe after this, you'll listen to me. You can't run a campaign without money. Yeah, I guess you're right, Judge. Well, I haven't got any. I guess I'm late. No, no. Don't be downhearted, Gildy. You've got a lot of friends in this town. Friends? How do you mean? Well, your friends will all be glad to contribute to your campaign fund. I don't believe it. No nonsense. Anybody that wouldn't give five dollars? At least no friend of yours. That's all. How much can I put you down for, Horace? The. Yeah. Let's start with you. Yeah. You see what I mean, folks? Good night, everybody. Music on this program is directed by Clark Sweet. This is Ken Carpenter speaking for the Craft Cheese Company makers of Marquee Margeron and a complete line of famous quality food products. Craft is by two. We'll listen to it again next week for the brother of by two, by the great Gildersley. And now listen real close, for here's the big, exciting food news of the day. Point values of Margeron have been sharply reduced by our government, cut from six points to only two ration points a pound. Think of it. Now, today, you can get your favorite spread-for-bread economical Marquee Margeron for only two ration points a pound. That is, grand news and sure to be welcomed by the millions of American families who enjoy Marquee Margeron every day as a delicious spread-for-bread. Great news, too, for you homemakers concerned about good family nutrition because Marquee is one of the best energy foods you can serve and is fortified by craft so that every pound of Marquee Margeron contains 9,000 units of vitamin A. So remember, it now takes only two ration points a pound for delicious nourishing Marquee, P-A-R-K-A-Y. Marquee Margeron made by craft.


Okay, we're going to get started now. All right, so last time at the very end, I told you about a quantity known as the binomial coefficient and the function in Mathematica is like this, binomial coefficient with two arguments which I refer to here as n and m and the definition of the binomial coefficient is given here in terms of n factorial, m factorial and n minus m factorial. There's a symmetry to the binomial coefficient. They're sort of the same when the numbers are equally spaced around the middle value. So it turns out that n over m is equal to n over n minus m and we'll see this in a minute when we evaluate the binomial coefficients with Mathematica. Now, does anybody remember what's the interpretation of this number or what is this number? Okay, I'll remind you. So we suppose we have a list of n distinguishable objects and we wish to separate them into two lists, one containing m elements and the other containing n minus m. And this binomial coefficient is the number of ways that we can do that if we don't care about the order in which the elements appear in the smaller lists. So let me give you an example of something that you can calculate using the binomial coefficient. So maybe you'll have a better feeling for what it means.  And each time I flip the coin there's two outcomes. It's either heads or tails. And what I want to know is, what I want to list here is all the ways that I can flip the coin four times and get only one tails, okay? So we can make that list. I could have the first coin first flip be a tails and the rest heads or the second one or the third one or the fourth one. So there's four ways. Now, but I want you to see if you can see here that that number should have been given by the binomial coefficient four over one. Because I can think about this, an equivalent question would be, how many ways can I break up a list of four elements into two lists, one containing one element and the other containing three without regard for the order? It's the same question. And we'll evaluate the binomial coefficient four or one and also four or three in a second to see that that's true, okay? So let's go ahead and have a look to see if that is indeed the case. And we'll talk about coin flips a little more in a second and we'll need to make sure that we feel comfortable with that statement. So I'm going to say binomial coefficient and then I'm going to put four. That's the number of coins, coin flips. And then I'm going to ask, I want to have one of my lists contain one, okay? So I get, whoops, that's to, oh, I'm sorry, it's not binomial coefficient, it's binomial, okay? So you see I get four. And as I said, you'll get the same thing if you put in four minus one, which is three, okay? So there's that symmetry. You can actually construct an object known as Pascal's Triangle from binomial coefficients. You might want to look that up. It's kind of an interesting mathematical result. Okay, so now let's do something, let's try it again. So now let's suppose I take 10 coins, 10 flips of a coin and I want to know how many ways are there for me to get exactly four heads. So what quantity should I evaluate? Binomial, 10, 4. Anybody have a guess as to how many that might be? Do you think it's a lot? Well, let's have a look. So binomial, whoops, 10, 4. 210 ways to get exactly four heads if I flip the coin 10 times. And just to check, it should be the same as binomial 10, 6, okay? All right, now I want to ask an even more specific question, again, about the coin flip. So let's go back over here and let me correct this. Sorry, that's not supposed to be there, okay? So the next question I want to ask is what's the probability of such an outcome, okay? So what we looked at here was how many ways can I flip the coin four times and get exactly one head? Now I want to know what's the probability out of all possible flips of a certain number of coins to get a certain outcome, all right? So to do that, I want to start with an even simpler example. So now I'm going to flip two coins and I'm going to look at all the possibilities, all right? So one possibility is both of them are heads. Another possibility is one is heads and one is tails, the second one. Or I could have got tails on the first flip and heads on the second and then the last possibility is that I get two tails. So there's four possible outcomes. What's the probability of getting two heads? There's only one way to do it, four possible outcomes. So the probability is one fourth. Now what if I ask what's the probability of just getting one head and one tail and I don't care about the order? Then I should combine these two and I get, yeah, one half or two fourths and then finally for the two heads it's also a fourth. And I want you to notice a couple of things. So first of all, if we did this right, these should add up to one and they do, okay? And the second thing is that I want you to notice that this is actually, no, sorry, that this is actually equal to one half times one half. Now why do I want to point that out? Well, because if I flip one coin, the probability of getting a heads is a half, okay? And if I flip two coins and I ask the question in the following way, what's the probability of getting heads on the first flip and heads on the second flip, the rule of constructing that probability is to multiply the probability for the independent events, okay? So the one fourth I could have equivalently gotten by saying, oh, I want a heads and a heads. So that should be a half times a half, okay? So or a half squared. Now the next thing I want to do is construct a more general result, okay? So I want to ask what's the prob of getting m heads, oh no, yeah, m heads in basically n flips, okay? So m is going to be a precise number, less than n, okay? Now let's think about what we have to know in order to get that. Well, first of all, what we have to know is that the probability of getting m heads is one half to the power m, but at the same time we have to get n minus m tails and since the probability of tails is also a half, we have a half to the n minus m, okay? So this is the probability of getting m heads and so multiply n minus m tails, got it? Okay, now there's one other thing we have to do and that is we have to multiply by the number of ways of dividing up the flips into two lists, one containing exactly m heads and what's that number? That's the binomial coefficient n over m and you can see that here the m's will cancel in the exponent so this turns out to be n over m times one half to the power n, got it? All right, so let's evaluate a couple of those just for fun to see what they are and then what we'll do is we'll forget about the coins and we'll do the more general case that I'll explain to you in just a minute, all right? So I'll go ahead and just, can you see that with the light on? All right, so let's try the, let's evaluate 10 coins and 4 heads, okay? So what do we need to do? We need to do binomial 10 comma 4 times one half to the power what? 10 and we could do n comma percent, all right? So if we flip a coin 10 times or flip 10 coins the chance that we'll get 4 heads is about 20%, a little over 20%. Let's try another one. Let's try the probability of getting 500 heads when we flip 1,000 coins times one half to the power 1,000. What happened here? That doesn't look right to me. Oh, right, because there's a fraction. That's right, thank you. All right, n percent, about 2.5%, okay? All right, so there are a couple of examples of using the binomial coefficient in calculation of probabilities of coin flips. But what about, let's talk about a much, much more general situation. And this general situation results in a probability distribution that's very special which is called the binomial distribution. And I'll tell you why it's special in a minute. But let me explain to you how we construct this one. Okay, so what we just did here was we considered a special case, heads and tails, okay? And we could think of this special case as a more general case where we have something that we're going to call a success which we said here we were interested in heads and then not success or failure is T, all right? Now, let's denote the probability of success as P. In this case, it's 0.5, all right? And the probability of failure has the probability of 1 minus P which also is equal to a half or 0.5, okay? Now what I want to do is consider an arbitrary situation. If you like, you can think of it as a loaded coin where instead of it, you know, fair coin has equal probability of getting heads and tails, so half and half. A loaded coin, we adjust it and just call it P. And if it's loaded in our favor, it would be P greater than 0.5, okay? But let's just leave it as P, okay? Now let's consider the case of arbitrary value of P. Now what we're going to construct is something I'm going to call P of M, capital P. And what this is going to be is the probability of M successes and we're going to assume that we have N trials, okay? Now we can look to here for inspiration. Okay? So what do we need in order to construct that probability? We need the probability of getting M successes.  And then we need to multiply that by the probability of getting N minus M failures. So that's 1 minus P power N minus M. And then we need the binomial coefficient to enumerate the number of ways that we can split our list of trials into two groups, one containing N and one containing N minus M, okay? And this is what's called the binomial distribution. And it's special because it's so general, okay? A couple of possible outcomes, arbitrary probability. And as we'll see a little bit later, this distribution is the starting point for deriving very well-known and ubiquitous distributions that occur in sciences and nature in certain special cases, more restricted cases, such as the normal distribution, the Poisson distribution. Those are special cases of the binomial distribution. Okay? So let's go ahead and see how we get this thing in Mathematica and then we'll talk about an important limiting case. Any questions on this? Anybody heard of the binomial distribution? A couple of people who took statistics. Okay. All right. So now, how do you refer to this thing in Mathematica, okay? So in Mathematica, that function there can be specified as follows. It's called binomial distribution and then it has two arguments. One is the number of trials and P is the elementary probability. Now, if we actually want to generate the distribution, what we do is we put this inside another function which is called PDF and PDF stands for probability density function, okay? And then we need an additional argument here to tell us how many successes we want. So if we want to keep it general, we say M, all right? And if you enter that, you get basically the formula that I wrote down over there, okay? 1 minus P to the power N minus M times P to the M times the binomial coefficient N over M, okay? And Mathematica knows what that means. If you refer to it like this, then you have exactly that distribution. Okay? And right now it's not defined with any particular numbers. So let's have a look at what it looks like for a particular case of P and M. And the way I'm going to do this is I'm going to actually look at it for all values of M so that we get the full distribution, okay? So I'm going to define N equal 10 and P equals 0.4, excuse me, okay? And now I'm going to make a list, a table actually, that I can plot and I'll call it lowercase binomial dist equals and then I'm going to tabulate this guy as a function of M, all right? So what I want to do is table, curly bracket, M and then we can mouse this in, okay, and put a curly and then we just have to specify the range of M. So M can range from 0 successes to 10 successes. So we could say M goes from 0 to N, okay? And I'll just put a semicolon there and then we'll plot the thing. It's evaluated at discrete values of M. We're making a table of discrete numbers here so we should use list plot binomial dist, all right? So let's enter that and see what we get. And I'm going to go ahead and make the point size a little bigger, so plot style arrow point size 0.02 so we can see them better, okay? All right, so what is the interpretation of this? What we've plotted is for an outcome for which success has a 40% chance of happening on an individual trial, what we've basically plotted is what's the probability of getting a given number of outcomes as a function of a given number of successes as a function of the number of successes? Okay? So the probability of one success is for, I guess that's 0, very small, 10, very, very small. And notice that the maximum occurs here at 4. And this is not a coincidence, 4 is actually what you get if you multiply the number of trials times the elementary probability of success. So the maximum in the binomial distribution, we'll see other examples, but this shows it, occurs at that number, the number of trials times the elementary probability of success. And now that we've got this all typed in, we can see things like that very easily. Let's just change this elementary probability to 0.6 and then you see the distribution shifts. Now, another thing that I would like you to notice is that this thing looks almost like a bell curve. You see, it's got the peak here at 6, which is 0.6 times 10, and then it's got some wings on it. And for this value, these particular values of parameters, it's a little bit skewed on the lower side, whereas in the previous one it was skewed a little bit to the higher side, but it's almost a bell curve. And that's significant because there will be a limit that we'll talk about in just a minute in which this becomes the bell curve, or in other words, the Gaussian or normal distribution. And one way to appreciate that limit is to increase the number of trials. So let's go ahead and do that. So now, let's change this to 100. And I'm going to put an option in here that's useful for you to know.  So if you put in an option called plot range arrow all, it will plot the whole thing. All right? So as expected, the maximum occurs at 60, which is 100 times 0.6. And now you can see that for n equal 100, it looks a lot more like a symmetric bell curve. So we can already appreciate the possibility that as the number of trials goes up, the binomial distribution becomes a bell curve. And that's convenient because as we'll see to some extent in this course, but you'll appreciate in other classes and especially physical chemistry and if you take probability, the bell curve, the Gaussian function, shows up a lot. And it has very nice mathematical properties that allow you to do exact calculations, whereas the binomial distribution is not so convenient. Okay. Let's go ahead and have a look at another case. So now let's go back to our coins example. A thousand coins. If it's a coin, a fair coin, we should put in 0.5. Notice the number that we get at 500 is the number we calculated before, about 0.026 or something. And notice that as we increase n, the distribution becomes more and more narrow. You see that? So there's an interesting connection to the chemistry issue here too. Let's make the number even bigger, 10,000. Let's go up to 100,000. Notice as the number goes up and up, the probability of getting anything but the value at the maximum decreases very rapidly away from that value, n times p. Now what the heck could this have to do with chemistry? Well, if I asked you what would, what happens? So suppose I have a cylinder of gas and I have a wall right in the middle of the gas and then I poke a hole into the wall and allow the gas to distribute. What's going to be the outcome of that? What's the situation at equilibrium? Well, this is like a coin flip in a way, right? If I have a really large number of coins, so suppose I have a really large number of gas molecules like Avogadro's number and I look at this plot here, I can appreciate that the most probable outcome by a lot is going to be the case where I have half heads and half tails. In other words, that half the molecules are on one side of the wall and half run the other. And that's one example that you probably heard about when you were first learning about entropy and its relation to microstates and most probable outcomes. All right, so if we think of our coins as being the gas being on one side of the container or the other, then the problem is the same. And what I'm showing you here is that if you had 100,000 gas molecules, that the probability of having 40,000 on one side and 60,000 on the other is for all intents and purposes zero. By a long shot, the most probable outcome is having half of them on each side, okay? All right, now you got it? Okay, now let me go back to the board and I'm just going to, we're not going to drive this. It's not too hard to drive, but I don't want to do it. I'll just quote for you a result that's very significant and we've already sort of seen an indication that this is true, all right? So, when the number of trials n is very large, so we'll say in the limit that n goes to infinity, but in practical terms it's much less than that, and if p times n, the position of the maximum remains finite and large, then in that limit, the binomial distribution goes to the normal distribution, which I will write for you here in some different symbols. So, it's 1 over the square root of 2 pi times sigma. I'll tell you what sigma is in a minute. And then e to the minus m minus n times, well, let me write it like this, yeah, n times p squared divided by 2 sigma squared, okay? And this is what's known as the normal or the Gaussian distribution, and it has a mean n times p, which is also equal to its maximum value. And the standard deviation is what sigma represents. Sorry about the squeaks. That's square root of np times 1 minus p, okay? So, this is the standard deviation of this distribution, and its mean occurs at n times p. All right, so now let's look at this. This is what's called the discrete Gaussian or normal distribution because m is an integer. We'll talk about the continuous one in a minute. All right, so what I want to do first is compare the binomial distribution to the normal distribution, and we'll start with a small value of n. We'll see that they're different to a certain extent, and then we'll increase n and see that they become indistinguishable. Okay, so let's go back to our original case here, which is 0.4 and 10, okay? And now what I want to do is I'm going to define the Gaussian distribution, okay? So, I'm going to put it right in here, and I'll call it g. So, g of m, a function, colon equals, and so then we have 1 over square root 2 times pi, and then times sigma, which I'll define in a minute, and I should put parentheses around the denominator to keep all these things together, and then times capital E, carat minus m minus n times p squared divided by parentheses 2 times sigma squared. And another parentheses, and I'm missing a parentheses up here, okay? So, that defines my normal distribution as written down over there, and now I'm going to introduce sigma using the same formula as on the board, all right? So, that's going to be square root of n times p times 1 minus p. And now I'm going to tabulate the Gaussian distribution, so I'll call it gaustist equals table, curly, m, and then g of m, and I'm going to do that, m goes from 0 to n, okay? And now what we'll do is we'll plot the binomial distribution and the Gaussian distribution on the same plot, so I'll put a curly here, add gaustist, and put a comma. All right, so let's see what we've got. So, which one is which? Well, we could put a legend if we wanted, but we know the blue one is the first one, okay? So, the binomial distribution is the blue points, and the Gaussian or normal distribution are the purple points, okay? So, notice that they're a bit different, but already for n equals 10, which is way far from infinity, they do look somewhat similar. What about if we crank up the number of points a little bit, number of trials? Now they're starting to look quite similar. So, already n equals 100 is getting pretty close to the limiting case for this particular value of p. What about if you crank it up to 1,000? And let's go ahead and make the point size back to normal so we can see if there's any deviations more easily. Now you see they're essentially on top of each other. Okay, so the main point here is, well, first of all, gives you a little practice with putting in the discrete Gaussian distribution, but second of all, I think we have convinced ourselves that the normal distribution, which as we will see in the course, and you'll see later, which happens to be a much more convenient function, is a great approximation to the binomial distribution for modest values of n. All right, now the next thing is, I want to tell you about the continuous Gaussian distribution. So now we're going to suppose that instead of having m as an integer, we're going to have the argument of the Gaussian is going to be a real number that's continuous. Okay? And we're going to call the variable x and the continuous Gaussian looks like this. It's very similar. And here I've just introduced the mean as angular brackets x. Okay? All right, so now we're going to see this function is actually predefined in Mathematica. So we'll see how to plot that. All right, so I'm going to go down here. And let's go ahead and redo this one again with 100. Okay, so the mean for this case n times p is 40. All right? Now I'm going to come down here and define something called mean equal 40. And then I'm going to define a plot of the continuous Gaussian function. And the way we access this is very similar to the way we access the binomial distribution. So we're going to say plot, bracket, pdf, normal distribution is what it's called in Mathematica. And then for the normal distribution we have to give mean and sigma. So in other words, the average and the standard deviation. And then I'm going to say plot it as a function of x or tabulated as a function of x. And now I have to say the range of x. And so I'll say x goes from 20 to 60. And I'll put a semicolon. And up here I'm going to define this plot as discrete equals. And I'm only going to plot the Gaussian. All right? So I do that, I enter this and I get my Gaussian. Oh, let me say plot range to 20 and 60. Oops, sorry. 20 and 60 and then I'll specify y goes from 0 to 0.1. Okay. Okay, so now we have a plot of our discrete Gaussian. And I'm going to make a plot of the continuous and then we'll show them on the same plot. And since I want to show them on the same plot, I'm going to specify the plot range here being the same. Okay, so I can just mouse all this stuff in and put it here. And finally say show discrete and continuous, enter. Okay, so now we see the blue points are the discrete Gaussian and the blue curve is the continuous. And you can see that they are coincident. It's just the continuous obviously is a nonbroken curve. And one of the points here is that if you want the continuous Gaussian distribution, then what you do is you say pdf normal distribution, you specify the mean and the standard deviation and then the variable that you want it to be a function of. Okay. All right, so to finish up all of the stuff, not quite finish up, one more little thing about the probability distributions. And there are plenty of others, but I think we'll leave, we'll stop at the Gaussian. There are others that you can define based on other limits of the binomial distribution. All right, so I just want to go back to using the symbolic forms. So I'm going to say clear n and p and then I'm going to redo something we did earlier. So this will be binomial distribution np and then comma m. And you may recall that that's going to just give us, whoops, what did I do? I spelt it wrong. That gives us the formula for the binomial distribution. But now I can actually put this into things like I can ask what's the mean of that? So if I say mean of all this stuff happened here. Oh, sorry, for the mean, we don't put the pdf thing around it. Okay, so the mean of the binomial distribution is, as we heard earlier, n times p. And if we want the standard deviation, let's put this in there. We get the formula that I wrote down over there for sigma. We can do the same thing for the Gaussian. So, well, let's just start over. Say pdf, normal distribution, bracket, mean, and sigma, comma x. Or I guess we can call it m to be consistent with our previous, or no, I guess it was x, the continuous Gaussian. And I'm going to clear mean and sigma before this because we have some numbers in there. Okay, so if we enter that, you see we get the formula that I wrote down for the continuous Gaussian, e to the minus x minus the average squared divided by 2 sigma squared with the factor out in front, 1 over square root of 2 pi sigma. And if we want the mean, what do you think we should get? Mean and standard deviation, sigma. Okay? So these are ways that you can use the symbolic form or if you put numbers in, you'll get specific values corresponding to whatever numbers that you put in. All right, now I want to show you an application of the Gaussian distribution. And this is something that you'll learn in Chem 131c. You'll talk about diffusion and transport, okay? So what I want to think about here is, let me go to the board again, so what I'm going to suppose is that I have a container, a one-dimensional container, okay? And it contains some solvent. And I'm going to call it coordinate x. And so here it will be zero. And what I'm going to suppose is that I put a one-dimensional sugar cube in there at time zero, okay? So I can imagine that all the sugar is just along x equals zero here, an infinitely narrow sugar cube. And then as the sugar cube sits there, right? The sugar, as you know, if you've ever dropped a sugar cube in your coffee, even if you don't stir it, after a while the sugar diffuses out of the cube, dissolves and diffuses, and at some point, what happens? What's the equilibrium situation? So if at time equals zero, I have all my sugar in an infinitely narrow cube at the origin. What's going to be the situation at time goes to infinity? The concentration of the sugar is going to be the same everywhere in the container, right? So that might be some value here that I'll show with a dotted line, all right? So at time equals infinity, the sugar has diffused and it fills the whole container with the constant concentration. What do you suppose the situation is in between? Well, it turns out, and this is a problem you'll learn how to solve in PCEM class, that in between, it's going to be a Gaussian distribution. So at some time, t1 greater than zero, the sugar will have, you know, started to diffuse away, but it doesn't diffuse away like a square, it obeys a Gaussian distribution if it's undergoing what's called, you know, just Brownian motion or diffusion, simple diffusion. All right? And at some later time, it'll also be a Gaussian distribution with the same area because the area under the curve is the total amount of sugar that we have, and this Gaussian distribution will broaden until it's flat. So that's one place where you find, say, a Gaussian distribution is in these diffusion problems. And it turns out that there's another problem, that has basically the same solution, and that's what we're going to, we'll actually plot this thing now. And that would be if you were to consider the position of a particle that's diffusing in a liquid, where it starts out at the origin, at time zero, what does the probability distribution, the probability of finding that particle at a given position and a given time look like? So the quantity that I want to consider is a particle diffusing in one dimension. I can ask what's the probability of finding the particle at a position x at time t, then that's given by the Gaussian distribution that has a time dependent width. If we start the particle out at zero, then that would be minus x squared over 2 sigma of t squared. And it turns out that sigma of t can be written, or again, for this Brownian motion, as 2 times what's called the diffusion constant, and then times t. So sigma of t, the width of the Gaussian, varies linearly, increases linearly with time. Okay, so now what I want to show you how to do is we're going to plot this, but we're going to plot it in such a way that we can animate it. So basically, we'll be plotting it at different time points on the same plot so that you can actually watch the thing spread out. Okay, so this will be your first introduction to what's called the animate command in Mathematica, which is kind of a fun thing to be able to do. But if you don't care about diffusion or whatever, the point is we're going to plot a Gaussian whose width varies linearly with the parameter, we'll call it time, and we'll animate it. Okay, so let's do that. Okay, so I'm going to clear sigma, I don't know if we've used d or t, but might as well clear them, and p. Okay, and now I'm going to, just to make the equation simple, I'm going to say that the diffusion constant is equal to 1, right, and now I'm going to define sigma equals square root of 2 times d times t, I guess I could leave the d out but whatever, we can change d if we want later. And then this should be, I'm sorry, this should be a function, sigma of t underscore, so it should be colon equals, all right. And now let's define p of x underscore and t underscore colon equals 1 divided by square root 2 times pi times sigma of t and parentheses here, and parentheses here, parentheses here, parentheses here, and then times e carat minus x squared divided by parentheses 2 times sigma of t and put some parentheses around it squared. Okay, now what we're going to do is we're going to make an animation of this thing showing how it varies from some early time to a longer time. All right, so I'm going to type a bunch of stuff in and then I'll explain to you the things that you may not already know. Okay, so the command is called animate, okay, and what we're going to animate is plot, a plot of p of x and t where we're going to plot that from x going from minus 10 to 10, okay, so that's our plot. Oh, wait, we want to put some options in here. All right, the options I'm going to put in are this plot range is going to be y going from 0 to 0.3, and these are things that I optimized by trial and error, I can tell you that. And then I'm going to say plot style, arrow, thick, black, this is the line that's going to be plotted, and then an option filling goes to axis. What that's going to do is just shade in the area under the curve and then I'll put some axes, labels, all right, so arrow, the first one's going to be x and the second one will be p of x and t. All right, so that's our plot. So, so far all we have is a plot command with a few options inside animate. Now what we have to do is put in a range for a variable that's going to define our animation. All right, so for us that's time, I'm going to say time t goes from 0.001, so some early time, to 100 in increments of 0.5. And then so it doesn't loop, I'll just say animation repetitions, arrow repetitions goes to 1. Oh, I don't need the curly bracket. Okay, now let's see if that works. Now I have this stuff here, back here. All right, so notice at the beginning that t equals 0.001, let's think about this. So when t is really small, that means the standard deviation of the Gaussian is really small, which means its width is really small. And we can see it's very narrow there. As time increases, the width increases, and so the Gaussian becomes broader and broader and broader, just like in the sugar cube example I explained to you. All right, and so if you push play, you're watching that happen from t goes from 0.001 to 100. So here's somewhere in between, and you can actually, you know, look at how it goes by moving the bar here. So you have this Gaussian spreading, spreading, spreading, and then at very long times, it's almost flat. And if you went to really long time, it would be flat, because the probability of finding the particle somewhere in the volume of the system, or the length of the system in this one-dimensional example at very, very long times is equal everywhere in the system, unless there's some special forces acting on it. Okay, but for us, this is mainly an opportunity to have a little widget that we can play around with to understand how the Gaussian works. Short time, narrow width, long time, broad width. You see how that evolves. And also, you got to see your first example of using the animate command. And like I say, this is something you will learn about in Chem 131c, diffusion. Okay, so now we are done with statistics, or what I want to tell you about statistics. All right, so you've learned how to analyze data in terms of mean standard deviation variants. You've learned how to make histograms. And then I introduced you to a couple of distributions that you commonly see when you histogram data. And in particular, the Gaussian comes up a lot. All right, are there any questions on what we've done with respect to the statistics? Okay, so I'm going to switch gears now. And the next thing that we're going to talk about is how to plot functions of two variables. Okay, so we learned how to make plots a couple of different ways for functions of one variable. So those are two-dimensional plots, y versus x. All right, so we've seen the plot command which applies to functions of continuous variables. And then the list plot which allows us to plot individual data points, sets of individual data points. Now what we want to do is plot a function that has two arguments. And I'll just write down an example for you. And this is an example that you will see. And some of you have probably already seen in Chem 131a. All right, okay, go back to the board. Okay, so there's a simple model problem in quantum mechanics that's usually one of the first ones that you get that you solve by hand when you learn how to solve the Schrodinger equation in Chem 131a. It's called the one-dimensional particle in a box. Does that sound familiar to any of you? And what is the model corresponding to the one-dimensional particle in a box? It's a quantum particle that can move in one dimension which we'll call x. And at x equals 0, we have a wall. And at x equals l, we have another wall. And the particle is confined between those two walls. And if the walls are infinitely high, of course, well corresponding to infinite potential energy, then this is a very easy problem to solve in quantum mechanics. And does anybody remember what you get out for the energies? The energies are discrete. Does that look familiar? H is Planck's constant and n is a quantum number. What does n range from? Okay. All right, so that tells you the ground state here, the lowest energy is n equal 1 and then it increases. Okay. Now, when you solve the Schrodinger equation in addition to getting these quantized energies, you get something else which is called the wave function which tells you the amplitude of the wave corresponding to the particle in this box when it's in a particular quantum state, n. And does anybody remember what that looks like? Well, it's a sine wave and then it has a factor out in front. Is that right? I think that's right. Okay. So then you get the one little hump for the first state and then a cycle with a node in the middle and then just higher numbers of oscillations as you go higher and higher in energy. Okay. Oops, and this should be a function of x. Okay. Now, have you guys done the two-dimensional version yet? Do you have? Okay. Good. So this is a function of one variable and if we want, we could type this thing in and plot it with Mathematica but that's kind of boring. We've already done stuff like that. But what we haven't done yet is to plot a function of two variables. All right. So if you treat the same problem except now instead of having particle motion in one dimension but say in two dimensions, say a square box, then that's also an easy problem to solve in quantum mechanics and what you get is that the wave function looks like the product of two of these, one for motion in each direction where I'll call the second direction y. Okay. Now, it's not so easy to tell what that looks like, is it? Well, now I'm going to teach you how to use Mathematica to very easily look at this for whatever values of n you want. By the way, I forgot to indicate that there's a quantum number for motion in each direction so these don't have to be the same. Okay. So let's just go ahead and do that and then we'll, I'll show you just very quickly how the 3D plot works and next time we'll discuss details of that but I wanted to show this to you because it's a nice fun way to end today. All right. So let's go ahead and define that function, that wave function for the two-dimensional particle in a box, psi x underscore y underscore colon equals, I'm going to suppose that l equals 1 so I'll just put in 2 times sine and then I'll say nx for the quantum number in the x direction. Oh, yeah, right, thank you. That would not have worked. nx times pi times x and then l is 1 so I can leave it out and then times sine ny times pi times y, okay? And now we'll look at the ground state first so I'll say n equals 1. Or nx equals 1, sorry, and ny equals 2, all right? Now the plot for making a 3D plot is called plot 3D. So we say plot psi of x and y and then we just have to say the ranges that we want so we'll say since I said l equal to 1, I'll say x goes from 0 to 1 and then y goes from 0 to 1 and now I get a plot. Actually the ground state is 1, 1 so let's look at that one first, okay? Now right now we don't know which axis is which so we'll look at how to make axes labels and things next time but I just want to show you this is kind of nice because when you're studying quantum mechanics it's kind of fun to see how these wave functions depend on the quantum numbers so suppose nx is 1 and ny is 3 then you get interesting things going on and you can move it all around like you want. You could say 3 and 3 and this helps you understand the nature of these wave functions, all right? So there's your first 3D plot and there's all kind of fun things you can do with them to make them look really cool and that's what we'll talk about next time and we'll also talk about another way of representing 3-dimensional functions which is called a contour plot, okay? So we'll see you on Monday.


Hoi Hoi and welcome to the channel. I'm Dr. Sumerian, not a real doctor, and today we're going to do a little reading of a tale I wrote last month. As a part of the gift exchange on the SCP Wiki, so it was a Christmas gift for somebody else. It is called The Previous Segment was brought to you by Grant from the Wondertainment Holiday Fund and by viewers like you. It is December 24th, 2023, and this is NPR News. A ceasefire between forces of the Global Occult Coalition and the People's Liberation Army has broken down on the Korean Peninsula. In Britain, the Queen announces an eternal empire unshackled by the limits of time and space, and the US President is defending herself from claims of executive overreach. I'm Thomas Lieberman from NPR News, and here are today's top stories. The ceasefire negotiated last June between Beijing and the GSE forces, established along the border of what was once North Korea, ended in gunfire today, as a Chinese expeditionary force crossed the demilitarized zone into South Korea. Originally, the force of approximately 16,000 troops was attempting to flee from an unnamed threat inside North Korea's former territory, but as soon as they were detected massing along the border, the GOC forces opened fire. Over 10,000 prisoners were eventually taken with unknown casualties amongst the Chinese forces. UN forces inside South Korea have begun to mass along the border as well in expectation of the unnamed threat crossing the border. But so far, nothing has materialized. Reporting from Chinese state news services has called this an unacceptable escalation and unnecessary provocation. The People's Liberation Army have begun to mobilize troops and ships in the South China Sea. We'll get you updates on this story as it develops. In Britain, the Queen has made a strange announcement in a public address. Josh Lanier in London has more. Today at a surprise speech in the House of Commons, the Queen has announced that Britain will form a new eternal empire unshackled by the limits of space and time. Following the speech, the Queen hovered over the House of Commons silently for approximately four minutes before landing and leaving with her entourage. What this means exactly has not yet been explained, but a number of news pundits attempting to better understand the speech and its aftermath were vaporized on live television by an unknown power. It is unknown if this is related to the speech or if it is other anomalous phenomenon. The House of Commons was dissolved by the Queen soon after the speech. Prime Minister Boris Johnson's last act before being dissolved onto the floor of the House of Commons was to call for a snap election. There were no other survivors. President Clinton is having to defend herself from accusations of executive overreach today after she made recess appointments to the SCP Foundation's governing board. The Foundation has not had an administrative council appointment confirmed by the Senate since 2018 and President Clinton placed Dr. Alto Cleff in the most recent open slot. Republic Senate Minority Leader Jack Riley spoke this afternoon in his home state of Washington. The president doesn't get to end run around the Senate just because it's inconvenient. The SCP Foundation governing board seats our Senate confirmed positions. If the president wants to appoint new members she needs to send us names that aren't tainted by past Foundation criminality. Till that time we will continue to delay these appointments. Thank you. White House spokesperson Anna Layman said in a written statement, Dr. Alto Cleff is one of the most respected authorities on anomalous science. If the Senate would like to reconvene during Christmas to prevent this recess appointment they certainly can. Until then the president is going to ensure that the government remains functioning. This is NPR News.  In the next hour more updates on the ongoing conflict in the Korean Peninsula and are you paying too much for avocados? Julia Hans has more. And special thanks to Billeth who helped me. You can actually hear Billeth's voice in this recording. And if you'd like to support the channel head on over to patreon.com forward slash decimarian and pledge at any level like everybody here on the screen already has including Sanjiriki who has pledged at a hundred dollars. It is nice to know that I'm not alone out here and I will see you all again on Thursday.


Hello everybody. This is Lance Coyke and today I want to talk about your personal autonomic issues that you're having. So if you're not familiar, autonomic is a branch of the nervous system that we we don't really control. It's kind of automatic, you might say. Autonomics controls all sorts of stuff. It controls your breathing rate, your blood pressure, your digestion, your libido, etc. etc. Now I want to discuss how all of these things relate to what we do as people who are trying to improve fitness and people who are just trying to, you know, operate at maximum efficiency. So first we have to discuss stress and stress is a very general term. It does not mean things are good. It does not mean things are bad. It is merely something that wears you down. So waking up, I would say in the morning is a good thing, but waking up is also a stressor.  It's crazy. On the opposite side, sleep helps you recover. So now we can start to look at things in this little balancing act of everything. So working out really hard is a stressor, but as we recover from it, as we stop doing it, we make our bodies maybe more resilient and maybe the term is actually not fragile, but anti-fragile. We get better as we deal with all sorts of random different things. So and that is one of the benefits of generality of training, of doing all sorts of stuff to keep the body guessing as I joke about, but I'm kind of serious about. Those things allow our bodies to recover from stressors and grow stronger. So more types of stressors. Let's list a couple. So waking up is one, working out is another. We could also look at screens. Screens emit a lot of light and blind us. That is a stressor. Staring at the sun is also a stressor on that note. Eating foods that don't agree with your body, that's a pretty big stressor. Breathing in a way that is maybe not appropriate for the activity demands of what you have going on is a stressor. So as we respirate, we use our respiration muscles and those can get more fatigued. Those can get tighter. Those can throw off our postural balance and steal some mobility from our necks, especially from our hips, from our shoulders, from whatever you want to do. Enter the thing that is important to you. If you want to squat deep, then it's gonna steal your hip mobility. If you want to bench press, it's gonna steal your shoulder mobility, etc., etc. So stressors, let's see if we can list some more. Injuries, there's one. Infection, that's another. Psychological stress, a loved one dying. There's a big one.  Those are all stressors. Those are all things that wear us down a little bit. Now what I want to talk about with your autonomics is that we have a certain threshold that we approach with these stressors. Most people can wake up and feel okay. So that's not putting them over the edge. That's not eliciting symptoms. But if we act up enough, if we stay awake long enough, if we eat the wrong foods, if we over eat there's another stressor, then we can elicit responses from our body that says, I don't feel very good. Why are you doing this to me? And to illustrate that, I want to now talk about this little threshold model. I want to discuss today with you stress and how stress works. So stress is general in our body and we accumulate to different kinds of them. So I like to think about things on a graph. So let's say this is time and this is total stress on the Y here. Okay? So later on down the line, more stress. So let's say just waking up gives me a little blip, right? My stress increases when I have to be awake. And let's say I do my morning routine. I have my coffee. I feel really good.  I wasn't expecting to get a call from my mom. It's a pretty good call though. So as we start talking, my stress levels go back down and we're all set. Now it's time. This is maybe eight AM. Now it's time to work. Let's bump this back up. Now I've got to solve my problems. Okay? And then maybe I work out. Ooh, big stress. All right. But it can be good. When I work out and I recover from my working out, generally good things happen. I get good chronic adaptations. But acutely in the moment, it is a stressor.  And bam, stress increases again. So let's say we have a threshold. So throughout this day, calls from my mom, waking up, I felt pretty good.  Now my stomach feels wrong. Now or maybe right, depending on how familiar you are with it. My stomach starts to get irritated. Maybe I have gas now. Maybe I have acid reflux. Maybe I this coincided with me eating some sort of protein bar that doesn't really seem to jive well with my body. Okay, once I cross this imaginary threshold, then I might have a symptom. And that symptom in this case, in this example that I've given you is acid reflux. It's that burning feeling in your chest, not when you're exercising. Or maybe when you're exercising, because maybe the exercise puts you over your threshold. Now, this is an example and I've walked you through different types of stressors that can happen. But what you need to understand is that there are many different types of stressors. And these many different types of stressors can still accumulate, cross an imaginary threshold and produce symptoms. Now, when you're dealing with your stressors, what's maybe the best case scenario? What are the stressors that you can effectively eliminate and still grow stronger? Well, depends on who you are. Best case scenario, maybe you just walk around with a little extra tone in one muscle and less tone in another muscle. And when you reverse that, you detonify the tonified muscle, you make the tight things relax.  That's, to me, that's the easiest thing because it's easy to fix.  That's a best case scenario. What are some of the worst case scenarios, though? Well, worst case scenarios, you never find out what it is. And so you can never address it. You never find out what that root cause of all of your pain and suffering is. And that that can be hard. But as we've kind of talked about already, there are multiple things. So maybe it's not even just one thing. So consider that consider that maybe another worst case scenario is I have multiple things that are really holding me back. Maybe my body, let's say this, maybe the other worst case scenario is I have something that I don't know that I'm willing to change.  That's hard. And from my perspective, trying to help you is very difficult. It's almost just we're going to do other things if we can and you're going to have to be okay with how you feel. What about some other stuff? So for me, I want to I want to draw on my experience right now. I have a an interesting facial structure where the upper parts of my bones have underdeveloped and it has left minimal room for my respiratory airway and my food airway. So I'll notice that I have trouble swallowing things. I'll get headaches. I have this little acrylic piece orthotic in my teeth to help stabilize my cranium a little bit help keep my neck a little more loosey-goosey. It alone does not fix me. What I need to fix all these things is I need to restore motion of the airway and motion can be in multiple dimensions. So maybe I need more width of my airway. In that case, perhaps I can get a somewhat minor but still surgery surgery where I expand my maxilla, my palate, my upper palate, my hard palate as we might say. Then maybe if the limiter for me is the width of this airway, maybe that's enough to help reduce my symptoms.  Maybe though it's not enough and then you need to take the next step. Maybe I don't just need width here. Maybe I need to bring this forward to get more front to back room. And so that surgery is then a little bit more involved and now we have a little bit more risk. How much of your face are you willing to have cut open Lance? The answer is not that much. So that's more of a more of a worst case scenario. Maybe you have something that is structurally ingrained and will be very difficult to manage. Maybe even so I started this asymmetrical pattern really early because I have allergies that have biased my motor positions all of my life. And so now as my bones were developing I have bony changes not just up here in my airway area but also you know my left tibia is externally rotated and my hip joint is a little retroverted.  So I want to illustrate here that your autonomic issues may be complicated. I don't mean to discourage you. I just want you to understand there isn't always a simple solution. Sometimes your cases can be very difficult and what I would generally recommend is accept where you are right now. Make a conscious decision of what you're hoping to get out of treatment of whatever sort and then try the least the most minimally invasive treatment that you can generally that is exercising then that is sleeping more then that is changing your diet. Now I have all this stuff going on but I'm not ready for surgery so I start to change how I exercise I start to change what I how I sleep what I eat all of these other things and what I notice is that when I sleep poorly when I don't sleep enough I have the worst pain that I have my hips hurt the most that they ever do my neck is tighter than it ever is and I'm more prone to getting headaches behind my eye and my right temple here.  So those are thoughts on your autonomic issues if I can help in any way please let me know but look out for all sorts of symptoms do you sweat early do you sweat a lot do you have to pee often do you have it something interfering downstairs with your libido do you have sensitivity to light do you have sensitivity to sounds do you have food intolerances all of these things can play into things and then you just have to evaluate each symptom on its own to help understand what's going on to help understand what parts of these are early developmental that you're probably not going to affect what parts of these are genetic which are also probably not going to affect and then rule those out and then look at where can I make the biggest impact


All right, I'm Dan Higgins. I've been living in Wineski for, since 1969, and I've been periodically documenting with photography the changing social life. And I have a new show of photographs that I would like to invite everyone to at the O'Brien Center. The show includes workers at the Four Quarters Brewery, Dan Linton, basketball players, musicians who've written a song about Wineski, then people who started the ANA market, Butanese Gardeners, Operation Bloom, Cocktail Walk. It's got the Friday morning coffee hour, the family room, the farmer's market, the volunteers who operate the food shelf, Girl Scouts, it's got international dinner, it's got women who have many years have worked at City Hall, a historic preservationist, an artist, Nepali dancers, new Americans at their lunch and learn, Pam at Chick's Market, Sally Tipson, volunteers for the school bus program, Scout Cafe, Sisters of Our Lady of Africa, Tinker Tuesdays, Trail Crew, VFW on St. Patrick's Day, Wineski Auto, the Wineski Press, the Woo Jam. So if you're in Wineski for waking windows and you're wandering around, come on down to the O'Brien Center on May 4th, three to five o'clock for a reception and a little talk about the show.


Hello everybody, HoodedCoverCommander788 here, and this is a special video. I recently picked up this sealed-in-the-box GI Joe 1993 Mega Marine's Monster Blaster. And I don't normally get sealed items like this, but I got a really good deal on it. I was inspired by GI Joe Berg, who recently got one of these, they put that up in a video and I thought it looked pretty cool, so I had to get one for myself. So I got it in the box, and what I'm going to do with this is, I'm going to open this and assemble it. Now I understand, to some of you, that is sacrilege. Opening a sealed vintage item is unconscionable, and please believe me, I don't want to offend you, so trigger warning if that will be disturbing to you. But those considerations are outweighed by the fact that I just really want to. I haven't opened a sealed vintage GI Joe vehicle since 1988, and I've never opened a vehicle from this late in the line, 1993. So I'm going to do it. I'm really curious what's in here. I want to see what kind of paperwork came with it, what the instruction sheet looked like, how it was packaged, and so I'm really excited about digging in here and seeing what's in the box. So here we go. This is the unboxing and assembly of the 1993 Monster Blaster. So let's open this up, and I apologize if you get some background noise. I'm trying to keep the editing in this video to a minimum, so you may get some noises from inside my house. I can't help that, but I'll try to skip those if I can. So here I am. I am cutting the tape on this end, and I am opening this vehicle for the first time ever. Now this will not be a review. I'm not reviewing it. In fact, I will not review this vehicle until GI Joeberg has had a chance to review it. They got theirs first, and as far as I'm concerned, they have dibs on it. Here's what this looks like from the open end. Looks like we have a cardboard tray. Let's pull that out. Is it a tray, or is it just a flap? Yup, it's a tray. So cardboard tray pulls out. All right, that's so cool. Empty inside the box now, and there's the tray with the vehicle parts. Looks like that's the cannon there. Main body of the vehicle looks like it's already assembled, or partially assembled. It looks like it's not quite all the way. There's the shell. We have a sealed ziplock bag with the wheels, the sticker sheets, and the instruction sheets. So I'll open that in a moment. We have another sealed bag, not a ziplock bag this time, with a tree with some plastic parts, but it looks like some of those have broken off. I think the first thing we need to do is open this because it has the instruction sheets in it. Now I'm a big fan of G.I. Joburg, so if you don't listen to that podcast, you should, and they have a great YouTube channel as well. I think they're great. I try to never miss an episode. The instruction sheet and blueprints. sticker sheet, and there we have the instruction sheet and the blueprints. Pretty standard. One thing that I've noticed that isn't in here, there's no literature, there's no catalogue, nothing to advertise other items that are available, which is a little bit surprising. None of that in this box. That's a little disappointing. Let's start the assembly, and we'll start with step one, the body assembly, which looks like it's almost already assembled. I think we just have to snap it in place. So let's see. Let's do that carefully. There we go. That is snapped in place. Step two is I got to open this. These are all loose. These are loose, and I'm actually, I'm a little curious about something because something doesn't seem quite right. This, I don't recall Ziploc bags ever being used for vehicles, parts and instructions.  This was allegedly meant sealed in the box, but now I'm wondering if this was repackaged at some point. Although if this wasn't really sealed, meant sealed in the box, I feel a little less bad about opening it and assembling it. It appears to all be present and accounted for, but if it had been opened before, then it was not as advertised when I purchased it. So interesting. I might learn a little less in there. Okay, step two. We're supposed to put this canopy on here, snap that on like so. Carefully. Looks like, almost got it. There we go. Okay, next step. We have a gun bracket and a gun. According to the instructions, this is a yellow gun bracket and a yellow gun. These are both green, so they must have changed the color at some point, but did not change the directions. Looks like it goes, yeah, looks like it goes that way, so like so, not quite. There we go. And gun assembly. Carefully snap that on. This looks fragile. This looks like it could break very easily. There we go. I managed to get it on without breaking it, so that swings at two points. That's kind of cool. Not bad. I did want to talk to you guys about just general stuff and I wanted you all to know. I really do enjoy doing this show. I love it. It's fantastic. You've all been so great to me and I can't tell you how much I appreciate it. Every once in a while, it's just the nature of doing a YouTube show. You get some negative feedback. If you are a content creator like me, it's hard to not let that get to you, but I'm not going to let it get to me, because by and large, I mean, nearly all of the feedback that I've gotten has been overwhelmingly positive. You've got to focus on the positive. One wise person once said that if you're going to do a show like this, you've got to do it for the people who enjoy it. Don't do it for the people who come along and troll and hate it. Don't do it for them. So if you are enjoying the show, I can promise you that I'm not going to change the show or quit doing the show just because somebody comes along and leaves a nasty comment. It's just not how we're going to do it. I will do it for you and I will always keep trying to improve the show, so hopefully you will enjoy it more. It took me just a minute to figure out how to assemble these rear guns, but I think we've got it. I think I understand now. The instructions are not clear, but just looking at it and how it's designed, I was kind of able to figure it out. So one thing that I guess I can complain about is I don't think the instructions are written all that well, and these guns are awfully difficult to get in. It was really not easy to get these rear guns on. I did it as instructed, but that didn't really work. So I had to kind of just figure it out based on the way it's designed. These rear turrets are also very tight. They just barely turn. So let's move on to step five, assembling the main gun, cannon assembly. Well the instructions say to assemble the trigger and trigger bolt, but that seems to already be done, which again suggests that this has been opened before. So yeah, the trigger and bolt is already assembled on this main cannon piece. That kind of takes care of steps five and six. All right, under here there is a slot, and I'm supposed to put this here on it, looks like that way, there we go, and that fits on here somehow. Let's see it like that. I see how it goes. All right, the support goes in here, and that clips on there. There we go, cool, not a bad little deal. All right, so you can prop the gun up like that, and then lift it and lower it. Very nice, I like that. That's cool. All right, so we've got that top canopy and cannon portion assembled. Now firing cannon, oh let's find out how we fire the cannon. Pull trigger bolt back, like so, looks like it's breech loaded, that's cool. Insert missile into cannon chamber, there, with Finn pointing up as shown. Finn is pointing up, push trigger bolt forward and over to lock and load missile. Okay, lock and loaded. Let's trigger to fire, ah yeah, works, cool. I like that, this is a really cool way of loading a spring loaded weapon. I like that a lot, I do. So we've got some missiles here, just put the missiles on, these tabs here, and then of course we've got to put the wheels on. The wheels, it looks like they just press on a mushroom clip, let's see, make sure I'm doing it right. Now four wheels, just snap them on, should be, there we go, there we go, one, two, right, that is fully assembled, it is now time to put on the stickers. This is the part I've been most looking forward to putting the stickers on, and so here are the instructions for that here, and so I'm just going to follow that. Looks like we have paper stickers, not our classic vinyl stickers, but I suppose that's okay. Now off the bat, something doesn't make sense, it looks like they want you to put this stay clear sticker right across this ribbed section on the cannon, and that doesn't make a lot of sense to me, because it doesn't look like it would stay on there very well. And there's no blank space for it, you would have to put it right across that ribbing. Alright, this is what the instructions say to do, so that's what I'm going to do. Let's carefully peel this sticker off the sheet, try to get it as straight as possible, make so, there we go, there's one on the other side as well, I'll just do that one now. Sometimes people tell me they don't know how I can put a show out like this every week, and I do admit it can be difficult sometimes, it's tough to keep up that workload, but I love doing it, and what keeps me going is the people, there's the fantastic people that I've met through this project and have been so kind to me, and so sometimes I get burned out a little bit, sometimes I get tired, but it really is pretty easy to stay motivated. You have so much positivity, so much positive feedback, that really keeps you going, that will make up for a lot of long days and late nights. There are a couple things maybe I should make clear. When I refer to you dear viewers, I don't call you fans, I don't consider you to be my fans, I do call you viewers because you are viewing this, but I don't want to use any language that elevates me above you. I don't consider us to be unequal in any way, you who are watching this and me making it. I'm a collector like a lot of you, I'm a G.I. Joe fan like a lot of you. I just happen to have a camera and I point it at myself sometimes and talk about these things. I see all of you as almost like an extended family, my G.I. Joe family. I've met so many great people and it's been very rewarding and enjoyable, but not fans. I don't have fans, I just have people who view these videos and who go on this journey with me and hopefully enjoy talking about G.I. Joe. So let's put that one on. It's another one where there's not really a good clear space for it. We're going to put it on where it looks like it's supposed to go. I think there could have been better coordination between the vehicle design and the sticker design. I think that is a little bit lacking, but it's still going to look pretty good when it's done. This project has given me the opportunity to work with some very talented people, just amazing people. You talk about Timmer and FormBX257, Joe Berg and Joefan82, just to rattle off a few. Just incredible people who do great things and I'm privileged to participate in that. Thanks to all of them for letting me collaborate with them, letting me be on their projects and coming in on my projects. All those guys really are as cool as they seem to be. There we go, the all-important mega marine sticker. Got to make sure that goes on well. Looks like we have some headlights we got to put on here. I'm not doing these in any particular order, but they'll all get on and they'll all get on properly. Lined up as well as I can do it. Of course, when I was a kid doing this, I wasn't nearly this careful putting on the stickers. I wasn't completely half-hazard with it, but if the sticker was a little bit off, didn't care that much. To be totally truthful when I'm buying a loose vintage item, I still don't care that much about the stickers. I like to have them, I like to have them in nice shape. However, if I get something and the stickers are not perfect, it doesn't usually bother me very much. That's not high on my priority list.  Like, let me make sure I do it right. This is another sticker that is going to go right over some of the sculpting. And I do not love that. That's not well designed there. I definitely would have done that differently. Let's do the other side. Another thing I try not to do on this channel is I don't want to make this channel about bragging about the things that I have. And I see some toy channels that kind of do this and it rubs me the wrong way. This channel is not about showing you how much more stuff I have than you have. You know, I'm still in a lot of ways a novice collector. There are a lot of people out there that have a whole lot more than I do. It's not about owning more stuff than the next guy. For collectors who actually enjoy basically lording their collection over other people. Well, I can't judge you. Everybody's got to collect for their own reasons. But that's certainly not my reason. So I try not to present my stuff, my toys, in a way that is going to make it look like I'm just trying to make people jealous of the stuff that I have. That is absolutely not my intention. It's not like I'm rich and have tons of disposable income and have been collecting for years and years so that I've accumulated just warehouses of GI Joe stuff, not at all. I have very specific collecting goals, most of which are related to producing this show. But other than that, I don't need more. I do not need to have a warehouse full of vintage toys. I just want to have the right toys to show you guys. And really, I don't entirely look at this as just my show. I look at this as our show. Now, of course, you know, I'm the one producing it and so I have to make all of the artistic decisions. But we have been on this journey together for a while now and I kind of view us as going on the journey together. We all, I hope, learn something through this process. And so, you know, I kind of feel like we're, in a way, partners. And some of you are supporting me on Patreon and in that sense, you're quite literally partners. And I've tried to show my appreciation there. I really, I can't say enough how much I appreciate all of the support that I've gotten from all of you. There was a time, not all that long ago, when I thought I was just going to have to stop doing the show. Because I had to leave the first job I had after law school and take a much less paying, much lower paying job. And I didn't really have very much money to spend on GI Joe toys at the time. And frankly, I was running out of things to review. And so it came to a point where I was going to have to make a decision about whether or not I was even going to continue to do the show. I would be left with nothing new to review. I guess I could just keep reviewing the same stuff I've already reviewed, but nobody wants to watch that. But yeah, it was pretty tight for a while. That is when I opened the Patreon account the first time. And that was like kind of a, you know, sort of a Hail Mary to see if I could get some kind of assistance in keeping the show going. And now I have a good number of supporters on Patreon. And that blows my mind. That is like some very tangible assistance that people are directly giving to the show. And it's made a difference. I have purchased equipment for the show that I have needed. And soon I need to purchase more equipment for the show because my camera and my laptop are getting a little bit long in the tooth. Their functionality is becoming questionable. And so I'm just going to have to replace them in the not too distant future. But the support of you guys makes that possible. So you have kept this show alive. And that has made a world of difference to me personally. That has just personally is very touching to me. And I want to make sure everyone knows how much I appreciate that. That's why, like when people send donations to the show, that is very deeply and personally meaningful to me. Because this show is meaningful to me. This show means something to me personally. I put a lot of myself into this show. And the fact that people respond and they like it and they show support is... Well, I don't really know. I can't really put the words to it. But thank you. And thank you for watching this. We have a fully assembled Monster Blaster. The more I've gotten into this assembly, the more I think this wasn't factory sealed. I think this was opened and then resealed. Because I do believe there should have been a catalog in here. And I think the plastic in which it was repackaged is not original. Or at least had been opened before. And I think all of the pieces were broken off of the accessories trees by a previous owner. That's what I think. But despite that, all the pieces were there. And intact. We had a good sticker sheet. We had a good instruction sheet. And we have a fully assembled vehicle. And I have to say this is really interesting. The colors are a bit different from what I would choose. But still, not bad. GI Joburg has dibs on this one for now. But at least you get to see it on this channel for a few moments. There is the Monster Blaster from 1993. Thank you everyone for watching. I will see you in the next review video.