Hello and welcome to this edition of Create a Life You Love. This is by far one of my favorite editions. I have Laura Robinson of Sparkle Spa with me today. This is going to be a great show and I'll tell you why. Each and every one of us wants to look as young as we feel. We all feel young and vibrant. Our energy levels are high, but on the outside we might be noticing physically, especially in the face area, that we are not looking as young as we feel. Laura of Sparkle Spa is going to give us some tips and pointers today to help us achieve just that. Hi Laura, how are you today? Hi Tony, I'm great. Thanks so much for having me. Oh, it's my it's it's my pleasure. I'm so grateful that you could make it today. I know this is going to be so informative for so many people that are watching us right now. So the first question, what drew you to skincare? It's kind of a funny story because I started out as an art student. I actually majored in painting and drawing and along that journey I discovered really through my husband, boyfriend at the time, that I had this passion for skincare and makeup and all things beauty more than I wanted to be a starving artist when I finished school. So he kind of helped point me in that direction and I started to investigate further I had never even had a facial before and I went to school to become an aesthetician, just kind of knowing in my gut that this was like the right thing to do. I always say that we know deep down inside we know we feel the direction we really want to go in. We really do. It really was just like a magnetic pull into that world that I didn't even know anything about but once I got there I knew it was the right place. Yes, you can feel it. You just feel like I'm home. Yes, I'm home. This is it. Exactly.  Yes. Your canvas just happens to be different faces. Absolutely. Yeah. Yes. So where did you end up going to school? So I studied at Pivot Point International in Chicago, Illinois. Nice. And so I started out in Chicago. That's where I was living for 14 years and we've been in Milwaukee now for about 10. So nice. Yeah. And so you how long have you been an aesthetician? I've been an aesthetician for 15 years now since 2002.  How would you say that working on your craft and putting more in your portfolio for a lack of better. So what are some of the areas that you've continued in? So I've been training at the International Dermal Institute which is in downtown Chicago. Nice. They have a lot of post-grad classes that we can take and it's a passion of mine going to education. And I feel like in this industry if you don't continue your education you're you're not going anywhere in your career. So you have to enjoy that part of it. There's lots of trade shows that we attend to every year. Chicago has a lot of them. And you know they are realizing and learning more about skin and how for lack of a better way of saying it again how it works and how it ages. Right. What works for the aging process? What worked five years ago? It may not work today. It might have been good five years ago but today. Right. It's a completely different ballgame. There's so much more information so much more research is done. So yeah education is really constantly changing in our industry so you have to stay on top of it. Absolutely. Absolutely. So I'm reading off these questions and I sent out an email that you were going to be on my show. Yeah. And I told people do you on my email list if you have questions send them to me so these are the questions that people have asked. Now I know personally that you because I've come to you and I love you I love your work but they want to know what are the unique services that we offer some of the unique services. Well in a nutshell I would say we really do focus on the skin. You know we're a spa we do skin treatments of course we do waxing services we do makeup but one of the more unique services that we offer is the lash lift which is kind of strange it's actually a perm for the eyelashes and it lasts anywhere from six to eight weeks and we can also curl them or I'm sorry perm into them yes tint them for you as well so they're lifted curled and then also tinted and it's kind of cool because it works with the natural lash you're not using extensions or anything like that which can really damage the natural lashes over time so it's just another way to better the way you look without any real side effects absolutely you know you know my eyebrows and lashes are white they're almost translucent so right I wish the color of my hair was like that I just save a lot of money on hair processing but exactly but so when for someone like me who has such a light brows and lashes this is saving and it saves so much time in the morning exactly and that curling it's pretty cool it really is because we try to do that we try to lift and that makes the eyes more open it does there are so many benefits for women to do that we've seen a lot of women come in to get that service done before they go on a vacation they really love it for like a beach vacation when they're swimming a lot because they get out of the water and their lashes look great they just look done already they feel yeah they don't feel so naked faced and then they get hooked on it and start doing it more that is that is one of the the things that people should know this could be addictive yes all of your services all of our services could be addictive so if you if now you do a number of different facials and skin care techniques yes what's one of your most popular skin care techniques let's just say for someone like me I I'm not using Botox I love Botox but I'm not using it right now so what would be a skin care technique that I could come in and have you do that would really make a difference right away and or over time sure basically we offer our signature skin treatment and that kind of covers everything very comprehensive treatment and then we have some add-on services and that's what kind of sets us apart with some of the anti-aging things that people are looking for we work with more holistic type treatments that are going to be cumulative results over time you will see some immediate results but it's all about that cumulative effect LED light therapy is one of those it's phenomenal for the skin what it does red light being the you know best for anti-aging it's helping to stimulate that collagen and elastin in the skin and that's what starts to decline as we age so it really helps to oxygenize all those cells and just gets the skin stimulated and looking healthy and youthful again another great technology that we're working with is called microcurrent similar to LED it's also helping to stimulate that collagen and elastin in the skin but it has a lifting and toning effect on the skin as well so you actually do see immediate lifting to the skin we like to call it fitness for the face it's just like if you go to the gym and you're working your biceps are you going to see a big difference after one visit maybe not but if you continue to do it over time you're going to see that effect right so it's not a quick fix nothing that we provide is really a quick fix we don't believe in that you know it you have to work at this stuff and but that's the important thing to know that is if you do work at it you will get results care for your face and get absolutely that you will see those results and they'll be long lasting definitely results which is really important to now the other part that's so important is the home care you know have to say that because it really it's about 80 percent of what happens you know you're only coming in monthly maybe um so what you're doing at home is so important because you're doing that every day twice a day exactly you're not using the right products you're doing your skin a disservice so we're there to help coach you and educate you on on all of that too absolutely yeah so you said about once a month is that what you would recommend for the amount of visits that somebody should cut like once a month for that facial or that that general maintenance for the skin we usually say about four to six weeks is great for someone that wants to come somewhat regularly but maybe they don't have the time or they can't afford to come as often we ask them to come in seasonally because our skin especially where we live here in wisconsin changes pretty drastically with the climate so we go from the force yeah to that cold outside exactly that yes absolutely my hands are totally suffering from it i know now what types of events or spa nights do you hold and how often do you hold them yeah um we try to do something a couple of times a year um we do have our big black friday sale coming up i love that too it's been very popular ever since i opened the business so that's going on black friday from nine to four um that's mainly all about product specials so the deepest discounts you're going to get at our spa is that day let's let me clarify because it is black friday if that nine a.m to four p.m or nine p.m to four eight no we're not that crazy so it is nine a.m to four p.m black friday special yes so that's like our biggest sale of the year now really quick i and i want you to finish talking about that can people it can people go to your website on that day and partake let's say if they're not in that area or they have relatives in and can't get in that day unfortunately not okay so make it in you need to make it in you need to come in yeah so worth it it's worth it it's worth it you can have a mimosa and shop and have fun yeah it's great they can bring their family absolutely and say oh this would make a great christmas gift most definitely yeah absolutely yeah sounds a great gift item so you have your black friday yeah which is coming up very soon as a matter of fact i know next week already oh my goodness we just did another event recently we called it our fall refresh event and we featured a new product launch that we had with Dermalogica where we had little mini treatments happening in our retail area and then we had our rep come from our microcurrent vendor that we use and she was doing mini treatments and then we had one of our wonderful skin therapists sienna doing makeup that night so we had three stations and each client went to each station and they looked amazing they felt amazing by the end it was also a shopping event so we we tried to do that a couple times a year i love that yeah and i know that you carry jane iredale do which is the best yeah this is a product line a makeup product line for women yes who want a more holistic clean clean clean clean ingredients yeah and you know it's comparable the finish is comparable to any high end absolutely and even better i would say much better looking on the skin than any other high end makeup line let me just put it that way absolutely you do have your nights where you have your your your spa nights where you have jane iredale makeup we've done makeup events before absolutely we usually do something around the holidays with that i love but the nice thing is you anyone can come in any time and we do complimentary color matching my the entire staff has been trained on how to do that nice so even the guest services um employees know how to color match so you can come in and we can help you select the best foundation for your skin and we'll match it true to your skin tone and try it on for you that's always a complimentary service that we offer because you have to try it on to to feel it and see it and you know and know that it's going to feel comfortable right on you now one of the things i know and i i did not know this growing up i think most of us did not know this growing up but something i learned later in life and our cosmetic companies and and uh lotion companies and skincare companies hide this they sure do that what you put on your skin goes in your skin so all these what they when they talk about these parabens and other things they go in your skin and we're trying to do something by by wearing makeup and paying for these expensive creams and foundations we're thinking we're putting the best on our skin yeah but when in reality some of these things can do more damage absolutely the chemicals most definitely in them where um the iredale line it's it's a it's a phenomenal line i did a lot of research before i brought makeup into the business because i i always had a love for makeup and really wanted to do it but when i started digging around i was really frightened by the ingredient ducks um of most makeup companies um a lot of you know fdnc dyes artificial fragrance just some toxic chemicals right you know and here i am teaching people how to take care of their skin and then i'm going to sell them makeup with all of the stuff in it that i just told them not to use so i you know i was like what am i gonna do yeah where do i go from here right so i actually discovered jane iredale at the chicago face and body trade show and was just like i can't believe this even exists you know it's like the skincare makeup yeah and then every ingredient has a benefit to the skin it's not coming to genic it's not going to clog your pores um every powder formulation is inert which means that it will never harbor bacteria and when i say never i mean never you could have a blush for 20 years and be okay with it it's it's not going to cause a problem just so amazing right so it's but there are products that you can put on your skin that are also good for your good for your skin you can feel good wearing it yeah and there are not a lot of product lines that can say that very few very few yes so some people i'm going to switch gears a little bit i'm going to go back to the facials because sure people think facials are for a treat sometimes very wealthy people pampering or and there are a lot of medicinal reasons and or just relaxation stress really absolutely we actually really don't like the word pampering at all it is a byproduct of what you will receive when you come in you're going to be relaxed beyond words i mean we have people that prefer our skin treatments over a massage any day of the week because there is so much relaxation with it um but as far as the benefits go they're huge um detoxifies the skin stimulates the skin deep cleanses exfoliates rejuvenates hydrates the list goes on and on i mean there's there's so many benefits and if you're a person that has uh some aging processes going on or if you're a person that has acne even yes adult acne or age spots absolutely facials kin can help yes definitely absolutely you know and if it's something that is more serious that we're having a hard time treating we're going to refer you to the person that can um but still what we do is the basis of all skincare you know you still need to care for your skin whether you've got acne or not and we want to teach you the right way to go about that absolutely absolutely education is a real foundation of sparkle spa i love that about your spa now my next question you also offer eyebrow care yeah i know this work bag do you do the shaping i like to call it artistry artistry so what are all the things you can do because i i'm going to tell you something a good brow will change your whole look your whole face it will frames the face it can take five years off your eyes minimum minimum right most definitely if it's done right absolutely a lot of people do not know how to manage their brows on their own we wish they would just let us do it for them i do not our favorite clients are the ones that come to us every four weeks and do not ever touch the tweezers they just let us maintain their brows for them we do a consultation for everyone that comes in talking to them while they're holding up the mirror and we're looking at what we have to work with what the goals are you know i call the brow boot camp some people have to go through that for a period of time can take anywhere from four months to a year i mean depending on how thin they are or how much growth we want to see absolutely but it is an art and and you must be skilled not just because somebody says they do eyebrows right no not they're not mean they can and because my eyebrows are so light i've had some and sometimes people they don't follow the shape of your face right they want to do what's trendy no oh lord basically we're just letting the brow become what it needs to be you know and we're hoping to to bring that out and teaching you how to keep them that way and also how to fill them in at home if you need to that's part of the service that we do i mean you know we do a really lovely um ice globe massage after all of our waxing treatments to really calm the skin very soothing feels amazing um it helps take the redness and sensitivity down a lot too um and then we always cover the skin with a tinted moisturizer with some protection and fill them in so you leave feeling like a new person just from a brow wax absolutely yeah absolutely much more than just a wax absolutely now i have nieces that range from three years old to oh my gosh she just turned 18 this past weekend what are the ages um for the services what would you because i know you know a three-year-old is not going to come in and get some of this as nor would she wouldn't want it she wouldn't need it but you know i also have an 11-year-old kind of on the edge there right yeah when's a good time to start getting brows done start getting facials to use the right makeup because some people think she's young she doesn't have to worry about her skin yeah i don't understand that one but right around you know when kids are hitting puberty is a great time to bring them into us um we do a lot of middle school girls brows it's nothing more fun to do a girl's first brow wax really those virgin brows they're so big and beautiful and then we can bring out the shape and they love them and they listen to us we're like no tweezing you tell your mom to bring you back in you thank your mom for bringing you you know um so many beautiful brows walking around um girl of young girls absolutely coming at a young age and they're not going to over tweeze like we all did in the 90s um or do that laser stuff right oh my goodness yes right so you know we we have seen kids as young as 10 11 12 years old um usually they're not coming in for treatments as far as skincare goes until they're starting to see some problems in their skin um and that's going to vary you know with ages and um a lot of it is hereditary with acne so we see a lot of teenage boys and girls and um i'm always so thankful that their moms bring them to us before they go to a dermatologist yeah that makes it makes a huge difference it really does it really does it does it really does yeah so we do we do i mean we do teen skin treatments all the time and we have a whole line 14s that's yes so it's geared directly for them and it's all about the compliance with the teens so they tend to listen to us more than they're going to listen to their mom absolutely yeah absolutely yeah so i want to ask you um what are your unique skills that help your clients some of the things that you do that maybe other uh estheticians or spas wouldn't do some of the things that you really get into um well from my experience obviously i know what i do and i've gone around to other places before um i don't feel like they're doing a very thorough consultation at a lot of places they're not really understanding your you know your background um but also the education is what i think brings people back to us you know i would i would agree with that i would agree and i know some of your unique um services like the eyelash left right some of those things i just can't say enough about that right i really can't i really can't and we're also very much of a niche business you know we don't offer tons of services we really kind of focus on what we do being skin treatments the waxing the brow artistry the lashes the makeup and you know we love to teach people how to put their makeup on it's not just you come in and we put it on and you walk out and go now what now i have to go home and remember all of that so it all for me i really think it does all come back to the education and the relationships that we build with our guests and i know you're as particular about your skin care products as you are your makeup lines and i absolutely there's i you know i know you have some of the most amazing you've turned me on to a few products that i am completely addicted to so this is the only warning you're going to get for these products are addicting grand lash oh yes oh lord i used to the first time i came to you to get my brows tinted and curled or lifted the lash right yeah my lashes lifted you couldn't do it because they were too short but look at these they look amazing yeah well don't do a close-up because we don't want to look at these but i'm just saying right grand lash is amazing one of our biggest selling products and the blink eyebrow moose yep we have a lot of little specialty lines like that but the main line that we carry with skincare is dermalogica which is phenomenal but around you know over 30 years just an industry leader company founded on education so of course i love that about them right and then jane iredale of course and then we have you know we have like a fun suncare line from california called kula we've got the blink and just a bunch of other little things yeah we're also bringing in a new line currently it's a called victoria dn peptides and it's a peptide line that pairs beautifully with any skincare line so it's just going to take everything that we already do to another level i love that very exciting i absolutely love that yeah so what i'd like you to do now is please tell people where are you located sure we are in elm grove wisconsin we are in the park and shop in elm grove it's downtown elm grove we're at one three four two five watertown plank road and then your web address because people can go online and pick out some of these products they can look at all the services that we offer there we even do have online booking too yeah so it's a really convenient service that we offer the website is sparkle-spot.com and we do love it when people call though you know so people can still call of course to book their appointments and i will personally say it's if you're not in their direct area it is absolutely positively worth the drive that drive if it's just once a month you can make a day of it in the area and just go in check them out talk to lora talk to anybody on your staff you will find out that this is this spot is very different because as much as they're you're focused on beauty you're also focused on care wellness wellness for your absolutely largest organ in the body we got to take good care of it you know absolutely absolutely yeah so lora thank you so much for being on the show today i'm so grateful to have you had been able to come i said that it's my pleasure having you here for you being able to come in today i really just i'm so grateful that you were able to get this information to everybody thank you for having me it's been great it's really appreciate it absolutely and i want to thank you for joining us today laura robinson of sparkle spa and myself tony green if you'd like more information on me you can go visit tony g t o n i g dot info and you can find out all sorts of information on me but definitely visit sparkle spa and let them make your skin sparkle thanks and have an amazing day


Video games, right? Did you know Nintendo didn't start as a video games company? From 1889 to 1956, Nintendo was a playing card company. In fact, they still manufacture playing cards in Japan and even have a bridge tournament called the Nintendo Cup. Interesting, right? And now you know!


Hello everyone, this is Alice Gao. In this video, I'm going to discuss the clicker question in lecture 8 on slide 17 I'm showing you right here So we have a perceptron and the activation function is the step function The question is asking you what should the three weights be such that the perceptron represents an end function In the main lecture video, I told you the answer that I came up with Minus 1.5 1 1 and there are also other possible answers. Now, let me show you how I derived these answers for this question, we are Essentially trying to learn a perceptron using a tiny data set, right? We have a data set of four point data points This is our truth table so the key idea is to realize what the data set looks like and Also, what the perceptron is trying to do to the perceptron is essentially a linear classifier linear function Which we're trying to come up with to separate the positive and negative examples Let me first produce a graph which can help you visualize what the data set is trying to do We have only one positive example, which is at the point 1 1 So let me use this shaded circle to represent that then all other three examples are negative So 0 1 0 0 and 1 0. These are all negative examples So I have three negative examples one positive examples Then the perceptron is essentially a line that we're trying to come up with to separate the positive from the negative examples As you can see, there is a fairly huge gap between These positive and negative examples, right? So we could come up with many different lines in this gap to separate the two Now to make our derivation easier and the numbers nicer I'm going to use one of the nicer lines. So I'll choose one Let me just add a few more things to make it easier to draw So I'm going to choose one way which Exactly goes through the middle of the gap. So it sort of goes through here Roughly here roughly here Like that Right now, we just need to derive an expression for this line So this line goes through the middle of here, right so the And the middle of here as well So if you do some calculation You will realize that this point is 1.5 and this point here is also 1.5 And this is exactly a 45 degree line. So the slope of the line is minus 1 so Equation which can represent this line would be if you think about this is why if you're not used to thinking about x1 x2 if you think about y and x this will be y is equal to minus x plus 1.5 a slope is minus 1 and y intercept is 1.5 But we can convert this to x1 x2 that becomes x2 is equal to minus x1 plus 1.5 and Let's move everything to the left-hand side This will make it easier to Convert to our perceptron later on So that would be x1 plus x2 minus 1.5 is equal to 0 Okay, so so far this equation is representing the line But remember that the perceptron is trying to do a classification So it's trying to choose one side of the line, right? So we need to make sure eventually we came up with the ways to choose the correct side of the line So how do I do this? Well, first of all, we want to choose the side with the positive example So we want to choose this top side right here So how do I usually figure out figure this out? I usually pick a positive example and plug it in to see if we have the correct number coming out from the left-hand side So let's try this the positive example is one with one one Right, so let's plug in x1 is equal to one x2 is also equal to one one plus one Minus 1.5. This gives us two minus 1.5 which is 0.5 If we apply the step function, this is a positive number So our output value would be one and that's the correct output value, right? Which means the correct inequality that we want is x1 plus x2 minus 1.5 is greater than zero Right, there could be the other case if you do the Calculation on this line right here and if you get a negative value That means we have to flip all the signs of all the coefficients Okay, hopefully we encounter an example later on in your when you're doing your own practice and you can practice that but for this example this Inequality is the correct one and it correctly selects the side with the positive examples So finally We can use this to figure out. What are the weights? All right, so the weights we have W11 that's the weight for x1 is one the coefficient is one W21 that's the weight for x2 The weight is one and then W01 The weight is the constant coefficient, which is minus minus 1.5. All right, so this is the entire process I used to derive the weights and By drawing the picture, hopefully you realize that there are many possible solutions available I just chose one of the nicer ones to make the numbers a little bit nicer To summarize, how do we derive weights for perceptron to represent the logical function? we can start by visualizing the data set and Our goal is to come up with a linear function that separates the positive and negative examples Once we come up with a line Then the expression for this line is going to tell us the weights of the perceptron That's everything for this video. I will see you in the next one. Bye for now


Find the focal length of a lens of power negative 2 Diopter so now we know that power is 1 upon the focal length So negative 2 diopter which is meter inverse is 1 upon the focal length in meter So the focal length in meters is negative 1 by 2 that is 50 centimeter here the negative sync device that this is the K-V type of lens and hence our answer is given that the focal length is 50 centimeter What type of lens it is? It is a concave lens. Thank you


Well, she's been part of this project from the beginning, hasn't she? You write in the introduction that these songs are part of a long conversation you've had with her during the whole first six years of her life. Well, throughout the research period for the making of this project, I would read poetry or recite poetry or nursery rhymes and lullabies, whatever, to my daughter. And then as the songs were developing, as I was adapting them to music, she was always in the room. So they became part of her childhood and part of her upbringing, her introduction to language and to poetry and to culture, history.


Hello? Mr. President? How are you, Hubert? Well, I'm fine, and how are you? Oh, I'm just kind of broken up. I'm aching all over.  I just called you because I hadn't bothered you, and I didn't want to, and I didn't think it, I didn't think it was a good thing to do, but I don't want to tell you first, but I told anybody else that you had no orders, and you had no instructions, and you had no mistakes, and I just don't know how anybody could do anything better than that. Well, Mr. President, you're wonderful to be. We worked hard, and I enjoyed it very much.  Well, we love you, Mr. President, Lady Bird, and we've been thinking about you. I haven't wanted to bother you either. I knew you were on the move every day, but we've been keeping in touch with your boys. Well, that's the way it is. We've handled it. You've handled it just perfect, and I couldn't improve on it, and I just give you a double plus, and you'll probably never get that good a grade again. We're going to have a big victory tonight, Mr. President. I don't pass many of them out, but I feel that way about it. I hope so. I don't know. I'm sitting near the Lomathon Bay, and they're rubbing me. I got a bad hip. I've been standing on my right leg. Your hip ever hurt you? Yes, sir.  Well, you just did the perfect. You wound it up happier. I told the press this morning you were happier. When you started ending, you were, and you started, and you were more effective. All that television, those television I saw, I didn't see them on TV, but I saw them on a practice thing ahead of time, and it was just perfect. Oh, you were so restrained and so effective. You looked like God just as fresh as a daisy. You must have done it. I felt good. I think we got some good licks in after West Coast, Mr. President. Well, I know. You seem like you had wonderful crowds. Yes, sir. We surely did. And I stopped by a Salt Lake City on the way home just to get in another punch or two on some statewide TV, and I was very careful and very restrained. I didn't go on any attack. I just talked about the issue of public morality in terms of public service. Oh, Hubert, I wish you'd see what these sons of bitches have done. They bought four full-page ads in most papers. Some of them just got 12 pages, some 16. Four full pages in this state, and it's all integrity and morality and Baker and Jenkins and Billy Saul Estes. I know. They had five full pages in the Los Angeles Times on Sunday. Five full pages. And they got out an instruction from the Negro Protective League that says that any Negro goes votes that the Protective League just wants to inform him as their friend. If he's ever had a traffic ticket, if he's ever been under suspicion, if he's ever been speeding, if he's ever had an over-parking ticket, if he ever hadn't paid his taxes on time, if he's ever been discharged from employment, that he'll have to report right away to the sheriff, and that these things will have to be settled before he can clear his record to vote. They put those out in all southern cities, just to mean this dirty, slow-down stuff that I heard. I ought to go to jail for it. It's just inhuman. Well, they've been doing it. I tell you, they were doing it out in the Mexican areas. The same thing in California. And I made several talks and teased appearances on the Los Angeles station, and I got some good cooperation from those commentators, letting them know that these people know that no one had a right to interfere with their right to vote, and that the Justice Department was standing by to make sure that the citizens' rights were being upheld. And we called Nick Canson back, and as you know, he issued some statement to the effect that the Justice Department was standing by to make sure that there was no interference with the citizens' right to vote. We got to set us up. The first thing you had to start looking about is how you're going to have a relationship with the Senate. Now, there's not going to be any jealousy between me and you. You know that. But I want you to try to figure out the problems we got, how we can get a committee chairman when they haven't got the three or four in there that's worth a good goddamn. We want to investigate these election things, and we want to have committees where we can refer things to that we knew something about. So we just ought to be thinking about who has the ability and who has the guts. That's right. If Howard Cannon's elected, he's won. Yes, sir. He's a good one. We've got a double. I tell you, one boy that's got guts, if you'll get in there and dig, is Johnny Pastore. Well, he won't do it. He wants this. He's got that Catholic wife, and he's got to get home every Thursday. Yeah, that's right. That's where you're so right about, Pat. Well, I'll look them over very carefully there. We're a little short on those kind of people. We've got to find them. And I'll see you now. We're going to have all of that 300 press down here. I'm coming down tomorrow. And you get in time for that barbecue. It's going to be out here at noon, and the helicopter. About 12.30.  And then you just stay at home, and you feel like it.  And thank your, uh, thank your sweet wife and all your children. Well, I will, Mr. President. And listen, you have good care. We're going to give them the damnedest liquor they ever had in their life. I don't know about that, but I hope, I hope that's right. How many states we're going to carry? I think you're going to carry about 40, 46. Okay. That we will. All right. Okay. And, uh, by the way, I just want to let you know that after the, uh, the latter part of the week, I hope to take off a few days. You ought to, you ought to. Now, what about that? You got to, you just got to. We're in trouble in Vietnam. Serious trouble. I told them to keep you informed. Yes, sir. Uh, we're going to have to hit back there. Yeah. Uh, the, um, uh, are you going to carry Minnesota? Oh, boy. I don't want to stop to do that optimistic, but we are carrying Minnesota by 250,000 boats or more. Out of how many? Out of a million three. That'll be the biggest one ever. Yep. We're going to get the biggest boat ever out of Minnesota. Well, now you encourage that tonight in all these states as a mandate because they're going to say, well, that's the meaning thing and so on and so forth. We're going to start that right away, Mr. President. They're going to do two things. They're going to say, boys, that even some of the distortion are going to say some of these papers say, well, this wasn't a mandate. This is just an anti-gold water. That's right. Now, what's the next thing they're going to say is, well, watch out for Humphrey. He's not going to be loyal. I'll bet one of those. Well, you just tell them that, uh, you just tell them that you've never seen such campaigning that people like Johnson. Like, God, you got the word. It's so contagious.   I know that. I know that. No, no, no. No, no. No papers ever going to come between us. Nobody else. Sure. You just tell me what you want me to do. Oh, goodbye. God bless you. Tell me or I'll call her. Tell me or I'll call her. Okay, I will. We went in, uh, me and my family went in 49 states and Mero took the 50th one. All right. All right. Goodbye. I'll tell her. God bless you. Bye.


Tomorrow, tomorrow, tomorrow, tomorrow, Tuesday, 4 p.m. Eastern Standard Time is the next episode of the Lions Den. Think Shark Tank meets the voice. You will have an opportunity to come on and pitch your existing business idea that needs either partnership, investing, or you're just trying to get someone to buy you outright, or if you have an idea or startup that you need the same thing, investment idea, looking for some capital, or you're looking for somebody to buy you right out. Do me a favor. Get me up now to my email address right here to get ahead on the auditions. Now what we're doing is we're having people get in line ahead of time in the green room. All we need is just a little bit of information about yourself, your name, your business, just so we can verify who we're going to be talking to, who's going to be pitching us. So we'll keep down all of the unnecessary back and forth and get us in and out. You'll have 10 minutes. That's right. 10 minutes to pitch us your best idea and see what happens. Remember, down in the comments section. Use my email address. Hit us up if you want to get on tomorrow's show. First six come in, first six gets chose. 10 minutes each. The lion's den with Ramil Amir. Tomorrow, tomorrow, tomorrow. See you later.


So, we're going to talk about typescript.net very, very, very, very early stage for game modding. But, you know, you can do whatever you want with it. My name is Andrea Gaitham. I am the editor tools tech lead at GitHub and formally I was at Unity and Novel and Xamarin doing monostaff. So, it's been five years since I've been here. So, this is fun for them. Okay, so let's get started. There are a lot of contents and I'm hoping to get through all of it, so it's fun for you. Languages and game development. So, games are like all other software built on tech stacks on layers. You usually have foremost software, one language, maybe two, maybe three, you might have some shell scripts for your build system. You use one language to do your app. You might have some data languages formatting like, you know, whatever, Jason, other languages that are accessory, but you do it all on one language. Games are slightly different because of the way of the disciplines that building games brings in. The game engine is usually on languages that have facilities for aligning data and memory so that you can optimize putting pixels on the screen, basically. Not that these languages are better or worse than anything else. It's just like, you can control how the memory is arranged, so the memory is layouted. You can send things to your graphics card at the fastest rate possible. So, you pick those languages, they're optimized for this. But, you're making a game and you're making it with there's game engine programmers, but then there's the gameplay developers, and then there's the game designers, level designers, scene designers, they are technical artists, everybody else building content on the game. They might have worked on the engine, they might not, they might not even own the engine. The engine is doing some things, and these people have to build content on top of it. Which means the language that gets used in these, in the scenarios is not necessarily the language of the game engine. You want to pick a language that is appropriate for the task that they're doing, right? It's not about data alignment anymore in memory. It's not about the most performance and most tasks. It's the one that's most expressive for describing what's happening in your game. And a lot of these people in these teams are not programmers at all. They don't come from a programming context. So, they don't even know how to code. But they can code. They need tools that they can use to express what they're doing with the game without having a full CS degree. So in the game industry, this is very common. You have multiple languages building on top of each other to provide the best tool for each job, right? And while C and C++ is very often on the game engine, C sharp, Luobasic, Scheme, F sharp, all of these languages that are expressive or functional or data oriented or have some other type of thing going for them is the language that everybody else is going to use to build the game with, right? So, here's the game. So, I got interested in this topic back when I saw some slides from a talk about, from Naughty Dog, about how they build Uncharted. If anyone has played Uncharted here, hopefully some, it's a game.  So, Naughty Dog is a Lisp house. They're very, very heavy Lisp pens. And they really didn't want to give their designers C to script their game. It's not efficient. So, because Lisp pens, they built a variant of Lisp, a scheme, a simple scheme language to give their designers so that the designers could just focus on making the game, reactive to events, talking to the engine, but not touching the engine. There's all of these advantages to having a completely separate scripting language that's running in a VM in your game engine. Like the engineering team doesn't have to directly be involved. And when we talk about engineering, we're talking about people maintaining the engine. Doesn't have to be directly involved with the content creation for the game. Code is data. It's easy to just change what's going on without touching the game engine itself, that the game engine becomes more generic. It empowers game creators and side effect. It empowers modding communities. Because when you have a language that's completely separate, that you used to build your game on, you can give that language to someone else to build things on your game. Because that's what you're doing, you're modding the engine. So, it's just the side effect that it just becomes very easy to provide tools for modding communities to build their own content for the game. This is the example that they have for their language that they gave. And I was very curious about this. So I emailed the person that gave this talk, asking how do designers have never coded before handle this? And it was like, they handle it just fine. They have no problems with this. They don't have a background in programming. So for them, this is just, it's easy. There's no side effects. They just react to things, trigger things, stop and play. Things happen, and they script, literally script the sequence of events that needs to happen whenever something else happens. They put things on screen, they attach scripts to things on screen. And for them, this is just a lot of parenthesis, but it's fine. They don't consider this programming. It's just scripting. So that was interesting. And sometime later, Neverwinter Nights. Not that Neverwinter Nights came later. I just looked at it later after I entered it. Neverwinter Nights came out in 2000 something. And Neverwinter Nights is an RPG based on D&D 30 editions. You usually multiplayer RPG, but it has one key difference. This is Neverwinter Nights. It is fully moddable as a lot of games are, but back then, not a lot of them were. And it has a full editor shipped with the game. So now, this is available for the people that are running the game, not the people that are building the game. The people that build the game also use this to build the game. But this is shipped with the game. The thing with Neverwinter Nights is when you're running the game, you can fire up the editor, create your whole campaign with all of the things that Neverwinter Nights ships, like all of the assets. They give you a license for all the assets, as long as you're not making money with the assets. You have all of the assets, like all of the characters and all of the tiles for terrain, everything. You have all of these things. So you can create a completely empty space. And you can build your own campaign to put all the scenarios together in the editor. And then you can script everything. So you can basically go into any of these objects that are in this area. And you can attach scripts to them. And the script is a C-like language, basically, that they have. Which allows you to make these things interactable. And then anything can interact with anything else, and anything can do anything. Which means you can just basically, you have a game and you just make a new game out of it at runtime. Let's just say this, right? You're not compiling the game. You're just building this content out of a shipped game. It also has all of these things that you can edit. Because if they have the tools, they had the scripting language and they had all of these tools that they built to make their game, it's free for them to just give this to the users. There's no overhead for them. There's no support that they need. It either works or doesn't work. The interesting thing about Neverwinter Nights, and I'll get to TypeScript and AL at some point, this is background for why I'm doing this, is that not only can you do all of this scripting at runtime, but the admin that's running the game. While the game is running, because this is a multiplayer game. So you can invite your friends to go into your server and play with you. Unlike the same way that you play multiplayer, but this time you're hosting the server, you control what comes in and comes out, it's your game. The admin that's running the game can go into the game while it's running and take over an NPC while another play is interacting with that NPC. Just override the entire dialogue tree of that NPC and start interacting with the player directly. And it's the ghost in the machine, right? And they can make quests, like on the fly. Like, yeah, we're gonna make a quest for you right now, cuz I'm bored and I'm gonna run a quest for you, but I'm an NPC. And this got me really interested, because there's not a lot of games that do this. In fact, there's none. Neverwinter Nights is 20 years old. There's still people running Neverwinter Nights servers. Because when you can do that, it's fun. It's a community, right? And we all know the popularity of Minecraft and other type of environments. It's about how you can modify the environment and interact with other people. This goes to a slightly next level, but it's an obvious next level. If you can control all the content and you're doing this at runtime, why not do it at runtime and control, literally override the system whenever you want. But Neverwinter Nights looks like, you know, old. So a few months ago, because of that, it was like, they would be so much fun. We could do something like this with better graphics and nicer engine, right? And just side effect, but it turns out that most D&D data, like all the monster descriptions and all the levels and all of these things, is about open source. Wizards of the Coast open sourced D&D 3.5 and D&D 5.0. Not the names of the characters, like the name characters, the bosses that you fight, but every single other data set from magic spells to names of creatures, like everything that you can find in the D&D book, all of it is under a license called OGL. Open given license. So it's all open source. Anyone can take that content and make things, which is how, forgetting the name, what the company that builds out of that content is. There's a company that builds entire contents out of this because it's open. So it's like, we have all this data and we can make this. And then we have Unity, which is a game engine that runs on C-sharp and Mono. So, we already have a VM that can compile things at runtime and reload because that's what it does. We have a game engine that runs on top of this VM. So we can put all of this together and recreate whatever winter nights did with a modern engine, modern language, modern everything. So, we come into scripting system. At this point, I'm still thinking I'm gonna use C-sharp for this because C-sharp is there. I know C-sharp, I worked on Mono, I know that part is easy. Doing a reloadable, recompilable system runtime is easy, loading all the data is hard. So, but then I had this problem, it's just Y type script. So, I'm gonna show you the little silly prototype of the system running. So you can understand my problem. So this is a very silly prototype of a thing that moves around. That cube is a trigger right there and this script is attached to it. This is the default content, it's not compiled yet. But if I compile it, I've compiled the script, I've reloaded all the data. Now, if my thing goes there, there's a bug. I don't know why it says activate instead of yay. But in any case, it now activates because the script is now attached. I recompiled it and did all of this. This is cool, and I mean it's nice, it's a one liner, I can just do it. Anyone can go in and write code, but code is not one liners. When you're writing games, it's never one liner. It's get this object and do some math on it and do something or other and update this state or react. It's multiple one liners, it gets complicated. And the problem with C sharp is that the code that gets generated is actually this. And that's why it doesn't stay longer, it didn't actually generate the right code. It's this, for that line to run, which should be in here, right? For that line to run, I have to have all of this scaffolding. Because C sharp requires it, this is what C sharp looks like, right? And now I have a new problem. If I just provide the users with an interface to type a one liner, they can't do more than one liner scripts. If I give them all of this because they will actually need to define some helper methods or to pull in other things. And all of these facilities that the language actually has, they can break everything, they're very easy to set themselves in the foot. Like method signatures become complicated, like what do I override? It's no longer the language that I give a designer so that they can quickly react to events, right? But if I go back and just give them, hide all this scaffolding, I'll figure it out somehow. If you take all of the code that you're writing in the little editor, put it somewhere else in an IDE, it's not valid C sharp code. Valid C sharp code needs this. So I don't get co-completion anywhere else. For co-completion, I need all of it. I don't need syntax highlighting all of these facilities. That is the reason why we use C sharp, because we have all of these things. So C sharp is not the best language for this. And I looked at Lua and I looked at other languages, but I didn't want to. We have that net, like unity runs mono and dot net. Like I have this, and then I looked at TypeScript. And it turns out it's perfect because TypeScript is a fully typed. It can look just like C sharp in a fully typed mode. There's all type information, but it's flexible enough. That doesn't require all of this scaffolding. So when you copy paste entire code into a VS code, you'll get the type completion.  Because it's JavaScript in the bottom. It types in TypeScript are a super set of what the thing actually is. And so it's flexible enough to be used for people, anyone. There's a lot of resources online for people to use it. It is typed enough for me to take it and throw it in IEL. Because I have all the types that I need to do this. So then it comes to the things that then people, these are the things that the designers and people that are making code need to do. Like integrated VM check. Like all of these things both C sharp and TypeScript can do. But defining types is the thing. In C sharp when you define types, you have to know what you're defining. You define classes and structs and there's a logic. And if you don't define them up front, nothing will work or compile until you do. There's no flexibility in the type system at all. It's type first and then script. And TypeScript, it's script first and then type. You can go like, trust me, it'll work at some point. It's fine. Which is, I mean, if the type is not defined at some point, it's not fine. But the IDEs will work. The IDEs will be very flexible, people not knowing exactly what they're doing until the point where you run it. But at least when you're prototyping and building, the ID is not getting in your way. It's helping you. And it's helping you learn. Because if you type one thing, it goes like, oh, I've seen this before. Sure, I'll help you again, even though it doesn't exist. But I trust you will always exist. So I saw all these things and thought, eh, TypeScript. I'm going to skip that all of that. So these are the things that I ended up with for TypeScript. TypeScript is transpiler-friendly. It's not a real language. It's a facade on top of another language. That means it comes with full tooling for IDEs, for figuring out what the code is, building ASTs, because that's what it does.  So that was my motivation for all of this stuff. So basically, actually, I have another slide that I can put up. So basically, what TypeScript gives you a TypeScript namespace? TS. That's the namespace for the ASTs, compilers, parsers, type checkers, and all of the stuff that's built into TypeScript. Like, this is built in. You don't need to pull in anything else. To actually get any code to be parsed by TypeScript, literally, this is what you need to do. You just do create source file, give it some name, throw in some code. You can read it off of disk, whatever. Throw in some code and then tell it to transform. You implement a little visitor pattern that will get called for every note that the TypeScript finds. TypeScript will build this AST. For those two lines up there, this is what TypeScript automatically gives you. It will give you calls for every single one of these notes. This is a little treat. The source file has all of these nodes, and then you can go down and you can decide whether to go down or not. I just recursively go down by doing that, visit each child. This is the visitor implementation that I have. I log what the node is, and I visit each child, and then this is what I get. And that's literally what you have. So you can see this is not valid TypeScript, or is it? This TypeScript actually care. Does the IDE actually care about this? It doesn't, because it actually thinks this is a property exit expression. It doesn't say this is gibberish. It actually says, hey, this is an object that has a property, and that is another property. If you provide TypeScript with more context about what these objects are, TypeScript will give you better information about what they are. So TypeScript doesn't care. They will still think that this code and it identifies the syntax, which is perfect. Because now we can write a class library access for .NET that TypeScript has no idea what it is. It won't complain, and it will give us type information on all of these things. And then what we get is, in this case, this simple line that TypeScript has no knowledge of, if I compile it into IL, you can see the tree that it provided. I'm not sure if you can see that in the back, hopefully. Those are all the nodes that I parsed. And I generate IL, and now we have .NET. And the IL that I generate is literally this, which is the equivalent IL for the TypeScript. So five lines of code, TypeScript Compiler. It's a bit more than that, but it's a good start. It was a good proof of concept. And this is where I started from to proof of concept, like is this viable? Does TypeScript have enough type information that I can take this and produce a viable IL from it? Turns out, yes, because JavaScript, there's only two types, string and number. And the TypeScript JavaScript model is literally containers of key value pairs. It's a dictionary. Every time you access a property, it's literally going in and look at the table and see if the thing exists. If it does, it won't complain at you. So putting TypeScript on top of JavaScript, you can do, because you can just build on top of the very simple string and number model, which is what they do with types. Taking that to C sharp is literally just deciding. It's transforming the syntax into IL, taking TypeScript.net is transforming the syntax into IL, and then deciding what is useful from the environment. Like TypeScript and JavaScript are not just the language, but they're also the ecosystem, JSON.parse, and all of those methods that you just take for granted. They're not actually part of the language. They're a part of the ecosystem that happens to come with a runtime that you're running in, in this case v8. When you're running TypeScript in .net, you're running in the .net runtime. So you get the environment that .net gives you, which is system console system, all of these things. And now you just get to decide what TypeScript it makes sense in this kind of environment. It is just like literal .net calls directly into it, or do you do some node facades to make it look like the normal JavaScript that you would see, but under the hood, you just call into .net to do these things, which are helpful libraries that once built, they're there, and you never see them. These are the questions that I'm considering now, and then handling any. When you have a type that is not a type, where TypeScript just goes like me, whatever. How do you transform that into IL? Do you just do JavaScript and just make a dictionary or keel-value pairs? Whenever you see property access to an any type, you just go and look up. You just create IL that goes look up into the dictionary. That's an option. You could use the DLR. That's another option for end-use dynamic, as you would in C-shark. So these are the questions that I have around TypeScript to .net right now, and then for game-specific step to actually pass data around, but that's for the game. So this was, this is the very last minute talk, so the code is not up yet. Well, it is up, but it's not ready for consumption. But ping me, email me, because I really want to start fleshing out this thing, because I actually want, I need this for the game. So, you know, and if you're interested, ping me on Twitter or email me or whatever, and I'll see about putting the thing that I'm calling T-S-I-L for now up in public. And we got, yeah, a few minutes for questions. We're going to set up while you folks have questions. Yes. Questions, please. Yes or not? What? Many people will just come up with questions. If they have them, yes.


Now why am I all of a sudden talking about these cases is because you are now going to study co-linearity, co-linearity of two vectors. What is the meaning of co-linearity? Co-linearity means they are parallel. So we say vector A and vector B are co-linear when they are linearly dependent. Vector A and B are co-linear when they are linearly dependent. What is the meaning of linearly dependent? That means if you do m1A plus m2B equal to null then m1 and m2 not all will be 0. Are you getting my point? In other words you could express A as minus m2 by m1 times B which is nothing but you can express A as lambda times B. So if you could express one vector where lambda is some scalar quantity. So if you could express one vector as lambda times the other then we say that the vector A and B are co-linear to each other. In other words they are linearly dependent on each other. That's why the concept of co-linearity evolves with the concept of linearly dependent. If they are non-co-linear my dear friends, let me write the reverse case also. If A and B are non-co-linear then they are linearly independent. In other words if you try to do this then it will only result into m1 and m2 both being 0. Let us try to understand the deeper meaning of this. Let's try to understand this through vector addition. Let's try to have another perspective of it. If let's say this is your vector A and this is your vector B. Are they co-linear? According to my diagram let's say they are parallel. Are they co-linear? Now if you see this, this is trying to say that if you manipulate these two vectors in such a way that their resultant becomes 0. That means if you do m1A plus m2B in such a way that the resultant becomes 0 this is possible without m1, m2 being both 0. How? Let's say this is double the length. So what I will do is I will half its length so that it becomes like this. Then I multiply it with a minus 1 so that it reverses its direction. Now if I add these two so 1 into A and minus half into B, 1 into A and minus half into B do you realize that this vector and this vector will close the path and it will become a 0 vector. So m1, m2 here both are non-zero. That is what this theorem actually says. It says that it is possible for you to multiply these two vectors with a certain scalar quantities that means you are fiddling with their direction and magnitude in such a way that they both cancel out each other. That is possible for co-linear vectors and hence these vectors are linearly dependent. Have I made myself clear? Yes sir. But if you have such vectors my dear friends like this, A is like this and B is like this. Can you try making the resultant of these two as a null vector? Can you somehow close this path such that this plus this ends up being a closed path? Can you do something like this in this case? No unless until you make both of them 0 isn't it? There is no way you can close the path. You try fiddling with the direction and length of these two vectors. Do anything you want. Says that they cancel out each other. Can that happen? No it will not happen. It can only happen when you have multiplied both of them with a 0. That means you have made them both dots. Then addition of two dots will give you a dot that is a null vector. But if you have any other non-zero quantities for M1 and M2 it is not possible to close the path between these two vectors or it is not possible to make them cancel each other out. So these cases are called these vectors would be called linearly independent. So two non-colinear vectors are linearly independent. Two collinear vectors are linearly dependent. Are you getting this part? Now a same concept can now be applied to collinearity of three position vectors. Collinearity of three position vectors or points you can say. Remember position vectors and points there is no difference. What is position vectors in vector is points in coordinate geometry. Getting my point. So many points here. So you say position vectors a b c. See guys we never talk about collinearity of two position vectors. Any two position vectors will always be collinear. So it's a futile effort to talk about collinearity of two position vectors. We can always pass a line through two points isn't it? So in order to make sense we will talk about three or more than three points. So three points let's talk about three points let's say point a, point b and point c whose position vectors are as shown. They will be collinear. That means they will all lie on a line. If. Now there are two ways in which I normally explain it. If a, b, c are collinear then construct any two vectors by choosing any two of the points. Let's say I take a, b and a, c. Then one can be expressed as lambda times the other. If this condition is satisfied then point a, b, c will also be collinear. Mind you you can take any two vectors you like. You can take a, b and b, c also. So even if you can express this as lambda times this, okay, any one of these conditions then these three points will be collinear. That's one way of understanding it and this is the easiest way. Okay. Normally I also choose this method to prove whether my three vectors are collinear or not. Okay. Second method is slightly tricky but you should also understand this. Second vector says that if you express the linear combination of these vectors, if you express the linear combination of these vectors as a null vector then m1, m2, m3 not all zero, not all zero must satisfy m1 plus m2 plus m3 equal to zero. This is slightly challenging way but this is easy to understand once you know the logic behind it. So what am I trying to say is that if a linear combination of a, b, c express as a null vector, okay, it should lead to m1 plus m2 plus m3 as zero but all of them should not be zero. That means of course m1 plus m2 plus m3 will be zero if all of them are zero. But here my situation is it should be zero despite m1, m2, m3 not all being zero. Then only point a, b, c would be collinear. Okay. How does this actually come about? It's very simple. It actually comes from the section formula itself. Let's say a is this, b is this and this ratio is let's say, let's say x is to y. Okay. So if I use my section formula, b would be nothing but xc plus ya by x plus y, correct. Now it can be minus also doesn't matter. Okay. If you cross multiply x plus yb is xc plus ya. If you write this in form of this term, if you write, if you express this as this, you write it as ya minus x plus yb plus xc equal to null vector. I can clearly see here that this is playing the role of m1. This is playing the role of m2. This is playing the role of m3. You can see that m1 plus m2 plus m3 will actually give you y minus x plus y plus x which actually is zero. That's what this condition is saying. But each one of them is not zero. You remember m2 and m3, they need not be zero all of them. Are you getting this point? Guys, is this understood? If it is understood, let me take a problem. Hope you can read this question. The vectors 2i plus 3j, 5i plus 6j, 8i plus lambda j have their initial points at 1 comma 1. Find the value of lambda so that these vectors terminate on one straight line. Done? Do you understand the question? First of all, see there's a starting point 1 comma 1. So one vector is like this. Let's say this vector is 2i plus 3j. One vector is like this. Let's say 5i plus 6j. Another vector is like this. Let's say 8i plus lambda j. All of these three vectors, they end on the same straight line. So this is the terminating point. Let's say a, b, c are the terminating point. So what should be the lambda values as that they all terminate at the same point? 11 by 3 is not the right answer. No problem, Aditya. See, let's say the position vector of a is not known. So can I say position vector of a minus i plus j is actually your given vector 2i plus 3j. That means position vector of a is nothing but 3i plus 4j. Similarly, position vector of b would be 6i plus 7j and position vector of c would be 9i plus lambda plus 1j. Now these three vectors, these three points are collinear. That means they are linearly dependent. Take any two of the vectors. The third could be expressed as lambda times the other. Okay, so let me take these two vectors and these two vectors. Initial point 1, 1 comma 1, right? Why does minus 1 comma minus 1 comma 1? I think you misread the question. Okay, so I'll use the formula ab vector is lambda times ac vector. I'll use this formula or the other way around. Ac vector is lambda times ac vector is lambda times ab vector. Anything you can use, not a problem. Now, I don't want to use lambda because lambda is already used. Let me use something like beta. Okay, so ac vector means c minus a. c minus a would be 6i lambda minus 3j. This is beta times ab. Ab will be 3i plus 3j. Correct? Now let's compare the coefficients. So 6 is equal to 3 beta. That means beta is equal to 2. And lambda minus 3 is equal to 3 into beta. 3 into beta is 2. So lambda is equal to 6 plus 3, which is 9. lambda is equal to 9. Okay, all right. So one last question we'll take up and then we'll call it a day. If a and b are two non collinear vectors, then show that these three points, points means position vectors are non collinear if the determinant given by that expression is 0. Okay, let's say I use the second method this time.  Since I was using m1, m2, m3, so I thought I would use the same, but I'm sure you would not get confused even if I replace m1, m2, m3 with x, y, z. Okay, let's say I equate this to null vector, then this should be true for x, y, z not all zero. Correct? Yes or no? Now let me first collect the terms a and b separately on my first equation. So if I take a term separately, so x, l1, y, l2, z, l3, a. Now let's collect the b terms. So x, m1, y, m2, z, m3. Okay. Now please note a and b are non collinear. Non collinear means they should be linearly independent. If they're linearly independent and you're equating it to a null vector, that means these two terms individually must be zero, zero each. That means, let me write it like this. That means l1, x, l2, y, l3, z should be zero. m1, x, m2, y, m3, z must also be zero. And other than that, we have x plus y plus z also equal to zero. Okay. Now remember, we have to find a situation where x, y, z all are not zero. That means this system of equation, this system of equation must have non trivial solution. Non trivial solution means at least x, y, z should be non zero in some cases. Yes or no. Now remember the condition when a system of equation has a non trivial solution. It can only happen when the determinant formed by their coefficient must be zero. Try to recall your determinants chapter. Okay. From determinants from, yeah. From Kramer's rule for system of homogeneous equations. Okay. Is that clear? And this is what we wanted to prove. The other if you know these three points, let's say I call this as l i cap, m1 j cap, l2 i cap, m2 j cap, and this point as l2, l3 i cap, m3 j cap.  And you want this to be collinear. That means the area of this triangle must vanish. Area should become zero. What are the area expression? Half l1, m1, 1, l2, m2, 1, l3, m3, 1 should be equal to zero. Okay. So even if you drop this half, it will be zero. Now you just transpose it. If you transpose it, it becomes this. Okay. Another way of understanding the same thing. Is that fine? So next class, when we meet, we will be talking about coplanarity of two three vectors, et cetera. And a similar conditions will now be seen in that cases as well. And then after I'll start with dot product. Okay. So today, mostly our session was oriented towards understanding the introduction part of vectors. Okay. More importantly, the concept of linear combination, linear independent, linear dependent is what you may have learned new in this part today. Okay. Anyways, I'll stop this session here over and out from my side. But yes, all the best for you tomorrow's exam. Do well. Avoid silly mistakes. Okay. Thank you. Thank you, sir. Bye-bye. Have a good day.