I serve because I'm a firm believer in to who much is given, much is expected and required. I've got a love and a passion for what I do. I'm lucky enough to actually be in a job and position where I enjoy getting up every single day. It gives me a chance to give back to others in their greatest time of need. Because I believe that planning for our future is important. I enjoy people. I enjoy being out in the public. Everybody needs that helping hand at times. I think serving your fellow man is very important and if we care about one another, we serve one another and that's what all of us should be about. I think that people would feel somewhat lost unless you have people in place to show you around and show you what is available and make people feel welcome. It's about giving back to the community and also it's about helping those who can't help themselves at times. One of the most important qualities a public servant should have is being a believer. Very open-minded. Trustworthy. Compassionate. We have to be patient. We have to be kind. We have to be humble. Seeing individuals as individuals and being empathetic to what they're going through. A believer that events, organizations, programs can get better and enhance the people's quality of life. Ironically, I think the most rewarding experience and enriching experience I've had was during the flood of 2015. I saw our staff step up with servant hearts and give them themselves like I had never seen before in the private sector. That attitude of we can't fail and to pull together and deliver like they did was very rewarding. Most public servants are not doing this for any financial reward or gratitude but I do think that they genuinely love what they do to be in the work that they're in.  Saving a picture or a photo or even saving an heirloom is gratification enough for us. I daily get an opportunity to connect with the citizenry that we serve and it's greatly rewarding to me and how I perceive my job myself. All the relationships and connections I've made throughout the years. Seeing those people when you're not working, when you're off the clock enhances your quality of life so much and I love every day I do it. As public servants, if we don't engage with community members, we're doing a disservice to our community as a whole because it's so important to be inclusive and to really understand where everyone is coming from in order to build a brighter future. We choose to be here, we choose to work with the City of Columbia to serve our citizens and it's a choice that we all make and we need to embrace that, enjoy that, but understand that we appreciate that very, very much. We're one team, one fight, everybody's trying to achieve the common goal which is to make Columbia a greater place. Folks get up every day ready to try to make life more pleasant for the community and everybody works hard. I can't say thank you enough to all those people because even though I'm also a public servant, I'm also being served by all those other people as well and so I'm very grateful for everything that all of us do here at the City. It's a great place to work and live.


I think it's quite fitting that we go to the steakhouse then. There's a lot of foot traffic though, eh? All we do to animals is absolutely a porran, and it shouldn't be illegal though. Um, no, I don't think eating meat should be illegal. We're gonna have a chat lads. Come talk about it. It's murder. Should be illegal. You don't? Oh really? Good work. Oh, good cuisine. Here goes, I'm from Ethiopia. They've got an amazing vegan food there. Hey buddy, how you going? Yeah, good, how are you? I'm Joey. Jack, nice to meet you. Jack, nice to meet you, Jack. So you're overhearing the last conversation? Yeah, yeah, yeah, it sounded really interesting, so yeah, I saw the sign. Yeah, no worries. What did you think of the sign? The conversation about it. Um, yeah, it's interesting. I think it's definitely a big topic at the moment. Yeah. So I think it's worth talking about. Definitely. Where are you from, Australia? I'm from Australia originally. Whereabouts? Adelaide. Oh, okay. Yeah, I traveled there, it's a great place. Yeah, are you from here? London? Yeah, yeah, yeah, from London, yeah. So, I would like you to start off and tell me why I'm eating... First off, do you oppose or support the statement? I'd support it, however, I don't know if it's practical in terms of it being illegal. Okay. I don't know if it would happen. Yeah, so it's more like should happen rather than will. I'm talking about more in principle. Okay. Yeah.  Yeah, I agree with you there. I don't think they're going to change unless there's a big demand shift and something's some type of direct action that attacks them and forces them into change.  If I went and assaulted anyone, there's laws protecting us basically for doing something that's inherently immoral. Animals are sentient, they feel pain, they suffer, they want to live. They're forcibly bred into this existence and then they're murdered and chopped up and sold into supermarkets. Consumer comes along and purchases that. That money goes straight to the slaughterhouse, goes straight to the animal agriculture and it fuels it, okay? So I'm saying if we made eating meat illegal on a grassroots level, on an individual level, that would definitely slow down what's going on because what would happen to demand, it would nearly completely halt here, especially in the UK. Yeah, well I think it's interesting because I think people should have a choice if they want to eat meat or not because it's been, people have been eating meat for a very, very long time. It's never been illegal in the UK, I'm pretty sure. No, it's never been illegal ever. Yeah, yeah, so I think that would, I think there would be a big fight back around it because people would probably say like if I want to, you know, they've been conditioned to think it's okay to do that. So that's kind of, it's all perspective end of the day. Interesting, we're forgetting someone else's perspective here. The victim's perspective. Yep, no. Do you think they should have a choice to live? Yeah, I mean, you know, it's an interesting one that. Because you're only talking about the, you know, consumer's choice. We're not talking about the victim's choice. It's true. I think it would be a good idea to make people more aware about how it's actually been made, what they're eating, because it might put people off. It's horrible, isn't it? Yeah, it's disgusting, man. Like if you see, yeah, you look at the footage and... I've got the footage here. Yeah. You know, this is called Land of Hope and Glory. Okay. A couple of friends of mine put this together. This is, you know, investigators get footage from UK farms. And, you know, this is a dairy farm here. They standard practice just to shoot bobby calves on their first day of life or shortly after birth because they're just not used to the dairy industry. I boycott these industries. This is tail docking, teeth clipping of newborn piglets. These are all standard practices. You can look all these up if you want to look up standard practice. They've got it all on there. Industry websites. You know, gas chambering of pigs. These are battery hens here. Free range hens are just in a big shed and, you know, a little bit more space and they're all murdered anyway. Yeah. It's not an ethical way to do it, how people are doing it, like trapping cages and all that. Like, I know some kind of meat is sold, but it's, you know, like free range, for example. So, like, they live happy, but maybe a quick death. They tell you they live happy, didn't they?  It's a propaganda machine we were talking about earlier. But these, you know, I look at this and instantly I just want to block it out like I do. And it's bad just to think that, right? Do you think most human beings would react the same to looking at this footage? Yeah, yeah, for sure. I don't know how you can look at this and then think it's all good. Like, there's definitely... This is pretty standard. I've been into these sheds myself and you see, you know, chickens that can't reach the feeding trays and they're just suffering and dying like this all the time. I mean, there's just so many of them. Do you think, like, this kind of footage should be shown in schools to make kids aware or do you think it's too much? I think everyone should be made aware. But obviously this is an industry, isn't it? They're marketing these products to us so they're trying to make people comfortable about it. That's why you've got the RSPCA, you've got Red Tractor and all these places that are constantly being exposed. Let's just say their lives were free of suffering. Let's just say... But I don't believe that's true. Let's just say that that's true. In the slaughterhouse when they're being bolt gunned in the skull and hacked up into pieces. How can that ever be viewed as humane or moral? It can't be, but I don't think there's enough of a substitute for it. I think, yeah, well, I don't think... If my sister was vegan for a while and she's very conscious about what she eats, and I don't think it's... If I wanted to try a vegan diet, I wouldn't know enough about it to do it. I think I wouldn't know what to buy, what to replace with. So you think there's a practicality issue with people switching over, even if they knew that this was bad, there's a practical issue with not having enough options available? Well, it's just being conscious what you're consuming. And I think the problem is... Well, it's not a problem, but the challenge is if you wanted to be more conscious about this kind of stuff, it takes a lot more effort, right? A little bit more. You have to... A little bit more. It's a meter from the soy milk to the dairy milk. One meter. You've got to do a bit of research. You've got to know what you can buy, what you're not. And in the supermarkets, you've got to be aware about what's in what. Like, my sister has to look at all the ingredients and make sure, you know, things like that. You've got to look at it once, and then you know that one's vegan. There's a lot more resources than what you'd think, and it's a lot easier than what you'd think. I just think people just need to be motivated enough to take that chance and just... It's a bit of work at the start, but I think it's completely worth it, like... Yeah, I do. I do. And as well, like, I watched a documentary Before the Flood with Leonardo DiCaprio. I don't know if you've seen that. And he talked about how, like, cows, you know, they produce the most, like, a lot of methane. Methane, yeah. So it actually has a damage on the climate. I've got a statistic here from Cowspiracy Facts page, which you can verify here. It's, like, up to 51% due to livestock. I've seen lower numbers. But it's more than all transport combined when greenhouse gas emissions. By eating a plant-based diet, you can reduce your carbon footprint by 50%. Up to 91% of Amazon deforestation animal agriculture, growing soybeans to feed to animals to get a small morsel of meat. Water use, land use, resource use. Yeah, that's amazing. That's... those are amazing stats, and massive change could happen, right? So I know, like, for a pig, for example, I've heard it has, like, the same amount of consciousness as a dog. Is that right? They rank higher in intelligence than dogs. They're probably on par with a three or four-year-old child, scientifically. Right. What about chickens? Chickens have around the same... I think they might even be ranked... They're very intelligent chickens. Right. So I was just thinking that could be, you know, because I know chickens, for example, are less of, produce less CO2.  So I guess maybe even in terms of maybe not making meat illegal, but actually having a compromise. So you could actually ease people into it a bit more. Because I guess climate is not just in one go. I think it just wouldn't work at all. Yeah, so swap the cows out for chickens? I think... well, obviously, I think it's still bad for chickens, but I think... More chickens would be murdered. Yeah. Because more of them, they're smaller. But they're all getting murdered right now. So I think if it was a slower transition... Well, that's why I'm saying we should just make it illegal. All of it. What are you going to do? They'll lock you up, mate.  Can't have your chicken. It's destroying the environment.  Do you think that making it illegal is the best way to teach people about it? Because, let's say drugs, for example, you know, it's illegal, but people do it anyway. And it's because they don't really... They see it more as a crime rather than, actually, it's not right, right? In some cases. Let's take drugs out of the picture, because that's more of a personal choice for me. I know that drug dealing has victims. Let's talk about child abuse. Child abuse is illegal, yeah? Yeah.  Yeah. It's victims involved in that consumer.  Yeah. Yeah. I think that should be illegal. Well, I think, again, it comes down to the conditioning of the place. Like, so I know in, like, Japan or China, like, that's not as frowned upon as it is here, right? So, from what I've seen online... I think it should be illegal, personally. What's your personal view on that? Um, I think... My products are... I mean, yeah, dude, like, I think it's disgusting that these animals are getting killed. No, no, no, no, animals. I'm just applying the same logic that I'm using for making meat illegal, eating meat illegal. Right. I'm using that same logic in the application of, like, products of child abuse. So, like, child porn, for instance, I think that should be illegal. And I'm just saying, like, for the same reasons that should be illegal, should be the same reasons that eating meat should be illegal because it's abusive to animals, it's murdering animals, and it's destroying the environment. So, I think, like...  We're humans. And so, I guess, sadly, I think we put ourselves first over animals, right? And what you're saying, if I'm right, is we should be completely equal with animals. No. No, I'm saying for the same reasons that we oppose products of child abuse should be... We should extend that to animals, not because we're exactly morally equal to animals in every way, but because they have many things in common with us.  So, all of these reasons, I would say that they deserve at least fundamental rights, like the rights to bodily integrity and not to be enslaved and things like that. I'm not saying that you're morally equal to a chicken, but I'm saying the chicken possesses these values. Yeah, for sure. They've got some level of consciousness. It looks like it took it a toddler. Like a toddler. They run around, they're drooling, ma, ma, ma. Look at pig. A pig's not much different in mental capacity. They're, you know, the ability to perceive the world. I think another thing to think about is some people actually eating meat is actually a good diet for them, I feel. I mean, I don't have enough research, but I know with the Jordan Peterson's daughter is a real supporter for carnivore diet. And my sister, she's always been plant-based, but she's always very weak, so she's thinking about actually trying that to give her more strength. So if it's completely legal, it might actually affect some people in being able to get the kind of food they need. Jordan Peterson's daughter has no scientific evidence for her claims that a full meat diet is in any way healthy. She's talking basically off of anecdotal evidence only. There is no scientific support for her claims. When you talk about a plant-based diet, there's a body of nutrition professionals, about 100,000 of them, and they make up the Academy of Nutrition and Dietetics, and they brought out a peer-reviewed statement supported by 117 studies saying that a vegan diet can be healthy for all stages of life, infancy, pregnancy, adulthood, even into your, you know, elderly years, if it's well-planned. So would you say that a plant-based diet can do everything which meat can do for the body? I'd say meat is the number one contributor to heart disease, just based on its saturated fat cholesterol content. It contributes to type 2 diabetes. It's doing the opposite of what healthy diets would do.  There's nothing in meat that we can't get from plants or from a B12 supplement, and that, you know, helps the environment too. I heard an alkaline diet that's really good. Have you ever tried that? I've heard about that. The only diet- Plant-based but alkaline. A whole foods plant-based diet is the only diet proven to reverse the number one killer, which is heart disease. So it's been proven in clinical study to reverse outflow sclerosis, hardening of the arteries, which is the number one killer of human beings. Yeah, well, I think it comes down to if there's going to be a change, it needs to be every individual has to be more conscious what they're consuming, right? But I think it takes time to change the conditioning of a place. Like, it does take time. So I guess really, I think just making it illegal, it just wouldn't work. It would have to be a slow process. Why wouldn't it work? I just think there would be uproar. There would be uproar. There'd be uproar. People would be like, no, this is wrong because they maybe haven't been educated. So practically, you don't think it would work? Let's just say, like, if it did work, would you think it would be a good solution? Let's just say it would, well, I think it would stop it nearly completely. Yeah, I mean, I can't see how it wouldn't make the world a- There'd be underground slaughterhouses, and they'd have to really do things in, you know? Yeah, no, for sure. I think at the end of the day, let's say it went illegal. There'd be more. Would you support it?  Come on, yeah. If it was illegal, yeah, I'd give it a go, actually, to be fair. Like, if it was more like, if they put it in front of you and said this is happening, then I'd definitely give like a plant-based diet. If you go by a steak, you're going to get one month in prison. Right, well, the thing is, if it was illegal, then it means it would be easier to get the right kind of foods in terms of plant-based diet. Everywhere would be plant-based. It's hard not to eat meat right now, because it's- It's easy to, it's just everywhere. It's much more convenient. So you have to do a little bit- Like, here's one, convenience. Do you think convenience should justify this and this? Like, what we're doing to the earth and the animals? No. No, it shouldn't. But convenience is the way the world's going. Everything for instant gratification. You want things fast. Like, it's much more of an inter-convenience to be on your way to a slaughterhouse or for us not to have an earth to live on. Yeah, I agree. I agree. So at what point should the government go, right, this is it? Eating meat's illegal. It's illegal. At what point? Like, we're nearly there with the environment being irreversible the damage we're doing. Billions and billions of animals every 2.7 trillion, sorry, including marine animals every year murdered? They won't because there's too much of a high demand for meat. And I think the only way was if someone created their own economy, which kind of duplicated a mindset around that. Otherwise, I don't think they'd lose too much money. There'd be too much uproar. I can't see it happening unless, like I said, someone started their own economy around it. On an individual level, you can do something with the impact that you caused to the animals and to the environment, but the best, the single biggest thing you can do for the environment and to help animals and for your health is to eat a plant-based diet. If, you know, would you say your sister? Yeah, my sister. If she's lacking energy, she's not counting her calories right? Or it could be something to do with she's not absorbing certain nutrients. That I wouldn't say that's inherent to the diet. Yeah, I think the struggle she's had, I think she's lacked in certain minerals and I think that's just a case of her experimenting on what food she should eat to get. Chronometer is a fantastic app which tracks all your minerals. So I don't know how much she's eating because a lot of the time when you're tired, you're not eating enough because plant foods have calorie dilute. So increasing your dried fruits and your starches and I don't know exactly what she's eating, but I wouldn't write off the plant-based diet just based on that one anecdote there because the science is in full support of this way of eating stuff. Well, that's that. I'm sure there's so many people who debate around this, right? And they say, oh, you know, actually, meat can be good for you in some cases, but I guess, you know, the facts tell, right? We've got three things, environment, animals, and health. Well, that's it. I think that's massive. I'm big one for the environment. I think I definitely want to make my own individual impact there. And yeah, I mean, you look at these videos and it's horrible.  So I guess maybe if it was illegal, then it would also mean that they'd have to be forced to change. They'd have to be forced to change, but there'd have to be some education around it as well because you can't expect people to stop having something without being... Without knowing why. Without knowing why. I think with all forms of activism, even direct action, there always should be education, which is what we just did here. If you made it illegal, you'd have to completely change the education process because kids would need to learn. You don't need milk for calcium. Yeah, yeah. Teaching our kids all of this. They're not showing kids this. But yeah, you know what, brother? Thank you so much for that chat. We really loved it. We let more of a debate to you, but no, I think it's a really good course. We were in agreement with most things, but I think we still covered a lot of things. I think it was great. Thanks a lot, brother. Joey Carbstrong, if you want to see. And challenge22.com. Challenge22.com. 22 Day Vegan Challenge. Try it. Okay. In a Facebook group, there are all a few of my friends run this organization. It's fantastic. Okay, cool. Give it a crack. I'll check it out, man. No worries, brother. Take care. We got three really decent debates. Conversate. I love talking to him then. What do you reckon? What should we call it?


This is an alert from the SCP Foundation, an international security organization, which has the support of your national government. You should pay close attention as this alert concerns your safety and security from an anomaly. An anomaly called SCP 173 has escaped from SCP Foundation containment, and is in your area. This anomaly is hostile to humans. It is extremely fast, and typically kills by snapping the neck, however it can only move when observed. SCP 173 has the appearance of a concrete statue with ribar protruding from it, covered in spray paint. SCP 173 may also be detected by its emission of blood and waste material if it stays in a single location for a long period. If you see this anomaly you must maintain eye contact with it, and back away as quickly as possible. If possible, travel in groups of greater than two so that multiple people can observe SCP 173 at once, for redundancy. When observing SCP 173, you must not even blink, as it may approach, and kill you in the time your eyes are closed. The SCP Foundation will have the anomaly recontained shortly. Secure. Contain. Protect.


Hi, I'm Zor. Welcome to Unisor Education. Today we will talk about rainbows. Well, strictly speaking, it's dispersion when the light goes through a sphere. But yes, it's about rainbows. Now, this particular lecture is part of the course Physics 14 presented on Unisor.com. I suggest you to watch this lecture from the website because it's part of the course. So the website has a menu. All the lectures are logically connected. And every lecture has notes, very detailed notes with pictures. So it's basically like a textbook which is divided into parts. And each part belongs to one particular lecture. So you have a video and textual presentation of the same material. The website has exams. You can take it any number of times. You want it just for yourself basically. Everything is free and there are no advertising. So it's just pure knowledge. Also the website contains prerequisite course math routines. Mathematics is a mandatory knowledge which you have to possess before doing the real physics. Okay, so back to rainbows. Everybody knows what rainbow is. Everybody probably saw it above the waterfalls, for instance, or after the rain. Just recently I saw the rainbow above the Victoria Falls in Africa. Very beautiful. Now rainbows have this circular shape and they have different colors, obviously. And we will talk today about why actually it happens. Well, the short answer is a refraction. But now let's just go into the details of this refraction. Yes, one more thing. There are actually a few kind of geometrical composition between sun observer and the water droplets which are in the air after the rain or above the waterfalls. Now this composition can be different, this geometry. And obviously different geometries have different results. Some of them just don't form any rainbows. Some do. And it basically, again, depends on how it's all arranged. Now I will address first a simpler form which is basically very rarely occurring. A simpler form is when you have the sun, you have some kind of water droplet here and observer somewhere here. Now this is a simpler. And why it's actually very rarely really seen? Well, because sun is very bright and the rainbow is formed somewhere in this area where the droplets are. And in this particular case when the sun is very bright you don't really see much. Another configuration where you usually see is something like this. Now the difference is that the light should go through a more complicated path in this particular case. So let me start from the simple one and then we will go to a more complicated. So the simple one is here. Now this is the sun and let me just enlarge this particular droplet of water. It would be easier for me to draw. Now from sun the light goes in, we can consider that the light goes in parallel white rays. So the parallel one goes like this. This is white light rays from sun. Now what happens in this particular case? Well, if you have the water droplet and you have some ray of light coming on its surface there are basically two things which happen. One thing is reflection of the surface of the water. Another is when it penetrates through the water but on the border between air and water the white light diffracts into different components because different wavelengths have different refractive index. And since white light is a combination of all the wavelengths from to the whole spectrum then this spectrum actually is opening up. And now how can I really draw it? First I have to have the perpendicular to a surface. The perpendicular to a surface of the sphere is obviously the radius. So this is my angle of incident. And angle of refraction is again different for different colors. Now the red light will have a smaller deviation from the original and correspondingly bigger refraction angle. The violet, so we will use just two opposite red and violet. Everything else is in between green, blue, etc. So this would be my red light. So it's a little bit deviated. This is my continuation of the white light. Let me make it with interruptions. It's deviated. Now violet would be deviated more. That would be violet. Okay, now so the beta is as I was saying a refraction angle. And obviously we have the law of refraction. Sine A times N air in this particular case, because we are coming from air, is equal to sine of beta times refractive index of water. So this is more or less unit one. And for water this is again different for different colors, but it's somewhere around 1.33. For one color it's less, another color is greater. Average is for yellow light is 1.33, considering. Okay, now let's just in this particular case forget about reflection, because reflection can occur here and it can occur here as well. But right now we are talking about a simple case, when there is no reflection everything goes through. So right now we have another refraction, because the light comes from the water to the air. Okay, so let's again put perpendicular reduces. Okay, so this is my, now this is my incident angle, beta prime for red. I didn't really put it for the violet, because the picture would be too complicated. So we are talking about red light only. So we will have this incident angle, and the refraction would be deviated from this particular original angle. So it will be somewhere here. So it goes, well let's put observer here. This is my eye of an observer, and it goes to the eye of the observer. Now violet obviously will go somewhere here. Okay, well, am I right with this thing? I think I should really put it a little bit less inclined than this. I would probably have to put it right here. Something like this, and like here. And the eye would be here. Now this is gamma. This is a refraction after the light. And now we can say that sign of beta prime times n water is equal to sign of gamma and air. Again this is about 1, this is about 1.33. So in this particular case gamma is greater than beta prime, right? Yes, and in this case beta is less than alpha. But now, look at this very important thing. Beta and beta prime are equal to each other. Because these are two radiuses, right? So it's an equilateral triangle. And therefore this is equal to this, which means these two are equal, which means alpha equals to gamma. Well, it's just an observation, not that it's very important. But actually yes, the incident angle of the white ray which is coming onto a sphere would be equal to a refraction index as the light goes out. So that's basically what it is. Now, here is what's important. If I see the red light here, will I see the violet which comes from the same ray of sunlight? No, because they are going into different directions. And if I see red, I cannot see from the same water droplet, I cannot see the violet as well. But there is a next water droplet from which, either on the left or on the right, from which the violet will actually come to me. So again, if on a smaller scale I have somehow light from one droplet and from another droplet at different, which basically diffracts slightly differently, I will have, so if this is red, this is violet. So I think of red and violet in two different places, because how I see? I see my red light on the continuation of this thing, right? So it's somewhere here. Now, if my neighboring water droplet sends me the violet in such a way that it actually goes from there, I see the violet here. So red would be in violet and everything in between, obviously. So I will see different colors in different places. And that's why we see basically different places for the colors in the rainbow. They are not mixing together, because if I see the violet from the same droplet, they would mix together again and make the white light for me. But that's not the case. The case is that red from one droplet comes to my eye. But into the same eye, the violet would come from another droplet, because there is a slight difference, and here we have a difference in angle, so I cannot see it at the same time, too, of them. But if I have somewhere here, I don't know, another droplet which goes with the same direction and hits the eye, then I will see the violet in different places. So basically my point was that since the light is basically split into... it's like one cone and then even wider cone, I will not see the same... I will not see different colors from the same ray of light. I will see red from one and violet from another, because the result of this one, again, somehow I don't want to draw it, it will hit my eye, or in this case. Okay, so this is about how the water droplet is reflecting light and it goes into my eye. What I was saying is almost impossible to see the rainbow when the water droplet in between sun and you, too bright sun, sun is too bright. So let's just draw another picture. Another picture would be a little bit more complicated, but nevertheless it's more practical. So now we have something like... we have sun here and the water droplet here. Now what happens is sun ray goes this way. Now let's talk about one particular color, let's say red. So in this case we will have this situation. I should really put it this way. Okay, this is a white and this is red. So the first things which should happen, it should go inside the water, because if it just reflected here, it will still be white. So it's not interesting, you're not interested in this reflection. So as I was saying, there is always part of the light is reflected, part of the light is going through and deviates from the original direction. Now here, observers somewhere here. So we don't see anything very bright over there, so we see the colors. Now here we have actually a reflection, so it goes this way. And now again, partially we have probably a reflection, it goes back into the water droplet and can again reflect, refract, etc. But let's just forget about this. Now let's talk about that it goes through. It goes through and this is my perpendicular and it goes somewhere here. So this is my eye. Now this is a red. Now the violet would be, well, kind of neighboring, but again it would be at certain angle in such a way that it does not go into the same eye. So the same white ray will produce only the red component which goes to me. It's a different white ray somewhere in neighborhood going against either the same or another, most likely another rainbow water drop. It will be again partially reflected, partially refracted and it will go into the same eye but it would appear to be, now in this case I see red light appearing somewhere here. This is my red light. Now the same violet will be reflected and refracted from another droplet which would be somewhere here and I will see it eventually in this direction. So this is more practical, though a little bit more complicated path of the light, partially refracted, partially reflected. And again as I was saying, I can actually have partial reflection here as well and it goes this way and maybe another reflection, again maybe somewhere I will see it, but it will be in a different place. So I will have more than one rainbow which is again, sometimes you have double rainbow which means that the lights partially reflected, refracted once and then if you have a second, then direction would be different obviously. It will still go into your eye from some droplet but again the red will appear in still another case. So one red light you will see as single reflection from inside the water droplet but if you have double reflection some other droplet will produce from the double reflection red light and you will see it in another place. So this is very important. It explains actually why you can see a rainbow concentric to each other. We will talk about why it's concentric too. What else? I think that basically explains why you have different colors in different places on the sky. So now obviously you understand there is nothing material except the water droplets in the sky and what you see as red or white light is a result of partial reflection, partial refraction of the sunlight from the water droplets. Now let's see now why do we have this circular shape of the rainbow. Okay, this is slightly different picture and again let me start from a simpler case whenever you have this is the sun and this is observer. Now obviously we need certain angle at which I see after the refraction, refraction whatever I see this is direction where I am getting the red light from some droplet. Now where are different droplets of water which are in exactly the same position relative to parallel ray of lights and an observer which give me exactly the same angle. Well, this is a sphere, right? So my point is that if you will have a circle of the same circle of certain radius now this is basically a cone if you wish. Now all these droplets which are here on this circle they all relatively to the observer are in exactly the same position because the parallel lights from the sun comes down all of them have the same angle so this angle between my vertical well we consider sun is on the top so between the vertical and every point on this circle this angle is exactly the same. So whatever happens here with this particular water droplets happens here and if the light from here comes here then the light from here also comes here and from there comes because they are all little spheres and they are absolutely symmetrical relative to this they are circularly symmetrical relative to the axis, to the vertical axis. So it's very important to understand that every one of these water droplets is in exactly the same position relative to sun and observer as any other. They are all equivalent which means if I see the red light from here I see the red light from here. So all the places in the space in the three-dimensional space where all the droplets produce the same red light or green or violet doesn't matter which color which comes to my eye. They are all on this giant circle with this angle being whatever like 40 degree, 42 degree doesn't really matter but some kind of a relatively narrow range of degrees. So these are all red. Now we were talking that the let's say violet I should really have from a neighboring let's say from here. So this is red and violet I will get from this water droplet. But again if I see from this I'm seeing from the same kind of circle of certain radius equal to the same value as this one and I will see all these droplets which are in the second circle concentric obviously to the first because it's all symmetrical relative to the axis. So all these droplets are in exactly the same position as this one which means that all these droplets which from perspective of observer are producing the violet light are on the concentric circle. So my point is that all the water droplets which are on a circle which is in the plane perpendicular to the direction to the sun and on the same obviously radius it's a circle with a center on the axis of symmetry they all produce the same light the same color of light so that's why we see reds that's why we see violets that's why we see whatever else green in certain order the order obviously depends on the wavelengths so from red to orange to whatever I don't remember yellow, green, blue etc. Okay, but why do we see only half a circle and not even half sometimes even a quarter well that's very simple actually it all depends on the position between us and the sun so if we stand on the ground this is the ground this is observer and sun is somewhere here now these circles which I'm talking about these are circles of water droplets so first of all there must be water droplets somewhere they may be here or they may be here but in any case if I see a circle which is perpendicular to this direction between sun and observer then the circle would be like this but I'm on the ground so I cannot see this piece obviously right so that's why I see only this piece and it all depends on the direction to sun again these droplets which produce the same color are on a circle which is in the plane perpendicular to this direction in the center lying on this line so that's why from the earth we see only maximum which we can see is half but what if the cloud is not there well then you don't see this and you don't see this you might see actually one piece and another piece now if the cloud of droplets is here then again it would be something like this circle and we will see this piece of rainbow now there are some pictures of the rainbow from the airplane now from the airplane now this is the ground this is airplane and this is sun let's say and let's say this is some kind of a cloud of water droplets then this is direction so you might see something like this so you might see the rainbow in different direction instead of this you might see it this way or if you have sufficient amount of rainbow of droplets you will see the rainbow for a full circle so sometimes you can't see the full circle rainbow it all depends on where are you where is the observer etc but obviously full circle can be only from the air because if you are in the ground then horizon obviously cuts the rainbow in both sides well that's probably about it I do suggest you to read the notes for this lecture because it has nicer pictures and also if there are certain exams which will be attached to the whole pot now this whole pot actually belongs to phenomena of light so at the end I will probably put some exam it's not ready yet but I will put it there so I suggest you to take exams it's very important actually to solve problems I think it's... you see most of the knowledge let's say about mass whatever is in this particular course mass routines or any other course you probably don't need it in your life the purpose of this education is just to develop your mind and solving problems is actually the best tool to develop your mind because the problems you will have to solve in your life are numerous and the skill of analyzing the situation and producing certain solution is very important for everything else in your life so mass is good as a tool I mean as much as you go to gym to basically increase your stamina, strength and something like this you don't really... I don't know... using the track for instance in the gym you don't use exactly the same track but you have to run sometimes you don't lift weights per se I mean there are some jobs where you have to lift weights that it's not such an often thing to do but you do lift weights just to develop your muscles so that's exactly what mass for your mind is it's what lifting weights and using the track for your muscles that's what mass and physics are for your mind but physics also has another aspect of this it's always interesting to know things about why things do happen around us it helps okay, that's it thank you very much and good luck


Thanks for joining me today. We're here to talk about volume, and specifically volume of a box. So remember what volume is. Volume is a numerical measurement of how much stuff we could fit inside of a box. So the idea here is that suppose all of you were to start with an eight and a half by 11 inch piece of paper. Now we're gonna make you think about this because you are older. You're not going to actually make a box yourself. We're gonna make you think through what would happen. So imagine you had a piece of paper, eight and a half by 11 inches, and we had you cut out from the corners different sized squares. And those squares could be really teeny, tiny, and only half an inch on the side, up to maybe four inches on a side, or maybe three and a half, okay? So we're gonna think about what would happen if we did that. Now I made some boxes just as visual aids for you. So the first box I made, I took an eight and a half by 11 inch piece of paper, and I cut out the square. These I did, I think we're an inch and a half on a side. So you can see where all the corners are cut out, and then I just folded it up to make my box. And you can see this one's a little shallow, not too tall, but the base is pretty big. All right, then I made another box. The other box I made, I made by taking squares that were three and a half inches on a side. So when I did that, this is what it looked like, and then I folded it up. And you can see how this box is much taller, but the base is a lot smaller compared to the last one I did. So I also have a computer animation that will show them side by side for you. All right, so this first one, the blue one, this one looks like maybe it was a box that was made by cutting out a teeny tiny square that was just half an inch on a side. And you can see how it's really shallow, kind of like a really shallow tray. The green one that's next, that one maybe was like an inch and a half, maybe almost the size I did. And then the yellow one you can see is definitely the tallest of all of them. Maybe that was a square that was three inches on a side or two and a half or something like that. But when you compare them side by side, you can see how different they look, even though all of them started out from the same size piece of paper. So what we're going to start investigating is, okay, so suppose we did cut out these squares of different sizes. What would be the dimensions, the length, the width, and the height of the box that got created? All right, so you should have on your handout a table that we're going to fill out now. So if I go to the table, and we'll start thinking through this together, but then I'm going to have you do it yourself. So I'll start you out. So suppose we started with an eight and a half by 11 inch piece of paper, and we were to cut out a square from each corner that was half an inch on a side. All right, so if you envision that, remember what happened when I made my own boxes. The height of the box comes from whatever the size of the square was. So in this case, since the square I cut out was only half an inch on a side, the height of my box is going to be half an inch. And all the heights are going to be like that. The height is always going to be the same as whatever the size of the square was you cut out. That leaves the length and the width. That's the part we have to think through. So imagine that the length is 11 inches long, and from each end we take off half an inch. That leaves 10 inches left over for our length. Now let's do the width. The width, remember, of the paper was eight and a half inches long. And from each end of that width, we take off half an inch. That leaves us with seven and a half inches for the width.  So now suppose we cut out a square that was one inch on a side. When we turn up the sides to create our box, that box ends up being one inch tall. So the length, remember, started out being 11 inches, and from each end of that length, we cut off one inch. That leaves nine inches remaining for our length. And the same thing for the width. The width, remember, started out as eight and a half inches wide. We take off an inch from each end. That leaves six and a half inches, right? So hopefully you've discovered the pattern. I'm going to give you a few minutes to get the rest of the table filled out. And then you can come back to me and we'll make sure everyone got the right answers. So let's see how you did. So the next one would be one and a half inches tall for a box in which the square you cut out was one and a half inches on a side. The length would be eight, and the width, five and a half. I'm just using decimals because since we are going to be doing this in our calculator later, I thought it would just be a little bit easier to do decimals. The next one would be a height of two. So when we figure out the length, that would be seven inches and the width, four and a half. The next box would have a height of two and a half inches, making the length six and the width, three and a half. The next box would be three inches high. It would have a length of five inches and a width of two and a half inches. Next we'd have a box that was three and a half inches high. That's the pink one I had made. The length was four and the width of the bottom was one and a half inches. And then finally the tallest box that we could have would be one that's four inches high. The length becomes three of the base and the width of the base is just half an inch. So I'm sure you noticed some patterns to the numbers here and what we're going to calculate next would be the volume.  So take a few minutes to calculate the volumes of all these boxes we would be creating and then we'll come back and compare answers. All right, so the first box, the one that was created by cutting out a square, half an inch on the side, that should have a volume of 37 and a half when you calculated it. The next one, the one that was created by cutting out a square that's one inch on the side would be 58 and a half. The next one should be 66 followed by 63. That's the box where the square you cut out was two inches on the side. Then 52.5, 37.5, 21 and six. Interesting that the tallest box has actually the smallest volume. So what we want to do is see, well exactly what kind of pattern do we have here. So what we're going to do is, in our graphing calculators, we're going to graph the data and the points we're going to plot in a scatter plot are going to be the X coordinates as the height of the box. Also you can think of it in terms of the sides of the square you cut out. And then we're going to go ahead and graph the data that we cut out and the Y coordinate is going to be the volume. So we'll talk about how to set that up in your calculator, how to create the scatter plot, and then we're going to take it a step further and actually use the graphing calculator functions to come up with what we call a regression equation that will model the path that you'll notice these points create. All right, so let me get my calculator and we'll go ahead and set up our graph. So on your calculator in the second row, if you hit the stat button, you should have a menu that looks like this and we want to edit because we want to enter the points. So we can just enter them all in one list. Under list one, we're going to put the height of the box and under list two, we're going to have the volume. So you can just type in the number and hit enter to get it in there. All right, once you have your Xs in, your heights of the box, just use your right arrow and that should take you to the top of list two. And now we're going to enter in all the volumes that corresponded to these heights. So when the size of the square, also the height of the box was only half an inch, remember our volume was 37.5 and we're just going to enter them down one by one. So when you're done, you should have eight points. All right, so now the date is in the calculator, but now we have to set up the graph. So the way in which we do that, if you hit the second button on your calculator, then Y equals, we need to tell the calculator to set up a scatter plot for us. So we're just going to do it in plot one. So if you just hit enter on plot one, you'll want to make sure that plot one is turned on. So you'll notice right now it's blinking on on. So just hit enter. And you'll notice the next line down, we have six different graphs that the calculator will make for us. And we want that very first one, the one that you see mine is blinking on right now. That's a scatter plot. All the other graphs that you see there, you'll learn about those in other math classes. The X list, we want that as L1, because that's where we put all our X coordinates. And yours should be defaulted to this right now. Y list we want is L2. And down on the bottom, you can decide for yourself what type of mark you would like your points to look like. I usually like the first one. You can pick whatever you'd like. All right, once you have that set up, simply hit Y equals for me. And what you'll want to double check, make sure you don't have any equations there under your Y1 and maybe kind of scroll down just to make sure there's none hiding down there. Because if we did, that could screw up our graph. So the easiest way maybe to get this graph, if you hit the zoom button and go down to it's number nine, you'll notice it says zoom stat. That's a really great one any time you've entered the data yourself. Zoom stat will decide a really nice window for you. So just hit enter on that one. And hopefully you get a graph that looks like this. All right, and what this is, this is a graph of all those points we just determined. Now what a lot of people find interesting, when they do a project like this, they think that they're gonna just keep getting a box that's of bigger, bigger and bigger volume. Well, when you look at the points though, what really happens is there is a maximum volume. If you hit trace on your calculator, you'll be able to jump from point to point. So right now you'll notice the little blinking spider. We actually do call it a spider. Right now it's sitting on that box that was half an inch high and had the volume of 37.5.  It looks like it's that third one, the box that was one and a half inches high and had a volume of 66. That looks to actually be the biggest. And it really just goes down from there. So what happens is, even though you might expect that the volume could just simply get bigger and bigger and bigger, that's not what happens at all. There's actually a maximum volume that you're going to top out at. So the next thing we can do is, okay, well what if we wanted to come up with an equation that would maybe allow us to figure out, well what if we did a box that was one and three quarter inches high? You know, how could we figure out what the volume would be for that? Well, the calculator will do that for us as well. Go across the top to calc. Now there's several different options here. These are all different types of regression to create equations, many of which you'll learn about in the future. The one we want is the one that says on number six, cubic regression. That's because, and you will find out later on once you've had algebra, that the equation that would model these points is a cubic equation. So bring that up and just hit enter on your calculator so you should be looking at this. And we want to take that equation and put it under y equals because we want to be able to see it on our scatterplot. So next to where it says cubic regression, hit vars. It's a button on your calculator. It says var s. Go across the top to y vars. And the first option for function. And you'll notice there there's all your y equal two options. So we just want to put it in y one. And then just hit enter after that. And this is the equation that would model those scatterplot points. It's a cubic equation, as you can see from the x cubed variable in the equation. So now go ahead and hit the graph button. And you can see how nicely that curve goes right through those points. So what this allows us to do, now that we have an equation and a curve, we can ask ourselves a whole lot of other questions that we couldn't really just do from the numerical data. So for example, what if we wanted to know the volume of the box if the square we had cut out was maybe two and a quarter inches long? So remember what that means is the height of the box would be two and a quarter inches. So to do that on your calculator, do second trace and you should see a menu like this. The first one is value. That's the one we want, so just hit enter. And next to where it says x equals, let's do 2.25. And hit enter. And you can see the cursor go right to where the curve is, up there sort of in the middle of the screen. And you'll notice that it says y equals 58.5. What that tells us is that when the size of the square that you cut out was two and a quarter inches big, the volume of the box ends up being 58 and a half cubic inches. And you can do this for any x value you want. Let's see, let's make up another one. How about four, let's do 3.75. And hit enter. And there you can see it down on the lower right, the volume would end up being 13.125 cubic inches. Now another thing we can do is what if we wanted a box that was 40 cubic inches big and we wanted to figure out kind of going backwards how big the square would have to be in order to give us a box of that volume. So we can easily do that on the calculator as well. If you hit y equals again, you'll notice there that long equation, that's the regression equation that the calculator figured out for us. So use your down arrow and go down to y2. And in there, type in 40, because that's how big the volume we want to be. Now just hit graph, and you can see that there's two places that that y equals 40 line intersects with the regression curve. What that tells us is that there's two different ways we can come up with a box that has a volume of 40 cubic inches. So let's find the first intersection point. If you hit trace, right now the blinking spider is sitting on the first of the scatter plot point. So just hit your up arrow and you'll notice that the spider jumps to one of the curves. Now use your left arrow and we'll go find that intersection point over there on the left. So all you need to be is close to it. Your numbers might not match up with mine. Exactly, that's okay. So once you're kind of close to the intersection point, do second trace, and we're going to go down to intersect. Hit enter, and it's going to ask you what two curves you want to find the intersection of. You'll notice at the top of your calculator screen, right now it's telling us the spider is sitting on the y1 curve. So hit enter, now it's jumped to the y2 curve. So hit enter again, and then enter one more time. So what this tells us is that one way we could come up with a box that has a volume of 40 cubic inches is if the side we cut out for the square was about .545 inches big. But there's another option because there's a second intersection point. So hit the trace button again. You'll have to use your up arrow to jump the spider back to the curve. And let's go over to the right and find the other intersection point. And again, you just have to be close to it. The decimals you have for your x value might not be the same as mine. Do second trace down to intersect again. And once again, it's going to ask you what two curves you want the intersection of. So just hit enter through those. And you should find that the second option for getting a box that has a volume of 40 cubic inches is about 2.922 inches on a side. So this is a little introduction as to how you can use your calculator features to really investigate different things and different characteristics about not only scatter plots and quadratic equations or other types of regression that you're going to learn later on. But you get to play with different things. And in this case, we investigated what effect different squares that we cut out from corners of a set size piece of paper are going to have on the volume. So later on, as you move on in mathematics, you'll learn how to take those equations and actually find the maximum rate from the equation. So thanks for joining me today. And hopefully I'll see you later when you get to those other levels of math classes.