Well, thank you so much. And it looks to me like a significant number of you were at my last talk, which is really great, because I'm kind of going to enter in with the assumption that we have that foundation and only do a little bit of kind of review and reinforcement. And so you can help me out. I encourage you to ask questions for Claire and for what I think of as grappling, right? Grappling to understand what I'm saying. We'll hold the kind of don't you think that this is the answer versus this is the answer. That kind of stuff will hold to the end. What I want us to do in the first part is to just do the best we can to understand what I'm saying. And of course, please ask questions, because I can forget how conversant and comfortable I am with these kind of topics, right? And I would say that racism is, if not, arguably the most charged and sensitive topic in our society. It's uncomfortable to talk about. It brings up a lot of feelings for people. I hope I bring up feelings for you, because if I keep you comfortable through our two hours together, then I can do a good job, because I just reinforce the status quo, which is overall comfortable for white people. And I want to interrupt that. And I hope that if you do find yourself feeling defensive that you can use that in a couple of new ways. You can use that to reject what I'm saying, right? And then just put it on me. I put defensive there for she's wrong. But there's no learning or growth for you in that. And you're just going to kind of come out of this room and just say, well, you're welcome. So rather than use defensiveness or emotion reactions as doors out, use them as doors in, be excited. Oh, OK, this is totally challenging me. I don't like that at all. Why? What can that help me uncover about the way I make meaning of race? Because there's so much depth under the surface. We live in a society that tells us race really has no meaning. It's really nothing. Focusing on race is the problem. We're post-racial, et cetera. And yet, by every measure, we have racial inequity. So this race has no meaning. This open-mindedness, all of this, has not challenged racism. It's not working. Or we could say it is working if what you want to do is hold racial inequity in place. And so try to move below the surface and get a touch with under there. Because not only does this niceness kind of post-racial attitude not work, but it's sitting on top. It's pretty shallow, but right under the surface is a lot of emotions. This is also part of what's so confusing about race. So many of us claim to be open and to see everybody the same, but yet it doesn't take very much to get us angry and upset. And I will just tell you that I've gotten some feedback that a couple of people that were at my talk, what they heard me say, what they took away, is that I was stating white people are bad. And I want to be really clear. I think racism is bad. I think we need to take responsibility. I think white people are the problem. In many, many ways, white people uphold the system, but often unintentionally. But it's not an issue of good or bad. That is not moving us forward, right? So please, if that's what you heard me say, try to challenge that within yourself because that's not what I'm saying. And actually, I have an image that I'll show you that I call the good-bad binary, that I think sets up that kind of defensiveness. Oh, okay, what did I do wrong there? So we are actually gonna start with the presumption that racism exists. So I don't tend to prove racism exists, right? I don't take the time if it exists. Okay, trust me, by every measure, people of color have an equity in the United States. And to be honest, there's a hierarchy. I don't want to say some groups experience more or less racism than others, but blacks or African-Americans are consistently at the bottom of every measure, right? And Latinos and Asians, actually, I would probably put Native Americans part of the way the impression plays out for Native Americans as they're using that on the chart at all. So a history of invisibility, right? So there's hierarchy within this broad category of people of color. And still, vast disparity, right? So we're gonna start from that presumption. And one of the challenges at trying to address this, and why hasn't this changed? I imagine every single person's room is against racism. Absolutely would never want to collude with it. And yet, it hasn't changed, right? We're actually almost back to pre-Brown versus Board of Education levels of school segregation in the U.S. And it was Brown versus Board of Education. And it breaks my heart that this generation doesn't know what that is, right? That's not your fault, but that's because teachers are not teaching that. So anybody, Brown versus Board? Yeah. De-segregation of public schools. Yes, so it was the legal page that basically, up until Brown versus Board, the claim was separate but equal. It's okay for a separate as long as we're equal, right? But of course, we weren't equal, right? We knew that. But what Brown said is that separate is inherently unequal. And then it made it illegal to not allow people to go to school together based on race, right? And that supposedly desegregated schools, yeah. Yeah, but right now, it's still sitting in the, in the way schools are still segregated. Yes. If you are, the neighborhood has to take whatever and then your methodology is still segregated. Yes. We need the school based on every reason. Yes. That's kind of the point I'm trying to say, right? Is that all of these unopposed civil rights changes have not resulted in changing in that way, okay? So one of the first challenges is that most of us don't know what racism is. Most of us use the terms racism, prejudice, discrimination interchangeably. And they're not the same thing. So that's our first challenge, right? We try to have a conversation. We're not even using the same language. And I will just say that mainstream discourse, mainstream kind of narratives are invested in us and not understanding this because that maintains the system. So prejudice is prejudgment. Every human being has prejudice towards other kinds of human beings. It's not humanly possible not to absorb ideas about groups to which you don't belong, right? We all have prejudice and we all act on our prejudice whether aware of it or not, right? The way we see the world will inform the way we respond to the world, right? And so our prejudice does come out through discrimination. And it can be, oh, here's a great example. If you give people an online course and they believe the professor is a male versus a female, they will evaluate the professor differently. So if they believe the professor is male, they'll get better evaluations, right? And if you believe it's female, they'll show you worse evaluations, right? It's not conscious. But there's no way to avoid absorbing ideas and attitudes that position some of us as better than others, okay? So everybody has it, everybody does it. But when we get into oppression, we're vacuuming a group's collective prejudice with control of the whole system. Now one group controls everything and they can embed their prejudice into the very fabric and foundation of the society, okay? And that transforms it. It's not dependent anymore on individual players. It's not dependent on intentions. It's not dependent on your self image. The system will reproduce the inequality, kind of the default will be, it'll naturally happen unless you consciously interrupt it, okay? So it's a system that works on all levels and results in an unequal distribution between white people and people of color overall with whites as the beneficiaries. There is no such thing as reverse racism. There's no such thing as reverse in any form of oppression because we're talking about, when we use isms, we're talking about systems of power and they're not fluid, right? The same groups who have controlled all institutions continue to control them. So the group that's oppressed just simply isn't in the position to oppress the other group, okay? So we can just drop. I'm only with this easy, but I can just tell you that we'll try, right? Drop that concept of reverse discrimination, of reverse racism. Everybody's prejudice, we don't need to put reverse in front of that, everybody's prejudice. People of color can have racial prejudice against me, but at the group level, they cannot oppress me. And so we have got to reserve some language so that we can acknowledge the difference between person prejudice and institutional power. And the example I used was in the last talk was when women got the right to vote. Only men could give us the right to vote. Only men could take away our right to vote. We couldn't do that because we didn't control the institutions and of course we still don't. Okay, got that? So I like this metaphor of birdcage because you have to understand that oppression is multifaceted, it's really hard to get past the sense of she's saying I'm bad or I do this or it's intentional, right? It's happening on every level. And so we look at all of these bars, right? If we put our face right up close and we take a really myopic or a micro view, we're not gonna see this cage at all. But if we step back and we look at the whole system, we begin to see why we're gonna be able to predict this bird is gonna have a very difficult time flying away. And I know if you were there, I used these slides last time.  Those are just some examples of all of the barriers to people of color that white people don't face collectively in this society. So let me just not make an assumption that you all know microaggressions. Those are those everyday little slights. Has anybody here that is Asian heritage ever had a white person ask you where you're really from? Okay, right? That's a microaggression. I think I'm just being friendly. I have no idea, but the message to you is you'll always be an outsider, right? That's a microaggression, it's a little mix everyday. Ideology, what's ideology? I've got a lot of professors in the community. Any student wanna take a crack at what ideology is? It's a really cool word to know. I love this word. Ideology are the big dominant beliefs that are reinforced throughout society. And so, consistently, then it makes it very difficult to avoid believing it. You don't even know the question because it's reinforced, right? So we're all unique individuals. Democracy is the greatest system on earth. Capitalism is the greatest system on earth. Prior to the Occupy Wall Street movement, you just could not question capitalism, right? That helped make a little space, right? Where now you can question capitalism. Prior to that, it was like, weren't it communist then, right? Ideology, these big beliefs that are reinforced and makes it difficult to question. So we're gonna look at some of those ideologies today that help prop up this cage, okay? So I think the number one most effective adaptation to racism, to the challenges of the civil rights movement, I would say, is this idea that a racist is bad.  I just said you were immoral.  This is the number one reason why it's so hard to talk in a group about racism is people get, you know, I wanna say people, white people get really defensive because we've been taught that to be a good person and to be participant in racism, that those things are mutually exclusive and we couldn't be a good person and be a part of the system. We also taught that we're all unique individuals and that I can simply decide to be unaffected by the society around me and see the ideologies that set that up. So we know how to fill this in.  Younger generation, you guys aren't racist. Southern, usually, right? This is our classic stereotype of a racist, right? So if you're not a racist, you're nice, you're open-minded, you don't see color, you treat everybody the same, right? So the story goes. You're educated and progressive and open-minded and good Lord, you go to the Evergreen State College. How do you possibly, young, young? All right, now some people heard me last time and they thought what I was saying is this is what we want and I'm saying this is wrong. This is what we're taught but it's wrong, okay? It just sets us up not to be able to understand how it actually works and it makes us defensive and it makes us, instead of looking within ourselves and examining the water and the messages, it causes us to reject and fight and push away. Have you, has anybody in this room ever had a discussion on racism and had it go really smoothly? All right, yeah. I have the melting pot. So I live in the South and being a person that is in the South, I live in this. I'm a brother that's been murdering my babysitter and her boyfriend. And when I'm in school and I'm hearing that we're all supposed to love each other regardless of what color we are, I ask the question then why are there white men inside the sheets and covering their face with pillowcases and killing people of color? I didn't understand that. So I got expelled from school for three weeks because I spoke out. But I needed to know that question and I still don't have the answer to that. Yeah. And so when I see this, it's explained to me why people, that's the way they actually looked at us up and it never was the proper thing to when you're teaching a child history. And in fact, in my time they had, they were teaching you about the black culture and they were teaching about Indian cultures and the different cultures of the world. So it did make any sense to me we're supposed to love each other, why would you kill each other? Right. I still don't understand it today. Yeah. And you can see that, okay Frederick Douglass's famous quote, power conceives nothing without a struggle, it never has and it never will. So the civil rights movement challenged this racism. And so one of the ways the system adapted and I think it's a poorly adapted application is this, you make racism so bad, no one wants to talk about it, no one wants to look at it, no one will be honest. Please just get rid of this idea. That's not my fault, I didn't choose it. I've been conditioned into it, I need to just start from that and go. All right, so all of this leads to these dominant narratives, ideologies. I just had a student write to me and I gave a talk about that at every. And the student caller and she said, what do I say to my white roommates that keep telling me they were taught to treat everyone equally? Right, and just try to imagine what it's like to be a person of color and be, here's these two white people that are arguing with you about a very vulnerable and sensitive experience and being defensive and basically just invalidating your life, right? And I find that heartbreaking and all of this leads to us behaving that way, right? As white people, often in these conversations. So let's look at some of the adaptations since civil rights, right? Here it is, right? I have this on here before I got that email from that student, right? This is a classic. So what I need you to understand is that you were not taught to treat everyone the same. It isn't humanly possible. You could be told, I can tell you that. I can tell you, you need to treat everyone the same. You can't do it. And there's no training into it, okay?  And human beings are not objective. We see the world through the cultural lenses we've been taught to see it through. And we receive messages 24 seven that influence how we see each other, okay? Thank you. Robin, could you talk a little bit about your example earlier that you were talking to me about if I was visually impaired? Okay, so first of all, we just simply don't like that. I'm looking at you or I actually have to be careful because there's all these matter judgments. You're closer to my age than something else. So I noticed that. I noticed that you present as a woman. I noticed that you look African-American. That's what I'm assuming about you. You look like your able body. Looks like he has a disability. I'm aware of all of this. And as we're interacting, it's filtering your responses. There's no way I see you in just some universal thing that's not gonna affect the way I talk to you, right? The assumptions I'm making about you. Somebody put it like this. It's like we have these barcodes in the back of our neck when we're born, all of our group assignments. And then we know how to read the barcodes. And then we're taught what it means that this person has this barcode. So, and of course you don't want to treat everyone the same because people have different needs. So, because I can see 12 point font, should I give all my students 12 point font when I have a sight impaired student?  I don't want to treat that person the same. Because you offered me 16, I'm kind of blind. Thank you. Yes, I would. I see people as individuals. I don't care if you're pink, purple, and polka dot it. Anybody ever hear that? Okay, promise me you'll never say it again. Why do I say promise me you'll never say I don't care if you're pink, purple, or polka dot it? Because even then you're denied. People don't come in those colors, it's so demeaning. And race is real in the sense of what it means in our society and so let's be real about it and don't just minimize me and say I don't care.   And you don't see. Here's the other thing is this is what you just have to trust me, there's so much research on this and you might think you see everybody as a unique person and you just don't. And this can be scientifically proven. All of this doesn't have meaning. These are my, that's students roommates, right? Everyone struggles, but if you work hard, does anybody know what this is called? There's an ideology that leads to this, are you figured? Good, I gotta give someone else a chance. The bootstrap, there's the book. Well the bootstrap myth, but there's another word, a fancy word, meritocracy, merit. That we have what we have because we worked for it and we earned it and we earned it through our merit. Do you think Bill Gates' son could work harder than you guys? How about Casey Apley, he's in a new movie, do you think he has anything to do with his brother? Right? All right, so this is an ideology, right? That's hard to question. My parents weren't racist, that's why I'm not racist. Do you remember anybody say that? Or my parents were racist, that's why I'm not racist. Cause it doesn't really matter what comes first, what comes second has to be I'm not racist because of the good, bad binary, right? Someone who tells me most of these things, this, this, this, is telling me that they don't understand socialization and they don't understand, I don't know why I just think our parents are the soul, are your parents the soul influence on you? Does music or movies influence you?  And then at what point did it stop and you're no longer influenced by anything? It never stops, it's ongoing, right? That's how come I know how to use my phone. We didn't have those, right, I figured it out, I kept it up, what else? So and so just happened to be black, have you ever heard that? Race has nothing to do with it, regardless of race, I hear that all the time and that's another one I'd actually take out if you look at it, yes, cause you just can't say it.  You might not know what it had to do with it, but it has something to do with it.  All right, so you and I, you know we're having a conflict and your voice starts going up, you think that I'm gonna be reacting different to you because you're a man than I would if a woman's voice is going up? Of course I am, right? So we have a conflict, the way we talk, the words we say, our bodies, how we use them, we're gonna be reading each other and whether I can map out exactly what gender had to do with it. Gender is in the way we're gonna have a conflict. And deeply socialized into gender roles, right? And we bring our histories, right? There's a history of harm between men and women, that's in the background, right? All of this, even the way we hold our bodies and how much space we take up. And we're gonna be reading those things as we fight. All right, now, if we're sophisticated Northwest liberals, we might not say those things, right? We're hippin' up, we know color blood's not in anymore, I hope you know that. So here's what we'll say, right? We're gonna be color blood, we're gonna do the opposite. We've got so many friends of color. All right, so what I'm gonna say, I work in a very diverse environment. I have people of color in my family. My second cousin married an Asian man. That's good. I'm just gonna make fun of you a little bit. I think it's worth being able to laugh at this stuff and maybe if we've kind of recognized it in ourselves. Someone who tells you this, how have you heard a white person say some version of that in a discussion of racism? A lot of hands are going off. So just notice, look how common it is, right? And as a sociologist, you wanna look at patterns. Patterns are really helpful. Not, when something's a pattern, it doesn't mean that it's true. It just means we've been conditioned to kind of say those things, right? So when a white person says some version of these things in a discussion of racism, they're giving you evidence, right? What in their mind are they giving you their evidence of? Here's my evidence that... I'm not racist. I'm not racist, right? Okay. If this is my evidence, how am I defining racism? What's racism to me that that would seem to cover me? That people can't be around each other. Diverse. Absolutely, conscious, dislike, intolerance, hatred. I couldn't bear the sight. Three cubes pulled down. I'm a person to cover. Or there couldn't possibly be any kind of racial dynamic between me and my intimate partner. This idea that these things disappear.  Oh, thank you. Oh, good. Have you ever heard that one? Okay, guess not.  So, you know, you saw people of color. That's why you're not racist, right? I do want you to see the ridiculousness, right? Because we rarely, rarely think deeply about this stuff. That's why I have it on a doc because it's so surface and superficial. And I want you to be able to think more critically about what are they really saying? What kind of framework are they drawing from, right? So then I know where to go with them. Do we say, this is real popular in Seattle. I live in the most expressive country in the US, Columbia City, which by the way is no longer here. Very gentrified. East of New York. My children are so much more open. I really do think that, but you guys are called millennials, are you? What is this 18 to 19 to 20 year old generation called? Z. Generation Z? Sorry, what is it? The Z. Yeah, Z.  And there's this idea that this young generation is open. And I'm gonna tell you, I don't see it. I see segregation, I see us not getting educated about race and racism. And there are this idea that children today are just simply, I don't know where you can be open because schools are getting more segregated, neighborhoods are getting more segregated, the Academy Awards, movie shape, all of our understanding about everybody, and the bass. Somebody just made a great parallel with us. Steve McQueen, who directed 12 Years of Slay. He talked about that when MTV first came out, it was 100% white music and then after 11 p.m. they played black music from action artists. Can you imagine that? And can you imagine if only white music ever, he were ever exposed to, what you would be missing? Think about movies. Not one single person of color was nominated for a award in pretty much any category. It is a deep apartheid, basically, in who gets to produce all of our images. So young people today are not less. They're more this. They're more, hey, it doesn't mean anything in my all white neighborhood, in my all white school. That's what it looks like. And by the way, by age three and four research shows, all children know that it's better to be white. We're gonna say that, I hope you understand. I'm not saying that it's actually truly better, but that the message of our society is that it's better to be white. And all children receive it. And if you're the parent of children of color, you actually have to take the time to try to overcome that message. In the same way that I wouldn't have to tell my son you could be anything, but I need to tell my daughter if you could do it, right? I have to tell her, because everything else is telling her that she's not. Okay, so all children get the message. So if we go under the surface of that dog, what we see that props up, you know, new racism, but what props up so much racial inequality where at the same time individually, most white people feel like they're kind of outside of any of this, is the good men binary. This idea that we're all unique individuals and I can simply decide to have been unaffected by all my conditioning. This idea that we're all God's children, on some level, of course we are, right? But we don't live on that spiritual level, right? We live in the physical world where it very, very much matters, right? And so just kind of insisting that it's focusing on racism and inviting us is actually just saying the answer to the problem is to pretend it doesn't exist and never talk about it. That's what that does. And we can see where that went with domestic violence, right? Right?  What kind of problem would we agree that the way to address is to never talk about it and pretend it doesn't exist? Internalized superiority, you can't, this is gonna be a hard one, but white people hang in there with me. You can't grow up in this society and not internalize a sense of being better than people of color. Whether you're aware of it or not, you just can't avoid that message. It's so constant and I spend a lot of time in my last presentation showing you those messages. I'm kind of jumping over that here. It's often unconscious. I don't want those messages, but I could never be lax about it because every time I walk out the door, every advertising, every movie, every all white environment I'm in, I'm constantly getting that message, right? And then segregation. Whereas on this campus, this is a very racially diverse campus. I believe not, of course, not in your faculty administration because that's kind of how it goes. But I don't know the south end, but I suspect that everyone in this room could name every neighborhood in the south end and then tell me what its racial makeup is because that's so segregation. This is what we're at the campus, right? Okay, and maybe I should say ideology, ideology. The way we justify and rationalize segregation is in ideology, right? It's natural. It's not actually, it's actually enforced through decades of policies and practices. Segregation isn't national, segregation is enforced in many, many ways. It used to be legal and now it's kind of under the radar but it's still enforced, right? So think about ideology as the way we justify and rationalize inequalities. Yeah. Could you say more about segregation that's distinct from the natural affinity people have for people who look like them? Yes. Which does have the naturalization. Yeah, and I'm not totally sure it's completely natural outside of being conditionative, but I do get that when you are a marginalized group, yes, absolutely, you just kind of want to be with other people that understand you and share your experience, right? And that are not posing on you, that need to behave the way I do need to behave, right? So that kind of affinity to be with your own can be strong and of course that has a very different impact than what I want to be with my own, right? Because I'm in that adult position. I also have to do is look at the distribution of resources and I think it puts the lie to this idea that it's natural that we all just want to be with our own because some groups want to be with their own all the goods and others want to be with their own in the, you know, no healthcare nearby, no grocery stores, no services. I mean, you look at the difference in the way we distribute resources to those places, that's where I kind of go, okay, something else is going on there, right? If they were equal and we were separate, but they're not, we hoard our resources. We love those good white schools, right? They're okay. We don't mind the schools being unequal as long as my kids go to a good school, right? I mean, if we didn't, why would we stand for that? If we didn't, those who control the resources that do this, yeah. Does that help? Yeah, yeah. Could you like, you have a really great concrete example I think in your last presentation about the tent cities and the what? The tent cities for the whole? Well, no, that was our gentrification panel. But on like how the north end, like how the north end and the south end dynamic kind of plays out, could you talk more about like how that type of segregation today? I think it came up where somebody said, well, what about, there's a period often where locations are switching and it looks like integration, but what it really is is now that white people want the cities back, right? We didn't want it before we banned them and we went out to the suburbs, loved those suburbs. Well, now it's not convenient, we don't want to be in the suburbs. So now we're looking back in and pushing people out. So there'll be a little bit of crossover. That's why people are so proud of zip code 98118, right? When the central district was gentrifying. But it's now, it used to be, I don't know the statistics, it's just in the paper, something we're like 90% African-American and now it's like about 10. So white folks know that it's really temporary, that kind of integration and soon it's precisely valuable because it's going up. What's making it go up? White, it's getting whiter. And oftentimes what we're in those periods of cross, we're not actually integrated. We're not supporting those small businesses that are owned by the local people in those communities. We're not building relationships with our neighbors, right? So it used to be legal to literally draw lines on maps and banks could do this and say, you can't give loans in these areas. Yeah, redlining. And so you kind of created ghettos and what we think of as slums. That's not legal anymore, but now we just do it with the good schools, the neighborhood. It has been proven that blacks and Latinos were targeted for the subprime mortgages just before the housing crash. Even when they qualified for better mortgages, they were pushed the really bad ones on them. There's a lot of ways we do it today without getting a pencil out and drawing on the map. Okay, so we can talk about these questions.  Or you're in a position of kind of authority on the campus, right? And you're in charge of the curriculum and the policies and the practices. And how racially diverse is your neighborhood growing up? So think about that. The vast majority of white people grow up in segregation. So the answer for most white people to this question is my neighborhood wasn't racially diverse at all. So we don't grow up near people of color. And we also get messages about where they are and what kind of place it is, right? I mean, this is part of why, is it natural that I just want to be alone or have my whole life I've been warm? Don't go to that, maybe, but that's dangerous, right? Yeah? The color is supposed to be dangerous because I'm racially. So I would like to know that because I'm not Indian and we have that black and we have that Italian, we have that green. I'm very Indian or I'm diverse. So please tell me how am I, because I'm a person considering my white person and I'm black, because I have an inch of black Indian. What makes me famous? It's a deep question, but I would just say, I've been conditioned to see you that way, whether I want to admit it or not. And I project that onto you. And this is, again, this could be measured even if I'm not aware of it, right? But I personally see it. Absolutely, look at Trayvon Mark. He was in a gated white community. But this is the difference between personal prejudice and institutional power. Which group has the power to control who gets what, who gets to go where, and who gets to tell the story. Who gets to write the story about what's safe and what's dangerous? That's the difference. This group is in the position to do that. And we're gonna do it in a way that serves our interests. This is where I want you to challenge. I'm not saying this as if it's, if we can't, we have to understand how all this works. So we can start challenging it, so we'll just keep going. And the next one is to think about when's the first time you had a teacher of the same race as you, or races, if you're multiracial? And how often that happened? And when's the first time you had a teacher of a different race? And the vast majority of white people's answer to this question is, from the time I began, I could even have gone through graduate school and never had a teacher of a different race. And for people of color, the answer is, I don't know if I've ever had a teacher of my own race, or maybe once, or maybe twice, or maybe not, or two college, right? Okay, so again, I'm wanting you to get the difference in how we get socialized. And so those teachers, the teaching force, which by the way is about 92% white nationwide, they answer these questions like most other white people, they grow up in segregated neighborhoods, they only have white teachers. So where do they get their understanding of people of color from terrible sources like movies and TV and reality shows and jokes and comments and warnings? And now they're the position to decide which children are good, which children are smart, which children should be pundit, who's naturally innocent and who's naturally criminal.  I was just watching, I started watching Training Day. How many of you seen Training Day? It's a very popular movie, and I couldn't watch it anymore. You've got your innocent white guy and your bad man. Even when African-Americans are always either cops or criminals, but even when they're cops, they're connected to, kind of, kind, and that's how, all of that, that's what I absorb, and now I'm looking out at this class of children and it's coming out in the way I respond, and again, this is empirically measurable in who gets punished for the same infraction, who gets picked up out of a chair and thrown across a room. All of that, right? And you have a school of prison white women and individually, those white teachers are nice people, they don't mean to be doing it, but they can. This is the problem. We grew up separate, we absorbed these messages and were in these really powerful positions. I showed this to you, I'm gonna show it to you again because I think it's so powerful and also I was thinking about the kind of questions you're asking me. These are the college champion's equity playoffs. These are champions. These are college educated champions. And look at the board, at the end of their round, there's a category not one of them touched. Obviously it was hard, they didn't wanna lose and they didn't feel smart enough to that category and for me that would be astrophysics or something like that. Remember, college educated. This is, this is, just take it in. I don't know how to explain the power of knowing our history but the further we get away from knowing our history the further we get away from being able to address institutional racism. And this is the result of a white teaching force that grew up separate from people of color that was trained, put it this way.  Do you get it? Do you get the weight of that? Trust me, I'm a professor of education, I'm waking up as fast as I can, but we have a crisis. Gotta understand what the problem is. And this is one institution, I'm not even talking about medicine or I'm talking about education. And I'm not even talking about the textbooks, I'm talking about the teachers. Do you see the cage? Do you see where anyone would say racism is a system that reproduces itself and that you've worked for? And that I can't help but be benefiting and participating and colluding if I'm not actively challenging. Yeah, please. So, Robert, when you showed this, I saw it last week, I actually turned to Kelsey and said, these are college educated, and I said to Kelsey, are they college educated? I argue whether or not they're college educated for the very reason that you mentioned. Their education is very limited, they don't know anything about African American history, so are they college educated and who defines what constitutes a college educated? And this is another example of how, who gets to define it? Mike, who gets to define it? Who's gonna get a good job? The ones that got that education, not the ones that didn't get that education. Who are very highly educated and don't know anything about it? Right? So I'm just, yeah, yeah, now thank you. That picture of the person is powerful. I've told you, you've gotta read between the world and me by Tana Heschikos. And then think about this. Okay, so all of this leads to common white patterns. So white folks, try not to distance yourself, right? All of this leads to us being a particular way around these issues, right? Preference and comfort with racial segregation and a lack of a sense of loss. No one who's ever been a role model for me has ever suggested that it would be a loss for me not to know people of color. Most white people don't have friends of color. And they don't see that as a loss. And that's white supremacy. And that's a message I've gotten all my life. And that's what I mean when I say white folks, you gotta look inside here and see what's in there. You can't miss it. Can't miss these messages. And they inform your responses, whether you're aware of it or not. So you need to reveal them so that you can challenge them, right? Lack of understanding about what racism is, seeing ourselves as individuals, not understanding that we bring our group's history with us. History matters. When I'm interacting across race, I represent a lifetime of a century of my group. And I have to be willing to own that rather than go, well, you don't know me. Why would you assume I'd be racist? Why would you assume I wouldn't be? How about I show you I'm not? Well, I can never show you I'm not, but I can show you I'm working on it. All right. Assuming everyone is having my experience, what a welcoming place, high-line community college. I'm not trying to put a high-line down, but that often kind of happens. The most accepting environment.   All right. Lack of racial humility, unwelvingness to listen, lack of authentic interest in the perspectives of people of color, inability to sustain long-term relationships with people of color, believing that we can be exempt from all of this just because we experience another oppression. Like, I grew up poor, I have clear, I don't have privilege, right? Or no, some people of color or took a class or were in the Peace Corps or what? Sorry, that's it. Wanting to jump over the hard personal work and get to solutions, well, okay, okay, you know, just tell me what to do. Yeah, yeah, yeah.  Confusing not agreeing with not understanding. There's a lot of this we just don't understand. You're trying to tell us your experience and why I don't understand it. And so, unfortunately, what we do sometimes is say, if I can't understand it, then it's not what you want. And until you can explain it in a way that I understand it, and you know, we need to just like, I may not ever understand it, it's true. And be willing to not know, which is a great interruption to all this arrogance that this sets up in us. Need to maintain white solidarity, safe base, look good. White solidarity is the unspoken agreement amongst whites that we won't hold each other accountable around our racism. We won't make each other uncomfortable. So that's why at the family dinner, when Uncle Bob says that thing and everybody cringes, but nobody says anything, because we don't want to make Uncle Bob uncomfortable. Let's protect Uncle Bob. I wanted to be aware, Uncle Bob is uncomfortable and five people are in there, integrity. Hilt, which paralyzes or is an excuse for inaction. I feel so bad, making me feel bad. You just want me to feel bad. How am I going to feel bad? Unless it motivates you. I'll take it if it motivates you. Just come on. The best antidote to guilt is actions to be careful. Yeah. So is the guilt arising from the unacknowledged knowing that racism exists in your density and then feeling bad, but not being, where's that coming from? Yeah, we're kind of a funny mix, right? On the one hand, we really don't see this and we're taught not to see this. We actually get punished for seeing this.  We do. And so after a while, we stop seeing it. And we don't really want to see it, right? So here's this, like, we really don't get it. And here's this, we know, we know, we know. We can never admit, because it conflicts with our sense of ourselves as good people. And that makes us crazy making us. That makes us irrational. That makes us, like, if we really don't know, we really do know, we can't admit it. We do feel bad and we never want to hurt you. I mean, I think that's sincere. I would never want to hurt you across race. At the same time, I'm deeply invested in racism in ways I don't even know, because all my life it's been, I don't even know where I'm from. Where I'm actually working against challenging it because it's too many people. We're a mess. Good. Well, peace isn't worth it. Are we not? But you notice that? It's been developed pretty good. Yeah, yeah. Cranker, right? Cranker. Cranker. Cranker. Cranker. Cranker. Cranker. All right. Bensiveness. Do I have another one on here? I mean, we want to focus on our intentions rather than the impact. I can actually, I think I have this on a handout that you're going to get. So, then you can email me for this. So, focus on intentions over impact, right? But I didn't mean to. Right. But I didn't mean to. So, based on what I'm saying, if I didn't mean to hurt you, it doesn't count. That's so sad. Not going on about it. I didn't mean to. All right. So, I called all this white fragility. We're really fragile around this because we live in a very racially insular bubble. I mean, I was valedictorian. I graduated soon after my, I delivered the commencement speech at Seattle University and I had absolutely never in my life had my racial learning challenge. I didn't even know I had racial learning. Until I applied for a job that I wasn't qualified for, but of course I got to be a diversity trainer. And I just thought, I won't qualify for that because I'm a vegetarian. Huh? No. You know what I'm saying? And I thought, that's over. That's what this is and I get this job and I don't, oh my God. Right? People of color are just challenge. Okay. Can't handle it. And we need you to stop and we will do whatever it takes. I'm gonna argue with you. I'm gonna cry. I'm gonna storm out of the room. I'm gonna redraw. I'm gonna avoid you. I need you to stop so I can get back into my comfort zone. Does this make sense? Have you seen this? I want that equilibrium back. So I think it functions as a kind of bullying. I don't make it so miserable but you're just not gonna do that again.  You ever seen any of this?  Has be open and receptive. And I once asked a group, I think I said this in the last episode, so it's so moving for me. I said, what would your daily life be like? You could just tell us when we step in and how this gracious thing we see reflect and try to change. What would your life be like?  I'm serious. This is about high blood pressure. This is about heart disease. Is this how tight it is? I have this kind of color, so can you, what would my life be like? It would be radical. It would be graciously trying to change. That's how hard we are. It's also how easy this is. It's inevitable. You've got blinders you don't know you have to start from there and then be thrilled that someone's willing to take a risk on you. Because most of the time you don't bother, right? Folks that call it room, how many times can you just say, I'm not even going to bother? It's too hard. So if you're going to bother with me, you probably saw something in me that's there. I'm going to take a risk, then she can do it. Then you probably spent hours agonizing, building up here and then processing and then going and trying. And then how I respond is going to really dictate whether we ever have a good relationship again. And if I don't respond well and you stop talking to me unfortunately I'll go, oh, there's no problem at all. She's never said anything. If you have a relationship with a person of color and you're not talking about racism, it's probably not as close as you think it is. If you're white. All right. So let's look at some of the triggers. And a lot of these triggers are challenges to ideology. This is why audiology is such a key concept to other media, right? So suggesting that a white person's view comes from a racial frame of reference. In other words, will you just say that because you're white? We don't like that, white people do not like that. Because you just challenged the objectivity in my whole life, I'm the one that gets to be objective. You are the one that has a chip on your shoulder and play the race card game, right? People of color talking directly about race. Whoa, we don't talk about race, right? People of color choosing not to protect our feelings just kind of calling it like it is. And that challenges my expectations and sends an entitlement to be comfortable. Not gonna like that. People of color not being willing to tell their stories or answer questions. This is, I'm gonna admit it, when I started that diversity contract and we were the trainer trainer and us white, just notice, I wasn't qualified if I didn't understand racism. I wasn't qualified to be a diversity trainer. But rather than feel like I better hide the fact that I'm not qualified, I took great umbrage that people of color wouldn't tell me how racism works. And I actually said, well, how am I supposed to know if you don't tell me, right? Without everything. I mean, can you know any other situation? I now understand that that's not your responsibility. That's for me. Essentially, you're gonna do my work for me. You take all the risks, you do all the hard work, you have the distance of your labor, and I will examine the same thing. A fellow white person not agreeing with you about what happened. That's a challenge to white solidarity. Receiving feedback that what you did had a racist impact. That's a challenge to white people. Suggesting that membership is significant. That that's a challenge to individualism. A acknowledgement that access is unequal. That's a challenge to meritocracy. Being presented with a person of color in a position of leadership, challenge to white authority. And by the way, a person of color is only gonna be in leadership if they keep white people comfortable.  Being presented with information about other racial groups, through, for example, movies. A challenge to white centrality, right? Black history, multiple friends, you have another one? So here's what I wanna do. I wanna give you a chance to talk because I've been talking for a while, but it's afternoon.   And what strategies might you use to counter it, right? How might you build your stamina because it's easier said than done. It's hard to receive feedback, right? But we have to make ourselves ready. If you're a person of color, well, to racial, how do you see white agility manifesting? And what do you wish white people understood? Okay, so at your tables, maybe just open my seat. What is your racial identity? So I'm Robin and white, and then take turns, yeah. Actually, that's a color about a racial identity, so it would be Caucasian. Would that be more ethnically consistent? No, actually, I really deliberately, because race is such a construct, right? So my ethnicity is Italian, but my race is white. And Caucasian actually comes out of the old scientific racism. So they have the like formus, coccyxoid, longloid, negroid. And if we think about it, we don't use those terms anymore, right? They're pretty offensive, and they came out of that early like scientific racism where they measured skulls, and they said, oh yeah, our brains are bigger than yours. So, Caucasian is actually kind of an updated term. I know a lot of people use it, but I would use- It's on the government forum. It's on the government forum. So I would say Latin, not African-American, for the purposes of this discussion. Oh, you know what, whatever your identity is, that's up to you, right? If yours is black or African-American, whatever, you get to decide. You get to name that. All right, have fun, talk. And on that note, I want to thank you. This is my two words about the richest discussions I've had in a long time. I think it's so much.


Welcome to NTI Nightly, I am Genelle Norville, this edition's top stories. St. Lucian's are called upon to maintain COVID-19 protocols as the ban on sale of alcohol is lifted. Donations keep pouring in as part of the national COVID-19 response, telephone and celebrating the island's latest centenarian. As of Friday 8th May 2020, the Government of St. Lucia reinstated legal licenses in St. Lucia for sale of alcoholic beverages. This measure allows for the sale of alcohol by only licensed businesses, from the list of approved businesses that are currently permitted to operate under statutory instrument 56 of 2020, namely supermarkets, minimats, small grocery shops, wholesalers and gas stations. The Substance Abuse Advisory Council Secretariat, concerned about binge drinking, has advised the public to be mindful of substance use and misuse, especially with the highly celebrated Mother's Day on Sunday 10th May. Coordinators at the Substance Abuse Advisory Council Secretariat Charming Hippolyte Emmanuel indicated that the harmful consequences of substance misuse are not only experienced by users but also their family and by extension the community. Persons are encouraged to be mindful of use so that exposure to smoking, alcohol consumption and other substance use can be minimized and if possible eradicated. The harmful consequences of substance use and misuse, including alcohol, pose harm both on one's physical and social health. It creates a means of depleting the existing health resources and also social issues like domestic violence and child maltreatment and abuse. Exposure to substance abuse further places vulnerable groups in a more susceptible position, thus compromising their immune system. The coordinator reminded the public of a popular slogan, be bright, don't light and she urged persons to be mindful that substance use and misuse will further complicate the existing situation. The Department of Health and Wellness encouraged persons to take this opportunity to bond with family and take greater measures to remain safe by following the hygiene guidelines, the use of the 311 number for additional support and services and the other toll-free numbers being circulated on social media. Donations keep pouring in as part of the National COVID-19 Response Telephone. On Friday 8th May, Desert Star Holdings Limited, DSH and the Royals in Lucia Tooth Club made a donation of $212,031. Chief Operating Officer of the Royals in Lucia Tooth Club, Ben Wildon and DSH's Project Director, Qi Chao made the presentation. We're just very glad that we can play a part in helping the government initiative in this effort in containing this coronavirus. It's certainly an extraordinary times, livelihoods affected and as a company we've been here five years now and we are very much a part of the community and we'd just like to play a part in helping the government's effort. I'm new to the island but in just four months I've grown to see her beauty and her incredible attributes both in her people and the island. The Royals St. Lucia Tooth Club looks forward to a great future here and it's a privilege to be here and in a position to help in a small way. Chairman of the COVID-19 Response Telephone Committee and Minister for Tourism Information and Broadcasting, Culture and Creative Industries Hon. Dominic Fede expressed gratitude for the donation, citing that it will go a long way in eating St. Lucia in its fight against COVID-19. We had an outpouring of private sector support which meant that we raised some in the region of about 2.5 million Eastern Caribbean dollars. Our GoFundMe page is still in activation and last time I checked it was over 70,000 US dollars and people are still giving and donating and the crisis has really mobilized and brought out the best of St. Lucia where the big companies, small companies, private individuals, St. Lucia in the diaspora, it's been an incredible outpouring of well wishes and support. Executive Director of the National Community Foundation, NCF Michelle Phillips expressed gratitude for the generosity. On behalf of the eight member committee chaired by Mr. Minister himself, I want to thank everybody who has donated to the National Response Telephone. To date we have collected approximately 1.8 million. As you know when you go into a telephone you get pledges but the proof of the pudding is always in the eating and collection is always the process that actually shows the support and we're doing very well so we want to say thank you. We want to also ask you to continue pledging. The pledging platforms are open. Our GoFundMe pledge platform will close on the 12th of May. You can continue to pledge at Bank of St. Lucia to account number 10451121 and if you're sending a wire transfer you can use the Swift code BOSLLCLC. Again thank you to everybody. Continue to pledge and I just want to say thank you to the frontliners and everybody who has been helping in this fight against COVID. Thank you. Executive Director of the National Community Foundation, Michelle Phillips. Bank of St. Lucia has partnered with the OECS Commission in its efforts to ensure member states are adequately prepared for the adverse effects of COVID-19. We get the details in this report. The details of the financial contribution of Bank of St. Lucia was announced by the OECS Director-General Dr. Didacus Jules. The OECS Commission applauds the contribution of US $40,000 from the Bank of St. Lucia towards the purchase of ventilators. The Director-General issued calls recently for private sector support in the fight against COVID-19 and Bank of St. Lucia through its acting management director Medford Francis responded positively. As a good corporate citizen we felt it was our obligation to make this commitment to the humanitarian effort that is needed at this time. Mr. Francis says the Bank does not only have an obligation to respond to any crisis impacting its clients but also has a responsibility to the people of the OECS. We have to do more to protect our people and hence our support to the acquisition of ventilators for the public health system. It is because we really want to ensure that once we have overcome this virus our workforce is intact and is physically, mentally and emotionally able to undertake the tremendous economic recovery effort that would be required. The OECS Commission has decades of experience in procuring pharmaceutical supplies for member states. This advantage is now helping to fast-track the sourcing of vitally needed medical equipment. We are now in a race against time and global demand to ensure that vital equipment such as testing equipment and reagents, ventilators and personal protective equipment for medical as well as police frontliners are brought in as quickly as we can. The $40,000 donated by Bank of St. Dushan will go towards the purchase of ventilators critically needed in mitigating the impact of the coronavirus in the OECS. From the Government Information Service, Lyssa Joseph reporting. The e-learning approach adopted by the Ministry of Education as a result of the COVID-19 pandemic is taking shape with students, teachers and parents becoming more comfortable with the medium. Paris Anissa Antoine. Due to the profound changes in social interaction and organization caused by the COVID-19 pandemic, the education system has adopted the e-learning approach to ensure the continuation of instruction during the absence of normal classes. Various online learning platforms such as Enmodo and Google Classrooms are currently being utilized to hold virtual classes as well as share information and instruction. Principal of the Kamenreni Memorial School, Sayana Noly George, explained that the flexibility to use various platforms has allowed teachers to use the most suited and convenient platform for their students. The principal gave insight as to what the transition has been like for the parents, teachers and students of the school. The fact that teachers do not feel pressured to do or to engage in a platform that they are not comfortable with, it gave us more leverage to be able to work with our students within whatever context is available. And like I said, it had its challenges. First and foremost, we had to put in a database so that we can contact our parents because most of our information is more or less on paper and it means that we had to transfer to an online database to be able to retrieve our parents email addresses and contact information and to let them know what our plans are as a school in terms of moving forward. And this helps significantly and I must say that is a plus for the whole transition because this is something that we've been wanting to do for a very long time and so having that database, it means that we can correspond with our parents directly. Amanda Jabatis, teacher of the Kamenreni Memorial School, explained the manner in which she utilizes the various platforms on a day-to-day basis to effectively communicate and engage with students. I have Zoom classes at 9 a.m. on weekdays. At these classes I present a lesson in my area of specialization which are mathematics, social studies and study skills. In these classes I use resources from the internet using the screen share feature. I also use videos to introduce the lesson and just as a warm-up exercise and I also use another feature which is the whiteboard feature. Although Zoom has a whiteboard feature I use Jam, Google Jam, Jam Board because it has other features for example I could upload videos from the internet. I could also use the different slides to include examples especially in the mathematics. Kairida Lionel, a student of the Kamenreni Memorial School, spoke on her experience with online learning. The quizzes are quite challenging but I think that I've done all of them so far. All right so how did you learn to use the various softwares like Zoom and Edmundo? How did you learn to use it? The teacher told us about how to use it and I just learned a little more by clicking unnecessary buttons. How are your parents helping you now? Well I don't really need help from my parents since I'm really good with working but sometimes I would ask them for help when I'm confused about certain questions. The Ministry of Education Officials encouraged the students to remain committed to their online classes and assignments. On behalf of the government and people of St. Lucia, the Eldercare Unit of the Division of Human Services has extended special birthday greetings to the island's latest centenarian, Ms. Rachel Stanislas affectionately known as Tease of Decretus Schuzel. Ms. Stanislas was born on the 8th of May 2020. During her lifetime Tease created many beautiful memories and notable accomplishments including her fondness for telling cruel jokes. At age 80, Tease was still climbing trees to get her ackee, plums and other produce to ply her trade as a local market vendor. She's the mother of 12 children, 11 boys and one girl, nine of whom are alive today. At 100 years old, Tease still enjoys spectacular vision and continues to assert some level of independence within her home. This is Ntnightly, up next, Primers-Hudgingston with the Ntn Nobel of We All. Welcome back. We join Primers-Hudgingston for the Ntn Nobel of We All. So, the Ntn Nobel of We All is the place where the Ntn Nobel of We All is located. Yes. The first place that we were told was not open. When all the cabbages were closed, all the locations in the country were closed. But these places, such as this supermarket, gas stations, minimats, the manufacturing were never closed. And these places were closed. Yes. So these places were never closed. So all that we were told was not open. And all the places were closed. All the cabbages were closed. But the most important in all that was for the world to be responsible. I would like to remind you that you can pay a good amount of money to drink alcohol. As a government, I would like to leave you alone. I would like to discuss with the director of the C.S. Forensic laboratory, M. Fernande Henry, the head of the G.S.A.C.A.P.O.T.E. for the world to be able to drink and drink alcohol. According to M. Henry, at the end of the day, they can drink alcohol, but at the end of the day, they can drink grape juice. The director said, It's not going to be a big deal. I would also like to give a big tribute to the director of the C.S.A.P.O.T.E. for the world to be able to drink and drink alcohol. I think that the decision that we make is the decision that we make. So we can't just do what we want to do to make a good time. So I think that the generation that we have, that we have to do what we want to do, all of them are going to start their little life. Ma'am Zell Johanna Joseph, who is your consultant on alcohol scotablism, has advised the public not to make costs to buy alcohol when the government has no permission to buy alcohol. Ma'am Zell Joseph has made it possible for the public to have a good understanding of the system of drinking and alcohol so that they can help you with your disease, coronavirus. We have a system of good condition. Even if the government has not opened it, it is for us to have control and support for our family, for all these people who live here. So, we have a lot of alcohol, we have a lot of editors. We have a lot of pauses, we have a lot of equipment. But our problem is already Maybe, because we have access to these six, seven, eight we cannot do that, we cannot do it our way, please, are you serious? Please, please. Please, please. Please, please, please. Please, if you would like to visit me, please, please, please, my lord, I would like to have a respirator, Thank you so much for your time and start fine. We're going to continue with the novel today, Mr. Otter, to guide me on how to do it, because I have a lot of news to share with you all. I wish you all the best. I wish you all the best. I hope you all have a great weekend. I wish you all the best. I wish you all the best. I hope it is a good weekend. I hope you have a good weekend. I wish you all the best. I wish you all a good weekend.


we have been discussing on various aspects of low Reynolds number hydrodynamics and so far we have considered only internal flows that is flows taking place through channels or ducts these kinds of examples we have primarily considered. Although we have considered some cases of external flows with regard to unsteady flows we have considered some cases of flows over flat plates and so on but mostly we have considered internal flows. Now external flows are important in the microfluidics context because of several reasons right. Let us consider an example of let us say that there is a charge species this charge species is moving say this species has a negative charge this charge species is moving under the action of an electric field. So let us say there is a fluid medium there is an electric field that is applied on this let us say that Q is the charge. So if Q be the charge and if E be the electric field then Q into E is the force that is acting on this charge species. Now if the charge species is not accelerating then what is happening that this driving force should be balanced by the viscous drag force this must be equal to F drag and this drag force is a function of the relative velocity between the fluid and the charge species okay. So what is the velocity at which this charge species will move relative to the fluid that will be decided by what is the drag force on this particular charge species. And to know what is the drag force on the charge species we may consider several situations. Now one idealized situation is an idealized model of the charge species where the idealized geometry may be for example spherical geometry. Now you may argue that spherical geometry may not represent all the charge species and that is true right while spherical geometry may represent some of the ionic species a spherical geometry may not represent charge species like DNA for example. So if you want to go for a very accurate model you have to consider the shape the geometrical shape of the charge species. However for simplicity for many complex shaped objects you may consider them to be of some equivalent radius where the radius defines the radius of an equivalent sphere and that radius can be thought of as the radius of gyration of the system. So if you are trying to model the situation by an equivalent sphere or sometimes maybe equivalent cylinder we will take that example of a equivalent sphere then for the equivalent sphere it may be possible that we can calculate the drag force by using simple analytical tools and that is a very classical problem. Of course for more complicated shaped objects we can follow the same governing equations but the same kind of analytical solution will not hold and numerical solutions may need to be obtained for complex shaped bodies. So the idea is that we are interested to calculate the drag force on a body of idealized geometry that is there moving relative to the fluid. Now the question is how is it moving? Now we are typically considering low Reynolds number hydrodynamics so we are considering that the Reynolds number based on the diameter of the sphere is pretty low. So I mean typically the Reynolds number much less than 1 so that viscous forces are dominant as compared to the inertial effects. So our objective for today's lecture is that we have let us say a sphere in a low Reynolds number background flow so it does not matter whether the fluid is stationary and the sphere is moving or the sphere is stationary and the fluid is moving because it is the relative velocity that matters. So let us say that the sphere is stationary and the fluid is moving past it and the typical Reynolds number based on the diameter of the sphere is low. So for that particular purpose what we can do is we can refer to a very classical problem which was solved by Stokes long back and the idea of the classical problem is to solve the velocity profile, the pressure profile and hence the drag force that is acting on this spherical object as you have a low Reynolds number fluid flow past the same. The Reynolds number of course is classically calculated based on the diameter of the sphere. We will try to solving this problem at this stage because this problem will require the use of a coordinate system with which you may not be that familiar with. So we will start with an equivalent problem description which we will represent in terms of a vector notation for any arbitrary coordinate system and then we will specify the particular case for this type of coordinate system. So to do that let us say that we are interested to write the governing equations of motion in terms of the Cartesian coordinate system okay. So now in terms of the Cartesian coordinate system let us say we write the Navier-Stokes equation although it is low Reynolds number I am still writing the full form just to give you the form of the Navier-Stokes equation in vector notation. We are considering incompressible flow I am not adding any body force here I mean you can add the body force in a way in which you like.  So if you take v dot del it becomes u del del x plus v del del y plus w del del z and the operator is operating on u okay. So this is the x component of the momentum equation x momentum similarly y momentum and z momentum let us quickly write y momentum it will be v dot del v and the z momentum okay. Now what we do is we consider this into i cap where i cap is the unit vector along x this into j cap and this into k cap and add. So that gives the vector sum of the 3 and if you do that then what you get rho del del t of ui cap plus vj cap plus wk cap so capital V vector plus v dot del ui cap plus vj cap plus wk cap so that is v is equal to minus i del p del x j del p del y k del p del z so minus grad of p plus mu del square of so see here the operator is Laplacian operator del square del x square plus del square del y square plus del square del z square of ui plus vj plus wk so this one right. So this is the compact way of writing the Navier-Stokes equation in vector form we have seen how to write it in index notation this is the compact way of writing that in vector form and writing that in vector form like index form is very much specific to Cartesian nature of the indices Cartesian tensor notation I mean the vector form the advantage is that it does not require the description of any coordinate system. So you can use it for a very general case and if you have a body force just add a plus b vector for indicating the body force. Now for low Reynolds number you can drop the LHS we will see later on whether the same is justified or not for the case that we are investigating but for the timing it is intuitive that if it is a low Reynolds number flow then the left hand side can be dropped this is what we have learnt from our previous experiences. Now so far as what we are going to predict whether that particular inference is still working or not we will discuss about that as we come to the end of the solution of this problem. So then you have null vector basically we will use a vector identity to simplify this problem but first of all before using the vector identity we have to find out a strategy of solving this problem. So the strategy of solving this problem see this equation has 3 components if we use some other coordinate system we may reduce the number of components by using some symmetry or that kind of thing but in a Cartesian coordinate system see we are not discussing this specific problem we are discussing about a general problem that can be described in terms of a suitable coordinate system we have not yet fixed up the coordinate system. So this equation involves how many unknowns in general 3 velocity components and pressure. So you have 4 unknowns and for an incompressible flow you have 4 governing equations also so that closes the system but analytically it is very difficult to couple the continuity equation with what with the momentum equation with the Navier-Stokes equation analytically difficult to couple numerically it is relatively more convenient. So what becomes the deterring factor the deterring factor is this pressure these governing equations are equations governing velocity but in that extra unknowns in form of pressure appear but we do not have an explicit governing equation for pressure. So one possible strategy one possible strategy may be so our origin of headache is the pressure.  So if you do not have head you do not have headache right. So you have pressure in this equation so you somehow eliminate pressure then there will be no problem with the pressure term. So how can you eliminate pressure from this equation? So one simple strategy is if you take curl of both sides you can use the vector identity that curl of grad of a scalar is a null vector. So this will go away. So take curl of both sides. So if you take the curl of both sides this becomes 0. Now we will use a vector identity this is a very commonly used vector identity and the interesting part of the vector identity is that you have a divergence of velocity in one of the terms. So if it is incompressible flow as we are considering for this case then this term will go away for incompressible flow not for all cases only for incompressible flow. So instead of del square v you can write minus del cross del cross v right using this identity and what is del cross v what is the curl of the velocity that is nothing but the vorticity. So let us this is vorticity. Let us say this zeta we use for vorticity okay. So we can write this is curl of vorticity and we have additionally taken a curl to make this term 0. So that is why curl of curl of this. Now we can now use the same identity here just replace v with zeta right. So we can write just I mean here instead of v we are using zeta. Now what is this? This is del dot del cross v and by a vector identity this is 0 divergence of curl of a vector this is 0. So we are left with del square of zeta is equal to 0. Now let us consider an example of a 2 dimensional flow in Cartesian system described in Cartesian system. We are starting with the Cartesian system not because that we will use the Cartesian system to solve the problem of the sphere but because of familiarity you can understand certain concepts which we will borrow for solving the problem of the sphere. Now for this particular problem now for 2D flow zeta this is the scalar component of vorticity. So for a 2D flow the vorticity vector is having an effect which is perpendicular the unit vector is perpendicular to the plane of the flow and the magnitude of the vorticity is this one. Now so this is zeta with respect to z axis the vorticity. Now for a 2 dimensional flow see we had said that for eliminating this term by eliminating this term pressure we are not having an explicit linkage of the continuity and the momentum equations. But there has to be some reference to the continuity equation otherwise how do you ensure that you are solving the velocity field from the momentum equation that satisfies mass conservation that has to be ensured. So somewhere continuity equation has to be brought into the picture. How we bring into the picture here is by defining this velocity in terms of stream function. So we define let us say u is equal to del psi del y and v is equal to – del psi del x. So what are these u and v? These u and v are the velocity components and psi is the stream function. So you can see that this definition of psi automatically satisfies the continuity equation del u del x plus del v del y equal to 0 for 2 dimensional incompressible flow. So you can write zeta z now for defining the stream function we have to be careful that right u and v have to be carrying opposite algebraic sign. So it does not matter I mean here we have taken this as plus this as minus but we could have easily taken this as minus and this as plus that would have made no difference. So this is in 2D this is – del square psi. So del square zeta z is equal to 0 that means you have del square of del square psi equal to 0 right. This is what we learn from our 2D experience 2D Cartesian. Now let us come to the problem of the sphere flow past the sphere. So if you now use a coordinate system which is radial r and angular coordinate theta then instead of u and v you could use the components vr and vtheta but because of the change in the coordinate system then this del square operator will not work. So instead of del square we will use a different operator which is called as e square operator. We will come into that. So just try to understand the analogy of the concept. The operator is simply different because we have to adapt to a different coordinate system but concept wise it is very similar. So e square of e square psi will be 0 and this psi is not the normal stream function in the Cartesian system but the stream function defined for this coordinate system which is also called as stoke stream function. With this background the definition of stream function will be different but that will satisfy why it has to be different because that has to satisfy the version of the continuity equation for incompressible flow in the rtheta coordinate system not the Cartesian system. Now next what we will do is we will try to assess that what will be the velocity field far away from the sphere. See we intuitively expect that far away from the sphere the effect of the sphere will not be important. So the velocity field if this is u infinity that will again become u infinity far away from the sphere in the downstream. So if you have this as vr then this will be the vtheta this is the resultant which is u infinity. This angle is theta and this angle is 90 degree. So technically here at r tends to infinity where vr is equal to u infinity cos theta and vtheta is equal to minus u infinity sin theta. Why minus? Because positive theta direction is opposite to this vtheta direction right it will see this vector triangle. So now the next step is we will write this vr and vtheta in terms of the stroke stream function. And then we will solve the stream function we will find out the stream function at r tends to infinity. So we need to now express vr and vtheta in terms of the psi. These expressions what we are going to write for the rtheta coordinate system are quite involved. I mean it is very difficult to remember this I never try to remember this. I mean it is up to your wish you may try to remember this but that will not give you any credit at least. If you are thinking of getting Nobel prize you will not get Nobel prize by remembering rtheta coordinate system equations. So I mean we will just write the standard form of the equation vr and vtheta as a function of or in terms of psi the stroke stream function and theta and then we will proceed. So I am not writing from my mind I am writing whatever is there given in the slide I am just copying from there. So do not think that this is to be written in written by memorizing it is not necessary. If these things are to be written or these things are required in some place some examination on somewhere assume that these things will be provided rather you apply your mind for analyzing the problem. So now vr is equal to 1 by r square sin theta del psi del theta. So which is equal to u infinity cos theta at r tends to infinity. So if you integrate this so psi u is equal to psi is equal to u infinity r square it is sin theta cos theta d theta. So let us say that sin theta equal to some z. So cos theta d theta is dz. So it is integral of z dz that is z square by 2. So that means u infinity r square by 2 sin square theta plus what? See we are partially integrated with respect to theta. So function of r is like a constant. So plus a function of r remember this is at r tends to infinity okay. We can write a similar expression for v theta is equal to 1 by r sin theta del psi del r which is equal to minus u infinity. So this is minus sin is there minus 1 by r sin theta del psi del r this is equal to minus u infinity sin theta at r tends to infinity. So if you integrate this now with respect to r this is u infinity integral r dr is r square by 2. So r square by 2 sin square theta plus some function of theta at r tends to infinity. Now look at these 2 expressions. If you compare now that those must be the same whether you have got it from the expression of vr or the expression for v theta psi should not be different. So that means you can assign f1r or equal to f2 theta equal to some arbitrary constant and that constant for a reference case you can choose as 0. So then you can write psi is equal to u infinity r square by 2 sin square theta at r tends to infinity okay. Now this is at r tends to infinity when r is not tending to infinity but r is a location which is somewhat closer to the surface of the sphere then what will what is expected to change r dependence or theta dependence. R dependence is expected to change as you bring the situation from a far field to the near field because that has not created a change in theta that has created only a change in r. So for a general case therefore we can write psi is equal to some function of r into sin square theta. This is the solution that we are this is the form of the solution that we are expecting this function of r we have to figure out what it is okay. So to get this function of r we will now use the governing equation e square of e square psi equal to 0. So what is e square the expression for e square this is the expression for e square. So what is e square psi first let us calculate the theta dependent term and then we will calculate e square psi we are calculating this term. So you can write this as sin theta by r square into del del theta into 1 by sin theta del del theta of sin square theta is 2 sin theta cos theta right this becomes del del theta of cos theta becomes minus sin theta. So this becomes minus 2 f sin theta sin square theta by r square. So what is e square f double dash see del square del r square of this particular term will become f double dash sin square theta. So sin square theta is common f double dash minus 2 f by r square sin square theta e square psi yes. So e square psi we can write f double dash minus 2 f by r square sin square theta this is say g of r into sin square theta then we have e square of e square psi is equal to 0. So another e square of this that means g double dash minus 2 g by r square that must be equal to 0 because sin theta is not equal to 0 in general.  Now one way of getting a solution of this equation is assuming that f is equal to some c r to the power n this is the trial solution for equations of this particular form that is a standard way of getting the solution that is you assume f is equal to c r to the power n. So f dash is equal to c n r to the power n minus 1 f double dash is equal to c n into n minus 1 r to the power n minus 2.  So this is n square minus n minus 2 so that is what n minus 1 sorry n plus 1 into n minus 2 n square minus n minus 2 right.  So now what is g? g is this one so this so g is equal to let us write it here maybe somewhere here. So g r sorry yes g r is equal to what f double dash minus 2 f by r square is equal to n plus 1 into n minus 2 into r to the power n minus 2 there is a c then you have g double dash minus 2 g by r square that is equal to 0. What is the difference between the form of the f and g? Now c is replaced by c into n plus 1 into n minus 2 and r to the power n is replaced by r to the power n minus 2. So the same thing will come another 2 terms with n replaced by n minus 2 right. So eventually this will lead to n plus 1 into n minus 2 replace n with n minus 2 so n minus 1 into n minus 4 equal to 0. So you will get 4 roots for n so n is equal to 1, 2, 4 minus 1. So if that be the case then what is your solution? Let us write the solution here is equal to c 1 r plus c 2 r square plus c 3 r to the power 4 plus c 4 by r. Each n is see the solution that we assumed is c r to the power n. So there are 4 n's therefore 4 c's. So now to get the stream function what we require? We essentially require to obtain the values of c 1 c 2 c 3 c 4 so we require boundary conditions. Now what are the boundary conditions? So boundary one boundary two boundary conditions you are obtaining on the surface of the sphere. What are the boundary conditions on the surface of the sphere? No slip and no penetration. So the boundary conditions number 1 r is equal to capital R let us say d is equal to 2 r so capital R is the radius of the sphere. So at small r is equal to capital R no penetration how will you write? vr must be 0. So instead of the rth theta system if it was xy system how would you express that? You would express that as v equal to 0. v is equal to what? So the question is how do you express this in terms of the stream function? Let us discuss in a little bit different way so that you understand it better. Let us say you have a flat plate forget about a sphere. So what will be a streamline which is representing the solid surface? Is it a streamline? First of all is the solid surface a streamline? It is always a streamline because the definition of a streamline is there is no flow across the streamline. So the solid boundary there is no flow across the solid boundary so by definition it is a streamline. So streamlines are lines with constant stream function. Therefore a solid boundary the no penetration boundary condition in terms of the stream function is equivalent to a boundary condition with psi equal to constant. What is the value of the constant? Value of the constant is arbitrary because see your definition u and v depends on the gradients of psi. So basically difference of psi is important not the absolute value of psi. So this constant can be arbitrary but for calculation convenience we take that constant to be 0 for the solid boundary. So at r is equal to capital R you must have psi equal to 0 and psi equal to 0 means f equal to 0. Then this is no penetration. What about no slip? No slip means what? Which component of velocity is 0? v theta. v theta how do you write? Del psi del r just like u is equal to del psi del y instead of y it is r. So del psi del r is equal to 0 that means what? df dr equal to 0 at r tends to infinity. What is f? This we have already calculated. What was f? u infinity r square by 2 that means what can we say from here? One of the constants we can. So c2 is what is c2? u infinity by 2 because this form should be satisfied even at r tends to infinity. Not only that we can make an additional observation. The additional observation is c3 must be equal to 0 because the highest order dependence is r square dependence. You cannot have a dependence with r of order beyond that. The infinity condition gives the highest order dependence. So you cannot have any order dependence beyond that. So you have c3 equal to 0. So see the situation is a little bit tricky. You have 3 boundary conditions and using that you are calculating 4 constants. Appears to be something which is not that straight forward. So that needs to be critically discussed. So with these conditions now it is possible that you can substitute these boundary conditions and calculate c1, c2, c3, c4. That algebra is quite trivial. I will not work out that instead we will go to the slides to see that what are the constants that you will get from there. So if you look into this slide, no penetration, no slip will give 2 conditions. Then at r tends to infinity, so the problem is here different notations are used for c1, c2, c3, c4 I think possibly. Let me see. No penetration, it is same. Okay. Same notations are there. Then it is fine. So whatever notations I have used in the board, same c1, c2, c3, c4. So we can use these slides directly. So at r tends to infinity, fr is u infinity r square by 2 that will give you c2 is equal to u infinity by 2 and c3 is equal to 0 that we have already discussed why c3 has to be 0. So if you calculate now c1, c2, c3, c4, so basically from the condition at r tends to infinity you are straight away getting 2 constants. So the remaining 2 constants you can calculate from the no slip and the no penetration boundary condition that will give you c1 is equal to minus 3 by 4 u infinity r and c4 is equal to u infinity r cube by 4. So you get psi equal to fr into sin square theta. So once you get psi, you get everything because once you get psi, you get the velocity field. Velocity field is expressed in terms of psi. Now you can also calculate the pressure field.  Now you somehow put your head back on the top of your body. So earlier pressure was eliminated. Now what you do is that you refer to the momentum equation where now the velocity field is known. You substitute the velocity field and integrate the momentum equation to get the pressure field. Not only that you can use the velocity field to get the shear stress and the normal stress. So getting the shear stress, normal stress and the hydrostatic stress in terms of pressure you can get the distribution of stress on the surface of the sphere and that will help us to calculate the drag force. So we will take up that in the next lecture. Thank you very much.