Welcome to the first of several enlightening discussions we have planned for you today. My name is Maika Samson and for the last eight months or so I've had the privilege of introducing myself as the Millennial Public Policy Fellow in the Family-Centered Social Policy Program here at New America. This panel, New Perspectives on Communities of Care, is split into two roughly 30 minute sessions with a Q&A at the very end. In the first half of the panel I'm joined by Elisa Dorana, the Senior Policy Analyst in the Better Life Lab and Rosalyn Miller, the Millennial Public Policy Fellow in the Better Life Lab. In the second panel, Jenny, the Millennial Fellow from the Education Program will lead a conversation with her colleagues, Ernest Nisuego and Abigail Swisher, members of the pre-K through 12 program and the higher ed teams respectively. So one of our goals for these conversations is to move past the whys, the justifications for care policy and to really get into the weeds of policy philosophy and design. We hope that by now we're in agreement that people need paid family leave, that the patchwork of American public assistance programs aren't doing enough to meet the needs and aspirations of their constituents and that of course American public and private education systems are failing to foster equity. It's easy to whip up a populist frenzy over what's obviously wrong, but it's much harder to focus our attention to the myriad of historical, social and technical considerations that must be taken into account if we were to ever get things right. Aliza and Rosalyn's work in the Better Life Lab exemplifies this commitment and depth to research in the field. They research and write about barriers to social and income equality, especially at the intersections of work, gender and social policy. Before joining New America, Rosalyn studied anthropology at Stanford University. Her studies focused on urban structures and their relationships to the public and private sectors. Before joining New America, Aliza's work spanned the Department of Housing and Urban Development's Promise Stones initiatives. She worked in social services in the Washington metro area and she did full bright research on social policy integration in the EU. Aliza, you recently authored an article that appeared in Slate on the Republican Plan for Paid Family Leave. I think it really highlights some of the issues we'd like to talk through today. Maybe the messy things that happen when we come to a consensus on a good thing, like paid family leave, but we have wildly different ideas about how to make that happen. And so to kick off our conversation, I wanted to ask the both of you if you could talk through some of the major points of this paid family leave policy proposal and some of the philosophical issues it raises in American approaches to care policy. Sure, so maybe to start, I don't know how familiar people are with paid family leave in the room, but there are currently two general proposals on the table there. The Family Act, which was introduced by Senator Gillibrand and Representative Delaro, would create an insurance scheme so that people would pay into the scheme about a cup of coffee, the cost of a cup of coffee a day. And then when they need to take time off to have a child, care for a loved one or undergo cancer treatment, something like that, that they would have the ability to take that time and not lose their source of income. So that has been introduced several times. It's basically a Democrat only bill at this point. There has been interest from the administration, which has now crossed over into Marco Rubio's office to author a Republican plan. And so that plan has come together as sort of an extension of the social security system. So in the article that we authored last week, we were looking sort of at the merits of that bill, surprisingly or not so surprisingly, it's not particularly well thought out and would exacerbate funding issues within social security itself and also not be inclusive of the needs that most families have. So in the case of that policy, the Republicans would like to fold parental leave into our current social security system. So not even though the majority of people who take time off take time off for their own personal medical care. This would just be limited to new parents. And if new parents were to take time off pulling money out of their social security, they would have to delay retiring. So there are, well, I have multiple concerns about that. Mainly that we already see a lot of discrimination of new parents, particularly women. The wage gap emerges when women are in their 20s and 30s. So that is one issue. And then the second is that the workers that probably need this the most who probably need to retire early because they are in very physically or emotionally demanding fields might not be able to if they take time off to have a child and then can't retire when they're no longer able to work. So, yeah. Yeah, I completely agree with all of that. And I just want to add that right now we're at a moment where people are finally putting family values first in the sense that paid family leave has not always had a consensus about its value. Right now in American workplaces, we expect people to adjust their lives, their families to the nine to five or to the shift work or to whatever it is that people are working in rather than making workplaces work for people. And that's a huge problem that I think paid family leave could be a corner stone of fixing. And right now about 14% from 2016, that's kind of an old statistic, but about 14% of Americans have access to paid family leave. Meaning that if you need to take six weeks off to give birth to your kid or to take care of a sick child or even an elder that doesn't have anyone else to take care of them, you have to sacrifice your salary, you have to sacrifice your position at work just to make sure that you can do those caretaking responsibilities. And that's not fair. And when we passed the Family Medical Leave Act, that helped with a little bit that provided unpaid leave for, is it 12 weeks? Up to 12 weeks. And even not all Americans have access to that. Not all companies are big enough. And yeah, why did we, you put policy forward and say this is important, this is valuable, but then not make sure that every worker has access to it or has the ability to take it?  So not to mention issues around people who are disabled or in the process of dying or there are many reasons why people need time to take off. But, yeah, so the situation is fairly dire at the moment. Yeah, definitely. I think part of the reason, I don't want to speculate too much, but part of the reason why this proposed plan pulls from Social Security is over concerns about its cost. Frequently, the argument against developing robust safety net programs is that the cost will be enormous. And could you speak to that sort of scarcity framework and how it's framed other social policies? Sure, I mean, Rosalind will also speak to this, but I think that we're in agreement that this is more a question of priorities. And Paid Family Leave would act as an insurance scheme where people would pay money in and then they would have the right to take that money out when they need to take time off. So comparatively, it would function similar to Social Security or Medicare. Other social insurance programs like that. I think it's partially a question of values and whether we think that people in the U.S. should live in dignity.  So it'd be nice to support them in that process. And at the same time, a lot of the people, we've been subsidizing a lot of the way that we live on the work of low income, mostly women and often immigrant women, who do a lot of the childcare, elder care, the domestic care work in this country for minimum wage or around there. So, yeah. I mean, in the end, we set our budget and what we decide is a priority for our nation is what we're going to have money for. And the policies that specifically paid family leave and then the family act, sorry, specifically those policies are created, they're well thought, they have a budget scheme in mind. And it's something, at least the family act, is something where employees and employers pay into and it's a social insurance fund. So there is money for it if we decide that we care about people's lives. And beyond dignity, beyond need meeting, we're allowing people to have freedom to live a life that they choose in a way that they choose. Beyond just meeting the baseline need, everyone deserves happiness. I think we can clarify what we really mean by our values in the policy making process. So I frequently think about David Elwood's original plan for welfare reform in the 90s, which was a lot more compassionate than the current cash assistance programs we have now. And I think a lot of his ideas sort of took on a life of their own and even though like he did espouse a lot of values about equity and fairness to folks looking for assistance and trying to get back on their feet, the tagline became and welfare as we know it. Personal responsibility is a goal of ours. That's independence is a goal of ours. It's a shared American value of ours. And those values really coalesce into something quite different than what you would imagine them to be. So my question is how do we really be clear about our values and clear about what we hope to achieve and not let our ideas get lost in the legislative machine? So I mean, I think that like framing this as a family issue, an issue that like people contribute to, I mean, it is both a public good and that like we want to invest in like the health and future of our country and our well-being as it stands right now. It's also something that exists both in the US and worldwide. So this is not some sort of radical idea we're not talking about. I mean, there are many other policy issues that are a little bit more far-fetched, but this exists in California. It exists in Rhode Island. It exists in New Jersey. And then there's new legislation in Washington State, Washington DC and a number of other places. So I think it's partially like how can we reframe this as like a way that Americans can support their own families and that also we contribute to child development, maternal health, which is worsening in the US, gender equality and other sorts of things. Yeah. Frankly, we need to start with culture change. We need to make it normal to value caretakers, to value domestic workers and shift workers and all of the people that make other work possible rather than sort of idolizing this one idea of success. Yes, by putting families first, we can get on the same page with values, but even if we're on the same page, if we do get a good paid family leave program, we're not gonna see equal utilization rates unless we address gender equality, unless we address wage disparities. Something you mentioned is sort of any unintended consequence of the proposed plan that it might incentivize employers to discriminate against young parents. What frameworks would you employ to sort of avoid some of those unintended consequences? Usually, I mean, in our work, usually what we try and think about is how would this policy affect historically marginalized communities by gender, by race, at the intersection of those two things, definitely able people, that sort of thing. I mean, what we know about the Family Medical Leave Act, for example, is that it did enable some mostly affluent, mostly white people to take time off when they need it, but only people that can afford to take unpaid leave. So in a way, it is exacerbated inequality, even though the idea behind it was to help families take care of themselves. So in thinking about any sort of future paid leave scheme or other types of social policies, like thinking through what incentives could be included in the policy or how this will affect different populations, one of the things that we have seen from other countries is that it's really important to try and get men in particular to take leave, so often to help so that women are not still disproportionately shouldering the majority of the care work in this country, both in terms of paid leave and unpaid leave as well and unpaid work in their families. So something, making sure that language around paid leave is gender-neutral, but that there's also an incentive for the second parent or caregiver in a family to take it and making sure that the pay is high enough so that our lowest income workers have the ability to take time off. When California first implemented their paid leave scheme, the amount of money that people would get if they took leave was just 55% of their wage. So if you're a minimum wage earner and you are only getting 55% of your income when you have a baby, it's still not really affordable to live in San Francisco on 55% of minimum wage, so bumping that up, especially for low income workers is really, really important. And California recently did bump that wage replacement up by, I think to about 70%. And in order to encourage men to take paid family leave in San Francisco, in San Francisco, men get 100% wage replacement rates for taking paid family leave and that encouraged utilization rates as well. I think this also brings up a question of the drawbacks and benefits to targeted versus universal programs. On one hand, targeted programs can somehow single out some of the most marginalized people in our society and really draw negative attention to them, but that's where we need to foster equity, right? So could you speak to some of the perils of that? The targeted approaches? Yeah, yeah. Well, you can't just capture everybody with a targeted approach and often you isolate the community that you're hoping to serve and there's a stigma associated with it as well, especially if you're getting vouchers for things and waiting in line forever. For example, if you're trying to get food for your kids and you have to wait in front of a food shelter for an hour early in the morning with people walking by in front of you, there's a certain stigma associated with that for trying to provide for your family. And we see this all the time in education as well with education voucher programs being offered for community colleges, but not for four-year universities. What we're doing is we're saying that people are worth a certain value and maybe the numbers show that that's where the impact is, but we're not centering the human, we're centering the statistic in that sense. So yeah, and then also universal approaches have a problem with ignoring marginalized communities. So I guess the big question is how do you balance both to make sure that a policy really does address the need that you want it to rather, and the people that you want it to serve rather than your stereotype or perception of what a population needs. And I think that we can do that by including people in the policy-making conversation and hiring the people with lived experience as well as in our research design actually incorporating qualitative research. Yeah, no, I mean, I think that's great. And I remember hearing Virginia Eubanks recently talk about her new book and one of the things she mentioned is like if you're implementing a policy or a research question and you would be unwilling to participate in that policy itself, so that's probably a good gut check as to like whether you're on the right track, but certainly I think including the communities you're trying to serve and the research and policy-making process, making sure, I think that I generally have more of a preference for universal policies than targeted. That's the approach that the Better Life Lab takes and thinking about paid leave, but making sure that we're, yes, designing policies or research with communities and for communities that have been historically excluded. Yeah, and I think a historical approach to policy-making is something that's often left out of the traditional policy-making process. We tend to speak in euphemisms when we design policies, like I was doing it earlier saying marginalized populations rather than talking about, if I'm getting more specific the way black women specifically were excluded from a lot of major social programs in the United States. And now that's a direct result of Chattel slavery in the United States. That is usually considered sort of irrelevant to our design process when it comes to social policy, but it's completely irrelevant. And if you can speak to the ways that your work often tries to integrate history when proposing policies, I'd love to hear that. Yeah, I mean with the case of the Republican paid leave plan and one of the issues with designing paid leave through social security is that a lot of the populations that we're talking about, it's like agricultural workers, domestic workers, like mostly like people of color, they're not a part of the social security, they were excluded from the Social Security Act, they're excluded from a lot of the labor protections in this country. As we think through the retirement security, like unemployment, paid leave, whatever the policy is, I think that looking at the construction of that policy, like where did it come from, who was included, who was not, how is that changing? I mean right now, more people work sort of in contract hourly work, and so even if they had been included in our safety net before, they're probably not included anymore now given the changing structure of work itself, so yeah. I'm curious about how this applies to your work as well with Family-Centered Social Policy. Yeah, Family-Centered Social Policy absolutely loves historical approaches to policy building, and I think a lot of that is not just like a sort of historical research, but directly bringing in the people who are going to use these programs to the policy making conversation. People who are going to benefit from these programs should have a say in how they're designed and how they operate, rather than sort of going to the technocrats and the people with fancy degrees calling out myself here, but including those folks at the table is really critical. Any other last words before we wrap up and go to our second panel? All right, so with that, I think I'm gonna welcome the education team out to the stage. Thank you everyone, can you hear me? We are gonna go ahead and jump right into our second conversation where I hope we continue to grapple with some of these same questions, but bring it into the education space. I've invited with me two of my colleagues from the Education Program at New America. They're working on two distinct projects that I think could serve well as case studies to begin to impact some of these questions around how do you intervene with care? How do you design policies with different communities in mind and ensure equity? So we have Abigail Swisher who is with our K-12 program and her work revolves around college and career readiness and today she's gonna be talking about some of the work she's been doing in the last year on youth apprenticeship and we also have Ernest Usuego who is a program associate with our higher ed team who does a lot of research and writing on a host of different issues but today he's gonna be talking about predictive analytics and higher education. So just to start off, can you guys give sort of a brief overview of what your work is and we'll start with some of the positive aspects, the promise, who, if we do this well, who can benefit and then also jump into some of the challenges and ethical concerns that are coming to the fore as you research this further. Okay, I can start. Yeah, so thank you, Jenny and thank you all for being here. Like Jenny mentioned, the topic area that I'm currently working on in New America is predictive analytics and its use in higher education. Predictive analytics being the idea that institutions are taking historical data and then using it to make predictions about what, or really I should say, forecast what student behaviors lead to success and learn more about what types of behaviors like students make in general. I think the great promise of predictive analytics and in general the conversation about data and higher education and data use is that data used ethically and effectively has the potential to teach us more about student success than we've ever known. It can inform the way that we learn, it can inform the way that we intervene when we know that students are off course and there are a number of other things, right? That having access to data can teach us but the key in all of that is ethical and effective use. I think if done properly, everyone, all students benefit from predictive analytics. I'll say all students but like students at the institutions that are practicing this because it's still relatively new work. I actually think that first and foremost students from historically underserved communities can benefit the most from predictive analytics and I'm sure we'll get into that through this conversation. And thank you, Jenny, thank you, Ernest and thank you all for being here today. So as Jenny mentioned, my colleagues and I have embarked on this year long project around the equity dimensions of youth apprenticeship and if you aren't familiar with youth apprenticeship or if your idea of youth apprenticeship is still like Benjamin Franklin slaving away in the workshop, youth apprenticeship has come a long way since our traditional conception of it although it is a many centuries old program design. The idea being that it's a partnership between three institutions, the high school, a post-secondary partner and industry to provide students with paid on-the-job learning along with classroom learning in a post-secondary setting for post-secondary credit and ideally at the end of it, it should lead students we believe in a high quality program to a family sustaining wage job and a path forward in a specific industry. So functionally what this looks like is a student either during the school day or after school going to a work site, getting paid on-the-job mentorship in workplace and either during the day or on the weekends, evenings, also going to a post-secondary institution to receive college level coursework in their industry area. At the end, they should get an industry-recognized credential or something that really validates the work experience that they've had. And as this program model has become more popular in the past few years, questions are really arising about who we see youth apprenticeship as for. There are a lot of potential benefits that it can accrue to a student. For instance, getting post-secondary credit early can reduce time and debt to a degree. It provides students a really stable pathway with built-in mentors to get to and through post-secondary into a family sustaining wage career. And it also means that for students who by necessity have to work while they are in high school, they're not working at McDonald's, they're not working at Subway, they're working in a workplace that will not only provide them with a living wage, but also move their careers forward. So that's, I think, a really tremendous potential. And so as we are thinking about who this is for, very often the discussion has come to this as a solution for students who we know traditionally struggle to get to and through college and into family sustaining wage careers. Specifically, very often this is put forward as a solution for low-income students and students of color. And as much as there is, I think, a tremendous potential benefit to that, we also have a pretty pernicious history as a nation around tracking and vocational education that has to be a part of the conversation today. And that was really the starting point of this project. It's a year-long sort of listening campaign across the country, done with the support of the Annie E. Casey Foundation, at the end of which we're hoping to have a better framework for what equitable program design would look like as these programs proliferate. Abigail. Ernest, can you say a little bit more about what some of the challenges are or sort of the wrong turns that have been taken with your particular work? Because I think it's quite interesting and would lead us to the conversation. Yeah, certainly. So I think right now the challenge that institutions in particular are grappling with in relation to using predictive analytics is this idea of practicing ethical and effective use while mitigating some of the effects and some of the kind of built-in negatives, unfortunately, that we know about using data. We live in unfortunately a time where we're still grappling with the effects of structural inequity. Earlier, Eliza mentioned the work of Virginia U-Banks. Kathy O'Neill also wrote a great book called Weapons of Math Destruction talking about the idea that currently, algorithms are, while they happen to the benefit of maybe rich and the rich and the wider communities, they're being sort of forced onto people from lower income and communities and communities of color. And I think what's key to understand is we're grappling with this in this time, this idea that the rich get people and the poor get algorithms is just this idea that prior to algorithms, poor people, it's not like we were getting fantastic service from people either. This idea of grappling with whether or not we're using algorithms individually versus whether or not we're really thinking through the human ways in which algorithms can affect us, making sure that we're looking at, make sure we're looking at how predictive analytics and data can have pitfalls related around tracking. All of that is key. I think that's the discussion right now that institutions are having. How do we use this data in a way that, and how do we make sure that we're not bringing to life all of the inequities that we know exist because we're using it? How we, and part of this is interventions too, right? What does this data tell us about the way that our students are and how do we practice the most human part of this intervention in a way that really does highlight the needs of our historically underserved communities? I think what's interesting and what I found interesting about both of your work is that there seemed to be this very slippery slope between wanting to do good and having well-intentioned policy and then tracking. And so there's a very thin line between this becoming sort of very paternalistic and reinforcing some of those deficit perspectives or stereotypes that we have of certain communities. Abigail, you wrote an interesting piece about vocational schooling and how that might haunt this new sort of resurgence of apprenticeship. Can you speak a little bit more about that? Yeah, so I think your points will take in especially, the anecdote that comes to mind was a time that we were meeting with the State Youth Apprenticeship Council in this past year and the college and career readiness person from the State Department of Education was talking about what she sees as the benefit of this program. And specifically to your point about paternalism, I'm thinking about what she said about who she sees program as forced. She told me this program is for the students who think they're going to college, but they're not. They don't have savings, they don't have the support and we know that they're gonna drop out within a semester so we want them to go into this program instead. And that strikes me as the height of paternalizing however well-intentioned it may be. I think very often when we were thinking about these programs that help guide students towards careers, we fail to think about their aspirations and that they have every right to the full amount of choice that students with the most privileged get in determining their career pathways and that as much as we have to balance the need to be practical and talk to students frankly about the challenges that they are going to face, no matter what they choose for their career, I think that there's a fine line to be walked between that and shunting students onto the path because we believe certain things based on data about their opportunities. Can we, this is something we often don't get to in these conversations, but how do you avoid that? How do we fix that? Have you all seen in your work people that are designing or implementing some of these programs well that have been able to avoid some of those unintended consequences? What are those conversations look like? Yeah, well so I mean that's sort of the million dollar question for this particular initiative and what we're trying to hear these programs are very new. They haven't undergone rigorous evaluation that tells us demographically how they're serving students yet. So it's an open question, but I think the first thing that people need to do when they're designing a program like this is to take care in what data they're collecting, how quickly they were reporting it before programs are scaled, and also actually know and be able to tell others who they believe their programs are for. And that to me is the first step in sort of figuring out what are tremendously complex and multifaceted equity concerns. I think so far I've really only spoken about equity concerns as they pertain to long-income youth and youth of color, but there are so many other aspects to this issue related to English language learners, to women who are disproportionately barred from certain apprenticable fields to students with disabilities, it's complex. So the short answer is we don't know yet. I think that's also the million dollar question with institutions grappling on how to use predictive analytics. It's just this idea that colleges are beginning to realize that you can have all the data in the world, you can have all the tools in the world, you can have the most complex algorithms, but the way that we interpret that data as humans and the way that we intervene, like the way that data forms interventions is critical to this work as well. I think an excellent example and probably the most talked about example in the field right now is Georgia State. They'll tell you that they worked with the Education Advisory Board to create this set of tools and algorithms that helped really pinpoint places where students were struggling and help them discover areas to intervene early and really touch on students, but they will also tell you that before, prior to having this whole set of predictive analytics, the ratio of students to guidance counselors to school was 700 to one. And after implementation, they took deliberate steps to also really step up the way that they were addressing human needs with humans, decreased their ratio to 300 to one, which is still large, but it's much better, right? And really begin to target interventions, really begin to use this data in a way that informed their interventions and help them focus on what to talk with students about leading from a wellness mindset instead of from a deficit mindset, starting off to simple things, like starting off emails as kind of nudges to students saying like, we're proud of you and we understand that this is hard work. Here are the ways, like here are the resources available and not just like warnings, you know what I mean? They're like, hey, you failed this test, you're now like 25, you're like in this group of people who are likely to drop out of school. And so, I think that's part of that work as well that's happening. And I think like schools are across the board from all like walks of the higher education landscape are discovering that data is critical, predictive analytics certainly help interpret that, but the way that we as humans take that and then interact with our fellow humans is also critical. I think that part of being able to have that forethought that was involved in being able to do something like that that was successful involves having, and we spoke about this earlier, diverse representation around the table when these programs are being designed. Who has been, in designing these programs, who has been at the table and what conversations have happened? Have people started using this historical lens in that work? Yeah, I would say that the number of the institutions that we've talked to who are really doing this work well are putting a lot of thought into who their personnel on this work is and who their team is. So not just like which vendors, outside vendors are you using, are they producing the type of tool that you think can serve your student body and are you talking with them about the effects of negatives and historical data on your algorithms, but also thinking at an institutional level from the student to the IT and IR institutional reporting departments, who's involved on this work on the inside and how are our teams like working together with these institutions to identify potential issues that might arise, identify unintended consequences that might arise as well. I think it takes like a certain amount of bravery to be able to acknowledge some of these problems at the onset and say these are the things that we know historically, these are the problems that we know can arise and start building from there and I don't think that's something that happens very often. Abigail, do you have anything there? Yeah, so I wouldn't wish to speak for all initiatives across the country, primarily because it's a really diverse landscape and these are highly localized programs. I will say that from what I have seen, we have a lot of work left to do to make sure that the policy and programmatic planning level staff working on these programs represent the students that they're hoping to serve. Primarily my observation with these folks is that they are mostly white and mostly male and I think that going forward that has like bound to affect how these programs will turn out in addition to thinking about the diversity of an inclusiveness of policy and programmatic level staffing. You also have to think about how you're trading people to confront implicit bias which I think is going to be one of the trickiest things to do with these programs. When we talk to people about it, particularly when it comes to the level, it's funny you mentioned counselors on the post-secondary level. On the secondary level, implicit bias from counselors is one thing that people bring up again and again that students are coming to them and saying, I know that the counselor recommended me for this because she doesn't think I can go to college or on the flip side, my teacher told me I shouldn't do this program because I need to go to four-year college to succeed. And so at all levels, there are issues both with inclusion and staffing and confronting the implicit biases of the people who are already in the room. I think it's probably safe to say in both of our fields that people are coming to realize exactly what was mentioned I think in the first half of this panel that if you're not talking to the people who are gonna be affected by these things, then you're not really doing this work as effectively as you can. So they just flagged me and said that we have three minutes. So maybe one person can answer this one. I wanna go back to this question that arose earlier about the tension between universal and targeted approaches. Have you seen that tension arise in your particular work? Do you think one is worked more effectively than the other? Have any general thoughts around that? I don't think I have a short answer to this question. Do you want me to go ahead? Yeah. So I think that in education in general, what we know about universal versus targeted approaches is that we need targeted approaches for students who are traditionally underserved in our school systems because they are getting less, not more right now than the average student across the board. So we do need those targeted approaches. And we also know that when we have universal approaches to interventions in education, whatever they may be, then in general, the people with the most social capital, the parents with the most social capital are the ones to immediately snap up those opportunities for their children. And I think about that a lot in the context of youth apprenticeship as it begins to funnel students towards high wage, high growth, family sustaining wage jobs that have sort of a greater level of prestige than say plumbing has traditionally had that a universal approach to these types of programs will mean that they're only utilized by the most privileged. Yeah, I agree. Did you want to wrap up? No, no, no. Cool. I can try to take a minute. I completely agree. Abigail, yeah, like one of the most frustrating things about policy, education policy in general is I think that there is like this pointing towards when I approach this all inclusive approach, but Abigail, you're 100% right. At the end of the day, when we do that, the people with the most social capital benefit the most. In predictive analytics, it's of particular importance to focus on structural and local interventions because different communities respond to different things, different ways. And if you're creating one-size-fits-all interventions for entire college communities where students are coming from different walks of life and backgrounds, you're guaranteed to rub people the wrong way and having those adverse effects and those unintended consequences. I think it also speaks to what Maya mentioned earlier about the scarcity framework and that if we really instill equity and that sometimes means that we're funneling resources, extra resources to particular groups of people because they need it. And I think that people are afraid that that means that there is less resources for them. And so that's sort of a question we also have to grapple with, right? That there is not a finite amount of resources that we really have to focus these where they need to be focused and ensure that people don't get forgotten in the design of something. I wanna thank you both for being here. This was a short conversation, but I hope one that sparks more conversations throughout the day, throughout our breaks and in our reception. So I just wanna thank you all for being here and listening to us and thank you both for coming on board and talking about the things that you're working on. So thank you. Really quick, we're gonna start a question and answer session, it's gonna be 10 minutes. We just wanna let you know to be mindful of waiting until you get a mic. But we'll go ahead and start right now. Okay, I'm gonna get a mic, yeah. Oh, sorry, we wanted to get Elise up here, sorry. And also in Mayaka, Mayaka is up here and Roslyn is around also if you have any questions for her. I'm trying to find out how you divide, determine the dividing line between the millennials and the successive generation. You use 96 or 94, how is that year maybe able to determine to be the boundary line between the millennials and, or you know, I'm trying to think where how they determine like 81 to 96 or 81 to 94. How those are the boundaries between the millennials and the other generations. I'll speak as a millennial. I think that, I don't know how they defined it. I think they just really drew a line in the sand and I think that's why the conversation we've had is how much can we really focus on these generational groups of people? How much can these labels really define us? So question to that is, I mean, we don't know. This question's for Abigail. What role do you think for-profit institutions play in the apprenticeship model that a lot of young people are going into, especially in areas where you see advertisements for these for-profit institutions that oftentimes pull resources out of people that are already cash-strapped and does that impact apprenticeship models or should they be nonprofit post-secondary institutions versus for-profit institutions? I think that I could safely speak for my program when I say that ideally it should not be a for-profit institution providing the post-secondary. I think that that to us wouldn't be a high quality model but to speak more to that it's funny that you bring up for-profits in the context of this conversation because we had a convening around youth apprenticeship here in this space last week and it's something that a participant brought up to us that youth apprenticeship actually has great potential for young people who are struggling to find their way into post-secondary institutions to avoid getting sort of into the clutches of for-profit institutions. The idea being that we make it easier for young people to access these programs and stay on sort of a safely guardrailed path through post-secondary so that when they leave high school they're not floundering and ending up sort of prey to those institutions which I thought was interesting and something I hadn't considered before. Any other questions? My question is for anyone from the first panel on the family leave. I wonder if you think the change in landscape of work in terms of the shared economy has what impact that has on policy? A little bit of hard time hearing you. Could you repeat that a bit louder? In terms of the change in landscape of work and the rising of the shared economy like Uber and Airbnb, what kind of impact that has on policies relating to families and equity? Yeah, that's something that we're actually very concerned about and interested in because a lot of our assumptions about paid family leave and other labor policies are, well, we assume that people are going to a nine to five job and that they have healthcare through their employer but what we know is that more and more workers, particularly millennial workers, they are working more hours, unpredictable hours, they probably don't have benefits and this is true not just for people or they work for Uber or Lyft but for others as well. So we're sort of trying to explore what the difference would be in terms of like a universal insurance model versus portable benefits, like how do we capture the most workers and also like our most vulnerable workers to make sure that they have access to those policies? It's not like an exact science because at this point, we're still like in the process of developing those proposals, partially because this is a phenomenon that is perhaps more prevalent in the US than it is in other countries that already have paid leave policies in place or already have more additional labor regulations around health insurance, paid leave and other policies. So ideally, I think in an ideal world, whatever the paid leave policy that we implement federally, which is probably not gonna happen in the near term but ideally that policy would capture both different types of work years, working different hours. So it's not like underpaid family and medical leave right now. You have to, in order to qualify, you have to work for an employer that has more than 50 employees. You have to have been at that employer for over a year. So already, like almost half the labor force it does not qualify even just for unpaid leave. So as we think about policies in the future, we wanna make sure that we're including part-time workers, hourly workers, contract workers, all the workers, like agricultural, domestic workers that aren't included in our current labor systems. So yeah. Hi, I have a question for Elisa. I was wondering how in your thoughts about, in BLL's work on paid family leave you're thinking about families that are not necessarily traditional and that they don't involve a birth but could be adoption or foster parents or older siblings taking care of younger siblings, anything like that. Yeah, so we, our approach to paid family leave, like we think that it's really important to be as inclusive as possible and this is part of our criticism of the Republican plan is that families take lots of different forms. So it is important to recognize the diversity in that structure and so making sure that we like to talk about the concept of family as something of love, blood, or choice. It might be that the person who's caring for your child is your neighbor. It might be a grandparent. It might be a same-sex partner. We wanna make sure that we're enabling people to care for those structures. So we've worked with organizations like a Better Balance to sort of talk through what that language should look like so that we include adopted parents, foster parents, LGBT community, or even, let's say, this is something that we've thought about a lot in response to sort of police shootings, for example, that often the people who end up caring for the children of people who have died may not be biologically related to those children. They may not be qualified, they might, because of that, under law, not be qualified to certain benefits even though they have lovingly resumed responsibility for these families that have been targeted by the police. So that is something that we're very much interested in further developing, yeah. So my question is for Abigail and Ernest. I'm curious about what correlations can be made, if any, with the New Youth Apprentice Movement and linking it in some way to the School Voucher Program and I know years ago it was meant to really support those in the lower income strata. And it's not really becoming a program that's really supporting that demographic anymore. It's really been, like the focus has shifted and others have really kind of figured out how to make it work to their benefit who weren't necessarily of that demographic that it was intended to support. And I'm curious with the Youth Apprentice Model taking hold and also just this movement for many students, millennials wanting to go to more trade school and even like non-traditional for your program, degree programs, like where you think there's a correlation if at all. And if it's an issue that needs to be thought about now as a possible potential problem later and if so, like what can be done now to ensure that that doesn't happen? Yeah, I think that's a fantastic question. And it's an interesting parallel one that I hadn't considered before, but I think there's a real danger in that as these programs become seen as I mentioned earlier, sort of more highly desirable and the type of education that people want to move into roles that they're interested in and how we guard against that I think is really an open question. And I think Jenny's framework of sort of targeted versus universal programs is one way to think about it, but it's a really thorny problem and one that we're excited to continue to work on. Regarding the earlier panel, we heard that a woman who's homeless has a family and has to wait on a long line or use a lot of time to get food for a family. Is there anything like Amazon Home Delivery, an equivalency that can be provided by the local jurisdiction that might make sense? In a case like that, there can't be too many cases like that, but something. And I wondered does this vary from jurisdiction or jurisdiction across the country? It must, I would think. Do you hear that clearly? Yeah, so your question is related to like how we provide food benefits basically and whether we can improve that or, okay. I also don't know if Roslyn would like to respond to that if she's in the audience, but yes, you're right. So I believe that was brought up in the context of stigma in accessing programs. So that would be cool, an Amazon delivery system that brought food to people, but you would have to make sure that you could get that to rural communities. You'd have to make sure that you, there's so many different aspects to that. And I guess in the context of this panel, which is about care and education and creating those inclusive policies, yes, there are technological answers, but we just need to make sure that we are considering the needs of the population when we are creating those technological answers and avoiding creating extra stigma or consequences that are unexpected, but we can check in on those by talking to the people that we are serving. Yeah, I think I want to add because I think that is something that had been proposed earlier. This year, somebody said about giving out meals like blue apron to communities. I think, I can't remember who, yeah. So I think you run the risk of again, having a paternalistic strategy, right? Like to dictate what food people are gonna get and then you have to dictate the quantity of food. And I think that's a slippery slope and I don't think that that's necessary. I think also like my concern is like, why do we allow so many people to endure the humiliation of being economically insecure and impoverished, which is not gonna be solved by delivering food to their house? Like they probably need money for other things, like medical care, they probably need money to pay rent. So I think that thinking about the whole picture of like a household budget, their emotional and other needs, like that is really, really important. And I think that to respond, I think to previous comments about targeted versus universal approaches, a lot of what we think about is whether there's like a yes and approach. So I'm thinking about paid leave. We want it to apply to everyone. We want it to be gender neutral, specifically since women have historically done more care work. But making sure, for example, that like the wage reimbursement rate is higher for lower income communities or that people who haven't done care work are encouraged to do so. So like making sure that we, that there's like additional supports for certain communities baked into the policy but that most people will have access to sort of the way that we like to think about social policies, yeah. Who has a mic? So for the education folks, it strikes me that a lot of what you are talking about or the barriers to some of the high quality apprenticeship implementation comes down to mindset and low expectations. And until replacing or raising the expectations of a workforce that has high expectations for students and young adults is a big task we've been undertaking for many, many years now. Have you seen any policy design or programs that have been able to make the shift to think about high quality apprenticeships and who needs the most sort of aside from getting in those adults who can think about it in that way of the design that you talked about, Abigail, in the beginning, have you seen any policy design that sort of helps to circumvent the adults with low expectation that still produces high quality outcomes for students? A short answer being, or are you studying it as part of this work? Yeah, so the latter, we are, we're studying it as part of this work, hoping to sort of over the course of years be able to lift up early success. I think like beyond, as you speak to the mindsets of adults, beyond that there also has to be some accountability to make sure that those mindsets aren't infusing program design. And so in these early stages, what we're really looking for and what we hope that people will do is collect and publish very clear demographic data about who they are serving and how well it is serving those students after they complete their apprenticeship. So that's what we're really hoping to see in these early stages. Thanks, I have a question about the paid family leave. You've referenced other countries kind of throughout your commentary and I would just be curious to know what countries you look to to kind of emulate their policies and kind of what is it about their policies that you think is particularly strong and that could maybe be adapted here in the United States? Yeah, so we, I think that there are, a couple years ago actually we had an event called paid leave leap progging and sort of trying to understand like what mistakes we can sort of see in other countries and what are things that we can learn. We did an evaluation last summer looking sort of the landscape of like how much, how long should paid leave ideally be in order to maximize infant well being and attachment, maternal health, gender equality and then business outcomes. And our conclusion and this has been reinforced by like public health officials out at UCLA is that we probably need at least six months for both parents of whatever gender they are to enable all of those things, especially for early attachment. There's also interesting data looking at the fact that if leave is too short, women won't take it. If leave is too long, it becomes very difficult for them to reenter the labor market. So there are countries that provide like three years of paid leave, but then they have a lot of issues with women's labor force participation. And then it's interesting, Iceland in particular, we always idealize Scandinavia, but like Denmark for example actually has an issue with like women's labor force participation because a lot of women will as the default just take paid family leave and the men will continue to work. And that's when the wage gap grows and inequality around who's taking care of children or the elderly or the disabled grow.  So if both partners take paid leave, then they will get additional time, which helps them sort of pay for infant care. And it's really in a very short period of time, bumped up the number of men taking leave. And what they've also seen is that when men take leave in the first like year of an infant's life, it helps to equalize the amount of unpaid care work they do in the household, either of the child or housework and that sort of thing. So it's really in a very short time period, like altered people's attitudes and perceptions of care work just in that context. So even within homogeneous Scandinavia, there's like a lot of diversity in terms of who's taking leave, who's providing care and how that affects the society at large. So yeah. It looks like we're out of time, everyone. So I wanna thank you all for your very thoughtful questions. It looks like we're gonna take a short break. There seems to be some refreshments outside and then we will be back in 15 minutes. Thank you.


Well, in case you haven't been on the internet in the past couple of days, you know that by now Eli Manning has been benched for this Sunday's game against the Raiders. That's just a hot topic that we're going to talk about for this week. Well, ladies and gentlemen, thank you so much for watching this episode of Time to Football. I'm your host, Hasan Khan. It's a sentence that I thought I would never say unless he officially retired on his own terms, but Eli Manning is no longer the starting quarterback for the New York Giants. First reported by Ian Rappaport of NFL.com, Ben McAdoo made the decision to start Geno Smith as their quarterback against the Raiders, ending Eli Manning's consecutive streak of 210 games started. In McAdoo's defense, he stated that over the next five games, he wants to start more players, giving them more opportunity to play, such as Geno Smith or the rookie third stringer Davis Webb. Like we said on top of the show, there's been a lot of mixed responses and emotions to the decision, mainly from fans who are outraged, but also former players such as Chris Knee, Sean O'Hara, Justin Tuck, O.C.U.M. and URA. A lot of players are speaking out as well. And even Tom Coughlin, who coached Manning in a little less than 200 games as a New York Giants, who now works in the front office of Jacksonville, says that he disagrees with the decision. Even current players such as Phillip Rivers, who was drafted in the same quarterback draft class in 2004 as Manning, said that the move is pathetic. As for our thoughts on Eli Manning, fans of the show know that we don't do scripts. Okay, I don't type something out before we go live. I don't read off the teleprompter. I'm looking directly at you into a camera right now, just talking. All we do before the show is I write down a topic that we're going to talk about and we talk about it. So, all it says right now is give thoughts on Eli Manning's bench. All it says. So, let's talk about it. Let's give you my thoughts on what I think about Eli Manning no longer being the starting quarterback for the New York Giants. I don't like it. The first game that I've ever watched, first ever NFL game was back in 2006. First ever Sunday night football game on NBC between the New York Giants and the Indianapolis Colts. Manning versus Manning and Peyton Manning and the Colts ended up winning that game. But that was a game that got me invested in the NFL. I fell in love with it after watching that game. And I loved rooting for Eli and the Giants throughout his entire career. Because a year later in 2007 when he faced the New England Patriots in Super Bowl 42, I was rooting for Eli. And then four years later in 2011 when he faced the Patriots again in Super Bowl 46, I was rooting for him again. Because throughout his entire career he's always been the underdog. Always has. He's always been ridiculed. He's always been mocked saying he's not good enough, saying he's overrated. He's always been compared to Peyton Manning, his older brother, when really his stats speak for themselves. Top 10 in almost every major passing category in his career. Being two and nine and making a decision to start someone else at quarterback, it makes sense. It really does. Only if your quarterback is part of the problem. Guess what? He's not part of the problem. Eli Manning is still a pretty good and solid quarterback. And the reason I know that is because I was watching the game about two or three weeks ago is when the Giants and the 49ers were playing this past year. And it was the most irrelevant throw in the world. It wasn't a touchdown. It didn't lead to the Giants winning the game. They ended up losing. Eli Manning was in the pocket and he was getting pressure thrown in his face. And he throws it towards the sideline. Perfect throw to Ricardo Lewis for the post-production video. We'll put it up on YouTube for everyone to see. But he had pressure in his face still through a perfect throw only where Ricardo Lewis could get the ball. And only the best of the best quarterbacks can make throws like that. When I saw that throw, I was like, dang, Eli Manning is still a pretty solid quarterback. You put any quarterback behind a bad offensive line with no run game so people are going to focus on the pass. With top two receivers injured, with a secondary that can't keep up and gives up a lot of points. Yeah, any quarterback is going to struggle in that situation. For Manning, it is sad. He has said that this is the hardest day for him as a New York Giants. And where will he be in 2018? I don't know. Is it going to be with Jacksonville? Because of Tom Coughlin? Will he be with Denver? Because they have a solid team around there just missing a quarterback? I don't know. We'll have to see. But I do think that the New York Giants for 14 seasons having him as loyal as he has been with the organization should at least give him the opportunity to finish his career if he does retire after this year or at least finish his career as a New York Giants for the next five games. At least give him that to finish the season with this organization that he's given so much, two Super Bowl championships to, so many memories for this organization. I hate to say it, but with Tom Coughlin gone, with Eli Manning more than likely gone as well, in New York it is an end of an era. And more than likely, McAdoo and Jerry Reese will not be back in 2018, so it's going to be a start of something new, something exciting, possibly we'll have to see. But for Eli Manning, I wish him the best.


What's everyone takedown here? Welcome back to another video. This is going to be the last video I upload before Christmas So I just wanted to take a minute to say Merry Christmas and thank you all for being part of my channel Also, it is that time of year again that I'd like to take two weeks off from recording any videos So this year I'm gonna do the same thing for the next two weeks. I'm not gonna worry about recording any videos I just want to take this time to spend time with family and really enjoy the Christmas season as of right now I'm planning to be back around January 5th recording new videos for you guys, but in the meantime I'm still gonna be uploading videos on my regular upload days, which are Tuesdays Fridays and Saturdays to still give you guys content I'm just not gonna be able to record anything in this time So I hope you guys all have a very Merry Christmas, and I'll see you all very soon


Hello and welcome to the session on Unified Modeling Language. In this video, we learn how to draw sequence diagrams for a software system to be designed. At the end of this session, students will be able to draw sequence diagrams representing designs to be used for software development. You have already learnt about the earlier UML diagrams that is class diagram, object diagram and use case diagram in the last videos. Now pause the video for a while and try to answer this question. What could be the next step after developing class diagram, object diagram and use case diagram in modeling a software system? Here is the answer. It is the interaction diagrams. There are two interaction diagrams namely sequence diagram and collaboration diagram. In this session, we are going to learn how to draw sequence diagrams. The contents we are going to cover are sequence diagram introduction followed by sequence diagram with an example. To start with, consider a scenario when we watch a movie. Instead of seeing continuous motion, we really see a series of static images played back fast enough to give the illusion of continuous motion. When directors and animators plan a film, they use the same technique. They build up a model of each scene sufficient in detail to communicate the intent to all the stakeholders on the production team. It helps the team visualize, specify, construct and document a model of the movie as it evolves from inception through construction and finally deployment. In modeling software systems, we have a similar problem. How to model its dynamic aspects? The value of visualizing the dynamic aspects of a system this way is quite limited. A better way to model the dynamic aspects of a system is by building up scenarios involving the interaction of certain interesting objects and the messages that may be dispatched among them. In the UML, we model these by using interaction diagrams by emphasizing the time ordering of messages and by emphasizing the structural relationships among the objects that interact. Sequence diagrams and collaboration diagrams are called interaction diagrams. An interaction diagram shows an interaction consisting of a set of objects and their relationships, including the messages that may be dispatched among them. A sequence diagram is an interaction diagram that emphasizes the time ordering of messages. We use interaction diagrams to model the dynamic aspects of a system. For the most part, this involves modeling concrete or prototypical instances of classes, interfaces, components and nodes along with the messages that are dispatched among them. All in the context of a scenario that illustrates a behavior. Interaction diagrams may stand alone to visualize, specify, construct and document the dynamic part of a particular society of objects or they may be used to model one particular flow of control of a use case. An interaction diagram is just a special kind of diagram that shares the same common properties as do all other diagrams i.e. a name and graphical contents that are a projection into a model. Now what distinguishes an interaction diagram from all other kinds of diagrams is particularly its basic contents. Sequence diagrams commonly contain objects, links and messages. A sequence diagram emphasizes the time ordering of messages. Graphically, a sequence diagram is a table that shows objects arranged along the x-axis and messages ordered in increasing time along the y-axis. We draw a sequence diagram by first placing the objects that participate in the interaction at the top across the x-axis. Typically, we place the object that initiates the interaction at the left and increasingly more subordinate objects to the right. Next, we place the messages that these objects send and receive along the y-axis in order of increasing time from top to bottom. This gives a clear visual cue to the flow of control over time. For example, figure shows a sequence diagram that specifies the flow of control involved in initiating a simple two-party phone call. First, there is an object lifeline. An object lifeline is a vertical dashed line that represents the existence of an object over a period of time. Most objects that appear in an interaction diagram will be in existence for the duration of the interaction, so these objects are all aligned at the top of the diagram with their lifelines drawn from the top of the diagram to the bottom. Objects may be created during the interaction. Their lifelines start with the receipt of the message stereotyped as create. Objects may be destroyed during the interaction. Their lifelines end with the receipt of the message stereotyped as destroy. Second, there is a focus of control. The focus of control is a tall, thin rectangle that shows the period of time during which an object is performing an action either directly or through a subordinate procedure. The top of the rectangle is aligned with the start of the action. The bottom is aligned with its completion and can be marked by a written message. In the sequence diagram shown in this figure, there are four objects involved, two callers SNR, an unnamed telephone switch and C, the reification of the conversation between the two parties. The sequence begins with the caller S dispatching a signal lift receiver to the switch object. In turn, the switch calls set dial tone on the caller and the caller iterates on the message dial digit. Note that this message has a timing mark that is dialing that is used in a timing constraint that is its execution time must be less than 30 seconds. This diagram does not indicate what happens if this time constraint is violated. For that, you could include a branch or a completely separate sequence diagram. The switch object then calls itself with the message root call. It then creates a conversation object C to which it delegates the rest of the work. Although not shown in this interaction, C would have the additional responsibility of being a party in the switch's billing mechanism which would be expressed in another interaction diagram. The conversation object C rings the caller R who asynchronously sends the message lift receiver. The conversation object then tells the switch to connect the call. Then tells both caller objects to connect after which they may exchange information as indicated by the attached note. When we model the dynamic aspects of a system, we typically use sequence diagrams to model flows of control by time ordering. Modeling a flow of control by time ordering emphasizes the passing of messages as they unfold over time, which is a particularly useful way to visualize dynamic behavior in the context of a use case scenario. Sequence diagrams do a better job of visualizing simple iteration and branching than do collaboration diagrams. In the next video, we are going to learn the other interaction diagram that is collaboration diagram. Now once again pause the video for a while and try to answer this question. What is a sequence diagram? These are the options. And the correct answer is option A that is sequence diagram is a diagram that shows objects along the top of the diagram and messages passed among them ordered in increasing time. These are the references referred. Thank you.


Hi, I'm Zor. Welcome to Unisor Education. With this lecture, I would like to start talking about trigonometry. Usually, I'm emphasizing that mathematics is more abstract, if you wish, kind of a science or a knowledge or whatever. It's more about mind rather than the real things which we are dealing with. Granted mathematics really started its own existence from some practical problems. However, contemporary mathematics is an abstract kind of knowledge. Trigonometry is something which is definitely having its roots in some practical problems. Before I talk about real trigonometry which is a strictly mathematical kind of a subject, I will talk about some practical problem which people were facing some time ago, I guess, which led to the development of trigonometry as a separate branch in mathematics. It's not like a definition or theorem or anything like that which I will talk about today. It's about some practical situations and maybe a little bit of geometry to justify the existence of trigonometry as a separate branch. What kind of practical problem think about led to the development of trigonometry? Well, I'm sure there were many. I'm just kind of fantasizing what can be the problem which led to trigonometry. Here is, for instance, a simple example. If you have some kind of a mountain, it has certain height which nobody knows what exactly the height is. We are standing here on the ground and we would like to know the height of this mountain. How can that be done? Well, obviously, you can probably go up the mountain and use your GPS positioning system or something like that. Well, it was not available at the time.  So, here is the way how people actually tried to solve this problem. People knew how to measure the distance. So, let's consider this distance is given, let's say a, from this particular person standing, watching, looking at the mountain. Also, people knew how to measure angles. So, if you remember, the angles can be measured by degrees. If you have an angle, it's divided into 360 degrees. So, this is 90 degrees and this is 180 degrees and this is 270 degrees and 360 degrees. So, they can measure the degrees of this particular angle. Another measurement unit is region. Region is an angle which has an arc equal in lengths to the radius. So, this is the angle of one region. So, no matter what the measurement is, whether it's a region or it's a degree, we can measure the angle. So, let's consider that we have this angle. Let's use letter 5 for this. So, with all this particular distance to the mountain and below the angle we view the top of the mountain. Is this enough to find out the height? Well, in theory, if you remember the course of geometry, these two characteristics are sufficient to construct a right triangle. Which means that yes, in theory, if you can construct the right triangle by using one catheters and an angle, it means this is somehow defined. But let's just talk about practicality of this. Practicality is that you cannot really construct it. It's not a piece of paper or anything like that. So, still you have a problem of measuring this particular height. But here is what somebody really understood the geometry of that thing offered. Let's have a rod or a stick or something much shorter than the length of the mountain. Now, if I will position it in such a way on the same line that I view these three points on the same line and I know the length of this particular shorter rod and I know this distance, let's call it C. What can I say about these two right triangles? Obviously, they are similar. Now, similar triangles have proportional sides. So, basically what I can say is that C over X is equal to C over A. Now, B I know, A I know, and C I know and that's how we can get to X. So, X is equal to C times A times B over C. Right? A times B over C. Now, this is how we can actually find the height of the mountain. A can be measured. B, we know, this is the rod which we actually have, we also can measure. And C is the distance on which if you would install this rod B, it will be viewed at the same angle. Okay, this is the beginning of trigonometry. And here's what I mean. Let's calculate B divided by C for all possible angles phi. Well, it's just 360 degrees or somehow in decimals you can have this ratio for one region for two regions or for 0.5 regions etc. and basically have a table of value of B over C B over C for any angle you have. Now, let's consider that B over C for any angle you have is tabulated somehow. So, there is a table which has the correspondence. Now, how can we construct this table? Well, basically we can have one particular B, one particular rod, and install it on one place, measure the angle, measure the C, and calculate. Put it a little further, angle will be smaller, B would be the same, C would be a little bigger. So, this B over C ratio would be a little smaller. So, basically moving B back and forth we can tabulate the values of phi, the values of this ratio for every phi. Now, when this is done, when this is a table which contains all the possible ratios B over C for every angle phi, we can say, you know what, we can measure the height of any mountain. How can we measure? Well, very simple. We install our viewing device at some place, we measure the angle phi, we measure the distance A, then we go to our tables for this phi we find this particular ratio, and now all we are saying is that X is equal to A times this particular ratio B over C, which we can found for this particular angle phi. So, this is all possible because the triangles are similar. So, for every fixed angle phi, this ratio B over C is exactly the same. This over this or this over this, this ratio is always the same. So, this ratio can be considered as a function of the angle. So, B over C, the ratio of the calculus which is opposite to the angle to the calculus which is adjacent to the angle is constant for every angle phi regardless of what exactly the size of triangles are. This can be bigger, this can be smaller, but the ratio is exactly the same. This is the beginning of the trigonometry. So, whenever people realize that they can calculate this ratio once and for all, let's say for every degree from 0 to 90 or something like this. So, it's just 90 calculations. Okay, fine. They did it once, they tabulated. And after that, they can measure the height of any mountain, any tree, any building or anything else using just a simple calculation. They have to know the distance from the observer to that particular object and the angle at which the top of the object is viewed from this particular thing. And the angle is also measured by somehow some device, obviously. And then you just multiply whatever the table says for this particular ratio, for this particular angle, by the distance to this object. So, this is the beginning of trigonometry, as I said. The foundation is similarity of all the right triangles which have the same angle, acute angle phi. And now people can actually expand it a little bit. Not only this particular ratio between the opposite calculus and the adjacent calculus is constant for a constant angle, acute angle phi, regardless of how big the triangle is. But all other ratios of different sides of this right triangle are exactly constant if the angle phi is fixed. Now, and here is something which they actually have defined as terminologies concerned. If you have the right triangle with these categories, and this is an angle phi, let's say. So, people came up with the idea that any ratio between these sides, if angle phi is fixed, is actually also fixed regardless of how big the triangle is. As long as this angle is phi, then the ratio of A over B, A over C, B over A, B over C, C over A, and C over B. All these ratios are constant for a constant phi, regardless of how big the triangle is. It can be this big or again to that big. As long as this angle is phi, then the ratio between these sides all are depending only on phi. So, people came up with terminology. This thing, A over B, which is opposite cartridges to adjacent, is called tangent. A to C is called sine. B to A is called cotangent. B to C is called cosine. C to A is called cos second. And C to B is called second, if I'm not mistaken. So, all these ratios are actually functions of the angle phi, of an acute angle phi. So, whenever we are talking about, let's say, cosine of the angle phi, what does it mean? Well, in this case, it means build a right triangle with one acute angle phi and take the ratio of adjacent cartridges towards hypotenuse. That's what it means. And regardless of what kind of triangle you build, as long as the angle is phi, this ratio will be the same. And that's why it's legitimate to call this ratio function of the angle. So, these functions are introduced, where introduced, in the beginning for acute angles in the right triangles. And again, there are some practical roots which we were talking about. Now, what's wrong with this definition? Well, it's okay for acute angles. No doubts about that. The problem is that, well, the contemporary mathematics again is much more abstract. We are not only talking about acute angles, we are talking about any other angles. What if it's angle 90 degrees? There is no acute angle of 90 degrees. There is no right triangle which has two 90 degrees angles. What if it's obtuse angle? I mean, then we are not talking about right triangles at all. And we would like to expand the functions and there were certain practical applications probably as well, but we are not talking about this right now. What's important is that this application is not really sufficient from mathematical standpoint. Since we have all different kinds of angles, we really would like to define these functions for all the values of the angles. Well, let me just give you an example. When people invented square root, they knew how to make square root of positive numbers, but they were basically completely helpless if we are talking about negative numbers. They didn't know what this is a square root of minus 1. So they kind of expanded the repertoire of their numbers and added complex numbers just to be able to apply the same function which is square root to any numbers which we know. And they knew about positive and negative numbers. So it looks like they were kind of restricted by having square root only to positive. So they expanded the numbers, expanded this set of different objects which they are dealing with. Same thing here. We have a function defined here for acute angles only. And this is actually not sufficient. Mathematicians were always not satisfied with these restrictions. So they always tried to expand the definitions in as much as possible. So the next lecture I will talk about the real definitions of trigonometry in contemporary mathematics. And that would expand the definition of all these functions to all kinds of angles. But that will be subject to the next lecture. Thank you very much.