I am so delighted to welcome to today's session Professor Vanessa Northington Gamble from George Washington University. Dr. Gamble is both a physician and an historian of medicine while at college at Hampshire College in Amherst, Massachusetts. Dr. Gamble studied medical sociology and wrote her senior thesis on the Tuskegee Syphilis study. That, in fact, would become a major area of interest for Professor Gamble during her career. She then completed her MD and PhD in the history and sociology of medicine at the University of Pennsylvania and completed a residency in family medicine at the University of Massachusetts Medical Center. Professor Gamble has taught at the Harvard School of Public Health, the University of Massachusetts, Hampshire College, the University of Wisconsin, Johns Hopkins. And recently, since 1997, has held the university professorship of medical humanities at George Washington University. In 1997, Dr. Gamble chaired the Tuskegee Syphilis study legacy committee. And some of you may remember that on May 16, 1997, President Clinton gave a talk in which he referred to the Tuskegee study as, quote, something that was wrong, deeply profoundly, morally wrong to our African-American citizens. I am sorry that your federal government orchestrated a study so clearly racist, end quote. During that talk, remarks delivered in the East Room of the White House, Mr. Clinton announced five reparations that he was prepared to offer in honor of the legacy of Tuskegee. And one of them was to establish at Tuskegee University a center to assure that medical research practices were sound and ethical. And President Clinton promised that monies would be made available for that effort. Some of you recall that it was Marion Secundi who trained with us in 1992, 93, who became the first director of the Tuskegee Center. And as Marion said at the inauguration of the center, I quote her now, the entire history of health care in the United States has been shamefully blighted by a long series of racial inequalities as a result, the legacy of distrust has been handed down from one generation to the next. But this bioethic center bears great hope. It takes us to the critical next step in changing the course of history for people of color. Tuskegee University serves as an ideal place to house the center both professionally and symbolically. The center will stand as a testament to those who suffered so unjustly in the name of science. End quote. Marion, sadly, is no longer with us. Some of you remember the book that she and Annette Dula and September Williams helped edit during their year here in the fellowship. It was a curriculum that they developed on African-American health care. And the book came out as it's called It Just Ain't Fair, The Ethics of Health Care for African-Americans. In addition to her remarkable work in the Tuskegee study and chairing the legacy committee, there's another aspect to Professor Gamble's work that I want to call to your attention. And that is that she has been a student of African-American hospitals in the United States and wrote two very important books about them. In fact, one of them, I believe, examines in some detail our local hospital. We'll see a picture, The Provident Hospital. The two books are first, The Black Community Hospital, Contemporary Dilemmas in Historical Perspective, and the second book, Making a Place for Ourselves, The Black Hospital Movement, 1920 to 1945, published by Oxford University Press. Dr. Gamble was appointed the head of the AAMC's division of community and minority programs in 1999. She's been a major contributor to committees and consulting groups at the IOM, the NIH, the CDC, and I could go on and on. It's a tremendous pleasure to welcome Professor Gamble, who will speak today on the topic that you see up on the board. Without health and long life, all else fails. African-Americans and the history of the elimination of racial disparities in health and healthcare. Vanessa, welcome to Chicago. Thank you. It's great to be here. I used to come to Chicago all the time as a kid when my grandmother used to drag me to church conventions. As a kid, I've spent a lot of time in Chicago, and when I was at the University of Wisconsin, I was down here a lot. And Dr. Sigler in his comments talked about my work with the CIFLA study at Tuskegee, and that it was my senior thesis, and it was my first introduction to bioethics. I was a student at the pacing center, but my friends like to point out that I'm milking my senior thesis 40 years later. So I'm, and I'm also milking something that goes today, something that goes even deeper, and that is my interest in African-American history. I grew up in Philadelphia at a place where African-American history was part and parcel of everything we did. It was not, first it was a week, then it was a month, but where when I grew up, it was a part of what our teachers wanted us to do. And I'm really happy that you mentioned Marion Secundi, because one of the things about Marion Secundi, which you did not know, is that we are both graduates of the Philadelphia High School for Girls. And so is Jill Scott, but all different generations. And what I wanna do today, and I have pictures here, and I have some comments, is that when we started talking about racial and ethnic disparities today, that one of the things we don't talk about, the history of these disparities, what are some of the programs that came in the past to address these disparities? And so I'm gonna focus on the African-American community, looking at what were some of the efforts in the campaigns of the African-American community in the early part of the 20th century. Because I really do think that many people think that it's only been in the past 20, 25 years, as I tell people, I've been doing work in disparities. And some of you, how I know in this room, how I understand this comment, I've been doing work in disparities before there's money in it. And so I just wanna talk about what the black community did to take care of itself. And here, and I have this life where sometimes I'm a historian, other times I do biotics, other times medical communities. So today I want to talk about history, and I've looked at what's been going on in this series. And I wanna start with the Heckler Report. The Heckler Report came out in October of 1985. This here is a picture of Margaret Heckler, who was Secretary of Health and Human Services in the Reagan administration, I'd like to add, who released the landmark report of the Secretary's Task Force on Black and Minority Health. And in this report, it detailed the stark differences, mostly between African Americans and other minority groups. The focus was on black health care, and we've changed it now to look at other underrepresented minorities. And in this report, it concluded that 60,000 excess deaths occurred each year in minority populations, and deaths that probably would not have occurred if the people had not, if they had been white. This report prompted the Department of Health and Human Services to establish the Office of Minority Health in January of 1986. I'd like to point out, the report came out in October of 1985. The office opened up in January of 1986. It's a different time in Washington. And that it also prompted the creation of offices of minority health at the state level. And one of the things that's been very interesting is that when I go around, everyone talks about, well, the Heckler report propelled racial and ethnic disparities onto the national research and health policy agenda. And I do agree that it did. And it led to many initiatives, work that's done here, sponsored by the Robert Wood Johnson Foundation. The fact that you've had this seminar for the past few months shows the interest in racial and ethnic disparities. But what I want to talk about today is what historical analysis shows you. I think one of the things that historical analysis shows is that the roots of the efforts to eliminate racial disparities in health and healthcare predated the Heckler report. The other thing I think historical analysis shows you is the tenacity of these disparities. And beginning in the early 20th century, African Americans, including physicians, social scientists, teachers, nurses, all developed programs to develop, to improve the black health status. And they frequently tied black health status to other events in the African American community. This was not just limited to health. This was an economic issue. This was also a political issue. Booger T. Washington, re-emphasizing here the Tuskegee connection, he once said, without health, it will be impossible for us to have permanent success in business, in property getting, and in acquiring education. Without health and long life, all else fails. Several years ago, there was a conference at the University of Wisconsin where I was a faculty member, and it was on African American Studies. There was nobody talking about healthcare. I took the chair's prerogative and inserted some comments. And I said it less eloquently than Booger T. Washington. I said, nothing happens if you're sick, dying, or dead. So the importance of how healthcare is so important, was seen as so important to the African American community. So in concert of what you've been talking about in terms of health disparities, I have two goals today. My goals are one, to demonstrate the agency of the African American community in addressing these disparities. And also to provide some background and historical analysis in terms of the contemporary campaign. This here is Dr. W. E. B. Du Bois. And in 1899, he published a book called The Philadelphia Negro. I'm a Philadelphian, so this for me, and my grandfather actually is mentioned in the book. He was a police officer at the turn of the century. And one of the things that Du Bois did in the Philadelphia Negro was demonstrate that how African American scholars and healthcare professionals combine not just scholarship, but scholarship and activism. That these were not two separate spheres. That in order to improve healthcare that African Americans also had to be very active in the political arena. And one of the things that Du Bois said in terms of looking at social problems is, we must study, we must investigate, we must attempt to solve. And in 1906, Du Bois published this book, The Health and Physique of the Negro American. And in this book, it was one of the series of monographs, research monographs that came out of Atlanta University, a historically black college university in Atlanta. And what Du Bois did was he used census reports, vital statistics, and insurance company records to document the poor health status of African Americans in comparison to white Americans. One of the objectives of this monograph was to refute the theories of Frederick L. Hoffman, who was the major statistician at Prudential Life Insurance Company. And one of the things that Hoffman said in his influential treatise, race, traits, and tendencies of the American Negro was that the excessive mortality rates of African Americans was going to cause African Americans to die out. So Prudential did not insure black people. So most of the people growing up in Philadelphia had metropolitan. Metropolitan did insure African American people. And one of the things that Hoffman talked about was that when we talk about things such as infant mortality, he saw it not based on social economic factors, but as part of the race traits and tendencies of African Americans. For example, he said things such as immorality was a rape trait and tendencies. And one of the things that Hoffman talked about was that because of emancipation, black people were going to die. And indeed, there were some people who thought that slavery should be reinstituted in order to save the life of black people. And these were sometimes seen in what we would consider mainstream medical journals like the American Journal of Public Health. Du Bois agreed that the health status of African Americans was worse than that of white Americans. There was agreement on that point. Where there was disagreement was what were the causes of what we now would call health disparities or health inequities. For example, Du Bois rejected Hoffman's argument that it had to do with racial susceptibilities. For example, he said the high infant mortality rate in Philadelphia was not a Negro affair, but an index of social conditions. And he contended that with improved education, improved social economic status, and better economic opportunities that the health status of African Americans would steadily increase. Dr. Charles Victor Roman, who was editor-in-chief of the Journal of the National Medical Association, the National Medical Association was the black medical society that was established in 1895, concurred with Du Bois. But he was even harsher in terms of his criticism of Hoffman, and he said that Hoffman's work, he contended that it was deductions and prophecies that gave solace to racism. The health of the physique of the Negro American served as the basis of the 11th Congress of the study of Negro problems that was held on May 29th, 1906. And in this, African Americans from all over the country gather together to study the health of African Americans. And there was a wide range of perspectives. One of the things I think is a challenge today when we look at disparities is, I do most of my work in healthcare, but then there are people who look at economic inequalities, people who look at educational inequalities, people who look at incarceration rates. There are very few times where we all talk together. We're all silos, but in 1906, at this meeting, people got together from various walks of life. And one of the things that Sam Roberts, who's a historian at Columbia University, talks about and he's written about the African Americans and tuberculosis focusing on Baltimore was that because of racism, black people had to work together in terms of there might be one black physician who would be alone. So you work with the nurse, you work with the social worker to try and address a variety of political, social, and health problems. At the end of the meeting, of this Atlanta meeting that was held in 1906, the conferees adopted several resolutions. The first was to call on local health leagues that the black community had to have health leagues to provide information about preventive health care and also urge existing health and social organizations in the black community to have health programs. The other thing that the conferees did was push Du Bois' agenda to not let the disparities in the black community be solely based on what people thought of as biology or race. That there had to be a spotlight also placed on socioeconomic factors. And the other thing that the resolution said that they did not find any adequate scientific warrant for the assumption that the Negro race is inferior to other races in physical build or vitality. The present differences in mortality seem to be sufficiently explained by the conditions of life. So they wanted the focus to be on socioeconomic factors. The other thing that the conferees did was to push for not just health care, but for research, but also activism. So it was this combination of you can study, but you also might act. This here is Dr. Virginia Alexander. She was a close colleague of Du Bois. I'm writing a biography of Dr. Alexander and I will tell you they were very, very close colleagues. And yes, that's what I mean. And throughout her career, Dr. Alexander epitomized the final resolution of the Atlanta conference. She spent most of her career look examining the links between socioeconomic status of African-Americans and crafted a career that combined public health and social activism. She graduated from the women's, she graduated as an undergraduate from the University of Pennsylvania, my alma mater. She then went and graduated from the Women's Medical College of Philadelphia in 1925. And then because of racial discrimination in Philadelphia, she could not get an internship. She left Philadelphia and went to Kansas City where she went to Kansas City Colored Hospital, also known as Kansas City General Hospital number two. We know who was in number one. And number two came about when they moved all the people out of the old hospital and moved them into one, except for white people who had infectious diseases. They got to stay with the black folks. In 1927, after finishing her postgraduate training, she went back to Philadelphia where she opened up a maternity hospital in Philadelphia. But in the summer of 1935, she was a Quaker and she got really involved in Quaker activism in Philadelphia and started looking at healthcare. And in 1935, at the meeting of the Institute of Race Relations, which was a Quaker organization, she, that was established to combat racism based on scientific strategies, she started getting really interested in healthcare issues. One of the things that Dr. Alexander did, she wrote a four-part report that was published in 1935 entitled The Social, Economic and Health Problems of North Philadelphia Negroes. And in this report, she painted a very, very bleak picture of the health of African Americans. For example, in 1926, black infants died almost twice as often as white ones. I mean, we're still dealing with that disparity in terms of infant mortality today. And in 1927, black Philadelphians died from pneumonia about four times the rate of white Philadelphians. And she, Dr. Alexander, attributed these sobering statistics to social and economic factors, such as inadequate housing, education and unemployment. She found that of the 500 black families surveyed, 47% of them had an unemployed head of household. And that 41% of the black families she interviewed in North Philadelphia were on welfare. And one of the things that she contributed this to was the discrimination in Philadelphia's hospitals. I mean, many times when I talk to students, they don't think about discrimination as being one, in healthcare, and two, discrimination being also a northern phenomena. And one of the things that she did in her report was document many instances of racism that people in Philadelphia experience. One patient talked about one of her fears and about not trusting a hospital. She said, I was told to go to Hanaman for an operation, but I was afraid to go because they always tell you that you need an operation when you don't. And then you can't have any more babies. This was in 1935. The other, and the existence of hospital discrimination in Philadelphia had been one of the primary reasons why Dr. Alexander opened up her own hospital. The other thing that Dr. Alexander did, she also asked black physicians and nurses about their lives. And she also talked about how, when she was on the phone talking to a nurse, a nurse was very nice. Then she shows up. The nurse is not so nice because they see a black woman as a physician. And one of the things that she strongly believed in, and I think because she was a Quaker, is that she thought that black healthcare issues should not be limited solely to African Americans, that it needed a broad interracial campaign in order to address them. And because she was a Quaker, she had inroads in the white community in Philadelphia, the way that many other black physicians did not. And so what she did, she used her connections with the Quaker community in Philadelphia to use that as part of Quaker activism in terms of desegregating, for example, Philadelphia General Hospital, which in the early 1930s did not have any black physicians at all on staff. And so between 1937 and 1940, three black physicians were named to Philadelphia General Hospital. And one of the things in terms of the campaign to desegregate Philadelphia General Hospital, it was involved that black people paid taxes. And since black people paid taxes, they should be allowed to have access to municipal hospital. And as her career progressed, Dr. Alexander remained an activist, remained a physician, but also got more involved in public health. And in 1936, at the age of 37, she became the first black person to get a master's in public health from Yale University. Now, one of the things that she talked about in her report was tuberculosis. And in the early part of the 20th century, in terms of disparities, the racial disparities, the focus of racial disparities in the African American community was on tuberculosis. And that the black tuberculosis rate was twice as high as the nationally, was twice as high as the white tuberculosis rate. And Du Bois says that the greatest enemy of black people was tuberculosis in terms of people dying from the disease. And so you find lots of efforts to try to prevent and also treat tuberculosis. Then the question was, why was it? And that's something that today, when we look at disparities, we have to say, why do we have these disparities in different groups? At the, in the early 20th century, there were a lot of people who said it was biology, that black people had inferior constitutions. There was one physician who was at Temple University by the name of Dr. J. Madison Taylor, who said that black people had more tuberculosis because they were structurally maladapted to live in northern cities. I guess he had never been to Chicago. And then the Washington physician, Dr. Edward Mayford Phil Boyle, vehemently criticized Taylor's theory because he said it incorporated widespread beliefs about the inferiority of African-Americans into medical discourse. So you see this tension about why, so why were the disease rates higher? And what do we do about them? What's very interesting, and I've been spending so much time looking at these disparities and seeing how African-Americans had higher rates of disease. And I just finished an article last year where I looked at the 1918 influenza epidemic. And there African-American had lower rates and so I had to wrap my mind around this, but it was still a racial disparity because white Americans had higher disparities there. So I think it's important to look at disparities more broadly. Now one of the things that happened in terms of, if you look at the discourse, a medical discourse in the early 20th century, is this tension. Was it biology? Or was it something else? And what we found is that African-American physicians and activists were pushing the socioeconomic status. That they were afraid to even engage in discussions about biology because of the widespread belief in eugenics. I don't know how many saw that, was the American Journal of Genetics Leaning that just came out, opening up their archives to looking at some of the eugenic materials that were published in their journals. That just happened the other day. And so you find this, not wanting to even address or think about biology because of so many widespread beliefs in the inferiority of black bodies. But even though there were these tensions about what caused it, there still had to be efforts to address the disease. So you find that African-American started anti-diberculosis league. There was a anti-diberculosis league in Denver that was started by African-Americans. The other things that African-Americans did in order to address health disparities was to start hospitals. That hospitals became important. And in terms of looking at the hospitals and in terms of trying to improve the black health status, one of the things that C.V. Roman, I showed you his picture earlier, who was at the Journal of the National Medical Association said, all history shows that ignorance, poverty, and oppression are enemies of health and longevity. And I think we can take that lesson today. And so between 1900 and 1940, African-Americans engaged in many strategies to address health disparities. One was to establish hospitals. It was easy to start a hospital at the return of the 20th century. And so they felt that they had to have hospitals because African-Americans, patients and physicians and nurses were not admitted to hospitals. For example, in Newport News, Virginia, for example, African-Americans were either not admitted or were accommodated in the local jail until a black hospital was established. And then in terms of segregation in healthcare, that there was some mechanism such as there was one hospital which in order to make segregation be more efficient, they said there should be slate blankets for the black patients and cream blankets for the white patients so that when you wash the linens, that the linens did not mix. And that was from a journal known as the Transactions of the American Hospital Association which is here in Chicago. But because of the intransigence of the color line in medicine, black people said we have to start hospitals. We have to take care of ourselves. This here is Emma Reynolds, who was from Chicago. Her brother was head of one of the African Methodist Episcopal churches here in Chicago and she wanted to be a nurse. And she was rejected from all the nursing schools in Chicago because of her race. And because of her rejection, Dr. Daniel Hale Williams in 1891 supported by had white support and black support opened at 29th and Dearborn Provident Hospital. And this was the first Provident Hospital in 1891 and Provident Hospital saw itself as a black controlled hospital. It was an interracial hospital, but it basically became de facto a black hospital. And because the primary impetus for the hospital was to train black nurses. In fact, Emma Reynolds graduated from the school and nursing school in 1893 but then went to medical school and went to Northwestern. It was from the women's medical school at Northwestern and spent most of her life as a physician. Daniel Hale Williams lived a professional life that was out of bounds for most black physicians. He graduated from 1883 from the Chicago Medical College.  He also was the first black physician on the state board of examiners. He had both black and white patients, but he also knew that his career was much different than most black health professionals. And so he called on the black community in 1910 to establish their own hospitals in order to improve healthcare. And he said, let us no longer sit idly and in namely deploring existing conditions. Let us not waste time trying to affect changes or modifications in the institutions unfriendly to us. But rather, let us seek to promote the doctrine of helping and stimulating our race. Let's start our own hospitals. And you see in the first part of the 20th century, African-Americans all over the country heeded Williams' warning. This here is Frederick Douglass Memorial Hospital and training school, which was in Philadelphia. And any of you who are familiar, Philadelphia, it was at the corner of 15th and Lombard in South Philadelphia. It was established by Dr. Nathan Francis Moselle, who I just like the three-piece suit and the fob. I think Dandy is probably the right adjective to describe him. He was the first graduate of the University of Pennsylvania Medical School. He graduated in 1882. Being a graduate of the Medical School of the University of Pennsylvania, I also like to point out he graduated in 1882. The first black woman graduated in 1968. But that's just a distinction. Yes, that's part of my history. So let's put it up there. But the thing is Dr. Nathan Francis Moselle, he too the same as Dr. Daniel Hale Williams had a very elite career, went to study in Europe, came back, could not get a hospital appointment. So he started the hospital. And here is a stage picture of his conducting surgery. Because a lot of these hospitals were established early on for surgery, where people can have surgery. So this is from the hospital's first annual report. You wanna see some? What do you, is that deep? Is there still not wearing gloves? Yeah, there's not wearing gloves. This was 1895. Yeah, there's still not, you know, even though it was a stage picture, I have some other pictures then where they were not wearing gloves. And you find gloves, not certain, it depended on the hospital because gloves were expensive. Those great Aikens pictures in Philadelphia of the gross clinic, also without gloves. Without gloves. And this one you can tell a stage is you don't see a lot of blood the way you see in the Aikens pictures. So, I mean, and... You don't see any black people in those pictures either. That's it, that's it. Especially doing surgery. Especially doing surgery, that's a point. But this here is Dr. Matilda Evans, who also graduated from the Women's Medical College of Pennsylvania. And she was the first African-American woman to practice in South Carolina. And in 1901, she also opened up a hospital. And here, this is 1901, still no gloves. And there she is conducting surgery in South Carolina. So the point here is in the beginning of the early 20th century, you see African-Americans starting hospitals. You also see the establishment of organizations such as the National Medical Association in 1895. The Old State Medical Society of North Carolina in 1887. And black nurses established in 1908, the National Association of Color Graduate Nurses. Now, one of the things about the establishment of these black hospitals is that you have to look at them in the context of segregation. That many black physicians just said, we wish we did not have to establish black hospitals. But if we wait to integration, the health of the race would suffer. And so we had to establish black hospitals. Not all physicians, even in the early part of the 20th century, believed that there should be black hospitals, but there should be, I mean, even when Provident Hospital was built, there was one minister who prayed that it burned to the ground because it was appealing to racism. This here is Dr. Louis T. Wright, who was a graduate of Harvard, one in Boston, medical school. Because every time I say people say Howard, I say, no, Harvard. So I just wanted to make it clear that he's a Harvard graduate, a medical school graduate. And he was also board chair of the National Association of the Advancement of Colored People. And he said that when we look at healthcare, the poor health status of African-Americans, and he said this in 1938, that we need to look at this, not as a racial problem, but as an American problem. That we need to do more and just look at it in terms of African-Americans. But African-Americans continued their self-help work if you look at the early 20th century. This here is Robert Rosamotin, who succeeded Booker T. Washington at Tuskegee as principal of Tuskegee. But before he went to Tuskegee, he started something in Virginia called National Negro Health Week. And part of this of National Negro Health Week was to have a campaign for African-Americans to take care of themselves, to have health brigades, to have education. And so he did this first in Virginia. But the other reason why he did it, he saw it as a business sense. One of the things when we talk about disparities today is that we're trying to get businesses involved in health disparities because they're paying for it in some respects in terms of health insurance or in terms of their workers being sick and not being able to work. And so one of the things he talked about healthcare was that the poor health status of African-Americans was a source of economic loss to the race and a hazard to the general welfare of the state. So he pushed businesses, the black business league, to get involved in healthcare. Booker T. Washington heard about National Negro Health Week and took it to Tuskegee where there's more of an infrastructure than there was in Virginia. And so Booker T. Washington has started to get interested in healthcare issues in large part because of the adverse effect of poor health had on the general advancement of the race. He got interested in it in large part because of the work of Dr. Monroe Work. Dr. Monroe Work was head of records at Tuskegee. And Monroe Work was a sociologist but had gotten really involved in what he called the gospel of health. The importance of taking the gospel of health to African-American communities. Now one of the things as a historian that Monroe Work did was every day he had his staff scour black newspapers. Then cut articles up and put them on five by eight cards. They used flour and water. So in terms of their lasting, it's been a problem. But they have now been microfilm. But one of the things if you look at what he did, you see one, what the concerns on healthcare was in African-American. This would be a great dissertation for somebody and I keep trying to get one of my students to do it and I haven't been successful. So I just wanna put it out there, great dissertation topic. And I'd help whoever wants to do it with it. And one of the things that Monroe Work did was he used data to look at economic loss. And he estimated that 45% of all deaths were preventable but also he estimated that 225,000 African-Americans died annually in the South and that about a half a million were seriously ill. So he painted this as an economic issue. Monroe Work prompted Booker T. Washington into action and he had a National Health Improvement Week that started in 1915 in April. And one of the things that he did was black churches, schools all over the country bought into this health week. Unfortunately, Booker T. Washington died before it took off. So actually this month is National Minority Health Month based on National Health Week. Booker T. Washington's work in terms of healthcare proved successful. The first Health Week 16 states held activities. Chicago was one of them. But one of the things that Monroe Work did was later was institutionalize it. So every April, black churches, schools, all over the country held health week activities. And the health week activities were like Monday was school day where they would do immunization. Sunday was church day. There would be sermons in church about healthcare. There would be complete health examinations for everybody. So the black community took in its own hands healthcare. This here shows what were the components of National Negro Health Week in terms of cleanup, mass meetings, school events, clinics. There was healthcare like in Tuskegee. When we talk about Tuskegee, when we talk about healthcare, we talk about the CIFL study. But Tuskegee also had a hospital, but also it had summer programs where black physicians from all over the country gave free examinations, but also got public training. This here shows the number of communities observing National Negro Health Week from 1924 to 1950. Excuse me. In the 1930s, Tuskegee realized it did not have the money or the infrastructure to run this. So they tried to get the federal government to run it. They tried to get the federal government to run it in large part because they felt the federal government had the resources and that having the approval of the federal government would put black healthcare issues on a broader platform. So it moved to Washington, where they opened an office of Negro health work in the federal government as part of the of a public health service. Unfortunately, most of the records of the office of Negro health burned in a fire. So there are, they did put out a bulletin every month called the bulletin of National Negro Health News. So you can get some ideas of what they were doing. But this was the first time since reconstruction after the Civil War where there was a Freedmen's Bureau looking at healthcare that the federal government said it was important for the federal government to be involved in improving the healthcare of African Americans. One of the things that, you know, there was, nationally there were activities. One of the things in terms of National Negro Health Week was here in Chicago. This is Dr. Mary Fitzbutler Warring who was a part of the National Association of Color Women's Clubs. She was involved here in Chicago with healthcare activities. This here is, and women were really important in the city's self-help efforts.  But, you know, this here is Luginia Burns Hope who started a clinic in Atlanta in terms of not just giving healthcare, but also political action around healthcare. Sanitation. They did petitions in terms of getting the streets in Atlanta paved because of the importance of sanitation for healthcare. But women's groups were very important in terms of looking at this. This here is Dr. Dorothy Farabee. She too graduated from medical school in 1925 and actually doing a dual biography of her and Dorothy Farabee to black women entering medical school in 1920. She went to medical school at Tufts. And in 1920, there were 65 black women physicians in the United States. And so looking at their lives. And she was involved in the Alpha Kappa Alpha, just let you know that for those of you who might be in deltas, that Virginia Alexander was a delta. Okay, so I got that covered. Okay, so just what you know, I'm not just focusing here on the Alpha Kappa Alphas. And those of you who don't know what I'm talking about, I'm sure someone would help you explain the differences in terms of the black sororities, okay? And those other sororities, I'm sorry. I don't have pictures of them yet, but I'm working on it. And one of the things that Dorothy Farabee did, she was head of the health committee of Alpha Kappa Alpha. And they had a Mississippi Health Project that went from 1935 to 1942. And a group of black women drove every summer from D.C. to Mississippi. The reason why they drove was a train conductor would not sell them tickets on a train. So they decided to drive. Now, I don't know how many of you are familiar with the Green Guides. The Green Guides were guides in terms of African-Americans traveling, like where you could stay at a hotel. Here it used to be Evans Hotel on the south side of Chicago. Where you could go to the bathroom, where you could eat. So they had to think about that, but they also had to think about whether there were hospitals in the communities they went through because they might have been in an accident and they could not get healthcare. So, but they decided that they were going to drive. And in the heart of the depression, the sororities of Alpha Kappa Alpha gave $2,500 to start this project off. I want to say in the heart of the depression. And so they volunteered. They went to, they went to Mississippi. And the reason how they got involved in healthcare, this is not supposed to be a health project. It's supposed to be an educational project, but they realized that when kids, as we know, when kids were sick, they could not learn. So they went, they went, they had to, sometimes they were, overseers were there with guns and they did their work. There were dentists, there were black dentists with them. There were some of the children who were there. And their first summer, they put over 5,300 miles on their cars. And by the end of the first summer, they did, they inoculated over 2,600 kids and they also did 200 physical examination. And by 1940, they had immunized over 14,000 children on their own dime. This was all pay, they did not get federal funding, they did not get county support. And the county supported them only so that the county didn't have to pay for it. This was, so they ran into difficulties. Here's Dr. Fairby with one of the children she saw. There's the sisters from A.K.A. in the middle, is Dr. Dettweiler, Walder, who was the health officer. There's Dr. Fairby again. And one of the things that started to happen in the 50s was that activities that looked at, that put black healthcare solely in the hands of African-Americans became under attack. In terms of integration. The office of Negro health work closed down because the federal government said that, that issues around black healthcare. And at this time, it was black healthcare. Actually, it was Negro healthcare. And in terms, it should be spread out within all parts of the federal government. But in the 50s and 60s, you start seeing the civil rights movement, the medical civil rights movements in terms of, no, we want to desegregate hospitals, that healthcare should be not just limited, even in the African-American community, should not be limited to the African-American. This picture is out a lot. This is a picture of the A.K.A. sisters in terms of some of the difficulties that they encountered in terms of getting their cars in the mud. And what they did with the cars, even though they hadn't planted the car, they made a medical caravan and went around. And something tells me that Dorothy Fairby took this picture, that she was not one of the people pushing the car. And I love the fact they're all in white, in their shoes, in the mud, just pushing this car. And so, what you see is that, especially in the 50s and 60s, you start to see grassroots activism, judicial decisions and laws, such as the 1964 Civil Rights Act and the 1965 Medicare and Medicaid legislation led to the desegregation of American medicine. One of the reasons why many black hospitals closed was because of desegregation. Yet, during the 1970s and 80s, it became increasingly clear that despite the significant impact of the medical-civil rights movement in securing access of black Americans to the nation's medical institutions, disparities persisted. And the gentleman, this here was Montague Cobb. He was an African-American physician at Howard, who was also head of the National Health Committee at, for the NAACP. He was a Latin scholar. I met him before he died. Good thing I remembered my Latin, because if I did not, I don't think he would have talked to me. But he really pushed for integration. And so you see in the 70s and 80s, this push for integration, and when thinking, and the belief was, you desegregate hospitals, the health disparities would go away. And we now know that's not true. And so Heckler's report in 1983, she did a health report to Congress. And in this, excuse me, she says, she talks about the continuing disparity.  The good news is the US health, the health status of most Americans is doing very well. The bad news is that there is this continuing disparity. And so that's what led to this report of the secretary's task force on black and minority health. And I urge you to look at all the volumes. It's a fascinating document in terms of trying to say what's causing it. And one of the things that it did was document. There's not a lot of information about what were the causes. But I think it was important to document. And so as I said, this report led to the establishment of the Office of Minority Health, not just black and minority health, but one of the things I think we need to do is get more data on other groups. The other thing that historians are starting to do is look at the health activities of other groups. Some of the resistance, say in Chinatown, in San Francisco, in terms of what Asians did to take care of themselves. So that we see what different communities have done, that these disparities have been with us for a long time. And that when we look at the history, we have to look at what the communities have done. And so one of the things that I have been very, as from this talk, I think you can see, is to say, what are the history of these disparities? What can we learn from how communities took care of themselves? But at the same time, I think that as we look back, we also need to look forward to the day when we're not talking about these disparities or these inequities. So thank you very much.  Just like that. I've got Dan Solmacy in medicine and the plane center. I missed you when you were in G.W. Recently. I just was interested. I didn't hear you say anything about the historically black medical schools. And I wonder if they were founded out of the same spirit and time, or do they have a different history? They have a different history. Because most of them, like Howard University, was established by the federal government. And a lot of Mahari was established by the Mahari brothers that were a group of, I think they were Baptists. And so a lot of them came from the schools that had been started by white philanthropists. Yes, there were some in the early 19th century. There was a small one, C.V. Roman, who I showed you a picture of, who was head of the Journal of the National Medical Association. He tried to start a very small medical school in Tennessee. So but they were mostly not coming up from the black community itself, but in terms of other people saying there was a need for black people. I mean, one of the things about the University of Chicago is that in 1920, the University of Chicago had the highest number, I'm sorry, Bill left because I wanted to tell them this, that in 1920, University of Chicago had the highest number of black medical students in the United States other than the black medical schools. And what started to happen was clinical education became important. So when clinical education became important, then people said, well, we can't accept black patients because black physicians, because white patients would not want them. And so Providence Hospital was actually between 1928 and 1944 was a part of the University of Chicago where they sent the black medical students. Yeah. So I have a question regarding sort of when you look at Chicago and the segregation and where people live, there's a question about what to do to improve quality because I was sort of very interested in the idea of self-help. And when people really were trying to help themselves, maybe they really actually could do better than when somebody else was trying to help them. And so you have this social policy that led to segregation and continued segregation and lack of resources to actually make hospitals function. So now that we have this health care reform, Medicaid, Medicare, all the sort of interventions that we thought would eliminate disparities have actually continued to widen the gap. And so what are your thoughts about the self-help and the idea of really thinking about community-based interventions that allow people to really see health and wellness as something that they have to take care of? Because it's very interesting when we went to do focus groups in the community and we were sort of asking the perception of hospitals around and why people really thought they should be coming to the University of Chicago. There was this constant feeling that they had inferior care in the community and they couldn't trust it. So they all wanted to come through the emergency room. So what is it that we need to do to actually provide care by doctors who care for people in their community and given that segregation is what we live with in Chicago? What are your thoughts about that? I think there's multiple layers to the question. Let me try to untangle some of those layers. I mean, I think it's interesting that when you talk about self-help, I think there's a difference between self-help and community that there's a combination between self-help and community initiation. Because in terms of what happens in the community, one of the things about these programs that I talked about, they were community-developed programs. And the reason why so many of them were not sustained were the lack of financial infrastructure. So that a lot of times when people say self-help is like, you could take care of that yourself and bring the money. So I think it needs to be this combination of community initiation but with support. The other thing, too, I think that your question points to for me is this whole thing that we have to also look at issues, broader issues around segregation. And I think that people today think that segregation doesn't exist. But those of us who look at this broadly, you look at census tracts, you know that's not the case. And so in the other thing about if you look and when you talk about segregation, I think, too, that we need to put more emphasis on class. Because when I grew up, I might have grown up with not a lot of financial resources in West Philadelphia, but down the street there was the housing project but also around the corner, the physician lived, because he couldn't go anyplace else. So there was a multi-class structure. So one of the things that's happening in a lot of communities is that they have become not just hyper-segregated in terms of race, but also in terms of class. And we don't collect a lot of data on class if it becomes a hard issue. But I think that the other thing that your question points to is in terms of solutions, I know Marshall knows a lot about this, is you have to look in specific communities. Because what works in Chicago might not work in Atlanta and definitely won't work in Tuskegee, Alabama, in terms of the history of the community. I mean, a lot of times people, sometimes, so what can I do to get my community to trust me? And one time I said to someone, I just got off the plane, I don't know your community, ask the people in your community, because the distrust might not be about the civil study, it might have been about something that was promised, say a clinic that was promised that was never delivered. I have a variant of Fumi's question, that most of your talk centered on the era of segregation and then sort of self-help and efforts within the community, although you hinted at the era of integration in the 60s and 70s. If you take a look at the current policy environment, even dating back like maybe eight years, where under the prior administration you had the first disparities report come out and efforts to suppress some of the disparities and censor that, to efforts now where there's a lot of transparency in terms of trying to encourage a collection of race, ethnicity data, performance reporting, as well as the most recent budget proposals, reaching from on one hand the Republican-Ryan proposal of shifting to the consumer, the burden and choices, versus more of the Obama approaches, which really rely upon expert opinions and choices. Can you talk a little bit about if there are lessons from the strains of history you've talked about, which inform more directly the current policy debates we're seeing and these major choices and approaches between Republican and Democrat? Okay, I think one way of looking at this is, first of all, we have to define, what disparities are we talking about? Are we looking at disparities in healthcare or disparities in health? So what are we trying to get at? If you look in the past that with the desegregation of hospitals, they were going after disparities in healthcare and they thought that desegregating the hospitals would lead to improvement of the health status and it turns out that was not the case. Some people maybe have gotten better healthcare, but I think one of the things that even these two proposals don't, there needs to be more emphasis on, and this goes back to Fumi's question, is the economy what's going on? And especially if most people get their healthcare as a condition of employment. That that's, so if you don't have a job and that even for some of the programs that, in terms of looking at consumer is that you might be out left in the cold, as we know there's some programs for kids that are doing better than others. But the other thing Marshall, I think where my concern is that it's almost akin, the whole consumerism thing, is akin to people's discussions on privatizing social security. You know, I have more knowledge than a lot of people about how I do my 401 program. How are people, how are we gonna do the education in terms of the consumerism and what do you need? And I still use your example from years ago Marshall, when you talked about getting patients to, you know, when they have their diabetes to come in and say I haven't had this yet, I haven't had, you know, I need to have my foot examination at this time. But I did not see a lot of efforts in trying to get people of all communities to understand, to be proactive in that way, despite what the funding mechanism is. And so I think one of the things that I think the past showed was people were going into the community saying this is what you need to ask when you go. Hi, thank you so much for the discussion. So you alluded to this a bit, but I'd like to drill down a bit further around the changing in the healthcare financing environment with the implementation of the Affordable Care Act, because one of the things that concerns me in its implementation, and particularly around poor populations are twofold. Number one, that there will be lots of increased demand without sufficient capacity. We see this on the South Side of Chicago in terms of the closing of hospitals consolidation and also the changing environment around healthcare financing without having those incentives aligned. One would think that with this implementation we would have a rising tide to lift all boats, but in fact it concerns me that the disparities will continue in spite of that implementation. And then secondly, because people have been delayed being able to get medical care on a timely basis due to a lack of health insurance, that there's actually going to be a tremendous influx of patients who have fairly complex medical conditions that will require a rise in the number of specialists that care for them without having the incentives aligned for those specialists to provide care because they are being supported by a Medicaid type of insurance. So if you could comment on that briefly. We know Medicaid's on the line these days. In many states. When, I remember some discussions before the act passed and I was invited to one of the talk backs they had. And I brought up the issue about what happened in Massachusetts in terms of, there wasn't the capacity. There were, you couldn't find a primary care provider being a nurse practitioner, physician or a PA. So in terms of the capacity, I agree with you that it is definitely an issue in terms of capacity. And one of the things that I've started to do, and earlier in my career, when I talked about getting more people of color in medicine, I was going on a social justice model. It's like affirmative action, social justice. Now I'm going on a preparedness of self-interest model telling people who's going to take care of you. A friend of mine says, wake up and smell the demographics. If you look to see who the young kids are in this country. In terms of who's going to take care of me when I'm older. So we start thinking about getting the capacity of more people going into healthcare. I mean, I think it's amazing what 10 years ago when I first worked at the double AMC, they were saying we don't need any more medical schools. There are enough physicians. They've kind of changed their tune on that one. But I agree with you, it really is a problem in terms of if you have the means but there aren't the institutions or the providers, it's just not going to, it's I think adversely affects disparities. Well thank you very much. Thank you. Thank you.


What is going on guys, today I am back with another Destiny 2 video and today I have something pretty epic and that is our first look at an Asylum's weapon that being a pulse rifle but before we go any further guys I am giving away a Rockstar Destiny 2 in-game exclusive gear called to win one simply drop a like on this video and leave a comment. Ok so thanks to Hardcore Gamer whose channel can be found linked in the video description We have some fresh new footage of Destiny 2 and the European Deadzone and the footage over on their channel shows many new things but today I want to talk about the pick of the bunch and let's start. Take a look at this weapon. How amazing does this thing look for damn sure. Now if we didn't know any of the wiser, seeing this weapon you would straight up think this is a Trials of a Cyrus pulse, yeah for sure that's what it seems to be but actually in my opinion this is not a trials weapon at all and here's why I think Firstly Trials of the Nine has been teased a lot, Trials of the Nine would also make a great addition to the game. Yesterday we saw the Playstation trophy dropped on the cyberwebs which also points and hints towards the Nine but then you are thinking what's this weapon and why is it themed around Trials of a Cyrus? Well let me explain, or Cyrus being the key word here, Trials of, let's forget about that part, most of us who bought Destiny 2 bought it with both expansion packs why wouldn't you? If you look at expansion pack 1 which is due out before this year ends, it's symbol you guessed it is Osiris so we will be getting DLC based around Osiris in some way or another and this weapon in my opinion is definitely a part of that DLC, it has to be, it makes more sense, it truly does but let's have another look at it in more detail, the thing is incredible in design it truly is, hopefully weapons in Destiny 2 are more designed around that which they represent and ain't just reskins as we used to in Destiny 1. In ADS with this weapon you actually see a sun symbol burning away below the sights which is a great addition but another great addition to this weapon is the Scallop logo under the sights, I am loving that for sure, in all honesty I can actually see this weapon being an exotic obtainable for doing a quest which comes with the first DLC for Destiny 2, I mean if we look at the weapons design it screams exotic in many many ways, might not be the case for sure but it does seem that way but what do you think about the idea I've put forward today? Do you indeed think as I do and believe this will be related to the DLC come the end of the year? Or do you think something else? Let me know down below but guys hope you enjoyed the video, thanks as always for stopping by, if you're new around here and enjoy Destiny videos be sure to subscribe and I will as always guys catch you on the next one.


Welcome back to our lecture series, Math 4230, Abstract Algebra 2 for students at Southern Utah University. As usual, I'll be your professor today, Dr. Andrew Missildine. In this lecture, lecture 15, I want to talk about the field of fractions, sometimes called the fraction field. It turns out that if you have an integral domain, every integral domain can be embedded inside of a field, and I want to explain how that happens. To begin with, I want to remind everyone, the important difference between a fraction and a rational number. So thinking of like integers, ratios of integers, simply put, a fraction is just an ordered pair of integers. So when I say something like two-fifths as a fraction, this really just means two comes first and five comes second. And so with that in mind, I can list lots of fractions. Two-fifths, I can take five-ninths, I can take seven-halves. It could be an improper fraction for all I care. Three-fourths, seven-sevenths, something like that. I can also talk about zero-thirds. I can talk about four-first. I can even talk about bump, bump, bump, 13 over zero, right? As a fraction, this is perfectly fine. Heck, I could even go zero over zero. This is a fraction that shows up in calculus all the time, but that's all that a fraction is. It's just an ordered pair of integers. Now, with that in mind, we don't usually write them that way. We write them like this, but that's not what one means by a rational number. A fraction is just this combination. And now we often are introduced to fractions as in the setting of rational numbers. So we're like things like, oh, things like this don't make any sense. Or we should write this as one, or we should write this as an improper fraction or whatever. I'm not gonna go through all those, but fractions themselves are just the first number. You have a second number and those numbers are integers. Now, of course, when it comes to the rational numbers, we're thinking of it as a ratio. We're thinking of it as division. And so we have to worry about some things. Like we don't wanna divide by zero. There's reasons to do that. We also have equivalency. Things like one half is equal to two fourths. Now, it's not the same fraction, but it is the same rational number. We consider those the same. And how do we know that?  And so two times one is two, two times two is four. So it's the same in that regard, but there's a lot embedded into that. It's like, well, why do we multiply the fractions top across top and bottom across bottom? That's not how you add fractions. Like it might take, for example, one third plus one fifth, this is not equal to two eighths as much as many early fraction users like to think. You don't just add across the top and bottom, but that's how we multiply. Why the difference, right? And why is two over two equal to one after all? So the real idea here is actually cross multiplication. These two fractions are equal to each other, because if you look at the cross product, one times four, that's the same thing as two times two. And so whenever that happens, we say the two fractions are equal to each other. Sorry. Two rational numbers are considered equal when their cross product is the same thing. So A over B equals C over D if AD is equal to BC, okay? And so really the rational numbers form an equivalence relation on the set of fractions where of course the denominator is never allowed to be zero. So you have to throw out some of the possible fractions, but then those which are considered acceptable fractions, including improper ones, right? Being improper can be acceptable sometimes. In that set of acceptable fractions, we define an equivalence relation where we say these are the same. And so really when we write a fraction, what we're meaning is this is the equivalence relation for the ordered pair AB, but there are other ordered pairs that can be considered the same thing and we write them as fractions because the fractions is to suggest division. So there's a lot loaded into that. And the reason I shared it is because I want to, I want to then generalize this to the setting of an integral domain. So note, if you're in a field F, then there's really in a field, since it's, every field is an integral domain, there's no proper divisors of zero because if there were, you could times it by a unit and that would imply that one is a proper divisor of zero. No, no, no, no. So there's no zero divisors inside of a field. So in particular, every subset of a field likewise has no, has any zero divisors, right? So in particular, if you take a subring of a field, it doesn't matter that subring has to be an integral domain. I mean, it could be a field, it could be something else, but every subset, every, excuse me, every subring of a field is necessarily an integral domain because if there were zero divisors here, then there would be zero divisors here, but fields don't have that. Okay, so that's an important observation. Every subring of a field is an integral domain. It might not be a field because the subring might not contain units. Like for example, Z sits inside of the field of rational numbers, it's an integral domain. That sits inside of that as two Z, sitting inside of that as six Z. All of these subrings are integral domains because they live inside of field, okay? What we wanna show is that the reverse direction is also possible, that every integral domain can be extended into a field. But how do you do that? How do you extend it? And it's like, there's nothing there. We have, where do I go? It's like you're in the darkness. What we have to do is we actually have to construct the field and we're gonna do that using fractions. So if you have an integral domain, say D, then, and again, this is the same D that's inside of a field. Take two elements, R and S, such that the second number isn't zero. Then we can define a fraction. What does this symbol mean, R over S? This means, oh, multiply by the reciprocal, right? R divided by S is the same thing as R times S inverse. So division can be introduced to a field because you multiply by the multiplicative inverse. Just like subtraction, when we define a field, we don't ever talk about subtraction because subtraction just means, if you take A minus B, this means A plus the additive inverse of B. Subtraction division are defined using inverses. Now, zero doesn't have an inverse, multiplicatively speaking, in a field so that we don't divide by zero, okay? So that's what a fraction is. So if we take the collection of all the fractions where the top's called the numerator and the bottom's called the denominator, so we take all the fractions where the denominator can't be zero, then the collection of fractions forms a subset of F and this subset is going to be a field, right? And we'll explain why that is a little bit later, but this collection of fractions, fractions coming from the integral domain, it forms a field and in fact, it's gonna be the smallest field that contains the integral domain, all right? So we can talk about fractions if we already have a field, but it turns out we can talk about fractions even if we don't have a field, right? Can we reverse this process? If we have an integral domain, is there necessarily a field that contains it? How do we construct such a thing? We're gonna construct it using fractions because a fraction is just, after all, an ordered pair of elements from the domain here, R and S, and we just apply an equivalence relation to that ordered pair and then those can make fractions and we can make a well-defined operation of addition and multiplication that forms a field. And so this is what we mean by the field of fractions. So this set, Fract D is gonna be this collection of fractions. After all, if you take the fraction field of the integers, you get back the rational numbers because after all the rational numbers are all the possible fractions of the integers excluding division by zero, of course, all right? So there's a couple of limits we have to prove before we can establish that this field of fractions is in fact a field. So what's the setting we're gonna live in? The setting we have to consider is an integral domain. So the first thing we have to do is you have to basically define what is Fract of D. So we're gonna first construct an equivalence relation on the set D cross D, but we remove zero, zero, okay? We wanna remove zero, zero. So we don't wanna divide by zero. Honestly, this zero over zero, if you remember from Calculus, this is an indeterminate form, it could be anything, right? It's sort of the same problem that we're gonna throw it out here. Now I want you to be aware that this set does contain things like, oh, I could have r comma zero in there. So in some respect, we are allowing division by zero temporarily. We'll throw it out later on. But we're gonna define an equivalence relation on this set D cross Z where we throw out zero, zero. And the equivalence relations what we saw before where AB is considered equivalent to the pair CD if the cross product AD is equal to BC. So we take A times B, excuse me, A times D and then B times C, that should be the same thing. If that's the same thing we claim this is an equivalence relation. So this is what we're gonna prove right now. Now, a little bit of notation that's not part of the proof, but this is really a definition. The equivalence class associated to the ordered pair A comma B, we denote that as A fraction B, right? For which we can write that using sort of like this notation or this notation, same basic thing, okay? So we're gonna denote the equivalence class of AB as the fraction. So a fraction is just an equivalence class of ordered pairs. We're also gonna show that if AB is equivalent to C zero then actually B was zero. So the only things that are equivalent to zero in the denominator were other fractions who have zero in the denominator. So with that then proven we will define the set of fractions of D to be all of these equivalence classes for which the denominator cannot equal zero. So we throw out when the denominator zero and since you can only be equivalent to zero in the denominator if your denominator was also zero that means we get the genuine fractions that we think about when we think of rational numbers. And so this generalizes the construction of the rational numbers. We can construct the rational numbers from the integers and it's this exact same construction. We build fractions as an equivalence relation on ordered pairs, all right? So why is this an equivalence relation? Well, we have to first prove it's reflexive. So why is the pair AB, why is it related to itself? Well, that's because AB equals BA. We're in a commutative ring. It's an integral domain after all. So since AB equals BA that means the ordered pair AB is related to AB. So it's reflexive. That was pretty simple, okay? Why is it symmetric? Suppose that AB is related to CD. That means that AD equals BC. But we're in a commutative ring. So AD is the same thing as DA and BC is the same thing as CB. And also it's an equation. So it's symmetric in that regard as well. Equality itself is an equivalence relation. So if AD equals BC, that means CB equals DA and that equation implies that CD is related to AB. So this relationship is symmetric. Why is it transitive? Well, suppose that AB is related to CD and suppose that CD is related to EF. Well, the first one implies that AD equals BC and then the second one implies that CF equals DE. This one I have to actually separate into a couple cases. So let's suppose that C is equal to zero. If C is equal to zero, that means B times C is equal to zero. And so AD is equal to zero. But also if C is equal to zero, that means CF is equal to zero. So DE is equal to zero. In that situation, we then get AD is equal to DE. And so since, you know, since D is not zero, notice here, if C is equal to zero, then D can't be zero. We threw out that possibility. So since C is zero, D is not zero, we can cancel out the D. And so you get that A equals zero. And so since A equals zero, that means the product AF is equal to zero. The product BE is also equal to zero. So we get that AB is related to EF. That's sort of a trivial case, but we have to consider it. Now let's consider the case where C is not zero. Why do I care about that? Well, if it's not zero and I'm in a domain, I can cancel it, all right? So let me actually scooch back up a little because I want to see the original equations all on the same screen so that you can follow along here. So consider the product AD times E, all right? So the original assumption is AD is the same thing as BC. So ADE, it becomes BCE, right? Redu parentheses on the left-hand side. This is the same thing as A times DE. And I'm just gonna remove the parentheses over here, of course, it's associated, it doesn't matter. Well, notice DE shows up as well. DE is the same thing as CF. So ADE is the same thing as ACF, which is the same thing as BCE. So moving the C around, we have C times AF, we have C times BE. Since C is not zero, aha, we can cancel it. And so we end up with AF is equal to, AF is equal to BE, which is what we're trying to check. If AF equals BE, that then means that AB is related to EF. And so we then have that this relationship is transitive. Since it's reflexive, symmetric, and transitive, this is in fact an equivalence relation like we were trying to show earlier, all right? Then the next part that's important to point out here, the other thing we gotta prove is that what if AB is related to C zero? So the denominator is zero. Well, in that situation, you have BC is equal to A zero, which A zero is equal to zero. So BC is equal to zero, okay? Now, because D is zero, C can't be zero because zero zero is not inside the set. So C has to be non-zero, so we can cancel the C, right? Because zero is the same thing as zero times C, we can cancel the C, and that's gonna get that B is equal to zero, which then proves this lima. This lima wasn't hard, it just was lengthy. It's some things we have to establish. So we know that we have this equivalence relationship on ordered pairs, and we then denote that equivalence relation using fractions. And so the set of fractions will be all of those equivalence classes where the denominator is not able to be zero, the denominator can only be zero. I should say it's only related to a zero denominator if you already have a zero denominator. So we've set up a situation which will never quote unquote divide by zero, even though we've never introduced division yet. All right, so we now have this, we have this set. So fraction D is in fact a set of equivalence relationships, equivalence classes, I should say, we then wanna put operations onto this. So we're gonna define the operations of addition and multiplication. And in this lima, we're gonna prove that these things are well-defined. And then we're gonna prove some other common properties here. So for example, if you, so okay, let's first define the operations here. We're gonna define addition of fractions in the following way. A plus B, excuse me, A over B plus C over D, that'll be defined to be AD plus BC over BD, right? So imagine when you add integers together if you don't have a common denominator, what do you end up doing? So you have one half plus like one third or something like that. You would rewrite this like, oh, I need a common denominator. This is going to be three sixth plus you're then gonna get two thirds. So this becomes five sixth, where six of course is two times three, the product of the original denominators. Where did the five come from? Well, the five is three times one plus two times one. So that's where five came from. So that's how we add these things together. So this is considered addition of fractions. Is this the usual rule we have when we add fractions together? Now I wanna point out that if the fractions already have a common denominator, you can just add the numerators together. We'll prove that as well. So this is the definition of the addition of fractions and then we'll prove that adding a common denominator is a consequence of that definition. But when it comes to multiplying fractions, we actually just multiply together the numerators and we multiply together the denominators. This of course will have the consequence that if you multiply a fraction A over B by C over C, right? Well, by definition you get A C over BC. I claim that this is then equal to A over B. So these two order pairs are equivalent to each other and these order pairs are equivalent to each other. Now, since the set of fractions is defined, well, fractions themselves are equivalent classes, there's always the concern that, well, maybe these operations aren't well defined. That's what we're gonna prove here in this lemma. So let's take two fractions, AB and CD. And of course, as they're fractions, we can now assume that the denominators are not equal to zero. So it should be clear that since B and D are non-zeros and we're in interval domain, the product of two non-zero elements is not zero as well. And so when you look at these fractions, AD plus BC over BD and AC over BD, their denominators are not zeros. So these are fractions that belong to the set. So as a function, it makes sense what it's saying. But of course we're concerned about, is it well defined? So suppose that AB equals A prime B prime. So these are two fractions that represent the same quantity. So like one half equals two fourths. We have that setting, that's what we're thinking of right now. So in that setting, if A over B equals A prime over B, then that means that AB prime equals A prime B. That's a statement in the domain D. Likewise, let's see that, where is the other one? What, C over D. C over D is equal to C prime over D prime. That would imply that C D prime equals C prime D prime. Okay, so imagine we have two representations for our two different fractions here. We have to prove that these different representations don't make a difference in terms of how we compute things. All right, so we have to prove, with regard to the addition here, we have to prove that A over B plus C over D is equal to A prime over B prime plus C prime over D prime. That's what we're trying to prove here, which of course this is defined to be AD plus BC over BD. This is defined to be A prime D prime plus B prime C prime over BD, B prime D prime like so. And so we have to argue that these two things are equal to each other. So what we need to show is that AD plus BC times B prime D prime. We have to show that's equal to BD times A prime D prime plus B prime C prime. So start with the left-hand side here. We can distribute the B prime D prime onto each of these and I'm gonna rearrange things. Take some liberty there using associative distributive commutative properties here. So we won't be distributed, we're gonna have A times B prime times D D prime added to B B prime C times D prime. Well, notice here, A B prime is the same thing as A prime B. So the prime basically moves to the other side. Same thing here, C D prime is the same thing as C prime D like so. And so then once we have these we're gonna move factors around. So put the A prime D prime together, put the B prime C prime together. So we have A prime D prime times BD. Then we have B prime C prime times BD. We can factor out the B prime and so then we get this. So that then proves the claim. These things are actually equal to each other, all right? So therefore that proves addition is well-defined. What about multiplication? Well, the same basic thing here. We have to prove that A B times C over D is equal to A prime B prime times C prime D prime. But what does the first one mean? It means A C over BD. And what's the second one mean? It means A prime C prime over B prime D prime. So we have to show that these things are the same fraction. So by cross multiplication, you should have that A C times B prime D prime is equal to BD times A prime C prime. So we're trying to prove this equation right here. So start with the left-hand side. A C times B prime D prime. If we reorder things, we're gonna get A B prime times C D prime. Because of the original assumptions, we can move the primes. So A B prime becomes A prime B and C D prime becomes C prime D. Then if we reorder things one more time, we're gonna get BD and A prime C prime. That then establishes what we're trying to prove there. So multiplication is likewise well-defined. Okay? Finally, I should mention that because we're associative or commutative, A times B C is the same thing as B times A C. And so notice what we have here. If you have A B times C C, by definition that's A C over B C, right? But then we cross multiply, you're gonna get A B C. And if you look at the other one, you get A B C. That's the same thing. So yeah, you can reproportion fractions in the usual way. And then next, what about adding a common denominator? Well, by definition A over B plus D over B, that becomes A B plus B D over B B squared there. You can factor out the B. So this becomes B times A plus D over B. And because of the previous property, we can cancel across the fraction bar.  And so this proves the usual properties of fraction addition and multiplication. The main topic for this video lecture here, the idea of the field of fractions of an integral domain. Let D be any integral domain. Then this set of fractions that we talked about before for which we've now put upon it a well-defined operation of addition and multiplication. This set of fractions is in fact a field called the fraction field of the domain or the field of fractions. And in particular, we can visualize D as a subring of the fractions. And when we identify D with the set of fractions of the form A over one where A is some element of that. And so we can embed every single integral domain inside of a field of some kind. A similar proof can also be done for domains can be embedded inside of a skew field. But we're not gonna worry about that. Having the commutivity makes things a little bit easier. And that's where we're going to land in this video right here. So because of the way we defined addition and multiplication for fractions, it essentially comes from the associativity and particularly the commutivity of addition and multiplication in the integral domain. So we're gonna have that multiplication and addition are commutative operations, okay? Second, these operations are gonna have additive and multiplicative identities. The element zero over one, in fact, you could take zero over any non-zero element of the domain, that's gonna serve as the additive identity, right? Because if we take anything, any element A over B, if you add to it zero over one, this is gonna become one times A plus zero times B over B times one. That simplifies just to be A over B. It's the additive identity. Same thing we get for multiplication. If you take the fraction one over one or in fact A over A for any non-zero element, you'll get the same thing. A over B times one over one, by definition of the multiplication, you get one times A over B times one, you get A over B. So we have identities, multiplicative and additive. Like we said, we have commutivity. We're going through all the axioms of a field here, all right? Then the next one to consider is going to be the idea of inverses, right? So we have additive and multiplicative inverses. In particular, the additive inverse of the fraction AB is going to be negative A over B. Notice if I take A over B and you add to it negative A over B, by definition, this will be AB plus negative A over B over B squared. AB and negative AB, these are additive inverses in the domain D, so you get zero over B squared. And like we saw before, this is the same thing as zero, the additive inverse. What about multiplicative inverses? Well, this is just the common rule of times by the reciprocal, right? If you take A over B, you're going to times that by B over A. Now, since this is not the zero element when we talk about multiplicative inverses, we know that A is not zero, so its reciprocal actually does make sense. You end up with A over B, excuse me, AB over BA. This simplifies just to be one with how multiplication works. So we have identities, we have inverses, we have associative, excuse me, we have commutivity. Commutivity was pretty straightforward. Associativity does require a little bit of an argument here. Multiplication is fairly straightforward because really multiplication is essentially just component-wise multiplication like we would with a direct product. Addition's a little bit more complicated, so let's look at it. If you have A over B plus C over D, and you add to it E over F, we'll do the first two first. This becomes AD plus BC over BD. Then when we add these two together, we end up with AD plus BC times F plus BD times E over BDF. I'm using associativity throughout here and commutivity as well. So distribute the F in this situation. We get ADF, BCF and ADE as terms in the numerator. So then we're going to regroup these things. ADF can be written as A times DF. The second two terms have a common factor, B factor it out. So we get B times CF plus DE. We still have BDF in the denominator. So notice that this right here is exactly the sum of A over B plus CF plus DE over DF, which of course this right here is then the sum of CD plus E over F. So it's fairly straightforward, just work through it. So addition is associative, like I said, multiplication is associative as well. So the last thing that we need to do to prove that it is a field is to prove the distributive laws. Since we've already established that multiplication is commutative, we only have to prove one of the distributive laws. So we're going to have here A over B plus C over D times that by EF. And we want to argue that this distributes throughout here. Let's first add the two fractions together. This becomes AD plus BC over BD. Then when we times it by EF, we'll times the numerator by E, the denominator by F, distribute that E throughout the numerator. We get ADE plus BCE over BDF. As we learned earlier with addition, we can break this fraction into two fractions. So we have ADE over BDF and then BCE over BDF, like so. And each of those are some cancellation we can do. There's the D that cancels here. There's a B that cancels here. So we have AE over BF plus CE over DF for which each of those we can factor for which you're going to get AB times EF and you're going to get CD times EF. And voila, we then have the distributive property. So all of the axioms of a field are satisfied. So this set frack of D is in fact a field and it will contain an isomorphic copy of D. So up to isomorphism, this is going to be a field that contains D. And we can also argue it's the smallest field that contains D. So I want to say a little bit more about that. So let F be any field and suppose that D, an integral domain necessarily, is a subring. Then we can identify up to isomorphism, the fraction field of D as a subfield of F as well. And the identification simple, every fraction A over B is identified to the product A times B inverse. So if you take a fraction like this, be aware that A and B are elements of the domain and necessarily B is not zero. So it has an inverse in the field. So A times B inverse is an F. And so this is going to show you that you're a subset right there. So we can identify the fraction field with a subset of the larger field like so. And so what about our operations? Does addition and multiplication of fractions coincide with addition and multiplication in the field? The answer is yes. If we add together these fractions, we make the identification A over B becomes AB inverse, C over D becomes CD inverse like so. I can insert in between the A and the B inverse, A, D, D inverse. I can insert between the CD inverse, a BB inverse. Really what you want to be thinking here is I'm multiplying by B over B and I'm multiplying by D over D, all right? And so removing things around by associativity and commutativity we are in a field. This becomes AD times B inverse, D inverse. And the second one becomes BC times B inverse, D inverse for which we have a common factor of B inverse, D inverse. We can factor it out by the Shusot principle. The inverse of BD is just B inverse, D inverse we have so. And so then if you have a product times an inverse, this is, I should say a factor times an inverse, that's the same thing here. So multiplication, excuse me, addition of fractions is the same thing as addition inside of this field. Likewise, when it comes to multiplication, if we multiply two fractions, well A over B becomes AB inverse, C over D becomes CD inverse. This is commutative, we can move things around. So this becomes AC times BD of B inverse, D inverse for which of course that's the same thing as BD inverse. I mentioned the Shusot principle earlier, but as we're multiplicative, the multiplications commutative, the order doesn't matter whatsoever. So we have AC over BD inverse, that's the fraction AC over BD, all right? So this fraction, this set of fractions behaves like, as to say they have the same operations, addition and multiplication are the same with the field, whether it's a field of fractions, it doesn't make any difference. So in fact, the fraction field of D is not just a subset, it's a sub ring of F, same multiplication, same addition, and associative to commutative distribution, this all is gonna work just the same, no problems with it whatsoever. And so one last thing I wanna mention is this idea of a prime field, okay? Because what the previous theorem told us, I guess the previous corollaries, what we call it, told us is that if any field contains an integral domain, then it contains its fraction field as well. So the fraction field is the smallest field that contains it up to isomorphism, of course. And so we can actually categorize the smallest field based upon a characteristic. Suppose F is a field of characteristic zero, that field will contain an isomorphic copy of the integers, okay? Because we just take the unity of the field, and so we take the smallest ring generated by one, the unity, that'll give you something that's isomorphic to the integers. Therefore, the field F will then contain an isomorphic copy of the field of fractions of the integers, which of course is the rational numbers. So every field of character six zero contains an isomorphic copy of the rational numbers. And so this will be referred to as the prime field of character six zero. It is the smallest field of character six zero, because any other, well, as we saw here, any field of character six zero will contain Q, it's the smallest one. We can do this for a field of characteristic P as well. Because if you have a field of characteristic P, we're gonna do the same thing. We're gonna look at the subring generated by the unity of the ring. That's gonna be isomorphic to the field, the finite field ZP, where P is some prime, of course. Now, the fraction field for ZP is itself ZP. It's already, ZP is already a field, so it's its own fraction field, it's important to mention. And every finite domain is in fact a field. So if I take the unity in F, it'll generate a finite integral domain. That's gonna be a field, it's gonna be ZP. And so we then refer to ZP as the prime field of fields of characteristic P. Every field of characteristic P will contain a copy of ZP. And so Q, the rational field, and the finite field ZP, where P could be any prime number, these are referred to as the prime fields because they are the smallest fields of each characteristic, a consequence of this field of fractions.


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Today, Lakshadeva is transforming into a model union territory under the visionary leadership of Honourable Prime Minister Sree Narendra Modi Ji, who took the country to new heights of development and the determination of our dutiful Administrator Sree Praful Patelji. To mark a momentous beginning to a promising tomorrow, the foundation stone is being laid for projects worth Rs. 31 crores. The new primary health centre in Kalpani Island is being constructed at a cost of Rs. 28 crore. This state-of-the-art facility is designed as a centre for healthcare experience, having 32-bed capacity with specialties of general medicine, pathology, microbiology, radiology and ICU facilities. This facility will ensure inclusive, cost-efficient and efficient healthcare to the people of Lakshadeva. The foundation stone of five Nandhgarh's Anganwadi's is being laid today in the five islands of Androdh, Chetlat, Khadamat, Akati and Minikoi. These facilities are proposed to have child-friendly infrastructure and shall sow the seeds for a promising tomorrow, ensuring holistic development of children aged 3 to 6. This day marks a crucial milestone as it unfolds a new era of development. A beginning of a transformative journey for the people of Lakshadeva. Committed to the ideas of inclusive development, Lakshadeva shall rise as a hub for prosperity, innovation and advancement, paving the way for Vixit Lakshadeva. Vixit Lakshadeva, Modi ki Garanti