Hi everyone. Welcome back to the forum webinar series. My name is Priya Chhaya. I am the associate director of content for the National Trust for Historic Preservation. In case you don't know, Preservation Leadership Forum is the professional membership program of the National Trust. This webinar series is made possible by the Campaign for Where Women Made History and members of Preservation Leadership Forum, and we sincerely thank all of you that are with us today. Today's webinar is the first in a series that we are calling Women Are Essential. This series focuses on interpreting the complexity of women's history and identity at historic places. For today's session, we will investigate the different ways of seeing women in every historic place. We hope you will come away from this webinar with an appreciation of the historic impact of women, as well as various strategies and case studies to shape a fuller and more honest American story. But before we begin, there are a few technical things for you to know. We will be taking questions from the audience at the end of the webinar. Please send the questions via the Q&A function on your control panel directly to the panelists. Don't put them in the chat. We'll only ask you to put them in the Q&A instead. You're welcome to submit your questions at any point during the webinar, but we will only be answering them at the end of the session. That being said, you are welcome and encouraged to communicate to all participants during the webinar using the chat function. We also have enabled the closed captioning function for this session, and you should be able to see it working right now. If you'd like to hide it at any point, you just have to check your settings or click the CC button on your control panel. Following the program, we will send out a recording of today's webinar directly to the email you used to register. And finally, all four webinars are archived in our forum webinar library, and we will share the link below. I also wanted to mention that in the reminder email for the webinar, you should have seen a link to hand out for the session. We'll drop the link for that in the chat during the conversations today, and also include that in the follow-up webinar, follow-up email as well. And so now I'm going to turn the program over to Chris Morris, the Senior Field Director at the National Trust for Historic Preservation, and also the Manager of the Wear Women Made History Campaign. Hi, Chris. Hi, Priya. Thank you so much, and thanks to all of you who joined us today for what I know will be an illuminating conversation that's going to change the way that you look at historic sites and cultural resources. As Priya mentioned, my name is Chris Morris, and in addition to my role as Senior Field Director here in Los Angeles, I've had the honor of managing the National Trust Campaign for Wear Women Made History for the last year or so. Next slide, please. The Campaign for Wear Women Made History is a direct manifestation of the National Trust's commitment to tell a more full and truthful American story. The trust, and in particular, my colleague Priya, along with many others, have long been committed to recognizing and elevating women's roles in our work. But over the past year, we've taken a much more focused and systemic approach to elevating the achievements of women and supporting the next generation of women preservationists. Virtually every aspect of our programmatic work, from our grant making to our historic sites, our corporate partnerships to our annual list of 11 most endangered places, our advocacy efforts, our storytelling, and our hands-on preservation experience has centered women in ways that also attempts to recognize the complexity and intersectionality of their identities. I hope you'll take some time after today's training to explore the many projects, people, places, and stories of women's achievement that are featured on our website. And of course, I hope you'll all come back and join us for the second part of this training on August 12th. Next slide, please. And now it is my pleasure to introduce our moderator for today's webinar, Dr. Heather Heich. Heather, join us on the screen. Heather is not only the author of the recent book, Doing Women's History in Public. She's an educator and a staunch advocate for women's history who has been leading the charge to reveal the essential roles that half of the population played in influencing every aspect of our society, through her work with the National Park Service and her leadership of the National Collaborative for Women's History sites. Heather has been absolutely instrumental in showing historic sites how to see, reveal, and communicate women's presence for decades. And she is the ideal person to lead us in this conversation today. So, Heather, thank you so much for helping to lead this discussion. And I'm going to pass the mic to you. Thank you. And thank you. I really appreciate it. Today, I would like to introduce my co-panelists and then make a short presentation. Dr. Emily Murphy is curator at Salem National Historical Park. In Salem, Massachusetts, she has a BA from Tink Johns College and a PhD in American Studies from Boston University. She specializes in early American decorative arts, material culture, and social history. And a book that includes a chapter of hers arrived today and is behind me on the bookshelf behind me. John Fowler, the second, is a park ranger and digital media coordinator of historic homes of National Capital Parks East in Washington, D.C. He has a great love for history and a desire to share that. He specializes in bringing the history to digital platforms by way of social media and youth engagement. And he has worked at eight national parks. Barbara Lau is the executive director of the Pauli Murray Center for History and Social Justice, a national historic landmark in Durham, North Carolina. She has 20 years of experience as a folklorist, curator, professor, oral historian, media producer, and author. And she has done exhibits, Pauli Murray, imp crusader, dude and priest, and also to buy the sun. She also teaches various courses. So we have a wonderful group here. And I will begin by talking a little bit about some of the essential finding essential women, a place based approach for American women. As we said, the trust is committed to preserve and protect and share our full story, one more complicated and much less certain than once taught, like national park service efforts, it builds on the 2020 suffrage centennial and seeks women everywhere. These two webinars ask different questions, such as who packed this copper miners lunch bucket? Or what happened to the girl who embroidered this sample? We will share tools and examples and how to find past women and their associated history to gain greater accuracy in understanding the past so that we can tailor our history to better fit what actually happened. Knowing what previous generations of women faced and accomplished empowers and encourages us today. In largest preservation audiences and advocates and encourages justice because omissions are also wrongs. Today's webinar features three distinct houses, a seaport house that was also a commercial space, a famous man's mansion, and a formative childhood home now under restoration. We will focus how we can learn about these places and find the stories and amazing women associated with them. The August 12th webinar will share how these three more sites have revised their interpretation to tell their fuller story, Fort Snelling, Shadows on the Tesh Plantation, and the Charles Russell home with dramatically different women. So we want to share the rich variety of American women's lives and how to research, preserve, and interpret them. These women and places challenge us to see more clearly the efforts men and women made. We want to show how essential they were in our lives then and now. Dr. Emily Murphy will discuss the Narbone House and Salem, Massachusetts, which provides a counterpoint to our image of male only seaports. In maritime communities, women provided continuity even under their legal and social limitations, because men were at sea or sometimes lost to sea. Nathaniel Hawthorne, who worked in the nearby U.S. Customs House, described in his House of Seven Gables, a scent shop, C-E-N-T, a convenience store that sold thread, yeast, flour, and candy. In the Narbone House, where two single women, Mary and Sarah Narbone lived, we can easily see their scent shop as they struggled to stave off economic disaster, their poverty and persistence intertwined with the goods they sold and the things they sewed. John Fowler will discuss Frederick Douglass. In 1878, Frederick Douglass, known for his strong dedication to women's rights, bought a mansion where his first wife Anna Murray Douglass and later wife Anna Pitts Douglass lived. Douglass could not have made the major transitions from being enslaved to being a newspaper owner and editor and later a national Black leader without many women's support. His newspaper, The North Star, had a motto which proclaimed his life mission, right is of no sex, truth is of no color. Barbara Lau will present the childhood family home of the Reverend Dr. Pauli Murray. Murray's experiences there grounded her life to become the amazing lawyer, civil and women's rights activist, poet, priest, and theorist. She lived and resisted cruel complexities of race, gender, and sexuality and profoundly shaped the jurisprudence of Supreme Court Justice Ruth Bader Ginsburg. Both Douglass and Murray combined writing and theology with fierce dedication to American democracy, demanding rights and respects for everyone. They broke trails we use. One of the joys of being a historian is encountering remarkable people and coming to know them. We are especially fortunate when we enter their homes and their lives touch ours. Places where they live provide insights. Douglass bought an estate overlooking the nation's capital during American apartheid. Murray's crib was placed on the stairway landing of the home of her formerly enslaved grandmother and wounded Civil War veteran grandfather's home which shows her family's love and determination. The 10,000 square foot building once the home offices and warehouse of Clara Barton, the American Red Cross and its workers shows her creative frugality when she stretched Muslim cloth across Joyce to create its ceilings.  Historic places show us stories and introduce us to amazing women. Next slide please. Preservation begins with the not so simple recognition that a place has significance, that the lives of American women are important. When Elizabeth Cady Stanton's classic Greek revival house was painted a bright turquoise, its color demonstrated its insignificance. Only recently, the modest but crucial gathering place, the San Francisco home of LGBTQ pioneers, Phyllis Lyon and Del Martin, founders of the Daughters of Bilitis, the first lesbian rights organization, had its significance recognized when it became protected as a local historic landmark. The physical work of preservation includes caring for tangible resources, landscapes designed or vernacular, architecture, both buildings and structures and objects of all kinds. Preservation prolongs tangible resources existence. Research in the knowledge base supports preservation of resources and interpretation with the use written sources from diaries to account books to census records increasingly use oral history, visual sources and quantitative big data. Those of us who work with historic places have the phenomenal advantages of researching the sites themselves, daffodils marking former gardens and doorways altered to create the Narbonne House scent shop. That's also why historic preservation is so crucial. Next slide please. Next slide. Let me turn to the women's lives chart and your handouts and the next slide, which is simply one way to analyze women's lives by their different activities. While deliberately basic, it shows women's key activities and provides a framework to appreciate their work. Today, if you want a cup of coffee, pop a pod into your Keurig, add some sugar or milk and drink it. Not so long ago, having a cup of coffee required pumping water, heating it on a cantankerous wood stove after roasting and grinding coffee beans, milking the cow, etc., etc. Typewriters once required every mistake to be hand corrected. In other words, we generally under-appreciate the complexities of women's work and all their forms, whether reproduction, care work, production and consumption, or social infrastructure. For many generations, women had to spend much of their time doing the myriad tasks required for sustenance, for basic production consumption and reproduction caregiving, as well as social infrastructure. As you encounter past women, consider how much expertise, skills, effort, and time were necessary. That time requirement helps us better understand their lives, as most women had so much work. As the old saying goes, a man works from son to son, a woman's work is never done. And consider that women work while simultaneously pregnant and how often they grieve when they lost children. It's crucial to consider the many variations of women's lives. Indigenous women, the 18th century Ohio River Valley, processed smelly beaver carcasses into skins, which were then fashioned into European men's hats. One historian has suggested that the fur trade, be renamed the cloth trade, as Wabish women insisted on trading beaver skins for cloth to their taste. And we need to seek other women. We must look past elegant in-town mansions to see large out-of-town income producing cotton plantations, where most black enslaved women worked and lived. Today, we are appropriately more aware of all the differences among women by race, class, geography, etc. We also need to see our commonalities. Historically, under Anglo-American common law, married women had no legal rights to their homes, which partly explains why so many historic sites are named solely for men, because legal ownership is confused with the actual occupants. Until 1964, U.S. women had no right to serve on then male-only juries. And in many states, contraceptive information was illegal for married women until 1965. If we look, we can find women at all historic sites and many other places, because women were everywhere, if not directly present, then indirectly so. If not highly visible, then still crucial, especially true for minority women. Consider how the women and men in these historic places shape our lives. They comfort us in our adversities and challenge us to respond to still unsolved problems. Let's thank them by preserving their tangible resources and interpreting their lives now. When we confront these systemic disparities, we can shape a more truthful and inclusive American story, as Chris Morris of the National Trust says, and be able to tell the whole story. Thank you. And next, we will have Dr. Emily Murphy. Good afternoon, everybody. So can I have my first slide, please? So this is number 71 Essex Street in Salem, Massachusetts. It's a modest house sitting perpendicular to the street, and it consists of two main rooms on the first floor and two on the second, with a lean two broken up into three rooms at the back of the house and a large attic and cellar. It's kind of odd looking. It's got a sharply peeked roof on one side and a gambrel roof from the 18th century on the other. And the building was acquired by the National Park Service in 1963 because of its age. The original part of the structure was built in 1675. But today, I want to talk about a pair of remarkable women, mother and daughter, whose lives encompassed the entire 19th century in that house, and witnessed nearly a quarter of Salem's history through those windows. One of the clues to the activities in the house is this space, if you could give me my animation. Thank you. It's the last major addition to the house sometime around 1820. And most likely, it was intended as a cent shop in Nathaniel Hawthorne's phrase, as Heather mentioned. It's got a very wide shop door that opens onto Essex Street, and that would allow interactions with customers on the major busy street, separately from friends and neighbors who would come in the front door down an alleyway between the Narbonne House and its next door neighbor. I have the next slide. So the Narbonne House was already a century old when Sarah Vincent Narbonne's grandparents bought the house in 1780. So Sarah's grandmother, Mary Gardner Andrew, was left a widow in 1783. And Mary's daughter, Sarah Andrew Vincent, raised her family in the house. So Sarah Vincent Narbonne was actually born in 1795 at the height of Salem's China trade to a family that was not wealthy, but was highly socially connected. So Mary Gardner Andrew was from one of the wealthiest merchant families in Salem, and was connected by marriage to the Darby family, another very, very wealthy and influential family. In fact, her twin sister was married to Richard Darby Jr., sort of the oldest son of the Darby family. And this is reflected in the astonishing quality of ceramics found in the backyard. We did an archaeological dig in the 1970s and found over 150,000 artifacts in the backyard. And many of them, as you can see on the right hand side of the slide, are actually whole vessels, so complete bowls, teapots, coffee pots, saucers and plates. However, the declining trade in Salem and the financial panics of the early 19th century really took its toll on the family. So Sarah's mother, Sarah Andrew Vincent, died in 1811 and her father at that point took off. Sounds like he actually hadn't been around for a little while before then. But that left the 70-year-old Mary Gardner Andrew to raise the 16-year-old Sarah Narbonne and her younger siblings. Mary then dies in 1820 and Sarah stayed in the house with her uncle. And in 1823, she marries Nicholas Narbonne, who's kind of a mystery guy. He's a mariner, shows up in Salem, doesn't seem to have any relatives in Salem, and hung around pretty much just long enough to have two children with her. And then she died and then he dies at sea around 1830. And so just as a note to this, one of the greatest concentrations or the greatest concentration of archaeological material in the Narbonne house dig is actually between 1780 and about 1830. And this is the time when there's pretty much continuously small children in the house. So as I always like to say, small children plus ceramics equals very happy archaeologists in a couple of hundred years. So Sarah is trying to deal with a lot of financial difficulties in the 1820s and 30s, as well as new widowhood. By 1843, she is listed as a seamstress in the city directory. And this is one of the few occupations open to genteel women who are well connected as she is. And she's living, as you can see in this photograph, she's living in a home surrounded by antiques inherited from important families. So the fact that she actually had to go out and earn her living like this is probably a little difficult for her. So you can see more of these amazing ceramics that did survive the children in the corner cupboard behind her. And then there's a portrait of one of her 18th century ancestors on the wall behind her, as well as some really spectacular pieces of 18th century furniture. Can I have the next slide, please? So it was Sarah Narbonne's daughter, Mary, who was born in 1824, who seems to have been the really active, actively working one in the house. After Sarah inherited the house from her uncle in 1844, she seems to have stopped working for a few years, although honestly the lack of occupation listed in the 1850 census for Sarah and Mary could actually have more to do with the most likely male census taker who seems to have not listed any occupations for women in his district. And there are a few women that I saw on there that I knew had occupations, were listed in the city directories with occupations at that time. By 1860, though, Mary's listed as a dressmaker. And the variety and number of sewing items found in the archaeology, like the needles, you can see here, it's actually very, very rare for needles to survive archaeologically, because usually they're so thin and the steel that they're made of doesn't last long in most types of soil. So the fact that we found 12 needles, and some of them quite thin is actually pretty remarkable.  We also found a number of late 19th century doll heads, which indicates that she may have been making dolls for children as well. We also found we also were lucky enough to acquire her pocket diary, which is really kind of a commonplace book that she returned to, it was printed in 1845. And then she returned to this book in the 1860s or 70s to record her work. So the diary indicates that she's that that she's doing a combination of sewing garments directly for clients. But also she seems to be doing a lot of pieces of like trim she talks about ruffling for gowns or buttonholes. So she's like subcontracting it seems for other milliners and dressmakers in town. So it's really fascinating we're uncovering more and more about Sarah and Mary. Unfortunately, we don't really have any direct evidence of what what they were doing with that scent shop. We don't have a ledger or anything like that. But the more that we examine the few documents that we have, and the more that we're combining them with what we found in the archaeology and analyzing the architectural evidence in the house, the richer the understanding we're really coming to about the Narbonne house and the families that live there. So now I'd like to turn things over to John Fowler, my fellow National Park service person from Project Douglas. Thank you Emily. Good afternoon everybody. Let me begin by taking a moment to thank Dr. Hyke for extending the invitation to us to participate in this auspicious occasion. And also take a moment to thank the National Trust for Historic Preservation for the amazing work that they continue to do. As has already been stated my name is John Fowler and I'm a park ranger and the Digital Media Coordinator for the Historic Homes at National Capital Parks East. National Capital Parks East is a conglomerate of national parks located east of the river in Washington DC and into the Maryland suburbs. And one of those parks is the Frederick Douglass National Historic Site. The Frederick Douglass National Historic Site is the property where the great abolitionist, orator, statesman, diplomat, civil rights leader, women's rights activist. This is where he lived the last 17 years of his life. The home was built between 1855 and 1859 by John W. Van Hook and Douglass boarded for $6,700. Douglass turned a 14 room house into a 21 room mansion originally with 10 acres of land he purchased in additional five making it 15 acres complete with vegetable gardens, a croquet court that was his favorite sport to play, apple trees, a peach orchard pear trees, black walnut trees, magnolia trees, I mean it was a sprawling estate. At the time that the home entered the national park system in 1962 it became just the third park created to honor the contributions of an African American. It took the National Park Service 10 years to restore and rehabilitate the property before it opened to the public in February of 1972. But let me be very clear without the pioneering work, activism, preservation, and stewardship of women, in particular African American women, the Frederick Douglass National Historic Site as we know it today would simply cease to exist. As we explore the way women's history is interpreted at sites, I want to take just a moment to showcase how we interpret this history at the Douglass home. Frederick Douglass as great as he was owes much of his success to women. Next slide please. In his three autobiographies, Douglass recounts the role women played in his early development. His mother from whom he was separated, his grandmother who raised him, his slave mistresses including the one that actually taught him how to read, and finally his first wife Anna. Anna was born free while Douglass himself was born enslaved. She sold her possessions which allowed him to escape and experience freedom. They later marry and have five beautiful children and while he is away for months at a time, in some instances, a couple of years at a time, she raises their children and creates a home for their family. Douglass recounted the beginning of their marriage as a partnership. After their wedding ceremony he recounted, I shouldered one part of our baggage and Anna took up the other. He described her as his help meet. And as historian Lee Falk points out in her book, while Douglass portrayed himself as the epitome of black, masculine self-reliance, that self-reliance included the ability to support his family and the self-reliance of the family depended upon both his and Anna's work. Now when Douglass met Anna, she was working as a domestic working in the homes of people in Baltimore and when they married she later took in laundry. You can go to the next slide. When she dies in 1882 after 44 years of marriage, Douglass preserves her memory by preserving her bedroom, which you can be seen in the bottom left hand corner. He marries his second wife Helen Pitts two years later and he does so not knowing that when his mortal time on earth would come to an end on February 20th 1895, Helen would set out and devote herself to making Cedar Hill. Douglass called the property Cedar Hill. Helen makes Cedar Hill a memorial to his life and legacy. Before Helen dies in 1903, she gets Congress to charter the Frederick Douglass Memorial and Historical Association, also known as the FDMHA, to carry on her preservation work. The FDMHA together with the most important Black women's organization up to that point, the National Association of Colored Women in ACW, take on the arduous task of preserving Douglass's legacy and Cedar Hill, making it the Mount Vernon of Negro America. Leaders such as Mary B. Talbert, Nanny Helen Burroughs, Madame C.J. Walker, Sally W. Stewart, Holly Quinn Brown, and Mary McLeod Bethune, just to name a few, performed the painstaking work, the fundraising, the launching of publicity campaigns to preserve and restore the property, installing the heat in the home, preparing the restore the brick walkways, the paveways, working on the windows, working on the steps, maintaining the grounds. Even after President John F. Kennedy signed public law 87-633, establishing the Frederick Douglass home as part of the National Park System, Mrs. Gladys W. Parham, who was the last caretaker of the property hired by the FDMHA and the NACW, worked closely with the Park Service, even becoming an employee of the Park Service in 1965 until her death in 1983. Beyond the actual women themselves, there are a number of objects in the home that help to convey the message that women were essential in the life of Douglass and the property. From the portraits of suffragists Susan B. Anthony and Elizabeth Katie Stanton that hang on the walls to the domestic parts of the home, such as the kitchen in the laundry room, which were vital to the survival of the home and the family at this point in time in history. We note the importance of washer women and and domestics in American history, particularly African American history. Dr. Carter Woodson writes about the role of washer women and Dr. Elizabeth Clark Lewis talks about the importance of domestics in her book Living and Living Out. To the sundial that was placed on the property by the married women's club of Pittsburgh in 1922, these tangible resources help us to interpret the crucial role of women at this national historic site. Seventy percent of the objects within the home are original and it's phenomenal that these people from these two groups, the FDMHA and the NACW, made up of a majority of women, particularly the FDMHA, had the foresight to preserve these objects, reaching out to Dr. Carter Woodson and his organization, the Association for the Study of Nigger Life and History, to come to the property and organize Douglass's papers. In closing, I ask that when you think about the great Frederick Douglass, and you go to the next slide to give me, when you think about the great Frederick Douglass and you think about his vast contributions and the role of the property not only in his life but in local history. For example, black women educators in the DC public school system teaching their students about Frederick Douglass and raising funds to preserve the property. The role in local history, the role in national history, again this was meant to be Negro America's Mount Vernon. People made pilgrimages to Cedar Hill to visit the property to pay their respects to the great Frederick Douglass. When you think about all of this, remember these three key things. His wives in particular Anna were essential to his success. It was African American women who helped to preserve Cedar Hill and the objects, the artifacts on the property within the home show the importance of women. Keeping those things in mind, you are left with the fact that Frederick Douglass, this great American leader, this great American hero, the patriarch of his beloved family. Douglass was a woman made man. Thank you. We'll now have Barbara. Thank you so much, John, and I want to echo your thanks to the National Trust and also to Heather for inviting us to be here. The Polly Murray Center for History and Social Justice is in Durham, North Carolina. My name is Barbara Lau and I have the pleasure to serve as the executive director there. The center is really a fantastic example. We are a National Trust success story. It was a National Trust field officer, Karen Nicholas, that came and visited us. I think 2014 might have been the first time, helped us become a national treasure, helped raise the awareness of the center, and then with the help of the National Collaborative for Women's History sites, we became a national historic landmark in the very end of 2016. So Polly Murray takes us to the 20th century, and as Heather mentioned, Polly was an amazing, accomplished human being who was the first African American woman ordained an Episcopal priest, someone who influenced Ruth Bader Ginsburg and developed really important legal strategies for the Brown v. Board case and later for many of the cases that undergirded women's rights in the Supreme Court. In fact, Polly's legal strategies and legal theories continue to be important to the fight in the Supreme Court for LGBTQ rights today. And Polly's life gives us this amazing opportunity to look at 20th century activism. There's a historian who said that when we look back at the 20th century, all roads lead to Polly Murray. Susan Ware was her name. And we see Polly's work as a writer and a poet, Polly's work as a protester, Polly's work as a thinker, threaded through all of the major human rights activities of the 20th century. And where did that come from? How did this person really come to be? We like to argue that this person, that Polly Murray became Polly Murray because they grew up here in Durham with their grandparents. As Heather mentioned, their formerly enslaved grandmother and their Union veteran, Union Army veteran grandfather, Robert George Fitzgerald. But they also in this site really began to understand both the power of opportunity. Polly Murray's great uncle, Richard Fitzgerald, by the turn of the century became one of the richest African-American men in the state of North Carolina. And the cruel oppressive hand of, you know, the enduring legacy of racism and in Polly's case as well, sexism, limiting their opportunities. Next slide, please. So we don't have very many artifacts. In fact, the House, Polly Murray's address book, and we are pleased to say that we have somebody standing by to donate one of Polly's typewriters are really most of what we, is most of what we have. So we also turn to archaeology to begin to understand our place, to understand its place in Durham's history and as well as in Polly Murray's life. And one of the things you see in these photographs, so this photograph on the left is this Spanish war cannon that's sort of aimed back at Polly Murray's house, which you can sort of see in the distance is right next to the property of Butts, what is a city cemetery. And this relationship becomes key to understanding how well this house is going to survive. It was built in 1898, but the sloping land that used to be a wheat field that Polly Murray's grandfather Leaston and grew wheat on would bring water down the hill underneath the house. And in fact, as we learned from both our inspection of the property and archaeology, it was pretty much on purpose, right. There was really a good case to be made here of environmental racism where the water was actually directed to the rear side of the house. And in fact, as we were doing the renovation, we had to jack up the middle of the house six inches, and there were what looked like little rivers under the house. But the archaeologists led by an amazing woman, Anna Agbee Davies from the University of North Carolina at Chapel Hill uncovered hundreds, if not thousands of small objects in the preliminary archaeology work. And one of the things they began to see, and this is one of Dr. Agbee Davies students, Colleen, was the family's efforts to divert the water to build bricks. And in fact, bricks were very important to the Fitzgerald family. This is where Richard Fitzgerald, Paulie's great uncle, began to build his business and make his money. Much of North Carolina is very clay rich. And so building bricks or making bricks for a budding tobacco industry really fueled a lot of growth and development in Richard Fitzgerald's businesses. And so in behind the house, we find these pathways that were meant to sort of divert the water from under the house that was flowing down the hill. But what's interesting about this and about the way that tangible objects help us to understand this amazing life is that there were many, many other objects there found there as well, buttons, pieces of glass, pieces of china, a dipper that we actually took out of one of the walls of the house. And Dr. Agbee Davies is really using these to also help us to begin to question ideas about gender, assumptions that we make about what kinds of objects were used by whom. Paulie Murray was to say the least someone who resisted the boxes, resisted the identity limitations that were often placed. Paulie Murray was born in 1910 and came to live at this house in 1914. And as they grew up, they really discovered that they did not want to conform to what society was saying girls and women should be like. They did not want to feel that they could only do the things that women were able to do. They grew up in a house of incredibly strong women who were educators and community leaders. But they preferred to wear pants and have a play basketball, have a paper route, and so often wore boys clothes. So knowing this, Dr. Agbee Davies is really using this site and some of the things that have been found there to push us to question what we assume about the gendered nature of objects that come from archaeology, which is a great linkage to the stories that we want to tell about Paulie Murray's life and legacy. Next slide please. So one of the things that we try to hold on to is Paulie's determination, which really came from this family of survivors and thrivers, people who are also fighting on behalf of the rights of their communities. Paulie witnessed these great advancement during the decades of their life, and as I mentioned, also the deep racism and sexism. But drawing from their own experience, Paulie resisted those boxes and began to create new language.  We now think about that sometimes as intersectionality. Paulie Murray changed their name. They were born in Annapolene and chose in their 30s to use the more gender neutral name Paulie. Paulie's ideas about being different but really validating their own experience gave them that opportunity to create new ways of thinking, began to challenge people like Thurgood Marshall and the people who planned the 1963 march on Washington to think more broadly, to invite other ideas from other people that weren't necessarily the folks that were generally on stage. We try to focus on what Paulie Murray saw as an integrated body, mind and spirit. So that determination that's reflected in this quote, one person plus one typewriter constitutes a movement. For Paulie, words were the weapons and Paulie fought through everything from legal briefs to letters to the editor to a correspondence with Eleanor Roosevelt that was transformed into a decades long relationship and collaboration to poetry. Creativity was a really important part of that. But that determination, that belief that one person plus the typewriter constitutes a movement, that really came from Durham, from what was happening in Durham as Paulie was growing up there and from that family that influenced Paulie. But the idea of Paulie's goal of a integrated body, mind and spirit is essential to the ways that we try to continue in Paulie's legacy to challenge what people think of as the periods of history, what people think of as appropriate ways to think about women and men, to think about straight people and queer folk and to invite other people into those challenges, into that idea that maybe what we thought we knew about American history is not what we know. Maybe there are many other ways to look at that. And we do that in a number of ways through a number of kinds of programs. Today just want to share briefly one program. Paulie Murray wrote a book, a family memoir called Proud Shoes, the Story of an American Family. And for several years we've been creating what we call Proud Shoes Labyrinths, where people are invited to decorate shoes and add information. And then they're laid out into this labyrinth, which then allows folks to reflect and to think about what they're proud of, to think about what's happening for them. Just this last year on Paulie Murray's birthday, we invited these artists and community members to help us create what we thought reflected where we are right now, connected Paulie Murray's legacy and ideas to the present in this lost hope and joy labyrinth. And so throughout this day, in a very carefully sort of socially distanced way, people came and brought objects. There was actually bricks that were brought, as you can see, flowers and shoes and other objects, and then to walk in the labyrinth to think about what was going on today and how we want to show up today as activists, how we want to channel Paulie Murray in our work. Paulie Murray's a relatively unknown person, but who is becoming more and more the object of great public interest in a new Netflix series. Will Smith talks about Paulie Murray's ideas about the 14th Amendment and the powerful advocacy that Paulie Murray was so involved in. And in fact, there's a new documentary film coming out that will be on stream through Amazon this fall that helps more people to learn about that story. And as they learn about it, as they're inspired with Paulie Murray, we hope, of course, they will come and visit us in Durham as we finish the interior of the historic home and add a welcome center so that we can be as welcoming as possible in terms of new visitors and new people who want to learn more about this history. So that's it for me. I think we're going to go to some questions and answers now, but thank you so much for your kind attention. Yeah, everyone doesn't mind hopping up. Heather, do we want to start with a question for you? I've got a bunch in the Q&A, so I can also ask those if you'd like. Well, I think one question we all want to think about for the National Trust, the National Park Service, and every other site and potential site that we know of, is what should be our next steps? How do we take what we keep learning, the people we keep finding, and how do we make them more available and relevant to visitors and virtual visitors everywhere? So I would like to start with that and then let's take some of the questions in the Q&A. Does that work? Next steps, y'all. Yeah, so I'm happy to jump in there just to say that we're learning so much about the power of technology. We have a monthly book club and we're now seeing people participate in that from other countries, and so trying to think about that sweet spot of using technology without discounting the power of putting your feet on the ground in the actual place, feeling how what it's like to be in those places, I think there's a really important balance there. Thank you. I would simply say just, you know, continuing to do the research, looking for connections with other sites is one way to bring this issue to the forefront. As I mentioned, there are National Capital Parks East, there are three historic homes and the other two homes are the Mary McLeod with the Council House, National Historic Site and the Carnegie Woodson Home National Historic Site. And ironically, all three of those figures, Bethune, Woodson, Douglas, there are connections in very interesting ways. And you find that in history, a lot of these figures are connected to one another in some form of fashion. So just, you know, getting out there and doing the research to see how these people, how these figures, the stories, get these connections. I think that's a great point. You can see behind me, everyone, a whole set of books. Those are books that have come out fairly recently dealing with Frederick Douglas and with Pauli Murray as well. And that's really important. And also you have two other sites. You have the Clara Barton National Historic Site and Maggie Walker National Historic Site, who are also part of this group of people surrounding Frederick Douglas. And you're absolutely right. Connections are important. Emily, did you have something you wanted to add? Thank you, John. Yeah, I think, you know, we have a slightly different thing going on with the Narbonne House in that, you know, neither of these women were either connected to great men or were really recognized in themselves. So I think for us, it's more about sort of, you know, understanding the commonality of their lives or how typical were they of women living in, you know, particularly the Seaport communities and the era of change that their lives cover, you know, in Salem, the transition period from the mercantile shipping primarily to industrialization and immigration movement and everything that goes on with that, there's some really interesting questions. So I think one of the things that we're looking towards is we need a really good historic structure report for that house. We have them for the other sites at Salem Maritime. There was a partial one that was written in the 1950s. It includes such wonderful phrases as, we're fortunate that these genteel women lived in poverty because that preserved the house and things like that. And it really focuses, again, on the male owners of the house, but not really saying much of anything about the women who were really, you know, the ones who lived and worked in the house and ran it for those years. And that's really important that we not only deal with those who are famous and well known, but we tell the whole story, including all the different women and all the different men and how people interacted with each other. Thank you. All those are great answers. I strongly think we need more research. We need more preservation. We need more interpretation. Priya. Yeah. So I'm going to actually take some questions and combine them to get to something that we talked about in our planning calls. Two of the questions have to do with sources and how do you find more information about women? And I think it would be great for you all to talk specifically about some of the non-traditional sources that you've been using. And you touched on it in each of your presentations, but the both questions have to do with archaeology. And then what do you do when you can find someone in one census, but you can't find them in a census later? And so I think helping them understand source material for finding women would be great. I think one of the things that all these presentations really show is how it's the combination of different sources that makes the difference and at the risk of whatever. I would say that when I wrote, when I spent five years writing, doing women's history, I spent a lot of time working to identify sources and how to use them to do these things. So there are sources out there that help us write them. We've got a fresh one here. I have the same. So I can, I can take the, oh, sorry. No, no, go ahead. I can, I can take the archaeology questions. I saw that one of them was specifically about the Narbonne house. So there was no garbage pickup in Salem until 1902. So what you did with your, with your broken, with your trash was you threw it in the backyard. A lot of most houses would have had a privy, an outdoor pit toilet, basically.  And you have not seen happy until you've seen the historical archaeologists hit a privy because everything's nicely in layers inside the privy. And I think it's one of the reasons we have an incredible number of chamber pots. Because there was somebody in the, in the early 19th century who kept dropping the chamber pots into the privy. And we're basically like, nope, I'm not going in to get that. So, so that's, and, and, and because we're an urban site and these things tended to happen in like, in like very close areas. I don't know if they've done any digs around Frederick Douglass, but you tend to have like very close areas. We have a lot of complete vessels, much more than you would have and say a farm where stuff gets spread all over. So I was going to say we're, of course, incredibly lucky because Paulie Murray was a packrat and someone who I'm learning from someone who actually helped Paulie edit their autobiography, that part of the reason they wrote that was to put in print the names of all the people that they had also met along the way that they felt had contributed to this work, but not necessarily been named. Paulie was savvy enough to make a decision prior to their death to put the materials in, you know, there are literally thousands of folders at the Schlesinger Library for the History of Women in Boston, because there wasn't necessarily a place associated for long periods of time. Paulie lived at 50 addresses during their life. And so, you know, this constant moving around makes the idea that they kept all of the, all these folders, letters, carbon copies of letters even more amazing. But I think it's not just about how much you have, but what you do with it. So we're discovering that there are so many more stories. We're now learning a little bit about Paulie's role with Eleanor Roosevelt in the crafting of the Universal Declaration of Human Rights, which is not a story that's been told or written, but is in that archive somewhere, right? Like, so being able to really look at historic material and think about it in different ways and question ourselves about the assumptions we might make about it. I think we'll also bring us much more and deeper history and deeper storytelling that we can then use at historic sites. There's also a bit of humor, which is that as she moved around, and sometimes it was because her typewriters were too noisy, the FBI was tracking her. And so you have FBI files that are showing, trying to prove that she was too radical. Yeah, she luckily applied for a federal job. I know you in the Park Service completely understand this, that when you apply for a federal job of any stature, you have to actually list all the addresses you've lived at. So she did some of the work for them, but again, I think it's also digging in, right, to what you have and thinking about it in different ways. And inviting other people who maybe aren't coming at it from an academic point of view who might be kind of seeing themselves in this person to give you their impressions as well. I think that's another really interesting way to think about using historic materials. Yeah, so it's four or two, so I know we're at time, but I wanted to ask one more question before we close things out. And one of the questions that came in was asking about balance, that as we tell more stories of women at these sites, how do you balance it with the original significance that was determined before? Especially since you're all Park Service sites, how is that working in the National Parks Service for large? That's a red herring. Yeah. But I think so far, at least at our National Capital Parks East, I think we do a decent job of balancing out and leading these stories together. And I think Heather's right. It is a red herring, right? Just because you add more storytelling in doesn't mean you're taking stories out. You can tell more stories. And all it is is telling the full history of a particular place. And it doesn't mean you're taking something away by putting more in. We're actually a private nonprofit, so while we have the designation, we don't have as much confines around that. So I think we definitely put one foot in history and the other one leaps into the present and the future. Great. I think you're also talking about multiple layers in the house. For many, many years, you would go into these houses and they wouldn't talk about domestic staff at all. And I think there's been a lot of folks more recently have been asking the questions. I think shows like Downton Abbey kind of make you more aware of the fact that there would have been domestic service in some of these houses. So you also want to make sure you're telling the story of all the women in the house, not just the head of the household. Because if you don't, you're seriously distorting everything. Great. Thank you, everyone, for being here. Barbara, did you have something to add? I just want to say I think it's our responsibility to the next generation. I think that if we're going to raise women leaders and non-binary people as leaders, we need to give them as much information to stand on as possible. And so doing our job to push those, to sometimes break the rules, to sometimes bend the rules, to sometimes just confront the rules and say, wait a minute, you might have done this for a long time like this, but maybe it's not the right way. I mean, and I know that that happens on all different levels, whether you're private, state, national, and I just want to encourage all the folks in all those levels to keep up that good work. Thank you. So before we close out, I have a few additional pieces of information. First of all, keep talking. One of the features of Preservation Leadership Forum is an online community called Forum Connect. It's free and open to everyone and is available at this link below, and I'll also share the link in the follow-up email. It's a great place to keep this conversation going. Right now, topics are about section 106. They're talking about issues we're discussing today related to integrity. And so just please join us. I'm the community manager for that, so you'll see a lot of me on that space as well. Next round, thank you. Keep learning. We have a couple of different webinars coming up. We have one using state historic tax credits to create affordable housing, which is just next week. And we also have the second part of this webinar series on August 12. I will share the link to our webinar page so you can register for both of those. And then also to learn more about the National Trust Campaign, where women made history. Follow this URL as well, and I will also share that afterwards. And finally, thank you. Our website is forum.savingplaces.org. This is where you can find out information about webinars, but always feel free to email us directly at forum at savingplaces.org. And I think Chris had just the last word. Yes. No, I just thank you, Priya and Rhonda, for all of your work in helping to put this together. But I wanted to offer a special thanks to our moderator, Heather, and all of our speakers, Barbara, Emily, and John, really appreciate everything that you've brought to this conversation today. And all you have done is just underscore the point of how important this work is and how women truly are everywhere. And there are so many ways that we can find them, understand them, and share their stories to help inspire and empower the next generation. So thank you all very much. And thanks to everyone who participated today. Hope you'll all come back and bring some friends for the next round of this, when we really kind of dig into the questions of how to start telling these stories in really in different ways. And that'll be on August 12th. So thank you, everyone. Thank you so much for having us. Thank you. Keep reading.


I'm very happy to stay part of this for a long time, happy to stay in this club, in this environment. Obviously I'm enjoying it, so that's the reason why I stay here. My goal as well, I want to be better in every single thing I can, so I'm trying to do... I didn't consider nothing special, but if I can choose, I think I'll try to be more dangerous to the opposition goal, try to score more goals and I'll be happy with that. The huge success we had made me like this even more and yeah, pretty much. I'm really excited to go again through all these things and I'm pretty sure that we can play on the highest levels and go one step further. So we still have unfinished job from Grand Finals, hopefully we can achieve that. And ACL is coming, that will be a huge experience for us. And all this trip in Japan will help us to get adjusted to these conditions. I'm sure we can do something in ACL as well, especially with our supporters. We'll bring things to the parameter to give supporters something different. They are amazing, they are something completely different than everything I experienced in my life and I'm enjoying playing in front of them, so somehow I would like to give them back that joy that I have because of them. On this experience in Japan, we've only been here a couple of days, but have you found it enjoyable? It was actually alright, I was afraid maybe because of the different conditions it would be harder, but I think all the boys adjusted pretty good and I think already now, after a couple of days, we feel like we've been here for a longer time, so it's good, yeah.


The objective of this study was to examine the baseline, 60-day and 120-day follow-up trust in research and researchers of Floridians aged 60 years and older involved in the University of Florida's Health Street Community Engagement Initiative. The study population consisted of 2,193 older adults who were assessed by Health Street Community Health Workers, CHWs. At baseline, 28.3% of participants reported having been in a research study, while 7.7% reported not being interested in participating in research. At all three time points, trust in research and researchers was high, ranging from 7.4 to 8.0 on a scale of 1 to 10, with higher scores indicating greater trust. Additionally, at all three time points, participants expressed high levels of interest in research. These findings suggest that older adults are willing to be involved in research and that their trust in research and researchers remain strong throughout the course of the study. This suggests that community engagement is an effective way to recruit older adults into research studies. This article was offered by Catherine Woodstock-Stryley, Shanta Lloyd, Deepthiefumma, and others. We are article.tv, links in the description below.


Now we want to explore, see we have seen, we do a demo, we can see that as the number of grid points increases that the number of iterations increases. So for given CPU time per grid point per iteration, the number of iterations increases in a very rapid fashion because the spectral norm is so large, it is getting closer and closer to 1, right, it is going to take forever to essentially come, remember we got a geometric series, right. So if you say that xn plus 1 is rho j times xn or en plus 1 is rho j times en, right and you want e to go to 0, the fixed point is 0. If this is very close to 1, if it is 1 of course it is not going to get there, if it is very close to 1 it is going to take forever for the error to go to 0, is that fine, okay. So it is a problem, that is a problem, right. So we have to think of ways by which are there ways by which we can make the code or the iterations go faster. So given that the cost the CPU time per grid point per iteration is the same, you cannot change that. You may not mind doing a little more work that is increasing that CPU time per grid point per iteration if we are able to converge to the solution faster, okay. So this is only Jacobi, I am not really going to sit down and work through this for Gauss-Seidel, but we did Gauss-Seidel and it does turn out that Gauss-Seidel is marginally faster than Jacobi, right. But the problem is that if rho Jacobi is 0.99 and rho Gauss-Seidel is 0.98, right, okay. You in fact this is twice as fast as that, right, it is ironical 0.98, 0.99 into 0.99 gives me 0.98 essentially, right. So this is in fact twice as fast as that, but in an absolute sense it is no use to me, right. It is only 0.98. I want something that is much smaller, right, I want something that is much smaller. So we have to think of, we have to come up with ways by which we can do this. What are possible ways by which we can make the program run faster, give me suggestions. What are possible ways by which we can make the program run faster or iterations converge faster? What are the things that we have done? We have an initial guess, so you could get an improved initial guess, right, we get an improved initial guess. Clearly, see if you manage to guess the solution, you get the answer in one iteration. So clearly an improved initial guess is something that is worthwhile, higher grade point. So one possibility is that you somehow use, you use the initial, make an initial guess which is a poor guess, 0 everywhere on a course grid, what we will call it, you call it a course grid, right. And use that course, use that as an initial guess for, so you use, you take the 10 by 10, you take the solution on the 10 by 10 as an initial guess for the 20 by 20, right. In fact, you can imagine that you use 10 by 10 as an initial guess for 20 by 20 and then use 20 by 20 as an initial guess for 40 by 40, right. So you could have a hierarchy of grids, we look at this at the later in the semester, there is a scheme called multigrid method which sort of exploits this, but as far as you are concerned, a good initial guess would get us to the answer faster, okay. So there seems a possibility there, but as I said we will do that a little later, what else, anything else that we can do, okay. So one thing that we, one thing that we will try, see all we have, all we have, if you think about it, for Gauss-Seidel, all we have is Vn plus 1 PQ is 0.25 Vn P plus 1 Q, you have seen me write this so many times now, Vn P minus 1 Qn plus 1 plus Vp Q plus 1 N plus 1, right. So this is Gauss-Seidel, this is Gauss-Seidel. Now this is all we have, we have phi, the latest phi and we have the prior phi's and the improved we are using, you know, what more can we do. So one of the things that we can try, right. So this is sort of like just try it out because this is all we have to play with is instead of calling this Vn plus 1, I will call this phi star and I will write Vn plus 1 at PQ, in fact is Vn PQ plus phi star PQ and I want to pick, I want to take a linear combination or what is called a convex combination of these two in order to form that, right. So I will pick a parameter omega and when omega equals 1, I want to get back Gauss-Seidel, okay. When omega equals 1, I want to get back Gauss-Seidel. So omega equals 1 means that this should be omega, that should be 1 minus omega, omega equals 1 will get me back the original equation, okay. And omega equals 0, there is no progress, okay. So now we have done a linear combination. You can say well what is the big deal, what have we gained by this, right. What have we gained by this process? It turns out that there is an optimal value of omega for which convergence is greatly improved, okay. There is an omega value for which it is greatly improved. There is an omega equals omega opt for which the convergence of this iteration scheme, right is faster than the original Gauss-Seidel, okay. It is faster than the original Gauss-Seidel, is that fine. Remember that this was called successive relaxation, Gauss-Seidel by itself is called successive relaxation. You can try various values of omega. For Laplace's equation it turns out that omega believe it or not is greater than 1, optimal value of omega is greater than 1, okay. And for that reason it is called successive over relaxation or SOR, successive over relaxation. So instead of successive relaxation which is what Gauss-Seidel was, right. Because omega is greater than 1 it is like over relaxation, right successive over relaxation, is that fine. So we have introduced this omega. Right now you have to take my word for it that it actually improves. It actually improves the convergence rate. The, as I said we are not going to go through this whole analysis for it to show that it actually improves the convergence rate. We will do it in a more empirical fashion. You can actually write a program and try it out. And the question would be, right, if you do not have an expression for omega for the optimal omega. As it turns out for Laplace's equation on a unit square with a uniform grid you can actually come up with an expression for an optimal omega, okay. Right? There are enough books out there that will give you, look at anything on matrix iterative analysis by RS Varga comes to mind. There are lots of books out there that will give you expressions that they have already derived expressions for an optimal omega, fine. But these things work for a unit square uniform distribution. What do we do when we are going to actually solve problems from fluid flow equations or something that is quite complex? There is no expression. So what you have to do is you have to get the, you have to, you have to find the optimal omega by experimentation. You have to hunt for it. Is that fine? The advantage is once you have found it, once you have found it, you are able to do production runs so to speak. You can make multiple runs with that optimal omega, right. So how do we find this optimal omega? How do we do this? There are two possible ways, two possible iterations. One of them may be better than the other. We will see that. There are two possible ways that you can do it. So pick values of omega and right now without an explanation I will say pick values of omega between 0 and 2.0. We look at where this 0 and 2.0 comes from. Pick values of omega between 0 and 2, right. Say at equivalent rolls 0.1, 0.2, 0.3, 0.4. Pick values of omega between 0 and 2. And then you can do SOR, perform SOR iterations, right. Perform SOR iterations. Now comes the critical thing. Perform SOR iterations till, right. There are two possibilities. Perform SOR iterations till En less than say 0.1. That is one possibility. Some predetermined value, okay. And then you can ask the question, so this N will be a function of omega. That is what we are saying. That N will be a function of omega. You will say allow it to drop by 0.1 and this N will be a function of omega. And what we hope is that if I get omega versus N omega versus omega, we hope that we get something like this and we know where there is a minimum, okay. There is a danger here though. I am always wary of this setting of value 0.1. What is the danger? Yeah, what if there is a value of omega for which it does not converge? You keep on running and it is going and it is going. You will never get to 0.1. It never drops by 0.1. See, there is always that danger. There is always that danger. Yes, I know for Laplace's equation, we just showed that the iterations are going to converge, right. But for SOR, we have not really done that. So there is always that danger. If you are solving the Navier-Stokes equations or whatever, there is always the danger that you try to get that 0.1 drop and it just does not happen, that the program runs forever, right. So in all of this kind of exploratory work, I am citing this example. I am citing this because this is a very important point that I want to make. For all exploratory work, you always bound the amount of computation that you are willing to perform. You always limit the amount of computation you are willing to perform, right. So you do not say, we do not say till en is less than 0.1. That is not the way to do it, right. What you do is you say we do say 10 iterations or 100 iterations. Then you have limited the number of iterations that you are basically going to say, I am willing to do this much and no more. In which case you can then plot what would you get? What would you plot? Number of iterations is fixed, right. So this would be en versus omega, right. And now you may get, again we hope that you get something of that sort. We do not know. We hope that you get something of that sort. We do not know. Is that fine? Okay. So we can run, we can run multiple. So you can take 10 values. For example, what I would do is I would take 10 values. I would then turn around and say that let me explore for the optimal omega. Having got this, right, having computed this graph, let me explore for the optimal omega in this gap, right. And it may turn out that I actually get something like this. I deliberately shown it sort of shifting to one side. Why have I shown it shifting towards one side? We will see whether this actually happens. This is those situations that they talk about math classes but you have not really encountered that often. This is a situation where you have non-uniform convergence. In fact, we want non-uniform convergence. We want for different omegas the convergence rate to be different, right. We are looking for a situation where the convergence is non-uniform. Specifically, we are going out and looking for it. Am I making sense? We have picked a parameter and we are hoping that I really, really, really hope that the convergence rate is non-uniform. If it is uniform, then we have not gained anything, right, okay. So we will hunt and we will try to narrow down. Now it is up to you how much effort you are willing to put in to narrow down that value. Am I making sense? And if the drop is sufficiently fast, you should be able to get an order of magnitude speed up or something like that, an order of magnitude speed up or more, fine. So that we will sort of look in a look at a demo, right and see what happens. We will try to figure out what happens. Now we have to address one issue. We have SOR. We have some mechanism and algorithm by which. So I do not want you to do this. Well, I want you to do this just for fun, right. If I say I do not want you to do this, then you should go ahead and try and do it just to see what is Ramakrishna talking about why should I do it. Just try to do this just for fun. But once the classroom, once the class, the learning process is over, you do not usually do this. What you do is you do this. You bound, you limit the amount of computation that you do in exploratory, right. You make sure that it does not, it cannot become unbounded, okay. So right now I will remove that. So we have an algorithm. You can find the optimal omega. Why is the hunt limited in this case, in this particular case? Why is it limited to 0 to 2.0? What is the reason? So let us find out, okay. Remember the matrix A, what is this matrix A? This is Af equals B. B had the boundary conditions. This is the discrete version of Laplace's equation using central differences. Nabla square phi equals 0 plus boundary conditions turned out to be right using central differences, the matrix of that form. And what was the structure of the matrix A? A was symmetric, right. A was symmetric. Remember that A was symmetric meaning A equals A transpose, okay. Now consider a function that I just casually introduced. A, well I call it x equal to phi. Q of phi is 1 half phi transpose A phi minus phi transpose B. You write this in the standard form because otherwise I will keep making this mistake of replacing writing x instead of phi. We just write this in the standard form Ax equals B, right, where x and B are vectors. So Q of x is 1 half. You could put a negative sign in front of it if you want but it does not matter. x transpose Ax minus x transpose B. This x has a little tilde in front of it to indicate it is not our coordinate. So what is Q? Given an x or given a phi, given an x or given a phi, it gives me a number, okay. What does Q? Given an x or given a phi, depending on which equation you are looking at, it gives me a number. Is that okay? Fine. It is mapping this vector into one number, into the real line, okay. It is quadratic. How do I find its minimum? How do you find the minimum of a function? Take the gradient and set it equal to 0. So what we want is grad Q and set it equal to 0, okay. We want to take grad Q and set it equal to 0. I think maybe this is better if we use index notation to do the gradient so that you do not get confused. Q of xi, i is just a subscript is one-half xj for xi aij xj minus xi. This has a summation over i and j and this has a summation over i. So the repeated index indicates that there is a summation. If the subscript is repeated, that indicates there is a summation. So I am not going to. So what is the gradient? Doh Q, doh xi is one-half aij, doh Q, doh xk, I am sorry, one-half doh xi, doh xk, aij xj plus one-half xi, aij, doh xj, doh xk minus, doh xi, doh xk bi. I hope all of you are familiar with your index notation. Doh xi, doh xk would be the matrix representation would be a unit vector. It would be an identity matrix but in index notation would be delta ik, delta ik equals 1 if i equals k equals 0 otherwise, okay. So doh x1, doh x1 is 1, doh x2 is 0, okay. Doh x1, doh x3 is 0, right. Doh x2, doh x1 is 0, doh x2, doh x2 is 0. The derivative of the thing with itself is 1. The derivative of the thing with something else is 0, okay. That is basically what it says. By itself is 1, if something else is 0, okay. And remember that repeated index means summation. So what does that mean? You can check this out. I will let you verify this for yourself.  Whether you sum over i or sum over j, it does not make a difference. So this in fact turns out to be one-half akj xj plus one-half xj ajk minus bk and you want to set this equal to 0. But because a is symmetric, akj is the same as ajk. Akj is the same as ajk because a is symmetric. That is why that symmetry is very important, right. Symmetry is very important. Is that fine? So what does that result in then? Those two-halves add up and you get Ax equals b. Writing it back in vector notation, you get Ax equals b. So solving Ax equals b is equivalent to minimizing q of x, right. When a is symmetric, solving Ax equals b is equivalent to minimizing q of x. Is that fine? Everyone? So we look at the problem in one dimension. It is easier to understand. We can draw figures, right. So we look at a problem in one dimension. For one-dimensional equivalent of this, so the tildas will go away. We will just use x because it is a scalar. So qx in fact will be one-half ax squared plus bx. This is q as a function of x. And what is dou q dou x or dq dx in this case because it is only dependent on one variable, Ax plus b equals 0 telling us that the minimum is that corresponds to minus b by a. From your understanding of quadratic equations, you already know that to be a fact. Let us graph this. Now in general, ax squared plus bx is not symmetric about the, figure is not symmetric about this.  That is if I were to draw a quadratic, the minimum is here. That is minus b by a, right. Minimum is there minus b by a. Of course if I were to translate the coordinate system by some c, I would get two roots about that minimum. And independent of the orientation of the quadratic, those two roots will be symmetric about that minimum. Is that fine? I want you to go back and check to make sure that what I am saying that you agree with. So if this is your xn, if that is your xn, because this is a scalar equation, life is very easy. After all that is what you are doing. You are taking a derivative and setting it equal to 0 and you will get this point immediately. That is what you are doing. You are solving for that point. This is xn plus 1. What I am saying is I call it x star, okay. I am calling it x star.  Is that fine? If I subtract out xn from here from this equation, I get xn plus 1 minus xn, which is delta xn, which is the correction that I need to add to my xn to get the new iteration, is in fact omega times delta x star, okay. So you just look at this. This is delta x star. That is delta x star. When omega is 1, this is the value that you get. When omega is 0, delta x star is 0 and what is the value of q that you get? This is q. What is the value of q that you get? You get the original value. When omega is 2, you swing over to the other side, symmetrically over to the other side and the q value is the same. For any omega between the values 0 and 2, you will get q values. If you choose omega depending on what omega value that you choose, you will get a value in between of x and the q will decrease. So these iterations for omega values between 0 and 2 will generate a sequence of qs, q1, q2, q3, so on. It will generate a sequence of qs which are decreasing and they are bounded from below. So you know that there is a limit. You know there is a limit and you are going to reach that limit. Does that make sense? As long as you pick omega values between 0 and 2, if you pick omega 2.1, it is going to take you there. The q is increasing. If you pick omega less than 0, you are going to go here which is also increasing. If you pick omega 0, you are not going to shift from this point and if you pick omega 2, you are going to oscillate from one point to the other point. So I would suggest that you try this out. You will see how this goes. Are there any questions? Thank you.


Welcome to every way woman so let's start with a little open dialogue should women who are the boss at work? Allow their men to be the boss at home Huh, well sounds like you've been in my house Say that cuz well my when I first got married I struggled with this because I was a manager of boss that I had a lot of people and then I came home And I started bossing my husband around and I was just really her and one day He told me he said you need to have a seat. He said what you do over at the city of blah blah blah is there But when you walk in this house, I'm the head of this house No, no, that's a lot of people but he got my attention turn it off. You don't run anything up in here We run it for you. You just step back and you like your man be the man of the house Yeah, you like that. Yes. He is the man of the house Yeah, I like a more traditional role but if if I were at Work every day and I was the boss and I was constantly having to stress out on Stress levels are high when you're making decisions. So if I came home and my man was like, hi honey, here's your dinner I got laundry done all the clothes are put away and we're gonna go upstairs and make magic in 30 I'd be like, yes So if I had the time and the energy which we don't we don't have the time and the energy to do all of those things and If he has the time and the energy if he's the one it that's at home It needs to be in charge then heck. Yeah, go ahead. I mean, I iron right and then do Well, you know, it's I find really interesting though is I think a lot of women Let their men think they're the man of the house kind of that the woman is the next that turns the That is correct. You will that is correct. We are the neck that turns the head That has no purpose without a head and a head has no purpose without a neck So you work in tandem, but I think what happens is is women sometimes and I know we're gonna get emails and text I'm sorry right now. We want chivalry, but then we want to wear the pants pick a mood Balance it right balance it. You can't be time. Oh, baby. Do this for me. Do this way and then I'll tell you Ourselves we're partnership. Well, how do you see it? How do you see your house? We know that you you have your eyes on having a career. Yes. I have well, okay again I want the best of both worlds. I am that classic. I want it all I do want the career I do want to be the boss at work And it is nice to be able to I would assume come home and let somebody else make some of those decisions But I can't imagine I would be able to turn it off and then just let somebody else step Let me add to that a little bit. Yeah, now you're out there dating right now And you're looking for men who have jobs who are successful are still in progressive careers where they are So what do you how do you see it if you're the boss and you're doing this and this and this and he's the boss And he's doing this and this and then he also wants to come home and take charge of the house. I Think you can let him take charge of the house Friday Girlfriend takes charge on Saturday and Sunday and let him have a little break and you can step it I mean it can't just share I think I left the wrong picture with you because I'm not saying that you just stop at the door And you become home and you come home with your docile. That's not what I'm saying. I'm an executive don't surrender No, I'm dog. I'm a manager at work, and I'm executive. I make very high-powered decisions, but in my home I'm he and I work together. I just don't come home and say this is what we're gonna do I will say that where I work. I don't have a time some time that this is what we're gonna do But I don't bring that same spirit and same energy in my home. It's counterproductive Do you think that's helped the success of your marriage? Absolutely, you know, I was speaking with a woman She's about 45 years old and she had just got out of relationship starting to date again And what she had said is you know, I have why can't I find a man who wants to take care of me? And but I she wants to be the strong independent person and then she said is and she juxtaposed that with I know women who are very Successful they date men that are very successful, but I'm not but her she like serves her man She goes to the buffet line or whatever the event and puts his plate together And make sure he has his drink and has all that just like what's wrong with that? Well, but see her point of view was is I I don't I'm a strong independent person And I don't need to do that and but yet here she is she's single and she can't find a man And jasmine to you that is the key. I can give you the secret about keep staying married listening My husband tells me all his friend men want three things. They want to know that they are valued in their home That they want peace they won't peace at all costs and that they want to know that you have their backs as their wife If you do that, you'll have their purse. You'll have their water With those three secrets, you're right CC because that's what she was missing. I think she was missing that Why do I have to serve him if I'm successful? He should serve me. That's right Why are you supposed to serve each other like I do to you as you do to me? It's what works in your home my husband rubs my feet I rub his head my husband likes hot dogs He doesn't want to wipe the necessary slaves over stowed. He wants me to talk to him my friend's husband She has to have her food on the table. It's what works in your home But as long as a man and you give him some He's got You will have a happy man Any words of the wise for Madison, I have to ditto Ladies I think I have a lot to learn Because I don't know what my household's gonna look like in the future, but I'm hoping it's a peaceful happy and give him some


South Korean President Yoon Suk Yeol visited Ukraine on July 15 for talks with President Volodymyr Zelensky, the South Korean presidential office said. The surprise trip came after Yoon attended a NATO summit in Lithuania and visited Poland this week, where he expressed solidarity with Ukraine and explored ways to support its fight against Russia's invasion. Yoon visited the site of mass killings in Bucha near the capital Kiev, before visiting Erpen, a residential area that received large-scale missile attacks. He was expected to hold a summit with Zelensky afterward, his office said. A US ally and rising arms exporter, South Korea has faced renewed pressure to provide weapons to Ukraine, which Yoon's administration has resisted in favor of humanitarian and financial aid, wary of Russia's influence over North Korea.


Hello and welcome to the session. Let us understand the following problem today. Solve the following pair of linear equations. AX plus BY is equal to C and BX plus AY is equal to 1 plus C. Now let us write the solution. The given equations are AX plus BY is equal to C and BX plus AY is equal to 1 plus C. These are our equations 1 and 2. Now given equations can be written as AX plus BY minus C is equal to 0 and BX plus AY minus 1 plus C is equal to 0. Now here A1 is equal to A, A2 is equal to B, B1 is equal to B, B2 is equal to A, C1 is equal to minus C and C2 is equal to minus 1 plus C. Now by cross multiplication we have X upon B1 C2 minus B2 C1 is equal to Y upon C1 A2 minus C2 A1 which is equal to 1 upon A1 B2 minus B1 A2. Now which implies X upon B multiplied by minus of 1 plus C minus A multiplied by minus C which is equal to Y upon minus C multiplied by B minus of minus 1 multiplied by 1 plus C into A which is equal to 1 upon A multiplied by A minus B multiplied by B which implies X upon minus B minus BC plus AC which is equal to Y upon minus BC plus A plus AC which is equal to 1 upon A2 minus B2 which implies X upon taking C common from these two we get C multiplied by A minus B minus B which is equal to Y multiplied by C multiplied by A minus B plus A which is equal to 1 divided by A minus B multiplied by A plus B. Now considering first X upon C multiplied by A minus B minus B is equal to 1 by A minus B multiplied by A plus B which implies X is equal to C multiplied by A minus B minus B upon A minus B multiplied by A plus B which implies X is equal to C multiplied by A minus B minus B upon A square minus B square. Now consider Y upon C multiplied by A minus B plus A is equal to 1 by A square minus B square which implies Y is equal to C multiplied by A minus B plus A divided by A square minus B square. Hence X is equal to C multiplied by A minus B minus B divided by A square minus B square and Y is equal to C multiplied by A minus B plus A divided by A square minus B square is our required answer. I hope you understood the problem. Bye and have a nice day.