Good evening and welcome to the 16th annual Ann Drummy O'Callaghan lecture on women in the church. The lecture has been endowed by the O'Callaghan family in honor of Ann, who worked tirelessly in the diocese of Bridgeport as a religious educator and advocate for the mentally challenged. Ann had been a vocal spokesperson on behalf of women, growingly troubled by the role and treatment of women in the church. Thus, the theme of these lectures. One of its primary goals is to bring together religious educators, theologians and students to discuss issues relevant to women in the church. With that, I am pleased to welcome our newest university campus minister to the podium to introduce Jeanine Hill Fletcher. Katie Burns comes to us from St. Thomas Moore Chapel and Center at Yale University, where she served as a system chaplain. Good evening. Ann was a vocal spokesperson on behalf of women and I am honored to have been invited tonight to introduce our speaker to join the impressive list of women who have given this lecture. The title of her lecture tonight is The Courage to Love Christian Witness in a Weighted World. Jeanine Hill Fletcher is a professor of theology at Fordham University. Her primary area of research in Christian Theologies of Religious Diversity has focused on the intersection with other forms of difference, including gender and race, with an interest in the material and the political impact of theological projects. She argues for a cosmopolitan Catholic identity for the work of faith and healing in a multi-religious world. Her books include Monopoly on Salvation, A Christian Approach to Religious Pluralism and Motherhood as Metaphor in Gendering Interreligious Dialogue. She serves as a faculty director of service learning in Fordham's Dorothy Day Center for Service and Justice. Her current work is informed by membership in the Northwest Bronx Community and Clergy Coalition, a multi-generational, multi-religious and multi-racial grassroots organization working for social change. Today's lecture comes from the work of her new book, Love in a Weighted World, on Racism and Religious Diversity in a White Christian Nation, supported by a grant from the Louisville Institute. Following the extraordinary choices of ordinary women, we'll see the possibilities for the ancient wisdom of Christian tradition to transform even our 21st century world when Christians find the courage to love. Following the talk, we will take questions. Please join me in welcoming Professor Fletcher. Thank you. Thank you for joining me this evening in what I hope is a tribute to Anne's memory and carrying on that conversation that enriches us. And I begin with my title, The Courage to Love, and I'm arguing that at the heart of the Catholic tradition, the Christian tradition, is the mystery of love. We may think of the word love as a simple term that captures the ideal form of relationships, but the practice of love is far from simple. Think about your closest relationships. To what extent are you patient, kind, not jealous, as first Corinthians would have it? How skillful are you in not seeking your own interests? How measured is your temper? And do you never brood over the injuries that inevitably come in this relationship? If our most intimate experiences of love pose a challenge, how much more difficult is it to love our neighbors, people we don't really know, but who share our lives and our space? Are we present to these people with kindness and patience?  And how about those we are told are our enemies? Don't we sometimes rejoice in the wrongdoing that's done to them? I think of the church as a laboratory for learning how to love, and the Christian tradition as offering an ancient wisdom to guide our being human in the world. When the first Christians wrote Jesus' life story, which come to us as their gospel accounts, they placed the central teaching of love from the Jewish tradition in his mouth.  This mystery of love is not only a human relational reality. Love is a divine reality. Indeed, in Christian perspective, it is the reality at the center of existence. As the words of 1 John would have it, whoever does not love does not know God, for God is love. And the text goes on to insist, since no one has ever seen God, if we love one another, God lives in us, and God's love is perfected in us. Putting this together with the Gospel of John, we hear anew this Gospel writer propose that while no one has ever seen God, Jesus, who is close to God's heart, has made God known to us. In the biblical sources of Christian faith, the central teaching of Jesus and those who followed him reflects a passionate and intense desire to be in right relationship, right relationship with others, that is through love of neighbor, and right relationship with the source of all existence, that is through love of God. When women and men in the first century patterned themselves on the love made known in Jesus, they often radicalized the proximal love of neighbor, as in Paul's suggestion that the whole law is summed up in one single commandment, you shall love your neighbor as yourself. The Gospel accounts suggest that Jesus and his followers, what we might think of as the emerging church, were not content for their love to transform their closest relationships. They sought to enact this love in such a way that it would transform the world. As the leader of a movement that announced a counter-cultural kingdom of God, where love abounded, Jesus posed a challenge to the kingdom of Rome and its imperial structures of exclusion that might place limits on love. Jesus' life and his death reflect what Mark Lewis Taylor calls adversarial stance toward religiopolitical systems of domination. The women who followed Jesus were part of a movement that challenged the systems of Roman imperialism, and after his death, these women were part of the project of spreading out this counter-cultural, politically adversarial practice of unconventional love. Paul named some of them for us. They were Phoebe, a deacon of the church, Prisa, who risked her neck for Paul's life, Mary, working hard on behalf of the Jesus movement in Rome, and Junia, who was imprisoned for her work as it challenged the religiopolitical powers of empire. And this is from Paul's letter to the community in Rome in the first century, so we know women were among those first members of the community who worked in spreading out this counter-cultural Jesus movement. Thinking with these women activists and leaders in the Jesus movement, I think of the church not only as a laboratory for learning how to love, but also as the continuation of this Jesus movement. And we might think of women in the church carrying on the counter-cultural practice of expanding the horizon of Christian love toward the ever-receiving horizon of love, whose source we call God. If God is love, but God is mystery, and Christians are to practice love, but love is also mysterious, it's the witness of Jesus that shows us the contours of love that are counter-cultural practice. In the Gospel according to Mark, the first Gospel written that we have access to, what love looks like is actually not spoken about in lengthy discourses, but it's enacted in Jesus, who models the work of love in his work as a healer. A mere 26 verses into the first chapter of this story, Jesus's fame as a healer begins to spread so widely after he drives out an unclean spirit that by the end of this very first chapter, of the very first Gospel we have, his healing is so well known that he can no longer go into a town openly. This is the beginning of a Jesus movement, as people come out to see him in the countryside, and Jesus gathers crowds as he goes through the Gospel healing. A paralytic in chapter 2, a man with a withered hand in chapter 3, driving out demons into herd of swine in chapter 5. He heals a woman with a hemorrhage and the daughter of a leader of a synagogue. As he performs this work of healing, Jesus is challenged by a syrophoenician woman not to let the boundaries of culture or religion be a barrier to his work, chapter 7. In chapters 8, 9, and 10, Jesus heals the deaf, the blind, he exercises demons, Jesus spends his time in this Gospel traveling around the region healing, and people follow him. As a reflection of the world that the Jesus movement sought to transform, the world in the Gospel of Mark is primarily full of people who are hurting. They are bleeding, they are withered, they have seizures and spasms, they are estranged, they are dying, they are dead. And the mode through which Jesus loves these neighbors is healing. So I want you to hold on to the idea that this Gospel sees the world primarily as inhabited by people who are hurting, and that love is found in a healing presence. In fact, in the closing of the Gospel according to Mark, the sign of those who carry on the Jesus movement, those who believe and will be saved is not what they confess, but what they do. When activists in the Jesus movement lay their hands on those who are sick, those who are hurting recover. That's from chapter 16 of the Gospel of Mark. The women who followed in the Jesus movement in the early years of what will become the church must have had this healing power. There's a great line in the Gospel according to Matthew, which explains that when Jesus directs his healing toward the particular people that he does, it's when he's moved by compassion because the people are the ones that are harassed. In the systems and structures of power in his day, these were those who were disempowered. And the storytellers have Jesus not only healing the harassed, but raising a critique of religious and political powers who make their situation worse, heaping disdain and harassment upon those already disempowered. Do not do as they do, Jesus warned, for they do not practice what they teach. Matthew chapter 23. In expanding upon the failure of prominent members of the religious community, this Jesus points to the dangers of a different kind of love. We're called to love God and love neighbor, but some he sees, quote, love to have the place of honor at a banquet and the best seats in our gatherings and to be greeted with respect in the marketplace, end quote. So deep is our desire to be known that we put ourselves in those places where we might be seen and receive glory, honor, credit, praise, fame. In response to this ever-present threat that our self-love will eclipse concern for the other, Jesus in this Gospel calls woe onto those who he says, quote, clean the outside of the cup and the plate, but inside we are full of greed and self-indulgence, end quote. Matthew 23. In discerning the contours of Christian love, we need to take seriously also the necessity, even the theology of judgment that Christian love requires. Through judgment and healing, the Jesus movement in his day and through Christian history drove toward the transformation of the world. Women as well as men have been engaged in the project of what Catholic thought has described as integral salvation. This is a way of conceptualizing the end goal or conceptualizing salvation that is not an isolated personal experience, but a transformative social reality. In the words of Pope John Paul II, the integral salvation that Jesus came to bring, quote, embraces the whole person and all humankind. End quote. It's with the notion of integral salvation that the bishops at Vatican II expressed what love in its social form would look like. Describing the measure of our love made real in social systems, the bishops insisted. And I quote from Gaudium at Spes paragraph 26. There must be made available to all people everything necessary for leading a life truly human, such as food, clothing and shelter, the right to choose a state of life freely and to found a family, the right to education, to employment, to a good reputation, to respect, to appropriate information, to activity in accord with the upright norm of one's conscience, to protection of privacy and to rightful freedom in matters too, in matters religious too, end quote. The concept of Christian love seeking an integral salvation allows us to employ the lens of judgment and healing to ask, how are we doing in our loving? In the last 20 centuries of the Jesus movement, as it extended around the globe, has Christian love created the conditions of full humanity, not only for ourselves but for all our neighbors? The Christian vision of an integral salvation that transforms the whole of creation with our love asks us to look out on our North American context and to see an epic failure of Christian love in our world. Economic disparity, religious injustice and racism reveals to us not the contours of a kingdom of God but the saturated reality of a persistent kingdom of evil. To see the disproportion that characterizes our epic failure to love, we might begin with the most basic realities of economic disparity and see what the Pew Research Center reports, that the median wealth of white households in the US is 20 times that of black households and 18 times that of Hispanic households. This economic reality means that while 10 percent of white children are poor, roughly 27 percent of black and Latino children are poor, and 40 percent of American Indian children live in poverty. Sociologists can help us look out on our world and to see the projects that continue this racialized disparity. When they describe, and I'm quoting, when African Americans continue to be discriminated against in the labor market, concentrated in blue-collar employment, and along with Latinos, particularly dark-skinned Latinos like Puerto Ricans, earn the lowest wages, end quote. In addition to persistent race-based discrimination, generational dispossession in home ownership also disadvantages people of color. When home ownership is the most important source of building wealth and transferring it generationally, we can see the structural evil of race-based disparity when 72 percent of white Americans own homes, while only 46 percent of Latino Americans and 42 percent of black Americans do. And as Alec McCoolidge reminds us, owning a home and housing location are critical to predicting access to quality education, development of personal wealth, employment, health and safety, democratic participation, transportation, and quality childcare. The housing disparity we can see is the result of economic disparity, but it also stems from the actively racist patterns in our nation's history of prioritizing housing for white citizens. Today's structural disparity also results from more recent patterns of targeting communities of color with predatory lending that has taken place in the last 10 years. The social segregation of white, black, and Latino neighborhoods that persists today is the fabric of a world where love has failed. Both private economic resources in wealth and home ownership and the geographic advantage that comes with owning a home in a wealthy neighborhood impact educational opportunities for people of color in the United States. A disproportionate number of black and Latino students are educated in under-resourced primary and secondary schools, and as the Georgetown University Report entitled separate and unequal makes evident, opportunities for college education, especially at elite private colleges and universities, continues to disproportionately favor white students. Lack of access to education and opportunity has racialized a disparity in employment and in incarceration. Conditions which are at odds with the bishop's call for the right to employment, the right to a good reputation and respect for many of our neighbors of color. This disequilibrium of well-being, where some enjoy the conditions of an integral salvation while others are denied it, is what contemporary theorist and theologian Mark Taylor describes as a weighted world. That is, we could be bearing the weight of the world evenly so that all would enjoy an equal amount of what is necessary for a life fully human. But instead, the conditions of our world is that weight has been shifted onto some, so that some bear more of the weight of the world while others enjoy a relative weightlessness. Recalling the portrait of Jesus' world in the Gospels, our world continues to be filled with people who are hurting, and many of our neighbors continue to be those who might count as harassed. On the criteria of human well-being in health, security, recreation, green space, home ownership, education, and the freedom of movement and respect, the weight of our world has been disproportionately shifted onto people of color a little early. If women in the church are to carry on the Jesus movement of a counter-cultural love, we need to recognize that we love in a weighted world. Where people of color have less access to the sources of human well-being, and white people in this country disproportionately enjoy a relative weightlessness. When our neighbors of color disproportionately earn less than a living wage, our educated and under-resourced schools continue to experience workplace and healthcare discrimination, are targeted by systems of predatory lending and race-based policing patterns. We might wonder how the Jesus movement today continues the legacy of the one who proclaimed, I came that they may have life and have it abundantly. The saddest part of this epic failure to love in denying the qualities of integral salvation to men, women, and children of color is the realization that these conditions of disparity were created by people who called themselves Christian. They were created by people who chose to mobilize their Christian identity in such a way that it dispossessed non-white peoples from before the country's founding all the way up to today. Prior to the founding of this country, non-white, non-Christian peoples were dispossessed of their land by a theological story that identified European Christians as the only people who could carry out God's plan. Only Christian nations could lay claim to land ownership in what would become the United States, and First Nations peoples were denied the economic security that would come from holding title to land. First Nations peoples would be colored as red as Europeans made note of the sacred body paint that indigenous people wore, and this coloring came to stand in for their non-Christian ways that were deemed less civilized than those of the white conquerors and white colonists. White Americans compelled by the stories of Christian destiny crammed their indigenous neighbors onto smaller and smaller sites reserved for them. Today, First Nations peoples suffer the highest rates of incarceration per capita, they suffer from poverty, a lack of access to quality healthcare, and high rates of youth suicide. The epic failure to love of Christians in the newly formed colonies that would become the United States was established on the basis of Christian supremacy when the criteria for identifying whether a worker was to be considered a slave or a servant was determined by their country of origin. If they were from a Christian country, they would be considered a servant. From a non-Christian country, they were assessed to be, they were assessed as bound for enslavement. This legislation from the Virginia colony in 1682, and affirmed again in 1705, shows how the ideology of Christian supremacy could become part of an ideology of white supremacy when it was dark-skinned Africans who had become destined for slavery, justified in part by their non-Christian origins. White Christians made the argument that it was, that this too was part of God's design, and that African slaves would be better off for having left behind their pagan ways of African traditions or Islam. Through several hundred years of enslavement, it was Christians who defended and benefited from the practice of treating other human beings as chattel, traded, and sold as property for the benefit of white Christian citizens and white Christian institutions. Even after emancipation, Jim Crow Christians enacted a kind of morality that instituted separate but equal, even in our churches, and kept African Americans distanced from the benefits of full citizenship in schools, in employment, in health and recreation, prioritizing well-being for whites, even through our governmental systems. For example, in supporting home ownership through the Federal Housing Administration, which prioritized mortgages for white citizens, black and Latino well-being was compromised, as both were kept from purchasing homes when the mortgage lending manuals set up a racial hierarchy for who would be granted them. And this is what's on the right side. What was used as the mortgage lending manual all the way up to the 1950s had a racial hierarchy, and those on the bottom of the hierarchy would be much more likely to be denied loans. Concerned to protect the investment of their homes, their parishes, and their communities, it was white Christians and white Catholics who defended the decisions laid out in the mortgage lending manual when they were the ones who refused to allow black and Latinos families to purchase homes in their neighborhood, as James McGreevy's study entitled Parish Boundaries recounts. What's important to recognize in the racist attitudes of white Christians is that the refusal to integrate schools and neighborhoods was a refusal of black and brown well-being institutionally and generationally. If home ownership and education create the conditions for economic security, but white Christians refused black and Latino neighbors access to homes and schools, their refusal not only has social repercussions, but economic and material ones as well. The persistent reality of segregated neighborhoods even in the 21st century means that white Christians have not yet repented of the sins of the past of racial segregation, and that the love of the Jesus movement in the love of neighbor has been seriously compromised. One more area of example to sit with the epic failure of Christian love. Just as our country was built through the stolen land of Native peoples and the stolen labor of enslavement, a documentary by Juan Gonzalez entitled Harvest of Empire helps us to see clearly that the pattern of exploiting our neighbors is ongoing, especially in relation to our neighbors from Mexico. Since the time when annexation of Mexico in 1848, since this time of dispossession, dispossessing our neighbors of their land rather than seeking their well-being, the United States has been continuing to exploit their geographic proximity. Our closest neighbors are the ones that we often are exploiting. First, in the era of railroads and the building of the West, Mexican workers were necessary, and so we invited them. But when the Great Depression hit somewhere around 1 million of our neighbors were deported. In the second phase during World War II, when once again the U.S. needed workers, our government legislated the Guest Worker Program and encouraged millions of Mexicans to cross the border to help in our work. But eventually, shifting economies and anti-immigrant sentiment once again restricted movements of Mexicans into the U.S. Now that so many U.S. production sites have been moved to Mexico and death wages can be paid for our neighbors' work, our neighbors once again seek well-being even if it means a dangerous crossing and dangerous work in a hostile land. Can American Christians continue to claim that they are practicing Christian hospitality and a boundary crossing love if our nation continues to compromise the well-being of our Latino neighbors whose labor continues to be exploited with dangerous agricultural work, a lack of economic security, and our broken immigration system? We need this lengthy excursion into the contours of Christian love and the reality of the epic failure of Christian love in order to envision what it means to be women in the church today. In all of these examples of legislation and practice in U.S. history, which created the conditions of disparity we see today, ideologies of white supremacy were at work and Christian theology was written in such a way that made prioritizing white well-being appear to be consistent with the Gospel. Christian communities have protected white interests as if economic status, educational attainment, and high quality of life were gifts from God, not unjust benefits of a history of stolen labor and stolen land. But seeing clearly this unjust enrichment and unjust impoverishment, we return to the heart of the Christian tradition as a love story, and our question becomes, how are we to love in a world weighted by economic disparity and racial injustice? More pointedly, we might ask, where have there been women in the church who might provide us with a witness of what it looks like to love in a weighted world? Throughout the long history of white Christian supremacy in this country, there were Christian women who denounced these injustices and were willing to find the courage to love in the form of judgment. One of my favorite witnesses for a counter-Christian perspective to this long history is the activist Fanny Barrier Williams, a leader in the women's rights movement, Williams also noted the ways in which Christian ideologies of supremacy and white ideologies of superiority intertwined to create the conditions of dispossession and dehumanization for non-white, non-Christian people. She openly criticized the leaders of the white Christian churches who had gathered at the Parliament of the World's Religions in 1893. She criticized those leaders who did not repent of their own histories and the times when, in her words, mothers saw their babies sold by Christians on the auction block in order to raise money to send missionaries to foreign lands. Chillingly, Williams reminds us that it was Christians and often ministers and leaders who participated in the death-dealing practices of enslavement. It was Christians and Catholics who bought and sold human beings for the purposes of individual gain and institutional security. Williams questioned her mobilizing love as judgment. Her question to those present at the World's Parliament in 1893 raises a question for us as well. Have we yet repented of the ways our own church and its institutions created the conditions of racialized disparity? Have we undertaken the repentance, reconciliation, and reparation for the times when Catholic churches and Catholic universities used the lives and bodies of black and brown people to sustain white well-being? This history and the Catholic response has been illuminated recently by the news surrounding the 1838 slave sale at Georgetown and Georgetown's response. But this was a widespread practice of Catholic institutions owning slaves and benefiting from inhumane systems of enslavement. Can we be mobilized by this love as judgment that we hear from Fanny Barrier Williams? Can we be haunted by those memories and mobilize love in reparation and reconciliation? Are we also haunted by our more recent, dangerous memories of the practices of white Catholic parishes mobilizing their parishioners to resist integration when black and brown families attempted to move in? In the same way that Fanny Barrier Williams brought the haunting of enslaved mothers into the consciousness of white Christians, she invites us to be haunted by white Catholic participation in policies and practices that killed. This moment of love as judgment is necessary in a weighted world. But too many of our Christian institutions have failed to take account of the white supremacy that has been death dealing for our neighbors of color and white Christians have been willfully ignorant of the judgment that has been raised. But it was hard to ignore the courageous call of love and judgment raised by one woman in 1955. When Mamie Till Bradley's only child, Emmett, was kidnapped and lynched murdered by white men in Mississippi and his water-blooded disfigured body was brought to her by train in Chicago, she had a crucial choice to make. She could have made the choice to follow the coroner's direction and retain the seal of the closed casket, but instead she opened the casket to review the disfigured body of her only beloved son, taking in the reality and the horror of the sin of white supremacy as it manifest on his body. As theologian James Cohn recounts, Mamie looked upon her son and said, Darling, you have not died in vain. Your life has been sacrificed for something. Instead of closing in on her grief, Mamie insisted further on the public viewing of an open casket and the publication of Emmett's horrific disfigurement in the national press. Again, Cohn describes, 600,000 people viewed his bruised body and attended the funeral and many more, many millions more saw the Jet Magazine photos that traveled around the world. This is not for Emmett, Mrs. Bradley said, because my boy can't be helped now, but to make it safe for other boys. The crystal-formed torture and death of Emmett Till enabled Mamie Till to hear the voice of the resurrected Jesus and she describes this in her memoir. She describes the way that her faith rooted in the witness of Jesus gave her hope. Hearing the voice of the resurrected Jesus speak of the hope that although white racists could take her son's life, they could not deprive his life and death of an ultimate meaning. As in the resurrection of the crucified one, it was God who could transmute defeat into triumph, ugliness into beauty, despair into hope, the cross into resurrection, and Mamie saw herself as a vehicle for God's power working in that way through her loss and through the horror of the experience with her son and the ongoing experience of white racism that it represented. Mamie Till continued the efforts of the Jesus movement to bring life to the dispossessed because in the haunting of Emmett Till, we hear Christ's words. This is my body given up for you. Mamie Till gave over her crucified son and the world would be haunted by the crucified one and empowered into the transformation of the civil rights decade that followed as Rosa Parks, Medgar Evers, James Cohn, and countless other leaders would be emboldened by the horror of Emmett's death and the humanity that was his life. Mamie Till was an ordinary woman, but she was propelled by her Christian faith and her love of her son and future generations to find the courage to love in the form of judgment on white racism and in the experience of those who were emboldened by his death and her witness to his death, we see transformation that comes through this movement of judgment. Where do we see the courage to love in the form of judgment of white supremacy that continues today? Ordinary choices continue the transformative work of racial justice when women raise their voices in our world and on our streets. Most of them we will not know. They are the unknown leaders who continue the movement of a counter-cultural love in the transformative work of racial justice. But some of them we do know, like Alicia Sonier, an undergraduate student at St. Louis University, who not only responded to the call to join the demonstration after the death of Michael Brown, but also lifted her voice for the transformation of her university community at SLU when she advocated for the development of a racial justice movement in the organization which came to be known as Tribe X. She and other demonstrators agitated for the transformation of their world, and it was only after their demonstrations with the signing of a 13-point agreement with the university that demonstrators who had led six days of teachings and conversations about racial equity and social justice peacefully packed up their camp at the clock tower and returned to their homes and residence halls. From out of this agitation and agreement, the university has committed to a wide range of initiatives that enact love in a weighted world, an increased budget for African-American studies, financial resources for African-American students, initiatives to benefit the local community and residents of color, ongoing internal work at the university in its curriculum and committees attentive to diversity. While Alicia doesn't self-identify as Christian in her social media persona, she is lifted up as a catalyst of Christian change in a variety of faith-based sources. In Sojourner's Magazine, for example, she's quoted as saying that her participation in the Ferguson protests and her work of campus transformation at SLU helped her to distinguish between quote, the people who talk versus the people who love, end quote. Perhaps she echoes Jesus' words of judgment that we can tell the difference between people who merely clean the outside of the cup versus people who allow God's life-enriching love to fill them and flow out into the world. Love in the form of judgment can propel love in the form of healing that is the transformation of a weighted world. But if Williams, Till and Sonia are not Catholic women, how are they witnesses for women in the Catholic Church? To be truthful, the Catholic Church has not had a strong record of racial justice with respect to African Americans. But these women offer a public presence that enters into Catholic consciousness through a witness that crosses denominational lines. In this case, Christian women outside the Catholic Church bring witness to injustice into the Church. They are in the Church insofar as we allow their critiques to transform us. As a faith-based institution of Catholic and Jesuit higher learning, St. Louis University was propelled by the activism of Alicia Sonia and others to bring their institution of the Church deep into the soul-searching required for judgment to flower into healing transformation. As the President of SLU, Fred Pastillo expresses it, it was the protesters gathered on campus that made the senior leaders of the University, in his description, it made them reflect upon what it is for which we stand and to make decisions with respect to how we act on that basis. Propelled by the judgment of the protesters, Pastillo and senior administrators actually asked themselves what would Jesus do? What would St. Ignatius do? What would Pope Francis do? And it was on the basis of that judgment by listening to the voices of critique that these senior administrators were called back to the values that they held. So it's by listening to the voices of that critique our institutions and our practices in judgment that the Jesus movement of the Church can continue to find ways of enacting Christ's witness in the world. We might also follow the trajectory of ordinary Christian women making extraordinary choices by considering also those Catholic women who are in the Church doing their work out in the world. While the Catholic Church is still learning from the witness of non-Catholic others who are leaders in the work of racial justice, there have also been white Christians and white Catholics shaped by the Gospel to name and to change the many forms of injustice that intersect with racism. We might think of the work of Dorothy Day who found the courage to love in the ordinary choice to use her skills in journalism to chronicle the everyday injustices among the working poor. She was a tireless advocate for the worker exploited by the systems of capitalism and we might remember her compassion toward the poor in the founding of the Houses of Hospitality that remain throughout the Catholic worker network today. But do we recall her politically antagonistic agitating in countless demonstrations as the work of carrying on in the Jesus movement? It was love that propelled her into these agitating encounters with politically and religiously oppressive forces. Thinking deeply with other members in the movement she transcribed in her journal and these are her words or these are her transcriptions of William Blake. We're put on this earth for a little space that we may learn to bear the beams of love. But enacting this love and bearing the beams of love is not easy. Dorothy Day also wrote and I quote her we must practice the presence of God and in following the Jesus movement in its practices of learning to love and presencing God even Dorothy Day had to pray with these words in her journal take away my heart of stone and give me a heart of flesh. The simultaneous commitment to political transformation and personal practice of self transformation run all the way through Day's writings recalling for us again the mystery and the challenge of love. But Day also witnesses the possibility that we might make the choice to find the courage to love in our everyday practices and the bold commitments we might make to ever widening the circle of well-being and having this commitment of ever widening the circle of well-being be rooted in our Catholic faith tradition as it was for Day. Such ever widening circles and agitating love of God and neighbor of the Jesus movement continues in the work of countless women and men inspired today by Sister Simone Campbell. Working for over 40 years with the lobbying body of network Campbell made the courageous choice for her faith to inform the work of social transformation as she and other women religious boarded a bus to bring Catholic social teaching to elected officials on behalf of struggling communities across our nation. The platform of network in this election year gives witness to the healing that comes through love as legislation and the issues that they raise are many and they intersect importantly with the concerns we've already seen raised from the perspective of racial justice and racialized disparity that we've seen in our weighted world. These are the issues that network highlights and they offer resources for thinking about this election year through these issues but these issues also are the ones that we've seen intersect with the racialized disparity in our nation. Issues of healthcare of housing immigration income taxes voting and women and families in a weighted world it's not enough to love in interpersonal relationships of care compassion and concern love in a weighted world requires social transformation made possible by legislation and importantly it's not just Simone Campbell not even just the nuns on the bus but the countless women and men motivated by love toward justice who are nurtured in the laboratory of love that is the church. These are the many countless women and men who continue the Jesus movement in our day and there's an important dimension in continuing to name this as a Jesus movement. As Detra Weisbaker a pastor and leader in the racial justice movements in Ferguson remarked the days of the individual leader are over there's just too much work to be done in her words and I'm quoting her the idea of one leader or one methodology that's dead the work's too heavy the work's too heavy and multifaceted for one charismatic leader there's all kinds of kinds of work that has to be done and there's all kinds of people doing it Simone Campbell echoes this sentiment when she calls for full participation in the Jesus movement quoting her whatever our part is just do one thing that's all we have to do but the guilt of or the curse of the progressive the liberal or whatever is we think we have to do it all and then we get overwhelmed and I can't do everything and so I don't do anything but that's the mistake community is about just doing my part end quote every day ordinary women doing their part whatever that is is the vision of the Jesus movement that might actually change the world network's website offers the practical steps that actual Christians might take in enacting our love as legislation for the integral salvation that is healing of the world who among us will have the courage to love that follows their program sharing the analysis of social injustice and economic disparity and mobilizing our local communities to vote for candidates who whose proposals aim to mend the gap of economic disparity and racialized injustice the network website gives a range of possibilities and they make it incredibly easy to be part of the Jesus movement in this way from the simple electronic messaging of our elected officials to the packet of full resources for mobilizing voters toward practices of legislation that might heal our world as these women move out into the world assembling to demonstrate their commitment to various forms of justice and to enact with their lives the project of justice they're working across religious and racial lines in the hopes of rebalancing the weight of the world they carry on in the Jesus movement as Christians and allies in our work bringing judgment healing and even enemy love to life in the 21st century when we see the dispossession and disparity of a weighted world we might be tempted to give in to what feminist theologian Michelle Saraceno has called existential fatigue the sense that our world is too far gone to be able to turn the tide of injustice racism interreligious conflict and environmental degradation but the women we've seen this evening raise for us the possibility of existential hope that despite the ways the world puts love to death love to the end is possible and that integral salvation the promising hope that the power of God the power of love can even change unjust institutions there is hope that that's available to us practicing the presence of God as love is not easy but it is the call of the Christian where love requires both judgment and healing and it needs to be a public presence Christians may call themselves people of faith but they ought to be called to be people of love and they ought to be putting that love into practice by now I hope you can see that my interest in exploring women in the church is not the solitary or exceptional women who stand out in church history but the everyday women whose courage to love has propelled the Jesus movement into all areas of our world it's good for us to return to the idea of the Jesus movement being a witness to the possibilities of a counter cultural love of God neighbor and even enemy and the church being a laboratory for our learning how to love but to enact the love of the Jesus movement in our world today we must keep clearly in view the structural reality of racial and economic disparity and we must ask ourselves how will we love in a weighted world how will we as women of the church continue to carry on the Jesus movement in the 21st century when our descendants our descendants in the faith look back on our world will they see Christianity's continued epic failure to love will they see the final decline of the Jesus movement as fewer and fewer young people see the church as part of their identity and worth their time or will they see the renewal of the Jesus movement in the early 21st century as women of the church refused to stand idly by and mobilized their networks in finding the courage to love what would it look like for us to bond together as people of love across the boundaries of race and religion to see ourselves intimately intertwined with all people of love to hear the stories of love as they are raised in hope by our sisters in the Black Lives Matter movement to read the stories of hope that are passed on through Buddhist tradition or through Hindu wisdom to listen attentively to the stories of our Jewish neighbors and our Muslim sisters and brothers as they enact love in the world and counter the fear they find in a white Christian nation how might we stand alongside First Nations peoples as their love for the earth places them in harm's way the person of Jesus offers wisdom for seekers after meaning that what it means to be human is to love learning to love together with our neighbors of other faiths we might follow the Christian call to love and so transform our weighted world in the darkness of days in a white Christian nation I hope that a new day might be on the horizon and for that new day we need to learn to love together for if we love one another God lives in us and the mystery of existence in love of God and love of neighbor becomes real in our lives so let's learn to love together so that the movement begun by Jesus the movement that became the church might continue its counter cultural work for the healing of our world as we anticipate the fullness of that healing and see on the horizon the integral salvation that is promised thank you so we have excuse me so we have some time now for questions and comments to Janine and we have two two microphones so put your hand up if you have something you'd like to ask or say then I'll ask you do we have the capacity as Christians as Catholics to mobilize and transform the world like do we have that capacity if we have that capacity what are we doing so the witness of women in the church is an invitation to us as women and men in the church to ask ourselves well what am I doing if I'm if I'm haunted by this weighted world what am I doing Jane I'm very much impressed by what you had to say your exposition of the failure of Catholics and Christians generally in dealing with people who are not like us I think is something we need to hear we haven't heard that I mean it may be stated here and there but it's something that most people don't think about we don't think about that I meet usually every morning with a group of old men who every now and then will indulge in racist comments and stuff like that but and I said to them the other day I said have you ever thought about being sold into slavery you know and that's something that I was just incomprehensible so this whole idea that we have created the problem that we're talking about I don't think we've most Catholic and most Christians I suspect don't even accept that or haven't acknowledged that and there's some element of needing to hear the dangerous memories right so my I remember when I several years back when I started to because I never asked these questions I was I say this to my students all the time I was trained as a Catholic theologian right I spent these years studying I spent these years writing and I could say not one word about racial injustice and racialized economic disparity and I could still be a perfectly good Catholic theologian right it wasn't it wasn't requisite right and so as I began this work I can't remember exactly what oh yeah I said to my mom okay so I'm really kind of puzzling through our racialized injustice and the history of racism in this country so yeah I remember when I was in the fourth grade I think it was I remember they announced a mass that the bingo money was going to be used to buy the house down the street so that black families couldn't move in right oh brother right and I said my dear lord mom what kind of parish did you belong to and then I found James McGreevy's Parish Boundaries which is a study of the regular pattern in northern cities of mobilizing right defending the parish boundaries and actually mobilizing against Latino black families moving in right so there's a certain amount of of judgment right and recalling those dangerous memories that we really need to do in order to in order to repair and so some of my some of my work also comes from you know we talked earlier right Christians are supposed to love right we keep mobilizing this idea of love right and it's kind of the love of can't we all get along right but it's not taking responsibility for the ways that white Catholics white Christians have done this damage right but I think that someone like so sister Simone Campbell is one of my heroes right that she says look we can't go on like this we can fix this we can fix this we've done this we can undo it right but until our until and I'll say women in the church but it's everyone in the church until we're willing to say okay yeah we got to have these difficult conversations right we have to do this work of healing until we say that you know we're not we're not going to move forward thank you so much for your talk Janine it was very very helpful and I think one of the things that I was so interested in is the way in which you clearly connect for us the idea that love is not a private feeling that I have that religion perhaps is not about my private life and so that when we talk about racism which you know is easily passed off as well sometimes people say unfortunate things is when you point out very clearly that there were systems that people established to make this country function in that way and these are these are publicly available systems that people acquiesce to and so the response to that needs to be not a number of individual pieties but a systemic response that takes responsibility for the kind of future and the kind of country we want to live in and I think connecting that to the religious impulse is very important well the other piece that is part of that that I am this is what I'm deep into at the moment is the way that Christian and Catholic theologies perpetuated those systems right there were ideologies of so the example with or the reality with First Nations peoples in this country right that there were theologies of well we can oppress them because they're not Christian the example of enslavement well we can oppress them because they're not Christian right so so the the theologies that undergird undergirded that that sense of racial supremacy that then became legislated right I think the theology is intertwined with that I think that the issue that you pointed out of apathy and just feeling like there's just so much brokenness that I can't move almost is a big issue with people kind of our age like what are some like just practical like how do so how do I choose what to do when there's just so much that needs to be taken care of okay so start seriously this was I'm so glad you asked this question I don't have the website I have somewhere in here I thought I had the website the network website it's on the bottom of one of these that weren't okay so then the so the network lobby who brought nuns on the bus to you has a whole website and I'm sure there are other organizations that have these sorts of things but what they offer is an understanding of the issues through the lens of Catholic social teaching right but then they also have these terrific links and I was able to click on a link and find out how my elected representatives were shaping up in terms of the principles of Catholic social teaching and then I could click on another link and I could send my elected representatives I could send one of them a nice email I didn't have to write it it was already written by network thank you so much for all of the ways that you are upholding right the values that we share because you have a hundred percent record of you know aligning on these issues that are going to move us forward and my other representative official got a different sort of email that said look your your voting records not so good on this and we need to see right so so so part of it is finding the opportunities right to ask the questions finding the opportunities to get information and then finding the people who are doing this work right all of the all of the data of economic disparity that's not something I have to make up right there's tons of studies right all of the data on how we or all of the visions of how we might fix some of these things there are all kinds of people doing that work right so how do I I think for me the place that I have have found is kind of trying to see what some of the major issues are right structural issues and then finding those resources that help me understand them and then how do I take you know a next step right and I think that that's what Simone Campbell Dorothy Day right another thing that Dorothy Day says is you know we don't we don't we don't say enough that all are called right we're all called to do this work and I think you couple that with Simone Campbell and she's like well yeah of course it's overwhelming of course it is right but what's the one thing you're going to do I think that the witness of Alisha Sonia on the on the campus at SLU right that you that that the one thing you might do is host a conversation the one thing you might do is you know is get more information and begin to ask a certain sort of questions in your classes or in your or in your classroom right I mean so it it's it really is kind of all right well I'm not going to do it all right what I am what am I going to do and then I and then I come back to the question how do I do this and do what I love right so I was trained as a theologian I was not trained in any of these questions right I was trained as a theologian right so how do I do my work as a theologian haunted by these questions with these questions in mind right and so whatever discipline Dorothy Day is a great example she's a journalist right whatever discipline um I'll throw this in here the the Jesuits since we're here the Jesuits have a concept of forming ourselves in a well educated solidarity right that is using the best tools of the variety of disciplines right and forming ourselves in compassionate relationships right that can be socially transformative right so it's that well educated part like what are you already doing that you would have openings right what systems are all are you already a part of that you could take one little step right what conversations in your churches what kind of justice groups are in your churches or or Bible study groups that are in your churches or whatever right what are you already a part of that some of this could be opened up in a different way right um and so I I think of my work as a theologian if I'm going to be part of a Jesus movement there's something I have to be doing there's some agitating I need to be doing right so where can you agitate you've mentioned the Black Lives Movement since you mentioned the Black Lives Movement um also wondering if you want to say anything about the Standing Rock Reservation and the issues that are going about but the Dakota Access Pipeline and and perhaps you I'm assuming you're familiar with a doctrine of discovery that was so if you want to comment on that sure in terms of the history I wish I had my map because to understand I wish I had my map because to understand the situation at the Standing Rock Reservation uh you have to see uh the map and the Standing Rock Reservation is one of oh actually let's go back sorry to give you a headache on that but here's a Standing Rock Reservation here I'm sorry runs through is the way that the oil company wants to transport oil and the the First Nations peoples have gathered at Standing Rock to say look you cannot put this in it is too dangerous to our water supply it is too dangerous to our land and to our livelihood and we and we we are you know we're refusing to let you lay this pipeline now I got to go back to the pipeline uh and the mobilization right of First Nations peoples to say we have a right to protect the land right that we have a relationship to that is sacred to us right we have a right to protect that land uh is being challenged right do they have the right to protect that land and there's two things I want to follow up on the doctrine of discovery the idea of the doctrine of discovery is that in fourteen ninety-two ish uh with the papal bull and other and other pronouncements the Pope at the time said look uh all of you Christian nations that are coming to this so called New World if you arrive and you find another Christian nation there you cannot take that land right it's their land they're already they're Christian and they own that they they have claimed to that land but if you arrive and you find a non-Christian nation there you've got the right to the land that's your land to have so the Pope says that fourteen ninety-two ish and it's practice right that's the practice of all of the all of the colonizing nation so the Dutch use it and the French use it and the and the Spanish use it that's their protocol right if you arrive and you find another Christian nation you have no rights to the land if you arrive and find a non-Christian nation you can claim that land well that doctrine of discovery was written into law in eighteen twenty-three and it continues to impact the ability of First Nations peoples to lay claim to the land right and so I don't I don't know exactly this you know exactly where that issue is arising with with the Standing Rock the the and the Dakota Access Pipeline I don't I don't know exactly where they are saying well look we can see that the doctrine of discovery is still is still haunting us but part of that is that this ideology of Christian supremacy right that laid the foundations for this law continues to have impact for non-Christian peoples but the really important thing for me in this Dakota Access Pipeline is that if that thing breaks in the Missouri River it's not the that reservation of people it's all of those people right who are affected by it it's the water supply for I don't know how many numbers but right not that not that purple spot but it's the water supply for all of that area if that pipeline breaks underground right between Standing Rock and Illinois if it breaks underground anywhere it ruins the ecosystem it is damaging for the people and the earth the people that live there and the earth but according to Dakota Access Pipeline reports the company that is it I don't know the according to their website and according to the state by state description of approval of this pipeline what they're saying is that 90 percent of the landowners from Standing Rock Reservation to Illinois have said yes sure go ahead lay that pipe right we don't care it's good it's good somehow it's good for us right we're not concerned about the possible environmental damage they're saying that 90 percent so that this little group of of indigenous peoples right who have been absolutely dispossessed right the level of poverty on these on the reservations is is astronomical and and and wildly disproportionate but of all the people who are going to say look this is our earth that we need to take care of because it sustains us they're the only people that you know they're the people that are mobilizing to do it and there are there are there are Christian groups who have stood with them in the NCR I think it was in their coverage of this they described all of the Christian groups but there was no Catholic group that was there there's a I read the same National Catholic Recorder article is October 4th and so the the headline was the Francis calls to it for an end to the era of fossil fuels and then they named the I think it's something called the 300 global Catholic climate change groups and and are they standing alongside the First Nations people that I don't know that's what I yeah that I don't know I do know that earlier it was the Sisters of Loretto I believe who had called for a repudiation of the Doctrine of Discovery no small deal right and and so to I mean that would be another example of raising up a you know a form of courage right that says look we got to do something right how do we mobilize our love as judgment as transformation and the and the you know there there have been Catholic congregations that have that have really been mobilizing to do this yeah and to your point about education in a Jesuit context and so on it's interesting because I think many people are not aware of either what's going on in Standing Rock or that Francis called to the statement for an end to the era of fossil fuels it's a big deal that we go back at lunch meetings or dinners or over the dinner table or you know at your local parish to to ask whoever is presiding you know can we talk about this can there be some kind of can we have speakers to address this because this is Francis calling for it and if we're going to be followers of Francis then there's some merit in doing what he says right and and and I'm I'm gonna shift your words from followers of Francis to members of a Jesus movement right to say I agree I think yeah that if we're if we're gonna be serious about being members of this Jesus movement in the 21st century there are things there are questions we have to ask there's information we have to have to pursue and then we have to do something right but why why not why shouldn't we be doing this last comment because I have a friend of mine who's a Lakota woman who's involved in this the Standing Rock Reservation and basically what she's talking about is the bodies of water in addition to the Missouri River there are like 30 rivers that are like I guess we call them tributaries of the Missouri River so they're feeding into areas all over so we really are the the leadership that the indigenous people are are offering us are doing us good and that's an example of being called by you know the non-catholic being called by uh those outside the church to transform our practices in the church yeah thank you so much I think that's it for this evening um and as is tradition every year um at the end of the O'Callaghan lecture we first thank Janine and secondly um announce our speaker for next year who will be Nancy Pineda Madrid so thank you all for coming and have a good night


And we're here with the visco here. Hi. Hi. So what do you show here? Hello, everybody. This is Daniel Huan and I'm the CEO of the visco garment and We have been in garment Industry for more than 10 years and you're right there and don't one with the factory. What is this SMT? This is the machine machine with the textiles And these girls working very hard very hard and now we have been busy and This year we have a new product. Let me show you and you can have a look at our yeah How style there's a lot of black and white? It doesn't matter if you black or white Yeah, it doesn't matter, but this is the most common one in the world most common What is special about your garment? My garment for example the light change So yeah, light change. How does that work? Give me a little light. I can just call. Let me show you Let me show you have a look. Oh My god. Yes. Yeah, it's green. Wow green, but actually it's What? Becomes blue. Yes. Let me show you the video. I think let me show you the video. Is it nuclear? Yes, it's using a fission Next let me show you the video. I think it's very easy to understand So when you go to a party you will be like the star. Yes Right Wow Oh, it's red blue. Yeah change the color under the Sun. Oh my god under the Sun Yeah under the Sun change the color. Otherwise, it's just white. Ah, yes in the shadow It's like these are white. They look white, but actually they're not. Yeah, they're not Because is it magic? What do you use? What is the technology? Can you explain? Actually, it doesn't matter about the material. It's about the technology we use On on on on the back on the on the components Oh, suddenly it gets little spots This is this is really I've never seen this before. Wow. It's very special. Nobody do this. I nobody do this So your invention. Yes, we develop. Is it dangerous? Not dangerous. The girls will not be sick. It is environmentally friendly So it's good And how about if I put in a washing machine it doesn't work anymore? Actually, it is From outside it is It is very normal normal sweater. Normal sweater and in the washing machine. No, no change. No change. No, it's zero change The color stay. Yeah color stay Okay, so this is this is very okay. Let me show you another new one. So this is black. Yes black. Okay, please wait a minute. Wow What? No, this is not the same shirt You go to the party it becomes green. Yeah, it becomes green So it is very good for the halloween and christmas.  Yeah, it's totally white And then and this is really become green Oh, yes, I don't believe maybe show again What happened when you light it up? You have the light No, this is you have to black Ah, you have to go in the dark next right. You cannot do it with the flashlight on here. I cannot It's that there are two different materials So this one is for disco in the dark. Yes. So this is night time disco night time with the club The club. Yeah, you want to be the cool guy in the club?  They will see a difference. Oh, is it during the day? It's white and during the night, it's green during the night is green so In the morning afternoon You will be a professor Wearing this one, but it at night You're the cool guy. You're the green guy. Yeah, green guy the cool guy in the club Wow Is it possible to mix some green some red some pink everything in one? Yes, can how you do it just We have because it is the knitting hand it so we can change this part to green change this part to blue It depends it depends on what you need. Is it very very expensive and not expensive? But compared with others. I think it's a little bit expensive like what? Not much price maybe What is moq is the moq our moq is 100 or 200 100 200 and kind of price you want to say or they have to contact you Please contact me contact you. You will make special deal Yes, depends where you ship if you ship to indonesia. It's not same price if you ship to germany, right? Yes So please contact me contact you visco visco. Can we see some other examples? So this is just black How can I change color? No color change also. No color change. This is the north This girl will not be the star of the disco. Okay, any of these change color? No change, but you can customize If you need you can customize the same style but to change colors You can make them change color those little thingy things or it needs to be a big white spot to do your magic.  Yes, you need white and then the white you can do stuff with it Yes, sure And then over here when we see those white things here, maybe they're changing they change they change Yeah, I have video so this is during the day and boom. This is during the night It's like neon Yes It's like the light spectrum right the something you play on it. Ah, yes, I think so something yes secret Uh, this is secret your secret innovation innovation innovation. So all right. Nobody else can do it. Nobody else only you Yes, how long time you do this? This is for sweater 10 years, but for this product. This is a second generation What's what's different between first second generation? We improve the I would say It's good to fix the color to fix the color So it's better. Yeah, it's better better to fix Okay, yes Improve our our components. Is it more brighter color or something like that more? luminescent Depends yes, it depends So okay, and there you have some colors and all these whites here or I think this is their their normal one actually it it doesn't matter what the components of the sweater it's about the The the the textile we we are using now you can choose cashmere. You can choose cotton But we put the technology on it So it doesn't matter Nice. All right Yeah, sometimes I've been to disco where it looks like my shirt is a little bit weird But usually it's because I've got dust on it and I look dirty So but uh It's because some of these clubs have a strange lights change your eyes But they need to have the strange. I don't know this deep blue Lilac lights. Do they need to have that for this to work or just dark? I just talk Doesn't matter. It doesn't matter. It doesn't matter. So every club will work every club Cool. All right. That's cool. So people can find you On the on your website. I will link under the video And here people should contact you right? Contact right here The whole world. What is your biggest market? Uh, biggest market is USA And uh, how many how many people you have in the factory? Uh, 100 people All right. So if it's just 100 200 How many they need you put their their logo on it? For the logo MQ is 100 enough So to support the customer because now you know the whole market Uh Is getting getting better So we we we hope to support our customers to grow up together And if they have special design they want to put their logo on the shirt Yeah, sure. This is simple for us simple. Yeah, very simple very simple MQ is 100 is enough So they can do merchandise like a cool band can do this And all their fans will wear it and at the at the concert everybody looks cool with different colors and everything Yes, yes We are trying to make a new video To uh for all the people like 10 or eight people to make an advertisement to wearing our new product Cool. All right. And it's for every weather or it's only for the cold Uh, I think uh for for the cold weather is better winter winter is better But actually for this one you see it is thin very thin so I I think uh spring spring or Summer should be okay. So Denmark, sweden is a good customer. Yes. All these countries. Yes, Finland. Finland. Okay. Cool. Thanks a lot Thank you so much. Thank you


Hi and welcome to this next lecture on data structures and algorithms. We will continue our discussion on shortest path algorithms. In fact, we will continue our discussion for shortest path with a fixed source. However, today we will discuss an algorithm that can deal with negative weighted edges. Recall that we discussed the Deistras algorithm which operates under the constraint that no edge weights are negative. So, the Bellman-Ford algorithm it computes shortest path from a single source, fixed source to all other vertices in a weighted directed graph. However, Deistras algorithm does not work for negative weighted edges. It is a greedy algorithm that makes use of the optimal substructure property. Bellman-Ford solves the problem of negative weighted edges, but is slower than Deistras algorithm that is the price paid and running time is order of number of vertices is to the number of edges. So, what is the idea? So, let us understand the algorithm with a simple example. So, we will try and illustrate the working of the Bellman-Ford algorithm through an example. So, let us say your graph with a source as we will consider a purely directed graph. Let us give names to these vertices v1, v2, v3, v4, v5 and v6. We will also give names to the edges and their weights w1, w2, w3, w4, w5, w6. It also helps to have an additional edge here to make the graph a directed cycle graph. So, let us say this is w7. So, Bellman-Ford algorithm iterates through all the edges of the graph and for every edge it determines the weight on the two nodes that it is part of. So, of course, if you have the edges to be undirected it is possible that the shortest path crosses that particular edge in either way in either direction. However, the edge is directed you expect the shortest path from one node to another node if at all to occur only along the direction that is permitted by the edge. So, the idea behind the Bellman-Ford algorithm is initially all vertices are infinitely far away from the source. The source is of course a distance 0 from itself. Now, you iterate over all edges for each edge E. You are going to check if let us say E is going from U to V. You will check if the distance the shortest path distance to V existing distance is greater than equal to the distance to U plus the weight on the edge U V. If this is the case then you update V to this new found shortest path which says I am going to look at the shortest path to U and then append the edge U V to the shortest path to U. This is the basic idea and you are going to do this for every edge. How many times will you have to do? Well, when you start the iterations initially you determine that for V 1 and V 4 or that is the edges W 1 and W 4 you are able to update the weights for V 1 and V 4 to say W 1 and W 4 respectively. However, for all the other vertices other than source of course in the first iteration over all the edges there is nothing to update. However, in a subsequent iteration you will also update the shortest path for V 2 say which is W 1 plus W 2 and that for V 5 which is W 4 plus W 5. So, you will have to iterate over all the edges number of times that equals the maximum number of hops to a node from S. So, number of times to iterate over all the edges what I mean by this is this iteration and this is the width of graph which is max number of hops from source node S to any vertex say this let us say V by the way we do not need the V 6. So, I am just going to do V 3. So, this is going to be V 3. So, the complexity is basically number of edges into this maximum number of hops, but I will convince you that this maximum number of hops in the worst case actually happens to be number of vertices minus 1. I will construct an example to show this. So, let us consider a simple linear graph S goes to V 1 goes to V 2 goes to V 3. So, my first scan over the edges I will be able to update V 1 the second scan I will be able to update V 2 the third V 3. So, there are 4 vertices and I need 3 scans over all the edges till I am able to reach V 3 and update its shortest path because I can update the shortest path for V 3 when the shortest path for its immediate neighbors are updated. Let us look at the actual algorithm as pointed out the first thing you do is iterate over all the vertices set the depth of every vertex the shortest path to depth to infinity the predecessor for all the nodes is not set, but the predecessor for the source is null and the depth for the source is 0. And then as suggested we are going to iterate over all the edges this inner loop iterate over all the edges and we are going to do that for a number of times that equals number of vertices minus 1. So, recall that this is in the worst case the so called bit of the graph and then it is a check that we already anticipated if du plus w w is the weight of edge e if this happens to be less than the existing shortest path distance to V then you update the shortest path distance at V you also update the predecessor of V to point to U. So, this is already motivated and explained what is the part here at the end but so far we have assumed that our graph is a directed a cyclic graph what if the graph has cycles and is therefore not a directed a cyclic graph abbreviated as dag even in the case that the graph has no directed edges it might just have cycles and here is a test if the shortest path can be further reduced even after V minus 1 iterations then it appears that there is a cycle that is there is a path from S to a node any particular node that involves cycle. Let us illustrate this with an example so we have S V 1 let us say this is weight 5 this is say 4 to V 2 V 3 minus 3 we already pointed out the negative edges are possible and say minus 2 minus 1. Now as you update the weights originating with S 0 V 1 is 5 V 2 is 9 V 3 is 6 and then you have 4 then you have minus 1 is 3. However, the next iteration when you update V 2 we will get 7 and then you will be able to update V 3 to 4 and that at this node V 4 you are able to update the weight for V 4 further and get it to 2 and then at V 1 get it to 1 you could do this again go over this 1 plus 4 is 5 5 minus 3 is 2 2 minus 2 is 0 0 minus 1 is minus 1 and so on. So, just by going around this loop you can actually get very very negative weighted paths from S to all of these nodes. So, what is a characteristic here well it turns out that this cycle itself has negative weight what is the weight of all paths on the cycle minus 1 plus 4 plus minus 3 plus minus 2 the whole weight is basically minus 2. So, the more you go around in this loop the more you will be able to reduce the shortest path and this you can do add infinitum. So, this is what we are checking if after so many iterations if you are still able to reduce the shortest path distance to any particular node then you basically cannot find a shortest path. So, you just return a false. So, that is what we see here returns false for negative weight cycle. Let us see this in action we start with infinite weighted shortest path to all the nodes the first iteration over all the edges we find that only the immediate neighbors of the source can be updated and we have done that then again we look at all the edges we are only able to update now the immediate neighbors of these nodes that we are updated. So, it turns out that B is also unable to A and you are able to get shortest path to B through A this is the latest we continue our bookkeeping find that the shortest path to C and E has been updated C and E has been updated and then to G and it turns out that you can actually find another shortest path G through C and in fact this also lets you update shortest path to E through G. So, let us analyze the Bellman shortest path algorithm we look at two characteristics one is its correctness and the other will be its complexity. So, we prove the correctness of this algorithm by claiming the following loop invariant and we state that for every vertex v within k hops from the source node s the value dv is indeed the shortest path from s after k outer iterations. So, we are claiming that at the kth iteration of this outer loop the value that gets updated in dv the end of this kth iteration dv contain the correct value the shortest path and it is easy to show that at initialization this is correct because the only node that is within 0 hops from the source itself and indeed depth of shortest path of source is set to 0. The next iteration we can easily see that we only deal with the immediate neighbors of the source and they get updated correctly. In fact, the maintenance can be easily proved because we know that to get to a vertex which is k plus 1 hops from the source s you need to go through a vertex which is within k hops from the source s. So, maintenance can be proved with the key observation that a vertex at k plus 1 hops from s is reached vertex at k hops from s and this can therefore extend even a termination. What about time complexity? Well, the runtime complexity is again straightforward as we had anticipated we are going to iterate over all the edges for a fixed outer iteration and number of outer iterations is basically the number of vertices or order of number of vertices. We actually split the cost here for each of the if blocks and the for loops and so on, but it is essentially number of edges into number of vertices and the final check is only order of number of edges which is basically to check for negative weight cycles. So, overall complexity is order of v e is the dominating term. Thank you.