It's really fantastic to see so many people here today and I just really want to give a particular welcome to the participants of UBC's program for open education scholarship, also known as POS who are joining us today as part of a unit on open education. My name is Will Engel and I'm a strategist for open education initiatives at the Center for Teaching, Learning, and Technology here at UBC. And I'd like to acknowledge that UBC, which is hosting this session, is located on the traditional, ancestral, and unceded territory of the Muslim people. And as we were meeting virtually today, I'd like to acknowledge that here in the lower BC mainland, we're often on the unceded territories of the Squamish, Tsleil-Waututh, and other Coast Salish people. You may be joining from different areas and I'd like to take a moment just to appreciate and give respect to the lands in which we are situated. And please don't hesitate to share the territory from which you might be joining us today. I appreciate the land where I am as it provides me with a lot of opportunities. And when I acknowledge being on the territory of the Muslim people, it's really rooted in the understanding that I, as a member of UBC, I'm really privileged to be learning and working on a territory that's not my own. Just before we begin, I'd like to note that the session is being recorded and you're welcome to turn off your camera if you don't want to be capturing the recording, particularly during the question and answer time, and that we have enabled the live captions. You can control the live captions at the bottom of the Zoom window. There should be a button that says CC on that. So in my role, which is centered on open education, I do often acknowledge that open education is grounded in Western notions of copyright law and ownership, and these notions can be intentioned with indigenous and traditional ways of knowing. And so with that, I'm really excited to introduce and learn from our speaker, Speaker Kyla Larson today, who will be exploring this topic in more detail. Kyla, or Kyla is a Metis and Ukrainian settler originally from Treaty 6 territory. And she is currently the indigenous programs and services managed, excuse me, the indigenous program and services librarian for Weewha Library here at UBC. She's also the program manager for the indigenization program, and she's also the co-host for the Ms. Nygan Iskwiak Book Woman podcast. I'm just going to put a quick link to that podcast in the chat because it's completely worth checking out to explore. If you're into podcasts, please do check it out. And with that, I'm going to hand it over to Kyla, or Kyla, sorry, to walk us through today. Thanks, Will. Hi, everyone. Good afternoon. Thank you for joining. And so today, the talk that I'll be giving will be focusing on indigenous OERs, what exactly an indigenous OER looks like and kind of the protocols or the considerations that need to be taken when engaging with indigenous communities on either the creation of an OER or when we are incorporating indigenous knowledge and worldviews into OERs that we are creating and how to have collaboration and consultation with communities if they have the capacity to do so. I'm going to ask to keep questions for the end. I like to talk to people. One of my roles as a librarian is always chatting with folks. So I'll probably go off on a long tangent if somebody asks me a question in the middle of the talk. So I'm just going to ask that I will answer the questions at the very end. And then also at the very end, if we want to have a little bit more of open discussion about indigenous knowledges in OER as well, we can have that. And so let's get started. So indigenous OERs, the six Rs of indigenous OERs. And hopefully by the end, you'll be like, you'll have a better understanding. What exactly do I mean when I'm talking about the six Rs? And how did I come up with the six Rs? And how can we start to begin to incorporate them into OER practices? But also thinking about how we can take worldviews such as the four Rs, which I will be talking about later, and incorporating them into our own practices and understanding our roles as academics, students, faculty members, and how we have to begin to think a little bit differently when engaging with indigenous knowledges. It goes outside of the kind of the Western norm that we're taught in academia about what is allowed to be shared, what is knowledge, who has authority. So welcome to the Indigenous OER panel. So first of all, I'd like to just start off like Will did in acknowledging that I am here joining you today as an uninvited guest from the Traditional Territory of the Humpminum-Speaking Musqueam Nation. Additionally, I live on the territories of the Musqueam, Squamish, and Tsleil-Waututh nations, and I am invited, and sorry, I am an uninvited guest, and an uninvited Indigenous guest on these nations, and I'd like to thank them for allowing me to continue to work and live here, and also to acknowledge all the communities who you are joining from and the lands that you're joining from, and the folks that have been there since time immemorial. So first off, when talking about Indigenous knowledges, and kind of coming into this virtual space that we're all joining today in an important way and in a way where we're getting to know each other, I think the first thing that I always like to do when coming into presentations is to really locate myself and talk about the importance of locating ourselves. And the importance of locating ourselves will come in later into OER practices and working with Indigenous communities. So when we locate ourselves, it reconnects us to ourselves, our people, and our stories as powerful forms of cultural resistance, and is the basic building block to having deep relations with others, and that's what we're doing today. We're all in this virtual space building relationships with one another. Now that you've gotten to see my face, hear my voice, and you'll be listening to this presentation, if you see me on campus, definitely feel free to wave or let me know who you are so that we can continue to build the relations outside of this virtual space. So when we locate ourselves, we often ask, who is your kin? So like it came up, I am from Treaty Six. I am from Treaty Six territory. I am Métis. I speak very little, so absis a bit of Nihiawayen, which is Cree. So when I'm asked who my kin is, it's Tante Otsikia. So that means where are you from? Who is your kin? But it doesn't necessarily mean exactly what lands are you from. It means where is your umbilical cord attached to? Who is your kin? Who is your mother? So that's what we ask. Additionally from that, we can ask what lands are we connected to? So where are you from? What territory are you from? What lands make you feel at home? From this, we can ask who are we accountable to? What nations and communities are we accountable to? Who are we accountable to right now? As well as what lands do we reside on presently? So we have the connection to where we grew up, the lands that we are the most connected to, our traditional territories, but also we have to think about the lands that we are on in the present. When we do this, it helps us to acknowledge our biases, our positions, and our connections. And this is important when working with Indigenous communities, especially as academics, faculty members, students, et cetera. It's really important to start to build those relationships and allow people to know where you're coming from and what your position is on whatever you might be talking about. So when I situate myself and to locate and position myself, I am from Treaty Six territory, Muscogee, West Nighan, so Edmonton, also known as Beaver Hills House, but I grew up more specifically in a Muscogee. So the area of the Beaver Hills, I grew up in a very small town called Tofield, Alberta. The area of Muscogee is a shared territory between the Sarsie, Cree, Anishinaabe, Nekotisu, Métis, and Blackfoot peoples and nations. And they've shared this territory for a very long time. Additionally, so when I'm talking about living on Treaty Six territory, my connection to Treaty Six territory is very strong. It's connected to my worldviews and my understandings of things like education, law, governance, relationship building, and protocols. So we can see here a photograph of Amosk Lake in Elk Island. I grew up not too far from Elk Island and Edmonton. So I'm very much so connected to Treaty Six. However, now that I'm here on the territory of Musqueam people and the Musqueam nation, I need to learn how to act appropriately as a guest on their territory, and to start to think about their own protocols, laws, and governance structures. And how do I place myself within that in a way that I can be respectful and responsible to the community? Additionally, just a preface where I also come from. So I work at La Cuihua Library here on campus. So on the UBC Vancouver campus, it is deeply tied to the Longhouse, and we'll talk about that a little bit later. So deeply tied in our protocols and our understandings, but also in geographic location. We are right beside the Longhouse. We are the only Indigenous academic library branch in all of Canada and respectfully internationally as well. And at the Cuihua Library, what we do is practice Indigenous librarianship. So Indigenous librarianship unites the discipline of librarianship with Indigenous approaches to knowledge, theory, and research methodology. Additionally, Indigenous librarianship, the major focus of it, is to provide culturally relevant library and information collections and services by four and with Indigenous peoples. Additionally, Indigenous librarianship is grounded in the contemporary realities of Indigenous peoples and Indigenous aspirations for self-governance and sovereignty. And this idea of self-governance and sovereignty is important when we talk about OERs later. A lot of the work that I do is connecting with community. My work is very outward. I have other colleagues, so Carline Deloria-Lyle, who's the Information Services Librarian. Also an Information Professional though, but the Information Services Librarian for the Cuihua Library does a lot more of the inward work. So working with faculty, staff, and students on liaison work. A lot of my work is more outward, working with communities, working with other organizations to have conversations around things like research and OERs. So it's always good to start off by kind of coming together on the same page of what Indigenous world views are, especially because we're talking about them in the context of open education and open educational resources. So Indigenous world views, and these are from Leanne Simpson, but in general Indigenous world views are holistic, cyclical, and dependent upon relationships and connections to living and non-living beings and entities. There are many truths within an Indigenous world view, and these truths are dependent upon the individual's experience. Everything is alive. All things are equal. The land is sacred. And relationships between people and the spiritual world are important. Within an Indigenous world view, often humans are seeing as being the least important thing in the world. And within Indigenous world views are Indigenous knowledges. So there's in general about three different types of Indigenous knowledges or how they evolve. So Indigenous knowledges are evolved from traditional knowledges, and so traditional knowledges are living chronicles and origins, trajectories, and achievements of Indigenous peoples. Empirical knowledges, so these are careful observations and relationships to humans and non-humans. It's ecological and accumulated all over time. And then also revealed knowledges. So sometimes knowledges are revealed through things like dreams, visions, and intuition. And then there's five characteristics of Indigenous knowledges. They're personal, orally transmitted with exceptions. So these exceptions might be like pictographs, pictographs, so carvings and paintings on rocks. Also tattoos can be a form of knowledge as well and a story on our own body. Experiential, so knowledges can be experiential. Often we see this with experiences on the land. You cannot actually know without being there. Not all of your senses are activated. So I can tell you what it's like to go to Lynn Canyon and hike in Lynn Canyon, but you can't actually experience without going there.  You can't hear the water rushing. You can't feel the softness of the earth underneath you.  Additionally, Indigenous knowledges are holistic. So they bring together the inner and the outer world, the physical with the spiritual. And then their narratives. So often Indigenous knowledges use metaphors to present moral choices and self-reflection as well. And then within these knowledges, we can break it down further to different types of Indigenous knowledges. And each type of Indigenous knowledge has different protocols and protections and ways that we engage with them. So the first off are traditional knowledges as we've talked about before. So traditional knowledges are knowledges, know-how, skills and practices that have been developed, sustained and passed from generation to generation within a community, often performing part of its cultural or spiritual identity. And often these are the knowledges that are most protected and especially when we're looking at issues within copyright. These are the more challenging knowledges for communities to claim ownership within a Canadian context over. But also it's important to realize that traditional knowledges are some of the most important knowledges within communities. Additionally, we have Indigenous cultural expressions. So similar to TK as it often includes traditional knowledges in the output of it and Indigenous cultural expressions include things like dances, regalia, design, songs, etc. So for an example here, we have a jacket, so like a Cowichan jacket and that would be an example of an Indigenous cultural expression. The meaning behind the design or any of the traditional knowledge or story that goes into the jacket would be the TK that's incorporated into it. In general, Indigenous cultural expressions are easier to cover under copyright law because they're more tangible. And so these are the things that we often see that being challenged within copyright law and copyright around designs, jackets, things like that. There was the case with Eritzia years ago when they had jackets that were along the lines of this and those types of things are more easily challenged within the Canadian court system. And then we have biocultural and genetic resources. So biocultural and genetic resources include things like microorganisms, plant varieties, animal breeds, etc. So this work with biocultural and genetic resources and when it comes to knowledge preservation around these items is fairly new. However, it's very important. A lot of the work around this is coming out of our relatives in Audra, so in New Zealand and Maori individuals looking at how they can take their own understandings and worldviews and incorporate that into genetic resource protection. With these types of knowledges that we've just seen, so traditional knowledges, the cultural expressions and the biocultural items, there are specific knowledge sharing protocols that go along with these different types of knowledges that differ from community to community. So often these protocols for knowledge sharing and data sharing use a collective knowledge and incorporate some type of law that is known within the community. And it's important to realize, especially within the Canadian context in having three different distinct groups, First Nations, Métis and Inuit who also within these groups have distinct communities and language representation. It's important that we work locally and we'll talk about this a little bit later, but it's important to also realize that all communities have different laws, they have different knowledge protocols. So what works for one community might not work for another and that's why keeping it local is always something good to do when especially engaging with OERs, but it's good to know the local community and what their knowledge sharing protocols are and to ask first, unless you're specifically working with data or knowledge from a community like a Cree community then ask that community. It wouldn't necessarily make sense to go to Musqueam and ask them about Cree protocols. So Indigenous knowledge and data sharing protocols often are dependent on things like ownership and inheritance. This can come at a community clan or family level they're earned can be dependent on age, gender identity, geography, season. So we're just coming out of the time of storytelling. So winter in a lot of communities is the time for telling sacred stories. And then we transition to more harvesting within the summertime and springtime. And then another another kind of knowledge and sharing protocol can also dependant on the type of technique that's being used. And all of these knowledges come together to form what in academia we would call data. And so it really is just a large blanket term for knowledges all coming together. So when we look at Indigenous data there's data on Indigenous resources and environment. So this is our land data water information. And then we have data on Indigenous demographics or social data. So often this is represented as legal data, health and education as well as this can be Indigenous created. So we can have Indigenous health surveys that are created by communities or we can have other things like Indigenous health surveys that are created by federal, provincial and municipal governments. And then we have data from Indigenous communities. So this can include things like traditional cultural data, archives or a literature ancestral knowledge or community stories. So all of these come together to form kind of the larger blanket of Indigenous data. And all of this incorporates into Indigenous research which is very different now than historically what we think about research or kind of a Western focused idea of research. Often the Western focused idea of research does not fit within Indigenous protocols around sharing of knowledge. And there was lots of problematic practices within more historic forms of research within Indigenous communities. So when we're thinking about Indigenous research more in a contemporary sense Indigenous research really is very community driven. It includes things like all of our relations. So when we talk about all of our relations that's those who are from the land, the sky, the water, it includes plants, animals, mountains and as well as the spiritual world so our ancestors and those who come after us. As well as Indigenous research is accountable so we are accountable to the communities that we work with. As an Indigenous person I'm accountable to my community but I'm also accountable to Musqueam. I am accountable to my co-workers at Kwikwa and now that we're starting to build relations with one another I'm accountable to the folks that are on this call as well. Indigenous research brings in Indigenous world views and includes Indigenous laws and protocols and all of this comes together and then we can talk about OERs and what exactly an OER is. Now that we kind of have a very basic foundation of what Indigenous knowledges are Indigenous knowledge protocols and Indigenous research we can talk a little bit about the star of this week open educational resources and I hope that you had a chance to visit some of the other sessions that have happened or some of the sessions that might be going on so you can learn a little bit more about OERs. I am not an OER expert I am very thankful to my colleagues such as Donna Langill at UBCO who works with OERs and is a specialist in open educational resources as well as the folks at the University of Alberta who I worked with that also worked with OERs and taught me about OERs when I was a student and coming into library and librarianships. But in basic if you missed some of the other sessions that have already happened this week here is an outline of what exactly an OER is. So open educational resources also known as OERs are teaching, learning resources and they're also research resources that are created with the intention of being freely available to users. They may include but are not limited to things like textbooks, readings, multimedia files and courses. Most OERs are covered by licenses that allow for the using remixing and sharing of items. As well as OERs break down barriers for authors when it comes to things like publishing. If you're a faculty member or a student we know or a graduate student even we know that there are issues for folks that are like IMPOC folks, queer folks when it comes to publishing and within the mainstream publishing industry. As well as due to their openness often things like paywall barriers are alleviated. So we all know how frustrating it is when we're trying to access information through a journal that maybe UBC does not subscribe to and then we hit that paywall barrier and we're being asked for money or even when it comes to just in general how expensive textbooks are getting um now OERs can alleviate that kind of financial burden for students of having very expensive textbooks and it's a great way also for academics to share their knowledge and in some cases sharing knowledge collectively between individuals and institutions. So when it comes to OERs there's five R's of OERs and these are important because these are kind of how we formulate an OER and how we look at them so there's retention retention is number one and retention is the right to make own and control copies of the content and then we have reuse so reuse is the right to use the content in a wide range of ways so that could be your class website study group video etc and then revise so the right to adapt adjust modify or alter the content itself number four is remix so the right to combine the original or revise content with another open content to create something new and then lastly redistribute so the right to share copies of the original content your revisions your remixes with others so really keep this very colorful image of the five R's in your head because this will kind of come into play later when we're thinking about indigenous aspects of OERs and how indigenous knowledge is maybe don't fit into this but in general these are the five R's of OERs that are used alright so here's the big one indigenous content in OERs I could have put indigenous knowledges but I put content in OERs because in some cases the knowledge can be coming from a community that's when I feel more comfortable in putting indigenous knowledges are coming into communities but sometimes it's indigenous content so that could be something like the TRC is called to action would be a content that could be in an OER or the ISP from UBC and if you haven't read the ISP the indigenous strategic plan for UBC if you are a member of UBC whether you're a faculty staff student please make sure that you do have a look at the ISP and the goals of the ISP it's a very important document that will play into courses relationship things like that here on campus so please please read that I always like to stress that people take a look at that so when we're thinking about knowledges and knowledges in OERs especially knowledges that come from indigenous communities black communities other communities of color from queer folks when we think about knowledge and how knowledge has been used over time knowledge is power and those who possess that knowledge are in power in that moment so when we're thinking about indigenous sovereignty and self-determination the ability for communities to be able to keep that power and that knowledge is important within the Canadian context indigenous nations in Canada are sovereign nations Canada and indigenous nations are two separate governing bodies living on the same land mass the Canadian government recognizes that indigenous peoples have the right to remain sovereign and practice self-governance through section 35 of the constitution as well as indigenous self-government is the formal structure through which indigenous communities may control things like the administration of their people land resources and related programs and policies so this can include education this can also include things like their cultural management and their land management which come together part of this sovereignty that is really challenging especially within an academic context and this also looks at power structures but one of the things that I'm trying to advocate for and use my voice and my privilege as a librarian and an indigenous librarian who has that indigenous knowledge and worldview but also lives in this world of academia here at UBC is to really advocate for indigenous data sovereignty and the principle of indigenous data sovereignty indigenous data sovereignty is not law but it is something that we can kind of remind ourselves about when we're working with indigenous knowledges indigenous data sovereignty is the concept that indigenous nations have the right to ownership and governance over data about them regardless of where it is held and who holds that indigenous nations have the right to govern data in a ways that align with their own protocols and laws and indigenous people have the right to access data that supports nation rebuilding so often this includes access to government documents both historic and contemporary and archival documents however one thing to note that with indigenous data sovereignty and sovereignty is that often it comes up in challenge with Canadian copyright law in general in Canada although it is changing and it's ever changing with conversations however there's no change to the Canadian copyright act but in general copyright when it comes to indigenous knowledges is hard to prove expressions of traditional knowledge often don't qualify for protection because they are too old and therefore supposedly in the public domain additionally the author of the material is often not identifiable and therefore there is no rights holder in the normal sense and additionally knowledges are collectively owned by indigenous groups and communities for cultural claims and not by individuals for corporate or economic claims so in one hand we have the government of Canada acknowledging that indigenous nations have the right to self-determination and to self-governance but then on the other hand and acknowledge that they are sovereign nations but then on the other hand we have things like the copyright act which challenges that sovereignty and governance when it comes to indigenous knowledges and who's allowed to use those knowledges and the protections over those knowledges so when it comes to indigenous knowledges in OERs we really need to think differently there's a different approach to indigenous OERs than there is in making other OERs mainly because of knowledge protections and sovereignty and making sure that we don't do wrong and replicate problematic practices of the past especially when it came to research of not asking a big thing that we often hear within indigenous communities when it comes to consultation is nothing about us without us and that's the goal here with indigenous OERs as well so when we think about OERs one place that we can start and this is a great resource and a great organization for people to think about because it does bring in concepts of open access but just kind of changed it is GEDA so GEDA is the Global Indigenous Data Alliance one thing that GEDA did is they looked at the fair principles of open access so the fair principles are findability accessible interoperable and reusable so they looked at those and created what I like to call fair plus but their little hashtag is be fair in care which is amazing because it's super easy to remember and they created the care principles that go on to fair so care stands for collective benefit authority of control responsibility and ethics so taking the fair principles of open access and thinking about it from a different lens incorporating those Indigenous worldviews about control responsibility and ethics and they have a website where you can learn more about the GEDA principles and GEDA themselves as an organization so when looking at OERs it's important to think who is the audience so who is driving the creation of the OER is it an Indigenous community is it the public is this for settler education because this will be different in how consultation happens or how even the front face of the OER might be or if there's any restrictions what is the age range that is going to be using this OER and what is the education level of folks that will be also engaging with this OER and the location is important too as I said not all communities so if this is a community-driven OER and you're helping to engage with the community to build it it's going to have very different protocols than where you might actually be located so like I gave the example of Cree folks and people from Musqueam as well so the location is very important and the protocols that happen within those nations and your geographic location context context is hugely important when it comes to what actually can be shared and not be shared so context and content the things we need to ask ourselves in this case is what kind of knowledges are actually being shared are there any specific protocols and think back to the protocols so what are the protocols that need to be adhered to when we are sharing these knowledges is there consent from the community to share this information is this primary or secondary information that we're sharing are we sharing elder stories are we sharing testimonies from important court cases or is this something else that we are sharing so secondary information and how can we actually support this OER what is the role that we need to take in the support for this OER are we simply just a user of it are we helping to generate content are we developing the OER so there's lots of questions that need to be asked when kind of working with OERs depending on if they're community driven if it's for settler education etc there's lots of questions that need to be answered one of the things though that we need to consider even if the OER is for not for community but for something else is that we need to allow indigenous peoples to take the lead especially when it comes to information being shared about their communities their lived histories and their knowledges the most important thing that we can do is consult with communities and take that and let them take the lead on what content and knowledges should be included in an OER as well as we need to allow for the building of capacity for communities to create OERs at all steps as well as building relationships building relationships is hugely important when it comes to OERs academia and building that also that trust and accountability with one another so question the five Rs this is the thing to do all right so let's start thinking when we look at the five Rs so retain, reuse, revise, remix and redistribute thinking about indigenous protocols protections of TK copyright kind of all the things we just talked about do the five Rs really make sense when it comes to indigenous OERs I looked at it and immediately red flags were going up with things like retain so if I am the individual that makes the OER technically within Canadian copyright law it can be altered but there is that kind of that I am the owner there's that kind of implementation that I am the owner as well as reuse we don't want all indigenous content to be reused or revised or remixed and redistribution can be highly problematic as well so we really need to think differently so as of right now there are no kind of federally, internationally accepted best practice for an indigenous OER indigenous OERs are fairly new and there's not even a lot of academic literature being written about them there are indigenous OERs that exist you can read the McCracken and Hogan paper and it lists all the indigenous that OER indigenous OERs that existed at the time of that publication however there is no best practice that is kind of like a standard that's been set out however the McCracken and Hogan paper did take kind of the first shot at what exactly and best practice for indigenous OER would be so their best practices are that relationships must come first again coming back to relationships and relationship building nothing about us without us integrating things like the principles of OCAP into the OER development so OCAP is stands for ownership control access and possession of indigenous knowledges and it was created by FNIGC which is the First Nations Information Governance Connect as a way for researchers to engage with indigenous knowledges in a way that is clearly defined by First Nations in Canada the principles of OCAP do they are meant for First Nations knowledges and follow First Nations principles they don't necessarily follow the principles of Metis and Inuit however we can take examples from OCAP and kind of bend it towards the knowledges of Metis and Inuit folks here in Canada and their world views additionally we need to consider that not all indigenous knowledges are open and it matters how the information is shared so I had mentioned earlier that the Huihua Library is very much so aligned and part of the First Nations House of Learning the Longhouse here at UBC one of the things that the Longhouse has is that they have their own 4Rs of and these are the kind of the protocols of the Longhouse and their respect relationships responsibility and reverence so these are kind of the world views that inform the Longhouse and those within it as well as we work with the 4Rs within Huihua Library and they inform our practices as librarians and the ways that we build relationships here on campus as well as our understandings of librarians and world views and respecting things like the sacred which falls under reverence additionally there's other 4Rs so there's another set of 4Rs that are the 4Rs of indigenous education and these are by Kirkness and Barnhart and so the 4Rs of indigenous education are respect relevance they're reciprocal as well as their responsibility being that my life my world view and my professional practice is so influenced by these 4Rs what I wanted to do was take these 4Rs and expand them take a world view that I already know and expand it to fit into indigenous OERs and take those 5Rs kind of forget about them and create the 6Rs of indigenous OERs based off of these two different sets of 4Rs of indigenous education and the longhouse so this is kind of how I came to the 6Rs and I would like to thank both the longhouse and Kirkness and Barnhart for kind of paving the way with this idea of the 4Rs and how we can begin to think of our role within academia so these are the 6Rs of indigenous OERs so the first one was respect respect for indigenous cultural identity communities and topics so we need to have respect within our open educational resources we need to bring in relationships so relationships connects to the concept of all of our relations and building relations with communities responsibility is hugely important we are we have the responsibility to share only when we are allowed and to publish in an ethical way that considers things like ownership protocols and community practices as well as revenants respect for the sacred we would not share sacred indigenous knowledge as sacred community knowledges or treat sacred knowledges in a way that they are lesser than academic knowledges as well as relevance so we need to legitimize and incorporate indigenous knowledges into curriculum in a way that makes sense and is controlled by community as well as reciprocity is highly important so reciprocity and the principle of giving back so for me as a librarian I can give back by giving talks like this helping with the development of OERs helping communities to develop their own OERs and building that capacity or helping to find information that might be relevant to the OER that is being created through my work at Kuiwa Library or connecting with individuals like Carleen, my colleague so these are the six kind of ours of indigenous OERs and I really hope that one day we have more of a better understanding and a group of practitioners that can come together to create more of a standard best practice for the incorporation of indigenous knowledges into OERs so that we can begin to do better with our OER practices and challenge the idea of what should be open and what shouldn't be open and so that is my presentation on indigenous OERs we have time for questions and dialogue after and I wanted to leave some time for that so that we could begin to talk a little bit more about this but I do have my contact I have my contact for here at UBC which is my work contact please feel free to contact with me about OERs or about indigenous research or things about the Kuiwa Library so the branch and then I have my Twitter so my Twitter is fairly active mostly with folks talking about indigenous research practices and data sovereignty but that is my Twitter anti-librarian one thing that you'll also find from my Twitter is often I like to retweet things from the indigitization program which I helped to run here on campus as well as from the Kuiwa Library so all of our events such as honoring indigenous writers which is happening this week but also kind of going through next week as well and all the events that are happening around that so please feel free to follow me on Twitter follow the branch follow indigitization hi hi thank you for being here this afternoon and I will stop sharing and we have time for questions and I hope there is not 29 questions in the chat also please feel free if you have questions put them in the chat or you can put up your hand I don't know well how you want to navigate this but feel free to ask questions thanks yeah I would just second that turn off feel free to turn off your mic and ask a question and put it in the chat so I see Michelle has her hand up yeah I'm trying to articulate my question here because I've been absorbing a lot of knowledge I attended a session on traditional knowledge labels from local contacts I think and I'm just trying to see when my job is to advise people on their open education resources and give them the best way forward and I know with a lot of OER it's about best efforts when someone approaches me with content that includes indigenous knowledge and are indigenous content and traditional which may pertain to traditional knowledge where should I tell them to start because I know attribution and copyright labels is a huge thing that people concern themselves with sure so for the group the local contacts group develop their traditional knowledge labels there's two different types of labels that we can use the TK labels that they've developed often act like a creative commons license or in addition to a creative commons license but they bring into frame kind of indigenous worldviews when looking at knowledges on digital platforms however there's been a lot of work of looking at how to use them in other contexts so I really I've done work with the local contacts group I think reaching out to Jane and the local contacts group is always great as these resources are made for kind of a digital or more open platform but take into account the protocols of knowledge sharing with the local context labels I would say for OERs it depends on who is creating it so if it's an OER that's being created by an institution or another agency there's a different license that would be used then if it's like a community creating the OER so there's the traditional knowledge labels which are community driven and decided by community so if the community's been consulted on the knowledge that is within that OER and there's been that collaboration and consultation then you can use the TK labels within it however if the community that this knowledge is not coming from has not been collaborated with the development of the OER or allowed for the sharing of those knowledges there's a different label technically that would go into it and it's an institutional label so it's something that the individuals who are making the OER would put on to say that they acknowledge that there's traditional knowledge in this and that they would like to collaborate with the community that this knowledge comes from I did pull up the TK label website for folks to see because they are very interesting and they are being used in different ways and have a lot of capacity for communities to alter them in a way that makes sense for this community so this is the TK label website one thing that you have to do now to use the TK labels is to be a knowledge hub or a local context hub Kuihua Library and a digitization are knowledge hubs as well as myself as a researcher is part of the knowledge hub you just apply to be part of it they verify you and then add you and that's also another way of connecting with other organizations communities and individuals these are the labels that are meant for communities to put on their own knowledge so we have provenance labels protocol labels as well as permissions and you can see here the permissions one look a lot like a Creative Commons license but the protocol labels are a little bit different so we can see that it's traditional knowledge culturally sensitive women etc so these could be important especially if you have like a community produced OER or you have that collaboration with community and we also have the licenses the traditional knowledge licenses and then the notices so we have the traditional knowledge notice which signifies that there is an understanding from the institution or the creator that there is traditional knowledge within the resource but it has not been verified by a community and then there's also institutional ones so UBC could use this if they were creating OERs that have Indigenous knowledges so it's attribution incomplete as well as open to collaborate with the community I think for those who are not new share for those who are planning on engaging in OERs this is a great resource and they are the folks at local contacts are always willing to have conversations about how their resource can be used and also lots of workshops training sessions they are I remember when the TK labels were first coming out it was like I heard them speak a couple times and now they're all over the place and it's a great resource and can be used in other contexts than open educational resources also for research other digital projects as well Thank you just by you explaining that some things slid into place I feel like some knowledge has been really when it just snaps too so thank you so much for this presentation Yeah, no problem Jen, I saw you had your hand up earlier I did I'm kind of wowed by this presentation and I don't even know where to start in a way so I don't want to sound like a blathering at it which I am my partner Zoe is here we're learning how to try to respect and honor the indigenous knowledge as we create an open education resource in biology and pathology and human human sciences and I was really struck with you saying about building relationship and respect for the indigenous culture I just don't know whom or how or see or where to start that from So I think kind of with that relationship building we're lucky here at UBC as we do have or we have like departments such as ERSI which is the indigenous research support initiative and ERSI is really great at kind of connecting communities and researchers together in a way that kind of aligns with those protocols and practices when it comes to finding indigenous content and being able to incorporate indigenous content into things like teaching, learning, OVRs and kind of that really important, almost like verified secondary information I would say definitely contact Carleen at the branch or myself as we do things in working with or folks like CTLT to collaborate on their indigenous initiatives and helping for like faculty members and folks like yourself for creating OVRs and being able to incorporate indigenous voices into those resources So I would say definitely contact ERSI for that relationship building part and then feel free to reach out to us when it comes to finding resources or even looking at LibGuides that we have we have lots of LibGuides that are absolutely amazing and kind of an area with tons of knowledge in it and also through CTLT they have their indigenous initiatives so reaching out to Amy Perot and her team would also be really helpful as they might be able to help you Okay, thank you that's just you just like jump where like 20 kilometers farther ahead than we were before so thank you Okay Nina, I see you have your hand up Yeah, I'm working on a I'm a settler non-indigenous person working on an OVR for my Japanese language class and trying to incorporate material regarding the indigenous people of Japan the Ainu people and I guess I'm looking for a little bit of direction on using resources that technically in terms of Canadian copyright law are now in the public domain published over 70 years ago or whatever and I can certainly acknowledge the author and that sort of thing but in terms of I want to incorporate the voice of the Ainu person's voice in that as it is basically right but how how how do I go about doing that with something that I know that technically I can use but I'm not sure where to direct you know how who to ask for permission in terms of someone from the community and that kind of thing Yeah, so in regards to asking someone from the community that might be a little bit harder I mean the one thing that we can always do is that within the creation of the resource and the OER is to just acknowledge where the knowledge has come from give some additional information about the community and where the knowledge is originate from and really thank them Additionally, this might be a good opportunity to collaborate with the Asian library and with the librarians there who work with the collections and they might be able to connect you to community members or somebody who might have more authority to be able to give you information about how you could better acknowledge that I knew community and where the information is coming from but I think in general that kind of locating and thanking of folks and for being able to use their knowledges and even if you were to put in there that you understand that within Canadian copyright law this knowledge is met is able to be shared freely but that this might not follow protocol and then adding something one of those institutional notices saying that would signify to somebody if there is something like attribution is missing or you're willing to collaborate or it just acknowledges that knowledge and the local context licenses it's not just for First Nations or in Canada it's a collaboration that really started with Maori individuals and our neighbors in the United States as well so it is used for multiple communities multiple indigenous communities so this might be actually a good chance to reach out to Jane and that crew too to see how they might be able to support your OER and working with I knew communities but I think checking in with the Asian library thinking about local context but also just doing that acknowledgement and that of how problematic copyright can be but also where those knowledges come from is kind of taking that first step to the redresses of the in some cases the sharing of knowledges that are not ours to share through academia I hope that helps I'm not an I knew specialist so it's a community I've never really worked with before but just thinking about what we've done with other communities that I work with that's kind of along the same same lines great thanks very much sorry Dagmar I see you have your hand up yes my question hi thank you so much for this session so much to think about and we had that a little bit I'm also part of this post-course and we had a little bit discussion about that in our previous session already when we were talking about open access and you know all this copy Western colonial copyright intellectual system which we kind of still have and follow in a way and we had some really interesting discussions there I myself work about Tibetan Buddhism and also Bhutanese Buddhism so I work a lot with Tibetan and Bhutanese communities and also partially indigenous communities within Bhutan and Tibet and so I felt like the six hours are so relevant for a lot of other areas as well and our things I'm struggling with as a scholar often also so what do I do when I have shared knowledge when I have knowledge which is supposedly for some of the community secret and other parts of the community allow me to use it and you know always you have this feeling like you're extracting something and you don't want to of course not do that and you don't want to follow this kind of yeah history of extraction so I think there's a lot of people who work kind of in culture that they are not their own basically you have to think about this all the time so do you have some advice how we can bring forward also this bigger discussion of changing the legal and you know other frameworks and learn you know how to bring in all these important aspects respect relationship collaboration responsibility I mean that that should be you know on the agenda for kind of responsible scholar anyway or teacher so yeah any advice maybe it's a very broad question I know but yeah when it comes especially to research and researching with a community that's not your own community and kind of ideas around protocol and knowledge sharing and what should be shared and not shared I think even starting to have conversations within your own unit so within the department that you work with having conversations with community members and then having larger conversations with things like research ethics boards it's kind of the place to start so having those conversations about where we're struggling when it comes to knowledge sharing what is not working within the institution and what might be working and then even looking kind of at what other institutions or what other communities are doing and then how can we find kind of a best practice that fits within the communities that we're working with or within our own research so just even opening up and starting to have those conversations I find that usually the starting of having one conversation leads to a larger thing and in some cases transformative change happening within organizations and institutions and I've seen that with lot with Indigenous data sovereignty in Canada when I graduated in 2018 with my masters not really anyone was talking about it since then it has become hugely popular it's something that often is coming up at conferences it's something that we're seeing lots of webinars on and something that the tri-councils are talking about now so even opening up and having those conversations with both our academic community and the communities that we work with is important and when it comes to working with knowledges that are not our own within the community having a very good understanding with communities on what knowledges we're allowed to engage with what knowledges we're allowed to share is the most important thing and building that relationship and building that trust with communities that we won't share something that they don't want us to share as well so it's all about the relationship building but also talking to each other which sometimes academics are not good at doing so not always great at talking to each other I hope that answered your question kind of So we're a few minutes past two and I just want to be very mindful of the time and really maybe at this point just really thank Kayla for her presentation today I think overwhelmingly I learned a ton today I think reading the comments I think people were really appreciative of your time and I really just want to thank you again for taking time to put this presentation together and to teach us in this area Yeah, thank you for having me With that I think we'll go ahead and in this session but we put your contact information in the chat and you posted it earlier This session was recorded and we'll send an email out when the recording is available as well It may be a few days


The House of Representatives on Wednesday raised the alarm over the Ramita platform through which the Treasury's single account of the federal government is operated. Through a motion by Jeremiah Umaru, APC, Acuanga, Nassarawa, and Gonwamba, the lower chamber said trillions of Naira had been passed through the Ramita platform and that the funds were unaccounted for due to the proliferation of subaccounts by the Central Bank of Nigeria CBN. The House is worried that if this is not addressed, the country will continue to lose its revenue. Joining us live to discuss this issue is Elvis Isar, legal practitioner. Good evening and welcome to our news, Elvis. Good evening and thank you for having me. Okay, well, a single Treasury account in the first place, is it working? Well, this is the first time that the National Assembly will be raising an issue, I would expect the operation of the Treasury single account. If you take a moment back to 2015, the Senate had raised several issues on the operation of the account, issues relating to the system that has been used for the purpose, the 1% commission charges, and of course, currently we are also hearing about subaccounts that have been created by CBN for the purpose of operating this Treasury single account. Again, in 2018, the House of Representatives also raised an issue on the same issue, again, 2019. So we've had these issues about so many challenges facing the operation of the Central Treasury account. What we haven't had is the political will and the genuine desire to resolve these issues. It is not enough for the National Assembly to always raise alarm over an issue as important as the revenue of the federation, which is actually a constitutional matter, because the constitution envisages that all revenues accruing to the federation will be in the single account from which there must be a budgetary allocation for spending. But over the years, we have seen instances where ministries and agents of government would open up all sorts of accounts and monies have been spent without the requisite appropriation. So this is the right time for National Assembly to do what is necessary. They have the constitutional rights to control the oversight functions on how this Treasury single account has been operated, because as it stands now, the proposal has been defeated. The proposal was to ensure transparency, accountability in public revenue, and prevent multiplicity of accounts that were being operated by various agencies and ministries, departments and parasitists of government. But the challenges we see today is that this is not being met, because there hasn't been proper oversight function by National Assembly. So my position is that it's not enough for us to just raise alarm like they have always done. This is not the first time. But this time around, there should be proper investigation. The proper authorities should be in court of question, so that the members of the public can see as any what's going on with the Treasury single account. Are you placing the blame of these discrepancies or things that are happening with this remittance on the system itself, or are you placing it on the human factor? Well, I don't think the system is never a problem. The problem is those who are charged with the duty of operating the system. Yes, the issues have been raised about the system, and that those issues have, you know, has raised from monopoly. There's this talk that remittance, I mean, system specs, which operates remittance, is monopolizing the system, and they are the ones that can, you know, they are involved in the transactions. People have also raised questions about the 1% commission that is payable on the phones, and all of that. For me, I don't think the system is a problem. I think the human factor, because right now we are seeing subaccounts. Your idea was to have a single account. So when you now have accounts that, you know, oversight functions of national assembly cannot reach, and, you know, we cannot see at a glance, then there's a problem, it's defeated your purpose. So for me, it's always the people, it's not about the system. We always complain about systems in Nigeria, we complain about democracy, we complain about, you know, SYZ. The problem is not the system, the problem is the people who are charged with the duties and responsibility of monitoring the system. And there has to be accountability, and that's where the oversight functions of national assembly come to play. And for me, I blame national assembly because they have the... This is a constitution, if you look at section 80 and 162 of the constitution, this is the third constitutional mandate. The traditional single account is a clear constitutional mandate. And the national assembly has the duty to ensure that that is being followed. So for me, it's really not the system, but the people that are managing the system. Yeah, I was going to ask the rationale behind the subaccounts because the aim seems to be defeated. If there are going to be subaccounts for something that we are applauding, I think it came in the time of Mohamed Buhari as the president of Nigeria. Single Treasury account, everybody was saying it was a good thing and all that. But from the experience we've had, whether it is the human factor or the system itself, wherever the problem is coming from that is making people to complain the way they're complaining right now, do you think a single Treasury account will really work in Nigeria? Transparency aside, because we can have more than one and still be transparent if we want to be. So, but do you think a single Treasury account will be the answer to the problems of our loose money being thrown about anywhere and being taken by people who should not? Well, it has worked, you know, I mean, it's not in Nigeria where we are operating the single Treasury account. It has worked in so many countries of the world. And so if it is not working here, then something must be wrong. So it's really not the single Treasury account as an idea that is a problem. It is how we operate it in Nigeria as a problem.  When they get to Nigeria, they don't work. So that tells you that it's not really the idea itself. It's the way or manner it is operated. So the single Treasury account can work, but that is if the CBI really wants it to work. There are even complaints that, you know, the funds that come through the single Treasury account through the commercial banks, money deposit banks. There are complaints that they don't even get to the CBI until a long time thereafter. The idea was to ensure that these funds, you know, the moment they are transferred to the system, they get to the CBI immediately. But we are hearing now that, you know, some banks, you know, delay in remitting these funds to the CBI. In fact, in 2019, the Senate had, I think it was the Senate or the House of Representatives had invited the Marine Director of Facebook, you know, to come and explain, you know, some of these delays. So, you know, I will maintain my position that the problem is not really the system, but the problem is the fact that we don't want, you see, at any point in time in this country where we try to come up with a system that will show transparency and accountability, we always, you know, find ways to defeat it. And that's what is happening right now. The right to cast within the system. Those who are beneficiaries of an opaque system, a system that is not open to scrutiny, they are at work again, you know, trying to score to the traditional account system. So, for me, it's really all part of the corruption that we have in Nigeria until we are really serious about dealing with the issue of corruption. We might not be able to, you know, no system will work. You know, I mean, the TSA as it is called is really not a problem. It's really just the fact that we are not ready to get anything to work, because the rest of us in the system, those who depend on the corrupt system will never allow it to work. That's where we are. And we need the political will. We need national assembly to just, you know, do what we're talking in order to fix it. All right. Thank you very much, El. This will come in on our news today and giving us your thoughts. Thank you for having me. It was a great deal. We've been talking with Elviz Asya, a legal practitioner, and we're talking about a single treasury account. Hello. Hope you enjoyed the news. Please do subscribe to our YouTube channel and don't forget to hit the notification button so you get notified about fresh news updates.


Welcome to another session of the NPTEL on nonlinear and adaptive control. I am Srikanth Sukumar from Systems and Control IIT Bombay. As always, we are looking at a very nice representative background of a rover on Mars. We hope that the algorithms that we sort of learn how to design in this course will eventually help us drive autonomous systems such as the rover on planets such as Mars or the moon and so on. So, without delaying any further, let us go into our lectures. So, where last time is that we had sort of looked at the notion of these nonlinear spaces. We had already defined different kinds of norms and we had also defined the structure which is a nonlinear space. And the idea that we sort of pursued last time was to prove that some of the norms that we have defined are in fact valid norms. What are the conditions? The conditions for a function from the vector space to reals to be a valid norm is that it is nonnegative is 0 only when the vector itself is 0, satisfies the scalar multiplication property and the triangle inequality. So, as we saw, usually the first three properties are not significantly hard to show and the triangle inequality property is what is a little bit more critical and difficult to in fact prove. All right, let us go back. So, we did prove all the conditions for the infinity norm the way we had defined it. So, the infinity norm was in fact proven to be a valid norm on Rn. So, we wanted to mimic the same for the two norm. We in fact started it, we proved the first three properties which is that the two norm is nonnegative, the fact that the two norm is 0 only if the vector itself is 0 and the scalar multiplication property. So, we were actually sort of there was a minor error, there was a slight error in how we were trying to prove the triangle inequality. And so, that is what we want to first complete today. We want to actually complete the proof that the two norm as defined that is the Euclidean distance norm as we said satisfies the triangle inequality property of norms. So, let us look at this. So, we started with the two norm of x plus y squared and this is nothing but the summation from 1 to n absolute value of xi plus yi squared. So, if I expand this, I get something like this that is summation from over i equal to 1 to n, I get xi squared plus yi squared plus twice xi yi. Now, notice that even before I go from here to here, this is actually because I have squared it. So, this is the same as taking the square of the quantity xi plus yi itself without the absolute value. So, I can actually get rid of this absolute value here and that is what I do. So, this is still all equalities. So, the xi plus yi absolute value square is sort of irrelevant here because I already took a square. So, this is also irrelevant. So, I get rid of this in this expression. And now it should be obvious that I can also plug back in the absolute values and this quantity is just the square of the two norm of x. And again, if I look at, I am sorry, I look at this quantity, that is the square of the two norm of y. And I am left with two summation i equal to 1 to n xi yi. So, now, this time we do not do what we were trying to do last time. We will do it in a rather simple way from the knowledge of scalar dot products that all of you would know holds true in the Euclidean space. So, I know that this expression right here is nothing but x dot product with y. So, this is just the scalar dot product of x and y. And what do we know about the scalar dot product? We know a couple of things. One is that the scalar dot product, well, it acts like a projection of one vector on the other if I divide by the unit vector. The other thing that we know is that it is a scalar value. That is why it is called the scalar dot product. So, when I take a dot product of two vectors, it is a scalar value. And that should be obvious. This is also a scalar value. So, this is in fact a scalar quantity. And we also know that the scalar dot product is evaluated as this formula norm of x times norm of y times cosine theta. What is theta? So, theta is simply the angle between the vectors x and y. So, whatever is the angle between these two vectors theta is that angle. And so, you have x dot y is simply norm x times norm y times cosine theta. Now, what do I know about the cosine? We know that the cosine lines between minus 1 and 1 for any value of theta. Therefore, the cosine theta is always less than equal to 1. So, using that exploiting the fact that cosine theta is always less than equal to 1, I can immediately create this inequality. That is, this is less than equal to norm x times norm y. So, we have very, very effortlessly proved that summation xi yi is less than equal to norm x times norm y. And this is exactly what we wanted because I will plug it back in here in place of this. So, it was, if you notice, it was all equalities until this point. But then it becomes an inequality because of this guy. And what do I have here? This remains the same. This remains the same. But here I replace 2 norm x times norm y. And it is easy to see that this is nothing but norm of x plus norm of y whole squared. So, now, if I sort of cancel the squares on both sides, I have exactly the triangle inequality that I wanted to prove. So, this is essentially complete the proof of triangle inequality for the 2 norm. Like I said, we are not really trying to, we are not really going to see proofs of for the 1 norm, 3 norm, 5 norm for any other p norm. But typically, proofs will follow in a similar way. So, one of the important, very critical things to note is that this piece of the proof that you saw here, I am actually going to highlight it because this is a rather critical piece of the proof. So, this piece of the proof that you see here is in fact, a proof of the Cauchy Schwarz inequality and Euclidean space. If you notice, the left-hand side is actually how we write the inner product. We will look at this notation a little bit later. x dot y is actually xy, the inner product of xy. So, this is actually the inner product. So, we have essentially proven that the inner product of two vectors is less than equal to norm x norm y, which is exactly the Cauchy Schwarz inequality. So, we have proven a particular case of the Cauchy Schwarz inequality right here. So, please remember this. So, this is an, by the way, this Cauchy Schwarz inequality is in fact, a rather key inequality which is satisfied by all norms. So, the Cauchy Schwarz inequality is in fact, satisfied by all norms. So, you can also do a general proof, but for now, we have a pretty good specific proof. We are quite happy with it. All right. Okay, let us move on. We have now proved that the norms that we have chosen as vector norms are in fact valid vector norms. Great. Let us look at the next set of ideas that we are sort of very keen on. We already spoke about the notion of convergence very loosely. We kept saying limit of a function or we said that the function converges to a constant, the derivative does not converge. Function converges to a constant derivative does not converge to 0 or the derivative converges to 0, the function does not converge to a constant. So, we use this word convergence a few times already in the lectures preceding right, but we have been using it loosely. In general, whenever even in the past mathematics courses that you would have attended, whenever you would have spoken of convergence, it is always associated with the notion of limits. So, there is of course, they are very closely connected. It makes sense that whenever we talk about convergence, the notion of limits also shows up. It is very natural. However, let us look at a more formal way of defining convergence. So, once we have a non-linear space, all these notions can be very easily defined without a norm because the entire idea of convergence is for terms to get close to a particular point. And there is no way to define closeness without the notion of a norm. So, it was very important for us to have a non-linear space. So, suppose I have a sequence. This is the notation for a sequence. I hope you folks have seen this before. If not, just look at, I mean this is very simple notation. So, each term is basically indexed by a i and i goes from 1 to infinity. So, a sequence inherently has to be infinite. There is no such thing as a finite sequence. As soon as they say sequence, infinitely many terms should come to your mind. So, the terms are all indexed. So, you have terms x1, x2, x3, x4 and so on and so forth. So, sequence in a non-linear space is said to converge to a point in this space x. If for all positive epsilon, there exists a positive integer, not just any integer. I would say z plus there exists a positive integer, such that xi minus x0, the norm of xi minus x0 is less than this epsilon that was given to us for all i greater than equal to this integer n. So, let us sort of reuse it. We want to look at this again. So, things are very clear in our mind. So, what am I saying? I am saying that any sequence in this non-linear space is said to converge to a point. If I am talking about convergence, I have to qualify it with a point to which we are converging, otherwise it does not make sense. So, I have qualified it with a point x0. So, sequence xi in this non-linear space is said to converge to this point x0. If for all epsilon, so if you give me an epsilon, so the user has to give me any epsilon and correspondingly I should be able to find an integer, a positive integer n such that all my terms beyond the nth term, all my terms beyond the nth term are at least epsilon close. So, this is an illustrative picture. This thing on the left here, this is an illustrative picture. And this 1, 2, 3 is the term number. I am basically writing i here. So, i equal to 1, i equal to 2, i equal to 4, 3 and so on. So, you note that as i increases, my terms are getting closer and closer to 0, x0. And this is exactly what is meant by this definition. It is not difficult to look at some examples. So, let us actually look at some examples. So, let us see. Suppose I have xi equal to say 1 over i. So, what does this? So, xi converges to, this is the notation, 0. And you can immediately see how it is connected to limits. Why can I say that it is going close to 0? Because if I have given any epsilon positive and I look at xi minus 0. So, in this case my x0 is 0. So, if I look at xi minus 0 and I want this less than epsilon, that is what is the requirement. I want to find an n such that beyond the nth term, everything, every term is epsilon away from the equilibrium, epsilon away from the point of convergence x0. So, I want to be epsilon away. So, what should I choose my i? It is very easy. Sorry, what should I choose my i as? So, it is very easy. I mean it is, all I have to do is that i should be greater than ceiling function of 1 over epsilon. What is the ceiling function? It is basically a function which gives me the closest integer bigger than a number. So, if I give you 0.7, ceiling is 1. If I give you 0.5, it is still 1. So, let us not worry about the halves. But the ceiling function essentially gives you the closest integer larger than the number. So, if I give you 5.9, 6, 5.26. So, the closest integer larger than the number. So, if I take i larger than ceiling of 1 over epsilon, then what do I know? I know xi is less than epsilon. Yeah, all right. So, I am done. Okay, as simple as that. Take an example xi is, let me repeat, xi is 1 over i. Yeah, I know just by my limit ideas that this is going to go to 0. So, the point of convergence x0 is in fact 0 in this case. So, how do I prove it? Or how do I find the corresponding n? Because in order to prove that any sequence converges, I need to actually be able to give an n. So, suppose I start with any epsilon, epsilon is arbitrary. Notice that epsilon is very much arbitrary. Yeah, and I want to satisfy this sort of inequality for i greater than equal to n. Okay. So, what is it? So, this guy here, I choose as my n. This guy here, I choose as my n just using the seeding function. Basically, I know that I want to have 1 by epsilon, anything larger than 1 by epsilon, but 1 by epsilon may not be an integer. So, I just choose the integer larger than 1 by epsilon. So, I take the seeding function. So, if I choose this kind of any i greater than equal to this n, then I know that x i is less than epsilon. And I am done because this and these are the same because all terms are positive in this case. So, the absolute value is really not much. The absolute value function does not play any role. Okay. Great. So, this is how you sort of look at convergence. Yeah. Of course, this is a very simple example. Little more to do when the example is slightly more complicated, but not significantly more to be honest. Yeah. Okay. What is a Cauchy sequence? Right. So, we've seen convergence. So, Cauchy sequence is a slightly different notion. It says that if I have a sequence x i again in a normal linear space, then it is said to be Cauchy if successive terms start getting closer. That is essentially what is quantified or qualified by these epsilon and n's. Okay. So, the successive terms get closer. What does it mean? That if I am given any epsilon positive, again, I can find an n. Notice all in both these cases, the n depends on epsilon. I mean, you can see n depends on epsilon. So, a sequence said to be Cauchy for all positive epsilon, there exists a positive integer. Let me again do this. Yeah. There exists a positive integer such that successive points are epsilon distance away for ij greater than equal to n. Okay. So, as you go, as your terms become, you know, as your i becomes larger and larger, successive terms are close. Okay. That's essentially what this is. So, you can see this picture. You can see this picture. In fact, the series that we just proposed x i equal to 1 by i is also a Cauchy sequence. It is also a Cauchy sequence. I am not going to prove this. You can actually think about. So, I will actually say this, find n given epsilon. Yeah. Please treat this as an exercise and do this. Yeah. So, if I am giving an epsilon, try to find the n corresponding to this. Okay. So, you want the successive terms to be small. Yeah. So, the n will turn out to be slightly different looking than what you have here. But the fact is this is also a Cauchy sequence. Okay. So, an important thing to remember is that, let's see. I am going to write this in red. Note, convergence implies Cauchy. But Cauchy does not imply convergence. All right. So, sequence is convergent, which is why the example I gave you works. I know. Yeah. Because the sequence is convergent. I know that it is Cauchy. Yeah. In fact, from this definition, right from this definition, you can prove that it's a Cauchy sequence. I am not actually showing that proof, but you can do that. Yeah. But for the specific case, I encourage you to find n given an epsilon to prove that this sequence is in fact a Cauchy sequence. The other way around is not true. If a sequence is Cauchy, it is not necessarily convergent. So, I can always construct funny examples and I have constructed one such funny example for you folks here. Yeah. So, my norm linear space is the open set 0, 1. What is the open set 0, 1? I really hope you know what is an open set. Yeah. Open set 0, 1 is everything inside the 0, 1 except for the end points. Yeah. The end point that is 0 and 1 are not part of the set x. Because I have essentially constructed this, if you may ridicule a set to prove my point that Cauchy does not imply convergence. Okay. So, if I take my sequence as 1 minus 1 by n, what happens is n goes to infinity. One might ask, right. You can see very easily that as n goes to infinity, your xn actually goes to 1. Yeah. So, this is where you converge to. But the thing is that 1 is not part of x. All right. So, this might seem a funny weird trivial sort of example, but it is not so trivial. Yeah. You, the series seems to be tending to a point, but the point is not part of the set. Okay. And if you notice the definition of convergence, it should be, you should, this should remind you of the fine points in any definition. The point where you converge has to be part of the set x. Okay. This is rather critical.  But there are, there can be many more realistic examples where the Cauchy sequence will not converge. Yeah. Okay. One good thing is most of the spaces that we concern ourselves with, yeah, they are in these spaces Cauchy sequences in fact converge. Okay. And such spaces are called Banach spaces or complete normed linear spaces. Okay. So, most spaces we consider like the Rn, Rn, Rn, Rm, Rp, whatever. They are all Banach spaces. Yeah. That is all Cauchy sequences converge to some point in the space. Yeah. This is rather useful. Okay. I mean, a set, a sort of normed space does not have this property can be a very troublesome space because we are always interested in doing convergence analysis and seeing where different signals converge to. Now, if, if you don't have a complete space property and your sequence or your signal seems to be tending to a point, but then the point is not part of the set then tending to a point which is not part of the set, then you will land in some trouble as far as I mean convergence analysis goes. Yeah. Because you have defined a, if you have defined a norm only on this set X, right. Outside this set X, you don't know if the norm is satisfied. You don't know if the norm works, if the norm exists. Okay. Say again, don't go just by this example. This is a sort of constructed cooped up example, but there can be more realistic and funny scenarios where you don't have completeness. Yeah. But also as an aside, I must clarify that everything we consider in this course are going to be complete normed linear space, which is essentially also called Banach spaces. Yeah. So, like we said, examples are Rn with the infinity norm or the 2 norm or any, in fact, any norm and it's all Banach spaces. Okay.  Once we have the structure of a norm on a vector space, we see that we can talk about convergence, right. So, which is rather nice, we can talk of Cauchy sequences, completeness and so on. Another structure which is a little bit more general than a norm is the inner product. Okay. So, again, we just saw it in the previous slide. I used this notation where we said that we talked about the dot product. Okay. So, dot product is the sort of the simplest inner product that we all know. Okay. In Rn, the dot product is the standard inner product. Yeah. And then it's also denoted like this. So, that's what is an inner product space. An inner product space is again a linear space. Yeah, we call it a special norm linear space, but it's actually a linear space, right, with an inner product operation. Okay. What is it? It's a function which takes two elements of the vector space and maps to the field. Okay. By field, I mean, where do each component of the vectors belong? Like for example, when I have two vectors in Rn, every component is a real number. So, the field is the field of reals. Okay. Vectors in the field of reals. And then you have a few properties of these inner products. Okay. So, what are these, just like we had properties for the norm function. Similarly, for the inner product function, also we have certain properties. Okay. And what are these properties? The first is that it is symmetric. Yeah. Again, we are talking about spaces in the reals. Okay. So, otherwise, there will be some conjugates and so on and so forth. Okay. So, the first property is that the inner product is symmetric. Yeah. So, inner product of x with y is the same as inner product of y with x. So, sequences doesn't matter. Then it has a distributivity property. So, x comma y plus z inner product is the same as inner product of x, y plus inner product of x, z. Okay. The third is the scalar multiplication property. The alpha, the scalar multiplier just comes out of the inner product. Okay. And the final property is that the inner product of x with respect to itself is non-negative and 0 if and only if x equal to 0. Okay. So, this last statement that you see should already start to remind you of norm because this is one of the norm properties. Yeah. Here you took one element x and you said that this function is now non-negative and 0 only when the vector itself is 0. Okay. So, this is also property of the norms if you notice. All right. So, what is an example I already said in the mystery is gone. So, I already said the scalar dot product on R n is a valid inner product in the field of reals. Yeah. So, and like I also said also hinted in fact, right, the x with this inner product is also a non-linear space. As soon as you give you an inner product space, you can always construct a non-linear space by defining the norm as inner product of x with itself. All right. So, given an inner product space, you always have a non-linear space. Okay. So, I will stop here. So, in summary, what we looked at today is the sort of we completed the proof of the fact that the two norm the way we define is a valid norm. Then once we have the structure of norm linear space, we were able to talk about convergence and we did. Then we looked at what is a Cauchy sequence and how the two are not exactly equivalent always. And then if they're equivalent, the fact that there's a Banach space. And then we defined an additional structure or a new structure, which is the notion of the inner products. Okay. And we also saw that the standard dot product that we have been talking about is in fact, the inner product. And this inner product space naturally leads to a non-linear space also just by virtue of this construction. All right. So, yeah. All right. So, that is where we will stop today. Thank you.


Hi everyone, Joe for Jasper's casebreaks.com coming at you with a random number block randomizer that'll unlock Flawless basketball first off the line pick your team to just a two team number block and that's how it works If you're not familiar with it This group is familiar with it though. Thank you. Appreciate it. There are the numbers right here Let's go. Let's roll it randomize names and teams six into two eight times one names and numbers two three four five six seven And eighth and final time got Kehun down to Dimitrios after eight six and two eight times for the numbers one two three four five six seven and eighth and final time We got five down to seven. All right, so here's how it shakes out Kehun with five and six David B with four Dimitrios with one Paul with nine Sean with zero So Sean, you'll get any and all redemption for those two teams. Actually, there probably won't be redemptions flawless So strike that Sean with two of these blockchain. No, I don't think they're a blockchain either Anyway, Sean you have zero and two Dimitrios with three David B with eight and Dimitri with seven. Let's order these numerically by number and Coming up in a separate video will be the break itself. Jasper's case breaks.com. Bye. Bye


This is looking pretty good, but I wanted to stress and why I made this video today is to talk to you about The risk that's involved and the narratives that are there remember just two weeks ago Weren't we not in a freefall almost especially when the SEC came out there sued Coinbase They sued Binance and things just dropping like a fly then all of a sudden we get a Bitcoin ETF Possibly from BlackRock now all of a sudden the narrative has changed So I will just warn you that even though this has changed There's other things that could happen. Let's say that Ripple comes out and they lose the case against SEC that wouldn't be too great Let's say that SEC moves forward and they start to really put a lot of pressure on Coinbase by an administration does something else that as far as like With regulation or different bills get shot down in Congress For clarity that could also affect it So it doesn't mean that everything's gonna be just going up and to the right We have to pay attention to the risk that is involved and what we should do about it


Have you ever wondered why some people seem to be very easily provoked even when you don't do anything bad to them? If you made any kind of mistake, then the person who got provoked would certainly have an excuse even if your mistake was trivial. But what about people who seem to get provoked for nothing? In this video, I will show you 7 reasons why some people are easily provoked. 1. They have serious insecurities. We all have insecurities. After all, we are in perfect humans, but some people have serious insecurities that force them to interpret every action and comment in the wrong way. Those people will always get provoked simply because they will see a different version of reality based on their own faulty interpretation. People who have serious trust issues might try to find a bad meaning behind every innocent action that people do. People with serious trust issues are very likely to interpret your words or actions incorrectly just because they believe you have bad intentions. A practical example is a mother's outburst whenever someone of the opposite sex visits her daughter or a possessive man's reaction when he sees his partner merely chattering and laughing with another male, who may even be a family member. 2. They have been seriously broken before. If a person was seriously hurt before in such a way that they never recovered from them, they will become extremely sensitive to any threat later on. In such a case, this person might interpret many of your innocent words as threats and so they might get provoked easily. One common example of hurt that can trigger easy provocation is grief. Grief can be an overwhelming emotion that is often associated with hardship, pain and personal loss. Grief can stem from the death of friends, loved ones, partners, family members or even a pet. Grief can also be caused by other hardships including professional or personal disappointment, the loss of a job, physical injury or even current events. When you are overwhelmed by grief, it can quickly turn towards anger. Grieving people are often frustrated by the cruelty and unfairness of the world, angry that a future they had envisioned is no longer possible and upset with people who aren't able to understand and sympathize with their suffering. Furthermore, anytime a situation that led to their grief arises in the future, they react in an extremely aggressive manner to avoid repetition. 3. They suffer from ACP. ACP is the short term for anger control problems. According to a study of 1300 people who were seeking treatment of mental health, the clinic found that ACP was just as prevalent as depression and anxiety for that group of people. If this rate holds true for the general population, it would mean that millions of people around the world are affected by ACP. People with anger control problems, ACP, often quickly react in aggressive ways when they feel insulted, wronged or injured especially when they think they are being treated unfairly. Everyone gets angry sometimes. This is normal and sometimes even necessary and helpful. However, people with ACP often react in a way that is more intense and aggressive than what is needed in the situation. Some of them may even physically hurt themselves or the other people around them. When someone is struggling with ACP, it's readily noticed. The person gets angry very easily, frequently and with great intensity and may remain angry for as long as an entire day. 4. Lack of good sense of humor. Have you ever made a joke that got people angry not because it was an offensive joke but because they just did not understand what you meant? Well, often, people who like to joke around get into trouble with others who are not humorous and people who are not humorous are so quick to get provoked if they are not around individuals with a healthy sense of humor. But the business and stress of our everyday life, having a good sense of humor, is paramount. 5. Filling powerless. Another common cause of easy provocation is powerlessness. This filling is often associated with a loss of control and filling of helplessness. Nobody likes to be in a position where they feel helpless. This people may react with aggressiveness when stuck in situations that are beyond their control. For instance, if you are suffering from issues with your health, struck in an abusive relationship or even just feeling trapped or just had a major failure, you might tend to get aggressive response to issues beyond your control. Be proactive rather than provocative. If you have a health issue and are frustrated with having to deal with it, then try to be proactive in learning about your condition and how to treat it or leave with it. If you are in an abusive relationship, gather up the courage and call it quits. If you do not find a way to manage that situation that makes you feel helpless, it will mess your mental health and you may likely start to experience anger control problems. ACP. 6. They have past traumatic experiences. A traumatic or painful experience can have long lasting effects even if you think you moved on from the event. Memories of past trauma can trigger anxiety, frustration and even extreme anger outbursts. For instance, a lady who was raped when she was still very young may grow up being bitter and hitting the opposite sex. Or still, if she was defiled by someone close to her, she may even detest her own siblings and her partner if she even agrees to have one. If she manages to get married, she may extend that hatred to her son and act aggressively towards him. Until she can heal from past trauma, she will continue to be easily provoked by any person of the opposite sex. To properly resolve past trauma, it's always a good idea to seek the help of a professional. Treating services can help you navigate negative emotions, control excessive anger and develop strategies for coping with painful or triggering circumstances. 7. They are afraid of change. Imagine getting into a religious conversation that is quite sentimental with its religious beliefs. If you try to point out obvious errors in his belief system, they would never agree to it.  Humans are generally overprotective of their beliefs. We hold on to what we were taught as kids, so much so that change seems so scary. So when we find that someone is discussing our beliefs either directly or indirectly, they might freak out and get provoked. Some people might actually consider simple statements to be a direct attack on their core beliefs and so they get provoked easily. If you have these kinds of persons in your life and you are confided about how to handle them or you just want to help them, the first thing you must do is to try to understand them, find out the root cause of their provocative action because you can't deal with a specific human behavior before you know the kind of intention they had when they did that behavior.