Hello, everyone. Good afternoon, good evening, or good morning, depending on where you're joining us from. Welcome to Engineering for Change, or E4C for Short. Today, we're pleased to bring you the latest in E4C's 2017 webinar series, Technologies for Connecting the Unconnected. My name is Mariela Hachado, and I'm program manager here at E4C. I lead a moderator for today's webinar. The webinar you're participating in today is part of E4C's professional development offerings. Information on upcoming webinars in the series, as well as archived videos of past presentations, can be found on the E4C webinars webpage, as well as on our YouTube channel. Both of those URLs are listed on the slide right now. If you have any questions, comments, and recommendations for future topics and speakers, please contact the E4C webinar series team at webinars at engineeringforchange.org. 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This is why organizations that are doing work in information and communication technologies for development, or ICT for short, are designing and delivering innovative technologies to ensure inclusive access to ICTs in areas without infrastructure. Today, Shurada Srinivasan from One World Connective will share with us an overview of dozens of case studies covering interventions to connect the unconnected and promote broadband adoption. These real-world examples will provide unique insights on new technologies used for providing last mile connectivity, including TV white spaces, the use of unlicensed spectrum lamps, and community networks. Shurada Srinivasan, and I hope I said that right, Shurada, is a CTIC research fellow working on One World Connective. Shurada holds a master of public policy from the National Law School of India University in Bangalore and completed her undergraduate degree in electrical and electronics engineering. She moderates the dynamic coalition on innovative approaches to connecting the unconnected and contributes to the intersectional work of the internet governance work. In the past, she has engaged with regulatory barriers to internet deployment in the developing world, cybersecurity, encryption policy, and network neutrality, and internships teams with the Global Public Policy Institute in Berlin and Center for Internet and Society in Bangalore. Without any further to say, I will pass the mic now to Shurada. Welcome, everyone. Welcome, Shurada, and thank you for joining us. Am I on the booth? Yes. Great. It's a pleasure to be conducting this E4C August webinar on Connecting the Unconnected. As Mariela already mentioned, my webinar is going to focus on technologies to connect the unconnected, and I will be looking at it both from the supply side and the demand side. Before we start the webinar, I wanted to go into what I mean when I said the supply side and the demand side. And in this presentation, we will probably cover a variety of things which look at what the context is when looking at connectivity and last mile connectivity in particular, and supply side being lack of infrastructure or lack of mobile network coverage or lack of electricity type problems that exist and demand side being after having coverage, geographic coverage, what are the other challenges that exist which might have to do with skills, with literacy, with affordability. So those are the two different sides that we will look at when we think of last mile connectivity and connecting the unconnected. But before we get started on all of that, just a bit of context. So to frame this entire webinar, we need to understand that right now, 53% of the world's population is currently offline. A lot of these communities are in the global south and Africa and Asia in particular are seeing flattening rates of adoption. What I mean is that the growth rate of more and more subscribers is actually slowing down in both Africa and Asia. And we are seeing that that gap that exists between the people that are connected which is the world internet users from internet stats and the number of people in the world globally is going to, like it has already reached 4 billion and is not really closing. And that trend has been seen especially in the last few years. So in that context, we need to ask ourselves what challenges exist to access. So of course there are going to be supply side barriers which is that there are communities that don't have access to electricity and communities that don't have access to mobile cell towers or infrastructure that allows them to get access to communication. But increasingly, surveys in the developing world in Brazil, in China, in India are saying that there is not just a problem of people not having access to a mobile phone signal, it's also that there is a lack of relevant content on the internet for them. There is a lack of skills that they have in terms of using devices to get access to the internet. And also they see a problem in terms of affordability. So they don't have accessible plans that they can use easily to be able to get access to internet or internet enabled devices. So these are supply and demand side barriers that exist. And to be able to surmount these barriers, we need to have an approach that looks at both of them. So the presentation that I will make today is going to look at case studies. Why case studies? Before like going into the case studies themselves, because we wanted to identify as a research project, one word connected as a project that I work with, we wanted to understand from the grassroots what is happening in order to bridge this gap. We realized that there were a number of initiatives that were ongoing, but there was very little knowledge sharing that really happened between these projects. Some of them were like, most of them were reinventing the wheel in Africa and Southeast Asia, in Latin America. And we really wanted to get empirical data and experiences from the ground to see, well, what is working in certain parts of the world in terms of connectivity and bridging that adoption gap? And how can other projects learn from it? What are the comparisons that we can draw? What are the lessons that we can learn? So that's the reason why we adopted a case studies approach to be able to understand last mile connectivity, because we saw that there was a paucity of systematic data gathering on such organizations, even though we found hundreds of them when we started looking for these organizations. So I'm going to structure this into two parts. I'm going to first talk about supply-side solutions, and then I'm going to talk about demand-side solutions. So supply-side solutions are going to be primarily about laying out the infra. And I'm going to look at two specific technologies that are used or that are innovative that you've studied that help in bridging the adoption gap in areas that have no mobile signal. So these are areas that are often so far-flung or have such low population that mobile network operators don't see a business case in going and setting up a tower there, because it's more expensive to go to a remote area and set up a tower when the number of subscribers that will use this tower would be a few hundred people. And the operational cost of getting that tower up and keeping it running is incredibly high, and unviable for that operator to keep track of. So you have these little innovative ideas called community networks, and in some instances, TVWide spaces that's a technology that's being used in very innovative ways to be able to bridge that last mile gap. So before we get started on a case study, what are community networks? So community networks are basically people, communities coming together, not a company or an organization, but more often than not just collectives of people that come together and say, well, we don't have access to the internet right now, and we should maybe just put together a bunch of routers, collectively own the network, and then buy a connection to the main access point. So a lot of people pool in the ability, pool in their resources to be able to get access to connectivity and to the internet more broadly. So they're often collectively owned by cooperatives or non-governmental organizations. They're socially managed in that people all come together and make collective decisions around it. They have open design in that they allow for more and more people to add to the network. They have open participation in terms of there is no exclusion of a particular person if they want access to connectivity, to not get that connectivity within that community. They promote peering and transit amongst their members. There's also a consideration of security and privacy, and they promote this development and circulation of local content. So this is an aspirational declaration of a number of community networks that came together and declared that this is how they recognize community networks there. And there are multiple versions of it that are currently ongoing around the world. NetCommon, which is a European consortium, research consortium found about 200 to 300 community networks in operation around the world. Some of them are not working anymore, but these are all set up at some point and have had some data on them. So we started studying some of them systematically, the ones that are working, the ones that we could get access to, and we started building our case studies. So the first one that I wanted to talk about actually happens in a very remote setting. In the island nation of Vanuatu, which is in the South Pacific Ocean, there is an island called Mevo, which until like 2014, 2016 actually, did not have access on the eastern side of the island to any mobile network, like literally none. And they tried very hard to get DigiSELF, which was the dominant operator in Vanuatu, and pleaded with the government to give them access to connectivity, but to no avail, they couldn't really succeed in doing that. So in late last year, a number of these people, like number of these people in the village, came together and built what they call their first community network with the help of two US Peace Corps volunteers that were there. And they created a Mevo Telecommunications Committee, which is the organization or the non-governmental cooperative that runs that network. And decided to basically connect their health center and school to a satellite backhaul that was provided by a disruptor in that market, called Pacific Satellite, and decided to get wireless last mile connectivity by that means. This was particularly important because Mevo did not have a hospital, the island did not have a hospital, and it cost nearly $400 US to get to Port Vila, which is the capital city, to be able to get treated. So Mevo Telecommunications Committee, the biggest need there was to help with the health and the education of the people that live there because the other problem that they also faced is in terms of getting a lot of educators given the remoteness of the island. So because of Mevo Telecommunications Committee, since the last year, they have built a community network that now has two villages, Kerepe and Navito, which have been connected to the internet for the first time, and this is like a short, this is a short snapshot of the impact that it has had. It's already provided access to healthcare in these two villages to 2,600 people, but all of this has been set up at a startup cost of just $6,000 US. Most of it was spent on equipment for the routers. The other success impact that they've had is that they've been able to convince the regulator to free up the 900 megahertz band and give them access to that spectrum to be able to connect that community. This allows people in Navito and Kerepi to get real-time updates from outside the island specifically to reach doctors. This is actually a nurse at the Navito Health Center who is connecting via Facebook to a doctor at the referral hospital in Luganville to be able to get advice on how to treat patients. The next case study that I wanted to go to is also a community network, except this time it's in the Democratic Republic of Congo in Africa. So basically, Iju is an island in the middle of Lake Kew, which is a large lake in Africa, and they did not have... It's a population of 300,000 people, most of which are about under 15 years of age, and they had no access to the internet at all until last year. So last year there was a non-governmental organization called Ensemble Port La Differance that worked with the community, the king of the island and the queen of the island, to be able to build their first mesh network there. And in the case of Vanuatu, like in the case of Vanuatu, the thing to note about the Pamohanet initial deployment is that it was used to connect primarily a weather board, weather updates board that filled a central marketplace on the island that served 10,000 people, as opposed to starting with provisioning of home broadband subscription, because the island had less than 10 computers on it. So like it wasn't like homes were really rich, most of them lived under one US dollar a day income, and therefore could not afford devices. So the easiest thing and the most effective thing in terms of getting internet connectivity to the island was to connect a node on the island to a base station, which was 60 kilometers away, and then like provide weather related and security related updates, especially given Congo situation, right? It allows, they also installed a small kiosk and now have, I think in the last year gained up to like 300 subscribers who like come to these kiosks and work on these computers that have now been provided. The impact of this again has been incredibly large because it provides the first internet access for the people at this marketplace. It provides travel and security related weather updates, which was incredibly important as a lot of people used to die in the lake before, and now they are able to get market prices on when to take the coffee that they grow on the island out to the mainland and be able to benefit as a consequence of that economy. They also get access to like accurate information and uncensored information, especially in Congo, wherein it's quite hard to get internet access often and there is a lot of shutdown. The last community network that I wanted to go through is the Nepal Wireless Networking Project. This is one of the older community networks that has been around for a while. It started in 1998, if I'm not wrong, in a small village in the Himalayas and now it's grown especially after the Nepal earthquake to include smart villages and provide a host of services, telemedicine, online education, e-commerce ventures, internet cafes, et cetera, which all are provided through this organization, the Nepal Wireless Networking Project, which again, sets up Wi-Fi routers in unconnected areas in remote hills of Nepal. This recently, especially in the last year, Nepal Wireless Networking Project has also started experimenting with TVWiP spaces, which I will get into more detail about right after this. So they, like the Nepal Wireless Networking Project in terms of impact, provides the first connectivity to 200 remote hamlets since 2001. 1998 was their pilot. So it also provides telemedicine and diagnostic facilities to small village clinics in these hamlets. And since 2015, after the earthquake, they have been working on disaster resilience in particular and provide smart villages where climate change, tracking, et cetera, can be like done in real time and data can be uploaded because of the connectivity that's provided at a lot of these hamlets. They also have helped the e-commerce industry by providing online bookings for tourists to come to a lot of these hill stations for vacation. The next technologies, and that was the supply side in terms of community networks. I wanted to go over a range of them in different parts of the world. The next technology on the supply side that I wanted to look at is TVWide Spaces. So TVWide Spaces are unused broadcasting frequencies in the wireless spectrum. Basically, earlier, legacy, because you had television channels that were broadcasting, you would leave space between the channels, like bands between the channels for buffering purposes. But the propagation characteristics of that spectrum are such that they allow for broadband internet propagation or use for broadband internet purposes. So the propagation characteristics are also such that they allow for long distance communication. This is incredibly important because in a lot of instances, middle mile is a huge problem. So you are able to connect to a base station, but then there is a long distance or far population for a very large distance or dense foliage, if it's a forested area. TVWide Spaces don't get obstructed by obstacles, which makes it much easier for them to use in areas with a lot of obstacles, with dense foliage, with like stone, et cetera. The wide-space spectrum typically ranges between 470 megahertz and 790 megahertz and they often require special devices to be able to use that frequency. So that's one of the challenges that exists with TVWide Spaces because there are very few manufacturers that are able to bring that cost down to a very affordable level for TVWide Space routers. The first example under TVWide Spaces that I wanted to go through was the Malavi TVWide Spaces Project, which was started by the University of Malavi in collaboration with the International Center for Theoretical Physics. They basically started connecting a start-apology hospital, school, airport, and research facility and they set the record for the longest operational TVWide Spaces link. So this was in 2013. So in 2015, they expanded that network from the university to connect another secondary school and the impact that it has had is on both the school as well as the community hospital that exists by providing them the ability to access telemedicine as well as access online educational content. The other really good impact that this project had was that it used the data to create or like facilitate regulatory frameworks that allow for TVWide Spaces to be utilized and be utilized in a manner that can be sustainable across projects, right? They created a dynamic spectrum allocation database in collaboration with different organizations in Malavi and Malavi is right now leading in terms of TVWide Spaces regulation in the region if not the world entirely. The next case study on TVWide Spaces that I wanted to go into was in May which is a state in the US. So rural Maine again has the problem that a lot of these rural remote communities have in that they don't have what mobile network operators would consider a critical mass to make a viable business case for connectivity. So there is a connected axiom deployment which serves like 40 customers in tribal Maine and that's supported by Microsoft's affordable access grant but they have like a very unique structure. So it's not like provided for free because these are subscribers, not necessarily public centers like a hospital or a school that were connected as in the earlier cases but they are like paying subscribers often home broadband users that get charged a discounted rate for the first year but then have to pay about $40 a month after that. The unique characteristic of this deployment is that they require mandatory digital literacy programs that allow for these subscribers, businesses as well as homeowners to be able to use the internet for their benefit. Things like how to use like emails like e-commerce platforms to market the goods or like communicate with people which I will like also cover later when I go more into the demand aspect. The impact that it has had is that even though it was like when I say 40 customers these are both businesses as well as home subscribers and a lot of these like businesses are able to serve larger demographics. So they've trained actually over 5000 adult learners since 2014 and allowed again for telemedicine to be implemented in one of the hospitals which is one of their customers but they also enable like closing of the homework gap which is considered a huge policy issue in the US by reducing time and travel costs of the individuals that now no longer have to travel long distances to go to a nearby library to access the internet for research for their homework. The next part of my presentation is going to focus on demand side solutions. So like I said, supply side and all of the work that you have heard of until now all of the stories that you have heard of until now are of instances where there's not even mobile network coverage but in a lot of areas in the world right now and this problem is particularly acute in Latin America there's already lots of geographic coverage like people, most people live within distance of a accessible mobile signal. However, they still don't adopt and that is mostly solved by demand side solution which is focused on training and capacity building on creating locally relevant content. And I wanted to go over a series of projects that we have studied that look at best practices to make this process of capacity building a lot more sustainable and the lessons that they have learned in doing so. So I'm going to first start with a Latin American example called S2LA Plus. So S2LA Plus actually provides like satellite educational content to rural schools in eight countries. It's started in Argentina and S2LA actually stands for school in Spanish if I'm not wrong and it used to produce like or provide like high quality content to like rural schools in eight Latin American countries but beyond that the project which is actually a CSR initiative of AT&T and Direct TV also trains teachers in audio visual technologies and use of multimedia in the classroom as well as allows teachers to record the programming that they're able to provide on this network. The channel also contains locally relevant content made collaboratively with the participating ministries of education out of the eight Latin American countries Columbia, Ecuador and Chile are currently participating in creating locally relevant content for the rural students in the local language in a context-specific manner which they then like are able to provide to the students and learn in a much more like systematic and of enriched way. The work that this has done has already connected two million students in eight countries of which 80% of the schools that they're connecting are actually rural schools and that's remarkable because a lot of these rural schools in many other parts of the world that we have been studying or have been researching on have absolutely no connectivity. A lot of them don't even have electricity outside of one staff room, right? So the STLR plus pedagogy is also trained over 65,000 teachers and an impact evaluation that was done specifically in Chile not by us but by an external evaluator provided us with the data that it improved academic performance at every grade level in Chile in particular. The next case study that I want to talk about is from Uganda and this takes the idea of a classroom to a new level. So in Uganda, they realized that there was a paucity of devices and a paucity of infrastructure to provide computer level training at every school. So mainly your foundation is a foundation or a nonprofit organization that works in Uganda that went around in jeeps like they basically took all terrain vehicles, converted them to have solar rooftop panels and provided devices in those all terrain vehicles which basically like go around the country, especially to rural school and train cool students and teachers in ICT. So they, this like basically because you're able to work in it with severe resource constraints, they're able to reach a lot of students or a lot of people that they wouldn't have otherwise been able to. So it's not always a requirement that training and capacity building has to be incredibly resource intensive or has to involve a large number of people. Uganda's example proof that a small, like they only have two all terrain vehicles but you will see the impact is huge because they're able to train over 200 children a day and that's like a mobile tent where they teach the children. So that's from the foundation itself. They're able to reach 5,000 people a year and they have like equipped over 60 teachers just in 2015 on basic computer like ICT skills which is a huge achievement for an organization that's been able to think quite innovatively and out of the box to be able to reach communities that are unconnected. The next example that I'm going to go into is actually just the capacity building program is also a content development program. So Intel at ACSR initiative that it tied with the government of India, especially as part of the follow the fiber initiative that was initiated prior to the national, like prior to the now new national digital literacy mission work which allowed for Intel to create content, mostly interactive content, easy to understand content that they could then do on flash cards or on Q cards to be able to impart ICT skills training and computer training. Like Intel didn't do this alone. It worked with 28 non-governmental organizations as well as key state governments including Karnataka and Tamil Nadu to be able to conduct workshops with this content that was developed by the Intel in-house team in collaboration, take it out to those people and train them using this new methodology. The reason why this was a particularly interesting case study for us was that they often focused on interactive learning and flash cards, Q cards and like even the online interface was very easy to understand and interact with for the people that were using devices for the first time or had very low literacy levels. They also focused on people that were like physically challenged and have reached over like almost a million people through face-to-face training in collaboration with all of these organizations. So again, Intel did a lot of the content development work but the face-to-face trainings are conducted by a lot of the partners. This is one of the ways in which digital literacy can be imparted, which is that you don't necessarily have to always surmount all the resources to be able to go out there to the field and be able to reach people. They've also trained, one of the organization that Intel works with has also trained physically challenged people like I said but they've also collaborated with state governments to reach another 120,000 people. Intel also worked to create all of these modules in regional languages because India's population, peace adversity of languages and English is not particularly comfortable for a lot of people from the country. So they developed this content that they did, the interactive content that I mentioned in six different languages and like were able to partner with relevant organizations in each of these states to be able to push out their training and train more people to be more digitally literate. The last, like a case study that I wanted to go into a Comcast Internet Essentials. This is a case study in the U.S. The, no, this is the second last case study but the work that Comcast Internet Essentials does is that it tries to actually combine supply and the demand gaps in a way. So it looked at the affordability gap in areas and both, and provides them with easy to access devices as well as very cheap internet connections for people especially in lower income strata in the U.S. As well as people that like are under study programs or like are under social assistance basically. They provide the online and in person training on internet use in two languages that is English as well as Spanish and work with almost 9,000 partners in various governments in civil society. They partner with libraries and district officials to be able to like train their people. The reason why Comcast Internet Essentials is I think quite like interesting to look at is also because they did longitudinal studies to measure impact in that they did a survey randomly selected Comcast Internet Essentials users two years in a row and studied what like the impact of them having Internet Essentials has been. So they've connected and this is as of last year they've connected 750,000 households and trained over 6.4 million people. This is combined like data for both face to face training through the partner organizations and people that have been supported through their website but the longitudinal studies that they did were particularly interesting because almost 95% of the respondents said that it helps them improve their child's grades and a lot of them reports that it was used in find it was like helpful to them. The internet connection in particular was helpful to them in finding new employment and employment sources. So clearly like providing access at lower, like at a cost that is easier for more people to access can be an incredibly valuable way to bridge adoption gap. Even in developed countries like the US it need not always be focused on developing world countries because there are like many people in the US that still don't have access to connectivity. One in five I think have home broadband access in the US and that's a remarkable statistic to remember as well. The last case study that I wanted to go into was on Ethiopia. It's actually the reason for including this case study in this presentation is because I not only wanted to look at ICT skills training for abled people but also for visually impaired people because the accessibility barrier that a lot of people have to the internet is often overlooked and should not be overlooked. So the adaptive technology center for the blind is actually one of the oldest organizations that is working in this area in Africa and in Ethiopia which has a high number of visually I think 20% of the population at some point has a visual disability and they provide internet access and training through a cafe of sorts to visually challenge Ethiopians. They provide vocational training through a collegiate that is associated with this internet center and they organize workshops in collaboration with a lot of international organizations to be able to serve specifically people with barriers of accessibility. So they have the ability to learn in braille, their keyboards are better suited for people that are visually challenged and they provide specific like curricula and tutoring for accessibility which is a part of the adoption spectrum that we should take more cognizance of. The impact that they've had is that they've translated about 2,000 texts into braille which obviously allows for more content to be accessed by people that have little or no access to this information otherwise. They train about 30 visually challenged people a year and they provide access to hundreds to the cafe that they've set up in Addis Ababa in particular. They've created or they've galvanized the movement around accessibility especially in Africa which again is a huge like momentum building factor that ought to be taken into consideration. The key takeaways from this presentation that I wanted to quickly summarize is that like connectivity, like I started my presentation with is more than just an infrastructural technical issue. There's a supply side barrier, sure, but there are also demand side barriers and we should keep that in mind while thinking about ways to connect unconnected communities or thinking about technologies to connect unconnected communities. There are innovative ways, I think I've presented about a dozen of them to bridge this adoption gap that exists but it's important to realize that like there is a lot of learning that can happen from local and context specific solutions that have been implemented. When doing this research, one of the biggest takeaways that I have had personally is that there are a lot of these organizations that aren't aware of similar organizations that are working in this area and may have resources to share. It might be in the form of digital literacy curricula, it might be in the form of actual, like implementation advice on specific topology, it might be in the form of how they galvanize volunteers to do some of their workshops and that kind of knowledge sharing can be really useful and I hope if some of you are considering either like working in this space that you will learn from some of the experiences that I have shared and I'm happy to put you in touch with the organizations that have been mentioned. The other thing that I want to emphasize and stress and I will illustrate this in a few last examples is that there might be a necessity to combine approaches. So recently I did an interview and this is not covered as a formal case study as yet in our research. I did an interview with an organization in Kenya called Tuna Panda Institute whose primary focus has been to create like to do digital literacy especially ICT training for entrepreneurs in a slum in Kenya. They realized very quickly that just providing them like training was not necessarily useful because they were constrained in terms of capacity by the room that they had in the institute. So they decided to now expand to create a community network in the slum so that like of 300,000 people in like that and in other slums in Kenya are able to get access on the supply side through the community network to content on the internet and to Wi-Fi hotspots that they can then access information through. So it's often that you need both supply side and demand side solutions to certain problems and the main example is again one of those examples where demand side like solutions such as digital literacy training is tacked on to the supply side solution providing them with their first connectivity to ensure that you have quick uptake and better uptake of the things that are provided. The other thing to note is that at a lot of times there might be a need to combine axillary products like for instance solar charging stations to these deployments. An example that I'm currently studying in Rwanda is a deployment by a company called Vandu which is trying to deploy solar powered small cell architecture in rural parts of Rwanda that have no coverage and they are like realizing that and our realization is that there has been a lot of these villages that have no electricity whatsoever. So it's often important to think about power sources and their ability of the people to access power while also providing them with connectivity infrastructure especially in some context like in Rwanda where connectivity rollout has far exceeded their electricity. Okay, I think we miss Charada for one second there. Charada, are you there? Yes, I am here right now. I was just saying that I'm happy to take questions because there may be any for the last 10 minutes. Okay, perfect. I think we missed that last part but I'm sure we got like most of the information of the key takeaways. Thank you so much for this amazing presentation. Personally, this is one of my main interests being a telecommunications engineer and working in ITC for development. So I'm really thankful that you presented all these interesting case studies. I have a couple of questions for you and we will leave the rest of the people to also ask questions while I ask you some of these questions. Please, again, if you have any questions put it in the Q&A and I will make sure to ask them to Charada. So the first question I had for you was you being in the field and for everyone out there, you have the privilege to talk to Charada who is in the field at the moment in Myanmar so she's doing these case studies as we speak. And what is the best example that you have seen in the field? So I know you mentioned community networks, you mentioned TV, white spaces. What is the best example? The one that you think has more or promise more for other implementations in other contexts? So I think- Especially the demand side. Yeah, on the demand side. Yeah. I think that, okay, I think on the demand side in particular, digital literacy training is a very amorphous term. So the best implementation often, I think is one that can be developed in collaboration with local context organizations and local community members. A lot of the organizations that we speak to in all of these contexts say that especially on the demand side, it's important to have a local trainer that you train, have a person from within the community that can be trusted to teach these skills. But also I think it's important not to be like blown away by a very fancy app-based training very easily. It's often that you need to teach them utility-based training. For instance, instead of teaching a person to learn how to write emails or how to use Microsoft Word, if you teach them the same thing with a purpose, say how do you apply for a job using emails? That might be a very useful way to conduct digital literacy training. In fact, we heard that in one of our case studies, Comcast, I think if I'm not wrong, said that they saw a quick uptake or a jump in uptake of digital literacy training. The minute they moved from very basic how to turn on, turn off computer and how to use basic applications to saying, how do you get a job on the internet? Or how do you sell your goods on the internet? And that kind of packaging in terms of digital literacy and ICT skills, I think makes a huge difference as long as it is very tailored to the local context. The other thing that I would say on the demand side is that it's important to have a more comprehensive picture beyond the basic skills. So things like protection from harassment, things like privacy and security and safety online should also be basic bare minimum that is covered in digital literacy modules. That's currently not the case, but often we hear that those are the kinds of things that people hesitate. When I spoke in the fields to villagers, they often have a hesitation to access parts of the internet because they associate them with bad things. And that's something that we should try to like, PM or try to at least educate people about through our digital literacy initiatives, whatever they may be. That's very interesting. It's interesting for me also that you highlight so much the supply side, because when we often hear connecting the unconnected, you always hear white spaces and all the demand side kind of initiatives. So there's one demand side question that we have in the Q and A from Catherine. Was there any pushback from regulators or service providers to use the TV white spaces? Different countries have had different experiences. India, for instance, currently has had faced huge pushback in terms of giving anything more than experimental license for TV white space projects. There is one TV white space testbed that is currently in operation and they are unsure. It's by IIT Bombay off the coast of, in the Gujarat Maharashtra border for those who are interested. But they are unsure if they will have the experimental license renewed or will be able to get any commercial license. On the other, and this has been from incumbent service providers. On the other hand, you see other countries that have had really good progress on TV white space regulation. Malawi comes to mind. I know Ghana and South Africa also have regulations that are in the process of consultation on regulation that are quite progressive and do allow for dynamic spectrum allocation to be a thing which allows for TV white spaces to be utilized. So in general, you don't think there's that much pushback from regulators or incumbent service providers? Again, it's hard to generalize. I would say that there are instances of pushback but not always. Okay, and another question I have from TV white spaces is are the equipment for TV white spaces expensive because as we know, the normal telecom hardware is very expensive. So how are these, in the case studies that you have seen, how are they funding and making it sustainable over time to maintain? So in a lot, if not majority of the TV white spaces that we have currently worked with, Microsoft has been a partner in some way or the other. They have been actually pushing for the adoption of TV white spaces more broadly. And they do get a lot of funding from the affordable access grants program that Microsoft runs. And Microsoft also has a TV white spaces like research arm that does a lot of collaborations with a lot of these. So the Malawi data went, I think was also like converted to the dynamic spectrum allocation table after collaboration, et cetera, with Microsoft. The, in terms of the router cost, yes, it is expensive, $5,000 to $6,000 per router, if I am not wrong, currently, which is quite high. And you like, and this is for ubiquity gear, but there is like, there are indigenous implementations that are, that we are currently studying. The Indian case is fascinating because the Indian case decided that the commercially available gear, which is primarily cars and adaptor or ubiquity is too expensive for them. So they built their own router. And in fact, I'm currently in the process of doing a cost effectiveness analysis of the deployment. These are the unlicensed spectrum deployment that they're also doing in parallel, which is proving to be slightly more cost in this, like slightly more costly for the reason that they have to depend on commercially available gear at the 2.4 and the 5.8 gigahertz spectrum. That's very interesting. So in India, they're kind of building their own hardware for the white spaces. Yes, yes, they're building their own router and it's currently being tested and piloted, but it's showing promise. The question still remains to be seen on whether or not they will get approval to use it beyond experimental purposes. That's super interesting. I hope they do get the approval because it sounds very promising. Okay, so aside from that, Shrad, I have one last question. I have two actually, and let's see if we can cover them. So the first one will be for community networks. I thought that was almost like democratizing the access to internet and having people from grassroots come with like we need this, like let's get together and work on it. Do you think at the long run, that's sustainable in terms of finance? Like as I mentioned already in a couple of times, I think my main concern or the concern of the sector is the financial sustainability of networks that are not connected to the bigger grid and to the telcos. So what are your thoughts about the financial sustainability of community networks as large or like mesh networks, WiFi mesh networks? So I actually think that a lot of the case studies that I've been studying show that financial sustainability can be attained in the long run of community networks as long as there is community buy-in. So in a lot of the community networks that I'm studying, there are like you need to attain like community and volunteer buy-in to be able to sustain the network, not just like financially, but also just physically sustain the network. The most successful example of a cost sharing mechanism for a community network that has been developed and studied extensively is the WiFi network deployment in Spain which has over 30,000 visible nodes and 44,000 in like total nodes if I'm not wrong. And that's like serving Catalonia. So yes, it is possible it's been active for so long like it's been active for almost 13 years now, 2004 if I'm not wrong. So it's possible, but I think a lot of the challenges that I've heard of when speaking to organizations that run community networks is volunteer buy-in. People don't want to contribute. People don't want to set up the routers or maintain the routers. People don't want to do the cost sharing. It's often a social problem, not necessarily a financial, sustainability problems or financial perspective. Okay, that's so interesting. Mikesh's answer or Kumar, I don't know what is the first name. Is there any way in which students can contribute to these projects? To the projects themselves, depends on the organization and depends on where you're based. But a lot of these organizations, especially if someone's in India, I know that there's digital empowerment foundation that does a lot of community networking in India and I'm happy to put them in touch with those people. The IIT Bombay deployment also, I think has some student involvement. But like I said, there are opportunities you probably need to be more specific about your needs and I'm happy to put you in touch with people that might be able to help. Perfect. Everyone has their Charada's email. We put it out there in the slide. We want to thank you for participating in Charada. Thank you so much for the work that you're doing for the space and for joining our webinar. Thank you so much. Thank you, it's been a pleasure. Thank you, everyone.


Alright so I have here a couple of examples of some functions. Now all you have to do is you have to figure out which one of these wave functions are allowed and which one of them are not allowed. Let's do this exercise and you can test yourself. Hello everyone welcome back I am Div Vishwati Das and this is for the love of physics. In today's lecture we will try to answer the question what is a wave function? You see in quantum mechanics the most fundamental equation is that of the Schrodinger's equation. It's a second-order partial differential equation. So if we want to study any kind of a physical system we have to solve this equation and if we solve this equation what we end up getting is this psi. This is a Greek symbol pronounced as psi which is a function of x and t because we have taken the Schrodinger's equation for a 1D case. We could have taken it for 3D as well but for simplicity I am taking it for a 1D case. This solution of the Schrodinger's equation is known as the wave function. Wave function. Now what is interesting about this wave function is that it's a complex function. This wave function is a complex function so that means it represents what exactly? You see the Schrodinger's equation is a wave equation that is supposed to describe the matter waves of microscopic particles. We know by this point that microscopic particles demonstrate wave particle duality. Its motion has a certain kind of wave behavior associated with it. So whatever that wave behavior is the Schrodinger's equation tries to be the wave equation corresponding to those matter waves. So now the question arises that if this is the wave associated with the particles motion then what is waving? What is this wave of actually? A quick announcement for my students who are preparing for CSI and net physical sciences or gait physics. We at Elevate classes organize live classes for these examinations every six months. The next batch is starting January. So this is a full-fledged live batch with live interactive classes recorded access test series and everything that you need. It's a complete package. So if you're interested you can check out further details at elevateclasses.in. You can avail the early bird discount coupon which is available for the first 50 students and if you're not really very sure about these online classes then the first week of lectures are free to attend upon registration. So elevate your physics preparation with Elevate classes. You see when we talk about let's suppose ripples on the surface of a pond then we know that these ripples are essentially atoms which are displaced from their equilibrium position. When we talk about light waves we are talking about electric fields with respect to a particular propagation of a wave. So when we talk about the wave function of a moving quantum mechanical particle what is this wave made of? Now that is a very important question and that is probably a question that many students ask themselves whenever they first study quantum mechanical theory and the sad part is the answer is it is nothing. At least nothing that is physical. No physical quantity is associated with this particular wave function. It's a mathematical function. Its existence only makes sense in the context of the Schrodinger's equation. It's a computational device. It's a tool. It doesn't have any physical significance associated with it or as you say physical quantity associated with it but it does contain some information about the particle because if it didn't then the whole point of this process would be useless because at the end of the day I'm trying to solve the Schrodinger's equation because I want to obtain some information about the system or information about how the particle is behaving in the presence of some sort of a potential. So if this quantity doesn't contain that information what's the point right? So no it does contain some information it's just that this quantity itself doesn't resemble a physical quantity. So we have to perform some kind of a mathematical magic on it to extract that information and one of the very first magic that we can perform was given by the Born's Statistical Interpretation which we explained in the previous lecture. So the Born's Statistical Interpretation simply says that if there is a particle restricted to moving in the x-axis we solve the Schrodinger's equation we come up with the solution. Then the mod square of the wave function which is essentially the complex conjugate of the wave function times the wave function gives us the probability density of the particle being found in a given region which means that if I integrate this quantity with respect to dx at a given point in time between let's suppose locations x is equal to a to x is equal to b then this simply gives us the probability of the particle being found along the x-axis in the region x is equal to a to x is equal to b. Thus the wave function is a mathematical function which let's suppose if I solve for a given situation and then I plot this mathematical function mod square and then that mathematical function may look something like this and then that mathematical function simply gives us an idea of the probability of the particle being found between two locations if we made a measurement if we made a measurement what is the likelihood that the particle will be found somewhere that is the information contained in the wave function as given by the Born's interpretation. So clearly the idea of a particle being found somewhere has something to do with the wave function yes but the wave function isn't exactly a physical quantity. So in a sense if the particle has a some wave function then there is greater likelihood of the particle being some found wherever the amplitude of the wave function is greater right. So if I have a particle and it has a wave function then wherever the amplitude of the particle is greater the wave function is greater the particle has a greater likelihood of being found there it has a greater probability of being found there. So, this all makes sense in the context of the quantum mechanics being in deterministic theory. The quantum mechanics that we are studying does not predict where the particle exactly is going to be in the next moment. In fact, the Schrodinger's equation cannot predict where the particle is going to be exactly in the very next moment. The only thing that quantum mechanics provides us is an idea about where the particle is more likely to be. Okay, so this is a theoretical prediction of where the particle is most likely to be. But if I made a measurement, I could as well as find the particle anywhere possible. It's just that if I made a large number of measurements, most of the time the particles will be concentrated wherever the amplitude is the greatest. So, thus the wave function turns out not to be a physical quantity, but a Pandora's box. It contains a lot of information inside. It doesn't really mean anything, it contains a lot of information inside, but we have to extract that information out of it. And the entire quantum mechanical theory is how we can extract that information. And this is the first piece of method of how we can do it. Now, it is not enough for the wave function to just be a solution of the Schrodinger's equation. There are other things involved. You see, the Schrodinger's equation is a differential equation. It gives us a mathematical solution. But is that mathematical solution even relevant to us in the physical world? Because at the end of the day, we will find that there are many situations where the solutions of the Schrodinger's equations are not useful to us. They cannot replicate a physical scenario. What I'm talking about is that the wave function is a function which has a lot of restrictions associated with it. There are a lot of criteria that it has to satisfy for us to be able to use it as a proper wave function for a particle. So, there are certain criterias that the wave function has to satisfy for it to be useful for us. And these are the following criterias. The first point is that the wave function must be finite single valued continuous. Now, why must the wave function be finite single valued and continuous? Well, it comes back to our interpretation of the wave function. The wave function basically gives us an idea about the probability of the particle being found somewhere. If the wave function is not finite, if the wave function blows up to infinity at a certain location, it simply means that the probability of the particle being found at that location will also become infinite, which doesn't make any sense. Like, if you look at the idea of probability, the probability can either be 0 or it can be 1. If there is 100% probability that the particle is there, then it's 1. If there is 0 probability that you'll never find the particle there. So, the probability of a particle is always between 0 and 1. It can never go to infinity. So, we cannot allow the wave function to be anything other than finite. It must be single valued. It must be single valued because there is only one probability associated with the wave function at a given location. Let's suppose there were multiple values of the function. It simply means that for one particle in one system, there are multiple probabilities of the particle being found in the same location, which again doesn't make any sense. So, we can't have that kind of an absurd behavior. So, we must impose that the wave function is single valued and finite. And it must also be continuous. Why must it be continuous? It must be continuous because we want the derivatives of the wave function to also behave well. The derivatives must exist and the derivatives must also be single valued, finite and continuous. Why? Because you see we have this second order derivative with respect to x. This must also exist and this must also give us some meaningful information. So, this brings us to the second point that the derivatives of psi, derivatives of psi. So, for example, we have d psi upon dx for a 1d case. And if we are considering 3d case, we will have del psi upon del x, del psi upon del y and del psi upon del z for 3d situations. They must also be, they must first exist, they must be finite, they must be single valued and they must also be continuous. But the question is why? Well, the answer depends upon two things. First of all, you see as I just now said the wave function contains a lot of information that we have to extract via some sort of a mathematical operation. Then one of the things that we are interested in is the momentum of the particle and we will see later on that whenever we are trying to find the momentum of a particle from its wave function, then essentially what we do is we take the derivative d psi upon dx if we are interested in let us suppose the momentum component along the x axis. So, because the momentum is an actual physical quantity, it cannot be infinite and it must also have a certain smooth variation and all these different conditions that are usually associated with realistic physical quantities, that is one of the reasons why the derivative of psi must also be finite. If it is not finite, it blows up, it simply means that the particle's momentum is blowing up or the particle's momentum has become infinite. If it is not single valued, again absurd physical scenario. If it is not continuous, that means the second order derivative will become infinite. Now, we do not want the second order derivative of psi to be infinite either because the second order derivative is present in the Schrodinger's equation. If this blows up then the entire equation itself doesn't make sense. So, in a way not only we want the wave function to be finite single valued continuous, we want its first order derivatives to be finite single valued continuous and its second order derivative to exist. Fine. So, these are some of the criterias that we have to impose. Otherwise, the wave function could be any mathematical function that makes zero sense. It could give us some very absurd weird situations which I am going to come to in a moment. But there are further conditions attached to it. The third condition that is attached to the wave function is that the wave function must be normalizable. Now, what is the meaning of this term normalizable? It has to do with normalization. I am going to come to that but essentially what it means is that if I want to find out this probability, right, if I am given a wave function and I take its complex conjugate multiply with the wave function. So, I essentially I get wave function mod square. I take it as an integral with respect to x. Then this between minus infinity to plus infinity must be a finite number. It must be a finite number. We do not allow this particular expression to either go to zero or go to infinity. These two conditions are not allowed. Again, it comes back to the idea of probability. If the wave function mod square from minus infinity to plus infinity comes out to be zero, it simply means that the probability of the particle being found in the entire universe is zero, which does not make any sense. The particle has to exist somewhere, right. And if it comes out to be infinite, it simply means that the probability cannot be made to be less than one, which again does not make sense because the maximum probability of the particle being found is one. So, it must be some finite number because if it is a finite number, we can make it to be less than one by multiplying that number with some sort of a normalization constant. So, this is basically known as the concept of the wave function being square integrable. This is called the wave function must be, should be square integrable. So, we should be able to integrate the square of the wave function and that should exist. Now, I am going to come back to this point of normalization a moment later. Let me first also mention a few more points. Another point is that for bound systems, okay. So, whenever a particle is bound in some kind of a potential. So, let's suppose the particle's energy is less than whatever potential barrier it is stuck in around it, all right. So, you can imagine a particle being stuck within some sort of a bound sort of a system. In that situation, the wave function should go to zero at infinity, okay. The wave function should go to zero as x tends to either positive infinity or negative infinity. You know the wave function cannot go to infinity or it cannot even be constant at infinity because it would mean that the particle then is not bound, all right. So, this condition is necessary for a bound system. And lastly speaking, for any kind of a system, the wave function must satisfy whatever boundary conditions comes from that system. So, psi must satisfy the boundary conditions necessary for that particular system, okay. So, for example, if I talk about particle in an infinite square well potential, then at the walls the wave function should be zero because if the potential is infinite at the walls the particle cannot exist. So, the wave function must also be zero. So, it must maintain these conditions imposed by the boundary conditions. It must be continuous, single valued finite. Its derivatives must also be single valued continuous finite. It must be normalizable. These are some conditions that we have to impose on the wave function apart from the fact that it's a solution of the Schrodinger's equation. So, it's not just sufficient that a wave function is a solution of the Schrodinger's equation. No, there are going to be large number of mathematical functions which are solutions of the Schrodinger's equation that we have to reject unless they satisfy these criteria.  I'm going to give you a list of different wave functions and you have to tell me which one of them are allowed or possible and which of them are not allowed, all right. So, let's do the simple sort of exercise, okay. All right. So, I have here a couple of examples of some functions. Now, all you have to do is you have to figure out which one of these wave functions are allowed and which one of them are not allowed. So, what you can do is you can pause the video right now for a couple of seconds or minutes, take a look at these functions and note down which one is allowed, which one is not allowed. So, if a wave function is not allowed, why is it not allowed? Just write it down. Let's do this exercise and you can test yourself. All right. So, now let's move on to the answers, okay. Let's look at these wave functions one by one. So, here I have in the first case scenario, okay. I'm not just giving you any mathematical expressions. I'm giving you a diagrammatic representation. So, in this first case scenario, what do I have? I have some sort of a wave function which is heading towards infinity. So, is this allowed? Is it allowed? It is not allowed. Why? Because wave functions must be finite. It cannot blow up to infinity because if it does, it means that the probability of the particle being found is going to be infinity, which is absurd, doesn't make any sense. Wave function has to be finite. So, that is not possible, not allowed and does not represent a physical particle. Let's move on to the next one. What about this wave function? If you look at it closely, this is not a single valued function because if you look at this region, any point in this region if you draw a line, the wave function has multiple values. See, this is not a one-to-one relationship between x and the function and we need a one-to-one relationship because the wave function corresponds to one probability value at a given location. It cannot have multiple probability values at a given location because then that is an absurd situation. What does it even mean? So, we want a one-to-one relationship. We want a finite and single valued function. This is not single valued. So, this is not allowed. Let's move on to the next one. What about this? This doesn't seem to blow up to infinity. This doesn't seem to not be single valued, but there is a problem with this. What is this? There is a sudden jump here at this location. That means there is a discontinuity here. There is a discontinuity in the wave function, but I said what? That the wave function must be continuous. So, this is not allowed. Why? Because if there is a discontinuity, that means the first order derivative of psi with respect to x blows up. We don't want that, right? Because of the second condition. So, therefore, this is also not allowed. What about the third condition? The third condition is that again it's going to infinity at as x tends to infinity. Again, it will it is not going to be finite after a certain interval of time and also it is not going to be normalizable if you notice because it is going towards infinity, right? So, this is also not allowed. What about the next one? The next one looks simple, but if you look closely, if I try to find out psi mod square for this particular condition, then what is psi mod square dx? It is essentially the area under this curve, right? So, what is this area under this curve? It tends to infinity, but we don't want that. We don't want that. So, therefore, this is also not allowed. What about the last one? Well, the last one is finite. It is single valued. It is continuous. It is smooth. Hopefully, its derivatives exist. Seems to be normalizable. This is a possible function. This can be allowed, all right? So, you see, out of all of these, only this one was possible and this one is allowed. So, now you can cross check with your answers and see how many of them matched with yours. So, the whole point of this exercise is to understand that the Schrodinger's equation could have many different solutions, but all those solutions are not necessarily allowed. They are not something that we want. We want the solutions which satisfy certain conditions and some of these conditions are written here. Now, let's move on to this next point of normalization. What is normalization and why is it so important? Many of the students who are studying this particular chapter in quantum mechanics is always stuck with this particular point. What is normalization? Even in examination, they might give you a problem of normalization. Normalize this function. What is normalization constant? So, let's try to understand what is this whole business about normalization of a wave function, all right? You see, there is no need to get scared of this process of normalization because it's actually quite simple. So, whenever we start a problem, we start with the Schrodinger's equation and we solve it, we obtain some kind of a wave function, all right? Now, we make the wave function pass all the tests that I mentioned, perfectly fine. If after all these tests, it turns out that this is actually a appropriate function, then what do we do? We try to find out the probability of the particle being found at two different locations A and B, let's suppose A and B, which essentially comes out to be the wave function mod square dx, it turns out to be some number. Now, if I ask you a question that if A is equal to minus infinity and if B is equal to plus infinity, okay? I am taking minus infinity and plus infinity along the x-axis because I am only interested in the particle's motion in the x-axis, all right? By definition. What is this probability going to be? What is the probability of the particle being found between minus infinity and plus infinity along the x-axis? Is equal to one, right? Because the particle exists somewhere in the entire universe along the x-axis, right? It exists somewhere, so the probability has to be equal to one. That's what it actually means. Now, it might happen that in certain situations, we might not actually end up getting one. Then, what do we do? Then, we simply multiply the wave function with some constant so as to make this condition true. Now, that constant is the normalization constant. To appreciate this argument a little better, let us take a classical example, all right? If I take a classical example, let's suppose in the classical world, we have a simple pendulum, all right? So, if a simple pendulum is present and we are interested in finding out the motion of a simple pendulum, then most of you may be familiar with the equation associated with a simple pendulum. It might be something like d2 theta upon dt2 plus omega square theta is equal to 0. This might be the equation corresponding to the motion of a simple pendulum. Of course, under the condition of small oscillations. Now, what is the solution of this kind of a second order differential equation? The solution of this kind of a second order differential equation is of course, theta t. Now, the most general solution is basically a sin omega t plus phi, where a is the amplitude, phi is the phase difference. These are constants that depends upon the initial conditions. Now, depending upon the initial conditions, I might have a different kind of particular solutions. For example, I might have a solution theta 1 is equal to sin omega t, all right? This is a possible solution, fine. I might also have a solution that theta 2 is equal to 2 sin omega t. This is also a possible solution. I might have a solution that theta 3 is equal to 3 sin omega t. Are you seeing what I am saying? These are all possible solutions for a simple pendulum and they all represent certain kind of motion where the amplitude is different. So, if I draw these sort of a graphical sort of a representation for this motion, maybe theta 1 representation could be like this, okay? This is theta and this is time. And maybe theta 2 could look something like this and maybe theta 3 could look something like this, all right? What I am trying to convey to you is that all of these particular solutions are perfectly fine. They represent a some slightly different motion for the simple pendulum. However, when we talk about the Schrodinger's equation which is also a differential equation and its solution, then we do not have this sort of a privilege. We do not have this kind of a window of a large number of particular solutions because it is not just enough for the wave function to be a solution of the Schrodinger's equation. We must also impose this additional condition. This is actually a very important condition because if this condition is not met, then the wave function is not going to make any kind of a physical sense. If the probability in the entire universe is greater than 1 or less than 1, then that wave function is absurd. So, out of all possible solutions which are different from one another by some multiplicative constant, only one of the solutions is allowed which satisfies this condition. Are you understanding what I am saying? In classical physics, we have a large number of possible particular solutions depending upon the initial conditions. But in quantum physics, the Schrodinger's equation might give us a lot of mathematical solutions which are different from one another by multiplicative constants. But only one of them will satisfy this and that is the answer we are looking for. So, what if you get a question in the exam that, okay, this is a wave function, normalize it. What is the process of normalization? The process of normalization is actually quite simple. It just involves us making sure that this condition is met. So, if I have a wave function, let's suppose psi, all right. Now, if I check this condition and somehow the probability between minus infinity plus infinity for that wave function is not equal to 1, then what I do is, I simply multiply the wave function with some constant. Let's suppose I call it n. This might be a complex constant. It's possible. It could be a complex constant. I simply multiply the wave function. So, let me write it like this. I have the original wave function. I simply substitute this, okay. I simply substitute this with n psi. That's it. Such that n star psi star n psi dx integration between minus infinity to plus infinity equals to 1, which gives us n mod square from minus infinity to plus infinity psi mod square dx is equal to 1. So, I solve this equation. I obtain n and then I substitute n here as a multiplicative constant for the wave function. So, then this is the normalized wave function and this process is called the process of normalization. So, this is a very simple step. I hope you have understood it. When we need to do the normalization, so as to make sure that the final function that we are dealing with is actually a function that can represent a physical particle. And for a physical particle, this condition is a must, all right. So, this is the sort of weird world of wave functions. Wave functions are not just mathematical functions of Schrodinger's equation. We must also impose a large number of conditions so that finally we can use that for some sort of an actual physical particle. So, in the next video, we will see something more. What other information does the wave function contain? What other magic can we perform to reveal further information about the physical system? Those things we will discuss in the coming lectures. I am Divya Jyothidas. This is for the love of physics. Thank you so much. Take care. Bye-bye.


Good morning everyone. How do I pronounce your name again? Niana mentioned I'm Paul and I'm a developer. I develop end-to-end dotnet solutions at work. Outside work I'm involved, I'm volunteer in two awesome organizations. Big Data X and Data Kind. In Data Kind we use Data Science to help nonprofits get insights from their data to help the communities better. And at Big Data X we aim to improve the data engineering literacy here in Singapore and surrounding regions. Hence we try to organize free workshops and events for this goal. And last year I went to Australia. I usually attend conferences because those are the things that make me happy. I learned about property-based testing from Zach who's speaking right here talking about hypothesis which is a library on property-based testing. And when I came back to Singapore of course I delighted about the library so I shared it with the community here. I talk about property-based testing with hypothesis. But today I'd like to focus more on the essentials. Like what really is property-based testing if you want to dissect it a bit. So I try to define it like it's a type of testing that asserts based on properties that describe the relationship between the input and the output of the function that is being tested. Is this clear enough? Yep, exactly. That's why I like examples better. So let's take a testing example. Let's try to test a simple multiply function. For this test function that we have, do you have any comments on the test? Yeah, don't do this. Don't ever do this. This is like implementing the functionality as part of your test, right? So if this is not the right way, what other possible approaches in testing that we can possibly do? So one of the basic ones is giving examples. So we give an example of the inputs, like two and three. And then we try to provide the example output. So here we have two of those examples. Example one, we have this group. And then example two, we have a bunch of inputs. And then the corresponding output, four times five equals 20. And we can choose to refactor it, make it look beautiful. So we have the common logic here. We're still comparing actual output and expected output. But it's nice to have all of our parameters for factors and expected output in one place that we can easily add. So that's still okay. But what we want to do is, is there a way that we can have a way not to depend on the expected output? Can we do a test just by depending on the inputs alone? So I use the multiply function just not just because it's a simple function, but it's also something that reminds me when I was in primary school. So in primary school, we learned about properties. Let's say arithmetic properties, right? You have like addition properties. You have the multiplication properties. And when we talk about property-based testing, it's really this kind of properties that we're referring to. It's the attributes and then the characteristics of the function that we're trying to test, right? Not the properties that is like a syntactic sugar for C-sharp or properties that you own. Of course, you have maybe like bungalows and stuff. But the properties that we're talking about here is something like this. So in multiplication properties, you have cumulative property, which you can reorder. It's still going to be having the same result. You have associative property, multiplicative property, and distributive property. So how do we apply this to testing? So if you notice here, we got rid of the output now. We're just going to depend on the input data that we have. But using this input data and our knowledge about properties, that's how we're going to improve our approach to testing. So we can do the cumulative property in this fashion. So we just rearrange. And then using the same function that we're testing, it should give the same result. So that's the property, and we're trying to test the cumulative property. And so on with the other properties you can do also in the same approach. But here, if you notice, what we're trying to do is we're now using property-based testing. But if you notice, I didn't use any framework yet, right? Why would you use a framework for such an example? We're still using predetermined inputs. So predetermined inputs, that means I have to set these inputs manually by myself. The thing is, here, for the multiply function, what is the population of our inputs? Can I do the testing in such a way that I can exhaustively test the function? It's quite impossible, right? Because you have, like, factors which can have, like, millions of samples, multiply millions, and all of these is impossible to me to manually write it down. So is there another way that we can deal with this sort of fashion? If your input is only a to z, I can just for loop it, right, and then test all the data. But if your sample input is too big for you to do exhaustive testing, we still want to test. But what you might be able to do is, instead of testing using the whole population, why not, like, test, like, sample at a time? Like, maybe 100 samples, test with that. If it's okay, then try with another randomized sample. So at least we might not test all the population, but at least we're moving there. And hopefully somewhere down the road, maybe some combination will spawn a bug or something that we'll be able to learn from, right? So that is using randomized inputs. So in this example, I'm using now the hypothesis for me to be able to generate a random set of integers and another integers for the factors, right? And for this, the hypothesis is just giving us, like, 100 samples at a time. 100 samples is the default size of the sample that the hypothesis is giving. So you might ask, why use a library? I can code the randomized inputs by myself, right? Why should I use a library? Well, there's nothing stopping you from creating your own library or function, right, if you want. It's just that why do you need to reinvent the wheel if there are lots of libraries that are doing this already? Even if you're using it for another language like Java or C sharp or F sharp, why would you recreate the same library, right? So perhaps before you create your own library, maybe you can look into the open source ecosystem and community. Maybe there is a library that's already built for property-based testing for your language and maybe it's not perfect, but we're in a community. We're here to help each other. If there's something that you notice to improve, maybe you can send a pull request and make the library better and then it will help the rest of the community as well. So apart from randomizing, what else can a library do? So at least let's say for hypothesis, it doesn't give you just randomized samples alone, but it also allows you to have more elaborate input criteria. So here, apart from integers, let's say you want to only include those that are greater than zero, all positive integers. You can do that or you can do arbitrary conditions. Think of formal methods, right? You can define your criteria in such a way. And apart from that, a while ago, we were doing example-based testing. Let's say you have a situation or a set of inputs that you really want to test, but you're already doing randomized testing. You can do that also using this property-based testing library. You can have an example. So what it will do, it will run with your example plus the randomized samples as well. So you have the best of both worlds, right? And from here, you don't have to depend on the default value or default size, which is 100. You can increase it to a few hundreds more. And in fact, if you want to do it with continuous integration, you might want to increase it to a lot more because you want the more samples that you test, the more probability that you will be able to catch the bug that you're hunting for. So you might ask, like, property-based testing is really good. Can I use it for everything? So this is my thought process. I'm always open to new ideas in case some things change. But currently, this is how I see it. So I usually ask myself when doing testing, is that function that I am testing, does it have testable properties from the inputs that I'm providing it? If there's none, then I just continue with usual example-based testing. But if I can derive a generic property that I can sort of use as a high-level way of testing, then I try to approach it in a property-based testing kind of approach. And then after that, I ask myself, can I afford to test all possible inputs to this function? If I can, if the input is maybe just A to Z, then I can just for loop it, and then use predetermined inputs for that manner. However, if the input is a combination of inputs are so large that I cannot really test manually, then I'll try to leverage on randomized inputs and then test sample at a time. Now that we have randomized testing, I don't want to be manually triggering this, right? You don't want to be manually triggering for bugs. You want it in such a way that you might be sleeping at night, but something is working for you, hunting the bugs for you so that when you wake up in the morning, first problem or some bugs, you'll be able to just get a report that, hey, there's something wrong with your function, you should fix this, right? So you can have some sort of system that you don't have to pay for it. It will do the work for you. So why not? So that hence we have this hunting bugs with CI. We have this normal CI. You can keep it there. It will do its job. The purpose of that is so that we have early detection of problems that is there, that's okay. But what we want to add is we want to have another CI pipeline dedicated for our bug hunting. So I call it the bug hunting continuous integration. So the difference here is instead of being triggered by merchant pull requests and so on, I want this to be scheduled. And if the CI platform that I'm using allows me, I want to schedule it as often as possible, maybe every hour or every day if it doesn't allow me. The purpose for this is for me to hunt bugs. Even if I'm away, I'm sleeping, it will hunt bugs for me. It will try to do those around my inputs and then probably give me a result with certain combinations. Maybe it fails that system. So let me do some demo. So I have some screenshots, but I'm not going to use this. This is only for backup in case the internet goes off or the electricity has some problems or the world as we know ends. I can't do much on the other two, but you know what I mean. So what we have here is a sample for arithmetic, the one that we discussed. So we have the multiply function and we also have a set of property-based tests with randomized inputs. So you have random integers and then this. So what I'm going to do now, I'm going to integrate this using... Who uses GitHub here? Anyone using GitLab? Which one do you like most? I use both of those. So for GitHub, because it has nice integration with Azure DevOps, Azure DevOps, by the way, is free. Yeah, I don't know why they put Azure there because usually when people think of Azure, it's the paid version, right? But yeah, all of my setups are free. So I tried to... Let me add a simple CI for this. So inside Azure DevOps, I can just build a new pipeline if that clicks. And then I'll just go to GitHub and then select my... This one. Multiplication. Because it's done in Python. Multiplication GH demo. And then once I have that selected, I just need to configure. And then this one, I'll need to cheat a bit. I have something configured already. Let me just... So what it does, once you have this configured, it's auto-checking into your GitHub repository. So I'm just going to copy this and then copy it here. So I included the test step here, where I use spy test to test using property-based testing using hypothesis. So that's part of the step. And then I'm just going to save and run. I'll just commit it to master branch. And then once that is done, I should be able to see it, check into the repository. And then once it's checked into the repository, I should be able to see the steps in the CI. So it will try to pull the necessary files and information. The normal CI steps that you usually see, including the building of artifacts and then also the testing. So it's currently preparing for the job to be queued. So while waiting, why not I can take some questions if there's any questions in the audience for now while we're waiting. So it's doing the normal CI, what CI needs to do, CI needs to do. It's quite fast installing the assemblies. So I did this setup both in Azure DevOps. I also did it in GitLab. So my GitLab setup I'll show you also later. So what we're trying to do now is we'll set up the CI first. And once the CI is done, you don't want to be manually kicking off the CI, right? So you need to explore whether your CI platform has ability to schedule the trigger. So I'll show that to you also. So it's done. What I want to show here is it has a step on testing. So in the test, you should be able to see it's so small. So if I scroll down, you should be able to see the hypothesis statistics where the first test that we have, I'm using 200 examples. The rest are just defaults. So you have like 100 passing examples. So this is fine. This is good. So once we have this, the next thing that you want to do is to be able to set the schedule so that it will trigger on its own every day or every hour. Unfortunately, I think for Azure DevOps, the granularity where it allows me to do the scheduling is only, I think, once per day. So it's okay. Once per day is better than nothing. I can just increase the sample to 1,000, right? So I can test more. So I'll just go to the releases. Oh, sorry. It should be builds. So in the multiplication, I'll just edit this. And then in the settings, under the settings, you have triggers. And in the triggers, you should be able to see setting for schedule. Here, scheduled. So I'll just add a schedule. It allows you to do scheduling every day. And then the thing that I want to uncheck here is only schedule builds if their source or pipeline is changed. We don't care if there's a change in the source code for this approach for bug hunting CI. So I'm going to uncheck that. And then let's say every 2 a.m. in the morning while I'm sleeping someone or something is doing the job for me in hunting bugs. So I'm just going to save this. Save and queue. So it will save it on its own. For GitLab, it has this similar functionality. You can set up your CI also. But the thing with GitLab is instead of allowing you to just do it like once per day, it allows you to do every hour. So if you notice here, once I set it up, this is GitLab, by the way. It's building and hunting bugs for me every hour. So you can set it up. So it's a choice whether you're hosting currently in GitLab or GitLab. And these are free public repos. If I want to go to my builds, this is where I can monitor the results of the builds as well. So in this multiplication GH demo, every build result you can see from here. The ones that I showed to you about how does the test result write. So if something fails, you should be able to see it here failing as well. And then let's say hypothesis found that for this combination, your function failed. And then you go and fix the bug. So with that, let me bring it in the summary. So what we've done so far is we've tried to explore on various ways of testing a function. We've tried with a basic example by providing example outputs. After that, we refactored and then tried to do it in a parameterized way. And then we explored at least two approaches in property-based testing. We're using predetermined inputs and then the randomized inputs. If we're not able to exhaustively test using all of the possible inputs to your function. And then we also explored the bug-hunting CI pipeline where it's a pipeline that is separate to your normal pipeline. Let your normal pipeline do its thing. But we use this pipeline to help us hunt bugs with those certain combination of inputs. You can reach me here. That's my Twitter and GitHub handle. And I've shared the links here for the previous hypothesis demo if you want to dig more into the hypothesis property-based testing framework as well as the demos that I used a while ago. And that's it for me. Thanks. Okay, I think we have time for one question. Yes? Yeah, you can give the mic. Yes? Give a real example of property-based because there's no, I mean, like, multiplication as it seems, the test doesn't really catch the bug where it's overflow, let's say, integer overflow or something. Because you test commutative and all this, you might not get it right. Yeah, that's true. So apart from randomized testing, there's also this approach called fast testing. And usually fast testing is usually you have randomized inputs and then your goal there is try to do as much input so that it breaks the system. That is another type of testing. But for property-based testing, you're thinking of a predetermined or deterministic result where you want to test that once you have this result, it coincides with the property of the function that you're trying to test for. So what I'm sharing here is property-based testing, it won't replace all the testing that you've done so far.  Plus, now we have another approach called property-based testing which we can add in our suite of kind of tests that we apply to the functions that we do. So other examples probably for this is just like multiplication, right? But other popular examples for property-based testing is, let's say, if you have, let's say, a list, right? You want to reverse a list. So one property there is if you reverse the list twice, it should be the same list that you input from the previous. So if you order like one, two, three, I reverse it, this is three to one, I reverse it again, it should come out as one, two, three. So the input and then if I reverse twice, it should be equal. And then of course there are like a few other approaches, like if you notice there's this diamond kata where it also teaches you on like how to spot properties from the inputs and outputs. Usually you try to look the input to the system and then output and try to check whether there are properties. The one that you shared, because people are also sharing that, hey, overflow is also a property or something, it might be case to case, I would categorize that maybe more appropriate for fast testing if that's the goal for that, but for property I want to have like deterministic expectation. Thank you. Okay. Thank you for the question. Thank you very much, Paul. Please give him a round of applause. Thank you everyone.


Dietrich Bonhoeffer once wrote, we are so afraid of silence that we chase ourselves from one event to the next, in order not to have to spend a moment alone with ourselves, in order not to have to look at ourselves in the mirror. I'm convinced that deep inner work leads to courageous outward risks. Bonhoeffer knew this all too well as he died in a concentration camp at Flussenburg, and we too every day get to take the deep inner risks and outer risks that he took.