A truism about any new technology, including drones, is that the technology is merely a tool, and that it then depends on how you use that tool. That's an oversimplification of the way that technologies interact with our social systems. The tools shape us, and we shape our tools. So this panel, we're going to talk a little bit about that process with respect to drones, with particular attention to privacy. But I think privacy oversimplifies the sort of complex set of questions we're trying to tackle a little bit. We're also trying to think a little bit about how the information that drones can gather reshape power dynamics, and reshape the employment market, whether that's a person who used to have a job walking down an electric power line, inspecting it doesn't have that job anymore, or whether it's a villager who was not able to sort of have a synoptic view of the area around his village, now can, which changes the way that that person interacts with their government. So privacy is one very large aspect, I think, of these set of questions. Shannon and Matthew Lippincott, who wrote a chapter for this primer that is available outside, framed the question as the political geography of aerial imaging, which is their framing, not mine. And I think that sort of encapsulates the set of questions we're going to try and tackle a little bit amongst ourselves, and then amongst the entire group. John Verdi is the director of privacy initiatives at the National Telecommunications Information Administration, or NTIA for short, which is part of the Department of Commerce, which is relevant to us, the part of the US government that the president on February 15th, I guess, put in charge of thinking about this set of questions. So we're very happy to have John here with us. Lisa Elman used to work within the government, and now, both at the White House and the Department of Justice, and now is at Hogan Levels, a law firm here in Washington, DC, and thanks, Lisa, for coming. And Shannon, as I mentioned, wrote part of this book, and is one of the co-founders and co-directors of Public Lab, which is a citizen science initiative, and it's many things that I can let you describe a bit better than I can, and a fellow at the Berkman Center for Internet and Society at Harvard in Cambridge. So thank you all for being with us. What we might do is each of the panelists will sort of speak a little bit about their own interaction with these questions and their history, and then we'll talk. Thanks, Shannon, do you want to start? Sure, I will go ahead. So I think probably the first thing that I'll start off by saying is that Public Lab doesn't deal with or work with drones in the typical sense of the word. We actually fly large balloons, weather balloons, and nine-foot kites that are tethered. So we escape FAA regulations around what drones fall into. But we started the organization back in 2010. I come from a long history working in community organizing and community education. At the time, I was working in fence line communities in the newest oil and gas fields of Louisiana, focusing on the BP oil spill. And during that time, we came together with about 250 other people to capture images via balloons and kites, sending them up about 2,000 feet in the air with very basic point-and-shoot cameras attached and collecting an alternative narrative about how the spill was affecting people in a disaster that had just a very large media blackout happening around it. So from there, we've been working for five years. Like I mentioned, we have a number of different tools that go beyond the imaging portion of it. But within our aerial imaging toolkit, you could say, we have kite mapping. We have aerial mapping with balloons, pole mapping. And then we also create open browser-based software. The kind of key one for us is called Map Knitter so that you can stitch images that you've collected from your devices. And it could be balloons kites or even drones. And then also Map Mill, which is an image-sorting platform as well. So I'll pass it on to you. Okay, yeah. Thanks, Shannon. Thanks, Konstantin. It's great to be here. Thank you, Peter, and all of you for having us. First of all, this is what I would call drone's fever. This is amazing. It's so great to see you all here. It's so great to see so much excitement and curiosity about this industry. And it's great to be here with you all. Just a little background on where I come at this issue from. So I worked for the federal government for many years. I worked both in the White House and at the Department of Justice as part of the Obama administration in a policy-making role focused on technology and innovations and emerging technologies and incorporating them into the federal government. In 2012, of course, when Congress mandated that the federal government integrate drones into our national airspace, the FAA, including our friend Jim Williams here, we're actively looking at those issues at the time. But the whole of federal government, all of a sudden with this congressional mandate, really starting to pay attention to what this meant and all of the various policy issues that come along with the task of integrating drones into our national airspace and what that actually means and kind of the first order policy considerations in terms of privacy, security, and safety that come along with that mandate. So I was asked to run drones policy at the Department of Justice and to participate on a White House inter-agency working group that was considering all of these issues, including with John and others that was considering all these issues at kind of on what should our privacy rules be with regard to drones? Our, do UAS present unique privacy considerations? And if so, what are those? If not, do we just need to update our privacy rules? Where exactly is all this concern coming from across the country? Of course, in towns and communities, we've heard concerns about privacy, about security, with regard to the use of drones and how should we handle those and think about those? So I worked there for a year running that effort both at Department of Justice, working on the Presidential Memorandum that came out on February 15th, of course, setting up what we'll hear about from John, this NTIA stakeholder process, which we'll deal with a lot of these issues in the commercial sector. And I now am in the private sector, where I'm working with the industry and helping the industry. Companies love drones and they hate drones.  So, which makes a lot of sense, of course, if you're an oil refinery, you want to be able to use them for infrastructure inspection but you don't want others flying over your power plant. If you're Disney, you want to be able to use them as fireworks in the sky, but you don't want others to be able to fly at your theme parks. So there's a lot of concern kind of in the community but also incredible excitement. And we're at such a unique time in American history and in history, generally around the world as people are considering these issues really now, for the first time, it's so rare when you're in policy making roles and working on these issues that you have very little data and whether it's safety data or privacy data, we haven't had here in the United States or we haven't had broadly authorized use of commercial drones, consistent use, it's very different than as a hobbyist which has been broadly authorized for many years, going and flying once a month in a local park is very different from what Amazon is looking to do. And so it's a very exciting time to be thinking about all these issues and I look forward to our conversation today and moving forward with all of you. Thanks, I appreciate the intro and I appreciate all the great work that Lisa and Shannon have done on this issue. My work focuses on convening stakeholders who are interested in unmanned aircraft systems and UAS. Folks from industry, technical experts, academics, folks from the advocacy community and others to try to develop some common sense best practices that can guide commercial operators and individuals as they roll out UAS within the National Airspace System. And the president asked the Department of Commerce through my office to do this as part of the February memorandum because there is a recognition that privacy issues, transparency issues, accountability issues have the potential to be triggered by broad commercial UAS operation and that there is also an opportunity here for companies and individual operators to build trust with the individuals and communities that these systems will be flying above and smooth the integration so that privacy and transparency and accountability concerns don't stymie the very real and valuable innovations that these platforms promise to provide. And so what we are doing at NTIA is essentially deferring to the stakeholder community. Folks who care about these issues, who either operate commercially right now under three through three exemptions or who intend to operate commercially under the FAA small UAS rule when that is finalized, working with those folks, working with privacy advocates, working with NGOs and working with technical experts to try to find some common sense solutions to promote privacy, transparency and accountability in this space while the operation is being rolled out. And we recognize that operators are gonna need to iterate in this space and we recognize that some of these questions are tough questions that folks are gonna need, as Lisa said, more data to form some firm answers around. But from the beginning, I think it would be helpful for folks within the community to have a common understanding of how best to address these sorts of privacy, transparency and accountability issues. And I think there's a broad recognition that lots and lots of UAS operation, whether it's inspecting pipelines, whether it's doing aerial photography on closed movie sets, whether it is working in the precision agriculture realm, doesn't raise a ton of privacy issues at all, if any, but that there are circumstances, particularly when UAS are being operated over populated areas and are capturing images and other data about individuals who are not participating in the UAS operation. There are privacy issues there, there are transparency issues there in terms of landowners and individuals who would like to know who are operating those systems that are important and that folks need to start grappling with as these systems are rolled out. So I'm looking forward to engaging in that process. We took public comment on that a couple of months ago and we received some really awesome comments from across the range of the stakeholder community. The first public meeting of that process is gonna be August 3rd. We have additional meetings scheduled through the fall. And we're also having conversations publicly at events like this and sort of privately with stakeholders, anybody who sort of asks for a meeting with us and wants to chat about these important issues, we always sit down and we're happy to talk. And we're excited about beginning the process and we're excited about what innovative solutions, industry and other stakeholders are going to develop as they grapple with these important issues. Right, so I might start first by pushing back against John in one small way. Awesome. That specifically with pipeline inspections, you say, oh, this doesn't really raise any privacy concerns. And arguably it doesn't if it's the owner of the pipeline inspecting it. If somebody else wants to inspect it, say a local community, it does raise, the company might say, oh, you don't have the right, for exactly the reasons that Lisa was just saying. That sort of minor point as a more global question brings me to both Lisa and John, you mentioned sort of this desire for sort of more data to drive sort of sensible regulation. It seems to me that to an extent, we need to reason from first principles here about what we want as a society. Like it's hard to get data about privacy to say, oh, my privacy was violated, you know, 7% and now I'm 7% sort of less free in my mind. So my question to both of you is when you say you want more data, what, and from an air safety point of view, that's a little bit less problematic. But from the perspective of privacy, what is it that you're thinking about when you're thinking about data? Sure, so when I think about data in this area, I think about the sort of experiential data that companies and individuals develop as they actually operate these systems in the commercial space, in real world environments, right? So you mean experience essentially? So, sure, experience, I don't know whether it's quantitative data or qualitative data, but for example, when we talk about privacy issues in other realms, when we talk about internet privacy issues, we have many years of experience with static websites, web applications and data flows within that ecosystem and within that business community so that we are able to, when we start from first principles, identify particular issues that pose privacy risks, that pose security risks and that folks might want to mitigate, right? And we have that level of experience. With commercial UAS operation, we don't have a similar level of experience right now. Folks who have 333 exemptions are building some of that experience right now. The FAA has test sites where folks are trying to collect data and build some of that experience right now. But what you don't have is several years of experience of actual in-the-wild commercial operation from which folks can draw qualitative data, from which they can draw quantitative data and so that we can take a look at those first principles and then say, all right, here are some really crucial use cases that we know are major issues that we need to address in the privacy space and the transparency space and the accountability space. Instead, what we have are really smart folks in the commercial sector, in the advocacy sector, in the academic sector who are thinking a lot about these issues and who have certainly flagged privacy issues, transparency issues, accountability issues that we can talk about and build best practices around. But what's missing right now is a really large volume of experiential data. So that's what I mean when I talk about it. Lisa, I don't know what you mean when you talk about data. Yeah, well, I would just add, just building on what you just described in terms of once we have this experiential data, what do the American people want? What are our preferences? And one thing that I saw, there was a University of Oklahoma, a few researchers from University of Oklahoma recently did a very interesting study, and it was in the use of public drones. So this is in the law enforcement context. But they did a survey asking folks whether they, how they felt about the use of drone cameras versus ground-based cameras that captured the same information, the same data, and took the same exact photos by the ground-based camera versus the drone camera and drone-mounted camera. And the level of opposition was way higher for the drone-mounted camera than for the ground-based camera, even though it was capturing the same exact information for monitoring traffic incidents, that kind of thing. So for some reason, across the country, there has been a part of it as a lack of experience with drones. We're all coming at this in the fact that a small hobbyist drone has the same name as a predator or a reaper that are flown overseas for very different purposes. And so there's a lot of confusion across the country in terms of drones and what their capabilities are and what we're talking about here. As the experience grows and as folks become more comfortable with drones and see all of their benefits, I think that that will shift over time. But it's not until we get there that we'll be able to. And that's why this national conversation that we're going to be having hosted by NCA is going to be very important in this regard. So I guess in response to those a couple points, and then I want to throw it over to Shannon. I mean, we live in a democracy, and public opinion is important. But there's also a reason that we have sort of courts that sort of deal with, I mean, this distinction you're making that the public opinion was very different in a drone mounted versus a street mounted camera, the public's opinion about that is not necessarily a reasoned informed opinion. And that may be something where it's useful, where there's a reason that Oliver Wendell Holmes sort of writes about privacy, and we don't sort of do it all by acclimation. That is true, but I think that that's why we see all this action in state legislatures across the country, since those people are directly talking to their legislatures. And going to the point of sort of the way the legal system has tended to treat privacy, in the US, broadly speaking, sort of having a reasonable expectation of privacy is an important legal consideration, which is what worries me a bit about this sort of quest for experience and data. Insofar as you mentioned the example of the internet, as a sort of analogy of how we might want to do things. To me, the internet hasn't been, privacy on the internet hasn't been a tremendous success story, right? There's our emails are not, there's no reason why everybody's email shouldn't be encrypted all the time, because we send letters and envelopes. We don't only send postcards when I get my utility bill. And this isn't done, and other people might disagree. To my mind, this is a problem. And one can disagree about that. But what I wonder about in this quest for experience, if a sort of precedent is set that, OK, this company does X, Y, and Z with drones, and it's done. And now we can learn from that experience. It's not very good, but hey, it's already there. So now I don't have a reasonable expectation of privacy because it's already gone, which is why I wonder to what extent the desire for data or experience, whatever word you want to use, sort of pushes the can down the road. And we don't confront questions now. So let me be clear. We're going to start confronting the questions August 3. And in fact, we have already posed the questions a couple of months ago. And I think the president and the administration are committed to engaging on these questions now, and I think it's critically important. That is not to say that the administration doesn't see the value in data as folks move forward and that the administration does not understand that the UAS industry, particularly the commercial UAS industry, has valuable things to learn about everything from safety to privacy to supportable business models as it becomes more lawful and more widespread to operate these things. I don't think it's an either or necessarily. I mean, on others. And I would go back to your, for instance, around why would a corporation want me looking at a pipeline? So I'm going to come at this from who I am as an activist and a person who works on advocacy and has done a lot of work with fence line communities. And we share our air. We share our water. You could maybe explain what fence line communities are. Sure. So fence line are communities that are situated directly next to industrial facilities, pipelines, other types of infrastructure and that sort. I think very key to the way that we approach work, though, is if we don't need to collect data, then we're not going to collect it. If we can come to the table as stakeholders, if we can talk to a company with the community at the table with representatives from the DEQ or an EPA fraction and come together in the initial sense. Sorry, Department of Environmental Quality. Someone states its protection. Environmental Protection Agency, EPA. If we can come to the table and reach conclusions without having to go into monitoring, I think that that's the approach that we prefer to take. When there isn't an ability to do that and when companies give communities pushback, data is an incredibly powerful tool to situate them as even players at a table. And so in that sense, I would say, well, you don't want us to monitor your pipeline, but this is also our land. This is our air. This is our water. It's a shared resource in a shared area. I would just add to that that part of it, too, is almost like we need a public education campaign kind of like the know before you fly, knowing what the safety rules are before you fly. There already are a whole lot of privacy rules that are not technology specific that are already in place. So if I trespass on someone's land, whether I go on there with a drone or myself, that's a trespass. There is nuisance laws. There's intrusion upon seclusion. There are various state laws, misappropriation of trade secrets, for example.  So whether it's happening with a drone or whether it's happening with a pole camera or any other technology, there are rules that do protect us already, but there has been a lot of, you know, this is what people are watching about. Did anyone see that modern family episode that with the drone? So the family was out sunbathing in their backyard and a drone came, flew above the swimming pool. The father to try to, they're all in their bathing suits. The father to try to, you know, get the net, the drone away, tries to take it out and the father's swimming trunks fall down.  Now this is what the American public, this is what the American public is seeing. And so yes, it is true that perhaps folks, you know, it might be based on some kind of fear, but this is what, as an industry, we do need to confront as a government, we do need to confront. And so perhaps some kind of public education campaign around these issues where recognizing that people are protected in many ways already. Perhaps we do need some UAS specific rules and we should talk about that, but there already are a broad range of privacy rules that are already out there. But I think this question of sort of what constitutes trespassing with respect to a drone has not worked its way through the courts yet, to my knowledge at least. So even if laws exist, how those laws work out in practice is still unknown. Sure, and to flag that those laws have been developed in an era where air travel is relatively expensive, relatively technologically burdensome, and largely in the manned aircraft space operated by giant devices that cannot hover over a pool in a backyard without making their presence really well known, right? If it's a rotary aircraft, if it's a manned rotary aircraft. And one of the real promises of UAS technology is that it has a lower cost of entry, it is more nimble, the platform is more flexible in a lot of ways, and with those benefits come different implications for state tort laws and a variety of other laws that have cropped up and analyzed over the years with the assumption that operation of aircraft is expensive, that the aircraft themselves are large and obvious, and how do courts sort that out? That's a great question, and I think we're going to see. All right, well, I'd love to sit here and ask you questions till the audience is all entirely asleep, but I will not. We'll start with Gregor here in the front and then work our way back. Hi, a lot of this privacy discussion comes around the talks about individuals and being monitored in their swimming pool. I think Lisa bring up a really important point about the privacy of corporations, and as Shannon coming from a social advocacy community organizing perspective, the question about the public's right to kind of monitor and document the activities of a corporation is important, and in Peru, the reason there was oil spills and the photograph there was largely because it went unreported. Nobody knew what was happening until the communities fought for their right to photograph and document what was happening, and the company did not want to allow it, and I see a similar battle happening at the moment as possible to take a balloon and fly over the BP oil spill and show what the company was not allowing people to do on the ground. Drones are kind of circumventing this and allowing greater transparency of the way companies are operating, but the real question for me about privacy is how much of those laws going to be leveraged to kind of cut off this new avenue we have of calling companies to account for making their operations more transparent? I think it's a great question. I mean, I think it's an open question, and I think that's a conversation that we're going to have at the NTIA Secular Session. There's a clear balance between our right to know and also like news gatherers, for example. They have a First Amendment right to report the news and want to be able to use drones for that, but then, of course, we also have the privacy concern on the other side, and so you have that tension, and we see that tension running through many industries, and I think that's something that we'll have to have a conversation about. I know that corporations themselves are worried about their own privacy, but then, of course, what is the public's right to know, and they run right into each other, so. Yeah, and this was, this point was made, I think eloquently and repeatedly, in the comments we received from the public, from companies expressing the concerns that you express, public and news gathering organizations and members of the public expressing the desire for greater transparency and greater information flows, and how that sort of structure maps onto the individual privacy issues as well, and I'm looking forward to a robust conversation about it. I don't know that there are easy answers, but my hope is, and my expectation is, that folks are gonna be able to make progress on those issues and try to identify best practices that will at least be able to guide operation as it rolls out. The question then is how the actual commercial operation and individual operation identifies issues that we don't even know at this stage exist, right, and then how we grapple with those, so I think it's gonna be an iterative process. And I think just quickly, this balancing between the right to gather information and the right to privacy is not, I mean, there's not a universal prescription that balances that, and I think there's a desire, certainly on the part of industry, a logical desire to harmonize rules across jurisdictions, whether within states, within the US, or within nations in the world, and I think the difficulty of balancing that argues for not pushing harmonization too much, that different places can experiment with that balance in different ways, and it's useful to have variety in that sense. Peter. Thank you. I think, Constantine, you touch on this in the primer, which is the idea of who owns the heir. And so the question that I put to you is, how is government thinking about the envelope of private property rights? We're one of the few countries that has the default position that we own to the depths of hell, to the heights of heaven, and there have been some adjustments to that. And of course, drones are driving changes in that regard, and your modern family example is California, so they use a net. If they're in Texas, they probably use a shotgun. Great. It's a greater effect. But how do you think, how do you think, because there's a whole new area of law, if you will, and how are you thinking about that idea of who owns the airspace? So I think that the framing right now within the government, I'm not gonna speak for our fellow agencies. I mean, one of the things that we're trying to do is actually reach out to the community and get input from everybody, not just one sector, but everyone who has an interest in this to see if we can find some kind of agreeable answer to that question. And I think it's a super hard question, right? In terms of how that issue can be framed, I don't think that there's any question when you look at trespass law and nuisance law at the state level that operating a UAS six inches off the ground on private property that you don't own or control and that is causing a hazard or a nuisance to the owner of the property is certainly outside the bounds of what tort law is willing to recognize as a lawful use, right? I think that there's also the issue of flying, a very large UAS 40,000 feet above private property is at the other end of that extreme. Those are easy cases because they're edge cases, right? Nobody wants a UAS chopping them off at the ankles and everybody understands that UAS at 40,000 feet implicate different concerns. And where things fall in between those two extremes, super hard question. And we're trying to get the framing right and we're trying to get the wisdom of the academics, the industry folks, the advocates who have been thinking really hard about these issues and see if we can get some sort of synthesis and some sort of consensus on it. Yeah, and I would just add there's been a very dynamic discussion in the community about this issue exactly. It makes a lot of sense that if I own the airspace in my own backyard and why can't I take photos of my property and want to be able to use those photos to sell it right now that would be illegal because it's a commercial use that's my backyard. There was of course the 1946 Supreme Court decision, Cosby decision, which said you have control of the immediate reaches of your land. Now that this is all considered navigable airspace, I think the FAA would say from the blade of grass up is navigable airspace and they have the ability to regulate to keep the airspace safe and secure. So I think on the safety side, one question would be well, even if you're flying 90 feet in the air, what if it's a flyaway, there's reasons perhaps that regulators would want to regulate in that area, but then there's of course also reasons that the owner of their property wants to be able to use the immediate reaches of their land for their own use. Now I've seen a lot of proposals, there is one floating around of course that would say that would basically give you control 350 feet, perhaps, maybe the right answer is 200, maybe it's whatever it is, of course also allowing where does, if an Amazon delivery drone is flying across, like where are they able to traverse the airways as well? So there's a lot of competing interests here and I think it's a very, very important topic for conversation moving forward. We're running a bit short on time, but I do want to give everyone a chance to talk. So the first four people to get to the microphone, if we'll just go in a row, keep your interventions brief, and then we'll give the panel a chance to conclude and then move on to the next panel. This is a fascinating conversation, but can you pose some hypothetical end positions on these, would it be a federal law, local law, guidelines, what exactly are we talking about like 20 years down the line, what would it be? And my other question is, is there an organized opposition to drones? Lisa, you can take the last one first. Yeah, the answer is yes, there's absolutely an organized opposition. I mean, look, there's a lot of concern about the use of drones, whether by companies or by law enforcement, or a lot of the laws that you see proposed across the country actually are aimed at public agencies, state or local agencies being able to use them without a warrant, that kind of thing. So you have a lot of the advocates that are concerned about whether the ACLU or others that are very, very organized and concerned about the use of drones. As far as your first question, I think privacy has traditionally been regulated at the state level, it's traditionally a state law issue. And there are some federal laws on privacy, but they're pretty focused in certain areas where there's a clear need. I think the best practices are a great place to start. I think we go from there and see what we need. But in the meantime, we're definitely seeing lots of different states come up with lots of different proposed solutions. And I think we'll have to see how those play out. And just to clarify, by my interpretation, at least the ACLU's writing on this issue has been fairly nuanced and sort of like, they're not like anti-drone. Yeah, just to be clear. But there is, but there is. We're down to two more. We went too long for that. I just wanted to understand this. So for instance, with the San Monica Bay, Los Angeles Basin, if there were three places that you thought about, let's say the Chevron Refinery, a private estate in Malibu, and a boat, either a small privately owned boat or a oil tanker in the bay itself, are these, what is the law now on covering or being close by to any of these sites? Is there any established laws? So are you starting from scratch with your legislation? Thank you. Well, California actually just recently passed. It's a platform neutral law, but it was geared at paparazzi using drones that would impede a reasonable expectation of privacy. So in California, if you're talking about privacy in California, they would actually have to abide by that law. I will mention a NOTAM that was, the FAA issues noticed to airmen and there is one that would apply, for example, to oil refineries. It doesn't prohibit flying over oil refineries. It prohibits loitering above oil refineries, power plants, dams, that kind of thing. So there are some protections, but there is nothing that says you may not fly over an oil refinery, for example. There are in general, and Lisa, correct me if I'm wrong here, restrictions about flying below 500 feet for like, for manned aircraft. So in terms of what already existed, this is all. And there's of course restricted airspace. So we can't fly anywhere here in Washington, D.C. But there's various restricted airspace around the country and you can't really fly unless you coordinate with local air traffic controllers you can't fly within five miles when they report that kind of thing. So, yeah. We'll have Walter analyze the microphone. I think the last one. So I'm coming from a completely different angle. I'm a land surveyor. I'm using drones for mapping. I think that's a bona fide application. So all of these privacy issues set aside. I've been in this business now since 2008, waiting for those ever-promised regulations to materialize so that I can have some direction in life.  I could have given you data, my flight data, since 2008 if only you didn't banish and ban me from participating commercially in this kind of activity. You could have had a huge pool of data by now, possibly even had the regulations in place. So I don't understand why we can't have an approach of let's wait and see how this pans out before we preempt and dream up all sorts of phobic kind of scenarios that make us all feel insecure and stop us from progressing in this field. All right, go ahead. So I very much appreciate the point. And what I would flag concerning the administration's approach to this is the FAA has a very serious safety mandate in this area. And I am not, I don't work at the FAA. I am not an expert on the FAA's operation in this field. I do have some of my best friends are at the FAA and they seem like lovely folks. But I think that that process is moving forward. It's working itself out and I would be happy to follow up offline and sort of make those connections and have those discussions about the pace at which integration is occurring. Privacy transparency and accountability, the goal of our engagement is not to dream up hypothetical scare scenarios that will stymie development in this really important area. What we are trying to do instead is work with folks on a voluntary basis to try to identify best practices that will really smooth the integration. And I'm hopeful that that community-driven effort is going to be successful. So, but I very much appreciate the point. And I would just add you highlight a very important point which is a timeless issue, a timeless question of policy always lags behind technology. Technology is always moving more quickly than policymaking. So, and I like to talk about the concept of polarization. Policymaking must promote innovation, but innovators must also work hand in hand with policy makers. And now in moving forward, we've seen a bunch of, we now have a proposed rule out there, robust conversation, we're moving. It's the 333 process has become streamlined and it's much easier to be able to engage or sorry, fly drones commercially. And moving forward, I think it's very important for all of us in this room, innovators as well as policy makers to really work together to craft technology solutions to some of the privacy issues, for example, that we've talked about today. I told everybody else participating in the day that I was going to be very strict with time and I've now lost all credibility having let my panel run over. So we'll move on to the next one, but thank you all very much. Thank you. Thank you.


Hello, this is Professor Steven Nesheva and I'm here to help you out with getting started with some spartan calculations and after you launch spartan, you can go over here to what's called the the the new builder icon you click on it and This appears on the right and the organic tab is what we want and the first thing that you'll be doing is doing stuff with with water with two ox water and To do that you click over here, and I can make it bigger or smaller by scrolling the trackpad and Moving it around now for this first part of the exercise actually I want several water molecules So all I'm doing is double-clicking in there, and then What you can do is do the molecular mechanics minimization Which is which is that little green guy and I also want you to turn on and hear this model Tab and it turns on hydrogen bonds this way. Okay, so there's that now I'm gonna want to have more water molecules and Every time you add some you can just do this and click on that minimization And you can start to see how it forms this hydrogen bonding network And when you want to go do the same thing with methane you click on here for another new build and that's There on the on the right. That's the that's the methane And you can do the same thing. I'm just double-clicking here. You can still turn on Hydrogen bonds, but you'll see that nothing ever shows up, but you still do want to do the minimization Just like that. All right, and so that's the general idea The next thing that you're gonna be doing is well once again We're gonna go back to water and just but only one wall water molecule I'm gonna click on it there and The first thing that we'll do is we're gonna go to calculations and So I'm gonna click that and we don't want Hartree-Fock. We want B3 lip and you press submit there And in just a moment it will it will Start the calculations. You have to decide where to where you want to save it so I'm just gonna let it save there and Hopefully it will all come back in just a moment and say that it's done and Soon as it is done. There we go It's it comes back and says that now what we're gonna be when I'm looking at is surfaces So that's the surface icon. I want to go to density first. You see the little box shows up and there it goes So now there's there's water as a as a van der Waals surface But to look inside it what you got to do is sort of click on it until this thing shows up on the right And we can do transparent. All right So now we're looking at the size of a water molecule a second thing I'm gonna want you to do is to go to the surface again and Add an electrostatic potential map which we then have to turn off the density to look at it So that's now what we're looking at and if you want to look at it inside We do the same thing go to transparent and so forth. Okay, so now the the last bit of calculation that I'm gonna want to what you to do is to I need to click off here off-screen not like that but off and Go to this thing called properties and when I do that if I display the dipole vector Then it shows up and I can see how how the dipole vector which points from positive to negative parts of the molecule


Hey everyone, it's Missy. Welcome back. Today's tutorial is this triple polter braid into a ponytail. Make sure to subscribe to my channel if you're new and let's get started!  Then I'm going to bring this ponytail forward and clip it out of the way to use later. Then I'm going to divide off a second section of hair from the temples to the back of my head and tie this off with another elastic band right underneath the first ponytail. Then I'm going to let down the first ponytail and I'm going to hide my elastic with a section of hair.  This is an extra step but it's an easy way to hide your elastics if you prefer. So now I'm going to take the first ponytail and divide it into three sections, a left side, a right side, and a center piece. I'm going to pull the two side sections aside, leaving the center piece at the back. Then I'm going to take the second ponytail and divide this into two sections. Then with the center piece from the first ponytail, I'm going to place this down the middle of the second ponytail. Then I'm going to combine the two pieces of the second ponytail back together and clip this hair up and out of the way. Then I'm going to let down the two side pieces from the first ponytail and I'm going to pick up a new section of hair from above both of the ears and combine it with the three strands from the first ponytail. I'm going to tie all of this hair together to create another ponytail. Now I'm going to let down the hair that I clipped up and repeat the same steps as before. So again I'm going to take the top ponytail and split it into three sections, a left side, a right side, and a center piece. And I'm moving the two side pieces out of the way. Then I'm going to divide the bottom ponytail into two equal pieces and place the center piece from the top ponytail down the middle. Then I'm going to combine the second ponytail back together and clip this hair up and out of the way. Now I'm going to combine the three strands back together from the top ponytail, pick up a new section of hair from behind my ears, and tie it all together to create another ponytail. And then I'm going to let down the ponytail that I clipped out of the way. And now that I have two sections done I'm going to go back over the braid and pull on the edges to make them a lot bigger. This is an extra step but it really helps accentuate the sections of the braid. So now I'm going to create one more section of the braid so I'm going to divide the top ponytail into three sections again, moving the two side strands out of the way. Then I'm splitting the bottom ponytail into two sections and placing the center piece from the top ponytail down the middle. And then I'm going to combine the three sections back together from the first ponytail and tie them off with another elastic band. And then I'm going to pull on the edges to make the section a lot bigger and more full. And then with the remaining hair I'm just going to combine it all together and tie it off with a hair band to create the last ponytail. And then I'm just going to hide the elastic band so I'm taking a section from the ponytail, wrapping it around the elastic band and pinning it underneath with a bobby pin. I love how this hairstyle turned out. I think this is such a cool edgy looking hairstyle and would be so fun at the gym during the summer. Let me know in the comment section where you would wear this hairstyle. I'm really curious to know. Let me know what you think of this hairstyle down below in the comment section. And if you have any requests for future videos be sure to leave them down below in the comment section as well. Also make sure to like and subscribe and click the notification bell so you never miss a video. Thank you so very much for watching and I will see you next time.


Hi everyone, Joe for Jasper's casebreaks.com coming at you with a brand new release. This is 2020-2021 Panini Mosaic Basketball Fast Break Edition. It's a two box break. Random team number one, one spot gets you three teams in this two box break. So let's triple up these names here, thank you. And all 30 teams are in. Let's roll it and randomize names and teams. Three and a five, eight times for names and teams. One, two, three, four, five, six, seven, and eighth and final time. After eight, we've got Tony down to Brian. Three and a five, eight times for the teams. One, two, three, four, five, six, seven, and good luck. Eighth and final time. After eight, we've got the Raptors down to the Nuggets.  All right, so let's alphabetize by team. I will pause the video in just a little bit for the trade window, but I'm going to flip away from the screen just really quick. So the two boxes is from a fresh case of fast break. You can see on the top camera, mosaic fast break, 20 boxes in this case, pretty heavy here. So let me lean that over and we're going to figure out, we'll do a number of dice rolls to see which two boxes we're going to do. And I think for subsequent breaks, I'm just going to grab random boxes and it turned out to be a lot cleaner than I thought it was going to be. All right, now, one, two, three, four, five on each column, huh? So how about I'm going to shave a box off the top of each of these columns. And so we'll go one, two, three, four, five on the dice roll. If I roll a six, I'll just roll again, two. So we're going to check out that stack right here. Let's remove the other stacks. This is as random as it's going to get. Now, let's take two right off the top here. So now we'll go one, two, three, four, five, six, six, one, two, three, four, five, six. So that's the stack we're going to do and this we'll save for next time. All right, now, we're going to flip back to the team list here. We're going to pause the video. When we come back, we're going to see if there's any trades and then the two box breaks stick around, BRB. All right, welcome back, everybody. A little tiny bit of trade chatter, but in the end, no deals were done here on Wednesday, the 22nd. Two box fast break box, random team break number one. Another two boxes in the store right now. Jasper's case breaks dot com. And it's a brand new release. So I think traditionally these will have. You'll just have those exclusive mosaic fast break mosaic parallels, a fast break, the autograph list is is is a little bit different. So a lot of fun stuff in here and a lot of different parallels to chase and what not. An all card ship. A lot more packs in this than I thought. All right, good luck, everybody. You got a little Orlando magic Atlanta Hawks on in the background. 10 minutes left in the first half magic up 2823. And speaking of mosaic, the hobby edition of this, the 12 box hobby edition of this is on the site right now. It says fast break, but they popped an H two, like a hybrid on the pack. It's kind of weird unless fast break is hybrid. Is that what they're saying? Don't know, says fast break on the case, says fast break on the box, but says H two on the pack. Did they always, did they always do that? Maybe I'm just late to the party on that. Either way, let's go and be a debut obi topping for the Knicks. That's going to go to Fred. So this is the traditional fast break pattern and there's Cole Anthony and Cole Anthony again. Nice 48 out of 85. How is Cole Anthony doing tonight? I think he's he's been having a pretty solid season thus far. Let's go to the box score here. Cole Anthony has not entered the game. Wait, is he injured? I don't think he, I think he's good to go, right? Oh no, he had two hours ago, said ankle will not play Wednesday tonight against the Hawks. So he's out, but he's not having a pretty good season though. That goes to Orlando. That's going to be for Sean Matic. I think in his last 10, last 10 games or so, averaging 20 points, almost five rebounds and five assists a game. He's really hard to look good. There's a Tyrese Maxi NBA debut, regular one here, Malcolm Brogdon, Halliburton, Josh Richardson. I like these national pride cards. I wonder if there's different countries too, whenever that applies. Braun James, Patrick Williams, and a Lamello ball. NBA debut rookie card for Brian Watford and Charlotte. Jayshon Tate's been looking pretty good too. Is he playing tonight? Rockets are playing. Yeah, he's just five minutes, just five minutes into the game. So we'll keep an eye on how Jayshon Tate's doing tonight. Tyrese Halliburton and Yannis, 1985. That's who Jayshon Tate's playing tonight. Rockets at Bucks. Yeah, with all these COVID protocol and people getting injured and stuff, Joe Johnson, did you see that? Joe Johnson signed a 10-day deal with the Celtics. What are some other old-school players? Not old school, but players that may have just retired or maybe just wasn't signed? Maybe we'll see some of them come back. There's Emanuel Quickley and a Lamello ball Mosaic card. Why was that flipped around? Is that a variation? I don't know. Either way, pretty cool. That is for Brian Watford. There you go, Brian. It's a nice-looking card. Oh, is that V for variation, maybe? And then, quickly, we'll go to Fred. Mike wants to see maybe a little CJ Miles. I mean, J.J. Barreo only just recently retired. Maybe he's got a job with ESPN, but maybe he'll suit up and take a little time off from his broadcasting, his day job, play a little basketball. There's Kelly Overy Jr., 7 out of 50 for the Warriors. That's going to go to Brian Watford. I think Sadiq Bae's been playing. He's been starting to put up some numbers recently, too. There's his NBA debut card. Anthony Edwards. And we've got an Isaiah Joe autograph, fast break auto. Rookie auto for the Sixers. Fred with the Sixers. Oh, CJ Miles, one of the guys who got signed because of all the hardship, the hardship rule. Anthony Edwards going to Shawn Matic and Minnesota. JJ Redick, I think is what I meant to say earlier. JJ, not JJ Barreo. Hollywood, so if the Mosaic sells on time, we'll be doing the St. Nick randomizer tonight, too. Why wouldn't we? That's the second question I've got on that. People nervous that we'll just be like, ah, we'll do it in a month. We'll do it in the summer. We'll do that randomizer next summer, Hollywood. No, like I said, at the beginning of the promo and many times throughout, listen, the schedule, how quickly we do this is up to you, ladies and gentlemen. If you wanna fill the last break tonight, we can. If you wanna do it in two months, we can do that, too. I don't think we've ever had a promo all year long where we have, where once the promo requirements are accomplished, we're like, yeah, we'll do it later. Nah, never, no need to wait, ladies and gentlemen. There, I saw some Charlotte colors. It is, so that, yeah, that must be, that definitely is a variation. This one, he's going that way. This one, he's going the other way. Different jerseys, too, very nice. It's another one for Brian Watford and Charlotte. It's Anthony Davis out for a little while and here's your autograph. It's Deandre Jordan. Oh, not the autograph, but the numbered card, 50 out of 50, Deandre Jordan. That's still Nets edition here. Nick with Brooklyn. He's on the, on the Lakers now, so he'll get some more playing time with AD being out. The Tyrese Halliburton, got some for Mike and the Kings. And we've got a Cole Anthony card here, bum ankle, keeping him out, but that'll go to Orlando, Sean Matik. Looks like that's a variation, too. Save those Patrick Williams zizzes as well. James Weisman, Anthony Edwards reveals a Charles Barkley. All time greats blue, 52 out of 85 for Phoenix. It's for Fred. Anthony Edwards base card going to Sean Matik in Minnesota. Matik, Minnesota. James Weisman for Brian and the Warriors. Obie Toppen, Jake McDaniels. Another Cole Anthony, NBA debut, Mosaic. Another one for Sean and Orlando. That's for Fred and the Knicks. Tyrese Maxi for the Sixers, Fred. Got a, another NBA debut, Cole Anthony. Obie Toppen reveals a purple Royce O'Neill for the Jazz. Fred with the Jazz, 34 out of 50. Perusho, and behind Steph Curry is a Tyrell Terry, nine out of 10, Fast Grey Gatto. Nice, the gold parallel. That card is gold. Fred Williams and the Dallas Mavericks. James Weisman, Nash, and Montage, Chris Paul. There you go, gang. That's the break. That was two boxes of the brand new Mosaic basketball fast break edition. We've got more in the store.  Also, we have a full case hobby edition in the store where we're giving away our final two St. Nick spots. So go and get it. Jaspeyscasebreaks.com. I'm Joe. I'll see you next time for the Hoops Break. Bye-bye.


Numbers. Human life cannot be imagined without numbers. How did the humans learn to count? And where did the numbers and their symbols come from? Numbers always, in the civilizational sense that we are talking about, came from everyday activities. How many people are there, what work they would do, if there is an exchange, how many chickens you will exchange, say, for how many boxes of grains. So the first simplest would have been just one number is all you need. And then one mark, two mark, three marks, this is how the number system would have started in different languages or alphabets that we have. Counting systems have been known from, first of all, because the Babylonians, Egyptians, another time from Mayan system, Mayans, Chinese and of course from India. Different civilizations came up with different ways of recording higher numbers. For instance, the Greek, Hebrew and Egyptian numerals were extensions of tally marks with new symbols added to represent larger magnitudes. If you can see, for instance, even today in what we call the Roman numerals, one, two, three are repetitions of just increasing the number of marks that we have. When you go to four, you start using actually five and one in the subtractive sense, if you will, by putting it on the left. So you start then six, again you start repeating. Then when it comes to nine, it's really ten minus one. That's how we would see the number. What we call the Roman numbers which are still used in some clocks and some things. So with those, it is not so easy to do calculations. This has to do with the fact that they are not using the way of writing for calculations. The calculations were actually done using the abacus, or abacus-like device. And it's only the recording that involved the representation. You want to compute, for instance, how much of grains have been produced.  Why is that important? Because you already have a concept of taxation, the kings, the temples, levy taxes. And with the levy taxes, they did not really know how much you could produce. But they would do levy taxes based on what is the land you have and how much you have produced. Therefore the percentage of your product would then be levy tax. Using those symbols, adding, subtracting, still possible. When it comes to multiplying and dividing, which we will have to do if we are talking about taxes, we are talking about, for instance, areas, it becomes increasingly more and more difficult. To write and calculate larger numbers, some civilizations came up with a more useful system known today as the Positional Notation or the Place Value Notation. Conceptualizing, subtracting the hundreds, the tens and one units and then composing the number. This is what is called the Positional System. This is the Decimal Positional System. So let us understand our own Decimal System. Take, for example, the number 231. Here, the number 1 is in the unit's place. The number 3 is in the tens place and the number 2 is in the hundreds place. What does it mean by hundreds, tens and units? What it means is that we multiply 2 by 100. We add 3 multiplied by 10. Let me put in parenthesis and we add 1 multiplied by 1. This is the same as 2 into 10 square plus 3 into 10 to the power 1 plus 1 multiplied by 10 to the power 0 because 10 to the power 0 is 1. So this is the Decimal System. The decimal becomes important because here as you see there is all 10, 10 and 10. In certain other cultures, the system has been different. The Mayans had basically a system based on base 20. The Chinese, on the other hand, had a system which was based on 10 as the base. So something very similar to what we did, what we had. Except that there is no position plotted to 0. A similar thing happened also in the Babylonians. The Babylonians did not have the decimal number system. They had a sexagesimal number system. Just like in decimal number system, we have the 9 digits 1 through 9 plus 0. And so we write 11 as 11, that is 10 plus 1. They had 60 digits and that is the sexagesimal system. However, they had a very nice way, a very clever way instead of remembering 60 digits. They have a very clever way of using 12 as a base to create the other numbers in the first 16 digits. 60 gets divided by many more numbers. So arithmetic is relatively easier with a base 60. But the disadvantage is 60 is a large number. It is not a small number. It still is there for instance in minutes, hours, seconds, which is still on a sexagesimal basis. The remnant of the Babylonian system is still there in our use. But we do not use it as a number base anymore. And the number base, it becomes more convenient if you have something called 10 as a number base. Of course, it originates from our 5 plus 5, 10 fingers. In India, people talked of numbers already from the Vedic period in powers of 10. So they had names for 1, 10, 1, etc. Early times it went up to 10 to 12 and then it was 10 to 17. In the Buddhist tradition, there were even much larger numbers, 10 to 54 for that order. But the Jains actually went far beyond that because they were trying to reach, shall we say, infinity in some way. And trying to reach infinity, their method was to construct very large numbers and say actually the universe is bigger than even this. So that's where it originates from the quest is really a cosmological one. And for that cosmological quest for large numbers, they need to express or show how large numbers can be written. Now, in regards to the concrete, the decimal representation of numbers, there are records. The epigraphic record, that's in terms of writing on stone, comes only from the 9th century. But there are some earlier records, again there are some disputes about them. In the study of ancient Indian mathematics, there is considerable degree of uncertainty about various sources and so on. So in a way, not much is written on stone, as one would say. So the systems were evolving through different various cultures. But this came to be practiced actually both in India and in China. The decimal system was being used. And the Arabs, this went to Arabs. I should mention that, see, Brahmahupta was the one who systematically wrote about how this arithmetic works. And some of these manuscripts made their way to the Arab and Persian lands. And they imbibed them and in fact developed them further. Then it spread to the west from there. The Arabs sort through Arab through Spain and then to Italy. And in the 13th, 14th century, this arithmetic from Indo-Arabic arithmetic was in fact a big thing in Italy. Because the trade was expanding and in fact, I mean, this was still not a part of the curricular education either in school or college. But people used to pay fair amounts to get a tutor who teach their words, their arithmetic in the style that we do today. In the first instance, when you repeat the number again from 11 to 19, the 10 was not represented by two digits. In fact, it starts in Babylon again with the place value notation originates from. It started by leaving a gap over there. So there was a place for a number, but it was left blank indicating there was no number. So the problem comes up is what happens if what we understand is 0 or the absence of a number is at the end of it. Now that space becomes very difficult to understand that there is a blank after this. And if it is in the middle of two numbers, well, you can approximate absence of a number. There is no concept of 0 in such a system. And that's why in our, if you see what used to be called the AD, BC way of counting years, there was no 0 year. Okay, there is one AD, there is one BC, but there is no 0 year because there's no concept of an absence of a year as such. So this problem arises with the place value notation when you try to write it. And then they decided that first let's indicate a sum marker to indicate there was, there is something here, but it's actually has no value. A symbol for the concept of nothing. I mean, why do you need to count nothing? But this really kick-started some extraordinary mathematics, things like the calculus, even our digital age is dependent on things like 1s and 0s. Well, amazingly, mathematics was really vibrant in the Indian subcontinent and we find 0 being talked about for the first time there. From say about 5th century BC to about 5th century AD, the most active mathematically seem to be the Jain monks or the Jains who did a lot of these enquiries and also talked about it and wrote it down. They start talking about the place value which is left empty as you need. And that's sort of the origin of even the word sifra, then it becomes 0. So all this cipher 0, a lot of these things originate from really in different ways. It comes logically from actually the void as the concept. Although the earliest use of 0 has been recorded in several historical locations in South Asia, the oldest so far is a series of birch bark manuscripts discovered in 1881 at the Bakhshali village in Khaybar area of the present day Pakistan. It is the oldest representation of 0. The modern symbol of 0 shall we say anywhere else. But here it must be understood when you look at the Bakhshali manuscripts and what is the mathematics that is there. The third century what have been dated in the third century text or we still don't have dated the all the pages of the Bakhshali manuscript to only a sample of them. They seem to indicate that in this phase, the third century phase because Bakhshali manuscripts is a combination of texts from different centuries. In the third century text it seems it was used basically as a symbol. Still the rules of arithmetic were not applied to the symbol 0. The Bakhshali manuscript is actually quite a complicated document because it isn't just one piece of mathematics. It's many pieces written over, it appears now, quite a few centuries. And it seems to be a document helping merchants to do mathematical calculations. So there are lots of examples and lots of numbers. And this is where we see the 0 because in some of these numbers we see a dot. This is a dot saying there is nothing here. And so this dot is the one that will eventually open up to be the 0 that we use today. The idea of 0 as a placeholder is actually very ancient. The ancient Babylonians, the Mayans had an idea of a 0 as a placeholder. So something like 101 means there are no tens. So we see 0 in the Bakhshali manuscript being used as a placeholder. But why is this so important as a moment in the history of mathematics? Because this symbol eventually gives rise to 0 in its own right. A number for counting absolutely nothing. And this is a revolutionary moment in mathematics. These could be applied to operations with 0. It's clearly enunciated first really in India. It seems that Arya Bhatta may have been aware of it. But clearly enunciation of the rules of arithmetic of the sense is really with Brahma Gupta. Brahma Gupta, Bhaskara Wan, Varaha Nihir. All these now are getting into enunciating the rules of arithmetic. With 0 as a number. So this is something which happens between 5th and 7th century. 0 gave us access to the negative numbers. How? Because just like we can say that 5 minus 3 is 2. But you could not say what is 3 minus 5. Now from 3 minus 5 you can go to and minus 2. You can go to the left of the line. So if you think of the line with 1 starting here, 2 here, 3 here, 4 here etc. What you have done is just added 1 to the left of it and called it 0. Minus 1 is the number minus 1. Just go beyond. Negative numbers were considered valid in a lot of the Indian works. But somehow in Europe there was a lot of resistance or lack of willingness to admit negative numbers. If you are doing borrowing and lending, if you are in trade, how much have you borrowed? How much have you given back? Chinese for instance had red and black sticks for negative and positive numbers. But it was mathematically very difficult for them to think about taking out something bigger than something that existed. As late as 20th century people wrote papers or articles saying that negative numbers did not make sense. Now it sounds like people believe in flat earth etc. But as late as 20th century there are European writers reluctant to admit, think of negative numbers. But on the other hand in India negative numbers are found from very old times. We talked about the evolution of numbers, the place value notation and the use of 0 besides the negative numbers. The story of Ganita or mathematics cannot be completed without exploring the developments in geometry and proof system. That is something we will discuss in the next part of our film. One of the oldest and widespread mathematical developments after the basic arithmetic and geometry was a theorem named after Pythagoras. Pythagoras theorem is something which all of you learnt in class 5. It says that if you take a right angle triangle with C being the hypotenuse and A and B the two other sides, then A squared plus B squared equals C squared. So suppose think of yourself as 10 year olds, you want to play football, you want to mark a field. So this is a typical football field, the world boxes, the line in the middle, the central line and the field. Suppose you have just a long rope and you want to do this. So what you do is you take the rope and you tie knots to divide it into 12 equal pieces. Once you've done that, then you take three of your friends, tell one of them to be on the third knot, another one on the fourth knot after that, and the other one on the end, who holds the two ends together. What you have now is a right angle triangle because one of the sides is 3, the other is 4, hypotenuse is 5. So 3 squared plus 4 squared equals 5 squared.  The first known evidence of Pythagorean theorem actually comes from Babylonia. The Babylonian civilization succeeded the Sumerian civilization and the Sumerians actually, their civilization was quite advanced. They had an administrative and legal system, they built irrigation condensers. They introduced writing using a cuneiform script, cuneiform means corners. They made clay and on clay with a reed marker, they marked things and then they baked it. And that's why Babylonian and Mesopotamian tablets still survive and we know so much about them now. So this is a typical clay tablet which exhibit lots of geometric pictures and there are various such things found. So in one such tablet which is again in the British Museum, there is a nice problem that 4 is the length, 5 is the diagonal, what is the breadth? Its size is not known and they are also given an answer to it in the same tablet. 4 times 4 is 16, 5 times 5 is 25, you take 16 from 25, there remains 9. What times what is 9? 3 times 3 is 9, so 3 is the breadth. There is also another Babylonian tablet, the cuneiform tablet, which in which there is a show the computation of square root of 2 represented in this hexadecimal system which they were following and that certainly involves the Pythagoras theorem to understand the magnitude, one had to know the Pythagoras theorem. There are marks on the side on the left and two on the horizontal diagonal of the square. So there are two marks on the horizontal diagonal and one marked there. What are they? They are the numbers 30, then 1, 24, 51, 10, 42, 25, 35. This is the hexadecimal system, so 30 is exactly like 5 in a decimal system and what we can think of 5 as being half of 10. So if you translate this and if you remember that 30 is half of 60, what is the red line is just half and below there are two things, one is the sixth decimal approximation of square root 2 with this approximation divided by 2. If you do an elementary Pythagoras, so the red line is half, the other line to its left is also of length half, half square plus half square, then square root of that becomes root 2 by 2. It is well known that the Babylonians had the table of Pythagorean triples. Now some people have debated it may not exactly correspond to Pythagorean theorem but on the other hand could be. It is called the Plympton 322. This is just a list of Pythagorean triplets. A 3, 4, 5 is called the Pythagorean triplet because 3 square plus 4 square equals 5 square and these are probably used in practical applications in land measurements and various other things in irrigation canals. So the Chinese civilization is the only civilization which has been uninterrupted. So we know a lot about it because of the continuity. Around 2700 before the Christian era, there was a Chinese emperor, Wang Ti, who took an active interest in mathematics and he is supposed to have composed the text but of course that's lost now but these are on astronomy and mathematics. Chinese call this theorem the Gou-Gou theorem. Gou is the hypotenuse and Gou is the side. So one of the pictures from the book relates to two proofs of the Pythagoras theorem. But till now the Mesopotamian everything, there was no mention of a proof. Here they do a mathematical proof in the modern day sense. One very interesting problem which they have in this book is called the Bent Bamboo Problem. You can see how global mathematics is from here. The Bent Bamboo Problem which says that there's a bamboo which is 10 chi. Chi is the unit of length in China. The upper end of which being broken touches the ground. So it was a rod like this, it broke here and so it has become a triangle now. And it says it touches the ground 3 chi from the foot of the step. They ask what is the height of the break. So you know it was 10 chi, it broke. So what is this height now? So of course you have a right angle triangle. You know that the hypotenuse plus this height is 10. You know this length is 3. You can set up the equation A plus C if C is the hypotenuse. A plus C is 10, the base is 3. So these are the two equations you get. And you also have the equation from the Pythagoras theorem A squared plus B squared equals C squared. So you can solve this quadratic equation and you get the answer A equals 91 by 20. It appears exactly same in Mahavira's Ganita Shastra which was around 850 Christian era. And later in Europe Arabs in this Philippi Kalandri's book called Arithmetic from 1491. The earliest explicitly stated statement of the theorem comes from the Shlva Sutras. Especially Bodhana being the earliest among the Shlva Sutras. Shlva Sutras are part of the Vedanga Kalpasutras of the Vedas. And Vedangas are the so-called appendices of the Vedas. There are nine Shlva Sutras of which three ascribed to Bodhiana, Agastamba and Kadyayana, the Vedangas which are rich in mathematics. The Shlva Sutras specify the construction of Yagye Bhumika or fire altars. Very elaborate structures were described in verse but without diagrams. The most famous of these is the falcon altar which comprises of certain geometrical shapes like parallelograms, rectangles, triangles and various other types. The Shlva Sutras are very specific about these sizes so that the brick makers could bake the exact shapes. There is this Sanskrit sloka there which basically translates to the chord placed along the diagonal of a square, produces an area double the size of the square. If I see this diagram AC square is double the size of the area of the square inside. The square inside is of length AB times BC but AB and BC are the same. Two AB times BC is two AB square which is the same as AB square plus BC square which is exactly the Pythagoras theorem for a square. They also talk about a rectangle. Here they say that the chord placed along the diagonal of a rectangle produces both the areas which the chords along the longer and the shorter sides produce. It's exactly the same thing. The main objectives of the Shlva Sutras was to convey how this structure, elaborate structure is to be constructed and the stipulations of various kinds first of all it had to be in five layers of bricks. Each layer was made up of 200 tiles. They could be of different shapes. There could be square, triangle and then sometimes even pentagonal and so on. For brick building purposes the sutras had to be more specific. So as in the Plympton 322 tablet where there was this list of numbers in the Vedas also in Baudhiana's universal sutra there are lists also given. So they write 3 and 4, the 5 will come 12 and 5, 15 and 8. These are all part of Pythagorean triplets. In the process of doing this kind of work they realized various geometric principles. One of the fundamental things in basic geometry is to be able to draw a perpendicular. Given one line and a point on that you need to draw a perpendicular. These are some of the first things that one learns in school. The method that we use in the school that is taught in the schools was in fact known at the time of Shiva Sutras. You know the Pythagorean triplets, because they are so basic probably originated in each of these three places independently. There is no reason to believe that there was a monogenetic origin for Pythagoras theorem. Unfortunately we do not know much about the Egyptian civilization in the sense that we do not have evidence of Pythagorean triplets but I am pretty sure that they would have had it because if they could build such elaborate pyramids and everything they would be sure they had it. If we could also get evidence from the civilizations in America because they were completely disjoint. Unfortunately again we do not have much evidence but there also they built pyramids, the Mayans, the Incas, the Steris farming and everything. So these are local variations but I would say that each of them are true in their own right that yes these are the areas which reached this conclusion and it is neither that the Greeks we gave the world the Pythagoras theorem and it is also an appropriation of the West to claim it is a Pythagoras theorem. It actually belongs to nature not to Pythagoras. The Greeks as I said because they have geometricized their mathematics more than others therefore they also were the first to establish a formal way of writing down geometry. When you go for statements especially in geometry which are a little more complicated if somebody makes them there is two things firstly there is some way in which they would have arrived at it and secondly having arrived it they would have some way of confirming or validation I would call validation. So proof has the main component in proof is validation. And if you look at what proof we have talked about the Pythagoras theorem it is essentially a visual proof. You move certain squares around you fit it in from one set of squares to another set of squares and you see okay you know they really fit in and therefore they are visually a proof therefore that the squares on the two sides are equal to the square of the hypotenuse. A mathematician will not accept a statement if it is not accompanied by a proof. The complete idea of proof as evolved from the Greek tradition is that you should be able to give a proof which is sort of independent of whom we are trying to convince including an adversarial participant of this debate. You cannot go back and back and back to prove so there are certain things you have to assume they are called axioms or postulates and then we have a certain system of accepted principles of what implies what and then you enter from there to deduce statements so those would be valid statements if you are hired by intuition at some statement being true then it was kind of a duty for you to be able to produce an argument which would lead to that. One such example is the infiniteness of prime numbers. What is a prime number? A prime number is a positive integer which is not divisible by any other positive integer except itself and one. Three is a prime, seven is a prime but fifteen is not because fifteen is divisible by three and five. So a question which is attributed to Euclid which he asked is how many prime numbers are there? There are infinitely many prime numbers. There is no limit. So one way of proving is what is called reductured absurdum or proved by contradiction. He says okay suppose there is an end to it. Suppose there is an end to the primes and there has to be a largest prime. Suppose for argument sake seventeen is the largest prime. You multiply all the numbers from one to seventeen. Then the product is divisible by one to three all the way up to seventeen but you add one to it. Now when you divide by anything there would always be a remainder of one. So this number plus one is a number which is not divisible by any of the primes either it itself is a prime or there is some other prime number larger than seventeen which will divide. So this is a proof. So in the Indian tradition they did go beyond the obvious statements and then they had means of validating that but the validation was not based on this systematic procedure or no systematic procedure was in fact laid down. So in that sense it is true that Indian mathematics did not have proofs. That does not mean that they simply contemplated and found every statement. They had means of, they had ways of arriving at statement. They had ways of convincing their counterparts. The world upapatti which means more like explanation or something like that which played the role of proof in Indian mathematics. If we give credit to the South Asian cultural area for the number system place value notation and zero as it is known to the modern world though each of them might have been discovered in different ways we have to similarly give credit to the Greeks for having reached this more model of proof which is really a powerful method of proof. The mathematics is something which is just completely universal. Nobody is shy of taking ideas from elsewhere or contributing to that. Having a geographical ownership of mathematics doesn't make any sense.


I'm going to be doing every time my boyfriend kisses me. I'm going to be removing a layer of clothing. Mm-hmm. Just want to show her some love What are you doing? Are you hot? Joe are you taking up? What are you doing? Are you taking out your shoes?  I'm here. No! I don't want to! Wait God today is going to be a crazy video.    And he's not gonna know because you guys already know this. Bill is very clingy He's very affectionate loves to kiss me.  We are inching our way up to Christmas I am super super excited. Also at the end of each video. We're doing a $50 giveaway So if you guys want to be entered into that pit-down giveaway, make sure you guys are subscribed Make sure you get a video big thumbs up like check in this video to 20,000 likes and make sure you guys are commenting down below You guys is cash app in order to be entered and we're super excited. We love giving back to you guys This is the month of giving so it feels really good to you know Bless your guys's bank accounts and just help anybody who is in need so alright guys And now let's go over and ask Alexa how many layers of clothing like I'm really praying Alexa comes through today I'm hoping Alexa has my back I'm just nervous because I know how much bill loves to kiss me and it's not gonna end well If I don't have a lot of clothing because then I'll be butt-naked Let's go over and ask Alexa and see how many layers of clothing Alexa pick a number one through ten Here's a number between one and ten I will go with seven Marvel Squad seven is perfect. So let's see. So I have this this is a shirt underneath. So it's one two three Four and then I my socks are five. So I need three more layers of clothing I need to figure out what it is So I'll be right back once I figure this out also you guys are wondering why I am talking so loud Bill is actually at the gym right now and this is the best time to fill an intro because he's not here So when he gets back, he's just gonna think we're vlogging for the day going shopping because we do have to go to Target And a few other places. So there's gonna be vlogging today doing some stuff I decided to do an intro while he's at the gym because the perfect timing guys I got it. I gotta do when he least expects it, you know, all right about what squad So I put on my seven layers of clothing. I have my jacket, which is one my hoodie, which is two the shirt three four Five six, which is my socks and shoes and then I have my scrunchie I have my scrunchie that's seven layers of clothing I'm not gonna count my bra because obviously I'm not gonna rip off my bra on camera Well, I might honestly have to if he keeps kissing me But I have my layers of clothing on and it's gonna be not as obvious and be having this flay their clothing on because right when He gets home He's gonna shower and we're going straight to Target because we have to get some things from there So I will see you guys once Bill gets home and he's showered and ready I am super excited this video on a roll because he is gonna be wondering why I'm removing all my clothing This is about to be crazy.  I guess we're just gonna have to see What is up Marvel Squad? Welcome back to our channel If you guys want to make sure you go down and hit that subscribe button, join the Marvel family Guys, literally we are on what vlogmas day? 18. 18 already. This is crazy. Yes guys. Happy Friday I hope you guys are having a great day and how many days till Christmas last day? Wait, we gotta change this before we say anything else Seven days till Christmas left. Oh my gosh guys. This is insane. Like honestly, it's inching up Unfortunately me and Bill will not be spending Christmas together this year But we will be opening up our gifts on the 22nd, but you guys will obviously see it on the 25th We're not gonna be missing any uploads. Don't worry about squad We're still gonna be posting after vlogmas Monday through Friday literally every day We're gonna be pre-filming like so many videos So we don't miss an upload because we got to stay tuned with our farmers We have not missed one day and I know you guys I love it after vlogmas We're also gonna be doing like we said five days a week model squad Monday through Friday They're gonna keep doing the everyday posting they will even do every day after if you guys want us to do We'll see how it goes. We'll see how it goes. We definitely are doing five days a week after vlogmas This is super exciting I know I cannot wait so guys stay tuned because we have amazing awesome content coming up And oh by the way the reason why I'm going without her because we haven't missed a trip together and forever It's because she wants to stay back with her family. I want to go with my family So it's just something you got to do when you're you know a couple But before we say anything else if you do not know where we're going in this video right now You have you are not subscribed to us yet. So make sure to subscribe to us because where do you think we're going? Where do you guys think we're going comment them below right now? What do you guys think we're going? I'm not doing a title. Let's yeah, let's not tell them Let's just show up at the place all right if you guys are not subscribed you obviously don't know where we're going So make sure to hit that subscribe button turn on post notifications. Thank you so much for being here We're on the road to two million Awesome Amazing love for you guys been showing on our channel every day just everything you guys are so supportive And we are so thankful to have such a strong arm. It's crazy. It's just a never-ending army All right now. It's time to go to the mysterious place that you guys don't know that we're going to see where it is All right, where do you think we are guys? Did you get it right? Should we tell no we didn't we're back at target guys we come here. Oh my god Good blow dryer and I've never heard of a Dyson, but it's like the best blow dryer you can get baby If you call that a good blow dryer you're lying. It's supposed to be amazing blow dryer It is an amazing blow dryer. It was very expensive, and it was worth it So I wanted to come here and get a bin Literally we're always like running out of stuff, and we're always going to target almost every day Target beat-ups hand-expressed those are the three things you need to know if you are subscribed to our channel You have to know those three things And that we love cars and you know just love you guys if you're new also look at her hair guys my right Amazing oh my Mmm, just want to show her some love. Yes, we're gonna be going inside But uh let's go inside see what we can find so first thing on the list We are in the bin section trying to find something cool to put her new fancy Nancy hair dryer in it All right, baby get it down Guys oh my gosh, right Good job little little baby right here guys literally she's always having me care. What are you doing? Are you hot? Right it's not freakin hot in here Why? Mariah did not change she just took her hoodie off for some reason but guys that literally do you show clothes That was a falling off right it came out this far. You're so lucky All right, it's actually really funny because we basically did all that for nothing we got this instead. Let me show you a picture Yeah, I know I'm sorry. I'm sorry.  We got this. It's a white thing It's not it doesn't come with these but we got these so they're white we're gonna put them in there And I think that'll be way better I think the black and then we'll mix so well with the white and think about it You won't be able to see this stuff in it.  You're gonna be throwing stuff in there left and right Yeah, we can put some cute like logos or something in there to make it cool. Yeah guys We just arrived home with everything. We also you did not see this, but we got a scale We thought this one pretty pretty good for the place And I want to start like weighing myself after every workout She was no no you want to grow you want to grow there Okay, we don't We're going to um about we're about to be start cook We're about to start cooking dinner pretty soon, and you know our dinners are fire. Wait. It's Tuesday our hello fresh you come in Wait, what are you doing? You're taking up? What are you doing? Are you taking out of your shoes right? Isn't it Tuesday our hello fresh guys if you don't know we make the most Amazing no I did not did you actually I have to look back But we make the most amazing dinners, and our food is in here today Oh, yeah, but it's gonna be fire I cannot wait Juicy juicy what I gotta get those after travel kisses. What do you mean? Why are you what are you doing? Do you not want to take my Why are you actually right you're being rude? Hey, do you not want to kiss me? My gosh, why are you? But why but I don't Okay, well can we film it like no I'm just saying every time I kiss you.  I'm not I just you know Why you have to take off my stuff all right? That's what I'm talking about What's wrong?  Can we film really quick? I want to I want to close this house because I'm making something in there, babe. Can you are you good? Yes, I'm better now because no I don't That's all off camera All right, let's get our dinner started all right Oh, the lighting actually doesn't look that bad, but it's kind of wack because it's yellow lighting up here We're gonna try to figure out how to change the lighting.  What's on the menu chicken sausage? Kibbutabi bolognese. I don't know anyways. It's with chicken sausage noodles. It looks amazing I cannot wait. I'm really super excited about this dinner. It's not one of my favorites, but it's probably gonna be good Oh, no, it's gonna be great I know we have everything out. We have the zucchini the onion We're gonna say we just talk about this that I'm usually the one that's cooking up in the kitchen yesterday I will give it to you. You did cook in the kitchen. I'm a good boyfriend. I literally cook this girl's meal So what what? That's what I'm talking about. Why are you taking it off now? Wait, hold on wait take it off and we're actually cooking I'm not gonna take it off now. Oh my gosh, babe. Why are you wearing that now? Because you I have to film up now because look at the camera. I'm gonna film like this I'm gonna film you don't all right. Oh, but as you were saying I'm a good boyfriend and I do things right Right, baby. I don't I do things right. No kisses. Why why? Why just wait hold on hold on what you've been asking weird all day. No, hold on Give me a kiss. No, give me a kiss. No. Why can you guess? No Come here. Come here. This is off-camera, babe.  No Come here. No Wait, are you you're actually serious right now?  Tell me am I wrong? Did I just figure it out or are we gonna figure it out? We're cutting this out. You're wrong. Why are you doing that? Oh, that's it. I figured out You did not just do that to me all day. Oh What do you mean, okay? Wait hold on hold on.  I knew you were being sketched, but I did not think it was for a video Mariah Had to come through with this babe. We gotta close the blinds. I gotta take off my pants, babe. Babe.  This wasn't like was this a challenge. It's a challenge. So you check wait So I challenged I made it switch to I challenged it by myself. I did challenge so you challenge yourself Participate in the challenge.  I don't know how she came up with that, but that's smart.  Can you get the gym? I have a lot of how many layers I can have how many I can have seven I don't know a lot. I only kiss you seven times scrunchie. Oh, I only kiss you seven times All right pop the bra off and no panties right now I'm surprised guys. I usually kiss this girl way more. So seven would be like in an hour usually Yeah, no, maybe not our but definitely More than Mariah Mariah's like get that Especially because it's that time of the month guys if you do not know when girls, you know, they get kind of Snippy little I got a little snapper turtle right here.   I was gonna try to see how many layers I didn't have to take off This is a lose for you. You know you were taking it out I don't wait was the goal to like if you like ended the day with clothes on yeah, you would have won Yeah, oh, I would have hated if I didn't win, but hey, I technically won team bill You set yourself up for failure. It's okay. I like to actually help me Babe But we're gonna go off and make dinner.  We're gonna be giving away right now. Let's get it. All right drum roll, please $50 giveaway of this video goes to Thank you so much for supporting us I also know you guys are probably like why is she wearing the same bra again? I purposely wear this bra in these videos because if I take my shirt up I don't want to have a normal on and it's the only like not normal that's still basically too much I don't even want to show it right now. I'm like trying to keep the camera up like guys But thank you so much for all your love and support. We love you We love you. Thank you for commenting down below your cash up liking the videos being subscribed and guys also to win The $50 you have to watch the video all the way through once we see that you guys are showing love liking it up Comment down a cute comment. You might be the next winner guys. We give away every day up until Christmas So let's so get ready tomorrow. You can be the winner and I need to come back guys. You do Stop I did yesterday was leg day. Oh yesterday was leg day at the gym babe. I was hitting the weights hard You know I'm saying I'm saying I was like I was pumping iron babe I'm trying to I'm trying to act too cool. She's trying to act like a baby Love you guys