Good afternoon everybody, hello, how are you? Can you believe it that it's raining today? And cold and miserable what happened to spring? I was just in DC over the weekend It was the sweetest scene it was all blue and that tender green on the trees. It was paradise But this is our intellectual paradise. We are here And I'm delighted to get the chance to talk to you about what is very much a work in progress what I want to talk to you about is how I want to spend my summer vacation and Here's the backstory. I'm Susan Crawford I'm a professor here at the law school and I'm one of the many directors of the Berkman Center and proud of my affiliation with the center, which was very supportive of me I'm a new professor just got here this year so The backstory the really really deep backstory is that I come from a very quiet Background extremely quiet. I now understand that I had an academic childhood I didn't really know that when I was going through it, but at the time I just noticed there was like Nobody talking to us and a very very very withdrawn very quiet And so when I was a young lawyer the advent of the internet the idea of the internet that anybody could communicate with Anybody else without asking permission that anybody could be in touch with anybody else introduce something new Was the most exciting thing that had ever happened to me? I was so lucky that in 95. I was sitting at my desk in Washington, it was a lawyer at Wilmer color and we suddenly had a browser and we're suddenly looking at websites And I remember distinctly the very first site I ever went to I'm from Santa Monica, California And this is a beach house called the spot that was online with this line saying Click here if you want to talk to us these 20-something people and I distinctly remember clicking And it was like the lion the witch and the wardrobe Unbelievable that you could reach back beyond the coats and see these people Extraordinary those of you grown up online. I'm an old curmudgeon now don't recognize how Amazing this is so there is the spot there my introduction somehow that brought me to be on the board of ICANN Which is a little different as an experience But it gave me a real sense of the importance around the world of a globally interoperable Internet and the desires of people to connect. I spent some time in the administration the very first year of Mr. Obama when It was all very entrepreneurial and I learned a ton I had a sort of a tech poop odd job there and what I learned was that there are all kinds of heroes inside government and They're all doing their best to coordinate But it's nearly impossible to get anything done and I had this alarming experience I often talk about these days of going to talk to a senior official in the administration about replacing subsidies for phone Access in America with subsidies for high-speed internet access and he they're all he's so I'm not giving anything away He looked at me blankly and said but phones are two-way All right, so that was alarming and that gave me the sense that there was a lot to be learned In government about the internet about internet access and I also learned that everybody does everything through meetings And I kind of like meetings. That was okay with me. I came out of that I wrote a book called captive audience about the role of the cable industry in America and in doing that I did a ton of interviews with people who all refused to speak to me on the record because they were too afraid of The power of Comcast Time Warner Cable and their brethren who had divided up the country Divided markets and had enormous Influence over the destiny of any business that wanted to be online and Any career of anybody who wanted to work in telecommunications policy learned a lot through doing that I became interested in how do you get politicians to respond to these problems? especially when no one's Boating in elections the worst voter turnout in 72 years last midterm election And the pull of democracy I began having these big thoughts about Democracy and I'd been at the international level and then at the national level And then I decided that cities were really the places where things happened And that because expectations were high because we're all getting used to the internet cities need to resist becoming anachronisms and learn how to govern themselves and give opportunities and understand technology So You're being webcast that's all I want to let you know So cities are big everybody's moving there and that this all led me Love of cities to this the second book the responsive city Which was also a great adventure and for which I did a gazillion interviews with heroes in city halls across America and has led me to be quite involved in the responsive city movement the idea that you use data and Sensors and smart people inside city hall to make better decisions and improve the lives of people in cities And this is a big moment for us cities. It's like our fourth era People were moving out of us cities between 1920 1920 and 2010 real hollowing out starting at 2 to 11 Especially with students and everybody like that. They're moving to students to cities cities are becoming the places for development Suburbs are starting to shrink. So we've been to the steam engine the electrical grid cars These are all eras of cities and now we're in the fiber data era of cities. I now have this Big push in my life, which is to talk about fiber optic communications And I'm going to bring this all together as you help me work on my summer project. So on the upper left is copper wire used for telephone calls our Phone system in the United States was the envy of the world when it was introduced The first national phone system to be beautifully functional We then saw the advent of the cable guys with their hybrid fiber coaxial cables. They are on the right You can carry much more information than the copper phone line And but was originally built to be a broadcast medium So you're sending TV over cable to hilly places in Pennsylvania that couldn't get it That's how the cable industry starts they then devote a little bit of their access to the internet But most of their digital channels are devoted to their own content their own ways of slicing and dicing want to hear more about that I can talk your ear off about it, but that's the cable wire and now we've got the future proof medium for Data as far as we can tell is fiber fiber optic these tiny glass tubes another dreamy slide about fiber That have are that are lit by lasers carrying as far as we can tell unlimited amounts of information If you get the lasers tuned right and split right they can carry gazillions of phone calls So you only have to know about four wires for my little talk Copper wire was used for DSL split into two frequencies and digital subscriber lines now known as the new dial-up People are running from it in droves That's the cable plant hybrid frap fiber coaxial little portion of the pipe Allocated internet access high capacity downstream really cramped upstream unless cable rebuilds everything fiber to the node Getting fiber deep into neighborhoods But the problem is that you then use copper 18 t does this to get into houses And so your ability to participate remember my lonely childhood to be part of the world is a little cramped relying on fiber to the node because You're you're have to be very close to a central office to have very high upstream or downstream speeds And then the gold standard, which is fiber to the home potentially unlimited capacity Easily symmetrical which means easy opportunity for creativity uploading as well as downloading Future proof all you do once it's in the ground is upgrade the electronics. That's it Here's the problem for the United States as a country our fiber penetration is far beneath Jet Japan Korea Sweden Estonia Norway were weighed on the list behind Luxembourg and the Netherlands and Only a step ahead in fact We're only step ahead of Mexico when it comes to fiber to the home penetration in the United States This is the OECD's most recent figures and as a country. We're stuck We're stuck. So here's the basic map if you talk about Internet access as anything over 20 200 kilobits a second like really minimal internet access Here's the story in very low density areas about 5% of the country Low numbers of adoption DSL that copper connections really strong Satellite and fixed wireless are also important. So if you grew up in rural Vermont This might be what you're relying on a satellite connection that's very capped Doesn't allow you to use a whole lot of data Somebody told us yesterday that you would burn through your monthly data allowance in one hour If you streamed video over your satellite connection in rural Vermont pretty pretty amazing Low density airport areas about 20% of the country Cable is not dominant. There's a very better value proposition than satellite fixed wireless or DSL Yeah, I'm sorry Universal service funding support is the federal government is subsidizing Copper line connections continuing to subsidize them. So that keeps them entrenched In the majority of the country, we've got a very static world where telco has about 30% of the subscriptions It's mostly DSL and the rest is cable and then in very high density areas like Cambridge, Massachusetts Cable dominates so you have no choice other than Comcast and Cambridge and there's a little bit of fiber to the premises Verizon has built out to Now about 8 million subscribers and has with its files fiber product It's actually sold off its systems in Texas, Florida and California Well, we have a little bit of fiber to the premises and we have no national path to make it upgrade to fiber The cable companies long ago divided up the country. They don't face competition between each other Not only that but in some of those big square states in the west of the country That they're telcos that don't themselves compete with anybody else either so lots of service level power Wireless I'm gonna speak more about wireless because that's one of the key decisions We have to make how to how to push forward with new generation wireless in company with fiber But it's it's complimentary. It's not a substitute for what you can do over a wired connection Most people who have a smartphone also have a wire at home It's very closely related if your smartphone only it's very likely that you're poor or have fewer opportunities And so the big picture so that whole script was about Broadband at very low speeds as we move towards the future anything over 25 megabits per second There really is very little choice 20% of homes can't buy it at any price and Taken together about three quarters of American homes have no choice in providers and prices are unperturbed and it's all cable Which is again very cramped on the upstream Complete pricing power and no particular incentive to upgrade to fiber Which is the better and future-proof technology around the world This is a particularly terrible problem in inner-city America 60% of Detroit residents don't have a wired home because it's too expensive Expenses very highly correlated with non-adoption in many of our big cities in America and smaller cities very low Internet adoption at home There are a bunch of cities This is a brave little map from the Institute for a local self-reliance A bunch of cities across the country working on installing fiber on their own sort of trying to do it And I'm very proud of team fiber and Dave Talbot here at the Berkman Center who have put out where as Dave I just saw you there you are a terrific report last week about the situation in western, Massachusetts where towns are trying to do this for themselves But it's very difficult So what's amazing about this in the big picture is that around the world fiber of the home is exploding China plans to have more people on but more new people on fiber than all the existing subscribers in South Korea today They plan this year to convert more people to fiber than everybody in South Korea that's huge and Fiber is growing by 60% over the last year that we know about 2014 to 2015 around the world cables very small in growth around the world big in the United States small every worlds People are fleeing copper. That's the diminishing almost 20% of copper There's there's some growth in fiber to the node Satellite grows wireless grows, but it's real That's the remarkable thing that around the world fibers a big a big deal and My vision of the future is that this becomes akin to the internet stack That every every city in America should have Fiber available on a wholesale basis. I'll talk more about that if you'd like Which means available for lease to any retail provider so that you have a competing thriving market in fiber optic two-way Unlimited communications sensors open data screens algorithms. This becomes the way we start seeing the world through a Multi-layered electronic visual, but this all sounds a little inhuman Let's do a little bit more Google self-driving cars going to produce a terabyte of data a Minute a gigabyte of data every minute Everything we want to do for science and agriculture and small businesses is going to depend on fiber Cloud storage data processing sensor data is going to be overwhelming We really need this no delays unending increase in capacity and it's cheaper in the long run if we upgrade because copper This rain affects copper badly That's why your phone service landline phone service if you still has it have it goes out when it rains And a fiber it doesn't get interfered with in the same way Wireless, you know remains a really interesting world, but you need fiber for wireless There's a big potential for fixed wireless point of sight communications to carry a whole bunch of data But that data needs to go somewhere And there's especially issues with availability of backhaul for wireless all what I mean by backhaul is just You have to think of a wireless system as 95% a wire and that the wireless that you're using is like an airplane That airplane needs an airport to land in and so if you say well all we need is wireless That's like saying all we need is airplanes no airports You need a wire for your communications to go to and travel around the world So there they're wireless is fascinating and we need to make some great decisions about that the fundamental one is fiber So this summer what I want to do is write the roadmap for the future for America and say This is what we won't be unless we make this upgrade now each chapter is going to be about one of these sectors We won't be the leading health care nation in the world. We won't have energy Interpendence we won't achieve a transportation revolution here in America. We won't have the best education available to everyone We won't be engaging our citizens because we can't the whole thing's built on sand unless you can move data around We won't be exploring space. We won't be building respect for people with disabilities We won't see the creativity explosion They'll see in other countries that have made or are making this upgrade and this all amounts to new jobs As well as everything else I got really fixated on the idea of human presence as the killer application for fiber If you've never experienced it if you're on a fiber connection with somebody else It's as if there's just a pane of glass between you and them No latency no jitter no delay totally human and what that makes possible is eye contact and That makes possible all kinds of engagement that we're not capable of carrying out over Existing cable connections Here's my example of this Researchers tested two rabbits for tricks the rabbits that's making eye contact with you is the rabbit you're likely to buy and How about that? How about that because eat we can connect to a rabbit right and kids That the cereal manufacturers know this and so they they have downward-looking eyes So that because the kids are in the aisle looking up and if the kids connect with the character they're gonna want the cereal Right how fundamental is that so fiber is gonna make this all possible? So I just went to struck Stockholm. So I got you right so you're not gonna forget the rabbit if you remember one thing You'll remember the rabbit. I just went to Stockholm. That's me peering because I'm too vain to wear my glasses I probably should be wearing them even now What they're showing me in Kischa Science City, which is this totally cool enormous innovation area outside Stockholm Where there are three universities thousands of startups and giant companies they're showing how? After you got home after having experienced a stroke a doctor using a fiber connection could be on the screen guiding you through your exercises, right You can connect with that doctor because again, there's eye contact compassion empathy connection And their suites their arms are all folded, but I'm totally excited I think this is a thrill and in in Stockholm. They're carrying out some pilots with older people trying to help them stay at home I have an aging parent here in Cambridge I care about this a lot help people stay at home and not have to go out and slip on the ice Go see a doctor because you can actually visit your doctor through that pane of glass I'm a violist so I care about this wouldn't it be cool if you could actually play together at a distance And you can do this with these connections There's no latency no delay you feel as if you are in the same room and until you've experienced it You're not going to believe me so I'm just going to keep talking about it. I Also heard this story in Sweden. This is called a synchotron. It's being built outside Lunds, which is a magical place in Sweden Synchotron pretty great, huh? That's it's a particle accelerator using magnets to focus light so intently We've never seen light like this before researchers go there to examine the atomic level of materials pause Imagine if you could see the atomic level of a drug of a Substance in nature. You could actually begin to understand how it's going to interact with everything else in our world This is extraordinary the researchers though when they go to Lund to the synchotron have Giant capacity hard drives in their briefcases because you can't stream this data over existing Connections in Europe you might within Sweden where there is a lot of fiber, but nowhere else Also, giant implications for research for everything else. We want to learn you have to have this point-to-point capacity in place Civic engagement also this is part of the story. This is something we won't have without making the upgrade to fiber Where we could possibly see our government acting? I'm enthusiastic about this We with a thick mesh of civic engagement people would remember what the role of government is in their lives And wouldn't be just you know, I pay you taxes you deliver me services, but a much richer connection They're also talking to me in Stockholm about wanting to be the smartest city in the world by you know next week Using sensors and electric cars all of a sudden this all requires fiber in order to work Understanding your environment understanding how things are moving around here city They're they're polite so they say target sport city question mark but they really do intend to be the the smartest and This is also a huge implications for energy being able to track energy use understand it And connect that to use some public spaces and Push a lot of this into open data formats so that businesses and citizens can understand what's going on all all all based on this substrate of fiber so That this is what I'm doing what America's future won't be I want to make it really optimistic And pull in all these stories from around the world. I have to go to apparently I've been told I have to go to Dubai and Singapore I've been to Stockholm and Seoul and last year went to Cuba, which gives you the other side of the story. It is wrenching so awful and China is also an interesting part of the story I have a couple more trips to make clearly, but a lot of this can be done with you know Bright people working with me just dreaming about what we could be what we could be as a country and won't be unless we make this move so That's that's my allotted time That's what I wanted to talk to you about and now I would like to brainstorm about what else We might not be or what I should be working on this summer because I'm just devoted to this I'm not going to travel and she says she always says that she does stuff But I really want to just sit down the only way to write a book is ABC apply bottom to chair You just sit down. Don't do anything and I have a whole bunch of material from trips and and learning and everything I've been doing with fiber over the last three years, and I'm trying to pull it all together, but if you were me What would you do? Come on. Yes What I would like to know more about oh, thanks beatbox time What I would like to know more about is this whole idea of data caps and how they came to be like You know from where I'm sitting it seems like it was a scam to begin with oh, yeah There's you know We've got point oh one percent of our customers using this much data Which is going to hurt everybody blah blah blah and then boom data caps, right?  Yeah, you put the cap way out here And you say well what could be more fair than that? You know Americans love fairness is one of our most treasured values and so you say well It's only fair that people that are using more data Should have to pay more after a certain part and as far as we can tell it's only about 2% of our users right now doing that So of course we should do well given all these developments that usage cap becomes incredibly helpful You you're able to replicate in the wired world What you have in the wireless world right now? This is why you wouldn't substitute your smartphone for a wire because you would hit your data caps and start incurring overages Very quickly if you if you tried to swap out all let's say the TV watching You're all too intelligent to be doing that but all the TV watching the most people do from a wire to a smartphone You'd pay $500 a month for that smartphone, so Yeah, data caps are enormous, and how did that happen it just happened and because we don't have a competitive market And the Commission FCC at the moment is not taking on things like rates We have nothing to say about it. So that's why I'm so interested in just Avoiding the cable guys. I should have put a big picture of Jim Carrey here I have a wonderful one avoiding them and moving right to fiber Yeah Where in places where there are multiple providers such as summer bell Which has both it has two cable providers serving the whole city or places that have both Verizon files and and a cable company Are things a lot better there and if not why aren't they two doesn't make a competitive market? What we see is it's like Shamu and Godzilla, you know They're both invented and huge and they kind of pretend to fight with each other, but they don't really Too much. So they're the pricing is is is more similar than it should be and I Economists will tell you that it takes for European economists often say it takes four competitors to actually fight with each other There's it's too easy to signal and it's too much in the interest of Remember they they have fiduciary duties to their shareholders To pay off, you know to keep share prices high To drive as much as possible into dividends Some of the highest dividend-generating companies in the country So they want us to feel as if this access is a luxury not a utility and so that's the way it's marketed That's the way it's felt and these cities that are taking the big moves to go towards fiber and make it more of utility We'll see giant spillover effects in other parts of their economy But that money won't go right back to the fiber company So it's just a totally different mindset different model and in Somerville and places on the east coast where there is some files and some Table we're not seeing huge competitive effects looking for yes. Can we have a mic over here? Sorry? I've got a mic over here I'm gonna trump you. I'm very gray. Hi I'm in charge. Okay I was looking at her because I knew she'd I I'm really excited to read this book and I want the book that will That will challenge Recentering fiber as the new technology that if we just have that technology there It makes all the difference like something that will with your analogy of the airport not just say Yeah, we need airports as and we need wire But that we also need roads to the airports that are support infrastructure for people to actively participate So even literacy we still don't teach, right? Basic tech or media literacy we treat it like it's a given or an obvious thing So I guess that that would be my push is to see how this can How this cannot replay a lot of the conversations around digital access and I think Paul Demaggio and Esther Hargatay's work on digital inequalities is the thing that I want kind of Worked through in this that there's still these inequalities that aren't about having access to fiber So sure although yeah, no, I got you and I talked to Esther a lot about that work when she was doing it.  I have I'm with you Yes Thank you so much for for speaking on this My name is Caroline Trone I'm a researcher up at the Fletcher School of Tufts And I work on a project called the digital evolution index measuring the rate and state of digital change around the world And this element of access is such a huge issue because you can't talk about digital evolution unless people have got access I was wondering how do you solve the the last mile issues and costs? And you brought up the example of rural Vermont, but we're seeing this even in New York City where The pass-by regulations make that people don't get fiber to their houses And as then wireless broadband going to be the stopgap issue to to help overcome costs related to the last mile All right, we've got three different things in there. So but I love this Yes, there is cost involved one of the great things that we're doing here at Harvard is is the team fiber effort, which is a Lot of it is devoted to Lowering the barriers to financing solutions for Whole sale fiber. Here's the problem. There's a lot of capital sloshing around That would be interested in being directed to Projects that will pay off until the sun explodes, which is what this is it doesn't pay off at 20% But it pays off a modest rate of return forever once you get people signed up, but we have to find ways of Lowering the cost of access to that capital. So for example, I've written about Taking a hard look at the buy America bonds that were set up at the beginning of the Obama administration that made available to a Foreign banks and Sarvons around the world and other kinds of corporations the ability to invest in American infrastructure and passed along to those borrowers Subsidy basically a small subsidy that made it worth their while to borrow the money The problem for municipals right now borrowing money is that they only have access to people who are looking for a Right off against their taxes and all those foreign banks and other guys don't need to write off against their American tax Taxes, so we're limiting our access to capital. We also just have to make it simple a lot of banks don't understand this product don't understand how it could be financed and I were hoping to put out lots of playbooks on exactly that New York City So I have a place in New York care a lot about New York and it has not happened One of the big problems there is that the city has not acted as the regulator It actually is city has regulatory authority over the conduit under Manhattan in the Bronx and has just Sat back and okay short story about telco consolidation There was a time when there were bristling wires all over New York City for telephones And they all fell down on the hurricanes. These were competing telephone companies kind of battling it out New York City said forget it We don't want to have all these wires all you guys have to cooperate and go into one tube underground conduit We're going to call it Empire City subway, so that was great So you still had a competing phone market, but they had to go under Under the sidewalks and the city was the regulator of that conduit. I'll say it's fast-forward all of those phone companies have Consolidated so it turns out that the entity that is Empire City subways is now a subsidiary of Verizon Yeah, and so it owes two allegiances it has a regulator, which is the city But when the phone it gets answered it's answered by an Verizon employee who has no particular interest in opening up new conduit or making it available at a reasonable price So all kinds of problems and the city could have been more emphatic Here's a huge problem for cities that the Danes are shocked by every American city gets five percent of the Pay TV revenue of your local cable company That's a lot of money and you could put that to very good use for all kinds of good digital projects You'd have to run the risk of cutting away from that Stream of income coming to you as a condition of moving towards an open fiber system Which in the long run would be much more Beneficial to your city than getting that little five percent, but mayors aren't in office forever They're in office for a short time. So they're they're a time rise is short So that's the New York story and it's it's a trail of tears Wireless could be a stopgap what I worry about is that everybody says oh, we're fine We've got wireless just as we said we're fine We've got cable and we're not fine and that's why these what's happening in other countries is more relevant to me Other markets that are developing that won't happen here. Yeah. Yes. So how over here Well Susan my two suggestions for your list would be addressing climate change in creating a more equitable sharing economy Okay, the innovative Economic development that goes along with both of those. Okay, that's great Yeah, energy independence is a kind of a shorthand for that, but it's got to be more, okay Thanks Hey, what else would you do if you were me? Well, it's all do I would worry about keeping all this Democratic that they're not be concentrations of data and sort of privileged surveillance enabled by You know all the sensors You particularly see that in the quote transportation revolution on quote where I mean Google's link New York City is actually You know, it's marketed as free Wi-Fi For digital equity, but it's really a you know a sensor platform and an advertising platform And Google has more transparent knows about how we move in ways. Nobody ever has and You know concentrations of data are going to be Concentrations of power just like concentrations of capital are That's very useful I think of uber along those lines too because uber has a ton of data that will be facilitated by all this and and could launch the only fleet of self-driving cars Based on all their data and based on what that concentration of data, you know The so up the stack you're right There are all kinds of problems that could emerge in concentration of data I guess I'm preferring to lay a little low and just say let's make the fiber as open as possible and then hope that our competition authorities And others I've realized that's a duck But I'm trying to look at the positive of this and that that's why I'm so focused on wholesale fiber The story in Stockholm is that 20 years ago the city fathers Decided they didn't want to be under the thumb of any one incumbent They wanted fiber and they only wanted to dig up the streets once they're very neat So they said we're going to do this. We're gonna gradually lay down Passive infrastructure so those glass tubes, but no lasers through them not lit not competing in the private market just a whole sale It's like a street grid Stockholm put that dark fiber It's called down first to businesses and now they reach a hundred percent of all businesses and all Residences in Stockholm every time they get a new flood of Syrian refugees. They said oh, okay And they open up more rail lines and more fiber. That's just it's just infrastructure basic infrastructure And there are a hundred competing providers Available in Stockholm when you flip open your laptop not just providers of internet access service also things like, you know Dedicated health services home security. Maybe they're not as worried about that as we are But just many many different kinds of things happening on top of that fibers The city made that possible it long ago paid for itself. It's now a source of revenue The leasing operation of that fibers a source of revenue of Stockholm. So it's a great story. It's so sensible and I'm never embarrassed to be an American. I'm very proud to be American but the when I met the mayor She said I'm just so I'm so sorry So sorry, you know, what can we do? How can we help? So you have to get used to that when you talk talk to them about our situation here because they they are stunned How bad it is? Okay, yes, Bruce It's our situation as a result of our politics and it's I think as you're writing this I'd be interested to know What is it about our politics that will make this a challenge in particular to the United States as opposed to Stockholm or Dubai or those other countries and What how can we prevent this move to fiber from being co-opted in the same way that? Wireless or cable was because I'm gonna read this and say it's gonna be the same old We're gonna come up with these promises and ideas and in five years. It'll be two companies again That's really how can we make that not happen? Yeah That's great. Yeah, it's this big flip I think I've got to somehow argue that that it becomes viewed as as a street grid But that takes enormous that takes videos, right? We got to do we got to reach people it takes Stephen Colbert, I mean something in his old incarnation it it takes What was who's the guy? John Oliver it takes John Oliver That's what we need is his explain it This is just basic stuff is just like running water and then if everybody agrees then the mayors have more Political cover and then they can take the brave moves and then gradually as percolates up to the national level What I'm really concerned about is that this doesn't appear to be on the radar screens of any presidential candidate It's not relevant and yet it should be because that's this is where all these future jobs are gonna come from in a future middle class But it's it's politically View it as pretty dangerous, but just ten days ago the president Criticized in a sense the cable industry by making a filing saying these set-top boxes. Why are we paying so much for them? And that that was quite a moment. I eight years ago unthinkable unthinkable that The cable industry was really viewed as untouchable and now they're more like big forma big tobacco Something is having a choking effect on the country And so we may be able to make this this political move, but I agree with Bruce. It's otherwise. We'll just recapitulate the whole thing Two thoughts Susan. Yeah, so one is I think your book is gonna have to Burst the Silicon Valley bubble like I think there's a perception that America is the most Innovative nation, you know Google and Apple are doing all these amazing things, right? You know look at them We're so far ahead. We don't need to worry, right? So you've got to engage with that I feel to show that there's a problem The second thing is I feel that Americans much less than Citizens of other countries like say Canada like say Canada Don't care about cross-national comparisons, right? The fact that oh, you know our we're like 26 on the OECD ranking on whatever Doesn't register as much as a our state is so far behind like look at our state compared to the you know The 50 state survey is sort of like a dominant mode of analysis And if you can find a case study other than Chattanooga of a place where you know things are happening in the United States There's been like, you know, maybe Chattanooga is good And hold that up. I think that would be really effective. That's really really helpful. You're right We're parochial. We don't care what these other countries are doing. Yeah, and there are some cities Unfortunately really is Chattanooga that's coming to mind because it's the most well-developed and they're using it for a smart grid Maria's doing a wonderful work on this as well as other uses and they're seeing big companies move to town But it would be good to get others get get more of a story The problem is if it's just you in America that has the fiber connection sort of say I'm here I'm here, but there's no one to talk to So in the Google Kansas City demo place, they took me to they said just zoom in on that painting. Well, that's fine But you know, it's not really, you know, the little pods. It's a critical mass problem. The little pods of fiber and that it's not everywhere Here's a cool experiment the librarians in Kansas City in Burlington, Vermont and Chattanooga all opened up fiber windows in their kids rooms So that the kids could play with each other talk to each other get used to having this fiber connection Among them and I'm excited. I want to know what that what happens there And a friend of mine with a string conservatory in Macon, Georgia's opening a fiber connection to string players in Miami so that they can do that string quartet thing and I'm really excited about that. So once we have some visceral Okay, string quartets are insufficiently visceral Something that grabs people's attention about music making what? So it's always sex there's this great book obscene profits that tell talks about the adult industry going ahead of everybody else every single time and with all this Kevin Kelly has just been exploring magic leap go look for this and wired and The magic leap is actually going to put little images on your retinas and it will overlay your physical world with other images Okay, so just imagine that plus haptic devices. Just let your mind wander anything's possible And that is probably a direction where we'll see some investment But eat that maybe I should go talk to some adult industry people and get them to be on my side. Yeah Okay, okay anybody have any contacts like it's That's like that's a good one. Okay What else? Yeah Here's my coming. I Just want to follow up on that thought because I think if we can change the Expectations of an upcoming generation right we will actually change what we do And I think we kind of seeing that in the election right where we really do have a generational gap Yeah between what you know one generation thinks we should be doing and what we're actually doing Yeah, that's absolutely right and for younger people this sounds like well She's talking about air of course we need more internet access of course we do it's essential for everything and they should expect Cheap, you know basically unlimited access that's my Mac talking to us and it would be good to Foster that make that expectation even stronger and not make it feel like perhaps the Sanders campaign may feel now like you're sort of Like my big brother five years older would put his hand on my head and I could flail away with my wrists But it made no difference and if you feel like that about this issue that could make it even worse But then everybody will flee America and go live in other countries Or go live in the places that have fiber. I do think you would be dumbed to buy a house these days They didn't have this connection and dumbed to move to community that didn't have it So that that should have a big effect In fact So what are some of the things that each of us in this room could do within our own little bubble? Over the next, you know five years to to help this cause and make sure that we get infrastructure appropriately well good question I think Every university should be a platform for convening the local officials people who know something about fiber the activists to Make sure that people are having the right conversation And are learning from this very friendly community across the country that trades information about fiber learning from best practices understanding financing possibilities Making it just a common question for every political race every debate of course we're gonna have fiber So what are you going to do to bring that about so for me the franchise model would be to have these neutral but really powerful sources of community organizing Everywhere and lend whatever expertise you had to it, but since you're here I'm gonna make sure that you you work on ours But they're gonna be gonna be others too. I hope that will emerge Yeah, you're a resident of any of those cities and aren't involved want to be you can talk to Saul or I about Yeah, that's important because it's hard to get people excited about this stuff and there are efforts going on Right, that's why we need this human story to get the more excited about it and lost opportunities lost generations All that is gonna help right now Yeah, so Patrick's on the Cambridge Broadband Council Task Force as is Saul so these are there's they're talking about it They have a consultant. They're working through their plans, but they could use I'm sure energy Yeah, it's all it's the so this region is starting to bubble up which is good and actually be happening everywhere in the country So yes, I was wondering are you think universities are doing enough? I mean like like here. We are at Harvard, you know, we have you know Presumably a connection to the internet backbone here and yet you're you're describing to us these things that that That if we could only see them we'd understand how great Fiber could be right and so I'm wondering why we haven't seen them here You know like like shouldn't fiber and you know the amazing things that that that this ultimate high-speed broadband can do Shouldn't it be like a visceral part of every curriculum and of every class so that when students leave Harvard or any every other university Can afford to do that they're going to their businesses You know their next places of employment there when they're looking to buy a home, you know Whatever it is they're saying I cannot live without this because I just had four years of this amazing thing And so, you know what what more can we be doing here at Harvard and at our peer institutions? To help create that kind of environment. It's a great question And we clearly could be doing more like even in Cambridge Why is why are Harvard and MIT not part of the Cambridge broadband task force discussion? What's going on here? Surely they they have assets to contribute Kira has your hand up Thanks for talking about this. I've loved hearing you talk about it all the time. Um So something that maybe you touched upon in different ways, but wasn't expressly outlined in this list is you started this talk with bringing up the massive shift to large urban communities and many of the communities that have sort of taken it upon themselves to build a Fiber networks for their communities have not been those larger areas, but actually more rural places and it could be You know, thanks to the potential for teleworking and Small and medium enterprises like you mentioned it could be a way to sort of Slow that shift to the super urban and also preserve smaller communities Allow them to be more robust in their economies and you know appeal to those people who Really don't want a large urban setting to live and raise their families But right now feel like they have another option. That is terrific. Yeah, great things come from small places And there's no reason why you should have to move away from your town Just because you can't work remotely and keep your next generation in place So tiny towns all over the country have done this kind of thing and talk about that value and it's very important to keep that On the list. I appreciate that Hi, season. Hi, this is fascinating I'm still astonished that our leaders and policymakers. This is hasn't been on their radar for the last 20-30 years at least, right? and I'm wondering if you Track this back somehow as another sort of fallout at the end of the Cold War and the sort of sort of loss of the sense of having to think nationally and get our all of our Young people educated in a certain way starting from president Eisenhower with the highway infrastructure, right, right? That is the exact exact analogy and you know gore was sort of laughed out of the room for making That exact analogy right once upon a time about the internet super highway Do you think that is tied to the political question that a couple of people in the room have asked the sort of just Dispersion of a lack of even just if you want to look at it as a sort of national egotism around prestige Right the idea that we're that far down the list Among our our peer countries and some we wouldn't consider or wouldn't want to be in the same room with yeah It's interesting. It was almost the image of the Soviet astronaut or or the Sputnik rocket The thing that could be seen that got there first. Yeah, this has been so so slow moving We don't have that totemic that moment that gets everybody into science grad school and drives money into it It's just as important I think But but you're right. We we need to make this like that Sputnik. Yeah, that's sort of economic regulatory Vacuum that opened up in certain sectors at the end of the Cold War. That's a big thought. That's a bigger thought than I've Had in months. It's big thought Yeah, thank you for that. That's really that's really useful Yeah, and Eisenhower had a kind of appeal that no national leader has you know He'd been a great general. He was sort of viewed as bipartisan tremendous leader Just so well, we need this and it happened So we don't seem to we don't do that and we're not worried about other countries because we just Say where we are except we are worried about terrorists, which makes us do things unreasonably sometimes. So I you know I don't know but you're right. There's there's some big shift Deregulation market will solve everything. We don't need to worry Industrial policies become kind of a swear word. You say something should be an industrial policy people say, oh, we don't do that in America and That's a problem because these other countries do and there's some things where it would really help to have industrial policy Oh, the dahlia. Oh, yeah Just kind of picking backing off the last two comments. I do think What you started with the human element about this I think is a critical piece of this I mean is what could tie together the drier elements of this thinking of the John Oliver narrative. I Think really doing and it's difficult research to do I think but doing some empirical research as someone who's experienced that Fiber to fiber and saying connection through like a Cisco conference room It's a very elite Environment and how that could impact individuals on such a Fundamental level I think is such a key Element of this conversation. So I definitely would spend some meaningful time on that just to Tie together why this is so important because I think that's where you get The local regulators to start thinking differently about this if they can think about how to talk to their own citizenry if they can think about How this impacts them in the short term to your point about they're only in office for x amount of time I think that human element is really important and to be able to Convey that would be really really powerful. Thank you. That's really helpful and every once in a while I think I'm thinking about compassion and empathy too much and I should stop But actually it's at the heart of this and I think it does connect people to the need for this I think the fact that here's some empirical stuff this enormous Blunk of older people that I'm gonna be part of How are you how are they gonna have you know a sense of connection and and this will reduce isolation? I mean that's the hope So that that's great. It's great and and also allow everybody to do their homework the homework gap. What's that? Right. Yeah, right, which is a much better place to be. Yeah Another one from Bruce unless they're new hands. Oh, here's a new hand over here on the right Hello Just a short point but one one element that could be very interesting is exploring a bit the paradox that we're having right now of Being at Bergman and always reeling a bit about big data and all of the problems that go with big data and at the same time advocating for big error data more speed more capacity and And and for example, if we have more data as you have shown the Example of self-driving cars. Yeah, we're already at a point where we have Nondiscrimination of data that's not usable anymore. Just store it in service somewhere more data will mean more capacity for servers for more more Storage as well. Maybe more power to the cloud entities that hold that hold these data So it would be nice to explore the sort of butterfly effects that could happen with fiber. Oh, I appreciate that and I I Think for me personally the benefits of data uses Could be so human and are so great and do touch so many different industries That I tend to be optimistic about it and also having more More competing providers lowers the risk. I believe of intense concentrations of data We'll see yeah Bruce. So the compassion point. I think it was really important Yeah, you're making an argument at many levels. Yes economic levels But fundamentally you're making a psychological argument making an argument about human connection. Mm-hmm, and I Think if you ground that argument well It'll motivate a lot of what else you're saying whether that's two stories or research or data or anecdote I mean, I don't know but you're making a very strong statement about the how this powers human connection That has all of these follow-on effects. Mm-hmm. Yes, really helpful I think it's really would be be a good motivator great and this really came home to me I went to see the young man who started the virtual reality meetup in Stockholm and I said, you know what? I'm really interested in his eye contact And he said he kind of like twinkled. He said well, yes We're working on that because it would be really great for people in virtual reality worlds to accurately track your eyes So they know exactly what you're looking at now, obviously the commercial Applications of this are enormous. We know what you want to buy where you're paying attention But the human possibilities are also enormous So this whole idea the eyes expressing so much and are not really being able to see them using existing Skype Connections I think it's could be a grabby thing and I want to I want to hang on to it And if the gaming industry is looking at it that means the adult industry is looking at it Which means there are other drivers that will Help the whole thing along. Yes, Adam Thank you so much Susan. I know I keep it positive So some other time I'll ask you about the privacy implications of collecting all the wonderful data Well, that's that's why I keep talking about wholesale fiber network So they're a whole bunch of competing providers. I mean that the censored city that sort of thing Surveillance aspects. That's why we need wise policy leaders who have been trained at Harvard Law School But I want to I want to follow up Bruce's empathy psychological right and the Sputnik idea and I think I think I would love to hear more about perhaps You've already been thinking about it. But is um You were saying who knows somebody in the adult industry. I need to get them on my side And it seems like the question you really need to be asking is To my ear as we frame this this is just Painfully obvious. Yes, it's been so much sense. It's be so wonderful. Why aren't we doing this? There must be someone who doesn't want it done, right? The status quo does not want to have it done So who do you need to get on your side? Oh interesting? People who are actually worried about national security will worry about this sometimes there are lack of a resilient communications Multiplied redundant communication network that conjures up how the DoD is at the forefront The point of the spear with respect to green energy because they know what it's going to take if in a petroleum Yeah, it's interesting they're just a few companies that are really benefiting from the status quo and everybody else is suffering and so if you could look at People who are worried about our national competitiveness You know big thinkers about the economy pension funds that have trillions of dollars. They should be worried about this It's the whole substrate for everything. So you're right I I should figure out who those other actors are and not just the niche ones People with power There's also people who are influence opinion shifters and the Sputnik moment thing made me think I know you're a Stevenson fan I am his software X speech a few years ago Where he said, you know, what why aren't we writing about moon shots anymore? You know why is all fiction and all Science naval gazing, you know the best minds of my generation writing the iPhone apps Yeah, and it just seems that maybe another aspect of this and I think you're already on track for it with team fiber is Who are the best people? constituency stakeholders, you know choose your collective now To be telling the inspirational stories. Yeah to shift opinion and perception Yeah, I want to get David Petraeus to talk about this There's somebody like that who really is thinking about the country in a big way and understands what we need Okay, we're just about out of time who wants to ask like the glowing wonderful question that sends us all in our way the lunched anybody, okay Yeah, so you say we need we need a Sputnik moment. Yeah, we've got it We've got this but we just need to package it on the other hand You say we've already you can look at this that chart and say well Sweden South Korea and Norway Estonia I forget what else but those are for countries everybody's heard of that are up that are above China's not a member of the OECD Right, so is there something we can point to and you'll make a big video saying you know, they do this in Sweden or South Korea every day We're missing this. Oh good. This is my inspirational moment ready to close on those other countries Especially I spent a lot of time now in Seoul and in Stockholm. Hey, they're wonderful, but they have some Faults that we don't have okay, so in Stockholm things are really too neat It's just way too neat and in fact they they said we need to import some grit They're not they're very polite, you know sort of standoffish not they don't have the entrepreneurial zeal They're trying to develop zeal they keep talking about zeal, but but it's good It's a little out of their character So for them they say well, of course we have fiber, but they're not thinking about all this other stuff all the time They're beginning to but they haven't so far. That's their problem in Seoul It's just too hierarchical Samsung just comes in drops on you if you start a startup.  It's just this it's just it's strange to my view and and not it doesn't feel like there's a whole lot of freedom to Do new things also a pretty small place as a market just 60 million people in the whole country We have 330 so We've got stuff that you know the people can be great at a very young age here They don't have to wait and address people differently depending on how old they are as you do in South Korea We have a lot of messiness. We're good at messiness. We could have more probably but so if America made this move We would see benefits of those other places haven't and that's what to me is so exciting about the possibility of an upgrade That our national spirit is what's gonna make this truly great. So thank you very much. I appreciate your


In this video, we are going to compute the lattice of subfields for the field e, which is which for us in this video is going to be q, the rational numbers are joined the square root of three and the square root of five. Now, notice that e is in fact the splitting field for the polynomial p of x, which is x squared minus three, and x squared minus five. Now, of course, if we view this as a rational polynomial, we get that x squared minus three and x squared minus five are, in fact, irreducible polynomials. They're quadratic, so we can check by the rational roots theorem, the only possible roots would be plus or minus three and plus or minus five, respectively, that doesn't work. You could also use Einstein's criterion to show, since three and five are prime numbers as integers, that this polynomial, these polynomials are irreducible. Okay. Now, of course, p of x, if we think of it as a polynomial over e, then these polynomials actually factor, you're going to get x minus the square root of three, you're going to get x plus the square root of three. You'll get x minus the square root of five, and then you're going to get x plus the square root of five, like so. And so we see that this polynomial does in fact split over the presumed splitting field e in that situation. And so yeah, that's what we're going to get here. We get four possible roots for this polynomial. We're going to get plus or minus the square root of three, and we're going to get plus or minus the square root of five. And so if you view these as complex numbers, right, the complex field is in fact an algebraically closed field by the fundamental theorem algebra. So every rational polynomial will split inside of c. And so oftentimes we go to the complex numbers to try to understand what the roots of these polynomials are. And so this polynomial p has four roots. There's the square root of three, negative square root of three, square root of five, and negative square root of five. Notice that our field e contains exactly those four elements, right? Because if you contain the square root of three, then you're going to contain negative square root of three. It's added inverse. And if you have the square root of five, then you're going to contain the negative square root of five. So we see in fact that e is the splitting field for p, because this is the minimal extension of where we joined roots of p to q, and we got this. So we're going to join all four of the roots, because as the roots come in these additive inverse pairs, once you took one from each, you got the other. And so I want to mention that because of the factorization of p right here into two irreducibles, you'll notice that these two numbers here, the square root of three and negative square root of three, these are conjugates of each other because they have the same minimal polynomial because that's x squared minus three. And likewise, plus or minus the square root of five, these are likewise conjugates of each other, because again, they have the same minimal polynomial, x squared minus five. So there is this relationship between the two. The two are very much close to each other in that regard. So to make conversation a little bit easier, we're going to introduce some other notation here. So we're going to introduce the field f one, and this is going to be the field q adjoin the square root of three, where likewise going to introduce the field f two, which is going to be q adjoin the square root of five. And so I want to analyze these fields for a moment. So if you look at f one, there exists an automorphism sigma, which goes from f one to f one, which be aware that f one as a set as a vector space it looks like the span, which we're going to take rational coefficients here, as there's lots of different fields that we might want to specify which vector space we're talking about. This is a q span here. This is going to be the span of elements of the form one plus the square root of three. Since the minimal polynomial, the square root of three is x squared minus three, we see that f one is going to be a degree to field extension of q. So f one over q. So it's going to be a degree to extension. It's a quadratic extension at situation. So coming back to sigma here, sigma is the map that is determined by the relationship. So sigma will, sigma will take the element a plus b square root of three, and it maps it to a minus b times the square root of three. So in a previous algebra class, like college algebra, intermediate algebra, so like math 1050 math 1010 at SUU, you would call this the conjugation map, right, you're replacing the number a plus b square root of three with its conjugate. Right, this notion of conjugate is trying to generalize that concept we're replacing the number with its conjugate. Essentially, this is the map that sends the square root of three to the negative square root of three. There is an onomorphism there. I want us now to return to the field e. We could actually represent the field e as f two adjoin the square root of three, because after all, f two is q adjoin the square root of five. So if you take the square root of five and then you would join the square root of three, that's exactly what the field e was to begin with. Right, so e can be written as an extension of f two. So in particular, we have that f two sits in between e and of course q, like so, and you can accomplish this by joining the square root of three. I want you to be aware that this map sigma, which we're viewing it as an f one map, automorphism, this can actually be extended to map on e. Okay, because in that situation, if you think of it not as if you think of e as a rational span, your basis is going to be four elements. But if you think of this as an f two span, this is exactly the same thing. And so e over f two is still going to be a quadratic extension, and we can do this exact same map as before. So for now, instead of thinking of a and b as rational numbers, we think of these as elements of f two. Alright, and so sigma, we very much can think of this map from e to e. But with this perspective, note that yes, sigma is going to send the square root of three to its conjugate the square root of three. But it's also when you restrict it to f two. This just gives you the identity map on f two. So in particular, sigma, we can identify with a map inside of the Galois group e over f two, it fixes f two. So in particular, this is a subgroup of the Galois group of e over f, which of course is q in the situation. So this map, which it fixes the square root of five, but conjugates the square root of three. So be aware that our map is looking something like the following. If we take an arbitrary element, we'll say that a plus b square root of five, like so. And then you have a c plus d square root of five times the square root of three. This map is going to send it's going to lead and so for each of these numbers a b c d. These are in fact rational numbers. This map is going to send the first number which belongs to f two, it's just going to leave it alone. And then with the second one, you're going to take the negation there. And so you get c plus d times the square root of five times the square root of three. So that's what that thing ends up doing in that situation. All right, I want you to note that this map is order two, right? If we take Sigma squared, you get back the identity on the identity on e, by the way. So this was the identity earlier on f two. But if you do Sigma squared, I believe the identity on everything, everything is left fixed in that situation. If you do it twice. Now, if you do it only once though, because after all now we're very interested in what's the subgroup generated by Sigma here. It will contain just the identity in Sigma. So as a group, this thing is isomorphic to the cyclic group of water two. I'm interested in what is the fixed field associated to this, this map Sigma right here because notice when you look at this expansion right here, we have this a plus b times the square root of five. We have negative c squared of three minus d times the square root of three times the square root of five, for which you can put those together and just think of it as a square root of 15, like so. If this equals the original number a plus b squared of five plus c times the square root of three plus d times the square root of 15 here, you'll notice because of the difference of signs here that since these things are linearly dependent, we have to have that c equals negative c, which implies that c equals zero. And so you see the same thing on the square root of 15 right here as well. We get that c equals d equals zero, if this is in fact a fixed element. But with a, you just get a equals a, so a could be anything b could be anything. So I want us to note here that if we look at the subfield of e that is fixed by Sigma, we get exactly f2. So the way we've constructed this Sigma conjugates the square root of three but it leaves the square root of five alone. Therefore the fixed field is in fact going to be f2, which was q adjoined the square root of five. All right, so that gives us one of the automorphisms in our Galois group. I want you to be aware that by a similar reasoning, we have some map tau, which is a map from e to e. And for what's it going to do, it's going to, it's going to send the square root of five to negative square root of five like so. And it's also going to leave tau when you restrict it to f1. Now it's going to give you the identity in that situation, the identity on f1. So in particular, if you take something like tau of a plus b times the square root of five plus c times the square root of three plus d times the square root of 15, like so. What this map is going to do, it's going to negate the square roots of 15. And so you end up with, in this situation, a minus b times the square root of five plus c times the square root of three. That's the square root of 15. It's the square root of five times the square root of three. So that square root of five gets replaced with a negative square root of five. So it also will conjugate the square root of 15, like so. Now, if this is a fixed element, if this is a fixed element, make a comment there about that. If this is a fixed element, then this should equal a plus b times the square root of five plus c times the square root of three plus d times the square root of five. These are different signs, their coefficients would have to be 0, b, and d are both 0, and so then you have no restriction on the choice for a coefficient a, no restriction on the coefficient for c. So in that situation, we see in fact that the fixed field associated to the subgroup of tau is going to be f1, which is q adjoin the square root of 3. Again, just like with sigma here, notice that tau has order two as an on a morphism. If you do it twice, you get back, you get back the identity right there. All right, so with that said, let's make a few other observations here. Let me move on to a new page here. What do we know? So we have that the Galois group of e over q, it clearly contains the identity. It contains this element sigma, it contains tau as well. I'm not sure I wrote them in the different order, right? Then there's potentially some other things going on inside of that. We'll come back to that in just a second. I claim that we know the order of this Galois group. The order of the Galois group is in fact equal to, well, since it is a Galois extension, this is going to equal e over q, the degree of that extension. Well, how big is that? Picking one of your favorite of the intermediate fields. So we'll take e over, say, f1 here, and then f1 over q. We can factor in that way because, like we already observed, these fields f1, f2 sit in the middle. So you have e, it contains f1, it contains q. We could also done f2 would make much of a difference. Now, f1 here, of course, is q enjoying the square root of three. And the middle of a polynomial we mentioned was x squared minus three. So this degree is two because we had joined a quadratic element to it. Now, I claim that when it comes to this one right here, this extension is the same thing as the degree of f2 over q. And the reason I say that is because e, and we'll leave that on the screen here, the reason I say we can do that is because in this situation, e is actually equal to the field extension f1 enjoying the square root of five. We did it the other way around before, but this one's also true. So e can be formed by extending f1 by enjoying the square root of five. And the square root of five does still have as its minimal polynomial x squared minus five. Its minimal polynomial over q is x squared minus five, which means that its minimal polynomial over f1 has to divide x squared minus five. As this is a quadratic polynomial, if it factors at all, it has to split. And so that would mean that f1 contains the roots of x squared minus five. That is f1 would have to already contain the square root of five or the negative square root of five, which it doesn't have that. You can argue that in fact that f1 does not contain any square roots of five whatsoever. So this is a proper extension. So it's going to have to be degree two as well for the same basic reasoning. And so when you put this together, the Galois extension has degree four, which means the Galois group has order four. Now, how many groups have order four in general here, right? If we take our Galois group of e over q, I'm going to call it just g for short. I hope that's okay right now. I'll do curly g right here. There are basically two options. This group is either the cyclic group of order four or it's the Klein four group. That is z2 cross z2. So those two options. And so it turns out with the information I have already, I can determine which of these two groups we have. Because notice, clearly we have the identity, but our Galois group contains two automorphisms of order two. Which of these groups can do that? Well, the Klein four group has three elements of order two, but the cyclic group though has one unique element of order two. Besides the identity, other two elements of the cyclic group are elements of order four. And so it turns out that our Galois group can't be cyclic because we have too many elements of order two. And as such, it turns out that this means that the Galois group has to be the Klein four group in this situation. So that's what we have here. Our Galois group is in fact equal to the Klein four group. And that tells us that the fourth element we haven't accounted for yet has to be the product of the other two elements of order two. So our Galois group is going to be one tau sigma and sigma tau. So what does sigma tau do though, right? If we look at that sigma tau or tau sigma, it turns out while functions in general don't commute, these ones will. If I take an arbitrary element a plus b root five plus c root three plus d root 15. Let's apply these two. Tau is going to conjugate the square root of five, thus also the square root of 15. So this is going to give us a minus b root 15 root five plus c root three minus d root 15, like so. Then what does what does sigma do in this situation? Sigma conjugates the square root of three for which, in that situation, then you're going to get a minus b root five. Sigma does nothing to that. You're going to get a negative c root three. But then the square root of 15 will be conjugated again. Because again, the square root of 15 is just the square root of five times the square root of three. Tau negated the square root of five. Sigma is going to negate the square root of three. And so when you do them together, you're going to actually do nothing to the square root of 15, right? So notice that the elements that got their coefficients changed. The b is now a negative b and the c is now a negative c on the square root of five and the square root of three. The square root of 15 actually was left alone. It has the original coefficient here. And so if this is supposed to be some fixed element, so this is what sigma does. Sigma will conjugate the square root of three and square root of five but not conjugate the square root of 15. Tau, remember, conjugates the square root of five and square root of 15. And sigma conjugates the square root of three and the square root of 15. Alright, so that's what's happening here. If this were a fixed element, this is supposed to equal a plus b root five plus c root three plus d root 15. Like before, we'd see that you'd have to have b and c both equal zero so they're going to vanish. And so we see that the fixed field, the fixed field e sub, the subgroup generated by sigma Tau here, this is going to fix the field q adjoin the square root of 15. The square root of 15 is the thing fixed by this element. And so we're going to call this field F3 for the, for the sake of discussion here. And so I want us then to see what are the, the lattices that we have been constructed with regard to the Galois correspondence. Let me draw the fields over here. So our top field was q adjoin the square root of three and the square root of five. There's the base field of q. And then we've discovered there were three intermediate fields. We had q adjoin the square root of three, which we called F1. We have q adjoin the square root of five, which we called F2. And we just recently discovered there actually is a third field, which in hindsight makes total sense. We have q adjoin the square root of 15. And so then when we draw this picture, this picture looks exactly like the lattice for the Klein 4 group, for which, just so we're aware, if we look at the Galois group of e over q, that gives us the full Galois, the full Galois group, which is v4 in that situation. If we look at the Galois group of e over e, that'll just be the identity. And so you get one right there. And then we have some intermediate fields based upon fixed fields. There's the subgroup sigma here. There's a subgroup generated by sigma. There's the subgroup generated by tau. Remember that tau, the subgroup generated by tau actually fixes the square root of three. And the subgroup generated by sigma, it fixes the square root of five. And then the subgroup generated by sigma tau, it fixes the square root of 15. And so we see this picture here as well. Right? If I mentioned the degrees of these extensions, these are all degree two extensions. And we see the same correspondence happening over here. We have two, two, two, two, two and two. And so we see this correspondence between the lattices. Now this example can be a little bit deceptive, because the lattice for the Klein 4 group is the same top down versus bottom up. The lattice upside down, you get the exact same picture. So it can give you this misconception that the correspondence looks like this. This field corresponds with this subgroup. And this field corresponds with this subgroup. The bottom coincides with the top and the top coincides with the bottom. So you do flip this thing upside down. And so therefore, this degree, this extension coincides with this one down here. You flip it upside down. And this extension coincides with this extension right here. And lastly, this extension coincides with this one. But there's so much stinking symmetry happening right now, it can be a little bit deceptive. Now this example, we worked with the square roots of three and the square roots of five, but there's nothing particularly special about those square roots. In fact, the example could have been done where you take the square root of some number p and the square root of some other number q, which basically we just require that p and q are not themselves perfect squares. We require that the GCD between p and q is one. So we want them to be a coprime, for which, you know, this would work if p and q are both prime numbers like three and five. And this actually gives us what we refer to as a biquadratic extension of the rational numbers. And it turns out that with the right assumptions that the Galois group of a biquadratic extension of the rational numbers will always be the client for group. So if you kind of botched some of those assumptions I just mentioned, then you'll get a subgroup of the client for group, or I guess maybe it's a quotient group, but whatever one it is, you might get like a Z2 as your Galois group. And these are biquadratic extensions of the rational numbers. If you do other fields, you can get things similar to this. And so this is a very well understood and one of the simplest types of Galois groups to study that are beyond just a simple extension. So this is a good example to get started with, despite the fact that one might be confused with the Galois correspondence because the lattices have symmetry from top to bottom there.


Hey everyone, are you a songwriter and you want to make your own music videos but you don't have the overly expensive equipment and or the funds we got you covered on this episode guys. Hey Freedom, what's up? My name is Nolden, welcome to Freedom Central, the home of all freedom content. On this episode, let's talk about how you can transform your low budget funds into a very professional music video. But before we do that guys, you know what to do, like, subscribe, and gong that bell. Let's get on to the episode of Freedom. Quick tips. Number one of course is to shoot with what you have. It's 2020 already guys and basically anyone can record with their mobile phones. I would dare say that there's some mobile phones that have a way better camera than the expensive DSLRs. If you don't have an expensive camera, an expensive light set, an expensive microphone, it's okay. Don't panic. You just use with whatever you have. If you have your own mobile camera, or DSLR, or point and shoot camera, that's fine. If you don't have any light set, use a sun shoot outdoors and use any available fluorescent lights to your light kit. For the microphone, you can use your mobile microphone and of course your DSLR microphone. You can also canvass cheaper props to your local hardware store. You're bound to get something that is within reach of your funds. Alternatively, you can ask from your friends to lend you some of your equipment. I sometimes do this when I need a good microphone. Just be sure to repay their kindness in the future. Number two is look for volunteers. You can ask your good friends, your siblings, maybe your parents, maybe your cousins, your best friends, or your loved ones. I'm sure someone will turn up. If you don't have the budget to hire a film crew, look to the people who you think will help you out. Alright, when you have your set of volunteers or your film crew, always make sure to keep a positive aura when you guys are shooting. Just a heads up, these are volunteers, not people that you paid for. They can actually just decide to ditch you when you're shooting. And we don't want that guys. Try to incentivize their time helping you out with the project. How you might be wondering, well guys, for starters, buy foods and drink. It's on you to feed them. Another way to incentivize their stay is to make sure that they will learn something from the shoot. Try to teach them some of your tricks, your insights, and how you do things. Number three, keep it to one day shooting. Let's face it guys, if you go beyond one day shooting, you'll have more costs. So before you shoot, you have to plan it out. Keep yourself organized and efficient. Pre-production is very important when you are on a tight budget. Number four, have a ready concept in mind. Okay, so in pre-production, you have to know what concept you will be doing in your music videos. Concepts are the theme behind the video. Now that you have your concept ready, you should be able to know what props you will be needing and the costs that are attributed to your needs. Is there another way for you guys to make really good music videos with a low budget fund? Let us know down below. Share this to your friend who has a tight budget, but they want to make music videos. Maybe you can help them out in the future with this video. Before you leave guys, please leave a like, subscribe, and gong that bell. My name is NoelGuys, bringing you tips on how to grow your channel. Always, always remember, freedom, quick tips. I'm going to be seeing you guys on the next episode. Goodbye!


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Hi guys! Welcome back to my channel. Today's video is going to be a little bit different. It's going to be filmed over a couple days and Cherie you want to tell them what we're doing? Well what we're doing is because of the coronavirus we have been sitting around eating a lot of stuff we don't normally eat and we see the scales creeping up a little bit on that weight so we want to try to do what I've been doing for the last two years but have not been doing it for the last two months is doing a low carb diet. Alex normally does not do anything low carb. She is a high carb gal so this is going to be a real challenge for her. We're going to do it for two weeks and see if we can make that scale drop just a little bit and then I probably will continue on and then we'll see if Alex wants to continue on too based on her results. And after pictures of results photo at the end so you can see before and after but I want you guys to watch this video we're just going to document what we eat every day and it's going to be interesting. I really want to lose like this poochie. Don't get me wrong guys I love how far I've come I love my body you should always be self-confident no matter what you know like body positivity but this is like pushing it to the next level and I want to just see because it's kind of like a challenge and whenever I video or document anything it really helps me be accountable for my actions so that's why I wanted to make this type of video. Before this video starts I also wanted to say please don't do this if you're like under the age of 18 consult with a doctor we are not nutritionists this is just what we're doing for fun so I just want to put that disclaimer in the beginning. So today is April 27th it's a Monday and we're going to go for two weeks um I think we're going to have one cheat day so you guys will see that in the video but without further ado let's get on with what we have been eating. Here we go! I also wanted to add mothers not here but that's okay I also wanted to add that I am keeping up my workout routine and Chloe Ting's workouts during this as well so just bear that in mind I'm not cutting out any workouts hence why I'm in the workout gear seeing like my little back rolls getting smaller slowly but surely um but anyway now let's really get on into the video. Okay so today is Monday the 27th correct Sherry? It is! And this is what I'm having for breakfast I'm kind of switching things up so for breakfast I'm gonna be having a lot of the same things just so you know so be prepared but I'm having hard boiled eggs yeah they came out a little funky couple of eggs cracked which is super sad and then over here we have some celery sticks I love celery always have always will and then my vitamin vitamin D and obviously I'm having some water and I'm having this before I work out this will probably be my breakfast for the next two weeks want to contribute anything Sherry? Uh no I think that's a very good breakfast you're having your eggs and have a little celery so get some of your favorites of breakfast okay so for lunch before I forget to vlog this I am having my salad like normal and I'm having my deli fresh meat mother's having a salad what else are you having Sherry? I'm having a oh so she's having an Adkins meal so this is what I'm having so far I don't know if I might have some nuts after if I might still be hungry and then I wanted to show you guys Sherry's little Adkins meal just to add that in there and these are the peanuts I'm gonna dig into a little bit now just for a little snack something salty for my palette I'm just gonna open this on up and start snacking okay here's chef Valerie hello and we have here a gorgeous filet mignon oh my favorite you guys know and in here oh wow she feels this we have some asparagus this is dinner on the 27th of April and and then Sherry said the hollandaise this is a quarter teaspoon or teaspoon no two tablespoons two tablespoons my measurements for carbs or whatever but I had to have some hollandaise with it here's the ladies plates they have some onions along with their meat and vegetables and look at that that's a huge piece well it's filling not that big it's not enough for both of us so yes hi you cool cats and kittens hi I do feel like we are big cats because now we're eating all this red meat here okay I also wanted to share that I'm having one of the shakes I'm having half and then Sherry's having the other half over there okay so today is April 28th and for breakfast I'm having my vitamin and vitamin D and I also have my eggs here like normal and my celery and water of course okay so I'm having some salmon this is a fit life foods meal I almost forgot to vlog this because I was getting distracted with KK and baby J's new upload so I'm having a fit life foods meal and I'm maybe gonna have a shake I don't know I'll let you guys know if I do okay and now I'm having a shake these are awesome I love these this is my favorite flavor which is the protein shake mocolate we also we had to get the milk chocolate delight that's what we had last night because they were all out of this flavor so I have a couple left of this flavor guys I'm only on day two and I almost forgot to vlog so I'm having my classic salad and the turkey and I know I had this yesterday but the thing is you're looking at someone who's eating the same thing for a while so it really doesn't bother me so I'm probably gonna have finish up this and then I might have some peanuts or we have some watermelon yeah okay and before I have my turkey we have this watermelon because this is on low carb so we're having some watermelon sherry has it like this okay so today is April 29th and it honestly looks like the same clip but I have my water eggs vitamin vitamin D and my little celery here that is breakfast okay so it is about 12 it's about noon right sherry yep on the 29th and a little hungry so gonna have these planters peanuts first snack and sherry's gonna steal some okay so this is lunch for April 29th I have the mixed chicken and vegetables the vegetables contain zucchini peppers and then that's chicken and then this is just lettuce I wanted to have like a little small something because this is a smaller size and I didn't want to be hungry after so I just have some Caesar dressing on this salad and I also have to refill up my cup I always drink after eight so it doesn't really matter that it's like not a thing right now okay so this is still Wednesday April 29th I'm having green beans and these cauliflower bites these are the adkins cauliflower bites and I'm also gonna have a shake after this I didn't bring it out because I didn't want it to like get all warm and everything so this is dinner like I said I'm gonna have this for dessert the mocha latte this is actually the last mocha latte we have so far because we have milk chocolate delight right yeah so I'm gonna have this for dessert I don't know why my camera is not focusing today is April the 30th and this is my breakfast it's the same as yesterday so I'm not gonna like repeat myself I'm sorry this video is kind of repetitive but it's just a documentation so I hope you find it a little interesting sherry is watching her days of our lives like normal but I almost forgot to vlog this I started eating and my camera was literally sitting right there and I was like oh I forgot so I'm having the salmon kale and asparagus for lunch pretty plain but it's really good it's a fit life food you know okay and I'm having a milk chocolate delight shake beside a cake and baby jay sorry my mom's talking in the background okay so this is starting to become a pattern where I start eating and I just come to a realization I need to vlog so I'm having for dinner my huge salad and my deli fresh turkey because you guys know I love this stuff but yeah this is not that fancy sherry over here is having a salad I haven't really been keeping track of what sherry's eating because I can't even keep track of what I'm eating half the time on to whatever I film next for dessert I'm having some peanuts because these are really good to snack on have a little salt in my life sherry over there is having a shake and a few peanuts it is May 1st and I'm having my egg celery and my vitamin vitamin D with um my water or so just wanted to I'll make sure I always have breakfast and like have something in the mornings okay so this is what sherry and I are having for lunch we're both having the same thing it's the chicken and vegetables from fit life foods for dinner sherry and I are having some salads like normal I was gonna actually have broccoli but you know I just copy what mother does half of the time because I don't know I can't really think so I have a salad and then we're changing it up a bit with the meats we got some hot dogs and apparently these little guys are two carbs per dog right yeah I think maybe not even that much but yeah yeah so that's good to know that's pretty much it I'm also gonna have a shake I know that okay so we're watching this documentary about Susan howl if you haven't seen it check it out it's on Hulu sherry and I are splitting the milk chocolate delight I can shake I didn't want a full one so we split them sometimes okay so it is May 2nd and I'm having my normal breakfast I'm not even gonna repeat myself this is just for the vlog okay it is still May 2nd and for lunch I'm having a small protein mixed grill I don't know what I'm gonna have after this so I guess you'll find out in 0.8 seconds I came to the conclusion of eating some peanuts after my small protein meal okay so for dinner we are having Piennese and I'll show you guys the pizza when it comes out sherry said that it was okay to have this for our low carb just so you know we're not doing strict keto this is just a fun thing that we're doing to see if it will impact our bodies so it's low carb it's not technically full on keto right sherry that's correct we're just cutting back on carbs so sherry and baller got the same thing they got a lot of stuff on there as you can see pepperoni olives some garlic anchovies double pepperoni here's my pizza oh my gosh they made it freaking perfect so happy my garlic salt and my barbershop cheese yes okay so we've made it to a week we are now on May 3rd this is the last day for this video and for breakfast I'm obviously having the same things I'm not even gonna mention what it is because you can kind of see but yeah I guess I will move on to what I had for lunch today okay so for lunch for the last day uh April May it's it's not April anymore it's May 3rd I'm having a salad and turkey kind of like normal I might have a shake I don't know but tonight we're having bonefish mother and I are gonna cheat a little bit and have a cookie so you'll see that in the next clip okay so for the entree we have here broccoli and salmon as you can see we're also having a few other things which I'll just show you before I eat it hopefully I won't forget to vlog but this is the main course so I put my salad in a bag because it's just way too much I already had salad today and this is hollandaise I have a little taste of it I eat it straight up because you know that's just how I am and then I'm having this little bread and I'll update you guys on dessert I think I'm just gonna have one cookie gotta have a cookie action more cookies more cookies for me okay so for the last meal item of the week I'm having one cookie because these cookies are so delicious if you guys ever have the opportunity to try one highly recommend okay so this is future alex coming in before I edit to talk about my weight log okay I wasn't gonna talk about numbers or anything in this video but I wanted to just kind of talk about my weight in a sense I've gotten a few questions on Instagram about my weight and what it is and everything like that and oh can you give us numbers to see like if you're losing weight or measurements I personally don't think anyone is like defined by a number you gotta also consider the fact that I'm working out I'm building muscle as well but I'm going to go through my weekly log I've only I kept track all week so on the 27th of April I weighed 137 pounds and six ounces and then on the 28th of April I weighed 136.8 and then on the 29th I weighed 136 just 136 pounds then on the 30th of April I weighed 136 pounds and three ounces so I gained 0.3 ounces but who cares and then on May 1st I weighed 135 pounds and nine ounces and then on May 2nd I weighed 135 pounds and seven ounces then on May 3rd I weighed 134 pounds and six ounces and today when I'm filming this May 4th I weighed 134.3 ounces so basically I've lost around three four pounds which doesn't seem like a lot but it's a lot for me that's insane and I do have a goal weight but I'm not gonna say it because people might say that's unhealthy but for me I kind of want to get back to where I was when I was like in college and everything because I was getting a lot more exercise when I was in school I think that is about it for this clip so back to the Alex that you were watching previously I actually curled my hair today it's kind of coming out I just want to show you guys the before and afters of last week compared to this week so I will put them on the screen now so here are the before and after photos on the left is the before and on the right is the after and that is with all the photos you can see a major difference on the side view I think the front looks the same and the back kind of looks the same hopefully you can kind of tell a difference so yeah I don't know if you can tell a difference or not but I certainly feel a change in my body I feel less bloated and just like cleaned out that's the best way I can put it that is going to be it for this week stay tuned because we are doing a week two update video next week so you won't want to miss out on that I hope you guys enjoyed this video and found it helpful and entertaining and just this is just meant to be a fun little thing for sherry and I to do so give this video a thumbs up don't forget to subscribe to my channel and I'll see you guys in my next video bye


And a non-governmental organization has taken advocacy and sexual harassment and how to prevent and respond to it in the campus. To this end, it has strained 50 female students from the University of Abuja on the prevention and response mechanisms for addressing cases whenever they occur. Plus, the Immanuel Ihejena report is presented from our studio. This is what we're talking about being brave. Sexual harassment is a global issue that has been addressed by governments and non-governmental organizations and civil society organizations. In Nigeria, legislation has been passed to reduce the prevalence of sexual harassment in various settings, including work, homes, schools, and tertiary institutions. However, an NGO is working to end these by sensitizing and training 50 female students at the University of Abuja. The campaign, titled Amplifier Female Student Voices, is now being held at the University campus. We have a voice as female students and as females generally. So all what we need to do is to amplify the voices. We need to be heard. The culture of silence is actually prevalent and that's why there's low reportage on sexual harassment. Or sometimes you look at it, people do not even know that what is happening to them is actually sexual harassment. So Gender and Mobile Initiative has been strengthening the capacity of students for them to know. So we're looking at, we've trained them on different types of courses, like the campus organizing. We've also trained them on, of course, the earlier when I said the bystander intervention and then the first state social support. We are seriously pushing for the passage by the presidency of the sexual harassment prohibition in tertiary institutions bill. We believe that bill is very vital to safeguarding environments of learning and to serve as that legal framework for institutions to look up to when it comes to addressing cases of sexual harassment. At the institutional level, we also have a national policy still on sexual harassment prohibition which we've designed in collaboration with the independent Coral Practices Commission, the ITPC for short. And we're looking to disseminate that policy. That policy has also been endorsed by the Ministry of Education and we're looking forward to disseminating that policy and ensuring that it's implemented in environments of learning. Some of the students share their experiences as they give reasons why sexual harassment still persists in institutions and why the training has been of great help to students but also calling for more awareness programs. They call them lecturer boys. Those ones that assist the lecturers to mark, they'll tell you, I have the right to mark your results so I can remove mark from you but you can even enter exam hall and touch you, do whatever they want and people are seeing but they can't do anything because they are scared of them and they don't know what to do so because of that I as a person I felt like there's a need to stop all these kind of things and even if they should report to the authorities there are some people that are friends to those lecturers, those perpetrators that are harassing the students, there are some people that are part of them that they can easily report and like this also students is reporting you to the management so because of that they can easily threaten the students with their results and the manifest function of every student that is the primary assignment is to have a good grade, graduate with a good CGPA. This initiative is one as such that it is like a blanket that has come to cover persons that have been sexually harassed. It comes to let people know that if you are sexually harassed you have a voice you should speak up you shouldn't keep quiet keeping quiet to give room for the perpetrators to begin to do more. Campus ambassadors receive certificates of participation enabling them to continue the campaign I institutions were encouraged to implement programs promoting student sensitization and reporting of sexual harassment ensuring perpetrators are caught and punished. Hello hope you enjoyed the news please do subscribe to our youtube channel and don't forget to hit the notification button so you get notified about fresh news updates.