Good afternoon and welcome My name is Raj Kumar. I'm the president and editor-in-chief of DevEx I'm delighted to be with all of you who are here in the room live in Davos And those of you who are following us from around the world for this issue brief on the state of the Humanitarian system in fact the official title is the Humanitarian system under pressure and I think maybe there hasn't been such an understatement in a long time This is a case where Humanitarians that I talked to and that we report on and and Look into around the world if you talk to them They will give you a sense that they have never felt so stretched before their institutions feel overwhelmed you may not know that from You're watching the news on the mainstream media because there are some very big crises which get a lot of attention But there are many many more that don't and we'll talk a little bit about that today You may know though that the world is in this state of growing Humanitarian crisis simply from where you live Even if you live in an advanced economy in a rich country you may find Refugees in your own country you may talk to them and hear their stories and people In historic at historic levels are fleeing. They're moving. They're moving sometimes internally because of conflict They're moving because of climate They're moving because of corruption because of violence There are many reasons but there are many people moving and today there are 360 million people in the world in need of humanitarian assistance and Over a hundred million that are displaced from their homes for some reason I'm joined by three people who are working at some of the most important institutions that are trying to address these issues to Provide assistance to people in need around the world and we're gonna hear from them what they think the picture is in 2024 going forward. So I'm joined by Philippe O'Grande who is the UN High Commissioner for Refugees You may know it as UNHCR I'm joined next to him by Kitty van der Hayden who's the deputy executive director for partnerships at UNICEF and David Miliband who is the president and CEO of the International Rescue Committee? Maybe I'll just start with you David if I can When you look at 2024 you think about the state of the humanitarian system such as it is How would you describe it now versus where we've been these past years? What's new? What's different? What's what's coming that people should be aware of? Thanks? First of all, I think we all three would Insist that while there is pressure in the humanitarian system or sector the pressure on our clients is quantumly different and what will run through my remarks is the unspeakable pressure That is afflicting 300 million plus people that you talked about just for context. We've just published our emergency watch list for 2024 85% of the people who need humanitarian aid are in just 20 countries 75% of the world's refugees are in those 20 countries So it's a massive problem, but it's also acute in particular places You had a session. I know at Weft today on Gaza just before I arrived Gaza is number two on our watch list and number one is Sudan and number three is South Sudan and 25 million people in need in humanitarian need in In Sudan, I would say there are three sources of pressure in the Humanitarian sector. There's a funding gap. There's a delivery gap and there's a political gap The funding gap is easy to talk about and actually easy to fix relatively speaking So I'm not gonna spend time. We're gonna want to know about that later. But yeah, it's good As a policy problem Funding is an easy thing is a much easier thing to fix than the second which is delivery gap How in the context of conflict is it possible to deliver humanitarian aid in a way that Gets the aid to people who need it is able to establish sustainable Basis for them to live not just under humanitarian aid not on humanitarian aid But off their own efforts and in some cases when they're in conflict how to survive impunity that is all around them and so that delivery gap has led us to work very hard in the context of the challenges of climate and conflict and poverty to Propose different models for the international system to work with international NGOs and with local NGOs We think civil society has a much bigger role to play than it's currently Afforded and happy to talk about that some more the political gap It is obvious and it's obviously the hardest to fix and takes us beyond the lanes that we're most Comfortable with but it wouldn't do justice to the topic not to recognize The West versus the rest as an increasing factor in global Politics the increasing breaking of international norms and in some cases laws about protection of civilians about aid for civilians So those political issues Are summed up by the inertia and the gridlock at UN and Security Council level just to finish and because I know you want this to be Interactive we're pleading with people in this week in Davos to remember three numbers And their numbers about solutions that we're pioneering not problems that we're describing number one. We took a An approach to treating malnutrition to Mali at the moment 80% of acutely malnourished kids in the world don't get help 27,000 kids were helped by our simplified protocol delivered by community health workers in Mali 92% success rate 20 to 30% savings on cost effectiveness Second 11 weeks the second number that I want us to remember 11 weeks is the time it took for Children engaged in our Alan Simpson early childhood development program to make a year's worth of pre-primary progress in their social and emotional and academic Progress so there's an we all know that Education is the least funded part of the humanitarian sector There are solutions even in that even in that area as well and then the third statistic is 15 15 countries in which we're running something called signpost which is a refugee for refugee information system It's currently been used by over 50 million refugees because information is the first thing that you need and it's a bespoke local Initiative with it's actually unbranded and it's a trusted source of information That's just to say that I'm sure My co-panelists here can speak about the amazing things that their organizations are doing Let's not allow ourselves to drown just in the the dysfunction Let's also think about how we can invest and seek investment in what is functional Yeah, I'm glad you you proposed some solutions. We'll get a little more into that but just in terms of this year kitty You've been in the space a long time and it seems like the trajectory year after year has been clear more conflict Climate having a bigger impact You know, so I guess if we're here next year It seems like this trajectory is clear unless maybe we can get some of the three areas that David proposed to change What is your take on what 2024 is going to look like what should people are interested in this space look out for in 2024? Look, I think if if the past predicts where we're going Then what we've seen is an increased number of Crises that are affecting children Worldwide many of these crises is are not sudden onset crisis many of them are protected 80% of them are protracted look at Syria 12 years of conflict look at Yemen nine years look at DRC Almost 30 years these crises are not always black swans They've been there for a long time and we have as a global community not been effective in Addressing them what I see if I look forward is a continuation of those type of protracted crisis also because climate change as an undercurrent to those crisis is not going away anytime soon actually We may be winning some wars some battles, but we're losing the war on climate currently Where where I see a huge problem coming up and it's been there for a long time and this is thank God We needed some disagreement in the room right Is an issue around funding because I think funding should be easy to fix the reality is that it isn't what I'm saying Is not necessarily that there isn't enough money What I'm saying is that that almost all that money is earmarked and going to a few crises in this world So as a humanitarian sector last year 2023 50% of the funding went to five crises right Afghanistan Ethiopia Syria and refugees from Syria in other places Ukraine and Ukrainian refugees elsewhere 50% How how many children do does anybody know how many children in Sudan you mentioned Sudan how many children in Sudan need humanitarian assistance And he gets 13 million Right 80% not funded Nobody talks about a place like Burkina Faso 3.2 million people need humanitarian assistance 91% not funded so we are looking at a crisis within a crisis We see increasing needs and a chronic underfunding and a funding that is very very earmarked to what hits the headlines and That leads to an inability of all of us together as a humanitarian system To deliver in an equitable way every child every civilian has a right to survive and to thrive and currently as a system We're not enabled To deliver that last point I want to make when it comes to funding what we see because there are so many Crises and that's only increasing and we need that lifesaving support But it is also leading to a much reduced portfolio within one fixed budget, which is ODA development aid Into addressing the root causes of some of these crises education health systems Basic services that people depend on for a life in dignity the more we do Humanitarian aid if that is within one fixed funding envelope The less we're able to deal with the root causes of deprivation and displacement of human misery and migration With that I think we get to Over to you that is a good segue to refugees Filippo you are people are moving people are moving there are refugees all over the world now and Your agency is responsible for serving them in many many places. So In many cases, these are people who have left home as refugees a very long time ago to Kitty's point about protracted crises In many cases, they are not getting the level of assistance that would be required that your agency would like to give them So there's a funding aspect there, too But what is the big picture when you look at 2024 and the status of refugees? I'm actually lucky that I can build on what my Panelists have already said so I'll add a few comments a bit also from my perspective The first one and I don't know I think this is also related to what David mentioned the crisis of delivery We spoke about this before in other panels. In fact One of the big issues this is nothing really new but new at the scale in which it's happening is the politicization of the responses and this has a very wide range of phenomenon of aspects of course in my area in our area It's very clear politicization of refugee movements for electoral purposes is common This actually makes delivery much more difficult because solutions that often are easy to find are made impossible by the politics Things like giving a work permit to a refugee, right? And we just had another meeting here on the same topic and this came up but also the issue of access because You know the traditional understanding always difficult, but that humanitarians Talk to everybody and must have access everywhere is now often Put in discussion. No, you know, you cannot talk to these people because they're bad and you know donors drive Some donors drive that discussion So this is an important aspects of the crisis in the humanitarian domain the other aspect is resources and I agree with what has been said and the key question here is, you know I often hear this comment have human humanitarian assistance has grown over the decades Has ballooned in fact because there were many needs Has it peaked? I think it's a bit of an absurd question because if you talk about Just the UN but the UN appeals, you know are a big chunk. What 30 40 billion a year This is this is small change in the world today And how can you say that it has peaked when it is important to save so many lives? But let's assume it has peaked and let's assume also that one of the reason why it has peaked as is often said in my Opinion in a manner that distracts from the real discussion Which is the responsibility of not having it peaked but often it's a you know The humanitarian model is so broken that we cannot put more money into it. I think this is a false argument Not least because actually the humanitarian model is evolving. I Every time I come to Davos every year. I always hear this mantra We need to have a new humanity. We've all evolved enormously in terms of Efficiency in terms of partnering with to making this more sustainable and and we just you know He just mentioned that So I think we need to recognize that and scale it up these new models where we work with development Organizations where we look at sustainability at sustainable care as I call it and and this brings me to my last point which is the importance in a world that is so fraught with crisis of Emphasizing not only humanitarian responses, but searching for solutions because we also know that the more you delay solutions from Climate change to the Israeli-Palestinian conflict Areas in which the world has been brilliant at you know Pretending there you know or putting it aside for a variety of reasons then it comes back with the vengeance in different ways, right? So that's is one track of discussion the other track for us final final final point I want to make is what do we do in the absence of solutions be they political solutions or Developmental solutions or both like in the case of climate and I think that there is where we need to become even better are at finding intermediate approaches where again Support to those that pay the price of this crisis is Sustainable and does not depend entirely on humanitarian assistance. That's a difficult one But I think that that's one in terms of delivery where we need to really work we are working on that but we need to really get more support and More space in order for because I predict that that Necessity to find in intermediate not even solution but intermediate ways to support people in distress Without a a solution that would allow them to go back to normality that situation is becoming the new normal almost everywhere Well humanitarian assistance may not have peaked but perhaps official development assistance has perhaps ODA Which is the larger basket from which humanitarian aid comes has we don't know But if you look at this year and 60% of the world has elections And many donor countries are moving more and more rightward and candidates are are winning who are opposed to official development assistance Perhaps that basket a larger percentage ends up going to the humanitarian community given the crises and the needs But the overall basket may itself be be shrinking or plateaued But I want to come back to a key point you made Philippa and bring David into the discussion on this And by the way in a moment, I'm going to ask for questions from the audience if you have them On this question of has the humanitarian system evolved is it getting better has the model changed Philippa says yes Obviously, there are things like cash transfers the IRC has been a big a big proponent of you do quite a lot of that kind of work And it's it's expanded in many agencies now What is the fair assessment from your standpoint David given that you're you're not new to the space even here a while But you are a relative newcomer and that you had an important political job before you took this one You're such a charmer and you almost said I was still young so Look, I think it's a very low bar to say is it getting better because it could be crawling forward The point is is there still a long way to go to make it much much much much better. Yes So I would defend what's done, but I would argue there's a long way to go to make it Did you put a grade on the humanitarian? No, but the I wasn't born yesterday. So I spent a lot of years dodging questions like that the but I think it's important to to be clear There are Interventions that we know work very well, but are seriously underfunded. I mean early childhood development is a Example of that malnutrition is another example of that. So That's really inexcusable Secondly, we also know that the poorest places get the least investment and one example of that is in the climate adaptation Space this is going to be a major new area of funding. We know the Secretary General has a decision rule That 50% of all climates for Secretary General of the UN 50% of all climate funding should go to France It should go to adaptation We say that it's essential that a proportionate amount of that funding goes to fragile and conflict states Which at the moment get the least and within those fragile and conflict states a fixed percentage at least goes through The civil society sector because we know that institutions like the World Bank historically have only worked through the Official sovereign sector. You can't do that in the fragile and conflict states. So that's an example of how delivery has to Move forward. Thirdly, you'd have to say that we're going backwards on civilian protection and on Human access to humanitarian aid and that those two areas are legal rights to be protected from war 90% of the casualties of war today are civilians and the access quote-unquote access is sort of strangulation rather than access the the the the limitations on Humanitarian aid delivery are growing not receding So if you were to measure by outcomes it sounds like at least in certain areas We are doing worse than we were before as a humanitarian. There are more people in humanitarian need I mean Filippo can tell you that the number of refugees and displaced people has doubled some of them like in from Ukrainian refugees in Europe are getting high standards of treatment But very large swathes of them are getting very low standards of treatment Let's see if we have a question or two from the audience. I See Sarah there. I'd like to go to her the woman in red and then we'll take one of the questions in the front row We'll take we'll take three if we can keep them really brief and snappy with ideally a question mark at the end And please share your name and organization if you would thanks. I just I'm sorry, Pateriano from ODI short and snappy Kitty talked about Sudan what we're seeing in Sudan is an enormous amount of Leadership and energy by Sudanese citizens themselves in a lot of areas where there is no access It is the Sudanese who are responding to the crisis Other loosely, you know organizing forms of mutual aid or through the emergency rooms How can we sustain these forms of very impactful very? Appropriate adequate, you know response to make sure that first they get more money second They're more involved in the decision-making around the response You can pass it right behind you. We'll take your question and then come back to the front row. Thank you I'm a global shaper from Kabul of Afghanistan Well, it one side of the coin is you guys talking about lack of funding when the other challenge We that has been persistently that has persistently existed in Afghanistan and when it comes to a distribution is that it not going to the right people because the regime hands over and you know a Pre-picked list to the UN organizations to distribute the aid so whereas it starts from a really good place With good wealth for the aid, but it doesn't reach the right people a recent example is our province where The aid was completely stopped because the regime was interfering What are the mechanisms? How can you make sure that the aid makes it to the right people? Thank you for that question. Just right here in the front row. We can pass the mic Hi, hello, my name is Antonina and I really related to what key to say because I come from a country Where it's in crisis that no one talks about anymore However, we're the second worst migration crisis in the world. So I think you can guess is correctly So I come from Venezuela and my question is very simple, but I have to ask why are with us the second Least funded humanitarian crisis in the world Well kidding me. We'll start with you on this question from Antonella about Venezuela And again, we have just a few minutes. So we'll try to keep our responses sharp if we can Venezuelan refugees are now all over the world Why is it not a place that gets a lot of funding? Look if I would know the answer We would have the funding we needed to address the crisis in Venezuela and in surrounding countries, right? I mean, this is not a UN problem We are being funded by donors and unfortunately as I said those donors create highly earmarked funding pathways for us And that is creating I mean you mentioned it. It's an equity crisis in the way We fund the humanitarian crisis We are the custodians on the convention every child is the same whether you're in Venezuela or in Gaza or in Ukraine or in Yemen doesn't matter every child has the same rights And we're unable to be there for every child everywhere all the time Because the way we're funded as a system means we therefore some children in some countries for some part of the time That is the equity crisis. We're dealing with that is something that our donors need to help us So if we can't do this alone, we will be advocating for every forgotten crisis every forgotten child is a crisis for us Filippo embedded in Sarah's question is a critique. I think you talked a bit about the delivery Getting better in some ways, but she's talking really about this idea of localization All right, and such a small percentage of humanitarian assistance gets to local organizations She's using the case of Sudan to say look here's a place where people are rising up on their own to do this work Why can't we as an international system fund them? What is the what is the barrier? Is it you know bureaucratic intransigence? Is it a is it a a different view of of you know How trustworthy local organizations are what's holding us back from truly? Increasing the amount of humanitarian aid that goes to local organizations, but before I answer Sarah's question Just one point on Venezuela It's a bit more of a mixed picture in a place like Colombia and This is what I I was referring earlier that we need to look at how these things are evolving Colombia is the country hosting the largest number of Venezuelans, right? Two and a half million probably more close to three million now. So it's a large number We started off a few years back with a very humanitarian approach money dried up very quickly You're absolutely right on that because this was not the priority etc. But in Colombia in particular to an extent in Ecuador and other places as well is are probably some of the countries where involving international financial institutions the Inter-American Development Bank even the World Bank in support of good state policies that include Refugees has been one of the most successful and we're talking about billions of dollars. So you see I think that we need to look at it There is if there is pressure on us to Embrace new models and we do embrace new models because we are largely the humanitarian They're largely responsible for having brought in Development actors then needs to this needs to be recognized and supported. Otherwise, we continue It's a spiral.  These are all real issues, but there are ways out that I think we need to Grow and on Sarah's, you know, I think this is an important point We are struggling with that as an organization struggling. We are Grappling with it as an organization at the last refugee forum in December last month two months. Yeah, last month We had 300 refugees participating So that was Still symbolic if you wish over 4,000 participants But a powerful symbol that they are part of the discussion This is in a way indirectly responding what you said about Sudan the question is you know I did one of the final sessions with four of them It was fascinating because I had to push back on certain issues Representation for example, how do you determine who represents what how might put the point I Sent back to them when they said we want to be more part of this meeting We want to part to be part of your governance structure The the message back is this is all well and good, but because it's so difficult to structure it globally It's at the local level that this needs to happen and this is what you're saying So I am now pushing my representatives in the field to embrace refugee participation In decision-making it's still difficult because you know Representation is political at every level who who does what to whom do you entrust resources to do things? It's not it's not a joke. It's quite complicated, but it's easier to do it at the local level where you have a better You know picture of the situation and it's actually as much more effective to do it to do it at the local level It's a very very big discussion, but one that I think deserves attention and deserves Experiments in order to move because we have seen it during COVID and we see it in this impossible situation where access is almost Zero or not next to zero that either you work with the local community or you don't work It's potentially one of the most important ways to do more with less when you have To find the right ways to do it because otherwise donors would say oh wait wait a minute Where is this money going because there is also that element that we need to factory David We only have about a minute or so left, but we had this colleague in Afghanistan So two things to end up 30 seconds on the funding picture in broad terms Half of the world's extreme poor live in fragile and conflict states but a quarter of the money That is earmarked for development and humanitarian aid together goes so you've got a mismatch there There's big room for a switch spend not least because we now know 30 40 years after the collapse of the Berlin wall There is a route to development in stable states that is about governance and markets not about international aid To the colleague in Afghanistan The we have five thousand people working for the International Rescue Committee in Afghanistan at local level In 12 different provinces including two thousand two hundred women despite the quote-unquote ban that was Imposed and your point about thinking local is actually borne out by every study Of where aid has gone in Afghanistan. Filippa has an extraordinarily distinguished record actually in Afghanistan There's more about it than I do but for 20 or 30 years But all of the studies show the big money that goes in for prestige infrastructure projects from the top doesn't get to the people who need it Seeding change at local level does and that's a very important message We think we're part of the local system because of our 5,000 staff 4,996 are Afghans and they make decisions about what to do and which grants to apply for so I think your point Isn't important. Yeah, I think so too And I think part of what you are calling Afghanistan is getting at is it's also about having to work with certain governments You talked about the the governments and fragile states that are very challenging to work with the reality this year is There are many governments many countries that are tough tough partners for the humanitarian community But there is no choice because as kitty says, that's where the need is So I hope we've given you a lay of the land for what is a very challenging moment for the humanitarian community And as David said especially for the people themselves who are in need all over the world So thank you very much for being a part of the issue


I'm excited to speak here today. I looked at the list of attendees, and it seems like every one of you is a leader in the education establishment. And you all have a very, very strong bias toward progression in the world of education. I'm sure that lots of people have covered lots of subjects that are education focused today. And I've got a particular perspective on it. But I thought I'd start with a few comments on the social, economic, and political environment that I think we're in right now. Because I think we've reached an inflection point that's particularly important to everybody in the education establishment. And what I always find fascinating when I read the news is not the things that are stated in the news, but rather it's the things that occur and the implications that are unstated in the news, or rather the news headlines that aren't written but should be. And I think this is the most momentous year ever in this business. So I want to make a few comments on that. And I'm going to discuss how this relates to education too in my speech. About two weeks ago, or three weeks ago, Apple came out with an announcement for a new smartphone, the iPhone 5S. At the same time, it released a product called the iPhone 5C. What was covered was 9 million units moved in the first weekend. What wasn't said was equally important. And at the same time, Apple released an operating system, iOS 7. And throughout the news organizations, it got barely a tweet, maybe one paragraph mentioned. Now, what did I see? Well, the iPhone 5S is obviously the biggest product launch in the history of Apple. It was and will be the most successful product Apple has ever created. They're going to sell 100 million copies of one computing device in 12 months. They're going to sell 100 million copies of it and generate about $75 billion in revenue. That much is very clear. Nobody wrote this. It's going to be the most successful product Apple ever created, but it's also going to be the most successful computing device ever created. And if you follow that train of thought for a bit, it's about to become the most successful consumer device ever created. And that makes it the most successful product ever created. And it all happened a few weeks ago. In the history of the world, Apple put a product on the market that's the most successful one in the history of the world. Now, along that line, something else happened which is fascinating. We saw in the area of mobile phones what we're seeing this transformation where it's increasingly clear that anybody that can have an iPhone wants an iPhone, but Apple came out with the 5C and the 5S. And it turns out that everybody wants the 5S. It's been a gargantuan success. 12-year-old girls want the 5S. 75-year-old senior citizens want the 5S. It used to be there was a bifurcation or a segmentation of the market based upon consumer preferences. And senior citizens would want something different than a 45-year-old professional. And that would be different than a rich person. And that would be different than a poor person. That would be different than an uneducated person or a young person or a male or a female. But we're seeing actually the collapse of all these segmentations in the area of computing. And it was very, very clear and punctuated by this product launch. That's, of course, one of the reasons why it's possible for Apple to create the most successful product in the history of the world. It's also the most profitable product, by the way, in the history of the world. They're gonna generate a 40% margin on $75 billion in revenue in 12 months. Never before accomplished with an airplane or an automobile or a television. Anything anybody can think to produce. We've never done it before. And the spectacle, by the way, what they put in that product was a 64-bit chip which nobody really wrote much about. But one of the implications of the 64-bit chip is now you can take slow-motion video. That means that every 12-year-old kid sits and takes slow-motion video of their friend jumping into the pool. They post it on Facebook. To tell all their other friends, they now have the coolest phone in the world. And I watched this happen. I watched college girls posting slow-motion video on Facebook because they want their girlfriends to know they've got the coolest phone. The iPhone 5C has a 32-bit chip and it doesn't have slow-motion as a camera option. You can't do it, therefore you can't be cool. Cool is 64-bit chip. Since when was cool ever a 64-bit chip? The iOS 7 got released on Thursday night. By Monday morning, there were stories that were 200 million downloads. Now what was that in iOS 7? Well, lots of interesting things, but two very powerful things. One was something called iTunes Radio. Apple shipped free digital radio to 200 million people in 72 hours. Another thing was an upgrade to FaceTime. FaceTime was Apple's, in essence, digital technology for video conferencing. They've had it in the product for quite a while, but it's never really been focused upon because lots of people, me included, don't want to show our face if we make a call late at night or early in the morning or we don't want people to see what we're wearing or if you're not wearing makeup, maybe you don't necessarily want to make a video call. So we use audio calls. Apple's known for being brilliant marketeers, but I find it very amusing to see their anti-marketing. They actually came out with a product called FaceTime Audio. And FaceTime Audio is merely the FaceTime without the face. But if you were to call it what it is, they came out with free phone calls. But they're not gonna call it free phone calls because Verizon and AT&T sold more than half of those nine million iPhones that weekend. And it's probably offensive to the telcos to release a product to 200 million people in 72 hours, which makes phone calls free. Now, why do I fixate upon this? Because that makes iOS the single most successful service delivery in the history of the world. And that's the headline that didn't get written that nobody focused on. And it's worth a 10-page journalistic piece, right? A company figured out how to release a service interesting to consumers ages three to 80, they delivered it to 200 million people in 72 hours. We've never delivered anything of substance or value to 200 million people in 72 hours. And they did it, right? And more to the point, it's now inevitable as you look forward another 12 to 24 months that will reach the iOS 7 point where they will release something to 500 million people in 72 hours. And that puts the writing on the wall. There's a global wave of technology coming. I wrote a book called The Mobile Wave, I wrote about three years ago, and the thesis was computing and software has become so cheap to provision that this technology wave's gonna sweep over the planet. And I think right now it's pretty clear that we're moving toward a world where five to six billion people have a mobile computing device. We're gonna have 950 million smartphones sold in the next 12 months. That means that we're moving toward a world which is about everybody of consequence has a computer in their hand or in their pocket. Now something else is happening, right? Two more headlines that you sort of read. Microsoft took a billion dollar write off on Surface about a month ago. Blackberry took a billion dollar write off on the new Blackberry smartphone. What you're seeing, by the way, and what you have seen is the implosion of Nokia and the implosion of Blackberry. What was the significance of that? Those were the two leading non-American telephone companies, right? The two leading non-American smartphone companies they imploded in the last 12 months. Now it's been coming for three or four years. Anybody in the tech business knows it's been coming. It was inevitable, like water flowing downhill, because as the value proposition of the phone became more and more software infused, if you didn't have the best software in the world, you couldn't possibly hope to compete. So Blackberry explodes, there goes one Canadian player, Nokia explodes. Nokia, for those of you who remember, in 2000, I actually declared somewhere here in DC that I thought that we would eventually get to the point where you could provision education for free online. And in 2000, Nokia was the most valuable company in Europe. 13 years later, Nokia is no more because they missed the software wave. It turns out it's easier to predict the future than is to make money off the future. For those of you who follow this, it's pretty inevitable that education is going to be highly automated. It's a question of when it would take place. But in those past 10 years, Nokia disappears as a player, Blackberry disappears as a player, and the entire mobile world collapses into a standard which revolves around Apple Computer as the leader, and Google is the number two. The number three is rapidly emerging to be Amazon. HP, Dell, Lenovo, all falling by the wayside. Another headline that dropped in the past 12 weeks that got a big ho hum, beyond was we've reached an inflection point, we sell more tablet computers every quarter now than we sell PCs. That means that the center of gravity of corporate computing has just flipped from the PC to the tablet computer. Most people didn't grasp that part. The center of gravity or the leadership in the entire software industry flipped to the mobile operators as soon as we shipped more smartphones than we shipped PCs. But the smartphone is not routinely used for corporate activity, the tablet is. At this point, that headline could be read as the last straw and it marks the end of the era of Microsoft and the beginning of the era of Apple and Google as the dominant players in enterprise computing. The stock market figured it out a while ago. Consumers figured it out a while ago. Corporations have been dragging their heels for 36 months and for the ones that didn't move rapidly, they'd said something like, oh well, we don't trust the iPhone, it's not secure, we trust the BlackBerry, that's secure. That's our standard for enterprise mobile computing. Or we're gonna wait and see what Microsoft is gonna do. The significance of those other headlines is just about everybody in the corporate world is throwing in the towel now and they're not waiting for BlackBerry to deliver anything, as you can see. BlackBerry's probably not gonna be a company in 12 to 24 months. They're not waiting for Microsoft to deliver anything either. And the significance of that is not that they needed Microsoft to deliver anything, we never needed them to do it, we just needed them to get out of the way. And Microsoft has in essence thrown in the towel and declared, actually thrown up its hands and declared it doesn't really know what to do. You couldn't really characterize as any other way it's a company that just spent $8 billion to buy Nokia because Nokia was the last company creating a Windows phone of consequence and if they didn't buy Nokia, there'd be no major phone manufacturers working in the Windows operating system. They'll throw $8 billion into that deal, they will spend another $10 billion trying to make it work, it will ultimately fail. Wall Street figured that out because the day they announced the deal, Wall Street knocked down Microsoft's market cap by 20 billion. And funny enough, that's kind of what I calculate they're gonna waste on that detour. And they didn't do it because of some brilliant plan because at the same time they announced that they have no confidence in their CEO, he's gotta go, they need some new guy, they're not sure who that's gonna be. Again, not a vote of confidence. Conclusion, everybody in the corporate world is now stampeding, avalanching toward the Apple standard if they can afford it and the Android standard if they can't afford it. If you look at all the segmentation in the marketplace, every person of economic consequence in the world with a 90% likelihood is stampeding toward the iOS. Apple is winning this market everywhere in the world on the high end and where people just can't afford it, where you can't get into that business, you go where the Android is the number two, the rest is going to become inconsequential. Now, all those facts mean different things to different people and most people, they can see the writing on the wall, they're just afraid to admit it to themselves because it's a little bit too scary. But let me tell you what I think it means. I think it means that we're about to move into an era, a global wave of prosperity and a global wave of trade, but there are certain global standards that are emerging, English, the dollar, American customs, American law, American commercial values and American cultural values. They're all flooding the five to six billion people on the planet that actually are literate. There's one billion people on the planet can't read, they can't read because it's too expensive to read, they will be drawn into the literal world and will probably get to stability at the seven to eight billion person point. Now, as you notice, I made a point, Nokia and BlackBerry weren't. We're seeing a collapse around networks that emanate in the Western world, especially America. Why Facebook, why Amazon, why Google, why Apple? For those of you who follow marketing, this was a salient year, a watershed year, the most popular brand in the world for the last 12 years and maybe for the past 50 years. It's Coca-Cola. And the greatest export of America was sugar water, and the sign of global trade was Coca-Cola for who knows how long. And this year, the brand became Apple. Apple became the number one brand that was written about, it's a big deal. Apple's number one, Coca-Cola's number, it's not number one. What wasn't written about, who knows what the number two brand was? Do you guys read this article? All of a sudden, Apple dethrones Coca-Cola. It wasn't just Apple that ran past Coca-Cola. Coke was number one, Apple became number one, Coke slipped to number three. Number two brand is Google. Okay, and people look at these things as, oh, it's just some marketing guys on Madison Avenue had something to say. It isn't. It means that Apple and Google are the two most trusted ideas on the face of the earth. The two most trusted, most credible ideas on the face of the earth. The reason that people trust Coca-Cola is they could crack the can and drink it and it wouldn't kill them and they know what it's gonna taste like. There's a certain comfort that comes with the credibility and the certainty of the brand. When the number one and the number two player in mobility and in computing become the number one and the number two brand in the world, that's a very interesting inflection point because it takes me to another observation, right? These are the two platforms across which every piece of software is gonna run over the next decade, maybe the next two decades. 10 years ago, right, and I lived through the first big wave of technology, the internet wave, and during the internet wave, something less than 5% of the economy dematerialized the software and the big winners were the e-bays and the AOLs and Netscapes and Amazon and Yahoo and the rest. Well, now we're living through the mobile wave and the difference is in the mobile wave, something on the order of 50% of the economy is gonna dematerialize into software. You know, the stock market still hasn't hit the exuberant highs we hit in 2000. However, people are starting to sense this, right? What happens in a world where half of everything of consequence or value on the face of the earth becomes software? Well, it's gotta run on something. What's it gonna run on? Well, I just told you what it's gonna run on, right? It's gonna run on smartphones and tablet computers. They're gonna be running Android and the iOS. It's really not possible for anybody to squeeze into that space easily at this point. Now, why this other global wave of consolidation? Well, the combination of the internet and technology and mobility tipped everybody toward American standards, American currency and American language. There's something else that happened. The rise of the EU broke down the currency and the customs and the languages of every major country in Europe, right? The French, the Germans, the Italians and the Spaniards entered into a voluntary coalition to trade with each other. And then they woke up and realized that they needed all to learn English to trade, okay? So Germans sell French cars in English. And they dragged the other countries like the Greeks into this coalition and the Greeks had to abandon their currency, the drachma. If you're gonna abandon your currency for a currency set by some bureaucrat in Brussels, why not just go ahead and abandon your currency for a currency set by some bureaucrat in DC? You think the Greeks trust the French or the Germans more than they trust the Americans? Well, we could test that hypothesis, right? There's $5 trillion worth of currency trading every single day. The UN recognizes 190 countries. There's less than 190 currencies called 100 currencies. That makes 100 by 100 matrix. You could trade the Euro versus the Yen versus the Russian currency versus the Brazilian Real. You could, in theory, there's Cartesian product, 100 by 100. 87% of all currency trades are against the dollar. The US economy represents 20% of the worldwide GDP. So on a GDP weighting, it ought to be 20, 25%. Maybe you go to 40%, 87%? Well, that means 13% is everything else. That is the rise of the American currency. For those of you who wonder, why is it that interest rates are so cheap? Why is it that the Fed can print a trillion dollars worth of paper every year as part of easing, monetary easing, or stimulus or whatever they want to call it? Why do we print $80 billion per month or something on that level? And the world absorbs it all. And we don't have inflation. Chavez had 49% inflation in Venezuela. That's this year, 49% inflation. What happens when you engage in irrational economic policies, your currency collapses? But for whatever reason, ours didn't collapse. And the answer is because the American currency has subsumed the entire world. And we've done it because all the Europeans gave up control of their currency. When they did that, they gave up control of their customs, customs meaning the trade flows. And with that, they gave up control of the law, right? Because at this point, if half the economy is software, and if you want to win that software war, you have to have the best product. And when you have the best product, you can ship it to a million people, 100 million people or a billion people, all for the same variable cost. Which means there's a dynamic that takes place. A Western company dominates the largest market, the US market, that allows them to win Australia, Canada, South Africa, all the global multinationals and everybody in the EU. Once you win that market, you've got 70 to 75% of the purchasing power on earth, then you take over the rest of the market. It's impossible. Name a company that came out of Japan in the software business that's of consequence to us. Now, that being the case, every single place that the software industry touches, it breaks down the local markets and the local providers, right?  There's not gonna be a Brazilian version of Google. You ask a question, by the way, in Google and the English language, you get a better answer than if you ask the question in the Brazilian language. Interesting.  There's just more, right? Where English is the Latin of the modern era and it's getting more powerful. But ultimately, what do we have? We have a billion person network. Google's a billion person network. Facebook is a billion person plus network. Those networks are infusing the rest of the world. China can't stop them, nobody can stop them, right? As those networks spread, people wanting into those networks have to play by American rules, American laws, American customs break and American law on gambling, American law on pornography, you don't get on the network. Somebody in DC, a regulator shuts you down, you get locked out of the network, you get locked out of the world's commerce. This is interesting dynamic because the other way to get on the network is to buy advertising. When you buy the advertising, you're gonna have to buy it in dollars from Google or from Facebook. Therefore, you better have currency that converts to dollars. If you don't play in our currency and if you don't comply with our laws and if the regulator is in the right way, don't wish to recognize your product or your service or the legitimacy thereof, you can't get on the network. If you're off the network, you end up like Cuba or like North Korea. What happens when I get things for free on the network and they cost money off the network? How many people are familiar with, well, you know, you notice there was some Google Maps, right? Google came out with maps that were plugged into satellites and satellite images. Apple decided they needed something better. How many people have used Apple 3D maps? Okay, if you take Apple 3D maps and you fly through Manhattan, you actually see the buildings. If you take Apple 3D maps and you zoom to South Beach in Miami, you can fly around the building. You can count the number of levels. You can see the swimming pool behind the wall. You can look at the shrubbery and the hedges. And so, how do they do that, right? They must have flown drones with 3D imaging cameras over every city. Now it turns out that they imaged South Beach up to 42nd Street. I have a house, 48th Street. So when you go from downtown up to 42nd Street, everything is a beautiful three-dimensional image. You can fly around. If you wanted to buy a house, you can actually see the house in the neighborhood. It's like taking a helicopter around the neighborhood. Helicopters cost $1,500 an hour. A rich person that wants to go shopping for real estate pays $1,500 an hour. That's what I did in the year 2000. I've got helicopters, I fly around. Helicopters are dangerous. They're scarce, they're expensive.  It's 20 times more dangerous to find a helicopter than this to fly in a fixed-wing airplane.  But if you have an iPad and you pull up Apple Maps, you now have something better and it's free. And you don't have that on Blackberry Maps. You don't have that on Nokia Maps.  Okay, so Ergo, it's a billion-dollar buried entry to be in the mapping business. It's going up. And here's the last point I have. I have a house on 48th Street. When you fly over all the houses south of me, they're all three-dimensional and vivid and beautiful. You get to my house, I'm living in Flatland. My image is a satellite image, which was magical three years ago. Today, I look at my house, I live in Flatland and I think no one would wanna pay as much money from my house as they'd pay for a house five blocks to the south. And it irritates me. It irks me. Apple put me in Flatland. Software is spreading everywhere on earth. Next time you decide where to live, you're gonna want to fly around and see the neighborhood. When you look at how good that school is, you can see the school in three dimensions if you don't live in Flatland. Everybody's probably gonna wanna move out of Flatland. Right? Now, what's this mean to education? Well, it seems increasingly clear we're moving toward a world where billion-person networks are going to spread, right? The first era of mobility was the era of consumer identity. The big applications are consumer apps, QtC ones, Gmail, you know, and Apple Maps and Twitter and Facebook.  But nobody ever got out of jail with their Gmail account, right? Nobody ever went to a bank and said, here's my Twitter ID, give me money, right? You can't do things of consequence with consumer identity. We're not moving the era of corporate identity and civic identity, right? And if you can identify yourself corporately with your phone or you can identify yourself civilly, I am a student and enrolled in elementary school, I am a police officer, I am a citizen of the country. At that point, all of the civic processes and all of the commercial processes that currently have been relegated to be non-automated procedures, they're all going to become automated. Right now, the standard for doing anything of the consequences I show up in person with a photo ID at a bank teller to take a test, right? To withdraw money, to borrow money, to get a fishing license, to get a driver's license. All these things have to be done to vote. Maybe people don't like you have a photo ID to vote, but most things. That's all gonna change and as that changes, we're gonna see a very interesting thing, a new era of process automation, right? And the procedures in our life that didn't get automated during the last wave, the internet wave, will get automated during the mobile wave, you know, getting a prescription from your doctor or writing a traffic ticket. If I can dematerialize your civic identity to your phone, then you can take that and you can open up a bank account in Oregon in 30 seconds while you're sitting here in this conference room. That's never before been accomplished, it will be accomplished. And that changes things dramatically. I think coming back to education, it's pretty clear here that we've reached a point where you can teach people things using computing devices. I think there's a classification of things we teach in the world that are more challenging than others. If you wanted to make it very simple, you would say we have science and we have humanities, right, one hand or the other. I went to MIT and there's science on this hand, there's humanities on that hand. And teaching ballet or teaching drama with a computer is a bit more challenging than teaching math or science. But it's an irrelevant issue because the primary economic value of education to the world today is science, technology, engineering and math, what they call STEM. And the irony is STEM has been used as a buzzword to get funding for educational organizations everywhere, aggressively, like a beating of a drum. But the one headline that I haven't read about STEM, which is the most obvious one to me is that that science, technology, engineering and math are almost certainly things that a computer can teach you better than a person can teach you.  So if there's anything that is destined to be completely 100% automated at science, technology, engineering and math. And I think you could probably show right now that a computer program would teach you mathematics a lot better than a human being.  Now tablet computers are going through the floor. Amazon just came out with a $220 tablet device. Why? Because they're number three, they have to. Bezos said, we don't intend to make money off the device, we intend to make money when people use the device. So what happens when you get to a $200 tablet computer and you have free Wi-Fi? If it lasts for four years, you're down to $50 per year. What, by the way, Bezos bundles a bunch of stuff into the tablet computer, Google competed with Apple by giving away Android for free, Google thinks about ad financing it.  And you might say, why would anybody do that? Well, the answer is why wouldn't they do that? LinkedIn trades at 20 times revenue. LinkedIn trades at 20 times revenue. Facebook trades at 20 times revenue. Zillow, Zillow, the fun application that we use to do home shopping on our tablet computer, trades at 20 times revenue. Okay, when's the last time this all happened? 1999, that's when it happened. And you remember what happened then? When things start to trade at 20 times revenue, it means an essence that the marketplace has become electrified, things hit a plasmatic state, there's massive amounts of energy to do anything that captures the public imagination. And at this point, you could argue that it would be in the best interest of LinkedIn to take $2 billion and embed a complete education curriculum, whatever it might be is give it away for free to the planet if you join LinkedIn. What's their monetization strategy? It's recruiting. It's easy, right? Facebook could do the same thing. Facebook's worth $135 billion. What if they just give you free K through 12?  Of course I can. How about how to build a bridge, right? If you play with cut the rope or you play with the games like water, things that teach hydraulics or they teach rotational physics, it becomes very, very clear that all of those things are taught better on a computer. Almost by definition, any laboratory exercise in an engineering school for an undergraduate has to be a very controlled experiment because otherwise we would burn our 19-year-old students to death, right? Think about the liability of letting kids construct their own bridge with real steel or play in a lab with a virus, right? We don't really let 19-year-olds or 21-year-olds play with fire, not a lot of it, little fire, right?  You know, I have two jet engines on the back of my airplane, they're 15,000 pounds of thrust each. That means technically it can lift 15,000 pounds straight up in the air. You got to let a 21-year-old play with 15,000 pounds of thrust, put a hole in the roof, right? So, bottom line, we have controlled experiments. There's no better way to teach people engineering and hydraulics and physics and math than a controlled experiment or a simulation running on a tablet computer. And there are no better simulations than the one we've seen. When Apple released their iPhone 5S, they showed a 64-bit chip. This is great, 64-bit chip. And no one has any clue what a 64-bit chip does. So they said, well, look at this game. This is a dragon flying through the air, breathing fire, and we've rendered it perfectly. Do the 64-bit chip. It's a simulation of you fighting a fire-breathing dragon. That's the best idea they could come up with. But I went to MIT and studied aeronautical engineering. I can think of some better simulations to put on a 64-bit chip would have economic consequence to the world. You know, the only other practical application we saw was I spent all weekend recording 12-year-old boys running and jumping into the water and I hit slow-mo and it captured 120 frames per second and you could see the kids spinning like this. Now, I said before it's hard to teach ballet on a computer, but I didn't say you couldn't do it, right? Because a 64-bit chip that captures 120 frames a minute combined with the M7 chip which keeps track of your time and motion at a gyro compass, combined with a watch that has Bluetooth may very well allow you to watch someone's motion of their arm as they conduct music against Beethoven and give them a grade, right? Or watch the swing and the motion of a golf club or capture the frames as you spin around or capture your center of gravity. All of these things are coming, but the most obvious thing that's coming is someone's gonna write a program that teaches you algebra and they're gonna release it to one billion people. And that's gonna be a better way to learn algebra than any other way we came up with the last 2,500 years. So, for education, I'm not gonna talk about individual education initiatives. You look around the room, there's a hundred different education initiatives going on here, right? All I'm gonna say is the obvious at this point. There's probably two billion people in the world that wanna learn something at any given time. There's seven to eight billion people on the planet. Just do the simple math. Somewhere between one and two billion people would like an education in something. The most economically valuable education you can get is a science, technology, engineering, and math education combined with the ability to speak English. All of these things certainly can be taught for a variable cost of zero on a piece of software running on the iOS or Android. Someone is gonna spend one of those programs and release it. If Apple may very well make iOS 9 the version of Apple that teaches you everything scientifically related, K through PhD. And then in 72 hours, 800 million people will get something embedded in the operating system called I, K through 12. And if they don't do it, then Google will do it. And if they don't do it, Jeff Bezos will do it. And if they don't do it, then somebody at Zillow or LinkedIn or Facebook is gonna do it because there's effectively infinite money running after good software related ideas right now. Those companies that trade at 20 times revenue do so because they're pure software plays. And the perception is, if they get it right for 10 million people, they'll get it right for 100 million people. They'll get it right for a billion people. And then they'll get the next five billion people and there's no stopping them.  That's not my point. My point is I think we're gonna see an incredible renaissance in the software business and you're gonna see dozens or hundreds of great international networks form. They may not all be American, but they'll be Western networks coming out of the first billion consumers because that's the marketplace capable of catalyzing the global dominant player in any given field or segment. Will there be one education network? Probably not, but there are economies of scale here that you can't look beyond, right? And we're transitioning from a world where for 2,500 years, we taught 20 people at a time calculus and algebra. And now we're gonna be in a world where one person can write a program or one team can write a program that teaches 250 million people at a time. And the other day I looked at just another one of these MOOCs that came out and just it struck me, it struck me. In this day and age, learning anything in a classroom of 20 people is about as good an idea as growing food in your backyard. Right, because a garden is a garden for 20 people. You're gonna grow food for 20 people at a time in your backyard. You're gonna have one person teach 20 people anything. Well, it is true that there are some things you can't teach to more than 20 people at a time. I get that. Those aren't gonna be the revolutionary things that drive the civilization forward. Cooking and ballet and your interpretation of Shakespeare, that's not what's going to drive the civilization for the next decade. The things that are revolutionary are gonna be the ability to teach somebody computational fluid dynamics for a nickel. The ability to create a, you can create a person with a PhD in mathematics for $50 a year. Right, we know we can do that at this point. Has it been done? No, but is it inevitable, we're gonna move toward a world where it costs about a million dollars to convert a three-year-old kid into a PhD. We're gonna move toward a world where it's gonna cost something other than $1,000. And every single field where you can do that is a massive amount of money you can make. Massive amount of money. It's an economic opportunity for a non-profit or for a for-profit. And that's my closing thought. Are we done at a time? Thanks for your time.


Who thinks that I speak too fast and then the lectures are too fast? Oh, come on, some of the different questions. Do I speak too fast? OK. Are the lectures too slow? OK. Are the lectures too fast? OK. Too slow. Good. OK. No. Oh, are the lectures right? No, you see, it doesn't match. There are too many undecided people. This is not correct. OK, so I think I'm going to start. So today, I think it's a key lecture because I think we really want to connect this rotation and Gauss map. And it's going to be our first example of renormalization. And it's really the basic idea of renormalization. But I think even though someone thinks it's too slow and almost all of you know continuous fractions, I decided that I made a mistake in skipping. I want to have on the board a couple of the properties that you almost all already know about continuous fractions because I'm going to need them today. So let me first start with this quick recall. So recall for almost all of you. Recall from continued fractions. So I need the notation. So we have alpha irrational. And we have, hence, alpha has a unique infinite continuous fraction expansion where these entries are positive integers. And I want to, probably you've already seen, I can define truncation. So I want to call pn over qn finite continuous fractions obtained by terminating the fraction at a n. So this is infinite, but I stop it at a finite level. And then I can clear out the nominators and I get the rational. So these are called convergence of alpha. And we are going to use them today. Actually, the denominators we are going to use. And let me recall you some facts about this convergence. So just three facts. So first of all, this convergence, you may well believe, will converge to alpha. So as n grows, you will tend to the infinite continued fraction. And actually, this convergence is exponentially fast. This I don't need, but it's just for your own. They converge exponentially fast in the sense that you can bound the difference between alpha and the n truncation. And this is less than some constant over something like square root of 2 to the n, so exponentially small. Maybe we'll go here. And then the key thing that you probably have seen, because it's one of the things you do in continuous fraction, there are recursive formulas. So especially the Qn and the Pn denominators and numerators both satisfy this set of recursive equations.  This is a recursive relation involving the denominators and the entries. And also you have initial condition. So Q0 is actually, you set it 1. And Q1 is A0. And the Pn satisfy actually the same recursive formula. So Pn plus 1 is also equal to An plus 1 Pn plus Pn minus 1. The same formula, but different initial conditions. So you want to take P0 to be A0 and P1 to be A0 Q1 plus 1. Doesn't matter so much. Just a recursive formula for actually, I don't need the P's, I will just need the Q's. Have you seen this when you did continuous fractions? OK, great. So if you want, in principle, you could try to prove them. So it's just a manipulation of continuous fractions. So if you haven't seen them, you may want to play with them. But I want today, we will see a dynamical interpretation. So this formula will have a dynamical meaning. So I don't care about manipulating continuous fractions. I care about giving it a dynamical meaning. And similarly, let me tell you the third property that you also know, probably, that these are best approximations. There are something called best approximation of the first type or the second type. I don't remember which one. But I say I want this one. So if I look at this distance, this is actually less. It's the best possible. So this is the best approximation among all rationales with denominator bounded by Qn. So this distance is less than, let's say, put less than or equal to have to be safe. But I think less is correct. Q alpha minus P for every P integer and for every Q1. One less than Q, less than Qn. As I said, put less or equal. I guess I want to put less or equal. So in any case, they minimize the distance from integers. So maybe you can also use this notation. You can write norm of x, z to be the minimum of x plus n as n is an integer. And then you can kind of read this as saying Qn alpha less than Q alpha for Q less than Qn. So this is like distance from integers. So this is all I wanted to remind you. And first thing I want to remind, I want to give dynamical more than geometric. What does this tree means? Dynamical interpretation of property 3. So what does this tree say about the orbit of the rotation? How do I find Qn if I look at an orbit of the rotation in space? They are best approximation, but dynamically.  I have to do many pictures today. So I'm going to put 0 on top of my circle, just because I like 0 on top. So if I look at the orbit of 0, if I look at the orbit under the rotation by alpha of 0, so this is just basically a fractional part of n alpha. Well, on the circle is whatever. On the 0, 1 is fractional part of n alpha. But say that I plot my, what is special about the Qn? If I look at the Qn iterate of the orbit of 0, how will I recognize that I'm special? You're just shy? Maybe my question is clearly unformulated. OK, maybe. So this property tells me that when I have the Qn, the distance from 0 on the circle is less than all the previous iterates. So I want to say, if I look at the distance between alpha Q of 0 and 0, this is nothing else than the Q alpha, this integer norm. It's the distance from integers. And Qn are successive closest returns. By this I mean, so if I keep iterating my rotation, at some point, well, I start from 0. I go far from 0. At some point, I get back close to 0. And this is actually going to be the first orbit at Q1. At Q1, I'm very close to 0. Then if I keep moving, well, I will again go farther from 0. And maybe when I come back, I actually come back but not as close as before. So I might have to keep going, keep going. And I come back, and maybe I come back again close, but not as close as Q1. So if I wait until Q2, I will actually be on the other side. And I will be, maybe I should draw it a little more. I would be actually Q2 is the first which is closer distance from 0 is less than the distance of Q1. And so on. If I keep going, it will take me longer and longer and longer number of iterates. But at some point, this will be the Q3 iterate. It will be even closer and then so on. And actually a fact that you can convince yourself and it also comes with a continuous fraction is that remark is that r alpha to the Qn of 0 alternate between left and right. So now I will get it wrong. Let's see Q1. So this is the left of the origin to the left of 0. If n is odd and it's to the right of 0, if n is even. So the closest return is once to the right and then to the left and then to the right and then to the left. And they accumulate towards 0. Great. Now I want to understand. So this is the dynamical interpretation. So I want to understand what happens on small scales. So in some sense, I want to zoom in around the neighborhoods of 0. And I will use these special closest returns to pick a family of neighborhoods of 0. OK, so let me define and let me set. Let me give a notation. Set in to be, this will be an arc to be an arc. But sometimes I will think of it as an interval. So we always identify the circle with an interval. So arc, but I will straighten it up and think of it as an interval. But for now, I want it on the circle because I want an arc with n points. N points are alpha to the qn of 0 and are alpha to the qn minus 1 of 0. This morning I was trying to get my indices consistent. And let me check my hook one. If it can be off by 1. But I think I checked it in the morning and I want it with n and n minus 1 to be consistent. Let's see. I lost my notes. Yes. OK, so I cannot tell you which one because some ones it will be one to the right, one to the left. And the other time it will be the other way around, right? So in my picture over here, this would be, for example, between 1 and 2, this yellow interval will be, did I get it wrong? I want it to be 2. I guess it's correct, I too. And i1 actually will be q1 is actually, sorry, q0 is 1. Is it right? q0 is 1, so alpha. So I have to take the point alpha. So if this is alpha, and this would be actually i1. i1 has n points at q1 and q0 and q1. Yes, that's right. Sorry, did I confuse everybody already? The n points are n and qn and qn minus 1 iterates to 0. So if I want the n points of i1, the n points of i1 will be q0 and q1. But q0 is actually 1, so this is actually alpha because 0, after 1 iterates, maps to alpha. And this one is this point that I have over there. So this is the first interval, and the second will be smaller. Essentially, what's happening is that I have an arc, which is my i1. Oh, gosh, this chalk is not good. There is 0 somewhere in between. And then at some point, one endpoint I keep, and one endpoint I keep, and the other endpoint I shrink. So I get another interval which contains 0, but it's smaller on one side. This would be i2. And then I will keep this interval and wait for the next closest return, which will happen on the left, and so on. So I'm getting a sequence n plus 1 contained in in. So these are nested arcs, and each one has one endpoint in common with the previous one, by definition. And this will be the interval on which I want to zoom. So I want to study the dynamics of the rotation on these smaller scales. And I will define in a second inducing. But before doing that, let me make a convention, so an easy remark. So by convention, I'm going to decide that i minus 1, which is not defined here, i minus 1, I'll take it to be, I write it. I take it to be basically the whole circle. Let me write it like this. It's s1 cut open at alpha. So if I have my whole circle, this is 0. This is alpha. I'm going to take my pair of scissors and cut it open at alpha. I can draw the little scissors. And so the interval looks like this. It's 0, contains 0. And here it's alpha. And here this length is 1 minus alpha. So this point is minus 1 plus alpha. This is my starting interval. And of course, it's just a different choice for opening up the circle. So how does the rotation look like when I cut open my circle? Well, we draw the graph. We said it's x plus alpha mod 1. In this case, it would be x plus alpha modulo this interval. So we had a plot, you remember, of the graph of the rotation. But I want to think dynamically. So dynamically, how does the rotation look like? I have two intervals, one of lengths alpha, one of lengths 1 minus alpha. And I want to just say that if you cut open a rotation, it looks like an exchange of two intervals. So what happens when I rotate the big arc? Oh, sorry. This point is minus 1 plus alpha. This is the length. So when I add alpha, this is just a shift. So I'm going to draw the image by the rotation of these intervals geometrically. And this is just shifted. And it goes exactly to the end of the interval. And the other one is just what happens to the other one? I'm adding alpha. And then I have to take the result modulo what I have. So when I do it, it just goes back exactly to the other point, right? So this is how a rotation looks when you cut it open. It looks no matter where you cut it open, it will look like an exchange of two intervals. So maybe let me write this. It has interval exchange, interval exchange map of two intervals. So the rotation is equivalent to this. In general, so if you have, and this is also called two IET, interval exchange map, in general, you could have a D IET. And this would be a map where you have an interval and you chop it up into these subintervals of any lengths you want. And then you kind of permute to them. In this case, you need to specify how you want to rearrange them. But you can kind of permute them so that each has the same length in the image. And you rearrange them so that they again form an interval of length one. I'm telling you this because I will give you an exercise later, which involves an interval exchange of three intervals. OK. And actually, I can tell you what the, OK. No, no, I cannot tell you yet. OK. And now I just want another easy thing.  So first I'll also, no. I want to tell you what does it mean to induce. So what does it mean inducing? Inducing. So if I, let me say in general, if I have a dynamical system from x to x, from x to x, and I have a subset of my system, y, and assume that I know, assume that for every y in y, or maybe not for every, but for almost every, with respect to some measure, for almost every y in y, the point returns to my set. And you just did one career recurrence this morning. So this is not such a big assumption, you will believe. So assume that y, for every y in y, there exists an n such that fn of y belongs to y again. So this is a return time. For example, this is true for our rotation for any interval, just because orbits are dense. So if I pick any interval, points will come back infinitely often, actually, to them. But for one career recurrence, this would also be the case for measure preserving. OK, assume that you know this. Then you can define the induced map. Then you can define, I will call it fy from y to y. This is the induced map. Sometimes we can also call it first return map. Sometimes we can also call it one career map. For one career, maybe I'd like to use it for sections of flows better. I'm not sure if it's. Let's say it's an induced map. And what is this? This is just you wait until the point comes back and define a map from y to y by setting fy of y equal to f to the r, let's call it r y of y of y. So let me explain this. So what is the r y of y? It's an integer. It's a power. So this is not a power. This is a composition. This is r y of y composition. It's the usual notation of f composed with f that number of time. And r y is the first return time. So it's the minimum n greater or equal than 1, such that f n of y is back in y. So this is first return time. I have all the statements to state what I want to show you and the algorithm I want to explain. OK, we'll leave over there. I want to see or I'm somewhere that I don't erase. So OK, maybe I'll do it here. I keep the n point. I keep the intervals. And what I claim is that maybe I'll take the way I wrote it. So the main proposition. So let me say the induced map of r alpha. Maybe let's give it a name. Let's call this induced map t to the n. I'm calling it t because it's OK. The induced map, this is the definition. The induced map, t to the n, t to the n is just the name of the induced map. The induced map of the rotation on this interval, i n, contained in S1, is actually an exchange of two arcs. It is an exchange of two arcs. And I'm going to call these arcs delta n and delta n minus 1. Again, I hope my indices are right. Let me just check my indices. Delta n and delta n plus 1, correct. And for n greater than 1, and for n greater than 1, I want to say, so let me let ln lambda n be the length. This is the length of this arc. This is the arc length. So we have that lambda n divided by lambda n minus 1 is actually the ratio of the length of these two arcs is actually given by the nth iterate of the Gauss map. So I see the Gauss map as ratios of these induced lengths. Moreover, you can also say what are the return times, the first return times are respectively qn minus 1 and qn, respectively. So and it's mismatched indices. So qn minus 1 is the return for delta n. And qn would be the return for delta n minus 1. Voila. And this is what I want to prove today and show you. But I want to first explain what this means. So what am I saying? I have my rotation. I have this sequence of nested intervals. And I claim that I look at this nth nested interval. The dynamic which I see as the first return map is exchange of two intervals. So the dynamics of the one-care map or the first return map will be something like this. I will have two intervals which are exchanged. So when I wait for my rotation to come back to this small arc, I see two intervals which are exchanged. And the iterates that I need to do of the rotation to come back are different for the two intervals. So in one case, I have to wait for one, and we have to wait qn iterates to come back. For the other, I have to wait qn minus 1 iterates to come back. But I just thought I spent some time to say at the beginning that the rotation, you can think of it as an exchange of two intervals. Because now if you want, I can glue back, glue to circle. So if I glue to a circle, this map, these two intervals, and I rescale the circle to unit 1. If I rescale the circle to unit 1, then this induced map rescaled is actually you get a rotation by Gauss to the n of alpha. So basically, this inducing is also giving me a map from rotations to rotations. And basically, this map is renormalization. So this map, we'll call it R, renormalization.  And this is actually equal to R of Gauss to the n of alpha. So on the parameter space of rotations or rotation numbers, this renormalization procedure is described by the Gauss map. Just to understand my time, I have only 20. How much time do I have now? Now we have to work. This is kind of all the introduction. OK, I made also some pictures because I'll try to make a picture on the board, but it's not clear that it will be as nice. So maybe I keep also pictures on top. And I would put these pictures on the web. So I would suggest that maybe you look and don't try to write because you can get a different picture and then you get confused. So just look at the pictures and listen, and then, OK, OK. And also, I will post some lecture notes. In the other days, we went from a course which I was teaching in the introduction to the dynamic system. But this part is not written in a lecture notes form. But I have some handwritten notes that I think are quite nicely written. And I scan them, and I'll put them online. So you can find this procedure described with all the details in the notes also. OK, so we consider our rotation by alpha. So this is our rotation. And the first interval I want to look at, I want to set delta 0 to be 0 alpha. Actually, all these intervals, you could make them semi-open if you want, so then you have. OK, so this is my red interval. It's red. No, no, no, no. It's the first green interval in this picture, OK? Maybe it's bigger in my picture. And maybe I'll do it green also here. So the first thing is how many iterates can I fit before overpassing 0? So how many full copies of? So remember that if I take a 0, a 0 by definition is if I divide 1 by alpha and take the integer part, this gives me a 0. So a 0 is actually how many times I can fit an interval of size alpha in a unit circle. So iterate, so I want to iterate delta 0, a 0 times. So this is what I did in my picture, 1, 2, 3, 4. I iterate a certain number of time. And this number of time, a 0, is exactly how many times I can fit a full interval. And then what is left is going to be a reminder. What is left is supposed to be, that's why I like the picture on there, that what is left, this is going to be my reminder.  So delta 0 was the original arc. And delta 1 will be my first arc. And let delta 1 be the reminder. And notice, notice that alpha is r alpha to the q1 of 0, because q1 is equal to 1. So this endpoint is r alpha to the q1 of 0. And that endpoint, what is it? And the left endpoint, the left endpoint of delta 1 is r alpha to the a 0 of 0. But a 0, if you remember this recursive formula, a 0 is q1. So this is r alpha to the q1 of 0. So the endpoints of these two intervals are exactly r alpha to the q, sorry, r alpha to the q0. And r alpha, did they write it right? q0, this is q, sorry, sorry, sorry, sorry. This was q0, q0 is 1 and q1 is a 1. So what I wanted to say that what I defined to be i1 is the union of delta 0 and delta 1. And I claimed that now I want to induce. So this is my first inducing interval. I'll do it yellow. The union of these two is exactly what I want to induce. And I guess I have a pointer, yes. OK, so this is where now I want to focus. It's my first induction. So what is the Poincaré map, the first return map of the rotation on the yellow interval? So let's see what happens to the red interval. So 0 is mapped to alpha, because I'm rotating by alpha, right? So 0 is mapped to alpha. So the other endpoint will drag along. And the red interval will just move to the end of the yellow interval, OK? So 0 goes to alpha. And the reminder goes, well, whatever it is. And this is already back. The red interval in one step is back to the yellow. So the return map just takes one iterate. So maybe I can say, well, if I want to write everything, because what do I want to say? I want to say that r alpha of delta, what is it called? Delta 1 is already contained in delta in i. So the return time is 1. But notice that 1 is also q. The first iterates are confusing, because 1 is also q0. So we proved that 1 returns in q0 iterate. What about the green bit? So the green bit, now I wish I had that. We can use think of the pointer. Does the pointer point? No. Oh, gosh, where is the pointer? Here. So this green, let me move it again. So this green bar, it's my green arc. So I can follow it, follow it, follow it, follow it, up to here. And the last time it comes back, it will actually follow this bit and exactly fill the spot to which I had. So delta 1, so what I want to say, sorry, delta 0 returns. In how many iterates did it return? Eh? What did you say? Who said? You said the green one. No, the green one moves, rotate by alpha every time. 5 in my picture, in general. What is the number? So it fits a0 times fully. So I start with one copy. I have to move to the second, to the third, to the a0 ones. And then I have to do one more iterate. So it's actually a0 because it's a0 minus 1 plus 1. So I return in a0 iterates, in a0 iterates. And a0 is q1 by definition. So we proved the first step of our assumption. So we proved that we come back in q0, q1 types, and then the induced map is an interval exchange of two intervals. What happens next? Ah, this is too fast. What happens next? So now I need to induce on the yellow, sorry, I need to induce on a smaller interval, which I don't know yet what it is. But first, let me remark that if I look at returns remark, if I look at returns of the rotation to this I1, every time I return to the yellow interval, I can forget what happens in between. When I return in the yellow interval, I'm actually doing one iterate of the induced map. So returns of I1 are iterates of t1. t1 is this induced map, this exchange of these two intervals. So let me just try to understand what happens of the red interval. I'll draw it here. What happens of my red interval when I apply my exchange of two intervals? So this is green. And my map t1 maps it here. And this is red. And my map t1 maps it there. So if I look at the red interval, the first iterate is here. What happens then? Then I have to think of it as a part of your original interval and drag it along with the green. So you have to plot some orbit of some interval exchange, especially if it's next week it will be good. So my map takes it here. Then if you want, think of it as part of 0, 1, and then you drag it along. So I want to say that this is t1 of my interval delta, what was it, delta 1? This is delta 1. And then if you look at t2, this is actually going to be a copy of Joshian to the left. Sorry, t1 squared of delta 2 is here. And then if I look more, basically every time that I'm applying t on the red interval, it's shrinking towards 0. And I can look how many iterates it takes me until I can fully stay inside. So for how many iterates? So for, ah, we didn't do the main thing. I'm so sorry. I missed one bit. I missed one bit. Sorry, I need to go back. I haven't proven the full proposition because I didn't show you the ratio of the lengths, which was an important part. So let's look at, sorry, I'm going to go back to the first step. So lambda 1 was the length of delta 1. And lambda 0 is the length of delta 0. What is the ratio? So lambda 0 over lambda 1. What do I want to prove? Lambda 1 over lambda 0. I want lambda 1 over lambda 0. So lambda 0 is alpha. It's a length alpha. What is the length of the reminder? The reminder is 1, everything, minus a0 times alpha. You agree? I have to remove a0 times my big interval. But now simplify. What is this? 1 over alpha minus a0. And a0 was the integer part. A0 was the integer part of 1 over alpha. So this is fractional part of 1 over alpha, which is the Gauss map. So this was part of the important part of the proof of the first step. And similarly, how many copies, the cardinality of copies of delta 1 in delta 0? How much are those? I need to take the length of delta 0, lambda 0, sorry, the length of delta 0, and remove this cardinality of copies of delta 1 in delta 0. It's just I have to take lambda 0, divide by lambda 1, and take the integer part. So this is what the definition I divide and take how many times it fits. Lambda 0, I hope I get it right. So I prove that lambda 1 over lambda 0 is Gauss of alpha. So this is integer part of 1 over Gauss of alpha. This is the opposite ratio. And what is the integer part of 1 over Gauss of alpha? No? So Gauss of alpha, the continue fraction was a0, a1, dot, dot, dot. Yes, a1. That's right. So what is the length? So now I claim that this point is actually, this point is actually, what is this point? I think I'm going a little bit too, let's see where I go. I think I can erase here. I want to keep the theorem. So I want to know if I do this a1 iterate. So if I apply my induced map on the red interval a1 times, what is the endpoint? So maybe let me draw it again. I have my, here I have r alpha to the q1 of 0. The left endpoint, I want to look at the left endpoint of the red interval. So the red interval, I have to cut it. Iterating t1 cuts the red interval as many times. Here there are a1 copies. And I want to know what is this point. I claim that this point is obtained by taking r alpha q1 of 0. Taking this point, first I have to map the interval here. To map it here, I just need to apply the rotation once, because this is the first time. So then I need to apply the rotation once. But then to go from here to here, I'm actually dragging along with the green. So the green takes a0 times to come back. So I need to apply r alpha to the a0. I hope I'm going to get it right. So sorry, I have to apply it a0 minus 1 times. Because I'm already in the first copy, and then I have to apply it a0 minus 1 times. So what is this point? This is r alpha to the q1 plus, sorry, it's not a0, but it's a1. So this number of copies is a1, plus a1 times 1. You should think of it like this as q1 plus a1 times 1, where 1 is q0. And so what is this iterate? Well, this iterate is q2 by definition. So the moral of the story is that the endpoint of reminder is r alpha to the q2 of 0. So what am I saying? Then now if I want to induce on the next interval, so if I set delta 2 to be the reminder. So delta 2 to be the reminder interval. So this delta 2 will be where am I? Delta 2 will be the small interval here. So if delta 2 is this reminder, this one is my interval i2. And then I can continue the procedure the same way. So let me just say set delta 2 to be the reminder. And then I have that i1 is equal to i2 will be equal to delta 1 union delta 2. So maybe what I did, I'll show you the pictures. So this is actually how the iterate of the rotation on the whole interval looks like. Do you see the red interval? It goes along many times. And this is the red interval, you should really think dynamically. So the red interval goes along, come back here, then goes around, come back there. And left leaves my little reminder. And now I want to pick the red and the green and induce on this arc. And I have one more step. Now if I induce the red and the green on this arc, I get a smaller reminder. And this is where I have to induce next. So I don't want to do the, of course, this is the beginning of an induction. You could try to prove this whole statement by induction. But I think I want to summarize what is the algorithm before stopping. Because otherwise, I think we are all confused on what's going on, because we did too many steps. So let me streamline what's happening. Let me streamline the algorithm for inducing, which is now very simple. And it looks like this. I start with what was right, it was long to the left and short to the right. So it starts with, this is alpha, if you want. It starts with i minus 1, if you want, which is alpha, which is the whole circle, which is length 1. So what my algorithm tells me, my algorithm, you can think of it like this. Take this arc and chop it as many times as you can. This will be a 0 times from the left. You are left with a little reminder. Call the reminder, so this was your delta 0, call the reminder delta 1. This is our first step. Now we get i0. I might have messed up. Was this i0? I think I messed up a little bit. I knew I was going to mess up. Was i0 the one which I did I define with minus 1 or with 0? I think I might have messed up. I knew I was going to mess up. So I think it's, I should have defined the, is it still here? No, the trivial one where I cut open the rotation, I should have called it i0. Did I call it i0 or i minus 1? Okay, because I changed the indices in the middle of refining the class, which messed it up. No, and I think delta, we'll say it again. I erase this and i1 has n points. I think i1 is a 0 alpha, right? No, I forgot. I see, I think, okay. I think whatever was minus 1 should have been 0. Yes, so I said that i1 had, I know it was qn and qn minus 1, the indices. So yes, so I think i1 was, I'm not, I'm getting confused now. Okay, in this module, the indices, the next interval will be, I can check them up later and I think on the nodes there, right? Okay, so in any case, now I'll have, I start with large, large and a big interval. I chop the, here the small is on the right. I chop it from the left and point as many times as I can. I'm left with the reminder and now I start chopping the reminder. Now I start chopping the reminder from the right as many times as I can and I'm left with the reminder and then I start chopping the reminder from the left. So basically for, from n odd, let's see if I can get it right or not probably not because the indices from one end or the odd or even, you chop, you chop the small interval from the left end point as many times as you can and you're left with the reminder and for n even, you chop the small. For m even, the small would be on the opposite side. The chop the small from right, from the right end point as many times as possible. So each time you take the small, you go to the opposite end and chop it until you have a reminder and then you look small becomes large, reminder is the new small and you start over, chop the small and one time you chop from the right, one time you chop from the left. So this algorithm which you can take as an algorithm is actually producing the induced maps of the rotation on the smaller and smaller arcs and that's what we try to convince ourselves looking at the dynamics. So this algorithm, if you want, it's like a Euclid algorithm. It's a kind of geometric version of Euclid algorithm and it is indeed a way to produce the continuous fraction expansion. If you have two numbers, you have the chop one from the other and it is also going to be next week, we will actually describe an induction for interval exchange maps and this is kind of the basic case for two interval exchanges. It looks like almost like this partial sum convention. So I think I will start from here tomorrow. So tomorrow we'll rewrite again the algorithm and then I want to show you also the Rockling Tower pictures and then I want to show you some applications. What can you do with this? So okay, so hopefully.


Disney plus just released their poster for the most overrated character in Star Wars history Boba Fett. Let's talk about it Before I jump into the video. I have to inform you that Mary Poppins Leia just Telepathically communicated with me using the force she says you need to subscribe and hit the notification bell So you get these videos right into your feed. What's that? Oh, she's gone Princess Leia just flew back into space to to fight aliens and punch asteroids and stuff What we're looking at here is a very fine poster. It's not setting the world ablaze by any means. It's not insulting. It's just a It's getting the job done. We have our lead hero the titular character Boba Fett. He's sitting on a throne of sorts I don't know much about Star Wars lore Outside of surface level stuff probably a little bit more than your average bear But not enough to really dive into this poster in any meaningful way So I will now if you take a look at this poster You'll notice there's not much light going on outside of the one source coming from atop often the distance It gives not only a sense of scale to the room or depth to the room But also the fact that this room is not very well lit for a reason. It's been lost to civilization He has rediscovered it. It tells the audience what they can expect from a show like this There's going to be some spelunking Fett's going to be traveling to new locations unearthing secrets and discovery not only hidden gems But also discovering himself in the process He's on a throne. He's a king.  Can we talk about this character? The guy gets bested accidentally by a clueless Han Solo who hits the side of his backpack jetpack He flies into the side of his ship and then falls into the pit below how embarrassing It feels like it's been an eternity since we've seen a painted poster And I can't tell honestly if this is fully painted or if it's just drawn on top of a photo It looks like it is it looks like it's it's painted or drawn somehow if we zoom in and enhance we can see that upon blowing up He's got his blaster pointed between his legs. He's showing his dominance showing his alpha male status He means business. He's testing you.  How was he still alive?  It doesn't matter don't defend this just like bringing darth maul back after he was cut in half Just like bringing emperor palpy back when he was thrown down into the dead of space after being electrocuted And nothing matters. It's space magic, right? I like the poster the only thing that's not really fitting is the logo It's fine. It's a little poppy for me. It's jumping out a lot I understand you you want the audience to go there and then see that obnoxious disney plus logo below I would have liked a little bit more shading on it. It's very flat You know give it some depth put some shadow around those letters Let it let it grow let it come at you a little bit more It really feels just kind of stuck on there and not part of the poster end of the day a poster is far More than this chump deserves. He got a great song by mc chris. He's had several comics and and Appearances on things like the mandalorian season two. So yeah, they're they're really trying to make boba fet a thing to appease the nerd fans I I just don't get it. I never will people criticized captain fazma when she was announced A lot of people were like, I thought she was gonna be awesome.  She was boba fet Where's her show? Where's her crappy show? All right, that's all I got. Are you excited for the boba fet tv series coming out? Or are you lukewarm? Like I am I love the mando. I love mandalorian. So, you know, this this has potential. I just Why why him let me know in the comments like the video if you had a good time Subscribe if you haven't and hopefully I'll see you soon Thanks again for watching the video if you like the little poster breakdown I did I have more of them on star wars You can you can find them on my poster playlist. I have amongst other movie related content here You could also join me at patreon or right here on youtube via the join button And if you don't want to that's fine, but you know what you do want to you will go to patreon.com Adam does movies and leave me some money Because You you you like me Right now Do it I don't think it's working