Hey, guys, if you wind up liking this talk, I'm going to be tweeting out links to slides and all that stuff later, so check out my Twitter. So I'm very excited to be here, right? I come down to San Francisco every couple of, or a couple of times a year. And every time I come in, I always feel like I'm flying into Starfleet Academy. You know, SFO is really aluminum and roundy and everything's from the future and the sky's clear. And then I go back home to Seattle and it's a whole different story. Little known fact, that's actually a young Aaron Patterson. So my talk is about the short but happy lives of HTTP requests and specifically with a specific focus on how to make those shorter. We all know how this works, right? You type in a URL into your browser, that triggers your Rails controller, which causes a view to be rendered, which causes a nice picture of a calming manatee to be rendered back to the browser. And so, you know, that's great. That's a mental model I kind of use when I'm developing. But if you've been at this a while, you might start to notice that this connection between the browser and the controllers and the views is a little bit mysterious. It's kind of like a black box. And if we're going to build fast-performant web applications, we kind of need to know us in that black box.  So let's talk about the internet.  As soon as you start to research the network, try and learn about the stuff, you run into this thing called the OSI model. It's very simple. There's actually a lot of dispute about the OSI model. Some people think it looks like a hamburger. At this moment in time, though, we're all pretty much in agreement that it's made out of cats because, I mean, how else could the internet be so efficient and transmitting pictures of cats? So to find an image of the OSI model that didn't involve some stupid meme, I actually had to go back to a 1995 issue of Dr. Dobs Journal and scan in a picture. And so what you see here is we've got a 10,000-foot view of the network stack. At the top, we have things that are more abstract. At the bottom, we have things that are less abstract. You and I are used to dealing with the application and presentation layers. Let's just go down the stack. The session layers, kind of like SSL, transport and network are kind of TCP, IP, and the data link and physical are kind of like Ethernet card and the wire, right? So I want to talk for a second about wires. It turns out that wires are surprisingly important to modern web development. Because your wire determines your latency. And latency is a time that it takes for one byte of information to travel from my computer to your computer. It's a time in the wire, right? It's not bandwidth. It's not measured in megabits per second. It's measured in milliseconds. And the thing to know about latency is that it's got a lower bound. It's got a lower bound determined by the speed of light, right? Which is great because the speed of light is like the fastest thing in the world. It's 300 million meters per second is the speed of light in a vacuum. And just like a little pro tip for you guys who didn't go to science school like I did, just call it the speed of light in a vacuum. Don't say S-O on a vacuum because that's like something completely different. But you run into problems when you actually, say, calculate the shortest distance between London and New York City or New York City and London. When you do this, you find it's about five and a half million meters. And do the math, that means that your minimum theoretical latency round trip between New York City and London is 37 milliseconds, roughly. So you're never going to send a message from New York City to London and get it back in less than 32 milliseconds or 37 milliseconds. And in fact, it's a lot shorter than that because we're not sending light through a vacuum. We're sending it through fiber. And light travels through fiber much more slowly than it does through a vacuum. So we find out that we have latencies that are kind of like this, right? New York City to London is about 79.6 milliseconds. That's really too precise. Let's say 70 to 90 milliseconds. Within the US, latencies of about 40 milliseconds are common. Japan, you got 16 millisecond latency. It's not because they're super highly advanced, it's because, well, the country is a lot smaller. And I bring this up because latency kills user experience, right? If I click on a button and it takes 100 milliseconds for something to happen, I know in my heart of hearts that I didn't really cause that thing to happen physically. And if it takes 250 milliseconds, it feels sluggish. If it takes 500 milliseconds, I'm wondering how the stock market's doing. Yeah, I just started investing in the stock market. I'm like $50 down. 1,000 milliseconds, I'm out of there, right? And this has real world implications because Google found that if searches took longer than 400 milliseconds, people didn't search as much. Big online retailers have done studies that show a correlation between conversion rate and latency. So how do you get rid of latency? There's an easy way, which is to move your service closer to your users. And that's why we use CDNs, content delivery networks. But you can't really do that for everything, right? Chances are you have a centralized database, you have, you know, the centralized infrastructure and it would be really a pain in the neck to duplicate that all over the world and keep those in sync. And so we're going to talk about the slightly harder task of eliminating roundtrips. Now, before we do this, I've sort of dissed on bandwidth a little bit. I haven't really talked about bandwidth. And I want to do that for a second. And to do that, we got to go into the data link. This is the creepiest picture I could find. The data link is your ethernet card, it's like your cable connection, right? And it determines your bandwidth. Bandwidth has to be super important, right? Because these cable companies spend millions of dollars trying to convince us that life at 10 megabits per second is at least 10 times better than life at one megabit per second. Only it turns out that's just a lie. Some smart people at Google have done studies measuring real-life page load times as a function of both bandwidth and latency. And they found that after you hit about three or four megabits per second, you get diminishing returns. Adding more bandwidth doesn't significantly increase or decrease page load time. However, page load time decreases linearly as a function of latency.  Why is this a case? Well, it has to do with the way that the internet has evolved. So the way we use the network has evolved, right? I just loaded up Slate.com. And Slate on his homepage makes 286 requests for 1.9 megabytes of data. This is the web we have now. We make a ton of requests for a tiny bit of data. And it turns out that lots of small files are a lot slower to download than one big file over HTTP. So why is that the case? It's kind of the case because, well, because of the way the protocols interact with one another, the way that HTTP uses TCP. And so let's blame the protocols for a second. I'm just going to run down the stack. You guys already know this, but the viewers at home probably don't. We have IP. The IP protocol just routes packets between computers. It doesn't make any guarantees of delivery or order or anything like that. And so we have TCP, which is an abstraction of a stable network that runs on top of this unstable network IP. And it guarantees delivery. It guarantees delivery in order. It's all about reliability. And finally we have HTTP, which is what we use to request and manipulate files over TCP. And so HTTP 1.4 sort of fundamentally is inefficient in the way that it uses TCP. And now we're coming to one of the big things. If you don't remember anything from this talk, just remember that new TCP connections are expensive. The reason for this is that, well, in order to be super reliable, TCP is also a lot more chatty than other protocols. For example, when you open a TCP connection, you have this thing called a two-way handshake that happens. Your client says, hey, server, we should talk. The server says, all right, sure, I'm fine with talking. The client says, all right, I see that you're fine with talking. Let's continue to talk, and I would like to see that funny cat picture now. So now we've got this connection established. And the good news is that you don't need to know about any of this to do your job as a web developer. But there is one thing you need to know about this. And that is that you have just incurred one roundtrip of connection overhead just to start up this connection. And if you're dealing with a latency of 100 milliseconds, you just added 100 milliseconds of time to your load time. And maybe this would be okay. Maybe we could handle this if there were just one extraneous roundtrip overhead per new connection, but you're not getting off that easy because there's this thing called congestion control. It's a very complicated subject. And so I'm just going to skip over most of it and tell you the one thing that you really need to know. And that is about the slow start process. Because just a second ago, when I established that connection with the server and asked for the picture of the cat. The server now has a problem. You see, it doesn't know anything about me. It doesn't know anything about how fast my connection is and how much data it can send me at once. If it sends me the whole picture at once, that could wind up overwhelming my network and all those packets would get dropped and now I would have to re-request them. If it sends me too little at once and it's not using, you know, my pipes to full efficiency. And so what it does is it kind of like dips its toe in the water. It sends out a little bit of data at first, maybe one kilobyte or something. And if I see that and I say, hey, that's great. I got that. The next time it'll send two kilobytes and the next time four. It's going to keep going until packets start getting dropped. And then it's going to back off and say, okay, now I know what rate I can send this data to this person at. You know, which is great. It makes sense. If you believe this graph, we just incurred 10 round trips to transfer about 250 kilobytes of data. And that's 400 milliseconds if you assume a 40 millisecond latency. Now, this is an example. It's a little bit exaggerated, but still, new TCP connections are super expensive. So we're going to focus on avoiding them, right? HTTP from even version 1.0 has this concept called keep alive. That is where the browser opens a single connection and then uses it for multiple requests. Like, I request a web page from a server. I make a connection to that server. And then that same TCP connection is used to send me the HTTP or the HTML. It's used to send me maybe some images, some other assets. And so we get to do multiple HTTP requests with only one startup penalty. But there's a couple ways you can get shot in the foot with this because your server controls keep alive. And it's possible that perhaps if you have a lightly loaded server and your users are staying on your site for a long time, there's lots of back and forth between your users and your servers. Perhaps you would want to extend the keep alive period. If you have a really heavily loaded server, you maybe want to shorten that to reduce memory usage by your server. And Apache and Nginx behave sort of fundamentally differently when you deal with lots of connections open. So just be aware of that.  But here, I'll give you one actual concrete suggestion. Most network stacks have this feature called slow star after idle. And what this means is that your network stack is going to monitor open TCP connections. And if it sees that those connections aren't used in the past half a second, one second, it's going to require that the next request that comes over that connection do this whole slow start process again. And that just defeats the whole purpose of your keep alive. And so the first command here is to check to see if you have this enabled and the second command is to disable it. So try that out. Also don't blame me if it goes wrong. So there's lots of ways you can tune your TCP stack. I'm not going to talk about any of them because as long as you don't have a super high network traffic site and you're running a recent version of Linux kernel, you're going to do fine. They've done a really good job there. So at this point, you may be wondering like HTTP, WTF? Like why is it so inefficient? And you've got to cut them a little bit of slack because originally HTTP was intended to be sort of a protocol where you could telnet into a server and you could type in a request and get back a resource. So we had very simple origins, right? You had this sort of single request model. And now it's gotten a little bit more complicated because now we have all these headers. We've got request headers that tells us what it should send us. And we've got response headers which tell us all the stuff about the stuff that was being sent. And we've got caching and we've got different content types and all that. Did you happen to notice that about three, four of those request headers were cookies? And just in case you didn't know, those cookies are going to be sent on every request you make to the domain that set them, whether or not that's an image request, a JavaScript request, CSS, whatever. And so if you have one kilobyte of cookies and you make 100 asset requests, you've just forced 100 kilobytes of probably useless data over the wire. Which on a desktop, it may not be a big deal. On a cell phone, it may be really annoying. So this is just one request. And normally, on average, web pages these days do 112 requests per page. This is what the internet has told me is true. And so now our job is to get this number down. So we already talked about headers. So we might as well throw in some browser caching there. Here's a link with a really good article about browser caching that you may want to look up later. It's on Heroku. And that's great for the second time that you load the page. But the first time you load the page, you still do 112 requests, which is crazy. So we have these best practices now. We concatenate our JavaScript and CSS. This is built into Rails. And so we take 40 JavaScript and CSS files in development, and we squeeze them down into one or two files. And now we're doing great, right? Because we've gone from 100 and something assets, we're down to maybe 30 assets. I do kind of feel dirty about all this, because I've just glommed together a bunch of code that doesn't logically go together, and I've made it so that if I change one line in my JavaScript, my user has to download an entire, say, 100 kilobyte JavaScript slug again. But it's OK. But what I'm really upset about is that I still have 30 requests. I just can't get any lower than that. And I was really upset about this. And Twilight Sparkle came to me. And she said, I apparently find this a lot more funny than you guys do. She said, could you do this concurrently? Because you do get six connections for a domain, and you do know how to make domains. I bet you guys know how to make domains, too. And it turns out, yeah, you can. This is a technique called domain sharding. It's used a lot by sites like Flickr, where you have a ton of assets being loaded. Essentially, instead of loading all your assets from one domain, you make 10 subdomains that all point to the same IP address, and you load your assets from them. So instead of six concurrent connections, you get 60. And I mean, it's really an ugly hack because it's not that great to have 60 open TCP connections in your browser, especially maybe if you're dealing with a mobile device. But what the hell, we do it anyway. We do this with CDNs. This is from my own website. It's some requests we make. We probably use six or eight different domains. And we buy the CDNs for the geographic distribution, but we get the domain sharding for free. So a slightly less hacky way to deal with this is to move requests out of band. These are some interesting new attributes that you can use in your HTML to tell the browser to, say, pre-fetch images, to pre-fetch a web page and pre-render it. Also, you can tell it to look up DNS records. But now this is really getting into perceptual optimization. It's really getting into DOM and JavaScript stuff. So I'm just going to wrap it up. Network performance. You want to move your servers closer to your users. So use the CDN. Check your server configuration files. Check your network stack settings to make sure that Keep Alive is actually keeping alive. Don't use a lot of cookies. And just do what you've got to do. Swallow your pride. Concatenate those files. Shard them across domains. Just, yeah, embrace the dark side of the force. But don't worry, because the Calvary is on the way, right? We've got this thing called Speedy. It's designed to be a lot better at this lots of small files problem, supported by, I think, the newest versions of all the browsers, although as usual, like IE really screws it up. The workaround is to disable Speedy. And but you still need CDNs to get the content closer to your users, because Speedy doesn't lower the speed of light or anything. And it requires SSL, which may be bad for some people. I don't know. And finally, our great hope is HTTP 2.0, which is coming soon. And hopefully within the next couple of years, we'll all be using that. And we'll be able to ditch a lot of these best practices that are really just workarounds for the protocol. If you want to learn more about this stuff, you should really buy this book, High Performance Browser Networking by Ilya Grigorik. It's available free. I just saw that online right now, so go check it out. He talks about everything I've talked about here, but in greater depth and more intelligently. And finally, if you have any questions, just feel free to just come at me, bro. I'm super friendly.  And yeah, so I'll be around. And that's it. Get to the slide deck from my Twitters. Is that it? Yes.


Two primary and two secondary schools are transformed into cultural hubs for young ambassadors from Taiwan. The Gordon and Walcott Memorial and Dane Pooley-Louisey Primary Schools and St. Joseph's Convent and Leonhurst Secondary Schools are playing host to Taiwan's young ambassadors as the group continues their week-long program of cultural exchange. The first stop is Gordon and Walcott. Young ambassadors are given an authentic quail style welcome. The visit is a proud moment for the principal of the Gordon and Walcott School, Miss Margaret Gabriel. She says the visit is also fitting since her school is the only one on island which is twinned with an elementary school in Taiwan. We feel very excited and special that Gordon and Walcott was selected as one of the schools to participate in this program and it is a continuation of our long relationship, our friendly and cordial relationship with Taiwan, where our school was twinned in 2020 with Gordon Elementary School in Taiwan and ever since we have done a number of activities with them to strengthen our relation and to share best practices, etc., with Taiwan and with Gordon Elementary. In 2022, one of our teachers did an exchange and a virtual lesson, social studies lesson with the students of Gordon Elementary. So today is the continuation of our relationship with them. The grade 3 and 4 students are captivated with the cultural display of games, dance and music. A culinary lesson and pancake making keep the young ones engaged. For Dante Charles, this was the best tasting pancakes ever. I was eating a good pancake, it was a nice one, the best one I ever tasted before. The cheese was the best thing about the pancake. I enjoyed the fact that I learned how to make pancakes.  Traditional Taiwanese music is featuring through all of these engagements, it is expected that music will also take centre stage at the cultural night on September 7th. The bamboo flute is a popular Taiwanese traditional musical instrument. It has a rich history and dates back many centuries. The traditional cultural uses of bamboo is a similarity that both countries share. Youth Ambassador Ben Senyang explains that the bamboo flute holds special value in Taiwanese culture. The flute is the most representative traditional Chinese woodwind instrument and its history can be traced back to bone flutes discovered 8,000 years ago. Through historical evolution, it gradually adopts bamboo as its primary material. In Taiwan, the dish is also refilled as pinna. In Taiwanese, it serves not only as a solo instrument but also as a melody for traditional Chinese opera. Thank you. For the girls at St Joseph's Convent, the visit provides a rare opportunity for communication in Taiwan's official language Mandarin. The language was introduced as a subject at the SJC last year. Intended initially as a pilot project, the subject is now in its second year. Language teacher Ms. Cooper says, the hope is that their students will be able to write the subject at the CAPE level. Rosa Emanuel is one of the students hoping to take the Mandarin exams at the CAPE level. She says, learning the subject is easy. Education Minister Hon. Sean Edward, who was on hand to welcome the youth ambassadors at the Gordon-Walkett School, says the visit to the schools will broaden students' world view and inspire them to expand their horizons. 40 students from Taiwan are showcasing their specialized skills as part of the International Youth Ambassadors Exchange Program from the Government Information Service and Virtual Leonity Reporting.


Welcome back. We were discussing properties of integrals, abstract integrals. So, all the properties of abstract integrals are proved in exactly the same way. You prove it for simple functions first, then you prove the property for non negative measurable functions and then you generate for any measurable function. So, that is the way all results are proved, all properties of integrals are proved. So, we were in the middle of discussing of number of properties. So, I think we were discussing property number 6, which said that if g is non negative and integral g d mu equals 0 equal to 0, then g equals 0 mu almost everywhere. This is the property we were discussing. So, the proof of this is as follows. Assume the contrary, let b be the set where g of omega is strictly bigger than 0 and assume mu b is. So, you want to prove that mu b is 0. To get a contradiction, you assume that mu b is not 0, that it strictly positive. Now, you want to show that this leads to a contradiction. So, then we defined, let b n be defined as the set of all omegas for which g of omega is greater than 1 over n. This is what we defined. Now, we also know that b n is increasing or decreasing. B n is contained in, is that correct? So, we have union i equals 1 through infinity b n is equal to b. We are saying that this set is equal to that set. In order to show this, you have to show that this is contained in this and this is contained in this. So, one way containment, the contain in that direction is very easy. Because, if you are contained in any of the b n's, it is immediately clear that g of omega is greater than 1 by n. Therefore, g of omega is bigger than 0. But on the other hand, if you want to show the containment that way that b is contained in this. For you take any omega for which g of omega is bigger than 0, then there exists a k for which g of omega is bigger than 1 by k. So, there exists a k for which omega is in b k. Therefore, it belongs to the union. So, these two sets are equal. Then we used, then what we said is we can use continuity of measures. So, we said mu b is equal to limit n tending to infinity, mu of. So, this is mu of the measure of that is equal to, I must actually write b i. So, the measure of that is equal to limit n tending to infinity mu of b n. This is the continuity theorem for measures for nested increasing sets, mu b n. So, this is an important relation. So, we have assumed that mu b is strictly positive. So, we have written a strictly positive mu b in terms of a limit of a sequence mu b n, which means that for all n greater than some n naught, mu b n should remain positive. So, you are approaching a positive number. This limit is a positive number you assumed. So, this guy, the sequence must be positive for all n greater than some n naught. So, actually all this we need is there exist thus there exist k such that mu b k is strictly positive. This has to be the case thus integral g d mu will be at least as big as see integral g d mu is the supremum of simple functions, the integral of supremum of the integral of simple functions. One such function would be to say that see the function 1 over k over b k will have this property. It is definitely smaller than g by definition. So, you will clearly have that g integral g d mu will be bigger than or equal to 1 over k times mu b k. Got that because this is a supremum of all simple, this is a supremum of the integral of simple functions. An example of a simple function which is less than or equal to g is the function which takes the value 1 by k over the set mu b k or the set b k rather correct with me. Because over the set b k g of omega is bigger than 1 by k correct. So, the function 1 by k the function which is constant at 1 by k over the set b k is a lower bound. This is a simple function which is a lower bound on g. So, this must hold. Now, what you know about that guy? This is bigger than 0. So, you take that k. So, this is a contradiction. Why is it a contradiction? You violate this. So, this assumption must be wrong. So, mu b equal to 0. Are there any questions in this proof? So, in particular for non negative random variable, if expectation of x is 0 then x is equal to 0 almost surely. Property number 7 is a very fundamental property of integrals called linearity. Integral g plus h d mu is equal to integral g d mu plus integral h d mu. So, this is the integral form of the statement. If you want to state it for the random variable, what will look like expectation of x plus y? Expectation of x plus y is equal to expectation of x plus expectation of y. This is always true. This is a very fundamental property. The integrals are linear operators on functions. So, linearity includes this, but the next one I am going to say is also is a scaling.  So, put together it is linearity. So, the proving this. So, again this is true for any measurable functions g and h as long as all the integrals are well defined. But, as usual the way you prove it is you first prove it for simple functions. Can you prove this for simple functions if g and h are simple? Can you prove this? The g you can write it as some of weighted indicators h also you write it as a weighted some of indicators. And you can from the definition itself you can verify that this is true. For simple functions this is very easy. Now, going beyond simple functions the next step will be to look for prove this for non negative functions which are not necessarily simple. So, that is very difficult to do if you take the supremum definition I gave. So, one of the things about say there are couple of ways of defining the integral. The way we defined it 6 of the 8 properties turn out to be very easy or 7 of the 8 properties turn out to be very easy, but linearity turns out to be very difficult to prove using the supremum definition. What we will do therefore, is we will prove monotone convergence theorem which is the very important theorem in integration theory. And then get back to proving linearity all right. So, because the definition we gave is not is conducive for proving many other properties, but it is not very conducive for proving linearity. So, we have to take a slightly difficult route through this fundamental theorem called monotone convergence theorem which we will do later actually we will do very soon may be next lecture. So, I will only say that this is easy to prove for simple functions non negative functions and more general functions we will get back later. Let me not worry about proving this and similarly for random variables this is always true as long as all the expectations are well defined. Again the proof will be along the same lines you prove it for simple random variables and then use monotone convergence theorem to prove linearity. So, this is. So, expectations are linear no matter what is what else is true x and y need not have any further structure to them x and y may be have any joint CDF what so ever they may have different distribution different marginals they may have any joint distribution what so ever they may not be independent or any such thing right. It is always true that expectation of x plus y is equal to expectation of x plus expectation of y. And similarly this generalizes to any finite sum right. If you have a finite sum of g 1 g 2 g n you can always write it as the sum of those n integrals. Similarly, if you have n random variables expectation of x 1 plus x 2 plus dot dot dot x n is equal to sum of the individual expectations prove for finite I am not saying about if this is finite if the number of terms you are summing is finite this is always true that is very easy. Because, if you have x plus y plus z you can write this as x plus y plus z and you invoke the same thing right. Any questions on this get to the proof later in scaling. So, this is scaling property of integration. So, you can this just says that you can bring the constant out of integration this is something you have been doing all along and it is true for abstract integrals as well right. And similarly for random variables. So, expectation of a is greater than or equal to 0 expectation of a x will be equal to a times expectation of x. How do you prove that? There is only one way to prove things right. So, you start off with simple functions again you take that g is equal to a weighted sum of indicators and write out. So, a g will also be a simple function whenever g is simple a g will also be simple that is because I assume a is bigger than or equal to 0 right. So, and then you write that integral out and then you verify that you write that integral out and verify that they are equal right. It is a very trivial exercise in. So, for simple functions it is easy. Now, for non negative functions. So, if so for non negative functions you have to apply the supremum definition. So, the way it works is this. So, a equal to 0 the result is obvious they are both 0 right.  So, prove assume a bigger than 0 clearly if q is in S of S of g then a q is in S of a g correct. Actually it is not just clearly. So, it is actually if and only if a matter of fact correct. What does that mean? So, any simple function q which is less than or equal to g right. If this is the case then a q is a q is a simple function less than or equal to a g and vice versa right. So, that is very clear right. So, now you apply the supremum definition. So, you have integral a g d mu right. So, I have to be a little bit careful here. So, I have to look over the supremum of all q let us say q prime in S of a g is not it of integral q well q prime d mu is that right. So, that is by definition see, but this q prime is a q for some q in S g correct. So, I can write this as supremum over q in S g integral a q a q d mu correct. Maybe I am skipping one step you can write it as a q belongs to S of a g right and then write the same thing right. So, this is ok with me. So, now what happens? So, this is a simple function now right for simple functions I can bring the constants out because you can explicitly prove that to be the case right. I can bring the constant out here right can I bring it out here. I eventually have to bring it out here right. So, bringing it out here is not a problem, but since a is non negative I can bring it out here as well correct. So, that is equal to supremum. So, supremum q belongs to S g a integral q d mu this is because q is simple right. Now, this a is non negative. So, the supremum of that set of numbers will be same as a times the supremum of that right. So, this is equal to a times the supremum of. So, this is because a is non negative q belongs to S g integral q d mu and this is equal to a times integral g d mu correct by definition. So, I hope this is correct right I mean look over this argument very carefully it looks like everything is obvious, but each step requires a little bit of thinking right you have to be careful in writing this term. So, this comes out because of q is a simple function and the a eventually gets out of here because a is positive all right great. So, I think I am done with properties. So, I am done with the basic. So, the elementary properties of integration I am actually done now. So, the properties that remain are the more fundamental theorems of integration right. So, we will do actually there is just one fundamental theorem and that is the monotone convergence theorem. The monotone convergence theorem which is regarded as the cornerstone of integration theory and if there is one theorem in integration theory which is I mean which is the single most important one it is clearly the monotone convergence theorem. We will also do dominated convergence theorem which follows as a corollary to monotone convergence theorem and there is also a result a very well known result called Fatou's lemma that is a result we I will mention, but not prove it is not included in your syllabus. But, monotone convergence theorem and dominated convergence theorem are very useful in practice and they are very important theorems. So, I will those we will do in proper detail. Before we get into that. So, I think there is one more little unfinished business from the past if you remember I mentioned something called the inclusion exclusion principle for probability measures. Remember what that says it is a probability of a union b probability of a plus probability of b minus probability of a union b and similarly for n such events. If you have union over n events you have to pull out the intersection add back intersection and so on right remember that formula. So, I what is said back then when I was dealing with properties of probability measures was that you can prove it using induction right. It is true you can prove it using induction, but now that we have done expectations integration with there is a very straight forward proof of getting the inclusion exclusion principle. So, those of you who actually bothered to write down the induction proof will probably know how messy it was it is doable there is no intellectual challenge in it, but it was a it is you have to sit down and do it carefully right. So, very messy exercise, but we will see that using indicator random variables you can prove the inclusion exclusion principle very easily let me just indicate that right now. So, inclusion exclusion principle. So, inclusion exclusion formula if you like. So, recall. So, this is from your first chapter we said that probability of A i is equal to sum over i equals 1 through n probability of A i minus sum over i less than j probability of section A j dot dot dot minus. So, plus plus minus 1 to the n minus 1 probability of intersection. So, this is the inclusion exclusion rule right we just recall this from memory right. So, you have to add all the probabilities subtract the probabilities of intersection 2 at a time add 3 at a time subtract 4 at a time and. So, on right. So, in order to prove this. So, I am going to prove this and I am going to finish it here this is all the space we will take. So, you will agree with me that indicator of this set. So, I am looking at the indicator of that event. So, this is the indication this is the indicator of that at least 1 of the A i is occurs 1 of the A 1 through A n occurs. And that is equal to 1 minus the indicator that all the A i is fail to occur correct. So, this is the indicator that all the A i is fail to occur 1 minus the indicator of that is the indicator of at least 1 A i occurring right this you will agree right. Now, what is the indicator of. So, what is the indicator of A intersection B indicator of A times indicator of B correct indicator of A intersection B is indicator of A times indicator of B. So, this can be written as 1 minus the indicator of well actually let me write this as product indicator A i compliment I equals 1 through n right. Now, indicator of A compliment is 1 minus indicator of A i right. So, I am going to write this as 1 minus product 1 minus indicator A i agreed with me so far. Now, one more step is all that is needed. So, you have to go from indicator to probability how do you do that. So, how do you go from indicator of event to the probability of event take expectations right. Because, indicator of I of A is equal to probability of A correct. So, you take indicator of this what happens you get you get this correct and then you have to take expectation here right. So, what will happen here. So, if you expand this out.  So, the 1 will hit with the first 1 here. So, if you expand this product out what you will get is you will get a sum of the indicators right minus you will get indicator A i indicator A j right all the all the i j's you will essentially get terms like this you take you take expectations you will get this.  So, in order to write it may be I will take a little more space, but I am sure you can do that right. So, you just expand this product out this is like 1 minus this indicators this will be 1 minus I A 1 minus I A 2. So, 1 and then there will be 2 terms 2 at a time 3 at a time and so on. Finally, there will be a product of minus 1 to the n minus 1 indicator of all the product of the indicators of all the A i's which will finally, give you that term finally, if you take expectation you get that term. So, this is a very simple proof of inclusion exclusion principle actually this is a very this is the most transparent way to see why this inclusion exclusion principle is even true right. The induction proof while it is a mathematically correct proof it gives you does not give you much more intuition about what is going on right this gives you a very structural intuition on why this inclusion exclusion principle is true are there any questions if there are no more questions we will start discussing monotone convergence theorem. Maybe I will not I will not finish discussing today, but we will start of discussing all it is about. So, this monotone convergence theorem as I said is probably the most important theorem in all of integration theory. So, the monotone convergence theorem qualitatively what does it do it just gives you a way gives you conditions a condition rather under which you can interchange limit and integral. So, normally if you have limit n tending to infinity integral f n you have a sequence of functions f n let us say you have integral f n d mu where I can think of it as integral f n d x if you like if you just want to think of integrating on the real line you know you probably know that you cannot always integrate limit interchange in limit and integration right. So, the integral limit of an integral is not always equal to the integral of a limit we will see some examples, but the monotone convergence theorem says gives one sufficient condition under which you can interchange limit and integration namely you can say that the limit of the integral is same as the integral of the limit function. So, in particular if f n converges to some function f integral of f n need not always be equal to integral of f in particular the monotone convergence theorem says if f n converges to f in a monotone way right suppose f n monotonically increases and converges to f or f n monotonically decreases and converges to some f then you can interchange limit and integration. So, in that case you will in fact have that integral limit of the integral is equal to the integral of the limit. So, that is what the monotone convergence theorem says it is actually a to state it is fairly simple, but before I state this properly I want to define some concepts convergence of functions.  So, point wise convergence of function is a this is what this is it means right you fix an omega in the sample space in your set omega and for every omega f n of omega will be a sequence of what fix an omega f n of omega is a sequence of real numbers well not including plus minus infinity not quite real numbers. So, this is a sequence let us just say it is a sequence of real numbers if it is true that that sequence of real numbers converges to this real number f of omega. And if this holds for every omega in omega then we say f n converges to f point wise this clear. So, this f n. So, this could be a sample space this could be random variables for example, f n could be x n some random variables and in that case you say that random variables x n converges point wise to x if for every omega in the sample space x n of omega converges to x of omega for example. Now, it remains to be well the one little thing that I have not really spoken about is that if you have a sequence of functions converging point wise the limit function is also a measurable function whenever this f n is a measurable the limit function is always a measurable function. This is something that can be proven I have not done it in class, but it is always the case that if you have a sequence of measurable functions converging point wise then the limit is always a measurable function this can be proven. So, the definition clear and then I will just put one more definition which is closely aligned let us say that. So, omega let me say that omega f mu is my measure space omega is this guy and I have f n mu on that space as well we say that we say f n converges to f mu almost everywhere if what you suspect it is what you think this will mean this convergence holds not necessarily for every omega in the sample space, but instead it may fail to hold on a set of mu measure 0 if f n of omega converges to f of omega for all omega except perhaps on a set of mu measure 0 this is also definition. So, this is slightly weaker definition than this this is saying that for every omega in omega you need this convergence f n of omega converging to f of omega here you relax saying or may be it is not always true that. So, it is not true that for every omega it holds there may be a few omegas or a countable set of omegas or some mu measure 0 set of omegas some small set some there were 0 measure set where the measure is mu right on that set you do not have convergence or you may not have convergence right you do you cannot quite say what f n of omega is doing on a 0 measure set, but outside the 0 measure set you have convergence in other words there is a set a subset a of omega which has full mu measure where convergence happens. So, in the context of probabilities this has a very important interpretation which will come to a little bit later again. So, this will become almost sure convergence of random variables had the have you heard that term before almost sure convergence of random variables. So, there we have a sequence of random variables x n you have x n of omega converging to x of omega not necessarily for all omega in the sample space, but on a set of probability 1 right there may be 0 probability omegas where the convergence does not happen. So, this is a this is almost sure convergence when you are talking about convergence of random variables I will write that down explicitly a little bit later when we study convergence of random variables. So, far definitions everybody find see now. So, here so this is point wise convergence right now the issue is if you have a measurable function converging point wise to f of omega f of omega is always measurable.   Now, the question is does that sequence converges at all right that is question number 1 if it does converge does it converge to the integral of f d mu that is the question we are trying to address. The answer is no generally that is not true even if you have convergence of f for every omega in omega it is not true that integral f 1 d mu is equal to integral f d mu not true. So, the question we are trying to answer is this can we interchange limit and integration. So, that is the colloquial question right i e if let us say f n of omega converges to f of omega point wise is it true that integral f n d mu converges to integral f d mu answer is no. So, what I am saying is so rather say another way of writing is if you want to write it more explicitly is it true that the limit of the integral is equal to integral of the limit function if this is a little more explicit you can take this it is not true that this is not true to see an example I will just conclude with an example. Let us say you take let my omega f p be my favorite 0 1 integral 0 1 interval endowed with borel and Lebesgue measure that is my probability space I want to define f n of omega is equal to n for 0 less than or equal to 0 less than or equal to omega less than or equal to 1 over n or less than 1 over n and 0 otherwise. So, that is my sequence of functions. So, f n of omega will look like that. So, if I plot it so everything is in all the action is in 0 1 interval this is 0 1 interval. So, f 1 will be 1 in 0 to 1 f 2 will be 2 in 0 to half f n will be n. So, this will be 1 over n solid dot here 0 everywhere here hollow dot here solid dot here actually does not matter what the here it is a hollow dot here it is a solid dot the functional value is n here you will see that. So, if you want to so integral what is integral f n d lambda. So, I am going to integrate f n with Lebesgue measure integral f n d lambda will be equal to 1 for all n this is equal to 1 on the other hand if you look at the limit function. So, the limit function f n will be so for all omega lying. So, for all omega that strictly bigger than 0 the limit function will be 0 correct at 0 the function will be plus infinity actually because I put a less than or equal to here actually if I put a. So, if I put a strictly less than here the limit function will in fact be 0 everywhere right, but yeah I mean. So, if you like so to avoid confusion let us just take this. So, let me just put the function at 0 here just avoiding confusion. So, let me do that and at 0 it is 0 the function is 0. So, the limit function is equal to 0 for all omega and omega correct because you give me no matter which omega you give me there will be some n beyond which the function is 0 right. So, the limit function is identically 0 correct. So, if I look at f defined as limit f n this is 0 for all omega and integral f d mu will be equal to what 0 right and this is not equal to 1 right. So, the so integral f n d lambda is equal to 1. So, this implies limit n tending to infinity integral f n d lambda is also equal to 1 right. So, this integral is always 1. So, the limit is 1 the limit of the integral is 1, but the integral of the limit is 0. So, it is clearly not the case that you can blindly interchange limit and integration very simple example says that you cannot do it right. So, I made this strictly lesser. So, even if this was strictly less than or equal to the limit function will be 0 for all positive omega and it will take the value plus infinity at only at 0 and because it is a function that is 0 every almost everywhere integral of a function which is 0 almost everywhere is 0. So, it would not have mattered even if I had less than or equal to here there will just be 1.12 the function is plus infinity, but that 1 point has measure 0. So, there is no difference that is the clear. So, you cannot interchange limit and integration. So, what you will see next is next class we I will state the monotone convergence theorem which says that if this limit where to be a monotone limit if f n converges to f monotone equally then it is always the case that you can interchange limit and integration. So, in this case monotone city does not hold right because f n will look like this and f n plus 1 will look like that right. So, it is not true that they are monotone in n right. So, we will see this next class.


All right. Thank you guys for coming in on time or not leaving the room We're gonna kick off the buff birds of feather So the idea is we have few people who have some topics that they want to discuss with other people So each of them will come up and announce the topics that they have and then we'll identify one of the tables Where we can go and gather around and have the discussion around that topic So for example, I'm proposing the first topic is how to do continuous delivery continuous deployment on mobile apps This is something I've been doing at a few places. So if you're interested in that I'm gonna grab this table over here and do the buff on that, right? So people who are interested in this topic, we'll just gather around and we'll have a good discussion around it for 45 minutes All right at the end of 45 minutes We will kind of quickly summarize what each group discussed so each group will come up and quickly summarize what they discuss So that way, you know, if you didn't attend a buff, you can at least get to know what other buffs discussed. All right Do we have anybody else who wants to propose a topic? Following on from my session on continuous integration for web and JavaScript projects If you'd like to discuss that in some detail will be at the table here on the left at the front, okay I think we had one other person cheesy who was talking about doing microservices for embedded devices so if People have more questions details. They want to know then that's that's a topic that I Guess cheesy will grab that table over there and kind of get started Any other questions that didn't get answered today that you would want to discuss I am talking to a dead room Scaled agile was yesterday not today. Sure if people are interested, but I think That was kind of yesterday's topic. So kind of mixing that up today might be out of Context, but if there are people who want to do that, sure Do you want to grab a table? Oh? You're looking for someone to talk about scaled Right outside in the booths any other topic. So any other topic that you guys wanted to discuss If we are entrusted we can continue that All right, so we'll get started and if there are more topics we can You know announce them later, but we'll get started will be 45-minute discussion amongst you and then at the end of 45 minutes your east respective table can come and present what they came up with


Okay. Good morning, everyone. Everyone's bright and early. I hope everyone's all nice and caffeinated or got their tea, whatever it is. It's a pleasure to see you all. Thanks for joining us. It's a real pleasure to welcome Carlos Mingeth back to GSAP. Carlos is an alumni of the CCCP program. And one of those people who had a, you know, when he was at GSAP, we all already knew that he was going to do great things. And of course, you know, he did and he went and he was at storefront for some time as a curator there. And then co-curated the Oslo Triennial of architecture, which brought him into the sphere of Scandinavia. And then he became chief curator at Arcdes, which is the architecture museum of Stockholm and Sweden, the National Museum. There he very quickly set up some incredible shows, a number of publications, which are all listed in his biography, but some incredible shows, having to do with some of the pressing issues that were happening in Sweden, but also more globally, social, political, environmental issues and how they really bear upon architecture and how architecture can influence those issues. And in particular, he became very interested in the north of Sweden. And the north of Sweden, you know, Sweden, like Norway is a very, very long country and was essentially, you know, inhabited by native peoples and was colonized very much like the west of America was colonized by, let's say, white Europeans. The north of Sweden was colonized as well during the 19th century and they founded a city there, which was a mining city called Kiruna. And Carlos became very interested in it because they were in the process of undermining their own city, they were literally digging out the city. And entered into, has just put up a really amazing exhibition, which I think just came down on all of the issues that this city's undermining brought up and the plan to move the city away from the mine. It raised all sorts of questions about preservation, which we thought were just so interesting and this is why we invited Carlos. Of course, this is a kind of managed retreat. And it is not the same as a climate change cause for managed retreat. But you as you will see the kind of tools and the questions that come up in managed retreat have to do with economics have to do with social attachment to place.  And so methodologically, the kind of methods and systems that were put in place in Norway really are a kind of sorry that I say Norway and Sweden were are really a model for the the rest of the world, and thinking about how to do this. So it's really a great pleasure to welcome Carlos back to Columbia and in this virtual setting. And Carlos, I'll just hand it over to you. Thank you for joining us. Thank you. Thank you so much for her for the introduction and thank you for the invitation. It's an absolute pleasure to be to be talking to the, well, in the in the in the school that it's so important for me but also about questions of preservation that I really became very interested in in those issues precisely by by being at Columbia by meeting also you and by really really thinking about how present and how relevant questions of preservation and in contemporary architecture today. And definitely some of those thoughts have been very relevant when when I was like starting to develop the research around issues and all the connotations that the current locations is experiencing. So thank you thank you so much and hello to everybody in the audience. So I'm going to share my screen so we can we can go through for a presentation I prepared. And we can see a little bit of about Kiruna. So here. Okay. So, so yeah, Kiruna forever. And that's the title of the exhibition and the and the project that that was saying, I've been working, I've been working on for like, since I arrived to Sweden that was like a maybe three years and a half ago. And it's, it's connected precisely with with some of the things that Jorge was saying like I used I organized like the Oslo architecture three and Ali with a with a group of creators. And I started to really understand, like, to be interested in the north as as a project like the north as a place where lots of things are happening and when I when we are talking about the north here is like the north of the north. And this is a, this is the Arctic. Kiruna is a city that is located in the Arctic in Sweden, so it's like a very far away from a Stockholm is a very long country. And, and definitely, and we like when looking at the specific questions that were happening in Sweden we recognize that Kiruna was a place where lots of different issues were happening at the same time connected to natural services connected to attachment connected to to questions of preservation but also questions of land ownership and indigenous population indigenous land rights in the in the region. This is an image of the exhibition that we we closed in this last February, and was like a trying to present all these different perspectives all these different voices and views that are at play in Kiruna, because Kiruna is this city. This is an image of the city of Kiruna that is basically built around the mining efforts that this is like Kiruna but it is the mount Kiruna where they were the mine is located. I don't or mine is like the biggest underground, I don't or mine in the world is a state of mind so like this, the state of Sweden owns the mind like the extraction processes and also of course the export classes. The state exports nationally and internationally is one of the biggest exports of Sweden, like really getting back a lot of money to to a state holders and basically to returning to all taxpayers in Sweden. But Kiruna is experiencing, as I said, like one of the, what we believe one of the biggest and like processes, urban transformation processes in recent Swedish history, because he's being located the mine is has grown so much is like he's is growing is is digging at such a big level that like the ground the formation that the mine is producing has started to jeopardize the structure of the city, especially the city center that it's what we see in the foreground of the photo. And basically the municipality in coordination with the mine company and of course the state gave green light in 2009 to to start like the process of relocation of the city center and therefore the city itself. The, the ground the formation has been growing over the years at such a level that basically this is an image from 2018. So all these like, like a whole that the mine has produced is actually growing and growing and growing and already affecting the first buildings that are in the first line. Closer to to the mind, this is the headquarters of the of the mind. And, and so we can see some images of like the basically the the status of things in 2019 again this is a process that is ongoing like these today, they're like all all these buildings already are demolished because a third of the population have to relocate. They are moving to another, another area of the city or to the new city center. There are a series of buildings that are being or demolished or moved. This is, for example, a heritage building a heritage house built by Gustav Tickman, a very important architect at the beginning of a center in Sweden that is being relocated to a new area of the city. This is like a lot of housing blocks have been demolished and another area that's building that's listed building that is being moved and relocated an area that is actually where all these houses those are like mining houses from the beginning of the century of the 20th century, that have been all like moving to the same area so they are kind of building like a quote unquote historical site. And, but, and this, this for example is them, this is the plan this is the new plan of Kiruna that was a competition and international competition that there was one way by white architects and health and architecture. And we can see, we can see here like what I mean by the location, this is like the area image of the mine, this is like the specific factory like basically where all the treatment on the treatment plan is. The mine of course is like is underground but we can see all these holes that are produced by like the ground that is being basically swallowed by the earth. And we can see like the areas of affection of the of the of the mine how that is like starting to really affect and reach like the first areas of the city. The plan that was like presented by in the competition and won the competition and that's the plan that is being developed right now is that basically the new city center of Kiruna is here. And the architects have imagined that by 2100 the what we know as of Kiruna will be basically like like located demolished and the city will be be will be growing in this direction. So, and this is like the new city center has been like started to be built already like the first buildings are already an app. This is a photo from 2018 today. Actually the buildings around this town hall this is the new town hall of the city is already surrounded by new buildings housing blocks but also cultural buildings etc etc. But all of this is happening in a land that has been inhabited by my linear by the indigenous population of the region that are savvy. So, all these, all these, all these different elements. And as I said, we tried to really bring like a specific, like understanding of the different voices a different perspective of what is going on with the location, but also trying to give bring some light to the historical and geographical context, because it's not. When we talk about Kiruna, we realize through the process that actually is not any building any city that has been built on this on the side of a mining effort is a very specific city. For example, we were looking at a specific geographical context, one of the, one of the lines of investigation of the project was to, and trying to understand what are the tangibilities of the, of the, of the mining industry, both locally originally and internationally so we commissioned to a team that is the one buying a one band and desing and he'll buy yourself to, to, to work precisely on what is what is the, the journey what is the journey that the stars here in this is the image on the top of the mountain where where the mind. Like treatment plan is to, to like to understand like what is the geographical location but also what are what are the traces of that iron. That is extracted in Kiruna, in, in the different construction sites around the world so basically they could find these are like a series of posters that we represented in the exhibition research posters that they trace back like how the nine, the item in Kiruna is actually could be found in the, in the subway in London in the construction site in the materials that are used in the, in the subway in London, or in the material that covers like the oil pipes that are in the Gulf of Mexico, for example, or in the high rises off of Dubai, for So, so clearly like the impact that has like in terms of starting from architecture and finishing in architecture and it's, it's, it's both local and international, but also, and it was also a way to understand the historical context of where this is the, this is a map produced by Adolf Zavok and Maristeva that working at Lulea School of Technology at the time, and then they basically mapped out how the location of Kiruna, Kiruna is the K in this map, and is actually part of what is called the North Potnian technological mega system that is an entire network of mines of of industrial settlements of power stations and railroads that go from Lulea, Lulea in the coast of Sweden to Nordic in the coast of Norway. Those were made precisely to be able to develop the settlements, produce the exploitation of the land, distribute and transport the material to the ports and those ports were capable to transfer the material abroad. And so, so, so, so Kiruna is also a form of, of looking at the region, but Kiruna is also is being relocated, but also is destabilized in many different scales, for example, we were also looking at the work of hands like Narmapisen that is a semi artist that has been devoting his life, basically to map out Sapmi that is like the region that some people like live in, that is a region that moves from Norway, Sweden, Finland and Russia. And, and what when we, when we look at those maps that was presented in the exhibition, we cannot find the word Kiruna, what we will find is the word Giron that is like the name that is, is used by some people for for for the city. So, like, the, the city is being relocated the city, the, the, the materials are being circulation, but also even the names and the, and the identity of the city is also being this in a, in, in, in, well, in a, in an imbalance, no, in, in, in changing engines and stuff. Like, and that comes back to, to some of the documents that we could find of the, of the origin of, of the first drawings that we could find of representing Kiruna or representing the landscape that Kiruna, or Kiruna is located today. And this is for example, a map that was included also in the exhibition that is a map from 1736. This is the first time that like the Mount Kiruna, but that mountain that we have we saw in the first image that mountain was today like basically completely broken cut out because of the mining efforts. This is the same mind that is being represented here, the same, sorry, the same mountain that is represented here. And the first time that the mountain is represented is precisely through, the representation of the landscape with a core with a body of gray area here that already indicates from the first time that it is iron included in that area. This, in that area, this is like a geological expedition, this is a document that was done for a geological expedition that was supported by the king of Sweden. And was a was a way to, to, well, to study the land and study the composition of the land and precisely after this document. There is the first efforts produced by the king of the kingdom of Sweden to start understanding that land not as a, as an area that was like unknown as it was before with some economical exchanges, but very few. It was understood to be understood as a place of resources, a place where that needed to be studied, needed to be controlled, needed to be claimed, exploited and developed. Like some years later in 1847, we could find also this document that is like a claim map is a map that indicates how those those sections of the mountain. In this case, this is the Alivari Malvedi, a very close by body of war to Kiruna, that with a very similar story that basically claims the land in order to be exploited. And that, like that process that lead that line of work ends up being in the first settlements of in the first industrial settlements, and around the body of war that is this this great lines over here. The first industrial settlements that are built on the site of the iron body in order to be mining the surface at the beginning. And this is a, this is a, this is the beginning of Kiruna, this is like the beginning of what we know today as the city of Kiruna, this is like the first settlements of that of that project. As I was saying, like what is interesting about about the city of Kiruna is that it really is a settlement that becomes an important city for Sweden. Because like, because we can, we could trace back how from the very beginning at the beginning of the century, like the city of Kiruna understood as a place where the most important architects and designers and artists are going to be working with the city, they are designing like buildings and thinking about Kiruna as a place that has like an image has a projection to the rest of the country. From those settlements that we have seen that are like very, very like a basic settlements, industrial settlements at the beginning of the century, automatically, and somebody like Petal of Halman and Gustav Pikman to the most important urban planners of the time. They imagine what would be like the, the urban, urban plan of the, of the city. Gustav Pikman would be also building like a, like a wooden church that is still today in Sweden, one of the most important wooden buildings, largest wooden buildings in the country. And like somebody like Helmer Osloond, Axel Tornemann, Carl Wilhamsson, they are all like first level artists of the time that I invited to Kiruna to represent the industrial effort and industrial like advancement of the city. So we kept on asking ourselves when we were doing this project is like why, why somebody like Carl Wilhamsson, like one of the most important artists of the time, like goes to Kiruna far, far away in the north of the north to draw, to do a painting like this one. And we come back to that argument like the argument that Kiruna becomes an image that legitimizes some certain forms of colonization, but also represents a specific forms of like an image production for Sweden is like as a place that really projects that it has a symbolism that goes beyond the needs of the mining efforts, it operates at another level. So there is like a kind of like an important value that is implemented in the city that has to do with not not the needs of the workers, not the needs of the exploitation of the land are connected to a state values to a state directions to the idea of how the state is perceived and projected to internally but also externally. And that continues to happen during the entire 20th century we there is like a digital all collections from the museum. There is like a series of projects during the 1960s that are like of very high quality Hakuna very like a built like a, you know, like a very banal building this is just like, you know, like a hoisting and separating plant, but is built designed build and photographed and disseminated as a work of art understood as part of a project of modernization of industrialization of the country and represented as such in many different magazines, or the LKB. And that's the name of the state company headquarters located in front of the mine in front of the mountain and like also kind of representing the modernity and as arriving to the to the north of Sweden. And, and there are many other examples of looning of Dahlström like industrial, industrial buildings that really like, like, would have been completely banal in other cases in the case of, of this battle that are like mining export efforts like in the same area. They are, they all have that kind of level of symbolism and years to it. The same happens with with Ralph Forskin a very important architect from the UK that moved to Sweden and developed like an entire practice and entire body of work connected to the north and taking Kiruna as the petri dish to imagine new forms of, of housing and urban planning in the in the Arctic, of course, with certain tropes of the north as that exotic space. So, I mean, we can spend lots of time talking about Ralph Forskin and the north. But the reality is that he also developed an entire practice, an entire distribution of materials also he became very, very, very well known precisely by the ecological Arctic town that he was inspired based on the studies that he did around Kiruna. So again, Kiruna is that space that's that city that many architects have imagined the future with. And, but at the same time, was was a place where all these all these transformations of the man were being produced. Well, first can end up building a couple of buildings one in his papawara. And today, and today is actually half of the building so like there is also like a big, big question, precisely, very present, very present in the discussion today of what happens with all these buildings that had great ambitions, but today, for example, the half of this building is already demolished. And because papawara is a very, very small town with even migration questions. And there is a big, big polemic and discussion about what happens with these buildings that are like today having like a different attitude and a different relationship with the population. And in Kiruna itself Kiruna in Kiruna Ralfersken build very recognizable building housing, housing blocks in the city center that are core or driven and this building that is considered one of the best buildings of Ralfersken in Sweden, it's going to be demolished very soon. If it's not next year it will be the following the following year, they are located in the in the area very close by to the mind. And we argue that actually that process of understanding Kiruna's that kind of symbol symbolic effort like in between the like giving goods for society but also legitimizing certain process of sacrifice that the area is producing. That continues today, this is like the new city hall, the new building, also an international competition inviting like many different offices internationally to imagine what the future of Kiruna will be are participating in that process and building a new city. And I mean like the, yeah, so the location of Kiruna is one of the most important European project as I was, as I was saying in recent Swedish history, and not only because of the complex operation of moving an actual city but also because it mobilizes critical questions of global relevance. The citizens of Kiruna have been forced to face extraordinary philosophical questions. What constitutes a city, where do I belong, what should we preserve what should we sacrifice big questions that conflate conflate transcendental issues between the old and the new between what needs to be demolished, and what needs to be built about who owns the land and who belongs to the city losses and hopes this placement and attachment. The location demands of reconciliation among different communities, and also among different communities needs, some of them struggling to detach themselves from a historical servitude and to the mind, but also some of them diametrically opposed to the fact that the land is being exploited at all, the challenges of building a new city also poses questions about the reasons for the relocation in the first place. Why should we prioritize the extraction of minerals over the stability of a city and its citizens. And what what are the limits of economical growth, how much longer can we continue digging. And one of the cases that I think for this composition can be interesting is the, the old town hall in Kiruna. This is a, this is an image of the old town hall that is a town hall that was designed by Artur von Esmalienzi. You know, like 60s, 70s, very, very important architect in Sweden, the building received, like it was, it was finished in 1963 and received like the most important architectural national award in 1964 the Casper, Casper selling price. And the building was really incredible with lots of different collaborations with many relevant artists with craftmen, craft women that were like first level in Sweden, and with a lot of different details in the building. And it was, it was listed as heritage, soon after, and, and, and also was very, very well, like a perceived by the, by Kydunians themselves like I was a place that was very well used with lots of events. It was like Kydunians used to say of it like that was like the living room of the of the city. Unfortunately, the building was located in, in, in an, in an area that was very, very close by to the ground deformation zone of the mine. And so after many, many different litigations, the heritage listing was lifted. And then, and the building was demolished in 2019. These are like a couple of photos of my class time and that we commissioned like precisely to document also like the demolition of the building for the collections at the museum. And like the, the, the, and this is an image of the exhibition because one of the, one of the big efforts that we produced for the exhibition is precisely this happened in the middle of the organization of the exhibition. This was 2019 we were about to open like a year after. And so, like, in order to really address this question, we, we hope, like the exhibition had an entire area of the exhibition that was called origin heritage that was precisely addressing what are the, what are the conflicts that really produce questions of in the city and taking the town hall as a case study. Because like an interesting point about the building is that it was not only an amazing piece of architecture with a really special like features architecture features and architecture like elements. It was like a place where many different events happened. As I said, like it was very well used by the community, but but also it was like a place where that served as a, as a, as the, as the scenario for very important events. So in, in, in the exhibition we could in collaboration with, with the community municipality we could save some materials from the demolition so so so the balconies that you see here the textiles, the lambs, the, like the, the entire lectern, the materials of the the sculpture balcony, all the curtains, all these are like a they are saved salvage from from the demolition, like a reconstructed in real scale in the in the exhibition, and then returned to Ketuna to be reused in other in other buildings, organized by the by the municipality. And we decided to to reconstruct exactly this section of the building, because as I was saying, some of the events that happened in the building were very transformational for not only for Ketuna but also for the region and for Sweden. And especially there was there was a very important event in 1969 that our series of general assemblies that happened in that building and that were holding all the miners strike, and that it's, and it's known by all streets by the great minor strike of the 69. So we had a series of, like a series of days, 57 days while cat minus strike of 1969, which coming with with miners from, from Ketuna from his battle era from my very it that we're all assembled together in the building in order to, to have like a general to make decisions and to push for decisions to the to the company of labor rights that is still today are in place in Sweden. Right, so, so we, we commissioned to include Hanson an artist from Sweden that has been working precisely on questions of minus strikes before. To do a film to do a piece that could be, could be a reconstruction of those days of those events that happened in the building, like holding hosting these discussions this strike so really putting into emphasis the importance of also not only the cultural details and physical components of the of the reconstruction on the building itself but also the events that it held as a, as a, as a building and emphasizing like the importance of preserving at certain level actions and performances that are part of the, of the history of the building. But we, what we do is that we reconstruct the entire section of that of the of the building where like the lectern were done were precisely the, the, the, the speeches that were given and were held so this is this Mike is, is this Mike and with the same lectern like the original lectern that we could bring from Ketuna from them, like say from demolition. And we presented the film exactly at the spot where you will be walking upstairs positioning yourself as if you would be talking to the general assembly, and you would see the reconstruction of that those days in that, in that screen. And the, and then there was like a like another level of the project that was also including like a performance that was also that's a work by England Johansson as well, that basically is like the reenactment of the speeches that were given in the strike in the minor strike. In Ketuna in 1969 by Sara Lindman that is like a super important like a writer in Sweden and talked in like in as part of those general assembly days. So, and so this is this is a case of, of how, like, you know, like a building that has like a specific story. So we try to really address what are what are the implications what are the questions of sacrifice and saving and preserving and keeping and including in the in the certain legacy and certain memory of of the discussion. Through the through the exhibition. And a second, a second line of work with preservation can be also understood with the work of your mango part of the project was also to commission new work commission new projects for for the for the exhibition. So we collaborate with your mango mango is today. I think like one of the most important Sami architects that are practicing. He's a he's an architect but also operates with architecture. And he's a great speaks person for the role of some architecture in contemporary architecture today. And he, he developed like he has been working with a with a long term project that is called you can be that is the Sami architecture library that is a is a is a nomad is a movable moving library that basically moves into different places opens up everywhere it goes and has like a more than 200 like volumes connected to architecture to Sami architecture to indigenous culture to indigenous architecture. And it serves also place of discussion a place of addressing the issue of the relevance of some architecture, and we invited him to, to have like another another iteration of the project. This was like independent here so we we we decided to move that that that library to to the virtual space so you can actually visit it is like a good to be that space and and is a way also to think about questions of preserving specific forms of culture and specific forms of knowledge for for Joe is very important to to think of this project as a place of keeping together certain knowledge and growing knowledge together about some architecture but also understanding and discussing what are the possibilities for for for some architecture to be relevant to be relevant today and to be important in the questions of how do we deal with nature how do we deal with resources and we are like like, as I was saying like the location of goodness along and complex threat going back hundreds of years and reaching from the northern lands of Sweden to the rest of the planet. So very real and striking sometimes dramatic experience for those living in the city, the dialogue around the relocation continues to have multiple strong just opposed often often contradictory perspectives. Here is the greatest dilemma, Kiruna is not only being relocated three kilometers, it is moving at a time in which Sweden and the planets northern regions face fundamental change initiated in 2004 beginning to find its forms into 2020 and plant until 2100 the current location construction and definition of the new city in the Arctic embodies the dreams and aspirations of contemporary Sweden. Kiruna confronts us with the need to totally redefine our values when it comes to how we address global warming and reinterpret the notion of attachment in a world of forced and non forced migration. It calls upon to renegotiate with indigenous peoples and to reconfigure our understanding of sovereignty. Ultimately, it forces us to address the ways in which we privilege economic growth above all else. We are witnessing how the relocation of Kiruna a challenge initiated 15 years ago is finally taking shape. The first buildings are being built, and the new city center begins begins to become a reality, but we should not consider the project finished or untouchable. Kiruna embodies the hopes and dreams of the 21st century and shows us the tools we need to equip ourselves here and elsewhere to face the challenges ahead. Fantastic. Carlos, thank you so much. This was what a number of issues that you put on the table that are really significant for us to think about. And we have a little bit of time for Q&A. So those of you that are on the call. I was just going to say, please, just type your name or, you know, if you want to ask a question in the chat, and then we'll call on you. You know, just say, I don't know, stack or question or whatever you want to say. I think that's the easiest way for us to handle this as you think about, you know, question or a comment or a thought. But I'll just get us started over here as everybody mulls over the, you know, their questions to talk a little bit about this question of your I wanted to hear more about this strategy that you put on the table of reconstructing but also salvaging certain key pieces of the that in a sense, the their pieces that can represent or encapsulate or be the charge of a symbol, you know, of the whole building, the lectern and other things and then you also reconstructed around that to kind of supplement that object with enough so that it could do what you wanted it to do. That's a, you know, a very interesting experimental preservation practice. You presented others in terms of the kinds of works that some of the artists did but I wanted to focus on that one in particular. The idea of saving a piece of the building, moving it to a different place and activating it through performances actions and so on as part of the museum. That is not if you go to a traditional let's say art exhibition. Normally the objects are looked at they're not used and performed.   Yeah, yeah, I mean like, yeah, I mean, it all begins with like the question of circulation in Kiruna is very important, but like a extraction in Kiruna not only is about the iron that is taken out from the ground and exported somewhere else. There is there is a lot of dynamics that have to do with periphery and center. So Kiruna is in the north of the north and it's, it's, it's the people living in the north, they have a very strong perspective and experience of how like a knowledge economy and materials are being extracted. Right, and that the value always ends up being in Stockholm in the capital and that relationship between the center and the periphery was very strong from the very beginning when I was, when I was doing research for the project. So, so the, the idea of establishing specific forms of circulation that was going in and out from between Kiruna and Stockholm were very important from, from, from the very beginning. That's why, for example, we developed like an entire collaboration with a museum in Kiruna, like the Consmos et in or that is a museum that is located in the new city center actually. And there was like a lot of exchange of information of materials. So, for example, there was like a lot of questions about original materials that the museum had that the Kiruna municipality didn't have about buildings that were done in Kiruna. So there was like a lot of work of producing certain form of exchange between the two institutions, right. So that, that idea of circulation that idea of how things move and how objects like travel from one place to the other was like very much into the into the table and and and and basically was a form of that's why we call it origin heritage because in the middle of doing the research basically will receive the information. Okay, the build the town hall is going to be demolished is going to happen is going to happen. It's a very approved is going to be happening in the next months. So, so, so we felt that that that story was like a very important to tell very, very. It was a good way to really bring up to the public discussion, something that is very striking that a building at that level was going to be demolished and is a building that all of us in Sweden have been supporting by giving giving it like a national award. I thought that the contradictions that were produced encapsulated in the building were really, really powerful and really capable to tell like the importance of architecture, the importance of preservation, how preservation is connected to all of us is not something that some specific professionals deal with. It's something that citizens have some sort of connection with what should we should we preserve or not in a city. So it's kind of it was like kind of a fast forward case study of what does it mean to to to have a specific attachment with a space or with a building. So, so, and that's where like all the collaborations with the different networks of people started to happen and we could, we could like one of my first impetus was like, I mean the National Museum should be like a preserving should be taking care of some of the materials that are going to be lost, because they're going to be demolished and they're nobody's going to, like, like have that space or that material or that piece of the of the of the building anymore. But then all the questions about what is the role of a National Museum in relationship to these questions, what can you preserve of a building that is enough to preserve the building questions of what are the limits of representation of a specific project with a specific building, fragments, all these questions came to place. So, so that's why all the questions about the actions the performances the events that were happening started to become very important so so is a combination of of salvage material that for me was very important that was like circulating back to Kiruna right so actually we haven't let we haven't put anything in the collections we thought that that was not the role of the museum in that sense was more like the role of bringing up the discussion, bringing up the conversation of what is important to preserve in a city, rather than that specific material. And that allowed us to to have like a very, it's true experimental cases of how art is perceived in a museum like that's why you could touch all these things like it was like a very direct you could sit in some of the we also have some benches that were original from the from the building you could also sit on them. So it was like a lot of like usability of those of those objects that for me was important because the career, like for like one of the goals of the of the of this reconstruction. For me was like the general audience should have like a some kind of like a physical connection to that building and how can we like achieve that and that physical connection, like I understood or I thought that like the lectern was the right spot it was the place where, like the public speeches were given, or the most public components of the building were performed in a daily basis that's where the mayor talked to the citizens when they were he was talking. And that's where all the main, you know, like the main public speeches were given so so that's why for me was like that that was the concentrating spot was the place where we needed to work around. And, and the work of England your hands on of the reconstruction of the striking of the mining, mine is a strike was also very important in that process because it was a, it was a way also to connect to two things of another time but important today that the still are are echoes from the past that are as important as the handrail. So that that also that understanding that that architecture is not only important because of its aesthetics is important of other components for me was also for us in the team was was very important so so yeah so I'm actually that that's one of the things that I'm more more excited about in the in the project we thought that we could manage to bring several several parts that for us were important to discuss into into one specific case study. Okay, we have a that's, thank you, Carlos, we have a question from the hell. Yeah, hello. Hello. Yeah, hello, I have a question basically about the relocation issue of the Kiruna. Because the reason like original reason for the relocation of Kiruna is because they want to expand the iron ore mine in that mountain right, so they need to leave more space for the development of the industrial stuff. So my question is, as for the new planning stuff of the town Kiruna. How the pen could reply to the environmental effect of the expanding iron ore, because I know that is have some environmental issues near the near the iron ore miles. How the plan, the plan can, sorry, I did sorry, can you. Yeah, yeah, like, because for example my hometown like my home also have very large coal ore mine. And like around it, it is always like it is very polluted water is very polluted. So how the pen of the new town can reply to this kind of environmental impact. Right. So, so, well, so that's, that's a very good question and I think that, in fact, it doesn't really respond to it. I think that basically separates from it. The new location is made to to relocate the city like three kilometers away, not as a way to address the impacts of the mine in the in the in its surroundings. It's basically to make sure that the houses that are built are not swallowed by the earth, literally. So the, and that really tells a lot about the power structures of a city like Kiruna in which there is like the Kiruna municipality that advocates for all the citizens of the city, but also LKV that is like the mining company that basically advocates for the mining company to be operative and yes, address specific sustainability processes right and and there is there are a lot of efforts that are made by the mining company to be less polluted on to work less with with materials and processes that are a little bit more sustainable. Yes, but in the at the end of the day, basically for me like the big impact that of course it's connected to the pollution that is produced, but the big impact goes much much beyond that, like the impact of mining in the land is is very very deep in many different layers of society. For example, like the whole like a semi culture is against the fact that the land where they have been living for so many times so many years is even touched. So the sustainability process that's a sustainability question that are is not addressed by any of those questions and definitely not addressed by questions of pollution pollution. Yes, isn't that is an element of that process, but not only know. So, so the new plan, I think that it's actually not responding to that point it's trying to imagine like a new future for the city, making sure that the process of mining continues and keeps on going. One of the big questions that I always ask everybody I met in the process is like, why nobody asks why we stopped mining, like why that question is not even in the table. And I think that that's that really tells a lot of of the of the of the realities of a city like these and and and I'm sure that you have a very good, good experience and with your, well, good, I don't know, but you have the experience with with your hometown for sure. That's a good segue to the next question that we have from Professor of Rami. Thank you so much for very provocative project and informative presentation and you know I commend your team for the depth and breadth of research that was done in order to bring this to fruition. But I'm wondering if you can expand a little bit on the, the use of, of we, when you talk about we sort of as architectural historians preservationists and others it's very easy for us to ascribe architectural value to a place and to use our archival, which are sometimes very exclusionary forms of research to identify social value within a place but how was public engagement conceived or undertaken before the exhibition. It's a great sort of interaction as a result of the exhibition and maybe that in and of itself is a way of understanding social value but I'm wondering whether there was anything in advance of the exhibition that really informed how value was being ascribed to that place and to its components. Yeah, thank you. Thank you so much for the question. I think, I mean, Kiruna, the relocation of Kiruna is is a well known event in Sweden. If you ask anybody, or you ask anybody before the exhibition was done, like, there was like a general assumption in, in, in the, in the, in the two thirds of, or in the third of Sweden that is in the southern area of Sweden that is basically where all the big cities are located that is where the capital is located. There is a general understanding of what is going on in Kiruna and the way media portrays the portrait that kind of location was by saying the city is being moved, right. So, and through like the first section of the research that we in the museum, when I say we here is like the museum team like a team of people working with National Museum of Architecture and Design in Sweden. So the first section of the research was about trying to understand a little bit better, like, what was the, what are were like the discussions and then the groups of, of, of, you know, of thoughts in locally in Kiruna. So that's why we collaborated with the Kiruna municipality and with the, with the Consmosity North with the museum. And, and was like, yes, they were like a specific discussions happening about questions of preservation precisely that was one of the biggest lines of discussion like there was like a lots of surveys produced lots of public engagement in terms of understanding what were like a references for example of location of the new city center. So there is a large legacy of local involvement of different communities in order to discuss the difficulties and the challenges of the relocation. But what we really perceived in that process was that the discussions were very, very present locally. The consequences of those discussions didn't necessarily have like a very big, large impact in the decisions that were made because the decisions jumped out to another groups of power that were like connected to the state and to the state owned companies, less with the municipality. And more importantly, the discussion about like the components included and part of the context, historical and geographical context of the relocation of Kiruna were completely absent of the public discourse. So one of the main intentions of the project is precisely to open to make sure that we didn't focus on the relocation as a house that is moving on top of a track that is basically the image that was constantly projected by the media as a form of celebration of technology. We are capable of moving a city and to a discussion that was more about, okay, the relocation of Kiruna today is only possible because of a historical and geographical and social context that is very complex and has to do with many questions that are not important not only for Kiruna, but the important for Sweden as a whole. And so, so like the intention of the project and the research line and the exhibition was to bring to the general discussion and the general public, that kind of complexity. But of course, like the precedents in Kiruna are long and complex and deep. They have been many, many different groups of people and many different communities that have been exercising like lines of thought and lines of pressure, precisely in different directions. And the reality today is that the city is being relocated and buildings are being demolished. So, so that's why that's we were trying to go to the facts of that and to try to open it up to the public to the general public. Thank you, Carlos. Thank you for sharing your thoughts your work with us your insights. This is such an interesting case. And the way you've as in your practice the way that you show us how museological methods can intersect with preservation methods. And, and bring put pressure on the forms of community engagement that Professor of Rami was, in fact, raising when they're not happening is so exciting so we look forward to seeing more of your exhibitions more of your work to bring break out of the museum into the world. Yeah, I think it's a constant in your work. It's really terrific. So thank you so much and thank you everyone for joining us this morning for the for this for this lecture. Okay, terrific. Thank you so much. Thank you. Bye bye.