Okay, let's start and let's just go down the line and everybody introduce yourself. Like, are those mics working? Okay, go ahead, try again. I'm Jeremy, Basecamp. That's what? I'm Aaron, I'm not a pony. I'm Godfrey. I'm Santiago, I'm the co-founder and CEO of Yorgz. I'm Guillermo, I'm from Colombia and I work in a company named Rhype. Hi, I'm Andrew, I'm Unboxed CTO and I'm Pixel Trek, some GitHub. Okay, I think, you know, we don't have a ton of time, so I thought what I would do is we talk a lot about, we could talk a little bit about kind of like upcoming changes and stuff, but I thought sort of going along with what we talked about during Ruby Heroes, we talked a little bit about how you ended up in, on Grail's Core. I think that's really interesting to a lot of people. So why don't we go, we'll go back this direction. How long have you been on Rails Core and how, like, how did that come about? Did you just, you know, just take a minute or so? I've been Rails Core since like 2012 and that basically came about through just contributing to Rails. So I've been contributing to Rails since 2007, where I contributed to Rails was, I had a problem with my app, broken Rails, fixed it in my app. Next version of Rails could have broke my app, I thought. But they fixed this in Rails, so it's a message of passion, just gradually worked from there. That's basically it. Okay, yeah, like Andrew, I started contributing to Rails, looking for the problems and the bugs that I found in my app. Yeah, I've seen that every new version of Rails started to break my app, so I need to fix this. And I am part of the Rails Core since like three years. Okay, I'm part of the Rails Core since 2010, I think, and I started to get involved with Rails development, basically based on issues I had in my applications. Also, once I joined to a hackfest or something like that, that happened during a weekend, like triaging the issue tracker and working on that, and that way I get involved with all the stuff. So we've probably noticed a trend by now, like everyone knows, I started contributing to Rails by finding bugs in my own application, like, why isn't this work? And I was like, well, maybe I can just fix it. So I brought patch to fix it, and then, like, some years ago, I came to the Rails Core, this hour, made Aaron merge my patch, and I started doing more, and that's basically it. So if you haven't done that already, we're still here, and you can still do that. My turn. You can say answer all of them, and that's okay. Yeah, so there were no bugs in my application. I just wandered in off the street. I don't know why am I here. How long have you been on Rails Core? I have no idea. I don't know. How long have I been on the Rails? Maybe five years. Maybe. Four years or five years. Seems legit. I'll echo the pattern. That's how I got involved in Rails, too. When Rails was first coming out and trying to port applications I'd written in Ruby and PHP and Java to do new development in Rails and finding missing pieces. And that's what I've seen with everybody coming into Rails, the consistency of noticing issues, addressing them, following up on them. It's kind of interesting because it seems like an easy thing, but it's also a surprisingly rare thing. The long tail of contributors. If you go to contributors.rubionrails.org, there are thousands of people who have done one thing, which is awesome. But doing two things or three things already gets you into kind of a rarefied territory, so I encourage it. So that's a good transition to my next question. We'll start with Jeremy. You probably have most to say about this. We'll pull the curtain back a little bit for a moment. Do you maybe say what the process was for introducing new people into Rails Core? Is it just like a discussion amongst all of Rails Core? Is it a formal thing or is it just a very informal process? It's very informal. It's gotten more formal. Sometimes I feel like people really introduce themselves. It's like the way that you fix issues and it's like people are there on the door. They're already in the core team essentially just by virtue of their contributions. It's like the way Aaron came into the core team. He was doing things and it became more of an issue to have him not on the core team. Basically if you hassle the other people too much ... Okay, so let's see. You've been on Rails Core for various amounts of time and one way that Rails stays fresh is change. It's not sticking with one thing. For instance probably not many people are doing RGS anymore. So this is sort of a two-part question and we can have everybody answer both parts at once. Probably what I'll say is since you've been on Rails Core the most interesting change that you've seen happen while you've been on Rails Core and the most interesting change that you're excited about coming up. I won't make anyone start because I've got a lot of like ... Does anyone want to start on this question? The most exciting thing that I'm looking forward to is Action Cable because I have no idea what the hell it is. What about since you've been on Core? What's one of the most interesting things that you've seen, maybe you did it or maybe you saw someone else do it since you've been on Rails Core? I don't know. All the work I did with adequate record is probably my favorite stuff that I worked on. Adequate record. Yeah, I think probably the most important thing to me is to focus on performance and measurement. We're kind of making now introducing all these benchmarks and then monitoring the versions different performance between versions and then hopefully make Rails more like the pastest version of Rails. What about interesting things in the past? I think back when you were like, finally, we're doing this. The Rails 2.3 to 3 jump was probably the most interesting thing. The thing that kind of got me contributing more to Rails. So that was kind of my most interesting for the past. Bundler and Asset Pipeline. These are things that people love to hate and it's for the most part turned out to be incredibly positive and constructive contributions to the way that I build apps. I remember going through Bundler issues and now I love it. I could not live without it. It's great for deployment and it's one of the kinds of things that I think everybody having been kind of patient through its growing pain really paid off. I think a shout out to somebody who's not here, Raphael, who handles most of our new people. He's our first contact for most people with Rails. New contributions is seeing Raphael comment on the pull request. He is our patch monster, our pull request monster, our comment monster, and our welcoming committee. So shout out to him. He's probably the best thing that's happened in the past five years. This is a just in time question generation. So sometimes I have to do a little compiler pause. Are you taking questions from the Twitter so that what's happening? No, but if you want to tweet some questions at me right now, I'll put them in the queue. So we can do that too. We have a whole slew of people who are all of a sudden wandering in. I don't know where they're at all morning, but come on in people of the hallway. Um, Guillermo Santiago, I've read anything about interesting things that you've seen change or that you're excited about? Yeah, I'm really excited about the work that Santiago is doing in the Rails API project. Finally, we're including the next version. So I want to congratulate Santiago. No, I'm excited about the performance of work we have been doing also. The integration test being faster and all that stuff. And having Ruby 2.2 as a requirement to run our applications. And also about Rails API, not only because I didn't work, but also because at Rails we work with several different kind of applications that some of them use Ember as in the client side. And this will enable I tend to think that this will enable these kind of applications to be first set in Rails. I must. Everyone else is talking about code changes, so I guess I'll talk about something else. Personally, I'm most excited and I've been pretty happy about some of the changes around the ecosystem, some process that we have. We have a much better process of testing our releases these days like we have. We test out latest version of Rails with discourse and with other open source projects. And Rust.Rail has been doing a music job managing the issue tracker. We now have a weekly newsletter if you don't know about what goes into Rails every week and stuff like that. I think I'm pretty excited about some of the changes around the ecosystem making everything better. That's excellent.  I know that when Rails progressed from two to three, there was a performance regression and a whole bunch of things because there was a whole bunch more code, whole bunch more sound ways of doing things. Does it feel like and maybe this was true last year when I think about it, that all of those things have been made up now and now it's sort of like all always better performance than previous versions. Does that make sense? Any thoughts there? I think we have much better tools now to monitor that. So you can now answer that question instead of... I think we just didn't know before in the two point three to three change. It wasn't until somebody kind of filed an issue saying, that's a record of five times slower than we did. I think there's also what we see is that the questions that are easy to ask are the ones that are easier to answer too. The active record gets a lot of attention because it's really glaring when there are regressions in it and the kinds of regressions that occur are often like in plus one or worse. So they're in your face and a situation like that is because there was some design change and less often because there was a regression in some micro-optimization that somebody might not have noticed. But we can often miss the things that affect the performance of our applications. What are the choices that we're making that makes the person who's using the application, what's their experience and how does Rails change that? Some things like asset pipeline can be kind of hidden stars and making things like delivering your entire application faster for real people rather than faster in our benchmarks. Well the problem is like the surface area at Rails' API surface area is so large that even if we have performance benchmarks we're not going to catch everything. There will be some use case that somebody has in their application that we didn't have a benchmark for and then eventually it's like that might regress. So it's difficult to keep track of that stuff. I can say too that we've really been helped by the improvement in Ruby itself. Going from 1.8 to 1.9 was a massive boost despite some small pains and going to Ruby 2.0 and then 2.1 and 1.2.2 each one has brought significant massive improvements that just work across the board. Ruby 2.2 symbol GC it's going to change the way that we write Ruby code just due to the fact that we can use symbols everywhere and it seems like kind of a small thing but those echo throughout the code base technically not everywhere. That's another good sort of transition you know it's a very, like I said, or else it's a very large surface area. There's tons of features and tons of things in there. How do you individually and as a group sort of decide what to work on?   For all I know you all have other jobs as well. But when you're like okay I want to do some Rails work. How do you decide what you want to work on? You can start anywhere on this. Yeah personally quite often I'll get on issues that are to do with time or routing so I tend to pick up those a lot or if I haven't got any of those then I'll just go and dig into the issue you're tracking and find something interesting. Do you set time aside in your week to work on Rails work? Or is it just that when it pops up you're like okay now I'm going to put aside a day or a few hours or whatever. I'll try and put aside some time. Not really I think I work mostly on weekends or on nights. But I see later in the work has become easier times to raffle. Yeah I think you can see the issue tracker and almost all the issue was already reviewed by raffle. We don't follow like a process or anything like that. I tend to work on stuff based on issues we have at work or from time to time I have to do list and put their pending things that I would like to fix and maybe at some point I just jump there or something like that. Yeah I think we as far as as a group I think we have a kind of loose list on base cam about some of the big areas that we would like to eventually work on. Individually for myself it's just whatever I bump into at work and yeah other things kind of find themselves on my list. I don't know how to get in there but they just automatically pop up. It's April it's time to do Google Summer of Code and make sure we have enough projects for our students and things like that. Random just random. Yeah just no usually it's it's a mixture of stuff like for me it's a mixture of things that will either be stuff like typically performance issues that we're running into on work apps or just things that I'm interested in. Either one of those two is just. I'll say that this actually isn't true. Aaron looks for the things that give the largest look of disapproval or the greatest table flip and then he dwells on them until they're fixed. So as a group do you set and decide and you know this is maybe a question for David that he's not here so we'll answer it is though maybe he would answer it. As a group do you figure out like okay what's going to be the next major release? Like the minor release is I guess a group. What is a group? Did I say something funny? Or is it I mean I know that he drives a lot of the big features maybe they're going to go into the releases. Is that still mostly the operating procedure? Let's just use Action Cable as an example. Action Cable yeah it's a different kind of example. We haven't really done something like that before. From my view we take a lot of what we've seen in working on Basecamp for the past number of years as it's integrated into each version of Basecamp becomes our legacy app and we get very intimately acquainted with the things that we'd like to do differently and so those are the things that come to mind when we do new development. Coming back to your last question about how we choose what to do like I'm often reactive also when there's an issue go fix it but during new development is also a great time to shape the way Rails is going to turn out and get on Rails master and find the things that kind of work on their own but don't quite work in concert together and make them work with your app and those are the times where you can make design contributions it ought to work this way versus things seem broken here I stub my toe. So within the issue tracker does it seem is it self? Oh I tried this and it doesn't work or it blows up for some strange reason or whatever. You're gonna have that presumably because it's software and then hopefully you're gonna also have some feature requests. Hey it'd be really nice if it did this, really nice if it did that. Is there a split? Like is it way more issues? Is it just a few features that actually feature requests that come in do you get a lot of pull requests? Do people try and scratch your own itch on the features a lot of times or I'd love to just know kind of how that split breaks down especially as you kind of said you're all sort of work on demand as things come up. That doesn't necessarily necessitate a lot of features except the ones that you personally say like oh this is a thing. So I'm just wondering how the community helps you figure out what features should go in and that kind of thing versus just pure bugs. The issue tracker on github we mainly use for tracking bugs and pull requests so just new feature suggestions. We generally direct them towards the mailing list so we can have a discussion about it otherwise they just sit there on github with nothing there. So if you want to send in a feature request you can send in a pull request. But if you sent one in it would behoove you to also start the conversation on the mailing list. Hey I sent in a pull request about this feature and here's my justification for it let's have a discussion but that's the place to do it rather than me. And does it feel like that happens often? Do you have a lot of feature requests a lot of feature discussions from the community on the mailing list? Very frequently. I wouldn't say it's high volume though. The difference between having something you wish for versus enacting your wish is a huge gulf and going from the first contact to github for something like an addition rather than a bug fix is a pull request which means that you've thought through a lot about how your idea needs to interact with Rails and with other people's applications which takes a lot more work. I wish this was here for me already which is easy to do and easy to say but when it's left on github issues there's not much anybody else can do about it other than just know that you had that wish. And if a lot of people have that wish great somebody can come and do something about it but there are a lot of wishes and not enough people doing things. Rails is also in a pretty special place in terms of its maturity as a project as you probably know a lot of people use Rails in a lot of different ways and we already have a very very large API surface and so some of that also boils down to how many people can actually benefit from this because we can't have too many things in Rails so like a lot of times people would come oh like I need this in my app like it seems pretty obvious everyone will need it while it turns out that perhaps not everyone will need it but it's still a very useful thing even though we couldn't justify putting into Rails perhaps you can put it make it into gem and that's actually how some of the new features in Rails was merged in and then over time this actually works and it would actually be beneficial for most people so it merged in Do you on that sort of on that note as people are in the audience or watching this some future time on the internet do you prefer if someone has an idea for a feature that they bring it up on the mailing list before they go off and write a pull request so that at least you can say well that's a good idea but there's all of these other things to think about before you do the pull request because I know that sometimes it could be that a pull request shows up and you feel bad someone spend a whole bunch of time on some feature that you're like well but it's actually really orthogonal to all these other things that we're doing and if we add it I know that you spend a bunch of time on it but if I merge it in it's going to cause all these other problems so do you prefer the discussion on the mailing list or do you prefer to just get the pull request and then have that discussion afterwards I think it depends on the size of the future like if it's a really big change then absolutely mailing list first but if it's like oh I just want to add I've got this really cool method I want to add to active support probably a pull request is fine Are there things that people shouldn't send pull requests for? New methods to active support I was hoping you'd say that that's why I asked I think it's a strong preference in any direction because I think that if you have something that you need to get done you really want to do then making a library or Ruby gym or a Rails plugin it's almost everything can be done that way these days unless you're trying to change something in the internals of Rails which I think is the less common case but you can implement it and you can prove it's usefulness by spreading use of the gym yourself there's been a lot of talk about especially with action cable and how people are writing web apps and the API work for inside Rails so you're all not just implementers of Rails but practitioners of it as well so maybe it would be interesting to find out a little bit about how you personally within your projects are using Rails are you using it using it for a lot of APIs and generating it using it for a lot of JSON APIs I'd love to hear what your personal philosophy is because that in itself helps drive what Rails looks like as well we can start however, do you want to start something? Given that we are a consultancy company we have several different projects and we don't have a strong preference of one way of doing stuff it's just the way that it's a better fit for the projects so we have some projects where we use Ember or Backbone and then we have a lot of more projects where we use the default stack so basically I mean it depends on the project what stuff we do Yeah similar to Santiago we're very much agnostic with micro services, separate Rails apps for different parts or a monolith depending on the application We've been working on a Pico service framework It's lighter weight Our apps at work are basically regular stack nothing amazing I'm going through the internet questions now so that's why I'm looking at my phone Any other thoughts there? Every time I hear monolith I just think of that Simpsons episode where he's like monorail What if I electrified five car monorail One thing that I felt after years of working on base camp was the power of small teams and what we can do with something that is well integrated, a monolith With a small number of people we're able to deliver an app to multiple platforms, we have iOS and Android apps that work from the same kind of canonical source We don't write a separate JavaScript app, we write one app that works everywhere and we can do it with a small number of people We have a workplace that I love and something that I've come to treasure like being able to design a workplace that can afford you that kind of flexibility where we can work on this whole breadth of base camp without needing tons of teams, people I don't know, we all work together That's a really good sort of quick question if anybody can answer if they have any thoughts there Obviously people building mobile apps and doing lots of things on mobile, do you feel like there are certain things within Rails that help you be able to build out interface with mobile apps or I'm just sort of throwing it out there to see if you have any thoughts The intersection of iOS, Android apps and Rails is a very interesting spot and I think a huge number of people are at that exact point in time Any thoughts there? Anybody? Merging the API stuff in the master will help I think going back in time a little bit for the technical end of things, doing content negotiation and being able to return multiple variants for each RESTful resource allows you to keep your representations close to your resource and the interaction and the controller and that single thing has turned out to we've gotten a lot of mileage out of it. We're going to adding explicit HTML only variants where we could serve a different page to mobile versus serving a different page to desktop we're able to build out entire apps from the same resources just with that tiny little feature How many miles? Ten? 15? Okay, so I have a couple of quick internet questions and then we'll get to one sort of pessimistic question for me if we have time. Ernie wants to know with 2.2 symbol GC, how soon will hash with a different access die?  Well, because you, I mean that would break the APIs, right? Because you have to be able to access with a similar way doesn't it? Right, the only thing that would happen there is if like symbols and strings all of a sudden became the same thing inside Ruby then you're like, okay, yeah, I guess it couldn't die now. Well, I mean we try to do it so I think with regards to hash with a different hash with in different wea with that we try not to use it internally so we don't use it internally but we use it for stuff that's user-facing so I don't know I like internals so I don't really care Most user-facing stuff is coming, like we're ingesting it from the outside world where it is strings too so it makes sense to build a hash of strings and address it within your program using symbols. Okay, I'll ask my pessimistic question and this will probably be the last question then so we'll try to have everybody answer you all have worked on, especially a number of you are consultants so you've all worked on a lot of different Rails apps that are probably in a lot of different states of usability, you know what I mean as you've been working on those is there some like specific smell some specific thing that when you run across a Rails app you're like, oh no they did this that you every time you see it you go, oh no they did you know, maybe it's overloading something weird I don't know, sorry what did you say Aaron? Concerns they concern me Any thoughts there, Andrew? Yeah, I mean you see people break models up into like loads of little files all over the place and you just don't know where stuff is, especially when you're coming in as a consultant Yeah, I've seen a lot of people that are still putting business logic in the controllers Yeah, that's hard I have seen models with 10,000 lines of code or controllers doing render text and all the HTML in the string, something like that So, don't break up your models but don't leave them as 10,000 lines it's just a very careful balance the feast of the famine of how big the makeup I think one of the biggest problems I've seen and like I personally sometimes have this problem too is not having a good grip of what you're putting in your app like whether it's like design patterns that you see at talks or what is gems, right like over time you have 20 folders in app like with everything, every pattern possible and like in your gem file there are gems that no one really understand like there's a block pose on top, if you put this gem into your gem file it magically makes your app faster, so you do that and then like over time you don't actually check whether that is still useful and turns out that well on latest version of Rails that actually makes things slower, right, like so it's those things like you really understand your app and be conscious of what you're doing Prune your garden, and your garden is your gem file, in other words is what you're saying Putting tons of actions in the application controller stuff I've seen, I was thinking about changing the route to just be like changing the router to just say CGI bin in that case but yeah actually a lot of, I was being kind of sarcastic when I said concerns but not that sarcastic like basically abuse of modules, so using tons and tons of modules mixing in tons of modules where you try to debug it, it basically becomes a debugging nightmare because you look at the module and the method in the module depends on an instance variable and you're like where did that come from, and then you're like good luck trying to figure that out, but honestly the worst is there's just so many methods, there's so many actions at the top level. Jeremy, you've seen code base evolve enormously over time. Yeah, I could speak to like past me and there's this perfect, it's base camp this is the reference application. I look at what we did with early Rails and some of those early things are hard to change, there's not much motivation to change things work and places where I drift from convention because I'm under time pressure or impatient and just want to get shit done and you can pay for that impatience and you pay for the next thing where you go touch that bit of code, but places where we've seen changes in Rails respond to that are like when we introduced RESTful everything it's now common to think of your controllers as resources instead of controllers that are like functional bags of stuff and so if you see any Rails applications that were born before that migration it's very common to see where you're like this kind of stuff happens here I'm going to have a bunch of actions that do that kind of stuff so it's organized like namespaces of RPC calls rather than nouns that you do things to I think everybody here is probably new enough that they don't remember that transition but I think that was one of the biggest feature that was added to Rails or the most impactful in my opinion which was what? Adding, introducing RESTful controllers just it was huge okay well I think that's we're going to call it on time thanks for being up here and fielding my ridiculous questions and let's give them all a big hand


I was glad to see at least one of my compatriots among the graduands. That was the one with the kilt in case you hadn't guessed. Chairman, ladies, gentlemen, colleagues, we honour today the intellectual achievement of a remarkable political economist. Over the last four decades and more, he has produced a large corpus of work in which great new insight has been provided into the nature of underdevelopment and development in his own country, India, and more generally. He has done that with a consistent determination to confront social injustice and deeply entrenched poverty, and always with analytical precision and scrupulous scholarship. He is one of the world's outstanding political economists. Prabhat Patnaik was born in Orissa in 1945. Through scholarship, he made brilliant academic progress at St Stephen's College, Delhi, at the Delhi School of Economics, and at Oxford and Cambridge. He obtained his BA and MA degrees in economics in Delhi, and his B-FIL and D-FIL degrees in economics at Oxford. He imbibed the ideas of Marx and was influenced by those of Keynes. As he says himself, when in Delhi he diverted the writings of Morris Dobb, and I know that he came to admire W Arthur Lewis and especially the famous Lewis model with its classical pedigree. He is deeply influenced by Marx, but he is no dogmatist. He has considered and seen the strengths of different systems of thought. He has, however, been a relentless critic of neoclassical economics. He was a member of the Faculty of Economics and Politics and a fellow of Clear College, Cambridge, between 1969 and 1974. Jawaharlal Nehru University had been founded in Delhi in 1969, and in 1974 he joined its newly established Centre for Economic Studies and Planning as an associate professor. He became a professor in 1983. He remained there until his retirement in 2010. His work has been in macroeconomics and in political economy. He has been a potent and illuminating blend of the two, at once technically brilliant, incisive and compelling. That work has been in five main areas. The first is in the macroeconomics of an agriculture constrained economy and a succession of papers, the first of which was published in 1972. The second area is the dynamics of a mixed economy. Many of the papers in these two areas were brought together in his 1995 book, Whatever Happened to Imperialism and Other Essays. That title signals his third area of interest, the theory of imperialism. And here, his brilliant 1997 book, Accumulation and Stability Under Capitalism, is an established classic. Fosley Marxist's theory has attracted his creative attention and he has revisited cogently the famous transformation problem and explored Marx's neglected contribution to monetary theory, which anticipates a good deal of kens. He's done that in his 2009 book, The Value of Money. In the final, the fifth area, he has mounted a formidable critique of neoliberal economic policies and he's advocated a range of measures to reduce poverty directly. In addition to the books I've mentioned, I should point to his Time Inflation and Growth, 1988, Economics and Egalitarianism in 1990, The Retreat to Unfreedom, 2003, and Re-envisioning Socialism, 2011. In each of those five areas, he has made powerful original and lasting contributions. From 2006 to 2011, he was executive head of the Planning Board in the Indian state of Kerala. A post he discharged with distinction and considerable success, presiding over an increase in welfare measures which have been associated with a very healthy growth rate. In 2008, in the wake of the global financial crisis, he was appointed by the President of the United Nations General Assembly to the four-member task force chaired by Joseph Stiglitz, charged with considering the crisis and recommending reforms of the international financial system. He has edited and he continues to edit the monthly journal Social Scientist, which under his editorship has successfully promoted radical ideas and published important research, both theoretical and applied and on both contemporary and historical themes. His work is characterised by clarity, rigor and elegance, which makes it a pleasure to read. Those are enviable qualities. In his case, brought to bear powerfully and with passion upon real issues. His writing is preeminently informed by relevance to real issues, social, political and economic relevance. It's not always that one can say this of economists. In his case, one can say it without qualification. Of all his many qualities, it is this that gives his distinguished scholarship special and enduring force. Chairman, it is my privilege now to ask you to present Professor Prabhat Patnaik for the degree of Doctor of Science, Economics and the DSC ACON and invite him to address the assembly. Dr. Miller, Professor Webley, colleagues, fellow graduands, ladies and gentlemen.  I'm extremely grateful to the School of Oriental African Studies for conferring on me the honorary degree of DSC ACON. I'm also grateful to Professor Terence Byers for the generous words with which he has introduced me. My association with the SOAS goes back a long way. In fact, one of my books that Professor Byers referred to accumulation, stability and the capitalism was written when I was visiting SOAS in 1990. To be recognized by an institution of such distinction and such cosmopolitan intellectual traditions and one of which I have such fond memories is immensely gratifying. John Maynard Keynes may have exaggerated a little but only a little when he wrote the ideas of economists and political philosophers, both when they are right and when they are wrong, are far more powerful than is commonly understood. Indeed, the world is ruled by little else. The obstacles to solving the material problems facing mankind may lie in our social structures characterized by the existence of privileged social groups with entrenched interests. But these interests are legitimized through ideas. The proximate obstacle to material progress of mankind therefore lies in the realm of ideas. Engagement in the struggle over ideas for ushering in a humane society is what makes the profession of an academic economist worthwhile. The importance of the struggle over ideas is greater today than at any time in the recent past. Humankind today faces a twin crisis. One is the crisis of recession and unemployment that began in the developed countries but is now spreading all over the world. The other is the food crisis manifest in the fall over the last three decades in per capita world food-rains production and availability. The first crisis implies that resources lie idle. The second crisis arises because peasants and petty producers over much of the world have inadequate resources. This combination of resource shortage in one segment of the world with resource wastage in another, both productive of human misery, reflects the deep irrationality of our social arrangements. But the very apocalyptic nature of the twin crisis also constitutes a source of hope. An improvement in the social arrangements characterizing the world economy can no longer be deferred. A denomah where all segments of the working people in the world can be made better off than they currently are is not difficult to achieve. What is required is a removal in the realm of ideas, of barriers to the achievement of such a denomah. The degree with which you honor me today gives me great encouragement to do my own bit in the struggle over ideas that is intensifying. Thank you very much.


Thank you to Stefano and thanks also to to Marcelo and Jean-Christophe for organizing this school and later this conference. So I came here several times it's always a huge pleasure. I followed many courses I learned a lot so now it's I hope this one could be fruitful for you so it will be with Raphael here. We wrote some notes that will be on the web page. There are some mistakes we are correcting so if you find another one you should tell us. Okay so let's start so the subject is partial hyperbolicity so but let's start with something a bit more general so we are interested by different shable dynamics so we are on a manifold which is compact on the relays and we are interested by discrete dynamics so a different morphism and the topic of this lecture is to discuss some particular class of this different morphism because there are few things we can say about general morphism but to start with let's say something general which is how to so today this morning will be more motivations so how to decompose the dynamics the composition of the dynamics so there are several ways I will I like one I will present now which is quite natural so to decompose the dynamics what you look for our attracting region trapping region so a trapping region is an open set which is whose closure is mapped into itself the manifold u is below and it's mapped into itself and now if you iterate the region any orbit here in you is attracted by your set a limit set the attractor of you which is compact and invariant and you can do the same in the past you define kind of repeller which is also compact and invariant and the other orbit have to to go through this middle region you have you decompose the manifold in three parts a and this region o even by the iterate of you minus f of you so points here are not recurrent at all so they they come from our and end at a so it's highly non-recurrent so you're mainly interested by orbits in our or in a so that's what you have if you have one such region but then you can change the region and again you're interested by the corresponding are and a and you trash the other point so if you trash all the points in the non-recurrent part for all the the region you what we mainly is what we called the chain recurrent set so this is the intersection of m minus o for all trapping region you you is open and invariant so this set is compact in invariant so we want to understand the dynamics in this set and he said naturally splits into a collection of invariant compact set so because you you may define a relation so if you take XY in our chain recurrent set you say X is equivalent to Y if each time you have a trapping region this cannot separate X from Y so either X and Y belong to you or X and Y belong to its complement so it's an equivalence relation and the equivalence classes are called the chain recurrent classes and they are compact in invariant because this relation is closed an invariant so this is something we would like to understand in general how does it split maybe there is a only one class maybe there are several ones maybe infinitely many one it's the first first property would like to understand okay there is another way to define there's objects which explain the the word chain so chain is another name for pseudo orbit so if you fix epsilon you say that a sequence in M is an epsilon pseudo orbit so for any n the distance between the image of Xn and Xn plus one is less than epsilon it's like an orbit but you allow some error at each iteration and then r of f is the set of points that are recurrent for pseudo orbit so for any epsilon there is an epsilon pseudo orbit from X to Xn well you have to specify that you have at least two points because otherwise it's trivial and then you may define the equivalence relation in another way so X is equivalent to Y if for any epsilon there is an epsilon pseudo orbit from X to Y and another one from Y to X again so something we could discuss in the tutorial is why this two notions are equivalent so I don't know for the tutorial we will see we can I propose something we can discuss any other thing maybe one indication is if you have if you fix a point and epsilon you may try to understand this set the set of point one that you can attain from X by epsilon pseudo orbit and again n larger equal to one so try to understand how this set looks like okay so this was something general even for homeomorphism it makes sense so now let's discuss some more particular class of systems so before talking about partial hyperbolicity let's talk about hyperbolicity uniform hyperbolicity so many of you maybe have no summer but uniform hyperbolicity I'm not sure all of you so I like to quickly give the definition and then give the main property hyperbolicity so we are still with a different morphism F and we consider K compact invariant set and we say that it is hyperbolic so for any point you may look to the tangent space at X if you want to simplify you may mention M is a torus and so okay and then so that this linear space have splitting into two linear spaces the property that so you have invariance for any X the image of yes is the space yes at the image and the same for you okay and then you have so you have contraction of ES there exists C and lambda smaller than one so just for any point and for any positive iterate so the the norm of DF at X along the space yes and any rate is smaller than C lambda n so this is contraction along ES and you have sorry the definition is symmetric in the time so now if you reverse time you have contraction along EU so this is a very classical what is less standard is how to define a hyperbolic different morphism so there is one definition I like and I'm fighting to promote this definition so with what I said before it's very natural you say F is hyperbolic any of its chain record class is hyperbolic is a hyperbolic set and there is another equivalent definition it's the fact that R of F can be decomposed as invariant compact set that are hyperbolic so I'm not taking and saying here that there are the chain record classes I'm not assuming a fine place of chain records classes for instance so to see the equivalence it could be an exercise no no no here the hyperbolic city is in restriction to the chain record set I will say give you example so what is more standard is to talk about what is called axiomay so I don't want to give the definition but for those who know more but we can discuss this if you're interested it's to show the link with a more classical definition so in fact it is equivalent to not axiomay but axiomay plus no cycle condition so some some very classical examples so one case is when the bull manifold is is a hyperbolic set a hyperbolic set so we say that in this case F is another famous example is this so linear automorphism on the two torres so this integral matrix matrix acts on R2 but preserves it too so you may take the question which is a two torres and it is a hyperbolic at the opposite you may have a very small chain record set so you may have a chain record set which is finite finite union of periodic point that are each of them is a hyperbolic set so hyperbolic periodic orbit so here it's almost what we call more smell different morphism in the definition of more smell different morphism there is another technical assumption I don't precise here so a very simple example on the circle you had some sink and some sources then you may have more complicated example maybe more complicated so you have the horseshoe is defined so on the sphere you have or in the plane you have a rectangle R which is mapped onto itself this way but inside R the horizontal and the vertical are preserved so you see the the vertical is stretched so it will give the unstable direction the the vertical and the horizontal is contracted so it's a stable direction and if you take the consider the orbit which don't exit you find a contour set and at last there are attractors so you may have periodic point that attracts there are things but you may have a more complicated attractors one example is a clicky attractor I don't want to give the the construction just to say that so again in the sphere or in the plane so you have a hyperbolic set so that so it attracts any point in a neighborhood but the set itself is locally homeomorphic to a product so to contour set times the line and the dynamics so stretch along this this line so you is here and contract to understand it's not so easy to to see how to build that we did some picture in the nose okay so let's summarize some important property because it's it will be our starting point for partial light of the city so one important property is the shadowing so it says that if you continue up so the orbit so an orbit with error it is shadowed by a true orbit so for any epsilon there is delta such that so let's consider K hyperbolic set and so each time you have an epsilon so the orbit in K then there is a point in M such that the orbit of x stays close to the absolute orbit so at any rate it is delta close so this which seems maybe technical it has many consequences so an important consequence for us is a spectral decomposition because it will be one of the main subject in this in this lecture so spectral decomposition tells that if f is hyperbolic then the number of chain recurrence classes is finite finite and then so each chain recurrence class has some recurrence but recurrence by pseudo orbits in fact in the hyperbolic setting it's better so any class is transitive so not only we can travel inside the class by pseudo orbit but we can travel by a single orbit so there is it contains a dense half orbit forward orbit which is the same as containing a dense backwater so two other consequences of this lemma one is so the stability f is hyperbolic then any G which is C1 close is also hyperbolic so hyperbolic city is an open property but not only that so there is so the dynamics on their chain reconcept are conjugate there is a homomorphism which conjugate is equal to G so the dynamics remain the same after perturbation and the last property related to the shadowing is the existence of coding or we have Markov partition so there is a symbolic representation of the system f restricted to the part that we want to understand just as an example for the horse shoe then it is conjugated so to a symbolic system which is a space of sequences of zero and one where the shift so we understand very well the dynamics so then some other properties that are important so one is to understand the geometry of hyperbolic sets it's a famous stable manifold serum it says that if K is hyperbolic and if you take a point in K then you may look to points that have the same feature as X what we want to call the stable set points whose future orbit gets closer and closer to the orbit of X in the future so this is so usually it's WS of X it is a so manifold is a an image so many emails because they accumulate itself then so another property is a description of a statistical description of the dynamic so let's take f hyperbolic deformer fission in general it's difficult to understand the future of any orbit but we are happy sometimes if we understand the orbit for almost every point so this is a case and we have some finiteness of the possibility so there are finitely many probability measures such that for almost every point so what does it mean almost every point it means if you take any volume it's almost every point for this measure and used by the volume if you change the volume you have the same notion of almost every point then the future of X distributes according to one of this measure there is I such that you look to the statistic of this orbit you put dirac masses along the forward a piece of the forward orbit this is a I normalize this is a probability measure and it converges to one of this measure for usual convergence of measures and then you may study the ergodic properties of this measure I won't talk about this now and the last property is the fact that okay we would like maybe to understand all the hyperbolic system and to classify them we are far from being able to do that but there are some reasons for example so the hyperbolicity could constrain the dynamics and the manifold so for instance there is one result by you have France and you have well I didn't give any name but so let's assume that F is another and M connected and that the unstable direction is one dimensional and then M has to be a torus and the dynamics is conjugated to a linear automorphism very similar to the one I gave at some moments so it's quite free another thing we understand so in dimension one hyperbolic morphism are exactly the those I describe in the second in dimension two hyperbolic morphism so according to the spectral decomposition breaks into finitely many classes and each of these classes has to so looks like one of the example I gave so either it's another or you have isolated periodic orbit or you have a contour set like the horseshoe or you have an attractor repelor which is similar to a click in but in higher dimension we we don't understand okay do you have question so let's go to partial hyperbolicity so one goal is to relax the notion of uniform hyperbolicity to address more a larger class of system so that the way this one so you first define what is a partially hyperbolic set so again you have fixed the morphism F you take a compact invariant set and you say it is partially hyperbolic if so for any point x the tangent space can be decomposed into linear subspaces so I didn't precise in the hyperbolic setting you had two spaces the first is called stable the last is unstable here you allow a third one called the center stable and you require so invariance as before here sigma would be s you are see you require that yes and you are contracted so yes is contracted by the f u by the f minus one as before and you have a center part which has which is dominated and domination domination means I really so this is a presentation but introduction but this afternoon I will describe in more details this notion so domination means each time you take vector so for any point x you want to compare what happens along the stable so you take a vector yes in ec and in you that are non-zero and you want to understand how they are contracted or expanded and so for instance if you look to the middle part this is a reason I took it non-zero it's less expanded that along you because you have this factor and it's more expanded that along yes similar so the hyperbolic case it just a case the center bundle is trivial we don't want that to have only a center bundle but in this case there is no information but sometimes we allow one of the extreme bundles to disappear because for instance in the hyperbolic case you may have only the stable if you have a sink attracting paradigm so so at least one one of this bundle yes you is non-trivial so for the moment I won't give more example so you have already hyperbolic example what okay a very simple example a nanosurf system on M and you and you do the product with the identity on M2 and another many products and you can check it is partially hyperbolic the center bundle is the space a tangent space to M2 so one goal is to understand how to extend the previous property to this more general setting this larger class of systems I want to discuss all all the properties I have introduced but there are also other motivation for studying partial hyperbolicity it's not just trying to generalize it's also because sometimes partial hyperbolicity appears a natural class so as I say one property we will discuss a lot is a spectral decomposition so what I mean is essentially the finiteness of the number of classes but there are system there are large class of system that are not partially hyperbolic but that have on infinitely many classes a famous example is a new house phenomenon so let me recall what it is so if you start with a C2 surface deformation which exhibits homoclinic tangency homoclinic tangency mean that there is a periodic orbit hyperbolic periodic orbit oh so just so it's hyperbolic set so you have stable and stable manifold so and there is a point P in O so that the stable manifold of P and the unstable manifold of P have a non-transverse intersection point okay something like that if you think to a fixed point saddle meaning you have one-dimensional unstable one-dimensional stable the so you have two invariant manifold the stable and looking to the past you have the unstable manifold and you may require that there's a manifold that are have a tangency in this case you may check that f is not hyperbolic and what new house has proved is that then there is an open set of system C2 so f is in the boundary of you and in you so energy in a dense subset of you not only it's dense but it's a g delta dense has infinitely many things or sources so since our periodic point that are attracting sources hyperbolic periodic point that are repelling so there are particular case of chain record classes so in this case you have infinitely many classes so this seems a wild behavior not only you have infinitely many classes but also to describe the so this classes here are simple but you have many other one which are much more complicated that could appear so to describe the system is very difficult subject so you would like to characterize system which have only finitely many classes so this is something we we don't know in full generality but let me just give a statement so one case is a case you have only a single class so let's say f so what one example you have a single class is when you have a dense orbit f is transitive anyway say f is robustly transitive any g deformorphism C1 close is transitive has a dense orbit and there is a theorem bonatti lia's puja's they have something a bit more general but instead that if f so if f is robustly transitive let's assume m connected then f is not partially hyperbolic but volume hyperbolic which is quite related so it but globally the whole manifold is a volume hyperbolic set meaning so to summarize you you have a splitting like for partial hyperbolicity but here it's not uniformly contracted maybe and here not uniformly expanded but you still have invariance and domination but what you have I want detail much that you have you don't have uniform contraction here but you have contraction of the volume along this space in the future in along ECU in the past and so for instance in particular in dimension 3 your partially hyperbolic m is partially this is one case another example where partial hyperbolicity appears so you see that homo clinic tangency may generate wide behavior so high complexity so you may want to characterize a system which don't exhibit homo clinic tangency homo clinic tangency so let me state one serum so I proved with Enrique Pujols Martin Sambarino that way young so it says that in this so if you fix the manifold in a space of C1 diffeomorphism you find two regions a closed region and open they are these joints and the union is dense with a property that if you take F in T then F is limit of diffeomorphism exhibiting tangency if you take F in O then F is partially hyperbolic in a stronger sense that what I have set up to know so any any class is either hyperbolic or has a splitting so ES EU and the center part splits into one-dimensional bundles and here yes and EU are non-trivial so this is a and so this forbid the existence of tangency close so this is a good setting to try to understand all this properties try to generalize all this property of hyperbolic system I have few minutes more yeah so what to say so one goal is to extend the as I said the previous property to this larger class of system another motivation for partial hyperbolicity is that we have many example natural example that appear in various setting so Raphael will talk about that tomorrow this we will discuss on on Thursday we will talk about robust transitivity and on Friday about finiteness for attractors then what about the other properties we talked about so invariant many faults so this will be addressed on Wednesday well I hope and there are many other subject with partial hyperbolicity we won't talk at all about so other subject so there are many ones but some in one that are been much developed in the past year so the problem of physical measure so there's measure that I described in the republic setting and in particular if the system is preserved the volume you have a natural measure and you'd like to know if it is ergodic so ergodicity when a volume is preserved and another subject that has been developed is a prime of classification and maybe we'll talk a bit about that tomorrow so mainly in dimensions but if you look to the literature you will see that partial hyperbolicity appear at many places because it's a very natural setting to extend some properties and usually the first case one looks at is a case of the center is dimension one and then a second case would be to address the case you have a sum of several one-dimensional center okay so and this afternoon it's more to discuss the definition and the basic properties so thank you


Hey guys, what is up? Welcome to my channel. For today's video, we have a luxury highlighter showdown. I'm basically just going to be giving you information about the most recent luxury highlighters that have come out. I'm going to give you my rankings for which ones I prefer. I'm going to tell you about the differences in formula and colors. And hopefully this video is helpful to you in deciding what luxury highlighter you've been wanting to pick up if you've been on the fence. So I really do hope that this video is helpful for you guys. So let's just get into it. Hi guys, if you're new here, my name is Morgan. I am a product knowledge enthusiast. I just love knowing anything and everything about all of the new makeup on the market and sharing my thoughts with you guys. And hopefully helping you make your decisions on what is worth your money. So that is what this video is all about. I wasn't sure if I was going to end up doing it, but you guys still seem very interested in it. Recently, a lot of luxury highlighters have come out. Today, I'm going to be talking about the Wangoss highlighters. I wasn't going to talk about these, but you guys wanted me to throw them in. So I figured it wouldn't hurt. We have the Natasha Denona. I need a nude highlighter. We have the new Dior Backstage Glow Face Quad. We have the new Charlotte Tilbury Holiday Highlighter. And then we have the new Pat McGrath Holiday Highlighter. All of these have something in common. They really are quite pricey. I'm not going to talk too much about value in this video. I really want to get more into the formulas, but I will give my two cents on value as well. So let's just get into it. We're going to start off from the most affordable to the most expensive. So the most affordable is actually going to be the Wangoss highlighters. So these are currently only available on the BeautyLish website. And of course, the two colors that I'm speaking of today are sold out. But I did want to talk about the highlighter formulas in here. So actually, since this is a blush palette, I did the math. Not really. I did math in my head. 19 grams of product. So we're going to say there's about nine and a half grams of highlighter. The full price of this is $45. So we'll say you're getting about nine and a half grams for $23. That makes this by far the best deal out of this entire video. However, you will only get in one color. So I have two highlighters to speak of. The first one is a blush peony. And then the next one is coral rose. Now of the two I'm telling you right away, I would highly recommend the coral rose highlighter. I think this one looks a little bit more smooth on the skin. It also swatches more smooth. His formula, I would say is a creamy powder. It's definitely a powder formula, but it does have a very wet, creamy feel to it. Compared to some of the other ones that I'm dealing with today. It is more on the powdery side. It's just we have a lot of fake gelay type formulas. I find blush peony to be a bit more powdery. You have to really kind of work it into the skin more than the coral rose highlighter. The blush peony is going to give you a pink shift highlight. The pink is actually quite strong, but this looks gorgeous with its corresponding pink blush. I'm not strongly recommending this one as much as I do love a pink highlighter. I just think that the coral rose is so much better. I feel like it applies smoother to the skin and more easy. I feel like it doesn't emphasize texture. This is a really gorgeous glaze highlight. This was in my most recent monthly favorites. I've been enjoying this one a lot. Now let's take a look into the next most affordable. That one is going to be the Natasha Denona. I need a nude glow highlighter. Now this has it is limited edition for the holidays. $42 is what it is priced at for eight grams of product. That's about twice as much the value of the Wayne Goss. This is the highlighter that I'm actually wearing on this cheek today. This is a nude champagne color. It's going to be a baked gelay formula. So there is very minimal fallout with this. It's quite mess free. I wouldn't say it's the most smoothing highlight. It definitely doesn't smooth texture, but most highlighters don't. I don't think it emphasizes texture any more than any other highlighter. Also, I just really love the ease of use for this. I feel like you get so much product on your brush, but it doesn't over apply to the face. But at the same time, you don't have to dig. And I think it's a really gorgeous everyday highlighter. It has a little bit more of a warm golden base to it, which makes it a little bit more wearable, but it still does have that metallic sheen to it. It actually swatches a lot darker than I feel like it applies to the skin. I do feel like it applies brighter. I think if you have a very fair complexion that you might have a cast with this one, but I do think light up to deeper complexions, you definitely can make this work. I can see this being a very versatile color. And if you look on my arm swatches, it is right here. It is definitely the most peachy out of every single one of the highlighters in here, but it has a very strong metallic shift to it. But you can easily blend that out or just apply a little bit for more of a natural sheen. So I've really been enjoying this one. So the next ones are the Dior Backstage Glow Face Palettes. So they already have two existing palettes in the line and Dior actually came out with three different colors. I picked up two of the colors. I picked out Pure Gold and then I picked out Rose Gold and I absolutely love these highlighters. I love the formulas. These definitely I would say are the most glitzy and glam. You can definitely see on my arm that these are the ones that have the most glitter and reflex. Now I do get asked all the time, are these highlighters glittery? The gold one if you absolutely hate those microfine glitters stay away from the gold one. This one is definitely more glittery, more metallic than the pink one. And I really do feel like though when you apply these to the cheek, you can make the glitter go away if you just swipe it away. But yes, you are going to get a little bit more of an extra sparkle than you are the other highlighters in this video when it comes to these Dior formulas. So if you're not into that, then definitely you want to stay away from these. But the gold one in particular, I feel like the shades have a little bit more of those microfine glitters Glitters is a strong word. I mean, if you just take a look on my arm, these eight shades are the Dior quads and you can clearly see they have more glimmer to them. Now, if you're okay with a little bit of glimmer, but you do want something more subdued, while there are a couple of the shades in this Dior formula that are a little bit more glimmery, like the gold color, I feel like the shade right here is a little bit more flat. So this palette isn't as glittery as the golden one, but this is a baked gelet formula that does have some glimmer. These are, amongst my favorite formulas for sure, but it's not going to give you that super seamless, smooth glow to the cheek. And by the way, not sure if I mentioned this, but these are $45 each. You are getting 10 grams of product, which I thought this one would be the best value, but it's actually not in terms of product, but you do get the biggest bang for your buck in my opinion because you get four different shades, which I prefer it that way. So this next highlighter, I was extremely hesitant to pick up. This is from Charlotte Tilbury. This is the Superstar Glow Highlighter specifically for the holiday, so it is limited edition. Now, this is $55. When I first bought this, I could not believe I paid $55 for a highlighter. You are getting 11.5 grams of product, which is the most that we've seen thus far in a highlighter, but it's like, why do you want so much product for one highlighter? If you look on the swatches on my arm, it very clearly is the most subdued highlighter. It has the least amount of sheen. And you guys, I'm going to tell you right now, this is my absolute favorite highlighter of the moment. It's my favorite highlighter of all the highlighters that I'm talking about. And I also believe this is the most versatile for the most skin tones. Now, the texture of this definitely has some kickback. You can see in the pan right here, there is a lot of kickback here. So it's a creamy formula, but you do get kickback with this formula where you almost just want to kind of press the powder in because you paid so much for it. The finish on the skin is unbelievable. It is a skin-like glow. It blends seamlessly into the skin. You can't see any trace of where you applied it at all. It just is a gorgeous glow. I'm floored by this highlighter. I've been recommending it the last couple of months. So if you watch me at all, I hope I've convinced you to buy it because I think it is phenomenal. So many of you guys have messaged me, thanking me for recommending this highlighter. I know $55 is a lot and I don't think it's for everybody. But I will say of all the highlighters that I have here, this one is by far my favorite. I've been enjoying it. I don't have another highlighter that is like this, finish-wise, color-wise. It's super unique for me. So I highly recommend it and I've seen it work on so many different skin tones. All right, so let's move on to the last highlighter, which is the most pricey. This is from Pat McGrath Labs and it is $65. This is the Skin Fetish Sublime Skin Highlighter. $65 you are getting, 6.5 grams of product.  I will say though, this is the most luxurious packaging out of all of these highlighters. It is super heavy, you guys. This metal 10 is so heavy and then you have to twist it. I don't really like this whole twist-off cap packaging. It's not cheap packaging. It is very weighty, very luxurious, but it's not necessarily the most practical packaging. And the inside looks gorgeous. This is described as like a golden champagne color. It definitely looks almost a little bit pink when you see it in the pan. And this is the highlighter that I have on this cheek right now and you can see the difference. The Natasha Genona has more of that gold warm base whereas this one has, I feel like almost more of a white base. It's a little bit more, dare I say, stark. It's not unflattering stark or too white or icy, but it does have more of a white base compared to the Natasha Genona. And I have to admit, I'm not crazy about this highlighter. It's more so of a cream formula. It's not a super creamy formula. There's literally no powder to this at all. You're not going to get any fallout whatsoever to the touch. It just, it feels like a cream to me. Definitely a hybrid for sure. I would say it's like 80% a cream product with a 20% powder mix in there. The color itself does pull brighter on the skin and it doesn't pull quite as pink as I thought, but I wouldn't necessarily call this like a champagne shade. I don't even know what to call it, but it is more so of a beaming highlight. Something to note about this though was it did take a lot of layering it up to get it to this intensity. The first initial application, I applied just a little bit and it was very, very natural. It's not necessarily very smoothing on the skin. It emphasizes my texture as any normal highlighter would, but I don't think it's anything to call home about personally. It's more so of a luxury experience, but I found it took me a lot of time to apply because I had to keep digging into it to get the finish on the skin that I wanted. I do recommend using a synthetic brush to kind of dig in there. I used a bling brush F17 to apply this highlighter and for $65 and being the worst value personally, I'm just not as into it. The only thing that's really unique about it is the packaging and something to point out the Dior, the Charlotte and the Natasha are all made in Italy. Wayne Goss is made in Canada and then the Pat McGrath is made in Taiwan, which I'm very surprised by. I thought she would source these from Italy like the majority of her great formulas. So I did want to do some swatch comparisons so you can see how the colors and formulas compared when they were side by side to each other. So quickly, let's take a look. So here's a swatch comparison of all of the highlight. We have the two Wayne Goss over here. This one is the Coral Rose highlight. This one is a blush peony and we have Natasha Denona, I Need a Nude. Then this is the Pure Gold from Dior, these four. This is the Pink from Dior, these four. This one is the Charlotte Tilbury and then this one is the Pat McGrath. And so here are the main differences as I'm going down with arm. I think that the Wayne Goss is clearly a more powder formula compared to the other products and they are a bit brighter. So they're going to fare better on lighter skin tones. That blush peony shade is extremely unique compared to everything else on my arm. The I Need a Nude shade from Natasha Denona is the most peachy and then you can clearly see the Dior shades are going to give you the most glitz and glam on your cheek. They definitely have glitter in there that the other formulas do not have at all. Like I wouldn't consider these formulas really glittery, but when you look at them compared to the other formulas, they look really glittery, much more metallic and much more foiled. So not for the faint of heart for sure. The Charlotte Tilbury literally looks like nothing special on the arm at all. And then Pat McGrath to even swatch it, I felt like I kind of had to dig into the pan to really get the payoff. It definitely pulls more pink on the arm than it applies on the cheek and it definitely pulls darker on the arm than it applies on the cheek. So just keep that in mind. So let me take a minute and rank all of these highlighters from my least to my most favorite now. We will start off at number seven, my least favorite, which unfortunately is the Pat McGrath. I love Pat McGrath. I had really high hopes for her first powder formula, but I just think it really is a bit too expensive for what it is. The packaging is just so luxurious, but the product inside, I just would reach for the other colors over this one. Moving in at number six is flush peony from Wayne Goss. This formula is a little bit more powdery and less creamy than the coral rose shade. And it's absolutely gorgeous. I really do love this highlighter, but it's just not a color that I'm going to reach for a ton. At number five, we have the Dior Pure Gold highlighter. I really, really, really, really love this, but when I compared it to all of these other highlighters, it's true this one is a little bit more glittery and it's not that I don't love glitter, but so many of the highlighters that came out this time of year are so amazing that this one just fell here, but I really, really love it. It was in my favorites video. Number four is the Natasha Denona I Need a New. This is a stunning everyday highlight for me. I can definitely see myself wearing this a lot just because it's ranked at number four doesn't mean I don't love it. I absolutely love this highlighter. The highlighters that came out are just so fantastic and this is a great basic everyday perfect highlighter. Moving in at number three, I just love the Dior formula so much and I prefer a pink highlighter. So that is why I love these pinky-based highlights in this pink quad. And I like this over the gold because I feel like you get a little bit more variation in formula because you do have this shade right here, which has zero glitter, but you do have some of the glittery shades, which I'm not opposed to a glittery highlight, okay? Ranking in at number two is the Coral Rose highlighter. For some reason, this Wayne Goss highlighter is better than the other one. I just feel like the formula is a little bit more smooth. It's quite a beaming highlight, but what I'm most impressed about with this highlight is I feel like it literally smooths my texture and it blends seamlessly into the skin. It is just so creamy, so I do highly recommend this shade. The blush is beautiful too, but the highlight in here is really phenomenal. And then of course, no secret, I already gave the answer away, but this Charlotte Tilbury highlighter, I have no words. I've talked about it so much on my channel that I don't want to talk about it anymore. It's just number one. All right, you guys. So that is all I have for today's highlighter video. I hope you found it helpful and it helped you make your decisions if you were on the fence about which one you wanted to pick up. Let me know your thoughts down below. If you aren't subscribed to my channel, I would absolutely love it if you would consider taking the time to do so. And I will see you guys in the next one. Bye, guys. Have a good one.