Okay, good evening everybody. Thanks for joining us tonight. I'm Lea Merose, the Director of the Finnish Cultural Institute here in New York. And I'm so happy to see you all here joining our programs together to hear it. We have been collaborating through a Mobius program, which is the program of our institute moving museum professionals, researchers in the fields of architecture, design and visual art across the Atlantic. So, from Cooper Hewitt, a friend, Andrea, Andrea Lips, has been to Helsinki about less than a year ago, but about a year ago, to do research there at the Design Museum. And Sui Salonimi from the Design Museum, Helsinki was here at Cooper Hewitt. And actually this program tonight, which is part of the series of design talks, is kind of like a fruit of the program. And we're going to have two Finnish designers who are participating in the beauty trial now, Kosta Saxi and Thomas Mark-Umbuilka, who are going to discuss their ideas, their concepts of beauty, and their creative work in the field of design. And Andrea is going to be the moderator of the discussion. I just want to use the opportunity to thank Cooper Hewitt for wonderful, wonderful collaboration. Andrea especially, and of course Kara McCarthy, who's also been a great help to us during this process. And also our project manager at the institute, Ilari Lamonen, who's been the driving engine behind the radius program. So, without further ado, and without taking more of your time, please, Andrea.  I'm Andrea Lips. Thank you, Alayna Maya, for introducing us. I am an assistant curator of contemporary design here at the museum, and the co-curator of the exhibition upstairs, Beauty, Cooper Hewitt Design Triennial. So I hope all of you would have had an opportunity to go upstairs and to see it. And tonight's program is generously sponsored by the Mobius Fellowship Program, by the Finnish Cultural Institute. And Mobius, as Lena Maya briefly introduced us, is a program for visual arts and museum professionals that is intended for transatlantic relationships and to foster and create those. And I was fortunate enough to have been a Mobius fellow myself last spring. I moved to Helsinki for a month where I was graciously hosted by the Design Museum. And there I researched and worked very closely with them to share expertise and knowledge about our institutions and about international design practice. I met with countless designers. I conducted studio visits. I attended events and exhibitions. I visited factories and labs and enjoyed Finland's ever-lengthening days. I was there in May and June, which of course is a very magical time of year to be in Finland. So that opportunity very much enabled me to appreciate Finnish design on a much deeper level. And of course that brings us to this evening. So I'm particularly delighted for this very special evening, exploring new frontiers in Finnish design, which brings together two designers from Finland whose work is included in the exhibition upstairs. So both Thomas Markenpoika and Kusta Soksi are two outstanding designers whose work is very much contributing to their fields in remarkable ways. So first tonight, Thomas Markenpoika will speak to us about his work. So Thomas creates everyday objects that seek to elevate ideas of function by exploring metaphysics and meaning. His projects range from industrial design to limited edition pieces for galleries and for collectors, and have been shown internationally in museums and galleries and in art fairs. And Thomas was trained as an industrial designer at Finland's Lahti Institute of Design. And after an exchange at the Danish Design School in Copenhagen and an internship with Marcel Anders in Amsterdam, Thomas pursued a more conceptual path for design. So he graduated then with a master's degree in contextual design from Design Academy Eindhoven in the Netherlands. And he set up his practice in Amsterdam where he currently lives and works. Our second speaker tonight is Kusta Soksi, who also curiously lives in Amsterdam. Kusta is an awarded graphic designer and illustrator whose practice has expanded to include textiles, environments, objects, and more. And all of these are unified by this very playful, almost psychedelic abstraction of nature that pushes at the edge of perception. So we'll see more about that in a moment. His work has also been displayed internationally at museums and galleries. And he counts companies such as Marimekko, Nike, Isemiaki, and LVMH, among those who have commissioned his work. Kusta is trained as a graphic designer also at Lahti Institute of Design before he then moved to Paris in 2004 and then later to Amsterdam where he also currently lives and works. So it's my great pleasure to welcome them both here this evening and of course to welcome each of you for joining us this evening. So the way that we're gonna run this is I will first invite Thomas up and he'll present to us for 15 minutes about his practice and his work. And then Kusta will come up and join us. And then the three of us will sit down for a conversation before we open it up to all of you for questions. And I will also note that as a part of the triennial, our next public program is in two weeks with Richard Neeson, who is a Dutch designer and I would very much encourage all of you to come in and participate in that as well. So without further ado, I would love to welcome Thomas. So my name is Thomas Mark, welcome. And I met somebody with a good introduction from me so I don't think I'm gonna do that anymore. And so the work you see upstairs is the cabinet that I graduated with to do the 12th of December in the high zone. And that project started out as, well, when I was studying in the Netherlands in the DeSanne County, my grandmother was at that time diagnosed with Alzheimer's disease. And for me not to be president in Finland also, they would support my family. And so I still was very much affected by the conditions and I wanted to somehow reflect that in my work. So I was starting to kind of ask questions like why, I mean also to criticize my profession and being like as a designer, like why do we make objects that are so different from us, how we're human beings, that we are fragile, we have emotions, we have feelings, we have dreams and we get inspired and what do we try to control our design ball in a way that it's contrary to how we're human beings. So for me the result was then to make a cabinet to start with and how I wanted to do this is to, I took an existing piece of furniture, in this case it was a wooden cabinet. And I started welding these metal rings around the object to cover the piece like semi-layer. And after which I have covered the piece, I set the whole piece on fire, which you see in this case in this picture. And so what I have left is this kind of exoskeleton of more like a memory of the former piece. And so this was my kind of translation to make objects that are more fragile because I think that's, I think fragility in objects is something that makes more precious to us, makes you more human and that we can really, really resonate with us, we care more about them and they have more of this kind of human aspects in them. And this is also another of my graduation work, so these are the two works I graduated with. And this is two pieces I did while studying and after which I extended the work to further to make more piece furniture. And in this case, this is a chandelier I made for as a commission work for a gallery in London. And I also have included a few other pieces as a commission work for private clients like mirrors and similar work. And here is the work I made a few years ago and it's called Amalgamated. And in a way it has a similar kind of aspect to the origins that I use very kind of industrial mass produce material, which in a way is very kind of anonymous and kind of commodification in a way. And I try to do with this is to kind of translate those into more of a language of my own. So your starting point was to take as the mass produce tool object and to kind of use it in a more holistic way to make the pencil something on its own rather than using it as a primary purpose. And here you see like the pens that are glued on one side to another to form like a large box. And then turned in a lathe to achieve shapes such as these. Maybe it's a bit of a jump there. Maybe it's good to show the video actually in the previous project. So this is like the making of one unit piece I made. And that's me. I was wielding around the chair and grab. Yeah, it's a lot of practice now following that. I think it's show you a video of this Amalgamated collection. So this is also more like a making of video. So it's easy to raise you to understand how the process goes. Also another very, very intensive work. Here. And this is the recent project I did about six months ago. It's called the Distant Lights. And this was kind of like the, it's a bit of a continuation on the topic of my graduation work which is what is kind of like escalating between this temporality and death and memories. And so I focused here a bit more on this kind of Japanese philosophy and aesthetics on like a part of Sabi. And. Who's playing with that? The video is still on. Still? Oh. Sorry about that. So the starting project was, the starting of this project was kind of a, because it is like, it's a cultural tradition that's not inherently mine. It's more like in the Eastern and Japanese form philosophy and metaphysics. So it's kind of a research on like how kind of Western designer approach these topics that are inherently part of my culture. And. So I focused on this kind of Sabi culture which is takes roots in permanence and irregular shapes and austerity. And it's very much opposed to kind of Western philosophy where we tend to take control of our surroundings and environments. So we, you know, try to master it and try to force it into something. And that we try to control it too much. And this, of course, I realized that to try to transfer this kind of very different concept of metaphysics and aesthetics to my view would be very almost silly to try to mimic or to use the kind of traditional materials or the traditional forms of making. And because then like, there's always like a pitfall of when trying to do so, it very easily turns in this kind of pseudo-send jargony and very like use of like just borrowed aesthetics and borrowed concepts and not really formulating your own. So I kind of focused on one aspect on this, what is Sabi culture, which is this rock gardens, cotton sweet gardens, dry landscape gardens. And there's one garden in Kyoto which I visited. I did like an excursion for about six weeks in Japan for this project. And there's a garden in Tokyo, I can't remember, sorry, Kyoto, I can't remember the name of it, but there's one, particularly in this garden and most of the gardens, there's like one way of looking at the garden. Like there's one perspective, one narrow place where you're supposed to be able to perceive the garden as it is. And that was a very interesting point of view that there's one way of looking at objects. But, and then you have these, in the garden, you have these ripples on the stones like they're from the gravel, which is reflecting kind of this pond, like ripples in the pond. And I was very, very curious about like how how these kind of translate into more like, my influence a bit more like western kind of like, scientific or more kind of logic in a way. And so I made these collection of lights which I used a freshener lens as a kind of a projector and a reflector. And because of this kind of a circular pattern, this is the diffraction, I suppose. And which is kind of the same as they have in the rock gardens. And also with these objects, the same way there's not really, there's only one perspective in which you see as intended. So this is the view from the back. So you do get this kind of like a symmetrical pattern from the lens as a reflection. And it always shifts on your perspective, like on your perspective how you move around the room. And on the wall, you see a projection of that light. And so also, this is also my way of putting it, like I didn't want to use traditional materials like clay and wood and all this natural zen marketed kind of magazine communications. And here are the collection of these pieces. So they come in different colors and lights. So I use like LED technology in these and this is the acrylic lenses. And also show you a video of these because it's very difficult to take a photo that would explain it like how the dynamic of the piece as you walk around, close this, so there's not gonna be another video explaining about that. Yeah, and here's the next slide. Hello everyone. First of all, I'd like to apologize that I might be actually forgetting some words because I've been on a really long haul from Hong Kong by Amsterdam to New York, so I haven't really slept a second last night. So like, if I pass out, please help me. So yeah, my name is Kusta and I was born in a small town that was called Govola in Finland. And at one point I wanted to study graphic design at the Lahtik Institute of Design. And I graduated from the school in the year 2000, which is one time ago. And after my graduation, I used to work a couple of years in Helsinki for different agencies. But then 2003, I think it was, I wanted to spread my wings and I moved to Paris. And in Paris, I was working with different fashion labels and did a lot of work for various companies. But I really, at that time, I really specialized in illustration and I've been doing illustration actually for the past 10 years. After four years in Paris, I kind of thought it was enough of that city and I packed all my stuff in a van and drove to Amsterdam instead and rented a studio over there and I felt that it's like a good place for me. And I've been there now for almost nine years and I'm still having my studio there and I'm working and living in Amsterdam. Like I said, I've been doing and specializing in illustration for the past 10, 15 years. And I've been doing a lot of different kinds of projects varying from stamps to posters, all kinds of big and small projects. Like for example, this one is made for a Finnish railway company, VR. So they wanted to have this sort of like scenery from the Finnish nature and countryside and I illustrated their cars in different illustrations. And this one is, a couple of years ago, this is a poster made for PlayStation. And my main material has been paper for the past 10 years and it's been pretty flat and 2D and I think at one point I kind of like got a little bit bored even of this material. But I've been also doing some animation work every now and then. This one is actually an animation work I did for an Italian fashion brand called Salvatore Ferragamo. So it was for their watch and sunglasses one. Then at one point I kind of like got really into installations but still for this project, I was using a lot of paper as you can see. This is a paper pavilion I did together with the Swedish, top Swedish architect called Gjert Wingord. And it was made for Stockholm, furniture and light fair in 2013. And it kind of like, it consisted of over 15,000 A3 papers and it kind of like formed this sort of like a dome. And when you entered inside, you could see this sort of like, it kind of almost looked like an altar and we were really like inspired by Mosaik and from this like old ceiling paintings from churches and temples around. So that really took some time to build up. There was a lot of people working for it for two weeks and it only lasted for two weeks. And then they took it down and all the papers were actually distributed to different kindergartens near Stockholm area. And actually like, because it was like poorly made out of paper, that they had to have the fire brigade patrolling there all the time, so the time being when it was built up so it was so easily planable. This is another installation where it's a shape of an egg and I made it for a Frankfurt book fair for Finnish department in the year 2014. And the shape of an egg kind of like resembles the Nordic mythology where the egg is actually the kind of like center of the universe and then it's been decorated with this kind of like Nordic mythology and all kinds of different creatures. At one point I started to put a lot of pattern design and this is an example of pattern design and it's for Nike's Jordan brand. They are always celebrating the Chinese new year and this is the pattern for the year of the horse and they use it for many different apparel as well. But this is the shoe box and sneakers. And then I've been of course working a lot with Finnish brand Marimekko as well. And I've done, this is actually from my first collection for them and I did quite many prints for their fashion line and also for their home line and tableware and a lot of different things. This is actually a pattern for the tableware tablecloth and here's the same pattern kind of like implied to the teapot and here you can see also some designs. And this is actually my latest pattern I did for them, this is for the summer 2016 collection. It's kind of like flower power. This is really where my current passion is at the moment. I was working with WuL for the first time around six, seven years ago when I designed a collection for an Italian knitwear manufacturer called the Gephard Corvapina. And I kind of like understood like how great material WuL actually is and I really wanted to make more out of it and to understand WuL better. But then like somehow like years just passed I didn't have a chance to work with that. But then at one point, I think it was around like four years ago, I decided to go to Holland's textile museum which is based in Tilburg. And I discovered their jacquard weaving technique and I started to study and I've now been studying for four or five years. And it completely opened up kind of new world for me and kind of like I could actually kind of apply my designs into something like more three-dimensional and I really kind of like the idea that I can actually touch the material and really feel something like instead of just using paper as a material. So I started to produce tapestries and that textile museum is actually very well known for making tapestries for hundreds of years for the castles in the northern France and in Belgium. So they have a long, long history and like the quality is really outstanding over there. But I really wanted to do kind of like contemporary tapestry partly because like tapestry culture is such a rich thing in the Nordic countries. It's also somewhere else, but like especially in the Nordic countries, people kind of like tend to want to use them on the walls at home. And it's such a kind of great culture, but I kind of like wanted to reinvent it a little bit. So I started to make this sort of like contemporary tapestries mixing a lot of different kinds of materials. I really like to kind of combine natural elements or natural materials with something like really high-tech materials for like for example, rubber or plastic or something. I mean, it can be a reflective material or neon because I think they usually tend to become quite interesting results. And this photo is from the Taylor's Museum in Holland. And I mean, actually making, this is actually my third collection of tapestries. And they're all kind of based on dreams. And I have a family member who is kind of like suffering from this like really kind of vivid dreams. They're called hyper-pompic dreams where she doesn't really kind of like know where the where the sleep ends and waking up starts. And I love to kind of like hear her stories from what she's been seeing. And then I kind of like interpret those dreams into my artworks. And this image is actually from a gallery called Siu Siu. It's kind of like an experimental architecture greenhouse slash gallery in Taipei, Taiwan. And I had a chance to exhibit my tapestries there last year. And here they are in Music Center in Helsinki. And actually like last summer, also Röktör Gudmann wanted to use some of my tapestries in their summer windows. And this is a close of that collaboration. And here's some photos of my latest collection, which is called Wool Gathering. And these were just exhibited in Hong Kong last week for the first time. So thank you very much. Yeah. I'm gonna take the mic that works. So you can hear me. Thank you again so much for being here with us and for presenting your work. And I have so many questions to ask you guys. But I do wanna leave time of course for our audience to also ask questions, because I'm sure many of you do as well. You know, I was really struck in both of your presentations by what seems to be this importance of material and process and how those contribute to narrative. And so for instance, Thomas, I'd love to start with you. The piece upstairs, I hope everyone has had a chance to see it. It's the cabinet piece. And of course you've used steel in creating that cabinet. As we were talking about earlier, steel of course is often used because it's perceived as this perfect material. It's often used mass production. But you've really mutilated it and through this firing process and hand cutting it. And so what I'm curious to find out is, you know, if you could talk to us about the importance of material and process itself in your work, where that figures in in your process. Well, I think it really depends on the project. Because sometimes I do start a project. Maybe it is based on a material that I find interesting. Maybe it's the fact that I like, maybe it's the texture I like. Or maybe there are some kind of metaphysics and other ideas I can implement on the material. And then I just kind of use the materials in the medium of bringing out those ideas. And I think it's really, really, really important. Our project plays like, sometimes I can go for months even just to look for a certain effect or not even think about materials. And go several weeks even without sketching or just about browsing the idea of what you wanna do and what you wanna say with the work. Well, and let me ask you about the engineering temporality, like the cabinet, for instance. So, of course, the entire concept behind the cabinet is this evocation of memory and impermanence. And so, did the concept come first and then you decided to work with that material and that process? I mean, how did that, what was that process for you? Well, I mean, it is my graduation work. So, I think most people can understand process is very chaotic. And, of course, the origin of that is it started as a concept, you know, a concept. And I want to work further with it. But I think in that particular case, it was more in the beginning I was much more focused on creating a concept that would be like, in a way understandable and it could have a reach for people that it's, it could translate something into physical work that is very tangible and also understandable to the audience. I think that the material itself came along at some point. And as you say that it was more like as an industrial kind of symmetrical, hard like process material, which doesn't really have these connotations of any kind of human aspect or anything related to human beings. And pencils. I mean, where did, how did you get inspired to work with pencils? Well, I always had this big jar jar in my desk which is containing hundreds of pencils. And I barely use them ever. Like I said, I don't necessarily sketch a lot. And when I do, I only use like a black ballpoint pencil most of the time. I mean, I'm not saying I don't like colors. I just don't usually work with them. But I just wanted to find some use for that. And somehow I, you know, I was showing the video a little bit when, when you started to sharpen the pencils. Like if you sharpen it a bit, not in a standard way, you start seeing that there's some kind of beauty inside of it. Like a structure that usually it's always hidden inside. So I thought, hey, why not do something that just reveals the beauty of the inside, you know, just and multiply that effect and make something bigger, like an entity of smaller units. Oh, that's lovely. And Kusta, materials for you. I, for the past, what, 10 years or so, you were talking about how you work with paper. And ultimately when you went into three dimensions, it was still paper, largely with that installation. I mean, can you tell us about that process for you of then moving into three dimensions and having all of a sudden this, this tactility to your illustration that hadn't existed before? Yeah, like I said, like, I think that completely kind of like opened a new world for me. And like, I was like, I started to be a little bit bored with paper material already. So I really felt that I needed, I needed something else. And I kind of like wanted to create something kind of like a bit more like objects than I can turn around and I can touch and like they feel something. And like... I mean, I'll throw this out to both of you. So does process, in a way, help generate narrative in your work in any way? I mean, Thomas, for you, for instance, with the cabinet, I mean, the process and the material, does that generate narrative? Yeah, of course. Like it's, I think within, if you develop any concept of working materials, they do work, you know, side by side. And I think it's a very good way of also working because the other one always affects the other one. And so it's not very, like my process is never linear. It's not, I mean, I might have an idea that's wanting to be linear, but it's just never going to work like that. So I think it's just accepting the fact that it's just, you know, kind of, oscillates between the concept and the material and it develops to another direction. And I think it just, you need to let it naturally flow as it goes. Yeah, also for me, I think the wall and the sort of like, like really soft yarns where it's just like perfect sort of base for creating artwork around creams because they kind of like, I like the idea that they kind of blur the sense it's a little bit and they kind of like unshark my images in a nice way. So they kind of like, they become much more blurred than if it was, for example, paper. Right. Well, and it's interesting because so much of your work, even on paper, the illustration and such, it seems to be playing with perception in a way. I mean, there is something that's very psychedelic within your work, whether it's on paper, within the tapestries. So where is that interest in perception? Well, I think it's like I've always been interested in kind of like a green world and also kind of like, a bit like weird kind of states of mind in a way and kind of like strange color combinations that, you know, you can, well, I've been also influenced quite a lot of like 60, 70s psychedelic era and like, you know. And Art Nouveau, I definitely see the influence of Art Nouveau as well in your work. Yeah, yeah. And what I really like about Art Nouveau and Art Deco movements is that like, they usually take inspiration from the nature. Would I, I mean, I always, well, many times like when I start sketching things, I usually kind of like start from the natural shapes, from the shape from the nature and then kind of like work on them and simplify them so that they all fit into my world. Yeah. Well, and that's what's so interesting actually, they're in a way, both of your works or practices seem to be about nature. I mean, whether it's, you know, really playing with forms and shapes inspired by nature and Thomas, for you very much seeking to create objects that are much more reflective of our own human condition and fragility in nature. And I'm really curious about, of course, your finished backgrounds and Finland itself, there is just such incredibly magical nature that exists there.  I think it has a lot of influence. I mean, like when I was a kid, like we were always like after school kind of like wandering, wandering in woods, you know, like that, that was great the place to go. You know, exactly. And so it kind of feels really in a natural place to be. And yeah, you could always find like surprising, interesting things in the woods. So. Yeah. Also, there were not really that many things to do, if you'll be honest. You said it. That's right. That's right. That's right. Wandering around, right? I mean, how is it for you? Was it similar? Well, I do have a bit of a similar kind of childhood. Yeah, I mean, it's a very kind of boring, concrete suburb. But it was in the middle of the forest, of course, Finland. So yeah, I mean, that was pretty much the pastime between things, always just playing forest doing stuff, going, swimming, building huts. I don't know. So yeah, definitely. I think it has much more like visually, at least much more effect on Gustav's work than in mine. Because I also tend to work on a bit like not so natural materials all do shapes that are now, not necessarily adapted from natural shapes.  No, I mean, the woods were kind of like the only kind of beautiful place in my hometown. Because my hometown is actually, it's many times considered the chair noble of the team. So it's kind of like having the same sort of skyline. But nature. But nature, exactly. That was the place so what you were just getting, so. But it's interesting, though, to even talk about in Thomas for you, I mean, going around and building huts and doing things in nature. And I actually see so much of your work is very much about the physical process itself. I mean, you're very much working with your hands and such. You see that. So what I have to say also struck me when I was just creating nature remarks for tonight is the parallel that exists for both of you.  You were born and raised in Finland. And now you're both expats. And you both happen to live in Amsterdam. So tell me about this decision to live outside of Finland and practice outside of Finland. Well, I think it was for me that this is more very clear or a summer, like second, third year of my bachelor's degree. I honestly don't think that there was anything from in Finland in terms of my profession. And it's very kind of limited. It's a very limiting thing you can do in Finland because of the more this kind of conceptual approach to sign. It's not really caught up there. I think it's a very kind of, it still lives on some kind of modernist hangover period. And everything is just, there's no fun. There's no joy in things. And it leaves very little room to work on. And I think it also has a lot to do with, there are very few international and renowned people kind of in Finland. It's in terms of Aalba or Aalba, for example. So it seems like this heritage is also a bit of a burden because you're always a little bit in the shadows of that. Everybody expects that this is something you need to do. This is something you need to be. It's given a very kind of restricted framework. This is how you're supposed to be because you're Finnish. This is what you think, this is what you're doing things in. I think it's a bit of a suffocating environment for me, at least. And I found that freedom outside that it's the only thing you need is a passport. And that's it, it's very easy to go and do what you want. Also style-wise, I think my work has never been typically Finnish. It's always been more of a maximalist.  And so I kind of, I also think that it was easier to find my audience somewhere else. Yeah. You know, it's interesting because actually when I was in Helsinki and meeting with all of these countless designers, we ultimately ended up talking about this incredibly powerful design history that exists in Finland. And I have to say, actually, the majority of them always talked about it as a bit of a burden. And that you were constantly in the shadow of these greats and sort of these heroes of design. So it's very interesting that you've taken this opportunity to step outside. But yet you still see these Finnish influences, I would say, very much in your work. I'm also curious about even your use of color. Because I mean, you'll have to tell me about this. But color, for instance, upstairs, you'll see the exhibition runs from its very polychrome worlds of multiple colors and collisions of colors to this monochrome world, black and white. And you see that actually in both of your practices. So Kuzda, for instance, you work with just these incredible color combinations. In what way does that respond at all to Finland? I mean, I can't help but think about, of course, the very long days that I experienced. But on the reverse side of that, the extreme long darkness that you have as well. Yeah, I mean, it's difficult to say where this color use, for me, comes from. I mean, it's always been kind of like used a lot of color quite naturally. And I don't know, maybe it does have something to do with a bit colorless kind of surroundings where I was as a kid. Or I don't know, it's really difficult to say where it comes from. Well, of course, I like these good examples of like great color use, for example, like Finnish brand Mari Benko, who's really known for amazing bright colors. And it's also quite psychedelic, actually. Bested up. I mean, that was so cool, seeing that, Mari, I could like, all down. Yeah, I think I spoiled it. Oh, okay. And, you know, the one thing also that I'm very taken with in both of your, actually the pieces upstairs is your inspiration from family members, actually. So, the Hypnopompic series itself, you've mentioned is inspired by a family member. Of course, the Engineering Temporality series, Thomas, is inspired by your grandmother. So, can you talk about the starting point for your projects and? Yeah, I mean, of course, it's like, because it's such a personal project, especially for someone who is actually seeing these dreams. It was a little bit, kind of, maybe difficulty in the beginning, especially when I started to make my kind of like, own interpretations of them. And then, like, then the person who is actually seeing the dreams, like, says like, no, it's not like that, you know. Oh, so you really have feedback. I do have feedback, yeah. So, like, but then I kind of like, then I wanted to go my own way. And I kind of understood that these are kind of my own artistic interpretations of the dreams. And I have the right to do it, so. Yeah. So it's fine, artistic license, right.  And what are, you know, how do you begin kind of your next project where you find your inspiration? Well. Convoluted. Oh. Hmm. Well, for example, there's something that kind of, I stumbled upon a little bit on the last project I did, which is Decent Lights. And for example, reading this book by Tani, the author is Tani Zaki. I think it's written somewhere, I think it's pre-war Japan. It's called In Praise of Shadows. And I, for example, in that book, like he explains, like how I cannot quote him very perfectly, but how is he's explaining, like how, hmm, I should have a book with me here. Maybe to summarize that book in a few sentences, to say that like, there is like this beauty in darkness, all the shape of the grave, and all these kind of murky areas of the house. And that by us, like to say that the introduction of electric lighting into Japanese culture, how it destroys certain cultural forms, art forms, because they were put under the, the, the floodlights, or like electrical lamps replaced oil lamps and candles. So the whole culture was, the whole cultures and art forms were developed under different conditions. So how, how, how, how like this destructive, this can be to a culture. But also like, of course it has practical, practical implications on like, adapting electrical lighting instead of oil lamps. But like, what, what is that we lose in the process of that? Like what kind of, what kind of feelings and emotions are also lost and gone with this kind of introduction with technology? So this is kind of the starting point of like, why? I mean, I'm developing a range of lights that are definitely not, has nothing to do with illuminating. It's more of this kind of, more like meditating or like creating very subtle, more like subtle, subtle shadows rather than subtle lighting. So this, this to take a different, different approach to that. So that would be one of my next projects, yeah. Well, I think at this point we need to open it up for questions. So we'll take any questions that you guys have. What's the fun? I have no idea. Hi, sorry. And actually, is this in Finland? This is actually in Amsterdam, it's a forest in Amsterdam. I mean, it's not a real forest. I was gonna say, you're still stinking out. Yeah, yeah, yeah, yeah. Question back here. All right, thank you for your presentation. I have a question which is not top of your mind, but it's something that's important for me or for us. We're kind of two European designers that just moved to New York. And I wanted to just objectively ask you about any kind of differences that you see between European and American style of design or processes or the way people are thinking about design. And I know that most of your projects are either self-initiated or for European clients as so we hear. Just kind of thinking about the world of design as we kind of live in and the age of internet, what are your thoughts on this topic? Thank you. Well, I think it's like overall, it's a little bit pity nowadays that wherever you go, the design tends to be kind of like similar everywhere. But I guess it's because of internet, like you see the same trends everywhere. And like, I mean, it probably was different before the internet, I hope so. But I think like, nowadays it's, you know, like when you travel far away and you kind of like expect finding something really kind of like unique things, you kind of like end up seeing too much the same. And I think that's a real thing. Oh yeah, I mean, I guess this is down to the topic of like a bit of like the originality of work in the sense that like if you are in this kind of flux of trends and fashion, and it's really an international style. I don't think there is certainly anything to say if this is like a European style or if this is like North American kind of thing. Or I think if by looking at the work, you could be basically anywhere from the world. I mean, it doesn't necessarily, the origin of the culture of the person, maybe that doesn't necessarily matter anymore than much. I really don't know what would be the difference, the main difference, for example, between European, European design and North American. I don't really have that much of a... Maybe the question was that the work that you're doing is so kind of, that the work you're doing has this kind of ineffable purity and poetic character that maybe you don't see that much here. That America is just so commercial and everybody is so just getting by, right? Is that really what you're trying to say? Yeah, yeah, yeah. Is that what you're trying to say? What's the point? How do you get to me? Yeah, so. Yeah, because that's, you do see much more conceptual type work in Europe than you do here. Well, I think at least in the case of Netherlands, I mean, I know I've experienced this firsthand that they, well, there used to be much more, but there still is some form of subsidies of support for artists. And so this really enables people, designers, you're nodding there. I guess you're agreeing this.  And I think that really enables artists and designers to work more freely and create something, something, giving more time to do things, giving more time to think over things. And I think it seems like here those kind of support is letting a bit. Yeah, you're kind of thrown out into the world and have to fend for yourself. Yeah, and after time to then start doing it. I mean, let's say like 10, 15 years ago, that was a very different thing, like you could do nettles.  And you had no commercial pressures. Wow. And you could almost live with that money. Yeah. And just freely create. And of course, if you're income rich, certainly I would need to pay something or not receive those funds anymore, but not anymore too bad. Stay here. Right. So there's a type of design that culture doesn't really exist in Finland. There were like reasons behind the logic that how people still behave. And they don't see the reason why the chair would cost 10,000 euros, for example. Why would I pay money for that? But they do see the reason by 10,000 euros there, right? That's the thing. It's a weird thing about it. It's just a way of like, how you spend your money, what's your priorities? And your car and your chair, I don't know. Like it's just... People in design, particularly in Finland, has always been incredibly democratic. I mean, when you look at Itala and Artec and you've got these incredible design heroes who are creating this very accessible design, it seems like the idea of design being somewhat inaccessible or too expensive seems... Yeah, I think it seems very like a little, it's just kind of a way like everything in a way is thought that it should not cost a monster to money and then everybody should be able to afford that. And well, I mean, it's of course just one way of looking at it and what else it is to be, but... I just kind of wanted... Well, it kind of happened. I think I always had good, kind of like supportive agencies that have been supporting me and who have been like finding me commercial work as well. So I think... Because especially like as a young illustrator, you don't really have the contacts. And I think at that time, especially, those agencies really helped me a lot to come back to find the right places to start to work. I mean, in the beginning, I was working a lot for magazines, but then it kind of like evolved more into... At some point a bit more to advertising. And then after that, to patterns. And so I know kind of like maybe more into installation. So it's been kind of like this kind of like evolving thing. So actually, thanks a lot for that and myself. When you started getting into your installation work with the Jacker atmosphere, were you originally working with a commercial manufacturer to do those things? Or, you know, we said you work for Nike, for example. Like a lot of times, like here, it's really hard to get connections with a manufacturer. I thought I would learn. No, I was working directly with Nike. So, I mean, and I was only kind of like designing the pattern for them. So they kind of like, they took it from there and like made the designs for the shoes, you know, and like adapted the pattern for them, for the products. And then into your tapestries, you have the good fortune of working with the Tilburg textile museum. Yeah, exactly. That's quite a unique place in the world, I think. It's quite an amazing place where the textile museum actually has this kind of like textile lab where you can kind of go with your ideas of making a lot of work and then like they can help you to kind of like realize it. I mean, of course, like they don't actually do everything, but like, but if you have a good idea, it's a great place to work with. All right, and I actually just, before we wrap up here, I have one more question because of course we're here because of beauty, our exhibition. And so we can ask you guys once for the book what beauty means to each of you and I'd love for you to share some of that here. So what does beauty mean to each of you? What does beauty mean to me? I mean, for me, beauty always has this kind of like a fraction, in a way. And you were mentioning earlier this one bit savvy kind of it's kind of like Japanese philosophy based on irregularity, austerity, yeah, oddity, yeah, yeah. And I, exactly. That's finished. And I think there's something really great in this Wabi-Sabi aesthetics that kind of like I completely share in my aesthetics as well, you know, like using like, you know, not making, not make things perfect, but kind of like a bit like asymmetrical and like leaving blank spaces or like things are not kind of, things are never finished in a way. And nothing really lasts and, I mean, yeah. Yeah, I think beauty for me maybe is more like a concept of something that evolves always and changes and kind of mutates. I think beauty is really more like a human interpretation of a thing or over a thing that really gives the meaning, you know, the meaning of beauty to you, whatever that is. And I think, yeah, it's also highly personal and very, very subjective thing. And I mean, I always only have to look at myself and like realize the things that I maybe loved some while ago. I just can't really tolerate that anymore. And yeah, I think it's, yeah, I mean, it's very interesting. Topic goes over beautiful topic, I mean, people's topic, sorry. But I made this a very difficult topic because yeah, I think the concept of beauty will change and it's on a personal level, or some cultural level or social level and I think it's, I think you can have topic beauty every year almost and it's going to have to be the same. But I think everyone is kind of like in a way like aiming to beauty all the time, like whatever they are doing, like they kind of like aiming to beauty.  Drink it by having a condition and essential part. So wonderful. Well, thank you, Kusta and Thomas. And thanks to all the people who came here. We hope you all have a wonderful evening. Thank you.


It's to the best of our knowledge, I'm Ann Strainchamps. Some people believe psychedelics will revolutionize the treatment of depression and addiction. But there is a troubling history that raises all kinds of ethical questions. We can't tell the true history of psychedelics without acknowledging the plight of Indigenous peoples, right? It was through the American Indian Religious Freedom Act that we even got our right to practice in ceremony and sit with peyote. This has always been a way of our life that was taken from us. This hour, can psychedelics be decolonized? Also the story of Maria Sabina, the Mexican healer who helped launch the psychedelic revolution without wanting to. Maria Sabina lived into her 90s. This woman who freely shared wisdom about psilocybin and died penniless and rather ostracized from her community.


Hi there. I'm Sandy Allnock, artist and paper crafter here on YouTube. And today I'm going to work on a Hobbit neighborhood card using Art Impressions watercolor. The Art Impressions watercolor stamp sets come in little groupings. This one has two Hobbit houses in it and it gives you an example on the cover sheet how to stamp some of those things and then I'm gonna use a selection of a bunch of the different flowers that I have. The way that I store the stamps that I've purchased over the years, because I have a lot of them, I'm kind of an addict. I put things like houses and bird houses and things in one and I have like 12 of these different ones broken into categories. I have all my little flowers from a lot of the little different stamp sets. So I've broken them all up. I know that makes some people apoplectic but there you go. I also use these little Art Impressions acrylic blocks a lot so if you're looking for where to get tiny ones like that they used to come with all those dollar stamps. I don't even know if they make those dollar stamps anymore but I had a bunch of those left over from years ago as well and they work great. So I'm gonna stamp both of the houses and I'm using my Tombow markers to just scribble a couple of colors onto the stamp itself. If it waits too long and it kind of dries out then you can huff on it meaning just go with your breath and let some of that hot breath kind of rewet the ink a little bit. It doesn't matter if it dries on the paper because you'll see how this is gonna work after I get some of the stamping done. The reason that I do the houses first even though the greenery that I'm stamping right now is gonna be in the background is because I want to be sure that I reserve the right places for the main image.  So I'm starting by just doing some very light background layers of a few greeneries and this whole thing is gonna be covered eventually so this is just kind of getting a start at it and figuring out where all these clumps of bushes are gonna be because I picture these little houses being like in the movie and the little hobbits in the shire that they have their little houses built into the hillsides next to each other. So these two are gonna be two little neighbor houses on the same particular piece of paper and with these stamps once you have the ink down and a lot of different markers will work once you have the ink down you take your wet brush and you just go over top of the ink and you can use a lot of water and really wash out that line a lot you can use a little water and leave the line more intact. I tend to leave some of them intact and get real washy with others because I really love with watercolor that lost and found kind of a look and letting some be really soft some be a little bit harder edged and now I switch to a different green and I'm just gonna add more of these greens on top the ones that are already there I have some damp paper underneath and you may have noticed that some of those when I stamped them splooched out a little bit right when I stamped them that's gonna give me more ink moving around the page. I shouldn't say ink I'm not sure what's in these markers in any of the watercolor markers it's not actually watercolor but we call them watercolor because it moves with water so then I'm gonna kind of move the move the water around the whole thing and then add more greenery this was a green I didn't like a whole lot but since I had started I didn't want to have only one splooge of it so I did a couple of them here and there switch to another one and you can see it doesn't matter a whole lot which one of the greens you use as long as it's some sort of a branch if you use the grasses that won't work quite as well for this kind of a hillside full of ivy and just a tangled thick brush that there that is on the whole full hillside but any of those others will work so if you have any the other stamp sets because some of them come with you know say a bird and a bunch of flowers or a bench and a bunch of flowers you can use any of those kind of flowers for this and now I want to start building in some richness of color because you can just stamp all over it make an all over pattern but I want to make it look like it's actually these these doors are carved into a hillside which means I need some darker color so I'm gonna put I put some color on a block itself I just scribbled with a marker and then I'm picking that color up with my brush and adding some of it in there my darkest colors gonna be right around the doors because if you picture all of those greens they're gonna be hanging out in front of the door so we need to create some space behind them and underneath each one of those branches and some depth right around the doors themselves so that they kind of sink in and then the door itself kind of pops so as I add layers of this and I'll keep adding more and more you'll see how this develops I love how it develops when you're doing speed coloring because you almost get the idea faster otherwise you kinda lose track on when that transformation started to happen so on a card like this you can certainly allow just this swash of color and then start working on the houses because I'm gonna start working on them a little bit more and put more into the doors but I decided I wanted to do the whole thing because I had somebody recently asked me how you do like a whole hillside whole mountainside full of trees if you're water coloring they weren't asking specifically about art impressions watercolor but hopefully she'll see this video I know that this is the same kind of an idea you would take all kinds of greens and just keep layering them like this and make little clumps of things so as I'm adding my darks I wanna add a few areas that define some of the places where those greens cascade into shadow and then let some of the rest of it stay in the bright front the light so they're gonna be lighter colors but I'm mushing all of it I'm just gonna soften all of it and as I put layers on top of each other the ones that are on top may get a little less water which means there's gonna be more detail on them and it's gonna give it that more lacy look I'm gonna add a darker color now and the color that I'd already painted right around those doors is dry and when I'm painting on top of dry I'm gonna have a little better success with getting a richer color so look how much those doors just kind of got carved into the wall behind them into that dirt wall by just adding that rich color right around part of it and I'm not adding it evenly notice there's different shapes so it's not an outline around it it's you know there's one part that is more like a triangle one that's more like a rectangle and then it stops it breaks up into a light area and then goes back into a dark that's gonna make it look much more natural like it's it's going in and out and there's some branches that are sticking out in front of the door and some that are receding behind so now I'm gonna take a break on the greenery and go to the doors and I've taken a couple of the browns and scribbled a little bit of them on the surface so I can have two different brown doors one is gonna be a solid brown door that I'll add detail on to later and the other I'm just gonna add the wood panels on the front of the door right now you can do those in any kind of order play around with them have lots of fun you can make them bright colors if you want if your hobbits are bright colored little hobbits but I'm kinda thinking these guys are gonna be trying to hide in the hillside having the little houses built in each one of these comes with these little rock stair things that come out from the front and I'm gonna add a few more of them just by adding shapes because I want them to kind of travel out to the same space and then I'm gonna add grasses all along the front as well and a lot of that is wet so I'm kind of having some struggles here with trying to get them to be on there and stay grass looking and you can see where some of them when they touch the water they end up just looking a little bit blurry and then the sharper edges are the ones that are stamped on the dryer paper all of this by the way is on Arches rough which for some people drives them bonkers in trying to create something like this I love the rough watercolor paper you can also use the hot press or you can use the cold press those are less bumpy and the hot press is the least bumpy of all but on something like this it really doesn't matter because I'm trying to create all of these layers and layers of grasses and brush and everything so that these two little houses are are pushed inside of the scene and now just gonna take more of that dark color and start to create more shadows in a few spots and those are the places that are going to draw your attention if you notice when you look at something like this the eye is drawn to the places where there's contrast that's why in lots of my stuff I'm always trying to find ways to add more contrast and trying to mix colors to create deeper shades and all those kind of things because that's what draws the eye in that's what draws you into the picture itself so don't be afraid to and remember that it's just paper so even if you spent a while on the piece of paper this is one of those designs that's really helpful to do lots of practice because you're just gonna cover the whole thing unless of course you decide to stop earlier as I told you before but when you're covering the whole thing with just lots and lots of greens you have one focal point and the rest of it is just gonna be a whole garden of greens it gives you that freedom to practice the layering of colors and all that sort of thing without feeling like you know you're you're wrecking it or you can't get it to bleed out to white or anything this really allows you to play around with it have fun and create a whole little scene here I have no idea what's gonna be the sentiment for it lots of people ask what my sentiments are on my cards lots of don't have sentiments at all because I just write a note inside I don't bother to stamp anything because it doesn't always need something like that I can put thinking of you or I can write a congratulations message or any kind of thing on a card like this doesn't necessarily have to be even a neighbor card or anything like that so I've die-cut my panel added it to another die-cut panel and called it done kept it really simple design-wise thank you so much for joining me I will see you for more of World Watercolor Month on my social media because I'm doing a little treat for you every day as well as I'll be back here in just a couple of days thank you much have a great day bye bye


Welcome back. We are looking at the theorem of Lagrange that if you take z by Pz and take a polynomial of degree D with coefficients coming from z by Pz then there are at most D roots. This is a result that we have looked just towards the end of the last lecture. So here is the result. A polynomial of degree D over Zp has at most D roots in Zp and we have also noticed these two remarks that the number of roots can of course be smaller than D and it is also essential then that we work modulo prime. So just to recall it for you I will make it clear that here you can take the example of x to the 4 plus 1 and you can take this example where P is 3. So here there is a polynomial of degree 4 and in Z 3 there are no roots at all or you may also take P equal to 7 even in 7 Z modulo 7 Z we have no root at all for x to the 4 plus 1. This is like saying that minus 1 is a fourth power. If you had any solution to this polynomial any root of this polynomial would give you a raise to 4 is minus 1 modulo 7 minus 1 is 6 modulo 7. So this would say that 6 is a fourth power modulo 7 but once is by computing squares that 6 is not even a square. So we do not get any root here and therefore the number of roots is indeed less than degree which is that 0. Whereas if you do not work modulo a prime and then we have seen that x to the 2 which is x square minus 1 modulo 8 has 4 roots. So this number is bigger than the number of degree this is your number of roots and the D here is 2 which is less than 4 which is the number of roots. So to have Lagrange's theorem it is essential that you work modulo a prime and not modulo a composite number. So let us go about proving this result the proof is not very difficult it is quite easy but before we prove this let me just remark one thing. So suppose I start with a polynomial f of degree D so what we have is we have it to be x ad x to the d plus a d minus 1 x raise to d minus 1 plus dot dot dot a 1 x plus a 0. This is a polynomial that we have and assume that we have some element in Z p then f x minus f a is x minus a into g x where g is a polynomial degree D minus 1. This is something which holds in general this is because what we have is that we have f x which is given by this formula and then f a would be also given similarly you will have a d a power d plus a d minus 1 a power d minus 1 plus dot dot dot plus a 1 a plus a 0. So recall here that these a i are taken as coefficients they are elements in Z p there is no relation between a i and a that is something that we should not forget about. So when you take the differences you will look at ad x power d minus ad a power d and this can be written as ad x minus a into a polynomial e in degree d minus 1. Similarly you will have this the difference of ad minus 1 x minus a into a polynomial of degree d minus 2. So what we are really looking at this at this point is that x to the i minus a to the i is x minus a x raise to i minus 1 and then you have some terms here and finally you will have a power i minus 1. This is the polynomial that we will look at this is the polynomial which is x power i minus a power i upon x minus a. So combining all these polynomials for different degrees will give you the polynomial g x this is what we get. So the most important thing for us from this point is this point that f x minus f a is actually a x minus a into g x where g has to be a polynomial of degree d minus 1 because if f is your polynomial of degree d minus 1 then that will tell you that a sub d has to be non-zero this is not equal to 0 and it is the same coefficient that you are going to get here when you look at the d minus 1 coefficient it is the same coefficient that you have. So g is also a polynomial of degree d minus 1 this is the most important thing that we need to remember.  So we have one less degree for g than the degree of f. Now so assume that as a root in Zp call it alpha. So we have an element alpha in Zp with the property that f alpha is 0 and then by applying this result where you put a equal to alpha what we get is f x equal to x minus a into some polynomial of g x where degree g is d minus 1 this is because instead of f a we will get 0 there.  So on the left hand side we simply get f x. So this is only f x and on the right hand side we have x minus alpha into g x. So what this tells us is that whenever we have a root for the polynomial f then x minus alpha divides the polynomial f. You can actually write f x as x minus alpha into another polynomial of smaller degree. This is the thing that we need to take ahead from this second slide that f x is now x minus alpha into g x where you have f alpha to be 0. So if alpha in g p is a 0 of f then f x equal to x minus alpha into g x. Now suppose that there is one more root beta. So if beta in g p beta not equal to alpha is a root f then f beta is 0 which implies that alpha minus beta or actually you will have beta minus alpha g beta equal to 0. But since you have that beta is not equal to alpha that tells you that this is non-zero and if this is non-zero what we should get is g beta equal to 0. What is happening here is that we are looking at elements in g p z by p z and once you put these values in the polynomial the g beta or beta minus alpha these are all elements in z by p z and these are all represented by natural numbers. So actually these are looking these are some natural numbers and we are simply going modulo the prime p that is what we are doing. So when we say that some product is 0 then it tells us that p divides the product because something is 0 in z modulo p z only means that when you divide by p the remainder is 0 that means p divides that natural number. But p being a prime has the property that when p divides a product of two numbers p has to divide one of the two and therefore if one of them is not 0 modulo p. So here beta minus alpha is not 0 in z p that means p does not divide beta minus alpha but p divides the product of beta minus alpha into g beta. So p has to divide the other thing which is g beta and therefore g beta has to be 0. So we get that if you have any such other root then beta is a root of g. Now g is of degree d minus 1 and we apply induction hypothesis we will start our induction with polynomials of degree 1 which are linear polynomials and those we have already observed that a linear polynomial where the coefficient of x is not 0 gives you a unique root. So the result is true for degree equal to 1 and then we apply induction hypothesis to the polynomial g g has degree d minus 1 and the polynomial and degree d minus 1 can have at most d minus 1 roots. Together with the root alpha which might also be a root of g in that case we will not have to count alpha separately but even if alpha is not a root of g you may have to just add that single root. So whenever you are counting the distinct roots of the polynomial f you are looking at the distinct roots of the polynomial g once you have taken one root alpha out and then you add this single root alpha to the list of the roots of g. So by induction hypothesis g has most d minus 1 roots and hence f has at most d roots that completes the proof. So you may wonder where does this proof fail when you have a modulus which is not a prime when you have a composite modulus and the point is exactly that you may have 8 for instance where we had 4 roots for it. 8 divides product of 2 but when it 8 does not divide 1 it does not imply that 8 divides the other one. So check this as a basic exercise check where this fails. So we have proved Lagrange's theorem which says that whenever you have a polynomial of degree d over the z by pz then such a polynomial can have at most d roots and when we are saying at most d roots we are counting the roots distinctly. If the roots come with multiplicity then of course this number will further go down but let us not worry about that. There is one very nice corollary of this result. So let us see this corollary. The corollary says that if you have a polynomial in degree d with coefficients coming from integers and suppose modulus sum prime you have the number of zeros to be more than d then p must divide ai for every i. So first of all we are starting with a polynomial which is defined over integers or you may also take a polynomial over natural numbers but integers is more desirable and then we look at modulo sum prime p. So p is a prime and suppose that the number of zeros is more than d then what we should get is that p divides the coefficients for all i. This is the basic statement which we would now like to prove. So consider the polynomial f tilde by reducing each ai mod p. So we will have a polynomial f tilde x which is given by ad x power d plus dot dot dot plus a1 x plus a0 but we are looking at not necessarily the ai but ai tilde where the ai tilde are congruent to ai mod p and you may assume that your ai tilde are between 0 to p. So we now have a polynomial over zp. We have a polynomial over the set z by pz and here by our assumption we have more than d roots. This is what we have seen that there are more than d0. So this f tilde has more than d roots in zp. So what is going wrong? Lagrange's theorem told us that whenever you have a polynomial of degree d it can have at most d roots. It seems that here we have a polynomial of degree d.  So since we have a polynomial of degree d it should have at most d roots but our assumption says that we are getting more than d roots. So what must be happening is that Lagrange's the hypothesis in Lagrange's theorem must not be satisfied. So there are many hypothesis has many parts. Let us go from the last part. The last part was that we are working modulo a prime that is certainly true here. We are looking at the prime p and we are working modulo p. So that is alright. Then we go further and we see that the hypothesis says that you have a polynomial of degree d. Somehow this must not be true. But clearly we have something of the type ad tilde x power d plus dot dot dot. How does a polynomial of degree d look if not like this? So if you are saying that this is not a polynomial of degree d then what must happen is that the coefficient of x power d must not be a non-zero element.  So the ad tilde should not be 0, should not be non-zero. Ad tilde should be 0 which means that p will divide ad tilde but ad tilde is congruent to ad modulo p so p will divide ad. Once you have that ad tilde becomes 0 modulo p the degree of the polynomial has reduced. And if any ai tilde had been non-zero modulo p you would get a polynomial of degree smaller than d and again the fact that the number of roots is more than p d would give you a contradiction. So what must happen therefore is that every coefficient must be divisible by p. So then p divides ai tilde for each i and hence p divides ai for each i. The only way a polynomial which is defined over natural numbers has more than d roots over a prime p will be where the polynomial when reduced to z by pz gives you a 0 polynomial and that would happen exactly when the prime p divides all the coefficients of the polynomial and that is what we have. So the corollary says that if you have a polynomial of some degree d and modulo some prime you have more than p roots d roots then the prime p should divide the all the coefficients of the polynomial f. We will this is a very pretty corollary. There are many nice applications of this. We will see some of these applications when we go to assignments but right now I will go ahead and prove one small result which is called Fermat's last Fermat's little theorem. This is also pronounced as fl t. This is also short form as fl t but this is not that famous fl t which was the Fermat's last theorem. This is the Fermat's little theorem. What does this theorem say? The theorem says that if you have any non-zero element in zp then raising that element to the power p minus 1 will give you 1. That is a very remarkable. You take any prime just compute p minus 1 and then for any non-zero number. For 0 of course you raise it to any power and you are going to get 0. You will not get 1 but if you raise any non-zero number to the power p minus 1 then you will get only 1. You are not going to get any other answer. So let us see one basic proof. There are several proofs of this. If you happen to know group theory then there is a quick proof which would come. The proof if I can just tell you orally would be this that the integers co-prime to p form a group under multiplication because when you have a and b in zp and both a and b are non-zero then the product is also non-zero. Return in other way whenever ab is 0 then a is 0 or b is 0 modulo p. So if you are taking both a and b to be non-zero the product is going to be non-zero. Therefore the set of the natural numbers from 1 to p minus 1 is closed under the product taken modulo p. Whenever you take product of any 2 you get it to be a non-zero element. So it is again an element from 1 to p minus 1 and this is a group because every element has an inverse and then the order of this group is p minus 1 and this is the basic fact from group theory that any element to raised to the order of the group will give you 1. So that tells that a power p minus 1 is 1 modulo p but since we are doing number 3 there are some nice number theoretic proofs. So consider this set 0, 1, 2, 3 dot, dot, dot up to p minus 1. You will immediately recognize that this is nothing but gp with respect to addition and product modulo p. This is the set gp that I have listed further since a is not 0 and it is an element in gp. What we get is that ai equal to aj for ij in gp gives i equal to j. You can cancel a from both the sides. So this tells you that ai is congruent to aj modulo p but since a and p are co-prime you can simply cancel a from both the sides and that will give you that i is j and therefore if I write the elements a into 0 which is actually 0, a into 1, a into 2, dot, dot, dot all the way up to a into p minus 1 then I am going to get once again p elements. The cardinality of this set is equal to p. We are going to get different p elements. So thus the non-zero elements these sets 1 or you may just consider you will have the sets i where you have 0 less than or equal to i less than p and a into i. The non-zero elements in both these sets are the same and hence when I take the product of all these numbers so I have 1 into 2 into 3 and I take the product up to p minus 1 I am going to get a into 1 into a into 2 into a into 3, dot, dot, dot a into p minus 1. On both the sides we should get the same number because these are all the non-zero elements coming from these two different sets. So when I have two sets and I am taking the non-zero elements in those two sets and take the product if these numbers themselves are same perhaps they will be permuted when I multiply by a but the set the numbers as a set are same then the product should give me the same value. So here we know this is congruent to minus 1 modulo p so this is in particular not 0 and here I can take a common from each term I will get it to be p minus 1 and I once again remember this is p minus 1 factorial and here I am getting the same number. So by cancelling the number p minus 1 factorial which is a non-zero number we get that 1 has to be equal to so we get that p minus 1 factorial is equal to a raise to p minus 1 into p minus 1 factorial but since this is equal to minus 1 which is not a 0 quantity we simply cancel it out to get that a raise to p minus 1 is 1 in Zp which is to say that a raise to p minus 1 is congruent to 1 modulo p. So it is a very beautiful small fact and this such a fact actually tells you whether a number can be prime or not because if you take some number 8 for instance and you raise some element to 7th power and you do not get the congruent to be 1 modulo 8 then of course your 8 cannot be prime. So for big numbers this is quite a useful test of primality that you take a number from 1 to n minus 1 and raise that number to the power n minus 1 if the result modulo n is not 1 modulo n then your number n cannot be a prime. However as fate would have it there are some naughty composite numbers n which satisfy Fermat's little theorem we will have to treat with them separately that is not part of our course we will perhaps talk about them in the next lecture but only to give you information about it. So I hope to see you in our next lecture. Thank you.


సిిఘక్నిసార్కిండిండ్స్ధోసికిండ్నిపి. How much is it? How much? Chicken chain? Can't that even go for my name? I'm just managing you all. Let's go inside now.  It is just... They might say they stand for everything. That's why I wait patiently for you all. All's well. Yeah, that's why I'm going. Let's go and wait patiently for you all to come. This is the right time. Mama, I'll try to... Pull up on my bed now. Let's go inside now.


This is FDA Patient Safety News. In this edition, a new type of drug to treat HIV infections, a product used to prevent adhesions is withdrawn from the market, new warnings on using lindane to treat scabies and lice, and new cautions for MS patients using beta interferons. These stories and more in this edition of FDA Patient Safety News. Welcome to the program. For the U.S. Food and Drug Administration, I'm Mark Barnett. And I'm Anita Rainer. Let's start with some medical products FDA recently approved. You can find information on all FDA-cleared medical products on FDA's website. FDA recently approved the expanded use of a laboratory test to detect human papillomavirus, or HPV, in the uterine cervix. HPV infection, which is transmitted sexually, is a risk factor for cervical cancer. The test, called the HC2 high-risk HPV DNA test, is manufactured by DiGene Corporation. FDA had previously approved this product as a follow-up test for women who had abnormal pap tests. The product is now approved to be used along with the pap test on any woman over the age of 30. The FDA announcement said that it's not intended to substitute for regular pap screening. It's an adjunct to the pap test. Well, why is this test only approved for women over 30? Well, the answer really is risk. There's a higher risk of cervical cancer among women over 30. Although the rate of HPV infection in women under 30 is relatively high, most of those infections in this age group are short-lived, and women under 30 rarely develop cervical cancer. On the other hand, women over 30 have fewer HPV infections, but cervical cancers are more likely to occur in older women. Well, Mark, what's the real message here for women about HPV and cervical cancer risk? Well, there are several things patients should understand. First, having the virus increases the risk of cervical cancer. But they should also understand that HPV infections are common, and that most of them resolve on their own, and that only a very small proportion of these infections lead to cancer. In other words, a positive HPV test can provide useful information for the woman and her physician, but it doesn't necessarily mean that cancer is going to develop. On the other hand, patients should understand that a negative pap smear and a negative HPV test can't assure that things aren't going to change. Infections or cellular abnormalities could develop in the future, which is why continued screening is important. The American Cancer Society has an excellent website that explains HPV and its possible health effects in late terms. It's called What Women Should Know About HPV and Cervical Health. It's a good place to send patients for more information, and you'll find the address on our website. FDA recently approved a new type of drug to treat advanced HIV-1 infection in adults and children age six and older. The drug is called Fuzion, and it's the first of the so-called fusion inhibitor drugs to be approved anywhere in the world. Fusion inhibitors work by inhibiting the fusion of viral and cellular membranes, thus blocking the HIV virus's ability to infect cells. Fuzion's generic name is infuvertide, and it will be distributed by Roche pharmaceuticals. What's this mean for patients? Well, actually, the key words here are drug resistance, a significant percentage of patients with chronic HIV develop infection that's resistant to many existing medications. By affecting the spread of the virus differently than current drugs, Fuzion can help reduce viral loads and slow HIV progression in patients who have developed resistance to current drugs. Since HIV must be treated with a combination of drugs, Fuzion can be used as part of a drug regimen for patients who have limited options. Fuzion should only be used in patients who have previously used other anti-HIV medications and still have ongoing evidence of viral replication. FDA based its accelerated approval of Fuzion on an analysis of six months of data from two ongoing clinical studies of about 1,000 patients. Patients who received Fuzion plus a regimen of other anti-HIV drugs had a reduced viral load compared to patients who received only the other anti-HIV drugs. The long-term effects of Fuzion are not known at this time, but they're being evaluated by the ongoing clinical studies. Anything to look out for with this drug? Well, actually, several things. Although bacterial pneumonia was uncommon in clinical study patients, those treated with Fuzion developed more bacterial pneumonia than the control patients. So patients taking Fuzion should be monitored carefully for symptoms of pneumonia. And they should be advised to seek medical evaluation immediately if they develop signs and symptoms suggestive of pneumonia such as cough with fever, rapid breathing, and shortness of breath. Fuzion can also cause serious hypersensitivity reactions. So patients should be warned to discontinue therapy and immediately seek medical evaluation if they develop symptoms of hypersensitivity such as breathing problems, fever, or skin rashes. And because Fuzion is administered as a subcutaneous injection, local skin reactions, which may be painful, occur in almost all patients. FDA recently approved a new anti-imetic drug to prevent nausea and vomiting in chemotherapy patients. The drug is called E-Mend. Its generic name is a prepitant. And it's made by Merkin Company. E-Mend is approved for preventing both acute and delayed nausea and vomiting. In fact, this is the first FDA-approved treatment that prevents the nausea and vomiting that occur more than 24 hours after patients receive chemotherapy. E-Mend reduces nausea and vomiting in a new way by blocking NK1 receptors in the brain. But it should always be used in combination with two other anti-imetic agents. It's one part of a three-drug regimen. Patients should be advised to report the use of any other prescription or non-prescription drugs and herbal products because these may interact with E-Mend and cause serious life-threatening reactions. For example, E-Mend may interact with certain anti-coagulants. So patients being treated with drugs such as Coumadin should have their clotting sedas checked after each chemotherapy cycle where E-Mend is used. E-Mend may also reduce the effectiveness of oral contraceptives. So women who use birth control pills should use an alternative or backup method of contraception. Now for an alert about a product that's been voluntarily withdrawn from the market. The product is the Gynecare intergel adhesion prevention solution. And it's used to reduce post-surgical adhesions in patients undergoing open conservative gynecologic surgery. Adverse event reports associated with this solution have included late onset postoperative pain and repeat surgeries following the onset of pain, non-infectious foreign body reactions, and tissue adherence. In some patients, a residual material is observed during the repeat surgery. Gynecare worldwide, a division of Ethicon Incorporated, is urging customers to immediately stop using the intergel adhesion barrier solution and return all remaining product and samples to the company. Gynecare is taking this action while it completes an assessment of the experience with the device. Part of this assessment will include adverse events associated with off-label use. For example, in laparoscopy and non-conservative surgical procedures such as hysterectomy. Roche Diagnostics Corporation has issued an urgent product correction on some of its AccuCheck glucose test strips because of a defect in the vials that hold these strips. The problem is that some of these vials may be cracked and allow moisture to get in, causing inaccurate results. The affected brands are AccuCheck Comfort Curve and AccuCheck Advantage Test Strips. The manufacturer believes that only a small percentage of vials are affected. Cracks may develop in these vials at any time, including after the vial has been opened. Roche is asking users to inspect the bottom of every vial for cracks before each use and not use test strips from a cracked vial. If there's no crack in the vial but blood glucose results are unusually high, low or inconsistent, the test should be repeated along with a quality control check. For more information, go to our website. In a recent public health advisory, FDA warned health professionals and consumers about the potential toxicity of lindane when it's used to treat scabies and lice. FDA has reports of neurologic effects from topical lindane products, ranging from dizziness to seizures, as well as several deaths. Most of the serious effects were due to misuse of the products, but there have been rare case reports of serious reactions from apparently normal use. Mark, as I understand it, lindane shouldn't be used as a first choice in treating scabies and lice. It's definitely not a first choice in treating scabies and lice. The FDA advisory stresses that lindane is a second line treatment that should be prescribed only when the patient doesn't respond to safer treatments such as permethrin or malathion products or if the patient can't tolerate these safer products. Well, before you mentioned misuse of the product, what type of misuse are we talking about? Mainly we're talking about overusing the product. Many of the serious adverse events reported to the FDA occurred when the medication was applied several times. And so the FDA advisory says that patients should be instructed that lindane products should be applied just once. Patients should understand that itching after treatment may be due to the lindane itself rather than scabies or lice and they shouldn't be tempted to reapply the medication. The FDA advisory also advises special caution in prescribing lindane products for specially susceptible population groups. These include patients weighing less than 110 pounds, the elderly, those with HIV infections and those on medications that may predispose them to seizures and lindane products are contraindicated and neonates. So what's FDA doing to make sure that prescribers and patients get the message? Basically there are three things to remember and those three things are warnings, package size and education. FDA is requiring a new boxed warning on the packaging of lindane products describing these precautions and the package sizes of lindane products are gonna be limited to one and two ounces to help prevent patients from reapplying the medication. Pharmacists should dispense only enough of the product for a single treatment, not to exceed two ounces and pharmacists must provide a medication guide to the patient with each new prescription. The guide describes the risks of lindane and gives instructions for appropriate use. You can get copies of the medication guide from our website. The prescribing information for three brands of beta interferon now contains new and strengthened warnings, cautions and information on adverse reactions. Beta interferon is used to treat multiple sclerosis where it's intended to slow the progress of the disease and reduce the frequency of exacerbation. The products are Avonex manufactured by Biogen Incorporated, Beta Seron manufactured by Chiron Corporation and Rebeth manufactured by Serono Incorporated. Some of the new information is based on reports of psychiatric effects among patients treated with beta interferon, including depression and suicidal ideation. Some patients develop psychiatric disorders for the first time, including psychosis. Others experienced a worsening of existing psychiatric conditions. The labeling now contains a cautionary note about using beta interferon in patients with depression, mood disorders or other severe psychiatric symptoms. There have also been reports of anaphylaxis, decreased blood counts, autoimmune disorders and liver damage in patients treated with beta interferon. And so the labeling now advises monitoring patients for signs of blood abnormalities, hepatic injury and possibly autoimmune disorders. The companies have developed medication guides for patients which are available on our website. FDA has received over a dozen reports of poor neonatal outcomes associated with the use of the Nelcor oxy first fetal pulse oximetry system. This system is used to measure fetal oxygenation during labor. The adverse event reports we've seen include three stillbirths, low apgar scores, acidosis and transient neonatal depression. As a result of these reports, Nelcor issued a Dear Doctor letter in February to clarify the instructions for use and to change some of the clinical management recommendations. The letter made four points. First, the oxy first system should only be used as an adjunct to fetal heart rate monitoring. It's not a substitute for clinical interpretation of fetal heart rate. Second, when a fetal oxygen saturation signal isn't present and readjusting the monitor doesn't restore the signal, clinical management of the fetus should be based on fetal heart rate and clinical signs alone. No inferences about fetal status should be made based on earlier values from the device. Third, the letter expanded the definition of what should be considered an ominous fetal heart rate. If the heart rate pattern is ominous, even when the fetal oxygen saturation values are normal, the company says that the clinician should deliver the baby. And finally, the letter included updated clinical guidelines for using the oxy first system, but reminded clinicians that these guidelines are recommendations that may not apply to every clinical situation. You can find the Dear Doctor letter on our website. Well, that's all for this edition of FDA Patient Safety News. Remember, you can get more information on all the stories you've seen here today by visiting our website. We also urge you to use the website to report problems you've encountered with medical products. That's how we learn about problems so we can alert others. We'll be back next month with another edition, so watch for us. Until then, for the Food and Drug Administration, I'm Mark Barnett. And I'm Anita Rayner. See you next time.


alright so we opened up this box check out the contents inside this is what's in there she had a lot of barbecue marinade but it looks like the rats were hungry and got in it chewed through the plastic three of the six containers look like that


Hi, my name is Brooke Berger. I'm a senior here at the STEM Academy and I'm the December student of the month. My shop is biomedical and what I like about it is that it's really similar to the real world in dealing with patients and making diagnoses, testing and treatments. In college, I plan to major in a similar career path like the biomedical life sciences and after college I hope to go to med school so I can become a doctor. Some fun facts that you might not know about me are that I'm a twin and I also foster kittens. So what takes up most of my time outside of school is mainly soccer. I play for a club team outside of school, but I also play for the high school team where this year I was made the captain. I'm also part of the National Honor Society, the World Language Honor Society and HOSA and lastly, I created my own SAT prep program where I tutor underclassmen at this school for the SAT. I would like to thank both of my parents for always being there for me, whether it's from driving me to soccer or keeping me motivated in school and basically doing anything they can to help me.


Hi, welcome to Good Lab Commit and to the DevSecOps stage. We're so excited to have you here. Software security has become a hot topic. I knew it had reached a new level of interest. And my dad called me and wanted to get my perspective and asked me what I was doing to help prevent new attacks like those he'd seen in the news. He wanted to be sure all of us in the software community knew that it's a problem affecting everyday people. The recent colonial pipeline attack certainly brought security to the forefront, especially for anybody on the east coast of the US. And now the US government is taking a bigger stance on the topic with last month's executive order on cybersecurity. If you think it doesn't apply to you, think again. I'm willing to bet the regulations and certifications that come out will be akin to the effort required of Y2K or GDPR. Those regulatory requirements forced everyone to take a deep look at every application to assess its architecture and potential issues. While GDPR was a European privacy requirement, you know that every company that might have European citizen data had to comply, which meant essentially everybody. The same will be true for the cybersecurity regulations that come of this action. It will affect everyone globally in the end. Because of the effort it will require, I felt it was important to have a deeper understanding of those requirements and their potential impact.