We've reached this era of touch computing and I would argue that we do less sophisticated things on our touch green computers than we did on desktops. And this sort of worries me because we've enjoyed this trend for 40, 50 years and all of a sudden we sort of nosedived in capability.


Hello everyone. Thank you all for coming. Welcome to the Elizabeth A. Sackler Center for Feminist Art. Today's lecture, as many of you know, is presented as part of the Helene Zuckersiemann Memorial Endowment. Let me tell you a little bit about Helene. She was an art lover, a contemporary art expert, and a great champion and mentor to many artists. Her career began at the Louis Meisel Gallery in Soho, and in 1978 she co-authored the book Soho, a guide to the community. This book is now classified as historical documentation of Soho. She later researched and documented a second book entitled Photorealism. For 23 years, she served as the director of the art acquisition program at Prudential, where she put together one of the great corporate art collections in America. In the years before her untimely death, she enjoyed being an adjunct professor at NYU and a very active private art advisor. Helene did everything with great enthusiasm and unbridled joy.  I am proud to have been her friend, as many in the audience today are. One of those friends is our speaker today, Leslie Dill. Helene followed Leslie's career for many years and remained fascinated with her work. She loved the fact that it was both whimsical and deep, that it was poetic yet concrete, and while informed by words, it remained visually rich, nuanced and ambitious. Leslie Dill is recognized for using a variety of media and techniques to explore themes of language, body and transformational experience through sculpture, photography and performance. Her work has been widely exhibited. She's had over 100 solo exhibitions. She's included in the collections of the High Museum in Atlanta, the Metropolitan Museum of Art, and the Modern Museum in New York, the Whitney Museum of American Art, the De Young Museum in San Francisco, and the National Museum of Women in the Arts in D.C., among many others. In 2009, the Hunter Museum in Chattanooga, Tennessee organized a 15-year survey of Leslie's work, and her show, Poetic Visions, curated by Barbara Madalski, is touring through 2013. Known for her performance work, Divide Light, a non-traditional opera by Dill based on the poems of Emily Dickinson, premiered at the Montalvo Artist Center in Saratoga, California in 2008. Leslie's represented by George Adams Gallery, New York, where she has an exhibit that just opened, and I recommend to you all, called Faith and the Devil, which also premieres a new musical collaboration with vocalist-composer Pamela Ordinez. She is also represented by Arthur Roger Gallery in New Orleans. Leslie has been the recipient of many awards over the years, but one I found very interesting. It's called The Anonymous Was a Woman Award, which gives her, I think, special credence for her appearance here today at the Sackler Center for Feminist Art. She has an upcoming exhibit at the Ducordoba in the spring of 2014. I so admire Leslie's work for being, I admire her work, and I admire Leslie for being a non-stop explorer and master of materials. She uses whatever it takes to bring an idea to fruition, sculpture, photography, drawing, printmaking, or performance, and she imbues it with a kind of philosophical magic. Leslie, please come up and share your work with us. I'm sure it. Thank you, Marilyn. That was so beautiful. I guess that about wraps it up. I know, so Fred Seaman is here and his son, Ford, is here, and I know this is wonderful and also painful to hear. We all love and still love Helene so much. Helene in my life is a yes, and to lead one's life in the form of a yes is tricky. So when you can find people that support that yes-ness, you cherish and you treasure them and you hold them in your heart forever. So what we're going to do here is I'm going to show you a seven-minute clip of selections from the opera Divide Light that I did in California. And I want to tell you that it's only seven minutes.  Is this going to be like 110 minutes long? And then she's going to talk. I want to tell you no, it's not. It's just seven minutes and then after that, look at the split, I'll go into my talk about my work over the last, you know, decades. Okay. Divide Light, if you meet while cubes in a drop, or pellets of shape, fits, builds, cannot undo, orders return, hold, force, play, and with a blunt push over your importance, let's steam. Stessy and stessy and stessy and die. The right outfits for the right emotions for when I go out in the world.  So I started making clothing as a kind of protection for the human persona. And in this dress, you can't read her when she's closed. You can only read her when she's open. And the poem, Emily Dickinson, dare you see a soul at the white, no, no, no, not yet. I heard as if I had no ear until a vital word came all the way from life to me. And then I knew I heard. When I was living in India, I drank a lot of tea. And I was working with cheery Cozo paper I'd brought from New York.  And I thought, you know, maybe this color is a very good global color. If you were to put all our skin colors in a blender, maybe this would be what would come out. Now, I say that because sometimes at the end of a talk, people will say, oh Leslie, why don't you use your own words? And the aforementioned is an example of why it's not a good idea. So, you know, so I made her and I embroidered her with horse hair again with an Emily Dickinson poem. I am alive, I guess. I am alive, I guess. But, you know, I like guys and I thought she was a little lonely. So I made her boyfriend and this boyfriend is based on a guy I knew for a little bit at the end of high school. And of course, when my mom is in the audience, I always say grad school. Because, because I wanted to address the idea of gender difference. And you know, at that time at 18, I had always thought that gender differences were in that mysterious genital place, the unknown other genital. And when I went out with Marvin, Marvin was one of those guys that had hair that started up here and then it went all the way down to his ankles. And being a rather pink and hairless person myself, I was quite interested and amazed at this masculine hair suit-ness. And you know, it informs why I would use horse hair and threads from this early imprinted dating experience. But I come to think of men quite affectionately since then, having done a dedicated study, forgive me, of male hair patterns through the years. And I found that I think of men now as snowflakes because no to our life. Now, my belief in words is very strong and my feeling is that if you were to cut us open, if you were to cut us open what would fall out would not be our pancreas and just our intestines. What actually would fall out would be words. The words that actually meet air in our lifetimes are few. Compared to the unlipped and untung words that we hold inside. A secret told ceases to be a secret. Those are copper lips up there and then copper teeth underneath with the words. So the process of making language itself is an essentially warm and human animal thing. Just to talk to you this afternoon, I have all these thoughts lined up in me like Boeing 707s, but to make them happen I have to bring them up somewhere here in my body to wrap my breath around the thought, to bring it up past my throat, my teeth, my tongue, my lips out into the air, onto your skin, into your ears and into your body. And I therefore think that the spoken or sung human word is one of the most important ways of communicating. And I know that you do know that this is true because the instant your cell phone rings, which I hope doesn't happen right this minute, but the instant your phone rings and the person on the other end goes, hi, and you know they are your mother, your father, your son, your beloved, your hated person. In that single envelope of air, every cell in your body knows who that is, that hi. You wake up and it's through sound. I am afraid to own a body, I am afraid to own a soul. Again Dickinson, this is how I started out, I am afraid. In India, my Indian women friends would henna my hands and feet and their hands and feet on special occasions with temporary tattoos of henna. And it really influenced me in coming back to New York. And I thought, how great, what a wonderful metaphor for the feeling that the words that we hold inside are staining through continuously from the inside of our bodies to the outside. So I did, I had people come out, friends come over and I would paint them head to toe with words, no Photoshop, and then photograph them and make a print and paint on them images of the heart or words close, close to their skin and their body. And this was the first piece that I made when I was living in India. Moving there and living there for almost two years, I learned a little Hindi, but not enough. And it was the first time that I'd ever been in a country, I don't know if you have ever been in a country where you can't read the writing, you can't understand what's being said, and there you are, alone with sound, you have no control over, because you don't know what it means. So I strained and tried, then I let go. And when I let go, the melodic musicality of human language in writing and in speech rose up and I was free and companion by this. And it has affected my work to this day, this kind of melodic unintelligibility in reading or in listening. Also I use the color white for this piece. I am a northern girl, I grew up in Maine, I thought white was a really cold color, but if you live through to 120 degree New Delhi summers, white becomes a shimmering hot color and the air is filled with the secret sound of Hindi swarming around you every day, night and morning. Also in India, it is a country that is devoted to a belief in the importance of the word, be it in prayers or mantras or pujas or especially in prayer flags. So again when I came back, I thought, oh, this I can maybe do something like that, taking big pieces of fabric, putting a photo on it with language. Now I did think, forgive me India, I thought that maybe it was a little naive that's putting words on flags and thinking that this language would go out into the air and do good things. But I think no, I think it is valid because of the sound, you know, the invisible sound formations that happen. Also, you know there is such a thing as drive by words. I was driving towards Seattle a little while ago and you know here in New York you also have that experience where you are walking down the street and you really don't want to, but the words that are somewhere on signage come into your body and you just really don't want them there, but they are there. So I noted this in this car ride to Seattle because there are a couple of phrases. One was carpet liquidators. I thought, oh my god, this is like textile destruction house. This is terrible.  But then you even see Burger King and all I could think of was some ground chalk king standing sky high. So I don't know, I just think words should be careful what we wear and what we hear and what we listen to. And again, living in India, this is actually a temple that's in Nepal. I went there and stood underneath this ribbon, this metal ribbon. And I had never seen this really much in temples in India. This was in Nepal. So I asked the man standing there. I said, what does this mean, this ribbon? He said, oh madam, that is the tongue of God. You stand here, you say your words and they go up and they go up into the sky and into the ears of God. And I thought, oh wonderful, that this, me, this complicated little messy nobles of flesh down here could like say something or think something and it could be rinsed out by like rising up and going up to the sky. And I'm a very prosaic level. I think this is one reason why I use threads a lot in my work. It just gives you one way to wend yourself into the world of metaphor. Example, these saw visions latched them softly. Okay, here's Larry, horse hair embroidered on the bottom.  So you lie down. This is not this gentle Swedish massage. This is a like whack massage, like bang, bang, bang, bang, bang, like that. Or that's what I got that day. And at the end of it, the woman, she said, close your eyes and I closed my eyes and she took her two hands and the very tips of her fingers. She said, clear eyes. I closed my eyes. And she started to gently with the most perfect exquisite touch to massage the pupils of my eyes through the eyelids. And it just felt like, one, I thought, oh my God, no one has ever touched me there before. And then I also thought, oh, this feels so good. As if all these images and loaded in my eyes are being released through this fingertip experience. And you too can do this at home after the talk. I often use those same words with different materials and different images. These saw visions latched them softly, thinking of words again, more like a song, a prayer, a mantra, over and over again in different contexts. A desire for secret rhythms, Kafka. Take all away from me, but leave me ecstasy, Emily Dickinson. All my photos are not there in real life.  We started to call them the SNM, you know, radiant photoshoots. But what I want to say about these two images is that I am a fingertip artist who is obsessed by touch. I think in a way we are societally deprived of touch.  Then we get on the subway and we check our iPhones. And then we go home and we turn TV on to relax. And then for a special occasion on the weekend, maybe we go to a movie. So much of life happens behind a screen. But we as human animals, we feel and smell and bite and touch. We have so many organs of feelings. We are not fish outside the fishbowl. We are living inside the fishbowl. Our lives are inside the fishbowl. We are like glasses of water in the ocean. I sent this photo to my mother and from India and told her I'd found a new guy. She was not thrilled. But it does look sort of like a match.com date that maybe shouldn't have happened. But I use this photo and this experience as a way to introduce my craving for the mysteries and the unknowable things of life. Going to the uncomfortable place is only uncomfortable until you are there for a longer time. So I was invited to do a community art project in Winston-Salem, North Carolina. I, of course, being inspired by my friendship with Helene, said yes. So I say yes. I, Helene, did so many things. So I said yes. I had no idea. I'll try to get more intimate with the mic. Okay. I had no idea what I was going to do. And then I remembered that I had a secret. I had a secret that I had never spoken about ever. And it happened when I was a 14-year-old girl growing up in Maine. And this is what it was. I was getting up to go to school and the sky was getting light with the leaves against the sky. So my vision was occluded with a huge blackness and struck through that blackness were like white streamers and things. I heard and saw the word pestilence, war, roughage, desolation. It was like a big black movie that was going on in this vision. But the other thing that happened in this vision was that this experience of pestilence and sorrow was actually overlaid and imprinted with feelings of rapture and bliss, which at the time at 14, I hadn't come nowhere near any concept of rapture and bliss in my life. So I got up to go to school, immediately forgot it, totally forgot the whole thing. And then I went to college. And then there was a class offered called Ecstasy. I was like, you know, really, who would not take that for credit? So I took it and the professor said, okay, here's a questionnaire. How many of you have had experiences you can't explain? How many of you have had a visionary experience that you don't understand? Where time has stood still or something you felt or seen something that you've never had. And then I remembered. It came to me like a swoon. And even though I'm an eager, obedient student, I did not raise my hand because I sat there thinking, oh my God, maybe I'm crazy. You know, so I never spoke about it really again until then decades later when I thought, let me see. I thought, let me go down south.  So let me go down and see what they have to say. So I went down there and I went everywhere with a wonderful education curator. And we went to Barnes & Noble, high schools across town, churches. This is the spiritual choir of the Emanuel Baptist Church, which ended up being sort of my home for this project. We did billboards, you see, the normal way to take a photographic image from we older people. There's Melinda and Angie. And here's a billboard with someone's language. Small changes change who I am, change who I want to be. I have left my body twice. I began to spin head over heels slowly. This was one of the curators. My name was called in darkness, I see, Reverend Mendes. Experience left me and I felt weightless. We install these billboards. I think it's called Route 55 and it's the road that traditionally divides the white from the black section of town in Winston-Salem. And also, the last thing is during the exhibition, the spiritual choir came to Sika, to the museum, and they had folded in the language of the community and married it to their traditional gala songs so that when you went there and heard them sing and you were part of the project, you heard your songs being sung back to you by this spiritual choir. This is another costume I did for another performance piece that we don't have time for you to see. But there it is. And Larry Goldhuber and Heidi Latsky invited me to join them and I made that skirt for Larry because I think guys don't get enough chance in our culture to wear skirts. So I made it really long and that's Heidi and me being dragged across the stage so much fun by Larry. And there's Heidi dancing with the first of projected images that I used. And there's Larry, the guy himself. And here are costumes from the opera, the fabulous Jorge. If we have time I'll tell you stories. And here's Andrew, the incredible baritone, who every day after rehearsal would come up to me like this, he would say, he's sung at the Met and around the country. And he said, oh my God, Leslie, I've never sung the word sperm before.  So here are more images, another dress. I didn't show you this was the finale dress, ecstasy. And here's the incredible string quartet, fabulous, based on San Francisco. And there's Kathleen, the mezzo, fabulous voice. And there we all are. Now, this took a lot of time. It took three years going back and forth to Colorado, working with different singers, composers, etc. So myself and my studio, we were tired. So, now Sarah, did you help with this next part? I think so. All right, yeah. Okay, so what does one do when you are exhausted from overwork? All right, here's my living room. These are the two dogs that we borrow in our house. Claudia is a big one and Aki is a little one. So I thought, let's make costumes for Claudia and Aki. Let's make Aki look like Claudia and we'll make Claudia look like Aki. So, ready? Here comes, here's Claudia and here's Aki. Right? That's good. Here's Claudia as Aki, looking very happy. Here's Aki as Claudia, not looking very happy. Something between Marat's sod and wounded soldier is what I would say. Anyway, I just include this. It's sort of a wind down. And then wound up again from a wonderful invitation from Gail Deere at the Maryland Institute printmaking department. And Scott Skinner from the Draken Kite Foundation. And we, the printmaking department and I, we worked together to make a 14 foot kite called Divide Light. So, you know, you think divide light, how does that happen? Well, the kite was perfect because just by its very nature, just by being alive when we walk out in the sunshine, we divide light as does a kite. And there it goes. So after that, that combined with my experience with music, I am very interested in things that rise up. So I did this piece at the New Burger Museum with the language collected from the spiritual choir from their songs and emitting from her back seated there. And of course, I have to go back to India to the original inspiration of the incredible fabrics that you find there. And let me go back there. Now that would be a very good image for the Sackler Museum, I think. You know, women, strong women, yeah. Okay. Then in the same exhibit, I did a little guy with hundreds of figures from around the world emitting from his back that 20 feet high by 65 feet.  And here's a sample of the metal figure and close-up that went into that piece. Sarah, one of my beloved assistants is here and she's probably feeling very tired just looking at this. Okay. Very tired, I'm sure, she's feeling. So then we did shimmer of kind of a puzzle-like waterfall of electrical wire. We used 2,592 feet of different kinds of wire for this. Your accounting studio. And now I'm going to show you a few bronzes and then a few things and then we are done. And you can ask me anything you want or not, or go. So this is a life-size piece called Rapture's Germination. And you'll see, okay, hold that and then, ah, I've done a number of pieces that are bronze with holes because I think when we listen to music, we open. We open up without thinking. Our whole bodies open up when we listen to music. It's not just our ears. And here is a guy, a big guy. And here is a woman, a bronze also. And here's a new bronze piece. It's actually up at the National Museum now, up in here in New York. And then this is called a Perfect Paralyzing Bliss. So up here I get to confide all strange things to you. So I was on a Buddhist retreat and I had, you know, ten minutes of this utter suspended feeling of bliss and rapture that I hadn't had as purely for a really long time. I thought, ah, that feels great. Eight hours later, it did not feel so great. It felt like a kind of spiritual viagra that I've never used. But, you know, it was like a state that was sustained for a very long time. I've since learned how to manage that. But, and then I went little. Here's little bronze guy. Here's little seven headed paper guy.  Jump, dazzle. Spit bite. Walking man. And this guy, big guy leaping off the wall with Kafka on him. Was he an animal that music had such an effect on him? Yes, he was. And then I did a show in New Orleans that was called Word Queens. And I have been so lucky in my life to know so many strong women and one of them was, was, is my friend and mentor Nancy Sparrow, who's dead now. But she would always tell me to amp up. Never apologize. Never speak for women. And in her own work, early on when I met her, I learned, oh, a woman can be the center of a story. A woman can be a center of the story and not necessarily be a victim that's the center of the story. So I wanted to do this show called Word Queens. And I did these in, I don't know, 2006 or something. This one is in Romania. And then this most recent show, and then this is almost it, Arthur in New Orleans invited me to do an installation down there. And so I researched and found that Sister Gertrude Morgan lived and did her spiritual work in New Orleans as a street preacher. So this whole installation was an homage to the biography of Sister Gertrude. She called the show Hell, Hell, Hell, Heaven, Heaven, Heaven, Encountering Sister Gertrude Morgan and Revelation.  And then there are necklaces. And it's her biography. The necklaces are big, a sort of homage to New Orleans. And in her vision that she had, she had a vision that she was meant to devote her life to the spiritual calling. And she, in her vision, she became the bride of Jesus. So I made her, I made in this exhibit, I made this dress on a figure in homage to Sister Gertrude with that helm. And this is from one of the drawings. And what she says is, My heart shall not fear the war should rise against me. My heart shall not fear the war should rise against me. Now, here we are in present day. I want to take this opportunity to publicly thank my many interns and assistants who have worked with me over the years. The generosity of these young women and their ideas is limitless. And they are fabulous people. And this is a show that's up now at George Adams Gallery. So there are just a few funky slides. So here's his team we had. Here is Elma, me and Maxine. And Sarah is the other person who should be in this photo, planning, planning, thinking. And we, you know, there are some disadvantages to having a camera in the studio. You just can't resist taking certain shots. But this was not posed. This is an actual photo. I mean, an actual experience. Right, Sarah? Uh-huh. Okay. And here we are at George Adams installing the show Faith and the Devil. A week and a half ago. Here is drunk with a great starry void. And here is big gal Faith.  And forgiveness, which is really a... Forgiveness is, I found, was the toughest one to work on. That one is lust. Easy. There's Lucifer. Last slide. This is Kafka. Faith, like a guillotine, as heavy as light. Now, faith is not a soft bunny of a word that describes slinky, jelly-like people preying on the floor to indoctrination. Faith is a strong, big word. The word faith, by its very nature, encompasses the incomprehensibility of evil, of murder, unmentionable acts of cruelty and rape. And these acts of evil coexist with thoughtfulness, reflection, and potentially even illumination. So I think, in general, for our lives, big, brave heart, big, brave mind, big, brave story. Thank you very much.  So actually it was, you know, I was only 45 minutes altogether. Okay, I'm sorry. Are there any questions or thoughts? No need. Thank you, Fred. Yes, fellow artist, woman, Leslie Wayne, wonderful painter. Sorry. I love it. I never knew that some of those like that tone of the temple was such a specific influence. And it's really interesting because we all look for information to take back to the studio. You're right. And I'm really impressed when you took those, just bits of visual and some information and then they... Thank you, sweetie. Another artist, another artist. This is a wonderful thing. I don't keep talking a little bit more about... And you can leave if you want to. Go ahead. How the poetry informs the visual image or how the visual image demands the particular words? You know, I always... Did you hear the question, how does the visual... I always forget kind of to mention that in the talk because I get so carried away with the verb of life. And so this is what happened to me. So my mother, when I was 40, you know, as artists, you know, working, making art, some good, some not really great. My mom sent me this book of Emily Dickinson Poetry.  I don't even like poetry. I'm down at the bottom of the page before it comes into my body. Give me a prose. And I thought, all right, but because it's my mother, you know, of course, I will read it. So what happened is I opened the book and then like my kind of electric blue frogs, these words, like, I felt my life with both my hands to see if it was there. Like jumped up into my body.  And then I opened the book again. I felt my life with both my hands to see if it was there. Did I just say that one? I did. See, I get lost in that. The soul has bandaged moments into my body. A wounded deer leaps highest. I've heard the hunter tell, bam, into the body. So I learned that I was affected by certain kinds of language, like a boom, boom, boom. And it was starting because the reading of the words actually then brought with them ideas for making artwork. So they came like fully loaded, like charged seed pods of connected words with an idea. And then with the train of the permission to use language in the work. I mean, I've always been a reader, but I'd never had this kind of almost experiential effect with language. You know, with four or five words linked together as a thing that comes up. So it was so strong that I just, and I was so dumb. You know, you don't know that this is going to become your whole life when you start with an inspiration. You don't know. You know, you don't know when you meet a guy.  You don't know that in a few years you're going to have three children with him. You know, it's things like that. So it continued to affect me. And I can't read late at night. I do research at different times. So it used to be the words would secrete the image and the idea. And then later on it became that I would get an idea and we need to be closed or I would start to match up. You know, as it became more of a world, a world of imagery and language and I became more confident in it. And it became more natural. Now it just stays kind of swim with it in many different ways. Pamela, the singer-composer who we are having a new collaboration with, we've been working for the last many months on just swimming with language and making songs from that. So does that go close to it? So it is the power of belief in the power of the word. In the power even of a single letter. Look, history. Her whole life ruined by one letter. Yes? Yes. Yes, Gracie. How many different writers have you used? Not too many. But for this new project of George's, I was poetically monogamous to Emily Dickinson for seven years. And then I strayed to Neruda, South Dark Esprit, behind just a few people. It would have a similar structure that would have the jump up frog thing happen. And then as I got more fluent with that, this show that's up now is from Dante, Milton, and also my good friend Tom Slay, who I'm a couple of artists here in the audience have also used his fabulous poetry. Maybe 12, 10, 12. Not too many. I still don't really like poetry.  Have you had such loyalties to Emily? I did. Was it hard to wriggle her? Well, I use it as a patterning device. A little joy, a lot of ecstasy, and some poison. Seems to work. That's my goodest. Thank you so much.


So there's going to be eight more months of this, of general election, that's 34 more weeks, 239 more days of the rematch that nobody wanted and everybody voted for. It's basically a toss up at this point. Trump's leading by a little bit in polls, depending on how you ask the question. Usually when the terrible reality of the general election being set between the two major party candidates, like hits, people reach for a drink or some hemlock or any possibility of a green shoot somewhere, a window into an alternate reality, where there might be a third party candidate, search terms go through the roof, people start looking around. So let's do ourselves a little heat check on some of the other names that are more likely than not to appear on the ballot. Heat and I understand rumor has it on the internet that you moderated a panel, not just the Academy Awards, but you were in South by Southwest with a certain RFKJ. So do you want to tell us a little bit about what you found interesting about him or his candidacy or his voice from a small L Libertarian point of view? Yeah, I was at South by Southwest. I was going to moderate a panel. That ended up not happening, although it had nothing to do with me, I hasten to add. But I did go to the event with RFK that they ended up doing at the University of Austin. So I saw him speak along with, my mind's going blank, your former ACLU. Nadine Strossan. Thank you, yes. Nadine Strossan, former head of the ACLU. Right. I saw their speech and then I went to RFK Jr.'s campaign cocktail hour after that. And that was my first exposure to RFK Jr. I have not followed him. This is the first time I've seen anything other than headlines. I came in with pretty low expectations because I usually do when somebody's famous for being the son of somebody else. But I ended up liking the guy. He strikes me based on what I saw in that speech as somebody who is probably fairly progressive in his economic bearings, but a civil libertarian very strongly. He had a lot to say about freedom of speech. He was very much in the absolutist camp when it came to freedom of speech. And you could hear him going towards, maybe not a libertarian position, but at least a very cynical, in a good way, understanding of the nature of power. He brought up at one point how horrifying centralized digital banking is and talked ad nauseam about the system they have in China right now where your credit card is now your face. You get scanned in an app and that's the identification for your credit card. And if your social score drops, the Chinese government will then limit the types of transactions and the geography where you can do them. So you can go to a grocery store, but it'll only work at the grocery store near your house. You can no longer use public transit, things like that. And he had a line of, I'm pretty close to quoting this here, any power you give the government will ultimately be abused to the hilt by that government. He had an idea that, he didn't strike me as the kind of guy that thinks that government is just when we all come together to help each other. He had an idea of the corrosive influence of power. And then topped it off by saying that trust the experts is not a feature of science or democracy, it's a feature of totalitarianism. So he does strike me very much as a civil libertarian. The other thing I'll add is I think he's running a real campaign, which surprised me. We'll talk about third party candidates here in a minute. There's varying degrees of vanity and colorful characters that go into these things. I'm friendly with vermin supreme. I don't feel like he's running a real campaign. I don't think he's sitting at night going, who would I make ambassador to France? I don't think he's doing that. Is that how we know it's a real campaign? Because in that case, I absolutely have run a real campaign. It's the most and bits are all of the sentiment.  I used to live in Washington DC, Catherine or anybody that's been in DC regularly, have you ever come upon Elijah the nature boy? Do you know who I'm talking about? Oh.   And he used to hang out. Oh, I've seen that too. Yeah. He used to hang out in Jackson Square, across from the White House when I was a Segway tour guide in this fair city. And so I became friendly with him. This paragraph is cursed, go on. Sorry. It's getting better and better. I wouldn't have lunch with him. And he would tell me that God told him he was going to be president. And I went, well, hey, if God's gonna make you president, I'd love to be an ambassador. And he literally went, Andrew, I really like you, but I can't just appoint my friends to positions in the State Department. It has to be based on competency. And I was really impressed with the quality control he was doing. He's not wrong. With Kennedy though, I did not get the impression at all from his campaign event that he is running a vanity project or he is running for Secretary of Agriculture or to sell a book or something like that. He had people that were very efficiently running the event. He had a lot of security guards. And it struck me as a thing where he's making an actual college try on this rather than just some board attempt for a spotlight. He has raised a level of money that we haven't seen in the third party candidacy. Certainly the third parties themselves don't really usually have much money at all, but you get independent candidates can get some money. But money can solve the ballot access problem to a great degree. Although one of the funny things that I didn't get into and I wrote about this about a month ago is that there is a third party ballot access signature gathering inflation because there's a lot of people out there. No labels out there getting signatures. The forward party. So they're bidding up the costs. I was talking with a Green Party, a really nice Green Party guys ahead of their ballot access. And he's like, yeah, all this competition is really driving up labor costs. Huh, that's fascinating. Can you, do the signatures have to be different for each party? I think they can be the same one on different parties. I think so. But I don't know. That's a good question, Mr. Gillespie. I suspect there is a lot of state-state. Dr. Gillespie. Other thing I'll say about RFKJ is that he is a championing self as a champion of free speech and absolutist in Dr. Heaton's terms. And that doesn't necessarily jibe with his long and storied career in free speech matters, which we've written about and talked with him about Nicted in the past where he was talking about the corporate death penalty for people who have wrong think on climate change. Well, and he also, it's a little bit slippery on the social media front. There's no question that his posts and things like that were suppressed or went through shadow banning, sometimes outright suspension over COVID stuff, but he talks a lot about social media sites as a new public forum that really needs to be restricted and regulated by government. And sites, various cases where either company towns or malls were limited in their ability to shut down speech, political speech. So he's a little bit cagey on that kind of thing. That was a clip from the latest Reason Roundtable. If you wanna see more clips, go here. If you want to see the whole episode, go here. Make sure to subscribe at Reason's YouTube channel or wherever you listen to podcasts. Thanks for listening, watching or both.


Dyna, ond y dyma i'r Gŵr yng Nghymru, ddechrau'r cyffredd. Yn hyffredd y Llywodraeth, ar gyfer o'r ffaith a'r hynny'n gwneud o'r ffordd, dyna yn bwysig, o'ch gwmpas oedd yn mawr, dyna yn bwysig, o'r bobl, o'r gwmpas, o'r ffordd o'r eich gwylliant. Yn ymgyrch ymddiad, o'r cyffreddau o'r gweithiau, sy'n gwneud yn dda'r rhaid i'r ffordd, yn ychafol o'r gweithiau, And he's become the bellows, and the phan, ... ... to cool at gyps' is lust. Look where they come. Take but good note and you shall see in Him... ... the triple pillar of the world transformed into a trumpets pawn, ... ... behold and see. If it be love you indeed!, tell me how much." There's beggary in the love that could be reckoned. I'll set a barn how far to be beloved!" Then was thine needs find out new heaven, new earth? Use my good ores and roads, great's me, the sun. Dweud i am Lent unig, Feit subsor yn fïn ychydig yng Nghymru. O beth y defnydd yng Nghymru sy'n seisi, Ddiwedd yr ydych yn yng Nghymru sydd hwn yn ymwyllfa'n gallu. Na haydyn nhw y gallwn iddynt yn galluEEeso i'r frangos Felly rydnos wedi'u wneudstaeth. Dwi'n cymhod! Mae'n Ei hwn, mae'n meddwl o'r Lent. Felly dych yn ymlaen, Mae'r ymgyrchu sy'n deud hynny. Ond yw'n deud ystod ymlaen. Feit eu proses fel Fylvius. Caesar's, I would say, both, call in the messengers. As I am Egypt's queen, thou blushest Anthony, and that blood of thine is Caesar's homager, else so thy cheek pays shame when shrill tongue full via skulls. The messengers... Let Rome in Tybur melt and the wide arch of the ranged empire fall. Here is my space. Kingdoms are clay, our dunny earth are like feet beasters, man. The noblness of life is to do thus when such a mutual pair and such a twain can do it. In which I bind on pain of punishment the world to eat, we stand up peerless. Excellent falsehood. Why did he marry full beer and not love her? I'll seem the fool I am not. Anthony will be himself. But stirred by Cleopatra, now for the love of love and her soft hours, let's not confound the time with conference harsh. There's not a minute of our lives should stretch without some pleasure new. What sport tonight? Here the ambassador. Five wrangling queen, whom everything becomes to shy, to laugh, to weep, whose every passion fully strives to make itself in thee fair and admired. No messenger but thine. And all alone tonight we'll wander through the streets and note the qualities of people. Come, my queen, last night you did desire it. Speak not to us. Is Caesar with Antonius prized so slight? Sir, sometimes when he is not Anthony, he comes too short of that great property which still should go with Anthony. I am full sorry that he approves the common liar who thus speaks of him at Rome, but I will hope of better deeds tomorrow. Rest you happy. Lord Alexis, city to Alexis, where does anything Alexis almost most absolute to Alexis? Where's the soothsayer that you praised so to the queen? But I knew this husband which you say must charge his horns with garlands. Soothayer? Your will? Is this the man? Is it you, sir, that know the things? In nature's infinite book of secrecy, a little I can read. Shine your hand. Bring in the banquet. Quickly. Wine it up, Cleopatra's house today. Good sir. Give me good for you. I make not, but for thee. Oh, but then for see me rather. You shall be yet far fairer than you are. He means and fairer. No, you shall paint when you are old. Wrinkles for birds. Ex not his presence. Be attentive. Shhh. You shall be more beloved than beloved. I'd rather heat my liver with drinking. Nay, hear thee. Good now, some excellent fortune. Let me be married to three kings in a forenoon and wither them all. Let me have a child at fifty to whom Herod of Dury may do homage. Find me to marry with Octavia Caesar and companion me with my mistress.  Oh, excellent. I love long life better than fids. You have seen and proved a fairer form of fortune than that which is to approach. But like my children shall have no names. Pretty how many boys and wenches must I have. If every of your wishes had a womb and fertile every wish, a million. Oh, I forgive thee for a wish. You think none but your sheets are privy to your wishes. Nay, come. Tell our assers. Well, now all our fortune, mine. And most of our fortunes tonight shall be drunk to bed. Well, the farm presage is chastity of nothing else. He has the old flowing nile as presage of the famine. Well, you wild bedfellow, you cannot sense it. No, if an oily palm be not a fruitful prognostication, I cannot scratch mine here. Pretty telephone. Sample complete. Ready to continue?


This is a mathematical mystery. Does this work? Yes, this works So this is something that I have been talking about a little bit with Travis Schull and Dan Schumow, so Street, so as you may notice from my shirt, I've been getting into blockchain recently in my way and As a side effect of a paper that I was working on recently We ended up looking for colliding ECDSA nonces in the Bitcoin blockchain And if you do this you notice that 99% of the repeated ECDSA nonces which gives you the private key are This value which happens to be n minus 1 over 2 where n is the order of the elliptic curve used for Bitcoin So this is an interesting thing what's going on so it turns out that the x-coordinate of This value times the generator of the curve which is the same as the x-coordinate of a half times the this point has 166 bits. It's this value instead of 256 bits So that's interesting This has been known to food sort of the Bitcoin crowd for some time and They're all like dude this magic valley decreases my transaction costs great Every time I give a talk to a room full of mathematicians about this they're like wait what? This this makes no sense like how is this how is this even happening? There's no way that this is this is random, but also this is not documented in like the specification for these curves So okay It turns out that if you look at a half times the generator the x-coordinate for the half times the generator For all of this family of curves the prime-order cobalt curves from sec to They have the same property So I mean okay for 160 bit curve you would expect to have 160 bit x-coordinate But the rest of them are all small and in fact they all share almost all of their bits in common so okay if you look at Sort of the the sec 2 standard that was produced by certicom This is all they say about the generation of these curves the recommended parameters associated with a cobalt curve Were chosen by repeatedly selecting parameters a binning and efficiently computable endomorphism until a prime-order curve was found Repeatedly selecting parameters. They don't specify like how they selected these parameters So you sort of the the natural Generation procedure that you would expect for this kind of curve is that you choose some prime modulus You choose some curve parameters and you check whether they have all the properties that you would want then you count some points And you hope for a prime-order curve and you sort of stop when you get a Prime-order group and then at that point you you search for a generator of this group and then you then then you publish in a standard so Okay, this 160 bit value that you find I mean we can hypothesize that this is a sha 1 hash of something You know if this is generated in 1999 then That's 160 bit hash function. So it seems natural Maybe the most in least for significant for bits have been changed since they're different in all of these points The other curve generators seem to be have been produced by changing the most in least to think for bits and appending some digits to the most new thing that's There's a mystery here, which is that you would expect to only need to try two values to get a valid point on the curve So why so many changes? Why are they appending so many digits? And then another unsolved mystery. Why did they double the point to get a generator? Because you know, you could have just published that like use the original hash hash value if it's a nothing on my sleeve value However, this property doesn't seem to be known to aid in computing of the curve discrete log in any way So there doesn't seem to be any advantage to having this kind of structure or either attackers or defenders so We have no idea if this is some kind of backdoor It doesn't seem to be but this does seem to be some kind of doc like undocumented artifact from the generation procedure That shed some light on how the generators were chosen, which is not documented in the spec So if you would like to contribute to our understanding Of this problem, did you work at sort of common in the 90s? It would be great to chat with you We have talked to Dan Brown and and he did not know that this had this property And Otherwise do you have any GPUs and can you help with Shaw when brute-forcing? So there's 256 possible values if we assume that the most at least significant four bits have possibly been changed I've been running John the Ripper, but I don't have really have GPUs and my cluster is down right now So I don't have that many CPUs either so if you if you have if you would like to run things and then that would be exciting too we might Hypothesize that this has been there's some ASCII seed, but we don't know Thank you


Hi, I'm Zor. Welcome to your new Zor education. I have completed basically talking about some theory behind similarity, and I would like to spend some time solving problems. First of all, as usual, let me just give a general kind of a guidelines about the problems on this website, Unizor.com. I think it is imperative that you first try to solve the problems offered on that website yourself. I'm not talking about exams. I'm talking about lectures like this one, where I explain the solutions to these problems. But before listening to me, read the notes where all the problems are stated. Try to solve them yourselves. Whether you're successful or unsuccessful doesn't matter. Then you listen to the lecture. I might suggest some new way to solve the problem which you have already solved differently, which is fine, or maybe you didn't find the solution that listened to me. After the lecture is completed, do again your solving problems exercise. Again, going through the same notes, try to solve the problems yourself. Most likely you will remember what I said during the lecture. If not, and you still cannot solve it yourself, listen to the lecture again. Basically, this is some kind of an approach which would enable you to remember certain ways and means to solve problems. Now, the next thing is, I'm usually putting the problems after certain theoretical materials covered, like in this particular case, the problems which I'm talking about right now would be about similarity. This is a hint already. So, any problem which I'm presenting in this particular lecture is about similarity and should be solved about similarity. It would be much more difficult if this problem is just given to you without referring to, okay, this is about similarity, kind of a hint. So, consider yourself in an easier situation than in, I would say, something like during the exam or whatever, where it's not obvious which tool to use. And speaking about tools, solving problems actually is supposed to develop a toolbox for you, so to speak. Every tool is basically the method you can use to solve certain problems. For instance, you can solve using algebraic equations, or you can solve using locus, the geometrical set of points which have the same property, or similarity, or I don't know, something else, whatever. So, this is a toolbox which I wish you developed by the end of the whole course, and it would be at your disposal at any time. All right, now, the problems. Problems are relatively easy, and as I was saying before, they're all about similarity. Construct a triangle by angle, a ratio between sides forming this angle, and an altitude from this angle onto the opposite side. Okay, so let me start the game. You have to construct a triangle knowing the angle, and then ratio between the sides and altitude to opposite side. Am I right? Angle, ratio between sides forming this angle, and an altitude from this angle onto the opposite side. All right, now, as far as the similarity is concerned, you basically understand that if I have a ratio of these sides, it means I can build a triangle similar to this one. How? Well, very easily. I have an angle, right? Now, on one side of the angle, I will put the point a prime, which is on a distance, I'll take the point b prime, I'm sorry, it's c prime, so that bc prime is equal to 1, some unit, whatever it is. Then, since I know this ratio, it's a numerical value, I will choose a prime b equals to a over b. Since I have explicit lengths of these two segments, this would be equal to 1, this would be equal to a over b, I can build a triangle a prime bc prime. And since the ratio between these two sides is proportional to these, an angle was constructed as a given, I can say that these two are similar to each other. Since they are similar, what I can do is I can just draw a perpendicular and continue it in such a way that I will have this bh equal to the altitude which I need. After that, now this is the right angle. After that, I draw a perpendicular and call these two points a and, sorry, c. So, now since these two triangles are similar to each other, these lines are parallel and that's enough for similarity. Since ratio between these sides is equal to a over b, ratio between these sides also will be equal to a over b, as was basically asked in the problem. And the altitude is also given, that's how I basically constructed the point h on the distance h from b. My problem is solved, the triangle a b c is the one which I would like to build. It has the angle, it has the ratio between the sides and it has an altitude. So, basically I would like you to just emphasize what I did. I was not able to build the triangle straight away whatever was required, but I was able to build a similar triangle using the ratio between the sides a over b and the angle. And then I just stretched or shrink whatever my triangle which I have built to the proper size so my altitude would be given. Basically all the problems which I'm talking about right now are that type. We inscribe a circle into a given angle such that this circle contains given point inside an angle. So, you have an angle, you have a point inside that angle p and you have to construct this particular circle. So, it will intersect the point and it will contain the point and it will be inscribed into the angle. How to do that? Well, okay, we cannot build this circle right now. I cannot construct it because I don't know the center. However, I can construct any other circle which would not go through the point p but would still be inscribed into the angle, like this one. How do I do it? You know all these inscribed into the angle circles are lying on an angle bisector. So, I pick any point on an angle bisector and draw these perpendicular and this is my radius. So, this is an inscribed circle. But what's the problem with this circle? It's not the one which I would like to construct because it does not go through the point p. So, what do I do? Let me connect with p and that's where it intersects my small circle, point m. Now, as you see, everything is scalable along that angle. If I will use b as a center of scaling and I will scale point m into p, as I told many times before, this center x would be transformed into a center of the bigger circle y. The reason is that when I am scaling bm to a factor which will convert point m into point b, my ratio bm over bp, I will use the same ratio. Now, obviously, since bx is proportional to by by the same ratio, that's how I can determine the by. So, all I do is, as far as construction is concerned, if I don't know this circle, I construct any circle which is inscribed into an angle, draw the line, take the intersection, and all I have to do is to draw py parallel to mx. That's basically enough because as soon as I draw it parallel, my angles are the same. Now, the triangle bmx is similar to triangle dpy because there are two angles. One is common and these two are corresponding with parallel mx and py and transversal dp. So, triangles bmx is similar to dpy, which means that bm relates to bp like bx related to by equals to mx related to py. Obviously, if I draw a perpendicular here, let's say these are c and d. I can see that my triangles bcx is similar to bdy from which radius is cx and a segment cd are in ratio of bx to dy, which is the same thing as this one, right? But now, since cx and mx are both radiuses, cx and mx are both radiuses, so equality between this bx over dy and this is obvious, so I can equate these two. And since mx and cx are equal, cd and py are equal as well. Not cd, wait a minute. cx to dy, I'm sorry. cx to dy is dx. So, which means py and dy are also equal to each other. And that means that this is a circle. Since this is the perpendicular, it will be tangent and the radiuses are equal to each other. That's why this particular circle will be inscribed and passing through the point p. Yeah, that's it. So again, the construction itself, after I did all the analysis, is just construct a small circle, connect BP and intersection m, draw line, the radius actually, from x to m, and py would be parallel to mx. Whenever it crosses the y-sector, that's the center. Everything else is just proof that this is correct. So first I did some analysis, I realized how to do it. Then I basically constructed and then I proved that the construction is what it requires. This is basically a typical way of solving the problems. You analyze it, you construct whatever is necessary, and then you prove that whatever you have constructed is right. Inscribe a rhombus with a given acute angle into a given triangle such that one side of the rhombus goes along the side of the triangle and two endpoints on opposite side of rhombus lie on two other sides. So basically this is the rhombus which you would like to build. a, b, c, c would be here, and this would be k, l, m, n. So what I know, I know that k, l, m, n is a rhombus and I also know that I am given this angle, the acute angle of the rhombus. And obviously, what am I saying? This is c, I don't know why I put d. So I have a triangle a, b, c as given and I have this angle and I also know that it's supposed to be a rhombus which means all sides are supposed to be equal. Okay, obviously it's not easy to create it immediately but however, if I have any other rhombus which, let me just do it this way, I pick any point here, let's say k' and I make the line here to n' in such a way that this is a given angle. So now I have the lengths k' and n' and I am using it to basically find my m' which is equal in length since it's a rhombus and I am building the rhombus this way and this would be l'. So as you see, k', l', m' and n' is a rhombus which is similar to klmn which we have to construct. Now, I can obviously construct k', l' and n' because I just picked the point k' and then used the angle. Now, construction is actually obvious right now after I have constructed any rhombus with this acute angle with one side lying on AC and one particular vertex lying on AB. Now, if I can stretch it along this line so I'm connecting a to l' and continue until it intersects with BC and that would be the point l. Now, this is the construction. So that's how I came up with this particular construction methodology. Pick the point, draw the line with this angle which is given and then using the fact that this is a rhombus I found the point m' and then l' which completes this particular rhombus. Then I connect a with l' until it intersects with BC. Now, all I have to do is that the resulting point l from which I can obviously put one line parallel to k' and n' and another parallel to AC that that particular klmn would be the rhombus which I need. Well, and it obviously follows from the fact that all the components here are similar to each other. A triangle let's say ak'l' is similar to akl. Why? Well, primarily because they have a common angle and since this is parallel to this one this angle is also equal. So ak'l' is similar to akl. Now, with the same similarity I can say that al'm' is similar to alm because again these are parallel so angles are the same and there is one common angle. So all these triangles are proportional to the ratio of al' to al which means if they used to be whatever the elements used to be equal will remain equal. Like for instance this line, this particular kl related to k'l' as al' to al'. But same thing can be said about lm to l'm' it's also in the same ratio and since these two are equal, these two are equal. So this is rhombus. Well, that's basically enough. I mean we can do exactly the same with two other sides. So I don't want to go into the trivial details but I basically understand that it's enough to build a small rhombus of required proportions and then stretch it such that the fourth vertex will coincide with bc. Okay, construct triangle by two angles and reduce of circumscribed circle. Okay, two angles and reduce of circumscribed circle. If I have two angles I can always construct a triangle which is similar to the given one, right? So I pick any base and construct a triangle similar to the one which is required. I'm actually constructing right now without analysis because it's kind of obvious. Then I find the center and circumscribed a circle around this triangle. So is it the one which is required a triangle? No, it's not. It's similar to the one which is required and the difference is that it has this radius. Now, there is a radius which is given to me. Construct triangle by two angles and a radius of circumscribed circle. So this is a circle circumscribed over a triangle which is similar to ours. It's not ours. Our radius is different. It's not this one. It's a different one. Whatever the radius is. So I take this radius. I use the same center and just continue each radius so that the new points which I have are all on this distance from the same center. So basically what I'm doing is I'm stretching my picture from this radius to this radius and these will be the new points. This is my triangle which I really need. Why? Well, obviously the fact that I'm stretching by the same factor triangles, let's say a prime, b prime, o is stretched into a, b, o and these two lines used to be radiuses of whatever the triangle I built and this is the one which I need so the ratio is exactly the same and there is an angle which means a prime, b prime, o is similar to a, b, o which means all elements are stretched by the same factor including a prime, b prime is stretched to this one. Similarly in this case b prime, o, c prime is similar to b, o, c and a prime, o, c prime is similar to a, o, c they are all similar to each other. Lines are parallel obviously because when I'm scaling segment a prime, b prime is parallel to a, b which means all angles are preserved all angles are preserved since all lines are shifted parallel to themselves and the distance from o, a to o, b and o, c exactly the ones which I need so o is still a center of circumscribing so that's basically the construction as you see every problem in this series I cannot construct directly the figure which I need I construct something else which is similar and then stretching or scaling rather the picture to the proper size construct a triangle by angle ratio between altitude from this angle and the opposite side this altitude falls on and a median to another side wow that's too many so again there is a triangle we have an angle ratio between altitude b, h, o, c and a median construct a triangle by an angle ratio between altitude from this angle and opposite side this altitude falls on and median to another side okay it's not this median it's different that's my telephone but it's just waiting to finish okay now angle, angle, altitude okay so let's think about this okay angle, ratio okay here's how we can do let's speak ac as any base whatever we want so since we have ratio we will put ac a prime, c prime equals to 1 now that's number 1 number 2 we know this angle which means I can build a circle around it which is a locus of points from which this particular segment would be let me just draw a better picture let's start with a circle okay so this is I started with this a, a prime, c prime which is equal to 1 then I draw a circle with which is a locus of points from which a prime, c prime is viewed at this particular angle now that's actually easy just in case you don't remember this is an inscribed angle so it's half the size of a central angle so if I have this angle I basically have this one which is twice as big and this is an isosceles triangle so I know these angles as well so I can build o, c a, a prime, o, c prime by this particular base which is equal to 1 and these two angles which are half of 180 minus this one half of 180 minus double this angle so I build the center and then I build the circle around the center radius o, a prime or f, o, c prime now I know this ratio and I know that a prime, c prime is equal to 1 which means b prime, b prime h prime b prime, h prime is equal to this ratio ratio which is given to me so how do I do it? from a, c, a prime, c prime and the distance equal to b to this ratio actually I draw a line and this is my real b prime so this is an angle it's the same angle as this one because this is the circle it's the locus of all points where this angle is the same but now my h prime would be here now I know that this triangle a prime, b prime, c prime is exactly what I need except one particular case it has the proper ratio between b prime, h prime and a prime, c prime it has a proper angle at the top but it does not have the median whatever we need now what should I do? well basically I should construct the median here that would be my median a prime, m prime basically stretch a prime, m prime to this particular length and after I stretch it let's say everything else should be just drawn parallel and I will get what I want now let me just summarize how I constructed before we go into the details so I take any segment a prime, c prime of the length not any at the length one then I'm building a circle around it so that this is a locus of points from which angle would be the same now how can I find the point of a prime? I'm taking this ratio and have the line on this side on this distance this would be my b prime so bh prime over ac prime is equal to my ratio angle is given and all I have to do is draw this median and to m prime and then expand it to whatever am is given and then I build parallel lines here and these are just continuation now obviously since this this is b and this is c since I built bc parallel to b prime, c prime the triangles abc and ab prime, c prime are similar the angle because it's parallel is the same and the ratio between the altitude and this is exactly the same between the ratio as the ratio between the big altitude and the big base because of similarity of triangles so that's why my abc is the one which we need to construct and again we have built a smaller or a different rather triangle which is similar to the one which I need and then we scale it using the only linear dimension we have linear dimension is the median so I ignore the linear dimension of this triangle which I have to construct and just use the rest which is angle and the ratio between altitude and the base to construct a similar triangle and then just scale ok so that's the same basically as all other problems and they have one left given an angle and point inside it find a point on one of its side equidistant from this point and another side so this is an angle which is given this is the point which is given we have to find an equidistant from side ab along the perpendicular of course the distance between the point and the line and mx so basically we have to find m such that mp is equal to mx well exactly the same thing let's just have any other point pick any one of them draw the perpendicular this will be p' connect since mx and mp are the same size this is a circle with a center m which is tangent to this line and intersects this one so here from m' we also make a tangent circle and that's where my ax is intersecting this is x' intersecting this circle so basically now it's obvious that ax' m' triangle is similar to axm so this is analysis now how to construct well we don't know point m so all we know is let me start from the beginning so now the construction itself we have a point x and what I'm doing is I pick any point m' construct a circle around it in such a way that it's tangent to this line connect x with a and now just do a parallel one xm is parallel to x' m' since it's parallel then these angles are corresponding with two parallels and ax as a transfer so this is the common angle these triangles ax' m' and axm so triangles are similar ax' m' and axm and that means that the ratio between xm and x' m' is the same as xa to x' a now what we can do is basically say that if I will draw this one and make this circle obviously mp would be similar mpa would be similar to m' p' and mp would be in ratio with m' p' as am to am' and these in turn because of those triangles similarity are exactly the same as ratio between this and this and that's basically enough mp relates to m' p' as am to am' that's from similarity of these triangles now and this is equal to mx over m' x' from similarity of these triangles mx' is equal to m' x' x' is equal to m' p' because these are ranges from which we have that mx and mp are equal to each other mx and mp are equal to each other and that proves that we have constructed correctly I hope it wasn't really very difficult you just have to understand that there is always one underlying principle in all these problems you just try to construct something similar to whatever you have to construct and then use the proper scaling to get to the object of your choice alright that's it for today now unizor.com as I was saying before contains all the information parents and teachers are encouraged to use this site to individually control the educational process of their students and thank you very much for your attention that's it for today


It's time to have a little holiday fun here in Monet Cafe. I'm artist Susan Jenkins, and today we're painting these cute little snowmen. These should be fun if you've got family in town for the holidays, kids or grandkids, and I've got some cute little sketches. You're feel free to use these. I'm also going to be providing attachments on my Patreon page, so I'll put a link up here. If you'd like to become a patron of mine, that would be awesome. I'll have these images there for you to use. Now this is just a sped up version, but in this video I will be sharing with you the materials that I've used and just some voiceover instruction to perhaps make it a little more simple. Now I will be sharing a more simplified tutorial on some Christmas trees after I share this video. Okay, so time to get started. Here are the sketches again. I wanted to give credit to artist Angela Anderson. She has a YouTube channel and I saw some sketches on her page where she did some oil paintings of snowmen, so she inspired me. Just wanted to give her a little credit. So I actually did four paintings in one session, two snowmen and two Christmas trees. Like I said, I'm going to be sharing in another video that's actually even more simplified or basic than this one. I think it should be good for all ages. But if you'd like to join along with me, what you'll need is some watercolor paper. Again, I did four at the same time, so I took a large piece of watercolor paper and I divided it off with artist's tape so that each opening or each space was five inches by seven inches. And the reason I use that size is because this is a common size for greeting cards and you can find envelopes to fit these. Now, while I will be using pastel in this, a lot of times you think, oh pastel, that's so vulnerable you can't package it up and send it. You actually can. I'll share at the end of this video how they make these little clear bags that you could put these in if you wanted to protect it and send it as a little greeting card and put a little note in it or whatever, make it a real personal gift. The other option would be to get a good photo of it and make a reproduction of it, print it out and send some prints of your little design as greeting cards. So whatever your purposes or your idea of what you're going to do, I just hope this is a fun project. Again, lots of family in town during the holidays and taking some time to just have some fun, get creative is always a good idea. And I purposely kept these sketches very basic because this is just a fun little design and we don't need to get too complicated or have an in-depth advanced painting tutorial here. So they're just fun and happy. I apologize that my pencil, I have a really light pencil here that I'm using and I won't even erase this when I go to add the watercolor and the pastel because it's really not going to show up that much. But you're just basically going to get your five by seven piece of watercolor paper and it is a good idea sometimes to tape it down. It can warp with the water. So if you could tape the edges down, give yourself a little, in mine I gave myself a little border. You'll see at the end the full card at the end is five by seven. But I came in a little bit on the edges about an eighth of an inch around each edge so that I have a nice clean white border all the way around. Here you can sort of see the tape where I've taped it off on my paper. I apologize, the paper's white so it's hard to see. The other supplies that you'll need of course will be some water and clean water and some watercolor brushes. I like to use a wide brush. All I'm doing for this is an underpainting with watercolor. It just kind of sets the mood. I'm using a set of Arteza. They send me these supplies and they're so nice and I like to give them credit when I make a video and I made a little color chart of all the colors on some watercolor paper. I have another video where I show how I do this. It's always a good idea because the colors look different on the watercolor paper than they do in the little pans. So this is their little 36 set. I like it. It's a nice little travel set too.  It's neat. It's a little brush where you can actually open up the back side of it. I think I do it here and put some water in it. So if you're just kind of on the go, I always like to have more water than I can just put in the end of this brush. But it's a neat way to have some water in your pen. The pen works, I mean the watercolor brush I should say works really great. It also has this neat little ring on the back. So if you want to hold it like a palette of paint or colors, you can hold it like that and it works great. The little pans inside are also removable so you could change the colors. You can rearrange them, move them around, whatever. So this is a great set but use what you have. It doesn't have to be a professional set. These are some other sets I've gotten over the years. This is a Windsor Newton set. It's going to be very dirty. This one's also very hard to open but I don't think I've cleaned any of this out. The same concept. You've got your little individual areas where you can mix your watercolor and kind of have it as a little holding area. This is another little one that you can add your own paints to. Oh yeah, this one's really messy. I used this for a painting not that long ago. It has some great colors in it. Same thing with this one. It's got a little hole in it. I filled it up with so much watercolor that I don't use it that way at all. My hand would just get so messy. Also, too, if you're very blessed to have some wonderful friends, this is a sweet, sweet, dear friend on my Monet Cafe Art Group who found me, I guess, through this YouTube channel. Got on the art group. Her name's Marisa and she sent me this little customized set of watercolor.  Again, she did the same thing which is take a piece of watercolor paper and go ahead and put all your colors down so you can see them. Okay, I know it's time to get started with this, but I thought that might be some helpful little watercolor info. Again, if you've got kids or grandkids in town, you can even use the little school watercolor kits or whatever. I want this to be fun, but if you have professional supplies, by all means, use those as well. Now that the sketch is done, I am just applying water with a large, flat brush. This is what's going to be called a wet-on-wet underpainting. I just wanted a mood of blue and I think I used some purples. Yeah, and kind of sometimes the messier the better with this because I like it when colors bleed into each other because if you overwork this with the brush, they all become one color. They mix on the paper. So I like it to have that variety. So notice I'm not overblending it. Now I'm just blowing it dry. You don't have to do this. You could just wait, but I wasn't that patient.  I don't want to get so messy that I go into the other side on the right where I'm going to do another painting, but now it's almost dry, pretty much dry here, and it's time to get started with the pastel. Now, if you know much about pastel painting, you know it doesn't stick real well to watercolor paper. So here's the little trick. This is Liquitex Clear Gesso. If you've watched my videos much, this is a really practical way to make an inexpensive paper into a pastel surface. It has little bits of grit in it, so it gives it that little sanded surface when it's dry. And I'm brushing it again with the large brush, just getting kind of a smooth application on it. And once it's dry, it's ready for pastel. Here are some pastels I've chosen. I basically just chose a lot of kind of neutrals and cool colors for the snow, and I wanted some little bit of bold colors that pop for the presence.  So you can kind of pay attention to some of the colors I'm using while I'm working here. Now, I added this little tree in the background, and I'm purposely keeping it. I'm not pressing down real hard here. This is supposed to look like it's far away. And basically, for evergreens, they're almost kind of like zig-zaggy marks that go from the top down, that go smaller to larger. So it's kind of a neat little simple way to do an evergreen tree. But I'm keeping kind of a light touch here, but I'm going ahead and getting in his little hat. You may have noticed that I put down a little bit of light, a lighter blue on top of that purple in the background, just to kind of push that background back and lighten it up a little bit. And I am giving a little bit of a shadowy color kind of down on the ground. I am going to add lighter colors on top of that, but it kind of needed something as a base, you know, to put on top of it. Now, I'm just going to continue to work here so you guys can kind of pay attention to the color choices I'm using. But you can choose whatever color palette you would like. Keep in mind, though, we have a tendency to want to paint the whole snowman just white. And just keep in mind that it's like any other three-dimensional objects. It's going to have shadows. So I'm making my light source where the sun or the clouds would be shining on him. The brighter areas are shining on his, to my left in this. And the back sides are going to be more of the shadowy areas, just like if you were drawing or painting an apple. There's one side, you know, where's the light coming from? And the other side will be in the shadow. So I'm giving kind of some cooler blues and purples on the shadow side and the lighter values on the left side, where the sun would be coming from. And also keep in mind that, again, even though there's a lot of white in snow and lighter, what we think of as white and light values, it still needs something dark to put it on. So that's why even like this little tree, I've got a little bit of a, I put down the darker value first to kind of emulate the shadows and the depth of the tree. And then I add the more of the evergreen colors kind of on top. I even added a little bit of light colors to kind of emulate snow that's kind of fallen on the branches there. So again, keep in mind that you've got to have something dark down in areas to put your, your light's not going to look light if you don't have something to put it on. I did keep the left side of the snowman where the lightest values are pretty light. I noticed I didn't put anything dark down first for that. But for the other areas, I typically, even with this scarf, I put down a darker kind of burgundy red. And then I added the little highlights on top of it. Pastel painting, I believe acrylic and oil painting, they have the same general idea. You work dark to light or darker values to lighter values. Watercolor painting, I believe you typically work light to dark because once you darken it up, you can't get that light back, that luminosity of watercolor paper. So anyway, working on this, having fun, doing the little arms. So just enjoy this part.  Now I'm wrapping up this cute little snowman. And I even added a little snow in the background. And one thing about snow, you want to keep it really a lot of variety in it. We have a tendency to make dots that all are equidistant in part in the same size. So, you know, just get real random with it. Now just made some little very simple bows on the package. And this was a really fun little guy. I liked him. So, and this is kind of how it looks again with the little edge after I tore off or peeled off the tape. Okay, it's time to get started on the next one. Same idea, a general sketch, a five by seven piece of watercolor paper.  This one, I'm going to have a little bit of a different color palette. I decided to go, I'm going to speed this up even more with the sketch to talk about the color palette more. Okay, so same idea. Unfortunately, I didn't change my water. You see, that's a little gray, but it didn't really matter for these purposes. I'm going to use a different color palette for the watercolor underpainting instead of the blues and the purples. I'm using magenta's bright pinks and oranges. Now, that might seem an unusual color for a snow scene that's usually very cool, but it makes, if you guys watch my channel, you know, I love warm underpainting. You use warmer colors for an underpainting and it made a nice warm palette underneath to lay down the pastels on. I still chose, you know, obviously colors and values that would represent snow, but I changed it up a little bit with this one and I'll talk about the pastel selections afterwards. Again, I'm keeping this really loose. I did keep the snowman and the little easel a little bit more of the orange tone with the pinks a little bit more of the background. All right, blowing this one dry. And of course, after this is done is when we have to apply the clear liquid gesso. I'll make a quick comment here. I like to point this out that why do we use clear gesso when doing this? Well, one, we need it to be clear. We need it to show through. If you have an underpainting underneath, if you use regular gesso, it's just going to cover up because it's not transparent like this. Another reason is clear gesso is the one that has the little grit in it, almost like sand that gives you the ability to put pastels down on top of it. The regular gesso does not. I don't know why, but that's just the way it is. All right, so you saw my little pastel collection or selection. I'm using a lot of teal colors. I'm making the snow instead of more purple and blue in the shadows. I'm making it more leaning a little more towards warmer blues, which would be teal in color. I decided to add some little evergreen trees in the background. Again, very simple, just kind of some zigzag marks. Lower marks are wider, upper marks are more narrow. Adding in some sky in between the trees, I'm using a pretty neat little bluish color in the background there. It gives a really neat color on top of that magenta, on top of that pink. Now, here's another one of those teal colors that I like, adding a little more of this blue in between the trees and even in the snow at the bottom. I think I add some of that in a minute. But see the palette of the teal that I'm using now? And you'll see when I add the shadows to the snowman. Yeah, there we go. I'm using more of the green and teal family rather than purples and blues like I did in the other one. And it's the same concept that on this one, though, I'm having the light come from the right side rather than the left side. So the shadows on the snowman are going to be on the left side. And the brighter parts of the snowman are going to be on the right side. I actually used for my, you'll see when I start doing the light colors, the white, I guess you call it on the snowman. I use a warmer white, more of a yellowy white instead. But also notice this mid snowman has two sections, a head and a body, whereas the other one had three. But see, I put down a lighter teal and now, remember, work dark to light. Now I'm putting down that more yellowy golden white rather than the colder looking white that was in these other snowman. So again, two kind of different color palettes for these, but some of the same general concepts. Also to a quick note, now I'm just doing like that piece of paper on that easel. A quick note is that this watercolor paper, I'm using the rough side. And so you get a little bit of texture, which I like. And also too, with the clear gesso, keep your pressure not too awfully hard because you don't get as much layering ability when you work on watercolor paper as you would if you're working on some of the other manufactured pastel surfaces. Now for the cute little hat, which is kind of like a little artist's beret, a beret, is that what it's called? A beanie.  And I will add the lighter values on top. Again, that gives it some depth and some shadow underneath. If I just put the lighter color down first, it would be very flat. Now this is a little bit of a lighter purple here that I'm using for the sash. And I add some little hot pink stripes to it. I know you can't see it all that great here, but just some cute little stripes to the hat and the scarf kind of made it a little bit more fun. I'll continue to work on this one a little more, give you some more holiday music. Let me see, I'll try to pick a different song this time. This might even be fun just to play in the background while art is happening with some nice holiday music. All right, here's some holiday tunes for your listening pleasure. As I'm finishing this up, I wanted to refer back to what I said at the beginning of the video that if you wanted to ship these as original paintings, a company called ClearBags.com does provide these nice little clear bags that you literally can put your artwork down in very safely. It has an adhesive flap and a little seal on it. And you can order them in different sizes. But in the description of this video, I'll provide a link for the five by seven size in case you wanted to get some of these bags yourself. They're pretty affordable. Now, wasn't that fun? I've just got to add some legs to this easel and I've finished up this little guy. So here he is all trimmed. The tape has been taken off and it's been cut. And I wanted to show you real quick here how when I pull the tape off, I do it very slowly too if you do this because you don't want to pull up the watercolor paper. Also, I have a big cutter that I use to cut the edges and also too as a note, I have this little, I wish I had it in the video, this little part that comes down to hold the paper. If you're using pastel and cutting, make sure you wipe that off each time. It can come down and contaminate your painting. So I'm always cleaning that little bar that's up on my cutter.  Once I got done, this was really neat. Each one didn't take that long. And it came out with four neat little paintings that you could either send as originals or get a good photo reproduction and print your own original green cards to send to friends and family. And also keep an eye out for the upcoming video with a really simple, fun artistic project you can do during the holidays. And if you love these videos, I pray you'll keep coming back. Please subscribe to my channel, like me on Instagram, find our art group on Facebook, Momay Cafe Art Group, and also consider joining me on my Patreon page, where for $5 a month you can continue to bring these art lessons to a hungry artistic world. Happy painting!


I just finished editing my first video back on YouTube and my god I disassociated so many times that I made a separate video of all the times I disassociated and the reason I did that is because I want to do a video where I show what it's like when I disassociate so that's what this video is I just wanted to do a more in intro.


The sad part about it was that she was on her way to help flood victims in West Virginia. And she came all the way from Maryland. And when she came this way on 119 from Pikeville, she said she thinks she went to sleep. And we just thank God. We know that sometimes in life we're faced with a lot of things we think we're prepared, but then you see this, you can replace brick, you can replace all of that. But I just think that no life was lost.