[User] Please transcribe this text

[Assistant] That centerpiece there, I don't even know the names of all those things, but all you have to know is how they work together.


[User] Please transcribe this text

[Assistant] Of course I just did that for, to explain that. We don't need all those dark things getting in our way.


[User] Please transcribe this text

[Assistant] Remember, we're going to be revising all these shapes constantly.


[User] Please transcribe this text

[Assistant] Because we're gonna be adding to that and you might lose them a little bit sometimes, you have to rescue them again. So, painting is this type of...


[User] Please transcribe this text

[Assistant] Game, you know, hide and seek, catch type of game, you know.


[User] Please transcribe this text

[Assistant] Top part, like people do like that when you're learning. And then the middle one and then the bottom one. These are not lips, okay? What you have to think of is...


[User] Please transcribe this text

[Assistant] Of it as if uhm, this here is kind of like a half a sphere, like a, kind of like half an orange.


[User] Please transcribe this text

[Assistant] Type of shape that goes from the bottom of the nose, let's say it's here, to


[User] Please transcribe this text

[Assistant] To the shin here, and then this area here, is kind of like a...


[User] Please transcribe this text

[Assistant] Semi-circular thing that goes out. We can see it in the skull.


[User] Please transcribe this text

[Assistant] All this has the teeth inside the structure of bones. It's just a circular, uh, shape that goes from side to side here, like that. And then from, uh, top to bottom going like that too.


[User] Please transcribe this text

[Assistant] Once you have that, if you know this here is lighter, because it's closer to us, so all this area here is lighter, and then the lip suddenly goes inward, so if this will be the center,


[User] Please transcribe this text

[Assistant] The division there of the leaves. This is dark just because it goes in, you know. Uhm.


[User] Please transcribe this text

[Assistant] And cast that shadow on there. So just by having these two areas of


[User] Please transcribe this text

[Assistant] of darkness coming in, and in the bottom, you already read the leaves within that form, circular form, and here, it's gonna be darker on the side and darker on the other, just because it's the deepest fold around the edge there, that's why we see them darker.


[User] Please transcribe this text

[Assistant] So always think of that. Don't, don't generalize and look at the difference in thickness because there is a color, uh, the flesh color gets pinker in the lips and you see that boundary and we tend to kind of outline them. But, uh, that's better if you don't do that. If you just understand the structure.


[User] Please transcribe this text

[Assistant] And why, why is, it does what it does.


[User] Please transcribe this text

[Assistant] So the closer we are to the middle of this in between the leaves, the darker it gets because it folds inwardly.


[User] Please transcribe this text

[Assistant] And then the upper part of the lips are just in light, almost like, like the top part.


[User] Please transcribe this text

[Assistant] So there is a difference in color, which is darker in the lips, and also the form, getting away from the light.


[User] Please transcribe this text

[Assistant] And after we understand that, then just to have reference for painting and kind of mark it.


[User] Please transcribe this text

[Assistant] This change of direction in the jaw, right under the ear, it's aligned with the lines of the mouth, with the center of the mouth.


[User] Please transcribe this text

[Assistant] So, it goes around, and that's when I change of direction, and here, change of direction. Remember, you have to go around it, not in a straight posi- way, but around the form. Going down. Here, and down there.


[User] Please transcribe this text

[Assistant] To have a strong drawing, uhm, also remember,


[User] Please transcribe this text

[Assistant] That is a combination between, because too many straight lines will make it lack of movement.


[User] Please transcribe this text

[Assistant] Straight lines are always gives us in nature, uh, that dignity, uh, strength, but it doesn't give us a lot of movement. So to add movement to the painting, you want to think of combining those straight lines that give strength, uh, and combine them with, uh, curves, because curves are always moving.


[User] Please transcribe this text

[Assistant] And, uh, you don't want to have only curves because then you're losing that strength. Everything is kind of curvy and soft and you lose the character.


[User] Please transcribe this text

[Assistant] And a place for movement is the hair, so good. There are things, uh, I just want to mention, there are things that you have to, uh, represent.


[User] Please transcribe this text

[Assistant] And there are things that you imitate. For instance, she's in front of me, and I am imitating her the shape of her eyes.


[User] Please transcribe this text

[Assistant] I'm imitating the nose, I'm imitating the skin, the shape of the head, that's what I'm imitating. I cannot imitate the hair because it keeps moving, so you have to kind of give the impression of hair.


[User] Please transcribe this text

[Assistant] And that is, it's like painting clouds, for instance. You don't copy each cloud or the foliage of leaves on a tree.


[User] Please transcribe this text

[Assistant] The same thing happens in this case with the hair or drapery. Uhm, you just represent them so they feel like hair. So as long as you know the difference, you don't have to follow


[User] Please transcribe this text

[Assistant] The hair, uh, in such a specific way as we follow other things, like the features.


[User] Please transcribe this text

[Assistant] Okay, so one last look, I'm looking around, see, you know, what I need.


[User] Please transcribe this text

[Assistant] Alright, I'm gonna give it a try and go to the next, uh, step.


[User] Please transcribe this text

[Assistant] So, the way I'm gonna do this is, of course, uh, this is, I just drew on the canvas, and just by touching it I can remove the charcoal, especially the raw umber charcoal that I added there.


[User] Please transcribe this text

[Assistant] So what I'm gonna do is get a fixative spray and I'm gonna spray the drawing so that it doesn't move when I paint because if I put paint on top of this as it is now, it's just gonna move the drawing around and it's not gonna be useful. So I'm gonna do that and I'll be back in 10 minutes.


[User] Please transcribe this text

[Assistant] And now, the drawing has been fixed to the canvas, so you see there's no more drawing,


[User] Please transcribe this text

[Assistant] You know, particles floating around, they're all in place. And I'm ready to go and paint my first layer of paint.


[User] Please transcribe this text

[Assistant] Now, this whole system is based on three layers or three steps or a process of painting.


[User] Please transcribe this text

[Assistant] Now it doesn't mean that you cannot go a fourth day and paint on it, but, or you cannot divide one, uhm, layer into two days or anything like that, but I like personally to divide it


[User] Please transcribe this text

[Assistant] Into a day. So a day of work, uhm, will get me done with one, uh, of the stages. I let that dry and then do the next one and the next one. The, the names I got it from my, when I started at the Angel Academy. The first layer is called the dead coloring stage.


[User] Please transcribe this text

[Assistant] In which, uh, you put the local color of, of the, of the...


[User] Please transcribe this text

[Assistant] Things you see in front of you, but you don't render the volume, you don't do details, you're just placing colors, uh, next to each other and making sure that the value is pretty close but very general. But before all that, the palette is our instrument.


[User] Please transcribe this text

[Assistant] Think of it as a guitar. You can get the best guitar player in the world.


[User] Please transcribe this text

[Assistant] Give him an out of tune guitar and he's not gonna be able to play.


[User] Please transcribe this text

[Assistant] Uh, at least until he learns how to do it, but what I'm getting at is that even if you know how to control


[User] Please transcribe this text

[Assistant] The instrument, if it's not organized to what you want to do with it, it can be hard to manage and hard to control.


[User] Please transcribe this text

[Assistant] So, and we can see that, for instance, we know how, you know, the palette of Sargent and the palette of Rembrandt and the palette of this and that. If you don't have them to really explain how they use that palette, it's pretty useless to us.


[User] Please transcribe this text

[Assistant] So thankfully, I'm here to explain how I set my palette, my tool, and it has to be organized and everything has to be there for a purpose, for a reason. In this case, I have white on one end and black on the other side.


[User] Please transcribe this text

[Assistant] That means that this is my darkest grey, because black is a grey, it's the darkest grey we have, and white is the lightest grey we have. So we have the two, these, uh, extremes greys right opposite to each other, also because


[User] Please transcribe this text

[Assistant] You wanna be, uhm, really careful going at them, and you, so you're consciously gonna go pick them up, so I just want them to be opposite to each other. The white,


[User] Please transcribe this text

[Assistant] It's, uh, it's gonna be more useful, so I have it closer to me, so I use it most of the time instead of going back and getting the white. The black is gonna be less used, uh, in this case maybe if I do a background then I'm gonna use another black, but in general when mixing flesh, uh, tones, the black is not the main color there. So, after


[User] Please transcribe this text

[Assistant] The white, this is just titanium white, fast drying. Here is the tube.


[User] Please transcribe this text

[Assistant] I use a Winsor & Newton Griffin Arcade for the reason that I want it to be dry by tomorrow. So I'm using a fast drying titanium white.


[User] Please transcribe this text

[Assistant] Uh, that is the name of the color. Don't ask me, yeah, but what's the name of that light red? That is the name of the color. It's made by Winsor and Newton.


[User] Please transcribe this text

[Assistant] And it's called Light Red, as you can see here. And it's kind of like a...


[User] Please transcribe this text

[Assistant] Color for the lights. That is the base color for the flesh mixed with the white.


[User] Please transcribe this text

[Assistant] Next to that I have Yellow Ochre Pell. Now that yellow is also from Windsor and Newton. And it's called Yellow Ochre Pell, the name of the color.


[User] Please transcribe this text

[Assistant] Raw umber is a type of yellow. I don't want


[User] Please transcribe this text

[Assistant] And this brown, it's a yellowish brown. How do we know that? Well, if you mix blue to it, you get a greenish color. The only color you can get green is by mixing, uh, yellow and blue. So those two getting green, then you know that one of them, if it was not the blue, it was the yellow.


[User] Please transcribe this text

[Assistant] Now what you see in the middle here are pre-mixed.


[User] Please transcribe this text

[Assistant] Uh, our premix of those colors. I'm gonna explain now how to get these colors.


[User] Please transcribe this text

[Assistant] Flesh is always different. There are different complexions. These mixtures are based on the purpose and what you're doing at that moment with the flesh and with the portrait. So it depends on the skin of the person. So this is not really scientifically, you know, exact.


[User] Please transcribe this text

[Assistant] And especially at this layer, when I'm gonna put just an, uh, an underpainting for, as a setup, so I can paint tomorrow.


[User] Please transcribe this text

[Assistant] But I wanted to say that I set my palette, my instrument here, I set it to what I'm gonna be working on, on this particular day or sitting.


[User] Please transcribe this text

[Assistant] I don't want to put here blues, greens, the reason is that remember when I started drawing it was very simple, circle, mark, lines, and I developed from simple to complex the drawing.


[User] Please transcribe this text

[Assistant] Well, I wanna do the same, I wanna have the same attitude with painting.


[User] Please transcribe this text

[Assistant] I have the colors I need. I don't need greens and blues at the moment because this, uh, stage is just to have a value, uh, and a general local color for the painting.


[User] Please transcribe this text

[Assistant] Tempt you to use them and then you're gonna have a rainbow kind of painting under it. It's fine if you want to do it, just make sure that you do it for a purpose and that it works.


[User] Please transcribe this text

[Assistant] For me, I rather control myself, keep myself a little bit, uh, you know, safe by not using so many colors. So all I need is, uh, one, two, three, four, five, six colors including those, uh, two grays, black and white. So pretty much the real colors are four here in between them.


[User] Please transcribe this text

[Assistant] The order in which I place them is, uh, is on purpose. We get the whites, which is the first one here, and add it here. We get a little bit of the light red, and mix it into it.


[User] Please transcribe this text

[Assistant] And you see, this light red with that white gives us a very nice kind of general flesh color.


[User] Please transcribe this text

[Assistant] So, I'm just gonna get a little bit of yellow and add it to it.


[User] Please transcribe this text

[Assistant] Okay, that way I have another variation. This one is getting darker. This one is just a lighter version of it. So I'm gonna leave it here. I'm actually gonna show you how I got the second one.


[User] Please transcribe this text

[Assistant] So I get white plus light red, which is the base color, and a little bit of yellow.


[User] Please transcribe this text

[Assistant] And you see, if you get that to this value, it's too orangey, too high chroma. You gotta be careful because you don't want your flesh to be too high chroma. And with all the colors available to us in art stores, uhm,


[User] Please transcribe this text

[Assistant] Our supply source is too much. We can easily be too bright and too, uhm, chromatic. You wanna make sure you tone that down. So what I'm gonna do is add a little bit more white.


[User] Please transcribe this text

[Assistant] And then we kind of have that flesh color. Here is a little bit chromatic too.


[User] Please transcribe this text

[Assistant] Also, if you, if you see that, for instance, this is, this came up grayer, and this came up a little bit high chroma.


[User] Please transcribe this text

[Assistant] Two ways to tone that down, either by adding, uh, raw umber, which is, uh, kind of darker gray or yellow, or you can get


[User] Please transcribe this text

[Assistant] And premix, always, if you need to grey it down, you wanna do it with a grey, with black and white. It's better if you mix a grey to that value.


[User] Please transcribe this text

[Assistant] Before you add it. You don't want to bring the black directly into it. Because you really have a little control how it's going to affect it. So first, you make


[User] Please transcribe this text

[Assistant] A grey, kind of similar in value to what you want, and just add a little bit to it.


[User] Please transcribe this text

[Assistant] It's just try paint, this is not paint, just so it's not confusing. I am mixing these colors that you see here, and premixing them. Normally in my studio, I premix all the useful colors into tubes, such as, for instance, this.


[User] Please transcribe this text

[Assistant] Uhm, so this is just an empty tube that comes, uhm, empty and I, and I fill it up with a color and I just name that one too and put a yellow kind of mark on it so I know where it belongs and I have


[User] Please transcribe this text

[Assistant] What I, so, these things that you see here, uhm, maybe they're difficult to see because my palette is just dirty, but I'm gonna, what I'm doing now is, uhm, going over how I get these mixtures.


[User] Please transcribe this text

[Assistant] And in art, there's nothing, uh, exact about it or perfect about it. So what I'm showing you is the principles of how I pre-mix the colors. You don't want to have too high chroma, uh, flesh. You don't want to have really gray and low chroma flesh. So what I'm showing you is how to balance them out.


[User] Please transcribe this text

[Assistant] A little bit. Uh, if I had, for instance, these colors here and I just pre-mixed a lighter one, I might use it for lighter areas. So it depends on what you're painting at that time. I'm just showing you how I mix and how I come to get my, my, my, uh, tints for flesh.


[User] Please transcribe this text

[Assistant] So let's go on. I've done two. Now, I can either


[User] Please transcribe this text

[Assistant] Keep going this hue, which is this color, and keep going darker.


[User] Please transcribe this text

[Assistant] As they get darker, because in flesh you want to make sure that the brightest high chromas are towards the center of the form.


[User] Please transcribe this text

[Assistant] It depends on the situation, uh, back in the day, that was most of how they did it, because the floors were, uh, wood, wooden floors, and they would, uh, kind of reflect this warmness into the shadow.


[User] Please transcribe this text

[Assistant] But nowadays we have very, a lot of white and pale floors and that can influence the shadow color. The most important thing is for you to look at the sitter


[User] Please transcribe this text

[Assistant] And, and really observe the, the subtleties of colors and temperature within the skin. So I'm just going to show you how I mix them with these simple colors here and you can try them at home.


[User] Please transcribe this text

[Assistant] Okay, so next, I'm gonna get the same base, white, and I already have, uh, my palette knife a little dirty, so, and I add


[User] Please transcribe this text

[Assistant] The base color for the complexion, you want to have two alternatives to that. You want to have a low chroma, grayish, it can be leaning towards green or blue, and you want to have a high chroma, a pink or a purpley.


[User] Please transcribe this text

[Assistant] Pink, orangey flesh color, whatever you have. And then they're gonna be areas of just cooler and areas of pink areas. And that's pretty much what I'm setting up here.


[User] Please transcribe this text

[Assistant] So you see, this one is a little bit, uh,


[User] Please transcribe this text

[Assistant] Warmer, and this is colder. And, uh, oh, cooler, cooler.


[User] Please transcribe this text

[Assistant] You want to have kind of similar, uh, values, so when you put them next to each other, they're not so different in values. Most of the time, the color is a little darker just because it's going away from the light. And for the shadows,


[User] Please transcribe this text

[Assistant] And that could be a nice color for the general warmth of the shadows. If you want, you can add lighter by adding yellow to it.


[User] Please transcribe this text

[Assistant] So everything is, uhm, once you know the principles, you can change it back and forth. And I'm, right now I'm gonna be very simple about this. They don't have to be very specific or exact. The more, the next days we're gonna be a little bit more, uh, attentive, uh, more specific about


[User] Please transcribe this text

[Assistant] What we miss to be more like the model. But for now, this is perfectly fine for what we need to do.


[User] Please transcribe this text

[Assistant] Okay, I'm gonna talk about, uhm, a little bit about the brushes. I've been asked a couple of times what type of brushes I use, what brand.


[User] Please transcribe this text

[Assistant] Really? I don't know exactly. I go to the store and if I see some brushes for sale, kind of get them, toss them around. If I like them, I just buy them.


[User] Please transcribe this text

[Assistant] You want to have a combination of synthetic versus natural. You want to have a red sable, you want to have a black sable. I have options because you never know when they're going to be handy.


[User] Please transcribe this text

[Assistant] The, what you want to have is different shapes. You want, you want to have round brushes because when you paint, they give a different effect than a flat one. For instance, this one. Or a filbert.


[User] Please transcribe this text

[Assistant] Actually, this one I remember. This is the Winsor & Newton Monarch series.


[User] Please transcribe this text

[Assistant] These are really, really good for all types of the beginning layers and the ending layers. Actually, the whole time in the, when I was at the academy, at the Angel Academy, the only type of brush I used was this monarch, monarch, uh, series. So you can see them here with the brown handles.


[User] Please transcribe this text

[Assistant] But the most important thing is to know how you're gonna use them.


[User] Please transcribe this text

[Assistant] I know you can probably do it with a smaller one too and go like that, like, if you were drawing, but...


[User] Please transcribe this text

[Assistant] All this is going to be covered and as a base I just want to go effective and quicker. So I'm going to get my biggest brother brushes and use them.


[User] Please transcribe this text

[Assistant] So, you wanna have a different varieties of brushes, and for this stage, you don't need many because you're gonna be painting over it, but you want the biggest brush that will do the job.


[User] Please transcribe this text

[Assistant] Uh, and uhm, and this is what I'll be using today. So don't ask me for specific brands or whatever because


[User] Please transcribe this text

[Assistant] The, you know, the cheaper and the better the better. Even though I have some good expensive brushes, but I just leave them for the last layers when I'm really gonna render and use the finesse of the brush to really render texture correctly. So, but for now, let's just go into it. About mediums.


[User] Please transcribe this text

[Assistant] Right now I have the, I'm just using the paint how it came from the tube. I'm not going to use any medium, I'm just going to use a little bit of


[User] Please transcribe this text

[Assistant] Uh, turpentine, if I, if I need to make it more, uhm, liquidy, uh, if I wanted to run more, which I will in the background and stuff like that, but I want the body of the paint to be strong at the beginning, so I don't want to put too much medium into it.


[User] Please transcribe this text

[Assistant] And since I'm using a fast drying white and it has been included in all these tints, it's pretty much gonna be dry by tomorrow. One thing that I recommend that you should do is first look at the situation here.


[User] Please transcribe this text

[Assistant] I have a pretty light, you know, maybe number three value, uhm, camping toura. And if I start with the lights.


[User] Please transcribe this text

[Assistant] It's too similar to the value of the canvas. So it's more effective and efficient if you go


[User] Please transcribe this text

[Assistant] And find your darks first. Simplify those families. Separate them all the time. The lights from the darks. And make sure they're clear and the note is, uh, is, uh, clear enough so that you don't put subtleties inside.


[User] Please transcribe this text

[Assistant] Think of a value at this stage as a clean white wall. If you make a little, uhm,


[User] Please transcribe this text

[Assistant] If you open a hole and just make a mark on a white wall, you will see it from far away. It's going to be obvious. But if you have a space or a wall full of different brush strokes and stuff, and you put that same little, uh,


[User] Please transcribe this text

[Assistant] You know, change or hole is gonna be hard to find.


[User] Please transcribe this text

[Assistant] That is that we're gonna appreciate more if it's clean, if the notes and the values are clean, we're gonna appreciate changes more than if we have a messy kind of tonality into it. But first I'm gonna go with the background.


[User] Please transcribe this text

[Assistant] And just make sure that I have that. I have my settings really kind of darkish in the background. It's not the darkest thing. Her hair in shadow will be the darkest thing.


[User] Please transcribe this text

[Assistant] Now, what I'm, uh, getting a little bit of when I go to the side here, I'm just getting a little bit of turpentine.


[User] Please transcribe this text

[Assistant] To dilute the paint a little bit more so it runs easier. I'm not using a secret medium that I'm not gonna tell you.


[User] Please transcribe this text

[Assistant] People always think, I mean, a lot, a lot of, I used to think that, uhm, the secrets were in the medium and, and the brushes and the paint, but it's really the principles, uh, of how you use those, uhm, elements that make the difference.


[User] Please transcribe this text

[Assistant] By the way, I'm using a fast-drying Ivory Black. Ivory Black is a very slow dryer, as you may know. Just like the Titanium White.


[User] Please transcribe this text

[Assistant] And they can take forever to dry. But I love the transparency of Ivory Black instead of Mars Black, which dries faster, but is too opaque. And for these early stages, I just want something more transparent.


[User] Please transcribe this text

[Assistant] Especially in the background, especially black. So I'm just using a fast drawing.


[User] Please transcribe this text

[Assistant] I'll keep Windsor & Newton Black so that it be dry by tomorrow.


[User] Please transcribe this text

[Assistant] Again, what I'm doing here is not the end result, this is just


[User] Please transcribe this text

[Assistant] Kind of like a set up to paint over uhm, tomorrow.


[User] Please transcribe this text

[Assistant] I'll probably warm it up later because black tends to be a little bit kind of flat and


[User] Please transcribe this text

[Assistant] Lacking life, so I probably add a little bit of warmth to it, uhm, just to have some variety in the background.


[User] Please transcribe this text

[Assistant] In, uh, you know, in my, the scene in front of me, the background is a little lighter.


[User] Please transcribe this text

[Assistant] I don't want that hair to be totally black and opaque now. I'm just gonna use raw umber, purely.


[User] Please transcribe this text

[Assistant] Just paint the hair very general. I don't want to make all these small differences right now. I just want to go and cover stuff so I can get to the fun part which is the flesh.


[User] Please transcribe this text

[Assistant] If you can, if you can see my brush strokes, they're just kind of going around.


[User] Please transcribe this text

[Assistant] You don't want to be stingy with your paint, you want to just put a lot of paint.


[User] Please transcribe this text

[Assistant] If you lose a drawing that you had in the back, you can rescue it later. Hopefully you know how to draw. And you can just go back.


[User] Please transcribe this text

[Assistant] You don't want to be afraid. The thing is that when people don't, are not sure of what they're doing, or they're insecure,


[User] Please transcribe this text

[Assistant] They tend, and they project for instance, what they do is that then they paint around the edges. They don't want to lose it. So there will be, you know, you don't want to be going around the edge like that, like try not to miss it. You just want to be.


[User] Please transcribe this text

[Assistant] Direct to the point and the point is to just mask in that color and that will make it faster.


[User] Please transcribe this text

[Assistant] I'm going to talk about the edges too at this point. You want to make sure the edges are soft.


[User] Please transcribe this text

[Assistant] You can always sharpen edges afterwards, but if you have a sharp edge that is dry, to soften it requires a little bit more time and it might become visible after


[User] Please transcribe this text

[Assistant] After oil becomes more transparent, you can see through it and see a very aggressive sharp edge there. You don't want to have that. So make sure you have control and soften the edges.


[User] Please transcribe this text

[Assistant] Before you let it dry. That way, when you come back, you know, the following day, they're all nice there for you to decide if they have to be sharper or softer.


[User] Please transcribe this text

[Assistant] And I know tomorrow I'm gonna darken it again, but just for now, so, so I can...


[User] Please transcribe this text

[Assistant] This area I can leave because there is nothing, uh, this is light enough to call it, to contrast, so.


[User] Please transcribe this text

[Assistant] So, for example, now I did a little bit of the background and the hair.


[User] Please transcribe this text

[Assistant] But we're not making that now. We're gonna paint that over. So this is just a base of a value. Remember that because it's hard to do it, I know, because I used to be hard for me to remember that I just have to simplify it and uhm, and just be efficient.


[User] Please transcribe this text

[Assistant] Okay, so I got the background, I got the darkest thing, which is this hair in shadow. And over here too.


[User] Please transcribe this text

[Assistant] So what do I do next? That's my thinking, that's my thinking process.


[User] Please transcribe this text

[Assistant] And I'm ready for the shadows in the flesh.


[User] Please transcribe this text

[Assistant] And I'm gonna use the color that I mixed, uhm, premixed before. I got it.


[User] Please transcribe this text

[Assistant] Becomes, uh, Mastin becomes the same family as that shadow there.


[User] Please transcribe this text

[Assistant] Yes, I see all these variations in the darks. For now, I'm gonna simplify it and make it only one value.


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[Assistant] All I'm doing here is simplifying, dividing that shadow versus light, and filling it in with one even value.


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[Assistant] You see what I did there? I'm just thinking, that's, that looks like a mistake, but...


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[Assistant] That's not a shadow, that's half tone. But what I'm thinking is that when I put the flesh next to it, I just want to mix it a little bit with that color and it will become a grayer color there and darker. So that's what I was thinking when I put that there and I realized that it might be misunderstood.


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[Assistant] Uh, in the video, Draco, he went outside of the, of the boundaries of the shadow.


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[Assistant] So I look around and try to find where I can.


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[Assistant] Even though the hair piece here is light, uh, this area here is pretty dark, so I wanna make sure I darken it.


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[Assistant] So I think, uh, we are ready to play with the lights. Now you see, since I started


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[Assistant] Uh, at first everything was the same values, uh, the fuel color that I had there, the Camping Tura.


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[Assistant] With a drawing, and then as soon as I started darkening things up, then that looks lighter now. Before it looked a little bit darker, but just by contrast it has become lighter. So now I think I'm ready to put the lighter notes.


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[Assistant] In my painting, the lightest thing would be the piece of cloth up here. So I just want to exaggerate that and make it so that I have the whole range


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[Assistant] In my painting, so I just wanna have that note of light.


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[Assistant] Before I move to the flesh because I just want to make sure that the flesh I do the best I can and that is only by having the surroundings correct.


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[Assistant] Of course this is going to look darker later when I add the little patterns and colors around it. But I just want for now to divide all this.


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[Assistant] And like I said before, it's better if you have a clean value so that tomorrow or your next sitting


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[Assistant] Uhm, when it's dry, you can paint variations in it.


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[Assistant] I see them, everybody sees them, you are tempted to go and make those changes, but I don't recommend them because you really don't know where they belong, you know, the values really on top of this, it's really hard, it's really hard to judge


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[Assistant] Uhm, what really the values are here, but if I have everything keyed in,


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[Assistant] Then I can paint on top of that and make those decisions. So that's why I recommend to, to wait and, you know.


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[Assistant] You can decide what you do with the brush strokes and the brush marks. Uhm, you see how I am painting that but you have your own way of approach and application and that's fine.


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[Assistant] I'm not going to teach you how to move your brush around because that should be intuition to you. Uhm, normally I follow the form. That's what I want to do. I like doing that. If I see the nose going up, I'm going to go up and then across. Uh, I can go down like that too.


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[Assistant] So there are different ways to do it. You can find your own way. Also, the amount of paint you put. Maybe you want to be more like thin and go like that. Maybe you want to be more aggressive and just get a lot of paint and just put it there.


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[Assistant] That's all fine, that's all style. Uh, I'm not concerned with style, that's up to you.


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[Assistant] I'm just, I just want to teach you the principles of how to have a successful painting in terms of representing


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[Assistant] Reality. After that you can just decorate that however you want.


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[Assistant] And as you can see, I'm kind of like block covering the drawing that I did before.


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[Assistant] Uhm, because, really, I, I just did it to get the proportions right, that were not supposed to be there, uhm, to as a end.


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[Assistant] Uhm, there was just, there were just reference for me to have a better...


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[Assistant] Now that ear is further back, so I want to make sure I can just incorporate it from now a darker value to it.


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[Assistant] So that it sits back there and doesn't want to come forward and compete with this which is closer to us.


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[Assistant] But this is on the dark side and since remember we're rendering, we're painting this as if it was a sphere or an egg shape. So I want to make sure I force myself


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[Assistant] Even though it's hard to see it, but I mean I can see it because when you squint, this area here disappears before this area. So that means that if I squint and this disappears before that, that means that this is darker. So I just put this area with, I just uhm, fill it up with a dark


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[Assistant] But also a clean note. You don't want to have too many variations in there.


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[Assistant] That's why it's a good idea to have the darks first, because if I put this color here from the beginning, it will look too dark.


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[Assistant] And it will scare you, and you will say, oh no, it's too dark, and it will light it up. When in reality, it was fine.


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[Assistant] That's why it's useful to have the darks first, and then you can judge this better.


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[Assistant] Again, all I'm doing is describing, describing the...


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[Assistant] The planes and kind of drawing the form.


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[Assistant] Making it as simple as possible, trying to make it look, uh, realistic.


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[Assistant] And you might see a little bit of the red and a little bit of this and that, but really what I'm thinking now is, because before I just dealt with form in drawing, now value. Yes, I have color, it's not only a grisaille, you could have done a grisaille, I could have done a grisaille now because it's under, but I think having kind of a general


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[Assistant] Complexion helps me for the future layers, but I'm really not thinking about


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[Assistant] Color right now, my mind is focused on values.


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[Assistant] And also, you have to know that at this stage you cannot judge what you're doing until everything is covered. Because you see the lips here are still with the under painting and all this, so it might look too dark what you're doing there. You cannot judge it at this point until everything is covered up.


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[Assistant] Uhm, player trains his ears and his fingers to hear the right note and put the right note at the right moment.


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[Assistant] Uhm, we, we do that as painters. We try, we put the, we train our eyes and our hands so we can put the correct color and value in the right place.


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[Assistant] So pretty much what you want to do is block in. You see how blocky it looks? Uhm, that's the purpose of this stage is just to make it, uh, to block it in so that you have important information, useful information for the future. That's all. You don't need more, more stuff.


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[Assistant] But I'm thinking value. How dark or how light is it? I'm not thinking how, how pink is it, you know. Just putting it there for reference, but uhm.


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[Assistant] I'm gonna think about it tomorrow when I go to the first painting on stage.


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[Assistant] This you can call, you know, blocking stage or dead coloring stage. Really doesn't matter how you name it.


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[Assistant] You don't want to fall into a trap of just having everything labeled and say, oh, what is that? What's the difference between an e-bodge and, uh, you know, an underpainting or what type of this, that's really, it's just, uh, common sense. You gotta paint that.


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[Assistant] Not that difficult, and you can get to thinking beyond that and get into more interesting,


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[Assistant] It's, it's normal that it happens because now look at the size of this brush and I'm putting color on it. So I kind of probably messed up a little bit of the proportions and stuff. But I'm gonna go back tomorrow when it's dry and I can just correct that, uh, while I paint and put more information.


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[Assistant] But this was really just the time. We spent a lot of time.


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[Assistant] Looking at proportions and shapes, so now is just the time to fill it up with a close


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[Assistant] So let's get some, uhm, greys for the, for the whites of the eyes. They're not white at all. Pretty grey, so.


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[Assistant] Sense of color and shapes and values in the head. I wanna go back and just make sure that I get the right shapes and values within the eyes. Because they, since they're, I left them behind, now they look a little creepy. So I wanna go and make sure I, you know, improve upon them.


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[Assistant] And the way I do that is by first adding darkness around the dark of the eye. There and there.


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[Assistant] So once I have the surroundings pretty close,


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[Assistant] I think of that as a, that's a kind of like a sphere in that eye socket. So you want to make sure it casts a shadow from the eyelid.


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[Assistant] And it's soft against the dark area there.


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[Assistant] If you put the highlights, just wanna make sure, just put them in the right place.


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[Assistant] I'm not rendering them, I just want to put the range of values so that I kind of know, uh, where they go.


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[Assistant] And also by having the lightest thing, I know how dark or how light.


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[Assistant] Uh, I mean, player one knows which to choose then. He's going to choose, uhm, down.


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[Assistant] Kids are now separated by intelligence. The weak are picked on. Girls you've known since kindergarten won't even talk to anymore. Okay, well...


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[Assistant] The cafeteria. Possibly the cruelest place on earth.


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[Assistant] Welcome back. In this week, you learned to implement a neural network.


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[Assistant] Before diving into the technical details, I wanted in this video to give you a quick overview of what you'll be seeing in this week's videos. So, if you don't follow all the details in this video, don't worry about it. We'll delve into technical details in the next few videos. But for now, let's give a quick overview of how you implement a neural network.


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[Assistant] Last week we had talked about logistic regression and we saw how this model


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[Assistant] Corresponds to the following computation graph, where you didn't put


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[Assistant] The features x in parameters w and b, that allows you to compute z, which is then used to compute a, and we were using a interchangeably with this output y hat, and then you can compute the loss function l.


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[Assistant] A neural network looks like this, and as I've already previously alluded, you can form a neural network by stacking together a lot of little sigmoid units.


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[Assistant] Whereas previously, this node corresponds to two steps of calculations. The first is to compute the z value, second is to compute this a value. In this neural network,


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[Assistant] This stack of nodes will correspond to a z-like calculation like this.


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[Assistant] Uhm, as well as an A like calculation like that. And then,


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[Assistant] That note will correspond to another Z and another A like calculation.


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[Assistant] So the notation which we'll introduce later will look like this.


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[Assistant] First we'll input the features x together with some parameters w and b, and this will allow you to compute z1.


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[Assistant] So a new notation that we should use is that we'll use superscript square bracket one.


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[Assistant] To refer to quantities associated with this stack of nodes is called a layer. And then later we'll use superscript square bracket 2


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[Assistant] To refer to quantities associated with that no really.


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[Assistant] That's called another layer of the neural network. And the superscript square brackets, like we have here,


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[Assistant] 1 and 2 refer to these different layers, layer 1 and layer 2 in this neural network. But so going on, after computing Z1,


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[Assistant] Similar to logistic regression, there will be a computation to compute a1, and that's just sigmoid of z1, and then you compute z2 using another sort of linear equation, and then compute a2, and a2 is the final output


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[Assistant] So I know that was a lot of details, but a key intuition to take away.


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[Assistant] Is that whereas for literacy regression we had this Z followed by A calculation and this new network here we just do it multiple times. There's a Z followed by an A calculation and a Z followed by an A calculation.


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[Assistant] And then you finally compute the loss at the end.


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[Assistant] And you will remember that for logistic regression we had this, uhm, backward calculation in order to


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[Assistant] So in the same way, in a neural network, we'll end up doing a backward calculation that looks like this, in which you end up computing


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[Assistant] So that gives you a quick overview of what a neural network looks like. It's basically taking a logistic progression and repeating it twice.


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[Assistant] I know there was a lot of new notation, a lot of new details. Don't worry about it, if you didn't follow everything, we'll go into the details more slowly in the next few videos. So let's go on to the next video. We'll start to talk about the neural network representation.


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[Assistant] About the millions of women who go to work in our homes every single day, caring for children as nannies.


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[Assistant] Caring for our loved ones with disabilities and our elders as home care workers.


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[Assistant] Maintaining sanity in our homes as cleaners. It's the work that makes all other work possible.


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[Assistant] And it's mostly done by women. More than 90 percent women, disproportionately women of color.


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[Assistant] And the work itself is associated with work that women have historically done, work that's been made incredibly invisible and taken for granted in our culture.


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[Assistant] But it's so fundamental to everything else in our world. It makes it possible for all of us to go out and do what we do in the world every single day, knowing that the most precious aspects of our lives are in good hands. But we don't think about it that way.


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[Assistant] It's almost defined by its invisibility.


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[Assistant] You could go into any neighborhood and not know which homes are also workplaces. There's no sign. There's no list or registry. It's just invisible.


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[Assistant] It's this work that is not even referred to as real work. It's not referred to as help. It's often seen as unskilled, not seen as professional.


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[Assistant] And race has played a profound role in how we value this work in our culture. Some of the first domestic workers in the United States were black women who were enslaved, and racial exclusion has shaped their conditions for generations.


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[Assistant] In the 1930s, when Congress was discussing the labor laws that would be a part of the New Deal, that would protect all workers, southern members of Congress refused to support those labor laws if they included protections for domestic workers and farm workers. That history of racial exclusion


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[Assistant] And our cultural devaluing of work that's associated with women now means that millions of women


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[Assistant] Go to work every single day, work incredibly hard and still can't make ends meet. They earn poverty wages without a safety net.


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[Assistant] So that the women that we're counting on to take care of us and our families can't take care of their own doing this work.


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[Assistant] It's about making these jobs good jobs that you can take pride in and support your family on.


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[Assistant] At the National Domestic Workers Alliance, we've been working hard in states to pass new laws that will protect domestic workers from discrimination and sexual harassment, that will create days of rest, paid time off even.


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[Assistant] So far, eight states have passed domestic workers' bills of rights. Yes.


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[Assistant] And during the Obama administration, we were successful in bringing two million home care workers under minimum wage and overtime protections for the first time since 1937.


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[Assistant] Which allows for domestic workers with multiple clients to give them access to benefits for the very first time.


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[Assistant] So really important progress is being made. But I would argue tonight


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[Assistant] That one of the most important things that domestic workers can provide is actually what they can teach us about humanity itself.


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[Assistant] And about what it will take to create a more humane world for our children.


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[Assistant] In the face of extreme immorality, domestic workers can be our moral compass. And it makes sense.


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[Assistant] Because what they do is so fundamental to the very basics of human need and humanity.


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[Assistant] They are there when we are born into this world. They shape who we become in this world.


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[Assistant] And they are with us as we prepare to leave this world.


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[Assistant] And their experiences with families are so varied. They have some relationships with the families that they work for that are incredibly positive and mutually supportive and last for years and years, and then the opposite also happens.


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[Assistant] And we've seen cases of sexual violence and assault.


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[Assistant] Of extreme forms of abuse and exploitation, we've seen cases of human trafficking.


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[Assistant] Domestic workers live in poor neighborhoods, and then they go to work in very wealthy ones.


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[Assistant] They cross cultures and generations and borders and boundaries, and their job, no matter what, is to show up and care.


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[Assistant] I want to tell you a story of a woman I met early on in this work. Her name is Lily. Lily and her family lived in Jamaica.


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[Assistant] And when she was 15 years old, she was approached by an American couple who were looking for a living nanny to come live with them in the United States and help them care for their children. They offered Lily's family that if she came to work as their nanny,


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[Assistant] They decided it was a good idea and decided to take the opportunity. Lily held up her end of the bargain and helped to raise three children.


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[Assistant] But all communication with her family was severed. No letters, no phone calls. She was never allowed to go to school. And she was never paid for 15 years.


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[Assistant] One day, she saw an article in a newspaper about another domestic worker with a really similar story to hers, another case that I was working on at the time, and she found a way to reach me.


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[Assistant] She also found a way to reach her brother, who was living in the United States at the time as well. And between the two of us, we were able to help her escape. And she had the help of one of the children. One of the children was old enough to realize that the way his nanny was being treated was wrong.


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[Assistant] She was essentially enslaved for 15 years. Human trafficking and slavery is a criminal offense.


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[Assistant] And so her lawyers and I asked Lily, did she want to press criminal charges for what had happened to her? And after thinking about what it would mean, she said no.


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[Assistant] Because she didn't want the children to be separated from their parents.


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[Assistant] Instead, we filed a civil lawsuit and we eventually won the case. And her case became a rallying cry for domestic workers everywhere. She was reunited with her family and went on to have a family of her own.


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[Assistant] But the thing that's so profound to me about this story


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[Assistant] Is despite having 15 years stolen from her life.


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[Assistant] It did not affect the care and compassion that she felt for the children.


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[Assistant] They're simply too proximate to our shared humanity. They know how your toddler likes to be held as they take their bottle before a nap. They know how your mother likes her tea.


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[Assistant] How to make her smile and tell stories despite her dementia. They are so proximate to our humanity.


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[Assistant] They know that at the end of the day, these are people who are part of families. Someone's mother, someone's grandmother, someone's best friend and someone's baby.


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[Assistant] Undeniably human, and therefore not disposable.


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[Assistant] That anytime a single person becomes disposable, it's a slippery slope. You see, the cultural devaluing of domestic work is a reflection


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[Assistant] A hierarchy that values the lives and contributions of some groups of people over others.


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[Assistant] Class, immigration status, any number of categories. And that hierarchy of human value


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[Assistant] Requires stories about those groups of people in order to sustain itself.


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[Assistant] So these stories have seeped deep into our culture about how some people are less intelligent, some people are less intuitive.


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[Assistant] And domestic workers know it's a slippery slope when we start to see.


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[Assistant] In the spring of 2018, the Trump administration announced a new policy at the US-Mexico border, a zero-tolerance policy to forcibly separate all children


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[Assistant] Children as young as 18 months separated from their parents after a long and arduous journey to reach the US-Mexico border in search of safety and a new beginning. Thousands of children separated.


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[Assistant] In response, I helped to organize the Families Belong Together vigil at the Ursula Border Processing Center in McAllen, Texas on Father's Day.


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[Assistant] Inside that processing center, there were hundreds of children who were being held, processed.


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[Assistant] And then prepared to be shipped all over country, to be jailed in facilities hundreds of miles away from their parents.


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[Assistant] I saw with my own eyes children not young enough for kindergarten.


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[Assistant] In unmarked buses being shipped off to jails hundreds of miles away. And as they passed us by, they reached for us through the windows.


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[Assistant] As we stood vigil to let them know that they are not alone and we are fighting for them.


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[Assistant] Domestic workers came from all over Texas to be a part of the vigil.


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[Assistant] They saw in those families their own family stories. They had also come here in search of safety and a new beginning, a better life for their families, and they saw in the eyes of those children their own children. And through our tears,


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[Assistant] We looked at each other and we asked each other, how did we get here?


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[Assistant] To putting children in cages and separating them from the people who love them the most in the world. How?


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[Assistant] was if domestic workers were in charge, this never would have happened. Our humanity would never have been so disposable that we would be treating children in this way.


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[Assistant] That love and compassion are necessities, not luxuries. Without them, humanity cannot survive.


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[Assistant] In other words, they are fundamental to human existence.


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[Assistant] Domestic workers are in charge of the fundamentals.


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[Assistant] As you go about your day, and you encounter these moral choices, think of Lily.


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[Assistant] Think like Lily. Think like a domestic worker who shows up and cares no matter what. Love and compassion no matter what. Show up like a domestic worker.


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[Assistant] Because our children are counting on us. Thank you.


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[Assistant] What's going on? Happy holidays! In today's lesson with Harry Potter and the Goblet of Fire, you are going to learn with a scene in which Ron, Harry, and Hermione attend a Christmas ball. That is a large formal party in which people dance, and that in the movies is known as the Yo-Ball.


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[Assistant] Now, yule is an old word for Christmas, which is used still in Northern Europe and North America in some specific context around the holidays. So this is a really great opportunity for you to learn all about British culture and some differences between British and American pronunciation.


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[Assistant] And if you're new here, every single week we make fun lessons like this one so that you can understand fast speaking natives without getting lost, without missing the jokes, and without subtitles. Just like this learner who says that they are amazed at how fast that their comprehension has improved by watching our lessons over the last year.


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[Assistant] And you're going to learn super fast too. All you have to do is hit that subscribe button and the bell down below so you don't miss any of our new lessons.


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[Assistant] In British English, the adjective bloody, when used as slang, like done here, adds intensity and emotion to a sentence, emphasizing what you are saying in a slightly rude way.


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[Assistant] So a common collocation with the word bloody is the slang expression bloody hell.


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[Assistant] A robe is a long, loose piece of clothing normally worn on very formal occasions, such as when graduating from college or when judges are working in court.


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[Assistant] In the wizarding world, it's common for wizards and witches to wear robes, as all Hogwarts students do.


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[Assistant] A dress robe is an old term used to refer to a type of robe worn for parties and social events, similar to the kind of clothes worn for gala events nowadays.


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[Assistant] So, Ron says Harry's dress robes are alright. Those!


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[Assistant] Ron is frustrated because his mother sent him very old, out of fashion dress robes to wear for the Yule Ball.


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[Assistant] Lace is a decorative cloth made of delicate patterns with holes in them. Collar is the part around the neck of a piece of clothing. If you describe someone or something as dodgy,


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[Assistant] You disapprove of them because they seem rather dishonest and unreliable. Example. The drive over those mountains can be quite dodgy.


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[Assistant] Well I expect yours is more traditional. Traditional? Traditional can describe anything that polished tradition, or a usual way of doing things for a long time.


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[Assistant] For example, traditional Mexican food includes tortillas and beans. A bag of corn chips and chili and fake cheese sauce, on the other hand, is not traditional.


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[Assistant] So here, Harry tries to make Ron feel better by saying he thinks his robes are more traditional. Meaning they fall in order and more classic style than Harry's robes. Well I expect yours are more traditional. Traditional? They're ancient!


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[Assistant] Ancient means very old, in a sense of being older than old.


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[Assistant] For example, ancient history normally refers to the time before the Middle Ages.


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[Assistant] You probably know a person's aunt is a sister of their mother or father.


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[Assistant] So a great aunt is a sister of their grandmother or grandfather.


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[Assistant] Murder me or kill me is a figure of expression said when you're so sad or discouraged by something you have to do that you would rather die than do it. This is a figure of speech not meant to be taken literally. Everybody smile!


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[Assistant] The expression, leave it alone, means to not interact or interfere with something.


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[Assistant] Harry's asking Ron to stop being worried about his clothes.


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[Assistant] We can also collocate this expression with people. For example, leave me alone, or leave her alone. Meaning a request to stop bothering somebody.


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[Assistant] Here, we can hear a word that is commonly mispronounced by learners, the function word of


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[Assistant] Many learners will actually make the mistake of pronouncing the sound of the letter F, as you should do in the word off.


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[Assistant] In reality, what should be said in of is the sound of the letter V. Of, off, of course.


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[Assistant] Now, one of the many differences in pronunciation between American and British English accents, as you probably know, is the R sound.


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[Assistant] When referring to how the R sound is pronounced, accents of English are divided into those that are rhotic, meaning they pronounce R in all circumstances, and those that are non-rhotic, which only pronounce it before a vowel.


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[Assistant] So they don't pronounce it before a consonant or at the end of a word.


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[Assistant] Non-rhotic accents can still pronounce it at the end of a word if the word is immediately followed by another word beginning with a vowel.


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[Assistant] So car may be pronounced ca, but car and bus is pronounced car and bus, similar to how Americans would normally say it.


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[Assistant] Let's check out some other examples of words with the R sound set in both standard American and British accents.


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[Assistant] Okay, do you want to improve your American English pronunciation and comprehension? Well then I highly recommend our Fluent with Friends course, where every week for 48 weeks, you will receive a fun lesson that follows along with the first two seasons of the TV series Friends.


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[Assistant] Plus you get 20 plus page PDF power lessons, vocabulary memorization software, access to our Fluency Circle global community, and so much more.


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[Assistant] Plus, you can try it for free right now with our three-part masterclass. What are you waiting for? Just click up here or down in the description below and you can sign up for that right now.


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[Assistant] Here, you can see a more informal use of the adjective pour.


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[Assistant] which normally describes a person who has little money and few possessions


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[Assistant] Ron believes her money is not going to the ball because she had no partner to go with.


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[Assistant] So calling Hermione a poor kid means he feels sympathy for her. He's expressing his sadness about the fact she's not going to the ball.


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[Assistant] The expression I bet means the same as I believe or I expect.


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[Assistant] What would be another informal way to say I bet in this sentence?


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[Assistant] Now, literally in another context, to bet is to risk money or an object on the result of an event or competition in the hope of winning more money.


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[Assistant] If somebody is crying their eyes out, they are crying a lot. Oh kid.


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[Assistant] To take the mickey out of somebody is an old and very uncommon British English expression meaning to mock somebody.


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[Assistant] It has a few different applications with positive and negative connotations.


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[Assistant] If you say you are proud of somebody else, you feel good about being responsible for supporting somebody else when they are successful. My perfect sister being who she was.


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[Assistant] It can also mean you have or show respect for yourself, recognizing that you are responsible for your own achievement.


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[Assistant] In the case of what Ron said, he put it as a negative idea meaning that she was being arrogant and overly respectful of herself. He's referring to a previous conversation they had in the movie.


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[Assistant] Here Padma used an informal expression to make an observation about Ron's looks.


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[Assistant] That means he looks stylish and attractive in an adventurous and exciting way. Obviously, Padme said this insincerely in order to be polite, as Ron is definitely not looking good and in style.


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[Assistant] Would you care to do something is a formal expression used to ask someone politely whether they want to do something. So, would you care to join me in our first dance as husband and wife?


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[Assistant] What's got your wand in a knot is an idiomatic expression from the Wizarding World which expresses a person's curiosity as to why the other is in a bad mood.


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[Assistant] This is not an actual expression that is used in the real world, but it may be a creative alternative to real expressions like what's got your panties or knickers in a bunch. Example. Don't get your knickers in a bunch, I will help you in just a few minutes. What other real expression could we use in this case?


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[Assistant] Both alternatives B and C are correct, and are said by natives to express the same idea.


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[Assistant] Check that out up here or down in the description below after you finish this lesson.


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[Assistant] Especially if that person is from an opposing side or team, or has a different social position.


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[Assistant] For example, in this scene from Friends, that happens at Ross's workplace, the Museum of Natural History. We say that the scientists don't fraternize with the tour guys.


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[Assistant] In the scene, Ron refers to Victor Crumb as the enemy. If you've watched Harry Potter and the Goblet of Fire,


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[Assistant] So here, Hermione makes a sarcastic comment, asking Ron, who wasn't wanting his autograph, as early in the movie, Ron was actually a fan of Crumb, who is a famous professional Quidditch player.


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[Assistant] If somebody explains and talks about the whole point of something, they are emphasizing the purpose for doing something, especially when they believe such purpose is not being understood or has been forgotten by other people. Example.


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[Assistant] I don't like the LEGO video games. I think the whole point of a toy like LEGO is using your hands to build things, not a mouse and a computer screen.


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[Assistant] Ron means Victor has second intentions in his relationship with Hermione, that he wants to be more than friends with her and perhaps become her boyfriend. He's using you.


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[Assistant] How dare you is an informal expression said when you are very shocked or angry about something that someone has said or done.


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[Assistant] So Hermione is angry with Ron because he's insulting Crumb and Hermione by saying that he is using her, meaning that he is taking advantage of her. He's using you.


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[Assistant] In this phrase, way adds extra emphasis to too old. It makes the meaning stronger.


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[Assistant] To pluck up your courage is an idiomatic phrase meaning to force yourself to be brave enough to do something, although you are frightened or worried about it.


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[Assistant] The term last resort refers to the only choice that remains for somebody after all other alternatives or solutions have been tried.


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[Assistant] You can do a brain biopsy but only as a last resort.


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[Assistant] If we refer to an argument or comment as off the point, that means it is not important or not related to the purpose of the discussion. Alright.


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[Assistant] Nevermind is an expression used for telling someone that they don't need to do something or worry about it anymore because it is not important or because you will do it yourself.


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[Assistant] If you are off to bed, you are going to go to sleep. It can also be used as a command as Hermione did here.


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[Assistant] In this sense, to spoil something is to destroy or damage something, especially when making it not able to be used anymore.


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[Assistant] For example, spoiled eggs would be eggs that are rotten and inedible.


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[Assistant] Hermione is referring to how Ron spoiled the moment, as she is now feeling sad and unable to enjoy the party.


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[Assistant] So after hearing this exchange between Ron and Hermione, Harry gets confused and asks Ron, what's this about?


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[Assistant] That is another way of asking what is the reason for this, or what's up with this.


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[Assistant] I'm Ron, by the way. Ron Weasley. I'm Harry. Harry Potter.


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[Assistant] In the last video you saw the equations for backpropagation. In this video let's go over some intuition using the computation graph for how those equations were derived.


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[Assistant] This video is completely optional, so if you either watch it or not, you should be able to do the homeworks either way. So recall that when we talked about logistic regression, we had this forward pass where we would compute z, then a,


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[Assistant] And then the loss, and then to take derivatives, we had this, uhm, backward path where we could first compute dA, uhm, and then go on to compute dZ, and then go on to compute dW and dB. So the definition for the loss was, uhm, L of A comma Y equals negative Y log A minus 1 minus Y times


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[Assistant] So if you're familiar with calculus and you take the derivative of this with respect to a, that would give you the formula for dA. So dA is equal to that.


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[Assistant] And if you actually figure out the calculus, you can show that this is y over a, negative y over a, plus one minus y.


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[Assistant] Over 1 minus 8. Just kind of derive that from calculus by taking derivatives of this.


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[Assistant] It turns out when you take another step backwards to compute dz, we then worked out that dz is equal to a minus y. I didn't explain y previously, but it turns out that from the


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[Assistant] Sigmoid of z is our activation function for this output unit in logistic regression.


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[Assistant] Right, so just remember this is still logistic regression, we have x1, x2, xv.


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[Assistant] And then just one sigmoid unit, and then that gives us uhm, A, or gives us y hat.


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[Assistant] So here, the activation function was a sigmoid function.


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[Assistant] And as an aside, only for those of you familiar with the chain rule of calculus, the reason for this is because A is equal to sigmoid of Z, and so partial of L with respect to Z is equal to partial of L with respect to A times dA dZ. But since A is equal to sigmoid of Z, this is equal to


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[Assistant] So that's why this expression, which is dz in our code,


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[Assistant] Is equal to this expression, which is da in our code, times g prime of z. And so, this is just that.


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[Assistant] So that last derivation would have made sense only if you're familiar with calculus and specifically the chain rule from calculus. But if not, don't worry about it. I'll try to explain the intuition wherever is needed.


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[Assistant] And then finally, having computed dz for Luthor's regression, we would compute dw.


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[Assistant] Which it turns out was dz times x and db, which is just dz when you have a single training example. So that was logistic regression.


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[Assistant] So what we're going to do when computing back propagation for a neural network is a calculation a lot like this, but only we'll do it twice because now we have


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[Assistant] Not x going to an output unit, but x going to a hidden layer, and then going to an output unit. And so instead of, uhm, instead of this computation being sort of one step as we have here, we'll have, you know,


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[Assistant] Two steps here, right, in this kind of a neural network with two layers. So in this,


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[Assistant] Two layer neural network, that is an input layer, a hidden layer, and an output layer. Remember the steps of a computation. First, you compute Z1 using this equation, and then compute A1.


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[Assistant] And then you compute z2, and note that z2 also depends on the parameters w2 and b2. And then, based on z2, you compute a2, and then finally, that gives you the loss.


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[Assistant] We don't need to take derivatives with respect to the input x, since the input x for supervised learning is fixed, so we're not trying to optimize x, so we won't bother to take derivatives at least for supervised learning with respect to x.


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[Assistant] And so, uhm, I'm going to skip explicitly computing dA2. If you want, you can actually compute dA2 and then use that to compute dZ2, but in practice you could collapse both of these steps into one, into one step. So you end up that dZ2 is equal to A2 minus Y, same as before.


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[Assistant] So this step is quite similar to for logistic regression where we had that dw was equal to dz times x, except that now


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[Assistant] Uhm, a1 plays the row of x, and there's an extra transpose there, because the relationship between the capital matrix W


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[Assistant] And our individual parameters w was, uh, there's a transpose there, right? Because w is equal to, uhm, a


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[Assistant] Rho vector in the case of logistic regression with a single output.


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[Assistant] D w2 is like that, whereas w here was a column vector, so that's why it does an extra transpose for a1, whereas we didn't for x here for logistic regression.


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[Assistant] So this completes half of backpropagation.


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[Assistant] And then again, you can compute dA1 if you wish, although in practice, the computation


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[Assistant] For dA1 and dZ1 are usually collapsed into one step and so what you can actually implement is that dZ1 is equal to W2 transpose times dZ2 and then, uhm, times an element-wise product of G1 prime of Z1.


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[Assistant] And just to do a check on the dimensions, right, if you have a neural network that looks like this, right, outputs Y if so, if you have


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[Assistant] And two by one dimensional is really going to be a one by one when we're...


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[Assistant] Doing binary classification and z1 and therefore also dz1 are going to be n1 by one dimensional.


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[Assistant] Right, note that for any variable foo, uh, foo and dfoo always have the same dimension. So that's why w and dw, you know, always have the same dimension.


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[Assistant] And similarly for B and D, B and Z and D, Z and so on.


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[Assistant] So to make sure that the dimensions of this all match up, we have that dz1 is equal to w2 transpose times dz2 and then


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[Assistant] Uhm, this is an element-wise product times g1' of z1. So matching the dimensions from above, this is going to be n1 by 1.


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[Assistant] Is equal to W2 transpose with transpose of this, so this is going to be N1 by N2 dimensional. DZ2 is going to be N2 by 1 dimensional.


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[Assistant] And then this, this is the same dimension as z1, so this is also n1.


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[Assistant] So the dimensions do make sense, right?


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[Assistant] By one dimensional, vector can be obtained by


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[Assistant] N1 by N2 dimensional matrix times N2 by N1 because the product of these two things gives you an N1 by one dimensional matrix.


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[Assistant] And so this becomes the element-wise product of 2.


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[Assistant] One tip when implementing backprop, uhm,


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[Assistant] If you just make sure that the dimensions of your matrices match up, so if you think through what are the dimensions of your various matrices including w1, w2, z1, z2, uhm, a1, a2 and so on and just make sure that


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[Assistant] The dimensions of these matrix operations may match up.


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[Assistant] Sometimes that will already eliminate quite a lot of bugs in background.


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[Assistant] Alright, so this gives us dz1, and then finally, just to wrap up, dw1 and db1, uhm, we should write them


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[Assistant] Here I guess, but since I'm running out of space, I'll write them on the right of the slide. dw1 and db1 are


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[Assistant] Given by the following formulas, this is going to be equal to


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[Assistant] DZ1 times X transpose and this is going to be equal to DZ and uhm, you might notice a similarity between these equations and these equations, alright, which is really no coincidence because X plays


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[Assistant] The row of a zero, so x transpose is a zero transpose. So those equations are actually very similar.


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[Assistant] This derives, and we have six key equations here.


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[Assistant] So let me just take these six equations and copy them over to the next slide. Here they are. And so far with derived back propagation,


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[Assistant] For API training on a single training example at a time. But,


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[Assistant] It should come as no surprise that rather than working on a single example at a time, uhm, we would like to vectorize, uhm, across different training examples. So we remember that for, for propagation, when we're operating on one example at a time, we had equations like this, uhm, as well as say a1 equals g1 of z1.


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[Assistant] And then we found that, you know, by stacking things up in columns and, uh, defining the capital uppercase version of these, we then just had z1 equals w1 x plus b and a1 equals g1 of z1.


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[Assistant] Right, and we define the notation very carefully in this course to make sure that stacking examples in the different columns of a matrix makes all this work out. So it turns out that if you go through the math carefully,


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[Assistant] The same trick also works for backpropagation. So the vectorized equations are as follows. First, if you take


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[Assistant] These DZs for different training examples and stack them, uhm,


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[Assistant] As the different columns of the matrix and same for this and same for this, then this is the vectorized implementation.


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[Assistant] And then here's the definition for, or here's how you can compute dw2.


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[Assistant] There is this extra 1 over m because, you know, the cost function j is this, uh, 1 over m of sum from i equals 1 through m of the losses.


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[Assistant] And so when computing derivatives, we have that extra 1 over m term just as we did when we were computing the weight updates for logistic regression.


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[Assistant] Uhm, and then that's the update you get for DB2.


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[Assistant] Again, sum of the dz's and then with a 1 over m. And then dz1 is computed as follows. Uhm, once again, this is an element-wise product.


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[Assistant] Only whereas previously, this was, we saw on the previous slide, that this was an n1 by 1 dimensional vector. Now this is a n1 by m dimensional matrix. Uhm, and both of these are also n1 by m dimensional. And so,


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[Assistant] That's why that asterisk is a element-wise product. And then finally, the remaining two updates perhaps shouldn't look too surprising.


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[Assistant] So I hope that gives you some intuition for how the backpropagation algorithm is derived.


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[Assistant] In all of machine learning, I think the derivation of the backpropagation algorithm is actually one of the most complicated pieces of math I've seen.


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[Assistant] Uh, and it requires knowing both linear algebra as well as the derivative matrices to really derive it from scratch from first principles. If you are an expert in matrix calculus, uhm, using this process, you might be able to derive the algorithm yourself.


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[Assistant] But I think that there are actually plenty of deep learning practitioners that have seen the derivation at about the level you've seen in this video and are already able to have all the right intuitions and be able to implement this algorithm very effectively.


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[Assistant] So if you are an expert in calculus, uh, do see if you can derive the whole thing from scratch. It is one of the very hardest pieces of math, one of the very hardest derivations that I've seen in all of machine learning. But either way, if you implement this, you know, this will work and I think you have enough intuitions to tune it and get it to work.


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[Assistant] So with that, uhm, there's just one last detail I want to share with you before you implement your neural network, which is how to initialize the weights of your neural network. And it turns out that initializing your parameters not to zero, but randomly turns out to be very important for training your neural network. In the next video, you'll see why.


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[Assistant] What are those? What are those?


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[Assistant] Better stand back. Let's go!


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[Assistant] Is used to return those who've been petrified to their original state.


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[Assistant] High garden. Give me your word.


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[Assistant] That completely changes the way we think about the Earth and Moon.


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[Assistant] In my lab, I can shoot at rocks using cannons like this one.


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[Assistant] In my experiments, I can generate the extreme conditions during planet formation.


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[Assistant] And with computer models, I can collide whole planets together to make them grow or I can destroy them.


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[Assistant] I want to understand how to make the earth and the moon, and why the earth is so different from other planets.


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[Assistant] The theory states that a Mars-sized body struck the young Earth, and the moon formed from the debris disk around the planet.


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[Assistant] The theory can explain so many things about the moon, but it has a huge flaw.


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[Assistant] It predicts that the moon is mostly made from the Mars-sized planet, that the Earth and the moon are made from different materials. But that's not what we see.


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[Assistant] The genetic code of planets is written in the isotopes of the elements. The Earth and Moon have identical isotopes. That means that the Earth and Moon are made from the same materials.


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[Assistant] All of the planets are made from different materials, so they all have different isotopes, they all have their own genetic code. No other planetary bodies have the same genetic relationship. Only the Earth and Moon are twins. When I started working on the origin of the Moon,


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[Assistant] They didn't see any way for this theory to explain special relationship between the earth and the moon. We were all trying to think of new ideas.


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[Assistant] The problem was, there weren't any better ideas.


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[Assistant] All of the other ideas had even bigger flaws.


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[Assistant] So we were trying to rescue the giant impact theory. A young scientist in my group


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[Assistant] Suggested that we try changing the spin of the giant impact. Maybe making the earth spin faster could mix more material and explain the moon.


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[Assistant] The Mars-size impactor had been chosen because it could make the Moon and make the length of Earth stay. People really liked that part of the model. But why does something else determine the length of Earth's day?


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[Assistant] Then there would be many more possible giant impacts that could make the moon.


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[Assistant] I was curious about what could happen, so I tried simulating faster spinning giant impacts.


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[Assistant] And I found that it is possible to make a disk out of the same mixture of materials as the planet. We were pretty excited. Maybe this was the way to explain the moon.


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[Assistant] The problem is, we also found that that's just not very likely.


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[Assistant] Most of the time, the disk is different from the planet. And it looked like making our moon this way would be an astronomical coincidence.


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[Assistant] And it was just hard for everyone to accept the idea that the moon's special connection to Earth was an accident.


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[Assistant] The giant impact theory was still in trouble. And we were still trying to figure out how to make the moon.


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[Assistant] My student and I were looking at the data from these fast-spinning giant impacts. On that day, we weren't actually thinking about the moon, we were looking at the planet. The planet gets super hot and partially vaporized from the energy of the impact.


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[Assistant] But the data didn't look like a planet. It looked really strange. The planet was weirdly connected to the disk.


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[Assistant] I got that super excited feeling when something really wrong might be something really interesting.


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[Assistant] In all of my calculations, I had assumed there was a planet with a separate disk around it. Calculating what was in the disk was how we tested whether an impact could make the moon. But it didn't look that simple anymore.


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[Assistant] We were making the mistake of thinking that a planet was always going to look like a planet.


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[Assistant] On that day, I knew that a giant impact was making something completely new.


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[Assistant] I've had eureka moments. This was not one of them. I really didn't know what was going on.


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[Assistant] I had this strange new object in front of me and the challenge to try and figure it out. What do you do when faced with the unknown? How do you even start? We questioned everything.


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[Assistant] What is a planet? When is a planet no longer a planet anymore? We played with new ideas.


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[Assistant] We had to get rid of our old way of thinking, and by playing, I could throw away all of the data, all of the rules of the real world and free my mind to explore.


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[Assistant] And by making a mental space where I could try out outrageous ideas and then bring them back into the real world to test them, I could learn.


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[Assistant] And by playing, we learned so much. I combined my lab experiments with computer models,


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[Assistant] And discovered that after most giant impacts, the earth is so hot there's no surface. There's just a deep layer of gas that gets denser and denser with depth. The earth would have been like Jupiter. There's nothing to stand on. And that was just part of the problem. I wanted to understand the whole problem.


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[Assistant] I couldn't let go of the challenge to figure out what was really going on in giant impacts. It took almost two years of throwing away old ideas and building new ones that we understood the data and knew what it meant for the moon. I discovered a new type of astronomical object. It's not a planet. It's made from planets,


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[Assistant] Planet is a body whose self-gravity is strong enough to give it its rounded shape. It spins around altogether.


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[Assistant] Make it hotter and spin it faster. The equator gets bigger and bigger until it reaches a tipping point.


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[Assistant] Push past the tipping point and the material at the equator spreads into a disk. It's now broken all the rules of being a planet.


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[Assistant] It can't spin around together anymore. Its shape keeps changing as it gets bigger and bigger. The planet has become something new.


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[Assistant] We named it after the goddess Hestia, the Greek goddess of the hearth and home, because we think the earth became one. The prefix means all together to emphasize the connection between all of the material. A synestia is what a planet becomes.


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[Assistant] In this visualization of one of my simulations, the young earth is already spinning quickly from a previous giant impact.


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[Assistant] Its shape is deformed, but our planet would be recognizable by the water on its surface.


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[Assistant] The energy from the impact vaporizes the surface, the water, the atmosphere and mixes all of the gases together in just a few hours.


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[Assistant] But these burning bright objects don't live very long. They cool down, shrink and turn back into planets.


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[Assistant] While rocky planets like Earth were growing, they probably turned into synestias one or more times.


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[Assistant] A synastia gives us a new way to solve the problem of the origin of the moon.


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[Assistant] That the moon formed inside a huge, vaporous synestia.


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[Assistant] The moon grew from magma rain that condensed out of the rock vapor.


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[Assistant] The moon's special connection to earth is because the moon formed inside the earth, when earth was a synesthesia.


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[Assistant] The moon could have orbited inside the synestia for years, hidden from view.


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[Assistant] The moon is revealed by the synesthesia cooling and shrinking inside of its orbit.


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[Assistant] The synestia turns into planet Earth only after cooling for hundreds of years longer.


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[Assistant] The giant impact makes the synestia. And the synestia divides into two new bodies.


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[Assistant] Creating our isotopically identical earth and moon.


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[Assistant] Senestias have been created throughout the universe. And we only just realize that by finding them in our imagination. What else am I missing in the world around me?


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[Assistant] What is hidden from my view by my own assumptions?


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[Assistant] The next time you look at the moon, remember the things you think you know.


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[Assistant] Maybe the opportunity to discover something truly amazing.


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[Assistant] Once again, you astonish with your gifts, Potter. Gifts mere mortals can only dream of possessing. How grand it must be to be the Chosen.


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[Assistant] We can't just do the same thing over and over. We can't if it's Zooey Mama. It has to be a little more sophisticated.


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[Assistant] I wonder what is in this cute little box. It's not a box, it's a brick you dumb moron. Oops, I've been trying to open it all day.


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[Assistant] No, it's not funny. Well, I think it is. I like Zooey, Mama. You know what? If you like it so much, then why don't you go do it yourself?


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[Assistant] I'm kinda in a tough situation. I know something, and if I tell the truth about it, it could hurt somebody. But if I don't, it could hurt somebody else. Well...