All right, let's take a look at this let's play the whole thing here. Oh shadows nice Cool. Oh, I like that ending here Very neat. Let's see It's cool. There's a little bit of a hiccup there Right there. Well, maybe it's the head too. It starts already here Be careful when you have head moves up like that and it comes to a sudden stop just for a little bit Goes back up there and it's right through there It's a bit of a bit of a hiccup let's play this again and We'll wait there. I Don't think it's the camera. Let's see the camera Cameras are pretty smooth. So watch out. It could just be in the head. There's just something right through there The kind of continuous through there where I feel like there's something I Think it's in there. There's something that feels like it's just kind of waving right there. That's cool Definitely not as High as I thought since we're seeing the shadow here That's cool. I would probably still have some Like some stone pieces around here and some sticks or something so you can kind of see the travel And I know we have this but just kind of always gives us some interest It's not just this gray surface especially through here You might even have some cool moments of I'm always a fan of foreground elements where you know Something else could come by here Even if it's past there and then you can have something here to balance it out and some things here Overall once you're done, I would probably also take the surface wherever he is not Landing and moving and just take those vertices and move them a bit So you don't have that super flat CG you've got geometries of those cool Elements here and you can imagine that the surface is just a bit more Irregular this is super picky by the way just has nothing to do with animation there Okay, the roar is cool. I think through there that is my my timer I Think there's something where Once you see these these legs, I know this is very Presentational where I'm asked I'm asking you to animate something that's technically you don't really need but in terms of I know if that's what the creature would do but in terms of visual entertainment and And again Presentational value this is very subjective I would have something where maybe he brings those or it brings those legs together maybe a bit of a Curling of these guys or something that goes on through here and maybe through here as well So they don't feel like they just parent it. They're not moving Even if it's kind of a Tightening or an adjustment imagine maybe they're a bit further out and then through here They kind of get a bit more together maybe this one because of the dragon overlap The momentum there and then I will probably take these and from here on They're very slow in their movements. I think you can also have a bit a stronger offset. Let's see. I think you have the right one Yeah, just a tiny bit more. I think it's very cool once you get into here How they're both moving separately and you got this here. I like that the legs are moving here That's cool. You can probably go a bit further with how close they are together So you can kind of get more in and out Just for variety and movements. It's just something that feels just a bit still Through this section. You can probably also go potentially Slightly lower so it doesn't feel like this is so aligned with that tail Cool. I'm gonna look at the tail later You have the legs here. I know I should be looking at the whole body, but I'm always kind of fascinating by feet and legs and claws Got cool stuff in there though. All right, let's do the the sensible thing of looking at your the main mass and the roots Cool Here's a bit of a weird thing Right there on that drop. I feel like it would drop this way and then you have a sudden acceleration this way So it's it's not quite following this line. It's going suddenly to the left, but also accelerating a bit too much I'll keep this right through there. You can see this goes this way and then this way There so I would smooth that out. So it's not this sudden acceleration right There and suddenly more screen left. It's cool, too. When you do this you might even Have a moment of the roar like this and then by here Imagine that the head could be turned away from us It was like tilting away from us. He also wants to lean into the turn, but again gives us a change of silhouette It's not It feels like this is in one orientation and then it just kind of stays there and just again just for visual interest You can open and with a little bit twist over That's cool much at the head here right there again, it feels like a bit of a fast Move up right through there it goes up and then it kind of stops and this in real time Right there has been On things like this, which I love when you heckles up work right there Don't forget again same as before you want a bit of a sideways rotation So that you know that horn would be here in the lower one would be the right one screen left one would be down here Just it's not just in one axis you want to engage all of them for a bit more complexity and then Right through there be careful Let's pretend you would want that fast drop for whatever reason like it has hooks and it's being pulled down terms of physics being true here if Even if you change the timing to be smoother it still has a Certain drop here where I would bring that head up here. There's just something where once you're to here right through there This whole section with the neck and the head feel like it's one Piece of geometry just kind of drops down With no drag anymore And I think if you would delay the head a you would have a nicer silhouette You can you almost have the chin here you can almost separate that up with my awesome drawing here And because the head is a bit higher is a nicer negative space in silhouette and then boom and then on that impact Here is so imagine the head will be here the neck The head will be here By now you can hit this pose so that the head drops for it for an overlap and impact rotation down and then That's cool During this I would try to potentially translate that more screen left so to its right It feels like if that's the chest that the head is Kind of turn this way doing this and this the roar versus chests Doing this I'm going to explain this right, but there's something where I feel like this This is the head right and this is this is your chest where I feel like that chest is here Even though the curvature is like that As opposed to that chest and head curl this way So this neck piece out more screen left which brings the head maybe a bit more here I'm only saying this just because when you bring that head up here and then over this way I Don't see much in here Except a up-and-down rotation. See that Just kind of goes down Actually, it's a translate up, but I don't see anything in why so the white Rotation is a bit miss is missing there, but I feel like that head has a bit of a move to its right So what I'm thinking is that pull that head over translated over a bit more screen left So that imagine again chests And imagine this is your neck and it did this move right to the right I will pull this more to the right so that a it's more angled this way and because you are pulling this more You will take the chest in y rotation here and rotate this over so this You would see more of this side here Hope that makes sense Translate over rotate the chest in y with the neck. I just feel like the neck is doing a lot While the body is basically just rotating down and then translating up not quite affected by this I know there's a long way to go from the head to the chest with this whole neck area, but a Bit more connective tissue there with that translate over affecting this chest would be cool Even through here you could technically bring those legs a bit further down and then by now Right through there that will get to this so they kind of go back during this section I'm just trying to make it slightly bit more interesting visually. So it's not just this one piece gliding speaking of Axis I feel like that tail is also just mainly going up and down Whereas here you can kind of push the side to side a bit more and then you got some moments be careful This I don't want to say it's all for polish But as you get into this when you curl this and then the tail goes down by now that tell me a bit lower There's something where the tail goes Down and now it's stuck right through there. You can see their rotation. It's kind of stops. It's kind of frozen there and Going back to the body, which again, I should have said that the very beginning, but I was kind of look at details It's very annoying for people listening So on this here Because that head it kind of goes up and stops you're gonna have to continue going up with that head Because of that I will bring up that chest a bit more also because of that flap down There's a bit more of this of an arc kind of flap goes up a bit more and it can drop into this and Look at this here. You're dropping and Here you're leveling out and already going up and to me you'll be dropping dropping dropping dropping until Here so the wings around here and that Gets the head up and the body up. This is cool right there This is really cool I like how your body goes up and they already starts to drop pretty quickly at the physics there feel really nice Well, you're right there Drop and then it really fights to get back up Yeah, and then it goes back to what I said with the head here because you got that high energy of the head going up And here I feel like it's really trying to reach up And you want to bring up that had a bit higher inside a rotation to the side just give it kind of that that try Yeah, then here that sudden drop and it's on move to the left and screen space Polished off you'd be offsetting wings a bit more Drag just tips a bit more and then watch out they kind of come up and they're kind of stuck there I Keep going up or we'll have those tips there. Yeah offsetting wings is going to be cool You get some good drag there Good rubber lap. That's cool Yeah, and just tail stuff, which I know you're totally aware Polish stuff but through here because you have so much room could be cool moment of the bit more side to side So it's not just up and down Impact trimmer on the on the tail there. It's cool. I'm gonna be incredibly picky So that this spiky thing of the wing could rotate that up. So it's more here Basically, so you're mostly like a separated from this so this tip maybe up here. This is super picky. I'm just looking at Tangent moments like that and also seems to go through the ground too. So either way you want to go up a bit higher It's not that connection there It's very cool though, definitely much much better And I be careful with moments like this where I will probably from here on with the neck as It goes up here. You can go a bit more in line with that upper body here with the chest area So you don't have this kink here So it's been hidden in the wings, which is cool. And then through there. I would have that neck a bit lower So it follows a bit more and then when you go up, you really have a nice rotation up in a pull So that when you're here again, you don't have that kink here You want your neck to I wouldn't say full-on go up like that. It might be too strong But definitely a bit more like that.  This just feels a bit broken there And then on that impact, I don't know if you have any rotations This way or the other way and it would be a shake basically on the neck area. So imagine it's kind of a neck jiggle for polish through there Even the head would be On that if it's tilted already like this On that impact by now ish or so you can say that Instead of like this they're already lying like that It's a bit of a dip this way just you can feel that impact Down but also sideways rotation wise on the head That's cool. It's a big fan of that. You can almost have a And right through there for that last end one more up to the sides kind of That's a one more thing But don't really need this. I mean it's already super cool It just feels like it's Then you relaxes or it or she so that's totally up to you You can do a raw and then it stops or you can do a raw and then raw about more totally up to you It's very cool though. And then in your polish you can have a bit of a Tongue animation in there a bit of a shake through there as it all shakes through here. Maybe even bit of a Raw curved tongue that flattens then through here There's some movement in the mouth and then all of that shaking as you would have it in the tongue as well since Let's see here Yeah, you got something here Now wonder how far you could go. It's probably enough to go through here with a little bit of jiggle here I was thinking maybe it's a tiny bit here in the membranes would shake a bit But I think that's too much. I would just concentrate On this section with a little bit of jiggle through here kind of fanning out that energy. I Think that's it. I'm gonna let this be like that. You're gonna get into all your polish stuff But overall so much better. It's very cool Yeah, it's really neat. So as always any questions, let me know you can email me. There's anything that is unclear And that is it. All right. Thank you All right, there's an email you can sign up you can start whenever you want you can submit whatever you want You get 16 submissions either way a like and subscribe would be awesome. All right. Thank you


Awesome, yeah. Cura, yeah. Adam Moriarty, head of collection information access at Auckland's War Memorial Museum, and today I'm going to talk about voice search. That was a pretty boring introduction to myself and my talk book. I think we've got all the key points in there, right? Who I am, where I work, and what I'm going to talk about. And if you were counting, which I know a few of you would have been, that was 30 words. Now, why on earth would you care how long my introduction is? Well, 30 words is the average response time of a system such as Siri, or the Google Assistant, or Amazon's Alexa. And I heard that fact a couple of months ago. That's the average response of these devices, and it kind of got the gears turning. So I thought about how much time we have spent as a sector working on rich visual content as a way of storytelling and sharing our information. Whether that's our topic pages, or blogs, or research articles online, or digital interactives in galleries, or exhibitions as a whole. We spend a lot of our time making things that are much longer than 30 words. One of the jobs of my team is to help manage inquiries at the museum. I kind of played with the idea of what would it look like if I challenged our curatorial team to only respond to every inquiry in 30 words, and they're not allowed to use any imagery. It sort of starts changing how we think about the content that we have. And so, yeah, I started looking into voice search, and I'm not going to lie, I'm not someone who really had used it before.  Kind of got some privacy concerns there. And I think it's quickly, right at the start, I want to say, acknowledge there are some privacy concerns when talking about voice assistance. I'm not going to be talking about that today. I really just want to talk about voice as a search. So, acknowledging, parking, moving swiftly on. But we will have a lecture in the background. So, yeah, I kind of didn't really believe that voice was going to be this thing. It feels like it's something from the future, right? We were promised flying cars, and we were going to talk to robots. And voice is probably the one thing that maybe it's actually there. Maybe this is the future that we were promised has come, has arrived. And there's a couple of facts there just to help support that. There are now 500 million Siri-enabled devices on the planet, 400 million Google Assistant. There are 20% of American homes now have an Alexa. So, this isn't some future trend. This isn't something that is coming, the next big thing. I think we have to start acknowledging that this is something here right now, something that we need to start thinking about. It's how people are getting answers to their questions. It's how people are using the Internet nowadays. Another stat that I quite like is I think Comcast reckons that by the end of next year, so by the end of 2020, 50% of all searches on Google will be conducted by voice. So, this is how people are using the Internet nowadays. And so, I kind of wanted to delve into those figures. I wanted to think about how we could start using it as a sector. And so, I bit the bullet for all of us, and I went and bought one of each of these devices, put them in the office and at home and sort of ignored the privacy. I just put that to the back of my head and just started interacting with them to see how they would go. And I'm not going to lie to you guys, I love them. I didn't want to.  But actually, it was really great. I mean, because they're really convenient. They're fast, right? So, on average, I think the average typing, so it's 40 words per minute, but you can do 150 when you speak. It's a much more human interaction.   When am I ever going to need that in the kitchen? I need it all the time. And just being able to get that convenience in the office, being able to answer an argument incredibly quickly by just shouting and getting that answer. And so, you're really, really enjoying that and thinking they were cheap. I mean, almost all new phones come out with them pre-installed. And if you want to put one in your home, it's going to cost you under $100 to do it. They're small as well. Small footprints, so you can hide them wherever you want. And it's not going to be taking up in ugly, I guess, where I'm going with that. And they deliver quite personalized results because they know a lot about you. They know where you are. They know the types of queries you've done before.  So, they can deliver quite personalized results. So, yeah, I started getting on the bandwagon. This is awesome. We should get more of them. And I started thinking about that. The interactions I was having. And realized that I wasn't dealing with a search engine anymore. And we've got really used to working with search engines. It's what we spent a lot of our time getting our content ready for. Keyword searching. But actually, now we're dealing with answer engines. Because these systems want to deliver you a packaged answer. Because it's convenient. It's easy for you. They don't want you to go searching.  You got 10 results. 10 blue links. Now, it was up to you to decide whether you chose that promoted link at the top. Or the one the SEO marketer had spent the most time trying to get into the number two place. Or whether, God forbid, you went to page two looking for an answer. But it was up to you. You got to decide what you chose. Now we've got a system. We've got the wealth of the world's information out on the internet. But now we're relying on a couple of devices, a couple of corporations to decide what's relevant. And to package up an answer and deliver it to you. And again, that kind of got me thinking around, well, is this actually something museums, the sector wants to play around with? Is that something we want to get involved? Or is it something one of those fads we can just let slip by? Another shiny new tech that we don't need to get involved in. And so what I want to do today is just go through the three questions that I went through, essentially. So are we going to do this? Are we going to try and work with these systems? How do we do it? So if we decide yes, what are the technical things that we need to do? And should we? Kind of ethical question there. And so, yeah, are we going to do it? Unfortunately, I think if you're online, if you put publishing content on the web, you're already part of it, right? We're already putting our stuff out into the world. It has already been sucked up into the Google Knowledge Graph or into whatever these systems are. And we're putting it out there and it's getting used. And we don't have a choice. That horse has left the station. I don't know. I've mixed metaphors there. But something has happened and it's already gone. And so we kind of have to. Because someone else will be doing it or be putting content out there if we don't. Now, good news, a lot of our content is already out there. Because we spend a lot of time getting things like our opening hours and our prices and our parking directions and our what's on. We spend a lot of time getting that into a format so that it appears highly anyway. And so that information has just kind of been sucked up and it's there and it's ready to use. It's also, if I admit the kind of stuff I don't really care about, because I'm focusing on that collection content. So what do we have to do to get our collections ready for this? And are we wanting to put our collections into these systems? I guess just a quick sidestep. I got the assistance. I brought them into the house. And it took all of three minutes, I think, for my son, who is four, to work out how to use the Google Home. And four minutes and he was just chatting away. It took him probably at the 10 minute mark. He'd worked out how to control all the speakers in the house and get the poor patrol soundtrack blasting at 100% in every room. It was just pumping. He loved it. And there was this amazing sense of power that all of a sudden he had where he was just like, oh, this is awesome. I don't have to use a keyboard. I don't know what a keyboard is. I don't know how to use an ISO. I haven't had to learn anything. I've just shouted at this magic box and poor patrol is playing in the kitchen. And yeah, you could see him kind of like really get excited. And I don't know if anyone else has got young children, four-year-olds in our house right now, but the Coast Guard is king. Like anything, any information about the Coast Guard is just if you've got stuff, share it. Because that's all he wants to know about. And all of a sudden he can start asking these questions and we just would hear him up in the kitchen kind of just asking, well, do the Coast Guard take an oath? What's the biggest Coast Guard boat? How fast can that boat go? And we realised he was just there kind of just asking all these questions. And of course, if he hadn't got that, he'd have to have asked his naively challenged father.  We have canals and shopping carts. We don't have a Coast Guard. I know nothing. And so he's able to kind of learn something. And then he was telling me he was giving that information back to me. I haven't retained any of it, but it was an interesting dynamic. And at the other end of the spectrum is my mother-in-law, who's 73, and is the only person I have ever seen use Siri in public. And she just shuts at her phone aggressively. And it's not because I think she wants to, but it's because she can't use the keyboard. Or she's trying to think in case she ever watches the video. She can use the keyboard. She just struggles if she can't find her glasses. And she doesn't know where her glasses are. Glasses in her bag. No one knows where the bag is. And then she has to use the stylus. Now I don't know if you have to find the stylus in a 73-year-old's bag. It's impossible. So it's just a lot easier for her just to shout at the phone. And again, so there's two user groups there using this and using it for reasons that I'd never thought of. And I kind of realised that maybe in the middle, it was just a novelty. I had no need. I much prefer using a keyboard than I thought I did. And maybe actually these two groups, we were in the middle, we were thinking about how we get our content on and how we online and how we use search engines. We're actually these two different audiences who we want to engage. We're using and having this big uptake and kind of, yeah, maybe I had my my blinkers on, hadn't seen it happening. And so, yeah, it's with that kind of make me again think, so are we wanting to do it? Well, yeah, because these users out there, that's how they're getting their information. That's how they're answering some questions. So, yeah, we kind of have to think about how we want to engage with them. And so how are we doing it? So then we spend some time thinking about, well, what's the, how do we start playing with these systems? How do we start seeing how we can try and get our content in there? And luckily one that what we've been doing so far, what we've been working, what we've been talking about here for like the last five years, a lot of us are kind of already on that journey. It's about looking at things like structured data. How do you tag up your content in a way so that both machines and people understand it? We've been talking about this for a long time. If you don't know what the schema.org is, that's your homework. Go and ask Siri. She will tell you. It's the way of tagging up your content on your own website so that machines can understand what you're talking about. They don't have to use keywords. That's something we've been, as a sector, as libraries in particular, have been working on to make sure your content is understandable and findable. Now, you could, if you want, with Alexa, there's a skills store you can go and upload some content to. And it's really easy.  And you can run them locally, which is kind of cool. So we created a couple in the office that do things that are no use to anyone. But we can run them in the office and we could test and see how they worked. Literally uploading like an FAQ kind of questions, answers and keywords. And we've seen a couple of museums out there using that. In the U.S. they're looking at voice assistants in galleries is where you can ask a question where in a gallery it gives you a response. Could be cool. MoMet and Met have created little apps that are on there, the public, so anyone can download them, which give you a what's on. So in the morning you can ask what's on at the Met and it will tell you, it will give you a response. And unlike the sort of tagged data of using Google, they've able to create a bit of a narrative around that. I mean, you're still creating an app and you're reliant on people downloading it, but it could work. There's 100,000 skills on the Alexa store, most only have one review, so maybe it hasn't quite got there yet. And I have to admit, I don't want to be standing here telling everyone to make the next version of an app. So I'll stop there. When we when we got the devices, we started asking them questions. We asked each one of them 100 questions. And we quickly discovered that if you had an FAQ page, that stuff would come out really come out at the top. Makes sense, right? You've already written it from questions to answers. You've already done all the hard work. But again, a lot of the time we focused on the physical stuff, like how to get here. Where do I park? Can I get gluten-free sandwiches? You know, it's kind of the very much focused on the physical visit and very sort of, I guess, low-hanging questions. It was very hard to find examples where broader collection questions were getting answered in an FAQ format, or maybe it's just one or two, not sort of rich content that could be delivered through these devices. So again, definitely some work that I think we need to do both in our museum, but also as a sector about thinking of the questions that people are going to be asking and providing the answer. So it's easy for people to get it. And I think there's also, sorry, just a side step, Alexa also has, I think it's AlexaAnswers.Amazon. You can go and see all the questions that people are asking. And they're trying to crowdsource the answers. And so it's kind of crazy just to see the types of things people are asking and the types of crazy answers that are being given. The question I searched this morning, the question is Wellington, the world's windier city is still unanswered. So there's an opportunity there if you want to jump in. But it's kind of did the types of questions. The one that we came up with is, can I keep squirrels as a pet? It's like one of the top questions from last week. Yeah, you can't, it's a leave I found out. But it's, again, interesting to see that there are enough people asking that incredibly weird question. And so yeah, that's another way for us to kind of start looking at the types of things people are asking and helping to start building the answer, you know, thinking of the answers for them. And then the other thing, asking 100 questions of these devices, sort of interviewing them. The thing that came out the, you know, at the top, the thing that was the most common thing that we found is 90% of the time it started with, according to Wikipedia, blah, blah, blah. So once again, I'm standing at NDF to tell you about the power and importance of getting your content into Wikipedia, because that's where our people are going to look for information. And it's, it's a powerful way of sharing our collection, sharing our stories and putting our content where people are already looking. So if you're not working with Wikipedia, again, the barrier now is, is quite low for us to get in and create those pages or enrich those pages, add some, add some new sources, references, images. And it's a great thing because when you put the information in there, you're concretely changing what the world knows about our subject of expertise and also increasing how people can find out about our collections. I mean, it's a stat from last year, but we have one collection item in Wikipedia that sees 250,000 page views every month. And it's never been viewed. It's been viewed like 12 times on our own website. This is a great way to amplify your collections and share them. That's it for my Wikipedia kind of sales picture. You should be doing it. And it's also it's an organization whose mission and ideology I think we can get behind. It's not, it's not, we're trying to support Amazon or Google. And so that, that last question around, should we, should we be working on 30 word answers for, for concepts and collections that are far too complex for 30 words? I mean, are we doing it? Well, I think we have to it's, it's already there. The technology has started. It's already been sucked up into the, the knowledge graph. How do we do it? Structured data, things we're already doing. We work with aggregators and third parties to put our collections where people already are. Should we? It's a, it's a tough one, eh? 30 words, it's, it's not a lot. And we spent so much time on these rich deep content. You know, do we, is 30 words really worth it? It's, is it really something we want to be investing our timing? And I, I don't know, I think about that. And so I ask you, I guess, is it acceptable if someone who is searching for Mardi Culture on an Alexa gets hit with a blank end, you know, they don't get anything? Is it acceptable if a school child who is searching for Auckland history on a Google Assistant gets a response from a corporate tour operator who's trying to sell a ticket around historic Auckland? And is it acceptable if someone who has a spark of interest in content or collections that we are the custodians of reaches a dead end? Is it not our role as a sector to ignite that spark? No matter where they're looking, is it not our role, our duty to put our information out in whatever content or context people are looking so they can continue their journey, their journey of discovery, their journey to answer their question? And of course, 30 words, it's not much. It's not a lot of room to play with, but those 30 words may lead to another 30 and another 30. But they definitely shouldn't just stop. If someone has a question about collections that we look after, about information and knowledge that we have, we should be sharing it. Isn't that what we've spent the last 163 or however old your organisation is? Isn't that what we have spent the last 160 years working to create the tools, the expertise, the networks and the trust to put our information out into the world? And isn't it now more important than ever to make sure that someone is putting out trustworthy and reliable information, even if it's only 30 words? I really believe this is something we should be doing. And so to that answer, should we be working with these systems? Should we be putting our content out into the world? Should we be working with aggregators and Wikipedia? Should we be marking up our content in a way that is usable for those people and machines? Should we do it? Yes. Sometimes you don't need 30 words to get a good answer, right? Thank you. Thank you, Adam. That was brilliant. We've got some time for questions. Does anyone have a question for Adam? Adam, thanks for that. There's a substantial difference between voice commands and voice searching. Yeah. So I think the first half of your paper about, you know, wanting to find out more about boats was kind of fun, but not really relevant to what we're looking at in the glam sector, which is actually a philosophically more profound problem. So you have really two approaches to organising information and retrieving it. And one is more structured data and one is better search. And somewhere in between that you've got these new search capabilities like voice search, which have severe limitations at the same time that they open up new ways of thinking about what it is that humans search for and how they do that. So I think I wanted something in there in that kind of middle space. Yeah, that's one of those things where this is quite a broad from both voice interaction and voice as an interface into collection. So thinking of it as a, yeah, how are people going to be asking questions of our collections and the types of questions they're going to be answering, asking and how do we answer them? And yes, that kind of the search, yeah, acknowledging they are two different things, I tried to try to merge them into one kind of into one narrative. Yeah. Any other questions? No. OK, can everyone please join me?


My name is Kent Vleager and I'm the state soil health specialist with the Natural Resources Conservation Service here in South Dakota. And I'm here today to do the rainfall simulator.  And then we're going to observe what happens. Okay, so we've got the first tray you'll notice we label it as continuous grazing. Where if you have livestock, you turn your cattle out in the past year, let's say April on a typical year, and you leave the herd out there all summer all the way until October, for example. There's no rest. The cattle are always out there. They're always able to access the green plants whenever they want, and they're always taken from the plants. The next thing we have is called rotational grazing. Rotational grazing is a little more involved on the rancher or the farmer's part. And so what that means is they have to monitor the grass. And when the grass gets to a certain height or an established level, they take the cattle off of there and move them to a different pasture. And when they take them off, it allows that grass to rest. Okay, and then they don't come back to that pasture until the grass is fully recovered. These two soils here have been in a no-till system for over 20 years. And he has a three-crop rotation, actually four-crop, corn, soybean, spring wheat, and then winter wheat. And he follows that winter wheat with the cover crop. So what you see here is the cover crop example, and this is the after-wheat harvest. The last tray we have is a conventional tiller system. And so what this producer does is he farms corn, soybeans, rotates between those two crops, and he does tillage in the fall and tillage in the spring. So what we're going to see today is when I turn this on, you're going to see what happens with these front set of jars and back set of jars. The front set is going to show you everything that runs off. So if water hits here, it rolls down the tray, catches through and funnels into this. That means that it has not gone into the soil. It's gone off on the surface. The back set of jars is going to catch everything that infiltrates. That means the water goes into the soil, goes through the pan. These are what these pans look like when they're empty. You can see they're all perforated on the bottom. So when the water hits here, through here, it can go through the holes. And then we have a catchment tray in the back that funnels it into one hole and drops it into those jars. Okay, so the first thing I would like for you to observe, when a raindrop hits the soil surface without any cover, it actually breaks apart the soil aggregates. And so aggregates are little pieces of soil that are bound together by the plant roots and by the glues and things that the low ground life exudes. So when it hits that, it breaks them apart. And it breaks the sand, soap and clay particles into small little individual particles that you can't actually see with the naked eye, especially when it comes to clay and silk. And when they do that, it clogs up the soil surface. So it can't get through where the roots are infiltrating, where the worms are infiltrating. Okay, so you'll notice, you'll notice we've got this one right over here it's starting to run off. And this one's running off, right? But it's not running off on the middle three. The ones where there's a little better management, the soil cover is better. So we've got the continuous grazing. So while that one is infiltrating, it's because there's constant livestock actions. We've got some compaction on the surface. We've got the soil a little bit exposed. Those last two trays were bone dry. I reloaded those trays. The soil was all dry. It goes to your logic that you think that it's really dry. It should be taking in the water really fast, right? But it's not. We've got one that's running off quite a bit of soil. And jar's not even catching all of it. You guessed which ones we're going to infiltrate the most. The rotational graze one did. The cover crop took in. And the no-till one took in.  So this year when it's really wet, everyone says, well, the soil surface is saturated. We can't take any more water. At some point, the soil profile does fill up. But in most years, we should be able to infiltrate just about any rainfall that comes. And you can see these trays are about two inches deep. So I'm going to need a couple of volunteers. So what these two girls are going to do is show that the influence of management and land use can do on your soils. How you can actually benefit yourself by having more diverse application, by practicing no-till, by doing better grazing management. Because in most years, we're wanting rain. That's the first thing you notice. Okay, so this one kind of looks like wet chocolate cake or like black cottage cheese. Right? Right? Like a mud pie or a cow pie. There we go. And what's this one? So this is dry. So this is one way that we can encourage better management. Now in years like this where you have plenty for rainfall, maybe you're not going to see as much difference. One other plus that you'll have in this is this better soil structure. You can actually get in the field earlier in the spring because it can support your equipment waste better.


Hey, Psych2goers!  Being manipulative can come from environmental factors. For example, if you were raised in a highly competitive environment with little to no room for steady growth and affirmation, you would likely resort to underhanded acts and mind games to get what you want. Chances are you have good intentions in mind. Manipulation usually becomes your survival tactic when you're not acquainted with healthy ways to communicate with others. In today's video, we will be discussing 6 signs that you're unintentionally manipulative, along with some tips to help. 1. You tweak facts or events to your advantage When you're retelling an event to someone, do you notice yourself leaving out parts or twisting events because the original version doesn't fit your narrative? This is a form of manipulation. You're probably twisting facts because you want the other person to go along with your side of the story. You probably don't want to be in the wrong because it puts you in a vulnerable position and may even change other's opinions of you. Try to catch yourself next time you're changing the facts of a story. It's not easy to change something you're used to doing, but the important thing is that you've recognized it. After a while, you'll probably notice it more and more and give yourself chances to choose a better option. 2. You've unknowingly mastered the blame game Do you always try to point out other people's mistakes? Playing the victim often ends up with more problems than solutions. It can brew anger, start fights, and even end relationships. It's good to hold someone accountable for their actions, but when it looks like it's always them who's wrong, there may be an issue. Before pointing fingers at who's wrong, try considering their side first. Mistakes will always be mistakes, but by considering their perspective, you're learning to look at things with a more open, less judgmental mind. Also, when you're the wrong one, the best thing to do is just accept it. Do your best not to blame others. It'll just repeat the cycle and complicate things. Mistakes are lessons, and each one is an opportunity to grow. 3. Your go-to line is I promise Do you have a habit of making promises and shrugging them off later on? Promises bear weight. It requires a degree of responsibility to uphold. It's basically a personal agreement or an unwritten contract that when broken puts the trust between you and another person at risk. So when you have a habit of making promises and end up breaking or forgetting them, there's a high chance that you're leading on and hurting the other person. Remember that you don't have to make promises, especially if you don't think you can keep them. If you notice that it's difficult for you to stick to a problem, that's okay. Trying your best and proving yourself through actions is always much better than false words and hope. 4. You do good things for others while expecting them to return the favor. Have you ever been super kind to someone because of an ulterior motive in mind? If the answer is yes, don't beat yourself up too much. Plenty of us have also been there. Now, the issue arrives when you're doing everything just for the benefits. When you're being nice to someone or giving them gifts because you want to gain something in return, that's already manipulation. Plus, it can greatly hurt their feelings if they find out it's why you were kind to them in the first place. It causes hurt and confusion when you're applying the same method to genuine people with pure intentions. Being strategic and having good people skills can get you far, but sometimes putting other people first with no underlying motives can help them and you immensely. It's good to be selfless sometimes. 5. You tend to exaggerate Are you the type of person who tends to speak in hyperbole? Do you exaggerate facts to the point where they seem more extreme than the actual truth? For example, you have a friend who borrowed some money from you and forgot to pay it back. Because you're angry, you tell the other friends about the issue and instead of saying the original amount of money borrowed, you declare a bigger one. This can cause conflict among you and other people. If your main intention is to persuade, it's always better to relay accurate information first before sharing your own opinion. Not adjusting the whole story itself to fit your narrative. That way, you're being honest and open about how you feel. 6. Everything always seems to go your way Do you notice that nobody seeks to contradict you anymore? Is everyone following what you want even if they clearly prefer something else? When everyone appears to be subservient to your every wish, it probably means that you've gotten the hang of manipulating them. Or they've grown tired of it. You may not notice it, but you probably display manipulative behavior when things don't go your way. The people around you may be trying their best not to let that happen by going along with whatever you want. Often, you unconsciously resort to these acts because you don't know how to communicate your needs properly. Direct communication is highly important, and it's good to accept that not all things will go your way sometimes. Do you see yourself in any of these signs? If so, then please take this as a reminder to not let guilt get the best of you. Every human is prone to being manipulative. You're already an amazing person for educating yourself on this topic. It shows that you have a better, healthier road ahead of you once you take the initiative to build better habits. The first step is to recognize this behavior and then make peace with it. Identify why you act the way you act, and be gentle with yourself as you take small steps in healing. It's never easy to face negative aspects about yourself, but there's no doubt that you can do it and come out a better person than yesterday. Thanks for listening. See you next time.


What's up everyone it's your girl Kenzie here from Layton Sports Cards and I am ripping brand new release today at 2021 Penini Donress Optic Football H2 five box break number two random teams. Again here's a look at the random results you can always find these at LaytonSportsCards.com underneath the results tab and the link is also in chat for you. All righty best of luck everyone here we go. Well Chris I mean it's a it's a really small Dunkin Donuts so like trying to get out of the line once in it is like almost impossible so I was kind of like stuck at that moment. Plus I really wanted some pumpkin spice so that's that but hey we got it and we were on time for work so we're good. All right we got a base Zach Wilson rated rookie so and a hollow Damian Harris Patriots looking at football cards. Yeah we break football basketball baseball hockey occasionally soccer occasionally we've got our red mojo rated rookie Keeney and Wong Woon Vikings and hollow retro series Roger Stalbach. Again can be no giveaways right now at this point. But be sure to go over to Layton Gaming where you can find one there. We've got hollow red hot rookies. Jamar Chase. E.T.N. Moray we've got hollow rated rookie Trace Sermon Niners. NASCAR breaks we have NASCAR personal CS not so much breaks it that's one of the harder sports to do you know for group breaks. Amon Ross St. Brown rated rookie. We've got red mojo rated rookie Quitty Pay Colts and retro series hollow Rich Ganon. I just ripped a couple Don Russ hobbies the other night for personals. Sean Wright JC Horne we've got pink velocity Davis Mills for the Texans. Nice one there Houston Paul. Oh 54 of 79 on that Mills. Nice one there. I've been picking up his cards on eBay for the low and trying to I think he's going to do really well this year. We've got another off color match here Frank Darby on the red mojo Falcons and gifted rookie Zach Wilson. So what's up tiktok you can buy into our breaks at LaytonSportsGards.com. Be sure to check us out on Twitch and YouTube to Trevor Lawrence rated rookie base and red mojo. Back Jones Patriots Jonathan L. Whoo back to back breaks with big rookie quarterbacks on the H2 exclusives. Congrats that is a beautiful card. Loving these red mojo rated rookies. There you go. Very nice. Well man that one for you Patriots Jonathan L. And Elijah Moore on the gridiron Kings rookies. Yeah talk mostly NASCAR we just stick to personals though. We're going to tell some of those Dallas with the with the centering on the mojos. Shai Smith Joseph and hollow Michael Vick. What's up Emma. So up tiktok hope everyone's having a great day. Jalen Waddle on the rated rookie base we've got red mojo rated rookie Josh Palmer and Dami Brown on the elite series rookies. Looking forward to some more preseason football this weekend. You know looking forward to it. Trace Sturman we got my house hollow Kyler Murray. Again I got tickets for me my fiance and my niece surprising my niece for her birthday taking her to the game Steelers game in Jacksonville this weekend. Super excited. Jabril Cox on the mojo rated rookie cowboys and Travis Etienne on the rookies. That game is tomorrow tomorrow night. Really excited. Jacob Harris Jake Funk hollow rated rookie Dami Brown Washington. Trubisky was named starter CSC. But hopefully you know all three will we'll get some playing time like they did last week. So we'll be able to see all three of them in person. Nice one here Broncos little ps2 on the red rated rookie mojo. You know Broncos and hollow retro series Lawrence Taylor. You don't think so Jesse. I don't know. I know about that. How pits rated rookie. We've got Jalen Darden rated rookie silver circles to 125 rated rookie to Sean writes cowboys. That one is 45 out of 125. Oh you're asking for a weak one. Um I don't know I really don't. Oh nice one here we've got red rated rookie mojo Zach Wilson. Jets another one another one. There you go. Very nice break so far Robert S with the jets. Very nice first box we had Mac and now we've got Zach. Mac and Zach attacks going on. We'll make that and rising sun CMC. Right. Okay call me crazy but how do you feel about a most fantasy football CMC. Like overall second pick. I just don't like he's always hurt you know like I feel like I drafted him last year in one of my leagues and he was out half the season. Like that's such a gamble I feel like for the second pick. Got Nash on right on the red mojo. Cowboys in nice hollow white hot rookies Mac Jones. They are not they're just an exclusive. Got Michael Carter paint and turner we got an auto here out of 50 for the chiefs on the pink velocity Cornell Powell. That confused me to the first pink velocity was out of 30 this one was out of 50. Some of them are numbered the same and some are different. Then we've got the base autos that are sometimes numbered out of five. Little confusing there and Santos for the bears on the global. Yeah Chris I'm sure Sam would love it you're busy auto. Rhonda Moore. We've got red raided rookie mojo JC Horne for the Panthers and gifted rookies Rashad Bateman. Got them cooks later. Got Callan Mons raider rookie and hollow drew blood so patriots up tick tock be sure to go over to our YouTube and Twitch and subscribe. Moho Sukura Moa Schwartz and we've got hollow Chris Evans for the bangles. Goodbye into her briefs elite sports cards dot com. J. Brevin Jordan and wow back to back to back. Let's go Trevor Lawrence on the raided rookie mojo Jags. Boom. Paul K. Everyone eating this break. Wow. Mac, Zach and Trevor back to back to back. We are heating up here y'all. Whoo. There you go. Beautiful. Really liking these red mojos. Congrats. Wow and legendary logos hollow rookie Javante Williams Broncos. Okay I mean we've got some breaks that go down so you know usually around 1999 for some pick your teams and other various sports as well. So the prices do range. We got Justin Fields raided rookie and we've got Aqua to 299 Lydian Tomlinson. I'm not sure how much it's worth you know today with it being release day it's always going to be higher than maybe it is in a week or two. But then again season is starting up too so prices for a lot of cards continue to rise. Rashawn Slater on the red mojo Chargers and the rookies Grinator Kings Justin Fields. Um usually the those ones are like baseball. Our baseball products. What's up Scott. Trying man. Trying. You think so CS. Oh no I don't know about that one. Jalen Waddle raider rookie Alex Leatherwood and hollow raider rookie Cadarius Tony Giants. Let's spread the love Chris. I'm with it. Let's let's continue pulling some of these big ones. We got Richie Grant on the red mojo Falcons global big poem for the Chargers. Smart Jefferson Phillips got Jerry Judy Holly hollow Holly Cadarius Tony raided rookie. We've got red mojo Jalen Phillips for the Dolphins and hollow retro series Joe Thysman. All right. We've got another auto here coming up Richie Grant shy Smith. We've got chiefs again another pink velocity here to 50 shambuchelle. The chiefs we go chiefs and white hot rookies hollow tree sermon on Jacob Harris. We've got orange semi fahoko for the Cowboys out of 199 and by a powerful ticket. Jake Fox we've got shy Smith on the red mojo raider rookie Panthers gifted rookies of Elijah Moore. We do. We do have a shot front. We're based here in Orlando, Florida. Central Florida. Cadarius Tony on the red mojo raider rookie. There you go. Giants with another off color match there. Nice hit. Giants Mike W. And dominators Dak Prescott. All right. Last box here. What's up jammer. I like the spelling on that sports cars rules here in Ohio. Yeah. Well, if you're ever in central Florida, be sure to stop by. Come visit Disney and lean sports cards all in one trip. We've got Micah Parsons raider rookie base. Tray Lans raider rookie base and hollow Eric Metcalf. Stevenson Javante Williams raider rookie and hollow raider rookie Alex Leatherwood. And mojo raider rookie Greg Newsom the second Browns and my house hollow Zach Wilson. It's cool how in the H two, these are like cars in the hobbies. I feel like they were all die cuts. Those really funky looking die cuts. It's cool how they have both. We've got red mojo raided rookie Remandry Stevenson. I can see that one. The center on that one is a little far right. The other ones have looked pretty solid though. Justin Fields elite series. I don't know. CSU depends on the day. He said which lines are longer Duncan for PSL or Disney parks. Again depends on the day. Legendary logos. Hollow Aaron Rodgers. Pens on the day. Big palm. Jibril Cox. We've got Aqua at 299 Earl Campbell Oilers. We'll go to the Titans. Appreciate a jammer. What about the Duncan inside Disney? Oh, good luck with that one. Got PS2 raider rookie base. Red mojo raider rookie Pete Werner Saints. And Rising Suns Jalen Rager. All right, last one here. Mickey Mouse to do a break. Hey, maybe it made me for Halloween. You never know. You might make an appearance. Chris Evans for the red mojo. Bengals and Kyle Pitts the rookies. All right. What a break. Wow. First three boxes got the exclusive red mojo raider rookies of the top quarterbacks. One second. We will do a quick recap here. All right. We had a couple autos as well. We had the shambuchelle to 50 for the chiefs on the pink velocity. Another chiefs taking home both autos. Actually another one out of 50 Cornell Pala on the pink velocity. We have a Trevor Lawrence on the red mojo raider rookie Zach Wilson on the red mojo raider rookie jets. Mac Jones on the red raider rookie Patriots. And then the pink velocity Davis Mills out of 79. What a break. Congrats everyone. We've got another one of these coming up in just a few. Thank you.


So Here we have some smart jewelry. So who are you?  How does it work? Connected Bluetooth with a smart ring So Bluetooth to smart ring. Yeah, and if you go in here, you can see the device is gonna blink. Yes And does it vibrate also inside vibrate and 12 LED light Nice can each LED can do different function The LED firstly it can show the clock What's the time is it then when you're cos calling the light will be Reminding you and the vibration will remind you the calling is coming Nice, and here we have a smart ring also. Yeah, can you take off? Yes Let's see how it looks There How long is battery life a six months six months Factory how long it lasts the battery six months. This is can charge in charge in the air nice charge. How often? Often need to charge Every day or every week or every week once a week. Yes, and this one for six months Three months to six months Can you do something by tapping it or no? Tell me it. There's no function to do like this No But there is a vibration inside and it's Bluetooth for Connecting to iPhone and Android. All right. You can download the application in Angel and LS download this And how much it cost? What's the price For how many pieces 500 pieces MQ and only this color would have different one There are three types So many Which one is most popular design Is it real gold? Yes There is Nice is it possible in the future there will be more function with the APK. Can we see? Yes, we see the APK Let's see something But you can sign to the different kind of people you wanted to save case Important call so when you get a call from Ella. What happened? Then there will be a if I like how your phone this black alert will remind you All right, and this can Drink alert you can sign to the internal time internal time 20 15 anytime you want drink alert drink alert. Yes. What does that mean drink? Reminding drinking water. What time drinking month every 12 minutes You have to drink What does it mean? Yeah, just drink later. It means if you walk a speedy so you forget to drink water this application can remind you to drink water in what time and drinking waters


In this video, we're going to prove the main result of lecture 17, that every principle ideal domain is in fact a unique factorization domain, or more particular, if D is a principle ideal domain, then D is a unique factorization domain. I guess that doesn't specify much more, but we're going to be talking about this domain D. It's a PID by assumption. We have to prove it's a unique factorization domain. Now, of course, to be unique, to be a unique factorization domain, there's sort of two things have to happen. First of all, of course, it does have to be an integral domain in the first place, but that's a non-issue for a principle ideal domain because both of those definitions assume the ring in question is an integral domain. So then the idea comes with unique factorization, which really unique factorization breaks up into two parts as well. So to have unique factorization, first of all, you have to have factorization. Every non-zero non-unit element has a factorization of irreducibles. That's the first part. So there's an existed statement of factorization, but then the unique part says that two different factorizations of the same element are really equivalent to each other with regard to equivalence of factorization. So they're not really different factorizations, you know, up to relabel or up to order of factors, associates of irreducibles and things like that. So that's how we're going to proceed forward. We're going to first prove that if you take a non-zero non-unit element of a ring, we're going to call in our PID, of course. We're going to call that element A, it belongs to D. If we take a non-zero non-unit element A, we have to first prove it has a factorization consisting of irreducible elements. Then we're going to prove that that same element A has a unique factorization, that two different factorizations are actually the same thing. So let's take this element A. So the first thing that we're going to claim here is that A has an irreducible factor. Clearly, to have an irreducible factorization, you need to have all these different irreducible factors, but does it even have one? Okay, that's a very important concept. And so that's the first claim we're going to prove here. So if A was an irreducible, it would be a factor of itself, because you can just factor A as one times A, so we'd be done. So we can assume that A is, in fact, it's a reducible element. Therefore, it has a factorization factor A into A1 times B1, where neither A1 nor B1 was a unit. And so what that then means because of this factorization, the principal ideal generated by A is contained inside the principal ideal generated by A1. And this containment must be proper. Since B1 is not an associate, well, let's say this way, since A1 is not a unit, that means B1 can't be an associate of A, but also goes the other way around. Since B1 is not a unit, A1 is not an associate. So we know that this ideal is not equal to this ideal, because principal ideals are equal to each other if and only if the two generated elements are associated to each other. So we have a proper containment. We also know that this is not the whole domain, because A1 itself is not a unit. Now, if A1 was an irreducible element, we would be done. So let's suppose that A1 is not irreducible. So it also has a factorization since it's a reducible element into a product of A2 and B2, where again we can assume that A2 and B2 are not units. Let me bring the words up here. And if by similar reasoning, this tells us that the principal ideal generated by 1 is properly contained in the principal ideal generated by A2. Because again, A2 is not an associate of A1. And again, this is not the whole domain itself, because A2 is not a unit. So if A2 was an irreducible element, then we could stop because that's the irreducible factor of A by transitivity of factorization here. So if A2 is not irreducible, that makes it reducible, and then we can continue to do this process. So we continue to factor, factor, factor. So we take a factor of A, call it A1, then we take a factor of A2, excuse me, a factor of A1, which we call A2, then we can take a factor of A2, call it A3. And if these elements are continuously not being irreducible as the reducible elements, then we have an ascending chain of ideals. At each step, this containment grows properly. And so we have an infinite ascending chain that never stabilizes. That's not possible in a principal ideal domain, because principal ideal domains are noetherian. And noetherian rings satisfy the ascending chain condition by definition. Therefore, that tells us that at some point this process has to stabilize. There actually is one of these factors, some An, that's in fact irreducible, excuse me. It's going to be irreducible. And we're commutative and everything. So what we're going to have here is that A factors as An. And then we have, of course, have all these B's floating around here, B1, B2, all the way up to BN, like so. And put those together, we do have a factorization where An is irreducible. Going forward, we're going to call this element P1. And this is because we want to think of it as a prime element in a principal ideal domain, primes and irreducibles are actually one of the same things. And so this proves that A does in fact have an irreducible factor. Now, I wanted to make a comment before we go on here. We didn't really use the fact that the ring D was a principal ideal domain. We just argued that it was a noetherian domain. So in this situation, a noetherian domain implies you have irreducible factors. Not necessarily an irreducible factorization, but every non-zero non-unit element had an irreducible factor because of the sinian chain condition, which a PID does satisfy. But more broadly, a noetherian ring, a noetherian domain would have the property that every non-zero non-unit element has a irreducible factor. So we're then able to factor A using P1, which is irreducible, and C1. Now, if C1 was a unit, we would be done because then this would be an irreducible factorization, because that actually would imply that A itself was irreducible. If you're an associate of an irreducible element, you yourself are irreducible. So let's assume that C is not a unit. If C was itself an irreducible element, then A would be a product of two irreducibles, so we would be done. So we then might want to consider what happens if C is a irreducible element. But if C1 is reducible, even if it's irreducible, that's fine. If it's reducible, you at least have an irreducible factor by the previous claim. So because C1 is not a unit, it's also not zero because that would imply A was zero, C1 has an irreducible factor, call it P2. And so we don't even have to consider whether C1 is itself irreducible because it could be that C1 and P2 are actually the same element and C2 is one. That's a possibility. But that then changes the factorization of A to be A equals P1 times P2 times C2, for which P1 and P2 are known to the irreducibles. Well, is C2 a unit? If C2 were a unit, then this would be an irreducible factorization of A because P2 times C2 would be, well, which is of course equal to C1 would have been irreducible in that situation. So if C2 is not a unit, then we could continue this process. But does this process ever stop? The answer has got to be yes. Because as we look at this chain that we've created, the ideal generator by A is contained inside the ideal generator by C1, which is then contained in the ideal generator by C2, which is then contained in the ideal generator by C3. And so every time that C is not a unit, this ideal grows. And we get bigger one and a bigger one and a bigger one. And so if C never becomes a unit, then we have an infinite ascending chain that never stabilizes, which contradicts the ascending chain condition. Which again, principal ideal domains satisfy the ascending chain condition because they're noetherian. So what this means is eventually this ideal is going to stabilize. And at that moment of stabilization, the number C had to in fact be a unit, in which case then a unit times an irreducible is still an irreducible. And so we then get this factorization into irreducible elements. A equals P1 times P2, all the way up to PR, where R was the step where this process terminated with this ascending chain. All right. So this then shows that A has a prime factorization. A does have a factorization inside of A, has a factorization into irreducible elements. So again, highlighting what we saw here, we haven't really used the fact that our ring is a principal ideal domain except that a principal ideal domain is noetherian. So if you have an oetherian domain, I want you to be aware that an oetherian domain implies the existence of prime factorizations. Although in a general domain, we don't necessarily know that irreducibles are always prime, so we should call it an irreducible factorization in that situation. So you can see of course the use we have of the ascending chain condition that principal ideals have. The ascending chain condition gives us that we have these prime factorizations for every nonzero nonunit element. So what about the uniqueness of factorization? So we know that PIDs like every noetherian domain have irreducible factorizations. Why are they unique? So the uniqueness of factorizations where we're going to see where the principal ideal component comes out here. Suppose we have A still, which is a nonzero nonunit element. And let's say it has two distinct factorizations into irreducible elements. One of them is P1 times P2 all the way to PR. Another one is Q1 times Q2 all the way to QS. And each of the PIs and the QJs are irreducible elements inside of the domain D. And for the loss of generality, or without the loss of generality, let's assume that R is less than or equal to S. We're going to prove that R equals S and that there's the one-to-one correspondence between the irreducibles that these are actually associates of each other. All right? So how are we going to do that? Well, if you take the first irreducible factor P1 in the first factorization of A, well, because A can be factored using these P's, that means P1 divides A. But A is also equal to the factorization Q1 times Q2 all the way up to QS. Now, we've previously shown that in a principal ideal domain, irreducible elements are prime elements. And therefore, a prime element, by induction, if it divides a product, then it has to divide one of the factors. And so let's say that P1 divides the irreducible factor QJ. One of those, it has to divide one of those by basically just prime elements by definition are those elements that satisfy Euclid's lemma. It has to divide one of the factors. So up to, you know, we can relabel things, right? So up to a rearrangement, we can move QJ up to the front and we'll then call that one Q1. And then the previous Q1, we can call that now QJ, whatever, just relabel things. We can assume that P1 actually divides Q1. And that therefore will make them associates because Q1 itself is an irreducible element. And so if we have a factorization here, Q1 equals P1 times something B, I will call B1. These are have to be associates because P1 and Q1 are both irreducibles of each other. So that's the first one. So up to a unit, let's actually, I guess I noticed down below I called that unit U1 for unit there. So if you have that, you can then replace the Q1 on the Q factorization with P1 times U1. You can cancel out the P's since we are in a domain. We have the cancellation principle. So then our factorization reduces down to this. These two things equal each other. We're going U1 is some unit here. But then the same principle happens as well. Q2 divides this factorization. Therefore it has to divide this factorization. So because irreducibles are prime elements, then that means P2 divides one of the elements QJ. Without the loss of general order, we can assume that P2 divides Q2 so that Q2 factors as P2 times some unit U2. And so then we can cancel P2 from both sides.  We then have U1, U2, which as U1 and U2 are both units, they're product as a unit. We then have Q3 all the way up to QS. And then we can keep on repeating this process, constantly canceling out all of the irreducibles in this factorization. We cancel in now with some QJ until we eventually get the following here that one on the left-hand side, because we cancel out all of the irreducible elements PI, is then equal to the following, which of course U1 all the way up to UR. That product is a unit because each of those U's is a unit. But then we also have these elements right here. But wait a second. If you take the product of QR plus one up to QS. If you multiply that by U1 up to UR, that equals one. This tells us that the product QR plus one up to QS, that product is a unit. And each of the individual factors in that would have to be units themselves, which means they weren't irreducibles. That would be a contradiction. That contradiction only happens if S is strictly larger than R. So we would have to conclude that S is in fact equal to R. We have the exact same number of irreducibles in the two factorizations. And this cancellation process we did earlier then determines the one-to-one correspondence between the irreducible factors PI with the irreducible factors QJ. And this one-to-one correspondence was always an association correspondence. And so up to reordering and up to association, it turns out these two prime factorizations were in fact unique. This then proves that every principal ideal domain is a unique factorization domain. And if we summarize, we did prove that every noetherian domain will have irreducible factorizations. But without the principal ideal assumption, we can't actually prove that a noetherian domain is necessarily going to be a unique factorization domain. In fact, there exist counter examples to the contrary, which we can have a noetherian domain that is not a unique factorization domain. Of course, our favorite example is going to be Z adjoined the square root of negative 3. We know this thing is not a unique factorization domain, but as we mentioned earlier, this is in fact a noetherian domain. So in a noetherian domain, you have irreducible factorizations, but they're not necessarily unique. In a principal ideal domain, those factorizations are in fact unique, which is what makes it a UFD. So every PID is always going to be a UFD. So the class of PIDs sits inside of the class of UFDs, but this containment is in fact proper. There do exist unique factorization domains that are not principal ideal domains. And an example of this will be provided some other time, not in Lecture 17, which we actually bring to a close right now. Thanks for watching. Like these videos if you've learned anything about principal ideal domains. Subscribe to the channel to see more videos like this in the future. And post any questions you have in the comments below, and I'll be glad to answer them when I can. Bye.


Okay, to this point we've taken a look at the basic parts of the chord, the root, the third, the fifth, and the seventh. And now we want to look at some extensions of those chords, mostly known as the ninth, eleventh, and the thirteenth. So we're going to take a look at a D minor 7 chord first and see how to extend that like this. Okay, so we're going to take our D minor 7 chord that we just played, and basically hopefully you've noticed by now that all of our chords are just stacked thirds, the interval of third, D to F to A to C, those are all thirds that give us that chord. Now we're going to continue to stack thirds, so a third above C is E. So if we play the third, the fifth, the seventh, and now the E we're going to call the ninth because if this is the seventh, seventh, eight, seven, eight, nine, gives us the E. Now you might say, well, isn't that the second scale degree of the D scale? It is, but when we go an octave above, we usually call that the ninth. So we're going to have three, five, seven, and nine. Now you might say, well, that looks like an F major 7 chord. It does, but the bass player is still going to be playing the D, so it really gives us a D minor 9 chord, okay, and here's the nine. Now if we move the thirds up once more, the fifth, the seventh, the ninth, and G is now the eleventh, then we get an 11 chord for the D. Now again you might say, well that looks like an A minor 7 chord or a dominant 7 chord. It does look like that, but it really depends on that bass note. So in this case we're calling it a D 11, and then finally 7, 9, 11, and 13 looks like what? It looks like a C major 7 chord, but with a D in the bass, we're calling it a D minor 13 chord. So let's take a look at all those together. Here is the D chord, just with a 7, we move our thirds up. Now we have the 9, the D minor 9, here's the 11, and finally here's the 13. And we're going to experiment with using these, even when the chord progressions don't call for 9s or 11s or 13s, sometimes we'll use those anyway because it makes the chord progression more interesting, and it also makes it easier to play on the piano from a voicing standpoint where your hands are going. So we'll do some more with that moving forward, but I just wanted to introduce to you what extensions are, and later we'll talk about how we're going to use those.


Worried about the United Nations? Anxious about those bills piling up? Want to get away from it all? CBS offers you escape. You are the victim of a native witch doctor. Pursued from the West Coast of Africa to the West End of London by the grinning face of a dead man. You are under the curse of a poor man. The Columbia Broadcasting System and its affiliated stations present escape. Produced and directed by William M. Robeson and carefully plotted to free you from the four walls of today for a half hour of high adventure. Tonight, we escape to the dark lowlands of West Africa and the mind of a man who scoffed at native magic as H.G. Wells paints it in his gripping story, Pollock and the Poor Man. I had spent considerable time in Africa, but I have given little credence to the many superstitions of the natives there. Voodoo curses, weird incantations of witch doctors and the like, had always seemed a pretty silly business to me. But that was before the affair of Pollock and the poor man. Even then, while the thing was happening, I took little notice. It was only when I got back to England some months later and went to see Pollock climbing up the three flights of stairs to his lonely bedroom that I began to realize the ghastly truth of it. One look at him was enough.  It was good of you to come, Waterhouse. Nonsense, old chap. I just thought I'd look you up and say hello. But I had no idea I would find you ill. Ill? Yes, I suppose I am ill. I suppose that's what you'd call it. What in heaven's name is the matter, Pollock? I, uh... I said come closer, will you? I'd barely see you. Oh, yes, of course, sir. I'll just drop a chair. Oh, no, no! Pollock, then. What's the matter? Oh, no. Take it away. Take it away! What are you talking about? What is it, then? That thing in your hand. Take it away, please, if I haven't said it. What? In my hand? Pollock, this is only my hat. Your hat? Why, yes, of course. Just an ordinary black humble. Now, if it's style is offensive, too, you ought to... Oh, no, I don't know. I'd... Just put it on the table, the floor. Somewhere where I can't see it, please. Of course, old man. Yes, I... I suppose you think I'm male. I don't mean... I know you do. Everybody does. I'm used to it now. And the worst of it is... Perhaps I am. I say Pollock. Only, I don't think so. Because I do see it. I don't care if no one else does. I can see it. See what? The head. That hideous face following me everywhere, grinning at me. And always upside down. Pollock, what are you talking about? You don't believe me either. Well, look at my wrist. It's broken. The bandage is still on it. That's real enough, isn't it? Yes, of course. Broken, you say? Yes. It did that. And my other accident. When I first got back to England, they said I walked in front of a bus, but I know better. It did that too. A head? Exactly. You wouldn't expect to see a man's head come rolling down the middle of a busy street in London now, would you? Oh, Pollock, you'd better lie back. Rest a bit. I'll call a doctor. You too. And I thought you might understand. After all you were with me when it started. It was you who first warned me, who sent me home. You don't mean that business with a poor man? Oh, yes. Yes, of course. You remember how it started? We were camped at that little village on the lagoon behind the turn of Peninsular. It was swampy and hot and I was bored to tears. Maybe that's why I did it. But anyway, when I got back, you were furious with me. No, no, no.  You've got to take it back immediately, do you hear? Oh, what possible difference can it make, Waterhouse? Why, all this fuss, old boy, it's only a little wooden statue. Can't be worth anything, except for a curio.  You know, very well, this is a porous idol. You must have stolen it from the hut of a witch doctor. Well, and what of it? Don't you see to them this is sacred, as sacred as an altar cross to a Christian. You've not only committed a crime in their eyes, but a terrible sacrilege as well.  I should be frightened to death. Before they can do anything, you're going to take this back where you found it and apologize to the poro man.  Pollock, I've had about as much of you as I can stand.  I can't turn my back but your running crossways to them, getting you some scrap or other. The third time this month and this time it's serious.  I honestly think it would be best. As a matter of fact, I'm all for it. I'd be very happy to get out of this sticky, dirty Godforsaken place. Very well. But before you go, Pollock, for the good of the expedition, you've got to take that thing back and apologize. All right. I don't think I'd better. Why not? Well, tell the truth. I don't think they'd give me a chance to apologize. All right. Tell me what happened. Oh, nothing very much, except... Well, as I was carrying the thing away, he went and those chaps popped up and saw it. He started yelling, trying to take it from me. Yes, go on. Well, we had a bit of a tussle. I got away. Go on, Pollock. We were on the bank of the river and I toppled him over, that's all. He fell into the river? Yes. I think he may have hit the rocks first. Was he badly hurt? I don't know. I didn't stop to find out. He was dead, wasn't he? I really don't know.  You know what was an accident? I had no intention... An accident? A lot they care. It was bad enough with the idol, but you've probably killed a man. We're in for it now. Well, there's nothing to be frightened about. Nothing! In the first place, I should think even your conscience would suffer a little. The second, you don't seem to understand about this poorer business. It rules the country. It's the law, religion, medicine, everything. And these poorer are the most vindictive men on earth.  And there's no telling what he will do. Oh, come now. You don't believe in these voodoo curses and things? Of course not. I'm thinking of something much more real than that. You mean you might try something rough. I can only advise you to lie low until we can get you out of here in the morning. I'll take you as far as Suleymane and see you're safe aboard a steward. You needn't. I can go alone from here. Not far. You still don't understand this business. You wouldn't get a quarter of a mile from this camp alone. I still thought you were making a mountain out of a molehill waterhouse. But I must admit I didn't sleep much that night. I lay there on the mat in my heart and listened to the sounds of the village. And then later to the noises of the night wakening jungle. Sometime after midnight I must have dozed off because I awoke with a start. For a moment I was confused, but I sensed something wrong. And then framed against the moonlight square of the door I saw a hand upraised and in it a knife. Stop it! Stop or I'll shoot! Stop!  Pollock, Pollock, what is it? What happened? I missed the beggar waterhouse. I missed who? Missed who? What happened? The poor a man. Waterhouse he was in my heart. He had a knife. He tried to kill me. Now wait a minute. Wait a minute. Wait till I find a light. There. Are you all right, man? I'm all right. I just saw it in time. He rode aside and I'm... Look. In my bed. The knife. That was a narrow one. Well, perhaps now you understand the seriousness of this. Waterhouse I saw his face. He stopped just at the door for a second. He was crouched down and he looked back at me from under his arm. His face was etched clearly in the moonlight. It was upside down. I'll never forget it. I'll get you a drink. Listen, Waterhouse. Listen.  See that in my dreams. Steady on, old man. Here you are. Drink this. All right. Waterhouse. The idol's gone. I've just noticed the idol's gone. He took it. It's gone. Yes. Well, then it's all over. He got what he wants. He won't follow me again, will he? I'm afraid there's more to it than that. But he's got the blasted idol back and he won't try it again. Will he? I've just noticed something too, Pollock. There's something here on the floor.  Too bad you aren't a better shot. Why? Why'd you say that? Because I'm afraid we haven't seen the last of this business yet. You were more right than you knew, Waterhouse. The next morning was only the beginning. We were standing by the river and supervising the parking. I'm glad we're getting out of here. There's something brewing or things wouldn't be so quiet. Oh, what would be brewing? In a copper pot, probably? Dancing in a circle of skulls, putting curses on you? Oh, that. What can he do? How the devil should I know? There are versatile people. They know a lot of rumdaches. The best thing to do... Look out! Oh, man, that was close. What was it? One of their beastly poisoned arrows and the tree behind you. Missed your head by inches. I came from over there in the bush. Let's do something. Let's chase him something. No use now. Never find him in there. The best thing for us to do is to get out of here quick. Well, we got out all right. You remember how we went down the river, keeping as far from the banks as possible? Huh? You thought I was safe when you got me to Selim and said goodbye. Didn't you, Waterhouse? So did I. You said goodbye and went back to the interior. Nothing happened. And for two days and I was beginning to feel that the whole thing was just a nasty dream. And then, then as I was walking in the compound, I was hit in the arm with a slug. It was a long shot. The bullet was spent. I only got a flesh wound. But I knew he was there. I decided to confide in Brea. Little Portuguese would rid me of hotness compound. He took it seriously. It is a personal question, you know. It's revenge, see? And he must hurry because you will leave the country. Yes, I'll be on the boat to Freetown in three more days than I'll be rid of him forever. Perhaps. Then there's this magic. Of course, I don't believe in it. Superstition.  You have any bad dreams? Well, there. Keep seeing the beggar's head upside down grinning at me, showing all his teeth the way he did not. That's nothing to be afraid of. It's not pleasant either. Then they say poor men send snakes. Have you seen any snakes lately? Well, only one. I killed one this morning on the floor under my hammock. I almost stepped on him when I got up. Of course, it is coincidence. Still, I would keep eyes open. Then there is the pains in the legs and arms. I thought they were caused by miasma. Probably they are. When did they begin? Well, three nights ago the night... Oh, blasted. It's nonsense.    Anyway, not yet.  Of course, it is our talk. You must not worry about it. No, of course not. But I wonder what he will be up to next. Perhaps it is I who should be up to something. What do you mean? Never mind. But I am not one to just sit and take this. That very afternoon I had a conversation with a rough-necked Mendei tribesman I found there in Salima. He showed me a little iron dagger and demonstrated how one struck at the back of the neck. He agreed to do the job for the price of a double barrel gun with an ornamental lock to prayers feeling better than I had in days. That night the Portuguese and I were sitting in his living room playing cards when suddenly the Mendei rough strode in without so much as a knock. What do you want? Oh, what's you? Have done what you tell me. Have proof. What is it you have in the package? Is that blood dripping? Proof. Here. His head? Oh, no. No, no. This man you want, now I get gone. You didn't have to bring this. I didn't ask for such proof.   Why should I? But he will not be able to take it off now. What do you mean, take it off? Look at the cards. They are all spoiled with this blood. What do you mean, take what off? You must send me a new pack from Freetown. Can't buy them there. Take what off? It is only a superstition, I forgot. The natives say if the witch, he was a witch, but it is all rubbish.   It is very silly. Gun. Now. Yes. I'll make you two guns if you'll take that beastly thing away. No. One gun. Now. No. All right. Friar, that gun you have for sale, give it to him. I have the money right here. Yes, sir. Over here. Take it and go. Thanks.  Just the way I saw him that night. Just the way I see him in my dreams. Like it was waited that way. You will take him with you when you go. Maybe take him now. My cards are all spoiled. There is a man who sells them in Freetown. You should have killed him yourself. Stop it. Stop it. Stop it. I took the thing to my hut. And no matter what I did, it always came to rest upside down and glaring at me. I got a shovel. I buried it in the soft earth behind the hut. But in the middle of the night, I was awakened by some sound in my room. What is it? Who's there? Speak up or I'll shoot. Oh, a dog. Only a dog. Yes, it is only a dog. But in the morning when I awoke and started to get out of bed, in the center of the floor glaring at me upside down, it was uncanny until I remembered the dog. I found his paw prints and then dug up earth outside and I knew how it got there. I took the thing down to the river. I threw it as far as I could into the current. At last I'd be rid of it. Late in the afternoon, a little steamer arrived that would take me away from this insane land of the power and Freetown and civilization.  Is that boat carried me swiftly away from the shores of the Bora land? At last I would be free and soon I'd be back where poro and curses and nightmares would be forgotten. I was standing at the rail sighing with relief when the captain of the steamer whom I'd met before strolled out and began to make conversation. After the usual exchange of pleasantries, he said, I picked up a rum curio on the beach this go. It's a thing I never saw done this side of Inge before. Why is that so? The head of one of these poro chips all ornamented with knife cuts. I say, what's the matter, old chap? The green in the face. I wouldn't have took you for a bad sailor. Oh, I'm quite all right. Well, this ill I was telling you about is a bit queer in a way. I've got it in a jar of spirits in my cabin.  Here I say, old chap, what's the matter? Stuart! Stuart! That was the last straw, I suppose. Something seemed to snap in my brain. For the rest of the voyage I lay there in the bunk, staring at the ceiling. And I had the strange sensation that the boat was made of glass. Transparent. And then I could see up through the ceiling into the captain's cabin. See the poro man's face floating in a jar of alcohol upside down, grinning at me. Of course, the actual head is still in the captain's cabin in Freetown, but it didn't matter the poro man's work had been done by then. Because now I carried it with me everywhere. In my brain. I saw it everywhere, anywhere. Any object that was round, like a hat or a pillar of ours, suddenly developed features when I looked at it. Ugly, scarred features with a grinning, mocking mouth. Features turned upside down. When I docked in London, I went straight to my banker's office in Cornhill. And the security is all in order, Mr Pollock.  Then to... I say, Pollock, what are you staring at so fixedly? That thing. Hanging from your mantelpiece. Oh yes, I see. The potted fern. Rather pretty one, isn't it? Oh yes. Yes, it's very pretty. I must do something about it, though. It's always dripping water down on the fender of the fireplace. Makes it rusty. I was wondering about that. It looks... Red almost like blood. Rust, you know. Yes. Oh, by the way, that reminds me, can you recommend a physician for mental troubles? I've got a little, uh... what do you call it, uh... hallucination. The poor man grinned at me fiendishly and I stared back at him. The banker watched me very curiously for a moment and then he gave me the address of a doctor and I left his office. That's when my accident happened. To a man who's been many months in the jungle of busy London streets, confusing enough. But when a head comes rolling down the middle of the street and between your legs... No! No! I was in the hospital for weeks. The only permanent injury, however, was the loss of the tip of my little finger. By strange coincidence, the same fingertip of the left hand that I'd shot off the poor man that first night. Well, even in the hospital, the poor man was with me all the time. Everywhere the doctors couldn't help me. My friends couldn't either. So I tried cycling in the country. But that thing kept rolling along beside me and getting tangled up in the wheels and spilling me. That's, that's, that's how I got the broken wrist. It... Well, the worst came only last week. I'd just come back from a long walk, hoping to be tired enough to go to sleep. As usual, that bronze vase was over there in front of the big French window. And it... Well, perhaps the poor man enjoys the view of the street three floors below.  Yes, Pollock. I am still here. What, what, what did you say? I said I am still here. And I always will be. No, no, not that too, not that, no. No, no, no. Now you understand, Waterhouse, I not only see the poor man, I hear him too. Pollock, old chap, this is frightful. No, it is, rather, isn't it?  Now, surely there's something someone can do, some doctor? What can any doctor do? Can he take off the poor man's curse? Pollock, that's nonsense. And you know it. Oh, is it? Of course, man, it's all in your mind. All, what do they call it, suggestion. The power of suggestion is strong. You're impressionable. You've let these stories prey on your mind, and you've got to snap out of it. Oh, I should have killed him myself. Pollock, I'd do it too, with my bare hands if only I had the chance. Man, you're talking rot. Look at him there, look at him grinning at me. Pollock, that's only a bronze vase. Always grinning at me more and more famously every day.  Pollock, calm yourself. Lie back, rest. Rest, rest, yes, yes. That's what I mean. If I'd only known, I'd never have left you there in Sulema alone. All this might have been prevented. Oh, might it? Listen, Waterhouse, when you came in, I was just lying here thinking I see him. I hear him, my sense of sight and of hearing is affected. And someday, my sense of touch will go too. When it does, I know that will be the end. I'll be finished. And the poorer man will finally have his revenge. Won't he? Pollock, old man. When you came in, I was lying here, trying to get up the nerve to walk over there and make the test. I'm going to do it. No, no, I won't let you. No, you can't stop me, Waterhouse, don't you see? I've got to. I can't go on like this. I've got to know. Have it over with. No, Pollock. It's beyond anything you can do. Stand aside. But stand aside, please. That window is open. If you have a view. Never mind. This is just an ordinary Bronze vase. Isn't it, Waterhouse? Pollock, don't do it. I know it's only a Bronze vase. I know that when I will feel only cold metal, when I reach out and touch it, I know. Pollock, look out that window. You're backing into that window. Pollock! Escape is produced and directed by William N. Robeson. And tonight brought you Pollock and the Porer Man by H.G. Wells, adapted for radio by John Dunkel, Martin Yarborough as Pollock, Louis Van Rooten as Waterhouse, and Bill Conrad as Berea. The special musical score was conceived and conducted by Sy Fuhrer. Next week... You are groping through the darkened corridors of a gigantic department store in the dead of night. And suddenly you realize you're not alone.  A hundred hands reaching for your throat. Next week, Escape with John Collier's eerie story, Evening Primrose. Good night then until this same time next week when CBS again offers you Escape. This is CBS, the Columbia Broadcasting System.


The holiday season was in full force at the 142nd Wing during a frosty December drill. Throughout the chilly weekend, 142nd Airmen and their families took part in a variety of festive activities organized by the resiliency team. At Santa's Workshop in the Resiliency Center, Airmen enjoyed a selection of free stocking stuffers and tasty holiday treats. It's all part of an effort meant to give back to military families and highlight important resources available to them. Our mission really is Airmen and family readiness, like the idea that you are ready to go to do the mission at any time and there are so many things that contribute to readiness. Connecting people with the things that really improve their life and enrich it and relationships themselves are really what's enriching and makes a community a community. The more family members we have in here, the more it brings the purpose of what we're doing to the actual job. On Sunday of drill, old St. Nick himself made a grand entrance on an F-15, giving kids and military families a chance to meet and take a photo with the Jolly Red Aviator. We have a really tight relationship with Santa, he really cares about our service members and their families and the kids knows what families serve to so we called him up and said could you make a special little trip, he was totally on it. While the holidays may only come once a year, organizers hope that the event works to strengthen the relationship between service members, resource partners and the greater Bayes community so that regardless of the season, Airmen and their families have the support they need. I think strategically speaking having toys and cookies and coffee over here really is a means to try to get family members and the service members over here. We really are trying very hard to entice people to come find us and to know about all the things that are here to support them. Reporting from the 142nd Wing, I'm Staff Sergeant Alexander Frank.