Digital online action and the research that we are doing and we would like to share it with you So first some introductions My name is Marlene. I Have been involved in the activist movement for about 12 years now And been involved in different movements from squatting movement to climate movements feminist groups And I mean in the end it's about system change. It's about movements that are connected Intersectionality if some of you know so if you start with activism you end up from here to there to everywhere Yeah, I've been involved in different social spaces. I love to cook vegan food I'm a vegan myself, and I love to share that with people Yeah, I'm school as a graphic designer have been working as a graphic designer not for commercial work, but often for the movement and for different organizations and The last three years. I am working at Greenpeace as an action coordinator Yeah, so we thought for the introduction it's nice to show An image of an action that both of us have been or me in this case have been involved in This was an action one of my first climbing actions at Greenpeace This is was me. I was on a on the roof of Shell HQ in The Hague where we were protesting against Arctic drilling and I was sitting there for some hours at some point you get arrested the police take you down So we were going through the building of Shell and I was wearing still this Big suit as a polar bear and it's walking like really big and heavy because it's big And then when I came down and I took off this Polar bear head the police was a bit shocked that there was a blonde lady in it And it was like the perfect picture that the photographer took and it's always nice to share So About Martin. Yeah, I'm Martin. I also work at Greenpeace, but I started after high school. I did study artificial intelligence And I yeah, I was always talking about left-right activists things But then I got into doing some privacy workshops and then I rolled into the student movement and from there It all went really fast and now I'm Well, very deep into the climate movement and the nature movement. I sometimes play guitar, but Yeah, it's it's it's a process and I also took a picture This is in the Steadibos last year where we occupy the forest And Yeah, and in this photo, I just got in food so there was really One of the highlights of the one of the 12 days So and yeah, this is not a talk about Greenpeace but just to give a little bit of background info because Maybe not everyone knows but Greenpeace is quite old for the organization that the type of organization that it is 50 years and we're all around the world and there's many offices in different countries and regions and We've been fighting to preserve nature and for peace For 50 years and we have a lot of experience in that so we do a lot of actions, but we also do Research we go to the nature areas and we fight court cases And this is why we think we're like uniquely uniquely It makes it possible for us to try to bring civil disobedience into the online world And if you know if you have Questions about Greenpeace then we can talk about it completely after the talk if you have questions about the talk itself We can do it There's room for that still Yes, so First we want to talk a bit more about how we get to this topic So in 2014 I I was a volunteer at Greenpeace and I also did some internship work I also came to Greenpeace and said like isn't it interesting to look at if we can do digital actions And that's already quite some time ago The year after I organized a hackathon Where we where the challenge was to look into the data or fishing vessels that go around the whole world And at some point they can take off their tracking system or turn it off and we basically don't know what they're doing in areas So the during this weekend there were more than 30 people We looked into the topic. We got a lot of data from AIS systems and we Learned a lot about what we can do if they turn off their system So that was for Greenpeace and for us a really valuable moment But also for the people who joined because they really liked it to be working together with Greenpeace and to Do something that would preserve nature preserve the oceans So after that we wanted to continue with like what can we do with data with online activism? And so together with a colleague with Bob I set up an e-activist team at Greenpeace and this is basically a team that does More innocent online actions So they write Google reviews. They put pictures At a bad company about their destruction And all kinds of actions we did they were very useful. They were it still exists this team So we're still doing these kind of actions often to support offline actions And it's it's really a nice extra new tool in our in our way of extra activism So yeah next Now or the last year. I've been looking into like how can we do digital disobedient actions? But before we really get into that we want to give you a bit more context about what disobedience means But also how Greenpeace does that and how we Have court cases how we win court cases because this is really important to understand why we believe it It could be possible Yeah, so first about What is civil disobedience and nonviolent direct action? because there's this concept in our society civil disobedience and it's meant to To fight things that are greater cost than yourself and you need to Well uphold a certain number of criteria in order to for it to match that civil disobedience definition For example, you need to have a lawful excuse, which is Let's say your neighbor's house is on fire and you break down the door or the window to save the baby sleeping inside Then you're breaking the law because you cannot break windows But you have a lawful excuse because the fire the house is on fire and for the same way It's like the planet is on fire. So sometimes it might be justified to block shell for example You have to be really careful about safety of everyone involved that's for our activists But also for the police people and for the workers at the sites that you do actions at and you have to Subsidiarity is when you First exhaust all other possible means to fight for your cause. So if you Start with petitions and then you do demonstrations and it still doesn't work then that might then you almost have to Take the next step. Then you're justified for that. But you also have to be proportional. So if you're fighting a very big thing then It's it's Proportional to for example with the Steadibus We have a big major crisis going on and then you sleep in a tree in the forest. That's that's a small thing See if I forgot anything with green peas were very and also for civil disobedience non-violent so Violence is a very vague concept We're very strict never violence against people and if you have to do violence against object Objects rather not but sometimes you need to maybe Break through a fence or for example, but non-violent as much as possible and as I said, there's no Personal gain to be had from doing civil disobedience. So it's really for the bigger cause and All this together makes it so that judges think like, okay, this is they're Changing the world. They're fighting for a bigger cause and that's just nice and NVDA is a Subset of civil disobedience where you directly go to the To the activity that's that's doing harm. For example, you shut down the coal fired power station It's a direct action and you directly stop the activity and So one example I can just play right? Yeah This is in Germany sound it would be nice if there's sounds So every year there are big actions in Germany called and the galena and they are really nice example of people power people doing action to stop fossil fuel industry in this case lignite mining And they're very Terrain a thousand fifteen hundred have come from all over Europe We're here to stop the trains from coming across the tracks because we believe in climate justice and we want the cold to stay in the ground I feel it's an honor to be here. So yeah, I'm I'm very happy We know that you're lying We act in every way we can and civil disobedience is one of this So yeah, that's that's pretty nice where thousands of people come together And if you want you can go again this summer there. They're organizing in August But one another example, this is Amsterdam. It's a really nice field of grass in the city center But what I didn't know at this is that it used to be a highway right through the through Amsterdam and People really didn't like this actually because they really didn't like cars And they thought yeah, we just should take the bike. So they got on the highway. They did like a die-in and They took their bikes as you can see and this is civil disobedience that changed the highway to a nice field of grass and I think that's important part of civil disobedience is has shaped the world around us for the better From you say implying to voting rights for women to the eight-hour workday to abortion rights It yeah, it has shaped the world around us. So We think it's important Yes, so Now we would like to talk a bit about how we do these actions at Greenpeace like Martha said Greenpeace has been doing actions for around the world for more than for 50 years now and There's a lot of experience and knowledge here in the Netherlands, but also in of course many other places in the world So when preparing an action at Greenpeace That's my work Basically every detail counts. So the moment we depart from our warehouse till the second we go on to Gas rig as we see here in a picture That we already prepare what happens if we get a court case We already do everything in advance. We know everything that could possibly go wrong or what could happen? And that's super important to be prepared especially in court So what happened in this case? I'm gonna take you to one action that happened in 2018 because it's just a very interesting example so There was a company called Hansa and they were planning to start drilling for gas In Schiemannik oog in the water say which is a nature area even a nature 2000 area The Dutch government has been working for years on it to get it flourished as a nature reserve And then suddenly there's this company saying so we're gonna get some gas there. It's gonna destroy the nature Besides destroying nature the people who live there. They didn't want any of this happening in their backyards They didn't want anything of this happening in this beautiful nature reserve so The people they contacted Greenpeace beforehand Greenpeace was already in touch with Hansa the company that was planning to drill for the gas To say hey if you're gonna do something let us know they said okay We will let you know if we're gonna start drilling because We need to tell that in advance Because we're preparing it because the government needs to know that's how it works But they didn't they just announced we're gonna start drilling next week So in a week time Greenpeace prepared this action often we take months to prepare but here was one week where we took off from Amsterdam all the way to Schiemannik oog and In preparation of this action like I said we think about every single detail so we think about How are we gonna contact the owner Hansa? But also we need to contact the authorities that we're doing an action So when you're doing an action in the area of oil rig, this is important for the legal case after There is a mining law and this means you cannot be in the area of this mining Activity in 500 meters so we had to stay out of this 500 meters And that's what we did with our big ship. We had a beluga with us. It's a sailing vessel And it was outside of this 500 meter border But we had also had our ribs with us and Those could go into this 500 meter area because The rig is supplied Also with small ribs that there's no danger of any anything Collapsing into the rig so we knew that and that's why we took the ribs to bring it to bring the activists to the rig and What also happened at the same time is the moment we start this action. We called the owner We called the authorities. We're gonna do an action. We weren't even on the rig yet, but we prevented Already that in the court case they would say you're there was dangerous. We didn't know we were planning to mine blah blah blah blah So we already knew we need to let them know in advance and we are so fast that they're unable to stop us before we're already on the rig before they're there so Um, this is very important in the legal process So here the activists go onto the rib. They go into the onto the the rig After 24 hours the activists were taken off the oil rig and that already Took care of a lot of media attention And it made the discussion Really start in the Netherlands about drilling for gas in a nature reserve So that's basically the goal For that action and it really worked but then after There is always the public prosecutor saying hey, I want to have those activists being punished because they did something that is not allowed um So what the public prosecutor said is that the mining law is more important than the right to protest that the action was totally unsafe And that there are less invasive ways of making your points So they say we shouldn't have gone on the onto the rig. We should have just talked to them. But of course it doesn't that doesn't work Um, this is a lot of text, but it's uh, it's just very interesting. This is What the uh, this is the verdict of the judge in the end all the charges were dropped the judge the judges basically said That the right to protest is more important than the mining law Which is already really exceptional. That's really really quite amazing that they said that because often Economy and money goes before ideological and activism um But what they also said and here I wrote it down a bit more concise um Is that again that the mining law is not absolute it's um The right to protest is more important um The mining company started to test unexpected That's why greenpeace couldn't do anything else To had like we said the subsidiarity. So we couldn't get into touch with them They were just on their way and we were too late to basically go into a discussion Uh, there was no safety risk. So this is all what the judge said, huh? Um, the action was well prepared and well documented And they even said greenpeace was it is a large and professional organization That should really address these kind of topics Uh, there was open communication with the authorities. Um, the action was limited Um, yeah, they had a clear target So in the end it was also for us It was really special that they really set this mining law aside and they said the right to protest is more important And that was really a big victory So again in this like I said essential is the subsidiarity and the proportionality because that's where The judge really looks at So why I'm telling all of this is Because basically what we're doing Uh Is if you think about it like if I am myself if I just go take a boat and I'm gonna row to a rick and I'm gonna climb on it I will probably be prosecuted. I will probably get a fine or a jail time because it's so Unclear what I'm doing there. I'm one person. They don't understand it But if you're doing that with a big organization if you have a clear story And if you have a clear goal it can change So the question now is the one I wrote down here Anyhow, so when we talk about digital action digital disobedient action, um, we think Digital action equals high fines and jail time Because that's basically what you hear a lot when people do something online That's not allowed that there are a lot of media attention and that people get high fines if they're found because often you're anonymous Um, yeah If it works, let me know Yeah, so the last year year and a half, uh, we've been doing really extensive research where we talk to Lawyers who are specialized in the right to protest but also, uh cyber cyber crime lawyers Who have advised us and we've been talking about like how Does that work and how do you could you move like a right to protest the european Right into a digital area and they say it's it should be possible. It should be It's very interesting to quest as this question because it hasn't been done like this before Of course, we know actions that are done, uh, anonymously by example anonymous But no one knows who they are But if you would do a digital action and say hey, we're green peas We've done that and we are standing for what we're doing and we can explain to you how we did it And how and what we done and why we did it Like copy what we did what we do offline And we often win and we always win those court cases offline How come you can't copy that to an online place? So again, we said We're still researching. We want to know everything about this If we can't guarantee safety if we can't guarantee the safety of the activist of Of uh, of anyone who's involved of even the companies that we might hack, uh, then we won't do it Um So basically what I'm saying is that I or we think that the risk Isn't as high as I expected before There are laws already made on this topic cyber crime crime and we've seen that of course in the news But there's also a part in this law that talks about ideological action Um So that means that there's already chapter a chapter written In it wet book from strafrecht. I don't know how to say that in english Saying that it's That they already thought about like what if you hack something with an ideological Stance with an ideological view and then of course we look into a jurisprudence So what has been done before have there been court cases? Done against activists who do digital actions And of course we look at the european context You can can look into money places in the world u.s. And there's often these things happened with Snowden and we're we are in europe so we look at european law And one action we did find was A ditos attack on lyft hanza Done by activists who didn't want Undocumented refugees to be deported And luft hanza was taking them and taking them to another location So they did us openly Hey, we did this. This is my name As a form of demonstration And they won this court case So they were not prosecuted for anything and that's the one case we can find in it was in germany That happened where activists said we did this It was a direct action But the judge said it is it is okay to do it because it was a demonstration And that's really interesting Yeah, so screens are not on yet So if we really want to start with doing actions, we really need to prepare Because how would you copy these? The things we prepare when we do a physical actions for an offline online action Like we say the subsidiarity and proportionality Proportionality nullity are very important Subsidiarity depends on the target Yes, that talks a bit easier because it's a lot of text Yeah, so the subsidiarity it depends on the targets for example if we want to do a digital action on shell Um, I mean we have we've got a history with shell We've done many actions on shell So we don't really need to explain why we're doing more heavy actions for example or digital actions on shell Because we have been doing that for years Um, so that depends on the targets, but if you want to do a proportional action That's a bit of a difficult one. That's something that we that I've been thinking about like what is a small action online What is something big? What is something that's really disruptive and how would a judge look at that? Um, and how can we track every every step we take online? So for example, if we climb a building you can basically say yeah, we went to the fence Then we went there we went to take that ladder and we're up the building But how would you do that online? How can you track that? How can you show that you haven't been looking into places where you find credit card data or anything else? Um Yeah, so again the thorough legal advice. We don't want any risk We want to make sure that no one gets in jail and if they are not Possible then we don't do it Uh, also something I was thinking about can someone experienced Um an experienced hacker prepare an action and that a green piece prominent for example the director presses a button And he does it. He does the hack Um, because that you know in the in the discussion that could really help Um and as always a risk assessment Yeah, so Now we're uh in the process of um All the technical stuff, but it's also Um, what are we actually going to do? Um We are very good at uh doing uh banner drops with what would the digital banner drop look like and um, we it's quite obvious if you block the entrance to uh shell But can we also do a direct action online and how would it look like and maybe the Most interesting one, uh, or challenging one at least is the mass action where you have uh, You saw the video of and the glen with thousands of people Can we do it online in a disruptive manner? um, and then Yeah, make it make it happen because, um The world is warming and nowadays, um, you have This is From the global south, but on the right side of the screen. It's it's in europe now and even in the netherlands where we have floods so there's no Escaping it anymore and something uh, yeah needs to be done and then We're the question part How much time do we have 15? Okay, so we have time for questions Um, and we would love to hear anything if you have any remarks or questions or Also, uh later. We have more time. You can also come to us. We will be here the whole day also on monday, so any questions Oh, yeah This oh, yeah, it's also like what you described is how can you prove that you're not hacking the company or not Accessing the database or accessing confidential information. Can you talk a bit closer? I can yeah, of course Yeah, um The most important thing with it is like what you described with a d-dOS attack. It's impossible to hack anything with it. It's just Disrupting their services, but it's not hacking it. You're not accessing the database You can prove this to everyone that there are certain types of cyber attacks which Which are impossible to Lead to an actional hack And that's the the most powerful thing of it also what you said like how can I have many people? Attack shell for example like take the most Busy page of cell the the page which takes the most time to load Maybe they're log in page to their oil platform or take some page which is very slow to load and speak of time Globally and everyone refresh the page constantly everyone everyone on the at the team Start refreshing the page and eventually it will stop working And then the oil consumers cannot log in but you can prove that you did not hack anything and if you Say like hey, we're green priests. We're gonna we're gonna use we're gonna like If you're gonna do a real hack you must Say i'm gonna use it from this ip address I'm gonna use this method And you can check this logs to make sure that's no database has been hacked But if you're using a DDoS attack you should not disclose your ip because then they can block it very easily But it's technically impossible to To access private information. So you're always in that site legal DDoS is not legal by the way, but it's at least a gray area. Yeah Nice. Thanks. It's very interesting Yeah, can we respond because uh on monday we have Uh a workshop where we are gonna try to really make the translation move for these kind of actions And really try to look like okay, maybe we can even find the page that you were talking about and let's let's find it on monday Now with the slides can you make them available online for download and with for instance all the cases you've mentioned Could you cite them and like tweet them or master done them or something that would be nice Is there a way we can see? Yeah, I think so. Yeah, we can also discuss with the organization How or where we can share it that should be fine. Cool. Thanks. Yeah I have one remark and one question a remark for the gentleman about DDoS in the website. It will not work I'm working I've been working in marketing for 10 years and I know how these sites are being built up So best case you would get one edge note You could maybe get down But everything is protected by like cdn or akamai or without any real Hacking you would just not get a result that's that's that you would like But I would like to talk more on monday about that Yes, yeah But Let's talk. Come on. Let's go after this talk also fine. My question is If if you do an action who gets sued is that green piece or are that the people performing the action If green piece acts as a protection for people doing the action That could attract a lot more people be willing to do civil disobedience If you're shielded by an organization Yeah, it's uh Actually all I think almost all cases. It's the activists And but it's also a combination because the activists do the action in the name to have for together with green piece So that means that they have an organization like green piece behind them supporting them also being there in court with the lawyers So it's green piece supporting them and green piece helping running the court cases But in the end they want to prosecute the activists Okay But we yeah, we don't have any Cases where the activists were heavenly prosecutors because of those preparations And that's where it starts it starts when we are at home in our drawing tables drawing down this action or at work And saying hey, we really need to take care of all these points because of a court case So that's already prepared in advance. Okay, thanks. Yeah Hey, so first of all cool talk. Thanks for sharing I do have a question regarding this preparation phase that you mentioned I would expect it's kind of easy when you're a dutch person Doing something on dutch mainland like taking an action But then when he gets online it gets much more difficult to grasp How do you make sure that it's actually dutch law that will be available that will be applicable How do you make sure that you do not fall under like foreign jurisdiction? And is it part of the technical analysis that that you have to conduct before Go taking such actions or is it part of like a more legal approach For the first question I think you're mentioned You mean that if you hack a company that has servers in the us for example Yeah, sometimes you just don't know you may have some hkc's where it has some impact on other companies on other Jurisdiction for example. Yeah. Yeah, we we also talked about that with the cybercrime lawyer for example, and he said That's a very difficult one, of course And, you know, if you would start doing these actions It would be smart to look into where our servers placed for the first times and see, you know To make sure you're on european area or european law and if not That's the next step, I would say because there is a chance that the us will say Hey, the activists need to come here because we want to prosecute them and that's a very tricky one, but Uh, I think what we said now we would try to focus on european law and everything that's on european ground Okay, cool. Thank you. And the second question. Uh, sorry. I missed I'm not sure there was a second question. No, okay. Sorry. I thought you had the second one. Sorry. Yeah Hello Think about that formulated properly So there's of course the tension between if you do something in public, it's nice But then people know who you are and we know that maybe sometimes Uh, like people that don't necessarily follow the law people disappear or stuff like this um I don't know if you could maybe comment on the difference between like doing something privately or like, uh securely, let's say so you don't know who's behind it so nobody can be specifically targeted because usually it's just A few people that know the very specifics and so like you just make their life horrible and there won't be More of these attacks, let's say So I think there's a bit of a tension between like doing something privately or like, uh, Anonymously versus publicly. I don't know if you thought about this It was partially on answered a little bit by the preparation stage. Yeah I think it's probably best to do everything out in the open. Uh, as as let's say in the light as possible Yeah, but maybe you can comment on this Yeah, we we um, we're still talking about this, but um, like I said before Um This form of action like what we're doing offline We can get away with it like we do it for 50 years. Um And I believe you can really copy that to an online place and if you do it anonymously online I think if they find you in the end, uh, I think the repercussions are harder and are um Because we're open and because Greenpeace is always saying this is the activist. This is the organization The judge is also more willing to be Hey that you're doing it for such a night such an important topic you're fighting climate change or whatever Um, it really helps So I I I know what you're saying that there's like not maybe not so many people who can do a really difficult hack for example Maybe there are I don't know or or even activists like fighting for the amazon I don't know what is like the highest number of activists disappear over there Yeah, no, that's true But that's also it depends on what action you're also doing right and what what targets and but with Greenpeace It's it's really like that that we always show who we are. Um, but we do um I personally think it's important that you can do anonymous actions, of course, but that's not how Greenpeace works Thanks Okay, so the last two questions and then we need to continue so, uh to me it feels that the goal with the Physical protest is to disrupt the companies to get their attention for a cause, right yeah On Monday, we're going to go into four tactics and sometimes it's also making public aware that something is happening Or direct communications towards the people who can influence decisions But we now we focused a lot on yeah Because the example is given people boarding a drilling platform You being in the trees all that is preventing people Their work right you being disruptive to that process because the money Time effort whatever If you translate that to online You will not accomplish that with a wiki leaks or ever snowed in You will not get there if you go with the DDoS. You want to get there? So that means that you're you're promoting to destroy Or disrupt their infrastructure And you feel that you can do that with your previous offline case in the physical space. So is that what you're advocating? No, um, this is what we want to dive into on Monday to see like hey Uh, if we do a better drop, uh, can we do a better drop online? Like I said, is it is it translated? I don't know. I think that I think that there's a lot of creative people maybe here Maybe on the camp maybe in the world who can translate it into different things Maybe it's true what you're saying. Maybe it's one of the tactics But I think that also civil disobedience comes in many ways, right? So I think there's ways to We have to hurry up To to look into that Destroying things is not non-violent and it's also not civil disobedience more sabotage And that's the point you made so so I'm I guess confused The room you give yourself what you are able to do so online Yeah, that's right digital processes, which I get. Yeah, but I think it's hard to accomplish with the Rules you give yourself. Yeah, but it's uh, it's not easy. Yes Thanks Hi, have you heard of the activist group distributed denial of secrets and some of the environmental data says that they release like mining secrets No, no, but that's a good tip. Okay. We um, maybe later you can say it again after the talk and we can write it down Yeah, okay. We have two more minutes. So one minute. Okay, so Uh, attempt to check a ratio hand if you agree with the statement and it's okay if you disagree But just to get a feel of the room What oh one question Um Can we first do this? Please and then we can do it afterwards Um, direct digital action should be normalized like offline direct actions Nice, that's also why you came to the talk maybe So, uh, what's next? Um, we're uh, we're gonna continue with legal research and we're gonna do it out in the open so we will uh, publish a position paper and we will host public events And uh, then we're gonna set up a team of people who can actually do this stuff And uh, we're gonna design the first low risk action. So we're not just gonna encrypt all the servers of some, uh, oil company Maybe we're gonna start it easy or we are going to start it easy And then on monday where like we said, we're gonna try to really see if we can find Ways to make this translation step um But hopefully all of y'all and your expertise That would be really nice Yeah, so we'll be back Yeah, and if you're um, if you want to contact, um Send me an email Greenpeace email is on google. So sorry for that. Uh, I have my other email, which is riseup, which is much Better. We also believe that um And uh, yeah signal me or to send the telegram Like I said, we will be here today and we will be definitely be there on monday the whole day So also just come come to us and talk to us Uh, and we had one last question. Is that still okay? I'm looking at Oh, when is the next hackathon? Um, I don't know. I didn't plan one. We can organize one. Yes We would like to join a hackathon if we organize one Some hands Okay, I think that's uh, that's it.  Nice, it will be fun Cool. Okay. Thanks. That was uh, that was it So before you all leave I have another announcement to make uh, first of all Everyone who has merged pre-ordered can now pick it up at the merge stand. It has come in. It was a bit late But it's hit there now Um, I'd also like you to ask to pick up the trash To leave everything cleaner than it was Be excellent to each other drink water use sunscreen and yet again give it up for the amazing talk of martin and martin


Tonight we have a speaker who is also a man of action and this is Patrick Puyone that you know and he is the head of the of Total and we have a entertained friendship relation and he's going to talk about the development of the energy landscape while taking a bit some distance with a perspective that would have a look at the past and will try to prospect the future and I am very happy to give him the floor


Welcome back to our lecture series Math 42-30 Abstract Algebra 2 for students at Southern Utah University. As usual, I'll be a professor today, Dr. Hinch and Missile 9. In lecture 29, we want to talk about the titular topic of splitting fields. So, as we've discussed field extensions previously, we know that by Kroniker's theorem that given any field, any irreducible polynomial over that field, we can always build a field extension that adds a root to that polynomial into the larger field. The algebraic closure is then essentially the union of all of these processes. That is, you take all of the roots of every possible polynomial put together. But in some sense, this is sort of like, well, as we've proven, this was a maximum algebraic extension that makes all of the polynomial split. Is there a minimal algebraic extension that makes certain polynomials split? That's what we mean, of course, by splitting field. But I keep on saying polynomial split. What is that exactly that mean? Let's make these definitions explicit here. Suppose that we have a field F. And suppose that S is a set of polynomials from the polynomial ring F for join X. And say that E is a field extension of F. We say that the set of polynomials S splits over the field extension E. If every non-constant polynomial that belongs to S, which I should mention that throwing constant polynomials into S is completely pointless. So for the most part, we can assume there's none in there. But if there is, our definition accounts for it. But the set of polynomials splits over E. If every non-constant polynomial factors into linear factors in the polynomial extension ring, E join X. So we say a polynomial splits if factors into linear factors. That's a set of polynomial splits if each polynomial factors into linear in that situation. We say that E, this extension field, is a splitting field for the set of polynomials S. If S splits in the field extension E, and this is the important part, it splits in no proper subfield of E. In other words, E is a minimal extension of F where S splits over E. This minimal extension is very, very important when it comes to the definition of a splitting field. Many students sometimes ignore this. So like, oh, E is a splitting field because this set of polynomial splits over E.  But to be a splitting field, you have to be a minimum split. This minimum algebraic extension in that regard. Now related to the idea of a splitting field, you have the idea of a normal extension. We say that E is a normal extension of F if E is a splitting field for some set of polynomials over F join X. So splitting fields and normal extensions are essentially the same thing. But when it comes to a splitting field, if we say that E is a splitting field, we're referring to some set of polynomials S. When we say that E is a normal extension, we're thinking of it as an extension of the field. But the set of polynomials is implicit in that situation that are splitting.  But being a normal extension, of course, depends on the base field. If you choose a different base field, might not be normal anymore, normal extension. We'll talk about these things in the future. And so the two notions, of course, are very related. Why do we use the adjective normal? Unfortunately, that's something we're going to have to talk about in the future. There is a reason for that terminology here. Believe it or not, it has something to do with normal subgroups. But I get a little ahead of myself here. Now of great importance is going to be the situation where your set of polynomials is actually just a single polynomial. Now if S is just a single polynomial, we often don't refer to it as a set. We just refer to it as an individual polynomial. And so we would say that the polynomial f of x splits in e or that e is a splitting field for f of x in such a situation. Of course, you know, e is in fact the splitting field for the set S in that situation. Now, I should mention that if your set of polynomials is a finite set, then really it's no different than just being an individual polynomial. Because if you have a finite set of polynomials, what you can do is you can build a polynomial S of x such that it's the product of all of the polynomials inside of your large set S, which is finite, but it contains several polynomials here. After all, each of these elements f of x belongs to the polynomial ring f of join x. And as such, the product of all of those polynomials is a polynomial in f of join x. And so a set of polynomial splits over e if and only if every root of every polynomial inside of S belongs to the field e. But all of the roots, if you look at the collective roots of the polynomials inside the set S, that's exactly the roots of the polynomial S, right? Because if, you know, let's say alpha is a root of f in the field extension e, then as f of x is a factor of S of x, then alpha is also root of S in that manner. And this goes in both directions. So the roots of the set of polynomials S is actually identical to the set of roots for the individual polynomial S right there. So the set of polynomials S will split over e if and only if the individual polynomial S of x splits over e as well. So when it comes to a set of polynomials, if that set of polynomials is finite, then without the loss of generality, you can just assume it's a single polynomial. So you'll often hear us talking about the splitting field of a polynomial. Now, of course, if your set of polynomials is infinite, then there isn't necessarily a single polynomial that can do all that lifting there. For example, you could take S to be the set of polynomials x squared minus p, where p is a prime number, p is a prime number inside of the integers. So we can think of these as a set of rational polynomials. Like so. This is an infinite set, because we know, of course, there's an infinitude of prime numbers. And there's no single, there's no single polynomial that will contain all of the roots of this polynomial, of these polynomials here. Because the splitting field for this set is in fact going to be q adjoin the square root of a prime, which this is an infinite extension. This is an infinite extension of q, for which if you have a fine, if you have just one polynomial, the field extension will always be finite, because you only have to adjoin finitely many roots for which each root worst case scenario extends the field by a finite amount. And so yeah, you basically have two options when it comes to sets of polynomials you want to split, either a single polynomial or infinitely many polynomials. Oftentimes, we'll be very interested in this lecture series, of course, just in the single polynomial situation. Now, of course, we should mention that when you look at the algebraic closure of a field, every polynomial in f adjoin x will split over the algebraic closure, f bar there. But usually speaking, f bar is not going to be the splitting field for a specific set of polynomials. And this is where the minimality comes into play here. Yes, every polynomial splits in f bar, but is f bar the smallest algebraic extension for which that set of polynomials splits. Now, there does exist, of course, such an example where f bar is a splitting field.  It's the splitting field of, of course, this set right here of f adjoin x. So if you take literally every polynomial in f adjoin x, then f bar, yeah, is the splitting field of that because no smaller field can do it. I mean, that's the whole point of the algebraic closure. Every polynomial splits in that situation. So yes, f bar is a splitting field for a set of polynomial. In particular, that means that the field extension f bar over f is a normal extension. That's a very important observation because it's a splitting field for some collection of polynomials. But be aware that just because every collection of polynomials splits in f bar does not mean f bar is the splitting field for every collection of polynomials. No, no, no, no. f bar is not the minimal extension there with that regard to make the polynomial splits. So it's not the splitting field for that set of polynomials. Although it is a splitting field, but implicit in the definition of a splitting field is a specific set of polynomials. f bar is not the splitting field for every set of polynomial. But it is the splitting field for the set of every polynomial from the whole plan words there. Alright, so we mentioned some examples of splitting fields, but let's look at some finite examples here that is for some finite sets of polynomials. Take for example, the polynomial p of x, which will take it as this quartic polynomial x to the fourth plus 2x squared minus eight. And we're going to view this as a rational polynomial. Now this quad, this quartic polynomial, excuse me, it's not irreducible, it does in fact factor into two irreducible quadratic polynomials irreducible over the rationales, of course, p of x will factor into x squared minus two times x squared plus four. And feel free to pause the video right now to verify that multiplication if you would like to. So we took a single polynomial p of x, but if you wanted to, you could take as your set of polynomials s these two individual irreducible polynomials x squared minus two times x squared plus four. So if one wants to we can always consider the pulse the set of polynomials s to be a set of irreducible polynomials. Because if you had a polynomial in s, that was reducible. Well, it'll reduce into irreducible factors. And that's because f of join x, it's a Euclidean domain, in particular, it's a unique factorization domain. So every polynomial has a unique factorization into irreducibles. So if you have a reducible polynomial factor into irreducible factors, and then you can separate the factors as if they were different polynomials in the set. So when it comes to the set s, you can make some important assumptions. If you want to, you could pretend, since s here is finite, that it's just one polynomial to rule them all. And in the darkness bind them. Or, of course, you can also segregate all of the irreducible factors. And you can consider you can consider s a set of polynomials that are only irreducible, you know, if it's beneficial for you, it won't make much of a difference really in practice. But just want to be aware you have those op, there's our options on the set s here, right? Given a splitting field, it could actually be a splitting field for multiple sets of polynomials. But if it's a, if it's a splitting field for any set of polynomials, that makes it a normal extension. And that's why we introduce this idea of normal extensions. Because the splitting being a splitting field, like I said, it could be a splitting field for multiple sets of polynomials. If it works, if it splits for one polynomial, then it's going to be a normal extension. Alright, so getting back to our polynomial p of x right here, it factors as x squared minus two and x squared plus four, for which we can factor this easy enough that if we have the square root of two, then x squared minus two will factor as x minus the square root of two and x plus the square root of two. And this is a factorization in the, in the ring q adjoin the square root of two, square root of two, adjoin x like so. So that polynomial would factor in that setting. Then when you look at x squared plus four, we can also factor that one x squared plus four. This is going to factor as x minus the square root of negative two times x plus the square root of negative two. And so of course, this would then factor inside of the ring q adjoin the square root of negative two, adjoin x. So p of x has four roots, those four roots, of course, are going to be plus or minus the square root of two and plus or minus the square root of negative two. And so the splitting field is going to necessarily have to contain these four roots. And so basically the splitting field means we're just going to take all the four roots of the polynomial and adjoin them to the rational numbers. So we're going to adjoin the square root of two because if you get the square root of two, then you'll get negative square root of two. We adjoin the square root of negative two. And so this gives us our splitting field because we threw in all the roots of the polynomial that will make sure the polynomial splits. And why is it a splitting field? Well, if we were missing any of the roots, then it wouldn't be and wouldn't split. And so in some essence, that's how one builds the splitting field. And we'll talk about that in just a second. That's how you build a splitting field you throw in the roots of your polynomial. Now we can think of it also as the splitting field for this polynomial is going to be adjoin the square root of two times i. Maybe this is a little bit more preferable here because notice the square root of negative two can be factored as the square root of negative one times the square root of two that is its i times the square root of two. So clearly this field contains the square root of negative two it clearly contains the square root of two. So this we go in that direction. And you can also show that both of these fields are in fact degree four extensions of the rational numbers. So these are the same field and thus they're both the splitting field of p of x. The splitting field is unique. This is the same field with two different representations of that splitting field. Alright, let's look at a degree three polynomial this time. Take q of x to equal the rational polynomial x cubed minus three. Okay, now clearly one of the roots of this polynomial is the cube root of three. Now, and that's pretty easy to see here, of course, if we take if we take this polynomial and evaluate it at the cube root of three here, you get the cube root of three cubed. Well, by construction, the cube root of three is when you cube it is three. So this gives you zero. So the cube root of three is a root. And we're of course, taking the real cube root of three as the root we mean right here. But if we adjoin it to the rational numbers, you do get the factorization that q of x will factors x minus the cube root of three there, but you'll also get x squared plus the cube root of three x plus the cube root of nine, which be aware that the cube root of nine is just the cube root of three squared, which does belong to the field q adjoin the cube root of three. So this gives us a factorization and you can make the argument that this is in fact, irreducible, it doesn't have any other roots. So our polynomial q of x doesn't split over the field q adjoin the cube root of three. Now this was a big difference between the quadratic polynomials we saw a moment ago, like when we adjoin the square root of two, the other root of the polynomial was negative square root of two, which is its additive inverse. So because the square root of two belongs to its to a field, its additive inverse had to also belong to that field as well. So if we were only looking at the polynomial x squared minus two, then if we take q adjoin the square root of two, we get one root of the polynomial, but we also get the other root of the polynomial negative square root of two. And so by adjoining one root, we got the other root. That was also true for the for the polynomial x squared plus four. If we adjoin the square root of negative two to q, we automatically get the other root negative the square root of negative two. So you get one root and you get the other automatically. That's not always the case. This is actually sort of a special observation here, because in these two quadratic situations, the two roots you have are in fact, additive inverses of each other. Does that always happen? Well, it turns out for a quadratic extension, the answer is going to be yes. Because by the quadratic formula, if you would get a root of a quadratic, that's not rational. The other one will just be its conjugate and up to, and since your field will contain the rational numbers up to field operations, it really comes down to adjoining the square root of a number, which is not a perfect square, which case its conjugate will be added in verse, you always get the second one for free. But for arbitrary extensions, that's not always the case. If we adjoin the cube root of three, we don't automatically get the other cube roots of three, for which what are the other cube roots of three? Take zeta three here to be the principal complex third root of unity. So we get e to the two pi i over three, like so. So this of course is cosine of two pi thirds plus i sine of two pi thirds. This is a complex number, in which case all of the complex cube roots of unity will be powers of zeta. So you have of course zeta, zeta square and zeta cubed is equal to one. So one is a third root of unity. I want to show you here that if you take the real cube root of three and you times it by any power of zeta three here, and then you cube that, what's going to happen as well by multiplicative properties here, you're going to get the cube root of three cubed, and then you're going to get zeta cubed to the nth power for which the cube root of three cube gives you three, and then zeta cubed is going to give you one, one to the nth power is still just one, this gives you three. So basically what I'm saying here is that the cube, a cube root of three is going to have the form, you take the real cube root of three times any third root of unity, any complex third root of unity. This will give you all the cube roots of three. Why is that? Well, clearly we just saw a moment ago that the real cube root of three times a complex root of unity does give you a cube root of three. Now the cube roots of three are in fact the solutions to the polynomial x cubed minus three. That polynomial has at most three solutions because its degree is three. And as there are three complex third roots of unity, you times each of those by the real cube root of three, we get all of the possibilities right there. So that tells us that if we take the field, q adjoin the real cube root of three times a principal complex third root of unity, that will in fact give us the splitting field. Why is it the splitting field? Well, because this field does contain the three roots to our polynomial cube. Alright, so the polynomial splits inside of that field. Well, to be a splitting field, it has to be a minimal extension, right? The field, the polynomial splits yes, but is there any smaller field that does it? Well, notice that this field has degree six over the rational numbers. How do I know that? That's because I can factor this thing as q adjoin the cube root of three zeta over q adjoin the cube root of three. Oh boy, let me clean up this a little bit. Give myself a little bit more space. And then we also have that it factors as that. And then we have the cube root of three over q, like so, for which this first one we already mentioned is going to be three, because the minimal polynomial of the cube root of three is q right here. And so that's a degree that's a degree three polynomial, which gives us a degree three extension. And this right here is going to be to degree two. And the basic reason for that is, since the cube root of three, I chose it to be the real cube root of three. And this zeta three is a non real number. The extension, the extension of q adjoin zeta over q, is it going to be two? Because this polynomial, excuse me, this root zeta does satisfy the polynomial x squared plus x plus one. You can show that's the minimal polynomial for zeta right here. This gives us a degree two extension over q. Now throwing the cube root of three into there doesn't do a look of anything, because these are all real numbers. This is a real field and so to adjoin a non real number is going to be just like you adjoin it over q, like here. So we're going to get that this is two, this is three, so the product is in fact six. And so if you adjoin one root, you get a degree three extension, but it doesn't split over there. And so divided by divisibility, we need to have an, we need to have a subfield of this field, which is divisible by three, but it's not three, which only leaves six here. So we do have in fact this is a splitting field. It's the smallest field extension of q for which the polynomial q of x splits over. Now we arrive to a very important property of field extensions, that field extensions are unique up to algebraic closure. And so suppose we have a field f, and suppose we have a set of polynomials s, then the splitting field of s exists and is unique inside of f bar there. So I do have to put a little bit of clarification here. When we talk about it's unique inside of f bar, given two algebraic closures of a field, you know, say something like f bar versus f hat. Okay, we have previously shown that these two algebraic closures are necessarily isomorphic to each other. And in fact, if we have some isomorphism fee between them, this map fee, when restricted to f, the base field, this is just going to be the identity map. Okay, fee restricted to f is just the identity on the set f right there. So we prove that such a nice isomorphism is going to exist between algebraic closures. Now, if you do have the situation where a field e is the subset of f bar and e prime is a subset of f hat, if these are two different splitting fields over f for the same set of polynomials s. So you know that these are the splitting fields for the polynomial s right here. So e is the splitting field of s inside of f bar and e prime is the splitting field of s inside of f hat. Then it turns out that this field extension, excuse me, this field isomorphism fee right here, if you take fee of e, this gives you a subfield of f bar. Okay, well, so this gives this will give us a splitting field of s because of the isomorphic property, the polynomials s will factor in fee of e and it will fact be minimal. So we're going to have to get that since fee of e is a splitting field for s, the uniqueness of splitting fields in f hat is going to guarantee that fee of e is actually equal to e prime. Therefore two splitting fields for the same polynomials are always isomorphic, even if they're contained in different algebraic closures. So in this theorem that we're going to do right now, we're going to say for a fixed algebraic closure, the splitting fields are isomorphic and so what we just mentioned a moment ago is if you have distinct algebraic closures since they are since they are isomorphic, that isomorphism will restrict to the splitting fields as well. Alright, so let's proceed to prove this. Note that a specific polynomial splits over a field if and only if all of its roots are contained and this is a consequence of the factor theorem. We alluded to this fact earlier in this video here. So suppose we have some subset of x inside of the algebraic closure of f, f bar and but more specifically suppose that this set f is the set of all roots to the polynomials s because the set of polynomials s it splits over f bar because it's the algebraic closure and so in f bar we have all the roots of s called that set x. Alright, so then in particular what's going to happen is the set s is going to split over any field extension k over f if and only if k contains the set of roots x because they like you said by the factor theorem if you split into linear factors you contain all the roots and if you contain all the roots it'll it'll split. So we look at the fields that contain the roots of the polynomials and s those subfields of the algebraic closure and so that's what we then defined the set e to be. We're going to take the intersection of all fields k for which what do we require of k well clearly it's contained inside this fixed algebraic closure but it contains the set x the set of roots of s right here now the intersection of field is a field so e is going to be a subfield of f bar now since each of the fields k contains the field f that means f is contained inside the intersection of the k's therefore f is a subfield of e so e is an extension field of f but similarly since every field in this intersection contains x we see that x will be a subset of this intersection so x is a subset of e so e is a field extension of f that contains x so by the above observations all of the polynomials in s must split over e. I claim that then e is the splitting field for s because by construction since we're using these intersections e is necessarily the smallest field extension of f for which s splits over because since e is a field for which s splits over because remember s is going to split over k if and only if k contains x so we define this set to be the intersection of all fields that contain x but we alternatively could define this set to be the intersection of all fields that extend f that s splits over okay since s splits over e e is actually one of the fields in this intersection um and therefore this shows the minimality of e right here that in fact e is the splitting field of s inside of f bar because it's the smallest field for which um s splits over because if there was a smaller field it would be in this intersection and therefore the intersection would have been smaller than e giving us that contradiction there so we do get that splitting fields exist okay well why are they unique up to algebraic closure here well by construction like we saw before this field e contains the field f it contains the set of roots x from the algebraic closure so in particular the set the field f the field e i should say contains the subfield f adjoint x so what is this right here f adjoint x here this means the set uh that that is the smallest field that extends f that contains all the elements x well this is a field that contains f that contains x so all the polynomials in s would split over the pollen over the field f adjoint x so by construction f adjoint x would be inside of this intersection would be one of those fields k so therefore e is a subset of that but also e contains it so in particular this splitting field e is equal to f adjoint x and so the splitting field is exactly that the splitting field is the base field adjoint all of the roots of every polynomial inside of s we alluded to this fact earlier when we talked about our examples but then this proof solidifies it and so as this set x is fixed um with regard to the algebraic closure that then determines uniquely the set e the splitting field the splitting field is exactly just the base field adjoint all of the roots of the polynomials which are contained inside of the algebraic closure so splitting fields are unique uh inside of an algebraic closure they exist which then finishes this video uh on splitting fields


Welcome everybody, my name is Lars Brunnes, I'm the Director of Education at IOHK and in this short video I want to help you get started with Jelle, the language designed by runtime verification to power smart contracts on Cardano. We look at a very simple example of a program written in Jelle and show how to deploy it to the Jelle testnet. You can of course write Jelle from scratch but to begin it's maybe easier to start with a contract written in Solidity, compile it to Jelle and then look at the resulting code and modify it. So we'll do just that and as an example I'll take the same example I used in another video where I showed how to compile Solidity using the command line tool mallet and then deploy it on the Jelle testnet. So let's briefly look at this simple contract, it's called counter, it has one int variable x of state, the constructor sets x to 0 and there are two functions, one to increment x by a given increment a and the other to return the value of x. Let's compile, we do that with mallet connecting to the Jelle testnet and the command is Jelle.compile, takes the file name, let's check the result and there we see the field Jelle code which contains the Solidity contract compiled to Jelle. So in order to save that we use node.js fs write file, file name, let's call it counter.jelle, we use c.jelle code and we must provide an error handler but we don't expect any errors. So let's do it like this. Let's check and there we are. Let's look at this in editor, so I'm starting with, okay, so first of all we notice that this is actually quite easy to read, at least it's much more easy to read Jelle than it is to read EVM and we can see the structure of our original Solidity contract. So we have the contract name, we have the store variable x, we have the constructor, the increment function and the get x function. So let's look at that in a bit more detail. So this status variable x is indicated with an add symbol, then function names also preceded by an add, then we have labels in this function in the constructor, we have three entry, return and throw. So labels are the destinations of branching statements. In the first line, we have a local variable, a register prefixed with a percentage sign and we assign to this register call value result of calling the special function Jelle call value which returns the value of the transaction. So register call value now contains the value of the transaction and in this line we do a conditional branch. So it takes two arguments, the variable to base the conditional on and the label where to jump to. So if this is greater than zero, so if this transaction has a value, then we jump to label throw which is down here and we revert. So we expect it to be zero, in that case nothing will happen and we reach this line where store variable x, this one here, our counter is set to zero. So the constructor first checks whether the transaction value is zero and if it is, it sets x to zero, otherwise it reverts. And after setting x to zero, it returns void nothing. In the increment function, we have an argument to the function also indicated with this percentage sign called a zero. We again check that no value is transferred, otherwise we revert here. Then we introduce a register x dot well, load the value of x into it, introduce a second register TMP and assign the sum of register x well and a zero to it. And x well has the value of x. So temp now contains the sum of x and the argument to the function a zero. And finally we store the sum back into x and we return void. Finally in the get x function, again we check that no value is transferred, otherwise we jump to throw and revert. We load the value of x into register x dot well. We introduce a second register underscore one, assign to it x dot well. Then we jump to label return. This now only has one argument, so it's an unconditional jump, it will always jump, so it jumps to this line and returns the value of register underscore one, which is the value of x dot well, which is the value of x as expected. Now that we understand how this works, let's try to improve on it a bit. First of all the double quotes around the names are only necessary to escape special characters, so as long as we stick with simple names, they are not necessary. So let's get rid of all the double quotes and simplify the names. We call this simply counter, this simply ink x, this simply get x. Then the variable names we can also improve, so here instead of a zero we just call it a, instead of x y, just call it x, instead of temp give it a clear name sum, down here same. So now that we have renamed the registers, let's look at other things. For example the labels to these entry labels, we don't need them because we never jump to them. We do jump to the throw, so we leave that, but we don't jump to this return statement, so we can get rid of that. Same here. Here we actually do jump to the return statement, but it's an unconditional jump and as you can see, you just jump from this line to the very next line, so we can get rid of all three. We remove the jump and the label and then there is one final thing we can do, this underscore one is unnecessary. Here we load the value of x into the register x, then we load the value of the register x into register underscore one and then we return underscore one. So we can simply return x directly and get rid of this one. Now that we are happy with the yellow code, let's generate bytecode, so we fire up mallet again and we again use yellow compile, only this time we give our yellow file as source and c.result is the bytecode we want, but just for fun, let's compare this with the bytecode we would have gotten if we had used the original version. So let's compare that with yellow compile where we compile the solidity and grab the bytecode, let's not overwrite our c and we see that was much longer. So our hand optimization indeed made the resulting code shorter and cheaper and faster. Now that we have the bytecode, let's quickly deploy and test the smart contract. So in mallet, I first have to select an account. So I simply list all accounts, grab the first one and select that. Now I use yellow create contract where I have to specify some gas, let's use 100,000. Then the value zero and most importantly the code, which is just our c.result, I must provide the password for the account and let's grab the receipt in order to get to the contract address. That's not available yet, that is. So the contract address is r.contract address, right? Now we have deployed the contract, now we can test it. So let's first increment the counter, yellow contract call, specify the contract address with this now counter, some gas, let's again use 100,000, value again zero. Now I need the function name, which is ink x and finally the arguments. So if you want to increase increment by seven, we use this again, my password, let's wait for the receipt to see whether the call succeeded, okay, status code is zero, so it succeeded. Now finally let's call get x to check whether the counter is now indeed on seven. So for that function, I don't need arguments, password again, get receipt. Let's grab the result, okay, and in the return data, the seven is encoded, so if I want to decode that, I can require the RLP library and use its decode function applied to r.returndata, and there we go, seven. So we deployed the contract and we tested it and it seems to work. So to summarize, we have seen how to compile a Solidity contract to yellow, we have walked through some very simple example and seen the most important commands like using local registers, assigning values to them, branching, branching conditionally, adding numbers, returning values, we have seen how you can optimize yellow code, make the resulting byte code smaller and faster, and we have seen how to deploy such a smart contract to the yellow testnet. And of course we have only scratched the surface, so if you want to find out more about yellow, you should have a look at the home page at runtime verification, yellow semantics on GitHub, and there you find lots of information like the complete syntax, the design decisions made, and a lot of more interesting things.


What's up everybody, Jason here for Jaspy's Casebreak.com guys, happy to release that again for another release. This is a 2022 Panini Playbook Football release. This is an 8 box half case break, pick a change number one guys. Again you get two autographs, two memorabilia cards and one additional autograph from memorabilia booklet. Four cards a pack. So my printer looks like it ran out of ink so here's the list of customer names I bought in and then last but not least it was David Duffy with the Patriots and the Bucks. So there you go right there guys. And here is the case. Nice, Jalen Hurts on the cover, I like to see that. Again, 8 box half case break guys, pick a change number one and two for this case, one, two, three for the left, four, five, six for the right, let go. Roll it. It's a three. One, two, three. These will be for number two and I'll put a two on it. I'll sell it out tonight, let's do it, if not, I'm sure we'll do it tomorrow. So here we go. We've got Christian Watson, nice packs there to 25 and again guys this is one of those bounty breaks so of course if you match up the numbers for the bounty, you guys are a customer that hits that will automatically win some break credit. So we're looking for 24 to 99, 100 to 199 and 196 out of 299. All right so there you go, Green Bay Packers with that one and that is Joe. Damian Pierce Relic out of 49, ooh a little like Chrome Fuel Acetate, like that. Houston Texans Victor with that one, we got a Chase Edmonds, 47 out of 99 and then this one was 48 out of 49, that is Denver Broncos and Scott and then 3 out of 15, Ty Law. Yeah that's pretty sick, on-card as well, nice patch right there for the Jets, 3 out of 15 Jets, Jets, Jets, Scott. Awesome book, first block's done. Yeah not the Jets book that I was expecting either but we'll take it. Ty Law, I don't even know if he played for the Jets. Joey B, 87 out of 99, so we're looking for 24 out of 99 there. You got Sam Howe, 8 out of 75 for one year so they decided you know what, I'm gonna throw in a Ty Law Jets. I don't think I've ever seen that. Washington Commanders, Justin. Doug Baldwin, goal line grabs 38 out of 49, Seattle Seahawks, Devin. And for the Tennessee Titans, 63 out of 99, how about a Chris Johnson? Nice, we got some cool vets though I will say right, CJ2K man that guy was so good. So good. Tennessee Titans, that is Eric. Alright next one. Like their Madden material, 7 out of 199, you need 100 out of 199 to get that bounty. So that bounty not hit yet there, but Browns is Shane. Kavion, whoops sorry, two cards actually. Kavion Thibodeau, that one looks like it's not numbered. That's gonna go to the Giants, which is Brian. Got a 49, 4 out of 49, Breez Hall. Let me have Garrett Wilson, Rookie Jumbo Vision. That is 90 out of 99. Another one there for the Jets. Nice break so far man, Scott with that one. Aiden Hutchinson, 91 out of 99 for the Lions. Detroit Lions, winner Robert. About a little A.J. Brown, 97 out of 99. Flagel's Fly Eagles, it's Jordan White. We have a Triumph Davis Price, 34 out of 49. 49ers, that's going to Raymond. And then 48 out of 99, Dat Nguyen. Looks like a little older cowboy there. Are they really going deep in the hard cast? Cowboys, that's it. Next four. Alright we got a nice three color pot, 74 out of 75. That's for the Saints and Justin. Alec Pierce, 49 out of 49. Colts, Jerry. Sam Williams, numbered out of 49, 47 out of 49. That's another one for Ed. And a Skymore to 299, 180 out of 299. The number we're looking for to 299 is 196. So we're off 16. Got to get more slider boxes. I'll put that in one at the end of the break. Alright three more boxes guys. Patty Mahomes, 109 out of 199. And we needed 100. We're off nine right there, that was really close. Kansas City Chiefs with that one. Jameson Williams, 24 out of 25. We need a 24 out of 99. We've hit 24 twice today though. But they've been either at a 25 or out of a 50 or stuff like that. DeMargo Murray, goal line graph, 7 out of 10 for the Cowboys. Going to Ed. 256 out of 199. Cowboys, oh he's already ran, it's not Cowboys. Rams is Patrick Davis. Alright we got 62 out of 99. Justin Jefferson, that is Vikings for Ed. Aaron Rodgers, 49 out of 49. Nice two color patch there for the Green Bay Packers. Joe. One of my favorite Eagle running backs. I was an Eagle for about one season or so. Is Ligera Blunt, nice one there, 29 out of 49. This is a Patriot though, addition. So David Duffy lost Palmojo. And then of course Drew Pearson to 99 for the Cowboys. Nice two color patch there. 41 out of 99. And that's going to Cowboys and Ed. Alright guys, one more box, here we go. There's a lot of vets on this side so far for the booklets. Not too many rookies. See what we ended up here with. Justin Herber, 106 out of 199. Ooh that one was really close. We needed 100 out of 199, 106. Off by 6. Chargers with that one, that's Ed. We have a three color patch, 66 out of 99. Green Bay Packers, sorry, 90 out of 100. Denver Broncos, Scott. Then we got EZ, not numbered, Zucanma for the Miami Dolphins. That's Kev. Ooh and we were off here by another 7. John Dott and 17 out of 99. Nice three color patch there. Washington Command and there's Justin. And there you go folks, a lot of nice stuff. The booklets have been pretty cool. A lot of old school names, a lot of names I haven't seen in a while. And the patches have been pretty nice for the cards as well. So again, the second half is in the store. If you guys want to run it back, jaspyscasebricks.com. Guys thanks.