Live from San Francisco, it's theCUBE, covering Google Cloud Next 19, brought to you by Google Cloud and its ecosystem partners. Welcome back to San Francisco, everybody. This is theCUBE, the leader in live tech coverage, and we're here at Moscone Center, Google Cloud Next 2019, hashtag Google Next 19. I'm Dave Vellante with my co-host, Stu Miniman, this is day two for us. Anthony Lai is here, Senior Vice President General Manager of the Cloud Data Services Business Unit at NetApp, CUBE Alarm, and Lewis Verzi, who's a Senior Cloud Engineer at Cloud Health. Gentlemen, welcome to theCUBE. I'm sorry, Cardinal Health. I got cloud in the brain. Gentlemen, welcome to theCUBE. Thanks so much for coming on. Lewis, let's start with you. A little bit about Cardinal Health, what you guys are all about. Tell us about the business. Sure. Cardinal Health is a global supply chain, medical product services company. We service hospitals, pharmacies throughout the world. Where our drivers are delivering cost-effective solutions to patients right throughout the world. Awesome, and we're going to get into that. Anthony, you've been on theCUBE a couple of times here. Almost a year since we last at this show, it's grown quite a bit. Good thing Moscone is new and improved. He's got all these new customers here. Give us the update on what's, look back a year, what's transpired, what are the highlights for you? Oh, for NetApp, we've achieved a tremendous amount. I mean, we were a Google partner of the year, which was quite nice to receive an award for the hard work. We have a very special relationship with Google. We actually engineer directly into the Google console, our services, the products that are sold by Google, which gives us a very unique value proposition. We just keep adding. We add more services and we add more regions, and we continue to sort of differentiate the basic services that customers are now using for secondary workloads and increasingly very large primary workloads. We're going to get into it and learn more about the partnership, but thinking about what's going on at Cardinal Health. Question for you, Lewis, is what are the drivers in your business that are affecting your technology strategy and how you're dealing with those? Sure, there's a few things, and I'm sure this is the same in many industries, right? We're facing cost pressures. We need to deliver solutions at a lower cost than we have been in the past. We need to move faster. We need to have agility to be able to respond to changes in the marketplace. So, on-prem didn't give us a lot of that flexibility to turn those levers in any of those three areas. Those three things have really driven our push into the cloud. All right, Lewis, let's dig into that a little bit. You can kind of, do you still have on-prem as part of your solution? We still have some, so we've been working over the past two years to migrate workloads out of our data center into the cloud. We're about 80% of the way there. There's going to be some workloads. iSeries doesn't run in the cloud very well. You know, we've got some... We were just joking about that earlier today. Yes, yes, yes, lots of things, but in the back corner somewhere, I've got that iSeries running under the main frame. Are you working on that, Anthony? Trying to, trying to. We're blessed, we're blessed. Lewis is a customer of ours, and we enable him to run some pretty heavy on-prem workloads that required NFS can now run production on Google Cloud. Yeah, and you're basically trying to make that experience seamless, right? As much as you can. I mean, talk about that partnership with Google. What are the challenges that you guys are trying to tackle? I mean, just going to refer to one. That's a great question.  In the cloud, it sort of pivots 90 degrees, and you have people that own workloads. And the workload people aren't experts in every single thing, and so they go to the cloud, assuming that the cloud itself will take care of a lot of that problem for it. So we worked with Google, and we built a service. We didn't build it for a storage guy to configure and undo the bolts and nuts. We built it like dial tone, that there is, the NFS is always on in Google Cloud, and you come and provision an endpoint, and you just tell us how much capacity you want, and how much performance, and that's it. It takes about eight seconds to establish a volume in Google Cloud that may take through trouble tickets and IT capital purchases about six months to do. Yeah, Anthony, actually one of my favorite interviews last year is I talked to Dave Hitz at your event, and he talked about when we first started building it, we built something that storage people would love, and you shot him down and said, no, no, no, this needs to be a cloud first cloud solution. Louis, I want to poke at, you actually said price is a main driver for cloud agility, absolutely, but bring this inside a little bit. I know you're speaking at the show a year, people always say, it's like, hey, cloud, is it easy? Is it cheap? Well, devil's in the details there, so would love to hear your experience there, and how less expensive translates in your world. Sure, so when we were looking for something, we tried to get away from NAS when we were moving to the cloud, and we just can't do it, right? There's, we have a lot of COTS applications, a lot of processes that you just have to have NAS, right? And we were looking for something, as Anthony described, that with a click of a button, our developers can spin up their own storage. The price point was lower than frankly, you could get just provisioning the type of disk that you'd need in the cloud, and that was acceptable for most of our workloads. The ability to tier, right? There's three classes of storage in the cloud volume services. Most of our workloads are running on the standard tier, but we've got some workloads where they've got higher performance, and we provision them right on the standard, and when they are doing their testing, they're like, hey, we need a little bit more. With a click of a button, they're at a higher tier of storage. No downtime, no restarting, no moving storage. It just works. So the cost, the agility, we're getting all of that out of the solution. How do you manage those SLAs? Is that sort of an automated way, or are you sort of monitoring things, and what's the process for managing which SLAs? The SLAs on the different tiers of storage. We provide them. Yeah, we're not monitoring that. We're on the whole floor. So it's all automated? Yeah, we run it, and we stand by SLA guarantees, throughput guarantees, and we take the pain away. So it's like to say, what people want to do in the public cloud is innovate, not administrate. And generally, when people say cloud's cheaper, it's because I think they've decided that their better use of the dollar is in application development data science, and then they can retire IT people and put application developers into the business. So what Google does, I think, incredibly well is it has infrastructure to remove sort of the legacy barrier and the traditional stuff, and then it has this wonderful new innovation that maybe a few companies in the world could use it, but most people couldn't afford to put TPUs or GPUs in their data centers. So they hit you with really two very strong value propositions. And maybe what they're saying is, when they say the cloud is cheaper, maybe it's better ROI. I'm spending money elsewhere that's giving me a better return. Yeah, I mean, do things that make you different and not the same, right? Right, right, so storage strategy, I mean, I'm sure there should be such a thing anymore. There's workload strategy. Back in the day, when you used to work at EMC, it was I buy EMC for block, NetApp for file. Things have changed in terms of how you run a strategy and think about your business. So what is your strategy when you think about infrastructure and storage and workloads? So we really don't want to have to focus on an infrastructure strategy, right? Right now, we're mostly running traditional workloads in the cloud, running on VMs. We're working towards getting a lot of workloads into GKE, using that service in Google Cloud Platform. Can you just step us back for a second? How'd you end up on Google? Why'd you choose them versus some of the alternatives out there? So we started our cloud journey a couple of years ago, started out with really the main cloud player in town like most people have. And about a year in, not all of our needs were being met. That company decided to enter our business segment. So it starts asking some questions, people start asking some questions there. So that prompted us to do an RFP to try to see, technologically really were we on the right cloud platform? And we compared the top three cloud providers and ended up on GCP from a technological decision, not just a business decision. Gave us the ability to have a top level organization where we could provision projects to application teams. They could work autonomously within those projects, but we still had a shared VPC, a shared network where we could put enterprise guardrails in place to protect the company. But Dominic Price was on earlier, he's with Google and he was saying some nice things about NetApp. But I'd like to hear your perspective is why NetApp, what's unique about NetApp, what's so special about NetApp in the cloud? Sure, a few of the things that Anthony talked about were really differentiators for us. We didn't have to go sign a PO with another company. We didn't need to commit to a certain amount of storage. We didn't need to build our own infrastructure, even in the cloud. The service was just there. You do a little bit of upfront setup to connect your networking. And we can provision storage whenever we want. We can change the speed, the throughput that we're getting on that storage at any point in time. We can grow that storage with no downtime. Those are all things that were really different in other solutions that were out there. I mean, it's interesting infrastructure was really still even in the cloud.  And what we always said was, people want to buy the pirate ship. They don't want to like have to dig in all these bins. And so we sort of said, let's build storage kind of like a pirate ship, that you just know that the end result is a pirate ship. And I don't have to understand how to pick all those pieces. Someone's done that for me. So, you know, we're really trying to sort of, I would say we like to create easy buttons. You know, people just hit the easy button and go, someone else is going to make sure it's there. Someone else is going to make sure it performs. I am just a consumer of it. So Anthony, we've talked to you and NetApp. You play across all the major cloud providers out there. And you've got an opinion when it comes to Kubernetes. Help give us the, you know, where, what you think about what you've heard this week at Google and how they differentiate themselves in the market.  I think that was an industry changing event. And you know, I think Kubernetes really starts to redefine application development. I think portability is obviously a big thing with it. But for an application developer, the VM was something that somebody added afterwards. And it was sort of like, oh no, we overbought infrastructure. So now we'll virtualize it. But the cost of virtualizing things was so expensive. You know, you put an OS in the VM and Kubernetes was built and was sort of attracted to the developer. And so the developers are coding and refactoring. And I just, you just look around now and you just see the groundswell on Kubernetes. CNCF is here. And the contributions that are being made to Kubernetes are astonishing. It's reached a scale way bigger than Linux. The amount of innovation that's going into Kubernetes, I think is unstoppable now. It's going to be the standard if it isn't already. Well, Lewis, I'd love you to expand. You said, it sounded like you moved to the cloud first, but now you're going down that application modernization. You know, how does Kubernetes fit into that and what other pieces? Because it's changing the application to typically be the long pole in the tent and modernization. Yep, so Cardinal took the approach of we need to get everything into the cloud and then we can begin modernizing our applications because if we tried to modernize everything up front, it would take us 10 to 15 years to get to the cloud and we couldn't afford to do that. So lifting and shifting machines was about 70 to 80% of our migration to the cloud. What we're looking at now is modernizing some of our applications. Our e-commerce solution will be running on Kubernetes very shortly and we'll be taking other workloads there in the future. That's definitely the next step, the next evolution. Okay, unicloud or multi-cloud? That is the question. We are multi-cloud. There are certain needs that can only be met in certain clouds, right? So Google Cloud is our primary cloud provider, but we're also using Amazon for specific workloads. And you use NetApp across those clouds? Correct. Okay, so what's that like? Is the NetApp experience across clouds sort of still coming together? Is it sort of highly similar? What's that experience like? So it's using NetApp in both solutions is the same. I think there's some stuff that we're looking forward to that where things will be tied together a little bit more. So it brings me to the roadmap question. That's presumably, got your best people working on that? Oh yeah, no, no. I mean, so look, I think storage is that sort of wonderful business because data is heavy. It's hard. It doesn't like to be moved and it needs to be managed. It's the primary asset of your business these days. So we have, you know, we release continuously new features onto the service. So, you know, we've got full SMB NFS support. We're adding NFS V4 support. We're adding a backup service. We're integrating NFS into Kubernetes, which is a very frequently asked response. A lot of Kubernetes developers want to build stateful apps and block has a real problem when the container fails. NFS doesn't. So we're almost seeing a renaissance with Kubernetes and NFS. So, you know, we just, we subscribe to that constant innovation and we'll just continue to build out more and more services that allow I think cloud customers to, as I said, to sort of spend their time innovating while we take care of the administration for them. 2006, Stu, Floria and I wrote a manifesto on storage as a service. I didn't know it would take this long, but I'm glad you got there. Last question, Lewis, cool stuff you're working on, fun projects, what's floating your boat these days? My time these days is the cloud. As I said, we went to the cloud for cost savings. You can spend more money than you anticipate in the cloud. I know it's a shocker. So that's one of the things that I'm focusing our efforts on right now is making sure that we, we keep those costs under control, still deliver the speed and agility, but keep an eye on those things. Anthony, put a bow on Google Next 2019, partner of the year. That's awesome. Congratulations. Thank you. You know, I would say, you know, to put on a bow on it, it's great to see Thomas again. You know, I worked for Thomas at Oracle for about six and a half years. He's an incredibly bright man and I think he's going to do a lot of really good things for Google. As you know, I worked for his twin brother, George, and they are insanely bright people and really fun to work with. So for me, it was great to come up here and see Thomas and I shook hands when we won the award. And it was kind of surreal. It'd be both like, you know, we're both at a Google event. So it was fun. I got to make an observation. I was saying to a student in the keynote today, say we're both Patriots fans. So Bill Belichick, he has progeny, coaches leave, they try to be him. And it just doesn't work. Thomas Curian is not trying to be Larry. I'm not sure they, you know, share a lot of the same technical philosophies but he's got his own way of doing things and his own style. So I really appreciate that. It's a great hive of Google, a great hive. Really is. All right, guys, thanks so much for coming to theCUBE. Appreciate it. Thank you very much. All right, keep it right there, everybody. Dave Vellante with Stu Miniman, John Furrier is also in the house. We're here at Google Next 2019, Google Cloud Next. We'll be right back right after this short break.


I Yes, Walter Ruther is calling the president of line. Oh the president asked the operators to get him I've ordered. How are you fine? I? Your labor boy is giving me such push today. I haven't been on the phone I just got through and I'm going over any dinner with John Steinbeck, but I thought a better call you in between I had away a night in today and John Lewis and all of his co-workers, and so I've had a pretty rough day You had a rough day.  Thank you. What I'm calling you about. I'll just take a minute I've been working with moon and our boys in the Texas situation We've been trying to help put that together down there You know so that the Conley forces and the Yarborough forces could work together and give you a united, Texas Which we need and I thought it was coming along and then the other day Ralph Yarbrough called me and Hank Brown has been trying to get me and he wrote me a long letter And I met this afternoon with our regional director who's a fellow that moon works under Teddy Hawks, and I Think it would be a great tragedy those boys are talking about walking out of the convention down there and so forth And I don't think there's really much difference between them as they they appear to be And Hank Brown and these fellows are talking about where they're fighting for your program and the Conley forces won't go along Well and either one of us know what our program is it hadn't been written the only thing they'd done the damn fools are letting Republicans Sick them on that's right. They want to try to take the convention away from Conley water and they can't do it He's got them beat two to one and Conley hadn't got a program of platform, and I haven't got one We're gonna write it up at the Atlantic City we're gonna write a platform and then they're gonna have another convention But all the Republicans done is they got a bunch of simpletons down there who really want to control this and the Arbors their agent he votes right up here, but he got absolutely no judgment What he ought to be doing is getting every Democrat he can Sport him cuz he's gonna wind up getting in a fight and running half of them over the Republicans Yeah, and ain't a damn thing in the world for him to gain Every delegate that's come to that convention is going to be a carefully selected London Johnson man from who laid the chunk and he's going to be ordered to instruct vote for me All the way down the line now what they're trying to make them do is say you give us a blank check To endorse platform and hadn't been ridden. Yeah, well I now they can't do that And if it did Conley would get beat by Republican right the point is the point is that why? Why can't there be somebody to work this thing out because they're fighting over nothing now number one? important thing is to get that convention United to support all the Democratic candidates starting with you Well, I'll tell you why I miss Randolph through the years is the good good soul But she ruled her runs if she can't if she can't rule it loose and then she'll run it now they have tried to figure out they went out First thing I tried to do is beat Conley, which was a terrible mistake for him to do they ought to be fighting with it Then I got in a fight with Conley because he said well if they're gonna beat me I'm gonna be in your bra, but I said you can't do that And he said well It's a hell of a thing to take my gun away from me and give them the gun to work on me with right and you can't keep down your brown But you can keep me out. Well, I made Joe kill go mad and I made Conley mad But I kept the album from getting defeated because anyone in the group Jim ride Joe kill go any of motive defeated your Conley had it right But I said why do I want to improve the situation when I get a man to vote 99 times out of a hundred Why don't want to change that kind of a man? and I Appeal to Conley's intelligence and he said well all right, but I'm still mad about it. Oh, it didn't be now Soon as they got by that thing they come out startified and say, okay We we can't run the convention. We've tried to beat you we've lost But now we're gonna tell you that if you don't do it We're gonna embarrass present by going up with a separate delegation Well, Conley don't give a damn but they take a separate delegation and I don't either for that's concerned because they got nothing to fight I had your word lunch today at White House.  If you want to fight about it going to September convention in Texas after we've had Atlantic City and try to Blackball everybody doesn't support a platform. I wouldn't give a damn heart to support it. I'd say you sport Johnson period Because we haven't written their platform. I don't know what it is I want to ask them to support Conley called me and said now what kind of a program you advocate What are you gonna put in your platform? Are you gonna are you gonna balance the budget or are you gonna unbalance it and I said well We're gonna have a platform because they didn't we're gonna write a damn good platform Well, they said don't ask me though to write a blank check before you ever meet because I don't appeal to anybody Well, yeah, the Arbor's reaction is that they after him and they're gonna beat him and come is after him So he's got a fight coming now.  I told you Arbor day I said I'm with you money marbles and chunk all the way all the time Now you tell me who you want me to call what you want me to do I'll do it and he said well, that's fine. I'll sure be in touch with you But so they really after me well, that's true. They are after each other Of course it was it's awful But we will get Conley and every conservative Democrat that's on that ticket connected with them They'll wind up voting for Johnson Voting for Conley and voting for the Arbor now the only one that's really important about it is the is the Arbor thing they're gonna vote for me the Democrats are and It'll pull the Arbor over but if he has a bloodlady and he gets them all mad at it And what he ought to do is start fighting the living hell out of Bush That's the man to fight not to fight Conley, but they don't do that And this is history of Texas and the liberal movement and that's why they always get back We had to we had him up when Conley was elected Where labor could make advances in Texas ten years ahead of what he'd done. They didn't wait two hours until they started threatening Yeah, well, you know are you a deputy boy support? That's right. They they have in the state problem down there now is our fellas are fine But then you got CWA and the steel workers and some other people and I and Hank Brown is calling me And I'm just trying to get these other fellas of the back sensibly what they ought to do is this They ought to realize that number one. Mr. Conley won the conventions. They had a contest over it They got 2700 votes and he's got about 1800 of them That's number one. So they They tried and the majority didn't win and they lost they tried down the Arbor and they lost Now Conley's there and the man that didn't lose was Ralph Yarber and the only reason he didn't lose because we wouldn't let a man run Against him and wouldn't let Conley and Conley's are Giving me some very bad publicity about it. They said Conley and I have fallen out and all that kind of stuff It's not true But Conley didn't like my telling him that he just absolutely couldn't Support Kilgore and then Kilgore called here and I was in the cabinet meeting and all the Jenkins talked to him And they had to make a decision at an hour before an ounce And Walter Jenkins told him that he thought it would be an insult to me if he announced So he went up and withdrew And that gave the arbor a unheard of opponent and he damn near defeated him And now the problem we've got is getting the arbor beat this attractive young boy bush And he ought to quit fighting with Conley and every democrat if a man's got democratic label on he ought to say Mr And the only ones he ought to cuss is republicans hell if I were him I wouldn't go to a county convention I wouldn't mess around the convention the convention is going to be for his candid for president His candid for president is going to win. He's going to have his program It's going to do what the arbor likes to vote for so why does he want to get Mixed off in the convention. He ought to try to win the senator ship. That's what we need Is john Conley prepared to adopt the broad general statement? Which is say they that they provide full support for president and all the democratic candidates I don't know. I don't know. I haven't I haven't talked to him because if they we could get an agreement on that hill That's all they need They don't need anything else John Conley is prepared To bring that delegation up there and support me either Who laid the hill I'm prepared to tell john Conley and everybody down there that We've got to go all out to elect the arbor, but I don't know whether I can keep them from just fighting at each other's throat because you're like two big pussycats Act like boys But connelly's been elected and connelly's got the votes and connelly's in charge And I've got to have connelly to care of the state myself and that they ought to recognize And connelly got 71 of the votes against don the arbor I didn't halfway try and didn't halfway campaign And uh a year ago. He only beat him to 26 000, but that's what they've lost In a two-year period And they'll get it down to 81 percent if they keep on but what they'll do they wind up having tower in the senate And having bush in the senate. That's the way they're going because your arbor is a very weak candidate Several rights and union labor and the negro thing is not the way to get elected in a state that elects connelly by 72 percent And your arbor votes right, but he's handicapped in that state Now he wouldn't be handicapped in michigan in new york, but he's handicapped in texas.  That's number one They're not going to send a man there. That's not agreeable to me So the the man that they claim that far is going to have the delegation they want.


Hi everybody. Good morning. Good afternoon wherever you are. And welcome to our all-day movie workshop. I'm Peter. I'm going to be the host today. For those who are new, welcome. I can let you know a bit about the day. But before I do, we have a larger group with us today. We have a online retreat happening this weekend. Miracles are involuntary. That's our theme. And so we have some people here from the retreat and some just for the movie workshop. So welcome everyone. So we're going to start with the movie with David. And then afterwards we have a 10 minute break. And then we're going to have a breakout room or breakout rooms after that where you can express any emotion or anything that came up. And then we have a 45 minute break and then we have a Q&A session with me. So I see David there. I'll pass it over to you now. Thank you Peter. Hi everyone. Welcome. Welcome. Exciting. We have our final two episodes today of another self, the Turkish series and it's part of our miracles are involuntary weekend online retreat. So, so that's really what we're aiming for. We're, we're aiming for a state of mind in which we just feel like we're flowing all the time, we're just in the flow. You know, like they said in the 1960s, go with the flow. We want to live in the flow, live in the flow. Always live in the flow. Be happy, be joyful, be free. And we have a great setup today. As you know, for those of you that are here. Every week on, on Saturdays, you know we have a poll of themes and the themes flow with with the movie or the series that we're presenting and they also flow with our online retreat theme. So today, the themes that were voted on. Number one coming in number one with the most votes direct communication. Say what you need to say. Isn't that lovely. That sounds like that John Mayer song, say what you need to say, say what you need to say. Yeah, we need to hear that song a lot. Because some of you have said, Oh, David, I'm a big people pleaser.  That's a way to rinse away some of that people pleasing just now today I'm just going to say what I need to say I'm just going to, I'm going to roll with it. I'm going to let it flow off of my tongue, whatever it is I'm not going to prejudge it or bite my tongue and hold stuff in I'm just going to say what I need to say. Coming in number two accepting I am worthy of love. That is so important. If we're going to give up private thoughts and people pleasing we have to feel we're worthy of open communication. We're worthy of sharing what's really important to us, and we're open to receive communication as well we're open to give and receive communication. And that's how I begin to accept that I am very very worthy of love. Number three embracing my function as a miracle worker. 43 votes. Number four, let it go and let it be. We're adding to the famous Beatles song let it be, let it go and let it be. Let it go and let it be, let it go and let it be. Yeah, we can we can remember that tune that happy tune today, especially as we're watching this series. Let it be ready when you make to the final scene. Just remember my voice, let it go and let it be. That's the only way to be happy. So that's, that's good that's our fourth, fourth theme. And the last one number five, all things work together for good. In the Bible. It says all things work together for good for those who love the Lord. And of course in miracles it says, all things work together for good there are no exceptions, except in the ego's judgment. And really the Bible in the course you're saying the same thing, you know, that it's all happening for our good, it's all happening so we can remember God's will for us which is perfect happiness. I did a little live stream this morning early early morning with my friend in Germany, but the, and we were just having such a good talk because basically that's our plan of life is. What is your will for me that's it. That's, that's the prayer. What is your will for me God what is your will for me to have an open mind and just be able to take whatever is flowing throughout the day. With the open prayer of God what is your will for me. I would accept your will for me. Your will for me is perfect happiness so that's why I want to know your will for me, because we all want to be happy right, who doesn't want to be happy. But we have to be emerged with God's will to to know that happiness. You know what we're looking at when we watch this series is where we're beginning to get a pretty good feel that the only thing we're ever upset about is when some unconscious darkness rises up from our subconscious from our unconscious mind. And when the darkness comes up, we are tempted to interpret the events of our world in a in a dark way. And these can be interpretations that involve abuse or neglect, some type of mistreatment. It can be interpretations that involve betrayal or rejection or abandonment. It can be interpretations where we feel offended, or where we feel like we weren't heard, or like we feel invisible. But all of these dark interpretations of the world were not created by God. These are just egoic interpretations. God's perfect love and perfect happiness and joy is not creating any of those things. God doesn't even know of abandonment or rejection or abuse. God is just pure love and pure oneness. It's eternal life is basically what God is and an eternal life is, you might say that's our that's our inheritance when when God created us as a perfect being of light as the Christ. Then we were we inherited the traits of God, eternal, changeless, joyful, happy, peaceful, pure love. We inherited all of the characteristics of God, and we even received creative ability but the ego is an attempt to use that power of mind for projections. And that's why this series is really showing us that as long as we believe the past is real, we're going to perceive things in a very distorted way. Imagine that you have a filter in your mind, and that the ego is is dark spots. And if you've got a lot of dark spots on your filter, you're not going to be able to see clearly. That's talked about in the Bible in Corinthians, where it's spoken that we are looking through a darkened glass, and we don't see clearly. Jesus tells us in the course. Yeah, that's right. You don't really see anything because your vision is so dim and you're not seeing with the vision of Christ. But once you see with the vision of Christ, you realize how wonderful light is and how wonderful love is. And then you'll go, oh my, I never knew. And Jesus will say, well, you did know you just forgot. It's not like you never knew you knew, but you forgot that a little case of amnesia, little case of time space amnesia there. So, so I want to try to make it simple because I think everybody can realize that whenever you get into an argument or you feel upset. Basically, because the the person either the projection onto you as a personality or onto other persons is basically saying you're not fulfilling the role that was set for you. And guess who set all these individual roles, the ego. So, before you even came into time and space, you picked it all.    And if you were aware that it was just a movie, and that you made all the choices, all these egoic decisions, then you probably would be a little easier on yourself and say, I'm going to cut my mind to break here. And I am not going to stick to judging the things that I picked, because I must have been lacking. I must have believed I was lacking something to pick all these specific things.   It's more than all right. It's absolutely necessary that you change the mind about what you believe you are. And we can tell what we believe we are by our, our contractions in emotion by our, our, our dark emotions whenever we're feeling upset is because we simply are believing that somebody let somebody down in terms of the roles. And again, God did not create these specific roles these were ego choices. So in the end, we're just here to let go of ego choices and make another choice. See the world in a different way with with the Holy Spirit. So, some of you have been following along we have three women who are besties three best friends. We have Ada and Laila and Sevgi. And at the beginning of this series which was about four weeks ago when we first started doing this, it became pretty clear that two of the women. Ada and Laila were married, and one of the women, Sevgi was not married and she started off being diagnosed with cancer. And then as we watched the characters develop in this Turkish series with all these episodes. What we saw was that there seemed to be private thoughts and secrets that little by little were being exposed through the interactions. Ada was married to Salim, but her former boyfriend was Toprak. And as soon as Toprak enters the scene. Oh, wow, we've got a love triangle, a married woman with a husband and an ex boyfriend. As soon as they begin interacting, we start to realize that there's private thoughts, there's secrets, there's judgments, and there are hurt feelings. There's gent jealousy, there's envy, there's anger. There's all these dark egoic emotions that are coming up. And seeing that also with Sevgi, where she started off being diagnosed with cancer, her girlfriends felt sorry for her. But she goes to see Zaman, and suddenly Zaman starts to bring in the family patterns that have been going on for generations which is just symbolic of beliefs and thoughts in the mind. There are real generations, but the the ego just projects the world, and then the generations just act out the beliefs. So if you believe in abuse will say are abandonment, then it just gets acted out generation after generation, until your mind finally goes. Yes, I am not. I'm entitled to more than abuse and abandonment, and then you let it go and then suddenly the world shifts the whole world shifts and looks different. So the world, the perceptual world of time and space linear time is just a motion picture, acting out the beliefs and the thoughts and the emotions in the mind. The good news is you can change your mind. And when you change the purpose of your mind to forgiveness, then all of your feelings and all of your beliefs and thoughts line up with forgiveness. And then you see the world in a completely different way. Remember, it's just a motion picture is just acting out what you believe. The temptation is always to blame characters, but the characters aren't doing any more than they were told to do. You know the ego passed out all the parts, and they're just acting out the part you should be going Bravo.   You really played that Oh to a T you just played the part just as it was written by the ego Academy Award. You're not angry. So at the end of the stage play at the end of a Shakespeare play like my best or Romeo and Juliet you know the audience cheers, all of the actors and all the actors come out and the actresses take a bow, and there's a big standing ovation. Bravo Bravo. Oh my gosh you play that so well. Now while you're watching the play you might occasionally identify with certain characters and feel some emotions and that's what happens with this world. You get too attached to the characters. Then you start wanting to protect them or defend them, you start wanting to correct them. You start wanting to tell them, you behave.  But the mind assigned the part from the ego so it should be going oh little Johnny. That was a great act that you just did.   And what you did. Bravo for that. Oh my gosh I see what I have to release in my mind. When you're blaming the child you actually thank the child for acting out what you needed to see what you needed to release. So you start to see the world is just mirroring. You can start to feel gratitude for everyone. Everyone right now in the world. So, Vladimir Putin is he's playing the best tyrant that he can I mean he's he's going all out because the ego gave him that part. So yeah you're going to go through this and this and finally you're just going to invade Ukraine, and then you'll break off communication with the West the world and do this and you have to go Bravo tyrant. Oh my gosh that's that's an Academy Award performance right there. But, but if it's acting out tyrant or a dictator or someone that some people would say is evil even, you know, that evil part was assigned by the ego, not by God. God doesn't give any evil parts out. God doesn't even know if time and space how could God be passing out evil parts. It's just we have to learn to take everything as a mirroring of what's going on in the unconscious mind, and you may say, Well listen, I, I may have some bad days but I don't have any tyrant thoughts in my mind. It's not even acting out a tyrant thought it's not in my mind and I say well it's unconscious. That's why they call the unconscious you're not aware of it. You believe it but you don't even know it's there until he acts it out and then you get a chance to forgive it. And then you see oh here comes a tyrant thought. Here comes a dictator thought here comes a war aggressor thought. Oh my gosh I didn't know I had any war aggressive aggressor thoughts left in the unconscious mind I must have. Oh there's one. Okay. Thank you Vladimir. I like that name Vladimir. That's really cool name. Thank you Vladimir. Thank you thank you thank you for helping me see that I couldn't be upset unless I believed. I believed in the ego. So, the other thing is is the Holy Spirit and Jesus want us to see the world in a holistic way. And that means see the big picture. Don't get fixated on any of the parts. Remember the ego passed out the parts so why would you think you could know God's love if you were fixated on the parts. Jesus instead said show me the whole show me the whole thing show me the whole picture show me a forgiven world show me show me a happy dream. I would rather see a happy dream than be right about the parts. But as long as we're focused and fixated on the parts then that's where the dramas come in. Some parts need to be protected or defended. Some parts need to improve. Some parts need to be less boastful and prideful. You know, basically, some parts need to change in order to for us to be happy and they don't. They're just exactly the way they were written. And yet this kind of series starts to show us. Oh my gosh. I just need to look upon the world and full appreciation. The very first one is direct communication say what you need to say, and that is like a tool for the sleeping mind to learn to wake up by not hiding and protecting thoughts. By not maintaining secrets if you say what you need to say that will unravel secrets. And of course you can do it with love to you know you you can do it with a state of grace and presence. Because when you're saying what you need to say, it's really to release it. It's not. It's not to make anybody right or wrong it's not to point finger and blame anybody is just to speak it up and say, This is what I've been dealing with, but I'm willing to let it go. And I want to express it or talk about it. And that works. It works. And this episode just as a little bit of a recap with audit and her husband Salim and toprock, you know, basically, we are seeing throughout the series that audit became a doctor.   So she's gone from being the medical doctor to now she's slowly becoming a little more open to what are the psychological causes in my mind, what are the psychological aspects of the past that are determining my issues that I'm going through in my relationships. And basically toprock represents the other all the men in her generations of women in her life that have been left or abandoned. And meanwhile, she became a doctor to try to compensate for this hurt by saving lives. So even the roles that we take occupationally or friend roles relationship roles family roles they're all projections of the belief that something's lacking.  The ego is of course going to project a seemingly dysfunctional family because that's what it is the ego is dysfunctional. So what you know what you get from dysfunction is is a distortion or seemingly dysfunction. But actually they just played their parts perfectly you know in the end you start to say thank you. Thank you dad. Wow, great role, Oscar for you. Thank you mom. Fantastic role. The best I've seen Oscar for you, and you start passing out the Oscars for acting out the thoughts and beliefs so perfectly, even though the emotions were not comfortable. We acted them out so that they could be forgiven and released. And then we see that. She has issues with her mother, Belgian who's passed away now in a recent episode, and she still is waiting to find out what is underneath these persistent issues that I'm having. Also, just to catch everybody up if you're watching this for the first time. Her mother's Belgian. She went to her grave she passed away with her secret, but the Holy Spirit will help that one get revealed through a photograph, and then Mucko, whose seven keys mother she's got a major major secret that she's not sharing. We've seen in some recent episodes, her eyes get real shifty. She seemed to really like them on. She was baking for him at one point and now in recent parts of the episodes. She seems to dislike them on. She goes from baking for them on to questioning them on and being very suspicious. What Jesus calls this is a love hate relationship. When we, when we hold somebody up on a pedestal. And we do special things for them. It's because we're trying to make them more valuable in our mind and make a special love relationship with them and the flip side of that is special hate. If they don't do what, what the ego wants them to do, then the hatred comes in. So Mucko is really a good example of special love and special hate she's, and she's just sitting on a family secret that she's not telling her daughter. And that's why she's so into protecting the family, keeping the family together at all costs. And, and pretty much seeing everything through the filter of the family, everything that's good is what serves the family staying together, everything that's bad is what is that breaking the family apart, and that's because it's special love and, and special hate. I think we're just enjoying the treat of this whole series, because sometimes it's better when you can see it acted out in other characters, it's less threatening, you can, you can see it. You can gain the insight by watching what the characters are going through. The thing about it is, we've been raised with a lot of fairy tales and, and sometimes people say, Oh, don't, I don't know whether to see this movie doesn't have a good ending. What's a good ending. What's a bad ending. You just more judgments, you know, basically what we're really asking for is, is, can I find peace in what I'm looking at that's really what the question is and I am I going to find the peace of mind that God wills for me when I'm looking at the world. And that's, that's always our question. So, I hope you can enjoy these, these next episodes. I'm going to cut my setup short because I'll have commentary throughout, and then at the very end there's this amazing song, I could just listen to this song over and over. It's definitely a song that teaches a course in miracles and it's so wonderful. And we'll play that one when the credits roll. Let's try to play that song. It's, it's just basically the key line in, and it is no one's born to die. None of us have been born to die. All of us have been born to resurrect this. We've been born to say, Okay, it's time to wake up to heaven. To leave the world behind by forgiving it, not by trying to fight it or battle it just by lessing it and, and, and releasing the ego and feeling the softness and gentleness of it. And then, usually at the end of the movie that's pretty much the end but I think we, I might have a bit of commentary coming through after the final song so it's such a deep series that I'll try to do a summary. When we make it through the final song. So sit back. Enjoy the ride have fun watching the characters and pay attention if anything comes up because you want to work with that you want to give that over to the Holy Spirit. See you very soon.


The study assesses the spectral consistency between a high-resolution UAV-mounted Microsense red-edge MX sensor and variable-resolution multispectral sensors on-board PlanetScope, Sentinel-2 and Landsat-8 platforms. It finds that a vicarious radiometric correction is more accurate than a linear empirical line method for UAV data, with the former improving relative root mean square error, RMSC, by between 1.6% and 20.11%. Spectral band misalignment affects spectral consistency, causing different reflectance values for the same object in corresponding UAV and satellite bands. Larger differences between UAV-derived normalized difference vegetation index, NDVI, and satellite-based NDVI are observed for different ground features in response to land cover boundary and shadow effects. As spatial scale differences between the UAV and satellite platforms increase, the impact of geometric misregistration on their consistency decreases. The study provides insight into the collective effect of spectral and spatial misalignments on the degree of spectral consistency that can be expected between UAV and satellite data, guiding radiometric intercalibration efforts and potential for improved synergy and interoperability between UAV and satellite data. This article was authored by Geologyang, Casper Johansson, U12, and others. We are article.tv, links in the description below.


What is going on guys welcome back to the channel Critical Overlord here's a time of Halloween ends in this video here again today So recently in a new interview with Collider Nick Castle gave some comments on the upcoming film that we know was coming out later this year In the month of October It's gonna be the conclusion of the David Gordon Green iteration of the timeline that he's been crafting since the 2018 Rebirth of the franchise with the horror icon Michael Myers involved and of course him now pursuing Laurie Strode who is not his sister heard the fact that it's a Sequel all of these are sequels to the original film and we know that wasn't established till the second movie So his recent comments seem to be teasing a shocking surprise ending that you might not be considering is a possibility going into the film and I know I've seen some people already kind of say they're worried about it He basically stated that I think there might be more and talk about the future of franchise I think there might be more because of all the success of this trilogy But green will have a very surprising storyline and ending for everyone is absolutely something I don't think you would have ever guessed in terms of the way. It's going to unroll now One thing I could I guess I could say many people are not necessarily considering is that What if this? This dream idea that I know a lot of us are considering we're considering that but we're considering it to be a Dream that is gonna undo everything that we've seen that would include the 2018 film That would include halloween kills and it would actually include the film we're about to watch It's gonna undo all of that and it's gonna be picking up sometime after the events of the first movie and Lori Strowed is in a completely different different spot in her life than we originally thought But what if they do something different than that? They could do something where it's just that the events of kills and ends are the dream scenario Halloween 1978 of course happened, but also halloween 2018 as well happened It's not going to erase the whole trilogy It's just going to erase kills and ends and you would establish it after the events of halloween 2018 Lori Strowed and her and her daughter and her granddaughter did indeed ride off into the halloween night Firefighters though never really came and discovered a live Michael Myers They did put the fire out, but they didn't discover a live Michael Myers. They could do something where We are teased that the shape is still out there And maybe that's how the movie ends the movie ends with again the idea that Dave McCrae brought up Which again, I think is brilliant where the firefighters actually arrive on the scene of the house at the night of halloween 2018 still that's how halloween ends could could end up ending and When they're going to put out the fire There's a voiceover that comes on where dr. Loomis says you thank you for the Michael but not me and Then the movie just cuts off Indicating that well did Michael Myers actually survive that fire from the 2018 film because basically what we've gotten ever since then is confirmation of that with kills Showing us that he survived and now in showing us that he survived, but what if they pulled the rug out from under us and we just revert back to that same night and It's basically gonna show us that Lori strolled is in the hospital and She's recovering from her from her wounds Everyone else has been treated but Lori got admitted to the hospital since she's up more up in age compared to her daughter and her granddaughter So she's in the hospital and she had just been dreaming at all. It's gonna be the same Halloween night of 2018 You'll have your Judy Greer cameo that way You'll have Allison in the room present when she wakes up and then when we realized that the events of kills and ends We're all just a dream and we're still in the same night. We could jump to a scene of the firefighters arriving on on the set of the or on the scene of the fire at Lori's house still the fire Rages on and when they go to set it out or put it out the camera starts to pan over It gives you like an aerial shot Observing the the fire from above and you can hear dr. Loomis speak from beyond the grave You fooled the Michael or something like that, but not me and then the movie just cuts to black You don't know if Michael survived that fire or not And you can actually throw in some little subtle breathings to confirm what actually went down in that house if he survived Does that does that mean that he survived and you constantly just have this idea or this conversation going surrounding Whether or not he survived that fire from the night of 2018. I Haven't seen many people consider that the most I've seen people consider is that they're going to completely erase everything and say that all three films were a dream What if it's just the last two that are part of the dream? Because if they were to erase everything and then just have us pick up 40 years after the events of the original movie And we're still with Lori Stroll's character, but she's in a completely different place in her life What if they even take it as far as rendering Allison a non-existent character Karen doesn't exist all of these things that they They could do if they were to erase those movies Tackling on to the fact that all the other timelines are dream sequences She's just dreamed all these different scenarios in her head where Michael Myers kept coming after her kept coming after her Daughter named Jamie kept coming after her son named John she dreamed that she was the head of a private school in California and Michael attached her there rendering all of the timelines a dream I think that will face more backlash. I think that scenario would face more backlash But I think that's of course another thing that I guess you could say many people as a whole aren't considering this surprise And they're talking about Most of us are considering, you know, Lori and Michael are gonna die together Michael's gonna die Lori's Lori's possibly gonna die Michael lives stuff like that. They're not really honing in on Dreams and a big a big dream being the big revelation at the end of hallowing ends If you do it in a way in which Halloween kills and ends are not canon. It was all a dream I think people be more accepting of that if you render Halloween 2018 kills and ends as a dream And then just pick up randomly 40 years after 78 movie and tell us that Lori dreamed all of that that would be I think far worse received and then adding on to that you can add in that all The timelines we've known in love those were part of this dream to in this timeline I think that would be a lot more backlash from the fans if they were to do that Honestly this surprise ending. I hope it's related to something just remaining canon. I hope it's not really related to dreams all these other things but I Think if they were to do it, maybe when we go back and rewatch it We could see that there were indeed clues Hinting to the fact that they were gonna take us down this dream route And the writing was on the wall and we just failed to recognize it But again, hopefully they don't do that. Hopefully the surprise is related to Mostly it's like a shocking outcome for Michael and Lori that maybe I'm not considering maybe you're not considering But let me know what you guys think about Nick castles comments down in the comment section below Are you looking into it as much as I am and as much as I've seen other people look into it Are you just gonna wait for the movie if you haven't already of course make sure you subscribe Turn on postification and then there's a video in the scripts. I have links to my social media How's my Facebook Twitter and Instagram you can message me there of course limiters any movies And those are usually I'm gonna cover in the future with all that in my guys. I will see you in the next video


I had double knee surgery and the bone and the metal starting to jab into my knee and it causes me to walk. Walk a little weird sometimes and my lower back and then my upper back and my neck and it's just all out of whack. And I just wanna be able to walk without this shooting pain in my leg. What do you want Jesus Christ to do for you now? Heal me whole. For the salvation of your soul. Always. After you're healing you follow Jesus Christ. Yes. In the name of Jesus Christ. Yes.  Be healed. Yes, thank you. Thank you Lord. In the name of Jesus Christ. In the might of Jesus Christ. In the might of Jesus Christ. In the might of Jesus Christ. Lose it, lose it. Lord, thank you Lord. How do you feel sir? Oh, I feel good. Yeah, praise God. Thank you Jesus.


So, I am Harsh from North Korea, India. I did my beauty tech from BIT University, Belarus, and I'm currently working as a blockchain developer at Anworks. The project that I was involved in was to give Ares the functionality to support fabric as a ledger. And the hyper ledger project that I worked with in this mentorship project was the Fabric and Ares. I was mentored by Kamlesh Nagwari, sir. So I would just first give a project description. Ares is basically a wrapper around Indy and Ursa, such that it enables businesses to build self-solving identity solutions. Now in these solutions, an issuer can issuer credential to a user. And this credential would only and only be kept in a wallet. And this user can verify to the verifier without even revealing the whole credentials through zero knowledge proofs. This works in two ways. Suppose say I'm a user and I have a credential of name Harsh and age 25. Now it's my choice that I can reveal that my name is Harsh to the verifier. And at the same time, it's my choice that I don't want to reveal my age. So the verifier would only check whether if my age is less than 30 and if my age is less than 30, it would be successful or else it won't be. This is what Ares, Indy and Ursa supports. These can be any types of, there can be any type of credentials and various types of verification can happen. Now businesses that are developing blockchain solutions using fabric, say suppose supply chain solutions or solutions in telecom industry, they also want to carry out some sort of verification process. And their need is that they don't want to separate the data that they're putting into the blockchain. So they don't want their domain related transaction to be in fabric and the identity related transaction to be in Indy. Once this project is developed, they would be able to use this Ares wrapper and only one blockchain platform they can use that is fabric for all their needs. It would work for supply chain transactions as well and also identity related transactions. So my objective here was to first develop a chain code in the fabric network and integrate that chain code with AFJ. Then I also had to write the test cases in Ares framework JavaScript that would test the module that is written in AFJ that is integrated with fabric. And the third objective was to demo whole, this whole process of issuance and verification with fabric as a ledger. One of my first deliverable was, see there are three transactions, there are three types of transactions that happen in the Indy ecosystem. One is domain, second is pool and third is config. So as fabric has its own similar types of pool and config transaction, we didn't need to support those transactions here. We only needed to support the domain transactions which are these, dead, atreps, schema, credit devs, revocation registry entry and revocation registry definition. So we needed a chain code of that to be present in fabric. My second deliverable was that there would be a module in AFJ that would interact with the chain code that was that we deployed in deliverable way. My third deliverable was to write test cases that would test this whole module and chain code thing. And the fourth one was to demo the issuance and verification with fabric as a ledger. So we have been able to write the chain code and the module. This project that I was involved with, first it motivated me to look into how the Indy Ares and Ursa ecosystem work and replicate some of that functionality in fabric. So we didn't need to entirely copy paste what Indy does. We picked up the SSI related part that Indy does and how it does it and tried to replicate that in fabric. So it gave me an understanding of how Indy works. And at the same time as I was working on fabric as a ledger and Ares framework JavaScript as a framework, I had to go and dig deeper into that also and to understand it. One challenge that I faced here was while establishing connection from AFJ to fabric, but this when we later solved it, it improved my understanding of how a fabric network works and gave me an understanding of what Docker networks are and how they work. We have some future work for it, like right now the domain specific transactions that I was talking about, there are six transactions. And currently Ares framework JavaScript only supports three of them, like dead schema and credential definition. They have plans for revocation and atrip transaction as well. Once that those are done, we would add that to fabric as well as AFJ. One thing here that we are doing is as we are using Indy wallet to store secret and non-secret records of credentials that are of credentials that are related to SSI solution to work and we are using fabric wallet to store client credentials. So we need to integrate, we can integrate that in the future and create only one wallet for it. And in the future, if the need arrives that any business that is using other blockchain platforms and if they want to do that identity verification process in it, we can add those ledger as well. Now this module would be added to AFJ. We have had a chat with the team and the chain code would be submitted to hyper ledger labs and it would be taken forward from there. Now, as I said, I had two deliverables that I was talking about earlier. I had to write a test case and the demo of issuance and verification through fabric. The second demo of issuance and verification, we are still working on it, but I have the test case prepared. So I would give a demo of it. Okay. So I am running fabric in my local system. This is logs of one of the peers and this is the logs of order. So I will just run the test cases here. Okay. So here it would write the DID schema and credential definition transaction in the fabric blockchain. And so you would be able to see the logs of three transactions occurring here. This gave me a minute. So now the process has started just now. Yeah, so just a second. Yeah. The order has created block six and it has come to the peer logs. The seventh block, the same year, we see block seven and committed block seven. Now one more block could come. Yeah. So the eight block. And here we can see that all the test cases have passed. It has registered the DID schema and credential definition on fabric legend. We are in the process of creating the issuance and verification demo. So now the insights that I gained from this project was whatever you're doing, first research on it and document the whole idea and a plan of how are you going to do it? Then plan it and then implement it. Then the implementation becomes very easy and in short, your life becomes very easy afterwards. And then try to have regular meetings with your mentor and exchange minutes of meeting emails from them with him or her. It would enable you to be in loop of what is happening in the project and what we are going to do forward. And if you're facing any issue, first try to debug it and if it is not being able to solve, approach the open source community through GitHub issues or Rocket Chat, they're easily approachable and very helpful. Last but not the least, thanks to my mentor, Kamlesh sir. He was available at various times and he was also looking at my issues and researching with me and also to the AFG team for the easy response, quick response for my issues, especially to Timo and Bernard. Any, I'm over with my demo. Any question and answers? So actually Kamlesh here, I want to add like because I was the mentor of the project. So working with us is really great and he's very dedicated, committed, even via schedule over meetings on the weekends, Sunday, every Sunday, 12 p.m. And idea about the project like because in the hyper ledger, we have number of projects, number of DLTs and we have libraries and the end goal of all these libraries and projects to work together. And able to use this as a library, like for example, Explorer currently we only use for fabric. So it should support like Beisu and Eroha and other sort of kind of project. Similarly, this AFJ, this Eris framework, Java, JavaScript only support the indie and indie as a ledger. So having a fabric as a ledger is really good move and that's why we started and we proposed this project. And as a future goal, I heard and I'm thinking to propose this as one of the hyper ledger labs. So yeah, thank you. Thank you both so much for presenting and Kamlesh for mentoring and supporting your mentee. And it's great to hear that you are planning to propose this as a ledger labs project. So we're looking forward to hear more about it. And also the other demos you're working on, the assurance and verification. Yeah, yeah, sure, thank you. Yep, thanks again.


This lecture is part of an online course on commutative algebra and will be about integral elements. So let's first define these. So suppose S is an R algebra. So an element S in S is called integral over the ring R. If it satisfies a polynomial with leading coefficient 1, so we have S to the N plus R N minus 1, S to the N minus 1 plus R naught equals naught for R i in R. So for example, let's try and find the integral elements of the rationals. So let's take R to be Z and S to be the rationals. Let's find the integral elements of the rationals. So suppose we've got an element S which is A over B with A and B integers.  And we can assume that A and B are co-prime, obviously. So now we multiply this by B to the N and we find A to the N plus R N minus 1 A to the N minus 1 B and so on, equals zero. And now we see that if P divides B for some prime, so then P divides all this because this is all divisible by B. So then P divides A. Well, A and B were co-prime, so B is a unit. So A over B must be an integer. So the integral elements of the rational numbers are just the integers, which is just as well because otherwise the term integral would be a bit weird. Notice that all we've used here is that Z is a unique factorization domain and Q is its field of quotient. So if we have any unique factorization domain as R and its field of quotients as S, then the integral elements of S over R are just the elements of R. So let's look at some basic properties of integral elements. First of all, if S is integral, this implies that R of S is a finite and what this means is finite as an R module. So you remember when you talk about things being finite, you can mean finitely generated as an algebra or finitely generated as a module or finitely generated as a field and these are all different. And here we mean when we talk about a ring extension being finite, we usually mean finite as a module or the terminology just is a bit confusing. And this is obvious because it's generated as a module by 1SS squared up to Sdn minus 1, where Sdn is equal to Rn minus 1, Sdn minus 1 and so on plus R0. So you can see from this that all higher powers are also in this module. Of course, it's finite as an algebra, it's just generated by the element S, but as a module, you need more generators, but you still have only a finite number. And the converse is actually also true. So if R of S is finite, then S is integral. In fact, we can prove something slightly stronger. If S is finite over R as a module, then all elements of S are integral. And I'm going to give two proofs of this. The first is if R is notarian, it has a very easy proof. We just look at the submodule of S generated by 1 and the submodule generated by 1 on S and the submodule generated by 1S and S squared. And this is an increasing sequence of R modules. So eventually, two of them must be equal. So 1S up to Sdn minus 1 must be equal to the module generated by 1 up to S to the n. But this says that S to the n must be in the module generated by all the things up to S to the n minus 1. So S to the n is equal to R0 plus R1S plus Rn minus 1 to the n, S to the n minus 1. So if R is notarian, this is very easy to prove. And normally, if something has a proof like this over notarian rings, it's generally not true over nonnotarian rings. But in this case, this is an unusual exception. And in spite of this easy proof of notarian rings are, it's still true for nonnotarian rings. And to do this, we're going to use the Cayley-Hamilton theorem. Well, you may have come across the Cayley-Hamilton theorem in linear algebra. And people who do the Cayley-Hamilton theorem for linear algebra wimps because they just work over vector spaces. And we're going to do the Cayley-Hamilton theorem for modules over arbitrary rings. So what does it say?  M is integral, fairly obvious, should be fairly obvious what that means. It just means phi satisfies a polynomial equation with leading coefficient 1 as an endomorphism of the R module. And to prove this, we suppose M is generated by elements m1, mn. So these do not necessarily form a basis. In fact, M might not have a basis, it might not even be a free module. And these might not be linearly independent. And then phi is given by some n by n matrix. And you've got to be a bit careful here, because this matrix is actually not uniquely determined by m1 up to mn because these might be linearly independent. So there might be several different matrices corresponding to phi. So this matrix is not unique. So if we're working over a field and took this to be a basis, then there would be a unique matrix for phi, but for rings we have to be a little bit more flexible. And this means that if we take this matrix here with just phi down the diagonal and subtract this matrix A and apply this to the vector m1 up to mn, this is just equal to zero. I mean, that's more or less what you mean by saying that phi is given by some matrix. So on this side, so this thing here is a matrix. And the coefficients are in R of phi, not just in R. And now we know that if we've got any matrix, and the matrix times it's a joint, which is some weird matrix you probably forgotten from linear algebra formed by lots of n minus one by n minus one minors is equal to the determinant of the matrix times the matrix with just ones down the diagonal. So in particular, if we take the determinant of this matrix with phi's down here and then subtract A, this acts as zero on the vector m1 up to mn, so as zero on the matrix m because it kills off a set of generators. In other words, this determinant is just acts as zero on m. And you notice this determinant is a polynomial in phi with coefficients in R and leading coefficient one because we've got a term phi to the n from the determinant down the diagonal. So phi is a root of the integral polynomial where you just take the determinant of this matrix x, x, x and so on and subtract the matrix A. So phi is integral. We can even write down the explicit polynomial that satisfies if we really want to. So from this, we can go back to the theme we're trying to show that if, remember, we're trying to show if S is finite as a module over R, all elements of S are integral. And what we do is we just take the module m to be S and if little S is in S, we take the element phi to be the endomorphism given by multiplication by this element S, which is an R linear map from S to S. And then if we apply the theorem, we see that the element S is integral over R because the polynomial satisfied by this transformation phi will obviously also be satisfied by S. So we see from this that S is finite over a ring R is equivalent to saying that S is generated as an algebra by the finite number of integral elements. So let's just check this. Well, this implication we've just done because all elements of S are integral. So you can just take a finite set of generators of S as a module and these will obviously generate as an algebra and they will all be integral. So that's easy. The other implication is also fairly obvious, but all you need to do is to show that if we've got two finite sub-algebras of S, let's call them S1, S2, then they generate a finite sub-algebra. Finite as usual means finite the generation as modules and that's very easy because if S1 is generated by elements A1, opt to AM as a module and S2 by elements B1, opt to BN as a module, then S1 and S2 are both contained in the module generated by the elements A, I, B and J and this is obviously also a finite module and it's also obviously closed under multiplication and addition so it's a ring. So any integral element will generate a finite algebra so a finite number of integral elements will also generate a finite algebra so this implication follows. The fact that in particular if we've got two integral elements then their sum and product is also integral. So for example in number theory we can take Z equals the sorry R equals the integers and S equals all, let's just take it with the complex numbers, then the integral elements of C over Z are the algebraic integers and these form a ring because we've just shown if you've got two algebraic integers they both generate a finite extension of Z and you can take the ring generated by both of those and that will also be a finite extension of Z. Notice that this is not really obvious if you just use the definition of being roots of a polynomial, for example suppose you've got the square root of two and you add the cube root of two and you add the fifth root of two and let's find a polynomial in Z of X with this as a root. Well I'm not going to do that because in fact the smallest polynomial like this is degree 30 and there's nowhere I'm going to write out a degree 30 polynomial so you see if you think of these as being roots of polynomials it's not at all obvious that adding two roots of polynomials is going to be a root of another polynomial but it is sort of obvious if you think of integral elements as being things generating finite extensions. So next we're going to look at the concept of normalization. So if S is the integral closure of R in the field of quotients S is called normalization of R so this is yet another example of the world normal being grossly overused by mathematicians. The interval closure is of course just all elements integral over the ring R. So let's see some examples of this for example let's let's find the normalization of Z with root five adjoined to it. So the field of quotients is just q root five which are the numbers of the form a plus b root five for a and b rational numbers. So let's find some elements of the normalization. Well it obviously contains all numbers of the form m plus n root five for mn integers and it's not at all obvious what else it could possibly contain in fact the obvious guess is that these are all of them but in fact it does contain some other elements let's try and find the normalizations systematically. If m plus root five n is in the normalization let's call this normalization S then pretty obviously m minus root five n is also in S and we've seen that the normalization is a ring so if we add these we find two m is in S. Now sorry that shouldn't be S that should be in Z no should be in S. So two m is in S so in Z because we've seen that any rational number that's integral over Z must actually be Z so m is either an integer or it's a half integer well the ones with m an integer we've pretty much found you can easily check that if m is an integer then n must also be an integer so this leaves over the possibility that m might be a half and in fact there is a number with m equals a half that's integral because we can take one plus root five over two and this is the notorious golden ratio phi and you can check that phi squared is equal to five plus one so it is integral over the integers and this shows that the normalization of Z root five is not Z root five as you might guess but Z one plus root five over two the same thing happens for Z of root D for D congruent to one mod four you find that you can get things of the form one plus root D over two which is a root of X squared plus X minus D minus one over four unless I've got a sign wrong here I can never remember what the sign there is let me put it plus or minus. So I think I don't usually give exercise in lecture but let me let me give a quick exercise here find the normalization of Z root D for D an integer and you may as well assume it's square free otherwise you can just take out the square factor without really changing the normalization. So next one other thing we should check is that the integral closure of the integral closure is just equal to the integral closure for example suppose you've got a root of say X cubed plus alpha X plus the fifth root of two equals zero where alpha cubed plus alpha plus one equals zero then this implies X is also an algebraic integer which again is not immediately obvious if you try and find a polynomial of the integer coefficient satisfied by S and this follows from the fact that if S one up to Sn integral over R and S to the n plus Sn minus one S to the n minus one and so on plus S naught this naught equals naught then then S is integral over R and this follows fairly easily because you notice that you've got R contained in S naught up to Sn minus one and this is contained in R S naught up to Sn minus one S and this extension here is finite as I mean that's the finite R module as usual and this extension here is finite and you can easily check if you've got a composition of two finite extensions like this then this extension is also finite so little s is integral because it's in a finite extension and finally we just mentioned that the ring R is called normal if it is integrally closed in the field of quotients I guess if I'm taking a field of quotients I should make R an integral domain so for example any if R is a unique factorization domain R is normal actually proved that at the beginning of the lecture we sort of showed that the integers is integrally closed in the rationals and commented that the same proof works for any unique factorization domain and we've also seen that something like Z of root five is not normal because its integral closure is Z one plus root five over two so what we're going to do next lecture is study the geometric meaning of being integral or being normal because it turns out that being normal is a sort of very mild form of things being non-singular it turns out that if you've got a variety and its coordinate ring is normal that doesn't mean it's non-singular but it means that all singularities have co-dimension at least two


promised our Jack Curry joins us now and Jack this date in history will be remembered forever 19 years ago everything changed today we honor those lost and their families and reflect on the role baseball played in standing up strong in its return 10 days later that night at Shea Braves Mets no dry eyes in the house so well said Nancy today is a sad and sobering anniversary as I watched and listened to the names of the deceased being memorialized today it was a chilling reminder of how much we lost on 9 11 with every name that was read whether it was someone I knew like Mike Armstrong or someone I wish I had known like Victor Sarasini or Patrick McGuire I thought about the dozens and even hundreds of people who love them and miss them Nancy we all know where we were in that agonizing day I was at Newark Airport heading to Houston to try and interview Barry Bonds after the first plane hit the World Trade Center there was an eerie feeling at the airport after the second plane crashed there was an announcement telling us to evacuate there was panic there was confusion but that was absolutely nothing compared to the devastation several miles away in New York City those early days we all remember them they were gut wrenching for so many amidst a lot of praying and hoping I remember wondering if baseball could eventually provide a modest distraction for many traumatized people after then Commissioner Bud Sealy declared that baseball was returning 10 days after terrorist attacks that met game that you referenced that Shea Stadium I interviewed him since I was based in New York Sealy said to me do you think we're coming back too soon I said no I think people need this in times of utter distress I do think sports can be a diversion even if it's only for three hours at the 9 11 Memorial Museum which I recommend highly people go and visit there's a quotation from the poet Virgil it says no day shall a ratio from the memory of time I think those words are beautiful and so appropriate thousands of lives were lost on that awful day but the impact those people had and will continue to have has not been erased they will never be forgotten beautiful tribute of course as always from you Jack thanks so much in this day of course remember throughout baseball today


For a patent, the front page includes the title, inventor, abstract, a drawing that summarizes your invention. After you flip past the front page, you'll find figures of your invention, numbers next to the illustrations, explain how your invention functions, and what each part does, field of invention, background, and detailed description are the parts of the patent that specify your invention. Here you can find inventions of similar inventions that may be out on the market and how your idea differs from them. This section will also reference those significant numbers that describe each part of your invention in detail. Finally, the claims are the end of a patent and determine the scope of protection provided. The claims of a patent that tell competitors how close they can come to your idea without infringing your rights. As you can see, patents are a complex document, which is why I always recommend hiring a patent attorney to draft a patent application for you if you want the best protection possible.