It is really hard to believe that November is so far gone already, and I can't even begin to tell you where time has gone. It's just like it's just zooming by before you know it's going to be like the 4th of the July or something. It's just absolutely nuts, but that's beside the point. Every single month I get together and find five amazing Linux apps that I can share with you in hopes that I bring some entertainment to your life, and the series seems to be fairly popular, so I continue to do them. I continue to go and find applications, and this month is no different. I have five really cool apps to share with you this month. I'm really looking forward to it. But before we jump in, let me remind you that there's this big red button right below my face, and you should hit that button, and if you haven't already, subscribe to the channel because I publish content pretty much every single day of the week. Some of it is good content. Some of it is not good content, but you don't want to miss the good content, so hit the subscribe button. You won't regret it, or at least I hope you won't regret it. If you do regret it, let me know, and maybe I can get better. Anyways, enough of my rambling. Let's go ahead and move on. Move into the list. You're here for the applications, right? Let's go to the applications. Let's jump in. Okay, so the first app on the list for this month is called Seahorse, and Seahorse is a very interesting little application. It's made by the GNOME guys, and its purpose is kind of to be a password manager, but not really to be a password manager. It's kind of hard to explain, but really what it's meant to do is create and store GPG keys and open SSH keys. Now, it'll also store passwords, but as you'll see in the video and the B-roll that you'll see in this section, the password functionality is a little weird. If you're looking for a password manager, this is probably not the one that you're going to want to go with because it doesn't store usernames or anything. It'll just store passwords. That's literally it. Write out the name of the password that you're storing and then the password that's all it will store. What this is really useful for is storing GPG keys. So if you use GPG in order to encrypt your emails or whatever, you can store your keys in this. This is like a gooey way of doing GPG encryption and SSH keys, which will allow you to connect to things via SSH. And the SSH thing is really kind of what I found most interesting about this because I have a hard time remembering how to set up SSH in the command line. I always have to look up a tutorial in order to set it up. This made it really, really easy. And I think that despite the fact that I usually prefer to do things in the terminal that going through and actually using a gooey in this case made it more enjoyable for me to maintain these things and easier too. So Seahorse is free and open source, obviously, and it's available as a flat pack, I believe. I'm not sure. Actually, when it is in the AUR, because I downloaded this in the AUR. So it is in the AUR. It is a flat pack, whether it's in your destroyer repositories is something that I can't answer, but you should be able to check fairly easily. So that is Seahorse. Okay, so the second app on this month's list is called Get UI. And for those of you who've been watching the channel for a while, you'll know that I pretty much despise using Get in the command line. There's way too many commands. It's way too confusing. And it's just not something that I've ever been able to really wrap my mind around, even though I've gotten better over at it over the last few months. So I've always been looking for an application that I can go through and just use to interact with Get in a more 2E slash GUI, you know, fashion. And for a while now, I've been using Get Crackin.  But I've been wanting to look for a false option. And Get UI is an option that I'm going to be trying out. Now, this is a 2E application, meaning it runs in the terminal. And you can do pretty much everything you need to do to interact with Get inside this application. Now, I've not used it extensively. I haven't set it up with my Get credentials yet, mainly because I just distro hopped because of computer problems. And I haven't set up SSH keys and all that stuff yet. But when I do, I'm going to be giving Get UI a deeper look because it seems at least a little more simple than something like LazyGit. LazyGit was very complicated for me, and I can never get it up and running and working well. So I didn't use it. That's why I was using Get Crackin. But Get UI seems at least a little bit easier to set up. Now, I will say that the help for Get UI is not all that great, at least in application. I can't speak to what it is on their website. I'm assuming the documentation is much better on the website. I haven't actually looked or haven't had the chance to look, but the help inside the application is not very great. And there's not a man page. There's a very rudimentary help page that just says help brings up this thing. And there's no options or anything. Now, it does give you a list of all of the key bindings and stuff that you'll need to know. And there are helper tags along the bottom of what you'll tell you where you can go and what you can do. So it's not that hard. And it's not as if you need a ton of documentation. But I really do think that I need to go and actually read the website before I dive into this. But from what I can tell and from the few things that I've read about it, Get UI does look like it's at least a little bit simpler than lazy Get. And that's something that appeals to me. And other than that, it's just a way to interact with Get. If you want some other way of interacting with Get, then just using the standard Get commands. So that is Get UI. OK, so the next one on the list is called Markets. Now, this is another GNOME-based GTK application. And it's very, very simple. There's not a ton that you're going to be doing with this. Basically, this is just a stock market slash cryptocurrency tracker that you can install and keep track of certain stocks. There's literally nothing more to it. Now, in the B-roll that you're watching, you can see me go through and add a couple different stocks. You can go through and you can see me go through and add a couple cryptocurrencies. There's not actually a ton of stuff that you can do with this. There's not a lot of preferences. There's things that allow you to set the amount of time to have it refresh. And there's a bit of dark mode, I believe, is the only other thing that you can actually change in terms of actual settings. Now, when you click on one of the items that you've added, it will actually take you to the Yahoo pages for the markets. So if you click on Apple, it'll take you to the Apple page on Yahoo Finance or whatever it's called. If you click on Bitcoin, it'll take you to the Bitcoin tracker on Yahoo Finance. And other than that, there's not much to say that. So if you're an investor in the stock market or cryptocurrency or whatever, and you want an easy way to track this kind of stuff and you want a gooey way of doing it, markets is a good option for you because it's very, very simple. So that is markets. Okay, so the next app on the list is called Petivi. And Petivi is a video editor. I've been looking for something as an alternative to KadenLive because KadenLive does way more than I really needed to do and oftentimes confuses the crap out of me and they tend to push updates that go through and just crash it for no reason. So I've been looking for something that's a little bit more stable and a little bit more simple. And Petivi is an option that I'm looking into. It is very simple. I will say that it has a very simple UI. It has some features. It doesn't have a lot of settings. It has quite a few effects, which I find nice. But it's not as complex for sure as KadenLive. So if you need something more complex in a nonlinear video editor, KadenLive is probably still the best option for you. But if you're looking for something that's a little bit simpler, Petivi is an option. Now I will say that it doesn't seem to work well with transparent background animations. As you'll see in the B-roll, if I get this edited correctly, you'll notice that the Twitter animation that I import just has a black background. Now in KadenLive, it takes that black background out and just uses the animation as I think it should. With Petivi, it just left the black background there. Now I could go through and add a green screen to that very easily. It would be easy to do. But it's just something that I noticed in my brief time with it. Now I'm going to give it a little bit more try. I'm not going to commit to editing this video which is like 12 different tracks in order to edit. I don't think that I'm that committed. I'm more used to KadenLive right now and I want this video to be edited fairly quickly. But for more simple videos, I'm going to give Petivi a try and see how it works out because if I can get used to it, the simple UI really does appeal to me. So that is Petivi. If I'm saying that right, I actually didn't know. I don't know if I said the name right. I could be butchering that. Anyways, that's Petivi. Okay. Now the final app on this list for this month is called TUT. TUT is a terminal based Mastodon client. Now, if you don't know what Mastodon is, it's a federated social media platform similar to Twitter. It's very much Wild West from my experience. So if you join it, stay away from the federated timeline.  And it's just not a good place to be. It's just really, really, really bad sometimes. But if you follow just like the Linux people on there, it's actually a fairly good experience. Plus there are actually useful bots on Mastodon where you can go through, set it up so you can get all of your Twitter feed in Mastodon through a bot. It just shows up in your timeline just like they would in Twitter. And that kind of saves you from having to go through and visit Twitter. So that's kind of cool. So I've been using Mastodon a little bit more over the last week or so. And I've been looking for a TUI application that I can use Mastodon with so that I don't have to keep going to the browser and actually using Mastodon. And Tut is that option. Tut is not the greatest from what I've heard, but it works for me. It's very simple. There's, you can do pretty much everything you want to do in terms of using Mastodon inside this application. You can reply to messages. You can DM. You can view threads. You can boost. You can favorite. You can share. You can do all this stuff. And it's good. Now, my biggest qualm with it is that the layout is kind of wonky. As you'll see, as you've seen the B roll along one side, you have the timeline and you have the notifications. And you can change those panels to whatever you're viewing, whether it's the federated timeline, whether it's a different, your DM timeline, whatever. That's where those two things reside. And then in the right hand panel, you have the message that you're highlighted over. And I mean, it's a simple UI, but it's not the greatest. The thing about it is that finding help is kind of hard if you don't have the website in front of you. So as far as I can tell, there's no way of getting help inside the application. If there is a way to do that, like I said, I didn't find it. Maybe there is. And I just, you know, missed it. I everything seems to be done through them like command line stuff. So if you do colon and then like TL space home, it'll take you to your home timeline. What I thought you would do is it, you know, colon help and it would bring up help, but it doesn't actually do that. So maybe there's a key binding for it. And I just don't know. But the application itself is really good. It's fairly fast. It's easy to log into. You don't have to log into it each time. So it remembers your credentials and it just works. Now, I wish it would, it does seem to auto update, but from what I can tell, there's no way to control how often it updates. There's, it's possible there's a configuration file. I didn't actually look. So maybe there is and I just missed it. So that is tut. If you're interested in using mastodon and you want to use it in the terminal, that seems like a good enough option. I'm going to look for other clients and see if that, how they compare. And I'll let you know in a future video. So that is it for this month's top apps of the month. If you have an application that you'd like to share and see on a future list, you can leave those in the comment section below. Just remember not to include a link because Google will go through and delete those things because they don't like links. So just give me the name and the developer, just the name. And I'll try to find it and add it to the list. I really do appreciate all the help everyone gives me with these application lists. Because if I use one of your applications, I don't have to then find an application to fill out the top five. So I really do appreciate any of the comments that you leave below. If you have interest in any of the apps that I shared today, also leave a comment. I love our discussions. You can follow me on Twitter at Linuxcast. You can support me on Patreon at Patreon.com. SlashLinuxcast. Before I go, I'd like to take a moment to thank my current patrons. Devon Chris, East Coast Web. Gentoo is fun too. Patrick O, Primus, Marcus, Megalyn Jackson. I'm cool Steve A, Sid A, Mitchell, Aaron Matthias. Merrick Kamp, Joshua Lee, J-Dog, and VSTsRock. Thanks everybody for watching. I'll see you next time.


Welcome to All Hands Update. I'm Pat after James Stilpeck with your headlines from around the fleet. The Navy recently committed to fully investigating the safety of its uniforms. Two uniform working groups were established January 14th. The purpose is to ensure the safety of sailors and to maintain operational readiness. The groups will decide if an update to our uniforms is necessary and determine future requirements for working uniforms at sea. Three guided missile destroyers in the Nimitz Strike Group, Surface Action Group, or SAG, departed for a Western Pacific deployment January 14th. Commander destroyer Squadron 23, USS Higgins, USS Stockdale, and USS William P. Lawrence will join USS Shoup already underway. The SAG will deploy with approximately 1200 sailors and will establish conditions for regional stability. You can rebore about these stories from Navy.mil. From All Hands Update, thanks for watching.


How's it going everybody? DottoDoy here with another video for you all today, and in this video I really wanted to take a few minutes of your time and talk to you about the newest fighting game soon to come out, Samurai Showdown. More specifically, I really wanted to talk to you about what Samurai Showdown is, what you can expect if it's going to be your first time jumping into a game like this, and just in general a few of the qualities that make it really exciting in my mind to play a game like this, but admittedly those same qualities could very well be reasons to stay far away from it if you're just not into that type of fighting game. A few of those qualities in my mind have to be the overall speed of the game, the relatively lower barrier of technical skill needed to succeed in this game at a high level, and of course the third and most important quality of my mind is the intensity of this game during the neutral, mostly as a result of all the big damage being swung around. I mean seriously, just just look at this hammer move. That is disgusting, but I love it though. Now I kind of want to go back to each of those points individually and expand upon what I mean when I say things like, the game is overall a pretty slow paced one. So in Samurai Showdown, a 2D fighter, you mostly retain all of the same movement options you can expect in a game like Street Fighter. It definitely isn't an anime fighter where you'll be dashing in the air, or in Dragon Ball Fighter's case super dashing across the screen. This one is much more grounded based, you're going to be using that slow walk speed, a lot more going back and forth, trying to space out those very important normals. Facing in this game, I cannot stress this enough, is going to be very important, you're going to want to really know those walk speeds, and how much you have to walk forward to get a certain move to land, while also being outside of your opponent's striking distance. In contrast to this though, the dash speeds in Samurai Showdown are actually pretty fast. So sometimes when your opponent's anxiety is at its highest, you're going to want to just dash in there and go for a throw or something like that. But even with those faster dash speeds, you'll find most of the time you're going to want to rely on the walk speeds, which are just a lot slower. And as you would expect, if you're going to be on the ground a lot more, the projectile game becomes a lot more important. So you can expect to have to jump over fireballs, things of that nature, participate in that fireball game.  Another reason why I say the game is overall slower paced than other fighting games is because combos in this game are relatively short. I'm talking like two to four hates is going to be like some of the bigger combos you can get with some characters.  If you are looking for something like that in this game, you can still enjoy it. Yoshi Torah comes to mind when I think of flashy combos and an overall faster paced game. So definitely look into that if you want to play a game like this, but you also want to impress your friends. Yeah, for most characters, you're just going to be looking for some slashes and some block strings and maybe a couple hits into a DP or something along that line. Again, I know I'm comparing it to Dragon Ball Fighters a lot, but it's the game I play the most. It's not like any character you pick up, their B and B is going to be 30 hits. And the point about the combos being shorter also has to do with my second overall point of the game requiring less technical skill than some other modern fighters. Overall, I see this as probably the point that most people will be able to agree on. Samurai Showdown is definitely not a Tekken 7 per se, where, you know, mastering a character can take many months, if not even years, if you want to be the top of the top. But it's not like the game is achieving this by dumbing down certain aspects of the game or getting more casual, as some people say. It really is just a byproduct of the combos you have to learn being shorter and not requiring too many special inputs or anything like this. Because of that, you can totally play Samurai Showdown on just about any peripheral you want while not really giving up any competitive edge. Just wanted to add a quick side note here that when I talk about requiring less technical skill, that doesn't mean skill overall. If you play against somebody that's been playing Samurai Showdown for a while, you will definitely feel that it will still be a struggle for you to get that win. Just thought I should add that on here in case people thought I was saying that the game was easy or something. Totally not the case. Moving on to my third and final point about what you can expect from Samurai Showdown, I believe I mentioned how high intensity the neutral is in this game and how that's mostly because of the damage. I 100% stand behind this fact. This is what makes me really enjoy Samurai Showdown. It's a feeling unlike a lot of other fighting games.  And that's really why I think the damage is there. I mean yeah, it does look flashy saying you can finish people off in like one hit or something or an unscaled super does 70% or even something like that hammer clip I showed earlier that just doesn't insane amount of damage. Really I think those big numbers are there as more of a scare tactic to keep you playing a slower paced game. You know one mistake could take 20% of your life bar and then you really only have three mistakes left until you're dead. Unlike my last point how I talked about everybody could probably agree on that one. This is what I think is going to separate people that really love the game from people that just aren't going to enjoy it too much. As a plus side though when you make a mistake in this game you're not necessarily being punished with a very long combo that you have to sit and watch. You're instead being punished by immediately being stripped of that life bar. So whichever one you prefer you should definitely know that before heading into this game. That was pretty much it for the overall basis of what you can expect on a ground level going into the game. Now I kind of want to talk about some mechanics the game has and how they affect gameplay. You know basically just the ones you're going to see a lot. So in this game you have three different types of supers. You have the weapon flipping technique. This is probably going to be the one you see the most often as it is a normal super that you can cancel into and it disarms your opponent which means their weapon of choice goes flying off to the side and then they have to fight with only their bare fists as long as you don't let them go pick that weapon back up. Super powerful allows you to control that space like we talked about in this game. That's going to be super important. Meanwhile your opponent is already fighting at an inherent disadvantage because they lose out on range damage etc basically everything that would come with their weapon. The other super is the one that you're going to see in a lot of online videos especially here when I start doing right videos because these are the ones that if you hit them unscaled you can expect to do 70% damage crazy stuff like this. They all have relatively cool animations. It's different for every character so you're going to want to get in training mode and experiment with that and see which one you like the best. The last sort of super move if you can call it that comes after your rage explosion which allows you to use your rage gauge once it's gone by the way that's it it's gone for the entire match. So if you want to use this optimally make sure you're using it where you need to use it like the last round of a match for example because what this move allows you to do is one while you're in rage all of your normals hit a lot harder and if you want to go ahead and spend that resource right away you can instantly slice through your opponent really quick. I'm talking like if you see your opponent click anything you could probably punish them with this and if you hit it unscaled it does a ton of damage. If you do it off of a grab of course that would make it guaranteed so that's scaled down pretty heavily but anywhere else this is going to be your go-to option when in rage and trying to snipe that last bit of health off your opponent. Apart from that the other mechanics I wanted to talk about were the defensive options in this game give your standard blocking which is going to be even more useful in this game because when your opponent does go for those riskier moves their character will yield back when they hit a blocking opponent leading to some very easy punishes. You also have your deflects which serves as the game's perfect guard system. If you hold back just as an attack connects you'll get this little spark and it'll be easier for you to get those punishes off. So already you should kind of be getting the picture here of how these systems influence the gameplay. It's very read heavy, very slow like I've said all video long but also very rewarding for mixups. That's another thing I should mention here just because the game is slower paced and more spacing oriented doesn't mean there aren't different kind of characters like zoners, rush down, balance all of these things, mixup characters all of these things exist within this game. Hanzo a character I've been looking forward to playing a lot specializes in throwing out one projectile and then immediately going into set play which basically means his mixup options you want to set up that vortex as soon as possible. He is a teleport that can hit overhead, a teleport that just keeps him in place and a teleport that does a low and you can also cross up on whichever side he chooses to. So yeah if you're into mixups if you're into reading your opponent this is also the game for you but that is pretty much all I have to say about Samurai Showdown in this video. Of course if you want to see more videos on it there should be some more ranked videos on this channel eventually. The game comes out very soon June 25th I believe so ranked videos will start coming in on this channel right then. I might even be streaming it over on my twitch page. Yeah I don't really know you can expect to see a lot more Samurai Showdown for me. If there's anything specific you want to learn about Samurai Showdown just let me know down below in the comments and I will try to make a tutorial like video for you on that as soon as possible. And of course if you just want to watch more Samurai footage gameplay right now the places where I got this footage from will be seen down below on the pinned comment so make sure to go check down there if you want to watch even more gameplay to really decide if this is something you want to buy into or not.


Why is Forty the favorite for the Kentucky Derby as Elise Meyers? I would say that's a great question I would love to tell you. That's him at two winning the Breeders Cup juvenile This is the best race for two-year-olds. Remember you have to be three to run in the Kentucky Derby But at two that's his owner accepting the trophy for champion two-year-old He was the best two-year-old of last year, but you know how it goes You're an athlete you might develop faster than others other people catch up you get to that next year You're in high school You're in college and are you just as good as strong as fast as the rest of the class now that they've all grown and kind of Caught up to you physically. He's just as good. He keeps winning He's undefeated this year. This is why Forty is the favorite for the Kentucky Derby. He can't be beaten He's beaten all the horses last year.


What's the worry y'all welcome back to the recap man. It's so crazy how this NBA season is going I feel like it is the most unpredictable season of all time. There's a lot of parody There is no heavy favorite like we've seen in the past couple years And because of that the narrative around teams can switch just like that It feels like just a couple days ago We were talking about how to use the rockets at the second best defense in the league after the james harden trade And now they got double digit losses in the row. It was just yesterday We were talking about the Miami heat struggling and now they are back on their grind So, you know, I do these recaps and and part of it is over reactions to an extent But we all know that the the landscape of the NBA can change very and I mean very very quickly I want to start off by talking about the Miami heat because they are back ladies and gentlemen Be sure to leave a like subscribe if you are new Let's talk about heat basketball because this one was a very important game for them They're going against the Utah Jazz Who's the best team in the league right now record record wise and one of the hottest teams in the league It seems like nobody can stop them. They are a legendary three-point shooting team All of those things and the Miami heat outplayed them. This was probably the best Miami heat game I've personally watched this season. I don't know. I can't really say it is the best game of the season for them But for me as a viewer, this was definitely um their best game They got production from pretty much everybody and and when they were struggling I think a lot of us kind of forgot at least If you aren't in heat nation, you may have forgot that Gordon dragic existed Right because Gordon dragic missed a lot of time and he was basically on his second game back And and when they went on that run in the bubble People were really questioning the reliability of what Gordon dragic had did and you know I had come on here like y'all will forget that Gordon dragic was just an all star two years ago So yeah, eventually you'll probably see him decline because he is an older point guard But he still got a lot left in the tank and today he showcased a lot a lot of great things And they really took advantage of the defense that the Utah Jazz were running Now, I don't really know if this is something the Utah Jazz normally do And I just overlooked it because they've been so dominant on the offensive side of the ball I have really paid attention to to how how their defensive strategy is But they were like dropping very far back on like the pick and rolls They were dropping very far back and leaving a lot of shooters and well the Miami heat Half shooters, you know I'm saying Duncan robinson slowly shooting out of his slump, which is great to see Gordon dragic productivity It will dial us in in threes, but the big thing of course is jimmy butler You know if jimmy butler had played more games He is he is a guaranteed lock in the all star game all star started when he's putting up performances like this Where he can dominate a game without hitting a jump shot The amount of bios defense is very good. Um tonight and the crazy thing is it's not like The Utah Jazz played bad like the Utah Jazz had a very good game as well The Miami heat just played better now he fans This is where things are looking up for y'all because let me look at the standings really really quick Right now they're sitting at the five seed at 16 and 17 And the bulls were just a six seed and now we're down to the 10 seed because we lost today That's that's how the standings are working today and that i'm telling you this season is just so so very weird Um, but they are sitting at the five seed on their five game win streak Let me read y'all their schedule coming up. You have the Atlanta hawks twice So you can argue is the most disappointed team in the league, especially after another loss today You have the pelicans the magic the bulls the magic the cavaliers the grizzlies Then the pacers and the things get a little bit more difficult But the next five or six games and nothing is a cakewalk in the NBA But the next five or six games can be locks of wins for y'all So you could potentially go on a double digit game win streak But again, you got it you got to go through the bulls and right now if you erase Tonight's game off the agenda the bulls have been rolling Um, but you have a lot of games coming up that are very very winnable So that that slow start is really turning around for you guys and It's exciting to watch definitely exciting to watch the next game. I did get to tune into was kings versus the pistons now I've been wanting to talk about this for the last couple. I guess weak or so But the kings were playing so bad It was hard for me to justify talking about them to a to a grain length And you know, I'm still not going to talk about them to a grain length But one of my favorite things about this season when it comes to player progression Is diaren fox's three-point shooting ability now tonight He was ice cold from the three-point range But overall in the season he has slowly turned himself into a respectable jump shooter And I'd even just like on a catch and shoot I got three seconds to get the shot up in the floor the office This man is hitting step backs and things like that which is which is great Which is great for the development of diaren fox today's game was very weird And I don't really know why I stuck around to watch this completely Maybe it was because diaren fox But they got like no productivity from their bench and they ended up getting the win And the last minute or two of this game felt like an eternity You know reviews things like that buddy heel with the template and dunk. Was it over the backfowl? Was it not Dennis Smith jr. Had a very good game, you know in his very young detrack pissing career But I just wanted to highlight Dear fox's three-point shooting ability had had it has got better. Let's talk about the bulls Last time I was telling y'all that the bulls have given me hope And it was the worst kind of thing to get hope from the Chicago Bulls And through the first three quarters, I was like, oh my god The bulls might actually be a good team Now I'm not stirring too far away from that But we we we got blown out in that fourth quarter the fourth quarter was crazy And it was it was cool to see because the suns are one of my favorite teams to watch for obvious reasons when you consider me being a Bit chris paul fan But when you see him doing the things that he do against your favorite team, it hurts It actually hurts And this is a this is the same chris paul that led a team on a comeback against us last year Y'all remember that bulls fans chris paul shakey else alexander and them came back on the bulls 20-point game and they came back and it's he did it again. He just hates us. He just hates us. Anyway Um, very good game for them that fourth quarter was dominated by chris paul being the point god really really taken advantage of The thing that he does best and that is just like Being able to control the game and then lastly Deondre Aiden at fourth quarter would look like an all-star He looked like the best player on the court for a lot of this fourth court And that's that's one of the biggest things about the chicago bulls because window carter is a very very good defender Do not get me wrong But when it comes to like one-on-one positional defense against another good big that is where he struggled as a team defender We cannot get much better than window carter The numbers will back me up on this window carter makes our defense very very good in comparison to when he's off the floor But it's when he's going against these big men that actually have a really good offensive game Or overall he may struggle because I think a lot of it has to do with his size I mean, he's he's matching up against a seven foot dude as like six nine, you know I'm saying So deondre Aiden took advantage of that Um, and it was cool. Um, devon booker came out guns blazing hot and then he slowed down In the bulls blew a game Yeah, yeah, yeah, the thing that the bulls are missing most is A chris paul light because it's only one chris paul But a god that can really control the pace and be able to settle things down When you when you need it and we don't have that on this roster in due time though I'm not saying this season particularly But I'm sure the people at the top offices are realizing the things that we need because I think every bulls fan Really realizes this that like as a we need a player that could just be like, we good as that Don't worry. Let's let's chew a little bit of clot. You know, do those type of things Um, the next game that we got to tune into was the thunder game I'm not saying it was the hawks game because the hawks disappointed me once again But the thunder game because I I somebody said on twitter You should tune in to uh to to teo maladon I want to call him teo, but I think it's teo maladon And I was like, all right, bet I'll tune in and tail was going off. I like like This is this team is so weirdly constructed It doesn't make sense for them to be as as solid as they are Who would have thought that this okc team would have the same record as the alana hawks That tells you Expectations are really weird because this is an amazing season for the for the uh for okc But also a huge disappointment for alana, but like teo maladon Very very good. I didn't know much about him coming into this season And I think in the very early of his career, maybe the first month or so He he definitely struggled george hill goes out with an injury Teo maladon comes to the start of lineup and he has been dramatic and I was listening to the broadcast This was ty Jerome's very first game a part of the team He looked great and it's so crazy that this man Lou get little door. I almost tried to pronounce his full name, but I can't do it door Be putting players in alcatraz And I feel like he's never really in foul trouble treyong was locked treyong didn't attempt a free throw did he attempt a single free throw On alcatraz on absolute alcatraz. So I really want to talk about the alana hawks is getting a disappointing me next game We should talk about oh I was really trying to contemplate if I wanted to start the episode with this player in this team specifically But let's get into a talking about draemon green Oh, yeah, if you remember draemon green cost this team a game the last time they went against this charlo hornis Same terrible year called game after draemon gets ejected after a loose ball. Yadda yadda yadda draemon ticket personal Literally ticket personal this man Is electric in the the most non traditional sense because he's not very athletic He is not speed. He is not electric by the normal definition But as an mba nerd watching the things that draemon green can do on the floor is mind boggling A lot of a lot of his assists and it did happen this see this game as well But early in the season a lot of the way they were running their offense It's like hey, here's a dribble handoff between me and steve cur. We're gonna do this 100 times a game The offense is way more free flowing than that. I think that kelly ubre had like seven dunks in the first quarter I'm not even exaggerating. He had like seven dunks in the first quarter draemon greens play making and his defense's ability is amazing And I feel like draemon's career is going to be like when it's all said and done People are gonna look back on it and be like man He wouldn't be the same if he wasn't playing with steve If he wasn't playing with clay his entire career and that might be true But it's taken away from all of the talent that really is draemon green There are not many people that can play that draemon green role Yes, it is elevated when you're playing with steve curry and clay Thompson for sure But the things that draemon green does as far as his playmaking his defense his intensity his coaching Can go across all of the other 29 teams. It's so happening. He's playing with steve curry So it looks a little bit better, you know, I'm saying, but this is another one of those games Very very ugly took a long time to get it done that fourth quarter was disgusting If you erased the fourth quarter, I'll probably come into this episode talking about draemon green And the warriors to start the show, but the fourth quarter was so very ugly Malik muck continues to get those minutes and opportunity and taking advantage of it, which is great for them Um, the miller ball another good game And I felt like miles bridges was trying to do another trace migrating impersonation late in this game after a miss free throw But it didn't really work out man This warrior team is it's so Crazy to to look at where they are now and compare it to the first two to three weeks of the season And that's why I try to talk about overreactions because I am somewhat guilty of it as well I knew that them being as bad as they were wasn't going to sustain himself But I didn't think they were going to turn into this good this fast Like right now they are they are good and they have a couple blown games like the draemon green when a couple more like that But they are good like the other night they had a game where steve curry shot like one for 10 from three And they were cool They won a game kelly uber I turn from the worst player in the league through the first two weeks of the season to being very very good again Very very good again Wiggins We always talk about wiggins as far as his defense and his progression of his defense. I don't know How true that was but it's still good. It's still good and that's what you can ask for and now that they got their centers back It's more synergy I love watching this team play and and something happens. James wiseman turns the ball over misses a rotation and draemon green gets into his ear That's what I would want if I was a player a young player And draemon bro, if you if you somehow come across these videos I'm gonna always leave the invitation out to talk about hoops on called game bro You'd be the perfect guest because when it comes to comes to called game and the visual idea I have behind this a lot of it is trying to learn from the best of the best Because even as a basketball fan, I can only see it through my eyes my own lens as a fan I will never understand some of the stuff draemon green knows and I want I want to try to understand those things And I'm sure people at home watching would love to understand those things Um, another game that I'm watching it was actually the first game of the day So I probably should have started with it Um, was he paces versus the Celtics the Celtics did a win after cardiac kimba looks like him again And for the most part the last five six seven eight games He's been really solid he had the one stinker on national tv a few days ago And that's when everybody was talking but for the most part these last couple games have been been solid The only problem with the Celtics as of right now, they can't get their three stars To all perform very well together daniel tice clutch daggers Um, robert williams timelord putting in quality quality minutes. They got a jeff teague performance two Um, but it was still close because jason tatum shot like one for nine or something like that And then when it comes to the paces bro They're they're late game offense is so bad And and you want to give it a slight pass because they traded victor lo depo and got back a guy that can't play right now I'm so happy to keres lavert Got traded because if he didn't I don't know what happens, you know I'm saying him getting straight to save his life But he's not on the court tj warren. It's not on the court and these are guys that will be offensive creators Malcolm bryden as good as he is I don't know if I see him really as a point guard. I think he's more of an off guard and I think that's where he's Strived the most um for me personally as a fan watching from an outside of looking at he strives the most as an off ball because There there are times where like he he is so good at to getting at his spots and getting to the paint Where you would want him to be maybe a slightly better playmaker to kick out to the corners We have dug mcdermot You have just a holly who had another um clutch couple shots in this game that of course didn't end up in the victory You want him to be a little bit more of a playmaker But at the end of the day, then maybe just not who he is right? He's been putting the roll right now due to injury and things like that where he has to do this type of things Either way them at 15 or 16 is a bit weird. So most some bonus though get that all start not Get that all start not and I think jason tatum has moved up to the starting lineup in the all star game The other games I didn't really get to um kawaii had a big one It looks like and then the lakers game I could not get myself to watch them because I was so focused on warriors versus hornets But didn't shoot it came back. You're right. If you enjoyed the video leave it a like um, I see y'all soon Hey hit up your favorite NBA player. Let him know I'm looking to talk to him for called game virtually, of course We have all the setup. We just tried to book more talent We got a few people that I think are gonna be super fun We already spoiled one with Duncan robison when I was on his podcast He'll be on an episode Um, some of my NBA friends like tyrese haliburn said he'll come back Because he was on the first official one or unofficial one But there are so many players that I would love to talk to Um, let him know I'm looking for my appreciate y'all. Love you call game


ੰ ੰ ੰ ੰ ੰ ੰ ੰ ੰ ੰ ੭ੱ ੠ੱ ੭ੱ ੰੱ ੲੱ ਖ਼ੱੱ ੓ ੲ੨ੱ ੰੱੱ,因为 I couldn't answer well for seven days before I became pregnant.


I want to thank everybody for coming to join to join in on our intention for the planet and for all of humanity. The intention of this harmonic emergence gathering is to have a heart expansion meditation where we can connect with our multidimensional selves and bring in those higher vibrational energies to earth. Grounding them into the planet and then expanding them out to the universe with a clarion call saying we are ready. What we're going to create today can encourage us to put aside our differences and spark a new momentum towards all humans finally getting along with each other and creating a thriving new heart based world. If you have any shoes on I encourage you right now to take them off and let your feet join on the sand for your legs whichever one you prefer but at least you're sitting in a chair put your feet in the sand. This 99% quartz 99.9% quartz crystal sand is what we're here for today in the vortex that exists outside in the water. Well it is now. So what Bill said is when we came here we created the vortex and when he walked to the water powered up and now we're sitting in a vortex. Actually what I've already said in the meditation here has already happened. So we're just reliving it. Bill what did you want to say? We didn't create a vortex. A vortex is naturally occurring. A portal is an artificially created vortex. A vortex is naturally existing right here. What I did what I got here has helped to release the resistance to it which allows it to power up and then it affects everybody. It allows the flow. It's like an electrical circuit kind of like a like just how electricity flows. When you put in resistors it does not allow the flow to work as well. And everybody who comes down here holding negative astral in their fields of vortex exchanges that negative astral that they picked up from their experiences. Their thoughts or emotions or whatever crap that they had and it'll pick that up as it's sending the light to them that the vortex naturally does. And then those of us that are earth keepers we go and we allow that resistance through our work to go and it allows the energetic flow of the vortex to flow more properly. And then what I always do is I leave the center point where I was doing my work and then come back to it and find it more powered up. And that's exactly what happened when we walked away and then came back. If I picked a good spot then. Right here. Right here. Good choice. So let's meditate on that for just a second and just take a nice deep breath. And inhale and exhale. I'm going to let Greg start off here. I'd like to set out the intention that all of our higher selves are connected right now. And I ask that creator, source, universe, spirit guides, guardian angels, friends and family on both sides of the veil. Galactic neighbors and friends, all of our higher selves and Mother Earth help magnify the intentions that we put out here this evening. Now visualize that you're in an egg of pure white energy around you. See the sparkles of gold and silver. While this energy completely surrounds you, it is also low and permeable to that which you invite to join you today or as you merge with each other. So what we're going to do is we're going to take a deep breath. Breathe in. Breathe out. Breathe in. Breathe out. Good. Now I want you to take your awareness to the part of your body that is touching the sand. Maybe your feet, maybe your legs. Take your awareness and connect to the quartz crystals in the sand. Just imagine that you're narrowing your focus down to the sand itself. Feel the magnificence of that sand. Take your consciousness and actually go into the sand itself. Imagine that you're just below the surface of the ground inside the layers of the sand. Connect and expand. Connect with the sand and expand. Now take your consciousness from the sand to the core of the earth and meet Mother Earth. Connect with Mother Earth and allow her love to connect with you. Feel what it's like to be in the love of Mother Earth. Now that we have the love of Mother Earth, travel back up through the sand to your heart center. Get your consciousness physically in your heart center. Be in your heart space for you that could be the chambers of your physical heart. For you that could be the space right below your throat in your high heart. Whatever is your spot exists in that space. Take a breath. Now you have the love of Mother Earth in your heart.  Now expand your heart energy out to connect with those here in the meditation. So as you inhale and then you exhale, imagine love sparks. Beautiful flowy energy coming out of your heart and connecting with everyone else's hearts in this circle. While in this vortex, imagine all of our energy creating a huge love bubble right here in this circle. So your consciousness is in this love bubble. What does it look like? What does it feel like? With your third eye, you can look around at everyone that's in the love bubble. And you smile and say thank you. Do you see the sparkles? Do you see the creation that we have made here? Now expand your heart center even more. And expand the love bubble even more to include everyone and everything on the beach. So we're expanding out, expanding out, expanding out. Together we're expanding our consciousness, expanding our love and expanding our energy to encompass everything on the beach. Now let's radiate unconditional love and passion and upliftment into the planet's whole energetic field as we continue to expand. Imagine a grid and imagine the light that our love bubble plays, infusing the grid and spreading it all across the planet. So the grid is connected and it's spreading, the light is spreading all around the planet, expanding, expanding. This is the human consciousness field and we are expanding with our love and light. Now we're so powerful that we can imagine now that that grid is so full of light, lightning fast, faster than the speed of light, that the whole earth now shines like a star. All of the earth is expanding with our love and our light. Take a few minutes to expand this love bubble as far as you can imagine. To the galaxy, to the universe and beyond. Together we're expanding our love as far as we can imagine, expanding and it makes us happy. Now we want to take an expansion and we want to come back. Now slowly when you are ready, drawing the love bubble that you made, you joined in with everyone else and you want to bring it back here into your body on the crystal sand. Now we're connected with Mother Earth, we're connected with the universe. Take a deep breath in, giving gratitude to the sand for helping you to expand your life. Gratitude to Mother Earth, gratitude for the vehicle, the body that you are in right now, takes care of this time on the planet. Are you sick from these beautiful love energies?  It exists right in your heart, everything is in your heart and just intend to connect to them. This would be what we call past lives that are happening at the same time on different levels of vibration. Allow all of your multi-dimensional selves to bask in the love and the light that we have created together here in this vortex so that they may be healed, that they may join you, that they may bring their wisdom, all of their experiences into this lifetime so that you can call on information as you certainly, as a light worker. Also, with your oversoul, this is the bigger part of you that is outside of this experience and it has the wisdom of all of these lives that you have, all of your multi-dimensional selves all tied back to this oversoul. So you're connecting on a higher and higher and higher level and you're saying, thank you, I love you, you can bear, ultimately everything is connected to source and this is all within you. Right here, right now on this quartz crystal stage. Now the love, the now of this love and light will release the concepts of the past. This will remove any aspects of what we think is the future because there is only now, there is only one and we are it. There is no separation, there is no time, all of that is an illusion.  You are unconditional love. Sit with that for just a moment and realize who you are in your heart space and where you've just been. And realize that it's all happening now in this vortex and we have expanded out into the universe which is within us. And when you're ready, open your eyes slowly, look around you and see the beauty of Mother Earth in the eyes of everyone in this group. Everyone around us, we are back in this reality and we have affected everyone here, not only on the sand but on the earth as well, very powerful. And what we have just done is to send a clarion call to all the multidimensional selves of ours to our over souls to our galactic friends and family and to source showing that we're bodying our true selves right here, right now. We are responsible co-creators. We are love and we are light and we are ready to create a new earth and rightfully claim all superhuman abilities. And so it is. I just want to say something, I don't know about anyone else but my crown chakra is just buzzing like crazy. It's just lit up, the top of my head is just buzzing. I don't know if anyone else is feeling that. What I would like to invite you to do is if you'd like to share your experience, if you did have any experiences, come on up and share. Tell us. But then it's down the road. That's great, that's great. Bill, would you like to add anything? No, you're pretty happy there, buddy. I'm happy with my field. That's how we transition as we go through what we're going through. As we're first recognizing the chakras, you'll feel it in your crown as you do something like that and later you feel it in your field going out and it's just like what I'm going to explain. It's like macro and a pearl. That's the same thing with war taxes. When we walked away and we came back, it was slightly more powerful. You get in closer to the circle, it's more powerful and it affects a different chakra. You get in closer to the circle, it's even more powerful and it affects even a different chakra and that's how I perceive it. There was supposed to be somebody coming to do the meditation and this morning I realized she wasn't coming and I thought, oh my goodness, after everything now, I've got to focus on the meditation but it really was very simple. It actually came to me and it's just a part of everybody can make up their own meditation to do something very similar. It's just my way of expanding my heart chakra to be earth, to be the galaxy itself, to be the universe itself and just expansion and that's what's going to keep you open and that's what's going to keep you connected and allow your body. I had no problem expanding my field, going out but when I came back and said bring it all back to your heart, I didn't feel like I deserved it.  It wasn't fitting. It's hard as hell to come back into a body, isn't it? This is a vortex here. Whether the star gate is out there, we create artificial portals. This is a natural vortex here. The way the vortexes work is you've got some type of conduit that can be salt, it can be water, it can be sand, it can be crystal, it can be silicone, it can be whatever that's coming up that literally goes all the way down topping off the magnetic magma chambers of Mother Earth and as the iron is spinning on the inside, it generates a field that goes up the conduit to the positive ether, from negative ground to positive ether. This is a natural vortex here. What I did when I came here is to release the resistance that had been placed in here.  Y'all can come here and do the work, help keep it powered. It affects every single person that comes past this point and it'll affect you too. It can help to raise your vibrations when you understand how to work with the earth, how to work with power centers and vortexes. You can do the work and allow it to help to heal and raise your frequencies too. So that's part of it. So know that this is a power point right here. And use it. Come back here. Come back here and use it. Know what you're doing when you're walking up. Be aware of what it's doing. And before you go into the expansion, be aware of how it's hitting your chakras and work to clear out those chakras in your body and you can put the stuff into the vortex and then turn around and clean it up too. So it works really well. It is the infinity sign. It is the one but yet the two. Okay? One thing I wanted to focus on is to share how I connect with my multi-dimensional selves all the way up to, you know, angelic realm to source and, you know, all the way up because we have a lot of lives that may have been killed for telling the truth, you know, burned at stake as a witch or whatever. If we haven't cleared that energy out of our field, then we're not able to run our energy like we just did. We went down to Earth. We brought it up through our heart and then we went from our heart, you know, up here through the vortex. We used the vortex as a tool in this case to, you know, to go all the way up. And so you can do this at home. You can do this on the beach for other people. You can keep doing this kind of work. It's very simple and you can create your own meditation just like I did this morning. I just created it. And just what you were just saying about the past lives and having the issues, when we go through traumatic experiences like that, battlefields are one of the places where you can really feel it. You can walk in and go, huh, not even know there was a field there, but you can feel the energies. And what we're doing is we're helping to release those fat resistance because that's what it is. Those old emotions, the negative emotions, the past experiences, that the trauma that people are got, they just want to go, God, I don't want it anymore. And the Earth will take it. But there's those of us, once we come to search, we hope to release it from the Earth. And by our working with the Earth, it works back with us. So here to heal the Earth, the Earth knows how to raise our vibration and heal herself. We are here to help as a collective raise our vibration with the Earth. So the Earth, any time you want to get rid of some junk that's not yours, just connect with the planet. Hug a tree under the beach. Use the water, you know. Put your intentions to do it and she will take it from you. And if you don't have a natural who it's actually to work with, create a portal. To create a portal is just to do a ceremony just like we just did saying, I intend to put an energy point right here. That's it. Thanks for bringing that, Andrew. Yes, that's exactly it. Anybody have anything they'd like to share? Right. Yes. You cover my score in the Earth, you make the analogy that it's like a negative neutral. When you take all this dust, put it down in the core, just then go neutral, and all this is canceled. Really what I mean by the core of the Earth is not a physical place, but the consciousness where Mother Earth has her being. Just like we have ours in the core of us in our hearts, a Mother Earth's heart. It's not really a physical place and you can send it. Energetically, you've got to understand it like a circuit. And just like putting a ground into here, you're grounding right there. It is an energetic circuit. It is electronics. No doubt about it. Your bodies are too. Thank you. You know, you tend to forget all the little steps involved, so I knew that I had to go to the core of the Earth, but didn't think of it as the word grounding and that's exactly what we did. Observations here. Look around. How many people are there? 22. 11-11. Totally unplanned. Yeah. I got goosebumps. My crown's going crazy. Another thing too, when I asked for my higher self to hook up with everyone else's higher self, and then we connect our Creator Source Universe, our spirit guides, guardian angels, friends of family on both sides of the veil. Even though there's only 22 people here, there are literally millions upon millions of galactic friends, neighbor spirit guides, guardian angels right down the line. This is huge. You guys have no idea how big this is right now, so thank you all for being part of this.


In this video we are going to look at two concentration terms and how they are related. So let's start with our first term which is molarity which is denoted by this capital M here and it is defined as the number of moles of the solute divided by the volume of the solution in liters. This part of having the volume in liters is important because sometimes in labs we use solutions in mls that is milliliters so you cannot directly plug in the value in ml here you have to convert it into liters before you calculate the molarity and the other concentration term to consider is the strength of a solution which is defined as the mass of the solute in grams divided by the volume of the solution in liters and apart from these two you would have also heard about mole fraction or maybe molality or mass percent so then the question is why do we have so many measures of concentration is it only to complicate exams well the reason why we have so many measures of concentrations is based on the application for which they are used let me take an example here we have a glass of water and for this water to be drinkable that is for it to be of good quality we know that the total amount of impurities which is also called dissolved solids should be less than 300 milligrams in one liter of water so we know of this number from the different studies that have been carried out on drinking water and now let's rearrange this unit a little bit so we can write this 300 milligrams per liter as 300 times 10 to the power minus 3 grams per liter and because we know that the density of water is one that is one gram will have a volume of one cc or one ml we can write this as 300 into 10 to the power minus 3 grams divided by 1000 grams so instead of this one liter i know that the mass of one liter of water will be 1000 grams and so we can simplify this and we see the units have gone off and we get 300 into 10 to the power minus 6 10 to the power 6 is called a million so if you think of this 10 to the power minus 6 you can take it down to the denominator so then it becomes per million so we can write this as 300 ppm or parts per million so what i've done is if we rearrange this unit of milligrams per liter in case of water we can write this as ppm or parts per million and you can realize how small this quantity is because let's say we have one ppm of something what it means is out of one million units of that particular thing we are picking out one unit another example is of carbon monoxide in air different studies have shown that if the concentration of carbon monoxide in air exceeds 35 ppm it becomes poisonous for us so when we're dealing with these very small concentration limits like in the case of pollutants ppm is a convenient measure of concentration to use on the other hand if we consider industrial usage so let's take an example that an industrial tank will be around 50 000 liters and the amounts of solute that is added to this solution can be in the order of tons so now in both of these cases where on one hand we're dealing with very dilute concentrations which are in ppm's and on the other hand we have extremely large quantities of weight by volume measurements using only one standard measure of concentration is difficult which is why we have so many different measures of concentration which conventionally come from the applications they are used in and coming back to our experiments that we do in the lab the gram per liter measure of a strength of a solution is a sensible scale to use for the amount of quantities that we work with in labs so now let's go back to the original comparison that we were making and let's see if we can find a relationship between molarity and strength of a solution so to get the relationship between molarity and strength of the solution let's start with the definition of molarity which is given by a number of moles of the solute divided by the volume of the solution in liters and we know that the number of moles of a substance is defined as its mass divided by its molar mass so we can plug this in here instead of the number of moles and we get the molarity to be equal to mass divided by the molar mass of solute into the volume of the solution but if we look at this expression we know that this quantity that is mass divided by volume of solution is what we defined as the strength of a solution so in that case we can write the molarity to be equal to the strength of the solution in gram per liter divided by the molar mass of the solute so now with this relation if we have the molar mass of the solute and the molarity we can calculate the strength of the solution and vice versa


What will be in this second chapter of these bridge notes that I'm going to post? It's a Fourier-Vire relation, essentially. So of course we have this description for Gaussian states. When principle we already have a bridge to the Hilbert space. I didn't really show it, but in order to get some of these results, like evaluate the covariances, you need to go to the Fock basis, which is already in the Hilbert space. But the most sophisticated, I would say, and powerful bridge between Hilbert space and by the way, you always need to go into the, even though Gaussian dynamics may be trivial, this is sometimes a point that is raised against these sort of continuous variable problems, right? Because people in the sort of a field theoretical tradition, they call this theory is quasi-free. They call them quasi-free because of the normal modic compositions that I showed, which is you can always diagonalize these Hamiltonians and solve the dynamics. That's true, but that's not the point. I mean, solving a problem in quantum information such as typically is a state entangled or not. It's not equivalent to solving some dynamics, so that objection is that it's unfounded, essentially. So these problems are still difficult, as we're going to see. And whenever you want to face those problems, you have to go into the Hilbert space. So one way to go into the Hilbert space is the Fox space that we saw, but a very powerful way is the Fourier vial, which is essentially the characteristic function. And by which I mean, essentially, that displacement operators that we saw already form a basis in the form of an orthonormal basis or a complete set with respect to the Hilbert Schmidt product. And the consequence, I'm going to state this only for a single mode, because stating it with many modes will be unwieldy and unnecessary at this stage. But what I mean is I can write any row, any state. Let's talk about a state. It could be any bounded operator, but as an integral of a C2 of the alpha. Let me just be sure I use the right, the same convention. Well, I'm not. So D minus alpha trace the alpha row. This pi normalizes this convention and where D alpha is the displacement operator, but written in terms of complex variables with ladder operators as a basis of operators. That would be this. You're familiar with this, I think, because you've seen our coherent states and all in the day before yesterday. But this is the same as what we wrote before with XMP and that omega. This product corresponds to coupling XMPs through the omega matrix. Check it out. Like, upon this identification. Yeah, this is alpha is X plus IP over square root of two. And then you get the same and A dagger and A are the ladder operators. Okay, I don't want to go into these details, but essentially what this statement say, what this statement is, is that you can expand a row in the basis of D alphas. Yeah, I know that mathematically this this this statement is lightly questionable, but you know, allow me the freedom to be a base lobby. And that's what I call Fourier vile. And this in fact is that's the characteristic function. There's a symmetrically ordered characteristic function of of the state row. Yeah So then if we Yeah, if we Fourier transform this, we take the complex Fourier transform, you get the Bigner function. And we already talked about that. I don't want to get into this. But as you know, there's a number of these quasi-probability functions, these phase space representations. And another one is the P function.  You don't know about the P function. Okay, cool. So let me let me get a bit more specific. I'm not going to show this relationship, how to prove it, because that will be a bit lengthy. But I'm going to give you one bit, which is this is based on a very interesting representation of the projection on the vacuum. This is equivalent to this, to an equation that we're going to need later. And which is proven in the notes. Oh, why am I, no, no, C2, no, C, not C2, C, so minus or plus is the same. Yeah, so I just mentioned that and this is proven in the notes. Yeah, so that's how you derive this. And use the fact that essentially the set of coherent states is an over-complete set. You can resolve the identity through it. Let me just mention another important equality, which is the identity operator in the Hilbert space, at the Hilbert space level is 1 over pi alpha, alpha. Let's create alpha. Whereas alpha is a coherent state, so it's the alpha upon the vacuum. Okay, so so that's a resume of quantum optics in a sense and and this is the, I think this is the most cultural of all the, it's something that all physicists should know, I think. If I had to pick one bit of quantum optics that everyone should know, it's not a Wigner function and all that, because that's just derivative and it's an elaboration, fine. But this is the most important bit and it's the one that bridges really between Hilbert space and the phase space description through this characteristic function, right? So you can prove that all the, so if we put the Gaussian definition that we have before, this is explicitly done in the notes, though it's a bit pedantic, but you get you get the following. So the big, the characteristic function of a Gaussian state, chi alpha, this is something, so it's it to the, no, no, no. Chi, let me go back now to my variables there where I remember formula. Hopefully. It should be this. You always come with an omega because of the way this canonic, this commutation relations work.  This should be up to a phase that. So that's the first moment of the state. And they act as a phase on the characteristic function. And this is the covalence matrix. So this is a characteristic function of a Gaussian states. And this will relate between our phase space description given by sigma and R and the Hilbert space operator through this. Okay, if I plug this one in there, I get the expression of another alternative expression of a Gaussian state. So this relates to standard quantum optical descriptions. What is it? Oh, yeah. And then if you take the Fourier transform of this, you get the sigma will go sigma to the minus one, obviously, like for any Gaussian function. And this phase will become a shift. That's what happens. Yeah, and then you get the vignette function, which is really, you know, for one mode is a Gaussian blob centered in R with some shape that is determined by sigma. Yeah. And then the grades imagine a Gaussian blob. Okay. And you have this phase space, which is given by X and P or alpha through that equation. Okay, so that's very, very briefly concise summary of all this and but I want to then go to the peer representation a little bit slightly more specifically. So you can define other characteristic functions and in particular you can define chi minus one alpha as same thing, the trace of the alpha row times this. Okay, so as you notice, we're making things slightly more difficult. Because this will be, so when you Fourier transform this, because we're making it narrower, we're taking the risk. Okay, this will be worse behaved than the big, so once we Fourier transform this, then it might be, it might behave worse than the vignette function, which is the Fourier transform of that. Okay, because we make it tighter as a distribution. I'll come back to this point because it has a relevance for that entanglement even for of these systems. It's okay. It's kind of an interesting side remark, but it was very instrumental too. And then the peer representation is the Fourier transform of that. So I think, how do I usually, yeah, I think I normally, this is normalized that way without the square root, but with a pi there. And then the square beta it's e to the alpha beta star minus alpha star beta of chi minus one beta. Okay, and the peer representation as a very interesting and this was, well this line was almost worth, not alone, but it was instrumental to get in a Nobel Prize for Glaube, right? So this is the renowned Glaube-Südarsson representation, which is that rho equals simply this. That's some really freakish equation that, so they're so over-complete. Coherent states are so far-reaching that you can even express any state as a mixture in a sense of diagonal of projectors on Gaussians, on coherent states. What's the catch? Some of you will know what. There's a problem, of course, in what I just said. That P alpha is usually not even a function, right? It's something nasty. Not only negative, but like could be derivative of delta functions, some distribution, but not a function. Yeah? So it can still be defined consistently that way. And let me mention how to prove this, because I want to, this is really interesting that, so if you add a D alpha there and there, yeah? We will get a D alpha there, and a D minus alpha there. D minus alpha is the same as D alpha, that guy. That unitary, so. And so this equals then projector on alpha. This will just, this will shift this operator by alpha minus alpha, so by zero, but will then give a phase. It should be familiar with this, that if I combine two shift operators, I get the operator, which is the sum of the shifts times some phase. That phase embodies the canonical commutation relations. Yeah? In this case, that phase sort of reads this way. So, so if I write down what I have on the right hand side there to square alpha, alpha, alpha, P alpha. This is an interesting proof, so I want to show it explicitly. This will be one over pi C, D squared alpha, and then I do the other integral in, I don't know, say gamma, there's a P alpha, which is this one, but the the projector on alpha, I want to write it with this integral, and it's, yeah, into the minus, and then I've got the phase, which is alpha, gamma star, minus alpha star, gamma. The phase is the effect of these two, and this is gamma. Why do I have minus gamma there? Oh, it's the same. I can choose both plus and minus there, because it's phase invariant, that statement, so. And then, and then I've got, ah, yes, this is really nice, in fact. Now, this, yeah, so, ah, yeah, so this integral will give me the counter, so I have, I end up with the characteristic function with this, because I'm counter Fourier transforming the P, and then multiplying by that. Yeah, but think about it. This is, because we got P by Fourier transforming that. Yeah. So then, that's why this works. So the integral in alpha is, ah, eaten up, and I get my chi, why is it chi, oh, maybe I should have called it minus one.   That's pretty bad. Okay, so that's why this, because I started to question myself because of this minus, and now it all works.  Yeah. Okay, so, sorry about that. So that's why this P is less regular. And whereas if I put the minus, you get the cure presentation, which is more regular, my bad. But fortunately, I went through this and then I found out about my mistakes. And just let me just be sure I learned this. Yes, chi one, now this is a gamma, and it to the minus squared. Ah, yes. And this is d minus, which is one over pi integral over c of this squared gamma. Fantastic, chi zero gamma. We counter food and transform this and get chi one times that. But chi one times c to the minus alpha squared is chi zero. And chi zero goes there. Now what's this? That's the integral of chi zero times this, the bases. Yes. By using the Fourier-Weier relation, which is the first thing I wrote, this is raw, which is exactly what we were set out, we set out to prove, okay. So this is how you prove this celebrated representation. Why am I making all this fuss about this? The reason is that, yeah, I was hoping this would be a bit more obvious to see, but like never mind. So no, actually it is. It is quite clear. Now in going from alpha to this x functions, you get a factor two because of this square root. Trust me, try it out. And then you see that essentially what this becomes, this factor there becomes e to the r t r over four, which is also equal. So this is equal really. I mean for a single mode, but it doesn't really matter. Omega t, omega one quota r. Now, so for the p function, for the p function of a Gaussian state to be well defined, well, to be well behaved. And we'll see what that means. And by well behaved, I mean not worse behaved than a delta function. It must be sigma greater equal than the identity. Why? Because see in order to get the chi one, I need to multiply this by one quote this factor. Yeah. So the quadratic part would be essentially if I want chi one, I need to simply put sigma minus one identity there as a matrix. Yeah. And in order to be able to then transform Fourier transform this properly, I want all the eigenvalues of this to be positive. And if they are zero, you get some delta functions. But if they are worse, then you can't define a proper function like that. So you can define this, but it won't be a function or a delta function. It would be like some other distribution. Okay. So at this stage, this will not tell you much, but we'll see why this is very important to us. Yeah. That's the one result I wanted to go through. And it's also useful you get some manipulation of these p functions. And after all, a collagen quantum optics. So now we can go on to discuss the entanglement of Gaussian states. And so first off, what is an entangled state? You probably know it, but you know, this has contained, let me repeat it. So, so row is separable if and only if. So a state of a composite system with Hilbert space A and Hilbert space B is separable if and only if you can write it down as a convex combination, probabilistic mixture of product states. These are all the states that can be, sorry, A, J. These are the states that can be formed from uncorrelated states through local operation and classical communication. Yeah. Because the hypothetical Alice will sample this distribution. And then when she gets a J, calls up Bob and instructs him to create the state row BJ, whilst she creates the state row AJ entirely locally. So that's how you do it. That's how you correlate two coins through this ignorance. Okay? And row is entangled. So you probably will know this, but if and only if is not, row is not separable. So then, okay, there are many tests to check entanglement. The whole extent of the study would be beyond the scope of this lecture, but I want just to mention one test, which is PPT, Positivity of the Partial Transposition, which is that if row is separable, and can the FOB be written that way, then row tilde will stand for partial transposition, which means we transpose only in one of the two Hilbert spaces. Which one is irrelevant? Why is it, why is it that each one, which one is it? Well, I'll come to that later. But that will be transposed in this. And of course, if you transpose the whole state, it's still a state. It's still positive specifically. And so therefore it'd be true that this is greater or equal than zero. So it's a positive semi-definite operator. So this is a necessity condition for separability. And it turns out to be therefore, because of the mutually exclusive definition of the two notions, nature of the notion, it's also sufficient for, its violation is sufficient for entanglement. So therefore if row tilde is not positive semi-definite, it has one negative eigenvalue, then row is entangled. Yeah? So then, and this criteria is only sufficient in general. It's only necessary for separability that is sufficient in general for entanglement is not necessary and sufficient. There are PPT entangled states which are called bound entangled, because they cannot be distilled. But that's more like quantum information theory really. So here to this extent, let me just say this is a test to check that whether this is entangled or not. And it turns out that for the most iconic type of continuous variable entanglement, which is a two-mode Gaussian state, that's what you have in the lab more often than not. Although now in optical comms they've got these like billions of entangled modes, and so the, which would escape this criterion. But basically in all the early days and most of the situation that we're still interested in now. For instance, if you want to check whether the light mode of an optimal mechanical cavity is entangled with a single mechanical mode, that's still a, that's still a two-mode Gaussian state perhaps. And you can still check it's, it's entanglement through the covariance matrix. And it turns out that this condition, which is what we're gonna see now, is not only necessary, but also, it's not only sufficient, but also necessary for Gaussian entanglement of two modes. That's no longer true for, it's still true for one versus any number of modes. It's still true if you have modes which are bi-symmetric, which means that they are symmetric if you exchange modes within the same partitions. But it's no longer true in general for, for any generic Gaussian states. So of many modes, yeah? M plus M modes. But for two modes, this is, this turned out to be necessary and sufficient. Like for two qubits or for a qubit times a Q-trip. In finite dimensions. So, and that's what we, we set out to prove. And okay, so the first thing I want to prove is, it's first a sufficient condition for separability. And it's very general. Which is, is it true only for Gaussians, this one? Yeah. Yeah, I think so. That's it. And then, Gaussian state with the, with the, with the covariance matrix which is greater than the identity is always separable. And why? Because we have it already on the white board. On the black board. Yeah? Because of this reason. Because then P, look at what, what would happen. So this would be the characteristic function. And it would be a well-defined Gaussian. Because we just need to, to, sorry, it's, it's Fourier transform that goes there. Sorry about the sort of mix up in notation here. This is complex notation. These are just real, but it's just, so that I don't write wrong formula. But because if sigma minus one is, is that way, and most you can get a delta function which, which is obviously the P function of a coherent state. Yeah? But a projector on a coherent state, see? But this will be well behaved. And this means that in the multi-mode case, you get a mixture of product states. A well-defined positive Gaussian mixture of, of tensile products of coherent states. Yeah? I didn't write the multi-mode case explicitly, but you can see that this all carries on over. And the reason why everything carries over very simply from the single-mode case is that all these vial operators are tensile products over different spaces. They don't let modes talk to each other. Okay? So it's all a direct sum. So the P representation give immediately these decomposition. So the state must be positive, must be separable. Right? So that's the first state. And besides being instrumental to what follows, this, this statement, yes, between any mode, any mode, any mode within this partition, you split this between any partition of modes, you always end up, which brings me to the underlying truth which, which runs quite deep is that you always need squeezing to have continuous variable entanglement. By squeezing, I mean an eigenvalue of this smaller than the, than one. That's a very nice and powerful statement though. It's very simple. I mean, it's got like far reaching implications, no squeezing, no entanglement ever in continuous variables for Gaussians because if you truncate the space and do things like infinite dimensions, you can get different effects that would not abide by this. But okay. So, cool. So this is the first thing. Let me, let me do everything quite in detail now because the second part is that let's now, this is for any mode, for any number of modes. Let's focus, let's now consider two mode states. As we saw in the previous lectures, we can disregard the first moments as far as entanglement is concerned quite safely because they can be adjusted by LOCC as we like. So, let's just consider two mode states and then we call sigma which is where we encode all the information about the state as sigma A, sigma B, and sigma AB. So we, sigma A is the two times two covariance matrix of mode A and this is the two times two covariance matrix of mode B and, and, and this is where the correlations are. Yeah. And the first remark is that you can always reduce it. There is always a set of local operations that leads this to the standard form through symplectic LOCC, let's call them. I mean, there's no classical communication need. It's just LOBA, which they're going to, and the standard form is also called Simon normal standard form and this, this expression here, c plus a minus. So why, how do we do this? Well, so first off, you have local operation based on the, on the normal mode decomposition for a single mode state. You can always reduce this to Williamson. That's also the normal mode form is also called Williamson form because this was, that's because in the 30s, these things were still being studied to some extent in the third, quite late, considering, you know, how fundamental this stuff is just quadratic Hamiltonians that would appear in classical mechanics. But the trick was that it's quite difficult to classify everything you can do through symplectic operations on any metrics that is not strictly positive. The strictly positive case that I discussed is the simple one. There's a very well known and notorious appendix to Arnold, the classical mechanics books were all book where all these, there's also mistake in the appendix, but all these normal forms are described and that was Williamson theorem. Williamson was interested in all the pathological cases that we don't care about at this stage. So that's called Williamson theorem in the literature often, although Williamson theory is about the difficult cases that are not just this. But anyway, through bi-virtual Williamson theorem, this sigma a and sigma b can be reduced to normal form through local symplectic and now see these local, these normal forms are invariant under rotations, under local rotations which are also symplectic. They are the phase plates that we saw before. And then through those, you can apply one on the left and the different one on the right of the off diagonal block and do it singular value decomposition that leads it to diagonal form regardless of what this is. And you can even, you have enough freedom in these orthogonals that you can choose C plus to be greater or equal than C minus. Yeah? Okay, so this is, it's always true that you can apply local operation and classical communications to achieve this normal form with all these zeros and four parameters which are relevant. And those are the four parameters that are invariant under global and local symplectics. Okay? So then another lemma, it's state with determinant of sigma a b greater or equal than zero, then rho is separable. And this is a bit technical and I don't want to get into that because what you do is you show that if the determinant of sigma a b is greater than zero, that is if C plus and C minus have the same sign, you can always define a set of operations that you can do local squeezing and global beam splitters that leads to a state with sigma greater than one. And then it must be separable. The details are irrelevant here. I mean, again, they're all spelled set out and spelled out quite, fleshed out quite in detail in the, in the notes, but I don't want to get into that. So that's an important lemma that we have. And now we're ready to go for the jugular, which is find the, establish that this condition, the, the, the PPT is necessary and sufficient for such, for, for Gaussian states that we do it this way. Well, we need some few more lines of preparation. So the first one is that there's a quantity. So, okay. So what is PPT? PPT is an expression about the positivity of the states, right? But if you remember, we had another, other ways of expressing, well, we had a Gaussian or phase space way of expressing this positivity. Yeah? Which was sigma plus i omega with the equal then zero, the Eisenberg principle. Yeah? So one ingredient that we need is this and its consequences. Yeah? And among which are the fact that all the simplistic eigenvalues, these are the same. All the simplistic eigenvalues must be greater than one. Not the orthogonal eigenvalues, eh? Those can be smaller than one and hence violate these and have some entanglement. But the simplistic eigenvalues must always be greater than one. They're one for pure states, like the vacuum. And, um, but this can be expressed also in another way, which we're going to do now. How do we see this, that this is the best way to? Yes. So it must be able to express this in terms of all the quantities that are invariant under symplatic operations, because, you know, you can apply a symplatic there, a symplatic there, and, and this will disappear. So this quantity must only depend on, on symplatically invariant quantities. And there, for an n-mode Gaussian states, there are n independent symplatically invariants, which correspond to the n-symplatic eigenvalues. Okay? Specifically for a two-mode state, there is one, it's very simple, it's just the determinant of sigma. I'm mentioning this because there are several problems where it's convenient to, to apply this, to, to use these invariants and to utilize them. So one is two-mode, eh? Only for two modes. One is the determinant, which is always an invariant, because symplatic, uh, because symplatic operations, by definition, because they have to satisfy this, right? So by Binet theorem, there must be invertible because they're a matrix group. So they cannot have determinant zero. And by Binet theorem, obviously they must have determinant either one or minus one. And it turns out they always have determinant plus one, by the way. But, so they cannot change the determinant of sigma acting by congruence. So this must be an invariant. And the other invariant is a bit more exotic. But it's just, you can determine all the invariants by taking the characteristic equation that lets you find the symplatic eigenvalues. I couldn't go into that. And, and constructing the characteristic polynomial. This will be all the invariants, the coefficients of the polynomials. But, um, but one of them is very simple to write down. And it's this one. It's this quantity. And it's kind of interesting to see how that, that turns out to be an invariant. Let me see how much time, yeah. Let me do that because I don't want to. So the reason why this is a, a symplatic invariant can be seen by looking at the standard form. So any state can be brought into standard form. So this must be through local operation, right? So this must be invariants because local symplatic operation are still symplatic operations. So, and then, so the invariants must be, the global invariants must be, uh, expressible in terms of these four quantities. And so if you look at delta, that would be, uh, you know, a squared plus b squared plus 2c plus c minus, which turns out to be if you regroup this as, if you take these two blocks, so reorganize this, this, this vectors as this squares. So shift the space and call this the x block. And the circles are the p block. That would just be trace the Hilbert Schmidt product between sigma x and sigma p. Yeah. And then you can show that you can bring any metrics from the standard form to, uh, from this standard form to the normal form by operations that do not change this. And this proves that delta is an invariant. And it must be determined by the, by the, the eigenvalues. And the reason is that the beam splitter that we saw, that we wrote before will just be rotations among this. And if you mix this beam splitter and local squeezers, you can do, you can bring this state into, into standard form, into normal form, into a state which is new one, new one, new two, new two. But I don't want to. I think, I think it's a good place. So let me just clarify what we established, a few things. So we have the PPT, the violation of PPT, our positivity of the partial transpose is a sufficient condition for entanglement in general. So for Gaussian states too. And then we have a couple of lemons, one that say, well, the most important one is to say is that e in a two-mode Gaussian state, if the determinant of sigma a b is greater or equal than zero, then rho is separable. And then we have a way to express positivity, which is this, oh, which then can be re-expressed in terms of the simplistic invariants as, as this is this equation, that sigma minus delta plus one greater or equal than zero. And then we have this final statement that the deter, because of the Eisenberg principle, I can't really, well, it's not difficult to show this, but you just need to express this delta, the fact that that sigma is the product of the simplistic eigenvalues, squared, and this is just a sum. And then this must be greater or equal than one. If you put everything together, you find this relationship. Yeah, so we have that this must always be true. We identify two invariants, and this must always be true for any covariance metrics to be physical. And then I'll come back and tell you how to describe partial transposition in phase space, and we put everything together and find a criteria and show that this is necessary and sufficient for two-mode Gaussian states, which solve that problem. And I think that's it for this lecture. We still, we have one lecture in the afternoon, right? Yeah, cool. Thanks.