Ie, rysw'r cyffredigau mae'r seyrdd wedi'i ddau drwy'r dda cofnod ddefnodd, mae'r seyrdd brosesr, Rodd trwy'r nodi am yfyrdd. Rydyn ni wedi'ch gwybod fe, gyda preffeso ar gyfan arno, ein bod chi'n ei hoffa i parff y brosesrach. Efallai, mae'r cwmhaen trafod gennym ei fofo a'r ddechrau o infringiogau maes o hyn o'r ffordd. Ac efallai, maes oherwydd yn wneud yng ngonch. Mae'r cwmhaen a'r preffeseo ar gyfan arno Felly, mae'r bwysig am ychydig yn ydym ni'n ddim yn rwy'n ddweud yr holl yn ni'n meddwl. Gwyddoedd yn amlwg yma yw ddych yn unrhywbeth, yn ddych yn ddod, yn y ddweud o gweithio. Maen nhw wedi'n ddweud o ddweud o'r ddweud o gweithio, oherwydd mae'r ddechrau, yn ôl ar y cyfnodd, o'r pethau, o'r ddweud o'r ddweud o'r ddweud, oherwydd mae'n ddweud o ddweud o gweithio. Mae'n rhaid oedd gweithio'r idea. Mae'n rweithio ffrig at de-mapwg ymateb, ychydig yn cywit i dynnu'r cysteiniadau ac yn bwg, yn ysgwmponol ydym ni i'w rai cystafellaeth o blaen o leiru'r cwrs i ddegwyddiol ar재ud a fi'r iawn i ddifenu'r mwyaf a'i dewb yn ddean i groesfodd ymdeilig a'r morgyrchu sy'n gwneud gan ylleu â cefn, mae'r de-mapwg yn bobl. Rwy'n amser, is the 10-10th of deep mapping of helping to think about what panaspoil project has evolved into. Of course, we're talking really about objects, but objects are already always in a place in the world, so it's different sides of the same coin rule. Also, given the session, the role of the digital within this, and again, I appreciate that some of what I say is probably not very sophisticated, and that's partly why I want to bring this session together with thoughts and feedback on this. So, the project really began, this is the Palace Boy Vessel, the original vessel at the time of the project. This is an Iron Age wooden trough, or a vessel that was then found in a peat bog in 2001, excavated by the Arshaftlers for Weapon Unit and Convert Dermed there. And this project came very briefly as the project to reconstruct or to recreate the Palace Boy Vessel, and that was where Mark came in as a woodworker. We kind of moved on from that to other wooden artefacts, prysod wood artefacts, notably the Balahoolish Goddess that some of you may be familiar with, which is in the National Museum of Scotland. She looks like that now, and she is definitely a she. This is the photograph of the Goddess when she was discovered in 1880. Absolutely really the only surviving evidence really in the art now. So, we went up to Balahoolish, and we worked within the community in the community hall there, saying we, again, said Mark, and did all the hard work. Mark really made the Goddess, and that's the Goddess, in situ near to where she was found. The original find is what remains of Balahoolish Goddess up there in North Balahoolish. What I found helpful in terms of thinking through this is the work that we're going to do in Springgate. I don't know if anyone is familiar with this paper, going flatter or deeper, connect and de-mapping, platontologies and democratising of knowledge. So, again, what I became very interested in is really the way that we can use and talk about the craft that's been mentioned, and kind of the role of craft, and what we've done with the project. It's just kind of grown like a fungus. And again, I don't pretend to have read a thousand plateau in depth, but I've really drawn to the idea of the riser because the project kind of grew rising like. It had all these kind of shoots that kind of came off it. So, as we went along, we had all sorts of connections and contacts that became interesting. So, we had other artists, this is an artist in court, we had a market at a workshop, a woodworking workshop, people made their own figarees. That's one of them there. We worked with students up in UCD, the Experimental Archeology Centre there. And also, children as well, we had fantastic interactions with children. And again, she's using these kind of artefacts to engage people. Sarah mentioned enchantment, and it's very much came out of this. We left the battle of Gould, she got us behind the community, and she did a tour of the new schools, and she's been buried back in the peat. So, hopefully at some point, we're going to go back and dig her up. And there's really no limit to these engagements. During the open day, we were helping the court of the museum, and someone suggested that vessel may have been crypt. We don't know what it was used for. We never know if it's really massive in the context of this. So, we had a test in inverted commas of the vessel as a crypt, and that was remarkable. The baby was willing enough to mention it. I've already run over time, so I'm going to hurry through the end of this. The role of digital in this is clear. Brian has documented all this. He's a photographer and an artist, so he has his own kind of artistic response to this project. We've had various outputs through the usual channels through Facebook and Twitter in the project blog. All there has been scanning both the remake artefacts and some of the original ones there. She's scanning the goddess herself, or remains the goddess who dried out now. I won't call them any images on Sketchfab if anyone's interested in the links to that. So, all these connections she's developed, they weren't planned. I'm not suggesting we set out with these kind of ideas to work in this way. I think that's really how it happened. We didn't have a plan. People just got rolled in if you weren't along. It's got some marbles about it and say joyous and wondrous, and everyone seems to get it. All the interactions just kind of happened. So, some of the reasons I'm talking about it is if anyone has any thoughts or wants to interact with them somewhere, that's the right word, then gives a shout. We've got all sorts of kind of ideas through the blog and all sorts of discussions that went in all kinds of directions. We didn't plan at all. One of these was this. We had a thriving experimental percussion scene. We had some experimental percussionists who played the Greek Destructed Bessel. There's a link to that. I won't put it up now. We're actually having another palace boy sounding in a couple of weeks' time, so this goes well. So, we've got all these kinds of interactions around the vessel, and again, it's been facilitated, the outputs, the communication that's been facilitated through the digital. And again, during the open day, we asked children for their responses. We provided a sheet that we just can't really see it. There was just the outline of the vessel. We asked them to provide their interpretations of the vessel. Now, it's fantastic. And this was, Cornelius's work, my first thought, but it's especially crafted for a child who can achieve from that time. It was fascinating what work we've got here. So, again, we're getting all the responses. Other iPodual colleagues have said, what's it told you? What's it told you about the vessel? What have you learned? It doesn't matter. We have learned some stuff. That, in experimental archaeology terms, is interesting. But I don't think that's the kind of key part of what's happening to our project. Right. I've run far over five minutes. I'm sorry about that. I've skipped over a lot of stuff there. But I'd be really keen for any thoughts, observations, or suggestions, as I say, within the session. I appreciate maybe not the least very direct kind of somebody of the thieves. But I have read all the papers. I've very much enjoyed them, and I've got lots of scribblings in my bag, in my bag, which is in the room. So, anyway. Thank you.


Hi everyone Joe for Jasper's case breaks calm coming at you with 2022 tops chrome black baseball 12 box pick your team a number of five Great stuff here. All card ship a lot of fun stuff really clean Real sharp looking set big. Thanks everybody here for making this happen on a Monday night Oliver you ended up with last spot mojo. You know what that does 70% 100% If you have a little rooftop next your name That means you won that spot in the team random big. Thanks. Everybody who helped fill that up Appreciate it. All right now. Let's pop this case open What we got I think most of you are familiar with this one encased chrome autograph and one refractor parallel per box And away we go first and we'll do we'll show you the case cards put this list right here I'm gonna start off with Matt Manning Brandon Marsh Not numbered and a Reed Detmerce 48 out of 150 for the angels. That's gonna be for Chad and our first hit Cal Raleigh rookie auto for the Mariners Nestor and the Ems Really like that's that sort of black-on-black design. They have their Really cool stuff Really sleek. Oh Mike's looking for a low-numbered Bryce Harfield parallel Let's see. Let's see what we can do Matt Olson Josh Donaldson and Jake Berger Berger's Howard with the White Sox All right, and then there's Ted Simmons Old-school Ted Simmons with the Cardinals Howard the Cardinals Miguel Cabrera to 150 Ted Simmons. Yeah, I think You may have to be of a certain Generation if you were to remember Ted Simmons in his playing days Yeah, play for the Cardinals between 1968 and 1980 Hall of Famer Inducted in 2020 by the modern baseball era committee 81.3% of the vote next is we've got a hitter. He's looking hitter ish. That's Pete Alonzo Nice Pete Alonzo. That is for the Metropolitan's. That's for you, Mike Pete Alonzo, you know Corbin Burns, Helio Ramos and Bryson Stott Rookie refractor to 199 for Mike and the Phillies and Ryan Sandberg Rhino 8 out of 50 Cubbies it's for Ed and the Cubs Joe Adele Gavin Sheets Ronald Acuna Jr. to 199 for the Braves. That's Michael Michael D with the Bravo's Here is Gavin Sheets Rookie Otto Gavin Sheets for the shy socks. That's gonna be Howard There is Aaron Ashby, Matt Chapman and Chris Bryant 45 out of 50 gold Like colors like that really pop against the black and it'll be for Oliver and the Rockies Then There's Ronald Acuna Jr. Michael D with the ATL Nice All right next side and Jazz Chisholm. I think this is this is my teal Aqua color is my favorite against the black background That's for the fish. It's gonna go to Kyle Harper 21 out of 150 Alex Kirloff For the twins that's gonna be For Travis Now we have bigger fish to fry and break seven Mike. I've got a bigger fish to fry there Joey Bart reveals a Miguel Cabrera gold and a Julio Rodriguez Would we call that a little color match there that's Nestor and the Mariners that's 94 out of 99 Will a Tom it refractor in the background. That's real sharp real sharp and Richard you've got the Tigers. You'll get that miggy It's Colton Welker Rookie autograph for Oliver and the Rockies last spot mojo 70% of the time last spot mojo hits a hundred percent of the time Jonathan India Cedric Mullins and all rise Aaron judge 80 out of 99 for the Yankees Greg got some orange We got a rookie We've got a Hoy Park 24 out of 25 for the Pirates It's gonna go to Travis. I sure yeah last spot mojo working out Ronald JT and bow one out of five Real sharp real sharp Alex picked up the blue jays straight up Alex B With the blue bird straight up and All aboard the big hit express whoo-hoo out of fives Nunder world famous train whistle Love it and a redemption All right. Good luck everybody congratulations You are due to receive a autograph gold mini diamond refractor parallel of K, that's Kansas City, right? Bobby with junior Kyle with the Kansas City Royals Nice All right, two more to go Bernadette at East jr. Blue parallel to 75 Will be for Michael D in the Padres Next one is 70 out of 99 and it's Yasmine grand all Howard with the White Sox Real solid case here real nice case. Let's see what we got in the final box Good luck. Yeah parallels look real nice in this There's Brian Della Cruz Jeremy Pena Videl Bruhan refractor rookie car to 199 for ed p in the race And let's see what we got Final one here. I saw a number 132 out of 150 and It's Eloy Jimenez nice break for the White Sox There you go Howard. Thanks for getting in appreciate you Thank you everybody. That's the break That was 2022 tops chrome black baseball 12 bucks picker team number five. I'm Joe. I'll see you next time for the next one Bye-bye


and that's just from last night for those of you who don't believe me about the bugs here on the prairies it's a party once the sun goes down did you guess baloney baloney baloney what try that again did you guess baloney baloney you guessed correct more of our friends have joined us again we gotta go wipe them off they're so insistent on being part of the vlog that they just keep coming back every time i wipe the windshield doesn't take long and they're back up i feel i clean the windshield i drink coffee i drive go to bed repeat yeah that's that looks good right there that diesel fuel oh that looks good oh the truck is gonna like that she's thirsty well it's not perfect but it's better right it's better i'm not lying i scrubbed it but i didn't scrub it that hard because i was i always say well what's the point you know you scrub it and spend 10 minutes scrubbing the windshield it smells like fish all the dead bugs sit out there scrubbing it 10 minutes down the road it's exactly the same so i talked to you about that the other day right that time you what's rattling in here stop rattling don't you hate that when something's rattling and it's just out of your reach and it won't stop rattling and then you stop and of course it's not rattling so you don't know what was rattling you just gotta deal with it till it decides to stop on its own complain on youtube and sometimes that helps makes me feel better anyways gives people in the comments something to complain about you're complaining again trucker charge i dropped this trailer and this trailer is going down to mississippi out of the truck i don't know why it packed for like a three week long trip i took everything all my clothes everything like what three nights i knew that too but i still packed everything so i gotta take everything back home at least i was prepared the rest of the month is gonna be go go go go i've been seeing some fields start to turn gold already i talked about that yesterday right combine on the fields in the us already online two crops a year down there why are you harvesting so early that's crazy you can fit two crops in in one year there's obviously i grew up in southern manitoba it takes a lot of education a lot of people in big cities seem to think that farmers are just you know redneck dummies that just grow a garden in their backyard every year you know no no no my friends they went through a lot of university and a lot of agricultural studies there's a lot of knowledge and wisdom that i don't have that they do that goes into growing these crops for your food it's not that easy different seeding seeds and pesticides herbicides when to plant when to harvest how to get the most yield out of it when to sell what to plant crop rotation planting a different field so that the nutrients in your soil don't get depleted by planting the same crop over and over again and then those machines that you see on the fields those machines they have millions and millions of dollars worth of machines on every farm you think my truck's expensive this truck i'm driving right now probably well it costs over 200 000 canadian tractors you see on the field are much more than that i'm thinking a combine would probably be what close to a million dollars for a good one 800 000 one million new farmers you can you know better than me it's a lot a lot and you rely a lot on the weather you got to be your own weather man it's nowadays saying that the other day i'm kind of a big fan of food eight billion people on this planet eight billion way too much food here in canada to feed ourselves we export it all over the world that we feed the huge portion of the world with the crops we have here same thing with the u.s i just bring stuff from there to over there we all have our part to play in this big machine we call an economy and we all do our best to do our best even when the government throws a wrench into the economy engine and it's not possible karen keep dreaming back though find a little parking spot drag ourselves into the timmies that's what you do the list lovely everybody's all nicely lined up here how did that guy get in here backwards how is that even possible obviously he came in the clearly marked exit it happens i guess go up here and park beside that brand new van trailer look at that shiny doesn't even have a license plate very nice very nice you're past me hope he doesn't park there that's the driveway where people need to drive through dude how are people going to drive through if you park right in the driveway oh man guy right there that's the only spot for trucks to come through and drive through to the exit parks right in the driveway oh man lots of part you saw it lots of parking over here you're supposed to park over this way i guess it's not clearly marked but still there's exit sign right there so you know that's oh well it is what it is i'm gonna feel much better once i have my timmies put me in a much better mood guaranteed you guys remember when i was on flatbed and i delivered all that those insulation panels to this building over here on the right just outside port of prairie looks like the building is completely finished now and operational i delivered a lot of that insulation on the top of the roof price there right some kind of food ready to go that's pretty cool south winnipeg we're after nine at night friends along with us on the window again that's okay because we're almost done our last traffic light all we got to do is get through this traffic light come on stay green stay the entrance to the right on rde putting north rte putting highway 59 south rte 59 bt lagimadir and then keep to the right and 400 putting meters what 800 meters take the entrance to the right on rte putting north rte putting highway 59 south rte 59 bt lagimadir and then keep to the right and 400 meters oh gotcha and from here we head home so thanks for watching this today thanks for clicking the video don't forget to click that subscribe button that is the most important button you can click on this page i'll wait i appreciate it thank you diesel is there anything you'd like to add we're already in the future here we're tired a little bit of home time footage coming up in the next couple of days and then uh we hit the road again going down south thanks for hanging out today everybody i hope you enjoyed that prairie scenery


Welcome to Toffy TV, it is the Everton News Daily. Reports today that Sean Dytter's job as Everton manager is safe, no matter what happens this season. A lot of those reports doing the rounds. Everton on a terrible run at the moment, one winning 15 games and Dytter's got a huge week coming up. Everton have three home games, Nottingham Forest on Sunday, Liverpool in the Massey side derby in the midweek and then Brentford the following weekend all of Goodersham Park. If the Blues boss can get two wins at least in those three games then it will go a long way to secure an evidence Premier League safety. Obviously at the moment everything's up in the air with the ownership as well and the manager will have found it difficult with all the turbulence going on at the top of the club as well so we'll have to wait and see what happens there. This obviously can't see the reports last week that 7-7 wanted to replace me if they got it so you don't know what to believe but he's got a great opportunity to get Everton closer to Premier League safety by winning at least two of those three home games. Everton have got coming up in the weekend. We need something positive Monday night. It was an awful performance, it was Everton's biggest defeat since the 7-0 of Arsenal 19 years ago so we have to follow it up with a positive performance and hopefully positive three points and let's open Neil Mopay on loan at Brentford to get a couple of goals as Brentford beat Newton and do us a big favour. Jarrod Branthwaite is reportedly on Manchester United's shortlist for the summer as the good news continues. A fee of around £93 million has been reported today for the young centre back who made it into Gareth Southgate's England squad recently didn't get on the pitch but he was there ever no sweating on the fitness of Jarrod Branthwaite. There'll be more on him at Sean Deitch's press conference ahead of the Forrest game. He left the Chelsea game early with an injury on Monday night. Fingers crossed there isn't too bad than he is available for the visits of Forrest at the weekend. Young Everton goalkeeper Harry Tyre has signed a one-year extension. The 22-year-old has been on loan at Chesterfield this season. He helped them get promoted to lead to keeping 11 clean sheets in the process. He's had an excellent season. The Chesterfield fans love him and he has signed a new deal with the football club and finally Everton's under-21 cyber knocked out of the Premier League international cup last night. The young blues were beaten four to a crystal palace. Jenson Metcalf getting both of Everton's goals. That is it for the news daily. Give the video a thumbs up and subscribe to the channel if you haven't and if you want to become a Toffy TV Premier member, which means no outfits on videos or podcasts. The link is in the description to sign up. Use the QR code as well. See you later.


Suppose that we have a group G that's acting upon a set X, so X is a G set. And suppose we have some fixed element G inside of G. Using this element, we can define what's called the stable set, sometimes called the fixed point set associated to G inside of X. This is commonly denoted as X sub G. X sub G is important to point out here. It's a subset of X. It's some collection of the points that we're acting upon. And this is going to be a set of all points which are fixed by little G, all right? So X sub G by definition is a set of all elements, little X inside of X, so that G dot X is equal to X. These are the stable set is all of these elements that G does nothing to, all right? In particular if G is the identity, right? If you take X sub E, this is all of X by construction, the identity doesn't do anything to the set. So the stable set associated to the identity is always the whole set. The kernel of a group action is defined to be all of those elements which stable set is nothing, right? So if you have some group action, it's so-called kernel, this is gonna equal all of the elements G inside of G such that XG is equal to X in that situation. So this stable set's a pretty big deal. It does say a lot about the group actions, what these do individually, that is these individual stable sets, these fixed point sets, what do they do? Now on the flip side of the coin, now let's take an element X inside of X. What does its stable set mean? These are typically called stabilizers. Sometimes they're called the isotropy subgroups. The term subgroup is somewhat getting ahead of ourselves. Why is it a subgroup? Well, we'll get to that in just a moment. So given an element of the G set X, we can define its stabilizer, which is commonly denoted as G sub X. So G is the group, X is the element that's getting fixed right here. And that's what G sub X is. This is a set of all elements of the group such that G dot X just gives you back X, right? So these are the things that stabilize X. And so like I said before, X sub G is a subset of X. These are all the elements which are fixed by G. Now G sub X is a subset of G and this is the collection of all elements G that fix X. So in both situations, the subscript is the element that's doing the fixing, right? So X is fixed in this situation or G is the thing that's fixing. And then the large set, the large set X and G, this is then the subset of X and G respectively. And there's some possible collection there, right? So we're taking, you take X sub G here, all the things inside of X that are fixed by G and then G X here, these are all of the elements of G that fix X. So there's always this relationship of stabilizing something, but the notation tells you which subset we're talking about. But like I said, why are stabilizers sometimes called isotropy subgroups? Well, that's because they're subgroups. That's our proposition that we're gonna prove right now. If you have a group G that acts upon a set X and you pick any element X inside of that, then it turns out that the stabilizer is in fact a subgroup of G and therefore it deserves the name isotropy subgroup. So to prove that G is a subgroup, well, there's basically three things we have to check. We have to show that it's closed under multiplication, closed under identities, well, there's only one identity, and then closed under inverses. So we'll do those bit by bit by bit. So let's take two elements of the stabilizer, call them G and H. So by assumption, G acting on X is X, and likewise, H acting on X gives you X as well. That's what it means to be in the stabilizer. They stabilize the element X. So what happens when we take the product? Well, because this is a group action, G H acting on X is the same thing as H acting on X and then G acting on that. But by assumption, H stabilizes X. So H dot X is just X. But also by assumption, G acting on X is just X because they're both in the stabilizer. So therefore the product G H also stabilizes X. So thus the product G H is inside of the stabilizer. G X is closed under multiplication. The next one's a pretty easy one. What about the identity? The first axiom of a group action is that the identity stabilizes everything. Therefore the identity will belong to G H for any X, well, excuse me, the identity will belong to G X for any X whatsoever. So G X always contains the identity. It's closed under identities. So the last one about inverses. Suppose that G belongs to G X. So that means G stabilizes X, G dot X is equal to X. What does the inverse of it do? Let's look here. G inverse dot X, we want it to be X and we'll see that in just a second. Since G stabilizes X, X is the same thing as G dot X. Using compatibility, we can re-associate and get G inverse G dot X, which G inverse G is the identity, right? The identity stabilizes everything. And so this then implies that G inverse stabilizes X as well. So G inverse belongs to the stabilizer and the stabilizer is closed under inverses. Since the stabilizer is closed under inverses identity and multiplication, the stabilizer is a subgroup again justifying the label of colon and isotropy subgroup. Let's look at some examples of these stable sets here, right? So let's take the set to be one, two, three, four, five, six. We're just gonna take the permutation action here. We're not gonna do all of S6. So I'm gonna take a subgroup that looks like Z4. So we're gonna take the identity. We're gonna take one, two, three, four, and five, six. So that's a two cycle times a four cycle. Then we're gonna have a two, two cycle, three, five, and four, six. And then another two, four cycle, one, two, and three, six, four, five, like so. And you can verify that this is in fact a subgroup and G is gonna act on X by the usual permutation action, okay? So let's look at the very stable sets. So as I go through these, as I go through these, excuse me, if I go through the elements of G, so we have the identity, we have this element, this element, this element, what are their stable sets? So like I mentioned before, the identity is gonna stabilize everything. This is the group identity just so we're clear here. Because the identity by construction fixes everything. So the stable set of the identity is always the entire G set. That's perfectly good. Be aware of that. Next, what do we get here? If we look at the stable set associated to three, five, and four, six, who doesn't get moved by that element? Well, notice that one is left fixed by three, five, and four, six. And so is two. Three doesn't get fixed because this element sends three to five, three to five here. Neither does five gets fixed because it sends five back to three. And then notice that four is not fixed because it sends, this element sends four to six and likewise six will go back to four. So the nice thing about permutation action is that when you look at the stabilizer, the elements that are present in the cycle composition are the things that get moved. Thus those elements, those letters which are omitted, that is going to be the stable set associated to that permutation. Then when you look at the other ones, the two, four cycle one, two, and three, four, five, six, nothing is left fixed. It moves everything. And therefore the stable set will be empty, right? So it's completely empty in that situation. Likewise, if you take the other element, the stable set is empty. So with regard to the permutation action, it's very easy to identify the stable sets because you just look at the cycle decomposition and then the stable set will be all those elements which are not listed in the cycle decomposition because we typically omit elements which are fixed. Now let's go the other way around. What are the stabilizers, those isotropy subgroups? So what is the subgroup that fixes the letter one? Well the identity fixes everything so it'll belong to that. But like we observed earlier, three, four, five, three, five, and four, six fixes one. So the stabilizer of the letter one is then the cyclic subgroup generated by three, five, and four, six. So this is a subgroup isomorphic to Z two. It turns out that the stabilizer associated to two does this exact same thing, right? Because one stabilizes two, three, five, and four, six stabilizes two. The other elements do not. They don't stabilize it. Then if we look at the other elements, the other letters I should say three, four, five, six, the only thing that stabilizes them is the identity permutation. No one else stabilizes them. So in fact, these six stabilizers are subgroups of the group there G. So you just get the trivial subgroup and Z two. All right, so before we end this video, there's one very important property about isotropy subgroups that I want to point out here. And it has to do with taking conjugates of isotropy subgroups. So we have a group action G acting on the set X take a fixed element G of the group, little G and a fixed element, a fixed letter X of the G set X there and we want to prove the following identity. If you take the conjugate subgroup of the stabilizer associated to X with respect to G here. So that's where conjugating by G, the stabilizer of X. This is equal to the stabilizer of G acting on X. Now these are both subgroups, right? Stabilizers are always subgroups and the conjugate of a subgroup is also a subgroup. So what this is basically telling us is that the conjugate of a stabilizer is also a stabilizer and they're connected by the element you conjugated by. But as these are subgroups of the group but as they're sets to prove equality, we only have to show that they're subsets of each other. We don't have to prove that they're groups or anything that's already established. So let's prove their subsets of each other and those are the two directions we have to go. So let's first start this direction. Let's show that the conjugate of GX is a subset of the stabilizer of GX. So let's start off the typical element of G, GX, G inverse, call the element H. Well, since H belongs to this conjugate here that means there exists some element H prime that belongs to the set GX such that H is equal to G, H prime, G inverse. So just the definition of what it means to be inside of that set right there. So what we're gonna do is then we have to prove that H belongs to the set G sub GX. This is the stabilizer of GX. So to be inside this set, H needs to stabilize GX. So if I take H dot GX, I need to get GX. What are the details of that? Well, H dot G dot X by compatibility is the same thing as HG dot X. And now I'm gonna use my formula for H above here, plug it in for H, excuse me. H then becomes GH prime G inverse. You type in that by G. So this is multiplication in the group. So the G inverse G will cancel each other out. We're then gonna get GH prime dot H, dot X, excuse me. Reassociate again, then you're gonna get H prime dot X and then you have a dot G over here. By assumption, H prime belongs to GX, it stabilizes X. So H prime dot X is just X right here. So when you take H dot G dot X, you get back to G dot X. So H does in fact stabilize GX. So H belongs to G sub G dot X. So that gives us the first containment that the conjugate of GX is a subset of the stabilizer of GX. Did I say that right? Let me say it again. The conjugate of GX is the subset of G sub G dot X. Now we wanna go the other direction. So let's take an arbitrary element of G sub G dot X. So something like this, right? So what we know is that H stabilizes GH. So this time if you take H and you act on GX, you get back GX, all right? Well by compatibility, the left hand side can be rewritten as HG, the product dot X. That's going to give you G dot X like so. And then what we're gonna do is we're gonna take this and we're going to dot both sides of the equation by G inverse. You know, we often say like you multiply both sides by G inverse where we're gonna act on both sides on the left by G inverse. Now on the right hand side by compatibility, you're gonna get G inverse times G dot X. This then becomes E dot X for which then simplifies just to be X. Compatibility on the left hand side is much simpler. G inverse dot HG dot X, this just becomes G inverse HG dot X. Again, my compatibility right there. So this shows us that G inverse HG dot X is X. It stabilizes X. So G inverse HG belongs to G sub X right here. Now, if this happens, then our original element H can be factored in the following way. It looks like G G inverse H times G G inverse. You know, for getting some of the parentheses, you have some products of G and G inverses or identities. So this is equal to H, but then look at it. We just showed that G inverse HG belongs to the stabilizer of X. Then if you throw a G in front and a G inverse at the end, this then shows that H belongs to G, the stabilizer of X G inverse, thus giving us the other containment, thus proving equality. And so then we have the statement we were looking for that the conjugate of a stabilizer is equal to a stabilizer and the equality comes from the element you conjugated by.


Hello, I am Antonio Vitorin, the head of the International Organization for Migration, IOM. We can all agree it's been a rough year for humanity. New fears, new restrictions and new challenges of all sorts have been sent our way. Our health, work, friends and families. Our job security, hobbies and the plans we have made are all in limbo. It's been a non-stop balancing act and our psychological and social well-being was taken at all. Even for those with good access to healthcare, water and food, an adequate home and a reliable source of income. Now, imagine the stress endured by migrants and people displaced by conflict or natural disaster. Women, children and men. Some who have suddenly lost their homes or jobs because of the crisis. Others who have found themselves stranded as borders closed overnight. Some are living in harsh conditions in a camp. Others in substandard conditions or in detention. Still more are stigmatized, discriminated against and abused. Many do not have access to health services and are physically cut off from support systems and social networks. As we celebrate World Mental Health Day, these 10th of October, more than ever before, it is critical that we raise our voices together and call for greater investment in mental health and psychosocial support so no one is left out. Mental health care must be available legally to all, regardless of migration status. Affordable and within reach, with dedicated outreach for migrants. And culturally and linguistically appropriate and diverse. As well as mainstreamed across all public sector services, be it else, education, social services and law enforcement, as well as religious settings and last but not least, to build capacity in migrant communities, to understand and respond to mental health needs and in the mental health care sector to understand different cultures and different needs of migrants. COVID-19 has demonstrated that one person's well-being is closely linked with everyone's well-being. We are all in this together, so let's mobilize and let's move for mental health for all.


Representatives from various military branches, as well as representatives from Cal Fire and West Coast City and state officials, met for the two-day defense support of civil authorities open house in San Diego, April 28th through 29th. We as the Navy Marine Corps team are here to be forward deployed and fight the country's wars. But if called upon, the President or obviously the Secretary of Defense determines us to support the homeland, it's important that we're able to respond to whether to save lives or help the civilian authorities during times of crisis. This is the beginning of a relationship, this is the beginning of a partnership. It's very hard to do things when you call it due to a crisis. But once we establish these relationships and we search trust, because you can search trust, then once it's time to go do mission, we can execute that mission very seamlessly. The open house took place at three of the San Diego Naval bases and included a ship tour, static equipment displays, and live demonstrations of the vehicles that would be used for Continental Humanitarian Assistance and Disaster Relief, or HADR, operation. You look out here, you see a lot of the equipment, you see a lot of the machinery and whatnot. But the story here is about the Marines and the sailors. Because without them, this would not be possible. When you talk to them, you can sense this pride of professionalism and not just what they do but who they are. And this is what our military is about. Not just going overseas and fighting battles, not just providing HADR offshore and overseas, but it's about here, right here in the United States, in support of our Americans when they are in need of our services and our support. From San Diego, California, I'm Petty Officer Brian Jackson.


The concept which is the oppression of the followers of Ahl al-Bayt throughout history. And we looked at several characteristics, inshallah we're going to have a brief overview of what we talked about yesterday, inshallah we can elaborate on that to look at other characteristics. And inshallah the essence of tonight's topic will be to discuss how we can act or what should we do as the followers of Ahl al-Bayt in face of such oppression, in face of such attacks. Whether we are to defend ourselves in a particular manner, whether we refrain from any sort of defense or whether we have to go out and have the whole concept of an eye for an eye. Now looking at it obviously from the perspective of our imams, how they reacted to specific circumstances, how they reacted to specific attacks. And inshallah we can analyze how we can better ourselves at the conclusion of tonight's topic. So please help me in starting tonight's topic with the loud salawat ala Muhammad wa aali Muhammad. Very briefly I'd like to touch up on the points that we mentioned yesterday in which we discussed a particular type of people by the name of the Khawarij. In which first and foremost we said that they have characteristics in which they used to pray in narrations the salat of the Fajr with the wudu of the previous Faridah meaning they were up all nights in worship, number one. And we said that this can be a problem within societies because someone may look at a figure that appears to be religious. However, when they come close towards him they take them towards the other path altogether. Now an example of this is and we are given is that there used to be a very pious man, a very pious man. All the day you'd find him in the mosques or the night you find him in the mosque. You find no one recited more than him the holy Quran. Now then you find that Shaytan every time he comes towards this man he tries to lure him. He tries to make him sin. He tries to make him think of something unethical, un-moral. Take him towards sin. He'd have no chance. That's the status of that man. Now let's look at the example that was given. How did Shaytan get to this particular person? The narration says that Shaytan embodied himself in which he became or appeared to be a man and he came next to this particular person. Shaytan, he saw this person was praying so he prayed more than him. This person appeared to be reciting a lot. He appeared to be reciting more than him. Therefore this person wasn't drawn to sin. However, he saw that this particular person which was embodied with Shaytan pray more than him, do more than him in the path of Allah and then he began to become inclined towards him because he doesn't know what he's doing, but he appears to do that which is pious. So he slowly draws towards him and draws towards him. And because he respected him in such a manner, because he thought to himself, you know what this person, it must be something great because he's praying more than me, he's doing more than me. Slowly, slowly he lured him away from the mosques. Slowly, slowly he lured him into sin. Slowly, slowly he got away from the path of Allah SWT. Now this is to give us an example of the danger that people such as the Khawaraj will have. Because they will appear as religious. You look at them, you see their actions, in particular circumstances, not in the holistic manner.  But in the perspective where you look at them, in the mosque environment, you say to yourself, wow, these are religious figures. So this was a danger because people might look at them and say the wrong things. Ali ibn Abi Talib has a statement in which he says, do not look at the length of someone's ruku and sujud. Don't look at that because that can be misleading. Look at what they say, what comes out of their tongues and how much they give charity. He says that should be the point in which you look at, to differentiate between that which is right and that which is wrong. Those people that are on the path or those people that are just pretending to be on the path. That's the second point. Therefore, we have to analyze in depth what kind of people they are in order so that we cannot be drawn to be like them. Now, someone may come forth and say, how is it that I can go away from such people? How is it that I can defend myself from such people? As you know, the examples that were given from the Khawarj at that time, they were known not only to be attacking the school of Ahlul Bayt, but only they were attacking anyone outside their school of thought. There used to be anyone, caravan coming past, they had stopped them. Now, look at this, and I want you to see if this reminds you of anyone nowadays or doesn't remind you of anyone nowadays. They would find Christians and Jews passing the desert. They say, what religion are you? They say, we're Jews. They say, you can pass. What religion are you? We're Christians, you can pass. People come forth. What religion are you? We're Muslims. Come, we're going to behead you. Does it ring a bell? Do we think nowadays anyone does that nowadays? You're Muslim, we'll behead you. So much so, that wasn't one of the companions. It wasn't the companions of our Imams, but one of the companions of the Prophet used to go past this particular area where the Khawarj lay in the desert because they were outcasted. Then he said to his whole tribe, he said, don't say anything. The caravan that he was in says, don't say anything, leave me to do all the talking because I know how these people think.  So the person, he starts to speak, he says, don't want to speak. He says, we're not Muslim. He says, oh really? And he still tells us people don't kill them, right? Let's see what's going on. He says, what's your story? He goes, we heard that there's a bunch of Muslims in the desert and we came to learn knowledge from you. Can you teach us so we might think about becoming Muslim or not? So they come towards them and say, this is Islam. This is what we believe Islam is. And the person says, okay, we'll think about it. Can you take us to a safe haven? And we'll think about it and get back to you. He says, okay, so they take them towards a safe location and they come back. The irony of this is that they supposedly were Muslims. However, the only way that you can go away from them and to be in peace from them was to say that you're not Muslim. That's the irony of it. And that's the people nowadays when we see such people holding the flag of Islam. We can see it on TV. We know about it. Holding the flag of Islam, but everything under that flag is against Islam. How is it that we can defend ourselves? What can we do in order to not fall in that trap? In order to defend ourselves from these particular traps in societies, it's fitness in societies. Now, people may come forth and there's so many different ways in which we can do it. Number one would be if we educate ourselves, obviously. That's the first thing someone will tell you, educate ourselves. Let's learn the misconceptions because when we're attacked, we have to know how to defend ourselves. If someone comes forth and says, you guys believe in ABCD, we have to know, yes, we believe in this. This is why we believe in this. What did we say yesterday? One of their ideologies is not to question. Just believe. Don't question. The difference is our school of thought says what? It says you must question everything and have a deep understanding of why you believe in what you believe. That's the difference. That's why we have the solid foundation and no one can falter it. Once someone has the love of Muhammad and Ali Muhammad and understands it, no one can take that love away. However, if you have a rocky foundation, if you don't even know what you stand for, how easy is it to take you away from that path which you're on? How easy is it, even in the time of our Imams, Imam Ali, Imam Al-Hassan, what happened? We celebrate his birthday in a couple of days. Imam Al-Hassan, Muawiyah used to buy, money takes you off the path. He used to buy out each and every one of his generals, not any normal person. Generals that Imam Hassan put as flag bearers, trusted them, entrusted them with the flag of Islam. Muawiyah buys them out with a couple of coins. I say a couple of coins because it's worthless, but he obviously offered them some amount that's remarkable to them. Now that's the level that we have to say, yes we can learn, yes we can educate ourselves, yes we can go on to learn what misconceptions there are. However, the most important aspect is the application. Why? Because on one level, we know of people in history that were very knowledgeable. We can learn all we want. However, how much do we apply it? I'll give you the best example that we have, it's Shimr. You think to yourself, maybe Shimr? Really, he had knowledge of course. Shimr, as we have in narrations, he sat on the chest of Aba Abdullah, he started crying. And I should say he started crying. Why? Why is it that we have the narrations that Imam Hussein was severed from the back of his head, not the front? Because Shimr couldn't bear to look at his face. His wording was what? When he put Aba Abdullah's head at the feet. Wa la'iyahatubillah. May the Imam forgive me for saying this. When he put the head of Aba Abdullah in front of Aba Abdullah Ibn Ziyad, what does he say? Shimr knew who Imam Hussein was. What does he say? He says He says, I know who I have killed. I have killed the best amongst you, with the best father and the best mother. And then he says it in his own sentence, what have I done it for? Few coins. Up to my knees put gold and silver and this is what I have sold myself for. What does Imam Hussein tell us? Your souls deserve only paradise. Do not sell them for anything less. Nothing less. You get offered. Shaytan guides you to a path. Shaytan puts an idea into your head. Remember Imam Hussein, that's why it's a definitive factor. This is why Imam Hussein was such a solid stance and this is why our madhab lives on, is because of the stand of Hussein. Because the stand of Hussein, when we have Aba Abdullah Ibn Ziyad and that's the example, when we have the main general, the main general of Yazid's armies. And this is a definitive factor because if we put this into our lives, and I've mentioned this, I think maybe two months ago, but it's a beautiful, beautiful analogy to put into tonight's lecture because it goes hand in hand. Imam Ibn Ziyad, before, he was going to fight Imam Hussein. He's in his courtyard. He's walking around and he's questioning himself because we all have the question with the sin. I'm not saying we're going to fight. I'm saying it starts off in a very small proportion. If you choose the right path in a small sin, you will choose the right path in the bigger sins that Allah will test you in. It's the choice that matters. If you always incline towards that which is bad, when you have the bigger choices, you will also incline towards that which is bad. If the small choices you make, the right decisions, that will carry on. Imam Ibn Ziyad, in his courtyard, what does he say to himself? He questions himself and he tries to make himself feel better. He says, he begins within himself the soul. He says, because he was given and he was promised the Mulk of Ray, which is the entire pleasure at the time. Imam Ibn Ziyad is questioning himself. He says, He says, do I leave this and everything that I dreamt is going to be given to me or, on the other hand, this is the price to pay. That's the balance. He's questioning himself. Do I take one, the worldly desires and my dreams and what to have? Or, on the opposite angle, do I go and kill Hussain? Will my hands be drenched with the blood of the Risaleh? That's the balance that I have. Then he goes on, what does he say?  Did they actually believe in Islam or did they not? Then I will repent over a duration of two years to my Lord and he'll forgive me. That's what he tells himself. Now, our question is what? Our question is, in every single day societies, and this is what we have to understand from tonight's topic, we are given a choice in every single circumstance whether we choose the path which is right and we become Hussain or we choose the wrong path and we become Whoever you want to mention, mention because when you are right, you will be with that which is right. Those who are right the Imam Sahib al-Asri was Zaman that's what he looks for. But if you take the wrong choice, you will be like the people that took the wrong choices. I'm not saying we have to become Ma'as or Meen. No. It says we are Bani Adam but we learn from our mistakes. We don't do the same mistake twice. We learn from predecessors. If someone in history made that mistake, I learn from it. I make sure I live in a manifestation of what the Imams have taught me and every single person and it's so beautiful the message of Islam. I have five more minutes with you and I want to wrap this particular topic up because of its utmost importance. In these five minutes, I want you to look at the wording because we encompassing two topics together. The wording of Sayyid Ahmad Shirazi when he talks about the concept of the terrorism and what's happening.   He says that when someone is poor, it's not that they don't have wealth or money. He says a poor person is a person that is poor in their intellect. They cannot comprehend. They don't understand. That's being poor. He says they think between one or two bombs that go off after a couple of the shuhadaa and they go straight to heaven. They can stop Imam Hussein and this march that's happening in Europe upon which it gets into the Guinness World records. It breaks so many records and it's increasing and increasing and increasing.  We know the story of Ibrahim Dizaj in which the first cuts his right hand. The second he cuts his left. The third and fourth he plugs his right and left eye out. They didn't have anesthetics back then.  Blood, bone, muscle. Imagine the pain they go through. Why? Just to go once to smell to see, to sit in the presence of our Imams and we are so gifted and they think to help us in that manner. But say the Zaynab says a beautiful line. And this is the line that will be echoing within history. It will be echoing until the end of time, until the Imam comes. Imam Sahib al-Asli was Zaman. What's that? When she finds Imam Zayn al-Abideen in a very sad and mana. She looks at him. She says, what is wrong or what remains of my family? Then she tells him about what? About Karbala and the effect it will have. The long reach in which Karbala will have. She says, who Wahdun min Allah li jaddika wa abik wa sayun sab futtaf alamun ala quroor al-ayyam wa ala quroor al-layali wa al-ayyam wala yashdahidanna a'immat al-kufr alamahihi wa tatmisih fela yazdad illa ulua Salah ala Muhammad wa ala Muhammad Tyrants in history will come and try to bring down this flag except it will not go anywhere except up and elevate and elevate. That's the message. That's what the stance of Imam al-Hussein had and its effect will be echoing within history. So tonight's lecture will be towards to take into perspective one particular instance in which we have to better ourselves. We have to be the best we can be before we can defend the religion. We have to be messengers for the religion. People that speak out without actually speaking by our actions, by our morals and mannerisms, by our transactions.  Everything will encompass your characteristics and the characteristics of your generations. Imam al-Ali says it in Safin when he is about to strike someone and this is the last story before I end for tonight. Malik al-Ashdar he says what? He says I want to count how many times Ali ibn al-Bitaleb kills and I want to match it with what I do. So every time Ali ibn al-Bitaleb would kill someone he would say Allahu Akbar. So Malik al-Ashdar counts. He counts, he counts. The narration says he killed a thousand and he's counting Ali ibn al-Bitaleb killed a thousand. He's questioning it in himself, he's just thinking. He says then there's no difference between me and Ali if he's killed a thousand I've killed a thousand. He says I was just thinking. I didn't say anything, I was thinking it. He says Ali ibn al-Bitaleb comes to me and what does he say?  Malik is thinking how does he know? He says I look in a person's generation their offsprings seven generations down the line if there's one good person I do not kill them. One good person. Imagine what the Imam was fighting who the Imam killed at that time. And I end on this Insha'Allah brothers and sisters let's aim and pray to Allah that he writes that we become the best manifestations of the muhabbin of Shia that the Imams want from us to be of the best characteristics that the Imam will be pleased with our actions. And if we are doing anything that displeases the Imams so Allah can allow us to let go of those particular traits and stay firm on the religion of Islam. In the blessings of the prayer in the blessings of the blessed Surah Fatiha of Muhammad and the people of Muhammad


The vice president of the United States, Kamala Harris, in this time of great challenge for Israel and at a time of horror for really Jewish people, primarily Jews on campuses who are being harassed and being beaten, being chased and experiencing what it is like to be in a hostile environment. In this period, Kamala has your back, don't worry. She is launching the country's first national strategy to counter Islamophobia because the real problem in America right now as we speak, the real problem in America is fear of Muslims. We're all terrified of Muslims and that results in really, really harsh behavior towards Muslims. You'd think that after October 7th, Islamophobia would be a term relegated to the dustbin of history because don't you think that after October 7th, we should be afraid of Muslims?   I mean, if you're not a little afraid of Muslims right now, there's something wrong with you and you would think that in the aftermath of October 7th, Muslims in this country would be what? Muslims in this country would be ashamed, embarrassed, maybe come out in support of peace, maybe condemn and denounce Hamas and everything Hamas stands for. Maybe they would come out for, I don't know, moderate Islam in opposition to the Islamist jihadist agenda. You would think, just like you would think they would have done that after 9-11 and the reality is they didn't then and they're not now, they're silent or worse. They're marching in the streets supporting Hamas. They're marching in the streets supporting the slaughter of children. The rape, the barbarism that we saw from Hamas. They're embracing it. Should we be afraid of Muslims? Yes. There is no such thing as Islamophobia which is just a smear term. There is such a thing as fear. There is such a thing as looking at the Muslim world and evaluating it. There is such a thing as condemning Islamic fundamentalism, Islamism jihadism, Islamic totalitarianism, call it what you will and you know, the vice president of the United States of America in her wisdom and this is obviously coming from Biden and coming from the strategy of the administration, they're losing Arab Muslim votes. They're worried that they'll lose that vote, two million or something. I guess they don't worry about the Jewish vote. That's there as Jews will just vote Democratic no matter what. They think at least. Maybe they're right, particularly if Trump wins, we'll see. But they think this is a good time to launch a national strategy to counter Islamophobia. I mean, I have a good idea of how to counter Islamophobia, flatten Hamas, destroy Hezbollah, eliminate the regime in Iran, crush whatever remnants there of ISIS and al-Qaeda, whatever they may be and come home. And we can all stop worrying about Muslims or at least worry a lot less, fear them a lot less because we will have won. Problem in the world today is not fear of Muslims. It's a so-called bogus concept of Islamophobia. The problem in the world today is that we embolden these radicals, we embolden these crazy Islamists, we embolden these suicidal, homicidal maniacs, we embolden them by our weakness, we embolden them by not being willing to name them, by not being willing to define Hamas as an Islamic organization, Hezbollah as an Islamic organization, and Iran as an Islamist state and viewing them as our enemy. That is the challenge of our time. That has been the challenge of our time for decades. And one more administration's field in doing what was necessary added to a long list going back probably to Ronald Reagan.


Hey there class, welcome back to Game Dev Academy. I'm Shane. Make sure you let me know you have a writing class by writing something down in the video comment place. In the last video, the following people let me know they attended by leaving comments there on screen now. In this video, what we'll be doing now is solving the problem that we identified in the last step, which is that the ball and the play field and the blocks aren't bouncy at all, so it kind of kills the pace of the game. So we're going to have to look at physical materials to do that. So let's get stuck in. In the last step, what we did is got it so that when we played the game, it'll fling the ball. It's not bouncy enough. And that's something that we need to sort out in this step. So it doesn't matter whether or not I can move my paddle side to side because that ball is never coming back down the play field. We need to sort that out with something called a physical material. So what I'll do is I'm just going to move into my content folder here, and I'm going to put my physical material in the materials folder so that I'm keeping everything together. So to create a new physical material, it's right clicking here. And then we go to physics to create it and then you'll see physical material listed there. So we'll give that a click and then you get this weird box with only one option. So we'll click that because it's our only choice and then select. And then we need to give it a name. So I'm going to call it PM physical material underscore no friction because there's going to be no friction on this material. It'll also be very bouncy as well. So we just need to press enter to name that. And then we need to open it up. Here it is. So it gives us some settings that we can mess around with. The first thing we want to get rid of is friction. We want there to be no friction on this whatsoever. So we'll take it from 0.7 to 0. And the other thing we need to change is this option here called restitution. And it gives you the name here. You can look in the tooltip. It's as restitution or bounces of this surface between 0, no bounce, and 1 where the outgoing velocity is the same as incoming. That's the one we want. We don't want it to lose any speed, any velocity. So we need to set that to 1. Boom, very nice. Okay, so that's actually all we need to change in this physics material. So I'm going to save that. I can close it for now, but we need to assign it to everything. And I planned ahead for this. So what I did is made sure that at the moment everything's got the same material applied. So we could actually, if we wanted to, go into the ball here. And there is an area here to add the physical material. So we can put it in there and there it is. But I'm not going to do it that way. What I'll do instead is open the actual material. So the basic ball colour that we created here. And if I click on the main material node here, at the top, there's a physical material option there. And that will do it for everything that's got that material applied. So I'm going to choose my no friction material. And then I'm going to save. There we go. And now that's saved, I'm going to test it out again. So let's play. And now we can see that the ball is not losing speed and it's bouncing very nicely. And it gives me an opportunity to, for the first time, really test the game. So what I'll do now is I will let the game run for a little bit. And you will hopefully see the problem that we need to correct in the next step by the time I'm done. Okay, so here's our problem. Basically, there'll be times when the angle of the ball would be too acute to make the game playable. This here is not fun and it's very unlikely that I'm going to be able to, there you go. So the ball will just kind of stop sometimes. And that, it can break the game. There are times as well, I've not managed to catch it on this one, but it will get caught on the side and you'll never be able to get an angle back into the ball, which again is not fun. So going forward in the next step, what we'll need to do is take control of the angle of the ball and we're going to clamp it so that it can only go at four angles. So it'll be going at 90 degree increments but kind of at a 45 degree skew. So that should mean that the ball, the bounce of the ball, the direction of the ball is always going to be predictable and we know it's not going to kill the flow of the game. So that's something that we need to pay attention to going forward. That's the end of this step though. We've now got kind of what I would call a minimum viable product. This is the absolute minimum of what the game is. It's a ball that we can hit backwards and forwards. There are no real mechanics yet, but this, if it feels fun knocking a ball up and down the play field then we know we've got something to build on and that's what we'll do going forward. I believe that quality education should be available to everybody and for that reason all of the classes at Game Dev Academy are completely free and we're supported by our very generous school governors over at Patreon. If you'd like to become a Game Dev Academy governor and support our work as well as helping us to steer the channel in the right direction then use the link in the description on the Patreon page.