Dragon Quest VIII. This was actually my first Dragon Quest game and my first RPG. I never knew a Dragon Quest was until I played this one. Back when I was a kid I used to subscribe to the American Shonen Jump magazine which was a manga magazine full of Japanese comics that I would get monthly. This is a nostalgia trip. Usually the magazine will be bundled with a little prize such as trading cards and sometimes game demos. So during fall 2005 I got my issue Shonen Jump in the mail that had a feature on Dragon Quest VIII and it included a demo disc for the game, showcasing the first town and dungeon and I played the hell out of this demo, beating it multiple times. Eventually I got the real game and the rest was history. Now Dragon Quest VIII had a lot of big firsts for the series. It was the first new game that was released after Square Soft and the Enix Corporation melded into each other and became the mucky pace known as Square Enix. It was also the first Dragon Quest game to release in Europe. Up until this point only North America got the localized versions. They even dropped the 8 from the title there and just released it as Dragon Quest, the journey of the cursed king so as not to confuse people. DQ VIII was also the first mainline Dragon Quest game on the PlayStation 2. No you don't count. This Dragon Quest game was a huge massive enormous leaping quality or the previous entry. Dragon Quest VII for the PS1. DQ VII was a good game but it was still using retro looking sprites for all the characters and monitors and we all know that sprites are old and boring and dumb and we can do better. Enter DQ VIII featuring stunning, cell shaded 3D graphics for the first time in the series. Dragon Quest VIII looked like a playable anime. The color balance, lighting, the architecture of the world it's all amazing to look at and seriously impressive for the time. I imagine that this was Toriyama's true vision for the series when they're making it way back in the 90s but they just never had a technology to bring it to life until now. With an art style like this the game is bound to be timeless. This was a major title for the PS2 and I still think it looks miles ahead of other games that release at the same year especially running in HD with widescreen support. So it's important to know that there's different versions of Dragon Quest VIII. Three versions to be exact. There's the original version on the PS2, the mobile phone port for iOS and Android and finally the 3DS version which released almost 10 years after the original. The PS2 version is the original version of the game and what we got in the West a year after the Japanese release was kind of like a deluxe version of DQ VIII being sold in this fancy cardboard slip cover which is not very common for games at the time. So you can tell this was a premium product. Square Enix actually made a ton of improvements dust for us which is crazy when you think about it. They did things like overhauling the menu system to look more modern while the original is basically using the same menu as the original DQ games. A lot of the 8-bit spell sound effects were replaced. They added a first person camera for closely observing important details in the world. We actually got a fully orchestrated soundtrack in the game while the Japanese version only had synthesized sound and the biggest inclusion in Dragon Quest VIII by far was addition of voice acting for all of the major scenes. Yeah, the original Japanese version had no voices. They completely dubbed the Western version in English just for us and the voices are great. They're all done by professional British actors they chose and they really gave the game that European fantasy feel that it needed. You what? It gives the character so much personality. Even some of the minor NPCs are memorable because of it. You want to get rid of. Absolutely one of the best features of the game. So the PS2 version is great. But what about the others? Well, there's the mobile port and you should honestly skip that one unless it's your only option. The game is running on a phone, which means a lot of corners needed to be cut. So all those cool features like the voice acting and orchestral soundtrack are gone. It's basically just the Japanese version of the game. The graphics were toned down a bit too.  This leaves the last version. The 3DS remake of Dragon Quest 8, which released a decade after the original. I am very conflicted on his version because there's a lot of new additions they added. Like a lot. The 3DS remake has optional faster battles, which I love. There's no more random encounters. The monsters are actually roaming the field now so you can avoid them finally. They added a photo mode with literally over a hundred different photo challenges. There's new dungeons, DLC items, new costumes, and they added two new party members, Red and Mori, who you normally meet during a story. That's not to mention additional story sequences that add so much more to the overall narrative and actually make so much sense and explain a lot that the original story only implied. That is a ton of content they added. There's so many quality of life improvements such as instant alchemy, the ability to save up skill points rather than have to spend them right away, and the mini map on the bottom screen for easier navigation. It should be a no brainer that this is the best version of the game. Well, there's a few things wrong with it, unfortunately. To start, there's no orchestral soundtrack in either version of the game, even the English version. It's all midi for some reason, which really sucks because the symphonic soundtrack really adds to the atmosphere of the game. But if you're brave enough to mod your 3DS, it shouldn't be a huge problem. The game also has a bit of censorship. In the 3DS version, they chose to censor some violence, humiliation, and the most terrifying thing of all, thighs. A lot of the sexy outfits in the game were adjusted to be more modest for our very sensitive eyes. Although the bunny outfit actually looks even more provocative somehow with an exposed midriff. So good job, whoever did this. But by far the biggest weakness of the 3DS version is the graphics. On the 3DS, the game is running at 240p resolution and they made so many compromises just to get it running on the handheld. The graphics are horrendously bad compared to the PS2 version. It's not even close. The character models all have less detail. The colors of the world look all saturated. There's way less trees and vegetation. The clouds don't move quite like they used to.  How on earth do you make a remake of a game? And it somehow looks worse than the original. I just don't understand. Putting this game on the 3DS was the biggest mistake they made. At this point, the new 3DS was already out and it was more powerful. They literally could have made it for that. It would have looked a lot better. Heck, they could have remade it on the Vita instead. That handheld was pulling off PS2 ports perfectly.  Okay, maybe I'm being harsh. It actually looks pretty decent compared to other 3DS games. But it could have looked better. And even though the visuals aren't great, I still play it because I'm a sucker for all the new content. It can't be helped. In the end, as much as a pain is me to say it, I usually prefer playing the PS2 version because a game like this deserves to be experienced on the big screen with these kinds of amazing visuals. And it is a tough call because the added scenes and features in the 3DS version make it an absolute joy to play. So make your choice based on what's most important to you. I tend to go back and forth depending on my mood. Man, if only Square and export this game to modern consoles and PC, that would solve all of our problems. We could have the good graphics and all the features from the original with the additional content from the 3DS port making for a perfect addition. Man, that would be such a good idea. I wonder why they haven't done this yet. I mean, it's not like they've been making remakes of every single other game that they've released on the PS2 or something. And it's not like this is one of the best selling games on the PS2 or anything like that. That sure would be a genius idea though, wouldn't it? Anyway, let's talk about the game. Dragon Quest VIII is a character-driven RPG focused on the individual party members and their struggles. Here, the crew is led by the main character, a former guard of Trojan Castle. I like to call him VIII because that was his default name in the demo. He is initially joined by his companions, Yangus and King Trod.  And this was all done by Duel Magus, a wicked gesture who infiltrated the kingdom and stole its greatest treasure. It's pretty straightforward.  He's very sensitive about his appearance and rarely ever goes into town with you out of fear of being attacked for looking like a monster. But this doesn't really affect the way he acts. He still pretty much bosses the main character around like a lackey, which makes sense since you do technically work for him. And Trod's most outward character trait is his affection for his daughter, Princess Medea, aka the horse who pulls your wagon around. Yeah, the princess is the horse and she still has her intelligence after being cursed and shown to be very brave protecting her father when angry townsfolk attack him. She will be really important later on in the story. You're also accompanied by Yangus, a former bandit trying to go straight. He's sort of indebted to aid for saving his life in the past, and he's just a great character. He's a ruffian with his cockney accent being voiced by a British comedian Ricky Grover. He's very lovable and he turns into a PNG image whenever he sees King Trod appear out of nowhere. King Trod and Yangus hate each other and it's really funny to see them constantly bickering and fighting for no reason. The team is eventually joined by two more party members, Jessica and later Angelo. Jessica and Angelo have their own sort of mini arcs that prompt them to join the players party. Jessica is a powerful mage whose brother Alistair was murdered by and she has issues with her mom due to her lack of being ladylike. So she joins you to kind of escape from home and kind of go on a revenge spree. Jessica is one of my favorite characters in a whole game for two very big reasons. Her personality and her great fighting abilities. She's a very headstrong and defiant person and definitely the most mature one out of the group in more ways than one. She's also a very powerful spellcaster slash whip user and has a habit of shooting giant fireballs randomly indoors which seems like a great idea. Angelo is awesome. He's a night Templar of the Maella Abbey who has a habit for gambling and getting himself into trouble in a nearby town. He's also a ladies man with a lot of charisma getting the affection of everyone around him. Hey no need to tell the whole world. I have a certain image to maintain with my admirers. His motivation is to avenge the Abbot Francesco who is again murdered by Dolmagus for some reason. He also has a brother who is head of the Templar guard named Marcello and he's a real piece of work. He hates Angelo with a passion and even through the party in jail while letting a creepy menacing clown man through the front doors no problem. So I'm not really surprised that Angelo wants to leave this place. Angelo uses swords, bows, and magic to fight with. Having four main party members is probably one of the best decisions they made for this game. Previous Dragon Quest games usually had at least seven or eight party members to choose from which could honestly get to be overwhelming while DQ8 only has four in the vanilla version at least. The 3DS version adds two more but I don't count them. They honestly feel like fifth wheels. These characters were originally in the story but they added them in the remake as party members just because they clearly don't belong in the game as party members and feel so forced into the story. Standing off on the sidelines, barely interacting with anyone, sometimes adding in their unwanted opinion, and not being acknowledged by anyone awkwardly. So yeah, they don't count. The OG party is the only real DQ8 party to me. Anyway, having four party slots and four main party members means your entire focus is just on these characters and their struggles, development, and equipment. It is a very honed experience building up these characters. The DQ8 team is so iconic and they have so much chemistry with each other. If you're ever lost or don't know what to do, you have the option of consulting your party and they'll talk to you and talk to each other. Their dialogue changes everywhere you go and every time a story unfolds. Even in cutscenes, you'll find that they have lots of interactions with each other. They get into fights, make fun of each other, and just overall feel like an actual group of friends which many RPGs fail to really get down and it's nice to see it's executed so well. And I shouldn't forget to mention Munchie, Ate's mouse companion who is always sitting in his co-pocket and can be used to squeeze into tight spaces to help to crew out in different ways. Throughout most of the story, you and your friends are chasing after but he remains one step ahead of you wherever you go, taking the lives of innocents in a seemingly random manner. Dragon Quest VIII starts off really strong, allowing you to explore the town of Fairbury to look for clues and honestly it's one of the best towns in the entire game. It's actually one of the best RPG towns I've ever seen as a matter of fact. Fairbury is such a lively town it teaches you how to explore and discover early on which is the bread and butter of this game. This game is all about investigating and finding secrets and there's just so much going on in every corner of town. It's absurd. Just from exploring, you find that there's a well in the corner of town that you can climb down and at the bottom there's a treasure chest with a leather shield inside saving you from having to buy that one yourself. Some bookshelves in town have books you can read, explaining the lore of the world you're in, characters in town talk about events that occurred recently. There are some treasure chests that are locked which hints that you might want to come back later in the game when you're gonna lock them. You can raid people's cabinets and steal their things which is a very heroic thing to do. Oh look, a pot lid and we can equip it on Yangus to use as a makeshift shield. There's a lot of cool things to discover in these towns and probably the standout feature of the game is the way the game uses NPC dialogue to give hints to the player of where to go next sort of guiding the player's sense of discovery. You see there's no quest log in the game you pretty much have to pick up clues from town's people and remember them for later and this is the most organic and realistic way for adventure game to guide the players around. Early on you'll hear towns people talking about rumors regarding certain people of interest, the shopkeeper in the back of the weapon store tells you rumor about a key that can open any chest and another shopkeeper town will tell you a secret location of a recipe to make the ski but only if you go behind the counter and talk to him at the right time of day. Oh yeah this game also has a dynamic day and night cycle as time goes by the clouds in the sky move around the sun sets and it actually turns the night in real time which affects quests the kind of monsters you encounter outside of town and even the sleeping patterns of the town's people. Yeah the town's people actually go to sleep at night is that immersive? And the game keeps track of every town's person in the game they all move around depending on the time of day and reveal different tidbits which is crazy attention to detail. For example during the daytime this woman keeps complaining about her ring she lost and how she can't find it. Well at night you can hear her husband at the end talking in a sleep about how he lost the ring by dropping it in a well by the castle. Little things like these make players aware of a larger world on the outside as way later on in the game you actually do find a town with a castle and there is a well with a ring inside it that you can return to the lady. There's so much life in every town in Dragon Quest 8 and this just isn't something people talk about enough. The towns feel lived in and realistic with unique NPCs that just feel authentic they each have personalities some of them have funny things to say and a story of their own and this is just one town the game is full of towns like this and if you decide to go back to these old towns for whatever reason the NPCs actually change their dialogue based on the events that occurred later on in the game as if they expected players to go back. Every time I play this game I always discover something new I didn't know about before it's like all the towns and cities in the game are connected to each other and every NPC is aware of a world on the outside sometimes you find characters referencing events and people from other towns when you visit them too it really makes DQ 8's world feel like a real world with history and connections and consistency I always feel compelled to talk to every character in the towns and explore every house just to find a hint or some tidbit of lore fleshing out the world of Dragon Quest 8 it's phenomenal how much attention goes into these little details this franchise just knocks it out of the park with its towns and people it's one of Dragon Quest's greatest strengths for its storytelling and it is just highlighted in the first town so strongly but the game really shines when you leave town and go outside here's whoever introduced the Dragon Quest 8's vast overworld with hills trails and trees to explore this game has an amazing adventure atmosphere that just begs you to explore there's this excellent majestic soundtrack for when you roam in the countryside and it's really great with the orchestral theme there's roads hidden pathways and it all feels so seamless there's also cows on the side and when you talk to them you get a bottle of fresh milk all packaged up like like the cow just hands you the bottle like it's the grocery store or something finding your way is simple there's signposts telling you what's ahead and you have a map with topography to kind of analyze and figure out where to go it's really nice having a system of discovery like this when most games nowadays are obsessed with giving you mini maps and flashing markers telling you where to go it's almost like the game is letting you get lost and find your own way and if you decide to go off the beaten path there's plenty to discover like treasure chests dungeons and towns the UI overall is very minimalistic all you have is a compass a map and your wits it's all about using these few tools you're given to get lost and find your way around game developers are just now realizing how refreshing this feeling is with newer open world games toning down the UI to put a focus on the world and the atmosphere around you and this world has atmosphere this game is a true open world adventure where you travel an entire world every mountain and cottage you see off into the distance you can actually go to and there's secrets all around maybe you get to a waterfall cave and notice a hut on top of it so you decide to venture around and discover a mysterious old man living there who asked you to find his toolkit it's this kind of moment to moment discovery and adventure that really sells the experience for me on the overall we also run into these enemy encounters random or roaming depending on the version you're playing and the monsters of dq8 are just amazingly expressive and super creative we all know dragon quest monsters are great but dq8 introduced some really good ones we've got a fencing fox with a little hat and cape he looks like puss in boots there's a gorilla that looks like one of those Kipling monkey keychains a chain nine who throws these spike dog collars at you just a lot of great designs but let's talk about how we beat up these creatures now dq8 is turn based and in the ps2 version it's honestly a little bit slow because of all the flashy animations which makes me appreciate that 3ds is fast battling all the more for the most part your typical dragon quest combat system you attack defend, use magic abilities and items but what's new is you can psych up which takes us to turn to sort of boost your attack power and you can keep psyching up until you get to a state of high tension to deal a huge amount of damage which is strategic for bosses I just love turn based combat it's strategic, it's fun anyone can pick it up and get good at it and it can be very challenging when it wants to be plus the game lets you live out your fantasies of fighting hipsters in the street you'll run to a lot of monsters and get plenty of practice fighting and leveling up when traveling from town to town which brings us to the leveling system dragon quest 8's progression system is based on skill points which is new for the series and very simple and easy to grasp basically each character has five different skill sets three different weapons one unarmed and one personality skill set hero has courage yangus has humanity angel has charisma and jessica has sex appeal every time you level up you have a chance of getting some skill points that you can use to upgrade each set which will reward your character with additional abilities for battle and on the field leveling up any of these skill sets unlocks you some very useful abilities such as the underpants stance or the puff puff which allows jessica to seduce the enemies usually my go-to is focusing on just one weapon for most of the game while putting enough into a special skill to get whatever moves you want for aid, swords and spears of grade yangus does really well with axes and sights jessica is best equipped with whips and angelo should use bows it's a really simple system that anyone could grasp but it works well and it's really fun leveling up characters in ways that suit your play style a bit into the game you unlock the alchemy pod which allows players to combine two or three items to create a new item using a recipe recipes can be found in books or from talking to people or you could just google them like a cheater yeah you don't actually need to find a recipe in the game to make something if you already know the recipe nothing is stopping you from just making things if you know how to you could also just blindly guess and come across something it's honestly great that they give you this kind of freedom to experiment around maybe on a second playthrough you might remember some recipes from before and be able to make some high level equipment early that's a lot of freedom they give you as soon as you get the alchemy pod you'll already have enough materials for a new whip or jessica and a thief scheme allowing you to go back and open any chest you miss which is a great setup the alchemy pod lets you make stronger medicinal herbs and consumables any kind of weapon and armor you can think of accessories and you can even make a different kinds of cheese for munchie using the fresh milk combined with something extra for an added effect so this game's main structure boils down to the player visiting new towns and meeting new characters of problems that intertwine with your own quest prompting you to help them you finish your side stories find out where your mark is headed and soon you're on the road again fighting danger and resting wherever possible and this is a common feeling you'll have that have an adventurer roaming around from town to town sleeping where you can constantly on the move it's a cool vibe you get you might have to help a depressed king see his deceased wife one last time or find a legendary jewel for a female bandit just to get closer to your goal this will usually result in some dungeon dive where you traverse a cave or tower with some admittedly creative puzzles that actually get you thinking three dimensionally followed by a boss fight some of these bosses are great there's a guy named Don Mole who's a giant fat mole with sunglasses and a southern accent who sings and you need to get a magical harp back from him that he stole the bosses in the game are often challenging and require a lot of critical thinking to beat and many of these story locations can be tackled in different order due to the open world nature of the game especially when you unlock your own ship which can sail and dock anywhere it becomes a true non-linear open world adventure game at this point and it's not just all fighting in the game there's plenty of downtime to be had and lots of distractions along the way a major one being the monster battling arena on the way to the town of Pickham you'll run to this weird Italian guy named Mori he asks you to find infamous monsters to recruit so he can watch animals fight for his amusement it's pretty easy finding them since it gives you memos clearly indicating where they each located and you can find them roam in the area you find these monsters, you beat the shit out of them and then they willingly join you out of respect for you yeah you don't cram them into a little ball and kidnap them from their habitat against their will they actually choose to follow you, isn't that nice? after that you get to join the monster arena there's different ranks to monster battling and it's all about making your way to the top you can even summon your monster teams outside of the arena which is cool this world has many things to do there's a guy named Dodgy Dave who tasks you with making different things they offer me pot for money there's mini medals all over the place to collect which you can trade in for prizes you can adopt a pet saber cat to ride around faster there's some optional dungeons for you to die with unique bosses and you can also check out the bunny girl show in the basement at the back of red hotel at night man what a bunch of sick freaks oh merciful goddess pardon my sin come on up there's plenty for everyone just look at the size of them someone tell that moron to get down in front I can't see the stage oh this one isn't jealous at all I'll give Dragon Quest Day one thing it's very realistic I don't think a medieval fantasy world would actually exist without a place like this for the locals to go to let's see what the bartender has to say oh so the slot machine to the right of the flower box is loose oh yeah there's a casino in the game there's actually two one to pick them and one in backer at at the casino there's slot machines roulette and a bingo game you can play the main draw here is the prizes there's a handful of prizes you can redeem with casino tokens that you can't get elsewhere you can get the falcon blade a sword that attacks twice in one turn for 10 000 tokens and the liquid metal armor which is one of the best armors in the game for 50 000 tokens so yes your crippling gambling addiction is finally useful for helping save the world for once one of the major locations you go to when you start exploring the world is the kingdom of argonia where you meet princess midi as a ranged fiance prince charmless it's charmelee let me tell you something they have created the worst NPC in any video game ever with this one this guy is the worst most unlikeable most punchable douchebag i've ever seen i've never seen a video game character so hateable aside from this fat piece of shit he is absolutely the worst dragon quest character ever at this point you and your party need to get the magic mirror which is the royal treasure of argonia and in exchange king clavius wants you to escort his son through the royal initiation which requires him to kill an argon lizard and present its heart as proof of his worthiness to the throne oh he's worthier right worth even ass whooping indeed i am you uneducated buckkin the problem is he's a cowardly piece of crap who keeps running away from every fight when he's not doing exactly one damage forcing you to do it yourself he's also a rude cruel little brat who thinks he's better than everyone else just because he's a prince even his father is sick of him by now every time you defeat an argon lizard he's not satisfied with the size of the heart and makes you fight another until you get a giant one and in the end he just ends up buying a heart from the supermarket which means you just wasted all the time hunting lizards for nothing just a completely unlikable character and i gotta give it to them for making a character so hateable because that was definitely their intention poor medea having to marry this guy and speaking of medea i just want to mention how heartwarming her relationship with the main character is in this game i mean she's a horse for most of the game but throughout the story she's still seen as being as courageous as her friends you start to get to know her more as the game progresses though when you go to sleep at the end after different story sequences she'll actually talk to you in your dreams through some astral projection here she has a bit of a heart to heart with eight every now and then revealing some previous history between her and the protagonist as well as their feelings for each other and there's always a song playing call over the sorrow which fits the dreamy longing feeling of the scene so well and these sequences you really get to learn more about her personality and they really help to show the love that the two share for each other they're honestly really great together and the added scenes in a 3ds version of the game showing how they met and how age started working at the castle only further cement that feeling even though the main character doesn't talk you can somehow understand his feelings for her just from his actions and everyone else's dialogue alone they reveal so much about her as the game goes on which makes sense because the game really is all about her if you think about it she's even in the logo if you look closely it is just so sad that you know she's gonna have to marry that asshole charmless in the end because of a promise her grandparents made it's overall a very sad and well done subplot in the game and only further motivates the player to hurry up and free her of the curse after meeting and helping many people across the journey gaining new abilities and honing in another target you eventually do face off against do make us an epic battle deep in the dark ruins and he's pretty tough too with a monstrous demon form and just when you think you've defeated him and that the game is finally over the true story has only just begun it turns out there's a greater evil behind the treasure trodding castle the god bird scepter there actually has an immortal ancient evil being inside of it that was controlling do make us and controls anyone wielding scepter and his plan is to free himself by using the scepter to kill all seven descendants of the original stages who sealed them away years ago with Rylas Alistar and Aber Francisco being the three of them did you get all that see this is where everything in the game comes together and all the mysteries surrounding the treasure finally starts to make sense and it is up to the player to get to the remaining stages before the evil dude to protect them though it doesn't always work out that well let me tell you this game is really sad and depressing at times there's so much regret and tragedy related to the last few stages you visit these character interactions are so well written and easy to relate to that you feel the loss that these characters have to go through I honestly think that this is one of the most depressing dragon quest games it gets to be a little too much at times the cheery adventure atmosphere that you've gotten used to up until this point starts to get a whole lot darker when you get near to the end game and have to experience more sad stories towards the end every event in the game just makes sense and you'll find that you have to backtrack to earlier parts of the game where certain details that you just can pay attention to have way more significance than they let on and I love the game for that how it uses the world it created to tell a cohesive story the party eventually finds a god bird named Empyrea who flies into the heart of darkness where you experience one of the creepiest dungeons in the series and find raptor and the lord of darkness the evil being behind everything though his first form is incredibly wimpy and silly looking like this is the lord of darkness and his voice is the best part just listen to this I've been waiting for you what you're so ridiculous sounding this is the final villain you should not have much trouble with this weirdo at least until he grows a triple chin and evil goatee looking like a purple Gabriel Egliseus now this is an actual threat at first you won't even be able to scratch raptor and when he's the embodiment of type 4 diabetes you have to use the god bird sector like 7 moves in a row to summon the souls of the sages of old just to be able to weaken him which is pretty tedious at first takes at least 10 minutes then the real fight begins and it'll take a lot of skill and determination to beat him but by this point you'll probably be such a high level that you'll have omni heal and kazing for multiple characters that'll let you consistently heal everyone and revive anyone who falls immediately I honestly had the party AI on and just kept periodically hitting the X button on the controller while eating a sandwich and I eventually beat him this is a very difficult game if you haven't noticed when you defeat raptor and the curse finally breaks and princess medea and trode are for turn to the former selves in a very heartwarming scene although trode berry looks any different than before he's just not green anymore but he's still like two feet tall and has the exact same face which I think is hilarious and even the characters notice this and it's funny because he was always so conscious about his appearance when he always just looked like a little troll medea however that's a sight for sore eyes she's finally a human again and now she can marry her fat fiancee at last yay also the curse on the whole kingdom goes away and everyone who's turning to a plan gets turned back and of course this call is for an obligatory celebration feast scene where we get a slideshow of still pngs with this ridiculous confetti filter over looking like windows movie maker it's like they ran out of money in the budget at the end and said hey screw it let's use this fancy new program microsoft paying to be done with this and so the day is saved and everyone goes about their lives then we fast forward a few months and eight is already the captain of the world guard for his bravery and rescuing the kingdom but he also has to escort medea to his novella cathedral on her wedding day to prince fatso and you can tell it's making him upset even though he doesn't say anything the other party members pretty much spelled out how he's feeling so you go to her room to escort her outside to the carriage but not before raiding her underwear drawer of course he's a hero after all now here's where it gets interesting dragon quest eight actually has multiple endings depending on certain requirements that are met in the standard ending the crew goes to the church with medea and sadly find out that they can't attend the wedding because fatboy won't allow any commoners to attend so the following morning after staying at the inn yangus clears away for eight to crash the wedding only to find that she's already escaped with king trode who finally grew a spine decided he wouldn't let traumas marry medea the dude was literally about to let a guy who almost gave him a lashing marry his own daughter could have spoke up sooner if i'm being honest eight and medea have their little ending together where they run away into the distance and traumas is finally confronted by his father by lying to pass the initiation the group splits up in the end and you have a happy ending which is where the post game begins the post game explains so much about the journey that was hinted at for so long it basically brings you back to the right before fighting rapthorne except the world is slightly different this time as there's a new area we can visit caledrogovian sanctuary which changes the trajectory here the party discovers a village full of elf-like dragon people known as the dragovians and we find out that eight is actually one of them who's cast away as a child so the main character of dragon quest eight is actually part dragon and his whole time munchie was actually eight's dragovian grandfather in disguise looking over him which explains why munchie was so intelligent his name is chen mui oh i get it it's like an anagram of munchie that's clever yeah wow there's such a development looking back there were actually so many signs pointing to this that i'm surprised i didn't realize it sooner this game is very very good at foreshadowing it doesn't so subtly that playing it a second time you notice so many things you didn't notice before anyway the crew is tasked with completing the dragovian trials by the lord of the dragovians and after passing the trials you find out the truth from chen mui that eight's father was actually king clavius's older brother who fell in love with the dragovian princess and munchie is extremely racist so he naturally objected and they both died of a broken heart or some shit i don't even know but what this really means is that eight is actually their rightful heir to the throne of argonia and he's charmos's cousin what this dude is your cousin are you kidding me i must take after his mom so chen mui gives you your father's argon ring which is proof of your royal lineage and when you refight the raptor and boss and get through all the events all over again this time you're able to visit clavius the night before the wedding and show him the ring he naturally gets pretty mad at you for trying to usurp the throne and tells you to go away however the following morning during the wedding he changes his mind i have reconsidered you are the rightful groom so in the end eight and medea actually get married and we have a happy ending between the two i love this ending dragon quest eight is like a fairy tale in video game form and this is the perfect ending for a game like that it's so nice to see medea saved by eight and the two of them getting to be together finally and almost makes you cry doesn't it well don't cry yet there's actually a third ending in the 3ds version when you present the ring to clavius at night and tell him that you don't like medea he'll assume that there's someone else you like and in the morning instead of medea showing up for the wedding it's jessica what so yeah in the 3ds port they made a new ending where you marry jessica just because obviously over the years people prefer jessica as the best dragon quest waifu and the dq team knows it which is why they added this to the game in this ending jessica is wearing medea's wedding dress which she uh certainly fills in and it makes that she loves you and medea is there wishing you well no hard feelings this ending also has more dialogue and his overall way longer and more detail in the other endings which is why i kind of like it the most plus i like jessica a lot so i don't mind this one bit it really shows you how much of an rpg this is because they allow you to make a choice of who you want to marry in the end because you spend about as much time with jessica as you do medea's and some people will rather marry jessica so i give them props for adding to this ending to the game whatever ending you choose they're all good in their own ways and they close off the game nicely and that's it that's dragon quest 8 there's a reason they're resonated with audiences at the time and made so many people become fans of the series to me it is hands down the best rpg of the playstation 2 era and an adventure that just doesn't get old i hope you enjoyed my retrospective on dragon quest 8 and what it means to me tell me your dragon quest 8 story in the comments too i'd really like to hear them thanks for watching and i'll see you next time


YouTube team keep it clean I had to start this video off with a little drink because you know exactly how thirsty Us Ravens fans can be when anybody of any type of significance Possibly hits the open market and even though Rokhwan Smith. He's not on the open market He apparently wants to be traded now It's not every day that one of the best linebackers in NFL Requested trade now. How did we get here? How do we get to this point where Rokhwan Smith is like, hey I want out of Chicago. Well, according to him the bears They they've been in talks about a contract extension But the bears apparently offered him something that was absolutely Disrespectful to him and absolutely disrespectful to the the market the linebacker market So he was like, you know what no, I'm straight. I'm good. I don't want to be here in Chicago anymore And maybe how cold it gets up there and how windy it gets up there. Maybe has something to do with it But anyway He apparently wants to be traded now this thing could go one of four ways One of the ways it could go he could hold out and be like, you know what? I'm not gonna play now Usually that's the way that it doesn't go. Well, unless you leave you on bill They've been one of the only people that actually stuck with that But other than that it just that really doesn't hardly ever happen people have they threaten it But they don't usually go through it another thing that could happen. He could be traded He could be traded to another team end up on somebody else's roster if the bears got a significant enough offer Another thing that could happen He could end up playing and they don't come to a contract extension and he either after this year He becomes a free agent or the bears put him on a franchise tag and they try to tag and trade him Another thing that could happen is if he's like, all right. Well, you know what? Let's just let's do it and the bears come back and they offer him a better deal and they end up reconciling this Relationship and they just move forward. He gets his money from them. They keep their player and everybody's happy Well, which one will it be? We'll see now for that fourth option if they were to end up keeping him Because we've seen this happen in the NFL. We've seen it happen this year in the NFL where players will request a trade Debo and players that I hope would request a trade DK Metcalf and They end up Resigning with their current franchises. So if that ended up happening, it would be very 2022 but how did the Ravens fit in and all of this? Well, I mean, you know, I know as soon as I saw Rokwan Smith was not technically available But he was looking for a trade It's like you just knew the Ravens would be interested in in him And I just feel like the Ravens they they are gonna do their due diligence They'll check around cuz they that's one thing about the Ravens. They may not make everything happen But they will certainly check in on somebody Nothing has come out that said that they checked in on him. I know I've seen a lot Seen a lot of people say that they expect if he does get traded they expect to see a report Oh, the Ravens were close But they just couldn't come to an agreement with the Chicago Viz on the terms of the trade and whatnot Cuz we we have seen that so many times before not only this year certainly this year but over the years So it's like a lot of Ravens fans have become numb to the reports like that, but they do still sting Every time so a lot of Ravens fans are not numb to it, but anyway With Rokwan Smith should the Ravens trade for a Rokwan Smith What could he do for this football team?    He has good speed He's a good blitzer Josh Bynes he has smarts because of course he's been around a game for a long time like he played with Ray Lewis He he filled in for Ray Lewis. So he's been playing for a long time But anyway, Josh Bynes, he got smarts. He's a pretty good tackler But just imagine Josh Bynes mixed with Patrick Queen Rockwell Smith There you go. Rockwell says somebody got good speed. He can cover. He got smarts here and he can tackle So that they two for the price of one well actually the price of Rockwell Smith will be a little more than for two but anyway he Would instantly upgrade the Ravens defense in a heartbeat. No questions asked Rockwell Smith would make the Ravens defense significantly better and he would provide them with so much less question marks At linebacker because right now obviously the Ravens they still have a lot because we're wondering.  Is that gonna be the same case here in the pros It's Patrick Queen really gonna take that next step as the Ravens inside linebacker because again It's so much riding on him this season in the Ravens I I don't feel like they're 100% in Patrick confident in Patrick Queen And that's not based off of anything that I'd say that I feel but that's based off of their actions They went out and they went all in trying to sign a Bobby wagon again. They even offered more Then the Rams did but Bobby wagon. Hey, these dudes just went Super Bowl. I Live there. I'm from there. So easy decision But I'm glad the Ravens tried to make it a little bit hard for but anyway So they tried to sign another lineback and then they end up bringing back Josh Bynes bringing them back and that could just be for just Stay ready. So you ain't got to get ready Or it could be like hey Patrick Queen struggled last year and then he got benched for Josh Bynes So let's just have Josh Bynes ready just in case he struggles again. So it could be that So I just I don't feel like they're 100% confident in Patrick Queen I hope Patrick quit man for his sake for the Ravens sake for everybody's sake I hope Patrick Queen really goes off this year. I really do but I just wonder What a linebacking unit would look like with Roquan Smith and Then Patrick Queen Roquan Smith being a Batman Patrick Queen being a Robin because again He was robbing at LSU and then when he became Robin last year seemed like a thing just slowed down for him So much and he played so much better. He was so much smoother. He played with so much more confidence Now another scenario with that Because with with Patrick Queen I wonder if if the Ravens were to trade for Roquan Smith, what would happen with Patrick Queen Would they keep Patrick Queen this year? I mean obviously next year. I don't I would not see any scenario where Because the this is the year where they had to pick up his fifth year option so I don't if they were to trade for Roquan Smith, then that would be Patrick Patrick Queen will be on the way out and They were they will probably end up trading him the following off-season possibly even now, but definitely the following off-season Because I just wouldn't I wouldn't see them keeping him to especially because they would have to pay Roquan Smith and If you paying Roquan Smith, you're not gonna pay Patrick Queen as well so that can that could be something but Roquan Smith would definitely help because Roquan Smith is a sure tackler and that is something that has been lacking on his defense Oh, it's been lacking for sure and because with with tackling y'all have seen it like with lying back is with cornerback Sometimes with safety, so if you don't tackle well Then it just it makes everything so much harder for your defense and it makes everything so much easier for opposing teams offenses If you don't tackle well an eight-yard slant can turn into a 60 yard touchdown But you're more chase last year. Yeah, I did too And we've seen it time-to-time last especially last year guys just not Tackling but if you tackle well, it makes everybody's job easier reason being give you I'm gonna give you example You got to play safe instance. You got it. The the offense is running the running play. They don't want to run and play Quarterback hands it off to the running back running back. Well going right up there. Okay, linebacker season Roquan Smith season Tackles them boom to your game at the most. All right, cool But safe instance same play Running back runs it up the gut Roquan Smith or whoever is that linebacker? They missed the tackle. All right, so now it goes from just a two-yard game Then it turns into a five-yard game now It's up to the corners in the secondary for them to make a tackle And they're not usually always as physical as linebackers some of them can be but most of them are not so now they got to make the tackle and If they don't make the tackle bone that looked what could have been a two-yard game It could turn into a six-yard game It could turn into a eight-yard game. It could turn into a 14-yard game all because of miss tackles So with a Roquan Smith, he would give you that short thing at inside linebacker as far as tackling now Situation is everything when it comes to so many players In the shuck the Chicago I don't know what I just said just now, but the Chicago Bears have not been a good team Um, they've been struggling for a little minute But he's still been balling and So you you just think about man He's balling on a bad team imagine what he would do on a good one So he would again he would certainly be an upgrade for the Ravens Um, I don't expect them to trade for him if they did cool But me if they were to make a trade I would rather them look for a trade in another area Of the team because with a Roquan Smith, I feel like he'll be nice He'd be excellent for Ravens excellent for Ravens defense give would give them a nice boost but Would he really put them over the top like that? In a question that I posed to some people yesterday Just something for you to think about Roquan Smith like and I'm still hoping for Malik Harrison. I'm still hoping that him and Patrick Queen They could end up being a nice little one-two punch like a little one-two combo But when Malik Harrison, I just I don't know what his role is gonna be and I don't even think the Ravens know what his role is gonna be So we'll see what happens there because again, they did bring back Josh Bines So it's not just about Patrick Queen. It's about the other linebackers, too And they they brought back Josh Bines So they did not feel comfortable yet moving with their young linebackers moving forward with their young linebackers Because they brought back something that was gonna team back in like 2012 and what? Like like Josh Bines been around for some different generations of football and shout out to him, too By the way for it's still bringing it still playing Wow, that's crazy. But anyway, um, I Just I don't know man I would rather them if they would make a significant move. I would rather be somewhere else Somewhere that I would really feel like would really push the Ravens over the top Oftentimes when whenever a defensive player becomes Available and I know he's not technically available available But he tried to make himself available whenever defensive player comes available and even when the Ravens trade for a defensive player Nobody's ever like oh man That guy's gonna take away snaps from the young guys. Oh man that that guy Oh, he's gonna stunt such and such growth on defense. You don't never hear that That there's never even a conversation It's never a conversation But if you talk about another Position and you talk about making a significant trade to acquire somebody there Who's gonna be really good player? Then that's when a lot of chatter comes about. Oh, it was stunt their growth. Oh It was gonna take away snaps from them and I would just rather those assets be put into Lamar Jackson And then Greg Roman. Hey because he's the offensive coordinator instead of the assets being put into Mike McDonald now, I just because I feel like with I Feel like we could still use more on that side Then on the defensive side on offensive side than the defensive side because I just again my thing is We always talk about making life easier making people's jobs easier And this it would be a luxury move really it'll be a luxury move They got Roquan Smith and hey if they got them a kudos to them Um, I don't think that they will I know again I'll it's all the top destination for Roquan Smith is Baltimore Raven. Da-da-da that It would be a good move But I would just rather Then make a move on the other side of the ball now if they did get him They had to pay him He had to come to a contract extension with him Well, I mean you didn't don't technically have to but I'm sure he wanted that agreed upon Raven he was already they got a certain contract that they need to get figured out First before you go dish the contract to somebody else to line back or ain't even on your squad Oh, you you you got a contract that's kind of important right now that you you best take care of ASAP or else Next offseason this thing I'll get ugly If that contract ain't handled in the next three weeks But before the season starts so about oh, yeah, what a next month if they handle it in the next month This next offseason could get real ugly It can get real ugly because once franchise tags start coming into play. Oh That's what stuff can get real nasty So let's just hope it doesn't get there but Roquan Smith wants to deal The more Jackson wants to deal priorities


How's it going everybody? DatoDoi here back with another Dragon Ball Fighters video. We are once again going to be covering the final DLC character for season 2 of DBFZ, that being Dragon Ball Super Broly. Now you may have already seen yesterday's video going over the text leaks for this character, but thankfully we got the visuals very quickly this time around instead of having to wait a couple days or even a week. We just got them on the very next day, so super grateful for that. And I'm also super excited because these scans are really, really good. Let's not waste any more time than we have to and go ahead and jump right into Broly's first scan, showing off a couple of things, obviously his overall power rating that they give him as well as his normal form that he will be playable in. Thankfully like we covered in the text leaks, it does appear like Broly is going to start off in his Saiyan armor, in his Wrath form. This is really cool for me, obviously this was one of my favorite forms Broly took in the movie. Love the Saiyan armor, super excited that we're going to get to play around in that form for at least a little bit before we jump into any of the other forms he takes, because it does look like there is going to be a couple of other forms. Before we leave this page though, I do want to talk about the image of Broly we see on the right next to his drawing that we'll see on the character select screen. And that appears to be something from his intro, I'm only assuming that because he hasn't lost the armor yet and it does look like he's charging in and rage. Maybe my hunch right now is his intro might be him charging off of the ship or something like that. Maybe something similar to Broly's intro that's already in the game where he just comes sliding in and poses. I could definitely see that working for this character as well. Moving on to the next scan, we are treated to a better look at Dragon Ball Super Broly's level one, aka Blaster Meteor. Basically Broly just gets super angry and starts firing off Key Blast everywhere. It looks really good for a level one obviously. I do wonder about the gameplay implementation of this, it looks like Broly has to hit a head on charge first, so it might be similar to like a cooler DHC level one where he comes out plays a little animation and then you can go into the next one. Or I mean there's always a chance that Broly just does the move solo, but it does look like you need that initial start off first, so that's going to be something to keep in mind when trying out Broly for the first time and trying to DHC with him specifically. Other than that there's not too much to say on this page other than the fact that it looks like Broly does go into his Super Saiyan form here in the picture. It might be just an issue with the quality or just the green lights messing with my eyes, but I don't know something about the hair looks a little bit more Super Saiyan to me and I have gotten a lot of people telling me that oh every form of Broly is playable after the level one you actually get the Super Saiyan form. What I haven't seen is any conclusive evidence that that is entirely true but I do think it would be a sick thing to have in the game and I could definitely see them doing something like this, especially when we jump into the third scan page here. This page contains images of Broly's level three where he powers up to his final rage form and lets go of that giant mouth beam that we've read about in the text like super good looking level three. I like how just from the image down here you can see that they're trying to capture that same wild movement that they had in the movie. That was one of my favorite parts about the move there so I'm really glad to see that kept at least in part in the animation. Now another thing with the scan is it is by far the most confusing and the one that I've gotten a ton of different stories about from people. I don't know if they've got it translated or they've read a translation somewhere. It's really confusing so I'm just going to tell you exactly what I've heard from random people and there's really only two different stories I've heard. One is Broly lands the move, he rips off his armor, does the mouth beam and as long as you land the level three you will continue to play in the legendary super sane form but if you miss the level three your armor still breaks and then you get to play as this weird full power version of Broly but he still has that wrath state going on. Very confusing. Broly is looking super buffed up there in the bottom left though it does look a little weird. The other thing I've heard is that when you land the level three you do get that power up and you do keep the armor off but Broly always goes back to this standard hair version. He just loses the armor and gains an attack buff. The text on the bottom does roughly translate to after your meteor super you will keep an enhanced power and the armor will stay off or something like that but it doesn't say anything about the super sane form. From what I could tell I really have been looking for somebody to just give this a full in depth translation but it does seem even then the wording is kind of loose. Right now though my thoughts are that you will always come back to this weird Broly form down here instead of the legendary super sane form. I don't know if I'm right about that or not. Again it could also be the fact that if you hit the level three you keep the legendary super sane form. The only thing that has me worried about that is it looks like part of the level three is Broly making contact with them. I don't know how you could miss a level three and then Broly will burst his armor off in a cutscene. I don't know maybe I'm missing something but I'm just a little worried you know. Either way though I do really like the fact that Broly has an evolving look over the course of the game so after you land a level three even if it's the case where you don't keep the super sane hair I do like the idea that he stays buffed up and does receive that extra damage boost. If we take a look at a lower quality scan but one that's a little more center you can see that DBS Broly does appear to have the same standing light as the legendary super sane Broly we already have which is very good that normal has super long reaching range and it's very easy to abuse so that is nice to see. A lot of people have also been using this picture to compare sizes and it does appear that Broly even in this buffed up form is slightly smaller than the other Broly we have which is overall a very good thing in this game. The other Broly we have is a little too tall for his own good and kind of gets fuzzied out. Not saying this one won't get fuzzied in fact he most definitely will but at least it won't be as bad. And with that image that concludes this month's look into Dragon Ball Super Broly. There were no release states anywhere around this imagery at least as far as I can see so the release state is unknown as right now it did say coming soon so we can only assume what that means but I'm thinking maybe sometime next month maybe we get one more Fee Jump maybe it covers a dramatic finish or not because again a dramatic finish was also another one of those things that wasn't really touched upon here so I could see them definitely taking out another V Jump article and using that to promote Broly again and again I'd like to apologize for this video taking so long to get out but I would be lying if I said that this wasn't one of the most confusing scans I've seen in a long time. Add all the Broly hype and the fact that he looks so good and it's covering multiple different forms that he could be taking and I just got a ton of different comments like oh this happens no this happens or translation say this or it doesn't say that it was super confusing whatever does end up happening though one thing is for sure Broly will get that power up boost and some form of a transformation I just don't know what that transformation is going to truly be at the end thank you guys so much for watching let me know down below what you think of Broly visually do you like the choices they've made for him so far visually do you like the fact that he gets that buffed up form without the armor and maintains the wrath I hair do or do you not just let me know all of your thoughts down below in the comments other than that while you're down there if you like the video and the channel want to stay up to date on all things Dragon Ball Fighters as well as more Broly news down the line make sure to the like button and subscribe and check out the other videos up top if you want to watch even more right away I've been Dr. Dwayne thank you so much for watching this video and I will see you in the next one


Please note that Tia's story contains references to infant death, bereavement, suicide and depression and may be triggering to some people. In 2021, we released our first ever comic strip, Journeys Through Mental Health, illustrated by Sabah Khan and made in partnership with Richmond Fellowship. The following is an animated version of one of the three stories featured in the comic, based directly on real interviews with young people with lived experience. This story started when there was a tragedy in the family. I'm one of 14 siblings. I'd rank myself in the middle. I'm not the youngest, but I'm also not the oldest. My mum and dad are still together, still married. It is quite unusual, but they're still together. I was really bad in between 2011 and 2012, and ever since then it's just been a struggle. I'm 21 now. The first time I remember when things were starting to go wrong was when I lost my nephew. He was my sister's first, the first nephew out of all the siblings. A couple of days before he passed away, he was running around my mum's front room, jumping from one side of the sofa to the other side. He was only five. I was probably about 11, maybe 12. I remember it like it was yesterday. It's something that's always been over my shoulder, something I can't forget. I remember one of my closest best friends came to see me after school. She had no idea what had happened. I went straight up to my room and she came upstairs with me. I sat down and cried for hours and hours. His name was Jay. I couldn't understand how it had happened and where he had gone. Nothing was registering. Then one day out of the blue, I decided to try and take my life, but I didn't succeed. At the time I thought, well at least someone knows now. My mum booked me an emergency doctor's appointment and I was put on medication for depression and anxiety. Over time I met someone and decided to move away from my whole family. I believed that he would have helped me, could help me. In fact, he did, for a while. But then things started to change within the relationship and I was around when he lost his dad. I was close to his dad. That was another death that I took.  A few years back I lost someone else, a best friend of mine. We'd lost touch. We used to call each other wifey. She had decided that she didn't have the courage to stick to life anymore. I blame myself. I blame myself for a while because she wanted my help and I wasn't there for her. Through all of that I didn't get any counselling. I was still back and forth at the doctors, getting medicated for depression and anxiety. Every few weeks they'd try different types and various doses, until the medications stopped having any effect on me whatsoever. It was only then, just the year before last, when they finally referred me to a mental health clinic. It was the mental health clinic that diagnosed me with a borderline personality disorder. There's no medication that can treat a personality disorder. I was given distress tolerance support and I was shown lots of coping mechanisms. But none of them actually helped. I met someone not long ago and we've been together for a little while now. He asked me to marry him a couple of weeks ago. I thought that would have changed things, but I still feel a part of me is not. I guess I don't feel enough for anything. I've tried to walk away so many times. I've tried throwing everything away because I don't feel good enough. But I'm trying to stay supported. I've gone without it for too long. I'm with a BPD support group now. In some ways we can all understand each other. We can all relate to how we feel. It has its ups and downs. Sometimes it can be triggering. But other times it helps to make you feel less alone. It makes you feel like you're part of something. That you're not the only one struggling in this way. And that there are others out there too. I've always had my mum, dad and sister by my side too. Mum has always been there. Wow. She's never given up on me. But sometimes I just like to be on my own. If I'm at my mum's and she has a spare room, I'll just sit up there. They don't understand why I want to be alone. Well, I think if you're in a family of 14 like me, being by yourself can be a healing space sometimes too, right? I'm with the council project now, which is part of Richmond Fellowship. If I could speak to a person who's feeling like I felt, in my honest own opinion, I would advise you to get help before it gets to the point where you can't. We know that finding routes to mental health support is not easy, but there are still ways. Tia found solace and comfort in community groups and in shared experience. The human condition in all of its diversity has so many shared overlaps. Getting support can help us see that. At the very least, it can be comforting to know we are not alone. This comic is based on interviews with young people with lived experience of mental health issues. The names and physical appearance have been changed to protect their privacy. Journeys through mental health is each other's first comic strip created out of conversations we've been having with young people with lived experience of mental health issues. If you or anyone you know are struggling with mental health issues, there are resources on our Spotlight page on young people in mental health. The address is www.eachother.org.uk backslash young-people-and-mental-health.


Hello, we continue from where we stopped last time, recall that last time we discussed Kronecker's theorem, namely if alpha is an irrational number and you take multiples of alpha, alpha 2, alpha 3, alpha etc., and take their fractional parts, these fractional parts are dense in the interval 0, 1. We proved this theorem, but the Weyl's theorem considerably sharpens classical theorem of Kronecker. Let me explain this to you. You take this list 3.6, the fractional parts of multiples of alpha and you look at the number of elements in 3.7, fractional part of alpha, fractional part of 2 alpha, etc., fractional part of n alpha. How many of these lie in a specified closed interval a, b? So, take a closed interval a, b and think of each time you take k alpha and it is take its fractional part. Think of it as an experiment and in the first n it rates of this experiment. How many times does this fractional part k alpha hit the interval a, b? So, it is like a game of dots where it is a linear dot board and the bull's eye is the closed interval a, b and in the first n it rates namely equation 3.7. k n is the number of hits in the interval a, b, number of points in 3.7 that lie in the given interval a, b. Then k n by n is the frequency with which you hit the bull's eye and you take the limit of k n by n as n tends to infinity. It is a asymptotic relative frequency with which these numbers enter the specified interval a, b. And 3.8 tells you that this asymptotic relative frequency is precisely the length of the interval. So, suppose for example, if the length of the interval is one fourth then the last equation 3.8 says that approximately one fourth of the numbers in 3.6 they lie in the closed interval a, b in the long term. Of course, the first few several iterates anything can happen, but eventually in an asymptotic sense roughly one fourth of the elements in 3.6 will appear in the interval a, b if the length of the interval is one fourth. So, now we see that Wiles theorem is a quantification of Kronecker's result. Kronecker's result is a corollary of Wiles theorem and it is a considerable sharpening. We want to prove Wiles theorem following the treatment in this book by Andrew Browder, Mathematical Analysis and Introduction, Springer-Walagh 1996. Now, Kai will denote the characteristic function of the closed interval a, b. Now you take the fractional part of j alpha and whether this fractional part of j alpha lies in the closed interval a, b or not that is decided by the value of the characteristic function Kai evaluated at brace bracket j alpha. If this value is one then the fractional part j alpha has landed in the interval a, b if it is 0 if it landed outside the interval a, b. So, now how do I count the number of times the elements in 3.7 land in the closed interval a, b simply add the values of the characteristic function at these points and that will exactly be K n. K n by n is the arithmetic mean of Kai fractional part of alpha plus Kai fractional part of 2 alpha plus dot dot dot Kai fractional part of n alpha 3.9. So, this suggests that we should look more generally for any given integrable function f of x we should replace the characteristic function Kai by f and we should look instead of 3.9 we should be looking at 3.10 we should be looking at the arithmetic mean of f of fractional part of alpha plus f of fractional part 2 alpha plus dot dot plus f of fractional part n alpha that let us call that expression ln of f. Let us look at theorem 3.5. So, let alpha be an irrational number and let f of x be a bounded Riemann integrable function on 0 1. The averages 3.10 converges point wise to the integral 0 to 1 fx dx. In particular I could take the function f of x to be the characteristic function of the interval a, b then I get exactly what I want then I will get that limit as n tends to infinity 1 upon n the characteristic function evaluated at these fractional parts brace bracket alpha the average is exactly b minus a the integral of the characteristic function of an interval is the length of the interval. So, we get the displayed equation 3.11 that is exactly what we wanted to prove we wanted to prove 3.11 instead of proving 3.11 we will prove this more generally we will replace the characteristic function Kai by a general Riemann integrable function f and we will prove that the right hand side is integral 0 to 1 f of x dx. It may be a little puzzling to you why is it that instead of proving a specific result we simply make life more complicated by replacing the characteristic function by general function we will see that this generalization is easier to prove rather than the specific example.  Obviously ln f is linear ln of c 1 f 1 plus c 2 f 2 is c 1 ln of f 1 plus c 2 ln of f 2 the second important observation is monotonicity f and g are real valued and f less than or equal to g implies ln f less than or equal to ln g these are two important properties that will be heavily used in the proof of theorem 35. Let us as a special case do a simple calculation let us verify the correctness of theorem 3.5 for some innocent looking function f of x what function am I going to take exponential of 2 pi i k x where k is a integer let us do it for this special case f is a one periodic function f s period 1. Now, why have I chosen this particular f x if you think about it if you take the function f of x and evaluate it at these values the brace bracket g alpha what are the brace bracket g alpha it is simply j alpha minus square bracket g alpha square bracket g alpha as an integer and exponential of 2 pi i k times an integer is 1.  So, what we have done is that we have calculated the left hand side of 3.11 instead of the characteristic function I use this exponential function the left hand side happens to be 0. Now we must calculate the right hand side the right hand side is integral 0 to 1 x of 2 pi i k x let us assume that k is not 0 and I immediately get that this is 0. So, the theorem 35 has been verified for the special case when the function f of x is the exponential function e to the power 2 pi i k x we assume k is not equal to 0 what happens when k is 0 when k is 0 the function f is a constant function function f is a constant function these l n's are all 1 and the integral is also 1 and theorem 35 is trivially true when you take k equal to 0. So, we have proved 3.13 and f is the exponential function e to the power 2 pi i k x. So, the theorem has been established for the special case and so by linearity it will be true when I replace f of x by a linear combination of these exponentials x of 2 pi i k x when I take linear combinations of these things what do I get I get trigonometric polynomials. So, the result has been proved for trigonometric polynomials trigonometric polynomials of period 1. So, far we have been working with trigonometric polynomials of period 2 pi how do I pass on from a trigonometric polynomial of period 2 pi to a trigonometric polynomial of period 1. For example, sin x is a 2 pi periodic function, but to make it a 1 periodic function I rescale the variable x. So, instead of looking at sin x I will look at sin 2 pi x instead of looking at cos x I will look at cos 2 pi x. So, passing from a 2 pi periodic function to a 1 periodic function simply means scaling the variable x to 2 pi i x. So, now when I take linear combinations of these I get trigonometric polynomials of period 1. Now, remember that as a corollary to failure's theorem we have established that when f of x is a 2 pi periodic function on the real line and epsilon is greater than 0 then I can find a trigonometric polynomial of I can find a trigonometric polynomial g x of period 2 pi such as supremum mod f x minus g x is less than epsilon. So, I told you now simply replacing x by 2 pi x will convert it into a corresponding theorem for 1 periodic functions. So, now we use this simple idea. Then now we take epsilon greater than 0 b arbitrary then there is a 1 periodic function g x such that sup 0 less than or equal to x less than or equal to 1 f x minus g x less than epsilon by 3 that is 3.14.  I am going to add and subtract a g.  Now, f x minus g x is less than epsilon by 3. So, when I integrate it over 0 to 1 this last piece is clearly going to be less than epsilon by 3.  So, I said because of 3.14 first and the last summands are both less than epsilon by 3. So, now we need to look at the middle summand what are the middle summand mod ln g minus integral 0 to 1 g x dx. Let us focus on this. The added advantage of this is g is one periodic trigonometric polynomial and the result has been proved for one periodic trigonometric polynomial. So, this expression goes to 0 as n tends to infinity. So, there exists an n naught such that this expression is less than epsilon by 3 for n bigger than n naught. And so, all three pieces are less than epsilon by 3 for n bigger than n naught. So, we have proved the theorem. So, this completes the proof for one periodic continuous functions. So, theorem 35 has been established for one periodic continuous functions. But now we wanted for all Riemann integrable functions. So, from continuous functions we must pass on to Riemann integrable functions and that is going to be very easy the moment you do one little exercise. And what is that exercise? That exercise has been described as theorem 36. Suppose f from 0 1 to R is a bounded Riemann integrable function. Then given any epsilon greater than 0 I can find two continuous functions g and h from 0 1 to R such that f of x is sandwiched between g x and h x on the interval 0 1. Second g 0 will be equal to g 1 h of 0 will be equal to h of 1. Third condition integral 0 to 1 the top minus the bottom one integral 0 to 1 h x minus g x will be less than epsilon. So, let us prove this theorem. Let us see how to prove this theorem. It is a exercise, but I will give you some hints as to how to go about doing this exercise. Of course, we are not going to stop with this we are going to extend g and h as one periodic functions that is exactly the reason why we ensure condition 2. Because g 0 equal to g 1 and h 0 equal to h 1 the one periodic extensions of g and h will be continuous. Therefore, I can use the result that we have proved for g and h. So, first let us select a partition of the closed interval 0 1. So, 0 equal to t naught less than t 1 less than t 2 less than t n equal to 1 and let us select this partition. So, that the upper Riemann sum minus the lower Riemann sum is less than epsilon by 3. Capital U f and capital L f are the upper and lower Riemann sums of f with respect to this partition. And as usual when you study Riemann integration we introduce these terms upper Riemann sum lower Riemann sum and we talk about this measure the partition or the norm of the partition and capital M j and little m j are the supremum and infimum of the function on the j th sub interval closed interval t j minus 1 to t j for instance and capital M and little m are the supremum and infimum of the function f on the entire interval 0 to 1. So, that we get this chain of inequalities little m less than or equal to little m j less than or equal to capital M j less than or equal to capital M. Now, we consider the step function. So, what is the upper Riemann sum? The upper Riemann sum is simply the Riemann integral of a step function. So, let us take the step function which assumes the value capital M j on this sub interval t j minus 1 t j. If you integrate the step function h naught you are going to get the upper Riemann sum capital U f. Similarly, integrating another step function I will get the lower Riemann sum. So, what you do is that you start with this step function h naught and we start modifying it appropriately to get the requisite continuous function h. How do we modify it? We are going to choose an eta bigger than 0 and the eta will be specified very soon. What we will do is we will cut we will take this interval t j minus 1 t j and we will cut a small piece from the left and a small piece from the right. So, we will look at t j minus 1 plus eta t j minus eta equation 3.15 and we will define h of 0 and h of 1 to be both M and on this sub interval t j minus 1 plus eta t j minus eta we define h of x to be equal to h naught of x. So, the function h x agrees with the step function over a very large part of the interval 0 1 namely on each sub interval it agrees with h naught except for a small tiny piece that I cut out from both the ends. Now, what we have is that we have a defined a continuous function h on the union of all these sub intervals 3.15 as well as the 2 end points 0 1. Now, how to proceed to proceed from there is very easy we can define the function h of x in whatever way we want on the remaining intervals t j minus eta to t j plus eta. So, I urge you to draw some pictures and see what is going on. So, the interface point is t j and I cut out a piece from the right and a piece from the left. So, on this open interval t j minus eta to t j plus eta the function h of x is not yet defined and I must define the h of x over here also. So, that it becomes continuous you must continuously join it that is all that there is to it and you can do it in whatever way you want as long as the integral is small. The contribution of the integrals from these pieces must be terribly small. So, let us do the following. Let us take the point t j. Let us see the interface point t j and declare the value of the function to be 2 m at this interface point t j. And then now we have to define it on the pieces t j minus eta to t j and t j to t j plus eta simply join them by line segments simply join them by line segments and you will be through and this function h of x will be greater than or equal to f of x. Similarly, you can define the other function g x starting with the lower Riemann sum take the associated step function modify the step function as I explained instead of working with capital M work with little m instead of working with capital M j work with little m j you do the same thing. Now, what you will get is that what is the difference between h x and g x the difference between h x and g x on the interval 0 to 1. When you compute this integral on those pieces on those pieces 3.15 it is going to be capital M j minus little m j times the length of the interval and then what happens is that you get if you add over all the j's the contribution of this integrals from those intervals 3.15 will be in total less than u f minus l f what will be left over we have to now look at the contributions from these open intervals t j minus eta to t j plus eta h x minus g x and I am summing over j, but remember that this difference is going to be this h of x is going to be at most 2 m this g of x is going to be at least twice little m. So, this difference is going to be at most 2 times capital M minus little m and then you are going to add the lengths of these intervals and then you are going to take into account the length of these intervals will be 2 eta. So, all in all this contribution from this sum is less than 4 n eta times capital M minus little m. Now we could have chosen the eta so small at the very outset. So, this whole thing is less than epsilon by 3. So, if you do that then this thing is less than epsilon by 3 this integral from 0 to 1 h x minus g x d x is less than epsilon by 3 and we would have proved the result that we are looking for. So, theorem 36 has been established and this exercise has been worked out except for some details such as drawing some pictures which I urge you to do ok. So, now let us see how this helps in completing the proof of Herman Weyl's Equidistribution Theorem. So, let us take a bounded integrable function f of x and let epsilon greater than 0 be arbitrary. Select g x and h x as in the last theorem.  I will add and subtract a g x term.   So, this will be less than epsilon this last piece will be less than epsilon. And so now there is an n such that the middle term is less than epsilon for n bigger than n 1 why because g is one periodic continuous remember we have proved the theorem for one periodic continuous functions and so that. So, this middle piece will be less than epsilon for n bigger than n naught. So, we get the 2 epsilon plus ln of f minus g now you must use monotonicity of ln f minus g is less than epsilon and so ln of f minus g will also be less than epsilon and we get that the whole thing will be less than 4 epsilon or something and the proof of Weyl's theorem is completed. So, this concludes the proof of Weyl's theorem and I think this is a very good place to stop this capsule. Thank you very much.