Hello and welcome to the Grand Line review, your source for everything one piece. My name is Liam and if you'd asked me to tell you the value of pi to seven decimal places, then I would say no. And today we are here to specifically talk about a little known arc that I and everyone else likes to call one no. Specifically, the wide array of incredibly mysterious plot threads that are currently dangling dangerously off the edge of the narrative. Because Oda has set up a ton of intriguing questions that we now have to answer. Or at least I hope we have to answer them because sometimes, you know, we don't do that.  None of those are particularly relevant to one O and actually just think about that's not true. The person in the hat is clearly related to one O because they're dressed entirely in one O gear but I'm sure we've talked about that elsewhere. Today I am more concerned with arc specific questions things that need to be resolved within one O itself rather than the grand scheme of one piece as a whole. And to begin this video discussion thing, we're going to start off with a quick round of King, Queen or Jack, a very simple mini game, the rules of which are as follows. I am going to draw a card from this here deck and it is going to be your job to guess whether that card will end up being a King, Queen or a Jack. Should you guessing correctly, then your punishment will be to subscribe to the ground line review, which will also result in consistent injections of one piece culture administered straight into your YouTube feed. Meanwhile, if you are correct, then you will be given a pair of horns and inducted into the beast pirates to serve Lord Kaido for all eternity. So which will it be, King, Queen or Jack? Make your choice now and we shall reveal the answer in three, two, one and bam, it's a Jack, also known as the most disappointing of face cards as well as the most disappointing of Kaido's calamities. So if you said King or Queen, then you know a thing to do and please do say hi in the comments below if you are a new member of the Grand Fleet, welcome. But if you did land on King, then I don't blame you because he all on his own presents a veritable gift basket of one O intrigue. First and foremost, we still have no idea what his race is. King is a member of this mystery faction of the one piece world, one which is heavily implied to be potentially extinct. I mean, it's quite vague. In the English translation, Big Mom States, there are still three races that I don't have in my country yet. One of them might have been lost in the midst of time, but you're still alive. The you're being King in this situation, essentially implying that King may be the sole survivor of whatever brand of creature he hails from. Creatures that have black wings in this perpetual halo of fire burning brightly right behind their heads, which is one of the most unpleasant characteristics I could think of just at my neck and are constantly on fire. I mean, maybe that's why King does wear his gim suit. Maybe it's heat resistant or something. Speaking of his outfit though, that's our secondary King mystery. His outfit is eerily evocative and perhaps even a straight up reference to impaled down. When comparing King to Magellan and Shiryu, these three share a very similar aesthetic with this professional dark full body guard. And while King does not have the impaled down coat of arms on himself as the others do, he does have these two square patches featuring a skull. Very intriguing because this exact same symbol can be found on the arm and collar of Shiryu. So at this point, there is next to no doubt that King has a connection to impaled down in some way, shape or form. Whether that means he was a former warden or even killed a former warden and decided that yes, that outfit looks cool and took it, this is definitely something that demands answering. And just to cap off the King before one oh ends, we also need to know his bounty. At this point, Jack, Queen and even Kaido's delicious numberos have been revealed, but for whatever reason, Oda has decided to keep King's exact bounty in the dark, potentially to be revealed at some sort of combat based dramatic moment. So give me that number. But King is a mere one character of Wano. And if nothing else, you could describe this arc as quite character sum. There's an awful lot of people doing an awful lot of different things. And while a lot of that can be hard to keep up with others are deliberately hidden from us. For example, hello Hiori, watch up too. Ah, you won't tell me. Fine, be that way, I didn't wanna know anyway. Hiori is such a strange character because for as goofy and as emotional as she can be, Hiori seems to act with a very strong sense of purpose. At the time of this recording, we have not knowingly seen Hiori since the end of act two, where she rather weirdly stated that she refused to meet with Kinamon and the others in order to avoid distracting them with frivolous feminine related sentiment. I mean, she didn't say that last part, but she may as well have. So we have two options here. Either Hiori is sitting in Ringo, just, you know, fingers crossed that everyone else is doing all of the work for her. Or Hiori has her own secret agenda to assist the raid. I mean, I personally think it would be incredibly unsatisfying for her to just sit out the climax and rock up at the end and go, you know, good job, guys. I'm glad I wasn't there to distract you. Plus I do find it very intriguing that Hiori has effectively refused to show herself to any of the characters who traveled forward in time. She met Kawamatsu, Zoro, and obviously spent a lot of time with Dendro, but due to quote, sentiment, she does not want to present herself to Kinamon, Momonosuke, Kandro, and Ryza, which, you know, cure the Toki conspiracy theories that I enjoy ever so much. But speaking of Toki, this is another thread that we need to solve. There is something very important we don't know about her and that point can be summed up with a rather simple word being why. Her motivations for traveling forward in time have been left completely in the dark. And now with every one related mystery I'll be posing in this video, I will admit that this one might not necessarily have to be answered during the Sark, just due to the fact that Toki and Odin are connected far more to the core of the One Piece Metastory than any of us could have anticipated. But this isn't one of those things that we can just, you know, leave. Toki had a very clear intention with what she was doing and I want to know what it was, which I think it's a simple request. For something a bit less wild shaking, we also have the question of the Kitetsu set. Many readers and watchers may have forgotten about this at this point, but very early on in Wano, we discovered the Nidaki Tetsu, the sibling sword of Zoro Sandaki Tetsu. And it can be very easy to dismiss its existence as just a bit of fun and flavor continuing to build and expand that world we love so much, except that in a really roundabout way, Odin made sure to have Luffy take the Nidaki Tetsu, seemingly simply for the purpose to have Zoro notice it for a second. And then later on at the tail end of Act Two, we have Zoro noticing it again for a second, even learning its name and its relationship to his own Kitetsu blade. All I'm gonna say is it isn't a mighty convenient that our Kitetsu set consists of exactly three swords and our swordsman, Mr. Zoro, happens to use exactly how many, one, three swords. Of course, what really threw me off is that Zoro did go on to inherit Enma, so there's currently no room for a second Kitetsu blade. And even if there was, the one to which Imonji is taking up the space for a third. Still, the Nidaki Tetsu is a strange minor story thread because other than show off that yes, it does indeed exist, there is very little reason for Oda to have taken it on this amazing journey that it went through. He could have just shown it at Tengyama's place and been done with it. So it's just another one of those things to probably remember. As is the Kuruzumi Clan. This is one of the more disturbing aspects of Wano actually and we've seen a lot of disturbing stuff on this island. However, this is the one part of the story that highlights that our supposed good guys may not actually be all that good after all. Because after a plot where the head of the Kuruzumi Clan poisoned his rival, Daimyo, in an attempt to position himself to be the next shogun before Sukiaki was born, we received a brutal, brutal massacre because this plot was discovered and as a result, the Kuruzumi Clan were purged by all, by which I do mean extraordinarily brutally hunted down and murdered, even those who had no affiliation with the plot like, say, Aruchi and the other Kuruzumi members who were children at the time. This is a pretty dark detail and it does leave the remaining families in very questionable positions, one of which are the Kozuki Clan who have been portrayed as the heroes of this Wano story.  And of course, the others whose names I don't remember right now, but unlike the names of those families, this is a question we should not forget. These past ruling bodies, including our beloved Kozuki Clan, were well and truly responsible or at the very least criminally indifferent towards this massacre and I don't know if that's something we're going to need to contend with during this arc going forward, but there is certainly another deep dark layer of Wano history that has been very underexplored. And attached to that layer is Kuruzumi Higurashi, the old lady who was forced to flee Wano or Elshi too would have been massacred. In any case, she had a very curious transformation via the Manamanonomi into a man who looks suspiciously like Golden Lion Shiki and the anime has all but confirmed that this is indeed Shiki because they've now shown him during this time and young Shiki looks exactly like the man who Higurashi turns into. By the way, slight tangent, the anime is very worth watching right now if you're a manga only reader because they are starting to add all sorts of stuff that actually expands the canon story of One Piece. Like it's actually at the point where I'm watching the anime to keep up with canon events because they are dropping some pretty serious stuff in what is technically considered filler. In any case, I would love to know when and how Higurashi interacted with Shiki. One of the stronger thoughts is that she may have been part of the Rock Spirits which also brings a connection to Kaido into the mix but I imagine that it was no easy task to get close enough to touch Shiki in order to save his body into the memory of the Mani Mani no Mi. Unless Higurashi used her feminine wiles to seduce the old Shiki but oh, good luck getting that image out of your head. You're welcome. Continuing with mysteries now, Onimaru, we both need to figure out what you are and why you are. Well, miraculously why you're introduced into the story. Right now Onimaru represents a very rare figure of One Piece which is the potential of legitimate supernatural powers. Which I mean, magic-y sort of stuff because he is a Komagitsune that is able to shape shift into a human form known as Gyukimaru and it really cannot be overstated just how weird this is even for One Piece. Magical creatures, they just don't exist. Sure we have a bunch of weird stuff like cowfish, panda fish, even fish fish but not even sea kings have these strange magical powers. It's just Onimaru right now which brings up the possibility that he is a devil fruit user because that's how these questions are usually answered and Wano is a huge hotspot for unexplained devil fruit consumption. Another sub-mystery is that we still have no idea how Kinamon and Ryza even got their devil fruit. At the moment they're just completely normal during the flashbacks and then after traveling forward in time they are now fruit users all of a sudden which is great but tell me how and when and why. Next up we're going to cover some manga mysteries by which I mean these are questions that cannot be asked without spoiling Act 3 of Wano for those of you who are not caught up. This basically means anime, you only watch this, I'm sorry guys but it's hard to make a video like this without addressing these. If you wanna watch something else that's fun here's a video, I promise it'll be great but for everyone else we are going to move on. First big thing we need to know who was that mysterious entity eavesdropping on Jinbei and Robin? That's something I frequently forget ever happened because it was just that one ominous panel and then it was never referenced again but here we clearly have someone lurking in the bushes just observing like a voyeur and many people have jumped to a ton of retrospective conclusions with this like perhaps it was Yamato watching the straw hats which sure that does make some sense but nothing has been explicitly stated yet. So the options are wide open for almost anything to happen be this person Hyori carrying out whatever it is she may or may not be doing or something more absurd is like Toki keeping a watchful eye on the future or even a character we have yet to meet or one that we do know and don't realize is on Onigashima as of yet. It was just a really weird panel and to join it we also have the companion silhouette from chapter 1004. I don't wanna talk about this too much because I bring it up a lot perhaps even to death during chapter reviews but this whole Kandro Odin thing was a huge red herring to take our attention away from whoever this is. This is a big question and it could very well be the same person who was watching Robin and Jinbei because the silhouettes they match as much as a silhouette can when you see almost nothing of them. Basically this person appears to be wearing a dark cloak which well it fits the tiny morsels of aesthetic information that we have available to us. Back to Yamato though man there's a lot to unravel here. Yamato possesses Odin's journal which clearly contains some wild information including whatever it is that has led Yamato to believe that Momonosuke is the one who is going to bring about the dawn of the world. A role that was previously assumed to be held by Luffy going from Pedro's whole K crunch. That's a big one and following the action pack climax of Wano I think that we should be ready for some series changing information spawning directly from the mouth of Yamato. Meanwhile one factor that still heavily eludes this arc is the location of Kaido's road Poneglyph. We've examined not one but two funky square rocks on Wano now one found by Brook in Archi's castle and one kept in the basement of Onigashima discovered by law. Neither of which is the road Poneglyph that we sorely need before leaving this island that is pretty non-negotiable. And one of the major reasons why we're on Wano in the first place is simply to pick up this information. So where is this thing if not in Archi's castle or Kaido's stronghold? Just as a side note it is interesting that Kaido keeps all of his Poneglyph separate. I suppose at the very least that does present a big mommening from happening here where one breach results in the theft of all Poneglyphs but now Basil Hawkins. Another question that may or may not have been lost in all of this recent rate hype is who is the 1% man? In chapter 990 Hawkins stated that the chances of a certain man surviving until tomorrow were a mere 1%. And just like any time we see a shadow or a silhouette the possibilities are almost frustratingly numerous. Common interpretations include Luffy, perhaps Kaido and even the startling idea of Diaz Drake who Hawkins was speaking to at the time may be acting as some sort of tragic foreshadowing for Drake's future within this raid. But to explore this idea some more I've made an entire video discussing who the 1% man could be. Very interesting stuff. So I look forward to seeing you there.


Welcome to the 33rd session and here we continue what we were doing in the 32nd session namely to carry out that operation between the two finite length sequences x and h to obtain y. We had obtained only one point in the previous session. But what we were trying to do is to establish a methodology. Let us put down the question once again just to recapitulate and to put ourselves in perspective. Consider with the arrow notation xn given by minus 1, 953 with the arrow at point 0 here and hn equal to 1 minus 1, 2 with the arrow at 0 here. And we had calculated y0 given a summation only over two points. Now we want to calculate a general yn. So we take for example a general n, y of n. Now you see let us write down the indices 2 over a large range. Let us write them down starting with minus 2 and let us write down x of k on top of that because x of k is not going to change. So it is minus 1 here, 9, 5 and 3 there and everywhere else it is 0. Now h of n minus k we need to reason this out. You see h of n minus k will become h0 when n minus k is 0 or k equal to n. When we increment k so for k beyond n we get values before 0 and correspondingly for k before n we get indices after 0. So let us for example put down h of 2 minus you see at k equal to 2 that is here. We put down h of 0 which is 1. For k after 0 we put down indices before. So indices before are all 0 so we get 0s here and for k before n we get indices after 0. So 0 here, 1 there and 2 here. This is how it is. And now we can calculate y of 2 based on this. We essentially need to look at the products of corresponding points. This point with this point similarly this with this and this with this plus 9 into 2 18 plus 5 into minus 1 minus 5 plus 3 into 1 that is 3. So 13 plus 3 which is 16. Now you know you get the general idea. You first put down whatever is at 0 at the point k equal to n. What was after 0 in h is put down sequentially before n in the same order. So of course you know at n you put down what was at 0 in h at n minus 1 you put down what was at 1 at n minus 2 you put down what was at 2 and so on go backwards. Instead of you see as you move forward in the sequence h you put the same values backward in h of n minus k on the k axis. And what was before so of course in this case there was nothing with all 0s before. So you keep putting those 0s after k equal to n. In fact we can see the same thing by a different line of reasoning. Let us now look at that. So for example we could choose to write down h of n minus k as h of first let us write h of n plus k. So h of n plus k is the same as h of k plus m. And remember here k is the index and n is a fixed integer. You are considering a particular value of n. Now h of k plus n is essentially h of k shifted backwards by n. And then we are making a replacement h of k plus n with k replaced by minus k. Now k replaced by minus k is essentially reflection about k equal to 0. So essentially what we are doing is you have this index of k here. Let us write down a few points there. And you make exchange here. We exchange minus 1 and 1. We exchange minus 2 and 2. And similarly minus 3 and 3. And so too minus 4 and 4. It can go on and on and on. So essentially it is a process of exchange. Exchange of corresponding positive and negative points. Now what may happen when you exchange it like this? You have shifted. Remember you have shifted the sequence backward by n steps. So now when you make this exchange, when you make this reflection about the point k equal to 0, effectively the 0 point which had moved to minus n would now go to plus n. And when shifting it backwards you would have kept the points in the same order with respect to 0. But now that order will be inverted. That is what we saw. We saw that the 0 point goes to n. Then the points after 0 go before n in the same sequence and the points before 0 go after n in the same sequence. So we have arrived at the same conclusion by a different line of reasoning. You could use whatever line of reasoning you like. But this is the essential idea. So let us summarize this. Essentially what we are saying is h of n minus k is essentially h 0 brought to n, h 1, h 2 and so on brought to n minus 1, n minus 2 and so on respectively. And similarly, h minus 1, h minus 2 and so on, 2, n plus 1, n plus 2 and so on respectively.  Now I have taken this for a fixed n. What will happen when I increment n by 1? The whole structure will move forward by 1 step. Increment n by 2, it moves forward by 2 steps. Once you have fixed this for a particular n, when you change the n, you are just going to move as it is. The structure moves as it is. You do not have to redo the structure every time. So instead of, if for example you had constructed h of 2 minus k, you were trying to construct y of 2. So you constructed h of 2 minus k. Now you want to go to h of 3 minus k. All that you do is whatever you were constructing as h of 2 minus k, you just put it forward by 1 step. Or if I wanted h of 1 minus k, I would have simply moved backwards by 1 step. So basically what I am trying to get at is that you could think of this whole h as a train and you could think of the engine lying at 0 and the engine is at position n now. And of course, all the other points are like bogies connected to the engine. The only thing is you have to think of the engine as being in the middle and the bogies on both sides of the engine. You know trains do run like that too. There is nothing wrong in having the engine in the middle of the train and pushing it. Little unconventional, but not impossible. So we have this train with the engine moving according to n and pushing all the bogies with it. That is the analogy which you should think of. And there is a fixed set of points. So therefore, this whole operation that I am talking about, I am now going to give this operation a name and I am going to use what I call the train platform analogy to explain the operation. I shall show you the entire operation for this particular sequence point by point and using what I call the train platform analogy. Let us do that next. In fact, what we shall do is to take this up systematically in a whole session because we want to illustrate this both for discrete and for the continuous independent value. So hold on until the next session where we shall use the train platform analogy to explain this whole idea. But before we go to the next session, let me at least complete one job that I need to. That is to give this whole operation a name. So we will give this operation a name, naming this operation. We will call this operation convolution that is the noun. We have heard this before, but I am just trying to repeat certain ideas. And the verb form is convolved. We will say we convolve two sequences. So we are saying we convolve the input with the impulse response to get the output and the operation that we are performing between the impulse response and the input is convolution. In the next session, we look at convolution in greater depth by using the train platform analogy. Thank you.


I hope to apply the skills that I acquire from here and the knowledge that I acquire back in my work environment. Knowledge and skills that I acquire can also be used to do some work in my community. I'm a journalist, so when I return home, I can put new perspectives into my work, how to shape the public debates. I make some change in my country, especially some services. The first thing I would do is try to be there, present myself as a tool to be used. Provide workshops for people that are in my industry or the professional area. Help my country to build a new democratic nation. Accessibility for people with disability. I want to build bridges, roads and panels and to see if people use all these infrastructures to increase the economy of the country. That's what I aim for.