In chapter 83 of A Wise Man's Fear by Patrick Rothus, there's a scene in which Quoth and his friends talk about riddles, and Quoth mentions that his father used to give him incredibly difficult riddles so that he would spend hours looking for the solution only for his father to reveal that he had made up the riddle, and there was no answer. One of his friends replies that this was a cruel thing to do to a child, but Quoth says that no, that it was fun. He explains that the harder the riddle is, the more you learn on your way to the solution, and if there is no solution, well, then you could learn forever. And to me, this is the heart of mathematics, trying to solve endless riddles and seeing what we can learn from them. Getting to the solution, if it even exists, is secondary. And for that reason, I have a special love for the unsolved problems of mathematics, like the Riemann hypothesis, the Navier-Stokes equation, and of course, the Collatz conjecture, also known as the 3M plus 1 problem. This problem is famous, at least among certain nerds, because it is incredibly easy to explain, and yet no one has been able to find the solution. It goes like this. So pick a number, any number, and then what you're gonna do is that if it's even, you're gonna divide it by two. But if it's odd, you're gonna multiply by three, and then add one.  And here's the thing. Whenever we do this, we find that we eventually reach one, at which point we go up to four, and then back to one, forming an endless loop. But does it have to be that way? I mean, for example, 82 starts a sequence that grows all the way up to like 9,000 or something like that, and then it comes down. But maybe there's a sequence that never comes down. Or maybe 4 to 1 is not the only cycle. Maybe there are other cycles out there. But if they exist, no one has been able to find these sequences, and the conjecture is that they don't even exist. We've tested every number of like 3 quintillion or something like that, and indeed, every single one eventually came down to one. But this doesn't prove that it never happens. It just proves that if it happens, it happens with some really, really big numbers. Veritasio made an excellent video covering the history of this problem and why it is so hard, and one of the comments stood up to me. Everyone here, but maybe I'll be the one to find the solution. Yeah, and it's really funny, because it's true. At least for me. At one point, I thought I could solve it. And of course, that's silly, right? Because if the solution is ever found, it will be via a very skilled mathematician who has spent years learning. But that doesn't mean we should let them have all the fun. Here's a thesis of my video. You should try to solve this problem. In fact, all of us should try to solve open problems once in a while, not because any of us will be the hero that finds the solution, but because if you try, if you honestly try, you will learn so much, you have no idea. That's why for the third summer of math, I want to try something different. I want to give this problem an honest try and show you how it goes, mistakes and all, and see what we can learn in the process. Spoilers, I was able to find a connection between the collage conjecture and the salations, the branch of geometry that studies how shapes fit together. And from there, I was able to create an algorithm that lets me find any finite sequence in the collage stream. For example, if I wanted to find a sequence that increases by three over two three times, but then decreases by three over four once, and then increases twice, but then decreases four times in a row, but those times by one over four, then here it is, this is that sequence. And by changing one variable, I can find infinitely more sequences with this exact behavior. Pretty cool, huh? And the link is in the GitHub, so you are encouraged to upload your improved versions, especially if you include cool ways to visualize it. And yes, I know that someone else must have found all of these things already, but I bet you that he didn't make a YouTube video explaining it. For this challenge, I will not look up anything about the collage conjecture nor mathematics in general. I will only use what I already know, because the fun is to figure things out on your own. And if I see all the dead ends other people have already reached, it would spoil the fun of getting there myself. But this also means that if I make a mistake along the way and I don't catch it, that's it. That could make everything that comes afterwards wrong as well. And I fear that the first comment is going to point something extremely obvious I missed.  But you shouldn't be the one to discourage yourself. You shouldn't be your own poly. So let's do this. Looking at the collage sequences, you can see that if they ever share a number, they become identical from that point on. So we can arrange the sequences into a tree like this one, whose trunk is the sequence 16, 8, 4, 2, 1. And then if the conjecture is true, all the other numbers are somewhere in this tree. Some of these branches actually stop branching, and they go on forever as a single line of numbers. And they are always made by some power of three, multiplied by higher and higher powers of two. These branches are not relevant for anything for the rest of this video, but I just wanted to mention them so that you know that I didn't forget about them. Let's establish some terminology. These three is a graph. Graphs are made of vertices connected by edges. Most numbers are only connected to two other numbers, the one before in the sequence and the one after. But some numbers are connected to three numbers, because they are the point where two sequences meet. These vertices are very special, and for that reason they need a special name. And since I've heard the word node used when talking about graphs before, that's the word I'm gonna use. Apologies to all the graph theorists out there if there was a better word I could have used. I didn't know about it. Now, something very important is that after another number, we always have a node. That's because if we do 3n plus 1, where n is all, we always get an even number. But that means we could have also gotten to it by halving another number, like how 16 is 32 over 2, but also 3 times 5 plus 1. But I don't like this condition of saying where n is all. Our running theme in this video is going to be that we want formulas and equations that work whenever we plug any integer number into them. For example, all the odd numbers are always one more than an even number. So they can all be written as 2n plus 1. And so when we multiply by 3 and add 1, we get 6n plus 4. This means that all the nodes in the collapse tree can always be written as 6n plus 4. This fact will be extremely important to the point that I would not call this the 3n plus 1 problem, but the 6n plus 4. Since I was already focused on the nodes, I began looking at their separation. And I noticed something really interesting. Sometimes there was a single vertex between them. But sometimes there were two vertices. And I couldn't find a single instance where this didn't happen. And from that little observation, I made my own conjecture. The distance between nodes is 1 or 2. And I set out to prove it. Notice that by this point, I have completely lost sight of the collapse conjecture. But that's fine. Sometimes you have to do side quests to advance the campaign. Okay, so if you are in a node, there are two possible ways you could reach another node. You could divide by two some number of times until you reach the next node. Or you could divide by two some number of times until you reach an odd number. At which point, you know for a fact that the next number in the sequence will be a node. Now we can write my conjecture more formally by saying that these three equations always have solutions. This one represents when you divide by two and you reach an odd number. This one represents when you divide by four and you reach an odd number. And this one represents when you divide by four and you reach another node. These are called theophantine equations named after Diophantus of Alexandria, an ancient mathematician who wrote many books about how much he loved integers and how much he hated fractions. To the point that mathematicians said like, okay, dude, we get it. If you like integers so much, then whenever we are looking for integer solutions to an equation, we are going to call it theophantine. Just chill. Simplifying these equations we get n is equal to 2k minus 1 over 3. n is equal to 4k over 3. And finally n is equal to 4k plus 2. If my conjecture was false, there should exist some number n for which no integer k makes any of these three equations true. A node made using such a number would need to be divided by 8 before reaching an odd number or reaching another number of the form 6n plus 4. Let's look at this table where I've calculated the value of n in each equation for each value of k starting in k0. As you can see, there are many fractions in this table. And that means that those values of k are not solutions for those equations. But before we jit them into the zone like Diophantus would have wanted, look, this number here starts at minus 1 but goes up by 2 every time. And this one starts at 0 and goes up by 4 every time. And that means that every third number, they will be multiples of 3. And that 3 will cancel with this 3 in the denominator, leaving us with integers. In this case, we will get all the odd numbers. And in this case, we will get all the multiples of 4. And then finally, this equation always gives us integers, but they are always 2 more than a multiple of 4. And that will give us all the even numbers that are not multiples of 4, which are the only numbers we didn't have already. And so with that, we have all the numbers. And so this means that my conjecture was true. Can we get a scoreboard? It is very easy to compete against their people because they cannot earn any more points. For every number you give me, if I make a node with it, it will be part of one of these families of nodes. So let's give them names. If n is odd, it will be a Stark. If n is a multiple of 4, it will be a Lannister. And if n is even but is not a multiple of 4, it will be a Targaryen. We can represent each kind of node as a sort of puzzle piece, and the collat streak can be made by combining them. I was editing this video and I realized that I should have explained how these styles work. Okay, so this represents a node. And then this notch represents a connection to a node number. And this knob represents a connection to an even number. That's why Stark and Lannister nodes end with a circle because they connect to other nodes through odd numbers. But Targaryen nodes have this moon-looking thing at the bottom because they connect to other nodes through even numbers. Okay, so let's go back to the video.  And I'm a man of my word. Unless someone has already discovered them and gave them some boring name. Anyway, using these tiles, we have transformed the collats conjecture from a problem in number theory to a problem in geometry, specifically in tessellations, which is a lot easier to visualize. This is how the collat streak looks when we use these tiles. Beautiful, isn't it? But we are not limited to only what we can see or what we can find in the collat streak. We can just start placing random tiles together, and we don't care about the numbers, not yet anyway. And so, for example, these tiles can represent these sequence of nodes. These tiles can represent these sequence of nodes, these tiles, these sequence of nodes, and so on. You get the idea. We need a name for these sequences of nodes that are independent of the numbers. So I'm going to call them constellations, because I like the idea of the collat streak as a huge starry sky above us. And we are just looking for patterns in the stars. This actually reminds me of Feynman diagrams. These are drawings of the different ways that particles could interact. But Feynman realized that if he gave a precise mathematical meaning to each element in the drawing, he could transform these drawings into integrals. And the solution of each integral tells you how likely that process is to happen. Something similar happens with these tiles. Each tile represents a number. And the position of the tile tells you how it is related to the other numbers. So it should be possible to transform every sequence of tiles into a single deophantine equation. And the solutions to that deophantine equation would tell you where to find this pattern in the collat streak. To figure this out, we are going to have to find formulas that tell us the relationship between a node and the next node in the sequence. First, let's analyze Targaryen nodes. I know that if I divide by 4, I reach another node. So we have 6n plus 4 over 4 is equal to 6s plus 4. And so we just have to find integer solutions for this equation. And to do that, I'm just going to use Wolfram Alpha. I know I said I wasn't going to look up anything about mathematics, but Wolfram Alpha is just like a fancy calculator. It does things that I could do on my own, but they would take too long, and it makes this video shorter. Okay, so using Wolfram Alpha, the solutions are that n is equal to 4a plus 2 and s is equal to a, where a can be any number. So any number from 0 up to infinity that you put in these equations will give you a Targaryen node. So these two equations actually define the entire family of Targaryen nodes. Neat. For start nodes, the equation is a bit more complex because we have to divide by 2 and then multiply times 3 and then add 1. But when we do the solutions are n is equal to 2a plus 1 and s is equal to 3a plus 2, it's larger than n. Oh, I see. So yeah, these are the nodes that actually make the sequence increase in value. Interesting. And finally, for Lannister nodes, we have that we divide by 4 and then we multiply times 3 and then we add 1 and all of this is equal to 6s plus 4. And we find that the solutions are that n is equal to 4a and s is equal to 3a. But wait, before we use this to try to find a constellation in the tree, we need to make sure that the constellation we are looking for will actually exist somewhere in the tree because I don't know, maybe there are some mathematical restrictions like maybe there are never five start nodes in a row or maybe the sequence L, S, T, S, L never happens. I don't know, something like that. To see if this happens, we have to check if the equations of the nodes are always compatible with each other and they are, they always are. There are nine possible combinations and we check for integer solutions in the same way we already did. I'm not gonna go over them, but if you want to check them for yourself, they are on screen right now. The important thing is that there are no restrictions. There's no reason any kind of node couldn't be followed by any other kind of node, even itself. And this means that whatever constellation you make with these styles, most exist somewhere in the collage tree and we can develop an algorithm to find exactly where. But to do that, we have to tackle a slightly different problem, the infinite constellation of start nodes. This lack of restrictions is dangerous when it comes to start nodes because the other nodes always decrease in value. So there's an inherent limit to how many of them you could have in a row. But start nodes always increase in value and there's seemingly no reason why we couldn't have an infinite sequence of start nodes and such a sequence would never come down to one. Does this prove that the collapse conjecture is false? Not at all. There is a limit. Let me show you what. Let's say that we were in a start node given by a number a0 so that the node can be written as six times two a0 plus one plus four. Okay, then we know that the next node will be written as six times three times a0 plus two plus four. But then if that next node is itself a start node means that there most exist a number a1 such that the node can be written as six times two times a1 plus one plus four, which means that two times a1 plus one is equal to three times a0 plus two. And then if we solve for a for a1 we get that a1 is equal to three over two times a0 plus one over two. Okay, but then we can do the same and then we get an a2 that is this and an a3, a4, a whatever. We can do the same process any m number of times. Luckily, I had already solved many problems like this when I was learning how to solve differential equations using infinite series like the Frobenius series. Basically, all we have to do is see what is happening at each step and then generalize the pattern. For example, we can see that this number is just getting multiplied by three over two each time, but it started as three over two. So it's just three over two to the end. And then this other number is also getting multiplied by three over two, but it started as one over two. And then we have to add this other number, which was calculated in the same way, except we multiply by three over two one less times. So then we can sort of like open it up and we see that it is a series of sums. And so we cannot represent it with just this single thing. And then we can just find the solution by using Wolfram Alpha, of course. And then we get this. Am is equal to three over two to the m times a0 plus three over two to the m minus one. This is an exponential Diophantine equation. And Wolfram Alpha wouldn't give me the solutions. So I had to find them myself like a person. But once I found them, they felt pretty obvious. They are just a0 is equal to two to the m times b plus two to the m minus one. And then a m is just equal to three to the m times b plus three to the m minus one. And this number b can be any number from zero to infinity. And that might seem confusing, but it makes perfect sense. That means that this constellation made of m plus one star nodes doesn't exist in just one place. It exists in infinitely many places all over the collage tree. But here is the crucial part. The places where these constellations begin and end are always given by these formulas. For example, let's say that you have a constellation made of three star nodes. Well, then three is equal to m plus one. Because remember that we begin with a0. So we need to find a1 and a2. And b could be anything. But let's make it easy and say that b is equal to zero. Then a0 is equal to three. We put that into a star node and we get 46. And indeed, we see that 46 is a star node. And so is 70. And so is 106. But 160 is a Targaryen node, because we only specified that we wanted three star nodes. Using this, we can find all other constellations made of three star nodes by simply changing the value of b. Try it for yourself. Just be a little bit careful, because these numbers can get really big, really fast. And the computer seems to struggle with numbers larger than 2 to the 64, probably because of how it stores the numbers in the memory. But I don't know what the engineers had well from Alpha did, but you can really abuse it. Like, for example, this is the number that starts a sequence of 10,000 star nodes in a row. But fair, you ask me telepathically across time and space. The formula you have for a0 always gives all numbers. But what if we make a star node using an even number? Well, boys in my head, in that case, that node won't be followed by another star node. Take 82, for example. This is a star node made with a equal to 6. But then when we put 6 in the formula for a0, we see that there are no integer solutions for b and m. Which means that this node cannot be followed by another star node. And indeed it isn't, because 124 is a Lannister node, because it is a multiple of 4. But going back to the problem of the infinite constellation of star nodes, now we can see that if m was infinite, then a0 and am would be infinite too. And this means that a finite number could very well start an extremely long sequence of star nodes, but never an infinite one. This is why there is a limit. But of course, this doesn't do anything for the Collatz conjecture, because there could very well be an infinite sequence out there. It just means that the streaks of star nodes in that sequence take a break every once in a while, before going back up. But who cares? By analyzing streaks of star nodes, we were able to get a formula to find all of them. If we get similar formulas for the streaks of the other kinds of nodes, then maybe we'll be able to find any possible constellation in the tree. The process for finding the formulas for the other kinds of nodes is pretty much the same, except the solutions for the Targaryen nodes don't need a number b, because any number can already be a solution to this equation. Because if you look at the tiles, you can see that you can always multiply by 4 to get to another Targaryen node. And this means that you can start or end the sequence anywhere. Now, the question is if we can use this to find any possible constellation. And we can. We just have to think of constellations as being made of multiple sequences of streaks. That's right, we are multi-streak drifting! To understand how we're gonna do this, we have to think about sets. At first, if you just want to find any constellation, but you don't care about which one, well then you can use any positive integer. So this is your initial set. But then if you want to find a constellation made of a streak of a single kind of node, then you can use the formula for that case. And now your set has become smaller. Now it only contains the numbers that are solutions to this equation. And then if you want to find a constellation that is made of multiple streaks of different kinds of nodes, well then you have to combine these equations in some way to get a single equation. And your final set will contain only the numbers that are solutions to that equation. For example, let's say that you wanted to find a constellation made of three stark nodes. Well then you can just calculate a2 of s. I'm using the s here to specify that it comes from a start node. And you know that the end of the last node in the sequence will be equal to this. Because remember that the last node in the sequence is always something else that we cannot control. But if you want to say that that node has to be a Lannister node, then you can just take the end of a Lannister node, which is for a of lambda and the lambda to specify that it comes from a Lannister node. And then you can just make these two things equal and then divide by four to solve for a of lambda. And then you have it. Not all numbers will satisfy this condition. And so for that reason you have reduced the set of possible solutions. Now if you want this to be a streak of four Lannister nodes in a row, you just plug this into the formula for a3 of lambda. And then you have it. The solutions to this equation tells you all the places where you can find this constellation in the collapse tree. And this is actually how my code works. Although my code goes node by node instead of using streaks, which I know makes it less efficient, but it was so much easier to write and I have so many other things to work on. This is how we can transform any constellation into a single deophantine equation. Kind of like a five-mind diagrams can transform these diagrams of particle interactions into a single integral. I call this process threading because in my mind it's like if every node was a bead in a color or a bracelet and we are threading them together, connecting them through restrictions in the set of solutions until we find the equation that links them all together. Trees, constellations, tiles, and now bracelets. My metaphors are all over the place, aren't they? But what are you gonna do about it? Subscribe? Like the video? Ring the bell? You wouldn't there? This threading is a recursive process and I think that means that the collapse conjecture must be related in some way to the Mandelbrot set and the logistic map in the sense that these are also recursive processes. And it has been known for a while that we can model chaotic systems using recursive equations and changing the initial conditions, which is pretty much the same thing we are doing here. This is probably the reason why the sequences in the collapse tree seem so chaotic. And in that sense, the super awesome tiles help us flow through the chaos. Instead of trying to predict if a number reaches one or trying to predict how many steps before it reaches one, like a sailor desperately trying to steer a ship through a storm, we just say where we want to go and the tiles take us there. Originally, this is where I was gonna end the video. I mean, I found a connection between the collapse conjecture and the constellations and I found an algorithm that lets you find any pattern you want in the collapse tree, mission more than accomplished. But then I had an idea. A question. Could I find the starting point for an infinite constellation? Because that's one of the ways that the conjecture could be proven false, right? Okay, so we are obviously gonna find that we cannot prove that such a constellation couldn't exist, but it will still be fun to try. Okay, so how should we approach this? Okay, so first idea. If we have a constellation, we can just keep adding tiles at the end. And in that way, we could certainly have an infinite constellation. Yeah, but that doesn't work because every time we add a new tile, we change the equation for the whole thing. And it changes scoutically. So this means that every time we add a new tile, we change the places where this pattern begins and ends in the collapse tree. And that doesn't work. What we want is an infinite constellation that has a fixed starting point. Hello. At this point, I forgot to remind you that the way we calculate these equations is by using the formulas for the streaks repeatedly inside each other, like the result of one streak will be a zero in the next streak. And this will be extremely relevant by the end of this section. So just keep it in mind. Okay, so let's imagine we have an infinite constellation. In that case, we could calculate its equation from the beginning up to some point in the middle. And what we should find every time is that the solutions for a zero are always the same. Or if the equation is different, it is different in a way that always results in the same solution. But a n changes in such a way that it can always be something different. Okay, this seems really difficult, but perhaps not impossible. But then if an infinite constellation existed, we should be able to calculate its equation and not up to any point in the middle, but all the way to the end. How would that look like? Like, would we have something like a infinity is equal to infinity times a zero plus infinity? Like, this is meaningless. This tells you nothing about the sequence itself. So the only way this can exist is if these constants eventually converge to something as you calculate the equation up to infinity. Okay, and this, that seems possible. Yeah, sure, these constants could converge to something. But then how does that make sense for a infinity? How can this number go all the way to infinity if these constants are finite? Well, maybe because it doesn't go to infinity. Maybe a infinite is actually a finite number. Maybe what happens is that this infinite sequence goes up and down and up and down. And it just never happens to reach this particular number. So it's not that it rises forever, it just rises and goes down. It just never reaches this number. But that raises the question, like, what happens if you use the collapse rules with a infinity? Like, because it's not an infinite number, right? So what would happen? Well, there are two possibilities. I mean, it's clearly not part of the collapse tree. So it could either start a new infinite constellation, or it could be part of a cycle. So it seems that if we find one a zero that starts an infinite sequence, we should find infinitely more infinite sequences, infinitely more trees disjointed from the main collapse tree. But the problem with all of this are these constants, because we have to understand how is it possible for them to converge to anything. And it can be really hard to imagine what's going on here because we have all these fractions raised to different powers. But what we are going to do is that we are going to write them using Euler's number raised to these logarithms. And I know this looks very different to a fraction, but trust me, it is the exact same thing you can test it for yourself. Okay, so now what happens is that as we do the threading process, we might not be entirely sure what's going on because we don't know the order of the constellation. But we do know that every time we thread through a streak, we are adding another exponent in the sequence, right? So in an infinite constellation, we would get these infinite sums in the exponent. And that might not seem like a huge deal, because infinite sequences converge to finite values all the time. I think they even teach that in Sesame Street these days. But the problem in the here is that for an infinite sum to converge, it needs to use fractions. And these are not fractions. These are integers because they represent the length of the streaks. And an infinite sum of integers doesn't converge. It cannot converge. Even if it was just one minus one plus one minus one plus one minus one, that diverges when you take it all the way to infinity. So this sequence here, this infinite sum, whatever it is, it doesn't matter the order of the sequence. It will diverge. We will get something to e to the plus infinity minus infinity. And that just doesn't make any sense. And so that seems to prove that an infinite sequence cannot exist, because it would require an infinite sum of integers to converge. Which means I must have made a mistake somewhere. Because, okay, in the veritasium video, Derek mentions that it is relatively easy to find any number that exhibits any arbitrary behavior, which are the notes we just found in this video. So people knew about this. Like I told you this wasn't new. Someone else had found it. I was just rediscovering it on my own. But if someone else found it, they obviously didn't disprove that infinite sequences are possible in the Colette Street. So they must have seen something that I'm missing. They must have seen a reason why this doesn't work. Unless it is me, the one who is seeing something new. And at this point, I have to share with you my greatest fear, to be a science crackpot. The internet is full of these people. They are people who claim to have made amazing discoveries and that all the other scientists are wrong, but only they are right. Only they have managed to pierce the veil and uncover the mysteries of the universe. I don't want to be like those people. I am a scientist. I am on the side of truth. I don't want to be wrong. And so that's why I insist so much that I could be wrong, because that's the one thing these people never do. They never consider that they could be wrong. And just to show you how bad it is, if you look for proofs of the Colette's Conjecture, you find many of them. Look at that. You think the Colette's Conjecture is the most proven problem in mathematics. But of course, it's not. Of course, all of these proofs are wrong. But the people who made them seem very, very confident that they are right. And they probably think that everyone else is wrong for not seeing their genius or something like that. And I never want to be like that.  Okay, so how can I know if I'm wrong in this case? Okay, we have a couple of options. The first option would be like to check my reasoning and find a mistake in there. But I'm not smart enough to see any mistake in here. I just cannot see it. Okay, so another option would be to get smarter people to look at your work and find a mistake for you. But the problem is that life is too short to look at all the wrong proofs of the Colette's Conjecture. So obviously I couldn't get anyone to look at this. So then the third option I have is just to look at common elements of wrong mathematical proofs. Okay, so Scott Aronson is a scientist and he has a lot of experience reading mathematical proofs. And he has noticed some common patterns in proofs that are wrong, and he made a list of them in his blog. So let's go one by one. Number one, the authors don't use text. Okay, so text is something like a coding language, but for writing text, like all the scientific papers and textbooks are written using it. And I used a version of text known as latex. So I think I clear this point. And I also clear some other of the first ones, but spoiler alert, I don't do very well in this test. Number two, the authors don't understand the question. I hope I understand it. Like, the Colette's Conjecture is really easy to understand. If I fail this point, I'm really in trouble here, but I think I clear it. Number three, the approach seems to yield something much stronger and maybe then falls, but the authors never discuss that. Well, I think this is just pretty much limited to this one problem. So yeah, I think I also clear this one. Number four, the approach seems to conflict with a known impossible result. I'm going to say that I have cleared this. Like, as far as I know, I don't think this is happening, but maybe it is. I don't know enough mathematics. Maybe this conflicts with some other results that I am unaware of. Number five, the authors switch to whistle words by the end. Okay, so if I understand this point correctly, is that these people are not entirely sure of their result, but they present it as if they were sure of it. And I don't think I did that. Like, I'm pretty sure that an infinite sum of integers diverges. Like, I'm pretty sure these equations are correct. That's a problem. I'm pretty sure of everything I presented here. I cannot find the problem. And that's the problem. But yeah, I think point five, clear. Number six, the paper jumps into technicalities without presenting a new idea. This is where I started going wrong with this test. Yeah, I mean, my tiles are interesting and they are certainly new to me, but they are not new in general. And even if they were, they are not advanced enough to count as anything new. So yeah, point six failed. Number seven, the paper doesn't build on or even refer to any previous work. Well, I mean, that was like part of the challenge, but okay, yeah, point failed. And I don't even know what other word I could even refer to. Like, I purposely didn't research the topic. So yeah, super failed. Number eight, the paper weighs a lot of space on standard material. Okay, so this video is intended for the general public, but okay, yeah, sure. Point failed. Number nine, the paper gets poetic and philosophical. Yeah, no, I didn't do that. If I ever mistake philosophy for science, kill me. Number 10, the techniques just seem too wimpy for the problem at hand. And yeah, I agree. Absolutely point failed. That's five points out of 10. And he says that six and 10 are the most important ones and I failed those. So it seems overwhelmingly likely that I am wrong. I'm sorry, I just can't ignore it. It's right there. We've come all this way. I have to at least try. I'm sorry. Okay, so if this was correct, which it isn't, but if it was, then what about cyclical constellations? Because that's the other way the conjecture could be false, right?  We cannot argue that there's an infinite sum of exponents because a cycle, by definition, is finite. And so we cannot prove that a cycle doesn't exist, unless... At this point in the video, I gave what seemed at the time like a proof that cyclical constellations have to use negative numbers. And it was pretty cool. I used the metaphor of an auroboros to split the cycle into two constellations, which I call snakes. And I reasoned that the values for the variable A have to go up and down until they reach the same starting point, finding that this was only possible if the variable A was negative. Sadly, while editing this video, I realized that hidden in my reasoning were a series of assumptions that are not true in general. So, keep this in mind for later in the video when I mentioned that this seems to prove the colatz conjecture. That's wrong, as expected. However, what I can do is tell you that if cyclical constellations exist, we should be able to find all of them using this equation. Let me show you who I found it. Okay, if there was a constellation, you could calculate its equation, right? And since it's a cycle, the first node and the last node are the same. So A0 is equal to An. And this is great, because we actually have the solutions for A0 and An. We get them using the extended Euclidean algorithm, which I'm not going to explain because there are a trillion other videos about it. But now we can solve for B. And there you have it. The integer solutions to this equation should help us find all the cycles of the colatz 3. In fact, alpha has to be a power of 2 and beta has to be a power of 3. But I'm too tired, so I'm not going to explain why. I mean, I mean, this is left as an exercise for the viewer, as if anyone ever does any of this. It feels disappointing not being able to give you a proof, or at least something that resembles a proof. But I guess one of the oldest traditions in mathematics is saying, I give up. If you figure it out. In fact, some mathematicians became famous not for the problems they solved, but for those they couldn't solve. Like Riemann, Goldach, Poncaire, and of course, Colatz, among many, many others. And if this equation can indeed predict cycles, then I am now a small part of that tradition too. Unless someone else has already found it. But just to be clear, the question is not to find whether this equation has solutions or not. It is to find all the solutions. Because we already know a couple of them. With positive numbers, we only have the 4 to 1 cycle. But with negative numbers, there's more than one cycle. There's three actually. You are seeing them on screen right now, along with their equations and how they satisfy my formula for b. And yes, my code can find all of them. Anyway, that's all I have to say, and now me from the past has a couple of cool things to say about negative cycles. But anyway, so with the two cycles that my code can find, I can see that they have b equal to minus one. But then when I change b out of curiosity, I found many other sequences that have the same structure. They have the same kinds of nodes in the same order. But the difference is that they are not cyclical. They don't loop around. And I think I know why. We can think of cyclical constellations as one cycle, but also two cycles and three cycles and four cycles and any number of cycles. And all of these represent different constellations of different lengths. And they obviously have different equations and different solutions. But for each of these possible constellations, there most exist one number whose prime coefficients are just right to cancel all the powers of two and three and make all of these equations identical. And so these constellations are disjointed everywhere else, except here in this one point. And if we were to start the constellation in any other node, we would find another family of constellations that are also disjointed everywhere else, except here. This seems to prove that cyclical constellations are impossible. And that plus my previous proof that infinite sequences are also impossible seems to prove that the conjecture is true. Which means that this video has become just one more in this large of fake proofs of the collapse conjecture that swam through the internet. But I hope this video can have more value than all of those precisely because I am scientist enough to recognize that I am wrong. And I welcome and indeed crave to know what I did wrong. And when I know you can bet I'm going to make a video explaining what mistakes I did so that we can all learn from my mistakes together. Okay, so what did we learn? Well, in the one hand, we went through a journey through the authentic equations and infinite series and set theory and I don't know what else to find the super awesome tiles and to find this algorithm that finds any pattern in the collapse tree. And all of this is really cool. And I'm pretty sure it is right because I've tested it a lot. But in the other hand, we also have this walkie walkie walkie, I don't know, false proof of the collapse conjecture. And you know what, this feels about right, because if we had not taken the risk of being wrong, we would have never found the stuff that is true. And so I think that the trick to being a good scientist is to always be open to the possibility that you could be right so that you take the risk and maybe you find this cool stuff that is true, but that you also never forget that you could be wrong so that you don't mistake everything you find as being true. And finally, I have to thank all my patrons, but especially Carlo Fascioli, Robert Bigman, Alec Luhman, Otimo Tiozum, Azuria Salia, Mattia Serdi, Ryan Roberts, T. Heidel, Valerie Hyde, Dan Babbage, Daniel McGillibright, David Saunders, Jadon Hansel, John Stein, Marlo Vron and Matt Zweig. All my patrons, thanks a thousand times, thanks a million times. And that is where I was when I end the video, but I just have to improve my code, right? Just have to improve it a little more. Okay, so here's what happened. Do you remember how 82 starts this extremely long sequence? Well, I wanted to test my code, I improved my code and I wanted to test it, I wanted to take it to the limit. And so I made this simple code that you give it a sequence of numbers. Well, you give it a number in the collapse tree and it not only gives you the constellation, right? Like the nodes. It doesn't give you like the numbers, you already know the numbers. It tells you what kinds of nodes you find here, all the way until you reach one. And it was like, great. And I started testing it with many things. But then I eventually thought, well, this is a very long constellation, I'm going to try with this one. Okay, so we copy this constellation, I already have it here. Okay, so then this is my code. You give it a constellation and it gives you the equation. And then when I run it, there it is. It works. So here you can see that we have the, ah, let me make this a little bit bigger. Okay, so here this is the equation. It has some very large numbers, so that's to be expected. Here are the solutions. And here it gives you one example of a sequence of numbers that matches this constellation, because remember, the constellations exist in infinitely many places all over the collapse tree. And I thought, well, all of this is fine. But I want the example that starts with 82. And I was very confused, very perplexed by this. Because as you can see, I'm using the constant B equal to zero. Well, zero over one, which is actually zero. The entire code has to work with fractions to avoid issues with floating point numbers. But anyway, so I was like, okay, but how can I, what else can I do? Because if I use a negative number, if I use B is equal to minus one over one, which is minus one, well, then I get negative numbers. I was like, where is 82? Like, if I use larger numbers, if I use larger values for B, I'm gonna get larger numbers here. And if I use negative numbers, I'm gonna get like, I'm gonna use, I'm gonna get negative numbers. So what number do I have to put in here to get 82? I was very confused. I was thinking that maybe I had made a mistake that maybe my algorithm could find many constellations, but maybe it couldn't, there were constellations that I couldn't find. And so, well, I went to, well, from alpha, of course. And then I said, okay, so this is the equation for B. I mean, for a zero, as you can see, this is a zero. And I just basically, sorry, I copy it. I paste it here. And then I know that 82 has an a zero equal to six, right? And that has to be true, like, regardless of anything else, right? And so I thought, well, okay, so tell me, well, from alpha, what value of B do I need to make this equal to six? And this was Wolfram's response. Not only a fraction, but a negative fraction. And I was very confused. But I thought, well, here goes nothing. Let's try it out. Okay, so here is the thing Wolfram alpha gave me. Let's try it. And it works. It gives me the right sequence, 82, 124, 94, blah, blah, blah, and so on, on the way up to the last node, which is four. I was like, extremely confused at this point. It was like, what, well, I'm still very confused. I was thinking, like, what I'm using everything is Diofantine, right? I'm using only integers. I made everything using integers. Why, why do I need a fraction to find this? And then I thought, well, what happened? Okay, so what if this was one? What happens then? And Wolfram alpha gives me another solution. So let's try it. And we get the sequence that looks starts reasonable enough, 10, 16, oh, I've seen this before, but then it goes 13, 20, 31. And very oddly enough, finishes with two, four, one, and then some decimal points. And then I thought, well, I can just put any number in here. I can just put any integer in here. And Wolfram alpha will find a solution for B. And then I can take that value of B and put it in here. And I'm going to get a sequence. And then it gets weirder because I was like, well, what if I try some other constellation? Okay, and then I decided to try this constellation. And I'm going to try it with B equal to zero. Okay, we get something that is reasonable enough, right? Only integers like to be expected. And then we put B equal to one. Again, only integers B equal to two. Like, of course, like, what am I saying? Like, of course, you know, this is going to get integers. But the weird part is what happens when we put a fraction one over two. Look at that. Not only, obviously, we got a result. But look at that. All of these are integers. All of these are integers. If you look for these, if you want to find these sequence in the collage tree, using this equation, you have to use B equal to one over two. And that's not all. One over three, it works. One over four, it works. One over five. Okay, now it gives us things that are fractions. But what happens if we go to one over six? Integers again. One over seven. Fractions again. One over eight. Integers again. One over nine. Fractions. One over ten. Fractions. One over eleven. Fractions. One over twelve. Integers. No idea what's going on. Okay. Okay. Okay. Okay. The only conclusion I can find here is that B is not an integer number. B can be any number from zero up to infinity, but it's a continuous number. So, B is a continuous number. It has to be. We have to allow B to be a rational number in order to actually find all the constellations, because if we only use integer values of B, there are sequences we are not going to find. But then, if we can, if we are allowing us to use some values of B that are not integers, what right do we have to exclude other values of B that are also not integers? Like, we have to allow all of the values of B. But if we allow all of the values of B, then we get these other sequences, right, that are not made of integers. And the only conclusion I can find here is that these are also sequences in the tree. Like, we thought this tree was made only of integer numbers, but it isn't. Using these equations, we can generalize the tree to all the numbers from zero up to infinity in continuous, all the rational numbers from zero up to infinity, not only the integers. And it makes sense, right? Like, we are using the same equations in both cases, and we are getting results that, yeah, make sense. They follow, they certainly follow the rules. So, yeah, I guess the collapse tree was just a much smaller version of a larger tree, which I have to call the super awesome tree, just in case someone else has not found it already, so that I can fulfill my promise. So, yeah, this is the first glimpse into the branches of the super awesome tree that is made when you thread using the collapse rules, but you allow the variable B to have values, to have any value. Yeah, that's what happens. Because, yeah, and the collapse tree is only when you allow the values of B that result in integer values of a zero and a n, and I don't know, I think this is pretty cool. And the best part is that all of this, like, is independent of whether or not I'm right about the collapse conjecture, right? Because, yeah, this is true, like, the algorithm works. The algorithm certainly works. I tested it enough to be convinced of it. So, the algorithm works, and if the algorithm works, and it also gives the sequences, then the sequences also have to be right. And so, yeah, even if I'm wrong about the collapse conjecture, I think I'm right about this. I mean, I would be, oh, okay, maybe not. But I think I am. This is pretty cool. Yeah, I think, yeah, that's all I wanted to say. I just wanted to share this with you and say, like, yeah, this is pretty cool. And this is the super awesome tree. Okay, anyway, thanks for watching. Hopefully, this time for real.


What's up, everybody? I'm Hill Rabbit. We're here on a set of Corsa in a public lobby in some World of Drift streetcars I'm in the 180sx that just got bumped by another 180 So we're here to digest take a look at these runs I'm so glad I was recording because these have had to be some of the tightest Best chases I've done so far that I think in a public lobby I hooked up with these other two 180s The lead 180 the red one him and I just started throwing it down I was doing transitions that were basically clipping this bumper back and forth to the SS here in me huh, and It was I got so comfortable chasing him that I stopped using the handbrake for a while because I was just using my brakes and Left foot braking and clutching because I kind of knew the line. He was good runs I didn't have to worry about it. I felt very comfortable following him and it show So I found an amazing lead driver and a couple amazing drivers in the service show so glad I was recording So we're gonna talk about it today. We got the pedal cam the wheel cam the third person camera and the replay angle camera We had a couple instances like that where we kind of bump all around or rack and we reset the pits But we hooked up with each other Well all the time right after we racked so we all spawned next bit So it was definitely an amazing time. We weren't in any time chat or anything like that. We were just throwing it down It's just we found an amazing you know Amazing runs together so and it's amazing when you find them in random lobbies with random people like right there Three 180s door dives. He kind of biffed it But when you find some a very good lead driver in an online session It's you definitely want to try and chase them because you can get very comfortable with them And you can just start throwing down massive lines with them and we just had a lot of fun And I'm sure they had a lot of fun I know I did for sure I can't speak for them trying to get in contact with these drivers and you know Be like hey, dude. That was awesome. You know, let's throw down some other times right there Little bump on his little bump on his wheel, but nothing major So another thing I want to talk to you guys about today is live streams So live streaming is something I used to do a lot on the channel with torque drift with live battles and stuff like that Oh, I think I uh locked up the brakes there. So I want to bring back live streams torque drift a set of Corsa uh, maybe fours of rising four and stuff like that. So That's something I'm going to be striving to do here very soon with Uh the torque drift coming to pc very soon if you guys don't have that on your wish list on steam Make sure you go to steam search torque drift add to your wish list so you guys can see it when it comes out As well as I'm going to be doing some more endurance racing So if you guys remember last year about this time I did a 12 hours of sea bring up for the motorsport seven with a couple of my friends And uh, it was a lot of fun. We streamed the entire thing We were doing driver changes and everything like that And it was a great time. So Imsa racing series is something I'm very happy to watch and I love this series So we're going to be doing some more endurance racing We're going to be doing another 12 hour next month of sea bring And then I'm going to be doing some shorter ones like the one hour and 40s the two hour and 40s with my friends either over a server with AI and stuff like that I'm breaking myself into getting more and more into racing Door dives see right there bumper scrape quick transition quick flick throwing a town So it's awesome. Just watch these tandem runs over again and see you know the placement and everything and how You know it was done Because in the moment you're just having fun with them. You go back and you watch you go Wow, I was actually really close So like I said, we're going to be doing some more endurance streams 12 hours of sea bring will be next month We're going to be running it with two of my buddies this time not for when we're running with two So a little more drive time for all of us. We will be on the fan attack wheel But we're going to be doing it in our factor two which has multi-class racing Cautions pits strategies everything like that. So it's going to be just like an actual Imsa race now. I'm not going to be doing it. I know a lot of uh people do the iracing endurance races I'm not to that level yet So this is a way for me to tap into more and more racing because I do love racing and doing endurance races But this is a way for me to tap into it. So we're going to do a lot more endurance races We're going to be doing some six hours some 10 hours and stuff like that I will be streaming those live on the channel as well as bringing torque drift battles back to the channel Because I know you guys a lot of you guys loved it. So we're going to bring them back Especially when the pc version comes out. We're going to be bringing out some live stuff there as well so I just wanted to talk to you guys a little bit about my Plans for doing live streams and stuff like that here in the future because I haven't done money many many many many Wow, I haven't done many here recently and definitely want to get more and more Live streams going especially some open lobbies. I do have my server and everything going on a set of Corsa But I only run it when I'm on online So if you guys Don't see it's because I'm not online running it So what I may do is actually put a server link up in the description So you guys can find it and flag it So whatever it's on you guys can actually see it that can be done through content manager and stuff like that I'll get more into that too as well as the cars that I've been building I am going to be releasing my car pack. Hopefully very soon some people rabbit cars I have a male 2j 180 one day one j 180 I have my 350z Which you guys got a glimpse of As well as some other cars that I've been working on with my friends So real world cars as well like their real drift cars So Like I said, I've been having so much fun just random thrashing lobbies So if you guys see me in a lobby and you guys know who I am and you guys want to start doors Feel free to start doors Let me know if I was in your lobby and you try and you were throwing doors with me Hit me up on instagram Let me know direct message me on instagram be like hey man I was just in a lobby with you You know because it's very cool to see because half the time I don't know who I'm in a random lobby was and I know Some people mess to be on instagram and like dude. I was in the lobby with you. I was trying to get your door But I couldn't well then I know you know What lobbies people are hanging in? I know a lot of people hanging the 80c's Driftland Aussie drift server they hang in the lone star drift server They hang in the tando buddies at drift playground and tomata circuit I do definitely like the 80c cars as well as the world of drift cars. They handle very well They're pretty good at you know mimicking a real car in a sense They don't feel as numb in the front as such as a tando buddy car But I know a lot of people on tando buddies with 180s are with the logitech because I mentioned that before Because it isn't as rough on the wheel so Definitely gonna be hopping into more public lobbies just to thrash with some randoms as well as running my own servers Which will bring in more of the t us guys that i'm hopefully gonna be running some servers with the t us guys In tow, you know, so we'll be running tandem g. I should run tandem with the t us boys And myself because they're definitely a great group of guys and very solid drivers and driving with them for the longest time has definitely increased My uh my chase as you can see there. He was waiting for me a little quick flick of my uh headlights and he was like All right, let's go. So we do switch off more towards the end Where I needed a little bit But he mostly wanted to lead and he was a very solidly driver So big kudos to that man because we were able to get some nasty So you should just follow me on instagram and twitter always found the description box below a little break a lock break, you know Too much heavy on the you know Left foot brake there kind of locking up the front wheels, but we were still able to do it Little less handbrakes handbrakes in certain sections. So I hope you guys are enjoying this basically Chit chat session Let you guys know what's coming to the channel as well as watching some awesome tandems that I was having because I know a Lot of you guys were asking for just more tandem video. Well This video is all about tandems. Yes, I'm here rambling and talking to you guys about the channel, but it's just it's straight tandems That's all it was for the longest time I think I was tanning this guy for about a half hour.  They're they're a very stable car so We were just throwing it down this new 2020 version of mayhem the rumbles on the outside do Axes rumble strips they uh, they vibrate my wheel. I go through them a couple times You guys probably noticed and uh, it kind of chatters a little bit. So this is a new version I will leave the link in the description box for the Track as well as these street cars because this server is definitely A fun server to drive. I'll leave the name of the server as well down in the description box below So you guys know what server this was. I think the server runs most of the time and there's usually a lot of people on here I loved on in the beginning and there was about 15 people in the server and then it boiled down after a while But there was a good amount of people all Rip I forgot we both went way hard into that Until I forgot I was in reverse so This man Like I said very solid lead driver I was wondering if he uh Biffed it and did something with his wheel and we were kind of just chilling I was chilling for a minute obviously and then he decided to uh come out and then we were Throwing more tandems as you can see So I'm gonna leave you guys with the rest of the tandem videos here So you guys can just enjoy the sights and sounds of uh the tandems We did get into a little bit of a tandem train So I'll leave you guys with this make sure you guys follow me on all social media I'll just find the description box below as always. I thank you guys for watching I hope you enjoyed the stand-ins. I'm evil rabbit. I'll see you guys on the track


Welcome to Toffy TV, the pre-season. We love a pre-season, don't we? We want it all to be confirmed nice and early so we can get out of these. We don't do that at Evan. We don't do that. Evan, keep your own your toes. Keep your own your toes. You don't know when to throw those all of these in. The good news is, after confirming trips to Berry and Blackburn, Evan have now confirmed they're playing in the Algarve Cup. They will face Leal and Porto on the Saturday and Sunday of July 21st, 22nd. It's a three team tournament over the three days Friday, Saturday, Sunday. Porto and Leal play on Friday, we play on the Saturday and the Sunday. I mean, from a sort of getting away point of view, it's sound pretty much, I can literally, I could probably hear the noise of people getting on the Al easy jet. Well it was 105 quid yesterday and it's 308 today. If only we'd known yesterday. No, anyway. We're driving there. We've got a van. We'll take the van. We'll be there at the 18. But a lovely weekend. The pre-season is starting to come together now. And yes, listen, it hasn't got any big shiny fixtures in it so far. There isn't a big trip away, commercial trip away. But on balance, it's got a nice sort of trajectory. We start with Barry, then we go to Blackburn, then we've got these two games and we finish off at home. He's in the middle of the Blackburn. Oh yeah, yeah, sorry. Barry, this one with Blackburn and then obviously got Valencia and hopefully another European trip, maybe Jamie or something like that. But they obviously start in Austria pre-season and then they'll do a week and then probably at the end of the week they'll probably just play maybe a local side in a, you know, like they've done before, almost just like get the cobwebs off is your reward for the tough week is a game of 40, which none of our fans will take enough for, cos they never do. Last year or the year before it was wasn't it? Yeah. You just ate them on the street. Tim, do you want what you want? What you want? It was like a field surrounded with a thing and then a picture surrounded with like a thing and like a little bar, like a few, like diabloos, just one another one and people go, Darren, do you want one? Snotch, do you want one? Do you want it? Do you want it?  He did on a step over and fellow it. That's when Cumin made his man up in Foulton. He did the post out as well, didn't he? Yeah. And then Brandon Galloway got the gold in it, me one won that. It's, again, it's, you like you say it, it's an upward trajectory, I suppose. I appreciate, listen, be lovely to go and have an American tournament and a glit and glamour. Please be awesome next year. But again, it's the whole Europa League thing kind of complicated for Everton, I think, because if we'd have finished 7th and dropped by on these routes, you know, in a month's time we'd be kicking off or something. Well, we would have, we'd have played, wouldn't we? So I suppose that has to come into the thinking a little bit of what you can book. Because everything's contractual stuff now, so the minute you agree, that's it, you're tied to that, you know what I mean? So I don't know how much that plays into it, but I'm pretty sure it does. I suppose it does because pre-season house, it's, like, I mean, it's getting big, it's becoming big business at the high end and that's what we want to be involved in. And I've said this loads of times, you know, pre-season is commercially a fantastic opportunity to go to places and play against teams that you normally wouldn't in a more relaxed sort of surrounding where you can go to places and camp out and make yourself known. And these are the things we'd ever do and it disappoints me, but I understand because every year for, you know, the last few years we've been in a bit of a mess going into pre-season. So then pre-season for whatever reason is being thrown up in the air, whether it be like last season with the Europa League, the season before, Cooman coming in, or just a mess by our own hand, Roberto Manez, who just didn't seem to appreciate the importance of pre-season, like he didn't seem to appreciate the importance of defending. But I just hope, yeah, I hope next season, I hope we get it right. I hope, you know, everything's, we're all settled as a club and we can plan for something good because, you know what, we scoff and we laugh and we go all, we hope it's a miracle, but we really hope we do go to somewhere like a miracle. So those fans get a chance to see Evan again. So we get to play some glamour ties. So we get to have the opportunity to go somewhere and spread the Evan name because we haven't done that for a while. And pre-season saves two roles, obviously. I mean, first and foremost, it's your chance to get your players fit.  And we haven't been using it for that hard in the last few years. The pre-seasons have been a mess and they've not really done the job they're supposed to. And the other side is the commercial point of it because you've got things like the ICC, which, like we were obviously in it a few years ago by default when Galatasaray pulled out and we took their place, which David Moyes' brother sorted out for us and then obviously Manez benefited from it. And that was a fantastic tournament. It was a fantastic opportunity. The players played top opposition, got fit. Some stars were created, like John Stones, on and off the pitch, and I just loved that again. And the ICC now is so big that I think it's in pro-evolution soccer now as a tournament. Tim FIFA. Yeah, you know, it's mad, isn't it? It's like it's become a premiere and I'm not saying, you know, we need to get in that because that's a, I just would. It would just be nice to be able to go into a pre-season, settled, have a plan before the end of the season. No where you're going. Tell that to your fans. Ultimately, it's got to be for the benefits of getting players fit for the season. So that's what could we have done this year, you know? This year is difficult because obviously Sam Allardyce was in. Manatees will have different ideas of what they want their pre-season to be. One might like a gravy vat and one might like salad and stuff away, you know what I mean? Yeah, but if we'd have gone, Sam Allardyce wants to do that. Now, behind scenes, Marcel Brans and Mark O'Shilderman, they go there. We say, what could we have done, said the Sam Allardyce going to this tourney? He's like, no, we're not going there. I don't want a book. Don't want a book. I like that. You know? It's difficult because you're right. We've been in flux for too many summers, really. You know, it's been a while since we've been settled going into that summer and pre-season to planned February, January. Like, as you look on ahead, summer planned a year in advance almost. David Moyes, because he was in the job for so long. Everything was settled. He loved America as well. So we want to go there. We want to do this. And he had this tried and test the formula. I think everyone have done well, particularly the likes of David Harrison and people like that. And Marcel Brans getting the games that we've got actually give because it's relatively short notice again. We probably still had, with a month to go, there was still an outside chance we could get the Europa League place. So that's why they've probably been a bit like that. You know, if your Liverpool say or Tottenham, you can kind of go, we're going to be in the top six, which we don't have to qualify for anything. Last season, essentially, start on the premise. So we can kind of commit to that. And hopefully, you know, in the future, we might break into that or whatever and be able to do it. But I think the other thing as well is obviously if we're settled going into a summer. So hopefully, like you just said, all things being equal next season come a March. Now, you've got time with settled, Michael Silver's doing well and the starting to go. Even any kind of tournament, Liverpool, for years when I played in that Audi tournament in Germany. So that's still a big tournament. Arsenal always have the Emirates Cup at home.  And you know what, listen, I know there'll be people saying, well, what does it matter? But it matters for me. I think it matters both ways. I think commercially you can do a lot from it. And the other point of it, I think if you're playing in games that really test players, you know, and you're playing in hot conditions, that's going to get them fitted. Well, that, Martin, there's one that Moise had sorted out. You know, we had the events, the slowness, and Seville was it? Was it Valencia? Valencia. So we played three big games, you know. One in LA, one in San Francisco and one in Miami. So you're playing tough conditions. Tough conditions against good players. You know, and we had other games. I think we went to Acherings and Stanley, one for one. I think the first game we played and we had another couple more. On the summer like that, we had a couple of them, a couple of big ones. And then we come home and we lost the Spanish home. Oh, we lost the Spanish home. Apart from the, yeah. So it was one of them, wasn't it? We kind of hit the season, ready to go almost, and we had a good season from it. And I'm not saying it was simply because of that, but it does help. And last year was a mess. Well, I tell you what, the other reason I think it's a good thing as well, is that it brings players together. That's the key. Well, you know, you have that kind of feeling having me talking about it. Imagine this summer, I know players come at different times, but if you get players in Italy, and then you get, I know they go, say, like, Australia for a week, but if you take them somewhere in America where they might have a little bit of downtime and away from the hotel and stuff, somewhere actually where they can have a little walk around and no one's going to know what they are. They have a little bit of time away, get to know each other. I think all those things are really important to get to bed plays in. Foster's this thing called Team Spirit, and that, you're right, Moise will go into the States. Moise will go to the States and not even play games. He just said it's the best facilities. It might have been Tim Kayle or Leon Osmond. I said summer out for when it was everything that was in flux, you know, Rooney was going and stuff like that, and everything went out to America. And it just, the only, I think the only, went for seven days or six days or something, but he went, and it was said, you know, we've got to do this together, and he come back, and I think we ended up, well, we did end up finishing fourth that season, and everyone got tight, and then because of that, Moise took them back again. So whenever there was the opportunity to go there, he would. And listen, it's great, but any time away is great. I would, and I've said this before, I'd go to America every single summer, right? I'd plan for it, and I'd do it, you know.  We went and played the MLS All-Stars. That's a big game now. It's a massive game. You played like a real man. Playing U-Vay this year. You get announced by the player. It's a massive game. All the teams compete, stadiums compete to host it. I think it's in Atlanta this year. It's a massive game. It really is a massive game. We went, and they hadn't been beaten, and we beat them. And we didn't have an away kit, right? So we wore training gear. This is how backwards our club has been in the last few years. In the last few years. We wore a training gear. It was the first year of the La Coche Sport East deal coming back, and we'd launched a blue kit, but we hadn't launched the away kit. So we wore a training gear with numbers on it. So it was a big opportunity to launch the away kit. Now, I'm not saying the game was as big then, but it was a big opportunity to launch the away kit. No, they wore training gear. Do you know that you've done it with my playing team? We've gone over that. I'd go every single year. I'd nail it down. I'd build the fan base like Chelsea have and other teams have. The fans keep coming back. If you're over there, there's a team for them to go much every year. They know they'll be there every year. I'd also have said this before. I'd go into a city that loves football somewhere like Seattle, or Atlanta. Atlanta is massive now for football. There's a lot of big teams over there. I'd hit them for a week. I'd take the women's team. I'd take the youth team. I'd send them into the door play games against the different levels. I'd send them into the schools. The schools would be off. What did you go to the summer camps? The camps would just set up clinics in the city to get kids in. Kids training with Theo Wolcott or whoever.  Getting training off some of the academy coaches or whatever. Get Howard there. Get Donovan. Bring Ted Peanard over. Get all the ambassadors. Make a big thing about it. Do it for a week and smash it. You know what? This is our city. Seattle, let's set up it. I know there's teams already in America. Seattle or someone. It's their club. Link up. You can come over and play. Do that. Do it every year. I'll tell you what, there'll be some traction in there. That's the way the club should be thinking. I think maybe it will move towards that. These are all the stuff they've got to identify. I think from a purely playing perspective. I think they've done well to get the appreciations together. Especially if they add another one. If they can add a team in Germany. Or Holland. Something like that. In a midweek kind of game. I think that'll benefit them as well. Just to get away again. Just to have another overnight. I'm glad they're playing Berry. I'm glad they're playing Blackberry. I think it's important to play those kind of teams as well. It's set it up nicely. There'll be six. There'll probably be half a dozen games for Marco Silva to really get his teeth into. Get his training. Seven probably if you include the Austria thing. So it's going to be able to get his point of cross.  That he loves to do in my new details. That's going to benefit the players. Getting away being together. Trying to get them a bit closer. Look when you went to Dubai. Look at the way Towson settled in. Probably because of Dubai. Now he came back from there. He had to go. If he came at the end of August. Say the transfer window. He might have struggled and struggled and struggled. Now say Sanzo would have still been there. When he went to Dubai. And he'd have got him here. What do you like doing? Whatever. You don't know. We listened to Derek Montfield on the show. When he was talking about the details. Like that, the things like that. He was suggesting them go out and have a scrap. Or a meal and a beffy and stuff. I think it's beneficial. Like you say, I'm looking forward to it. 21st, 22nd. That's this tournament. 8 o'clock kick-off. The better game is. The 18th. The black bean is the. 26th. The 30th isn't it. The Premier kicks off on the. 11th. Valenti on the fourth. I think they were looking at a game between the 26th and the fourth. So there's a week. So there's a week and a bit there. Where you could throw another game. And then obviously the finish. The Valencia thing. And then it's preparation for Wolston. It's a decent little pre-season. To be fair considering. It's an old school pre-season. I like it. That's the way it is. Warren's sign as we've ended up with. We've got a good little tournament to go on and have a game in. Early on in the pre-season as well. See the other thing just very quickly. The thing with America. Why couldn't they go. And start the pre-season in America. Well that's what I'm saying. That's what Moys used to do. That's what I'm saying. That's what I'm saying. Maybe not faulted you. That would be a pre-season. But ladry for early on in a week. And then at the end of it. And then even if you're out of Europa League. Qualify it. And then it's a preparation down for that. Then you can play three. It took me a bit different as well. I honestly think they will be looking towards those markets. I think it's been enough. I think it's been a mess for ten years. We've seen the changes are a fault. It's still a noise. We basically can't help but be annoyed. If you keep looking back. I'm moaning. I'm just saying it should be happening now. I think things are changing. I want them changing now. Because I think these are the most basic things. That other clubs. That requires planning. That's what I'm saying. Marcel Brans might say. I don't see any value in dragging players off. I've said this before. The problem is sometimes you've got to take those decisions. I don't think a lot of clubs think there's value. A lot of managers of clubs think there's value. He's a commercial. He's someone who's very much involved in the football business. I think sometimes you've got to take these things at the hands of those people. This is where we're going. We're going every year. Pontons. See what happens. That's the pre-season anyway. Hopefully there'll be at least one. Hopefully two games. Because again. You've got a 25 man squad. You want everyone to get optimum playing time. You want more opportunities to look at the kids. Because they're going to form part of your squad. You're not going to be trying them in Premier League games. You've got to see if you can do it in these first. One or two might catch you, right? Yeah, do you have it? Are you a Evertonian abroad? Would you like Everton to come to your country? Your city? Let us know. Is there opportunities there? Let us know what other people are doing that we're missing out on. Are you going the Algarve? Nice to hear. Have a bit of that. Let us know in the comments. Thanks for watching Soffy TV. We'll see you later.


All righty, let's watch this in full first So good Right, I think overall. It's fantastic. I still really really love it I wonder if we could push the timing Into a slightly more cartoony realm just with some pushed Timing elements by that I mean This is This is all cool So it's a time to the sound I hope you have controls to fix intersections and stuff like that It's cool. And I like the Pushing down with a slight pause there That's all cool and I like the Timing of opening up holding a little bit and then going through I think that's very cool Also already detail stuff on the fingers on that door. So the first thing to me will be There's something where this is might just be me But when he comes in for the punch And this is going to be accentuated once you spline this I would do a punch With a couple things a you're coming in the straight line And it feels like we're coming out Fairly in a straight line as well where this fist just goes back And only at the end goes down, which is good for silhouette. Here's my my my thing here Would you consider? That you start here and then with that punch you have a little bit of a twist So that we see more of the side of that punch Maybe here Basically you have a frame or two linger of that of that punch there that fist Maybe a frame I mean it's tricky, but I would just play once you spline it that he punches with a translate this way and a rotation of that wrist and forearm that way, but what I would do then is Is it about faster? I think you can cut out these two frames this and this And maybe only have this that's my only thing and especially Maybe cut out this and this to me feels like keep this and take out this So it's a zip in slight hold zip out It's almost like I'm seeing too much. I feel like once we spline this we see too much of him And here's my reasoning you have this And it's fast and then then that's the quick Second entrance with the big surprise. Oh, that's what it was Or we almost know too much of what that punch wasn't by whom and what that person looks like it's very subjective But that's kind of my thought for that This will be for spliney stuff where maybe you want to do How many gets punched here that you push the nose up so it's kind of like Where it's That face goes sideways But imagine has a bit of a dip and then up just a bit more complex in that turn and the timing thing the overall time I think it was mentioned before is what if You're for power and it's almost a bit of a faster turn. It's kind of And then you have that hold a longer hold on the body But the head goes back a bit and a bit of a faster drop in the body. So instead of doing Drop it would be That type of thing I'm really talking about three or four frames or maybe two or three from two or three more frames Taking out in terms of just pushing the timing where it's just ever so slightly pushed of faster hole faster drop just a bit I Think you can also afford it by coming out maybe a frame or two soon because of the sound not that it's a killer I Think that should be fine, but I think just timing guys. I want the way it would look like if you had a That type of thing This is so great. I love this with the sound That's all great. I love the look here. I love how quickly you get up there and Get against the wall And I love all this. I love the poses how you switch over the very distinguished little hand pose there Opening up here looking down That hop is great And it's great with the audio too With that little inhale that that happens while he jumps Forgot to knock and then you mentioned in your email that you wanted to try you tried putting the arrogant look But then you put it here during the knock, which I think it's totally fine It's a pomegranate we can't see the eye, but then again, he's like me. He's got a big nose. It's a bit tricky But I will probably cheat this.  That's a horrible example Maybe here a so we see more so it's not so so edgy there and a bit more pretending that It's actually looking down. I forgot to knock And I love this I love that he has that That look and Then into that more serious look is ready and back for action there. Thank you. Pardon. I forgot to knock Forgot to knock One of the ones we splined this Maybe you have to add three or four more frames to this with a slight hold or leaning over and leaning back Or just leaning moving hold then cut. I don't know I Think it's great. I just wonder if we need like I said three two three or four frames I don't know if he needs a little bit or just enough of a beat to really read this and mainly to enjoy it I think it's such a cool change Going from here to here. I don't wonder if we could but you already have the sounds turning off So you might as well add a couple more frames to really linger on this and maybe you can have like I said a bit of a with this that's a bit of a move and then a bit of a hold and almost shifting weight going this way and Again, this is not enough. You can't shift weights in four frames But I just wonder can we hold this couple more frame to really enjoy this and I wonder if you want to It's nice and subtle again. Not that this is a killer. I'm just curious What if we push this mile by 15% so there's a slight bigger contrast of smile to serious Was there fairly similar? But it works like I'm always a fan of subtleties, but this is not again not the shock kill I'm just curious throwing it out there you can decide if you want to push this smile just a bit more and I don't know if you need to push this eyebrow, but curve this one maybe just a tad more For contrast again because you're so serious here But you have the heightening you have this here hold on knock No, I think it's fine. I don't know. I was I'm wrong because you have that already here That's a transitional phase into the series. So I don't know. I take it back. That's all good to knock And actually the same with this month, sorry, I was lingering here and I was should have should have lingered here To knock.  I'm just at this point rambling It's a really really cool shot. I love seeing this every time so cool. All right. Thank you All right, there's an email you can sign up you can start whenever you want you can submit whatever you want You get 16 submissions either way like and subscribe would be awesome. All right. Thank you


So guys I am back with another Starfield video and today I'm going to showcase to you guys a crazy glitch and exploit which is definitely broken and will be patch. It's not too much raise about it. This does work after the latest patch though so probably within the next patch or one coming after that. This will be nerf so take advantage of it while you can. It consists of three chests not one you've probably seen in Achilles City I'm thinking of the one chest know the three chests here I'm going to showcase to you how you get each and every one of them how you reset them what you can get it's ridiculous stay tuned. How's it going guys my name is dpj and if you do enjoy the video leaving a like really helps out and if you like what you see and want to see more be sure to subscribe so if this is new to you you need to come to Achilles City I'm going to showcase to you exactly where this is okay so let's go to the star map let's go out to uh here we go so you want to come to the Cheyenne Cheyenne destination this star right here and I can see if I zoom out it's actually too far from where you start we've got Alpha Centro over there Olympus there so come up here guys come up here so click on Cheyenne Cheyenne whatever that says and you want to come to Achilles click on Achilles and you want to come to Achilles City so just land here whether it's your first time here or not it does not matter okay so now we are there you'll end up right here guys your ship behind you and then you want to come this way now you want to go into third person for this now one of these chests I believe you can get and not being in third person but the other well especially one you need to be in third person so it may just well just run this in third person it's as simple as this okay so the first chest guys is right outside Shepherd's shop now you've probably seen this already this is the one many people have made videos on so to get this perfect guys you want to come up to this this is the one you can get in first person by the way it doesn't matter about being in third person with this one so if you want to go in first person you can so you just want to come up to this thing right here right outside Shepherd's watch and you just want to walk backwards until you see this puddle right here this first puddle you see now you want to crouch and it's somewhere around there you go right there you can see it there we go now this one in here's got credits take the credits it's got all kinds of ammo which is just what we want so I'm just gonna go I actually need to restock on my ammo so I'm gonna do this anyway people no I'm saying you know yeah yeah just go on okay so med packs digi picks everything you need is in here ship parts I mean they're kind of heavy I'll crop now I'm in comfort oh wait doesn't really matter okay so yes I'm gonna show you these I ain't gonna but there's so much stuff in here I mean look at all this there's so much stuff and this resets people I'll show you how to reset this it's crazy absolutely crazy okay so probably people want the credits which is fine but this still is unbelievable so we're just gonna come out of this one and we're gonna go over to here and I can see this one right here this shop here does that say the hitch impulse I think that's a H and the I either way so this is the way you want to come to so you can see it's like blue rug hanging up is that a rug I think it's a rug I'm not sure this one I believe you do have to be in third person for so I'm just gonna go into third person anyway and it is somewhere around here there you go right there see it's right there this one actually quite easy to get this one's got 1200 credits in it now see it's always just like a little bit boggy of it once you get it down those should be right this one isn't great it's just the credits from this one I mean unless you want to get drunk but other than that so we've come out of this one guys you want to come around this corner here so you can see this shop there rolling arms so you just want to come around here guys and you'll see these two tables so you want to position yourself just by this railing crouched down and it's somewhere around here this one's a probably the boggiest one to get get out my way Sarah I'm sacking that woman off she does my knot you know she does this complain they were right there you can see where you're at and you see this big rock there's that big rock and you can see there's that big rock basically you probably use that triangle for reference and they can go right there and we're seeing here guys we've got weapons might as well grab them while we're here we've got credits we've got ammo more ammo everything you need everything you need from these three things I'm just going to grab all these because I need that ammo I need that ammo more than anything I'm running out so I'm just going to grab these that's probably about that for that okay so to reset the chest you have to skip time by 48 hours on this planet you can do these two ways one way can come to this chair outside of shepherd shop and wait 48 hours this is probably going to take you a minute or two in game or to make this faster for yourself you can also go to skink which is another planet within the shion galaxy once you get here guys you simply need to just skip time by one hour this can be done quicker if you build an outpost here and create a sleeping bag once you are done head back to akila city and there we go guys you'll see now that the loot will have reset well actually there's one more thing you need to do before the loot resets because I've seen people actually say well my loot doesn't reset my loot doesn't reset so I'm back outside shepherd's shop here not watch what the hell am I talking about now if you come down here crouch come back to this portal you'll see that the credits are not there even though I've skipped time what you need to do is actually that anything I took out of here will not be there what you need to do is you need to speak to the vendor once you come in here and speak to the vendor so I'll click on his name show me what you have for sayo once you get to this point let him talk let him say what he was saying us back out of this and you'll see guys now when you do it the loot will have reset inside of this you'll see the credits will come back they can see them right there along with all that beautiful ammo as well as everything else and this is exactly the same thing for all vendors you need to speak to well I actually have seen people say that you don't have to speak to vendors for me of any kind of glitch like this with chests when you loot them from underground or whatever you always have to speak to the vendors to get them to reset may not be the case for you but it's definitely the case for me and most of my power so yes that loot is not there for you when you go to check the chest again speak to the vendors and it will reset and there we have guys remember one by the rug here and one around the corner here by this rolling arm shop simple as that guys and that is how you get infinite well credits ammo even weapons I mean there's so much you can get from here ship parts or whatever guys if you enjoyed the video leaving a like really helps out if you like what you see want to see more be sure to subscribe and hopefully guys I will see you on that next one


Did you ever feel the need to level up your game on your front forks, but don't want to buy an entirely new set of forks? Maybe you should consider a cartridge kit. But how much better can a cartridge kit be compared to a Revalve? Let's find out. Most dirt bikes come equipped with pretty good suspensions, but on some bikes, Revalving the forks won't be enough due to the limitations of the technology itself, like more hard-endure-oriented bikes. But buying a full set of forks is far fetched. This is where cartridge kits come into the picture. MX Tech is an American company focused on making high-quality suspensions, shocks and cartridge kits that fit on most OEM suspensions and bikes, and go the extra mile in performance and adjustability. And how do they do that? Well, they not only use some of the best raw materials available, but also focus essentially on low volume and high-quality production. This is a generic quality cost chart. Every manufacturing company has its own total quality cost for every part they produce. The total cost is determined by the sum of the prevention cost, which increases according to how few defective parts we want out of the manufacturing process, and the failure cost, which is the amount of parts that don't meet the standard. A quality-driven company will figure out how much it will have to pay to achieve a certain level of quality for the volume of parts it produces. A high-volume manufacturer can improve the quality of its manufacturing process by investing in better tooling, increasing the batch of parts that are under manual inspection, or even having automated quality control. A low-volume manufacturer tends to use its manufacturing threshold to its favor by inspecting almost all or even all parts that are produced. MXTech focuses on build quality and light materials, but they also have one of the most innovative and well-rounded cartridge kits around, the Raven cartridge kit. On the outside, the Raven is equipped with hex key-damping adjusters to prevent the wear of regular flat-screw driver adjusters. On the cartridge itself, there is a set of grooves to adjust the preload of the spring. The higher it is, the less preload there will be on the spring, simple yet effective. The compression base valve follows the same principle as any other compression base valve from a closed cartridge system, but with an additional cup with shims on its base. On the damping rod, besides the rebound valve and mid-speed valve, there is an additional smaller piston, which, combined with a cup on the base valve, provides position-sensitive compression damping that dramatically improves bottoming resistance, called the Huck Valve. Let's see how the Raven cartridge works throughout its whole suspension stroke. When the forks get compressed, the damping rod slides up the cartridge and the oil is forced to flow through the low-speed compression-damping orifice. As the oil pressure keeps increasing between the mid-speed and compression base valve, the low-speed shim stack opens, allowing more oil flow and reducing damping. On the piston rod, the float on the mid-speed valve allows an initial damping bleed. The shim stack is engaged shortly after, allowing more oil flow and reducing damping. If the oil pressure keeps increasing, the high-speed shim stack opens, increasing the oil flow and providing less damping. When the Huck Valve piston enters the cup on the compression base valve, it means the forks are near the end of the stroke. Oil inside the cup has nowhere to go and is forced to go through the Huck Valve, increasing the overall damping of the forks and dramatically improving bottoming resistance. On rebound, the play on the Huck Valve piston allows an oil bypass through four small holes, allowing the cup to be refilled without any significant rebound damping. On the piston rod, the oil is initially forced to go through the low-speed rebound damping orifice. If the oil pressure keeps increasing under the rebound valve, the rebound shim stack opens, allowing more oil to exit the chamber below. This will generate rebound damping and control the forks extension. The Huck Valve makes the Raven cartridge kit a speed and position-sensitive damping system, providing massive bottoming resistance that keeps the rider safer and makes it possible to have the forks set up for a much wider range of applications compared to traditional close cartridge forks and without sacrificing any comfort or performance. As you can see, a cartridge kit can bring a lot of benefits for weekend warriors looking for a cost-effective improvement of the forks or a racer wanting to improve the performance. As for MX Tech Raven cartridge kit, you can expect a lot of bang for your buck, being one of the lightest cartridge kits on the market with innovative features that improve performance, comfort, reliability and adjustability. And talking about adjustability, if you want to finally learn how to take full advantage of your suspension adjustments, take a look at our online suspension courses available on our website. If you have any questions, leave them in the comments below and thank you for watching. Knowledge is power.