As I make this video, I am on the traditional unceded territories of the Comox and Qualicum First Nations. I acknowledge that and I thank them for the use of their lands. A couple of months ago, I made a video about the Colatz Conjecture. And in that video, I essentially proved that if you had an integer that was within the tree, it was within the tree and it was connected to all the other integers that were within the tree. Which is great but it doesn't really address the Colatz Conjecture because the problem with the Colatz Conjecture is you're trying to prove all integers are in the tree. And if you just prove that the integer you're looking at is in the tree, you're not actually proving it for all the other integers. This was pointed out to me through comments by a number of individuals. One in particular goes by the name of Scruffy Egg who was particularly good at explaining to me where my deficiencies were and how I could improve them. And what we came to at the end was that I should probably be looking for loops. I should be looking for ways to prove that all integers were in the tree. Okay, the whole plan here is we're going to construct the Colatz Tree from integer equivalence groups of modulo 6 and show that the only loop in the tree is 1, 4, 2, 1. And that the tree contains the set of all positive integers. So starting off with the Colatz even rule. If you were wondering before about what equivalence classes are, well 2n is the even equivalence class. 2n plus 1 is the odd equivalence class. You can divide things into even or odd depending on whether they have a remainder of 1 or no remainder when you divide by 2. That's what an equivalence class does. We'll look at that for a modulo 6 in a second. Right now we're just looking at the Colatz even rule. So Colatz even rule says if I've got something that's even, 2n, I'm going to divide by 2 and get n. That's pretty straightforward. But I want to construct a tree so I want an inverted Colatz even rule and what that says is if I start with n which is any integer I do the inverse, I'm going to multiply by 2n, not divide by 2n, I'm going to multiply by 2n, and I'm going to end up with 2n. So n through the inverse inverted Colatz even rule becomes 2n. We'll do the same thing for the Colatz odd rule. Here you see the 2n plus 1. That's the equivalence class for odd numbers, remainder of 1 when you divide by 2. The Colatz odd rule says I'm going to multiply the starting number by 3. So I've got 3 times 2n plus 1 which is 3 times 2n which is 6n plus 3 times 1 which is 3.  So if I start with any odd number I'm going to end up with an equivalence class of 6n plus 4. 6n is part of the Modulo 6 equivalence class. But again because I'm trying to construct a tree I don't want to do the direction this way. I want to reverse it so I'm building up from the bottom. And that means my steps would be I would subtract 1 from 6n plus 4 and then I divide by 3 and I'm going to get 2n plus 1. Well that tells me that 6n plus 4 equivalence class integers are the only ones that are going to create odd integers because 2n plus 1 is every odd integer. So 6n plus 4 is going to have a precedence of 2n plus 1. So from these two rules we can see that any integer has even predecessors. So any integer, all of the integers will have an even predecessor but only integers of 6n plus 4 can have odd predecessors. So there we are right now. Remember that. This means that 6n plus 4 integers are the only ones that can have two distinct predecessors which is a requirement for initiating a loop in a tree. Well okay so think about what a loop in a tree would look like. It's going to have two paths that join. And at the lowest point that joining point will have to be something like this. It will have to have two predecessors. So the only integers that we have found that can have two predecessors they have an even and they have an odd, that is the 6n plus 4 integers. And so 6n plus 4 can have an even predecessor and an odd predecessor and that's what we're looking for to initiate a loop. These others can be any modulo class but they're not going to initiate a loop. They might be part of a loop but what I'm looking for is where loops can be initiated because if you can't start a loop in a given path there is no way you're going to have a loop in a given path. So that's kind of my structure here. So now we're going to look at equivalence classes of modulo 6. So if you were confused about modulos I'm going to show you now how they work and how they work is I'm going to put up these numbers. Now I want to sort these numbers into the different equivalence classes and the way I do that is I'll take each of these numbers and I'll divide them by 6 and I'll look at the remainder. So 18 divided by 6 is 3 with no remainder. That means it's going to show up into this equivalence class. 135 divided by 6 is 22 plus 3 which means it's going to come down here into this equivalence class because the 6n refers to I'm dividing it by 6. If you don't care about the 22 it's the 3 that's going to make it into the equivalence class. So now I'll just do a little bit of fancy animation. So we already know that there is a loop that occurs at 1 which means that we will construct the tree based on the value of n greater than 0. We will show later that there's only one loop where n equals 0 and we'll do that by inspection. So what's this about the n greater than 0? If n was 0 then one of the integers I'm going to be looking at is 1. Well I know there's a loop at 1 so I'm not going to get very far proving that there are no loops in the tree when I know there's a loop in the tree. So as a result to get around 1, that 1 that I know has a loop I'm going to take n greater than 0 so if n equals 0 you can see down the side here. If n equals 0 this will be 0, 1, 2, 3, 4, 5. So I'm going to do those ones by inspection later on. But I am going to look at n greater than 0 so that would start at if n was 1 it would be 6, 7, 8, 9, 10, 11. And then so on if n equals 2 then 6n becomes 12 and it keeps going on and on for all the integers that there are. So now I'm going to look at the even predecessors of module 6 and even predecessors are really simple it was what we were talking about. You just take the number and you double it and then you take that number and double it and double it and double it and double it. And what this table kind of shows it shows a kind of some interesting things that you might not really notice right away. One is sort of by definition each of these bottom equivalence classes is going to be distinct. They have to be distinct. That's how they're defined. If you divide a number by 6 you're not going to get a remainder of 1 and a remainder of 5. It doesn't work that way. You get one or the other. That's why it breaks up that way. So these are all distinct across the bottom. But when I double them now I've got double here. Notice here these are all distinct across this row and when I go up the columns they're distinct as well because I'm doubling each time. They're never going to be equal to what the 6n is. So what I'm looking at right now are these values. I could substitute any number in for n and then suddenly this would be populated with actual numbers and they would all be distinct and I'll be looking at the even paths going for module 6. So let's take a look at this because I can find out a little bit more about this right now. Just looking at this a path at a time. If I've got 12n there's another way I can write 12. I can write 12 as 6 times 2. So 6 times 2n, 6 times 4 and 6 times 8n, 6 times 16n. These are not equal values. I'm not claiming that. But they are all going to be in the same equivalence class. So all of these will be 6n equivalence class. Everything in this even path, even Colatz path is going to be a 6n. Do the same thing for 6n plus 1. So look at this 12n plus 2. It becomes 6 times 2n plus 2 and I double it and I get 6 times 4n plus 4 and I double this and because 4 doubled is 8 and 8 is 6 plus 2 I end up having to put a 1 in here for that 6. So it's 6 times 8n plus 1 plus 2 and then I double again and 2 doubled 4 doesn't get me out into the 6s again so I just have to double all these up. So again I end up with the equivalence classes from module 06. 6n plus 2, 6n plus 4, 6n plus 2, 6n plus 4 it continues on that way. So I started with 6n plus 1 then I got to 6n plus 2 and then the pattern starts. We can probably guess if I start with 6n plus 2 I'm going to go to 6n plus 4. I did there, I'm going to do it here. I'm not claiming these values are the same, they're not but they are the same equivalence classes. Something interesting happens with 6n plus 3. I double 6n plus 3 and I get 12n plus 6 but in a 6 module equivalence class I'm going to get 6 times 2n plus 1 and so 6 times that, doubled all the way up all those are just equivalence class 6n. 6 times a number is going to, there's no addition there, there's no remainder that I'm going to be dealing with. It's going to be a 6n equivalence class. So it's like this 6n shows up over here and that's all I get. Once I get to a 6n it repeats to infinity. Once I get to a 64 or get to a 62 it alternates with 64, repeats to infinity. I see that happen here. Now you can see I sort of gave away the game didn't I? So if I do the same thing with the modular classes here 6n plus 4 is going to go to 6n plus 2, 6n plus 4, 6n plus 2 and again on up to infinity. And here, what's interesting here is when I double it I get 12n plus 10 but if I want to change that to 6n 10 is 6 times 1 plus 4. It's going to be a remainder of 4. So I can't do 6n, I can't do 6 times 2n plus 10 I'm going to have to do 6 times 2n plus 1 plus 4 and then of course 4 goes to 2 goes to 4 goes to 2 so I still end up with that same pattern in here. So you've got this really interesting thing happen. These all go to infinity. These are all distinct values. When I put any n in here all these will become distinct values and because I can put any n in this represents all the integers. So remember I'm looking for loops. Well, right away if I'm only dealing with the even predecessors I have no loops. They're just straight lines. They just go vertically up doubling each time. That's how they work. So in the case of these ones, these even ones all they can ever be is there can't be loops in them. They're just going to be every time I hit an even I'm just going to divide by two. It's just on to the next one, on to the next one. I'm not going to be generating an odd if I'm in an even. Now if I'm in an odd that changes things a bit. So here are my even predecessors of module 6 but only the odd ones. So together these represent all the possible odd numbers. 6n plus 1, 6n plus 3, 6n plus 5 you do those equivalence classes you have all the odd numbers. All the odd remainders that you can have. You can't have more. There's 6n plus 2, that's even. 6n plus 4, that's even. 6n plus 7, that's not module 6 anymore. 6n plus 7 is actually 6n plus 1. So I have all the odd numbers represented here at this level. Now let's take a look at the and they go on infinitely. The little dots up here. They go on infinitely. So now let's look at the equivalence classes that they represent.  So I have some patterns here. What's really interesting is I have no 6n plus 4s in 6n plus 3. An odd number that's divisible by 3 will have no 6n plus 4s in its preceding even path. With no 6n plus 4s it can have no odd predecessors. These guys over here and these guys over here can. This we'll see in a second. This will generate an odd predecessor. There can be no odd predecessors for odd numbers that are divisible by 3. Just straight lines straight up. No odd numbers. Because there's no 6n plus 4s there can be no initiation of loops. There's no loops with 6n plus 3. Get rid of it. So now I've got 6n plus 1, 6n plus 5. Let's look at what happens at those 6n plus 4 points here. So I'm going to convert back to the values. Again I can sub any n in that I wanted and I'm going to get real values up here. These are all just multiplying by 2. It's all straightforward. When I get to here I'm going to subtract 1 and divide by 3. That's what I'm doing here. Now notice I can go as far up here as I want. This is to infinity. Which means this is to infinity as well. And this is to infinity. And this is to infinity. So what I've got here is I'm looking at 6n plus 1 and 6n plus 5 which are the only initiating classes that can have loops in them. And now I'm looking for where could the loops be. So the construction from any odd integer to the preceding odd integer is really central to this investigation. And I'm going to refer to it in the future as a precedent step. So I'm not going to worry about going past that next odd integer. When I get to a preceding odd integer I'm not going past it. I'm stopping there and I'm only starting from one odd integer and going to the preceding odd integer but as we can see there is a whole host of preceding odd integers. There's infinite preceding odd integers here. And so I'm just looking for the step from here the originating to here and this includes all of these. It has infinite preceding odd integers. So let's take a look at that. Let's take a look at the equivalence classes. The equivalence classes I start from 6n5 6n plus 4 2n plus 1 I'm getting an odd number. 6n plus 4 I'm always getting an odd number. There's always going to be an odd number here. I'm not going to get some other number. They're always going to be odd here. This is significant in the next couple of steps. So what I'm doing here is I'm just swapping out graphically because it's easier to show just how things work than it is to put all the numbers in places. So just to show you this can go on and on and on and on and on and on and on and each step from this one I'm going to get many preceding odd integers. So this is a one to many relationship. The one of course is the originating integer at the bottom. The many are the preceding odd integers up the side. Key point here is that in this precedent step there are no loops. I have a straight line up through the even precedence. I have a single edge across to the preceding odds. There are no loops here. There can be no loops here. If I stay within that precedent step get outside the precedent step I can't say but inside the precedent step there are no loops. Let's flip this on its side because this is where the fact that these are all odd comes in and I'm just going to look at one of them. I could look at either because they're both really based on having an odd a 6n plus 4, 6n plus 2, 6n plus 4 as I go through that's what's generating these odd numbers but this is what's really important. I've generated this odd numbers and there are no loops in here. It's a one to many. There are no loops in here. I stop here but say I wanted to say well what if this one was 6n plus 3? I'll put it there. Now I've added 6n plus 3 I've introduced no loops. There's no possible loops here because there's no loops here and then this is distinct these numbers will all be distinct and there's no loops. Okay, so what happens with 6n plus 5? Well, same thing no loops in here on this base I'm just putting an odd number in here it could be any odd number but right now I've shown if it was 6n plus 3 there's no loops if it's 6n plus 5 again I just showed there's no loops because it's one to many all the way up here and to wrap things up pop 6n plus 1 and same thing one to many with no loops based on no loops each of these and 6n plus 1, 6n plus 5 and 6n plus 3 that's all the odd numbers so any odd number put into this tree that has no loops, this one to many tree is another one to many tree or it's just a list of even numbers if it's 6n plus 3 so essentially I've shown that there are no loops using Agilo 6 equivalence classes to construct the tree but there is a loop at one so I will need to show that there are no loops for 6n, 6n plus 1, 6n plus 2 6n plus 3, 6n plus 4 and 6n plus 5 when n equals 0 I'm going to do this by inspection well before I even inspect for 6n, if n is 0 I get starting point of 0 and 0 actually isn't defined for the Colatz conjecture that's how I get rid of that 6n for n being 0 it's just not defined but let's take a look at 6n plus 1 that gives me 1 6n is 6 times 0 is 0 plus 1 I'm starting at 1 so from 1 I know I can generate all these even powers of 2 up above me I did that before this is just the Colatz conjecture going up the string here now there's my loop so this is just by inspection I just look at it and I go okay so if I started with 4 now this I'm working my way down the tree not back up the tree but if I start from 4 I go to 2, 1 and I go back up to 4 well when I'm building the tree I go 1, 2, 4 takes me back around to 1 so there is the one loop I've got but I'm okay with that because I knew it was there and I just have to prove by inspection that the other numbers, the other odd numbers are not involved in loops I'm not really worried about 2 or 4 and here are some of the other odd numbers I have to get to the odd numbers I can only in this case get to the odd numbers by going up the chain and using these higher 6n plus 4 to get to these other odd numbers notice that this is a 6n plus 5 this is a 6n plus 3 this is a 6n plus 1 this is a 6n plus 5 and these actually repeat all the way up but it depends on where you start from so we're just concerned the fact that these are odds so let's go looking next for the next odd in the initial sequence and that's 3 so I get to 3 by way of 5 and down to 3 so now I've got 3 and 3 of course is 6n plus 3 and that means that it only has even numbers above it so no loops no loops with 3 now I just have to check out 5 so I look at 5 and all the even numbers up above it all the 6n plus 4s generate odd numbers but again all of these numbers and in this case the number is 3 and then I go up this chain here the same way here my first number was 1 and then I went up this chain so this kind of throws you off a little bit as does this but actually if you're actually thinking about the precedent step you're just going up next odd up next odd up next odd and each time I do that precedent step I'm not introducing any loops all these numbers are distinct now by proof by induction for the 1 to many branching precedent steps in the Colatz tree the base case of n equals 0 was just shown and now the inductive steps so I've shown this tree just as a 1 to many and in the case I think depending on it's 1 or 3 or 2 depending on each step I'm I if I really want to do a Colatz tree each of these levels branching points would be infinite and then this branching point would be infinite again and this branching point would be infinite again well in terms of just showing how it works I don't really need to go into the infinities and they're hard to draw so what I'm going to do instead is just show this schematic to give you an idea so I can select any odd p that's not within a loop now in the Colatz conjecture that I'm dealing with 3n plus 1 there are no odd numbers within the loop the loop is 1, 4, 2, 1 1 is an odd number but I'm starting with 1 so I don't have to worry about that but at the end we'll see with other 3n minus 1 for instance which is the negative Colatz tree there are multiple loops so if I select the p and select it within a loop and that p has to be connected back to 1 but basically what I'm saying is if I'm applied m applications of the precedent step from 1 I'm going to end up at this p and this p could be any p in the tree that's not it's odd and it's not in a loop do that and gold so the next step I apply the precedent step now I've applied the precedent step to all these and they go on to infinity all these guys up here they go on to infinity the point is from this point on the precedent the odd numbers that are proceeding this odd number are going to be disjoint from all these other numbers because this number is disjoint from all these other numbers and when you apply the Colatz rules they're very determinative they will only apply the numbers you can't have multiple results from the same number you give it one number you're only going to get one result so now I apply the precedent step at m plus 1 time bang there I am there's my m plus 1 the resulting all predecessors are distinct from the rest of the tree and I've introduced no loops so the precedent step can be done an infinite number of times and that could create a tree with infinite distinct integers a tree with infinite distinct integers contains all the integers so all integers converge to the 1, 4, 2, 1 loop and that's pretty much what the Colatz conjecture says so there you have it that's what I found by constructing the tree and essentially the Colatz tree ends up as a whole series of n to infinity trees that have disjoint edges stacked on each other that means there's no loops and because you're doing it inductively it means all the integers are there at least that's my understanding of what I've done now I may be wrong, I'm not a mathematician so certainly make any comments that you want about whether you think I've gone wrong no, maybe I got it right I think I'll be honest I think it's probably too simple to be right but I can't find holes in it so if you find holes in it please let me know one of the things that came up on the previous video was negative numbers if I put negative numbers in the Colatz formula the 3n plus 1 or the even 1 dividing by 2 put negative numbers in I do get distinct disjoint trees I get a number of loops and that is true but when I do that I'm actually creating a new tree a new form that's equivalent to the 3n minus 1 the tree shapes are the same for 3n plus 1 with negative numbers and 3n minus 1 with positive numbers so what that means is this is actually a different tree than the Colatz tree and that different tree this the logic I've used still applies to it except you have to use modulo 18 because modulo 18 gets you up to cover all the initiation of all the loops the biggest loop is at minus 17 or 17 if it was 3n minus 1 you have to get above that so modulo 18 gets that to you and then the same arguments apply with one other exception that other exception is now you've got a loop when you do your induction step you can't be inside of a loop because in the induction step you're saying these are separate there's no overlap but if you're in a loop some of your successors are going to be equal to your predecessors because you're in a loop you come around and they're going to be there again so that induction step doesn't happen until you get above where the loops are and as soon as you get above the loops are the logic stays the same and it all works the same way but that's the difference so for 3n plus 1 which I just showed 3n minus 1 which I just talked about it seems to me that this works find holes in it let me know I'm absolutely open for comments this has been a very fascinating journey this Colatz conjecture is well in some ways it's so difficult but in other ways it's so interesting and I've learned so much from it by playing around with it so thank you for your attention and I look forward to your comments


Hello and welcome back to the craft box. My name is Brent and today on episode 113 of the Wizard 101 death walk-through last episode if you haven't checked it out already We went into The quarry area and we defeated this kid and we saved the professor But yet we're going into the elephant barge today So yeah, let us do these I think this will be the last episode of the drum jungle Which is really cool because then we just have the elephant graveyard And then we're a lake and we're done. So Nearly done with Zafari, which is really cool Look how many pallets of bricks and shadow artifacts they intend to bring back. No good will come of these relics Okay You are the outsider causing the Omra Queen so much grief Yeah, I am okay. We need to feed him. Let me just check if he cheats Are you okay feints blades cool? No cheats Can both myth and an earthquake Whoo, what a bit of health as well. So do we have you we do? That's cool. Okay Let's go boys. We can do this Don't don't do to do to do Okay He starts off with a lot of pips, but you're gonna start by doing this blade And I'm hoping that earthquakes or whatever Minotaur that's cool. Knock yourself out, brother We can also Medusa, so that's the two rounds done yikes Rebirth already what man He's going man boys And then there's all okay. Luckily Death get around absorbs by doing a drain because they don't block against strains, which is really good But yeah, let us Do this we can enchant hue We will get you up life blade, okay that cool and What do we got now? I'm a few earthquakes.  Oh All first that's even better Okay, any bad thing about all first as it takes forever And we have a nice wee empowerment. Okay, that's cool Useless spell, but that's fine Whatever floats your boat and we have another Have a faint and another blade we will faint Trying to get as much damage on as possible. Hey and foul.   That's how much this does No correct, but we still have four blades three blades four blades Eight thousand by four thousand by oh that was good. Okay. Let us talk to him No more the Umbra Queens agents took the elephant Prince through the mammoth doors to the numinous graveyard beyond She ordered them to cover their tracks the pedestal at the feet of the great statues must be able to see all who enter Her minions pulled out the pedestals gem eyes and hit them nearby You need a local guide to even have a chance to find them You tap into the energy of the eternal flame and burn a powerful glyph into the border Okay, let us head back to um Lilo. I'll be back when I'm at um Lilo. Okay. I am back and we're at um Lilo Hooray, I could see the barge burning from all the way over here Axel black drunk said they hid the pedestals eyes in the jungle who might know Perhaps Coco smoke sign will have an idea Back to Coco That's here on over to Coco That doesn't really look very bent to me, but that's That's cool Whatever floats its boat, you know, or whatever doesn't float the boat Let's head back to Coco Do-do-do-do-do around the black toss because they're bad Do-do-do Poop-poop-poop Do-do-do Coco more Gantz agents did what I Know a ritual to find the missing gem eyes, but you would need shungo's blades to find them Shango is the spirit of war and strength who cleaves through deception But his tomb was robbed and his blades are stolen the blades Shango's thunder and shango's lightning were stolen by a gorilla spider, which named Oya bloodstorm Track Oya bloodstorm to her cliff cave and get the blades from her then return to me Okay, let me head over to Oya and I'll be back when I met Oya a wizard. What a delicious morsel Okay, we are back and we are at this person a gorilla thing And just fill up our TC's which I haven't done and Hopefully that should be good. Let's go Okay, we will thank to start Might as well Mainly because the myth minion has quite a few pips Yeah Interesting choice She yeah, I'm not too bad. You're doing you're doing a minotaur There we go, okay, how much hath those we I have Ah 6,000 that's okay Not too much You'll just start blading slowly and hopefully Probably probably we'll need more than three blades Maybe three blades. Maybe yeah, we'll try three blades. We can try three blades And we've already got two So that's why the good start No, I thought it depends how many pips we get or don't get so Yeah, basically when we have the pops all hurt, so meteor And an infel Nope an ample amplify. That's cool Um, but I'm but I'm really want. Yeah, do that do that just so we can save some pips so we can hit next Okay, and I'm good another one might as well. Let's just do max, you know, why not? The only worry would be if they earthquake, so you just do this We've got four blades, it's good enough and a faint so we should definitely kill the boss Definitely kill the boss plus it's good unless you like your humongous. We might do max We'll do max but it's just how much damage we can do why not Let's do it for the lows Just for fun No, do I want to finish quickly? Oh such a hard decision. No, just to just do it. Just do it Pew Scarecrow Didn't crit again, but we have four blades and a faint So this should be gg. Yeah just Awesome as impressive at last time But that's cool Fine you win take the silver sword take shingo's lightning the other blade. I'll never tell. Okay. Okay. I'll tell I gave it to one of the umbra queens agents a goliath called runs on it dwells in a jungle clearing nearby Interesting some pierce don't need that though. Um, okay. Let us head on over to runs on who I believe is a goliath I think which is kind of kind of a worry But um, should be fine Should be good. I was wondering why they gave so much exp for this quest, but now it's understandable because we have to defeat two people I'll be back in a sec. Okay You track ranzan to this jungle clearing the smell of rotting plants and meat is almost overpowering Okay, let us um Do this one now Yeah, I've fled that little I didn't really want to get into um I didn't really want to Get into that fight. I mean last time it took forever to finish. So I didn't have prisms in their death So I just like nope now doing that uh, luckily None of them can earthquake so we can just basically full out blade Which is fantastic Wow That critical though that crit dough Oh Um, okay that crit what what why what? Okay, let's just keep blading I suppose weakness. No, that's good. If it's a little unlucky Blade Nice and blady Another cheeky blade. Yep Do this one And then I think we will go for a wow. Okay, that's cool Cool, bro We'll go for a faint then we'll go four blades in the fame How much he boosts how much health does he have who knows find out in a bit Wow, of course that death shield Geez 6,300 Gonna need a lot a lot of blades man a lot of blades Older blades Jesus Christ, you love judgment, don't you? Yeah, you do Except that one didn't do any damage because you didn't crit and you didn't have many perps. So that's unfortunate for you Um, okay There is one two three four blades we can do five um If I do faint now, hopefully we get a blade next which would be good. May not though It should be unfortunate, but um Don't think anybody can kill us at this point At this point it is um Yeah, we're very low on health for us But um, we can't die at this stage, which is good. They have like four perps and Four perps and three perps Unlucky. Okay. We didn't get another hit another blade. So we're just gonna go for it I'm just gonna go hunt full honours, bro And see what happens man. This could do a bit Blade hits a kind of natural attacks a kind of OP Um, okay Ha ha ha ha ha Okay Nearly dead Nearly dead And I have no pips though. So that's unfortunate and we're gonna get health from this No matter what happens, please crit Nope didn't crit that's unfortunate Okay, I'm not dead. I'm fortunate Got full health though. Yeah, boy Okay, let us try again Probably go for a Uh, Wraith probably just blade blade blade Wraith most likely At least you did another shield and that would be annoying That would actually be really annoying if you did Um, okay Blade blade and Wraith I don't think we'll need a faint but How much health do you have you have 2000? Yeah, we'll do faint just in case just in case Yum Hello Not worried anymore because of full health.  No, no fizzle good. Yay Here we go Yay No, no Bye 4200 nice Noice There we go We're taking health Once you defeat ranzan you find a crude but effective looking iron blade. This must be shango's thunder Okay, let us hit on back to cuckoo. In fact, I'll be back when I am at cuckoo Okay, I am back cuckoo. Good job Let the blades guide you they will cut away whatever obstacles are in the path then return to me Okay, um, we're just gonna leave a mark here for measure Uh, I don't know where we're cutting but we are Somehow we've defeated so many bosses today. I think there's still more to come as well. This is like a Kill all the boss episode Which is better than kill all the mobs episode, which is what zafari is usually like Um, so yeah, I'm not complaining, but it's kind of weird Um, but also cool. So yeah, let us cuddle the webs I don't know where we're going where we're meant to be going but um, we have to go down here Seriously Not the what Well get around the thing Whoop dodgy Whoop that was good. Okay, we're to walk go over here. Okay You feel the blades pulling you this way towards the waterfall. There's an unusual looking rock here You slot the silver sword into the rock and you can hear stone grinding. There's a cave behind the waterfall Oh, okay Next guy to the fate told you it's a boss filled episode. Haha Um, so yeah, let us defeat this fella What do you have cheats and stuff find out He's nice. Oh, yikes. Yucky doesn't even have nothing. Okay. Yeah, okay You can touch it. That's unfortunate, but we should be fine. Let us just put in A couple of you in and we should be fine Okay No myth, which is good. We will Faint to start with actually that's probably a stupid idea in case he shields, but that's unfortunate. We'll just do it anyway Um We'll probably have to head again. That's fine. That's fine That's fine boy. That's fine. Yeah Okay What this be? probably the worst thing you can do is either first try or Freeze us Um, yeah, so he can stun us a bit, but that's cool. We're used to being stunned. Um, stunning isn't Bad basically means we can get more pips. Um, essentially just kill them. So that's fine As long as he doesn't use up all of his perps He has less of a chance to use eye shield because they tend to only use one No, zero perp spells if they have no perps. So, yeah Speaking of getting stunned Welcome to the land of being stunned Um, okay Yikes Uh, what are we gonna do? We're gonna discard you And we're gonna draw you and just in case We are gonna do that. Nope. Okay, that's unfortunate. Oh, well Okay And what's this this is uh, I squabbling Okay, and we will blade again Doop What is he doing? What's he doing? Without sure. Okay, that's interesting. Oh, I played so weird. Um Okay, Blizzard not too bad And what can we do? We can blade or blade or blade just basically blade or blade 40 40 40 Yum, okay pass. That's good And we have this blade Just really sticking up these blades boy. He hasn't even tower shielded yet. I'm so happy I don't want to jinx that though because as soon as I say that he's gonna tower shield Just you wait Okay No, yeah, here's nope. Not here's a tower shield. Here's a four to five even worse to be honest Um No, look finally we get one of you Uh, what can we do we got? Yep, we just need I think it's one of the the item card player that we're waiting for so we'll just pass and wait Hopefully it's four rounds or he does another he does another Fortify not fortify like vengeance or something because I think he knows another one He should be able to know another one. It would be better if he doesn't Yum, okay, I'm not dead at this stage, which is good. Um Just cut you Just because we can always um You can always use a tc, which is better. So yeah Cause the same amount of pips but does more so it's cool Oh seem to like 300 probably 400 400 Um, and what's this? This is a Ice colossus, okay Probably like 400 again Probably maybe closer to five depending on how much he does About three. Yeah 400 Okay, slowly getting low on health Um, we're gonna do this Got no perps. He can't do anything but his fortify will run out. So that's cool What's this? Oh blade. Nice. Okay, and yay, we can hit and hopefully kill Let's do this Thank you so much game. Love you two pieces. What's the chances of shields? This game hates me.  Yeah, that's honestly Any crits. Okay, just to put this off in the wound. I get it Oh, okay Just as well. We got so much health off the minion. Um, oh god 2000 Triggered Let's see how much this does. I don't know if this will kill, but we'll try. We will try, won't we? You have nearly a hundred percent damage where it likes 75. I think so. Okay, he's dead. That's good Unless he blocked, but he didn't so that's cool One for one You could on me. I could on you. Yeah, that's what I'm talking about He didn't die He didn't die, did he? Nope, I'm lucky Oh, this is a struggle of a battle Geez Better get some decent XP for this one, eh? Oh Yikes, um 116. Okay game I see how it is Just as well. We had lots of perps Scarecrow to the rescue 954 We do nearly a thousand We're just damaged alone. That's kind of impressive Take the GMI for the mammoth doors. You are cursed wizard Just as well. I left the mark. Geez That was a struggle That was a struggle Coco, hello Well done Where does the iron blade changos thunder point you towards kala silverberg shock? I am not surprised His lair is guarded by the spider bridge if you tried to cross it you would get stuck fast And then he'd have you I can't protect you with a simple spell But to make it I need you to find my iron pot Someone swiped it when I was imprisoned I also need my wooden spoon that one of the blackback soldiers took and we need a pinch more eternal flame from umlilo Okay, let's get the iron pot Um Yeah, we'll do that. So it seems easy peasy Who knows your pot. Oh, you're in pot. Where is this iron pot? Oh, we have to defeat no, I don't think it's you. I think it might be the life people which is fine because they Don't put up a fight. So that's cool Um, where is this pot? Where are we going?  I'll be back once I've collected um the wooden spoon Okay, I am back. We have the spoon and now we're talking to umlilo You need another spark of eternal flame. I can do that for you I must thank you again for freeing me from that dire cage. I'll head back to beabab now Okay He'd back to drum jungle to koko who I left the market after defeating the soldiers You got everything I needed. I can make your spell now With this spell in effect You can walk safely through the webs covering the bridge to kala silverback shack cross the bridge Use shango's thunder battle the big boss and get your prize then return Hic The spell seems to work and the spider webs slip right off you still ick Okay, um shango's thunder cleaves through the magical ward like it was no more substantial than smoke Okay, this guy cheats.  Um, like I don't even know why They do it because it literally Doesn't change anything. Basically. Um, how did you get in here? Why aren't you stuck to a web having that life bled out of you? I'll just have to toss the spiders your carcass um Basically, if you hit him with a single target attack, so basically not a aoe Um, without a prism He will interrupt cast a minor blessing on himself so I I I don't know. Um That i'm kind of confused as to if it's meant to be like if the wiki's wrong and it's meant to be like all single Spells that do just anything like if you just select them then it is but um I don't know. Um, and I mean your unaltered spells won't even scratch my fur Yeah, right. Um because like I'm kind of confused because We'll see what what happens if I faint him, but I mean a minor blessing isn't much anyway, so Like literally minor blessing is 65. No, that's fine. Yeah minor blessing is 65. So I'm not worried Oh, just as well. I didn't play That's the new he was gonna do something cheeky critical. Okay. I see how it is I'm gonna have to get now with five seven two Um, this guy was for the mastery of balance fire life and myth Uh, um, but he's star school So he doesn't actually use any star school spells. Oh, no, he does use amplifying fortify. So yeah Otherwise he doesn't use any star school spells, which is kind of ridiculous um He can also What can you do? He can satyr, which is kind of bad and he can also madusa which stuns for two rounds. So that's kind of bad.  Yep. Yeah Luckily he can't um spirit Spirit shield, which is fantastic, which is a death shield. So I'm happy with that Uh, but he does the elemental shield. So be careful And I don't think anything boosts on him. So yeah, we're just gonna Pretend that nothing goes, you know And just see how it um because it doesn't sound like anything boosts. So yeah, all I know is you can't stun them So who knows Do do do do Yeah, we use this one up. Why not? Why not? Amplify he's trying to get a really good, um Really really good. Um, what's it called? Um earthquake on me and I bet He just wants that earthquake Just to slap me around a bit.  Well, that's the waste of his turn Could have tried to stop me, but nope Unfortunately he didn't Because I think I'll be hitting next round. So that's unfortunate Unless it's Let's hit and see how much we do Probably not gonna be too much Um, we didn't crit, which is A bit unfortunate, but it's fine Killed him, which is good We don't boost Okay, that's cool. We did a lot of damage on Who's that minor blessing, huh? Oh wait, they do work on you. Haha Who knows?  That's quite more than I thought Oh well Nope, not one for one.  Nothing? Fine.  Because I'm proud of us Coco Coco Coco Hello You fought bravely and well Kala Silverback was no minion, but a trusted lieutenant of the ombra queen With both gem eyes You can restore sight to the pedestal at the mammoth doors The door should open for you Once you are through to the elephant graveyard, look for the spirit of the elephants You'll know her to see her Okay, so next episode we will head on into the elephant graveyard, which is actually this way. Whoops Um, so yeah, thank you for watching. We usually leave a like and subscribe And if you're very subscribed, press the bell so you know exactly when I post another video and remember craft Outside the box


Ukrainian Army successful in offensive in two directions near Bakhmut. The Ukrainian forces are conducting offensive operations north and south of Bakhmut and are successful in two directions. Spokesman for the General Staff of the Armed Forces of Ukraine, Andrey Kovalev, said this. In the directions, Bila Hora, Andreevka, and Bila Hora, Khadyumivka, the Defence Forces have achieved certain successes they are entrenching themselves on the achieved lines, the spokesman said. According to him, the Ukrainian soldiers inflicts artillery fire on the enemy targets identified and takes counter-battery countermeasures. The enemy is putting up strong resistance, moving units and troops using reserves. At present, Russia is continuing to focus its main efforts on the Kupyansk, Lyman, Bakhmut, Avdeevka, and Murinka fronts, where heavy fighting continues. According to the NBC channel, Ukraine has not yet sent all its forces to counterattack. The conflict may continue for many months. Ukraine has not yet sent its troops to the counterattack. This means that the number of Ukrainian servicemen will increase until the end of the counterattack, it was said. On June 4th, the Ukrainian army launched a counterattack from the south of Donetsk, from the directions of Bakhmut and Zaporizia.


Looking at our income tax formula, we're focused on line one, that being income. Remembering that the first half of our income tax formula is in essence an income statement, which makes sense. This being an income tax, although a strange income statement, normally an income statement has income minus expenses is net income. Our goal is to maximize net income. So typically we would like to see income increase and expenses decrease in order to maximize the net income. With taxes, everything is flipped on its head. We still have income minus expenses, but the expenses are basically called deductions now to get us down to not the net income, but the taxable income. Unlike with normal net income, our goal with the taxable income is to be as low as possible. Therefore, we want to be able to decrease our income to lower the income the better and we want to be able to increase the equivalent of expenses or deductions because that will also result in a lower taxable income. So that's the general goal. Now, obviously in practice, what we really want to be able to have is to have income that we actually get, but which we're not required to legally report as income on the taxes, right? So we want to have our reportable income to be as low as legally possible and our reportable deductions or expenses to be as high as legally possible.


What is a marble squad welcome back to our channel. How is everyone's day going if you're new make sure to go hit that subscribe button Turn on those post notifications, so you don't miss out on any single video our squad is called the marble squad My name is bill my girlfriend's name is Mariah Mariah Phil Marble Marble Marble get it get it now you guys are part of my squad. It's that easy I'm gonna be getting my girlfriend back. She's been non-stop Stacking on these pranks. I need to put an end to it I've seen so many DMs from you guys and do not stop sending them anyone that's new here Anyone that's old here no matter who you are send me DMs Prank ideas that I can do on Mariah because I've been slacking lately. I need to get her back I am so looking forward to setting a different girl as my wallpaper. Basically. I'm going to go on Google images I typed in cute girls Mariah you are the most beautiful girl in the world Don't worry, but I did find this picture earlier that I'm actually going to use To set as my wallpaper. I'm not going to set it until I get there. It's not going to take long She's going to see my phone. Hopefully start freaking out My main goal is to really just make her freak out, but anyways mobile squad if you have not liked this video yet What are you doing give this video thumbs up welcome to any new people that are here part of the model squad now I'm going to give our post notifications shout out right now if this video post notification shout out goes to Riley Dunn She says come on bill step it up team Mariah in the house No, everyone in these comments. Make sure you're writing team bill I know Mariah's a little bit ahead, but I will get her back It is my turn to start pranking the living crap out of my girlfriend and um, yeah I'm not gonna let this down So I'm gonna do whatever it takes to get back in the lead team bill needs to get his name back on the board Good luck Mariah with my cute girl screensaver. I hope this doesn't hurt your feelings too bad Mariah I love you to death, but it is my turn so scooch on over and let me slide in I will see you at Mariah's house guys Thank you for tuning in. I hope you liked the video. See you there All right guys so Mariah is in the bathroom right now I'm at her house It's been about an hour since I got in and I'm gonna set this camera up right now I just set my phone to the wallpaper of the other girl It is low key weird seeing another girl has my phone screen so I'm gonna get her reaction I'm gonna leave my phone out in the open and hopefully she starts yelling because that's my main goal hashtag team bill Let's get it Look at the video No What they didn't send me anything No, get your hand off. Who is that? It's just a wallpaper. It's clearly not just a wallpaper. Who is that?  It's one of the random wallpapers that they had It's just Who is that dude? Who are you even texting now? You're probably deleting messages. Who is that? No, back up. Who is that? It's a it's just a girl My cousin That is not your cousin because I met everybody in your family. It's my cousin. It's my cousin So why would you say your cousin has your lock screen? That's weird because it's her birthday.   I don't hear it. Stop. Why won't you let me do what I want to do? It's my phone my lock screen. I'm obviously gonna do with you, but like she just looked cute I don't care if she looks cute. Who is that?  Then who is it? It's just a girl on instagram. Well, I don't care if you think girls are pretty and stuff like You're setting another girl as your lock screen I was your lock screen and you switch it to a different girl has it. How did that make me feel it? What if I switch up my my lock screen to another guy? You would be okay with me switching my lock screen. I mean no, but answer would you be okay with that? Okay, then why are you setting another girl's lock screen? Who is it? You're not telling me who is it? It's like it's just it doesn't matter who it is, but she she counted on my instagram posts And that's why I found it. Okay, so she kind of reached out to me. I honestly took a deer. Where are you playing to the deer at? uh in our DM So the deer was a setter as a lock screen Huh bullcrap Tell me no you're not getting your phone back. It's I'm a girl I'm investigating. I'm gonna see Okay, no back up just Stop no, I'm not gonna touch you right now. You're not telling me. I'm sorry. You're telling me one thing than the other It wasn't even supposed to be on my phone. I just forgot about it.  I forgot about it I'm sorry. You forgot about it. What do you mean? You forgot about it literally took the time to press the set as lock screen I didn't mean to I just didn't mean to build you take it was in my camera roll. I thought it was a different picture I'm sorry. What do you want me to do? Give me my phone. No. Give me my phone No, until you explain to me the full story. Don't touch me. Don't touch me. Give me my phone. Then leave Then leave because that's messed up.  It's a little weird and you're not telling me why if you told me why and it was a It was a real it wasn't actually a deer.  Who is she? It's just it was a random Picture of my camera roll that I saved off instagram. No, it's just weird that you're setting some random girls your locks, right? I mean if it was like a celebrity like Ariana Grande, okay, I support you 100% She cute. But okay, so that her is your locks. You why are you saying some random girl?  How'd you know her? Yes, it doesn't matter. Yeah, it doesn't matter Because you're setting her locks great. I will set you're setting her as your locks No, no back up. Stop. Give me my phone. No, you're clearly hiding something.  Back up. What is funny? This is not funny.  Tell me No, where are you leaving?  Don't throw my phone. Okay. Well back off Okay, just don't throw my phone. Tell me who this is She's pretty. But who is she? I'm gonna go look. I'm gonna investigate. Okay, stop. You don't have to I'm gonna investigate because there's seriously stuff that you're not Why are you getting pushy right now? I have to get a snapchat. Why are you getting pushy right now? No, I'm not gonna let go. I'm sorry. I'm sorry. Why do you have to look at other girls? Because she's cute She's on instagram. She's coming on my post. I thought she was my same age I was just like, yo, we'll get along. You're older than me. So it's hard to talk to you about things I've been DM'ing her What did you just come out of your mouth? Did you just?  How do you hear that again? You're older than me Okay, Ian. You can't talk to people all the time then Are you okay? Are you going crazy?   Calm down Did you just say that because I'm older Yeah, you can't talk to me about things Actually calm down. Are you okay? Really say that you can't talk because I'm older. I'm more experienced since I'm older So why would you talk to something that's younger instead of making a lot of screen because she's more talkable Right, calm down.  Is this you going crazy?  It's not funny.     Are you okay? Are you going crazy? I'm fine.  Because that's it. That's annoying. It's annoying why Leave no, I want you to leave. Come here. No, come here.  Just leave me. Come here.  Stop joking me. Stop pulling me. Come here. Babe, I don't want to. I don't want you. Okay, why don't care? I don't care. I will set you back as my wallpaper. No, it doesn't matter.  Babe, come here.  She's just making it. When you Okay, do I don't know the real reason do I don't know the real reason come here Just come back the reason why I look at her is because when you annoy me and make me mad It makes me happy looking at it like her That's so messed up Really? Yeah, that's messed up. Okay, then go and leave since I don't satisfy you enough. I'm sorry.  Get out. You didn't see it. Okay. Bye. She look at she's not yelling at me. You're yelling at me Babe, come here. Come here. Come back down. Come back downstairs. Come here. I want to show you something That's why I'm trying to get you to explain to me. Who is that? Look at it. It's the same picture as This girl on google. It was just a prank. I saw the random girl at the luxury This is how you react It's just fake. It's it's fake It's the same picture as the girl on google I'm so annoyed Look at it. Look at it. Look at it. It's a random pic like I typed in cute girls and I I sent a random girl Is that all paper and any? Look at it. It's just a random google girl. Okay.  I got you a little point I'm sorry, babe. Oh my gosh. Hey Hey, hey, hey, guess what guess what I get to say Hashtag team bill. Yeah, look it. You're all happy now.  I'm back in almost the lead, right? This this beat out all of your other pranks Okay. Yeah, you're so right. It did. No, it didn't. I swear to gosh It did rob a squad. Don't even okay Honestly, how did I do on this prank? Hashtag team bill in the comments She was pushing me. She was like, oh my god.  I'm like, who is that our center in my life? Okay, you were being all weird about it. Come on.  It was a good prank Second of all, no, there are no cuter girls in the world in you. You are the cutest girl in the world See points you got to get points you got to say you you got to say cute things like that guys to get points So, um, even if you don't mean them just say them because it makes your girl from jail good Did you hear me? No I'm just kidding, but no, I totally like think you're the cutest girl in the world. Um No, thank you Anyways, I got your little booty button I hope that you were just as mad as me when you I didn't wake up on you. I pranked you When you didn't wake up on me.  Shout out to you, Brittany Bertagna Thank you so much for being the person we gave shout out and showing love on our channel We love you guys so much. Thank you marvel squad for being so supportive and I'll see you on our tiktok instagram Um youtube and everything all the above just we love you guys Yeah, and uh like the last video there are gonna be more giveaways. Yes we're we're dealing with our merch right now and Apple watch the apple watch. Stay tuned for that. So we still have a giveaway left. Yes. All right, Marvel squad. We'll see you guys in the next video


The Inspector General of Police, Osman Barba, has ordered the mobilization and deployment of adequate police personnel, among personnel carriers and technical capabilities of the police airway for the AKT State Governorship Elections slated for the 18th of June. Also deployed by the IGP are the force marines, mounted troops, K-9 sections and other operational force spokesman C. S. Pio Lumoyawadejabi in a statement said the RGP also deployed deputies back to General of Police in charge of the force criminal investigation department FCRD, the IG Johnson Kokomotir, the IG who doubles us, supervised with the IG for the Southwest geopolitical zone, is the coordinate security component for the election. Subscribe to our YouTube channel and don't forget to hit the notification button so you get notified about fresh news updates.


Welcome back, everyone, to the next generation evolution of storage. I'm John Furrier, host of theCUBE. We're here with Pure Storage, precautions in the house. CUBE alumni, general manager of the digital experience business unit. Great to see you. This is like seventh time on theCUBE. Welcome to come into the studio. Thanks for coming in. Yeah, thanks for having me back. The title of this series is next generation storage, evolution of storage, but basically the waves are coming in, generated by one season. Another tsunami of more data is not stopping. This is a key part of how companies are re-architecting. User experiences are changing. The apps are changing and cloud continues to grow, which means that the consumption, how people buy technology and consume services is right there. You're heading up a business unit that's doing the service for storage. Explain your business unit because you have a really successful and growing product and we'll get into it. But explain what you guys do. Yeah, we're building up storage as a service. So a lot of our customers are using it as a distributed cloud. So if you can think about storage, traditionally it was like, I buy a box, use a box, right? And then when the box is old, buy another box. Well, there's a lot of inefficiency and waste that goes into that. So if we apply the cloud like concepts to it, what if you could get the cloud wherever you're at? Because applications sit everywhere, whether it's on-premise or in the public cloud, and you should be able to get that cloud experience anywhere. So we deploy a storage endpoint the way we like to think about it. And so in the customer's data center, we would, they don't buy the gear. We guarantee performance and capacity SLAs. They can do reserve commits, pays you go on demand, that whole type of model. But they don't have to worry about managing, running or operating asset or asset life cycles. They can just use storage and get the benefits of the cloud operating model and consumption model wherever they sit. So it's a dream scenario, basically, if you're a customer, because one, storage is gear. You got to buy stuff. You got to deploy it, got to connect it. In the past, it's never worked because it's hard, right? It's hard to do.  You got to swap that out. Some systems were tied to each other. AJ just talked about some of the things that are going on between challenge, between disk and controllers and it's, but it's evolved with flash. You guys have an advantage. Why are you guys successful? Because customers want to consume this way. They don't have to take a risk. They can consume like cloud, pay for what they get. Why are you guys successful? What makes it so unique that you guys can pull this off? Well, I wish I invented it, but I think I've only been with the company five years. About 13 years ago when the company started, some decisions were made architecturally to build this concept called a nevergreen architecture, which means what if you could build a system that never got old? Meaning, usually when you buy an asset it ages out, right? What if you could build a fountain of youth where that same asset would be newer 13 years later, right? So the way you have to do that is you monitor every component and anytime a component wears, you can swap that component with no degradation to performance or no data migration or no disruption to the customer. So that concept was built into our technology. So when we decided to build the storage as a service business, we realized we had a unique advantage and that we can actually deliver a service that just like a SaaS service, just like your Salesforce gives you new features all the time, right? Your Salesforce CRM gives you new features all the time. We could do the same thing in storage. Your hardware gets better over time, your software gets better over time, your security gets better over time, right? So that's the concept that we bring into it and we're unique because of this evergreen architecture we have. So the efficiency flexibility is there. You get that easily. Customers pay for what they use. What are some of the things that you see around the questions that might come up around security, meantime between failure, the normal stuff that people talk about in storage? Well, so like if you think about it this way, there was a point in time in storage where everyone's like, well, the network will protect me. Like as long as the network's secure, everything's fine, right? And I don't want it, once storage is like working, don't touch that, right? And what would happen is people would be like, okay, I'm only going to patch my storage once every year or change controls, windows because it was clunky and cumbersome. This day and age, a Linux, Linux, I don't know, in a week, there's like seven to 10 major Linux vulnerabilities. Every storage operating system's built on Linux. What do you think is going to happen, right? So imagine that, you know, if you apply the SaaS based security principles, you probably need to update your storage system daily, right? Like really think about it to secure your environment. So that's customers, are they going to keep up with the operational overhead to do that? Probably not. So what we do is now we, because our evergreen architecture allows us to update components non-disruptively, that applies to our software stack as well. So we can do software upgrades with no performance or customer downtime. So we now can just push updates to those IoT endpoints directly from Pure One, our cloud management plane, and customers can benefit from rapid software innovation cycles. And we've changed our software release cycle to actually now ship monthly as well. So our purity feature releases are coming out monthly where customers are actually getting new capabilities monthly. So this is not, I wish I talked to AJ, I didn't have a lot of time, but one of the things about, you mentioned the software stack, you're seeing that as an advantage in all the hot areas, whether it's GPU, GPU clusters, the software stack to build that developer and or agility angle is huge. Talk about your software stack and why that's so important to the evergreen model and also to getting new features. I'm sure AI is going to have some unique things about inference and training, making data available, controlling data. I'm sure there's going to need to be an upgrade on the stack on that piece. Well, so that's interesting. Later, I think it's probably coming soon, probably in the next few months, we're just doing a purity software update to introduce GPU direct support for FlashBlade, right? That's just, okay, now we support GPU direct, right? So next, so like those types of things are things that we can bring. But that's the key, you guys are just pushing software updates. There's not a lot of hardware or is there hardware, is there just swapping out, and it's going to develop? The good news is we build our hardware where our hardware life cycles, typically with evergreen have about a two to three year like generational life cycle, right? There's always this new memory, new DRAM, new NAND flash, et cetera, that has this kind of two to three year TikTok evolution. The good news is people don't have to wait because as it becomes available, we can swap it in to continually make sure your energy and density and... Because you're phoning home, you're getting a sense of it, you're phoning home, you get a sense of it. So you guys are getting ahead on the predictor side. So that follows its own innovation cycle.  They both get better independently over time and the security updates also get better over time because we're constantly pushing those. So that's kind of a layer and I know you brought up AI. So what's fascinating is in this type of approach, right? When you're thinking about, obviously, people talk about GPUs, burn GPUs, let's go. Like, you know, but... It's like, go, get me more GPUs. I want to talk to them. How do you actually like, there's kind of to get a good outcome. And I think we've been talking about this in kind of statistics and predictive and that was hot before AI was hot is there's only two vectors, right? More data or more compute to get better answer, right? So are you going like the more data you have to input the better your prediction model will be or the more simulation you can run against a data set, the better your answer will be, right? Those are the two vectors you're playing with. Now, if you can't get the data into the compute fast enough, you're going to have a problem, enter a flash. I don't know how you do any of this without flash, right?  But that thing aside, the next element then is in the optimization of enterprise data, my internal data, external public internet data, you got to cleanse the data, you got to bring it together. And if you've created storage silos, like we see storage is a very fragmented market space today, where you've got, these are my archive systems and these are my mission critical application systems and these are my analytic observability platforms and that type of thing, you are trying to build, like bringing everything together for AI will require data consolidation. So storage fragmentation is the enemy. And if you can go ahead and consolidate. For AI, I mean horizontal is the better play for AI. AJ mentioned that earlier. That is critical. What's available, what's addressable? AI is based on data quality and availability. I mean, high availability, highly available. These are storage terms applied to AI now. So AI and storage now is symbionic in the relationship. There's that connection is going to be even more tighter. It's the enabler to allow you to do that. So how do customers are thinking about that? Take us through the subscription. Okay, I'm a subscriber. I'm using the solution. Thank you very much. If it's my budget, I use it. Now I'm in the AI planning phase. How does Pure help me? What would you just subscribe to an AI module? Is there AI? Let's say you're already on a green one. Well, you're already on a model where as you scale, like you don't even need to buy more. Like you can actually just start using. And because we're the vendor managing the hardware that sits at that endpoint, we always maintain about a 20, 25% buffer headroom. So if you're using more, we're always landing more hardware than you're actually you need. So you have the ability to grow as you need. And in the consumption model, you'll have volatility, right? You might say, okay, I'm gonna spike and do a big training thing where I'm going ahead and I need spike. And I'll just pay for on demand for that because that's not my steady run rate. In the consumption model, you're not buying anything. You're not owning anything. So for AI, you can just say, hey, this month's gonna be hot. It's fine because I've built my training models. Now that I'm kind of running at a steady state around the inference, then that's where I'm gonna set my reserve commits and off I go, right? So that model allows customers to get started immediately with AI, just jump into it and go with. And obviously, we haven't talked a lot about it. And I think just like many years ago in cloud, people were talking about like, okay, I'm going to the cloud. And then people were like, well, maybe I'm coming back because it's too expensive. Like there's this repatriation trend because people realize like running full tilt was expensive. Like AI is very powerful, but it also could be very expensive. Is that repatriation or is that net new use cases that they wanna have on premise? Because that's where their data is. That's proprietary or- I think it's both, right? I think we see both happening just because cost models. And I think in AI, just like there was like DevOps and then FinOps for cloud cost management, right? I think there's gonna be AI FinOps as a market segment that's gonna happen being like, okay, I know AI can do that, but am I willing to pay a billion dollars to do that? You know, like there's a cost to doing this. Or will it, if it gets viral or something hits, am I ready for it? And what's the cost envelope look like? And by the way, is that what I want? And am I prepared for it? So again, I think cost is huge, we've seen that a lot. I have to ask, because this comes up a lot from customers that I talk to is that they say I'm experimenting on prem and then maybe I'll do cloud, but I'll do cloud. And then once I'm up and running, I'll do a little bit in the cloud and on prem, but I want my data to be here on premise. I want my GPU clusters to be there. I want bare metal. I want a GPU cluster. I want my storage on premise as the use case today from a development standpoint. What do you guys see? So I think I see all of those types of scenarios happening. Now, the easiest, like we always talk about this, like hybrid multi-cloud world is like, you know, the perfect scenario, but it does require some deliberate choices. One, you need consistency between your on-premises and cloud environment. So we have operations and technology. Operations and technology. And we have that now with our cloud block store product. So you can run cloud block store in the public cloud. You can run a flash array on prem. And we've even had customers that could run cloud block store on AWS and Azure with Oracle running on one. Oracle running on the other, active-active, right? So we provide replication technology across hyperscalers today. So all of that, those things exist from a storage standpoint. But then you also need to think about, you know, your application deployment, which typically is you VM or container, right? So, you know, VMware's created that common space for VMs that can be deployed. And Kubernetes has pretty much become the standard for how you can deploy in a cloud agnostic way. And with that, we have our Portworx capabilities that allow us to do that. So, I think, you know, where I see this going, right? Is if you think first, you know, services and consumption first, you layer on principles of flexibility in cloud operating model, then you make technology choices that are more container first. I think you're gonna get to the point where you're gonna be ready to give your business agility. Prakash, I think that's really a key point. And I would just say, we're seeing some validation in the marketplace because you mentioned Portworx, even in Kubernetes as it becomes like Linux, the conversation shifted from, how do you stand up Kubernetes clusters to, okay, what's the end-to-end workflow look like? What's my platform engineering look like? Which is essentially a pretext to app developers, who are gonna need store stuff on storage. Okay, so I see that. The question I have for you is, okay, we believe that to be true. Okay, so let's go to the next level. Pure has always been a product leadership company, good innovation strategy, investment in R&D, good expertise in Flash, you mentioned all the evergreen stuff and all that, and AJ did as well. Okay, great. But I want to subscribe to a platform now, because remember, I don't got platform engineering conversations happening, so assume best-of-breed is table stakes. Check, you guys done that. What's the product look like at a platform level? If I get this holistic view, is there a subscription for that? Or is it like a collection of subscriptions, or how does the customer motion look for you guys when they're thinking, okay, I'm gonna start looking at my entire end-to-end process. I got GNII coming, I'm gonna have a data engineer soon, I got platform engineering in full throttle. Kubernetes is now under the covers. I'm looking at pipelines, about native services. The way we think about everything is, in storage, you care about performance, capacity, and availability, right, and resiliency. We'll give you SLAs for all of the above. Meaning, what service level do you want, right? So the platform is the service level at that point, right? So, because should you really be worried about what hardware to deploy for the service level? No, you just need a service level. And we've instrumented that service level where customers actually have visibility to that SLA right in product. It's monitored and they do it. If we miss the SLA, there's a service credit built into the product. Two, we've enhanced those things. We have a zero data migration guarantee. So we're not even, we're not gonna bait and switch, tell you like saying, okay, here's our new hardware platform that we did that doesn't qualify or whatever, right? Like we're not doing those things that just a lot of traditional storage vendors do. Some guarantees aren't really guarantees. Yeah, you know, oh here, I'm gonna take this old product, rebranded as a new product so it doesn't apply as the, you know, under terms and conditions. We don't do any of that, right? So that's kind of the second thing. Third, because we're running these services within customer's data centers, not only are we giving you SLAs, whatever power and rack space we use, we actually pay for. So customers know that it's a real service because you're gonna treat it just like you treat a cloud, right? So you see yourselves as the easy button for platform engineers just to plug in what they need because man, they're thinking about the developers who are going to need to store at scale. So it's not like the developers will call them and say, I want more storage. Like, you know, the previously developers needed to just provision. They're like, okay, I just want to do things because money is no object, right? I think that, like it's, I run an engineering team right now. I have platform engineers and I have a. It's a good experience to provide but money is an object. Well, so it's funny. I have this guy, his name is Vivi on our team and his title is DevSecFinTestOps. He's a kingdom builder. Yeah, so I was like, wait a minute. So why did we create a role called DevSecFinTestOps? Right, if I got that right, I think that's his title. But so the head of my developer platform engineering that runs systems is also responsible for my cloud costs. Why is that? Right, because he needs, when he provisions a service for developers, he needs a rate. So by tying everything to an SLA, you actually allow developers to say, when I'm making this provisioning request for the storage, do I want the $3 version or the 50 cent version, right? And they can tie it to their SLA's for their applications. So it puts responsibility of the outcome directly in control in the hands of developers. I think that's the key to that money is free quote, as you got out because like, if the platform engineer does his job, it will seem like the developer has access to storage. That's the job of the platform engineer, your point. Yeah, before it used to be, oh, let's go build it and then we'll optimize it later. That's yesteryear. Modern developers actually need rates in products. Prakash, it's always great to have you on theCUBE. What's your vision for your business unit? What's next? You're always working on some new things. So you've got the generative AI wave coming, more storage is still needed. It's going to be different. We've been saying on theCUBE that the script will flip on data management as scale kicks in and you got automation. Automation basically is what AI is doing.  That generative AI starts doing work, whether it's the code whispers on Amazon or co-pilots every place else. You can have a lot more augmentation for the humans to help provision, manage all that good stuff. What's your vision for your effort? Yeah, so I've got like, it's interesting because I have one for customers and then I have one for our own internal team. For our own internal team, right? If you're running the service, right? Like running a service has always been about SREs. So generative AI can replace SREs. I'm pretty convinced of that, right? So building and training models for generative AI is to replace SREs for running and operating a remotely distributed service just moves more capacity into innovation on the development side. And then as we're developing for customers, previously people used to think about application-specific storage. Now you've got general-purpose storage that can do a lot, but with the advent of where the technology space is going, where we think in a few years we'll have a 300 terabyte all-flash drive and a similar form factor to this, right? At that point, you'll need to start doing micro-application understanding. And I do think these service SLAs will become more application-aware. Where you can say, just let's apply retention policies and these SLA policies to these applications. And the storage system itself will be aware of which application is working on it and optimize for the way it interfaces, the way block size is right. And even extend the life of the media based on the application type. So I think it's fascinating in that, to do the new service economy, storage will have to become more application and context-aware. And I think to your point to make that happen, you gotta know the underlying data because that's the AI fee there right there. The data needs to know exactly what to do when and where that's going to be driven by the application. Hence the developer is going to have to be data savvy. Not just know there's a database out there but know a lot about or rely on systems that can treat data with intelligence. Yeah, every developer starts with observability nowadays. Great, well great to see you. Thanks for coming on theCUBE. Really appreciate you for coming on. Thanks for coming on our next generation storage series, appreciate it. Thank you. Okay, we'll be back with more after this short break. Thank you for watching. We'll be right back for this next generation of storage. I'm John Furrier, host of theCUBE. We'll be right back.


It's all about college basketball right now and in the spirit of March Madness, we've been rolling out some super fun brackets like this one, Best Retro College Sports logo. Now all of these are pretty fun, you can't go wrong with any of them, they're all great. On the left side, I love the Florida Gators logo. An alligator with the sweaters just doing something more than the other ones are. And on the right, I love the ASU Sun Devil, classic. And I love the little Hawaii rainbow. In Miami's is really good too. But I think for me, it's gonna be the Arizona State Sun Devil logo. Who do you guys have in this Best Retro Logo Bracket? Let me know.