I'm gonna talk about twisty little passages and rediscovering the joy in programming. How many of you have had fun programming in the last week? Awesome, I love it. Like, even maybe yesterday. How many of you had fun yesterday writing code? A few more hands? Not everyone, okay. That's okay, you can't enjoy it all the time, right? Well, for me, actually, you know what? Before I go any further on this, I need to do a shameless plug. As Mike mentioned, I am writing a book. It's called Maze's for Programmers. And I have a free copy to give away, electronic only, so it's not gonna like grace your bookshelves or anything. But if you're interested in this book, and you all should be, because it's awesome. So to introduce this slide, it was probably about the last year or two, I really started feeling burned out on writing code. How many of you have ever felt burned out on writing code? Yeah, it's not a good place to be. It's really kind of scary, especially if coding is your livelihood, right? It's not a fun place to be. So I really struggled for a long time. So what I discovered is in order to conquer that burnout, one of the things, there's a lot of different things I had to do and try, one of the things was to rediscover what made programming fun and enjoyable for me. And that's kind of been a journey for the last year, as I thought about this. And so what makes coding fun for you? I don't know what's gonna be fun for you, but for me, these are some of the things that I particularly enjoy that make coding fun. For one, it has to be intellectually challenging but not intimidating. Like ray tracing, I went a period about 10 years ago where I wrote a ray tracer. How many of you have ever used a ray tracer? Does anyone know what I'm talking about? Okay, good. How many of you have ever written a ray tracer? A few hands. So you'll know what I mean when I say that it is definitely intellectually challenging, but it's also a little bit intimidating, especially when you start moving beyond spheres and you start wanting to do things like parametric surfaces and things like that. It definitely starts to move into the intimidating realm. So that meant part of it for me, but it's something new. Like after a while, after you've ray traced a dozen spheres, the joy starts to wear a little thin. Also, I mean, fractals. How many of you have ever played with fractals? Like iterated function systems or different things? Those are always new. Like you can do so many, it's new every time you do it, it's great. Rapid feedback cycle is something else that's important. Like you can't spend days getting to where you have something to show. You need something quick. That's another big win. Easy to experiment with. I need something where I can go in and change one line and get something totally different. Fractals were great for that. Like the iterated function systems, you change one little thing and you get a totally different fractal. Like that is a lot of fun to experiment with. For a bonus, if it's visually interesting, that helps a lot too. Like if it's something exciting to look at, that plays a lot towards what makes things fun for me. And if it's shareable, that counts a lot. Can I share it with my coworkers? Can I share it with my wife and kids? Like ray tracing. For me, it's great. You get that sphere up there and it's reflecting the checkered plane and it's great and you're excited about it and you show your wife, show your kids and you're like, dad, it's a ball. And you're like, I know it's a ball, but the light went over here and they just don't get it. So I appreciate it, but it's not as shareable as fractals or like, ooh, pretty colors. So there's a lot of different projects that I've played with, like ray tracers and fractals and generators and Celtic knots and making my own programming language and playing with grammars and genealogical databases. I've done a lot of things for fun, but some of them are more fun by the previous slide than others. And today I'm gonna focus on mazes because it nails every single one of those points for me. Challenging but not intimidating. These algorithms are so easy, you can fit them on, like some of them, two lines of code, some of them, a page of code. They're not hard to understand. Every time you run the maze, you get a different maze and there's so many different ways to experiment with it. You get the rapid feedback, you change something, you generate the maze, you get a totally different thing. They're visually interesting, they're really shareable. Like my kids love these random mazes. I made a maze on a Mobius strip the other day and my seven-year-old, seriously, he spent hours just tracing the maze around that strip over and over. So there's a lot going for this. I'm gonna show you what I mean by this. This is where it's gonna get tricky because I need to do some code while I'm holding this mic. Thank you. I won't need, we'll say I just need to type something here. All right. You sure? All right. There's a reason he's called Mike. Wow. So what we have here is a binary tree algorithm. The way it works is I create a 10 by 10 grid of cells. Then for each grid, each cell in that grid, I'm going to say, okay, take the neighbor to the north and the neighbor to the east, choose one of them at random and then link those two together. And what you get when you run that is a maze. Like it's a real bona fide maze and it's so straightforward to do. Now this next bit, this is what I'm talking about where I talk about how easy it is to experiment. One of the easiest things to do with these is to change the dimensions of the maze. So here we went from a 10 by 10 to 40 rows by 80 columns. We run that and once again, we get this maze. It's so straightforward and easy to play with, easy to experiment with. Another really easy thing to experiment with this, instead of choosing north and east, we're gonna choose south and east. And you look at that, you say it's about the same thing, but one of the big differences is instead of there being a big long row along the top, now it's on the bottom. You see over here, there's one on the east, that column there. If we switch and say, let's do south and west, now when we run it, oops. Now when we run it, that thing switched over here. So just by changing one thing, we get different textures of the maze, different features, different aspects of it. Another thing to play with, maybe. There we go. What if we prefer one of the directions over the other? So this time we're gonna say, let's take the south and the west still, but we're gonna put the south in this array five times and then choose one at random. So obviously that south is weighted a lot more. So what happens when we do that? When you choose south more often, well, you get a very different texture. Suddenly everything wants to go north to south all over the place. You could do the same with the east and west and get the same thing just horizontally biased. But now here's a cool thing. What if going from the left, where let's say on the left side of this, we're gonna prefer east to west and on the right side of it, we're gonna prefer north to south and in between we're going to gradually shift from one bias to the other. So for the south, we're gonna choose south based whatever column we're looking at and west is just gonna be however many columns in the grid minus that column. We set that up and we choose one of them and we get this. So from one side, it gradually shifts to the other. This is a game of what if.  What if I change that line? What if we make this do this? I wonder how I could make the maze behave differently. Really easy to play with. There's other ways to vary this. Instead of changing the algorithm, you can change the way things are displayed. The ones I've shown you before, the walls of the maze are just single lines, but you can change that. What if we render the walls as blocks? You get a very different look to the way it's displayed. You can change the colors, you can change all kinds of things like that. Another way to change it is you make insets. So instead of having the walls but right up against each other, you say we're gonna separate the walls, we're gonna inset them a little bit so that there's some separation there and you get something like that, which is similar to the blocks, but now the walls can be a different thickness from the size of the cell itself. Another way, instead of drawing the individual walls and the passages, you can pre-render a bunch of tiles and then draw each cell based on the corresponding tile and you get something like this. This is really simple. You could get really elaborate with, you could theoretically say for a given intersection, five different ways, five different types of tiles and randomly choose them. Lots of different ways to experiment with this. Let's move on. Here's another algorithm. This one's called the growing tree. This one works by basically setting up a list of seeds and starting with one. We're just gonna choose with a random cell in the grid. We're gonna put it in there and while there are any seeds in this array, we choose one at random. We look for all of the unvisited neighbors of that and if there are any, we link the seed that we chose to that, add that new one to that basket of seeds and go around again. If there aren't any neighbors, then we remove that seed from the list and go around again and that way eventually we'll run out of seeds. When we run that, you get another maze. Surprise, right? I'm sure you're totally boggled by that. But now there's lots of ways to vary this one. For instance, in this case, we chose one at random from that but what if instead of choosing at random, what if we take the last seed that we put in and always choose the last one? Well, we get another maze, obviously.  So what we can do, actually before we get there, you can also randomly switch between them. So half the time we're gonna choose the last seed and half the time we're gonna choose a random seed and surprise, we get another maze. But as I was saying, there's a difference there but it's hard to see. So what happens if we render these side by side? Here's another what if. What if we take it and we render two mazes with these different methods? One we're gonna choose randomly from that list. One we're gonna choose last. Let me just stop selecting text. Okay. Well, there we have the one on the left here is chosen, the seed is chosen randomly and the one on the right, the seed is, I always choose the last. How many of you see a difference between those two? It's a little subtle, isn't it? Some of you maybe you're like, no duh, it's really obvious but others, I mean, if you don't know what you're looking for, it's a little hard to see. So what we can do, we can make that easier. We can use Dijkstra's algorithm to actually color the cells based on distance. So what we do is we choose a single cell inside this maze, measure the distance of every other cell from that one and then color the cells based on that distance. How many of you have ever used Dijkstra's algorithm, what I'm talking about? It's a really cool algorithm. It's like the Swiss army knife of pathfinding algorithms. I don't have time to go over into it now but it's worth learning. So if we run this now, now the one on the left is the seed is chosen at random. The one on the right is we always choose the last seed. Now it's a little more obvious that there's a difference there but we can make it more obvious. Let's go by a 40 by 40 grid instead of 20 by 20 and now the texture kind of pops out a little better. There's a lot more movement over here on the right versus here is over here. It's basically just a radial gradient moving outward. That's kind of what you get when you choose at random versus always choosing the last cell. We can make this even more obvious. Let's do an 80 by 80 grid and we're not gonna draw the walls. We're just gonna draw the colors and you start to get some really cool artwork. Like this is stuff I wouldn't mind hanging on my wall but that's cause I'm weird. You can animate this. This is another cool thing. You've seen the results now of these algorithms. What happens when you actually animate it and you show step by step how these things come together? Well, let's look at a binary tree. Let's animate how it comes together. This is the binary tree being constructed cell by cell in sequence but the cool thing about binary trees you can actually do is visit the cells in random order and get the exact same result. So it doesn't matter what order you do it. It still gives you a maze. Bam. Let's try a growing tree. What happens when we choose at random with the growing tree? Every time we add we're gonna highlight that seed and every time we remove it we're gonna basically return it to its previous color. So the cells that are currently in that big seed bucket we're gonna see those in yellow. This is what happens. There's a reason it's called the growing tree. You can see how it kind of organically moves outward from that starting cell and at the end of it and you can also see this is why you get that radial texture like the flooding outward. So what happens is when we switch that to last we get a totally different behavior. It becomes very snake like. We're always choosing the last one and it chooses a random neighbor and it just goes around like a snake. In fact, this algorithm is also called depth first search or recursive backtracker. We'll try it. Does that work? All right. So now, yes, thank you, Mike. So now what if we take this growing tree and we actually show dikstra's animated on it to show how dikstra's algorithm works. It works by flooding outward from a cell that you choose but we can really see how that works by animating it, showing each individual step as a frame. Let's make that a 40 by 40 grid and we'll take the walls out so you can really see how things flood outward and there it goes. See it's following the different pathways all the way to the end and the darker it is the further it is from that starting point. It's really kind of hypnotic. I love this aspect of it. All right, now there's nothing sacred about these rectangular square cells. We can do all kinds of different shapes of cells. We can do hexagons. We can do octagons and squares tied together. We can do triangles. We can do polar grids. A polar grid is just a circle with like nested circles with spokes radiating outward. This is a polar grid but it's a grid. We've got cells that are adjacent to each other so theoretically we could run any of these algorithms on it and get amazed and sure enough if we run growing tree on it we get a circle maze just like that. And you bet there's a ton of stuff we can do to experiment with this. We can change the size. Instead of a radius of 12, we're gonna make 24. So there's 24 nested circles inside of it. That's the kind of thing that would give you a headache. But now we can compare those two. We can do diastres on these and compare them side by side again. And again you can see on the left and see what was it. I switched it around this time. Okay on the left we have the choosing the last cell and on the right we have choosing the random cell. But we can increase the resolution again. Go 24 and you start seeing more of these patterns. We can go even larger. Let's go 48 and we're gonna take the walls off again. This time you can really see the difference. The how the choosing last gives you more of the winding and the paths that, man, I'm losing my English today. Whereas on the right, what I'm trying to say, on the right you get more of the smooth gradient. That's what I'm trying to say. Now the cool thing is once you have a polar grid you're almost to a sphere because if you take a flat polar grid and you poke it up in the middle you get a hemisphere. And if you take that hemisphere and you join it with another one you got a sphere. So we're basically to the point where we can do a sphere. What does that mean to render a sphere maze? This is kind of one way to think about it. This is a cylindrical projection of a sphere grid. You can see the distortion at the tops and the bottoms. It's just like looking at a map of the earth. Iceland and Greenland look enormous compared to their actual sizes. And that's because of the distortion near the poles. Well, this isn't quite as exciting. Like you say you wanna see a sphere maze and people are like sure and you show them this and you're like that's not what I was expecting. So let's map that onto a sphere. Well there we have it. We've taken that grid and mapped it onto a sphere. And like I said, once you have a grid you can make a maze. So let's apply a growing tree on that. And there you have a maze on the surface of the sphere. And we can start doing a lot of the same experiments that we did with the flat rectangular or the polar mazes. We can color them using Dijkstra's algorithm. And we get that winding pattern in color on the surface of our sphere. And of course, the very next thing we wanna try is what happens when we make it bigger? 50, right? Pretty, okay. And red of course because Ruby Conference. Well, that's one thing but what we would love, we're seeing this in 3D now. Let's actually see if we can rotate it. Ooh. If you're fast you could probably solve the maze while it's rotating. I can't. Okay, so now, obviously that was a ray traced sphere. And I didn't write the ray tracers using Pavaret. But ray tracing kind of falls down when you want things in real time. What I would like now is to say, okay, we've got this sphere. What if we could render the actual geometry of the walls and actually watch that thing turn around in real time? Well, OpenGL kind of excels at that. So what we've got here is now a grid where we're gonna build the geometry of the walls and then fly.  We're just gonna sit and stare at it from some distance above the sphere. But those are the real walls. Well, okay. What if we increase the resolution on the end? Let's do 40 instead of 20. Ooh, wow, yeah, we're exciting. Okay, but we can do better. We can play with how high the walls are because this is real geometry now. We're not just painting a texture on a 3D sphere. We've actually got triangles and quads that we're playing with here. So we can change the wall height. You can go way nuts with that. In fact, let's do it. What if we change that to like 0.5? This number is relative to the radius of a unit sphere. So a unit sphere would have a height of one. So we're making these walls half the radius of that sphere. Whoa. And you can take it way down. But this is what I'm talking about. It's that immediate feedback. You can change the wall thickness. Make them thicker, oh, that kind of was wimpy. We can do better. There you can hardly even see the passages now. But you can combine them. It's a wall height. And it's just, I love the immediacy of this. This is what makes it fun for me. I'm like, what happens if, and you change something, you can immediately see what happens there. So now that we've got this, we can actually start doing some real animation in real time with this. We can rotate it like that, you know? Yeah, we're getting somewhere. We can rotate it around y and x simultaneously. This is cool because you can actually see what it looks like at the poles. And I'll admit, my OpenGL, I had to learn OpenGL just for this presentation. So I'm obviously doing something wrong with the lighting. If you're an OpenGL guru, I'd love to sit down with you and have you teach me how to do this right. But now the black background is kind of dull. It'd be nice to have a little skybox in there. Give us a background to see it on. Serene, just make you wanna like relax. I need some like elevator music. But now here's where we can really have fun. We've got this. We can compute paths through this grid, just like any other grid, thanks to Dijkstra's. How about we actually move our camera right down inside that maze and actually walk it. Now this is where I need to warn those of you prone to motion sickness. You might want to avert your eyes because it gets a little, yeah, you'll see. We're gonna walk from the north pole to the south pole. And I actually won't do the whole walk, but we'll get started on it. There we are, walking the surface of a sphere, a maze on the surface of a sphere.  Yeah, so again, we can play with this. We could change the resolution on this and do it again. The walls are a little closer together now. We could fix that by changing the wall height to make them feel like they're not so close together. Anyway, you just immediately play with that, but we can do really cool things now. Because one of the first things when I got this working, one of the first things I wanted to see was, well, I want to see, I want to fly in from outside and land inside the sphere and start walking it. So, of course, I had to implement swoop, which we'll do that. It's gonna swoop us in, land us on the north pole of our sphere and start walking that. We plop, and there we go. Let's do it again, because it's fun. And one more time. Every good special effect deserves to be shown at least three times. But now the problem is we're always landing on the north pole. It'd be nice if we could just choose a path that starts at some random cell and goes to some other cell. So what we've got, let's just find the longest path through our grid and walk that one. It's gonna land us at a random location, and so here we go. I am. See, I mean, that never gets old until you get motion sick. Let's try it from a different location. There we go. So that's what I'm talking about. I went from a simple binary tree algorithm step by step, what if, what if, what if, following the chain, and it got me all the way to an OpenGL animation where I'm walking around on the surface of a sphere. That's not where I expected to be when I started out, but that's where I wound up. And I'll admit, implementing the whole OpenGL thing was not the rapid feedback I usually desire, but by the time I got to that point, I'm gonna walk around a little bit, by the time I got to that point, I was willing to invest a little more time because I'd seen how things had progressed so far. The rapid feedback to that point had encouraged me to try bigger and bigger steps. Now, will this type of thing cure everyone's burnout? Not by itself, no, but it's one thing to try. Find something that's interesting and exciting and fun and play with it. How many of you came to programming because it was fun initially? I love all the hands there. That's how I found it. My mom had an ancient Tandy computer with GWBasic on it, and I was like, okay, let's see what we can do. And so I made a Choose Your Own Adventure game. I made, I implemented the card game War. I did all kinds of simple little things, but it was fun. And playing with these mazes helped me rediscover a lot of that fun. But what else would you try?  What if you were to change this? What if you were to alter that? It really is as easy as changing one line to get something totally new. It's exciting, it's playful, it's interesting, it's challenging, but it's not intimidating. If I can do it, seriously, it's not that hard. Rediscover or discover the joy of programming because that's what's gonna take you to tomorrow, like the next day. It's gonna carry you through the doldrums of your daily programming jobs. Because let's be honest, you may love your job, but it's not always this thrilling adventure, right? But find the joy, look for it. So don't forget to tweet, Mountain West Ruby Conference mazes, MWRC mazes, and I will announce the winner just before.


Yeah, so I'd like to thank the organizers for giving me the opportunity to speak here and for organizing conference. So yeah, I'm going to be talking about vibration theorems for fatigue and pollution of structuring spectra. What I'm hoping to do though is draw a lot of analogies to a much more classical story which takes place just in spaces like good old fashioned spaces and good old fashioned homology. So this does come with a disclaimer like Duncan's talk. I'm more of a homotopy theorist, but I'm hoping to keep things a little bit grounded. So first we're going to just talk about this classical notion of completion for spaces. And the idea here is that homotopy groups are often very hard to compute, but homology is often easier. So you might have the idea given a space X, I want to build the part of that space that homology sees. And I'll say more specifically what I mean, but let's assume we could build such a gadget and let's just call it X bar. There's a couple of desirable properties. If X bar is supposed to be capturing just the homological information, we would want that construction to not be able to distinguish between two spaces with the same homology. So if I've got a map X to Y, inducing a homology isomorphism, I would want this construction, I would want them to be weakly equivalent. And I should point out from now on, NEH star UC really means reduced homology with integer coefficients. If we're trying to build a part of a space that homology sees, though, we want some sort of comparison from the original space to this new construction. So we'd want a map from X to X bar and at the very least, we'd ask that it be a homology isomorphism. So how could we build such a thing? I'll just remind you this is what we're sort of after. And a good place to start, excuse me, is with the Heritage map. That relates homotopy to homology. And one way to construct the Heritage map is as follows, I can start with the following assumption. So when I say space, I really mean pointed simplicial set. If you're not familiar with that, it's just a delta op shape diagram and sets. And it's a model for regular spaces, there's equivalent equivalence. So how this adjunction works, well, each set I can take and form the free abelian group. So that would then give me a delta op shape diagram and abelian groups, which is also what we call a simplicial abelian group. So that's the left adjoint here on top. And then, of course, I could forget the extra structure of being the group. I could forget back down to being a set and that's this right adjoint U. And like any adjunction, this comes with a unit map. So I get a natural transformation from the identity functor here to this UZ tilde gadget. And now I started this whole discussion talking about the Heritage map. So where does that come in? Well, to this map, I could apply homotopy, by pi star, and ask what happens. And what happens is I get the Heritage map. So there's this natural isomorphism between the homotopy, the UZ tilde y, and the homology of y. And this composite is exactly the Heritage map. What that tells us is that this construction, UZ tilde, satisfies that first property that we wanted. That's not too hard to check. On the other hand, it's also not too hard to pick up an example that shows we usually don't have the second property. We usually do not have a nice comparison from X to UZ tilde X. But it's a place to start. And to improve this, to build the completion, I'm going to just sort of fatten this construction up. So I'm going to iterate this construction. So remember, we start with this adjunction. I have this unit map. This is sort of this Spaces level Heritage map. But what we can notice now is that I could stick another unit map here or here, like there's two ways to do it. So I would get, that's better. We would get two maps up to UZ tilde, UZ tilde. And then again, I could stick another unit map here or here or here. So I'd get three maps up to this UZ tilde cubed. And I haven't teched it because it gets a little gross. But the co-unit map associated with the adjunction gives me a map down. And I actually get two maps down here. So this whole thing is a delta-shaped diagram. And that's good because we have lots of tools to deal with those. And so to define the completion, I want to just sort of glue together all of this stuff in some homotopy meaningful way. And that's just really what homotopy limits are for. So I take this red thing and I glue it all together. That's just if you're not familiar with homotopy limits, just think of this as sort of homotopy meaningfully gluing stuff together. And we call that the Z completion of a space. And this eta map induces a natural comparison from X to its completion. So this is our stab at constructing the part of the space that homology sees. And these are the things we wanted. So I wanted these properties. And one can check that, yes, I have the first one. That's good. The second one is more subtle. But surprisingly enough, often you get something even better than just a homology equivalence. Often you get a weak equivalence. And this should be a little surprising because remember, this completion is just coming from iterates of these guys, which only see the homological information of X. So somehow, if I glue together in the right way things that only see the homology, I can actually recover the space up to weak equivalence. That's just up to homology. And that leads us to ask the related question, well, when exactly does this happen? When can I rebuild a space X out of much, much simpler components by just gluing them together in this formal process? And Bousfield and Kahn in the 70s gave an answer, which is that this happens if and only if a space X is nilpotent. The key step in their proof is understanding what completion does to certain vibration sequences. So in more detail, a space is nilpotent if and only if morally it can be built out of a sequence of principal vibrations. They show that completion preserves these principal vibrations. So they ask, well, when does a fiber sequence remain a fiber sequence after completion? And that it's an inductive argument up a post-Nikot counter. But the real technical heart of what they do is understanding how completion plays with fiber sequences. So now I want to introduce that's the classical story. And now I want to retell this story in a newer context of structured ring spectra. So I'm going to talk about completion of O-algebras with respect to P2 homologies. This is very much in the same vein of Duncan's talk. But the thing to keep in mind is this is an analogous story of Z-completion in structured ring spectra. If you're not familiar with spectra, I hope hopefully Duncan's talk enlightened that some. But you can just think of spectra as sort of a better version of spaces. Like the theory of spectra encompasses the theory of spaces, but they can have much richer algebraic structure on them. So remember, for spaces, we started with this adjunction, some partial sets, the central of even groups. And this is the analogous adjunction that we're going to have in structured ring spectra. So algae O, what this morally is, is just spectra with extra algebraic structure encoded by a reduced operand. So this is exactly the category that Duncan was talking about. So we can think of commutative ring spectra, associative ring spectra, EN, all different kinds of algebraic flavors. Because this is so general and so algebraically rich, though, it's not necessarily the best category to be working in. So what we do is go to a nicer category, which is this algae tau 1 of O, because tau 1 of O throws away a lot of information. So it agrees with O at level 0, but other than that, it's trivial. So we've lost a lot of information, but the upside is it's a much nicer place to work. So again, this is the adjunction. This is the analogy we've been thinking of. And the TQ topological and homology of an O algebra, we define as what I get when I just take somebody in here, go over to the nicer category, and come back, just like we define ordinary homology of a space. In the same way that we tried to build the part of a space that homology sees, like ordinary integer homology, we can build the part of an O algebra that this TQ homology theory sees. And we do it in the same formal way. That is, I take my O algebra A. I have my unit map that's acting like a Haravich map. And then I iterate it to form this cosine-pushal gadget. And then to define the completion, I just glue all that stuff together. So I glue together these TQ homology spectra. Just like in spaces, we can ask, well, when can I recover, excuse me, my O algebra A up to weak equivalence by doing this? When can I throw away a lot of information, but still through some formal process, recover the space that I started with, or in this case, recover the O algebra that I started with. Ching and Harper give in 2019 sufficient conditions. So they say if A is zero connected, then I can recover this. But that's not a complete characterization.  And we expect that we're gonna need to know, just like basketball and con, what does TQ completion do to fiber sequences? So the motivating questions of this project is, well, okay, how does completion play with fiber sequences? Or even as a warm-up, are there O algebras that are not zero connected? So not covered by Ching, Harper, but which are nevertheless TQ complete? And it's worth noting basketball and con's proof really relies on a characterization that's unique to spaces, that I have a free group action on the space, and that's something we don't have in our setting. So there is definitely a new proof required. So we're still working on a complete answer, but this is the theorem that I wanna talk about, which is that if you hand me a fiber sequence in O algebras, where the total and base objects are zero connected, then after I hit it with completion, I still have a fiber sequence. And so with the remaining time, I just wanna give you a flavor of the proof, we're gonna skipping details left and right, but just wanna give you sort of the strategy and attack here. So the first thing we do is consider sort of the canonical diagram. Well, I started with this fiber sequence FED, and then I look at what happens when I complete those. We know these maps are weak equivalences because E and D are zero connected, that's the Ching Harper result. What we don't know is this left-hand map. I don't know if that's a weak equivalence. And to show this theorem, to put this theorem on, it suffices to show that this is a weak equivalence because then this bottom, right, the fiber sequence after completion is weakly equivalent to the fiber sequence we started with. So that's now the strategy. I wanna show in this case that F is complete. So how are we gonna do this? Well, this is the thing we're interested in analyzing. So let's try, let's remember how I built this. So how did I build the conclusion of B? Well, I took B and I iterated that hereditary map to get this cosimplitial gadget, same thing with E and same thing with F. So now you say to yourself, well, okay, this left-hand column, that's a fiber sequence, life's good, that's what I gave myself. The issue that you run into right away, though, is that this next column is not gonna be a fiber sequence. There's a couple ways to think about that. Either you can say to yourself, well, I started with a fiber sequence, which is a limit, and I hit it with this Q-funker, that's a left adjoint, generally left adjoints don't play well with limits. Another way to see it is, well, I took a fiber sequence and I applied homology, and in general, that's really non-trivial to ask what happens. The serospectral sequence gives us some idea, but then you're gonna have this infinite sequence of serospectral sequences, not to mention the fact that we don't have the serospectral sequence in our setting. So this diagram is not quite what we want because we lose control of it too quickly. So what we're gonna do instead is just take homotopy fibers vertically. So whatever the homotopy fiber of this map is here, I'm gonna stick that here, and same thing here, and same thing here. What this gives us then is this diagram. The good news is that each column is a fiber sequence, so I have a good amount of control over the diagram. However, that came at the cost of having the thing we were interested in being the diagram in the first place, right? The thing that constructed the completion is gone. So somehow I need to get the completion of F back into the picture, and to do that, I'm gonna just consider this top row here, and stick it at the bottom of something. Now I was interested in getting the completion of F in here, so let's just draw it. There's the completion of F. And then the natural thing following your nose is to resolve each of these other objects with respect to TQ. And then I have all these maps here. Now we're ultimately interested in analyzing this map, right? I wanna say that that's the equivalence after applying Ho-lim, and I'm gonna conclude something about that by looking at some other maps. So that is to say, first I look at these vertical maps. It's fairly formal that these give you a weak equivalence after applying homotopy limits. I then look at these horizontal maps, and through some careful cubicle diagram analysis, I'm able to conclude that these induce a weak equivalence on homotopy limits. And it's sort of a two out of three argument to then say that this map that we were really interested in is also a weak equivalence. So what we get is that in this case, F is TQ complete, and that proves the theorem. I should also say what we get is actually a little bit stronger, which is that it's not just a weak equivalence after applying Ho-lim. I can say something about the various stages, which is that I get a proisomorphism here. And I also, which should finish by mentioning that there's a generalization of this that we're able to provide, which is that TQ completion preserves pullback squares, not just fiber sequences of this form if the X and Y are zero connected. To get the fiber theorem result, all you need to do is replace B with a point. So this is sort of a first step in the program of completely characterizing TQ complete O algebras, and that's definitely the subject of future work. And that's all I have. Thank you very much.


Yn amlu'r ychydig, Fyllte, yn ymdyn nhw'n mynd i ddechrau'r cyntaf? Felly, nid yw'n gwaith ymlaen o'r ddechrau'r cyntaf. Yn ymdyn nhw'n mynd i gael ymddangos ar y cyfnod, mae'n gweithio'r cyfnod sydd ymddangos. A'n dweud o'r cyfnod ymdyn nhw'n mynd i'w ddechrau'r cyfnod. Mae'r gweithio'r cyfnod yn ymdyn nhw'n mynd i'n meddwl â'r gweithio'r cyfnod. Mae'r mawr yn adlwyr i'r cwmau. A'r gwahag i'r rhag Laetd i'r stadium. Ac drwy'n adnwysig swydd, mae eto'r han wrth iawn gwyl i'w ardoedd. Mae un sylwag i ddechrau am ychydig, a rwy'n dechrau i'n gynhyrchu arwydd. A yna'r Clwp yn cael eu prosiectau bwysigol yn pob, oeddech chi'r cael ei wneud o'n gwybod? Rydyn ni saeth am gyda'ch gael a gennym ni yn gwneud ym mhwn agliwyd. Cymru rydyn ni'n ei gael i'r llei i gyr spineig, I could see the outline and where they wanted to go as a football club. And that's the biggest thing, what direction are clubs going in? For me these clubs are only going one way from now. That was enough for me. Of course I'm looking forward to seeing who the head coach is going to be. But following the dates, it's Edin and Greg that have signed me and are part of the football club. We'll have to wait and see who that's going to be. But no it wasn't too much of an issue for them in the interview. I was just very pleased to get it over the line. And what do you feel you can offer to roughly city's midfield? Mae'n candwch. Rwy'r cyfennau ardwm i ddiddordeb yn gwi falech yn feddwl. Rwy'n mynd i ni, ac rydw i'n go iawn i'r gwlad a chael gwybod yn cael eu golygu a gwybod. Dyma wedi ddangos eu cyflawn i gyd, yna eraill yn digwydd yn ôl yn gwybod hynny. Wrth gyd yn rwy'n cael eu gwlad am gyfer a'n ystyried gyda chi'n femonhau, ac mae'n edrych yn dweud o'i mynd yn gallu bobl yma, ond rydyn ni'n cael ei gwybod. a'r adeiladau, ar y cwm ymlaen, am adael fe, mae'r adeiladau a'r adeiladau. Mae'n erbyn gwneud yn dweud i'r llawer yn ei gymplo chi a'r adeiladau. Mae'n iddyn nhw'n unig i'r gwneud yma, a ddim ysgol i'r adeiladau a ddim sydd y fan yn ysgrifftdog lle ei gael ei chael i'r adeiladau a dwi'n ei gael i'r adeiladau i'r ganwain i'r adeiladau, a'r adeiladau i'r gennym. Rwy'n meddwl i'r adeiladau a'n adeiladau a'r adeiladau. i'w medri gweithio dwy'n medri ac yn cymryd i'r llwyth wrth wgwylol o'r cymryd ymwneud. Felly mae'n gwybod i gyd yn dweud i'ch bod gyda'n gynnwys ar y newydd. Ond o'r dda'r dda, ydych yn gweithio, mae'n gweithio i'n gweithio, mae'r ddweud i'n ddweud i'ch dweud i'r dyn am hyn o'r cymryd, ac mae'n ddweud i'r ddweud i'r ddweud i'r dweud, That's what I wanna see. That's not just the fact that Bradford's pitched. That's anywhere. There's nothing better than a nice surface.  As I say, I love getting on the ball. As I'm sure many other players do at the club. And I really am looking forward to getting out there and showing what I can do. And you mentioned dealing in the view of a campaign where you had the chance to get four or get a few goals. I think you're probably referring to the 16-17 season of dealing where you've got 14 goals oedd yw rhai y peth oedd yn daeth i'r rydym ni. Yw'r peth wedi'u gweithio am y llwrs a'i hyrraedd? Yn gwybod, mae'r gweithio fydden nhw, ond mae'r cyfnod yn y gweithio, mae'r cofodd cofodd cofodd cofodd, bydd yw'r gweithio i mi, mae'n gwybod yn y ball, byddwn i'n ei ddim yn ei ffildio'r gweithio, a'r gweithio llaw i'r rhaid, yw'r gweithio i'r gweithio. Mae'n gweithio i'r gweithio i mi, Dyma lle fel y byd yn fath o'r parodi ond mae'r holl arno, a ydych yn aml ei wneud ond rhesiwyr Inclusio i chi, mae'n rhai. Ond gaf i mi, rhaid i chi'n holl gennych ar gweithio, i chi gaf! Rhaid i chi i chi dda chi'n wneud i chi wneud i chi'n holl ac mae'n bwysig i chi'n ei wneud i chi. Rydych chi'n rhaid i chi'n holl, ond at y merwydd, ac ychydig chi'n ei wneud i chi, yr wydd gael arall i chi a rhaid i chi gael ar ôl, Mars Cymru, I've got goals in me, and that's what I'd love to continue to do now from now on in. You mentioned there obviously time of drilling himself in as well last season. Is it fair to say you know what league one level is all about? Yeah, for sure. I've played quite a few games in the level above, and also the level below, but this division league one, I've played many games in it now, and I know what it's all about. I know what you come up against week in, week out, whether that's home or away, it's not just ability that can win your stuff, make you successful. You need a lot more, you need a good change of room, you need good experience, you need to know what's coming on the pitch that day and who you're up against, and there's a lot more to it than just going out there and playing football. So I can bring not just what I've said but the other side to it as well, and I think that's key in a change of room and at a club. You need to touch on that there. Obviously I've got that league one experience. The experience in the championship has always come up. Do you feel your experience is so fine football? You can bring that benefit to the dressing room and around the training area as well? Yeah, definitely. I remember going out alone from such a young age and that taught me a lot. I went out at 17 to a football league club and there was nothing better than that experience, and I always tell whether it's people I know or just people in and around the game that a lone move is crucial because it tells you what men's football is all about because no matter who you are or where you are, play youth team football one to 23 football. It's not the same and getting out there on a first team match day and then being around a match day first team side week in, week out, it's completely different. As you say, I've played championship and I've tasted that. I've played many games in that and many games at this level and you have to bring that experience and you have to, if you've got young boys around you or boys who haven't got as much experience, you can bed that in them and you can make them aware and it can make that extra percent and take you that bit further. We talk about experience but equally though, you're 28 years old. Do you feel you're getting into your best years? Maybe your best is still to come in your career? I think so for sure. I think you hear a lot. I think maybe quite a few years ago your prime was maybe 27, 28. I think the way fitness levels and the way the games go and involving with athleticism and athletes in the game now, it's your prime and the way people look after themselves is, I think now 29, 30 maybe, so I still think I've got the best years to come ahead of me and I'm hoping that I'm only going to get better from now. You know, with experience, with ability, fitness and drive, I've still got a lot more to come. And we talked about the pitch at Ballet Prey. We know you scored at Ballet Prey before. You look forward to kind of being in the surrounding because then a breath of city shirt this time around? I can't wait. As I say, it's one of the stadiums, no matter whether it was the championship level or league one level, it's one of them stadiums you look forward to coming to because if you've got that character, not everyone, some people want to shy away from it because it's such a big crowd, so loud, but the one thing I've always felt I've had good games here I've been successful with, as you say, with the goal as well, that I thrive off of a big crowd and a budge, you know, and I can't wait to get out there and do it in a breath of city shirt. And the goal we're on about obviously was it was in a Jillingham shirt. Also during your Jillingham time, you had the notable achievement of a hatchet of penalties. Are you going to be fighting to get onto the penalty kicks come back on the start of the season? Oh look, I'm sure there's a few players that have taken them or fancy them and I'll definitely throw them a hat in the ring and we'll have to see how it goes, but if I can get as many goals from outfield play and just play in the game, that will do me, but penalty is always a bonus, so we'll have to wait and see. And I have to ask as well, throughout your career, certainly the last couple of clubs you've been at, you had the score number of 44, is there a story behind that? There's a little story. There's four or eight. I've always been my numbers growing up more and so because of the position I play, so you're giving them numbers from coming through at a young age. So it always stuck with me a four or an eight, but then I went with a four. No, I went with 44. My first time I had it was at Merewall and I just felt my first season, season and a half at Merewall, it brought me a lot of luck. I changed a four and the luck never really stayed, but someone at Merewall, the kick man said to me, hopefully you'll be the first player to like it with the number four because the last three or four haven't had much luck whether that was injuries or just successful in terms of playing. I went to the four and I never quite had that luck, so that was the last time I went with one. I've had 44 since and ever since then I felt that it's brought me a lot of luck and it's stuck with me, it's a bit of a tag now and I'd never want to change so I'm hoping that it should be fine that I can go and get the 44 again. So you're going to be knocking on the kick man's door and when you introduce yourself say, for sure, yeah, I like the way it looks as well as the four, I like the boldness of it and I always wanted to stick with me now so hopefully the kick man will be fine that he can print the 44 on my shirt. And obviously you've signed for Grafton. Now we understand your plans for the off season not finish now, you've got a certain big day coming up in a few weeks time. I have, yeah, it's been a busy summer so far I've just arrived back from Ostagda which was very enjoyable and now I've got a busy few weeks ahead because I'm marrying a lovely girl called Holly and I've got the first part of the wedding in England next week and then we fly out to New Yorker with many friends and family where we've got a bit of a holiday and the big celebration if you like. So it's a busy summer but a summer that I'll be keeping myself fit, keeping myself ready to come back obviously to Bradford for pre-season which I'm really looking forward to already so I've got some exciting times ahead. Yeah and you've seen the trainer so he's had a sign for the club about you you mentioned that pre-season trainer he was impressed, obviously I was made aware of what it was like before I was signing and I believe the pitches are being relayed there as well so there's some big plans ahead and I really can't wait to be part of it and I was obviously looking at the training round today can't stand looking forward to running round the running track if we'd be doing any of that but I'm looking forward to working very hard and meeting my teammates, getting together and playing some football.


Going on everyone Sam you're at late sports cards have been two boxes of 23 penny legacy football hobby for Kyle Z It's good luck Kyle. Let's do it buddy. So Kyle See you baby See you dare to tear. I'll be fire Orange Joe Montana to $1.99. Geez That is CJ Stroud silver rookie. Nice one there Hutchinson Will Anderson Orange Mini Josh Downs to $1.25 Good Lord Anthony Richardson to $2.99 clean tune this one Aurora and Oh, yes, what you should be looking for too. I would say Ethan solace is gonna be the main guy Jordan Addison to 25 nice one there yellow ice auto Grats on that one good stuff Jordan Addison be Ethan solace Who else would say you entry Vargas Felman Celestin? Yeah, yeah, well been Francisco Brandon my Alfredo Duneau Ries hall to 100 nice one there Luis Guanipa Honestly the all other ones do where you can get like the rookie stuff that'd be huge on the light Zach Evans Travis Kelsey Mini one of one plus everything else was number. That's pretty solid Debo to $1.99 the one of ones in this are darker black I think you might have been here be the day up That was nasty out of this, but I think it was in 10 bucks to Andre Reed It's going to be an RPI It is to 100 trait Tucker 94 of 100 rookie Jersey auto for the Raiders Nice one there Nate picking up a Chronicle soccer break tomorrow Nice, thank you Nate Trenton Simpson Chrome rookie and Yeah, three X tiered three X tiered Greg did Yeah, Greg you did win one of the 10 case pots actually Go Greg horse. We'll see you in the morning, Greg. Oh, yeah Dare to tear John Randall nice one there to 65. That's sick. Yeah, it's on that one Tank Bigsby Every polar though Sean always go at least a little bit That is a remand Ray Jimmy Garoppolo to 100 on the green is a Trenton Simpson rookie auto for the Ravens nice one there See simp. Yep. Hey Sean beauty to 149 on the orange Pats CVS receipt. That's pretty funny to 199 past moms. We were here all day, so No idea man. No idea TVH Jaden's winning right now Jaden big time to Jackson Smith and jig bus silver rookie with a baker to 120 whoa to 125 This thing's wrong man. Yeah, hard dude Randall Cunningham to 150 Quentin Johnson to 149 rookie to The Cardinals on the orange Smudge it a little bit roommate Packers dual jersey auto above That is Aiden O'Connell to 149 nice one there What year is it from if it's from this it could be Muzzgrave. I just watched highlights of its shorts I was here, so I didn't get to catch it. Well, 249 is Bruce Smith Chant Bailey and face stuff do for your break there Kyle. Thanks again for the sport buddy. Get right out to my man


Typically they would require teams of people coming together because they bring different inspirations and sometimes it is from different disciplines. So let's take the problem of water. Water is not just a science problem or an engineering problem or a policy problem or a business problem or a cultural problem or a social problem or a behavioral problem. It's all of the above and more. So then if you really want to find a complete solution, a comprehensive solution to this problem, you need to bring all of that thought processes together to be able to find a true solution.


Let's go over to our M. Mr. Tim or as we do each and every Tuesday and Thursday and don't forget folks You can reach Tim every trading day At odd or D dash oracle comm. That's odd dash oracle dot com Tim or what's going on brother? Yeah, I guess you got my charge. Yes, sir. I do All right It's kind of a repeat, but we can kind of go over chart one real quick. Okay. I have it Yeah, and okay, the bottom window we talked about this probably I don't know three four or five weeks ago and That bottom window is the 50-day average of the up-down boiling percent. Yes, and we talked about well when this indicator gets below minus 20 Normally the market flip sideways and flip sideways You know Last three times was six months then it went sideways for about four months We'll made minor new lows. Okay in the current time in the current time frame We want sideways two months because we got that signal Right, it's like July 1st or something anyhow come what sideways and usually you kind of touch a new low But nothing real significant then once this indicator closes above 50 Which is all that blue area. I see that on the chart That's when the rally starts and I did this this morning and or it plus 98 or so almost one plus one a house above zero and this is a longer term chart This is a 50-day average and the ones we last time we on Tuesday We showed the 18-day average and it was you know Both of them closed above We're at the up-down ball includes above Minus 10 on that indicator. This one needs to get above zero this one. Okay, where are we right now Tim? We're plus one So so the 50-day Needs to be above zero Above zero plus one. So this is you know generating that signal right now. Oh, right. That's what I thought Okay, I guess that's that's my point. That's what I was that I was looking at in the blue It's okay. It looks to me like it actually hit. Okay. Cool. Okay. Yeah, so let me ask you this What it when it when it hits there, right? Is that saying that you're at the beginning of the rally versus? the consolidation maybe yeah, okay Look at the last signal, you know last signal of July of last year. Yes We got down below minus 20 right and in in October It finally got above zero and that's you know, maybe late September and so it it rallied all the way into first part of This year, then you know went down below zero stuff. So any of these signals usually you laugh, you know The one back in 2000. I don't Look like about 20 or something where you wait till after the chart, you know, that's gonna last a long time It just kept going up and up and even with the March of 2000 COVID crash It actually stayed on a bullish signal even though the market kind of crashed It was kind of a big hiccup and it came right back and went up to new highs. So right well, I'm saying here We probably this is probably a multi-month type signal, right? So because you know, it's so intriguing on this one Tim is that you know when you actually look at, you know The the gold contract. I mean we have hardly done a retracement at all You know since going back, you know in the middle of April I mean, you know compared to what we have done going all the way back to you know, 2020 you know what I'm saying? It's like we had that nice run, you know prior to 2020 and then you know That consolidation always had deep retracement and this one hasn't had a deep retracement at all Yeah, you know, you're right about that and actually I've got some other signals that actually I got a But now we'll show it on the show with that. Yeah, I'm around to know I got a bunch of type Longer-term signals that were triggered last July August And so and even though the market has actually moved up from you know, the blows up last July August Oh, yeah, that's where that four months is, you know and made right our highs and right So this is a little shorter-term signal, but the longer-term signals are bullish So that's a flip to chart number two. I okay reason why I'm kind of putting this out It's something I think it's pretty intriguing here. This is a monthly chart and At the bottom window I want to point out This is a monthly chart of the up-down boiling percent It's not a 50-day average is a monthly chart. So this really looks at the bigger time frames and what's going on Yes, and What I want to point out I got that shaded pink area there. Yes Kind of up-down volume is kind of like an advanced decline, you know, if you got Zero advances and everything's decline. It really can't go lower, right? That's same with the volume. You get you get You know, no down volume at all and only up volume it would be registered You know extremely high infinite and the same thing with we got all down volume You can only go so low because you run out of chairs being traded. So it's kind of like that It would really be hard to get below the 2016 low. Yes, that was a major low off of a major high and it went back there and tested in 2019 and in currently we're at the 2016 low now for the up-down volume in the care okay something What I'm saying here something is Extremely sold out. It's it's you know when it's the worst of the worst is usually the best of the best Yes, but especially the market whenever I just hate it so much, right? You got a sold-out market and you get basically all the sellers that we're already sold Yeah, and they don't pay attention to the market, right? That I mean, that's how it goes, right? Yeah You know remember that one chart I showed you on bullish percent index. Yes, every time it got blown Five another five percent of the market was on bicycles. That was a major bottom, right? It happens the same way as top with the bullish percent index is up 95% You know it's hard to get any better than that That's usually a top or it kind of works with up-down volume It just stay right there. I hear this. Yes. Stay right there one second Tim and I gonna be coming right back Don't forget folks you get hold of Tim at odd dash oracle.com We have the doubt on 124 Nasdaq's up 52 S&P's a flat Tim and I come right back Welcome back folks to doubt down just shows right now trading down 120 that the Nasdaq up 57 S&P's a flat We talk what I'm am is the Tim or we are talking markets right now. We're actually talking the gold market Okay, Tim. We're ready All right, so when you know is what I'm thinking on this This is still chart number two. Yes that base that's building 2016 What I'm saying is the up-down volume a community of up-down volume really can't get any worse than what it is right now And that's you know that 2016 low was was You know, it's just an ugly low and actually 2019 was low with this one It's just as ugly and and so I'm thinking this whole thing is a big base You know, it's just building a base for the the next rally I don't think this up-down volume can get any worse than where it is right now we're minus five five zero zero on that chart and Historically that's pretty low. So That's that's my point that hasn't turned up yet, right? But this is on a monthly time We got you know, we've got some other indicators that have turned up. So this will probably we start responding Next month in September will probably start to spawn. That's kind of lagging in the care. I've went across is the Mid-Bowlinger band that's where all those lines up blue lines red lines our signal and we had a come across back in in mid 2022 probably on that July period went above it and kind of closed below it again So But anyhow this this I think will turn up because I got a lot of the indicates are turned up and when they do turn up It's usually a multi-year rally because you look at all those lines, you know, you got You know most of them are about two years apart. Yes, so I'm thinking this could rally into 2024 maybe 2025. Yeah, you know, that's what history shows. Yeah, you know, it's interesting Tim is that I did a Workshop for this gold subscribers last night, right? And when I was going through them the the gold contract itself, right Versus the equities, you know the gold contract itself even going back ten years The most it did was I you know a 50% retracement on a five-year at point three a two retracement on a You know a ten year, right?  I'm saying to myself This is interesting and then Silva like when I'm looking at Silva You know basically seems to be stronger than gold right now But on a longer-term shot if we just take the retracement value, right? It is not So it's like okay, this is gonna get you know We know that you know the metal market in general is always challenging But I'm saying I was like it was a heads up.  Well, the XAU gold ratios is kind of what you're talking about. I don't you know, yes That's just yes to an equity and right you quite a few studies with that too and and that thing has been Haven't gone anywhere to I think was 2014. It's just been facing in a small Pattern so I'm kind of watching for that to turn up. Yeah, and Actually the next show we'll do next to the I'll bring I'll bring that chart and we can talk about it Well, you know, I was thinking so listen to this. This is this gets intriguing folks, okay? So and in the gold and silver, you know, mining business, right? Mexico has always been one of the great jurisdictions to do business in right? Well, they put a law through last year Tim, right approximately only eight months ago right now and What has happened is that that law is pretty intense because the taxing structure Has gone up dramatically and go up a lot more and so what has happened is that equities Mexican that are doing a lot of business in Mexico. They haven't moved So it's really intriguing.  It's like and it's not only the thing that's crazy is that they went from In 2021, you know, they were an exploration stock. They went from Doing no business to 215 million to doing 428 million And the stock can't move You know, so I'm just I'm just throwing it out there in the context of that could be one of the reasons that You know the gdx the xa you, you know people literary now of you know, the whole Mexican deals You know what I mean? So you're dealing with, you know, the United States Canada Australia those are still great mining communities Where the equities do business there, you know, you because do you remember, you know the first run tim that we had If you remember in 2011 what happened folks is this and I never thought this would be happening in the United States But it did happen when we went from 2001 2002 That's when we had bgo with like 10 cents and 20 cents and cde and all that right Yeah, what happened folks in 2011 That was almost at the high 2010. It's not happening. I congressmen and senators start saying in Congress that hey man, we're gonna start charging, you know all these taxes in Nevada was like this came out of nowhere So it's always intriguing. You know what I'm saying? It's like, okay, you know, you get the gist of it It's like things can change pretty quick But right yeah, well, I'm thinking you know, they're they're pushing all this battery stuff out Which is basically all made up of precious metals. Yes, and you know, we're buying all that stuff from You know our amenities, you know or people that don't like it, right? So I'm curious, you know how this is all gonna swing around because You know, we got a lot of those men a lot of that stuff right here in the united states, but You know So we'll have to wait and see if kind of a political winds, you know may change Yes, I never remain the same for all the time. I'm with them. I'm thinking I'm thinking what's going on right now All these political winds are winds are gonna Change that's the reason why all these charges are you know, especially these longer term charts Are calling showing some bully signs, so right? Um, right be back to 2000 again. I don't know.  So absolutely time will tell Time will tell We gotta do one more chart real quick. Okay A chart three. I'm there and uh, yep This is just a weekly chart of the xa u or no, it's a monthly chart of the xa u going back to Uh, look at about 2016. It's just a big Channel going up You had a couple of shakeouts and we're bottom of that channel And so I'm thinking we're going to go back up to top of that channel And uh, that you know, we talked before on on your show that we think Uh, there's a possibility that xa u gets around to 180. Yes, there's some other charts Yeah, and this is kind of a sporting chart here. We kind of build a base Really haven't gone anywhere for most of a year now And so we're either going to break down which according To a lot of charts I have we're not going to break down. We're going to break up right next logical Target is back to the top of that channel. Yes, so I'm thinking that's where that 180 uh, or higher may may be reached No, I I can see that It just just stay there tim uh tim oid tommo brian folks who do appreciate your crowd on a prowl Unless we're going to be coming right back. We have that out industrials right now Down 136 nasdaq is off 52 s and p's are down one and a half I want to say hi to bill bill. What's going on? Bridget, what's going on? Love you guys Tim and I come right back Welcome back folks. Uh, tim uh oid tommo brian don't forget folks You're going to get hold of tim every trading day at oid or d dash oracle.com We have the down industrials right now down 116 nasdaq's up 61 s and p's Are up one and we're looking at the uh xa u monthly chart tim Yeah, uh, yeah, that's all I wanted to say about that. Okay Um, we can go on the s and p's now if you want. Yes, please. Yep. There we go. All right uh, okay, the first chart four is just the daily chart and um I don't know what today right now. We're up five days in a row when I did this chart We're up four days in a row You know, if you're up four days in a row the market's higher 73 of time within five days I say five days in a row that jumps up to 83 higher within five days. Wow. So um, so you So even though we're testing that previous high of may second I got a red line drawn there. Yes that that may second high had uh Uh, I think was 93 million shares or 94 million shares. Yeah 92.1. Yeah Yeah, so yeah, so we're testing that high most likely on lighter volume But since you're up, uh Four days in a row at least there's a good chance. We're probably going to get to that gap area Which is that pink area. Yeah, and that's the potentially where that signal potential cell signal may generate also the the week of um Next week is labor day And the week up is the week up before labor days up and the volume is like going into friday a lot times Labor day week week which is next week is a down week I see so okay, so i'm kind of looking for a signal here But there's a good chance. I don't know what today's going to do yet But if we don't hit a high Uh for a five days in a row most likely that Gap area is going to be tested if not going to be tested Uh, you know probably not this week, but probably next week So Monday or Tuesday is probably going to be up or Monday is a holiday Either Tuesday or Wednesday be up in the last several days might be down week next You know wait next week. I'm thinking nothing real significant But at one point I thought we may go all the way down and maybe test the lows I don't think that'll be the case. I think we'll find support Where that blue line is which is basically the previous highs of that bearish and golfing pattern I think we may find support there Okay, oh, let me look at that one one The bearish yeah, is it yeah, it's 444 area on the sdy's Oh, I see it. I see it. Yep. Okay. Okay. Yeah, which is kind of uh, so that's gonna be a really small consolidation Yeah, I got it. Okay. Yep So as I'm thinking that's what's going to go on then In premier, I don't know the whole thing's kind of just garbage. Yeah, this is It's kind of um Because I don't think we're going to break out to the upside. I think Um, actually go to chart five real quick. Okay This this is the reason why I don't think we're going to keep breaking up Is uh, this is uh the bottom window the six three day average of the trend. Yes And we get around what get around one or lower usually You know, there's always a section to the case. There's one time in in 2021 Uh, or 2020, I think you got there, but normally when you get this low on a six three day trend It's at least a high period. It's not at least consolidation and so I put those times for the uh, the pink areas and red lines And we kind of been there over the last uh, since uh, July We've been hanging around this point one or lower On a six three day trend and so we're you know, we're having difficulty here trying to keep going What we need to do is get that six day trend up around 1.1 And that's where an impulse way can get going Okay, I'm thinking we're probably going to move sideways probably all the way into october And uh, I think the worst still may come Uh, because I think 4200 on the sby is still possible so We'll kind of see but It's a bigger trend so if you flip back to chart number four again, yes That's the reason why I don't think this rally's going to just continue. I think it's going to fade out Um, it's certainly going to be interesting because it's amazing that you know like We're Just about at all time highs still and we're talking about going into september first, right? Yeah, yeah, the mark is strong. I mean, yeah Uh, I'm thinking we got garbage made for another month month and a half right but after that I'm I'm thinking You know, we're starting to build a base. We'll probably you will get back into that blue area I got shaded there. That's where all the The trend and tick readings. Yes got blowout The lease will get back into that area maybe we'll break a little bit below it And but we need the trend and ticks to really get negative scan to get enough energy going to build You know build a base to get to Throw the market higher and right now, you know with a six of eight trend Just setting that one which is kind of neutral but bearish on the bigger time frames You just don't have a Fear to drive the market higher remember Joe Granville, you know, oh, yeah, you know It the market clock climbs a wall of worry. That was his word That's right the generals and the you know the generals leave first and then the you know the private So whatever too. Yeah, right, right. Yeah, there's soldiers and stuff soldiers. Thank you. Yeah, so anyhow, that's that's So, you know, I can see that that's that's intriguing. We need fear in the market here And we really don't have it yet Right. And so what you're saying, which is pretty cool is that you have to get some fear in the market even to get higher That's that's the reality and I can see that there's no, you know, exactly what the deal Yeah, and so and so, you know, we're down. We're sitting here for two months But the six of eight trends, you know setting near bearish levels We don't have the power to break above the highs other than, you know, we may test those highs Right, but that'd be the most you're gonna get Right, so Wow if It's it's a trading range. So it's uh, I'm kind of looking for a sell signal here, but nothing significant I think the big sell signals, you know Is coming probably in october Yeah, I think you get a decent sell signal that That minimum go back down and and if you look to last low we had back in august Yes, that that low was on high volume. Yep 98 million right volume lows are tested right 98 million is lame Well, listen, man, it's always a pleasure. You have a great Holiday weekend kind of cool that we're going into, you know, labor day, right? No doubt. I mean, yeah You talk about a fast summer, right man. Holy cow. Yeah It really went fast. It did so So what like what type of weather do you get coming into the fall, Tim? Well, actually, it's usually really nice here, you know, today is probably going to be about maybe 85 at most nice All week's been really nice, but Nick this weekend it gets kind of it gets up to like 95 Okay, and unusual for this time of year. Yeah, but normally As you get september, you know, you start, you know, 80s are kind of the highs and evenings gets in the 60s and Then in November or october, you know, you're getting starting to stay in the 60s instead of maybe 70s So it's that's good. Oh, you get a nice one.  Yeah That's when you're gonna have to come visit us in florida, but that's that's that's good We're looking forward to it. Yeah, totally, man. So well, listen, don't forget folks You can get hold of tim every trading day at odd rd dash oracle.com. That's odd dash oracle.com Tim we always appreciate the education man You have a great weekend safe weekend and we look forward to talking as soon as we get back from the labor day weekend on tuesday All right, sounds good. Thank you


So design is everywhere and everything needs to be redesigned and rethought and it's something that you know in your position as you know the director of the AAD program here at GSAP. You know you're bringing all of this to the program which was already very much a sort of space of critical engagement, a space of argumentation, a space of experimentation, but you've expanded that to sort of push or invite students to consider questions of scale and how to work collaboratively with other disciplines etc. Tell us a little bit about some of the transformations you've brought already to the program. Well, I think the program is a legendary program that brings together some of the most interesting students around the world that already have a degree and already have questions and sensitivities. What I think is the great potential of the AAD now is that it's putting together an ecosystem in which people can bring here their questions, not only what they know but what they know that they don't know and that they want to develop and they could find a place to do that. And basically we believe that architecture is relevant and that architecture can make a change basically and we're supporting all these sensitivities to grow at something that could transform the world. And we're in the center somehow of many discussions by being in Columbia, by being in New York but also by being in the world in the way we are in a very independent way in a way that we believe that we can reinvent the way things work. And that means also to break down the discussions into a number of new terrains in which architecture can find and it's already finding an opportunity to grow and to bring relevance. The AAD program is being able to mobilize probably some of the most exciting and intelligent and equipped people to discuss this and we're very happy to convene the students that have those questions and that can bring them to this ecosystem. I mean the school has always been kind of a sort of space of experimentation with drawing and with digital sort of expression etc. And now, I mean the drawings that are coming out are like just kind of so, they're planetary is what I like to think. And do you think that you know through these new modes of representation and kind of hybridizing analog and digital again in new ways that we can kind of find ways to recast this question of scale? Yeah, I think this is a little bit of the core of many of the discussions that we're having. In a way we see that in the past there was this distinction that architects would work at a very particular scale and they would care about that scale only. And there would be planners, urban designers thinking of the larger scales and then there would be industrial designers or other people looking at the smaller scales but that's not the case anymore. And we're here in G-SAP and in DAJD championing a change of paradigm in which basically we understand that whatever architectural artifact to gain a role in transforming contemporary times basically needs to operate simultaneously at many different scales. It doesn't mean that it has to be at the same time an urbanistic project and a tiny microscopic project. It's that at whatever scale it operates it's somehow creating an effect and gaining an agency in those other scales. And that's why we think we believe that there's a great need to look carefully to what is the way architects design buildings because what we're doing basically has the possibility in what we're doing looking at transformations that could happen at tiny scales, at large scales from the work that we do. This is something that somehow it's a reflection on the world and the way it's challenged now. And what is the way that the times that we operate are not only the kind of 10 years of a building to be kind of assisted but it's something that also have a geological dimension that has to do with the materials that it mobilizes that has to do with its consumptions and therefore needs to be taking care and catering for processes that are thousand years long. But also it's about the way for instance tiny, tiny transformations chemical processes or biological processes are happening in microseconds and what is the way that the decisions that we take at the scale of the building are also transforming and making an impact, having an impact in those other scales. This is something that was not the discussion 10 years ago and that's something that I love that the AAD has the speed to grab these things and to champion them into the discipline.


The Arctic boreal region of western North America is experiencing increasing levels of oil and gas exploration and extraction due to climate change. This activity is causing significant environmental damage, including the release of methane into the atmosphere and could have serious implications for local communities and ecosystems. This article was authored by Luise Klotz, Oliver Solentag, Ziming Wang, and others.