You couldn't tell me when I'm supposed to start. OK. Welcome to the second session of the day, right? It's a pleasure to introduce Ling Xuan Ma from Purdue University. Ling Xuan got his PhD under the direction of Mel Hoxter in 2014 from the University of Michigan and has taken off. And while he was talented as a student, has only become even more talented since. Now at Purdue University, he was awarded a prestigious Sloan Fellowship. And on his website, you can see, has already over 40 papers and preprints, all right? It is a real pleasure to hear him speak about Direct Summands, and take it away, Ling Xuan. OK, thank you. Thank you for the very nice introduction. It's my great pleasure to speak. And sorry, my other device have some issues, so you cannot see me. But I'm just using my iPad right now. But after the lecture, I'm happy to handle any questions. So all right. So the title of, OK, so this lecture, I'm going to, the lecture that was assigned to me was about Direct Summands of Regular Rings. Actually, I feel a large part of the materials, a large part of the lecture, was already contained in this Kevin's Notes and Neil's Notes. So I'm just going to, perhaps, I'm going to do this question from a different point of view. So let me change my title slightly. So the title of my talk is going to be this lecture. We will focus on strongly F Regular Rings and Direct Summands of Regular Rings. All right? So, OK, so to start it off, let me just quickly remind you some basic concepts. So first of all, throughout my talk, all rings are commutative noetherian with multiplicative identity 1. So I'm not going to move beyond this noetherian setup. And so we will focus on rings of characteristic p. And so if r has positive characteristic p, so then there is a natural Frobenius anamorphism, then we have a natural Frobenius anamorphism f, which goes from r to r. And of course, it sends little r to r to the p. And sometimes we will iterate this map f to the e. And then the map is going to send little r to the p to the e. And at least in my lecture, I'm going to use a notation you've probably already seen in Kevin's lecture. That is important that we need to distinguish the source and target of the Frobenius map. And so the notation I'm going to use is OK. So here's a notation. So I'm going to use fe lower star of r to denote the target of the Frobenius. So in other words, instead of writing down this fe, that map goes from r to r, so we're going to view the Frobenius map fe that goes from r to fe lower star of r. OK. And so let me just quickly remind you. So in this notation, this one is esomorphic. This is the same as r as in the bidding group, but the r module, if I view this copy as a module over the left of the source, maybe let me just even write it down.  And the r module structure on fe lower star is defined using the following. So if you have r1 times fe lower star r2, it's going to be fe lower star r1p to the e times r2. So this is the Frobenius. But on the other hand, let me also point it out. So this one is also esomorphic to r as a ring, obviously, because it's just, in some sense, it's just r, but I just used this awkward, a little bit awkward, so this is the same as r as a ring. So it sends fe lower star r back to r. So that's the ring isomorphism. OK, so now here's the definition. I believe you've also seen this in Kevin's talk. So a ring r of characteristic p is called f finite.  So in other words, a finite means the Frobenius map is a finite morphism. OK, so I will leave this as an exercise to show that in this definition, you can require this for some e, or you require this for all e bigger than 0. It's the same thing. It's not hard. So let me just give you, OK, let me just mention some examples of a finite, and so for example, if you just have a field k, a field k of characteristic p is a finite, right? So k to the 1 over k is a finite dimensional vector space over k, so it's a finite extension. So this is because, well, I didn't mention that, but hopefully you already see this in the earlier lectures. While this one r is reduced, you can view this Frobenius map as the natural inclusion from r to r to the 1 over p to the e. And so for field, the 1 over p to the e is just the field extension. So for example, a perfect field or algebraic closed field are always a finite. And I leave an exercise that hopefully you have seen this before, that if r is a finite, then all rings. Maybe let me just write it down here.  So in summary, so for all rings, essentially a finite type over r will be a finite.  All these procedures are preserved at finite property. And let me also, for example, so then I mean, you can start with a perfect field, and then you'll get lots of examples. All the essentially finite type algebras over perfect field. Just a comment. You say that a field is a finite if and only if, if you consider the extension of k by k over 1 over p, it's a finite dimensional k vector space. But then you can also say that k is a finite if and only if k is a finite dimensional k to the p vector space. Both things are equivalent, and maybe this is a more direct point of view. Yeah. Or if and only if this is a more straight point of view, if you want to avoid p roots at this point. Yeah. OK. Good. Yeah. You can also say k is a finite dimensional kp vector space. OK. So are there any other questions, comments? And so the other thing I want to point out, I just want to give you plenty of examples of finite rings.  So this also follows from one of the exercises. And basically you use the co-instruction theorem. So you write this complete ring as a quotient of the power series ring over a coefficient field. And so as I said, adjoining a power series variable will preserve the finite assumption. So this is going to be fine. But anyway, this is an exercise. OK. So and throughout my lecture, when we talk about strongly irregular, just go back to this title, when we talk about strongly irregular rings, I'm going to assume the rings are always a finite, just for I just want to avoid this technical issue. And there are some results saying at finite rings are nice. For example, I'm going to just state it in words. So Coons have proved that at finite rings are excellent in the sense of words indeed. And Gabber has shows that at finite rings are homomorphic image of at finite regular rings. So these rings are, so in particular, for example, they admit canonical modules, et cetera. These rings are not pathological. OK. Now let me recall you. I think this already shows up in Kevin's lecture. But because this is a key concept that I will study. Did I label this? Or I didn't label this. Let me just remove this. OK. So here's the definition. And at finite ring R of characteristic P, of course, is called strongly irregular. If for every c inside R, not in any minimum prime of R, there exists e bigger than 0 such that the map R to f e lower star R sending 1, 2, f e lower star C splits as a map of the homomorphic. So this is going to be the definition. And so clearly, let me just put it out. So OK, let me let's perhaps stick with the definition a little bit. So the definition requires that for any c not in any minimum prime, the map R to f e lower star R sending 1 to this map, sending 1 to f e lower star C, this map splits as a map of our modules. So in particular, let's just try some simple case. If you take c equals to 1, let's see what happens. If you take c equals to 1, then the map is going to be 1 goes to 1 f e lower star 1. So this is just if you take c equals to 1, this is a natural Frobenius map. So in particular, let me just say remark, so strongly irregular rings are always f split. So f splits just means the Frobenius map splits.  So in particular, so whenever the Frobenius map is split or even much weaker, as long as the Frobenius map is injected, it's an easy exercise that you can show the R is reduced. So in particular, strongly irregular rings are always reduced. They are always reduced. OK, so and remember, well, I mentioned this earlier, but I didn't write it down, but you can view the Frobenius map as the natural inclusion from R to R to R to 1 over p to the e when R is reduced. So and so since here, all the rings we consider, the ring we define, there will be automatically reduced. So this condition, if you don't, this is in particular, if you first see this or if you don't like the f e lower star notation. So this condition is really saying what? It's saying if you identify this one with R to the 1 over p to the e. So then this condition is really saying strongly as regular, this is really saying what? It's saying like the map, the condition you want to put is that for every c, not the n minimal prime, not the minimal prime, not the n. So the map, the natural inclusion R to R to the 1 over p to the e. Well, but I'm not going to use the natural inclusion. I'm going to send in 1 to c to the 1 over p to the e splits as a map of R module. So this is completely equivalent to this. It's just a different notation, but same thing. So f e lower star R is identified with R to the 1 over p to the e. And under this identification, this f e lower star c is identified with c to the 1 over p to the e. So saying this map splits is the same as saying this map splits. But of course, the only small point I want to make is that if you want to use R to the 1 over p to the e notation, your ring better be reduced. But it tends. So strongly as regular rings are always reduced. So there's no ambiguity using this 1 over p to the e notation. But throughout my lecture, I prefer to use this f e lower star R notation because this, so first of all, it's compatible with Kevin's lecture. And secondly, it's going to be more compatible with the modern language that in the character p coming around to it. OK, so here's the definition. So I gave you the definition of strongly F regular rings. And the first remark is that they are always f split. In particular, they are always reduced. And so the first lemma is that, so for local rings, you can actually say more. So they are not only reduced, they are actually domain. So let me just state this. So I let R mk be an f finite and strongly regular local ring character p. Then R is an integral domain. OK, so let's prove why is this. So since R is reduced, to show is a domain, you only need to show there is only one minimal prime. It is enough to show R has only one minimal prime. OK, so now suppose you have more than one. So let p1, so we're going to prove a contradiction. We assume you have more than one minimal prime. When p1, pn, you have minimal primes of R. And let's say, at least two, let's just try to arrive at a contradiction. So the idea is that you want to, OK, so the only condition you have is the splitting condition. So you want to split off some elements not inside all the minimal primes. So you have to pick this element sort of cleverly, OK? So now we pick. So now you pick. So for each minimal prime I, you pick fi inside all these other minimal primes. But it's not in the PI. It's not in the I minimal prime, OK? So then if you look at the sum of all these fi's, so this is not, so then this is not, I claim this is not contained. This is not in any minimal prime, right? Because I hope this is easy to see because this is basically by the way you choose all these fi's. So for example, let's just look at p1. So f1 is not inside p1. But all the other, like f2, f3, fn, so all the others will be inside p1. So there's only one element not inside p1. So the sum is going to be not inside p1. And you do this for other i's too, OK? So you choose this element not in minimal prime of r. And so now by the assumption, you can pick some e such that split this element, OK? So let's just write it down. Since r is strongly, I will use sfr to be a short hand for strongly F regular. So since r is from F regular, you, so there exists e bigger than 0 and an r linear map from f1 lower star r to r such that this, let me call this map phi, such that phi sends this element to 1. So phi of fv lower star is 1, OK? So this is just the concrete meaning that the map r to fv lower star r sending 1 to fv lower star of this element splits. So I'm just writing down, so split means there's a map back sending this element to 1. OK, so now let's just try to arrive at the contradiction. So far, we haven't used any of this. So far, we haven't used the local condition r. And now I'm going to use the fact that r is a local way, OK? So well, so OK, so first of all, this map is additive. So this is certainly equals to phi fv lower star of f1, OK? And so now, of course, this is equals to 1. Remember, this is by our assumption. And so you have a sum of element, which is a unit. And so now I'm going to use the fact that I'm working in a local way. And so at least one of these elements must be a unit, because if otherwise all of these will be contained in a unique maximum ideal, so this can be a unit. And so since RMK is local, at least one of this phi fv lower star fi is a unit, OK? And so therefore, well, without loss of generality, let's assume, we may assume just phi fv lower star f1. It's u, which is a unit, OK? And now where is the contradiction coming from? So remember, we have at least two minimal primes. So this little n is like this 2. So what I'm going to do, I'm going to pick an element, OK. So let me just write it down. So but since f1 times f2, so this is equal to 0. So this is, again, by the way we choose this element. So I choose this f1, f2, fn such that their sum is not inside any minimal prime. But if you take the product of any two of them, you got 0. And so the reason is that if you let's just look at f1, f2, f1 is in all the minimal primes except p1, and f2 is in all the other minimal primes except p2. So f1, f2 is inside all the minimal primes, but r is reduced. So the intersection of the minimal primes is 0. So if you take f1 times f2, or more generally, you'll take the product of any two of the fis, you got 0. So f1, f2 is 0, OK? So then, well, you almost see the contradiction. So we have, OK, so now I'm going to, you look at u. So this u is this phi of f e lower star f1. So you just think about what is u times f2. So let me just write it down.  But phi is an R linear map. So phi is an R linear map that goes from f e lower star R to R. And so I'm multiplication by f2 outside. So you can pull this f2 inside. So this is phi f2 times f e lower star f1. And so now, what is f2 times f e lower star f1? Well, this is, remember, there's a Frobenius f e lower star here. So when you have f2 times f e lower star of something, if you want to pull the f2 inside f e lower star, you have to raise it to p to the e. So this is phi of f e lower star f2 to the p to the e times f1. OK. But now this is 0, because f1, f2 is 0. So f1 times f2 to the anything is 0. So this is phi of f e lower star 0, which is 0. So this is a contradiction, OK? Because u is a unit and f2, we suppose f2, I mean, we begin with f2 not 0. So this is a contradiction. OK. So I do this little lemma here basically just to, well, first of all, show you like for local rings, strong F regular rings are better. They are domains. And we'll see later, actually, like they are always normal. But let's just stick with domain for the moment. And also, I want to get you familiar with this f e lower star language, because it's useful. OK. Any questions? Sorry, I cannot see the chat. If you have questions on the chat, maybe the organizers can remind me. But feel free to just unmute yourself and ask questions. OK, so let's just, we define strongly F regular rings. The maps like r to f e lower star r for any c, OK, so for any c there is just e such that the map sending 1 to f e lower star c splits. Excuse me, there is a question in the chat asking why strongly F regular implies reduced. Right, so let me just repeat that part. So if r is strongly F regular, so the condition is that for every c, for every c not any minimal prime of r, this map splits. So in particular, the map from r to f e lower star r sending 1 to f e lower star 1. So this map better be splits for some e, OK? And so, well, so this means the natural Frobenius map is split. So in particular, I mean, to make sure that this map splits, it better be injected. And it's fairly easy to see. Actually, I think I leave it as an exercise. If the Frobenius map is injected, then the ring is reduced. This is, well, you will see that it's not a hard exercise. But anyway, OK, any other question? OK, so we have this definition. There's an easy remark that the F regular implies the strong F regular implies F splits, and they are always reduced. And now for local rings, you can do a little bit better. These rings are always, the strong F regular local rings are always domains. OK, so the next thing, because we want to study strong F. I mean, we want to use, so basically, the goal of my lecture is that I want to use this theory of strongly F regular rings to study this, well, to prove that the X amount of regular rings are comacodyl or whatever. So this is like the final goal of this lecture. And so we want to study some basic properties of strongly F regular rings, first of all. OK, so here's a lemma, the second lemma. So it says strongly F regular ring is a local property. So let R be an affinite ring of keras of p. Then R is strongly F regular if and only if Rp is strongly F regular for every p inside spectrum, for every parameter. OK, so by the way, let me just make a comment. So perhaps you have learned in this Niels or maybe Kevin's lecture that there is also a notion of weakly F regular. So obviously, because of the name that we define them, so strongly F regular always implies a weakly F regular. So weakly F regular is defined in terms of tight closure. And so actually, in my lecture, I leave it as an exercise to I will ask you to show that strongly F regular rings are always weakly F regular. So this is indeed a stronger notion. But you can see that. So for example, this lemma is like one reason, at least, like why strongly F regular rings behaves better. Oh, of course, it is conjectured that the weakly F regular strongly F regular, they are ultimately they should be all equivalent. But we still don't know that. And so this lemma indicates the strongly F regular rings are some sort of easier to study because it is indeed a local property. Well, for weakly F regular rings, we still don't know whether they localize it well. So I hope you have seen that open question part or some of the mentioned that before. But anyway, to check strong F regular, to check something, some ring is strongly F regular is really check it locally for any prime. OK, let's prove this. So there are two directions you have to show. So first, let's suppose R is strongly F regular. So suppose R is strongly F regular. OK, I want to show all the localizations are strongly F regular. So let P1, P2, Pn be the minimum primes. So OK, so now I fix the prime P and I want to show, let's say I want to show Rp is strongly F regular. And so now we want to use the definition. It is enough. OK, so let me just say, so what's happened? OK, so to show our local as a P is strongly F regular. Let's just think about the definition, what we need to show. Well, we need to show for any little C, I mean, maybe I should say, for any C, not inside any minimal prime of R local as a P. So any C whose image in R local as a P is not in any minimal prime of Rp. So you need to show for any C like this, there exists e bigger than 0 and an Rp linear map. From f e lower star Rp back to Rp, sending f e lower star C back to 1. OK, so this is definition. So to show something strongly F regular, I basically just copy the definition for it. You need to show exactly this thing. OK, all right, so now what's the, there's only like one, OK, this is the easy direction, by the way. So the only small subtlety that you have to think about is that, OK, so if you can, if this little C is not inside any minimal prime of R, it's not inside this P1 to Pn. If this is not inside any minimal prime of R, you can do this. Because we assume R is from a regular, you can pick a splitting from f e lower star R back to R, sending f e lower star C to 1. And you just localize that map. It induces a map from f e lower star R local as a P to R local as a P. OK, so if this C is actually not inside any minimal prime of R, this is obvious. You have a map on the level of R, and they will localize that map. That's pretty straightforward. But the only, as I said, there is a small subtlety here is that we are only assuming that C is not in any minimal prime of R local as a P. So what are the minimal primes of R local as a P? Those correspond to the minimal primes of R that are contained in P. So there could be some minimal primes that are not inside P. So this is the only small subtlety. So the claim is that you want to avoid those cases. Because if your C is inside some minimal prime of R, so you can't apply your assumption to split C off under R level. OK, but this is not a problem because the idea is that you can always replace C by some other. You can replace C. So the idea is that you can replace C by something else whose image in R local as P are the same. But the other thing is not inside any minimal prime of R. OK, so let me just give the details. So the claim is that we may assume C is not in any minimal prime of R. OK, so let's explain why is this true. So suppose C is contained in, let's say, P1, PI, but not in, say, the other, not in the other minimal primes. So I mean, remember, I'm assuming P1 to Pn are all the minimal primes. And so, for example, if you pick your C whose, I mean, the image in RP is not inside any minimal prime of RP. But unfortunately, C is inside some minimal prime of R. That could happen in prior. Let's say C is inside P1 to PI, but not in PI plus 1 and Pn, since it's not that. And so now the trick is that, so now we pick C prime inside the intersection of, OK, so Pj, j equals to i plus 1 to n minus the union of PI. Let's say Pj, j equals to 1 to i. OK, so this is by standard prime avoidance. So you pick a C prime inside all the other minimal primes, but not inside P1 to PI. And you replace C by C plus C prime. And replace C by C plus C prime. And the advantage of doing this is that, so there are two things we have to track. So the first thing is that C plus C prime is not inside any minimal prime of all. Because, well, C is not inside these Pj's. And you add, so C is not inside minimal prime from i plus 1 to n. And the thing you add is inside the other minimal primes. So C plus Ci is not in the other minimal primes. But this is also not inside any P1 to PI, because C prime is not in these minimal primes. But C is inside these P1 to PI. So this is the first thing I have to check. And the second thing I have to check is that, so C plus C prime have the same image at C inside our local asset P. OK? So maybe I leave this as an easy exercise. So check. You have to check this. Well, maybe let me just say C prime, the image of C prime in our local asset P is 0. OK? So this is just basically by the way we choose C and C prime. You notice that none of this P1 to PI, none of these PI's could be contained in P because we assume the image of C in our local asset P is not inside any minimal prime of our P. So P1 to PI cannot be contained in P. You have to use this fact to show this. OK? All right. But anyway, so the idea is that you can modify your C. You replace C by C plus C prime to assume that the C is not inside any minimal prime of our. And the image of C plus C prime and the image of C are the same in our local asset P. And so then once you do that, so now you use your assumption, as I said, then it's very easy. But since R is strongly irregular, you can split off this C. So there exists E bigger than 0, such that R to Fv lower star R sending 1 to Fv lower star C splits as a map of R modules. And then we'll just localize that. So and localize this splitting. We get RP linear map sending it was our C to 1. OK. So this direction is the easy direction. So as I said, the only subtle is that you have to modify your C a little bit. OK. So that's all right. So now we prove the converse. This is a really interesting direction. So now I'm going to assume all the localizations of R are strongly irregular. And I want to show R itself is strongly irregular. So let's see why is that. OK. So now we prove the converse. So now we fix a C inside R not in any minimal prime. OK, so now this time our assumption is that so we know for every P inside spec R, there exists E bigger than 0. Well, let me just emphasize this little E may depend on P, OK, such that Rp to Fv lower star Rp sending 1 to Fv lower star C splits. OK. So we want to show OK, so now our assumption is that all the localizations of R are strongly irregular. We want to show R is strongly fixed C not in any minimal prime. So of course, this time since C is not in any minimal prime of R, the image of C inside Rp is not in any minimal prime of Rp. So you can use our assumption. So for every P, you can find E, but E may depend on P, such that this map sending 1 to Fv lower star C splits. So this is our assumption that our local P is strongly frag. OK, so now you want to sort of spread out this splitting. And what do I mean? So since R is at finite, OK, so if you look at the harm set, so harm Rp, Fv lower star Rp, Rp. So this is equal to Rp times R, harm Fv lower star RR. OK, so this is the easy fact that harm commutes with flat base change if the first module is finally presented. But our rings are no theorem.  And our assumption is that this is the finally generated R module. So we are using the affine list here, OK? So once you have that, this is a flat base change. So you can just say it's the harm R, Fv lower star R, tensor with Rp is the same as you just tensor each thing inside with Rp. So you get this, OK? So I'm sorry. All right, so what was the upshot? The upshot is that, so OK, so we know that there is a map. OK, so we know like the map Rp to Fv lower star Rp is sending one to, we know this map splits, OK? So that means there is a map here sending Fv lower star C to 1, OK? And so now every map here is essentially, well, what I'm telling you here is every map here is essentially coming from a localization of a map of this level, OK? So the conclusion you get is that there exists a map V inside harm R, Fv lower star R, R sending.  It sends Fv lower star C to 1. And what you know, you know that before you localize, it must send Fv lower star C to something outside P to F, which is outside P. Because after you localize, you want this map to be subjected. Fv lower star C have to send to a unit. So before you localize, you know like it must send Fv lower star C to something outside P, because otherwise it's after you localize, it's not going to be a splitting anymore, OK? So this is what you can do, right? But then what you know is that our localization app to Fv lower star R localization app sending 1 to Fv lower star C splits, OK? So while this is, sorry, I'm already so I will stop after I finish the proof of this lemma. So the point is that so you have a map from Fv lower star to R sending Fv lower star C to some F not inside P. So as long as you localize this map at F, so the map is going to send Fv lower star C to a unit. So in particular, this map sending 1 to Fv lower star C splits, OK? So now for every P inside spec R, we can find F. So for every P inside spec R, we can find such an F. In particular, well, maybe I should really say an Fp here because F depends on P. F is not in P, not inside P. And hence, if you take the union of all the basic open sets, so that's equal to spec R. So to take the union of all these basic open sets, it really contains all the prime ideas of R. So this is equal to spec R. And so now since spec R is quasi compact, this is the very first thing we learn in community of algebra about the spectrum of community of rings. So hence, there exists like F1, F2, to Fn, such that the union of the basic open sets is spec R. And for each Fi, there exists an EI bigger than 0, such that the map R looks at the Fi to FeI, lower star Fi, sending 1 to FeI, lower star C splits. Because this Fi is coming from some P, so we have it, OK? And so now, so this is another exercise question. So now it's easy to see that you just take the E that are larger than all these EIs, so then the map will be split. So it is then easy to check. This is an exercise that for E0, which is the maximum of this E1, En, so the map R2 of E0, lower star R, sending 1 to Fe0, lower star C splits. So this has finished the proof. So let me just explain a little bit about the last step. So the point is that if you pick this E0, OK, so this exercise that I assigned you is that, so if this map sending, if you have some EI sending like 1 to FeI, lower star, there's a typo, RFI. So if you have some EI, such that R2, FeI, lower star, sending 1 to whatever FeI, lower star C splits, so then you can always enlarge the EI. You can pick for every E bigger than this EI, the map R2, Fe, lower star R, sending 1 to Fe, lower star C also splits, OK? And so now basically, if you pick, so now the upshot is that if you pick this E0 to be the maximum of all these, so then the map from R to Fe0, lower star R, sending 1 to Fe0, lower star C, it splits after localized at each of the FI, OK? And then again, it's an easy exercise that if you know it splits after localized at each FI, so then it has to be split because the obstruction, just look at the harm set. So if it does not split, then the image have to contain in some maximum ideal, so you just localize it at that maximum ideal. But our FIs, they cover the spectrum, so you can't find any maximum ideal, OK? So anyway, so I'm a little bit in rush, so maybe this last step requires some exercise, but anyway. So we prove that the strongly afregal ring is a, packing the strongly afregal is a local property. OK, sorry, I will stop here today. I'm not entirely sure who the chair of the session is, so let's clap for Ling Xuan. Are there any questions? There's one in the chat. In the statement, can we replace spec R by max spec R? Yeah, you can replace, that's a good point, because if you know it's true for maximum ideals, you also know it's true for prime ideals, but for any prime because it localizes. It's the same information. Another question. So this shows the strongly afregal localizes, but we say that weekly afregal doesn't, and we know the call me call it does. No, no, no, I mean, weekly afregal, we don't know. I mean, you don't know, right? That's what I'm sorry. But what about afrational? Afrational localizes too. OK. Do you need to assume that the ring is local? Yeah, well, OK, so first of all, I don't know whether people have already defined afrational, but for me, your first defined afrational for local rings. Are you defining local rings? Yeah, and then you just define it. OK, for non-local rings, I would just define it to be all the localizations are afrational, because I don't know how to define afrational. Well, maybe you can, you can use the canonical. But yeah, but in either case, I think afrational is also a local property, at least under some excellent type assumption. But it will be afrational. Yeah, it's a local property. And Florian will of course go over that in a lot more detail. Right, I think the next lecture will be focusing on afrational rings. Thank you. OK, if there are no more questions, then let's thank Klingchon one more time, and we'll resume again on Wednesday.


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Hello, Mojo. Nobody's in here. Alright, so this is where we left off yesterday. I don't think I filmed it, but I used a giant torch, a cutting torch, and cut off the bolts of the sink because they were too rusty. This is a frame that we have so far. Justin is a very good learner, a very fast learner, and a very proficient welder, and I was happy to share the knowledge that I got from Mike and Badge and the guys at Colorado Custom Coachworks to show him my remedial welding skills, which is good enough, right? Like, this is going to be covered, so it might look ugly, but it's not in display. It's structural. So, today we are going to cut up some metal. It looks like these guys are already at it. We have a plasma cutter. We're going to try and cut some metal pieces, and we're just going to continue rebuilding with the steps here, and it's pretty cool. Let's go take a peek. I just want to take a brief second to thank Rafe Langston. I know I always get his name wrong. It's a little hard for me to pronounce, so I think it's Rafe or Rafe, but thank you so much for joining Patreon. So a couple of videos ago, I had a little rant, and I was a little frustrated, and I was trying to communicate as best I could a couple things going on as far as people getting harassed online and things like that, just because people have a Patreon. Now, me personally, I've invested tens of thousands of dollars. I have made tens of thousands of dollars from sponsors, and that's how I keep myself on the road. And so, with a hypothetical situation of having a breakdown, actually one of my friends and someone I look up to drew some similarities between it, and I just want to say I apologize for throwing out a hypothetical situation, because in fact, I was definitely not referencing this person or anyone in particular when I was mentioning the I'm-up-a-creek-with-out-a-paddle type of thing, and I guess what I was trying to do is differentiate my... The way that Patreon is seen, for me, like I said, it's easier to think about it as like a tip jar. You know, I used to open a can of beer, someone would gladly give me a dollar or two, and it was like nothing. And so I think what I was trying to communicate was that I'm out here spending hours and hours on videos, tens of thousands of dollars over almost three years, tens of thousands of miles, and thousands of hours working on this. And so it's like a double-edged sword because us YouTubers definitely feel, you know, we feel under attack sometimes. And really we are putting out content from our own pockets for people to consume without any payment whatsoever. And to be quite frank, the ads from YouTube, unless you are a very large channel, 50,000 or above, do not pay the bills. And it is essential that if you want to continue with a type of lifestyle, for me this personal dream of traveling and sharing it as entertainment, you know, it's very helpful. And so I just wanted to apologize to my friend for any sort of similarities with that because I was, at first I didn't understand the message I was reading, and then I was like, oh crap. Absolutely not am I trying to, you know, infer that someone is not deserving of help when they have trouble. It was more just a kind of to let people know this is a situation and trying to be transparent and throwing out my situation as an example and nothing more than that. So I was very, I was just overly apologetic and cautious of me explaining that situation. And I hope that makes sense because I'm definitely not trying to call anyone out whatsoever, especially not a friend of mine. All right, so he is just going at it right now by the way. Glenn told him how to operate this thing, didn't show him how to operate it, and he's just going for it. So I think I know what he's doing, but to explain, he's cutting the metal to recreate part of the lip where it touches the doors. So if anyone hasn't noticed, I put a gigantic list of thank yous at the end of my videos from now on. I didn't know how to properly thank everyone on a regular basis, the people who have helped me out with different jobs along the way. And so I put them out to all at the end of them, and there's a lot of people who don't even know that they're thanked. So if you've helped me out on this video, please watch it to the end of this video because you might be pleasantly surprised. And if I forgot someone, please let me know, and I will gladly include them in that because I, as you know, this took a completely different direction. It's been this giant collaboration, and I am so thrilled to have had such an amazing experience, you know, building with so many just fantastic people.  I do get a little frustrated from time to time, but that's just all about managing expectations. And honestly, if you can manage expectations in life, life just becomes a little bit easier to deal with, you know, and also prepare for the unknown. Thank you. Wait, was I supposed to put the washer on the back? Yeah. Did you put it on the front? I did. Don't worry, you can edit this. I like to keep it real on this channel. I put the washer on the front. That's just a fact of life. Usually it's someone else when I say we, but this one's on me. I am putting and bolting back on, I don't know, we'll just call it the swivel mount for the steps, which don't exist yet. All right, so the thing that Justin Plasma cut is just to bump out and make flush this, I don't even know, bottom step, I guess we'll call it. So the door shut. Yeah. So anyways, we'll fill a weld, so it doesn't really matter if it's off, it's just more of a consistent width or something we could work with. All right, so we just clamped angle iron on angle iron, and Justin's just gonna weld it up. And after. I don't know, what do we think? Pretty good for a first timer. I am not speaking from a wealth of knowledge, but my small amount of knowledge was enough for mojo bus to complete this job. All right, here is an update on the oil. Let me take a sample, let me take a sample out of the tank. It is coming out the color of, that just gonna like this one. It's coming out the color of maple syrup, look at that. Nice amber color maple syrup, completely clear, and it just gorgeous, right? No debris whatsoever, if you can see that.  Like a good beer. So, many people are wondering about the denim jeans situation. Let me just show you how well the denim jeans filter out debris. I'm just gonna scrape on the inside of the denim jeans with my fingers, and I'll show you all of the residue left over from the jeans. This is all the nasty bits. This is the sludge that was coming out of the bottom of the tank when I first opened it, if you did see that video. It is all sorts of carbon. There is a little motor oil in this batch, but it is, this is all, everything denim jeans are catching is right here, and this was what was previously clogging my filter because it was not sufficiently filtered enough.  People recommend filtering down to the smallest amount possible, 1 micron, 0.5 microns, 2 microns, and then putting it in your tank and then having a 10 micron filter on the way to the engine. So this is all sorts of already clogging, injector clogging garbage. So I just want to give you guys a little update on that. Picking up where we left off, this is the following day. I donated some rattle trap. Mojo is welding in the side supports. I just heard rumor that you might put astroturfers, is that right? That's a terrible joke from Glenn.  It's alright. I changed his name at Ace Rewards, so I got him good. Anyways, a little thank you to these guys for all the hard work they've done for me. I got them an upper radiator hose, thermostat housing, and a fuel filter. Alright guys, here's the update. I took off my suit. Why? Well, I got this off, and guess what? I snapped the nuts or the bolts in there, so I'm going to go buy a new water pump. We got the water hose off. That's a newer version, the kind that is not supposed to rub into the AC right here. But I feel so much more comfortable doing mechanics than I do carpentry. It's kind of funny, just kind of where I gravitated towards. But we're going to get Mojo bus all fixed up, and just a small token of my appreciation. And he's going to help me out and try and finish the rest of the bus next week. So it's a great trade in my opinion, and also a little payback for all the custom cabinetry as well. He's proud of the stairs that he's made. Looking good. You guys might recognize some of the rattle trap. He's going to cover the whole thing with more rattle trap. Yeah, and then build in a little shoe cubby. Alright, we are midway through. We got off the fan clutch, fan blade, sorry, the fan. And then, yeah, all the lower radiator hose, sensor. So we just have, it's basically just, you take the bolts out, you put it back on, that's it. To simplify it. Look, Mom, I'm learning. This is the first water pump I've ever taken off. And it is nice to learn how to do things like this, even if you accidentally break off a bolt like right there. And like right here. Sorry, I broke your bolt, dude. We're going to do water pump, right? There you go, water pump's on me. Alright, so we got the bus back put together, just like we started, but we just went in reverse. Let's check down here with Justin. Wait a second, Justin, why are you draining the coolant again? Just sound like a good idea. You're not going to believe this. We're going to have to do the whole job over again. I'm just leaking from the water pump. I know. I know what you're thinking. It's going to be an awesome time. Are you excited? At least we know what we're doing this time. Water pump times two. Well, I was getting myself ready, grabbing a new gasket. And sleeping in. Thank you, Glenn. This is what happened to our gasket that came with it. For some reason it got sucked up and one of the blades chewed it and spit it back out. And so Justin took all this stuff off by himself in one hour. That's what happens when you do things. When you go to water pump boot camp, we'll call it. So anyways, we got some water pump gasket maker, and I'm sure somebody already knows that we should have done this to begin with. People like Badge and other mechanics, like this around where the gasket is, and try not to make two mistakes twice. Alright, you see some shiny new things. We got a new belt tensioner and a new thing. It's called an idle pulley. That bad boy right there. And since I was on the bottom yesterday, we were swapping. So my back hurts. I haven't used muscles I haven't been using for a while. Make sure all the mechanics know what I'm talking about. And yeah, so we got a new one of this, a new one of these. You know what's funny, buying this whole part here was just as expensive as buying these individual parts with bearings. So yeah, a lot of new shiny parts on this bus. On a scale of one to old man, I'm feeling like retired, maybe just tired. But we got it done. Thank you guys for all your help on my bus. And like I said, it is a pleasure that I could assist you guys with everything we did here. Thank you. No, thank you guys. I still have a big debt going on with these guys here. But we're going to end this video. We finished up, we put it back together. Everything is life is puppies and ice cream. We got that done. We're still going to work on the steps. That's pretty minor because they're already welded in. We'll let you know after we drive. See you.


Now there is a little bit of sketchiness with the internet connection. So if I come in and out, I apologize wholeheartedly. But that is the beauty of living in Puerto Rico right now. Sometimes the Wi-Fi isn't that great. So let's jump in, shall we? So the whole thing, before we start to talk about this million, $1.8 million mistake I made, just to let everybody know, we finally did a deep dive video on Farcana. Farcana is a gaming project that we were introduced to by TenSet, which is a launchpad. I think this one's going to be great. And there's multiple reasons for that. First of all, the game itself is already playable. I mean, look at this. This is a good looking game. And this is a triple A rated studio. And there is a lot of people behind it, Animoca brands. You've got Polygon and Arbitrum and a whole host of people. And then you got a lot of different KOLs and people pushing this project. And oh, yeah, one of the biggest things about it is that not only is it it's free to play, first of all, which is essentially what Fortnite is. And that made a billion dollars in 2018 in the first five months. It is free to play. But in the tournaments and the leagues, you actually it's a win to earn. And what are you winning? You're winning Bitcoin. So with this one, I think it's going to do extremely well, but it could be wrong. There's a link in the description you can check out for this video. This is over on Dan Degen, which again is one of the more riskier plays you can possibly do. But just so everybody knows, I invested into it. So do your own research. All right, so today here's the market kind of a red day. I think everybody was kind of poo-pooing because like, oh, we didn't get our ETF. Yeah, whatever. So maybe we'll get it on Tuesday or Wednesday. Nobody knows, but it was looking pretty good. I'm again, my stance is I'll believe it when I see it. But I hope it does because then I get to wear a really cool shirt and I get to go on Simon Dixon's channel, which is fantastic fun. Anyhow, here's the thing. So today, actually, a couple of days ago, me and my wife were talking. We we are living in Puerto Rico, we vacation in Texas. And we've got real estate in both locations. And we decided recently to sell one of our condos.  And we're like, that's pretty good. And we're going through the actual paperwork, taking a look at like what we spent on it and how long we've had it. And the profits and loss, which we already knew, but we're just kind of doing a refresher. And we said to look, we're like, man, maybe this wasn't a good idea, even though it was profitable. But again, it's about how much is profitable? So let's just talk about real estate in general. This is Ben's website into the cryptoverse. You'll see that there is a 10 percent off for the first month. Link in the description, all that great stuff. But I use this his site extensively. What I want to show you is this thing called Purchase Only House Price Index for the US. Now, I can't tell you what it is globally, but I got to tell you, the amount of homes in the United States are skyrocketing in price. I don't know if it's a value, but price certainly has gone up. And what this is telling us is this is based on data from tens of millions of home sales from all 50 states and over 400 American cities that extend back to the mid 1970s. And the FHA serves as a accurate indicator of house price trends. Downward trends of the index generally mean the house prices are falling like for likewise for when the index is rising or is it overheated or is it collapsing? And we can just see that, you know, of course, in the big, the great recession, which is all pretty much about housing and mortgages and differentiating things that were going on. You can see that, yes, it was hard to become undervalued because obviously the house market totally crashed and it bottomed out around 2011 and then came back, came roaring back.  And now here we are just going up and up and up and up and up and never stops. So the question then is, OK, so that's the index looking at it. What are we taking a look at as far as like home prices sold? Now, I don't know where you're at. The United States across all the different 50 states and the Commonwealth and the different locations that I've been to. I can just tell you that the best time to buy a house was probably 1968 when you had it was 24000.  It's just how it is. And that's what's called inflation. It's not because the house went up so much because it's so awesome. It's just the way it is. And there's a money printer and there's quantitative easing and you have the Fed to thank for that. But that's another that's another video. But we're going to see that the prices have just gone up dramatically all the way until again, the great session when we had a nice little recoup. And now here we are. And did you know I didn't know this until I took a look. The average price, the sales price, the median sales price of houses sold in October, does 22 with almost half a million dollars I don't think that's sustainable and it wasn't and it went down to only four and 18000 and now we're on our way back up. So again, house prices, it depends on the time that you actually bought it. Like right around here in March, when we had like a little bit of a pullback March of 2020, April, 2020, maybe July, 2020. Yeah, it was a pretty good time to buy because everything just kind of went up astronomically in prices of real estate. But was that the best play? I want to tell you what I mean. My wife took a look at we realized it really was. And of course, you can see this is new houses for sale or sold ratio. We can see that again for every one house or every nine houses sold. There's nine more waiting in the wings. This is the new house for sale sold ratio monthly. OK, so that is that part. And what we did with this these condos is we've done short term rentals. Now, before you run into and go, yeah, short term rental is great. It is great, but be aware of the cost. There is a link in the description for this website. It's free app dot air B T I C S and the kind of that we bought. We bought it outright at two hundred and sixty thousand dollars. And when you do this, you can kind of you can put it into the location of where you want to do a short term rental. And it'll tell you like on average, the revenue is going to be thirty one thousand dollars a year. Not too bad. Occupancy rate, Natalie rate, so on and so forth. But that's if you bought it outright. If you've had two hundred and sixty grand, quarter of a million. You make a pretty good, pretty reasonable money. Then roughly six years or so, you'd.  Eight, ten, ten years, roughly. No, no, no, thirty, sixty, ninety, one twenty. Seven years or so, seven, eight years, you'd get your money back, which is not bad. I mean, considering like if you're doing like a startup for a business. OK, but if you want to say like I'm going to take a loan, you just switch this on, whatever your down payment is. I just got to break it to you. That's usually if it's an investment property, you're looking at 15, 15, 20 percent down depending on where you're at. And of course, that'll lead into your profits. So your net profits, if you did that was only eight thousand dollars roughly and that's the headaches and so on and so forth. But there are good things. The only property, trust me, I've owned a few. One of those is tax reasons and one of those is stability as markets collapse and flow and ebb and flow, it's just a truth. But in this situation, not so much. Now, again, if you're an Airbnb, I also link this in the description to blog and travel guide. Apparently this has just been this has been rolling out the last over so many months. There is a new type of tag that Airbnb is using. So like the people that get tagged is like not just a super host, but a new type of like preferred host or something like that. If you don't have that badge, then you are going to be the 75% of people that are not going to get a lot of bookings. That's going to be bad for you. So again, this is all Airbnb stuff, not crypto, we've done a second. And I'm not saying that real estate is bad. As a matter of fact, it's good. The question, the thing that I have a problem with is that it's just so damn expensive right now. It's just not a good idea in my personal opinion. Start buying into real estate even back then. Of course, we had an interview with the founder of Boxable links in the description. I can see something like that moving forward, especially for the younger generation, because no one's buying a house for $400,000 when you're making 20 bucks an hour, 15 bucks an hour, 10 bucks an hour, whatever else it is. And I think the federal minimum wage, I think is between $7 and $9 an hour. So again, I don't see that being sustainable. Anyhow, all that aside, if I had to do it all again, because there's a big thing about lump sum, lump sum and buying it at Bitcoin and things like that, it's scary, right? But it's all about timing. So we know that the four year cycles are still intact. It's one of the few models that actually has sustained. In 2012, we had a having. 13, we got an all-time high dip and a reset. 2016, having. 2017, all-time high dip reset. 2020, a having. 2021, all-time high, beautiful times. 2022, 2023, dip and a reset. And we're due for a Bitcoin halving, April or May. I forget in the comments. You can tell me in the comments section. But we're due for a having. And that year is usually pretty good and the next year is even better. Now, does it mean that 2025 is guaranteed to be the most stellar thing of all time? No. Is 2024 the guarantee that everything's going to blow off? No, it's not. And that's the whole thing with investing. There's plenty of risk. So when I show you this next graph, I don't want you to go out in FOMO and go crazy. Having said that, sometimes I think people get ahead of them themselves and they think that Bitcoin is the end all be all and that's all you should own. You shouldn't. I mean, people get crazy. Let's just be honest. This is from Udi. A lot of Bitcoin maximists hate his guts. I think he's progressing and doing things with the ordinals and that's just how it is. But he did a pretty good post. He says, look, a lot of people say, don't all home or chairs or clothes? Because they're all scams. Alls I need is my precious Bitcoin. Like somebody who just can only have that and live on that. It's not all about that. It's living your best life, whatever that is, and your investment. I can't say that for you. Having said all of this stuff, let's take some numbers. So we paid $260,000 cash. And it doesn't really matter. You could say, you have $500 in grand scheme of things. The time to lump sum is not usually in the all-time high years. That's not good years. If you lump sum $260,000 at the price of Bitcoin at $67,000, you'd still be under water. And that's the truth. However, right now, maybe it's not such a bad idea. Obviously, before anybody says in the comment section, well, Rob, you know the best time to buy was probably when it was an all-time low. Thanks, Sherlock. I didn't know that. But yes, it would have been a great time at all-time lows. That's why a dollar cost average. But as time goes on, we kind of see where things are going, and this narrative is looking pretty good. So let's just say $260,000. This is what I showed my wife. I go, you know, we bought that con over $260,000. We lump summed in Bitcoin. Not in 2017. That wouldn't be right. It was 2020. It was July. July. Again, this is after the halving. The halving in 2020 was either April or May. I always forget. I think it was May 10th to 12th, somewhere around there. So this is in July after the halving. So I wouldn't have even hit the bottoms. The bottoms would have been November 2018, I believe, after the 2017 low, which would have been like $3,000 or $5,000. So I'm not even hitting that. But I think it was, let's say it's a 24, I don't remember. So check this out. I bought $260,000 at this point. I would have been underwater here at negative 0.6%. Whatever reason, only 25th. But after that, she's doing pretty good. Maybe, maybe, maybe. So I'm showing this to my wife and she's like, hmm, looks pretty good. And she's like, well, why don't we just put everything into Bitcoin? That's not a bad idea. However, just because something happened in the past doesn't mean it'll happen again. And look at this. So you come up here, you're at $1.7 million. The problem with this is that you think to yourself, wow, this just did a 5x. If it did a 5x, it'll probably do a 10x, right? Or a 20x, because everybody tells me even Digital Asset News said it was going to go to $100,000. And he's never wrong. And down you're down here. But you're still at $865,000, not too bad.   But it did a 6x, so it'll probably do a 10x. And it didn't. And you'll hold it. And you'll hold it. And you're still up, though.  And you still have $1.2 million for the big lump sum. Now, obviously, I know it's not like people can say, oh, well, that's great for you doing these things. But the point I'm trying to make here is that if I could do it again, and I had $500, $1,000, whatever, I personally think this is not a bad time to lump sum. And of course, people say, well, you know, you should have lumped up when it was $17,000, because I did. And I called it all the way. Great. Good for you. We're here in the present. I can't time travel. And I don't think either can you. So as we look forward, and hopefully this ETF gets approved, whether it gets approved on Wednesday or Tuesday or in March or in 2025, it's going to be approved at some point. Again, I'm just a wait-and-see type of person. So we can go from there. But I think that the narrative has been set. Traditional finance is here. People are starting to really finally start to understand it and kind of wake up to it. So I think that's not a bad play. Now, having said all that stuff, let's take a look at what this would be with Ethereum. Ah, little DGEN stuff. Okay, watch this. So $260,000, July 24th. Let's say I didn't want to do Bitcoin. I just did Ethereum. Well, if I held it all the way to the first top, I'd be at $3.8 million. And I did the second top, $4.4 million. And if I came over here, I'd still have $2 million at $260,000 I could have put in. But there is this thing called diminishing returns. All right, that's nice. That's cute. It's adorable. How about BNB? This gets even more ridiculous. And again, when I'm talking about this, remember that you can lose everything because you can. It's very risky. There's something to be said for crypto, just how it outperforms. If I would have held the first one, I had $8 million or $8.2 million. And today, I would still have roughly $4 million earlier to get in. Hey, you know what else? I got a friend. His name's Diddy. You may know him as the Bitcoin family. Diddy was an early investor. You know what he did? He went in all in on 2017. I think he said it was February. Let's just take February 28th, 2017. He sold his house, his cars, and his business. I don't know if he did 100. Let's just put in $150,000, huh? Geez, always. That means that Diddy in the first run-up had $2 million. If he didn't sell anything, I don't think he did. He's probably got $7 million. And $7 million here, and then $5.6 million. I know Diddy didn't do just... I think he did a little Ethereum as well. Anyhow, you can play around with that.  It's 100% free.  And do my favorite parts here. I like the DCA. I also love some. This is called Dynamic DCAN. Links also in the description about that video. But that's it for today. So look, if you like today's video, and hopefully didn't give you too much of FOMO, consider subscribing. Thumbs up, all that great stuff. Now if you want to stick around, I'm going to answer all your questions at the best of my abilities, and we'll go from there.  It's a beautiful sunny day. Thanks so much for stopping by. I do appreciate you. All right, everybody. What is going on? Let's see. Hey, the soul. No, if I did Solana, that would look too ridiculous because I think Solana came out in 2020. So it was like less than a buck. That's just unfair to show that type of gain. It's just to make people go crazy. I can time travel in my bed when I sleep. Yeah. 3x max before bear markets again. Yeah, could be. Let's see. If anybody says anything else about tectum, I'm going to ban them. T-E-C-T-U-M. Brass, I just banned three people. I'll ban you two. I think you're a bot. Let's see. Sorry, you can use a hot walk at your letter. Ah, let's see. Let's see. And it's doing a dominance video. I saw that. Yeah, be a good one. Okay, let me go up here. I know I missed a bunch of them. Ah, I don't know what that means. Rabbit says, I believe the ETF will be Wednesday, not because they can't do it Monday, but because it's like a bureaucratic entity to do everything last minute. Probably so. I will see. You are my research. I wouldn't depend on me. That's for sure. I get a lot of things wrong. Ooh, Barrow Beach. Cat, very nice. Ben's chair is here. Tesla is here. Panda Pi, usual suspects. Thanks for hitting the like. I appreciate you. Urgent Sky says, if Bitcoin bear low is 15K, and the previous cycle low was 3.5K, and on top of 6.9K, imagine the cycle top. Remember though, Ben's got a great series about diminishing returns. So every cycle, you see less and less on Bitcoin. Because remember in 2013, it went from 10 bucks to 1,000. And then in 2017, it went from 1,000 to 20,000, 20X. And then from in 2021, well, the low was 3,000 to 67,000. So you have a point. But remember, that's massive amounts of market cap. The market cap of gold is roughly $11.5 trillion. We're looking right now for Bitcoin at roughly, it's over, well, the total market cap is $1.7 trillion. I think Bitcoin, let's just find out. Yeah, Bitcoin's market cap is $861 billion. So I mean, for it to double, but it still doesn't work like that. Because it doesn't double, Bitcoin's price doesn't double just because it doubles in market cap. It says an exponential factor because of the amount that actually gets taken out. And the scarcity that it is because you can't create it anymore. So even like a couple of billion will raise it substantially. So I take that back. So maybe we'll see. Yeah, let's see. Lexx says BlackRock owns everything and everybody. I'm assuming they want ETF way before much. I know they do. They definitely do. But let me tell you, wouldn't it be great if they said no? Let me ask you a question. How does everybody feel? Does everybody feel like that you accumulated plenty of crypto and don't need to buy anymore? You're like, yeah, that's good. Feel pretty content. Did it all? Did everything? Or do you think yourself, man, I can use another month or two? If it doesn't get approved, there's a thing though. If it doesn't get approved in January, then the 10th might get approved in March. It doesn't get approved in March. It'll get approved at some point. And it's not like, there's another thing. It's not like we really need, need, need the ETF. We did pretty damn good the last 12, 13 years without it. Abdullah says, bro, lump sum now then. If you had 10K, do invest now. Me? Yeah, I'd probably want to, you want to play it really safe? You could dollar-cost average, or you could play in the middle, value-cost average, where you just take 2,500 bucks and put it in today. Then wait for that announcement to see if they actually get, if it gets approved or not. And then if it does get approved, well, actually, you can do it this way. 5,000 right now, because everything's in red. Not financial advice. Do not do what I, this is what I would probably do. 5,000 right now today. Wait to see if it gets approved. If it doesn't get approved, just wait for it to drop, and then put it in. But if it comes, does come out and says it's approved, buy as fast as you can. And that's just Bitcoin. Any thoughts on Trader Joe? It's a great dex for Avalanche. I've used it a couple of times, works pretty well. Doesn't work as smooth as say, Jupiter with Solana? Well, pretty comparable. Lax got a good question. Who has more influence on SEC's decision? Warren or Blackrock? The biggest question is, who's got more influence? Warren or actually Blackrock or Biden administration? That's the question. Call it a K. Are you going to get a boxable? I don't really have a need for it right now. The only place I could see it, I talked to the founder, was to put it on our sports facility. We have this place in Texas. It's a sand volleyball, sand soccer facility. And I think it would do really well in the middle.  As they're drinking. So, yeah. Thoughts on Immutable X? I own it. Have you heard about Luxo? Yeah. Everybody tells me about how great it is. I'm sure it'll probably do well. Mark Yusko said tomorrow's the day. Another prediction. Let's see if that works out. Ivan says, my tangent arrived. It's great. I use your discount code. Yeah, tangent's great, man. Am I right here? This is my cold storage wallet. Look at that. Let's scan it and that's it. Here's my Oli Pal. I need to do another video on this one. And my ledger. Let's see. Shark puncher. Arbitrum on the move. Arbitrum, another one that I invested into. L2 solution for Ethereum. Talk to those people at length for our projects. Pretty good team. Knows what they're doing. And it actually works. So, it should do quite well. Arbitrum price prediction. It'll be between $0.02 and $700 this cycle. Nailed it. Yeah, Missouri. It's cold and jury. Yeah, I remember Missouri. That's where I did my basic training. Fort Leonardwood. Worst place ever. Sorry, just the truth. Well, the base was. People are great. Panapai. There are again some rumors and fud around Kraken. Anyone impacted? Haven't heard too much. Is it solvency? I haven't heard anything about it. Yeah, Mike's right. It's going to be a crazy week one or the other. It is. If it gets approved, great. Wouldn't it? Great. And then, but I will warn everybody. I don't think that we see like a sky rock. It's like people think it might. Some people think it might. And the more rational people are like, okay, that's good. Now let's give it like six months to a year for everybody to flow into for all the people that are in the black rock, the fidelities, the arcs, to teach all their investors about what it actually is and have them come in at a slow, reasonable pace. I think that's kind of where I'm at. And other people are like, okay, Bitcoin's not 100K. I'm out. But see which one's right. Yeah. Sean says, we also got to hand out free STEMI checks during that run up to 69K. Yeah, that's true. But then the problem with these STEMI checks and the free money was that it's free money. So people were like, oh, it's free money. I'll just put it into this Bitcoin. And then, you know, that was in March 2020 to June, July 2020. Maybe maybe later. It's got enough funds to do that on a wide swath. Equities went up. Crypto went up. And of course, the sale of real estate also went up because everything went up. But if you give money to people for free, they don't know what to do with it. Because mentally, they've never had that.  And I don't need to save it. I don't want to invest it too much. And I don't have to go, the smart people will do it. But then even when they do invest it, they're still not used to it.  Bitcoin just went down 5%. I got to sell this stuff. This is going to zero. And it became so volatile. Bitcoin's not volatile. The people that hold Bitcoin are volatile. And that's the, that was the truth. So I think it's a cascade effect. I'm glad the tourists are gone.  I appreciate all you who are like even kilter and cool and fine. I just don't want to get a bunch of tourists again. I know it's inevitable. That's why I'm stepping down from this channel on the next bull run. And I'll come back on the bear. Yeah, me too. Waiting for the chiefs going to kick off. Sweet. Big buys and V. All right. Jerry Sloan one is correct. Gold ETF at an eight-year run. Have you ever seen this chart? Let me show you something. Yeah, this guy. Let me scare my screen. Because people were, they would talk about this chart and they're right. Gold didn't really do too much. I mean, it did really well when first came, you know, after course, the government stepped in and now took it from everybody. But then the 90s, it was pretty much flats, 2000s flat. A little bit of a run up, especially after the dot com bust in 2001. But then here November 4th was, November 4th, 2004 was the ETF. And one thing I want you to notice here, what happened to the launch of the gold ETF? Immediately after, I'm guarantee that the gold bugs were like, this is it, baby, we're going to the moon or whatever they used back then. We're going up a hill or whatever. And what did it do? It dropped. Now I don't know if these candles are monthly candles. Yeah, monthly, monthly candles. Look at that. Two months straight, down. Then a little green, then down. Then flat, flat for like half a year, like we just talked about. And then we start to see the rapid rise. All right, and dips, so on and so forth.  So just be aware that even though we get an ETF and everybody talks about, well, gold had an eight year run. They did and good for them. But it's not in a straight line, just like everything else out there. Good question. And Scott says, is it buying opportunity? Scott is correct. Well, here's what Dojo says, no ETF is coming. We should hang out. Like I'm still on the fence about it and everybody's telling me what a moron I am, which is par for the course, but that's fine. I'd rather be wrong and rich than right and poor. Born as a hit man for the masters, perhaps. Are you still positive I made it? Sure, look, anything that you guys invest into will probably do pretty well in the crypto market. Everything, it doesn't really matter. The question is, which ones will run far and wide and which ones will just spike and drop? That's the big question. But yeah, I think everything's going to do quite well. All right, what's your thoughts and influences bias and ICP coverage? I don't know if there is a bias. I just know they don't really cover it too much. I own it. It's probably do well, but it's, I want to say it's like 97% down from its all-time high, maybe 95%, I forget. But we'll see. People seem to love it. That's why I bought some. I don't really care about the tech, honestly. I know people will say that, but they're just lying to you. I want things to work out. I do, but I think things are so young and as far as like mass adoption, I'm like, the best shot we got is big thing. Right now, I think it's going to be great. And gaming, yes, that's true. I stand corrected. AI, okay, I can see something like that. Yeah. And then zero one to four with AI and automation, they will push UBI, universal basic income. Let's hope not, but probably. Well, maybe I can't say. Chris says, the tourists are the ones we sell to near the top. There's a price of admission. And those, like you guys get it, right? The price of admission, even in traditional equities, is the same thing, right? Gary Gensler can go and talk about, oh, we need disclaimers and we need this documentation so people know, understand the risks. The risks. Newsflash, Gary. Nobody reads the disclaimers. Nobody really cares. It's one ear out the other. It's all gambling. So when we get the tourists in, they're going to learn a hard lesson. Did you learn a hard lesson? I know I did. There is no free rides. And if that's the case for the tourists to come in and they're like, hey, what happened? I thought it was going to go up forever. This influencer told me he's going to go to a million dollars. He must have lied to me. Yep. That's exactly what happened. Duke Juan. Duke Juan. Is there another channel during the bull run categorized as knitting or the crypto coming? No, no, no. There's a lot of great people out there. Ben's great. Guy's great. CTO Larsen. Cito. Lady of Crypto. James is great. CTO Larsen. And a host of Tommy Crown. I mean, there's a lot of good people out there. And I'm not really needed, honestly. I'll probably still, like I said, I'll still shoot some videos on loop, like things to avoid, watch out for these scams, why I sold. That'll probably be on loop. The Dan Degen channel might stick around for like the most risky, degenerate plays you can possibly think of. And I've got a group that I'm involved with that I will stay active in, but I will leave when things get a little bit crazy. If you want to know when I think things are going to be crazy, watch that video in the description when I'm going to sell 80% of my crypto. Once that happens, I come on here. I say, hey, everybody, good news. I sold my crypto. And if Bitcoin hits 100K, I jump in one of these pools and I go. And that's it. And then I become like a tour guide in Puerto Rico or something. I don't know yet. That's the problem with retirement. You don't really, you got to have something to do. Three top cold wallets. I can only see the three that I use. Like Guy loves Trasor. I've never used it. I've seen it in like, I don't know. Seems reasonable, but mine is Tangem, Ellie Powell and Ledger. Those are the ones I have right now with me. Yeah. Roger Gennarite, that'll probably do well.  Everything did great. It was after the bull run, everything collapsed. Because all the, because you've like, more above it says you find out who's swimming naked. Because all the different shenanigans that were going on in FTX and Voyager and Celsius and all that stuff, it came to pass in the bear market, didn't it? And everything collapsed. Luna collapsed. FTX. All that's the collapse.  And they were Ponzi's and they were scams. That's what it is. 2017 was no different. There was nothing but a white paper and a hope and a dream. Those are called ICOs. And those all collapsed too. When that happened, after the bull run. So when the bull running comes in, like I had done my job, I calm people down, told them just to stick it out, write it out, it'll be okay. I sold some. Here's my profits. I made 2% or 1,000% or whatever I did. And then I'll see you in the bear market when everybody's crying. That's it. And I leave and come back. Michael says, class of 2019, I've had some online lessons. And still here. Those are the ones that win. The ones that keep showing up. It ain't easy, but it happens. SolDude says, any great deals in real estate, out there in Puerto Rico. And he mentioned a couple of past. I got a couple of real estate agents, Efrain. Great guy. He was at Meetup. I'll introduce you to him when you get here. And then a couple other ones actually too. But there's deals to be had just around San Juan and Guainabbo. Not so much. But if you get in the outer areas, yo, yeah. Oh, yeah. TimeCone says it correctly. Biggest learning in crypto is a need to sell. We can all buy. The question is, can we sell at the right time? Esquire says, Dan Degen and Shorts Channel. Perfect for bear. Yeah. Yeah. Puerto Rico is very nice. Treasure and ledger, golfer poker. I don't, I barely can golf. I'll play poker, but it's just, it's just, it's a, it's a tamer version of investing in crypto. That's what poker is. The government, I believe, raised the minimum to $70 and $20. And then it was interesting. It's sunny where we are. That's the beauty of living in Puerto Rico. Still, show bag says, I started as a tourist and outstayed my visa. You'll probably be successful in the next one. And that's it. So everybody, so again, as a quick reminder, check out that video over on Dan Degen. Links in the description for Farkana. It's just, they've got, they've got way too many people. They've got way too many investors. Like, like I said, Anamoka brands, Polygon Studios, Arbitrum, and a bunch of different V, not V-cell, V-season institutions. And the people, the angel investors are a bunch of influencers, mostly web three, but have huge, huge, huge following. And I got to tell you, in my personal opinion, it doesn't matter how great a game, and this game is really good. It's how much can you get that message out in marketing? And they've got that down. And then of course, the game is playable. You can do it right now. It looks smooth and slick. And it's free to play. So you're not going to get the Axie Infinity effect. But in leagues and tournaments, you can win Bitcoin. It's perfect. Damn, it's really good. It's a really smart idea. So that's it. And just so you know, you got like 24 to 48 hours to figure this out because the ideal launches. So don't delete LA. That's it, everybody. So everybody, Sunday, thank you. Appreciate it. Like this video, thumbs up, subscribe. And let's see what happens next week. Be prepared. It's going to go crazy either way. All right, everybody. Thanks so much. See you on the next one. Adios.


Once you're able to do your bubbles and relax here it's shallow you need to learn how to float. The step number two is learn how to float or learn how to fly in the water like a bird. In the water you are floating. A lot of people believe they're gonna drop down touch the ground and they're scared to feel then if they don't touch anything they just gonna drown which is not the case.  So to feel that you need to relax this is the key point to learn how to float you need to relax and start where it's very easy for you. Here no stress I can touch the bottom so I'm gonna start here and learn how to practice how to float. I'm on the stairs and I can look in the water blowing my bubbles. The only little difference is you're gonna push with your feet to glide on the surface and to reach the point where I can just feel comfortable because I can grab it. So I'm here I blow my bubble five seconds. I play my music with my mouth and then I will push with my legs to try to glide on the surface once I'm in the water. Wow I can fly like a bird. I can fly like Superman, like a bird, like an airplane, whatever you want to believe that you will not fly. Put your feet on the surface on the wall here. Get ready, blow your bubbles and just let yourself fly away and catch something just nearby just to feel then when you don't touch anything you're not going down. Just feel it. It's simple. If you are too afraid to do it here learn how to do it where it's super shallow. Here is super shallow. My hand can touch the ground. See? So I will practice here. Just feel it where you feel great. Okay? One more time it's simple here. Just touch the ground all the time, look down, push slowly and glide on the surface. Wow no need to go fast. To practice this skill try to go slowly and try to go easy. I'm going to do it here which is easier. I'm going this way. Okay? And I go there. Very good. One more time. Easy. You can glide with your hand on the front or you can glide with your hand open like a bird. If I open my hand I just feel my body gonna float.  Look, slowly and easy. If you stress, if you move fast, you need to practice until you can go slowly. You can even do it if you don't move at all. Okay? I'm not going down, I'm floating, I'm flying. Because I feel it I can go where it's a bit deeper now. This skill I can practice here. I'm gonna practice the same skill where the pool is deeper because I know I can control. I know I can blow my bubbles five seconds and I know that everything is all right because I can slowly, I go easy. I'm gonna fly from here to here about two meters. Okay? You need to move your hand, you need to kick, you need to do stress movement. Just fly. Okay? If you can do it for five seconds you can fly very far away from here to here.  Deep breath, no bubbles, push and glide on the surface. Okay? No fast movement, slowly and easy. That's the key point. So when you can do that, you learn how to float, you learn how to fly five seconds by pushing or by staying on the water. Okay? But that's simple. This is the step number two. Learn how to fly like a bird.